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 6 
 
MICROCOPY RESOLUTION TEST CHART 
 
 (ANSI and ISO TEST CHART No. 2) 
 
 1.0 
 
 I.I 
 
 !.25 
 
 2.8 
 
 1^ 
 
 If 1^ 
 
 !^ 14.0 
 
 1.4 
 
 2.5 
 
 1 2.2 
 
 2.0 
 i.8 
 
 A APPLIED IM/^GE I 
 
 ^S"^ '6-3 East Main Street 
 
 r^S Roi r;ester. Ne* York 14609 USA 
 
 '-^ (716) 482 - 0300 - Phone 
 
 ^5 (716) 288 - 5989 - Fax 
 
CONCRETE BRIDGES 
 
 AND 
 
 CULVERTS 
 
 FOR BOTH 
 RAILROADS AXD inUHWAYS 
 
 BY 
 
 II. (rRATTAX TYRRELL 
 
 Ch-il Eitgiiircr 
 Graduate of Toronto I'uivcrsilv 
 
 CIIICACO AND NKW VdKK 
 
 Thk Mykon C. Ci.akk PiHi.isnixc, Cd, 
 
 i;. Lt F. N. Spo.v, Ltd., 57 Haymarket 
 
 I'joy 
 
Copyright 1909 
 
 BY 
 
 H Grattan Tyrrell 
 
ri{Ki Ad:. 
 
 Hri(l<rcs of solid 
 
 Jlll.V () 
 
 tli( 
 
 niati'rii 
 
 cHiirn'tc iiic siii)(.ri(.r to those of 
 
 Tl 
 
 JUiil have i\ \ 
 
 K'v arc as pcriiiaricnt as st 
 
 one 
 
 ilu<-ts built l»v the Hoi 
 
 <''<s <-<)st. .Masoiii-v l)ji(h 
 
 :('s and a«|ii('- 
 
 sniii.'of tliciii in use. A tVw old cast 
 main, datinjr l,j„.|< ;, ..cntury ov uun-o. but 
 
 nans arc still stainlii 
 brid 
 
 iron 
 
 «'f the modern ones built of 
 
 lave ji very limited existence. Fort 
 
 bridy 
 
 ami 
 •'cs re- 
 
 a nujjority 
 wi-ou]L,dit iron and steel 
 
 es Avere 
 
 y years ago, steel 
 
 but It is now well I 
 
 i)''Iie\ed to be permanent struct 
 
 nown that thev do not 
 
 ;ist lonjrer than from twenty to tliirt 
 
 urcs. 
 
 },'cnerallv 
 
 y years. 
 
 Soli 
 
 <1 concrete bridge 
 
 wliich rein fore in;,' metal 
 
 tensile stresses in the arch riii?.' ('out 
 
 soal ' 
 
 are su|»erior to those in 
 is re.|uired for resisting 
 
 inuous water- 
 
 K'.ifT reduces tlu' adh(>sion of concrete to steel 1 
 
 illx.l-; 10') ,„.,. ,.,.„t. ;,,„l tJ„. ,.ft-,.,,j ,,f 
 
 )V 
 
 'so tends to dest 
 < furs that crach.s develop, sufTiciently ] 
 
 •ihoeks and yi- 
 n>y the bond. It fre- 
 
 t" ml, Mi! water, and when water and ..., 
 llie reinforcing' metal, it is then only a i 
 f'X'c the metal is d.-stroyed by rust! 
 An ohi Avire suspension bridw that 
 
 arffe 
 
 moisture reach 
 ew yeai's be- 
 
 \viis ex 
 
 xamined and reported on by tl 
 
 \v;is found that fail 
 
 recently failed, 
 le writer, and it 
 
 I'll-' Jind breaking of th 
 
 ure occurred because of tl 
 
 le rust- 
 
 e wire cables embedded i 
 
 » '" anchorage. AVhen the bri.lge was buil 
 'l^'ubtless considered that the cables when 
 
 111 
 
 n 
 
 as 
 
 t, it w 
 painted 
 
rKF.FA ('/:. 
 
 cind «'iiil)t'il(|((l ill fniHTi'lc. wtTt secure iij^iiinst cor- 
 nisioii. Siirticiciil eiiulion wms not t,-il;en t<i cxclud'' 
 moisture from tlie jiiiehorjiKcs. nnd the nridge failed 
 as stilted above, liy llie rustiiit; and l)i-eaking ot tlic 
 eml)e(ldi'(l metal. Il is esideiil. Hiei'etore. that 
 the most eiiduriti<r l)i"id<ri's are those of solid masou- 
 ry. whore tio metal is reijuii-ed. 
 
 Many (>r the larjrest masonry hridyfes built in re- 
 cent years, have m-eh rinj;s hiiill of solid conerelo, 
 without reinfor«'iii<r metal for resisting direct stress- 
 es. Details of some of these iire yixcn in Tahle No. 
 I. Hven in arches with reinforcemeiit. the best dc- 
 sijrners are now proportioniiijr the anli riiijrs. so the 
 line of pressure foi- uniform lojids will at all times 
 fall within the middle third of the ;M-eh rinj;, and 
 re(|uire no reinforcin*; for these loa«ls. 
 
 Tn the Enjrineer's l*o(d<et-riook. My. Trautwino 
 makes the followin<r statemenls: — "Nearly all tlu) 
 s<'ientific principles wlii(di eoiistitute the foundation 
 of Civil Enffineerinjr. are susceptible of complct*; 
 and satisfactory explanation to any ])ersoii who 
 I'eally i)ossesses only su(di knowled^'e of arithmetic; 
 and natural philosophy, as is tau<rht to boys in pub- 
 lic s(diools. The little that is beyond this, may safe- 
 ly be intrusted to the savant. lict tliciii work out 
 the results, and <iive them to the eiiirineer in intclli- 
 irible lariprn:i«re. We can afford to take their word, 
 because !^ di thin<rs are their specialty. The object 
 has been to elucidate in phiin En«,'lish, a few ii;.- 
 ])ortant elementary ])rinciples, which the savants 
 have enveloped in such a haze of mystery, as to 
 
PREFACE V 
 
 iviid.T piiisiiit hop.'lfss to ajiy hut « cmfirnu'd nuifli- 
 I'liialicijui." 
 
 Scvcnil complete and very comprolionsiv.' tr.-ji- 
 tis.- have already been ^vritton, covering tlio mat he- 
 iiiatieal tlieory (.f urches, and as far as this feature 
 of the subject is concerned, there is little left t) 
 be desired. 
 
 In til • preparation of this manual, the effort has 
 therelore been made, to as far as possible eliminate 
 iiiathenmtieal I'ornudae, and to jtresent the subject 
 ill the simplest possible nmnner. Only such material 
 IS jriven as is directly re(|uired in the design and 
 eonstruction of ordinary concrete or masonry arches, 
 so it will i)e unnecessary for the busy engineer t(» 
 spend valuable time and thought in the perusal and 
 study of obstruse mathenmtieal treatises. ]»racti- 
 (•ing en«riiieers have but little lime for nuithematical 
 investigation, and generally iimst accept fornuilae 
 as given to them by others. 
 
 A real need for this book is believed to exist. ();\ - 
 ing to tb.e increased use of concrete l)ridges. 
 
 The designs and data tables for culverts and tres- 
 tles are original with the author, and are here pre- 
 sented for the first time. They are the result of 
 his own practice in the design and construction of 
 railroad structures. 
 
 Tn the preparatio of this manual. I have receive.! 
 valua])lc assistance from my wife. :\raude K Tyrrell 
 a graduate of the Chicago Art Institute, ami cx- 
 peneneed in architectural design. I am indebted 
 also to the following gentlemen for assistance as 
 
VI 
 
 Ph'EF.lCF. 
 
 noted:— To .luliiis Kahn f..r t 
 
 trestles, {() Whitiu'v W 
 
 wo views of eonerote 
 
 arn-ii, Areliited. for v 
 
 iew8 
 
 <»f the proposed Hudson Memorijd Mridge, 
 to Messrs. Leii and Felpite f(.r views and 
 
 drn 
 
 w 
 
 inifs of the Hoekv Hiver Hridjre. to (J,.,. 
 S. Webster for a plioto{?raph of the Walnut I 
 Mrid< 
 
 illiistratiofis and draw 
 
 
 (• at Pliiladeli)hia. and to II. Hawfrood for th. 
 injrs (.f the Santa Ana Bridge 
 
 1 am also indeM..| to the Engineering News f 
 
 or 
 
 drawings of the pr.-ix.sed IIuds(.n .Alenurrial Bridge, 
 the Spokane and th.- rjrand Aveime Bridges, and to 
 the Engineering Kcc.rd fur two drawings of the 
 Kocky iJiver Brid-o and drawing ut Edn.ondson 
 Avenue Bridge. 
 
 r , ,„. . H. 0. Tyrrell. 
 
 Evanston. Illinois. 
 
 November, lOOO. 
 
TAULr: OF CU.\Ti:\TS. 
 
 I'AKI I -J'LAIX COXCRKTi.; 
 
 AKCIl liKID iS. 
 
 C'dnijH 
 
 ■-•Itloii 
 
 PaKe 
 
 .\(l 
 
 N.iiiianis ot MaMniiy Coil 
 
 iKirtainty ui Ala 
 
 iinii 
 
 '•"iiry ArcFu-; 
 
 struction. 
 
 IliiiKid Aril 
 
 us. 
 
 Mtioi) ot Siiriiigs 
 
 A'Mitiiunt I'itr 
 
 il 
 R 
 C 
 
 "^■iKlit ut IJri.ly. 
 
 iM- aiK 
 
 I Sp;, 
 
 111. 
 
 rowii lliickii 
 
 Thick 
 
 iicss u 
 
 f L 
 
 nnvii I'illiug 
 
 10 
 11 
 11 
 1-^ 
 
 r.' 
 It 
 
 Spandrels l<i 
 
 Varit 
 
 Kll 
 
 ip-c 
 
 us Forms and How to Dra\V Tli 
 
 em. 
 
 ulii-CenttTid Arch. I lirce c 
 
 Multi-C 
 
 I'arahoiic Arcl 
 Hvd 
 
 t-ntinil Arcli. l-uc C 
 
 enters, 
 enters. . 
 
 les. 
 
 16 
 20 
 20 
 20 
 
 ros 
 
 Sel 
 
 tatic and (leostatic Arcl 
 
 Kxt 
 
 eetion of M„st Snitahle I 
 
 les. 
 
 ernal I.nads and J 
 
 orni. 
 
 Matl 
 Stahility K 
 
 orces. 
 
 uniatical nuory of the Arcli! 
 
 ■23 
 24 
 27 
 29 
 
 Ih 
 
 Worl. 
 
 imate Valnes. 
 
 efpnrenients. 
 
 '"iiij,' I'nits. 
 
 L; 
 
 ine of Res-ist; 
 
 me o 
 
 f R. 
 
 '"ii't of R 
 
 "Hx-. I-ull I.oadin 
 
 33 
 
 34 
 3,^> 
 
 sistance. Partial Load 
 
 3t> 
 
 npnire 
 
 K'ing 4.f; 
 
 Hetermination of Arch' Thickneis: '. ■ • • ■ • 5i» 
 
 '••ickniR 51 
 
 \\aterpr<,onng' and ' Drainage.' .' ." H 
 
 I'lteniudiatc Piers . . •^- 
 
 A!)iitmint Piers 
 Aliiitn 
 
 53 
 54 
 
 K-nts < 
 
 Finndations 5o 
 
 E 
 
 xpansion 
 
 Snrf 
 
 aco Finish 
 
 Cost of Concrete Arch li 
 
 ridges. 
 
 vu 
 
 .58 
 60 
 60 
 63 
 
 «* 
 
 ffi 
 
VIII 
 
 C'OXTHXTS. 
 
 Dosisn for a .io ft. Arch Bn.iiro ^T- 
 
 LiicvL'u i.oailiiiir "•> 
 
 Riquired Arch An'.-i ^ 
 
 IntcTiiR'diatc J'iers. *'" 
 
 Ahiitnuiit riiTs. ^p 
 
 Tonte Kotto. Rnnu -Masonry Urulgcs 71 
 
 Bridge n{ Augustus a. ■Rimini," Vtni; Ij 
 
 Hudson Memorial Uridge W-w York- ■(•;;,■• i? 
 
 A'u-klan.l. X,.v Zealand. P.ridL ^ -"" '^ 
 
 Rocky R.vcr Bridge.. CIcvcIan.lOhiu " " f ? 
 
 ^Valn„t Lano Brulgc. Philade pi i" ?J 
 
 Snmn \ -"^ p'- r '^'■"'R^"- Illinois. . . .^ J' 
 
 San a Ana Hndge. Cahfornia . . ^? 
 
 i able ot Lc.icrete Arch Bridge^ Jl 
 
 ''^''^ "mSufS^^^^^ coxcRETE'ARai 
 
 Historical ( )ntiim' 100 
 
 Advantages of Rdn f^^c^d' Voncrae !'!; 
 
 Adhesion and Bond 106 
 
 Metal Reinforcement. . .., 1'"^ 
 
 Reinforcing Systems. HI 
 
 Concrete Conifx .sition 1 1" 
 
 Loads 120 
 
 rnits-L-ltimatc "and" \\V„-kiV'g |-'! 
 
 1 hcorv of Arches l'2> 
 
 r.ciicral ntsign 1^8 
 
 Hinged Arches. 136 
 
 Rililiod Arches... NO 
 
 Intrados Form. . 1-H 
 
 Spandrels !■!•'> 
 
 Piers and Ahntments 1-1" 
 
 c™.. ot _Roi,,f„,c„i concv;;^ ■ Xr.:,; nri„„„ ::::::: I ^ ^ 1^5 
 
 Appro.vimatc J'lstiniating' ivices V'^ 
 
 1 a hie of Approximate Ouantitie^ .' .' .' I'J'' 
 
 I otoniac ^(enional Bridge D-si-n }. 
 
 .lanv>f,,\vn Exposition ISridge. ^ ',7 
 
 I'rnnkhn Brid-re, Foresi P-,rl- kV'i ■ l''l 
 
 TcfTerson St. Br id-H- S m, f P.^ ' T^ '^1 
 
 r.arv, Indiana. BJidge ''' ^"'''■'"■' l''l 
 
 O-imo p:,rk Foot Prrid"-e St ' P-,,'.! "'-^ 
 
 B,.dde. Faced Bridg!^^^^^^^ S 
 
 ^1 nn;l Rapuls Arch Bridge 1"» 
 
 ^-^ !(]G 
 
 '. -^'msi^'^^^'^^msm 
 
COXTF.XTS. 
 
 IX 
 
 T^ridgc at V 
 
 I'll ire. 
 
 Calif 
 
 nartiiM Park l',ri<Itji- C 
 Suin-Toiifcn l',rii|"i. "s 
 
 Tal>I 
 
 >{ i 
 
 oriiia . . 
 'iicay<' 
 \vit/cr!a;i(|. 
 
 Page 
 
 xtiiit(,ri\-(l C.ncn.-tc .\roIi 
 
 PART ITI.-IHrjIW.W HHA 
 
 <>nii)ansnii ot ,\rcli and li 
 
 M HRIlXii; 
 
 It;') 
 . Wi) 
 .17.{ 
 
 174 
 
 Htani IWulii 
 Mcthud of D 
 
 •cam. 
 
 I'Slgl! 
 
 ■\RT ly-COXCRFTE CLTAT 
 
 .181 
 .183 
 .18.j 
 
 TKKSTI.i;s 
 
 R'lS 
 
 AX I) 
 
 cqiurc.l Si;^f of Culvert On, 
 euitorcrd Concrete I" 
 
 eiimg. 
 
 Load 
 
 >x Culvert 
 
 .18!) 
 . 1!»1 
 
 I- 
 
 coiU)inK- i.c'iiKtli for Sial 
 
 Reinf 
 
 ii'.s and Sial)-1 
 
 orced C. m-rete Slal. Tal.le \o. \-l 
 
 >eanis. 
 
 nRle Box Gdv.ns, Slal. T;pe.Tal 
 
 I>i)llMe UnK Clll 
 
 )Ie \, 
 
 \'l!, 
 
 ingle l!,,x (u! verts/ R 
 DouMe Ho\ C-.dverts. V, 
 
 vtrts, Slab Type, 'ial.ie X,,', Vlij 
 
 earn 
 
 Otl 
 
 ler C 
 
 T'ltne Ciihert Co>t.s. \'ri 
 
 uul Slali, Tahle Xo IX ' 
 am and Slal.. Tal.le Xo. X..' 
 
 ""lion Culvert !• 
 
 irious !• 
 
 I .rnj-. .... o 
 
 Culvert Data. Tahlc Xo. XI 
 
 ornl^^. 
 
 Con 
 
 Crete Railroad Trestles '. -'-' 
 
 .1!)4 
 .It).-. 
 .I9i< 
 .198 
 .2(1.'', 
 .207 
 .209 
 Ml 
 13 
 
 m 
 
 097 
 
 
 
 conomic Span Lengths 
 'escription of Various Tresile'Dei 
 csign A.. "-^ !'«.. 
 
 B . . . 
 
 C 
 
 n.,.. 
 
 K... 
 
 F ;;;; 
 
 G and li 
 
 28 
 
 igns. 
 
 .2.30 
 .230 
 .230 
 .235 
 .23.5 
 .2.38 
 .2.38 
 .2.38 
 
 oniparative Trestle Costs -^? 
 
 242 
 
LIST or /J.J ISTR.ITIOXS. 
 
 PART I. 
 . . Solid Concrete Arch Brihges 
 
 trontispiece-Potomac Memorial Bridge, Washington. 
 
 Pig 
 1. 
 
 •1 
 
 4. 
 A. 
 
 <j. 
 
 I . 
 
 H. 
 
 !<. 
 10. 
 11. 
 12. 
 13. 
 14. 
 lo. 
 Hi. 
 17. 
 18. 
 19. 
 20. 
 
 21. 
 '>■; 
 
 23! 
 24. 
 
 20. 
 27. 
 2f<. 
 2!» 
 30. 
 31. 
 32. 
 33. 
 34. 
 35. 
 36. 
 
 37. 
 38. 
 39. 
 
 21 
 22 
 23 
 26 
 27 
 ■S8 
 
 Ellipse P^Kf- 
 
 Three Centered .Arcli "^ 
 
 Pive Centered .Arch 
 
 Parabolic Arch 
 
 Hydrostatic Arch ..........'. 
 
 Comparison of Above Curves 
 
 Pressure Curve, Full Loads. ^ 
 
 Alternate Pressure Curve. Full Loads.' .' 44 
 
 Pressure Curve. Partial Loads it 
 
 Design for Twui Arches.... To 
 
 Abutments ^2 
 
 Design for Railroad Bridge ?-!) 
 
 Ponte Rotto, Rome "o 
 
 Bridge of Augustus at Rimini,' Italy 7^ 
 
 Hudson Memorial Bridge -r 
 
 Monroe St. Bridge, Spokane. "Vvasli .'.'."".' 70 
 
 Rocky River Bridge, Cleveland .... L, 
 
 Rocky Ruer Bridge, Cleveland 00 
 
 Rocky River Bridge. Cleveland .... qa 
 
 Walnut Lane Bridge. Philadelphia at 
 
 Connecticut Avenue Bridge. Washington." .' 88 
 
 Big Muddy River Bridge. Illinois. . f 
 
 Santa Ana Rrid,q:e, California 
 
 Santa Ana Bridge, California .".'.'.'.'.". 
 
 PART II. 
 Design for Concrete Higluvav Bridge on 
 
 Theory of Arches ' ,04 
 
 Grand Avenue Bridge Design, Milwaukee: .' .' .' 43 
 
 James own E.xposition Bridge.. . ,Mn 
 
 f/ff^''" g"''^'''-/:r^t Park. St. Louis.':.',;.:: m 
 
 Jefferson Street Bridge. South Bend. Indiana 64 
 
 Gary, Indiana. Bridge.. J.". 
 
 Como Park Foot Bridge. St. 'PauL' : : : : «? 
 
 Boulder Paced Bridge. Washington . . laL 
 
 Grand Rapids Arch Bridge . . }2° 
 
 Bridge at Venice, California {-, 
 
 Garlield Park Bridge. Chicag.i: ::::::::::: 172 
 
 PART III. 
 Three Span Beam Bridge.... ,o(\ 
 
 Single Span Slab Bridge.. ]fl 
 
 Single Span Beam Bridge. }^ 
 
 l>0 
 92 
 93 
 
LIST OF ILLUSTRATIONS. 
 
 XI 
 
 Fig. 
 
 4". 
 
 41. 
 
 \1. 
 
 43. 
 
 41. 
 
 4"). 
 
 4i;. 
 
 17. 
 1.^. 
 1!>. 
 •Vt. 
 
 r.i. 
 
 .V2. 
 •VI 
 
 .ji. 
 
 ■V'(. 
 
 •It;. 
 
 "m . 
 
 '0, 
 
 til*, 
 (ii. 
 lii. 
 (;:r 
 
 ti'i. 
 tit;. 
 
 PART IV. 
 
 Page. 
 
 Richmond. Va.. Trestle 18ti 
 
 Augusta, Ga., Trestle 1!)0 
 
 Relative Cost of Slab and B.anis •_'()<> 
 
 Single Box Culverts. Slabs -202 
 
 Double Box Culverts, Slabs -joS 
 
 Single Box Culverts, Beams 2(i4 
 
 Culvert Cost Chart 213 
 
 Culvert Cost Chart 217 
 
 Concrete Box Culverts, Slal)S 218 
 
 Concrete Box Culverts, Beams 22i) 
 
 2eam Top Box Culverts 221 
 
 Concrete Box Culverts, Slab Type .222 
 
 Concrete Box Culverts, Beam and Slal) 223 
 
 Rail Top Culverts 224 
 
 Reinforced Concrete Arch 22.') 
 
 Beam Top Culvert 220 
 
 Paraliolic .Xrch Culvert 22(5 
 
 Sewer T\ pc .\rch Culvert 227 
 
 Concrete Trestle. Design .X. Rail Top 231 
 
 Concrete Trestle. Desifjn B, Ream Top 233 
 
 Concrete Trestle. Design C, Steel Beams 234 
 
 Concrete Trestle, Design D, Beam Top 236 
 
 Concrete Trestle, Design E. Slalis with Rods 237 
 
 Concrete Trestle, Design F. Beam and Slabs 2.39 
 
 Concrete Trestle, Design G. Slabs 240 
 
 Concrete Trestle. Design IT, Beam and Slab 241 
 
 Concrete Trestles, Comparative Costs 243 
 
 li 
 
 I 
 
1 
 
PART I. 
 
 PLAIN CONCRETE ARCH BRIDGES. 
 
 Composition. 
 
 Masonry arclios vcrc fontiorly Diiilt almost on- 
 tircly t)f brick atid stone. In recent years, however, 
 owitifi to the increased prodnction of cement and 
 modern methods of making c»»ncrete. including the 
 crushing of stone and the mixing and handling of 
 materials, a large nund)er of iiir modern bridges are 
 built of concrete. P>rick andies hudv the bond of 
 stone. They a.*e usually laid in concentric rings, the 
 I'dge of the brick appearing in the soffit of the areh. 
 ()<'('asionany the bri(d<s have been laid dry. and 
 irrout run in to fill solid all cavities. As brick is 
 a softer uuiterial than stone or concrete, its use does 
 not appear to have any special advantage. All 
 masonry arches, whether built of brick or stone as 
 blo(d\ structures, or nuule of conert-te in a solid 
 monolith, carry their loads entirely through com- 
 pression in the arch ring, and while the uiortar 
 joints would doubtless resist considerable tension if 
 so re(|ui>-<'d. no reliance slumld be placed on the ten- 
 sile strength of such joints. 
 
 Advantages of Masonry Construction. 
 
 In niany respects a masonry arch is sui)erior t<» 
 ritlier a steel l)ridge or a combination of steel and 
 concret(\ Some of these advantages may be enu- 
 merated as follows: — Cenu'nt hardens with age. ami 
 co!isefpiently the older the bridge, the stronger it 
 iHM'omes. Therefore, if it successfully sustains its 
 first test load it will always be secure. This 
 condition is reversed in steel structures, which 
 
 ^^n 
 
 "^W>JE>i.if 
 
2 COXCRETi: BRIDGES .IM> ClI.rEKTS. 
 
 (Ictcrioratc with aire llirt>u<rli the iictioii oT 
 nisi and Ihc loosciiiiij; ol" rivets and pins. As 
 travel increases, enncrete l)rid<;es Ix'conie stronj^er 
 to support it; neither is there any yearly 
 expense for paintinj; or ntliei niainti-nance. 
 Tliey ean <;enerally he built from l;»eal nia- 
 tei'ial, and iarfrely hy local and unskilled labor. 
 The buildin*,' and completion of such bridges 
 is not dependent on mills, shops, or the operation 
 of trusts, as is fre<|uently the case with steel struc- 
 tures. In this respect, concrete bridjjres have an 
 advantaire over those of cond)incd steel and concrete, 
 for in the latter case, it is fre(|uently necessary to 
 await the convenience of the shops for the reinfor- 
 cin<^ steel. A consideration that should appeal to 
 the purchasers of bridjres is. that local labc ■ and ma- 
 terials for concrete structures can usually i»e secured 
 and used, and the money expended by a miuiicipal- 
 ity <;oes back to its own people, instead of j;oin<; to 
 distant points in payment for nuinufactured steel. 
 
 Arches in jreneral. which form is usually adopted 
 for masonry bridj^'es. present a more substantial and 
 !)leasinti appc .i'a!ic(- than can ])e secured by any 
 foi'm of truss, even thouj;h an andicj truss be con- 
 sidered, for in a truss, the outline of the arch is not 
 so evident as in a solid stnicture. F(>r railroad 
 brid<;es the arch of solid concrete is superior to Ww 
 reinforced, in that its ^'reater weijrht and nuiss more 
 readily absorb the vil)rations and shocks due to the 
 passajre of heavy traiidoads and euf^ines. Concrete 
 bridges require no lioor renewals as steel bridges 
 
 k 
 
; 
 
 /7..//.V coxcRirrii akcii briikjus. :'> 
 
 frcqiicnlly do. and they will jr«'iu'rally cost from l'> 
 to :}() per ci'iit less than stoiu'. They ai-c tiro proof 
 ;iii(l liav(> no sttM'l. cithor i.i the form of priaei|>als or 
 iciiiforcemeiit. to rust. They can be Aviil( iied at rny 
 lime without tearing; down the orif^'Uial hridjjes, as 
 mist he done with brid^'es of wood and steel. 
 
 I'.ridjres of solid concrete are particularly suitable 
 lor permanent railroad structures. Many railroad 
 coiiipanies are roali/.in<? their suitclor advantages 
 jiiul are replacin<; their steel bridiL^es with new ones 
 of masonry, and while thes<' concrete bridges arc 
 fre(|U(>ntly reinforced with steel, the main arches 
 are in most cas .s. designed to resist only compres- 
 Xwv stresses, with no need for steel in tension except 
 to better utiite the arch and to prevent cracking from 
 change of temperature. .AFany iron and steel rail- 
 road bridges in America have been replaced two or 
 three times l)y licavier st.'el ones during the past 
 thirty or forty years, in order to renew worn out 
 sti'uctures or to provide for heavier loads. When 
 it is rcDiembered that several nujsonry bridges in 
 Europe that were built 2.000 years ago, arc still 
 standintr and in use. it is evident economy for per- 
 manent roadways, to rebuild ordinary spans in ma- 
 sonry. Views of two old Roman bridges are shown 
 on subsc'iuont pages. Ponte Rotto at Rome, shown 
 on page 73, was first completed in the year 142 B. C, 
 and while it has been danuiged several times by 
 Hoods, owing to its unfortunate location, three arch 
 snans still remain in good condition. The Bridge of 
 Aiigustus at Rimini, supposed to have been built 
 
 "M^^t m -jl-A r-.c-^i; 
 
4 COXCRE'IL DRIIKil-S .IXP CI l.rERTS. 
 
 filiout 14 A. I)., (lurinp tlic n'ifrii o\' Kmpcror Aiifrus- 
 lus. has five arcli spniis. Tlw i>i«'rs an- very hoavy 
 and support scniirivcular arches. The hridfie is fine- 
 ly onianicntfMl. is still in -rood coiidition and in use 
 at the i)resent time. A view is shown on papje 75. 
 
 Uncertainty of Masonry Arches. 
 
 As compared with sttM'l frames, the desifjn of ma- 
 sonry arches is uncertain. The hypotheses upon 
 whifdi the desi<.Mi is hascd are only approximate as- 
 sumptions, and Avhen constructed, the action of th" 
 andi under loads is unreliable. In the former case, 
 with single truss systems and truss lines meetiti-r 
 in points. Avitii workin«; unit values (dosely known 
 by lon<^ series of exjierinuMits in both tension and 
 ('(•mpression. the desi<rnin«r of such frames has be- 
 come almost an exact science. It is dif^'erent with 
 iiutsonry andies. as their conditions under loads are 
 ^oo little known to arrive at any exact metho<l for 
 l)roportioninjr them. Moreover, even if these con- 
 ditions were more lofinitely known, the same incen- 
 tive for reducing the (piantities of material does n<'t 
 exist in masonry as in steed structures. ])ecause of 
 the coniparalive cheapness of masonry. Some of the 
 indefinite factors in the design of masonry arches are 
 as follows : — 
 
 (1) The condition and amount of the external 
 forces are n(»t definitely known. For instance, ui 
 an andi with spandrel earth fillinfr. the amount of 
 the conjugate horizontal pressure of the earth against 
 the extrados of the aridi is comparatively unknown. 
 
 •^^^rrs^m 
 
!'i..ii\ coxcNiiiii ARCH BRinans. 
 
 ir till' tillinjr wore ii li<ini(l. the oxt(>rnal pressure 
 would then be tioniial to the extriuh)s and its 
 ituouut would he definite. This eondition does not 
 ordinarily exist, and the nearest approach to liipiid 
 pressure is from s|)andrel tiUin<r of (dean dry sand, 
 it is well known that earth tillinjr. whicdi. when new- 
 ly phi'-ed. will stand at no <rreater slope than om- 
 iiiid onedialf to one, will after it heeonies set. su|>- 
 port itself for a time, at any rate, with alnu)st verti- 
 cal faces. Ilenee. eonjuirate pi'essure whi(di may 
 have existed at first, while the andi was under eon- 
 ^tru(•tion. may vanish hiter. In the case of an arcii 
 under a deep embankment, it is plaiidy evich'iit that 
 such an andi does not sui)port the entire wei^dit of 
 earth fillinjr above it. as the earth to some extent 
 andies itself. The case of a tunnel andi is an excel- 
 lent example. Such an andi is proportioned to 
 carry only a small jiart of the load above it. de- 
 p('ndin<i- upon the natun' of the overlyinj? material. 
 Further, where the masonry is continuous over the 
 piers, especially where a l;tr<rt' amotuit of ba(d<inj^ 
 is used, the material tends to cantilever itself from 
 the piers, and thereby relieve the andi of miudi of 
 its load, or if the amount of backing,' and filliii'Jr 
 above it be lar«re. these materials may to a «rreat ex- 
 tent andi them.^elves from pier to pier, and thereby 
 relieve the real masonry arch. The external span- 
 drel walls may also act as arches and carry a con- 
 sideraiile load. The above remarks ai)ply to liridge 
 andies. In he case of arches in buildinjis, the con- 
 dition of the external loads or forces is even more iu- 
 
 ! M 
 
 •i ! 
 
 , 1 
 
 ■HKHi 
 
i; COXCKlill: HRIlHiliS .IXP CIIAERTS. 
 
 (li'linitf. Take, for fXiiinplc. tlu' case of aiiarchcar- 
 ryiii<r a wall lna<l a^ov.- it. It is custoiiiary to con- 
 sider that the arch carries the entire weight of such a 
 wall The fact, however, is that an unbroken wall 
 supports itself almost etitirely, hy actinj; as a mason- 
 ry beam or hy archiiijr itself, anil the only portion 
 snitported hy the arch is a trian«;ular piece of ma- 
 sonry directly above it. This is true for a wall 
 without ojK'niiijrs. When openinjrs occur the above 
 consideration will be etlfected. depending' upon the 
 location of the openin<rs. If they occur in such i)o- 
 sitions MS to evidently interfere with, and destroy 
 tli( beam or arch-action of the suiterimposod nni- 
 sonry. then the entire wei«rht of masonry may come 
 on the arch. There are many bridfre arches now 
 standinj; that W(»uld doubtless fail, were they sub- 
 jected to the entire weiy:ht of the materials above 
 them. After strikiniL' center, the andi itself has set- 
 tled. ;'nd nnich of the imposed load is transferred to 
 the piers by the cantile\« . or andi action, of the 
 backinir and fill, or the arch action of the spandrel 
 walls. 
 
 (2) Another unknown factor in the desi<,Mi of ma- 
 sonry arches is the strenjrth of masonry. Experi- 
 ments have been made ])rincipally on small sam- 
 ples tested in machines with pressures normal to 
 surface, all of which c(Miditions are (|uite different 
 to those of a'-tual arches nmler loads. The material 
 is th(Mi concentrated in l)nlk. Avith pressures inclined 
 to bearing,' surfaces and with loads more or less of a 
 vibratory luiture. 
 
 ■\S. 
 
PI..HX COXCRliTIi .IRCII nRHKir.S. 
 
 it 
 
 (\\) It is usually assiimcd by .'iijriiiccrs iind ai 
 iilysts. that til.' .joints ».f hlock structures sui-li a^ 
 masonry arclu's ^vill resist no tensile str.'ss. This 
 is a pr'eeaution on the side of safety, hut may hi- 
 lar from true. With a rieh .lualily of eoiierete. we 
 know that i)roi)erly formed points will actually re- 
 sist c..nsi(h'rahle tension. !)rovided they remain in- 
 tact. 
 
 (4} The position of the line td" resistance in the 
 arch is not detinitely known. This is lar<,'.'ly du.' to 
 the continuity of the andi at the ceider. and the 
 sqr.are heariufrs at the piers or spritifrs. To obviate 
 this difticulty. some European enjrineers have l)udt 
 masonry arches with hin«res at the crown and 
 springs! thus fixing the position of the line of resist- 
 ance at these points, but in America such provisions 
 are not generally used. 
 
 (.")) Tmi)erfect workmanship in the cutting of the 
 stones and the littiiig of tlu' joints is another factor 
 .•ausing the actual line of resistance to m()V(> from 
 its supposed position to a different one. where the 
 joints come to a firm bearing. 
 
 ((5) The removal of the andi center and the se^ 
 tling of the arch to its pormanent position, al u> 
 effects to some extent the theoretical considerations. 
 It appears therefore that any effort at ultra re- 
 finement in arch design is a waste of energy, for the 
 actual conditions existing in a completed structure 
 niay not even approximate those assumed. 
 
 1 
 
^ 
 
 8 C(>\i'h'i:ii. nk'ii'ciis .i\i> CI i.n:h''s 
 
 Form. 
 
 Tlif riinii or trt'iicriil oulliiK' is tli<" iicst cuiisitli'i'M- 
 tioii ill the (|('si<,'ti t\^ ;i iiiiisoiiry jin-li. Sciiiicir- 
 nilnr jiml sciiii-i'llipliciil ;ir<lii's. i (»iiimi>iily kiinwn as 
 full (M'!il('i-('(1 jiii'lirs. s|)i-iii«r from liorizniitiil ln-tls, 
 uliilf scjrnit'iitji! iin-hcs spi'iiiy: fmiii iin-liruMl ImmIs 
 ciillctl sK('\\ harks. Tlic nld IJoiiiaii arches wtTc iicai'- 
 ly all sciiiicirtMilar. In hridjrt's and \iadiii'1s whci'i 
 P'km's art' used, lull ct'iitcrcd archts or thosf which 
 spriiif; from hoi-izontal hcds. ai-c prct'crahlc lo sc(»- 
 mciital an-lics spriii^niijr t'l-oni inclined hcds. for \\w 
 reason that full centered arches prodnce a less over- 
 tnrninjr luonient on the pier, and their attachment 
 to the i)iers \vifh hoi'i/ontal hcds is simpler than 
 with inclined sprinijs. The thnist on piers, however. 
 d( pends upon tlu' I'ise of ai'ch. which is not neces- 
 sarily the distance from sprinjr to center intrados. 
 Tlie c!Vecti\(' rise is the vei'tical hei<rht from sprin;4 
 lo crown, mi .isnred on the lineal" ai'ch or line of 
 pressure and any minor curve .)o.inin<r th.' a''ch sot'fit 
 to the pici-. is not ctTective and nuist not he con- 
 sidered as part of the ris( . Se>iiiiental ai'ches li.ivo a 
 shorter curve than elliptical for the same span, or 
 for the same lcn<:'1h of soft!', the sej^montal arch 
 results in a wider span. For sm:dl spans such as 
 conuiionly used f«ir culverts. se<rinental ai'ches con- 
 tain from 2.') to 4n per cent less masonry than senii- 
 eircular nrchos. thcup-h common jtractice makes the 
 scETmontal arch riii<r 10 to 2.") per cent thicker than 
 tl;e soniicircular. For lluid pressure the proper 
 form of arch is the semicircle. The effect of earth 
 
 \ 
 
/7..//.V cowis'iri: .INCH nk'in(;iis. !• 
 
 fill or other loads at tlic liauticln's. tftuls to raise the 
 line of pressure to the appntxiniate t'oriii ot" an el- 
 lips '. while the efVeet of a unift»riu l(»a(l. siieh as the 
 we. -lit of earth fill and pavement above the crown. 
 to<j:eilier with a uniform live load, tends to dej)ress 
 the line of pressure to the apj)ro.\inuite form of a 
 parabola. The eomltiJU'd efl'ect oi these two loadings 
 is to briiiir the line of pressure more nearly to the 
 sej^men* of a eirele. The most economical form is 
 a lineal' arch >>[' the <,'iven span for the reipiired 
 loadintr, in which the thickness is proportional to 
 ihe thrust. In such an ai-ch every part of the cross- 
 section would be stressed alike. One authority ree- 
 omnu'Uds that the form of intrados for an^hes with 
 cai-th filled haunches be midway between a circular 
 sejrment and ellipse. Any variation from re«rular 
 curves that is sufVicient to be a[)pareiit to the eye, U 
 a violation of a principle of desijjn and should not 
 l)e permitted. The many three and five centered 
 fhit arches already in existence are sufficient to ch r- 
 ly prove the utter failure of such forms to produce 
 artistic or satisfying: efTeets. If multi-centered flat 
 arches must be used, they should be drawn from as 
 many centers as possible. Thre<- and five centered 
 arches are suitable when the form approaches a, 
 semicircle. 
 
 An economical form of arch with cantilever brack- 
 ets at the ends has lately been built over the Vermil- 
 lion River at ^Yakeman, Oiiio The bridge has cross 
 walls with open spandrels, a clear si)c.n of 145 feet, 
 and end cantilever brackets 37 feet long. The reth- 
 
 "r!». 'LvwH'iMa'rjn 
 
o( 
 
 ioxcRiiii- HNiiH.iis .ixn cri.riih'Ts. 
 
 1 nc'issitiitcs llic use (if rcinCon 
 
 <'iiii(»rciii<r Jiictiil at tho 
 lt()(.i- li'vcl for tlic purpose of tyiii«,' the l)ra('k-('ts to 
 l!it' iiiaiii span. A sotnewliat .similar plan was adopt- 
 ed in liie Topeka hridtre. l)ut in the latter ease the 
 eonerete cantilevers were for retainin*; walls only. 
 The eanlilcvers were tied tojrether with rods to pre- 
 vent spreadin-r from the i)ressnre of the earth filling. 
 In the case of arches such as culverts under high 
 end)ankmeiits. the se^'mental arch Avith its horizon- 
 tal thrust is economical. The arch thrust resists and 
 counteracts the earth pressure on the sidewalls from 
 without. 
 
 Hinged Arches. 
 
 A i)ractice tiiat has lon<r l,t.,'n followed in Europe, 
 is to i)rovide stone (.r metal hinges at the crown and 
 springs. The use of such hinges locates definitely 
 the position of the line of ])ressure at these points, 
 and tliereliy removes om> of the common uncertain- 
 ties i,( masonry bridges. Hinges are particularly 
 desirable wliei-e the nature of the soil is yielding or 
 uncertain. Any lateral movenu-nt of the abutments 
 ciuises the andi to siidx at the crown when the centers 
 iii-e remove,!, and such siiddng produces cracks that 
 are unsightly ami [)ossibly dangerous. When hinges 
 are used, the joints are filled in solid with cement 
 niortar. after tii(> .•enters are removed and the arch 
 ri!!ir has assumed its final position. For additional 
 loads, the entire area of both hinges and nu)rtar fill- 
 ing will then be available for resistino arch thrusts. 
 
 V 
 
p/.j/.v co\CRi:rii .ih'cii nk'i/H;i:S. 
 Position of Springs. 
 
 U 
 
 The arch spriii«rs slioiild he located as iioar 1(» 
 the f(»iuulati(»ii as conditions Avill permit. This will 
 reduce the overtiiriiiiijf effect on the pier to a niiiii- 
 nmni. and jiroduce a more staltle construction. S(»me 
 of the conditions fjoverning the position of the 
 springs are as follows: Over streams the sprinj? must 
 be sufficiently hij;h to allow ample water way. and 
 clearance for the passajje of boats or drift: over 
 roads or hi«?hways the sprinjrs must be sntlficiently 
 hifrh to provide proper head room and clearance for 
 the [tassage of pedestrians and vehicles, and over 
 railroads, for the passajre of cars. In the last case 
 there must be a cb-ar head room of at least 21 feet 
 at a distance of five feet from the face of ])iers. 
 This allows clearance for the lar<rest box cars and 
 additi(»nal space for trainmen on the roof. 
 
 Abutment Piers. 
 
 For ]()n<x bridires or viaducts with a series of 
 arches, abutment piers, oi- those of sufficient thick- 
 ness to resist the pressure of a sin<;le arch, should be 
 l)laced at frequent intervals. Where the spriujr lin.' 
 is located so near the f<»undation. that piers need not 
 be excessively thick, it may ])e dcj^irablc to have all 
 ])iers of the abutment tyjie. Then, during? the 
 coui'se of construction, the spans may be built indc- 
 ]»endently aiid false work renu)ved when desired, 
 without reference to the adjoining spans, or after 
 the completion of the bridge if oiu> span should be 
 destroyed by flood or othei" cause, the other spans 
 
12 (oxcRirn-: liKiiKins .ixn cri.rnh-rs. 
 
 would still ivmain iiitii<-1. IF iill piers in ati arch 
 \ ladiict arc of the ordinary type, to support vertical 
 loads only, and one span should he destroyed, then 
 Iho nMn;)i?iin<r spans would also fall, one after the 
 other in succession, hy the ovcrturninjr of successive 
 piers. 
 
 Height of Bridge. 
 
 In most cases, the heijriit of Uw hridj^c or level of 
 the roadway will he previously deteniiined. In s(.nie 
 cases, h. n-ev.'r, tli.' Iloor jri;,.Ie may he varied nu)re 
 or less hy jrradiim" the approaches to suit other con- 
 ditions. It may In- that money spent in raisinjr the 
 iippi-oachcs and the level of the hrid^H' floor, will he 
 saved many limes in the cost of the masonry. 
 
 Rise and Span. 
 
 The span is the clear distance hetween vertical 
 faces of piei-s or ahntnuMits. and the rise is the 
 hciirht (.f crown ahovc s[)rin,irs. measured on the 
 
 hii 
 
 •' o! pressure, nd not <.n the arch ititradc 
 
 )S. 
 
 Curves joininL' lh,> arches to j)iers are not part of 
 the ct^'ective rise. 
 
 The lenirlh of span and rise of andi will he amoni,' 
 the first c(.nsiderations. In many cases, the natural 
 • •onditions will determine cnie or hoth of these di- 
 ni.'nsi.u.s. If the hrid.-e is short, a sin-l.' span mav 
 he sufficient. If it spans a street or rapi.l stroan'i. 
 where piers are impi'acticalde. the conditions will 
 '■''''"''■'■ ""'y <>•>•' ^Pit'i. In h.n- viadu.-ts. the 
 dividin- of such a structure into spans of proper 
 length IS an imjH.rtant matter. The economic span 
 
 V 
 
/7..//.V coycRiiiii .ih'cii iik'inci-s. 
 
 in 
 
 the total li 
 
 f 
 
 l('ii<;tli (Icpoiids cliioHy iipop. the total liei»j'il o 
 slnjctiirc above foimdatioiis. (iciicrally, hi<ji:li stnie- 
 tiii-cs i'('(|iiir(' loiijrer spans, juul lower strnctiires. 
 shorter spans. For steel bridjres with vertieal reac- 
 tions, the eeononiie length of span for various 
 iiei^'hts is Avell known or may easily he determined. 
 l)ut with ai'ches there are other considerations. The 
 usual i)ractice is as follows: — IMace the sprin<;in}» 
 lines on the piers down to the lowest point jjossihle 
 i-onsistc!;, -\vitii the necessary clearance, and tifter 
 allowiniT for the thickness of the arch rinjr and fill- 
 intr at tlie crown, draw in spans, the len«rth of whi(di 
 ;ire from two to five times the rise of the arch. ])ref- 
 erence beini;' <iiven to sjtans of twice the i"ise or to 
 semicirculai' arches. Certain other conditions, how- 
 ever, may determine the leufjth of span. P^)r exam- 
 ple, in a lonj? viaduct over railroad yards, it nmy 
 he desii-ed to span a certain number of tracd^s with 
 each andi. or to have as few piers as possible t'' in- 
 terfere with additioiud tracks or switches. Tn ihat 
 ease, the len^rth of span may be fixed arbitrarily re- 
 u'ardless of the rise or height of bridge. 
 
 Tn fixing the lengths of a series of arch spans, the 
 Romans made those spans nearest to the center of 
 the river, loiiger than the shore spans. The plan is 
 still in general use. and it has the merit of causing 
 the span at a distance from the shore observer, to 
 it]!ii(ar at least as long as the nearer ones. "When 
 a uniform s|)an length is used, the eiTect of perspec- 
 tivii is to cause those spans near to the river center 
 
14 
 
 coxcui'.Ti-. BRinci-s .i\n crf.rrRTS. 
 
 I 
 
 ihich should I) 
 
 100. to appear 
 
 which shouul l)t' of jjrrcator iinpoi 
 shorter than they really are. 
 
 To balanee the pier thrust from unequal s|>ana. 
 the shorter one may have a smaller rise with greater 
 earth tilling and eonsecpiently greater loads. 
 
 Several of the large railroad eompanies have re- 
 cently adopted standard segmental culvert arches 
 having a rise of one-fifth the span. Tn many othei- 
 bridges this proportion is exceeded, especially 
 where natural or (»ther conditions govern. General- 
 ly speaking it will be found cheaper to make long 
 spans with few i)iers, provided sufficient rise is 
 available. 
 
 Crown Thickness. 
 
 Tn the preliminary design it is necessary to know 
 approximately the retpiired crown thickness or dei)th 
 of keystone, and also the amount of earth filling 
 over the crown, to determine the remaining distance 
 from crown to spring or the available height for 
 the rise of arch. The crown thickness may be found 
 approximately by reference to tables of existing 
 arches, (tr from some reliable empirical formula. 
 Trautwine's formula for such thi<d\nf>ss is as fol- 
 lows. ;i development of the formula for various 
 sjians aixl rises l)eing given in the Engineer's Pocket 
 Manuid 
 
 Deplli of key in feet ^ R adius+ lialf span ^,o f^ 
 
 4 ■ 
 
 The above is for the jirst class cut stone work, 
 either circular or elliptical. For second class ma- 
 sonry, increase the results from the above formula 
 
PLAIX COXCRRT/i ARCH PRIDCFS. 
 
 1." 
 
 by ono-oi{?lith. for briek, l)y oiio tbinl; for lar<r<' 
 elliptical arclu's sonic ciitriiiccrs iiicrciisc also the 
 ;il)ovc values by onc-tliii'd. 
 
 Kaiikine's nilc for crown tbicl<ncss is: — 
 
 For sinorlc spans \A'l Radius 
 
 For several spans . .17 Kadius 
 
 Tt bccomos necessary therefore to determine the 
 radius at the crown. This can be done jTraphically. 
 The crown radius for an ellipse can be found as 
 described later and sliown in Fi<rure 2. Tt is com- 
 mon practice with small se«jmental arches to maU'^ 
 the arch ring from 10 to 2.') per cent thicker than 
 semicircular ones. 
 
 The crown thickness nuiy also be found approxi- 
 mately by first determinino; the approximate crown 
 thrust. This is easily computed by findinj; the cen- 
 ter bending moments for all loads, the same as for a 
 beam, and then dividing by the rise, or the approxi- 
 mate crown thrust may be found from Xavier's 
 rornuila, Tr^/r, where T is the crown Ihrust, p the 
 average pressure per sipuire unit on the arch, and r 
 Ihe radius of arch at crown. Tt Avill be noted that 
 the proper value for the crown thrust is that one 
 which produces e(piili1)rium about the point of rup- 
 ture, and not about the springs. 
 
 The experience of the writer in using Trautwine's 
 tables of sizes and quantities for masonry arches is 
 lliat Trautwine's figures are about one-third larger 
 than the best practice now in use by the large rail- 
 road systems for tlie design of concrete arches. 
 
 I 
 I 
 
 Mil 
 
16 (T).VC7v'/r/7: HKIlHIliS .IXD Cn.rr.RTS. 
 
 Thickness of Crown Filling. 
 
 An assumed (lei)th for tliis filling is re<iuired as 
 noted above, in order to determine the available 
 heifjht for the rise of the areh. For highway 
 bridges, a depth of filling ineluding the pavement, 
 of from one to two feet will be suffieient. but for 
 railroad struetures a greater depth is neeessary in 
 order to form a eushion for the ties and absorb and 
 ilistribute the shock from passing trains. For this 
 purjutse a depth of from two t(» four feet, or ordi- 
 narily of two feet below the ties will be suffieient. 
 To secure this cushion effect, the filling in some re- 
 een{ (-inerete railroad bridges has been as great 
 as five feet. 
 
 Spandrels. 
 
 Bridge spandrels are either filbnl solid with earth 
 held in place hy side retaining walls, or the fioor 
 over the spandrels is supported on a series of in- 
 terior walls and arches, which may or may no* ap- 
 pear on the exterior. The solid earth filling h, gen> 
 erally use,] f,,,- small spans and fiat arehes. Hut for 
 large arches and espeeially semicircular ones, the 
 op.'n eonstruetion will be cheaper. In eertain eases 
 of eomparatively flat arehes, even where it would 
 '"' inor.. expensive than solid filling, the open .span- 
 drel construction nuiy be desirable fur the purpos.^ 
 of reducing the load on the foundations. This 
 was the ease with an elliptical arch bridge recently 
 
Pl.AIX COXCRETE ARCH BRIDGES. 
 
 17 
 
 built by tlio Illinois Central Railroad Company over 
 !>i}; Muddy Rivor. containing three spans of 140 feet 
 caeh. with 30 fret rise. It was found that the open 
 sparulrel construetion reduced the loading on the 
 l)iles by about six tons per pii<'. "Which one of 
 llicsc methods to use in any particular case, can be 
 determined l)y juaUing comparative designs and es- 
 timating the costs. In many cases, however, the 
 clioice caTi l)e made by inspection. 
 
 liy building open (diainbers crosswise of the bridge 
 and having the openings appear oi the spandrel 
 faces, a design is produced that presents a lighter 
 appearance and at the same time shows plainly the 
 plan of cnnstruction. When a heavier and more 
 massive appearance is desired, theti the side walls 
 may be nsed and all spandrel openings closed. In 
 large arch's ai)proaching the semicircular form, if 
 open spandrels are used and the interior spandrel 
 walls run parallel with the axis of the bridge, these 
 walls then act as backing and produce the necessary 
 conjugate thrusts on the haunches below the points 
 of rupture. The jieed of i)r()viding for necessary 
 con.jugate thrusts is important and muse not be over- 
 looked. Cross spandrel walls and open chambers or 
 arcades may be used above the point of rupture. 
 l)ut below that point the construction must be solid. 
 This type of construction is well illustrated by the; 
 Connecticut Avenue bridge at Washington, shown 
 on page 88. 
 
18 
 
 COXCRlSTIi BRinCI-.S ASH CII.II'.RTS. 
 
 An iiiij)r()\('(l method (tf dcsij^iiin^ spaiidrcls is il- 
 lustrated in the Piney (Veek Paraholie Arcli bridjje 
 in Washington. The (loor slabs are carried on an 
 interi(>r system of beams and columns supixjrted on 
 the arch iiii<r. an<l the spandrels are enclosed witli 
 thin curtain walls. A desijrn similar to this for a 
 sejrniental arch was prepared by Mr. Thaeher for 
 llie Hcllefield bridfjre in Schenley Park. Pittsburtr 
 'Phis system is a v<'i'y economical one and has the 
 advantajres of lea\ inj; the interior construction open 
 at all times foi- inspection, and of producinj? a less 
 amount of load in the spandrels f(.r the arch to 
 larry. T!ie curtain walls are also thinner than re- 
 tainin«r \\alls for earth, fillint; and cost proportion- 
 ately less, and the pavement nmy be laid at once 
 without waitinj; for the Hllin«r to settle. When the 
 pa\-ement is laid, there will never be any liability 
 of the road settlin<r. as often does occur when pave- 
 ment is laid on earth fillinjr. even thou<rh such, fill- 
 in;,' be well rammed and permitted to settle a lon^' 
 time Itefore laying the roadway. 
 
 'Pile use of the open spandrel construction with 
 cither ei-oss Avails or columns avoiils any uncirtainty 
 in i-efercuce to horizontal <-on.jugate pressure from 
 spandrel tilling, and also prevents water collecting 
 and soaking into the arch masonry. When it is de- 
 sired to secure a greater diversity in design, the face 
 walls may be omitted and the interior arcade or 
 colonnade construction artistically treated for the 
 
 
PLJix coxCRi'.rr. arch PyRinci-.s. 
 
 19 
 
 purpose of prodiu'iiig a iiioro pleasing arehiteelural 
 clTect. In eoinpariiig the relative eosts of colon- 
 nade and areHtle eonstruetion for spandrels, en- 
 closed column construction will jjeiu rally be found 
 the cheaper, for the beams and columns nuiy be left 
 rough, and the spandrel curtain wall only will need 
 a finished surface. Cross arcade construction has 
 the economy of snudl dead load, but all open span- 
 drel walls are exposed to view and nniy rerjuire fin- 
 ished surfaces or possibly architectui il treatment. 
 Open chand)ers may be enclosed at tlie lop. either 
 by means of arching or by using Hat slabs of 
 stone or reinforced concrete. The upper surface is 
 then waterproofed by ai)plying a layer of rich mor- 
 tar and surfacing with neat cement, on top of which 
 is poured a layer of tar or pit(di. The surface may 
 then be leveled with gravel and sand, and the pave- 
 ment laid. 
 
 Another reason for selecting either the solid or 
 the oi)en spandrel type is for the j)urpose of adjust- 
 ing the ijnposed loads on the arch to the form 
 selected. This may be necessary to secure stability 
 and will be considered later under the head of load- 
 ing. In designing the side spandrel walls to retain 
 earth filling the usual rules for retaining walls will 
 apply. Practice is to make the thickness of such 
 walls at the base 40% of the height. They should 
 be firmly doweled or otherwise secured to the arch 
 niasonrv. 
 
 Si 
 
 4 
 
20 C().\(h-i:iii liKiiHii-.s .\\n cri.ii-.Ris. 
 
 Various Forms and How to Uraw Them. 
 
 Tlic roriiis iidnptcd I'di' tlic iiitnidos of inasonry 
 iin-li Itr!(l<.'t's i\n> jri-iicrjilly circnliir. scj^incntal, 
 t'lliplic.il. or iiiulti-ctMitcn'd. TIm'sc foui- types <'im 
 Ih' reduced to two.cireliliir and elliptical, for tliese;.'- 
 iiieiilal areli is iiier(dy a sejrment of a circle, and the 
 iindti-<'eiitere"( areji is merely an approximate ellipse, 
 'i'lietwt general forms are. therefore, the circu- 
 lar and the elliptical. 
 Methods of drawing 
 the ellipse and the 
 multi-eenteredcur\ e 
 are as follows: 
 
 Ellipse. . 
 
 Lit A!) and CD 
 
 »' 'he semi-major 
 fill .spuii-minor a\es 
 of an ellips»> at rijrht 
 anirles to each other. 
 Draw circular arcs 
 with radii AD and ('D. nsijectively. From points 
 where a common radius intersects the two circular 
 arcs, draw vertical and horizontal ordiuates. The in- 
 tersection of these ordiKates<,nves points on the ellipse. 
 
 Multi-Centered Arch— Three Centers. 
 
 These curves are sometimes called hasket-handlod 
 arches. The uiethod of drawing a throe-centorod 
 
 Fig. 1 
 
 J 
 
PI.. \i\ c 7 ) \-( h-r: Ti- . / A'( 7/ liRii h:es. 
 
 21 
 
 ^iin-li is as follows: 
 I.i't AD iiixl (M) 
 l»o tlio si'iiii-iiuijo. 
 a ii II (1 sciiii-miji ir 
 ax OS. respectively. 
 ^ of a true ellipse. 
 The form of the 
 true ellipse is first 
 <' r a w 11 by the 
 method <r i v e ii 
 above. This is 
 shown ill Fifrurc 2 
 l>y the full line. 
 T h e appro.xiinate 
 form is then 
 o drawn as follows : 
 Assume any two e.,iial distanees ("B and AK less 
 than half of the semi-minor axis. Joi,, BE and biseet 
 tlie lin<> P.K at F. Throu<rh F draw a perpen.' u- 
 l;ii- t(. BK. interseetinjr th.e line (7) at (). The two 
 I'"ints O and K will be eenters of two eireular ares 
 which will form an approximate ellipse. By first 
 seleclin- the position of the point E so the circular 
 ."v describ(>d fro,,, E as center will conform -.^ 
 •losely as possible with the true ellipse, satisfactory 
 '•urves will easily be found. The full line on Figure 
 1' shows the true ellipse and the dotted line the ap- 
 I'l'oxim. te. 
 
22 COXCKETB BRIDGES AXD Cri.rUNlS. 
 
 Five-Centered Arch. 
 
 A iiM'flHMl fur (IrjnviiijL' a fivf-cciilcn'd iirch is as 
 Tollows : — 
 
 Til order \<> dicfk nn tin- v oik. it is advisable to 
 llrst draw the foriii of tlif tnu* ellipse by the iiietliol 
 
 •riven above. Tn 
 Fii,'iire :{ the two 
 curves so elosely 
 eorrespond that 
 ojdy one oan bi' 
 shown. On th'' 
 transverse axis 
 A() draw tile 
 reetanjrle ACICO. 
 (Mliial ill lieiirhL 
 to the senii-iiiinor 
 axis OC of tlie 
 ellipse, and dr;: w 
 the diajjoiial A' '. 
 From G draw n 
 line OIID per- 
 l)endlcular to AC! 
 and intersect i II <r 
 the center lir.e 
 
 FiK. :j 
 
 CO of the span produced at D. From O as cen- 
 ter, with radius OC, draw th(; circular ([uadrant 
 as shown. Describe the stniicirclo ARL and 
 imKluce the line OC to it.s inter.st-ctiou with tho 
 semicircle at L. From O as center, describe tho 
 arc at M with radius equal to CL. and D as center de- 
 
/V..//.V c-().vcA'/ //: .ih'cit liRincns. 
 
 23 
 
 scriho jirc (f.M, \\\\\\ DM as ni<l is. On the axis AO 
 liiy off AX tM|ii)iI In Of,. TIh'ii fn.iii II ns cciit.-r. 
 with nuliiis IIX. (Icscrihc the jirc X(/. ciittin}; M'l 
 jit a. The three poii.ts IT, a and I), with corrfsixtiHJ- 
 inp OIK'S ill the otlicr «nui(lriiiit nrc the tive desired 
 eeiiters from wliieh to draw tlie approximate ellipse. 
 This method of drawing a five-eentered arch as ap- 
 proximate to an ellip.se must not he eonfouiided with 
 the method piven later for drawin<r a hydrostatie 
 arch. The eroM-n radius of the e]Ii{)se will l>e less 
 than the eorrespondinj; radius of the hydrostatie 
 arch. 
 
 Parabolic Arch. 
 The paraltnja is not fretpiontly used in masonry 
 hridjres. hut the formula for drawintr it is jjiven. If 
 
 is as follows : — 
 ' o \ he various let- 
 
 ters refer to di- 
 meiisinns shown in 
 the a<'eompanyiii^ 
 Fi''ure 4. 
 
 y 
 
 1 •«. » 
 
 J-2 h 
 rt2 
 
 The line OK is divided into any numher <.f 
 convenient e(iual i)arts, whieli are luunhered 1. 'I, W. 
 etc., be<;iuuiuj,' at the point nearest O. Tlien jo 
 find the value of y, for the various ordinates x. the 
 numbers 1, 2, ,*{, etc., may be inserted in the above 
 ecjuation for values of x, and the total number, wliieli 
 in the illustration is ^^, will be inserted for the value 
 
24 
 
 COXCRETi: HRinCES AM) (.77./ 7:' A' 7 .V. 
 
 of a. Tilt' upjHT line ill Fiirurc 4 shows tlir corn's- 
 poiitliii^ rorm for n tnir ellipse. 
 
 A \ ei'v simple jri-jipliiciil luellHxl of (Irjnviii<r the 
 piirahol.i is t(» hiy ollf on llie \-eftie;il line h'S the 
 sMiiie iiuiiiher of eipuil divisions jis di'invn on the 
 liorizonliil axis OR. and fi'oiii () draw radialinjr lines 
 to the various division points on the xcrtical axis 
 liS. From the various points on the horizontal lini' 
 Oil di'aw vertical lines iiiterseetinjr the radiatiiiir 
 lines from (). The |)oiiits at which these vertical 
 lines intersect the i-adiatin<r lines iwv |)oints on the 
 rctpiired paraliolic cnr\'e. 
 
 Hydrostatic and Geostatic Arches. 
 
 In selcctiii!.' the most snitahle form for the iii- 
 trados of an ar(di. the followin<;' i-onsideration of 
 the ahove two forms of curves will he serviceahle. 
 The hydrostatic ai-ch is the form of a linear arch 
 under varyinjr pressures wlii(di are always normal 
 to the line of arch. This condition corresponds t) 
 that of an andi suhmer<r(;d Ixdow the surface of 
 water. As the dei>th bi'low the surface increases 
 tlii'se normal pressures increase propoiM ionately. and 
 as the external pressures are always normal to the 
 snrfa<M'. the amount of pressure in the arch is con- 
 stant, and is ecpial to the produce of the external 
 pressure at the point by the radius of curvatur.'. 
 The (Mjuation is T^-f^r. and is known as Xavier's 
 Prititiplc. Since the essential priiicipit! of the hy- 
 drostatic arch is that lluid pressure is normal to 
 the surface, the thrusts at all points of tlie arch 
 
/7.J/.V coxck'F.ri: arch hridgi-.s. 
 
 i'iii<» iirc. tlicrol'iirc. constiuit. jind ciniiiot \ iiry with- 
 out the iipplicatioii of > '.'liuf or taiiffciitiiil pres- 
 sures. Since T is cot >;aiit. / \\\\] -jiry directly as /> 
 Tliese radii may \w f litid for va yiuj; de[)ths belcnx 
 water level, and the . < i .•-^! -Midinj; curve plotted. 
 It will be noted that tht> thrust T at the crown, is 
 equal to the total horizontal pressure on the e\- 
 trados of half the arch. 
 
 ('•rdinarily. liowevtM-. arches are subjected to earth 
 pressure i-ather than water. The external forces 
 !.re, therefoi-c. no lonjjer normal to the oxtrados 
 of the arch, but ])ear a relation thereto, dependinjr 
 on the nature of the overlyini; nuiterial. Tn the case 
 of earth or <_M'avel tillinpr. haviiifr an an<rle of repose 
 of one and one-half to one. it is known that the hori- 
 zontal pressure exerted atrainst vertical surfaces is 
 about one-third of the wei^'lit of the material above 
 
 the point under consideration. Tho formula is H = ^. 
 
 The linear andi suppoi-tin<r a filling of clean dry 
 sand would be the true form of the geostatie arch. 
 If /> is the horizontal intensity of force in the 
 hydrostatic arch, and p' the coiresponding force in 
 the geostatic arch, then />r:r=r/''- It will ])e seen, 
 therefore, that the ureostatic andi bears the saiu" 
 i-elation to \\\i' liy<lrostatic andi as the ellipse does 
 to the circle. A linear geostatic arch may. there- 
 fore, be drawn for any assumed value of (", sueh as 
 ^. which ex|)erimeiits show to be about the right 
 factor for earth or gravel filling. Tn drawing this 
 linear arch all the vertical co-ordinates of the hydro- 
 
2<; 
 
 (.oxcRF.TE liRfncrs .ixn cn.rnRr.'^. 
 
 stntic iircli ;u'(' rctiiiiicd. iind coiijnjrjitt' prossni'os 
 cliaiifri'tl jici-onliiin' to the foninilji p^-Cp'. Foi" 
 ;ii-clics iukIci' liciivy l)iui]<s ((f cartli the geostatic 
 anil can be drawn from the liydrostatio areh. Tl* 
 tilt' h('i<rlit is fixed, the form of em-ve and proper 
 width can he found to properly witlistand the earth 
 pressui'i". For lii'idjrt'.s. these principles are iiscful 
 •■liictly for arches under hifrh ciiihankments. 
 
 In his hook on Civil Kn^nneci'ing. pajje 420. Ran- 
 kine irivcs the following' approxiiiiat.> method for 
 drawiiifr the form of a hydrostatic curve al)out fivo 
 centers by means of circular arcs. Tlie two radii ;' 
 
 ~x amir" are first coniputt'd 
 from the acc()nii)anyinLr 
 formula. Thi.s fixes two 
 «)f the centers and the 
 tliird is found at E as 
 shown. The e«[uati<»n.s 
 for radii are as follows: — 
 
 T 
 
 r^ - 
 
 " ii + ': 
 
 a 
 
 r I -f 
 
 •» \ !>■■ 
 
 HP y 
 
 l)E AF— BI) 
 
 a 
 
 b'—a'j 
 
 ^ 
 
PL.UX iOXCRETF. ARCH BRIDGES. 
 
 27 
 
 f! 
 
 Ill Fitrurc '>. let FB bo the half span and FA the 
 i-isc of tlio proposed arcli. Make A("=::=;-^, and 
 lJn=:i^;'', the radins of '•nrvatnro at the crown and 
 sprinriii'; as ealeulat.v. from tlie ahove fornmlae. 
 Tlien (' -will be one of the eenters and D another. 
 About 1), witli th(» radins I)E. describe a circular 
 ;ir<'. and about C", -with radins CV. describe another 
 
 circular arc. Let 
 K be the point of 
 intersection o f 
 these arcs. Tin- 
 points D, E and <J 
 Mill be the re- 
 ([uired centers. 
 
 ]\rany semi-ellip- 
 tic arches ap- 
 l)roach very near- 
 ly the form of a 
 hydrostatic arch. 
 A comparison be- 
 twt't'U Kaukine's approximate curve and the true one 
 aie shown in Figure (!. The upper or outside curvf* 
 is llie api)roxiiiiate eurve as given by Rankine. The 
 (•('liter curve is the true hydrostatic arch plotted 
 from a succession of radii, and the inside curve is a 
 1 rue ellipse. 
 
 Selection of the Most Suitable Form. 
 
 Full centered arches, either circular or elliptical, 
 produce the least overturning moment on the i)iers. 
 and will generally require less pier masonry than 
 
 l"lg. G 
 
 1 
 
 i 
 
 ■ii# ; et!. .« - « 
 
28 
 
 cnxckniT. BRincrs axd crr.rnRrs. 
 
 
 s('<;mf'iit;il ardics. If tlic arch thrusts iijriiinst iiat- 
 iir;il )-(K'k sk('wt)iicks or al)iitiiu'iits. the niuouiit of 
 siicli tlinist is then a iiiattcr of little iinportaticc as 
 far as the aljutiticnt is coticfnicd. The altafhiiicut 
 of sejrineiital arches to piers usually re(|uires tilted 
 heds to l)riii<r the joints at ri^'ht aiij,'les to the liii(> 
 of jn-esstire. This is a condili.Mi that does not occur 
 ill full (-entered arches. In flat ellipses the i)ier 
 thrust is ^'■reater than with seniicii-cular ar(dies, the 
 position of thrust api»roachin<>: more lu-arly that of 
 a seoiii(.nt;d ai-(di. It has already been shown that. 
 for andi culverts carrying' i envy earth banks, the 
 sejrnieiital form of arch Avill be more eflfectivo and 
 less expensive. It produces heavy thrusts on the 
 abutments, which thi-usts counteract the inward 
 pressure of tl;e earth on the side i-etaininjr walls. 
 At the same time there is a shorter lenjjth of curved 
 work to build than with a semi-circular form. The 
 cost of seii'mental culverts has been shown to ])e 
 only about (iO^; of tlie cost of the correspondintr 
 semicircnlar ones. 
 
 After drawin<r a trial linear arch or line of re- 
 sistance for any particulai- case, the form of this 
 trial curvi' will sufrjrest the most suital)le form for 
 the intrados of the structure. For a brid<;e with 
 spandrel filling' jnid londs increasin«r from the center 
 to the spring's, the elliptical form or a correspond in.t? 
 multi-centered arch will probably lie lu-arest to the 
 linear aicli. while for an andi with open spandrel.-! 
 the condition of loadinjr will be more nearly uni- 
 form, and the curve will be flatter at the haunches 
 
PL.UX CO.VCRF.Tf: ARCH BRIDGES. 
 
 29 
 
 * r 
 
 If 
 
 ;ui(l approncli the form of piirabola. Tn such oasos 
 llio scs^iiiPiital form would probably bo iisod instead 
 of the elliptical. The elliptical form requires less 
 filliiij? in the haunches than the segmental arch, and 
 lias, therefore. l(>ss weijLrht to carry. At the same 
 lime it <?ives a jrreater amount of (dearanee under- 
 neath. \ semicircular or Roman arcdi with a lar<.'e 
 rise generally re(iuires the smallest piers, and in a 
 high viaduct, where the piers are an important part 
 of the total cost, tliis form will be economical. The 
 exact line of resistance for an arch luider a high 
 eiidmnknuMit is the geostatic arcdi. Tt may. how- 
 ever, be assumed as an approximate ellipse. The 
 form of the intrados under earth whose angle of 
 re|)ose is :]0 degrees Mill then be determined by the 
 iMluation : — 
 
 Vertical axis ■- 
 
 H(n"izoiital axis A 
 In designing culvert arches it will be advisable for 
 the engineer to consult standard plans for such 
 structures. ]\rany considerations will appear that 
 might not at first occur to the designer. 
 
 External Loads and Forces. 
 
 Tt has already been shown that both the amount 
 and direction of the external forces acting on a 
 iiuisonry arch are indefinite. Tn an arch supporting 
 a masonry wall it is usually assumed that the arch 
 carrie.s the entire weight (»f wall above it. This 
 is on the side of safety, but is certainly not correct. 
 The wall will, to a great extent, snnport itself. 
 
 .»■ ii m 
 
 m 
 
 ' " " . m 
 
?,0 
 
 coxch'iyrii hkiih.hs .\\n cri.n-.Rrs. 
 
 citluM- iicliii<r as a bfaiii di- ardi. and tlic ]ir()liability 
 is that till' wcijrht of only a small porlioii of llic 
 wall (lii-cctly ahovc llic arch is iill that is cari-ic 1 
 directly l»y it. Arches under hijrh ('nd)anknionls 
 certaiidx' do not siippoi't the entire wei^dit of earth 
 ahove thein. The earth coi'hels oi- arcdies itself, as 
 is plainly seen in the case of a tunnel, where oidy 
 a small portion above the crown is sni)])orted by 
 the tuiuiel center. It is customary to consider that 
 andi bridjres \\\\\\ spandrel (illinir support the entire 
 weiurht of such filling- on the ar(di rin^r. The fact 
 is. however, that the l)ackin«: and fill either arch 
 thenisehcs. to some extent. fi"om pier to pi(>r. or if 
 the hacking' is continuous over the pier, the backinir 
 itself wiil then form a cantilever and carry much of 
 the s|)andi'ei loads. 
 
 The Knjilish enirineer. llrunel. uiany years n<ri> 
 desiijiied and l)uilt a semi-arch of ])rick. with hoop 
 iron bond. (iO feet in len^Mli. whicdi supported itself 
 entirely by cantilever action. S;in(>e the introduc- 
 tion of reinforced concrete as a <lesirable material 
 tor ai'ch construction, it has becon;(> common })i'ac- 
 tice to build cantilever arms oi- bivud^ets on. the 
 shore ends of andi spans. showin<r that the eanti- 
 lever principle is just as sure to come into action 
 when contiiuiity over the j)iers exists, as it is that 
 the andi thi'ust itself is in operation. A jrood illus- 
 tration of this cantilever construction is shoAvn in a 
 bridjrc recently built o\er the ^ rmilHon Kiver at 
 \\ akeman. Ohio, and di^seribed in Eufirineerinfr-Con- 
 tracting. February 1, lOOf). Somewhat similar eanti- 
 
PI.AIX COXCRF.'I i: ARCH BRIiHlI-.S. 
 
 31 
 
 lever firms were used t'cr retaiiiiiifr walls iit the e\\i\^ 
 of Die reinfnreed eoiierete iirell hridfje at Topeka. 
 Kansas. 
 
 N'dt only is llie aiiiouiit of vertical loading from 
 the tilliii<; unknown, I -'t the horizontal eon.jujjrate 
 jii'essnre on the masonry haunches is also indefinite. 
 AVe know that neai'ly all semicircular arches, or 
 those (jf similar form, after the centers a.re removed, 
 will settle at the crown and recede laterally at the 
 haunches. The effect of this settlement is to briny; 
 i-onjujrate pressure on the l)ackin«rs. and, therefore. 
 it is certain that pressure exists there, but the 
 aiiiount of such pressure is unknown. Semicircular 
 arches re(|uire backinj* below the point of rupture 
 to produce conjugate pressure eipial in amount to 
 the crown thrust. This must be secured, either from 
 l)a(diing. fill tu- spandrel walls. If the i)()int of rup- 
 ture in sefrinental arches is at or near the skewbacd\, 
 the conjufrate thrust then comes from the abutment, 
 and little or no backing or corresponding walls will 
 be ref|nired. While conjugate pressures are neces- 
 sary for stability below the point of rupture, it has 
 lieeii ilemonstrated that conjugate tensions are nec- 
 essary above that point, and to secure that result, 
 rods have been used. The intensity of conjugate 
 thrust from eai'th lilling with an angle of repose 
 of :W degrees is oiu'-third of the vertical. It is good 
 practice to cut the voussoir stones on the extrados 
 of the arch into steps with horizontal f.nd vertical 
 faces, so the pressures on these may be normal to 
 the surfaces. 
 
32 
 
 coxch'f-.Ti: BRinr.rs .ixn cci.ri-.RT<!. 
 
 Sclicnicr's 'riicorciii ;issuiii('s llijit ,ill external 
 liiiidintr jicts verlieally. 'i'liis is an error uii llu' safe 
 side and will i-e(|nire al»nliiients sli<;hlly heavier 
 than when e()njn«rate horizmital forces are consid- 
 ered. 
 
 Tt has already been stated that elliptical arches 
 have less fill or material ahove th(.|ii. and conse- 
 qnently less weijrht to carry, than either se<ifnuMital 
 or parabolic arches. 
 
 Tn the case of arches snpportinp: earth filling, the 
 form of such tillinjr will, to a lar<r" extent. dete»'- 
 mine the proportion of weijrht that bears upon the 
 arch. A lon<r brid<re will carry the entire weijyht 
 of material al)ove it. while a cnlvert nnder a hij;li 
 bank will carry only a jxirtion of the nnterial above 
 it. Sewer arches exist Avhich would be unstable 
 without earth jiressure. showinjr clearly that con- 
 ju'jate eai'th pressure does exist. 
 
 Mathematical Theory of the Arch. 
 
 The theoi-y of arches is very complex and in- 
 tricate. Analysts have <riven much thou«;ht to the 
 matter and nuiny voluiiu's have ])een written, when 
 in reality, the complete determination of the force 
 polyj^on. and the correspon(lin<r line of resistance in 
 the arch, constitut.- all the c;>lcidations involved in 
 the practical (lesi«rii of a masonry arch. All methods 
 of comi)utation are approximate only. The thick- 
 ness of arch is first assumed by comjiarison with 
 tables of existing arches , ■ by the use of some em- 
 pirical fornuila. Twines of resistance are then drawn 
 
ri.UX COXC'liTIi ARCH liRlDGIiS. X] 
 
 for this iin-h. and if these lines (!<» not fall within 
 tho mid lie tliird of the arch rinj?. the form is 
 elian<re<l and a new lin«> of resistanee is drawn for 
 the revised fonu. The ealenlations resolve them- 
 selves into a series of trials. Xo effort will be made 
 here even to review the many theories of the areli. 
 For siieh investi<?ation the student is referred to the 
 writiiifrs of mathematicians. Their eonelusions oidy 
 will he iriven in this book. The theory is based 
 upon the assumption that joints will i-esist no ten- 
 sion. 
 
 Stability Requirements. 
 
 The re(|nirements for complete stability in a ma- 
 sonry andi are three in number: 
 
 (1) There shall be no rotation i>f one part of tin' 
 arch about another. 
 
 (2) There shall be no sli(lin<r of one surface upon 
 another. 
 
 (•'{) The unit pressure shall be such that no crush- 
 ing of the arch nuitei id shall occur. 
 
 To insure the first re(iuirement it is necessary 
 that the line of i-esistance shall lie entirely within 
 the arch rin<r. and to insure further that the pres- 
 sure shall be distributed across the entire section 
 of the arch, and no tendency to openin<r of the joints 
 occur, it is necessary that the line of resistance shall 
 lie within the middle third of the arch rin<r. To 
 avoid slidinjif of one joint ui)on another, all joints, 
 includinjr those in tlie arch and in the abutment, 
 shall make an<rles not less than TO deirrees with the 
 
 i I 
 
?A 
 
 COSCRETE BRIDGES .IXP Cll.VERTS. 
 
 liiif oi" resistance. The frietinii eoeffieient for ma- 
 sonry joints is from 407r to :^{y/, . To avoid crush- 
 injr of the areh material, the eross-seetion of the arch 
 shall 1)e sutlficient.so that the intensity of pressure at 
 the outer edtre shall not «'.\eee(l a certain safe work- 
 injr unit With these three re(|uirenients fulfilled, 
 the stability of the arch is assured. If a line oP 
 resistance cannot be drawn within the middle third 
 of the areh rin<r. then it is ru'cessary to change 
 either: — 
 
 (1) The thickness of the arch riujr. 
 
 (2.) The form of the arch, or 
 
 (.'}) The distribution of the loading;. 
 
 Practii'c in tli lesijjn and construction of con- 
 crcfc arches \,ii. , in reference to the absence or 
 presence (»f joints in the areh ring. In large struc- 
 tures, where the entire c(»ncrete cannot be placed 
 from one mixing, it is customary and sometimes 
 necessary to provide joints in the arch ring, and as 
 an additional precaution against slidinj; of such 
 .■•lints, they may !)(' (btweled or d(»vetailed together. 
 
 Ultimate Values. 
 
 The ultimate crushing values of the common arch 
 materials are as follows: 
 
 (iranite ....l.OOO to IS.OOO ponnds per s(piare inch 
 
 Limestone .4.000 " 10.000 " " " <• 
 
 Sandstone .;}.()00 " lO.OdO •• " '• << 
 
 Concrete ..2.000 " 4.000 " •• " '« 
 
 Brick ;100 " (iOO " •' ■' '< 
 
I'l.AlX COXCRETH ARCH BRIDGES. 35 
 
 Working Units. 
 
 Tli(> workiiiir unit strcnfrtli >f flicsc mnti-riiils nt 
 the outer ('(Ijrc is tnUcn at one-tenth of the ultiniate. 
 iuid its tlie inaxinmni pressure at the outer edpe 
 when pressure at tlie inner edfre is zero, is twice the 
 mean or averajre pressur*". this correspomls to usin^' 
 a mean unit i)ressure of only one-twentieth of tlie 
 ultimate. The necessity for this hijrh factor will be 
 seen from the following: considerations. Experi- 
 mental (lata on the strenjrth of masonry in bulk is 
 comparatively small. .Most experiments have been 
 made on sample pieces of the material held properly 
 in position with pressures applied normal to sur- 
 faces. Also the crushing' streu*rth of masonry in 
 bulk is nuich less than that of the separate material 
 of which it is composed. Ix-cause of the presence of 
 mortar joints. On the other hanjl. experiments were 
 made on sami>le cubes of material, while in the 
 arch the mjileri.il is used in btr<;e mass, ami is. 
 therefore, stron'.'er than cubes. Errors in workman- 
 ship and in fittinjr of joints may cause excessive 
 |)ressure to occur on sonu' i)arts of joints, and little 
 oi' none at all on other i>arts. The entire system of 
 external loads is, Ihcrefore, uncertain. Working? 
 luiits may safely be taken as follows: 
 
 (•ranite .')00 to ]..")00 ])ounds per square inch 
 
 Limestone .. .300 " 1.000 
 
 Sandstoiu" 200 *' SOO 
 
 Concrete 200 '• .lOO " " " " 
 
 T.rick 80 '^ 100 " " " 
 
 I 
 
:!fi 
 
 LoWRi.ii- iii<iiH,i:S .ixn cri.i i.h'is. 
 
 A iiiiixiiiiiiin pri'ssiifc of |(Ht |iiiiiiiils per si|ujir<' 
 iiH'li is irund inMclicc for ('(HHTt'lr jin*li rinjrs. and 
 is suitjihlr for a iiiixtui'c of 1-2-4 •\V(>11 and carefully 
 laid. 
 
 Tlic alxtvc pressures refer to the niaxiinuin pres- 
 sure at llie (Mitef edjrc and not to the mean or avor- 
 ajre pressnre. whieh wonld he only one-half of the 
 ahove. These niiits will ffive a faetor of safety of 
 ten in eonipi'ession. The re(|nirenient that the line 
 of resistanee shall fall within the middle third of 
 the joint prodnees a factor of safety ajrainst rota- 
 ti(»n of three, and the re<piiremen1 that the an<rle 
 hetAVeen the face of joints and tlx' line of resistanee 
 
 he not less than 70 de<ri s prodnees a fa<'t<M' of 
 
 safety a<rainst slidin<r of from one and one-half to 
 
 two. 
 
 Determination of Line of Resistance. 
 
 < )r(linarily. the consideration of two cases <<[' load- 
 ing' will he sut!icienl. (1 i A nniform dead and livi' 
 load ovei- the entire strnctnrr. and (2^ the entii-' 
 • 1' load with a maxiimnii li\<' load over one-half 
 of the span oidy. The ahsolute maxiiiium stresses 
 fr<»m i)artial loadin<r may he ohtained when the live 
 load is applied to somewhat less than one-half th(> 
 span, as .4 to .4."i of the lenjrtli. l)nt for practical 
 pnrposes; it is snfticiently a<'<Mirate to consider half 
 the span loaded. In certain cases it may he neces- 
 sary to consider the maximiun dead load with a 
 siiifxle concentrated liv(> load at the center. 
 
f'L.iix coMki.ii: ih'iii nh'iiH.i s ?,i 
 
 V\Ui\ first tlic line uf i-csislaticf Ww lln' ninNiimiiM 
 (Icjid nud Ii\(' Idjids oxer tin- I'litirc stnicliirc An 
 !ij)proxiniato tliickncss will linvc Ixmmi assumed for 
 the iircli rin? nt the confer, also flic tlepfli of flic 
 ciirth filliiitr above as previously described, and an 
 approximate f<irm <>f arcli will bave been selected. 
 11" fbe l)ridjre lias spnndrel tilling flie first operation 
 M ill be to divide fbe loaded ai-en above fbe intrados 
 into a lunnber of vertical strips, to compute fb" 
 weijrbt of material in ea<di of tbese strips and tbe 
 live load (>• tbem. i.: order to simplify : ' -iilafions. 
 a portion nf fbe bridjre one f(tot in leti '■> ; t rijrbt 
 ansrles to fbe paper will !»(> considered. Eacb re- 
 iiiainitifr p< rfion will be a dui)licate of fbis. Tt may 
 be necessary to draw a separate line of resistance 
 under tbe side spandrel walls, because fbe weifibt 
 of wall uuisonry is {rreater fban eartb fill. The 
 amount of eon.ju<;ate pre sure of fbe backintj on the 
 bauncbes is then considered. For prravel and eartb 
 fbe intensity of this pressure ))er sfpuire foot or 
 otiier unit may be taken at one-tbird of tbe weifjht 
 of fillinjr and live load above tbe extrados at fbe 
 strip under consideraf ion Then the prodnct of 
 this horizontal intensify and fbe area of the vertical 
 projection of that i)orfioii of the extrados nnder tbe 
 strip will jrive fbe amount of the conjnjjrafe fbrusf. 
 This will be repeated for all other strips and a 
 complete set of loadings found, which slioubl all be 
 written in their respeetise places. 
 
 Ill 
 
 if 
 
 MM 
 
I'! 
 
PI.AIX COXCRr.TIi .IRC! I BRinCES. 
 
 no 
 
 I'rncood next to construct a forc(> jiolygoii 
 by drjnvijifjc tlie varioiis loadiiifrs to a convenient 
 scale. As arches are frenerally synniiotrical about 
 tbe center and liorizontal at that |)oint. the crown 
 thrust for uniforni loadin<rs will likewise be hori- 
 zontai. The pole in Ihe force j)oly«;on will, there- 
 fore, be on the same hoi'izontal line with the upper 
 end of the first load line a1 A. The amount of this 
 crown thrust is unknown, and the pole distance can, 
 therefore, be oidy assumed for the present. Tako 
 any pole, as that shown at V on Figure 7, and draw 
 the corresponding force polygon. Draw also the 
 corresponding line of resistance or funicular poly- 
 gon in the arch ring, starting from any point within 
 the middle third at the crown. The resulting funic- 
 ular polygon is that shown at ay'. Tt is evident 
 that the pole distance assumed was uo\ the correct 
 amount of the crown thrust, for the line of resistance 
 or polygon falls entirely outside of the arch ring. 
 Project the last line of the funicular p<»lygon till it 
 intersects the line of ci'own ]iressure produced at 
 the point ir. This gives the jiosition of the resultant 
 of the assumed loads, and its direction will be pai'- 
 allel to the line \\\ in the force jiolygon. The posi- 
 tion of this resultant is constant, regardless of the 
 forc<> polygon. Tlierefore. the corresponding line 
 of any other funi<'ular polyiron produced, such as 
 that through y. will likewise intersect at the same 
 point. Therefore, through y draw such a line, and 
 
 ! 
 
40 
 
 COXCRllTE BRIDGES AXD CVU'ERTS. 
 
 1\ 
 
 from B in the force i)oly«.'on draw liP. iiitersoctins: 
 the horizontal throu*;li A at P. Tlie distance Al"* 
 measured to tlie same scale as the load line will 
 represent tlie true amount of the crown thrust. The 
 (tlher lines radiatinj; from V to the various points 
 on the load Ime will tndy represent the amount of 
 thrust at the various points in the arch. 
 
 A check on the crown thrust may be made by 
 findinir the bendin«r moment at the center for all the 
 loads in the same way as for a beam, and dividing 
 this moment by the rise of the areh. It will be 
 remembered, however, that the rise is not neces- 
 sarily the distance from spring to crown, for in 
 flat ai-ches. arid es])crially in elliptical forms, the 
 line of rt'sistance does not fall as low as the springs. 
 The correct rise of an arch is the rise of the line of 
 resistance and not the rise of intrados from spring 
 to crown. 
 
 It Avill be seen by iiisp<'ctioii that a positiou of 
 the ])oiiit y was selected so the line of pressure 
 would not pass outside of the middle third of the 
 ai'i'h. It approaches iicafcst to the limit under the 
 strip (/. The point opposite to this limiting position 
 is caUed the point of rupture, and is the point 
 at which the arch fii'st tends to open at the cx- 
 trados. If the line of resistance from the assumed 
 ])ni!it V h'ld fntlen oi/si(l(> tlie middle third of ihe 
 arch ring at (/. a new point would then have been 
 assumed so as to bring tlie line of resistance en- 
 
PL.^IN C0\' CRETE ARC 1 1 BRIDGES. 
 
 41 
 
 tiroly witliin the iniddk' third at the point of rup- 
 ture. As this point v would ap{)roa('li vory close 
 to the niiddlo third for an arch of uniform thick- 
 n''ss from crown to sprinjr. the rinj; is thickened 
 at tlie hauncdi to keep the line of resistance well 
 within the middle third. The line ay, which falls 
 entii'cly within this limitinjr space, is, therefore, a 
 true line of resistance for the maxinunii assumed 
 dead and live loads. It Avas necessary to determine 
 the crown thrust or pole distance liy trial, because 
 there are four unknowu (piantities, the two vertical 
 and the two horizontal reactions of the a..'h, and 
 to determiiu' these there are only the three equa- 
 tions of eciuilihrimn, .^'ar- 0, ^y—O, 2m~ 0. The 
 line BP applied at the point y. represents truly in 
 both direction and amount, the thrust of the arch 
 on the abutment. This may be resolved into ver- 
 tical and horizontal comj^onents as shown. 
 
 Xumerons injjenious methods aave ])een adopted 
 for simplifyiiif? the computations. For instance. 
 " Avriters prefer to construct what they call a 
 I .ced load contour. This consists in first finding 
 actual loads of arch rinj?. fill, live loads, etc., 
 •"or cacli vertical strip, and reducing; the height 
 above the extrados to a correspondinp: height, pro- 
 vided tlie load was caused entirely from stone or 
 matei'ial of the same nature as tlie arch ring. Plot- 
 ting these various heights to scale abo'c the in- 
 trados, and coiuieeting the points so found, pro- 
 
42 
 
 COXCRETE BRIDGES A\'D CVLVERTS. 
 
 (lucos n liiH> which is cnllcd tli<' rodiiccd load eon- 
 four. TJicn l>y iiinkiiig the divisions two feet in 
 width, and scaliiij; the leiijrth of the two sides of 
 each strip, the sum of the len<rths s<'aled will repre- 
 sent the area of the enclosed strip. Sometimes the 
 areas are i)lot1ed on the load line of the force 
 polytron instead of the weights. 
 
 Practic(> varies somewhat in reference to the 
 selectin<r of tlie jiroper jxtint in the middle third 
 of the arch crown from which to draw the line of 
 resistance. ^Vhen a h'njre occurs at the crown there 
 is 'hen no uncertaint v as to the correct position of 
 the line (tf thrust. Some designers consider that 
 the position of the line of resistance is such as to 
 make the crown thrust a minimum without causing 
 tension on any i>art of tiie section. To satisfy these 
 conditions, the line woidtl pass through the upper 
 extremity of tlie middle third at the crown, and at 
 the si»rin,<rs or at the points of rupture, the line of 
 resistance would pass through the inner extremity 
 of the middle third. Professor Church says that 
 the trne line of resist.nnee is that one corresponding 
 most neai'ly with the center line of the arch. 
 
 Tin intensity of the unit pressure on a surface 
 may he I'ound from the following f ornuila : — 
 p ^ W OWd 
 
 "^ L L-' 
 
 \vli(>re p is the niaximnm unit pressure at any part 
 of a joint. W the total pressure, d the distance of 
 
PLAry COXCRRTP. ARCH nRIDGF.S. 
 
 n 
 
 p = 
 
 the ocjitcr of pressure from the center of the areli 
 ring, juxl L the depth of the jirch ring. The formula 
 is general for all positions of d, provided the joints 
 can resist .ension. Tf they cannot resist tension, 
 the formula is still general for the values of d up to 
 one-sixth of L. Tf d exceeds this amount the max- 
 iiinim pressure is tlien given l)y the formula: — 
 
 .'{ (one half L - rf) 
 The amount of crown thrust or i>ole distance may 
 he found analytically by taking moments succes- 
 si\('ly around the various load ])oints in the arch. 
 The crown thrust will be found a maximum wlien 
 monu'nts are laivcn about the load point opposite 
 to the point of ru]itnre. This is an analytical 
 method of locating the point of rupture. 
 
 If the arch had hinges at the crown aTid springs, 
 as are commonly built in Europe, the crown thrust 
 eould then ])e detinitely figured. The presence of 
 such hinges greatly facilitates the computations for 
 partial loading, for then. Tiot only the amount of 
 the crown thrust, ])ut also its direction, are un- 
 known. It is no longer a horizontal thrust. 
 
 The above method of drawing a line of resistance 
 for uniform loads applied to a pair of scgmentul 
 arches is illustrated also m the left hand arch of 
 Figure 10. 
 
44 
 
 coxch'r.rr. HKincr.s .\xn cuij-rr-'s. 
 
 A iii<»(li(icati(.ii c.f llio abovo nicthod of dplorrr in 
 in«; the crown thrust and drawing the lino of ro- 
 sistanco is shown in Figure 8. The space above the 
 arch ring is divided as l)efore into ten equal divi- 
 sions and the t<.tal load on ca(di calculated and indi- 
 cated in the proper places. Beginning at the point 
 IJ. which is the upper extremity of the middle third 
 at tlic crown, the loads for half the arch are meas- 
 
 ly:: 
 
 FlK. 8 
 
 ured off to scale on a vertical load line \\c. From 
 R and c di-aw lines at 4.-) degrees with the vertical 
 intersecting at 0. and from O draw lines to tiic 
 points a, b, c and d. Construct a polygon with sides 
 i>'n-allcl to the lines Oa, 0^;. Or, O,/ and Oc and ex- 
 tend the two extreme lines of this polvgon to their 
 intersection at D. Through D draw the vertical CE 
 
 
PL A IX coxck'iirr. arch bridges. 43 
 
 intorseetins tli,. horizontal line R at C. The line CK 
 marks the center of jfravity of the loads on the five 
 areh divisions. Thron-h C draw the line CS so 
 that the line of resistance, when drawn, will lie 
 within the middle third of the areh rin- After 
 drawinprthe line of r.'sistanee, if it should be found 
 that any part of it falls without the middle third 
 a new position must then be assumed for the point 
 S. Throu-h c draw the horizontal line EF, inter- 
 seetin- f'S prolon-ed at F. The line FC will' repre- 
 sent truly to seale the amount of the crown thrust 
 From R lay off <,„ a horizontal line through R the 
 distance RI>, oc.ual to FE, and join P with the points 
 a, h, c, d and c. From R draw the line of resistance 
 with sides parallel to the lines Pa, Vb, etc. If any 
 part of this line of resistance falls outside of the 
 "•'ddle thinl of the arch ring, a new position must 
 then be assume<l for the point S, and another line 
 of resistance drawn, falling entirely within the mid- 
 dle third. If no such line of resistance can bo 
 drawn, then cither the form of the arch or its thick- 
 ness must be changed until a line of resistance can 
 »'•' drawn lying entirely within the middle third. 
 
 I* 
 
 \ 
 
 i 
 
 Line of Resistance— Partial Loading. 
 
 Consider next the case of a maximum live load 
 "v<>r half the span, acting in conjunction with 
 
.1^ i' 
 
PI..HX COXCRETF. ARCH BRWCP.S. 
 
 47 
 
 1 
 
 the inaxiinum dead load. Tioth lialvcs of tho arch 
 iimst then Ik- considered. As before, the portion 
 of the bridge above the intrados is divided inti» 
 vertical strips, and tlie vertical and conjugate load- 
 ing's written down in their respective places. A 
 load line, AHC, is drawn, and any trial pole, P', 
 assumed. With this position of pole, the funicular 
 polygron shown in dotted lines is drawn. By usinj,' 
 a little care, the point .r may be selected, so the 
 curve on the left will fall within the middle th.rd. 
 or tangent to it. It will be .seen that this line of 
 resistance shown dotted, falls outside of the middle 
 third in two places and intersects the outer vertical 
 through c' at y. This cu* ve cuts the center line 
 of arch at /'. See if it is possible io draw another 
 line of resistance, so that it will cut the center of 
 the span at the point / and pa.ss through the point \. 
 From I" draw a line i)arallel to /' y' intersecting 
 AB at D, and from D draw another line DP parallel 
 to ty. The new pole will lie on the line DP. Also 
 through P' draw a line parallel to xy' intersecting 
 the load line in Q, and from Q draw another line QP 
 I)arallel to .ry. intersecting the line DP at P. The 
 point will be the correct jiosition of the jiole, in 
 order to have the line of resistance pass through 
 the three points, .r. / and y. The distance II in lh<* 
 force polygon may be verified analytically as fol- 
 lows : — 
 
u 
 
 Cij 
 
 :i 
 
 •j5 
 
 g 
 
 >» 
 
 L. 
 
 ^ 
 
 
 it 
 
 "J 
 
 
 
 
 
 
 
 
 
 3 
 
 
 •^ 
 
 u 
 
 L« 
 
 •J 
 
 n 
 
 
 
 
 X 
 
 '^ 
 
 - 
 
 t 
 
 
 2 
 
 c^ 
 
 m-: 
 
 w 
 
 ^ 
 
 :5 
 
 *" 
 
 
 •^ 
 
 ^ 
 
 
 r3 
 
 
 
 
 
 !>•, 
 
 ri 
 
 7* 
 
 n 
 
 
 J2 
 
 .5 
 
 w 
 
 :: 
 
 
 c 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3 
 
 3 
 
 "( 
 
 w 
 
 
 >, 
 
 c 
 
 s 
 
 
 
 c 
 
 
 i 
 
 
 
 -/. 
 
 
 I.*: 
 
 
 a 
 
 ~ 
 
 ?■ 
 
 rr 
 
 
 
 -3 
 
 .2 
 
 
 
 
 /. 
 
 
 
 
 
 
 
 
 fl 
 
 ■r 
 
 
 
 >, 
 
 
 ii 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 -^ 
 
 
 •^ 
 
 V 
 
 — 
 
 
 
 
 
 
 
 
 M 
 
 •^ 
 
 ■r. 
 
 
 ~ 
 
 
 
 
 
 
 
 
 ^ 
 
 r3 
 
 
 T 
 
 ■^ 
 
 *> 
 
 w 
 
 u 
 
 h 
 
 ^ — 
 
 «*-« 
 
 *i 
 
 i: 
 
 iJ 
 
 
 <«-) 
 
 ■^ 
 
 '•I 
 
 •J 
 1 
 
 > 
 
 
 
 ■i 
 
 
 
 E 
 
 4>^ 
 
 3 
 2 
 
 5 
 
 £ 
 
 K 
 
 tr 
 
 i 
 
 
 
 
 
 
 
 
 r. 
 
 •3 
 
 *-> 
 
 •^ 
 
 V 
 
 
 
 '< 
 
 h 
 
 ^ 
 
 
 •-C 
 
 4>J 
 
 
 •^ 
 
 \j 
 
 s 
 
 "'j 
 
 
 
 ^ c^ 
 
 
 '7 
 
 
 */: 
 
 3 
 
 
 :i 
 
 
 w 
 
 '— 
 
 •J 
 
 S c 
 
 ,a 
 
 w 
 
 
 
 
 •S 
 
 S, 5 
 
 5^ i 2 
 
 2 H 
 
 2 '^ 
 
 o a 
 
 ■A ^ «3 
 
 I ^ 3 « 1^ I ^' 
 
 ■A 
 
 ^ 
 
 ? 
 
 ^ 
 
 Ci 
 
 s 
 
 7i 
 
 
 >■* 
 
 
 1- 
 
 •<-> 
 
 
 n 
 
 
 2 
 
 V-> 
 
 4-1 
 
 :; 
 
 
 ^ 
 
 
 .«.j 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 •S 
 
 .^* 
 
 ^ 
 
 <J 
 
 
 ■^ 
 
 
 >i 
 
 *^ 
 
 J^ 
 
 ;!^ 
 
 ^ 
 
 >•* 
 
 3 
 
 S 
 
 3 
 
 ^ 
 
 <<-i 
 
 
 
 :; 
 
 u 
 
 
 ^ 
 
 
 i3 
 
 C 
 
 
 
 S 
 
 '^ 
 
 ii 
 
 
 
 -. 
 
 c 
 
 
 3 
 
 rs 
 
 
 
 w 
 
 w 
 
 ^ 
 
 
 ^ 
 
 - 
 
 rt 
 
 p 
 
 t£ 
 
 ri 
 
 ^ 
 
 <«H 
 
 't-j 
 
 X 
 
 
 *sZ 
 
 
 
 
 
 
 
 
 H 
 
 J5 
 
 73 
 
 -1 
 
 1 
 
 - 
 
 '^ 
 
 — H 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 ^ 
 
 V 
 
 4^ 
 
 > 
 
 
 h-i 
 
 ^ 
 
 •J 
 
 •4^ 
 
 s 
 
 r 
 
 
 
 
 V 
 
 cS 
 
 :5 
 
 •w 
 
 4^ 
 
 fr 
 
 ■ 
 
 1 
 
 iKl^ 
 
PLAIX COXCRETE ARCH BRIDGES. 49 
 
 H'X/'A:' = HX/A-. 
 From this oriviation th(> valuo of II may ho found. 
 Mii'I the point I' will lie on the line (^I* at a distanci' 
 II from the load lino. Tho lino (»f rcsistanct' xt\ is 
 tan<ront to tho lino of middle third in tho strij) </. 
 Tho point whoro linos hooomo tanjront niljjht havo 
 boon takon as tho rocpiirod point throufrh whioh. 
 with .r and /. it was dosirod to pass a lino of ro- 
 sistanoo. Tho oorrospondinsjr lino would havo boon 
 found in a niannor similar to that dosorihed. It 
 will 1)0 soon that tho lino .i7v lios ontiroly within 
 the middle third of tho aroh. and tho aroh as drawn 
 is, therefore, stable. If it had boon found impossible 
 to draw a line of resistance within the limits of the 
 middle third, it would havo been necessary to 
 chan^'e either (1) the form of tho arch; (2) tho 
 thickness of the arch; or (:}) the distribution of the 
 arch loadinj?. A similar method applied to soj?- 
 mental arches is shown in Fiijuro 10. In this 
 case the bridfjo Avas desi«rned to carry a double 
 line of railroad, with tracks ],'> feet apart on 
 centers. It was assumed that the ties and earth fill- 
 in£j distribute the weight of each track aiul tho live 
 load thereon evenly over one-half tho Avidth of the 
 liridge. This assumption iiuiy not be true, but it 
 is as reasonable an y\ h ixinuition as can be made. 
 The live load was assumed e(pial to Cooper's stand- 
 ard E 50, and for 3'-foot spans is equivalent to a 
 uniform live load of 10.000 pounds per lineal foot, 
 which was considered evenly distributed over a 
 width of 15 foot, fimounting to HfiT pounds per lineal 
 
 1 
 
|^_ -^Pliq 
 
 .-,0 
 
 cowRf-ri: ni.i!>(,i:s .ixp cniiii^is. 
 
 ! 
 
 font in widll n\- 1, ii1u.'. For i>nrti;il loa.linjr. the 
 • •"iniviilriit iiriifuiiii li\.' load on linlf tin' span was 
 assniiicd at ll.r»(lo jM.nnds [xt foot of track. 
 
 I'oint oi Aupture. 
 
 Tlic point of r i! ,:■!• .^ tliat point of tlio ai 1) 
 I'liij: at tlir hantniM - '••;<•?• tli.' joints tend to oppii 
 al the cxtrados. m vhi"f t i.' Imc of rcsistanco li<-s 
 
 '•loscst to the idiht ..,)m-. ,,; fl ' ardi. I5y s. • 
 
 writers this poiiu ;., coi, ,. [fri'd fhc real sprin«,'i! j? 
 point of tin- arcli. ;i,id an; i rt ..f the an-h Ix-l.-w 
 IIk' point of niptnrc iv cons h-rci as part of • he 
 pier ..r al)ntni.'iit. [is position -an l»(>st ho dotcr- 
 iiiiiu'l irraplii.-ally when drawi- - the r.'sistaiH'c lif,.-. 
 .Hid. as Tar as tiie ardi itself is eoneerned tlie lin^^ 
 of i-esistani-e is re.piired oidy al)ove tl:e |)..inf of 
 rnptnre. It is. liowcver. coiitinned fnrtlh \' .v de- 
 lerniinin-^'- the stability of the pier 
 
 Tl'e folloMinfr empiric d rule <riv( approximately 
 
 the re.inir.Ml thickness for eircidar sof?ni' :tal andi 
 
 rin<rs at the point of niptiuv. Tn the idlowinir 
 
 '■-piation t--^ '-mw-n thickness. (/ re(|nired tliicdiiiess 
 
 at i)oiiit of rupture, wlieu 
 
 rise , , 
 
 ^ '-■ \ tliea rf = 2.0(1 t 
 span 
 
 ~ I th.'ii d --1.40 t 
 
 i then d=1.24 t 
 
 V, then d 1.1 -)f 
 
 " ■ ,'iv then d 1.10 / 
 
 In reference to the nee.ssary thi< i !ioss of the 
 
 anh rin<jr at varioi'< points hitween tf crown and 
 
 i? 
 
/'/.//" ''()Xih-/:i i: .I'y'if nh'/iH.i-.s. 
 
 51 
 
 spriii^is lie \ (■?•! leal |(rujcrt ioii id' (>\ iTy sci-|i< " ciif- 
 tiM'; l! aitli tr ^ nor lal to lli«> lin' of res lain-f 
 iiuisl in- at li.i-^ as ;r. it a > tin; viTtical ilcp h of 
 arch nny: at I ' ■■ crouii. 
 
 Till' jiositioii of tilt |i( iiit of t'lii 'ire •." KTitlly 
 
 <ici'iirs at al)(>iit I hat '<)i. t of IIk ..rcli wli re ''i. 
 
 iiiu'iiial to tl'c I of oi IPC 's an anirlt' of 
 
 t") ,lcj.Tci- witli 'ii. lion ((I I. • . liiy he sail that 
 
 t !M'\r!' t.iiJM h,\\\ ih- i|. ■ ,- (if :{() (l(;,'n>(" 
 
 N'ith tlii h< i/oiita a?i t hct^v .'il '•)') and 
 
 •i' (Icjriii's ' 111 tho j =1 
 
 i 
 
 y 
 
 Dett mina i of ah xhickn 
 
 iiiii' of ! -. ^ui. the variolic points of 
 
 the h 1 ( . .,.f| (Ictrriiiiiicd. It will bo soon 
 *iiat tilt sc ju't -sh icrcasc from crow?) to sprinir 
 
 ii! prop, "lion to he rise of tlic arch. \n si 
 circiii;! arches ■ tlii'ust at the sprin-r nia; 
 'lu'c foMi- tlif thrust at the crown. 'I'l 
 
 •«'l tivc pos 11 •enter of arch and the lim- 
 
 of resistant t Ix xaniined and suitable unit 
 
 press^"-es scic< - (1 foi' she various points. If the 
 liie ol -esista ee is at eitluM" limit of the middle 
 »' d. mc,..i unit pressure will then be one-half 
 
 o h' aximuin at the outer edye. This is the 
 '!sn .. ass Miipt' 'U. Then the a.Ta obtained by 
 ividiii',' •■ t "t'l pressures by the workinsr units 
 will be II , lired an-a of nuiterial at various 
 
 points of ti,. ;.rch. .Most authorities on the subject 
 recommend liberal sizes, not only because the usual 
 arch matei-ial is not expensive, but also on account 
 
II 
 
 52 
 
 coxcRiiir. liRinci-.s .ixn criAi'.RTs. 
 
 of the iiiKM'iiiiiiity of so many (■(niditions iu (tomicc- 
 lioii willi the Avliolc matter. 
 
 Backing. 
 
 Kcrcrciicc lias already hccti maile to the point ol" 
 I'upture. Jt is tliat jxtint on the extra(h)s of the 
 arch where the joints tend to open, and it occurs 
 opposite that point where the line of pressure ap- 
 |>r()a(dies nearest to the intra(h)s. It is known in 
 the failure of Hat arcdies that the joints open at th<' 
 intrados of the crown, and extrados at tlie two 
 points of rupture, and the haunches recech^ later- 
 ally, allowing' the central part of the arcdi to fall. 
 In onh'r to resist ami counteract this lateral move- 
 ment of the haunches and apply horizontal conju- 
 irate thi-nst thei-eto. that part of the extrados from 
 the point of rupture down to the pier is filled fren- 
 crally with l)ackin<r of rubble masonry or concrete 
 laid in horizontal layei-s. Semicircular andu's re- 
 ijuire ha(d\iii<r sufTii-ient to produce conjugate pres- 
 sures e(|ual to the crown thrust. Segmental arches 
 whi(di have a hoi'izontal thrust component at th'* 
 spring re(|uires less ba(d<:ing than semicircular ones. 
 
 Waterproofing- and Drainage. 
 
 Previous mention has already been nuule of 
 waterproofing. This is iHccssary to prevent water 
 soaking into the joints and freezing, thereby 
 teiuling to disintegrate the masonry. Waterproof- 
 ing is necessary also to |)revent drainage water leak- 
 ing through the artdi and discoloring or otherwise 
 disfiguring the structure. To prevent su(di leakage 
 
PL. {IX COXCRIi! li JRCIl PRIDCES. 
 
 53 
 
 it is oustoiiinry to <'ovr>i- llic iii>|)or surface of the 
 iircli and hackinjr witli a layer of bituminous eoii- 
 <-ivte or clay pu. l.!lr. ( Iny sliouhl eontain enough 
 sand to pivvcnt llie day from craekinjr wlien dry. 
 Walerproofinir may he acfomplished by ai)plying n 
 layor of rich moj-tar and surfacing it with neat 
 •M'ment. on top of whiidi is poured a coating of tar. 
 pitch or asphaltum. The upper surface of the back- 
 ing must have sutTicient slop(> to carry drainage 
 water 1o tlie gutter, where it may be discharged 
 tlirough pipes luiilt into either the arch soffit or the 
 side spandrel walls. 
 
 Intermediate Piers. 
 
 In making preliminary designs of piers, use may 
 I)e made of empirical foiMiiula to delerm;ne approx- 
 imate sizes. Kaid<ine"s rule is to make the thick- 
 ness of piers at spring from one-sixth to one-seventh 
 of the span or arch for intermediate piers, and one- 
 fourth of the span for abutment piers. Tntermediat- 
 piers must Ix- of sutTicient area to resist crushing 
 from the maxinmm loads, and in proportioning the 
 base of pier the weight of the pier itself must be 
 lidded to tiie imposed loads. Intermediate piers 
 must also have sufificient stability to resist the over- 
 turning eflTect of unbalanced thrusts on the adjoin- 
 ing spans. Such unbalanced thrusts will occur if 
 the adjoini.ig spans are of different lengths, or if 
 
 one ordy 
 
 tioiis the 
 
 IS sut) 
 
 .jcct to live load. F 
 
 or such condi- 
 ••enter of pressure shall fall within the 
 
 middle third of pier baf^e. Pier.s must b 
 
 e given 
 
 ^^oY< 
 
54 
 
 lOXCh'/ilfi BRIIH.I-.S AXn CriA liRTS. 
 
 siiflicitMit sprcjid sit the base, so the pressure on Ihe 
 fouiulntioii Avill ii(»t exceed a safe unit. To neutral- 
 ize the efll'eet of unecjual thrust on the piers from 
 spans of different lenirths. the siiortcr span may 
 have a less rise Avitli a correspond infrly <r>"<^*iter 
 amount of fillinir. This Avill tend to produce a thrust 
 from the smaller span sufticiently lar<re to e<|ual 
 that frcMU the loiifjer one. Another method is to 
 incline the short«^r span upward so the thinist will 
 act on the pier at a point somewhat hij^her than the 
 correspondiuf? thrust from the lonnfer span. In 
 writiiifT on this sul).iect. Tiankine says: "Kach pier 
 of a series should have sutlicient stability to resist 
 the thrust which acts upon it. when one (»idy of the 
 arches which sprinj; from it is loaih^l with a travel- 
 injr load. That thrust may I>e roujrhly computed by 
 midtiplyinjr the travelin<r load jxm- litieal foot by the 
 radius of curvatui-e of the intrados at its crown in 
 feet.'' The mathenuiti( ;d investifration of piers is 
 shown in Fiijures 7. !) atid 10. 
 
 Abutment Piers. 
 
 Hridires havinj; a series of spa. is s! uuld have abut- 
 ment piers at intervals in order that the possible fail- 
 ure of one span would not cause the entire strnetur'! 
 to fail. Abutment i)iers are useful also in allowing' 
 false work centers to be removed from some of the 
 spans, without waiting: for the completion of the en- 
 tire strucrnre. AVhen spring lines can be located 
 close to the foundations, it may be advantageous to 
 juake all piers, abiitinent i)iers. This was the case 
 
 ! 
 
 f 
 
 ^^S^T 
 
I'l.Aix (nxcRiii r. .\Rcii nh'/ncr.s. 
 
 55 
 
 ill llic loiiiriiuisonry viaduct ivci'ully l)uilt sit Santa 
 Ana in California. ..n tlic liiic of the San IVdn*. L(,s 
 AiiL'clcs & Salt I>ak(' Kailroad. (Sec Enf^inccrinjr 
 IJ.'cord. Scpt.-ndxM- f). lOor,.) Whon it is" inipra.-'^ 
 tK'iihlc to make al' piors al.utincnt piers, it Avill tlicn 
 1»" well to have every third or fifth one of the type. 
 Sneh piers may l)e desijjnod ^vith a factor of safety 
 iijrainst overturninir of from one and one-half to 
 tv.-o. Ti Avill b(> noticed that the point <»f intersec- 
 tion of the arch thrust with the load line throu^di 
 <Ih' <-<'nt<'r of frrnvity of the piers, falls lower in the 
 ;!l);itiiierit pier than in the intermediate ones, owinj? 
 1o the irn.ater width of pier. This is an advantajje 
 .hkI will hriufr the resultant pressure nearer to the 
 ••enter line of the pier base. Trautwines approxi- 
 "i;i)e formula for the thickness of abutment piers 
 ;'t 11|> spriniriiifr is to make the thickness c.pial to 
 •>Mc-Mrth of the crown radius plus one-tenth of the 
 '•ise. |. .IS two feet. 
 
 Abutments. 
 
 In proportionin-r abutment piers, it is n<»t neces- 
 sary t.. keep th,> resultant pressure Avithin the .uid- 
 <il<' third of the base, if the maxinunn pressure al 
 t!ie outer edse does not exceed the allowable unit 
 !>'-essnre. Trautwine's empirical rule for the thick- 
 ness (.f , l.u,,,H>nts at the sprinjrs is the sauu^ as was 
 U'lven ai ^, for abutment piers. This approximate 
 siz(^ will .. isist in establishinf? the correct or tinal 
 one and the rule gives a thickness intended to be 
 sufficient without depending upon the existence of 
 
 ■MMi^fll 
 
56 
 
 coxcrhth nRinciis .ixn cri.i'HRTs. 
 
 earth ])iv'ssuro from Ix'liiiid. Ahntmciits siisliiiniii<? 
 liiirh hjiiiks of loose iiuiterisil. must lie proportioned, 
 not only for the areh thrust, hut also as retaini!i<,' 
 walls. 
 
 There is fre'|ueiitly mor(> masonry in the abut- 
 ments of a bridjxe than in the span itself. For this 
 i-eason it is desirable to consider carefully any op- 
 portunities for satiny nuiterial in the abutments. 
 IMacinjr the arch sprinj; down mar the ^n-ound. 
 •rreatly reduces the ovorturuiiifr moment on the 
 abutnu'nts and causes ■,: considerable savinj? of ma- 
 terial. Tn brid<rcs Avith several arch spans, even 
 thouprli the spring,' lines on the piers must be hij;h 
 to secure a clearance undei-neath tlu» bridfje. the 
 s|)i'in<rs at th<^ end abutments may sometimes be 
 kept down lower than the correspondiufi sprinjrs on 
 th(> pi<'r. ( " if abutments must be hiirli. it may be 
 ect)nomical to use ribbed ab\itments. cored out and 
 reinforced with metal bars, if necessary. 
 
 The use of ])avement ties of either wood or metal, 
 will cause the arch thrusts to counteract each other, 
 and thcr'>by ijreatly reduce the size of abutments. 
 This (expedient has not been used to any jrreat ex- 
 tent until recent years, and even now is used cdiiefly 
 for bridijes of reinforced concrete. 
 
 A wide and shalloAV waterway is more etfeclive 
 than a narrow but hitrher one of the same area. Fi<?- 
 ure 11 shows some possible abutment forms. At 
 A and (' are shown abutments where the concrete 
 in front of dotted lino, not only is of no swvice or 
 benefit, but actually decreases the area of waterway 
 
 'I'^i. Wi'ST 
 
 V9r»»«»j 
 
/7..//.V COXCRllTr. ARCH HRlDCrS. 
 
 57 
 
 {111(1 at tlio samo tinio adds 1o the cost of the stnie- 
 tiin'. It Mill bo seen, howovcr. that the abutment 
 A is one of the most eommon forms used in nearlv 
 
 Fiir. 11 
 AK( H AUl TMENTS. 
 
 all old andi brid^'es. If fm- any suffieient reason, 
 vertical sides are desirable or neeessary. it will be 
 eci.iiomy to build independent side walls, as shown 
 
: 
 
 •'■•8 (owRijh: liRiiH.i-.s .i\/> (i/.r/:h'Ts. 
 
 at J5. rati.,.,, ll,,,,, w„sl,. .M.-.l.-rial l.y uu.kii.jr tl.o 
 wliolc iihiitniciit solid. 
 
 Al K an. sli.nv. „|,1 ami n.-w nidlKMis of const ni.-- 
 tKMi. The (lottcl Ii,„.,s sliowinjf an al.utni.M.t l.iiii; 
 '"" l<'V("] fonn(lati(.n is die inctlio,! j;ivi'n l.y Traiit- 
 winc and tlic one .generally uscl ii.itil riMM^nt vcars. 
 Tt will l„. scMMi. li<.w..v(M-. that the f,.nns shown" at K 
 ". full l.M.-s is oinally ..ffVctiv,' in trans.nittin-^ 
 thrusts to tl... soil, a.i.l r..<,nir..s somewhat less n.;i- 
 t.'nal. 11 vertical si.les are not re(|uire,l. son.e a.l- 
 « 'I'nnal ...aterial ,„ay he save,] hy „.sin- the ...etho.l 
 shown l.y ,lott...l lin,. at ('. 1) is suitable for arelu-s 
 M-.lh e,.nsi,l,.ral,].. ris,. on har,l soil ,„• loo.se ro,-k 
 an,l Fslmwsa l\m,^ of ahutni.Mit in whieh th,' an-;, 
 thrusts ayainst s,>li,I i-oek. 
 
 Tm (l.-sifrnin- abutments, it is saf,.r to ,lisear,] the 
 •'tt.'et of e,.n.,uv„te .-arth pressure on th,' ar-h ex- 
 tra(l,.s. The al.utm,M.ts will then h,. sonunvhat 
 heav„-r. hut the error will be on the side of safety 
 Jumkin,. says that the [hiekn.-ss of abutments is 
 ••ft,.n from ..n,-thir,l to ,.ne-fifth of the ra,lius of 
 ••urvatur,. at the en.wn. Flarinjr wing walls. 2.-) feet 
 in h,.,irht or less, rigidly e,.nn,M.ted to the abuf.u.Mt 
 tae,. wdl or.linarily !.,■ safe with a base e.,ual in 
 NVi.lth to on,.-fifth of th,. h,.i.},t. This is ,.ulv half 
 |l'" thH.kn,.ss usually giv.M, to retaining' walK and 
 
 '' '""' ' ■■'"^'" «'f <1"' an-ular ,-onne,<tion t,. th.> 
 
 Jtbutment face. 
 
 Foundations. 
 
 riors and abutments must have suffieient spread 
 »t th.. bas,.. so th,. lua,l on th,. f,.undation will not 
 
s 
 
 I'l.AIX COXCRHTE .IRC/ 1 imiDCF.S. 59 
 
 ';xn..I a safe unit. For s.,il, this will not ordinarily 
 •X-..1 nun two to fonr tons jn-r s,,uaro foot at the 
 "-.-•• ,..I,.o of the pier, where pressure is the .nvat- 
 -^ ■ n p.les are used, the same precaution will b. 
 •''-';• Slop.njr piles have o.vasionally been useu 
 " " .-h foun.lat.ons for resisting the areh thrust 
 I the;,' are n.ore diffieult to drive than plumb 
 I hs Th. Jan.estown Exposition bridge. Figure 
 
 •'•''\"^'"t- "... .uaxunun. allowable load on piles 
 sl.ouhl not exeeed fro,„ 1.1 to 2.1 tons eaeh, depend- 
 ".g upon tlu. penetration of the pile at the last blow 
 ;;' \'- ';'""—•• AHowanee nn.st be nu.de for the 
 ■'■s..ltant pressur,. on the base falling outside of the 
 -''••<•• Tt need not .H-eessarily be eonfi,.ed to the 
 ■<''"<' n..nl, p,.ov.ded the pressure on the founda- 
 1"'"sar the outer edge is not excessive 
 
 In h,s treatise o,, Masonry Construction, Profes- 
 •s-r Ii*.l<.r giv,.s the following values for safe bear- 
 ing p.»wcr of soils : 
 
 Tons per 
 
 Rock e^ual to best ashlar ""^Tto^'io 
 
 Rof'k .qual to best brick .nasonrv. ... " " " 'n to ?0 
 Rock ec.ual to poor brick n.aso,.'rv. . . .W" :, to 10 
 Hay, dry thick beds " " [ J^^ ^[, 
 
 Clay— n,()de,-at.>ly dry thi.-k Ix^ls o to a 
 
 Clay— soft " "^ 
 
 ^ii-avel and coarse sand well cen'.ented .'.'.' " 8 to 10 
 
 ^and-er,n.i,act and well .emented 4 to (i 
 
 Nand— clean and dry . . o t • 
 
 Quicksand, alluvial soil etc , " . , 
 
 ' •> to 1 
 
m 
 
 I '' I 
 
 hi 
 
 «0 COXCRJiTi: BRinCl-s AM) Cri.lERTS. 
 
 Expansion. 
 It is well to provi.lc for possihli- expansion, so 
 cracl-.s will not appear in the finislied surface. In 
 til.! ease of the Conneelieiit Avenue i5ri(|<re at Wash- 
 ington, shoM-n on pa<rc SS. onr-haM" inch expansion 
 j(ints are provided thronjriiout the entire hei<,dit of 
 th.i spandrels, from sprinj,' to the ll.x.r over the ])iers 
 and across the roadway. These arches are 150 feet 
 in len«rth and semicircular. After the completion 
 of the concrete arch hrid^'c over iJijr .Muddy Kiver 
 on the Illinois Central IJaili-oad /See I':n<rineerinfr 
 .\<'ws. .Xovemher 12. VM):\) an examiiuUion was 
 made durin<r a i)eriod of several months, and almost 
 no expansion whate\er was discovered. 
 
 Surface Finish. 
 
 Various methods have been ad<.pted for procnrini? 
 satisfactory surface linish on concrete structure! 
 Among these methods may be mentioned cement 
 washing, tooling, sand blasting, rough casting or 
 slap dashing, scrubbing, cold-water painting. "and 
 acid treating. The Connecticut Avenue liridge at 
 Washington has corners and moldings made of con- 
 crete blocks, and to remove form i:;-.rks the body 
 and tiat face work were bush hammered. 
 
 The Walnut Lane Uridge at Phihulelphia has a 
 rough surface finish similar to pebble dash, but of 
 coarser grain. Tin. surface shows stone chips not 
 larger than thre.'-.ighths of an inch in diameter, 
 lornied. by washing the concrete face before the ce- 
 ment had har.lened. A more expensive method of 
 
 §3,V^:^^^^^ 
 
 5'V'^vOS 
 
/7..//.V Co.XCh'/iTJ' Aiail HRinCES. 
 
 CI 
 
 K 
 
 •s-Minnjr a fitiisl...,! surfiKM- is to build all oxposed 
 siirla.M's ,.f ,-ut-st()ni. work, or a .M.inhi.mtion of 
 stoiu' and brick, usin- coiicrct." Tor the body of the 
 Wyi-k only. Till. (ircMi Island Concrete Hridgc at 
 Xiairara Kails l,as surfa<-in^' <,n the spandrels" and 
 pi.-rs of cut stone, and other bridf,'es have been simi- 
 larly bnilt at Indianapolis and elsewhere. :^Iany 
 hridfres generally known as stone masonry bridges 
 are stone only on the surface, with the body of pu^rs. 
 arch.'s and backing composed entirely of' co.H-ete. 
 The Rocivville stone arch bridge built' by the Penn- 
 sylvania TIailroad Company over the Sus(iuehanna 
 Kiver IS of this construction. Tt has stone facin*' 
 thnrnghont. including the soffits, spandrels and 
 pH'rs. [n budding an ornamental concrete foot 
 bridge over two lines of railroad at Como Park. St. 
 i'anl. to avoi<l the appearance of form marking on 
 the finished surface of the bri.lge. the entire surface 
 <»t the lagging and -noulds was lathed and finished 
 Avith fine plaster. In tlie National Zoological Park 
 ^^ashlngton. is a concrete bridge faced on the span- 
 drels and parapets with natural boulders, which ex- 
 tend down s;x inches or more below the concrete 
 soffit. In San Francisco are .several concrete brid-rps 
 Avith rustic surface finish, made to represent natural 
 bonlders. but really fonncd of moulded concrete 
 These boulder and rustic surfaces are appropriate 
 tor certain wooded pai-ks or rural places, but are not 
 isiiKable for general adoption. 
 
 Engineering-Contracting for January 6, 1909, con- 
 tains dlust rations of concrete surface effects secured 
 
\v. 
 
 V '^ X _ . _ 
 
 it i s: c « c 
 
 - t. ?■ 
 
 «i 
 
 _ — 4, 
 
 ~ ~ »N 
 
 ~ x''^ = ? ^ 
 
 ~ • - -- ? c 
 
 - ;" ~ " § h «^ 
 
 i t a: C/ IS s, ei 
 
 ;o t •- S !== if c. ? 
 
 r _: i c ~ cc 
 
 " tC tC *- "" i; 'C 
 
 _ - i. CC „ " 0- 
 
 cd 
 
 O z —" .= i — 5 
 
 - - = ;:• ?^ ^ n •= 
 
 -*. :: ~ ^ K 
 
 ■ r i . ^ '5- 
 
 0) i'- ~ 2 > ^ i< 
 
 o - j: r " c ^ 
 
 t :r _ o 
 
 »— "— ■ ;; 
 
 " — C ii -, 
 
 «« ? - ? C ,• -. = 
 
 C C '^ 
 
 S ^ £ 
 
 - >—c'= = = c 
 
 :r x = 
 
 Q tL — *" ^ 
 
 o 
 
 c 
 
 — _^ - f" -t- — C- 
 
 " ~ — !r >- I— 
 
 ^ •*• X "tr -^ — "■ ^" 
 
 r _z -I c c ,£: 
 
 
 v. w 
 
 = - = r "i «*-! 's^ 
 - ~ = -= ? c j: 
 
 ?*-- .r 
 
 3ifii^. 
 
/•/. //V tY>.VC,V/r/7, ./A', // HuiiH.l.s ,;:] 
 
 l>y v„ri..M.s „M.tl,<Mls „„ lahon.tnry samples. It will 
 •" 'm,l..rstno.L iM.MM.v.r. tlw.l h.iWv .vsulfs ^umh\ 
 
 ' '''"""'•' "•"'"»• <1'<'^<' <'on(litions than cnnl.l 1 x- 
 
 IM'ftcl o„ larir,.rs„rr;MM.s mI,..,v <„„. of its ,.l,i..f .lini- 
 
 ••iilfi.-s IS to j)n)(lti(M> iitiifonu cfTccts. 
 
 Sto„y IJrook Itri.li:,. i„ tl„. iJostcu. F.Mnvavs l.as 
 
 frramt,. tnn,„ii„irs m tl, spn-rkl,..! Lri.-k fa.-in- whil.- 
 
 I"" •"•<•!• ^"Hifs aiv linnl with -Ia/<.,1 hri.-k of varv- 
 
 I'ly pjitlcnis and colors. 
 
 ''''"•;••' i;< i< very artisti. thn-.-spa,, an-h hrLlfro 
 :'\"'-/ '<' nv.r at I)..s Moi„,.s. Towa. that has vitnfir.1 
 '"'"•J^' :'-"^'. Th. spans a,v,.a..hl..(MWti„h.„.,h 
 "':'' '■"'''."••"' '■"<■'"•'"• 'H... hri.-k nn-inir with tri.M- 
 """jrs ol a Iij,h|.T ,.olor p,,.s,.nts a v.-rv pl.asi,,.. 
 iipp<'iii'ann'. 
 
 Anoth.-r ,n..tho,i of prcv.M.tin- forn, marks fron, 
 ;''•'•"*"'■'"- "" <'"■ •••UMTot.. surfa.M- is to ,.ov,.r th.- 
 l."-'i:.nir with a lay.r of fi,,. Hay an.l ov.vUy tho 
 siuiic with bnil(liri«r paper. 
 
 Cost of Concrete Arch Bridges. 
 
 The cost of coacrPto IumM-oh varL-s witl, l,.ral rr- 
 Munvn.ents and conditions. The foll-win^^ ori.nnal 
 ;'nnn]a.,vcsthccostnfs. Id concrete arch h.-id..,, 
 ^'l• Ix.th railnrnds and liii^hways. The fonnnhfi. 
 
 ^ ~ * \ 100 y 
 
 where C is the cost in doHars p,.- .sc^uarc foot of road- 
 ^^ay H tlie ^.encral heii,d,t of the hrid^r^ at the center 
 ^^ the total widtli and F a vari«l,le factor givn by 
 the followinj,Mable: • 
 
64 
 
 
 ((>\t h'i:i/: nun 'I. is- IXf) (7 7,;7:A'/'.V. 
 
 When A is •^»()(i. tli.-?i !■' is I..-. 
 .">(»( I. 
 I (Kin. 
 
 •.'()( 11 1. 
 
 .'.Mm. •■ 
 
 ."lood. 
 
 ;i;.(t(i. 
 
 1(1(10. 
 
 :.n(i(». •• 
 
 Cdoo. 
 
 ;(i()(l. •• 
 •• •• soon. 
 '• '• :i(i(M». •• 
 1 1 num. 
 
 •• !1(I(M. • 
 
 I •.'(»( to, 
 
 i:;o(i!). 
 
 •• I4(i<:;). .. .. 
 
 As tlw- lH..,,ht .,{• i!,.. ]>rll:r ,nulii,.li,.,l l.v its wi.ltl, 
 .rnt-s flu. cn.sss.M-ti.mal aiva. tlir fuMcti.,u HW mav 
 he ivinvsont,-,! hy tlu- l.ttrr A. Factors V ivtVr to 
 an-hl.n.l.vswith (■on.j;l..t.. soffit slahs. wl,il.. factors 
 1' refer to an-h l.ri.l.vs with partial soffit slabs, such 
 as used m the Walnut Lane l.ri,l-^e in Philmh-lphia. 
 'in.lthel),.tn,it Ave. hrid-e in ( •l.-v.-lan,!. 
 
 The eost of concrete l.ri.Jircs is atrccted more by 
 natural conditions an<l the sele.-tio.i of the economi;. 
 torn.s than by the live load to which these bridges 
 
 .(» 
 
 
 
 .<;:. 
 
 
 
 .IS 
 
 
 
 .4-2 
 
 
 
 .;;<; 
 
 
 
 :;•.' 
 
 
 
 .•js:> 
 
 
 
 . ■.•(;•.' 
 
 and !•"' 
 
 is .m; 
 
 •.'•J I 
 
 .. 
 
 .'.i:» 
 
 •.'!• 
 
 .. .. 
 
 .!•! 
 
 IS 
 
 .. 
 
 .;i;; 
 
 \m 
 
 .. 
 
 .'.fv* 
 
 l.v.' 
 
 .. .. 
 
 .!il 
 
 Ill 
 i;!:! 
 
 • • 
 
 . ss 
 
 .Sli 
 
 1-:.-. 
 
 .. 
 
 .S.") 
 
 11 :• 
 ii:; 
 
 ;.■ :: 
 
 .SO 
 
 ■msm,^ 
 
 kr. 
 
 
/7..//V iOXCh'/m. ./A'( // HRIIH.ES 
 
 6 -I 
 
 nrc siihj.clfd. This is sliowji liy tli.' al».vi' fonmilH 
 .•ipplyiii^' <M|ually to (-(.iicn'tr jirdi bri(l;,'t>H fur Ii..fh 
 r.iilntads and !ii;;liways. 
 
 TIk' w«'i;rlit of concnli' and (itluT niati'rials is 
 •rrrafff than tlic iiiipos.-d live load and tlif live loads 
 .••If not. tlit'n'forc. fr,' chiff caiHid. -rat ions in drter- 
 niinin;,' tli.' ultimate ('(.st. 
 
 Tli.> formula clrarly shows that conrn't.' anh 
 l»ridurs vary in .(•st in ])roi)ortiou to th.' jn-.Kln. t of 
 th.-ir w. i-rht and width. Bridjjrs with a small m.-sH 
 st'ctioMal arra cost as low a price as J!2.ri(> jmt sijuan' 
 foot of tloor surface, while lar^re monumental hridfres 
 may cost as liiirh as 510.()0 \)vr sciuare foot. 
 
 The formula also ch'arly shows the ^n-eat ectmomy 
 in nsinjr ])artial in place (.f com{)lete sotfit sIh})8, nnil 
 tliis economy may be still further increased by the 
 us( f ribbed arch (h'si^m^ ^fl)l)ed an-hes are not, 
 how. r.^'enerally suita))h 1,^ ^^tructi.m in solid 
 concrete and the treatment .w l!,;,-, . tyle of an-li will 
 ti .refore l)e taken up later, > i',. i],, desi.irn of arches 
 in reinforced concrete. 
 
 Table No. 1, jrivinjr details of concrete brid.ires, 
 j,'ives also tlie total cost of these structures. 
 
 Design for a Concrete Arch, 60 Feet Center to Cen- 
 
 ter of Intermediate Piers. Clear Span 53 
 
 Feet. Rise 10 Feet. 
 
 The hi idgo consists of a series of arches to carry 
 a street over a number of railroad tracks. The span 
 y,-as arbitrarily fixed at 60 feet center to center of 
 intermediate pi. rs. or 53 feet in the clear. This 
 provides clearance for four lines of tracks, 13 feet 
 
<;<; 
 
 coxcR/://: nianciis .i.\/> cri.irMTs. 
 
 "l-'o„ ...„,..,,. l-'ur;, Wsln,..t,nvuni.isl.,.i.l,t 
 1^ -.• - sp;u,s Mn.ht lun-o lKv„ „.Hv ,vononn..I. l.„; 
 -s I....tl. w.s sHn.,.., tl:.t tl... ,.I..nra„,.,. whv for 
 
 •■;•-; <s"-nI.lM.,t,,,. too .n.,tlyol,stn.,.t..,l\viti. 
 ' '!• """ ''"'•'<'••"•'"> un,l,.nH.,f|. is shown .m Fi.-- 
 
 |-«- s,..,,H,,tinMs.lH.i„,,21 f,..tfroM,thMnp;,fraiI 
 "' "'." -'"<"'• "f tnu-k n.nnvsf to tl,o pi.r Tin- 
 
 ;''Pt;-MV>rn, was s..]..,.,, for th.n.nson that, with 
 - ^iv..„ H..,,-a,H.o. it alhnvs the spHn^i,,. li,.. to 
 
 .^1 Wr than any oth..,- fonn and i„ this .aso is 
 '•'♦"r/"'*"^"''"'^"-'"""!- ^Vs tho via,lu,.t is a lon.^ 
 
 V ;, ;' """,""""; '•'^" ••^' -"-fif^'^ the spa., 
 
 A\...s th n.fon. s..l..,.t,.<|. anionnfin,. to 10 f.-ot front 
 ;|;;.- o ..-own. Th. Hs. is tho s.ni-n.inor L : 
 
 P -ssn, whH-h ,s „s.Ml h,t.M- in dotonninin^ th. 
 "•-owti thrust an,] [,i,.r reactions TI. 
 rule fui- tl„. ii- 1 "'"Tions. I he approximate 
 
 '.;;•'. '"'•'<-- of intennediate piers is to 
 
 iH 1; •"";'"•' ^'""- -r'- -onid produce 
 
 ^t hK„,,,,, ,,. "toSf.vtatthesprincand 
 
 ' ^-^ ;^-^ -l".-t..<l i-or a trial. To detennim. 
 "l>I';-nnate crown thickness. K.,d<ine's .T ^ 
 •;^^;<1- K.ra series of .rches. it is ,.17 Kadius. 
 
 Ths rcp.ires that the radius he known. I.av out .,n 
 : ;;-^'-=.;i.-myhyn. n^thodoftive'c:^^^^ 
 •""f ^''" -'Jnis ,s found to he 72 feet. Rankine's 
 
i 
 
 /V..//.V COXCKliTIi ARCH /BRIDGES. 
 
 rule. ;i.s iil)()\ 
 
 ('. <r 
 
 n 
 
 \\i's }i thickness (.f ;}.:,, wliih, Traut- 
 
 ine's rule f„r the Jipproximatc thicl. 
 
 kncss IS L'lvcfi 
 
 . «' •■■•■••■' lUM-KIH-X.S IS jL,'IV(MI 
 
 m Ins book. paj,^. (il7. and is 2.2 feet. Try a thick 
 lu'ss of 2..-; f,.,.t. Tho jrradinj. of fh. hri,!?. „p to n 
 hifrhcr lev.) in onh-r to sc-ure a -n-ator ris.- for the 
 i>rch was consider..!. h„t as this increase! the (,uan- 
 tit.-s of ,„atcrial i„ the superstnicture. and would 
 <'(.'H.t a savin- only i„ the abutn.ont piers, the pbn 
 was not adopted. A thickness of crown fillinfr of 
 2..) foet was assuniod from the extrad(.s of the arch 
 to the pavement surface. 
 
 The entire portion of the hrid-e j.hove th<' intri- 
 dos was then divided into strips, and the weif,.ht 
 for ,.ach <.f th(.s,. strips calculated, on the assumn- 
 t.on that earth fillin,^ weicfhs 100 pounds per cubic 
 f'H.t. and masonry IfiO pounds per cubic foot. A livo 
 load of l.-,0 poun.ls per scp.are foot was assumed on 
 th.. roadway. The w.Mfrht was .-ompute.! for each 
 stnp and noted on Fi-ure 7 in their respective 
 places. The a.nount of con.ju-ate thrust was then 
 fo.ind by taking the intensity of such thrust at one- 
 th.rd the weip:ht of earth and live load above it. 
 These wer(> also noted in their proper places. re,.t<-r 
 lines wer.. th.Mi drawn throuj;!. each strip. an<l a 
 load dia-ram constructs by drawin- in (,rder th.. 
 various vertical and horizontal loads from A t.. P. 
 as shown in Figure 7. A trial pole P' was selected 
 and lines drawn conn.M-tin- each of the loa<I points 
 on an with P'. The corresponding funicular poly- 
 
 •mBr^'^iif^mrmirfim''i 
 
If 
 
 ! 
 
 
 r.s 
 
 COXCRllTE BRIDCrS AM: CriA'HRTS. 
 
 fron ay wjis dnnvn with lines pan.llol tc Iho linos in 
 the n.ree p„lynron AI". BI>'. ,.te. This is ..vi.lontlv 
 not the correct position of tlie pole, for the result- 
 injr fnnicular poly^^on lies ahnost entirely outside 
 of the arch. Hy i)rolonjrin<i the last string of tho 
 funicular polypron f,, its intersection at ^ with the 
 horizontal throiifrh the arch center from a, wo find 
 the point of application (.f the resultant of all the 
 imposed loads, which is at -. The direction of th.. 
 resultant pressure would he jiarallel to AB. As tho 
 positi.Mi of this point is constant for any other posi- 
 tion of pol,.. we may draw throu«rh v a line vt;. This 
 will represent the direction of the actual "pressure 
 of the arch on the abutment. Throujjh R in the 
 force polyjron draw a line parallel to v^ intersecting 
 the horizontal throu-h A at P. Tho point P will be 
 tho correct position ^^f the pole, and the distance AP 
 measured to the same scale as tho line AP. will rep- 
 resent tndy the amount of the crown thrust. In 
 this case it is 42.000 i^ounds. This investigation is 
 for a portion of th.- bridpr one foot in length at 
 rijrht an?les to the dia?ram. Pressures at the var- 
 ious points in th(^ ;irch correspond to the lengths of 
 hues in the fore- j)oIyjro,i. At the pier for full 
 loadmjr, the pressure is 4S.000 pounds. 
 
 Uneven Loading, 
 
 Tiines of resistance wer- next drawn f,,r unsym- 
 wietrical loadinir ;is shown in Fi<jure f). This has 
 .ilieady been .piite fully desenbed under the head 
 of I'artin! Loads. 
 
/'/..■//.VrO.VC-A7:y/: ./A.r///^A7/.(;/:.V. 
 
 Required Area in Arch. 
 
 ti!» 
 
 Tsin- n niaxinuun prossuro (,.f 400 p.,,,,,,!. ,„.,• 
 
 SMnar.HM.h.sas.fowoH<in.unito,...o,K.n.t,.. 
 t'-n.ter ed.e, or 200 pounds p.. s.n..n> indMn..;;, 
 P>-..ss„n.. tlH. n..,uin..| ,„•..„ i„ tli,. .n-h is :^'"i!i' 
 
 or21(,s,uan.i, „ 'Hus r.,uU:s ., ,.,,u „r 'Z. 
 
 lo 'r .,"'""' ^''"■'•'^^•''■^•^•'' "<i-pti...r 
 
 ^N.thaaopthof:50in,.hos,thomoaMpn.s.s,n „ tin.' 
 
 or the 200 pounds whidi is propos,.,!. 
 
 Intermediate Piers. 
 II'" ar,-h.s ,„„l tl,.. livo l,„-„l is .-,4.0,,,, ,„„„; '"" 
 
 :;7",'™""- -ii- Mo,,,...,,,,.... ,"' i,i,- : 
 
 "'™f"^ """ I"--"' II,.- o„„., ", 
 
 MT-Hss,,,,,.. ,„„r„f „,«„„„„„„ „^,„;l'^ 
 '"" I" "I'^l- lil-'''-t loil.ls is lli..|-..f.„,. -1"^" 
 
 (ir 
 
 "';"'™"-'-""|<i"'s'"v.-n,i„,..„,„i,i,.,.„i '"- 
 
 thr,'.'" '''"*■'!''■,'"" '■'■'■''"'''''I"''- 1'"" •-'".. 
 
 «,tl. .U-a.l l„a,l „„|y. Tl„. ,i,r„s,s i,i ,l,vs,. 
 
 .^ 
 
If 
 
 TO co.vt'A'/://: nKinai-.s .;.\7> cn.rnRTs. 
 
 Iwo cMscs jirc 4?<.()(l(» j)ii(] 42.000 ixmiikIs respectively. 
 'I'lii' lotiil liijul (Ml 11i(> pier iit llie li'vel (if tlie fjtrouiKl 
 is I Ik jM'Tcn ;is lollows: — 
 
 rounds. 
 
 I'r<!il I'lllly l.i;iflc(l sp;i'i 2ti.000 
 
 I''rniii p.'irtly Injidcil span _':!.000 
 
 Wei^'lll nf pier IS. 000 
 
 Tni;il t;i.(H)n 
 
 l>y (■(iiiil)iiiiiii,' iliis lo;i(I witli llic iii'clr tlinist . we 
 liiid Hie i-'siilljuil prcssi:iT. 1] ,■ lim. of which inter- 
 sects thi' li.-jsc at irrmilKl level one foot Troiii the ceii- 
 t''i" <'t" tlie piei-. which is well within the Mii<l(lh' 
 third. This icskII ii;ay \ ei-y easily he ehe(d<e(l aiiii 
 lylically The width d" piei- at hase is II feet, whieli 
 was i'oiind as rolhiws- - 
 
 The tiital pressiil'e i n t he Sdil is : 
 
 Pounds. 
 From lit idu'e .")4.()0() 
 
 I'"riiiii piei- 27.000 
 
 Tnial S1.000 
 
 -Mliiwin^'' a mean pt'essure ol' (i.Od!) pdnnds per 
 
 S((iiare foot on the soil, the iVMpiil-ed width of piei' is 
 
 SKHK) 
 
 - ,, "•' 1"^'> feet. If the soil will not sustain 
 
 (IdOO 
 
 • i.OOu pounds pel- sipuire foot. wlii(di. allowiii.ir I'm- 
 
 uiiexcn pressure, crpials 4 to .') tons per sipiare foot 
 
 ilt the outer edye. piles will then he I'etpnred 
 
 Abutment Piers. 
 
 In i)ropo!'tiotiiiitr the ai)iitiiien1 pier, st.ihijity is 
 the (diief coiisidei-atioii. It must he stahle aj^amsl 
 
I 
 
 /V..//.V COXCR/n/: .iRC/f HRinGIiS. 71 
 
 tlic Ihnist of arch from o.io side onlv. This arch 
 tlinist intcrsocfs tho .M-ntcr of fh." j.i.r at a distanc 
 "f U fcot al),»v.> the -r<,„„,i. Tho ovorturninf; 
 I'lonicnt from this thrust is therefore ."^OOOXH. foof 
 l-MMuls. rsinjr a faetor of one and one-half against 
 "verturnuie. th.' neeessary moment of stability is 
 •Ti.OOOXHXi,:.. ,, ,n.,oo foot pounds. Next pro' 
 <-"<'d to tind the half Avi<lth of pior base at -round 
 l"vel. fallincr this half width x. the re.juired mo- 
 iiuMit of Stability in foot pounds is 
 ^i:mOx+{'lxxnxm))x- .;!..;{00 foot pounds In 
 tli" above. 22 is the totnl JH-ijrht of the pier from 
 til.' top of the -round to th- top of the baekin- and 
 K'O IS the weijrht of the pirr material per .Mibie foot 
 1-rnm the abov.> we obtain a .pundratie e.|uation. and 
 sulyuM'. we find the vnlue of .,- to 1„. 8.4:. feet. 
 This would br for a pier with vertieal sides r.,r 
 Nb.l>injr sides, take a half width at the base of !) 
 <'"•». as shown in Fi-ure !>. This siz.> .,f pi.-r is 
 tlieii amply stable ajrainst uerturnin- 
 
 <'<'nn,ir .M.t Ihe haunehes by means of i„f,.Hor 
 spandrel w.lls. w<.uld <"vid..ntly W ,., ......m.mv in 
 
 so flat an an-h. The eost ..f snrh walls and nrehin- 
 ^^"••1,1 b.. -reater than th.. savin- m the areh rin- 
 l.-.n the redueed dea.l load and the b-ss amount of 
 nllin-. 
 
 Illustrations of Concrete and Masonry Bridges. 
 
 ''''.e fon.-oin- ta(,b. -ives a list <.f areh bridf,es 
 ^''" •"«•"" anl,,s of which are built of solid eoneret..' 
 
r ' 
 
 1 1 , 
 
 ) * 
 
 '- (('Wk'l.T/: lU<llH,i.s .l\/> Cri.lhRlS 
 
 witlinut iiiriiil iviiiror.M.n,..,if. Tn ono cf tlK'sc. Iiow- 
 "v.'f-flir n,iln.,„| hri.!-.' oviT tlic Vcnnilli.^n Kiver 
 ;it I);mviII.-— iTinrnrc..nH-ii( w;is jicliiiillv i-scl i,i fho 
 '"••"" '"-Hi. hut w.-.s\-,<I,.pf,,l ,,„|y for 111,. ,„n-i...s.. nf 
 Ix'tt.T iniifin- fl,,. ..uM.Mvtr .-uhI pn.v.Miti„jr n-M-ks 
 ''••"" ••liaiiir.- of 1..ni|...|-;,tmv. In s.-v.-nil ..f f|,.. 
 '•*'"''■ '"•i<l^«'"<- nni,.,I i„ ,|,., i;,i,J,, „iHi.l .■.■infom>. 
 ""•nf W.MS ns,.,I in spiui.lrrl ;,.vli..s. ,„• ofli,.,- ininoi- 
 P"i-ts. hut ns .•iln.Hly sf;,l..,I. tl... .„;,!„ mvlM.s lu,v.. 
 '>•'••" •l"siu-n.Ml ^vitl, UM pruvisi.Mi for tension in i.nv 
 part .,1 tl„. .,n-|, s-.-ti-.n. .•.n,I .-nnsniu.M.tlv no n-cil 
 i:<.r iTuitoivin- nictiil to ivsist .Iiiv<-t stresses. 
 
 Tlie tiil.le is not intend. ',1 to I,,, coniprehonsive or 
 Oninplete. hnf uHves so„,e .jetnils of ;, few ..f tile 
 
 Jnrirest .-onen-t.- spnns. the ni.'iin an-hes of whieh 
 fire .h.s.o-ne.l without n.inr..ree,uent. In ivfeirneo 
 1" ;'": '>'"1-"" M..n,ori;,l l-.ri.l-e. noted in this tiihle 
 :<'i.l illustnite.l on pfiuv 7:. th.- ,h-sij,-n enlls for .i 
 ''■""-"'■ ■"""""' "'■ "let.-il reinfoiv.MiH'nt. not for the 
 purpose ,,r resisting ■.my tensih. stresses in the jireli. 
 '"It nither to snpph.ni.'nt tlie ,.,nierete in r.'sistin.' 
 •'"•''••< --npression. This is ;, new prineiph- in „reh 
 '•"iistrnctioii. not pr.nioiisly use,]. 
 
 mnstnitions nui\ deseript ions of two ohl K,,nuin 
 
 '"••dues aiv .-dso ojven \\,V the p„rp,»s.. of e;diin- 
 
 ■•'""'"'■'" '" 111- sup,.riurily .•,n.l p.-rnn.n.-.ie,. ,.f ma- 
 sonry hndnes over those of .ny oth.-r known tvpe 
 '"■ •"■•"'■'•'■•''■ They h=ne exisie,l for .-."ut nri,.s. iin-l 
 -^H'-'! !.i id^vs sliuuhl ,.ndnre after inetal hri.luvs have 
 dis:ippcai-e(]. 
 
 ^ 
 H 
 

 J l! 'ill 
 
 ' !!. 
 
 M. 
 
 p li 
 
V 
 
 nil 
 
 74 coxcRi'Ti: itk'iiHir.s .ixn cn.iT.RT!!. 
 
 Ponte Rotto, Rome. 
 
 As it stands to-dsiy. tliis old liridsc lins tlirco stone 
 arch spans, and a suspension bridj^c, spanning; the 
 {?ap where oflier arehes (>ri«rinally stood. The pres- 
 ent bridjre stands on the site of tlie (dd Tons Aeniil- 
 ins. Itnilt H. (\ 17S-142, Avhieh was the first stone 
 hridfje over the Tiber at Koine. Tlie tliree reinain- 
 ijijr arehes date fi-om Julins TIF. and are richly orna- 
 mented. Two arehes were carried away by a flood 
 in 1508, and have nev<'r been replaced. The bridfr<' 
 H+'cnis to be nnfortunately located, as it has been 
 carried away at least fonr times, tlie first time in A. 
 T). 2S0. It was erected by fains ^'lavius, and is 
 probably tlie first appearance of the arch in brid«rc 
 construction. Tt has semicircular ar<'hes and a 
 level roadway. The two end arehes were shorter 
 than the three intermediate ones. It i;. called also 
 I'ons Palatiiuis. Senators' IJridfre, and Pons Lapi- 
 deus. Th<' bridjre is similar in construction to the 
 other old stone bridjres of Kome. and is built of 
 peperino and tufa, faced Avith blocks of travertine 
 anchorecl into the body of the masotiry. Tt will be 
 seen from the illustration that the spandrels ai;d 
 parapets are liijrhly ortuunented with <'arved panel 
 work aiul each of the ])iers above the arches and 
 foundations an- ])enetrated with snudler andi open- 
 injrs. The panel work has disapi)Pared from the left 
 shore s|)an and i)lainly reveals the plan of eonstnii-- 
 tion. It will be seen that the arch rin<r is built of 
 

 'A 
 
 
 16 
 
• lid'cn-iil iii:it>riiil .mil diffcrctilly laid than U\o 
 fil!iii<r :il)nv(' i!. ;ii)(i tluif minuTous openings (iccur 
 in till' l)ackiii«r wliicli were .Imihllfss used for the 
 
 puvposc of jiti.-Iioriiitr tl niiimcntai fnciuf; to the 
 
 ImhIv nl" tlic sf ciictiin'. Tf is \vell l<iiowji that, in the 
 eoiistnictidii tpf l)ri<l^'.'s iiiid n«|Ue(lu<ts huilt by the 
 TfiiMwMis mill utlier-s in .ai'ly times, a lart't- amount of 
 coiiel-t'te was used. 
 
 1^ ^ 
 
 f 
 
 ! ! 
 
 ) 
 
 u 
 
 1 
 
 t i 
 
 \i^l 
 
 Bridge of Augustus at Rimini. 
 
 The old Koman I)rid<re erossiiiff the River ]\Iara- 
 ••liia at l{iniini. is supposed to liave been huilt durin«» 
 th.- iviu-ii (.r Kmp.-ror .\ufrustus. about 14 A. D. It 
 has five ai-ch spans, with xci-y heavy piers. The de- 
 tails that still i-emain show that oriffinally the 
 bridi;.' Avas very ornamental. There are niehes at 
 tlic pie!-s. ami the heavy stone corniee is earried 
 on nui.'i. -roils 1. rackets. The arehes are all semi- 
 '■'"' ':"■• <li.' end ones havinj? a span of 2') feet, 
 whih' till' three internie.liate ones have spans of 28 
 
 lert. 
 
 Henry Hudson Memorial Bridge. 
 
 (K'eiid'oreed ('onei'ete Design.) 
 
 It is proj.osed to erect on an extension of River- 
 side Drive ill the City of Xew York, a Aremorial 
 liiidiic over Spuyten Dnyvil Creek, to eommeniorate 
 tl'e cxploialiuns and discoveries of Ileii.-y Hudson. 
 The desijrn aeripted by tlie Municipal Art Coiiinus- 
 
 I 
 \ 
 
 -i 
 

 
 
 y. 
 
 7. 
 
 n 
 
MICROCOPY RESOLUTION TEST CHART 
 
 (ANSI and ISO TEST CHART No. 2) 
 
 1.0 
 
 I.I 
 
 
 3.2 
 3.6 
 
 4.0 
 
 2.5 
 
 1 2.2 
 2.0 
 
 1.8 
 
 1.25 
 
 1.4 
 
 1.6 
 
 ^ /APPLIED IN4/IGE Inc 
 
 ^^. 1653 East Moin Street 
 
 r^ Rochester. Ne« Vork U609 USA 
 
 .SS (716) 482 - 0300 - Phone 
 
 S^ (716) 288 - 5989 - Fa« 
 
n 
 
 t'-- 
 
 I 
 
 ! ; 
 
 Ts (<)\ch-i:ii-: liRiiHiiiS .i\n cn.rr.NTS. 
 
 si(.ii of the (Mty of N'cw York is lUTcwitli shown. 
 I'n'vions (l«'si'_'ns showiti«i: the priiiciiial span fraiu(Ml 
 in steel Avere rejected as hein^' inappropriate for a 
 •jreat memorial brid},'*'. There Avill be one span 
 with a elear len<rtli of 70:] feet, and seven other 
 semicirenhir areh spans with elear lengths of lOS 
 feet. The tolal lenirth of the strnetnre will he 2,S40 
 feet. The main aich span will have a rise of 177 
 feet, and will contain a larfre amonnt of steel, used, 
 not as concrete reinforcement ordinarily is. to i-e- 
 sist tensih' stresses, hut rather to assist in resistin'Jf 
 the compressive stresses in the concrete, and there- 
 by reduce the amount of masonry. The arch will 
 have a crown thickness of IT) feet. There Avill be 
 iwo decks, the upper one carryinjr a ."0-foot road- 
 way and two l.Vfoot sidewalks, while the lower deck 
 Avill be 70 feet in width, and will carry four lines 
 of electric railway. It is the intention to <nnit the 
 construction of the lower de(d< at the present time. 
 The desi«:ii ])rovides for a clear headroom of 18.3 
 feet luider the main andi. The nuiin pieis will be 
 ISO feet in width. The estinuited cost is ^'^.SOO.OOO. 
 Tlie illustration shows the bridge as it Avill 
 ai)pear to an observe)' btoking out over tlie Hudson 
 iriver. with the Palisades in the distance. The do- 
 sign Avas made by the bridge department of the City 
 of XcAv York, at which time ('. M. Tngersoll Avas 
 Chief Engineer. I.. S. :Nroisseiff Engineer in Charge. 
 Wm. H. liurr. Consulting Engineer, and AYhitney 
 
/V..//.V coxcKirrii arch BRinci-.s. 79 
 
 Warron. Architect. The ncx^ lonjrcst iiuisoury 
 iirdios of tlic worlil arc as follows: 
 
 Foot, 
 span. 
 
 Stono arch bridjro over Adda Kivor 230 
 
 Stono arch hridirc at liuxcniburjr. (ioniiaiiy 27S 
 
 Stono arch hridjjc at I'lancn. Gonnany 20.") 
 
 Concroto arch bridjro at Oruonwald 230 
 
 Conorote arch bridjro at AValnut Lano. riiiladd- 
 
 phia 233 
 
 r>toin-Toufcn bridge. Switzerland 259 
 
 Concrete arch bridtre at Kocky River, Cleveland. 280 
 Aulxland. New Zealand 320 
 
 Aukland, New Zealand, Bridge. 
 
 A reinforced concrete arch bridge is being built 
 on the North Island, at AnUland, New Zealand, with 
 a dear span of 320 feet — the longest in existence. 
 Several longer ones have been i)ro.jected. one over 
 the ^Mississippi l?iver at Fort Snelling. ]\Iinn., with 
 two si)ans of 3r)0 feet, but none built. The Aukla?id 
 bridge has, besides the 320-foot center span, two 3.')- 
 foot and four 70-foot spans, with a total length of 
 010 feet. It is 40 feet wide, and the roadway is 147 
 foot above the valley. The two arch rings are hinged 
 at the springs and center. Tt was connuenced in 
 February. 1008. and the contract calls for comple- 
 tion in two years. Tt ad.joins a residential district, 
 and at one end are the gi-aves of New Zealand 
 pioneers. 
 
I : i 
 
 ; i 
 
 S(» COSCRIiTE BNIIXJliS .IXP CriAllKTS. 
 
 Monroe Street Bridge, Spokane, Wash. 
 
 Ill tilt' city (»f Spokane, Wash., plans are prepared 
 lor buildinjjf a four-span c'onerete bridge to carry 
 ]\ronro(' sIriM't at a lieight of 140 feet above the S])o- 
 i<ane Kiver. Tlie main areli lias a clear span of 281 
 feet, and is divided into two ribs. U) feet wide and 
 »i feet thick at the crown. It will have open span- 
 drels and ovei]ia!i«>ino: sidewalks, with Dutch towers 
 ;it the ends for public la\atorii's. The bridge will 
 replace the (»ld steel cantilever built 17 years ago. 
 It will have a 50-foot loadway and two 0-foot side- 
 walks, making a total width of 71 feet and 
 a total length of 701 feet. The main arch 
 will be segmental and the remaining ones semi- 
 circular. The deck will be carried on solid cross 
 spandrel walls, 20 feet a[)art. The ground on the 
 north side of the river is naturally suited for an 
 arch bridge, but on the south side the plan proposes 
 an abutment carried down to 140 feet below street 
 level, consisting of four parallel walls, each 4 feet 
 in thickness, joined by numerous cross struts and 
 braces. See Fig. Ki. J. C. Ralston. City Engineer. 
 
 Rocky River Bridge, Cleveland, Ohio. 
 A concrete arch l)ridge with the longest masonry 
 span in America is now being built over Rocky 
 River on Detroit avenue, at Cleveland, Ohio. It will 
 have a central span of 280 feet and five approach 
 spans of 44 feet each. It will carry a 40-foot road- 
 way and two sidewalks 8 feet Avide each. The total 
 width over r; lings will be t.O feet and the total 
 length 708 feet. The main span consists of two sep- 
 
 1 n 
 
 ^::"^JKW*i^2 
 
17. a: 
 
 ^^ 
 
 i a 
 
 - + 
 
 1 
 
 _ l_1 
 
 n 
 
 } 'JS^--r''>£l^y"^f^S.'!'T 
 
 '•^!mt'J9im^^ss.wir:''i^iMj:t 
 
 117 
 
^r 
 
 III 
 
 fcii \ \ 
 
 y. 
 
 82 
 
 iWL;. 'tfi 
 

 83 
 
 il 
 
 "•^H^^^^^-Vf^iWr-^' "'«!^^*F'?f?W!K?^'"J^a>"W:'- 
 
84 
 
 cosch'i.Tii liRinci-s .\\n cci.iiirts. 
 
 
 1 I 
 
 ! i 
 I. i 
 
 ! 
 
 ai-iilc arcli riiu'-s :s f,.,'t wide ;il ili(. crown, atul 
 plaiMul Iti feet apiirt. On tlicsf arclics tlic deck is 
 In 1h' carried on cntss-sparidrcl walls. The roadway 
 level is !M feel above tlie surface of l(»w water and 
 til" pavement will be of brick, with two lines of 
 traek for heavy suburban ears, lieneath the floor 
 ve to be two subway chand)ers. :i feet by 11 feet 
 /• the placitiir of pipes and wires. The main arch 
 ring's will contain no steel reinforcement, as the cal- 
 eulations show that n(» tension can at any time oc- 
 fur in any part of the ani. The sidewalks i)ro.ject 
 out over the face walls about five feet, and are sup- 
 ported on brackets. The entire strueture will b;; 
 built of concn^te. Jt will be (piite similar to and 47 
 feet lon«r< r than the Waliuit I.ane Bridfre at Phila- 
 delj)hia. The oidy lon<rer uuisotiry arch span in ex- 
 istence is th(> one at IMfuen. in (Jermany. with a 
 span of 2!)() fe.'t. built of hard siate. Other pro- 
 jeeted ioiifr-span bridfr<'s are that over the Xeckar 
 River at ]\ranheini. with a span n '*->et. and the 
 
 Hudson .AFemorial Uridjre in X. City, with a 
 
 span of liV.] feet. The Kocky Kiv. P.iMdsre Avas de- 
 sisrned under the direction of A. ]i. Lea, (Vmnty 
 Engrineer. hy A. :\r. Fel«,Mte, Bridjre Enirineer. It is 
 under eonstruetion by Schilliufrer Brothers, con- 
 tractors of Cliicago. Wilbur J. Watson, Engineer. 
 
 Walnut Lane Bridge, Philadelphia. 
 
 Walnut Lane crosses the Wissahickon valley on 
 a new concrete bridge at a height of 147 feet above 
 the river bed. At the time of completion it was the 
 
ta ^ 
 M 2 
 
 U 
 
 t« 
 
 ft&W^ 
 
 -w^f^n 
 
f 
 
 8(; 
 
 CO.Vt /«•/; //• liUllHil.S .\\n CUI.rKRTS. 
 
 loiifft'st concn'tc iiijisonry hridjjc, haviti>» u clear 
 spiui of 2'.H feci. It consists of two soparate an^li 
 riii«rs, IS feet wide at the crown, increasing; to 21 
 fc(-t (i inches at the sprinf,'s. At the crown tlie two 
 ring's are separated by a space of l(i feet. The 
 double rib consl ruction is siniihir to tint used in 
 the .stone arch bridjre sit Luxendjiirp, (lerniauy, hav- 
 ing' a si»an ol' 27.') feet. The main arch is an 
 •ippn. viniate ellipse, has a rise of 7:{ feet, and 
 carries ]() cross walls which support the tloor 
 system. There are also five semicircular approach 
 arches with clear spans of T),} feet. The bridj?e con- 
 nects Gerniantown and IJoxboroujrh. two residentinl 
 .suburbs of Philadelphia. It has a 40-foot roadway, 
 and two lO-foot si(lewalks. The entire structure is 
 solid concrete, not reinforced, except inj; in certain 
 minor details. TI - surface finish is rough, sinne- 
 what sin-Mar to pebble dash, but of coarser grain. 
 The exposed surface shows stone clips of not over 
 three-eighths inch in size, formed by washing before 
 the cement had Jiardened. The total length of 
 bridge over all is 58.') feet, and the cost $259,000. 
 (reorge S. AVebster, Chief Engineer. Bureau of Sur- 
 veys. II. ir. Quimby. P,ridge Engineer. Reilly & 
 Ividdle, Contractors. 
 
 Connecticut Avenue Bridge, Washington. 
 
 Connecticut Avenue, one f the chief tlummgV 
 fares of Washington, is carried over Rock Creek 
 valley near its junction Avith the Potomac on a new 
 concrete arch bridge, about three miles from the 
 
//: 
 
 
 87 
 
 ,« »^-^'5»*' 
 
88 
 
 coxcNini: hkiihus .i\n cii.ii.hTs. 
 
 lii ■ • 
 
 l'<\ \ 
 
 ('Hpitol l)uil(liii<r. The nunhviiy is 1l'i> fii-l jil)(»v<' 
 the vaih'V Ik'Iow, iiiid is ciirritMl l>y live sriiiirin-ii- 
 l;ir an-lics of loO-fuof spiin. aiid two end iirrlu's of 
 S2-f()<it spjMi. It has ;i .{.Vfont I'oadway. and tun 
 Kid. 'Walks S feet wide carli. niakitiLT a total widfli of 
 iVJ I'cct. a clear Iciifjlli hflwccn almt iiii-nts of l.(»»iS 
 ftH't. and a tnfal Ictifrtli of l.:{41 I'fcl [t was .•oiii- 
 iiHMiccd it) iSSf), and ('oiiiplctcd in l!M)S. The main 
 ai'r-hfs at'!' Iiinjrclcss with no i-ciid'on-intr. hut tin 
 spandrel an-lics have steel reinforcement. As the 
 bridfje is located in a tine residential disti'ict, 'U 
 aesthetic appearance was a matter cd' consideral»! • 
 importance. The face rinjrs oi tlie aivli. pii^r cor- 
 ners, mould in<rs and all trimmiiijxs lielow Iheirranit.' 
 
 t'opin<r. an )ulded concrete hlocks. The remaininir 
 
 part of the cNposed concrete surface is hush ham- 
 merpd. for the purpose (d" present injr a moie uniform 
 and pleasiiiff appearance. The cost (.f the falsework 
 was about !fir)().0()(). hut on this there was a sal\a«,'e 
 of about $13.(»()(). The cost (d" fraiiiin<r the false- 
 work was -t!) |)er Hi .usand feet of lumber. .Moulded 
 cement blocks cost .+ 1.') per cui)ic yard. The total 
 cost of the structure complete was i;^ ■)<>.(><)< ). equal 
 to $(;;}*) per lineal foot, or .tl2.;^(> per s<|uare fo(tt of 
 Hoor surface. It is built from a modili.-ation (d' tlic 
 prize desifrn submitted by the late (icor-re S. Morri- 
 son. The orijrinal c(mi|)etitive desijrns estimated 1:. 
 cost from .t-lTO.OOO to >:1.1()().()()() were published ii; 
 En<?ineerin^ News Jatniaiy 27. 1S!)S. j) xvjis bull' 
 under the direction oi Col. dohn Hiddl,'. Hntrineer 
 Commissioner of the District of Cohnnbia. AV. J. 
 
 ffi- 
 
 'sir-v^^-'W ■•'taAi 
 
8B 
 
 O 
 'A 
 
 -J 
 
 it 
 
 a 
 
 
 
 .i-A 
 
90 
 
 coxcRRTE RRincr.s .ixn Cri.lI-RTS. 
 
 I ; 
 
 i ! 
 
 l)()n<;liis. liridii*' Kii^iiiccr. K. 1'. Casey Coiisiiltiiii? 
 An-liitfM't. 
 
 Big Muddy River Bridge, Illinois. 
 
 Two tracks of the Illinois Central Railroad are 
 carried over l>ig ^Mnddy Kiver near Grand Tower, 
 Illinois, on a new three-span concrete arch bridge. 
 It was huil' in 1003 to replace an old steel bridge, 
 and for this reason the piers remain in their original 
 location. The liridge has three clear openings of 
 140 feet, and a total length of 4():{ feet between faces 
 of abutments. It is ')2 feet wide, contains 12,00!) 
 cubic yards of concrete, and cost complete .tl2-">.000. 
 The arches are true ellipses with semi-minor axes of 
 :U) feet. The old piers were to 10 feet in thick- 
 ness, and the new ones, which were built around the 
 old ones, are 22 feet thick. The main arches are 
 solid concrete, the only reinforcing being in the 
 spandrel arches snpi)orting the floor, and this was 
 used for convenien<'e in erection. As built, with 
 spandrel arches and oi)enings. the cost was some- 
 what greater than if it had been filled. The de- 
 signer explains that open spandrels were used for 
 the purpose of reducing tlu^ load in the foundations. 
 P.ig ]Muddy Uiver P>ridge was designed by TI. W. 
 I'arkhurst. Engineer for the Illinois Central Rail- 
 road Comi)any. 
 
 Santa Ana Bridge, California. 
 
 This structure carries the new line of the San 
 Pedro, Los Angeles and Salt Lake Railroad, over 
 Santa Ana River, near Riverside, California. The 
 
 [1 : 
 II ' 
 
 .V 
 
 .ir?aEBs^r'.« /""if^s^mi 
 

 n 
 

 ^- 
 
 »."--:-'"«• 
 
 wm^ 
 
rL.UX COXCN/iTIi ARCH BRIDGliS. 
 
 93 
 
 bridgrc has a total length of 984 feet, and the deck 
 is 5.') feet above the -water. It was l)uilt during the 
 years 1902 to 1904 under the direction of Henry 
 IIuMgood, who was tlien Chief Engineer for the 
 above railroad company. It contains eight senii- 
 circnhir arches of 'f^Cy feet clear span, and two end 
 spans of :i8 feet. The piers are 14 feet in thickness, 
 making the distance on centers of main piers 100 
 fei't. It is made of solid concrete without reinforce- 
 ment, contains 12.r)(>0 cubic yards of concrete and 
 cost .tlS.').:500. The thickness of arch at crown is 3 
 feet <; inches, and the width across soffit is 17 feet 
 and inches. 
 
 A leltei' from ^Ir. Tlawgood to the author in ref- 
 ("•cMce to tliis 1»i-idge states as follows: — "The Santa 
 Ana viaduct has given entire satisfaction from an 
 o[)crMtiiig standpoint. There has been no cost for 
 maintenance during the five years it has been in 
 service, whereas a steel briilge would certainly have 
 involved some ex[)ense during the same period. In 
 positions such as the Santa Ana Viaduct wher" 
 liiei-e is no limitation as to headroom, I consider the 
 simple concrete structure without reinforcement a 
 better structure than one reinforced. The greater 
 weight of concrete retpiii-ed forms a much heavier 
 nuiss to take up the imi)act of heavy high speed 
 (i-ains. The absence of vibration is very marked. 
 It is a tu'i'idlel condition to a heavy ai.vil under a 
 st'-am hammer — the heavier the anvil, the longer it 
 will last." 
 
 VY i 
 
94 
 
 coxcRF.ri: nh'incEs .ixn culverts. 
 
 J 
 
 TABLE I 
 
 LIST OF CONCRETE BRIDGES 
 
 li' i ! 
 
 t J 
 
 t ] 
 
 i 
 
 I.(M.ATI()\. 
 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13| 
 
 14 
 
 1.'^! 
 
 19 
 20, 
 
 2]| 
 22 
 23 
 21, 
 
 52l 
 
 2 
 
 28 
 
 Over. 
 
 Hudson Mem., New York. 
 
 ti il tt tt 
 
 Auckland, \. Z '. 
 
 Spuyten Duyvil. 
 
 Detroit Avenue, CleNelaiid . 
 
 41 H tt 
 
 Walnut Lane, Philadeiiiliia 
 
 Ciruenwald, Rasaria. 
 
 rirn, (iennany 
 
 Keinjpton, (ierniany. 
 
 Kocky Hiver.. . 
 
 n tt 
 
 Wissahickon. . . 
 tt 
 
 Tsar 
 
 Railway Yards 
 Iller Jtiver 
 
 LaufrMi'h, " 
 
 Nec'^arhausen, 'Jerniany 
 
 Munderkimjeii, A\ urteinhurtr. . 
 Connecticut Ave., Wash imton. 
 
 Neckar .... 
 Danube. . . . 
 Reck Creek. 
 
 Porfljinil, IVunsylvania ' Delaware River . 
 
 Vauxliall, London 
 
 'irand Tower, Illinois 
 
 In/.i(rliofen, (Jertnany | 
 
 Edrnondson Ave., Ba!tiin>(re I 
 
 Thames 
 
 Big Muddy River; 
 
 D'lniibe 
 
 Gwvniis River 
 
 7 Rorrodale, Scotland I Borrodale Burn 
 
 1 ^ 
 
 
 
 
 .1 
 
 c 
 
 1 
 
 : 1*703 
 
 177 
 
 2840 
 
 7^108 
 
 
 
 1,320 
 
 
 910 
 
 2 35 
 4 70 
 
 
 
 
 
 : 1280 
 
 80 
 
 708 
 
 5 44 
 
 22 
 
 
 ' 1233 
 
 73 
 
 585 
 
 5l 53 
 
 26.5 
 
 
 2'230 
 
 42 
 
 720 
 
 1210 
 1211 
 
 
 
 87 
 
 500 
 
 3 68 
 1187 
 
 
 
 32 
 
 280 
 
 l|l65 
 
 13.5 
 
 
 1164 
 
 16.4 
 
 
 r)ir,o 
 
 75 
 
 1341 
 
 2 82 
 
 41 
 
 ■ > • ■ < 
 
 5150 
 
 40 
 
 1450 
 
 2120 
 
 
 1450 
 
 2 30 
 
 
 1450 
 
 1144.6 
 
 18.5 
 
 
 3140 
 
 30 
 
 483 
 
 1141 
 
 14 
 
 150 
 
 1139 
 
 44 
 
 542 
 
 3j 60 
 
 30 
 
 542 
 
 1127. C 
 
 22.5 
 
 
 2 20 
 
 
 
I'l.AlX C(K\\h'l:H. .\RCIl iu<iih;i'.s. 
 
 <j5 
 
 TABLE I— Continued 
 
 LIST CF CONCRETE BRIDGES 
 
 su 
 
 4;/ 
 
 (50 
 fiO 
 
 m 
 m 
 
 2.i 
 46 
 54 
 
 " I 
 147 
 
 94 
 
 94 
 
 147 
 
 147 
 
 ('. 
 E. 
 C. 
 
 C. 
 
 
 
 Hcfcn-iice. 
 
 
 c 
 
 N., 
 
 Ellg. \ews 
 
 
 "5 
 
 H.. 
 
 " Ueronl 
 
 1 
 S 
 
 i9;;8 
 
 ti 
 
 1909 
 1 <»()<) 
 
 If 
 
 1904 
 1905 
 1900 
 
 H. 
 H. 
 
 II. 
 TI. 
 
 II. 
 
 H. 
 
 ;i,.SOO,00() MoisseifT 
 
 .\., Nov. 21, '07 
 I l{., Dec. 2S, '07 
 
 1 
 2 
 
 ■i 
 
 \ 4 
 
 N., Jan. ;il, '07; N 
 
 20,S,;i00 loliiate 
 
 2(;2,0()') AVebster 
 
 " N., Jan. :}1, '07j 9 
 
 05,000 I Munich N., Feb. 2:i, '05:10 
 
 45,00<i I X., Mar. 1.5. '00 1 1 
 
 12 
 
 i:i 
 
 14 
 15 
 10 
 17 
 IS 
 19 
 20 
 21 
 '22 
 2;i 
 24 
 
 U.8| 
 15 8 
 
 40 Sen. 1900 l{. 1! 
 
 52 
 
 120 
 
 V. 
 
 52 
 
 
 c. 
 
 :n 
 
 05, 
 
 El. 
 
 ;m 
 
 65 
 
 
 ;ii 
 
 05 
 
 
 
 45, 
 
 E. 
 
 L? 
 
 i9o;i 
 
 1S9;5 
 
 ii9or 
 
 H. 
 H. 
 H. 
 
 21,000 
 
 I eibbrami 
 21,t2f) ; Leibbran.l 
 8.50,000 MorrLxon 
 
 \., May 2, '07 
 X., Mar. 20, '08 
 
 1908;K. J{.' 
 
 Bus 
 
 12.5 
 00 
 •lO 
 
 70' 
 70i 
 
 >e^ 
 
 1908 }{. K.I HiLsh 
 
 1908 1{. ]{.! 
 
 1899... .1 
 1902 1!. R.i 
 1V95 H. 
 1909| H. 
 
 12.., JO 
 
 «),0.->0 
 
 ]S'5,.X00 
 
 I'.ush 
 IMiinie 
 Parklmrsf 
 Leibbrnmi 
 
 |{., -Viifi. 15, '08 
 i{., .\up. 15, '08 
 R., .\u>;. 15, '08 
 
 .\., Nov. 12, '(W 
 N., Sept. 17, '90 
 H., June 19, '09 
 
 lS98iH. H, 
 
 iO 
 
 Siiiiii.M.p \., Feb. 9, '99 27 
 '28 
 
Bi; i 
 
 Ml 
 
 9c c().\\'h-i:ri: nuincr.s .ixn chahrts. 
 
 TABIE I— Continued 
 
 LIST OF CONCRETE BRIDGES 
 
 ; I 
 
 I.(X ATIOV. 
 
 er. 
 
 29 
 
 30 
 
 31 
 
 32 
 
 33 
 
 34 
 
 35 
 
 36 
 
 37 1 
 
 38 
 
 39 
 
 40 
 
 41 
 
 42 
 
 43 
 
 44 
 
 45 
 
 46 
 
 47 
 
 48 
 
 49 
 
 50 
 
 51 
 
 52 
 
 53: 
 
 54j 
 
 55 
 
 56 
 
 Sixteenth St., ^^'ashiilKt<)Il I'iiiey Creok. . 
 
 Kirchheini, Wurtembiirj;; Xecktr 
 
 Ilainsburw, New Jersey I'.iulins Kill.. . 
 
 Miltetiburj;, (leriiiany Main. 
 
 PittsbiiiL PeiinKvlvaniii Silver Lake. . 
 
 Thebes, Illinoi.s Mis.sissii)i)i. . . 
 
 11 11 I 11 
 
 Dainille, Illinois Vermillinii. . . 
 
 Meclianicsville, New York .Anthony Kill 
 
 1 12.-) 
 
 4 >4.(; 
 .■ 1 JO 
 
 2 KM) 
 2112 
 2107 
 2 102 
 1 1 00 
 
 5 SO 
 1 l()!i 
 
 11 (•.;. 
 
 1 100 
 
 2 NO 
 2 100 
 
 Ininaii, Havaria Eyach. ... ... 
 
 WyotriiiiK Ave., I'tiilailel|>hia ' Fraiikford Creek. 
 
 Hrookside Park, Cleveland \ \\\^ Creek 
 
 Riverside, California Santa .\na 
 
 Boulevard, Philadel[ihia ' Tacony Creek. . 
 
 Lonj; Key, Florida \tlaiitii' 
 
 Mannheim Neokar 
 
 Larimer Ave., Pittsburg Peechwood Boul 
 
 Spokane Spokane 
 
 .Mmendares, Cuba 
 
 1 50 
 
 1 9S 
 
 2 »S 
 1 92 
 S ,S(i 
 
 I 2 38 
 ' 3 80 
 180 50 
 1 365 
 1 300 
 1281 
 2120 
 1100 
 190 
 
 I 
 
 39 272 
 19 450 
 60 i 1100 
 
 : 1100 
 
 17.7, 7.33 
 
 50 , t;oo 
 
 40 
 
 50 I 
 
 32.5 
 
 40 I ;};{() 
 31.' 
 
 us' 110 
 
 2.N I 200 
 
 9 : 125 
 
 43 '■ 984 
 
 19 
 
 14 i 350 
 
 25 10500 
 
 115 791 
 
 60 
 
 50 
 
 ii 
 
PL.ilX COXCRI-TI- ARCH BRIlKlhS. 
 
 97 
 
 TABLE I Continued 
 
 LIST OF CONCRETE BRIDGES 
 
 ^ ^ 
 
 lit 
 ,{4 
 
 .■jl 
 
 2S' 
 
 40 
 
 11 
 
 11.- 
 
 •)0 
 
 7( 
 70 
 
 :v\ 
 
 90 
 
 ;}:; 
 
 
 • • • • 
 
 
 
 N 1' 
 
 .'.) 
 
 Sf 
 
 :v2 
 
 12 7 
 
 12 
 
 17.0 
 
 o.j 
 
 KM) 
 
 ••in 
 
 IT) 
 
 ;«) 
 
 Par. 
 
 c. 
 
 C. 
 V. 
 
 c. 
 
 1006 
 
 IS98 
 
 H. 
 H. 
 
 190S 1{. I{ 
 
 1S99 
 
 H. 
 
 r;i." 
 
 c. 
 
 {'. 
 
 Seiz. 
 V. 
 
 •)(),000 
 46,600 
 
 101,000 
 
 190.-) K. H. .. 
 
 i9n;^i{.jV. ;; 
 
 1N96j"h." 
 I90S| H. 
 190.-,^ H. 
 1904 R. H 
 
 1904 H. R. . . 
 
 1905 H. 100,000 
 1904 R. RJ 
 
 4,2S.-, 
 102,000 
 
 18.i,0C0 
 
 Rcferpnrc. 
 N-, Enp;. N'pws 
 R-, " Record 1 
 
 e 
 
 Fleischiiin 
 
 J5n)\vn 
 
 Nobel 
 
 Diiar.e 
 
 Lfibbrarid 
 Quimby 
 Ze.siger 
 Hawgood 
 
 Webster 
 Cvrter 
 
 R.,Jan. 
 X., Mar. 
 R., Aug. 
 
 n N., .Iniv 
 
 '1 14: 
 
 '«:!9 H. wi.itpd 
 
 I ,. lial.-.|(iii 
 
 R., May 
 'n.,"\ov.' 
 
 R., Mar.' 
 
 'N.,'i\ov.' 
 
 X.,'iVb." 
 W., Feb. 
 N., Mav 
 
 R., Sept. 
 
 R., iviar.' 
 X., Oct. 
 Proposed 
 Projected 
 
 26, '07 29 
 29, '00 SO 
 
 15, '08 31 
 32 
 
 25, '01 33 
 
 34 
 
 35 
 
 6, '05 36 
 
 37 
 
 20, '02 38 
 
 '39 
 
 3, '03 40 
 
 41 
 
 5, '03 42 
 '43 
 
 16, '99 44 
 27, '09 45 
 10, '0646 
 
 9, '05 47 
 
 '48 
 
 13, '0949 
 19, '05 50 
 
 51 
 
 52 
 
 53 
 
 56 
 
u 
 
 * ! •< 
 
 I i 
 
 1 I 
 
 I 
 
 In 
 
 ' ^^n\— . 
 
 
 ->^— H 
 
 - ~ y r Z. '- Ji. - '- - 
 
 
 
 tr. 
 
 fi 
 
 
 
 liH 
 
 
 
 
 w i^-^|i H il-il 
 
 = it 
 
 - tf = 
 
 
 
 
 HI! \l 
 
 >^— h!" 
 
 
 — , / 
 
 ■•^ — ^ 
 
 '4L' 
 
 Trn 
 
 
 P b 
 
 •y: v: 
 
 r 
 
 b(. y: 
 
 V. 
 
 
 -r'-^---!i 
 
 
 -^ ~ ■■'^ i- 
 
 
 
 T v. 
 
 C — 
 
 .r-->-; 
 
 / 
 
 _ -t- X - — — -^ 
 
 »« 
 
 'vi^rf^ r^i'^rtl. v-4 
 
 ^aSTll^eM^^xT 
 
PART II. 
 
 Reinforced Concrete Arch Bridges. 
 
 H.'ininr.MMl ...m.-n-f.. nv.-h hri,!t;,.s „s usuallv built 
 "'■'" •' 7"'l'i""ti"M of ar..|. .-n..! 1„„„.. nn.l .'....fnin' 
 |"«.st of tin. pn.,M.rti..s of l»„th lyprs. fl,,. ;,n.|, .„• 
 "'Hiu properties pr,.,lon.i„i,li„j, a.-eonlitiK ns Uwv 
 li.Mve a lar-e or small rise i„ proportion to tlieiV 
 span Flat an-hes aet n.ore lik,. lM.;„ns. n'-anlless 
 ot tlieory. 
 
 Reinfo.ee,! , oneret.. was first eonsiclen.] n.ereiv 
 » '-Iioap sul.slif„te iW stone. l,nt its own n.erils 
 are now reeojrnize.l and it is use.l in a nuunn-r ae- 
 ('(»rding Mith its properties. 
 
 A principle of arehite.-tnral .lesijrn .len.ands that 
 ■nnatum of one material l,v the nse of another 
 shall not be ma,le. ami. th.-refore. in .lesijrnin? eon- 
 ^•n'te bridges, there shonhl be no effort to in.itate 
 stoms but to treat the design simply and t^-uth- 
 ful y. keeping all lines in han.u,ny with the mate- 
 iiiil used. 
 
 The e.xtent to whieh eonc-refe and reinforeed eon- 
 -n'te are now being used in ,»ref,.renee to ston.. or 
 
 ste.!u.a>M)o jndged from tl.. f-aet that, during tin. 
 :-'ar 190^, there was at least twenty tin.es more 
 -nient manufaetured an.l sold than in the e<,rre- 
 spombng period, ten years previ.,us. As n.ethods 
 "t design and eonstruetion beeo„K. -e„erallv lui 
 |lerstood and as workn,.., beeome more aeeusiom, d 
 '- liandl.ng conerete. then' will be a still ..reat.-r 
 'Hunber of bridges built of this material. L.... 
 
 99 ' 
 
 SCIENCE & ENGINEERING LIBRARY 
 
 : 
 
 
I 
 
 100 
 
 !ve^!;>«i/AM>(i 
 
REIXFORCED COSCKIili: .IKCIl HKHH.I.S. 101 
 
 spans oxopedinj; tin to four liundn-.l f.-.i. uill 
 
 probably contimu' to b." framed in uM'tal. hut thcr;' 
 is reason to bcli.v,. n,,,, .,11 ,„.,[i„,,,.y t(.wti jind 
 .•ounty bridjres and tli.- uui.jority <d" r.ilroad brid«r.'s 
 will be l)uilt as poruiaiu'nt structures. 
 
 Kcinforcod concrptc is a jrood couddnatiou of 
 inatcrials. Concroto has a hifrh .'ouip.vssiv.' 
 stronRtb. but is Moak in t.Mision. Steel rods im- 
 iMMldod in eonerpto have a hi-rh tensile streufrth. 
 but are weak in compression. The steel, therefore, 
 sfrenjrthens the concrete, and the coiK-refe stilTerH 
 the .steel, the streuffth of ..iie thus suppleuientinir 
 tin; weakness of the other. 
 
 Since the bejrinninj; of the cmnpetitive i)ractice 
 ill bridge In Ildiuir. many bridfres have been built 
 which are deficient in both stren<r1h and desi;;ii. 
 There is no doubt that competition is responsibb" 
 for many economic features in steel brid^'e desitrii 
 and has helped to a prreat extent iu developiufr ,.,m.- 
 nomic methods. It was found about the year"l!)0(). 
 that steel bridges were being built entirely too 
 light and competition was responsible f,.r the con- 
 dition. Previous to that tinu-. the various bridu'e 
 ••ompanies were accustomed to submit competitive 
 plans, an 1 generally the lowest bid and cousc- 
 'jiiently the weakest bridge was the e-ie aecei)ted. 
 From that date the policy begnn to change. i,n<l 
 nistead of calling for competitive designs, a com- 
 iM'tent engineer was employed to prepare plans and 
 co.npejilive prices w.-re then received on his plans. 
 The policy of employing an engine<.r wjiosc prin- 
 
 0\ 
 
 I 
 
'♦ 
 
 I 
 
 III 
 
 i I 
 
 lo: 
 
 iOXCRi-.n: Hh'inai.s .ixn ci lihnts. 
 
 cipiil motive wMs f.) protliicc Jiti ci'tMinmii' dt'sipn. 
 has resulted iti <i niiieli better ehiss (if hriil^es than 
 inider the oM e(Mn|»etitive s./steiii. 
 
 ("uiieicte liridjr<'s are ikw in the same sta^re of 
 (h'\el(»pmeiit .IS were steel h'idjres ten years ajfo. 
 Many eojierete l)riil^'es have been and <ire still be- 
 iiijr built, which are laekiiifr in architectural de- 
 sij;n and some are lackinj; in sti'en«rth. Th«' prin- 
 cipal reason for these defects is that reinforced 
 concrete bridjrcs are oblijred to compete with struc- 
 tures of wood and steel. When towns and other 
 nmnicipalities reali/.<' tlie chances they are taking 
 in acceptin<; competitive desijrns. the method of 
 securin<r an aceeptal)le one will then be chun'^ed 
 and a competetit enj:ineer will be employed to pre- 
 l)are the plans. Competitive prices will then be re- 
 ceived on these plans, but comix-tition will cause no 
 red\iction of the cost by weakenin<r any parts of 
 the bri(l<;e. At the present time, stone ami con- 
 crete bi-i(l{;es exist, havinir fadoi-s of safety varyinj^ 
 fn..ii three to one hiuidred and fifty, and there is. 
 therefore, a very evident need for better and more 
 rational methods ol desi<;n. 
 
 Historical Outline. 
 
 Since the early ilays of stone bridge buildinp;. 
 rods and bands of hoop iron have been used near 
 the extrados of tiie arch from the piers anil abut- 
 ments, to or slii;litiy beyond the point of i-uplure. 
 It was foinid when the temporary arch centers were 
 removed, thai the arcli settled at the crown and 
 
 i 
 
REIM-ORCEI) COXCRHTI- ARCJl HRID(JL 
 
 S. 103 
 
 there 
 
 (I< 
 
 f< 
 
 MTC WHS H K'rid 
 
 ..,,...w,,,^, ,|*'aill.^ IIP 
 
 "P''ii at the oxtrados linujichcs. To prevent these 
 joints from opening, iron rods have lonjj been used. 
 There WHS then n<. p-iieij.l effort made to stren^tlhen 
 the niHs..nry arch, except injr as stated above-. Con- 
 
 erete an-hes are reinfor 1 with metal not only at 
 
 Hi.' extrados from the i)iers to the points of "rup- 
 ture, but are also strcnj,M hened at all places where 
 there is any pc.ssibiljty of fusion in the areb ring, 
 .lean .Monier first betran usin«r rcinfor; on"ret(> 
 
 in fJenuany in the year ISfiT. :• jng large 
 
 tlower pots and urns ..f ccnu>nt and uicrete" within 
 sinrrl.. lay.T of wire lu'tting eud)eddcd therein. 
 .Alonu'r was a gardener, but he foresaw a success- 
 iul future for this combination, and in the next 
 ten years he built a innnber of tanks, bins and 
 other snudl structures of the composite nmterial, 
 Hnd secur.Ml patents from the Gernuin Government 
 on his invention. Tntrodu.tion of this construction 
 m Ger .any. was slow, and it was not until 1804 
 that t,.c Moiiicr patents were introduced in the 
 ''"it.'.l States. This system of reinforced concrete 
 conlained a single layer of wire n.esh with wires 
 of the .same size mi both directions. Professor 
 :^lelan realized the weakness of the .Monier svstem 
 and patented another and improv(.,l method of re- 
 ii.torcnig arches, by which curve.l steel ribs wer<> 
 placed Icnglhwise of the arch and imbedded in the 
 coru'rctc two ,u- three feet apart. T his first do- 
 s'gns. curved 1 beams wer.' used ..n.; ai, -r used 
 under his patents for small spans, For Inrgor .-nans 
 
 .-i*B4_ '..!-4tt;j:\»i--i 
 
 mm 
 
101 
 
 COXCRBTE BRinai-.S AXD CULVERTS. 
 
 \\\{\\ a jrrcatt'r lliickiicss df arch ring, he proposed 
 a system of li<»:ht latticed <rirders spaced from three 
 to five feet apart, which system is still in use. 
 These patents were introduced in the United States 
 by TIerr von Enii)er<rer in the year 1893. and under 
 these patents many of Am(>rica's best concrete 
 bridjjes are built. In the year 1S!)4, when American 
 eri,t;ineers beiran to seriously consider building and 
 replacing old l)ridges in the new type, it was esti- 
 mated that Kurope had not less than two hundred 
 of these bridges built mostly on the Monier system. 
 A bridge Avliich is believed to be the tirst of rein- 
 forced concrete in the United States, was built in 
 (Jolden Gate I'ark. San Francisco, in 1S89. It has 
 a 20-foot s[)an. 4 feet o inches rise, and a width of 
 {'4 feet. It is an ornamental bridge with curved 
 wing walls built with imitation rough stone tinish. 
 A second one in the same park and of similar de- 
 sign was built in ISHU In U^95 a 70-foot span arch 
 was built by Ilerr von Emperger, carrying a drive- 
 w;iy over Park Aveinie in Eden Park, Cincinnati. 
 Tlie bridge is located in the i)ark at a place nuich 
 I'rtMjui'nted. and an effort was made to make it both 
 sli'ong and beautiful. The balustrade is highly or- 
 nameiilal and llie spandrel ualls are decorated with 
 panels. The iiitrados of the arch is much flatter 
 tlian app<'ars neces.-ary and certainly a greater rise 
 would have presented a more pleasing effect. 
 
 During the first ten years after the introduction 
 of the Mclan patents in the United States, there 
 were not more than a hundred reinforced concrete 
 
REIX FORCED COX CRETE ARCH BRIDGES. 105 
 
 bridges built. Tho fact that a nion- gcuTal intro- 
 duction of this system was not nuule, was probably 
 due to the lack of more definite kuowledjje anil 
 data in reference to the action and behavior of this 
 construction und(>r live loads. European en,irineers 
 were likewise embarrassed by lack of knowledjre, 
 so much so. that durinir the years 1890 to 181)5, tlie 
 Austrian Governnu'iit undertook extensive experi- 
 ments on full-sized concrete ar-dies. The result of 
 these experiments was entirely satisfactory, and 
 complete reports of the investigations were pub- 
 lished in many of tiie engineering journals of Amer- 
 ica and Europe. From the completion of these ex- 
 perinuMits in 180r, to the present time, the building 
 ol bridges in concrete an.l reinforced concrete has 
 been on the increase, and there ar<. now more than 
 a^ thousand of these bridges in the I'nited States. 
 Previous to these experiments, no satisfactory 
 progress was made eitlu-r here or abroad. 
 
 At first it was customary to use reinforcing steel 
 id the arch ring only, hut later structures and nu^st 
 ol those now being huilt have metal reinforcenuMit 
 throughout. .Alasonry bridges and Imildings are still 
 ••xisting that have stood for many cnturi.'s. while 
 steel bridges built less than forty y.-ars ago, have 
 iilready worn or rusted out and have been replaced. 
 Two of these bridges have already been illustrated 
 in Part I of this book, and there are positive rec- 
 ords of many others .,uite as ancient which are .still 
 1.1 existence. Pont dn (Jard, an old Koman a.pie- 
 duet bringing water to the city of \imes, France 
 
IOC 
 
 COXCRETr. BRIDGVS AXD Cril'ERTS. 
 
 
 I; 
 
 if 
 
 is sn[)posed to luivo boon built about tbo time of 
 Augustus in tho yoar 19 B. C. Tlie Acjuoduet of 
 Vojus. consisting? of a series of hi«;h arches, and 
 tlie dome of the rantlioon at Rome, \vith «'i s[)an of 
 140 foot, are at b'ast 1,800 years ohl and all of 
 these structures are oven now in a fairly good con- 
 dition. Those and many others (juite as old are 
 built of coarse concrete masonry. 
 
 Several American railroad companies, after re- 
 peatedly renewing their metal b"idgos to support 
 increased loads and rolling stociv, have at last re- 
 sorted to building their bridges in masonry, know- 
 ing that when properly built, they will remain as 
 pcrnuuient struclures for centuries. 
 
 Advantages of Reinforced Concrete. 
 
 The general advantages of masonry as compared 
 to steel framing have already boon referred to on 
 page 1. These advantages r(>ferred particularly 
 to plain concrete rather than to reinforced con- 
 crete bridges. It was stated there, that arch bridges 
 (•f solid concrete v.ore superior to all others, and 
 particularly superior to arches wlioi'o tension oc- 
 curs in any part of the arch ring. In pointing out 
 the commendable tjualities of solid concrete, it is 
 not intended to deny tho nu'rits of i-einforcod con- 
 crete. On tlie other hand, reiid'orced concrete 
 arches have sonu' decided advantages over solid 
 concrete. Some of these advantages are as follows: 
 (1) Working units for reinforcid coticrete nmy be 
 higher than for i)lain concrete. 
 
h'f'.ixioh'cr.n C(K\-CRi:ii-: akcii uRinaiis. 107 
 
 CV) Ilijjlicr units pruiliicc a lliinnor arch riii<», and 
 conscMniontly less dead load and lighter al)ut- 
 nienls. 
 
 ('■V) Fhit arches may be safely used, which would 
 be impossible in solid concrete. 
 
 (4) l>ecause of their lighter weight, it is practica- 
 ble to bnild si)ans of nuich greater length. 
 
 (:")) All cracks of every description can be avoided 
 in reinforced concrete arches. 
 
 (T)) They have the strength of steel with the solid- 
 ity and substantial appearance oi stone. 
 Bridges of both plain and reinforced concrete 
 
 have also the following merits: — 
 
 (1,> They have no noise or vibration and are not 
 only cheaper l)nt more duralde than stone. 
 
 (2) Concrete bridges with solid decks permit the 
 
 use of ordinary ties for railroad tracks, which 
 caiHiot be used on steel ])ridges with open 
 decks. 
 
 (3) T'.ie tloors of concrete street bridges over rail- 
 
 road tracks are not danuiged by the action 
 of gas and fumes from locomotives, as is the 
 framing of these I)ridges when l)uilt in steel. 
 
 (4) Concrete bridges reciuire but very little skilled 
 
 labor. 
 (.'>) A concrete arch bridge so designed that ten- 
 sion cannot occur at any time or under any 
 condition of loading, is the most permanent 
 bridge of all. If no tension occurs, eraek.s 
 will not form to permit moisture to reach 
 and corrode the reinforcing steel, and when 
 
 t , V 
 
 J 
 
1 M 
 
 
 108 
 
 COXCRETP. liRlDGIiS .1X1) CILVERTS. 
 
 tlu; iiictiil is perinaneiitly protected and 
 sccMiro rroin the atmosphere and moisture, it 
 sliould endure for eenturies. 
 Deck l)nd(rcs are in nearly all cases preferable to 
 those where the travel is carried between lines of 
 side trnssiii<^ and l)eneath systems of overhead brac- 
 ing- ^iich truss and braeinj,' systems are a danger 
 anil menace to travel, particularly on crowded thor- 
 (Mijxliriii-es. iiiid obstruct the space required for 
 vehicles. Trussing' and bracing are also an ob- 
 struction to oI)servati()n and the clearance retpiired 
 throu«,'h the bridge revents the use of lateral brac- 
 ing necessary to sti.Ten the frame. Concrete arch 
 bridges, when deck structures, are free from the 
 disadvantages mentioned above. Through bridges 
 should never under any condition be used for im- 
 portant locations uidess the underneath clearance 
 or structural re(|uirements positively prohibit the 
 use of a diH'k bridge. 
 
 For all (U-dinary locations and length of span, 
 there appears, therefore, to be no good or sufificient 
 reason for l»uilding unsightly frame structures 
 when more permanent and artistic ones can be made 
 at the same cost. 
 
 Adhesion and Bond. 
 
 Kick cement concrete in which iron or steel ig 
 embedded has an adhesion thereto of from 500 to 
 fiOO pounds per s(juare inch of exposed surface. Ad- 
 hesion of concrete to metal occurs only when the 
 metal is thoroughly embedded and the concrete has 
 
A'FJxrokCE/) coxch'inii arch bridgi-.s. 
 
 109 
 
 opportunity to surnmnd and grip H,,. h^rs. If a 
 metal bar is jWaccd sinii>ly in contact with soft 
 concrete there \vill he but litth' adhesion. For the 
 purpose of illustration, if steel plates are placed 
 on edge and concrete tilled in between, but not un- 
 der or abov.' then., after the <-on.-rete has hardened 
 It \vdl be a comparatively easy matter to h.osen 
 the concrete and break the adhesion. This weak- 
 ness is due lo the fact that the concrete is simply 
 in contact with the metal but does not j,'rip or sur- 
 round it. In contrast to this condition, if a bar 
 be thoroughly embedded and surrounded with rich 
 eoncr;-!.'. it will adhere so securely to the rod that 
 a pull of from r,00 to GOO pounds for every square 
 ineh in contact will be recpiired to extricate the 
 rod from its bed. In order to develop the full 
 strength of the rod u]) to its clastic limit it is 
 necessary that the end)edded length must at least 
 e((ual twenty to twenty-five times the dianu^ter of 
 the rod. This is on the assumption of perfect ad- 
 hesion between the metal am", concrete. The mix- 
 lure as ordinarily used, instead of fine mortar, con- 
 tains more or less voids, which may be considered 
 e(pial to 50%. of the entire surface in contact. To 
 allow for watersoaking, a still furtiier reduction 
 of r.0% must b<- made. In ordinary work as found 
 m actual structures, the adhesion between the con- 
 crete and metal, instead of l)eing fn.m .lOO to COO 
 pound.s j.cr scpiare inch, as for fine test .samples, 
 would, therefore, not exceed from 125 to 150 
 pounds i.er square inch. IJy using a factor of 
 
 i 
 
I 
 
 i 
 
 1 .1 
 
 i i 
 
 110 
 
 C(>\ci\'i:ii: i!h'iiK.i:s .ixn cci.rnRTS. 
 
 siifcty ot five ;i workiiif? adhesive unit will not ox- 
 ciM'd from -M) to 40 pounds per scjuarc ineh of sur- 
 face ii< eontact. The letigth. therefore, that rods 
 must l)e eniheilded in ordinary eonerete to develop 
 their fidl slrenglli up to the elastic limit is about 
 four times t w i-nty-nve. or one hundred tinu's the 
 diam<>ler of the rod. 
 
 It has been positively prove'i by numerous ex- 
 periments that concrete adheres as securely to 
 Knu)oth rods as it d(;es to rou»rh ones. Fretiuent 
 and conliiHied shocks and vil)i',itions tetul to de- 
 stroy the union between the two nuiterials, and ex- 
 perinu'uts show that contiimous watersoakinj? from 
 six to twelve months reduces the adhesion by about 
 lOO'/f. P(H)r woiknuinship in placing and ranuning 
 file concrete is also iti'obable aiul for these reasons, 
 it is desirabli' to use reinforcing rods that are 
 roughened or twisted, so the bar it. ay have a direct 
 mechanical grip on the conen'te in addition to its 
 adhesion. ^Vhen this roughening of the bars is 
 secured wiliiout decreasing llieir cross-sectional 
 area the entire area of the bar is then available 
 for tension and no strength is lost by the expedi- 
 ent. Tioughening the bars can. therefore, do no 
 harm and it may be a source of extra strength. As- 
 suming that the rough rods cost more than plain 
 ones, the consideration in making a choice between 
 the two, is simply whether the extra expense for 
 rough rods is warranted by llic additional slrength 
 that they may give. While watersoaking decreases 
 the ailhesioii between the two materials, the upper 
 
 ^f 
 
RlilX FORCED COXCRETIi ARCH BRIDGES. Ill 
 
 concrete surfaces are usually waterproofed, and 
 the prohahility is, that instead of weakeninj? from 
 watersoaking, the strength of the concrete and its 
 adhesion to the steel will increase. The conclusion, 
 however, is that rough rods are preferable. They 
 <'ost but little more, ean do no harm and may be a 
 Ix'iiefit. 
 
 Metal Reinforcement. 
 
 Reinforcing steel in concrete bridges is intro- 
 duced for any or all of the following reasons:— 
 (1.) To resi.st tensile stres.ses due to bending mo- 
 ments, 
 
 (2) To preve. cracks oecurring fnMii change of 
 
 temperature. 
 
 (3) To form a temporary working |)latforin at the 
 
 roadway level. 
 
 There is no sufficient reason from a scientific 
 standpoint for the use of high tension bars or 
 rods for concrete reinforcement. After years of 
 investigation and experiment, brittle metal was dis- 
 carded for structural use and the only reason for 
 a return to the use of high tension bars now. is a 
 commercial one and not scientific. It is well known 
 that in r(!-rolling bars to produce surface roughen- 
 ing, the tensile .strength of the metal is increased 
 Instead of admitting the inferior (lua'.ity of their 
 products, interested parties have endeavored to ex- 
 plain that this increase in tensile strength, and cor- 
 responding decrease in ductility is a benefit. 
 
 ^Medann steel with an elastic limit of 32.000 
 pounds per s(piare inch, or soft steel with a corre- 
 
 i 
 
!f 
 
 112 
 
 COXCIdim HHlDGliS AS I) CriA-URTS. 
 
 I i 
 
 I •; 
 
 spondinf? claslic liinit of 2.S.(M)() [xmnds, are the 
 pnipcr fi;ra(K'S of metal for all ordinary eoiierete 
 reinforeeineiit. These may safely be stressed up 
 to half their clastic liinit under workinj^ loads. If, 
 for any snlTicient reason a hif?h tension metal is 
 desirable, then some ^rade of wire is preferable to 
 bars. It is dii'fii-ult. however, to secure f,'ood con- 
 tact between wire mesh and concrete, for the small 
 openinj,'s in the mesh nuike it difficult to tamp the 
 two nuiterials well together. If a mesh must bo 
 used, then a large mesh is preferable to a snudler 
 one. In nearly all positions, whether tensile stresses 
 are liable to occur or not, the presence of metal 
 in concrete will add to its strength and perma- 
 nence. Only in such places wlicre there is insuffi- 
 cient space for its insertion, will it be a detriment. 
 The rule generally is "when in doubt, use rein- 
 forcement ". 
 
 The old Monier system of arch reinforcement, 
 consisting of a single layer of wire mesh with wires 
 of the same size in each direction, is evidently 
 wrong in princii)le. The amount of metal required 
 crosswise and longitudinally of the arch is not nec- 
 essarily the same, for the area in each case must 
 be suited to its need. For resisting bending mo- 
 ments in the arch ring, when the line of pressure 
 falls outside of the middle third, the size of rods 
 will depend on the magnitude of the bending mo- 
 ments. 
 
 It was customary at first to reinforce only the 
 arcli ring, but now all parts of reinforced concrete 
 
REIXFORCE!) COXCRETli ARCH BRIDGES. 113 
 
 bridnrcs. oxeeptinor perhaps the halnstrade and othor 
 orna mental features, are provided with metal for 
 the purpose of hotter uniting the whole into a solid 
 monolith. It is partieularly desirable that rein- 
 foreement be placed at all points where loeal loads 
 are liable under any circumstances to produce 
 bending or tension. Where cross spandrel walls 
 bear upon the arch -in- these walls should not 
 only be well anchored to the arch, but ad.litional 
 metal may be required beneath these concentrated 
 loads. The best practice at the present time in 
 reinforcing concrete arch rings is to use two com- 
 I'lcte systems, one at the extrados and the other 
 at the intrados of the arch. Some designers prefer 
 to reinforce the extrados only from the sprin-s to 
 or a little beyond the point of rupture, ondttin.^ 
 the metal at the extrados crown. The saving by 
 this omission is not great and generally is not suffi- 
 cient to warrant it. 
 
 At all points where light walls or sections join 
 to heavier concrete masses, heavy reinforcement 
 should be used. In setting and drving. concrete 
 acts much in the same way as cast iron, and unless 
 ttie light sections are well tied to the heavier ones 
 cracks at the junction will occur. This is illus 
 trated where ring walls join to the abutments If 
 lor any reason, it is impracticable to anchor the 
 wing walls to the abutment face, it is then i)refer- 
 able to leave an open joint, for otherwise an irreg- 
 ular crack will occur, showing weakness either in 
 the design or in the construction. 
 
1 1 
 
 1 ( 
 
 |!i ! 
 
 1 
 
 i 
 
 i 
 
 114 COXCh'Lli: liRllHil.S ASn Cn.VLRTS. 
 
 As llic iiliioiint ul" iidlifsioii brtwct'il slci .. .;! coii- 
 crt'tr (IfpciKls directly u|)(ni tlu' amount of steel 
 surface ill contact with the concrete, it is prefer- 
 able for securiii<,' the "greatest bond, to use a larj^er 
 iiundxr of small bars rather than a snuiller iRUuber 
 o^ lar^'cr ones. It is desirable also to have tho 
 cracks in the concrete as small as |)ossible, so water 
 will not Ciller the cracks and corrode the metal. 
 I'ljon this feature the duration of a concrete struc- 
 ture depends. 11 water is allowed to soak into the 
 cratdis and corrode the reinforciiij? metal, it will 
 then be only a few yejirs \uitil the streiifrth of the 
 member will be destroyed by rust. It is necessary, 
 therefore, that sutTicient reinforeiuf; metal bo used 
 in order that cracks will not be excessive. Several 
 leadinj; desi<rncr« of reinforced coiicn^te are now 
 specifyin<r that tension in the concrete shall be 
 consi(len>d. and cno:i{rh metal used so the tension 
 in the concrete will not exceed a safe unit, which 
 IS usually placed at ai)out .")() pounds per scpiare 
 inch on the cross-sectional area of the concrete in 
 tension. The object in this is to prevent eraeks 
 from formiii<r and to c^xclude all moisture from the 
 metal. This is doubtless the ideal condition, for 
 when |ierfectly cm])edded and protected from mois- 
 ture, steel is known to be indefinitely preserved. 
 When insufKcient steel is used, large cracks will 
 form on the tension side and the bridge is then 
 no tiiorc a }>rrni;;.u'nt one than an ordinary steel 
 bridge, or not even as permanent. "When a steel 
 bridge is exposed to moist ui'c *he steel can be ex- 
 
RLIM-OKCEI) cose KE IE .IRiJll OKI DUES. M'o 
 
 Jiiiiiiicd iiiKi pjiiiitcd. wlirrt'iis in ji n-iiifoivcd con- 
 
 cn-tc l»ri(lK'(\ the sti-d is concealed fi i view, ciin- 
 
 Mot he inspected, nnd its collapse is the tirst warn- 
 111^' friv II tlial I'le nielal reinforeejuent has been 
 <lestroyed. The best results are. therefore, secured 
 i>.v allowinjr no cracks whatever, hut if cracks must 
 form, lo have these cracks so snudl that water can- 
 not enter ihem. It is better to have a larjre num- 
 !m'1- <»f very small cracks than a suuiil nuiubcr of 
 lar<?e ones. 
 
 '^ '•<'M>iire nf upon which the streuKtli of rein- 
 forced concrete directly depends, is the amount of 
 .'ontact between the two composing materials. 
 Every elfort should be made to have this contact 
 as perfect and complete as possible. In decidiiij,' 
 upon a workinj-: unit for adhesion of concrete lo 
 steel, it is customary to consider that imperfect 
 workmanship in ordinary structures will cause only 
 •iliout one-half of the exposed metal surface to be 
 actually <,'rippcd by the cement. If a hijjhcr de- 
 iTi<'(' of workmanship l)e secured, then the stren«,'tli 
 of th structure will be increased acc()rdin«,'ly. It 
 is (•■iisidcred that walersoaking still further de- 
 creases the adhesion by another lOO/r. Therefore, 
 if perfect adhesion on rich samples between the two 
 materials is from r)00 to bOO pounds per s(|uare 
 iiieh. the ultimate adhesion in actual structures can- 
 not b. taken greater than fnun 12.") to 150 pounds 
 !><'r sriuare iiich. To develop the full tensile strength 
 of bars endx'dded in concrete, it is easy, therefore. 
 ^ -nmpute the length that these bars must be em- 
 
 ifl 
 
il 
 
 116 COSCR^.Til BRIDCr.S .IXf) Hf.rERTS 
 
 h'Mldcd. I'siiij; iiti iillimalt' ii«lln'si\f' unit for ordi- 
 nary stnu'lurcs of !.')(> |)oinids per sfiiunv inch, one 
 inch sijuiirc bars '.vonld he ^'ripped to the extent 
 of <ino j>..nn<ls per lineal inch of bar. Therefore, to 
 s'cnre tlie fnll elastic slren>;t!i of the har up to 
 •{2.n(K». the rod must he enihedded a nuniher of 
 inches. (Mpial to :{2.(M»() divided by (i.OOO. or .').{ 
 inches. ^Vhere arch riiifjs join fo piers and abut- 
 ments, it is customary to run the reinforcini? steel 
 v.-eli into the piers t(» deveb»p the fidl stronprth of 
 the metal. 
 
 Kxperimeuts show that ailhesion to steel is much 
 •rreater before the steel is pauited than afterward. 
 A sli<,dit c(»atinjr of rust has been foinid to add to. 
 rather than to (h'trjK t from, tlu- adhesive stren<ith. 
 T..oose scales or Hakes of rust must not bo permit- 
 ted, but a slijrht rustinfr is no disadvantage. Kx- 
 perimeuts have been made on vusted steel imbedded 
 in ricii cement, and after a period of several months 
 whvn the steel Avas renu)ved and the cement broken 
 away, it was found that the steel ai»|)eared clean 
 and free from even tlie slij,'ht rusting that existed 
 when it was first imbedded. 
 
 Lij^ht reinforcing frames are freciuently >ised in 
 the spiindrels of reinforced concrete bridges, not 
 only to strengthen tlie concrete, but also to provide 
 a temporary working platform at the roadway 
 level. This plan is illustrated by the Illinois Cen- 
 tral Railroad Company's bridge over liig ^Fuddy 
 River near Grand Tower. Illinois. Bridges built 
 by Ilerr AVunsch in CJcrmany were mostly of this 
 
Rf.lXrORCED COXCRETE ARCH BRIDGES. 117 
 
 type. The metal in sueh eases must have sufficient 
 slren^'th to act as eompressive members. In the 
 fiij? ^UuUy River hridfre, the et.^rineer used old 
 rails for the spandrel frames, and when completed 
 these were eneased by the eonerete spandrel col- 
 umns. 
 
 Reinforcing Systems. 
 
 The principal reason for the existenee of the 
 many patented systems for eonerete reinforcement 
 IS the patent royalty secured therefrom. There are 
 ft few essential requirements, and where these are 
 I'ulfilled. the reinforcement is satisfactory. Chief 
 among these refjuirements are: 
 
 (1) The metal shall be rough or have a mechanieal 
 
 union with the concrete, 
 
 (2) Reinforced beams shall have stirrups for trans- 
 
 mitting shear components from the main ten- 
 sion members into the web of the beam. 
 In connection M'ith the latter requirement, it is 
 preferable that the stirrups be rigidly connected 
 to the tension member, in order to secure a positive 
 transmittal of the shear components. 
 
 The various reinforcing systems may be roughlv 
 classified under two headings. 
 (1 » Slab Iieinforcement. 
 (2) Beam Reinforcement. 
 
 Tnder the first heading are included the various 
 kinds of expanded metal. Light rods are suitable 
 for slabs, as are also twisted bars and j^lain fiats 
 with rivet heads thereon. For beam reinforce- 
 ment, the opportunity for patented systems is 
 
3^ 
 
 ^ 
 
 
 118 COXCRETE BRIDGES AXD CVLJ-ERTS. 
 
 greator, niul a large iiumk'r aro now on the mar- 
 ket. Among these may be mentioned Twisted ro; > 
 Corrugated Itars. Diamond l)ars. Tliaeher ban Ciii) 
 bars. Twi.sted Lug l»ars, ete. All of these ar r ,ds 
 and i)ars without provision for stirrup eonno tuv-. 
 Tri addition to these, there is quite a varietj' of 
 patented bars on the market, either in the form 
 of truss frames or with stirrup conneetions. Tn this 
 latter class may be placed the Kahn bar, the Cum- 
 mings Girder Frame, the Unit Reinforcing Frame, 
 the Luten Truss, the :\Ionolith Frame, the General 
 Fireprooling Company's Girder Frame and others. 
 P'or slab reinforcement, a coarse wii-e with its 
 high tensile strength and corresponding high 
 elastic limit, is economical. It does not have the 
 disadvantage of high tension bars, for while bars 
 are brittle and lack ductility, wire is elastic and 
 has always been and probably will continue to be 
 a desirable tensile metal. It bends easily, will not 
 crack in handling and gives a large external con- 
 tact area in proportion to its section. Certain kinds 
 of wire mesh have the principal strands in one 
 direction, united by a lighter weave at right angles 
 to tliein. This type of wire mesh is made with the 
 principal wires in various sizes and is well suited 
 for reinfoi-cing bridge floors. Where floor panels 
 are sijuare and floor beams in both directions, it 
 is then economical to use a wire mesh with wires 
 of the same size in each direction. Most of the 
 various expanded metal systems, while they have 
 a lower tensile strength, have sufificient stiffness to 
 
RiifXroRCf.n COXCRhlE .}RC/f BRinCES. 119 
 
 support their own weight .luring constructicn, and 
 i«n" rougJior Hn<l have a gn-at.'r ineehanieal bond 
 than win". An excelh-nt examph'. showing the vari- 
 ous methods oC reiuforeenient for eouerete hrid-'es 
 IS a nhhed design, for (Jraud Avenu.' Viaduet'in 
 Ahhvaukee. shown in Kigun- 27 and more fullv de- 
 s.-nbed iu the Engineering News, Februarv 14 
 IftOT. • ' 
 
 As the shearing stress in curved areh slabs is 
 qnite small there is but little need for metal in 
 the web. The .Alelan system has continuous lines 
 of double angle bars at the extra.los and the in- 
 Irados of the arch, connected by light lattice work 
 ;nid these are manufactured complete in the struc- 
 tural shop and shipped to th<' l)ri<lge site ready for 
 ••iretion. These frames are l)locke,. up vertically 
 oil th.> arch centers from three to five fe.>t apart 
 ••••osswise of the bri.lge. an<l they are connected at 
 '■nervals with bars ..r franu-s which take the place 
 "I .'xpansu.n ro,ls. Tl„.s.. shop-riveted frames con- 
 sulerably snnplify the w(u-k of (i.dd erecti..n an.' 
 avoul the complexity and eonfusion which is liable 
 to occur when a large nund)er of .lisconnected small 
 i>ars are used, but much ,.f the web niaterial an.l 
 tiic shop la])or of riveting is unnecessarv for re- 
 Nistuig stresses. In sonu' of the designs. Mr. Tluu-her 
 l:as used plain flat bars adjacent to the extrados 
 and intrados placed about two feet jipart. These 
 I'ars are roughened by having rivets driven at fre- 
 quent intervals, rivet heads projecting to form the 
 luechanical bond. 
 
 
wn 
 
 1 20 
 
 al:,:*ai,J":. 
 
 COXCRETI: BK/l>GIiS .IXP C[-UT'^TS. 
 
 The Kahn bar with li«rht comn'ctod diagonals, is 
 v,.'ll suited for ai'cli reinforocmont, as the web 
 iin'inl)ers securely lie the reinfor('in<; bar int' "^he 
 ])(»dy of the areh, but any sysieni of rough bars or 
 rods Avhic'h are completely imbedded in and sur- 
 rf)unded with concrete and which have the neces- 
 sary cross-sectional area, regardless (>f whether they 
 have a web connection or not, are suitable for con- 
 crete arch reinforcement. 
 
 i • 1 ! 
 
 Concrete Composition. 
 
 It is customary Avith some engineers to specify 
 scNcral degrees of richness for the concrete in a 
 single ])ridge. ^lixtures varying from one part of 
 fctuent with two of sand and three of gravel and 
 stone, varying through several different grades to 
 corresponding mixtures of 1. ~i and 10. are all 
 specified in the same liridge. the richer concrete for 
 the spandrel or arch ring and the poorer for the 
 abutment foundation. The policy is generally un- 
 warranted. Anyone^ who has observed the ordinary 
 methods used, and the way in which concrete goes 
 into structures, should realize that exact methods 
 w'liich can reasomil)ly ])e ap[ilied to single truss 
 systems, and specifications for various grades of 
 metal. ar(> not ajipropriate or suital)le for use in 
 the design (»f conerete bridges, (ienerally it is ([uite 
 sufficient to specify oidy one or two kinds of con- 
 ivrtv mixtures, the rieher for the sui)erstructure 
 and the i)o()rer grade, if another, for the founda- 
 tion. Examination of test records on the strength 
 
REJXFORChD COSCRETli ARCH BRIDGES. I2l 
 
 of concrete iiiixtnres, varying from 1, 2 anu ;? to 
 1. ;{ and 6, does not show enougli variance in 
 strengtli to warrant a change of working unit. 
 Therefore, instead of several mixtures witli only 
 slight variations, it is better to specify a single 
 mixture. It is frequently cheaper for the con- 
 tractor to put in all mixtures of the richer grade, 
 than to nmke numerous changes. A more impor- 
 tant consideration than the <iuality of the concrete, 
 is the securing <if contact between the concrete and 
 the metal. In proportion as this is well or poorl} 
 done, the permanency of the bridge depends. 
 
 Loads. 
 
 The i)rincii)al loads on masonry arches are the 
 dead weight of the arch itself and the sui)erimposed 
 material '>ove it. It is better to consider only 
 verticid k , as acting on ordinary earth filled Hat 
 arches, for ihe conjugate horizontal forces are small 
 and nuiy be neglected. The amount of horizontal 
 thrust from earth filling is indefinite, for the earth 
 will recede more or less horizontally, allowing the 
 arch to settle at the crown. Therefore, neglecting 
 liiese horizontal earth pressures is an assumption 
 on the side of safety. It nuist l)e noted, however, 
 that the above statements api)ly only to flat arches 
 when the proportion of rise to span is small. AVhen 
 the arch has a greater rise ecjual to or approaching 
 iialf the span, the conditions are greatly changed, 
 for below the point of rupture the horizontal thrusts 
 are so great that solid nuisonry filling is required. 
 
UBSiL, 
 
 m 
 
 ' f' 
 i 
 
 12£ COSCklilli liRllH;i-S .1X1) Cll.niRIS. 
 
 The side rilaiiiiii<,' walls of <'ar1h filled arches fro- 
 (luently act as arch ribs and earry a large j)r()i>or- 
 ti(»ii oi" the weitiht of the earth tilling. The distri- 
 bution of lo 1 earth tilled arehes is nneertaiii 
 and the proj ,iiion borne separately by the arch 
 ring anti the side walls aeting as areh ribs, is un- 
 • •ertain. To avoid this uneertainty some engineei's 
 are now designing the side retaining walls with 
 one or more expansion joints in each wall, to pre- 
 vent these side walls \v<,,n having any areh aetion. 
 The entire dead weight and imp(»sed loads must 
 then be supported l)y the ar.-h ring. There is no 
 doubt that the side retaining walls are capable of 
 su!)porting large loads as andi ribs, but it is im- 
 portant to know definitely which members of a 
 sirncture are in action. Any type of construction 
 in which Mie action of stresses is indefinite, is in 
 many ways undesirable. The condition is similar 
 to that of multiple system^ for metal truss bridges. 
 .Multiple systems are no doubt econoie.ical. but it 
 is usually impossible to know what i)roportion of 
 the load is carried by each system. This lack of 
 definite knowledge is often the cause of failure, and 
 it is desirable in the design of masonry as well as 
 steel structures to have the condition of loads as 
 nearly fixed as jxKssible. For this reason many 
 arches are designed with cros.s-spandrel walls elim- 
 inating entirely any possibility of external hori 
 zontal pressure on the arch rinsr. 
 
 The weight of earth filling varies a<-cording to 
 its nature from 100 to 120 pounds per cubic foot, 
 
RELXFORCED COXCRETE ARCH BRIDGES. 123 
 
 Jind the weight of conerete from 130 to 160 pomvls 
 per cubic foot, depending upon the density of the 
 stone. Other loads such as that of pavement, rail- 
 ing, ^vater pipes, etc., must be taken according to 
 their actual weights. Approximate general rules 
 for moving live loads are as follows:— 
 Ci ) Light carriage travel is equivalent to 100 pounds 
 
 per S(iuare foot, 
 'b) Heavy carriage travel is equivalent to 200 
 
 pounds per square foot. 
 (c.) Electric railroad travel is equivalent to 500 
 
 pounds per square foot. 
 'd) Steam railroad travel is equivalent to 1,000 
 pounds per square foot. 
 There is usually sufficient earth filling above the 
 iireh ring to distribute any concentrated loads, and 
 particularly for railroad bridges where the ties and 
 rails assist in spreading the load out over a greater 
 area. It is usually safe, therefore, to consider all 
 live loads as uniformly distributed. These rules 
 apply only to earth tilled arches, for the loads on 
 arch rings which have open cross-spandrel cham- 
 bers or arcades occur beneath the spandrel walls, 
 and are plainly concentrated loads. The system 
 of loads should be carefully considered for' each 
 ease, and the designer should be satisfied in refer- 
 ence to the safety of his assumptions, for local loads 
 might easdy occur which would require special pro- 
 vision. 
 
 The bending moments on arch rings for moving 
 loads are a maximum when the uniform live load 
 
124 COXCRETE BRIDGES AXD CULVERTS. 
 
 
 
 I :i 
 
 i >■ 
 
 ,1 -J 
 
 covers from two-fifths to throe-fiftks of tlic span, 
 but it is usually eonsiderpd as covering one-half of 
 tiic span. 
 
 The Aveiglit of loaded electric ears varies from 
 1,000 to 3,000 pounds per lineal foot of track, or"- 
 half of this load being borne on each rail. The 
 weight of ordinary light electric cars fully loaded 
 will not exceed 1.000 pounds per lineal foot, but it 
 is now customary to proportion the better class of 
 street railroad bridges to carry loaded freight cars 
 which it is often convenient to switch over electrio 
 railroad tracks. The additional cost of proportion- 
 ing bridges for this extra load is comparatively 
 small. The electric railroad companies themselves 
 so often re(iuire large quantities of coal delivered 
 at their power plants, that they are usually will- 
 ing to pay the extra cost of a bridge over which 
 their tracks run, in order to have coal cars deliv- 
 ered directly to their plants. 
 
 Temperature stresses in masonry arch rings are 
 frecpiently as large or even larger than the bending 
 stresses from partial live loads. Masonry bridges 
 are not subject to so great a range of temperature 
 as metal bridges, for masonry is a poorer conductor 
 of heat than metal and the intrados of an arch is 
 not exposed to the direct rays of the sun, neither 
 is the extrados or any part of the arch ring ex- 
 cepting the ends appearing at the spandrel. For 
 this reason it is safe to assume a maximum tem- 
 perature range of from 50 to 60 degrees between 
 the highest and the lowest temperatures of the 
 
RHixFOh'cnn coxch'ETi-: arc it bridges. 125 
 
 ar.'h material. Temperature stresses may be en- 
 tirely eliminated by the use of hinges at the sprinf?s 
 and erown, but the praetiee with Ameriean engin- 
 eers is tc spend more money in making the founda- 
 tions secure, and thereby avoid the need of hinges. 
 The money that would be spent on building liin'ges 
 is put into the foundations. 
 
 As temperature rises, the arch expands and rises 
 at the crown, but when the temperature falls, the 
 arch contracts and it nnist necessarily fall at the 
 erown. This rise and fall of the arch, due to at- 
 mospheric conditions, is the cause of temperature 
 stresses. 
 
 Addition nuist be made lo the live loads to pro- 
 vide for the effect of impa.-t. The amount of this 
 niipact is determined fn.m the formula 
 
 L+D 
 
 where L is the live load and 1) the total dead load 
 per horizontal square foot on the arch. 
 
 Units— Ultimate and Working. 
 
 Permissible Avorking units for i)lain eoncret.- 
 arches have already been given in Part I. Rein- 
 forc.^l concrete arches nuiy have higher values, 
 owing partly to the fact that the reinforcing steel 
 will resist some compression and also because rein- 
 forced masonry is a more secure monolith. Con- 
 crete l.as an ultimate compressive stress of from 
 2.000 to 2,800 pounds per sciuar.' inch. A working 
 unit for plain concrete in compression was given 
 
 Impact load 
 
jr— ' 
 
 U ii 
 
 i! : 
 
 \l W t 
 
 ,.4;; 
 
 3 '•* 
 
 !|^ 
 
 120 COXCRETE BRIDGES .IXD CULVERTS. 
 
 Jit 400 pouiids per squai-o inch; for roiiiforcod oon- 
 iTcto it is s;if<' to J isuiiio r)00 poiiiicls per s(iiian» 
 inch for (omijiiicd. direct and live load bendinj; 
 stresses. For conihined. direct, l)endin<>: and tem- 
 perature stresses, it is safe to i'ssunie a workiiij; 
 unit of from (iO/O to TOO pounds per scpuire inch. 
 
 American enjirineers «renerally are accustojned to 
 nsinj? nnich lower work in-,' units in concrete than 
 are used l)y European enjjineers. There is probably 
 suftieient reason for these lowei units, for the qual- 
 ity of work done in Anu'rica is not so fine as is 
 produced in France an<l Germany. In dcsi<?nin^' 
 the Grand Avenue bridijfe. now beinjr built in Mil- 
 waukee, the concrete Avorkinjr units used were r>00 
 pounds per scjuare inch, and GOO pounds includinir 
 temperature stresses. IVrfeet adhesion of rich 
 conci-ete to steel varies from ."iOO to GOO pounds p(>r 
 square inch. Tt has already ])een shown under Hi- 
 headnig- " A-lliesion ". that 30 pounds per scpiare 
 incli of I'xposed surface is a safe and usual work- 
 ing adiiesivt' unit. 
 
 The ultimate shearing strength of concrete is 400 
 pounds per sipiare inch and a safe working unit is 
 50 pounds per squai-e inch. 
 
 A safe working stress for steel in compression is 
 one-half its elastic strength, or 14,000 pounds per 
 square inch for soft steel and IG.OOO pounds per 
 square inch for medium steel. The ultimate tensile 
 strength of good concrete is 200 pounds per square 
 inch, and for the purpose of preventing cracks 
 forming on the tension side of beams or members 
 
h'fjxroh'c/.n C(K\Ckiiii-: akcii bridghs. 127 
 
 sul).i('«-f to heiidin?. provision iiuiy be iiiadt' for 
 tension in tin- concn'tc. tiol cxcccdinjr .'>() pounds 
 p<'r scpijirc inch. Tli.' oh.jccl in this is plainly t-. 
 l»n'V('nt cracks from fonninj,'. Avhich would admit 
 water (,r moisture and expose the metal to the daii- 
 •rer of .'orrosion. The provision is a safe ojic. but 
 iis the modulus of elasticity for steel is not more 
 than twenty times ^n-eater than for concrete, the 
 steel in the tension side of the beam would then 
 I'e stressed 1(. (udy twenty times the tension allowed 
 «>n the concrete, or 20 times ,')(). which is l.UOO 
 l»".nnds per s(|uare inch, instead of Ifj.OOO pounds 
 pel" sipiare inch. 
 
 Some ent,Mneers j.ropc.s.' a method of proportion- 
 iii',' c<.ncrele sections by the use of ultimate units 
 iipplied to thne or four times the actual loads. This 
 method is inconsistent. Hrido-e enj,'ineers have long 
 been accustome.I to usiii'? safe workin<r units for 
 structures which are only a iVaction of the ultimate 
 values, using diflPerent working values where neces- 
 sary for the dead and the live loads. The same system 
 used in designing steel bridges should be applied also 
 to concrete bridges, and all sections prop(.rtioned 
 a"cording to .safe working units after addition has 
 been made to the live loads for impaet. It is evi- 
 dent that when a tension unit of IG.OOO pounds pet 
 square inch is used for dead load stresses and a 
 -'•'n-esponding tension unit of only S.OOO pounds 
 'or live load stresses, that i)rovision is made by 
 these varying units for impact amounting to 100%. 
 It is simpler and more accurate to follow the method 
 
 3J 
 
 A 
 
 5; ■ 
 
 i i 
 
 li 
 
If 
 
 \ 
 
 
 12S 
 
 cu.xCRLir: uriik.i-.s .ixn ciwerts. 
 
 of tlif iiiiii'i' I'ccciit sict'l hrit'ii^c spi'i'ificatioiis and 
 jipply iiii|)a( t addition, usiii«; th<' same unit stresses 
 tor hiitli dead and live loads. 
 
 Theory of Arches. 
 
 i'lu' oxat'l theory of arelics is very complex. Sev- 
 eral coiiipi-eliciiNive hooks have l)ee:i written on 
 the suh.ject and the theory will be referred to only 
 briefly lit re. For a frdl discussion and explanation 
 of the \aiMous theories, the reailer is referred lo 
 any of the niatheniatical treatises on the elastic 
 andi. The sul).)cct has been treated {generally l)y 
 two niethods. the analytical and the graphical. 
 ]\I()st. if not all writers and designers using the 
 analytical nictlu><.l follow the theory as developed 
 and explained by Professor ( harles E. (Jreen in his 
 l)ook entitled "Tj-nsses and Arches", while expo- 
 nents of the graphical method use the one out- 
 lined by Professor \Yilliam Cain in his ''Theory of 
 Elastic Arches". 
 
 The coniidexity of the subject is responsible to 
 i. great extent for the lack of a more general in- 
 troduction of reinforced concrete arches. They {"-e 
 really a cond>ination of arch and beam. I'lain con- 
 •reti- arcdies have already been discussed in Part I, 
 and reinforced conci-ctc i)cams are considered in 
 Part 111. The reinforced concrete arch is propor- 
 tioned to act both in direct compression and as a 
 l)eam, to resist bendinu stresses from uneven load- 
 ing on the arch ring. 
 
 The arch is distinguished from the beam by hav- 
 ing liorizontal or inclined thrusts at the springs, in 
 
REISFORCi; COXiRI.l/i .IRCII /iRIDGES. 129 
 
 juMition to tln^ vortical ronction of the iihiitnionts. 
 Arches jirc clnssificd under three headings accord- 
 inj; as they arc fixed or hinj^'cd. 
 (] < Arches with no hiii<j:cs, 
 (2 I Arches with two hinges at the sprinj,'s. 
 (3) Arches with hinges at the two sjyrinjjs and 
 Jiinge a I the crown. 
 
 They are chissified also under two general heads 
 into (1 Slab Arches and (2, Ribbed Arches. 
 
 The stress conditions in the arch vary greatly, 
 depending upon the presence or absence of hinges. 
 The space allotted to this book will not permit of 
 more than a very brief review of the principles 
 involved. The principal part of the computation 
 for a reinforced concrete arch consists in finding 
 
 (a) the horizontal thrust. 
 
 (b) the end reactions and 
 
 (c) the bending moments at various points in the 
 
 span. 
 After these have been found, it is then a compara- 
 tively easy matter to proportion the metal and con- 
 crete to resist the stresses. The method consists in 
 drawing the correct line of pressure for th(> given 
 arch and loading, and determining its proper posi- 
 tion in the arch ring. AVhen this has been done, it 
 is easy to find the bending moment at any point of 
 the arch. 
 
 ]\rost of the uneertainties of masonry arches 
 which have been enumerated in Part I apply equally 
 to reinforced arches. The elastic theory applies 
 not only to arches in which bending moments are 
 
 ■I ! 
 
M 
 
 
 iri 
 
 u 
 
 ■i '' 
 
 130 
 
 coxch'hii: iih-iiH.iis .1X1 > cri.r/.h'is 
 
 n-sist.'.l 1,\ il„. ;,,.,. Ii nllu^ hut ni.iy !».■ iiscl iils(. 
 I'nr iin-lics III' si.li.l (•.iiicirlc with no fciisinn in any 
 pnrl of the ill-ell rintr or when- the line of pn'ssiirc 
 Ih's in iill ciiM's within tlic Miiddh' tliinl <»f its (lc|»lli. 
 The tiKM.iy is ii|)|.li.-jil)I.- l^.tli for f wo-liinj;,.,! j,n,| 
 for (ixcil .Mid jin-hcs. 
 
 rcli.'s with fixed cn.ls have live nnknowii .|njiii 
 tilics. 
 
 i») 0(iui\] hori/on1;d thiMisIs at fithei- end. 
 
 (b) two v.'i'li. al I'nd n-a.-tions and 
 
 (el two hcndiiiK iiioiin-nls at the sprin-js. 
 
 Where tlicn aiv no hiiijres in tli- an-h. .!. n-a.-- 
 
 tioiis are not tniiisl"<Tr.'d to tlie .. .ntnients in ae- 
 
 eordilllce with the law of the h'Ver. Sinee there 
 iire five nnknown (|nii(itities. th.-n- must in additi.>n 
 to the two ('(luatioiiHof e(|iiilil)riiiin. :ia-=^0an(12i> 
 l)e llu-ee nion" e.|niiti..ns round. These are d.-ter- 
 
 iiuiied from the iditions (.f e(|Milil)riniii for Hxod 
 
 end iirehes. wliieh ;ire as follows:- 
 
 (1,1 The jinjrle of inelination thai the spriiijrs make 
 
 with eji'-h other must not ehan^'e. 
 (2) The relative elevation of the two end ahut- 
 
 moiits must not eh;in<jre. and 
 (;^^ The let^th of s|)an iiuist not .•Imiiire. 
 These are mathenuitiejdiy expressed by the f(.rmn 
 lae : — 
 
 :i^iM 0, :i7,«Mx 0,2:f,nMy n. 
 In the above foruudae. .M is the jjeueral value of 
 the bendin<i niomenls. u flie ien^'th of a short por- 
 tion (.f the areh rinj,r an<l x find y. the horizontal 
 and vertical coordinates to iJie center of n, nieas- 
 
R/:i.\rORCEP COXCRETIi ARCH BRIDGES 131 
 
 tin'd from the (>ri<riii jit the s|>riti),'H A or H. Kixi'il 
 end arches have hi^h l('iu|)eraliire stresses, tw.. to 
 four times greater tliaii for t\vo-hinjri'<l arches. 
 
 The abutment reactions for ardies with either 
 two or three hin<,'es. i'oUow the law of the lever, 
 vvhi.'h greatly simi)lilies the mathemntieal ealeula- 
 tiotis. 
 
 Two-hinged arches have only three sets of un- 
 iviiown forces. 
 
 (]} The horizontal reaction and 
 (2 The two vertical end i-(\ic'tions. 
 'is there are hinges at the end and a condition of 
 continuity cannot exist there, the two additional 
 unknown quantities, the two unknown beiuling mo- 
 uicnts at the springs do not now exist. This is the 
 theoretical a.ssuinption, but it is not exact, for even 
 with pin bearings at the end. there is a large 
 amount of friction on the nins and the bending mo- 
 ments will not entirely disappear. The assumption, 
 hoAvevcr. for two-hinged arches is that there are 
 tinly three sets of unknown forces. Therefore, in 
 addition to the two usual eciuations of e(iuilil)rium 
 ^> and ^y = 0, there is only one other eipia- 
 tion required, and this can be found from the cun- 
 dition that the length of span must not change. The 
 span length should not change or no sliding of 
 either abutment should occur in order that the arc'i 
 ring between the springs shall remain intact. 
 The third e(iuatiou reiiuired for the solution of 
 
 1 
 
 iiii 
 

 1^ 
 
 f : 
 
 1 
 
 5.3 
 
 •, ; I 
 
 132 COXCRETE BRIDGES AXD CrL]-ERTS. 
 
 the two-hinged arch is. therefore, expressed as fol- 
 lows : — 
 
 2UM^ 
 
 Hinged arches are not fre(iuently built in America, 
 hut some designers for the purpose of simplifying 
 ejilculations, consider the arch ring as hinged at 
 the springs. 
 
 The condition of stress in three-hinged arches is 
 definite, for the moments both at the springs and 
 crown are zero, and the position of the line of pres- 
 sure is, therefore, fixed at these three points. Tlic 
 equations of equilibrium for three-liinged arches 
 are, therefore : — 
 
 2fx = 0, vj/ =^ 0, :^M = 0, 
 
 The thrusts, bending moments and shears may be 
 found most easily by Professor Cain's graphical 
 method, after which the section may be most easily 
 proportioned analytically. It has already been 
 stated that the graphical method consists in draw- 
 ing the correct line of pressure for the given arch 
 and loading and determining its proper position in 
 the arch ring. 
 
 The following method is used for determining 
 the form of arch and the thickness of the arch ring 
 for uniform loading. It avoids the usual trial 
 method given in Part I for solid concrete arches. 
 The position of the springs must first be as.-:nmed 
 as well as an approximate crown thickness and the 
 depth of earlh filling above it. The remaining 
 height from spring t(» crown intrados will be the 
 
 ' .j^^i^i^^&ii^^imrftiiSL^ ^i™ki .. 
 
 -•.■v>...*A. 
 
REIXrORCED COXCRRTE ARCH BRIDGES. 133 
 
 rise of tho ;irch. The method (Icp.Mids upon tlio 
 
 equation, M HT, wlunv 
 
 M is the bcndiiifr nioment, 
 
 H the erowii thrust or poh' «list;in<-<' of the foree 
 
 polygon, and 
 T tlie verticjd ordinate to the pressure curve at the 
 
 point where the moment is taken. 
 The hending moment at the center is tlie same as 
 for a simph> ])eai;i and dividing this moment by the 
 areh rise gives the crown thrust or pole distance 
 II. The bending moment at any other point of the 
 •irch is e(|ual t(^ the imle distance II multiplied by 
 the vertical intercept at that point in the funieular 
 I-olygon. The moments are. therefore, computed 
 for as many points as desired and dividing these 
 moments l)y the pole distance II. which has already 
 been found, gives the recpiired ordinates T to the 
 funicular polygon, which is tlu« line of pressure for 
 the full assumed loading. The pressure curve is 
 then plotted from the ordinates found and this will 
 give a curve for uniform loads. 
 
 The height T referred to above is the distance 
 to the line of pressure measured from a horizontal 
 line through tlie point of rupture, wiiich is not nec- 
 essarily at till' abutment face. The correct crown 
 thrust cannot be obtained l)y using a distance T to 
 any point below the point of rupture. When the 
 point of rupture falls within the abutment face, 
 the span lenglh must Ije taken as the distance be- 
 tween the points of rupture, and not the clear dis- 
 tance between abutments. 
 
 f' 
 
hi 
 
 >i 
 
 • I 
 
 \ 
 
 I i t 
 
 
 (3 
 
 II: 
 
 III 
 
 3; 
 
 5: 
 
 14- 
 
 l.*?4 COS'CRETE BRIDGES AXD ClIJ-ERTS. 
 
 For full (.lead and live loads, the line of pressure 
 should wherever possible, lie within the middle 
 third of the arch rinj?, and reinforcement used oidy 
 for resisting bending stresses due to partial live 
 loads. In Figure 20, the weight of the arch ring 
 may be assumed at its mean thickness at the quar- 
 ter point, and the arch ring weight assumed ap- 
 proximately as a uniform load. The weight of earth 
 filling, pavement and other material between th" 
 
 extrados and roadway levci. as well as the uniform 
 live load, is also uniform, and the center bending 
 moment for these uniform loads is expressed by the 
 equation: 
 
 W S' 
 
 M. 
 
 8 
 
 For a parabolic arch, the spandrel area shown 
 
 l! 
 
 «iiJ!'?fc^?S^ 
 
REI\ FORCED COXCRETE ARCH BRIDGES. 135 
 
 hatched in Figure 2G is equal to ^^. The center of 
 
 6 
 
 gravity of this area is e(|nal to one-eighth of the 
 
 span length from the al)utnient face. Therefore, 
 
 the l)encling moment at the center from spandrel 
 
 25 R S" 
 filling is equal to — The total moment is, 
 
 therefore, equal to the sum of moments from uni- 
 form loads and from the spandrel filling. Dividing 
 the center moment by the rise gives the crown 
 thrust or pole distance K for the force polygon. 
 Thi'^ is a very convenient analytical method for 
 determining the correct arch form for any system 
 or arrangement of loads. A combination of the an- 
 alytical with the graphical method will simplify 
 computation, as some results, like finding the crown 
 thrust, may be determined most easily by the an- 
 alytical process. 
 
 In practice, it is usually sufficient to find the 
 sum of all moments and thrusts at three different 
 points— the center, the quarter points and springs. 
 
 The thickness of arch ring at other points below 
 the crown must be such that the vertical heights D, 
 shall not be less than at the crown. 
 
 The bending moment at any point of the arch 
 ring from partial loading is equal to the pole dis- 
 tance or horizontal thrust at the center, multiplied 
 by the vertical intercept between the neutral plane 
 and the line of pressure at the point considered. 
 Tiic correct position of the line of pressure for 
 partial loading will already have been drawn upon 
 
I: ^i I 
 
 \ \ 
 
 HI 
 
 ■I 
 
 :i" 
 
 ! 
 i I 
 
 *4* 
 
 13G COXCRETE BRIDGES AXD CULVERTS. 
 
 the arch ring, and the vertical intercept may bo 
 scaled and will be positive or negative according 
 as the pressure curve lies above or below the neu- 
 tral axis of the arch. 
 
 The determination of the thrusts and moments 
 may be simplified l)y considering the arch as a par- 
 abola. This is approximately true when the rise 
 is small in comparison to the span. 
 
 The stability of an arch is secured when it will 
 resist the stresses resulting from thrust and bend- 
 ing from any system of loads, x^hen the line of 
 pressure is drawn in such a iiosition as to produce 
 the least possible bending moment, or when the 
 line of pressure is drawn the nearest possible to the 
 eenter line of the arch. 
 
 General Design, 
 
 The introduction of bridges of combined metal 
 and concrete has thrown open a wide field for im- 
 provement in design. So long as it was necessary 
 to build bridges of stone, the art showed no great 
 i'uprovement over the Avork of the ancients." In 
 recent year^. however, the increa.sed i)roduction of 
 cement Avill, its decreased cost, as well as the in- 
 vention of improved stone-crushing machinery and 
 appliances for mixing concrete, have tended to 
 )nake larger structures possible, even in solid ma- 
 sonry. The greatest j;rogress in the art has been 
 made since the completion of the Austrian experi- 
 ments in 18!)."). Ki'inforced concrete has made it 
 possible to discard old, conventional forms and to 
 introduce new and lighter types of bridges sup- 
 
 ■^SF^N^E^ 
 
REINFORCED COXCRETE ARCH BRIDGES. 137 
 
 ported by arch ribs, carrying open spandrel framing 
 to support the roadway. The enormous reduction 
 in the dead weight of the superstructure has caused 
 a i.roi,ort,onateIy large saving in the foundations. 
 A large nund)er of improved methods of design 
 have already been tried successfully and there is 
 prospect of additional progress in the future With 
 the new material designers are following to some 
 extent the outlines used for metal bridges, so there 
 me now inimerous examples of bridges built in con- 
 ••rete-steel, not only in the form of light ribbed 
 arehes, but also as solid and ribbed cantilevers, 
 girders, trusses, etc. The new material is, in fact 
 being used according as its own properties will per- 
 mit. ^ 
 
 The general subject of arch bridge design is 
 divided nito four parts, 
 
 (1) The parapet or deck, 
 
 (2) The spandrels, 
 
 (3) The arch ring and 
 
 (4j Temporary arch centers. 
 
 In beginning the general design, the final object 
 •should at all times be kept in view. The first and 
 •■Hi''t object in building all bridges is to construct 
 ^>id support a platform at the proper elevation, of 
 suihcient capacity to safely and securely conduct 
 travel over certain openings. A second object 
 which is too often neglected, is the desirability of 
 making the bridge pleasing in appearance, in har- 
 mony with Its surroundings and a credit to its 
 builders. 
 
 Ikxl^; 
 
11 ;i 
 
 
 
 r- 
 
 I A ri li 
 
 1> COSCKETE BRIDGES A\D CCLrERTS. 
 
 AVhe.i ',;;•!• started, the tlt'sigii should he eontiu- 
 iied in logical sefjucnee. The width of hridge and 
 the kind of pavement reiiuired, should be selected 
 with tJie necessary filling beneath the pavement to 
 support the roadway or the railroad ties. After 
 deciding upon the kind of deck required, the most 
 economical method of sui)porting this deck must 
 be determined. It may be carried on solid earth 
 filling or on a series of walls or columns, and these 
 may be continued to the ground in the form of 
 a trestle, provided the height from deck to ground 
 is small. If the height be great, these walls or 
 columns may then be supported on other ribs or 
 frames, such as arches or trusses, and the loads 
 from these may in turn be transmitted to the 
 ground through Malls or piers of the most econom- 
 ical form. There is no good reason why the span- 
 drel columns of a concrete bridge cannot be sup- 
 ported in other ways, excepting on slab or ribbed 
 arches, "^'russed frames or girders are possible 
 forms, though they would not be as pleasing in 
 appearance as a continuous arch. It is possible 
 that arches with double ribs or drums separated 
 by systems of framing may be used, following the 
 outline of a double-braced metal arch. If the de- 
 sign is developed in successive steps, beginning 
 with the roadway platform, and transmitting the 
 loads continuously in the most economical man- 
 ner through various kinds of framing into the 
 foundations, the result will be both scientific in con- 
 struction and satisfying to the engineer. It is a 
 
 Mi7^' 
 
 .•.A- ■i.-^fst' 
 
REINFORCED COX CRETE .IRC 1 1 BRIDGES. 139 
 
 drplorablo fact that tlio design of many bridges 
 is begun by first b.eating the foundations and de- 
 veK)ping the design upward froni the ground, in- 
 stead of from the deek downward. This one error 
 aeeounts for the absence of economy in many struc- 
 tures. 
 
 The old empirical rule.s for masonry arches, 
 which required more masonry in the abutments 
 than in the arch, are unscientific and useless for 
 reinforced concrete. All through bridges are ob- 
 jectionable. They are a menace and an obstruction 
 to travel, are lacking in lateral stiffness, and the 
 trusses or framing interfere with the river view, 
 which is generally and should always be an inter- 
 esting feature of a river bridge. 
 
 If a bridge has several spans and one span has 
 movable bascule leaves or other kind of draw, the 
 »)utline of the draw span should conform and har- 
 monize with the rest of the bridge and its pres- 
 ence should be indicated by piers or towers at 
 cither side of the opening. The underneath out- 
 line for double bascule leaves in a single span may 
 easily be made in the form of a continuous arch, 
 corres|)onding to the intrados curves of other spans 
 in the bridge. 
 
 rnsymmetrical arch spans may be used at the 
 ends of viaducts cro.ssing deep ravines. They cause 
 a large .saving in the abutments by permitting 
 higher springs at the abutments than at the piers" 
 The half shore span adjoining the pier may be made 
 with intrados curve to correspond with the next 
 

 if' 
 
 i-»(» 
 
 (■(>\CR/.i I-: nkinci-.s .ixn cr/.i / rts. 
 
 ailjomiMK spmi. flm, pn„l„M„jr syunnctrv ;,l,nuf the 
 !"<•'• "■"I<"r. As tl... ,.,hI n,v|, spai. Ii,.-ks svinim-trv 
 111 th." ;in-h. it is M.M-.ssary f(.i- apiM'arancc. that tli".- 
 (l''sij,'ii sliail he syiiiUM'trical about the pi.-r. 
 
 Til.. Kissi.ijrn- ilri.I^'... twelve ,„iles soi'Mieast 
 »i*"iii Wal)asli. IiMliaiia. is ,.f mmsiial <lesij,Mi. It 
 liiis a l(;-r.,..t eunerete n.a.lwav slab halaiieed ...i 
 a sin-le ernter eonerele wel, 12 inehes in Ihiek.iess. 
 supported on a sej^iiiental eonei-ete areli, S feet in 
 \VKltli. It is a sin<rle span liijrhway hridj^e. with 
 '•O-loot openin-r ami was built in 1!)()7. 
 
 All town or eity bn,ljr,,s should have open ehani- 
 bers beneath the Hoor for pip,,s and wires. They 
 may either have removable iron eovers, or })e pa veil 
 over, with maiili..].-s or entranees provided at either 
 ond. 
 
 Hinged Arches. 
 
 Then 
 
 !•<' IS a din'erenee of opinion with regard to 
 ;i"; use of hinjred or fixed arehes for ii.asonrv 
 l>n«!^^.'s. llu.^vs. by whieh is meant the insertion 
 <'l iH;.ivy ston. or in. tal bh,eks at ..r near the een- 
 trr line ot the aivh. remove one of the priueipal 
 uneertamtles of arch eouslrueti..n. bv tixin- the 
 posit Km ',!• th.. lin.. of pressure at the springs" The 
 "'ivsenee of a Iiin-,' at the erow.i tends to^.-onsid- 
 '■ni il.v reduce the n-idity and inen-as- derieetion 
 
 ••nid IS m)t ahxays to !,e .mimen.led. U\u<n^s may 
 
 hv introduced at th.' s,,rin-s in sm-h a manner an 
 to lusnre absolutely v. it bin small limits the posi- 
 tion ot the line of pressure there. Fixed ends tend 
 to greatly nu-rease the amount of temperature 
 
RHINFOKCr.D COXCRin/i .IRCIl HRinCES. 141 
 
 stivss.N and llu-y hav,. „„ advai.ta-.'s ..vcr |,i„jr,.,l 
 •'IkIs. Alt.T f|„. .-..nhTs an- n-iiiuv..,! an.l the arcli 
 r-nifT has ,.(„„.■ t(. ,.,• nraH.v to its final pcsition the 
 -P'-n .loints at the hin-.-s should th.-n he tiUfd s„li,l 
 with ...MHcnt. so tl... .Mitiiv ,.ross-s,.,.tion at thr 
 liin-."s wdl h.- availahl,. f„r f„ll h.adin-. The pros- 
 ">i(M' or hinjres or th.' assumption nf th.-ir pivsouce 
 Id 111.' spring's, siniplifit's the (•on.pntati<.ns and re- 
 
 '"••'■''•^ ""<" "»■ tl l'i''f" uncertainties of eonerete 
 
 "'■'•'.' •'''•^'^'"- '''"' AoH'i-iean praetiee has been to 
 av(Md any .>xtra expenditure on hin-es. hut to jmt 
 It into the foundations, insuriufr their stability 
 ajrainst niovenuMit. Then- are nunu'rous unfortu- 
 >'Jde (.as.'s Mhere the foun.h.tions hav been in- 
 suttieienl. Several spans of a bridge over the Illi- 
 nois Kiver at I'eoria were nvenlly destroyed, owinj; 
 to the undermining of foundations. Hinges are de- 
 sirable ehieriy where it is k„(.wn that "the soil is 
 yielding and the abutnuMits ar.' liable to recede lat- 
 ''i-ally. allowing the arch to fall at the crown and 
 cause inisightly and possibly dangerous cracks A 
 method employed by certain (i.'rmau engineers is 
 to place hinges at the point of rui)ture. This was 
 •1""" "1 a bridge built at Kempten. Bavaria, over 
 "'•' lller River, and described in the Engineerinjr 
 News. .May 2, 1907. 
 
 Ribbed Arches. 
 
 The principal economy in reinforced conorete 
 bridges comes fro?n the use of ribbed arches. Most 
 of the surplus material, both in the structure itself 
 and in the spandrel filling, may then be eliminated,' 
 
 * ! 
 
 m 
 
"2 coxCKiiir. iiKin<;i:s .ixd cn.niKTS. 
 
 I I' 
 
 i! ,- 
 
 if' 
 
 and as wcijjlit ol' siiiMTstnirturc dec rouses, Ihc cost 
 of foundations dtcrcahes in proporti(»n. The use of 
 ribs instead of slabs, is a more scientific type of 
 construction and allows the strongest supporting 
 nieiuhers to he placed exactly where re(|uirod. 
 Kihbed concrete arches are purely a product of this 
 new material and are possible in concrete only when 
 properly reinforced with metal. Concrete ribbed 
 bridges are built mostly in the form of arches, 
 though other forms, as cantilevers, have also been 
 used with varying degrees of success. :Many bridges 
 designed as arches have cantilever action also, or 
 when the rise is small in proportion to the span, 
 the stresses are chieHy the result of bending, and 
 regardless of theory the span acts then more as a 
 beam than as an arch. The uncertainty in refer- 
 ence to cantilever or !)eam action of arches can be 
 removed by building an open vertical joint between 
 the arches over the piers, the presence of which 
 will positively prevent any cantilever action. "While 
 such a joint removes a seriiuis uncertainty of de- 
 sign, it is very doulitful whether or not this expedi- 
 ent is desirable, for the cantilever action frequently 
 adds as much strength to the bridge as does the 
 .irch and when properly designed and built to re- 
 sist both sets of stresses, the i>resence of canti r 
 action adds greatly to its strength and permanence. 
 The Walnut Lane bridge at I'hiladelphia. and 
 the Rocky River and Piney (reek bridges now un- 
 der construction, illustrate to some extent the sa\- 
 ing which may be accomplished by the use of ribbed 
 
i; 
 
 Ijl 
 
 • { ;; 
 
 " i' 
 
 1 c 
 
 '1? 
 
 144 
 
 ( ' >.\ ( A7; / /; liUll<u!-s .1 It , I lAI ■•TS. 
 
 iM pl.-icc of sK.I) ar.lirs, ,in.l yd A\ ..f tins., tliivo 
 »»ri(!f;..s nrv only M.-.rtiiilly til>l..'.' Tl.. y . ,rh .■..!i- 
 
 Slst (.r Jl |,;,;i- nf luii, jipch ri|._'S S.-Jlil!, ;' ,1 ! ^- i 
 
 •''^^"" »■ '■'■'■"! 10 tu L'O IVrl. whi.i .;.„. ]..- 
 
 tu.'.Mi the 1 r.sfs is spiinncd l.y siniplr i,.,,,- , ,,- 
 stru.'ficr Tlh wavitiK' in tli.- a.vli riny i.,- i],;^ . ^. 
 
 ("•(li.Mii ,. fn.ni 2:. : to :{(k; ,.. ,i,,. ,.,,st of * ,. .-ii - 
 whi.-h sji iiijr would i... <till nrllH m,- ,.,1 iT 
 using ... in- ril,l„ ,1 ,|,.si-n- Tlh I.,, ., ,„l„.r- .ton 
 arch bn.lp. i-i (icrniany itii a M.a: of 27: fc. 
 and (onipl.-tcl n h.- y.-ar I'm:{, j. ,',f , , x.,„„, ,., 
 An unusual .'xaniplc ,,f rii,!M.,j ,.,,vi, .i,.s,^,„ .„,, 
 pared l.y Mr. Turner of Mi,, ,.;,., oii- sh. Wi 
 
 Figure 27. Ft is one <.f sev. 1 ',1,..;^., ^ub. ,1 
 
 i-i the I'rand Avnue \ i,,du, n y ... ,1, . he 
 
 Tuain eonipressi-n nie-ibc! ■< ai- .x-ta-ou ,1 
 hoojH'd. 
 
 Tfn- use of ribs instead of' slah^ makes it ,ssihle 
 to phu-e niend)ers ol' the piui,. r -nL'tl ■,. p,.- 
 
 • luired, as for exanipir uiui v nes uf . \y y 
 
 trark. M-h.T, heavier ribs are ii<ually i .,i tl i 
 
 under other parts „ ih.- r, mUv-.^v 'si.i.-- .i^. ,„. ,. 
 be braekete.i u, ti. . Hb. „n.I ^n .erlv tied 
 
 into or across le ('<> . ,, the ole si-n exe- 
 
 '■"l!;^' '" ;' "" ' ^"' • ^" oniical manner. 
 
 Uw pnncit>a, obje. • n to m- u^e of ri'.s is the 
 extra cost ui ii, required ooden f as. vhich of 
 <.nu-sc,snu..b greater i., for pj.dn .v d slabs. 
 Notwithstandn: - this obi. tion. impo, eonerete 
 
 ar.-h.s ol the ,ure will possibly b^. , uilt with 
 nbs. partieidarl: ^vhen le proportion of the rise 
 ^o span IS larg-e. 
 
 tre 
 
klilXlUh ,:!J COXCRI.TE .11 CH PRUXil-S H^ 
 
 Intrados Form. 
 
 A low lliit ..pcniiiK is the best form f'.r Wv p.is- 
 ^'''-" 'I' « f. A roctjingiilar opfiiirifr >r eii! verts 
 with tlu- hciijlit i,'n'atcr tluin the widt! wiH cost 
 1<- than when the width is the groat. t of th»- two 
 (111, I'll lis. This is <'h'arly show by the < ulvert 
 <lcsi}.'n t-iv.',, in Tiihlcs VH, VIII, IX and X (.f 
 Pat' I\', I lit tiw (hcn-asod cost is secured a. the 
 expense ( (Ificiciicy. 
 
 Iiitradii Ills should be as nearly as possible ex- 
 
 ;i< t math. ,,iical curves, but if shcse cannot l)e 
 MM-ured, tiny should I lien approad so nearly to the 
 • xact curves that tin lack of re<rnlarity may not be 
 detected hv the ey-. Three an<l five centered Hat 
 arches as pproximation to the ellipse, are usually 
 unsalisfa'- \-\ because the breaks in the curve can 
 ''^' tlp^ if a Hat ellipse is desired, the curve 
 
 exact ellipse and not an approxima- 
 which are too flat are not artisHc. 
 nil. -fourth t.. one-sixth of the span 
 •r appearanc(>. Natural conditions 
 or grade lines will frcpiently prevent even this 
 amount of rise, ami it must then be determined by 
 stability rc.piiremeiits. which should not be less 
 than fi'.)!)! oiie-ei,<,'hth to one-tenth of the span. The 
 st(>el arch.s of the bridge across the Mississippi 
 Kiver at St. Louis have a rise of one-eleventh of 
 the span and then; is at Stcyr, Austria, a reinf 
 e..n.-rete bn.lge of ]:J!)-foot span, the rise of 
 is only one-sixteenth of tlie opening. 
 Earth filling in the haunches tends to m. 
 
 sliouh 
 tioti. K. 
 A ris.' ol 
 will give 
 
 * I * 
 
 miMH 
 
li »! 
 
 1 |l 
 
 ■ ^ 
 
 ■ m 
 
 146 COXCKIiTE BRlDCIiS .1X1) CVLVEKTS. 
 
 lino oF pi-i'ssurc jipproacli the form of an cUipst", 
 while the nnifonn loads including the weight of 
 arch ring, filling above the extrados, pavement and 
 full live load lends to depress the line of pressure 
 fo the approximate form of a parahola. The eom- 
 I)in('d etf'eet of these two tendencies is to produce 
 H curve ai>i)roxiinating a circular segment. The 
 resulting curve will lie nearer to the ellipse or to 
 the parabola, according as the effect of haunch fill- 
 ing or uniform load predominates. 
 
 The trial method of determining the intrados 
 curve is no longer necessary, for a direct method 
 has been given. Under the head of "Theory of 
 Arches'', a method has been explained for deter- 
 mining the amount of crown thrust by dividing the 
 center bending nion)ent by the rise. The simple 
 beam moment at any other point is ecpial to the 
 crown thrust or pole distance II multiplied by the 
 vertical ordinate in the funicular polygon, which is 
 the intercei)! b<twecn the closing line and the pres- 
 sure curve. Therefore, dividing this bending mo- 
 ment i)y the crown thrust or pole distance, gives 
 the prop"r ordinate or rise for the center line of the 
 arch at the point considered. This method makes 
 it iiossible, after having first assumed the approx- 
 imate form, to di'termine directly without trial, the 
 exact intrados curve for uniform loading. AVhen 
 the exact linear arch has been found, the bridge will 
 present a bett"r appearance if a regular curve be 
 tlrawn, such as a segment or ellipse, even though 
 the use of a regular curve makes the arch some- 
 
 ia 
 

 RE/XI'Oh'CJ:.') 
 
 lOXCRliTIi .IRC 1 1 
 
 BRIDGES. 
 
 147 
 
 wilt 
 
 t thicker 
 
 ill 
 
 certain 
 
 parts 
 
 tha 
 
 1 is 
 
 requi 
 
 red. 
 
 Aft 
 
 •r haviiij? 
 
 drawn the 
 
 correct 
 
 linear 
 
 arch, 
 
 the 
 
 tiiicUtiess of tlie ring for uniform loads should l)e 
 proportioned directly to the thrusts. 
 
 The computations are much simplified if the 
 curve be considered a parabola, aiul this assumption 
 is api)roximately true when the rise is small in 
 comparison with the span. Parabolic and seg- 
 mental arches require little metal reinforcing, while 
 elliptical and other fiat arches may require a 
 greater anu)unt. 
 
 Some designers prefer to use an intrados curve, 
 lying half way between a segment and an ellipse 
 and found by bisecting the vertical intercepts be- 
 tween these two latter curves. 'Sir. Burr's Potomac 
 Memorial Design No. 3 has an elliptical intrados, 
 with a rise of one-fourth the span, and a segmental 
 extrados. 
 
 Spandrels. 
 
 The principles already given for the spandrel de- 
 sign of solid concrete arches, apply also to arches 
 of reinforced concrete. If side spandrel walls are 
 used, provision should be made for expansion or 
 these side walls will crack. A dovetailed expan- 
 sion joint is the most satisfactory one, for sufficient 
 space can be allowed in it for expansion, while the 
 two wall sections are held securely together. If 
 an expansion joint is not provided, an open crack 
 is liable to develop between the spandrel wall and 
 the arch, and if an effort be made to prevent such 
 an opening by clamping the spandrel with metal 
 
 T^? 1('rj«P^HPr,««ra«i 
 
 ■Hi 
 
148 
 
 t 
 
 Ml 
 
 ; 
 
 fi 
 li 
 
 I 
 
 [' 
 
 1' 
 
 1! 
 
 ! , 
 
 •I 
 
 
 COXCRP.ri-. BRIDciis .IX D Cl'IJ-ERTS. 
 
 ^^^'^ lo 11... iMvli rin^r. ,i„. ,,,,.,, i„ ^,„. .,^.^.,^ j,^^.^^ 
 ''<■';;•>"<•.. iml.h.nMiM.l... .s ;. portion „t' t!,,. W.u\ 
 •»v. I,r .-Mrri.Mi by ll.r mv), ;,<.ii,>„ „r ,,,, s,,;,n,l,vl 
 
 Willi. 
 
 -'••inls in .MMitimions wmIIs should on-ur sit in- 
 te-rviils nol (■x.M-,.(|i„j: 20 f,, 25 feet. Jt has bccM, 
 ;onn.i l,y rxponc.,,.,. llmt t.M.UHT.tnre cracks occur 
 m solul Malls at al.ont these int.-rvals and if artifi- 
 
 •■" •."•'"^•^ •'*' '■'"•""•<'• <l'<' ^l.'vcloping ,>f unsi^M.tlv 
 {"ii.l inv-nlar .-racks will he avoided. 
 
 All expos..d flat c..n<-r..te s-.nfa.H's slioidd he pan- 
 H(''l lo av..id nion..t..ny. If is ditTi.-nlt to build 
 plain surfaces perf.vtiy straight or pl.nnb, and tho 
 use of panels with pilasters and b.dt courses assists 
 to c.n.eeal irregularities an.l in.perfe,.ti,.ns in Hat 
 ■surfncos, that otherwis,- might be .p,ite apparent. 
 
 Open spandrel an-lu-s in the haun-hes prodnc.. a 
 ight and arlisti.' app..arance, bul th.n- are n..t pra- 
 tu^a bl.. tor Hat arch,>s. 
 
 Spandrel walls may be built c; ut as curtains t. 
 obscure the op.Mi chamb.-r fran.ing, or as retaini.r^ 
 Avails to support ..irth filling. As retaining walls 
 thoy may be built .Mther as s.,lid gravity walls, or 
 as lighter r.-infonvd walls witi, .-ounteWorts In 
 nnx .vase it is b.-tter that the centers be re,nov...l 
 JH.d h.. arch alhuvd t.. settle before building the 
 spandrel walls. 
 
 Piers and Abutinea' 
 
 On the stal)ility of the f.»undatif. .. 
 of the whole sup.-rstru.-tu.c d.^pends. Th. „„-. , 
 and abutments include all of the structure from 
 
 the strength 
 e piers 
 
 ^; i^/S9v:^J?jsi)W, .vivf *«,*£* :i-,<«i. 
 
 ^<:i.^ 
 
 •.a ■ -it^■.•" -^i 
 
REINFORCED COX CRETE ARCH BRIDGES. 149 
 
 tlK> grouiul up to the point of rupture. The totiil 
 Hii<rle iru hided between normals to the points of 
 i-upture. never exeeeds 120 dejjrees and is usually 
 from DO to no dcrrrees. the real theory of arehes 
 api)lying only to material between these limits. The 
 part below the points of rupture must be designed 
 in eonneetion with the substructure. 
 
 The neatest eeonomy in the design of abutments 
 is secured by using low springs. If higher springs 
 :ire desired, they eau be secured by false side walls 
 i!s explained and illustrated in Part I. Great sav- 
 ing can l)e effected in high abutments by coring 
 out the rear and transferring the thrust to the 
 soil through vertical walls bearing on a foundation 
 slab of leinforeed concrete. Abutment wings may 
 I)e l)uilt as cantilevers from the arch, extending 
 into the embankment only far enough to hold the 
 slope. They contain nuu-h less masonry than the 
 old style of gravity retaining wing walls. Cantilever 
 wing walls should be tied together with rods be- 
 neath the roadway, to resist the outward thrust 
 of filling. Thi.s method Avas adopted in the Topeka 
 l)ridge. 
 
 The recent failure of the Peoria bridge over the 
 Illinois River, has called attention to the need of 
 having absolutely secure foundations. The Peoria 
 bridge was destroyed, not beeause of any lack in 
 the design of the sui)erstructure, but beeause of the 
 undermining of its foundations. 
 
 Flaring gra\ity wing walls are more economical 
 than straight ones of the same type and better 
 
 k 
 
 1 
 
1 
 
 s 
 
 j I 
 
 n\ 
 
 I 
 
 j ii 
 
 !fii 
 
 ^ 
 
 150 COXCRETE BRIDGES AXD CULVERTS. 
 
 direct water to the opening, but straight wings 
 usually present a better appearance. 
 
 River piers require eut-waters at the upper end 
 which should be capped with stone or steel, well 
 anchored into the masonry. 
 
 Some bridge piers have been given a different 
 batter on the two sides for resisting the une.pial 
 thrust on the sides from spans of different lengths 
 The piers must have sufficient thickness to resist 
 the uneven thrust caused by full live loading on 
 one span and no live load on the other. Piers must 
 bo designed, not by empirical rule, but accordin-' 
 to the stresses that they actually have to resist 
 
 The presence of reinforcing rods for resisting 
 temperature stresses in piers, is desirable thou-h 
 not necessary. Piers are usually well protected 
 from the direct rays of the sun, and rods are more 
 usetul to unite the mass into a solid monolith than 
 for resisting temperature stresses. 
 
 The design of piers for reinforced concrete 
 bridges does not differ greatly from the design of 
 piers for masonry bridges, and most of the discus- 
 sion of this subject for Concrete Bridges, applies 
 equally here. 
 
 Cost of Reinforced Concrete Bridges. 
 
 There are numerous considerations that affect 
 the cost of reinforced concrete bridges, among which 
 are the nature of the soil, the nearness or accessi- 
 odity of materials, presence or absence uf .switch- 
 ing facilities, the design of the bridge whether solid 
 tilled or open spandrel, the height, width, finish, 
 
RFIXFORCED COXCRP.TP. ARCH BRIDGES. 151 
 
 |>Hvin|yr, wiiifrs. otc. TIm'v will, however, rarely if 
 -vcr cost iii(»ri' I hail hridjrcs of solid concrete. An 
 • •rijriiial formula for the cost of solid concrete 
 l»rid^'cs has l)een driven in Part I. but for -onveniencc 
 it is repeated here. It is as follows:— 
 
 HW 
 
 C-F 
 
 100 
 
 Where C is the cost of the bridge in dollars per 
 
 s(iuare foot of roadway, 
 W. the total width of deck 'n feet, 
 II. the height of deck above valley or river bottom, 
 
 and 
 
 !•'. a variable factor the value of which is as given 
 Ix'lo'v, 
 
 The function IIW, or the product of height by 
 width, is the cross-sectional area, and may 
 be represented by the letter A. Factors F. 
 it re for bridges with solid slab arches, while 
 factors F' are for bridges with partial slabs, 
 like the Walnut Lane bridge at Philadelphia, 
 or the Rocky Kiver bridge at Cleveland. 
 
 Values of Factors F, and F'. 
 
 When A is 200. then F is l.T) 
 500, •• 1.0 
 
 1000, '• .nr) 
 
 1500. •• .ts 
 
 2000, •• Al 
 
 2500, • .;{0 
 
 3000, •• .:J2 
 
 3500, •• .285 
 
 A 
 

 ' 
 
 ji 
 
 jij 
 
 :i 
 
 :H 
 
 « 
 
 « 
 
 .224 
 
 Mo 
 
 .200 
 
 .lU 
 
 .ISO 
 
 .<J8 
 
 .104 
 
 .<J2 
 
 .152 
 
 .91 
 
 .141 
 
 .S8 
 
 .183 
 
 .86 
 
 .125 
 
 .85 
 
 l.'»2 CONCRETE BRIDGES AXD CULVERTS. 
 
 When A is 4000, tlu'u F is .202 uiul F' is .0« 
 
 50(M), 
 
 r.(M)(>, 
 
 7000, 
 
 8000, 
 
 IM)00, 
 10000, 
 1 1000, 
 12000, 
 
 This fonimla uill give costs that should rarely if 
 ever bo exceeded, (ienerally. however, eeonoiii- 
 ieally desipied reinforced concrete bridges shouhl 
 c(.st from 2."»9^ to oO'/, less than the costs given by 
 the formula for bridges in solid concrete. In a few 
 cases, the cost of bridges in reinforced concrete 
 liave exceeded tliat given by the formula, but these 
 eases are rare. Where the height (h>es not exceed 
 IT) to 20 feet, the cost will usuallv -.wy from .$2.00 
 to .$4.00 per s<iuare foot of lioor surface, while for 
 greater heights it may be twice these amounts. 
 
 The total cost, as well as the cost per square foot 
 i»f deck for a miscellaneous lot of reinforced con- 
 crete bridges is given in Table Xo. II. The square 
 foot cost is based upon the total length of bridge 
 over parapets or foundations, and not upon the 
 length of opening. If based on the latter length, 
 the costs per sipiare foot would then be greater. 
 
 The cost of IS concrete areh highway bridges, 
 biiilt by the city of I'hiladelphia, is reported in 
 Engineering Record January 23, 1909. The report 
 states that the bridges Avere mostly single si)an with 
 
REIM-ORCEl) CO.VC'i :/..'/• AUCIl BRIDGES. 153 
 
 oi'nanii'iilal balustrade, washed ^'ranolithic surfaeos 
 and i)av('d decks. The costs based upon the total 
 length of bridire vary from $1.7:? to $7.;5!) per s(puire 
 loot, or ati {" -re of if;:!..')!) per s(|uare foot, while 
 the costs ));• .ipon th.- width multiplied l)y the 
 dear length .>f pening vary from $"?.1() to .t!).74, or 
 an average of $0.2.") per s(piare foot. The total cost 
 based upon tlu^ yardage <>f concrete in the structure 
 varies from .tS..')0 to $11.2.1 per cubic yard. The 
 report stales further that if large spalls or stones 
 were embedded in the concrete 1o save cement and 
 mixing, the cost would then be i-ednced bv abojit 
 207; . 
 
 ("omj)ared with steel, reinforced concrete bridges 
 usually cost about the same as steel bridges with 
 solid tloors. The report referred to above states 
 that those built in Philadelphia i)roved to be cheaper 
 in fir.st cost than plate girder bridges by about 
 2.")^, but if maintermnce expense is considered, the 
 saving is still greater. 
 
 Comparative estimates for the Memorial P.ridge 
 at AYashington. one design for which is given in the 
 frontispiece, showed that the reinforced conerete 
 designs cost 45^ more than corresponding designs 
 in steel. 
 
 A bridge over the Hudson River at Sandv Hill. 
 X. Y., consisting of L") ribbed arch spans of GO feet 
 each, cost only $2.30 per scfuare fo(>t and a steel 
 i»ridge for the same loads would have cost as much. 
 
 Bids received for a bridge over the ]\lississipi)i 
 River at Fort Snelling Minn., consisting of two arch 
 
 ii 
 
 mm 
 
! 
 
 j 
 
 13 ' 
 
 I '. 
 
 
 154 COXCRETll BRIDGES AND CULVERTS. 
 
 spans ;{50 feet in length each, showed that the 
 bridge could l)e l)uilt in either steel or reinforeetl 
 concrete at about the same cost. 
 
 A concrete design for the Richmond trestle shown 
 in Figure 40 is reported to have been accepted in 
 I-reference to steel, simply because it was the 
 cheaper. 
 
 Estimating. 
 
 It is customary to estimate the total cost of tioor 
 slabs, including concrete, metal reinforcement and 
 forms, at 2.") cent • per square foot of floor for the 
 slal) only. This figure is nuide up as follows-— 
 concrete, r. inches ,,,,,, 
 
 woodforms:::::::::::::::::::::::::::::::::;::j-;g 
 
 Total o- „„ » 
 
 2o cents 
 
 The cost of forms varies considerably, and for 
 iloor slabs may cost from 8 to 20 cents per square 
 foot of floor. If the slal)s are estimated separately, 
 then it is necessary to estimate also the cost of 
 floor beams and spandrel cohunns. It is u.sual to 
 estimate the cost of forms for beams and columns 
 of ordinary size, not exceeding about one and a 
 liiilf foot in cro.ss-section, at 50 rents per lineal 
 foot. To this must l)e added the cost of the con- 
 cr.-le and steel in the member. The total cost per 
 lineal foot of girder or columns would then be as 
 follows : — 
 
 Concrete 1 cu. ;V t nz 
 
 Sterol f ? <^ents 
 
 Forms ...'.'.'..'. l^ ^^"'^ 
 
 oy cents 
 
 Total 71 
 
 90 cents 
 
 '^^miM:mm^ 
 
 :UiifK:«d^Maij 
 
 <V. 
 
REI.\ FORCED COX CRETE ARCH BRIDGES. 155 
 
 TABLE II 
 
 APPROXIMATE ESTIMATING PRICES 
 
 Price delivered. 
 
 Karth filling ' 
 
 Kxcavatintt, ordinary ' 
 
 under water (including cost 
 
 of cofferdam) I 
 
 Wood piliiiR I 
 
 Sheet piling ' 
 
 Concrete pMini; ' 
 
 Concrete in foundations '■ 
 
 in arc-h rincs ■ 
 
 includins steel reinforcement . . ' 
 
 Concrete imludine steel reinforcement 
 
 and centers ' 
 
 Steel reinforcement, riveted worii | 
 
 rods, plain ' 
 
 patented rods ' 
 
 Brick, common !*ti OOtoSlO OOper M. 
 
 Price in Place. 
 
 " face. 
 
 " moulded 
 
 " enameled 
 
 Concrete blocks, 10 inches thick 
 
 .Sand 
 
 (Iravel 
 
 Cement, Portland 
 
 non-staining 
 
 Crushed limestone 
 
 granite 
 
 Bedford limestone 
 
 Cartilage limestone 
 
 Kasota or .\Iankato stone 
 
 (iranite 
 
 Bedford ashlar facing, 4 to S inches thick. 
 
 Bedford stone carving 
 
 Concrete floor siaba i concrete, steel, forms i 
 Concrete girders and columns (concrete, 
 
 steel and forms) 
 
 Concrete columns, spiral wound 
 
 30 00 " " 
 50.00 " •■ 
 70.00 " ■■ 
 .25 cu. ft. 
 .75 to 1.25 " yd. 
 1.25 " " 
 1.35 per barrel 
 3.25 " 
 1.20 per yd. 
 3.00to3.50 " " 
 1.30 per ft. 
 2,00 " " 
 2.50 " " 
 2.50to3.00 " " 
 
 10.50 to SI. 00 per yd. 
 .SOcu. ft. 
 
 4.00 cu. ft. 
 
 .351in. ft. 
 
 40.00 per M. 
 
 1.25 per ft. 
 
 6.00 •' yd. 
 
 8.00 " " 
 12.00 '• '• 
 
 18.00 " " 
 70.00 per ton 
 30.00 " " 
 50.00 " " 
 20.00 per M. 
 45.00 '• " 
 70.00 " " 
 100.00 " " 
 .SOcu. ft. 
 
 1.60 per ft. 
 2.30 " " 
 2.80 " " 
 3 30 " " 
 1.00 sq.ft. 
 4.00 " " 
 .25 " " 
 
 l.OOlin.ft. 
 1.70 " '• 
 
 u 
 
156 COXCRETli BRUX.l.S .\\l> (II.IHRTS. 
 
 TABLE II -Continued 
 
 APPROXIMATE ESTIMATING PRICES 
 
 \ I ' 
 
 BriilgF pavftnents, wood block. . 
 " " Krani)litliic »!»lk^. . 
 
 brick 
 
 " " asphalt 
 
 " " stone block. 
 
 " " uranitp blork. 
 
 Railitie, three linos pipe 
 
 " plaiti iron lattice 
 
 " fancy iron lattice 
 
 " artificial stone 
 
 Balusters, turned Rciiford stone 
 
 Hand rail and base rail. 
 
 Stone coping 
 
 Intermediate rail iwsta 
 
 End newels 
 
 Limp posts 
 
 Trolley fxJes 
 
 Lumber in co!Tenlani.< 
 
 " " arch centers 
 
 " " forms 
 
 Beam and column form.s 
 Metal lath and pla.'iter, int( rior 
 
 ' " cMcriiir . 
 
 Expanded metal No. 10, 4-in(li mesh. . 
 
 •■ li?ht 
 
 Nails and spikes 
 
 Tar pap'r 
 
 Torh Bros, waterproof paint, No. 10. . 
 Bay i'tate coating (for concrete surfaces) 
 two "oats ' 
 
 $22.0t> 
 
 O.'ijpcr sq.ft. 
 .02 " " 
 
 03 per lb. 
 005persq. ft. 
 125 "pal. 
 
 .02 '• s(). ft. 
 
RElXl-URCr.I) COXCNl-.Tl- IRCff BKIDCI-.S. 1S7 
 
 If tlie girder or column is larger than 12 inches 
 si(uare, the cost of the concrete will then increase 
 in proportion to its area. 
 
 In making up a tender on a prospective contract, 
 
 it is necessary that all items of expense he included 
 
 and provided for. Some of the extra exj)ense items, 
 
 that are not inckuled in the regular estimate, are 
 
 as follows : — 
 
 Sui>erlntendent. 
 Foreman. 
 Timekeeper. 
 Traveling Expenses. 
 
 Bond. Cost is 1 per rent, on amount of bond, which is 
 usually 25 per cent, of contract. 
 Telephones. 
 Watchmen. 
 Fire Insurance. 
 
 Liability. Cost is 2^ to 3 A per cent of amount of pay roll. 
 Permit and License. 
 Water. 
 
 Setting <uit survey. 
 Rent of, or depreciation on plant. 
 Office and Storage sheds. 
 Material tests. 
 Models. 
 SigHiil lights. 
 Pumi)ing and Baling. 
 Refilling and Leveling. 
 Shoring. 
 
 Removing Rubbish. 
 Incidentals. 
 Surfacing. 
 
 These items must be provided for and the amount 
 of profit desired added to the total. 
 
 The appi- ximate estimating prices given above, 
 should be changed to .suit local conditions and the 
 varying slate of the market. Prices of nuiterial and 
 labor change according to location and time, and 
 prices that are suitable in the East may not hold 
 
 
w.m^ 
 
 i 
 
 i 
 
 'I: 
 
 !! 
 
 I' 
 
 i'pi! 
 
 158 
 
 coxcuini-. HRinci-.s .ixn i( i.niRTS 
 
 for work in lli(. W.-st or S„utli. The j;n-at.-st ran- 
 is iKMM'ssiiry in .•stiniatint? the fonn-lations. I'or tho 
 pari fliat is nns.'.-M is imc-rtain. If is w.-ll to niak.' 
 unit pric's for a <rrcat.T or l.ss amount ..f founda- 
 tions than is slionii on the plans, for fre(iut'ntly 
 more is rc()nii<'<l tlian is anli.-ipat.d. 
 
 Table of Approximate Quantities. 
 
 The f(»ll(nvin,<r lahh' </nvs the approximate ,,uan- 
 titics in IJcinforcd ( oncn'tc Ardi Ili^'liway Hri.lf^.'s 
 for clear spans varyin',' from L»() to 150 fwt, an.I a 
 ••har width of roadway of l(i feet. 
 
 They have solid earth filled spandrels witli rein- 
 forced eonereto side refainin«,' walls and the rise of 
 arch is one-tenth Die span. 
 
 They are proportioned for a live load of 200 
 pounds {..>r square foot on the » .adway. The quan- 
 tities of material in the abutmen ^ are only approx- 
 imate. 
 
 _I^^"^ OF APPROXIMA re QUANTITIES. 
 
 ' livir Sp.'i 
 
 III 
 
 tVct. 
 
 20 
 
 ;«) 
 
 4(1 
 .">() 
 00 
 70 
 80 
 
 go 
 
 100 
 110 
 120 
 130 
 140 
 150 
 
 ('ri)Hii 
 Tlil<kiicHs 
 rn Iticlu's 
 
 •) 
 11 
 i:i 
 i:. 
 
 16.5 
 
 is 
 
 19 
 21 
 22 
 24 
 26 
 -.8 
 30 
 32 
 
 ■•■./.».' .t.-.< 
 
t.l-jl. 
 
 i^.l 
 
 Rn/.xPi cm ((KWh'nTE arch URinc.r.s. i-'.!> 
 
 Por^mac Memorial Bridge Design. 
 
 This is ( ic of several »l('si«;ns sjihiiiittcd to tin' 
 I'liited St}i( >; (ioveniiiieiit ill tlu' yciii" l!K)() for ii 
 ;ii'(i|»ose«l iiieiMoriiil l»ri<lf;e aei-oss the I'utomne UivtT 
 ;it \Viishiii«:l(ni ft liais a clear width of ()<> feet, con- 
 sist iii}; (»r a 4«i-t'o()t roadway aMd two lO-i'oot sith- 
 wulks. The tnial h-nptii of open hridsrt' is :i,400 
 feet. It has one deck ami no provision for car 
 tracks. There are six sejrniental reinforced con- 
 crete arch spans of 1!I2 feet clear len^'th and 20 
 fet t rise, with •');; feet clearance nndei'neath. A 
 donl)le leaf trunnion bascuh* draw span is centrally 
 located hi t ween the arch spans, having a elear open- 
 ing of 1.")!) feet and a distance between centers of 
 trnnnions of 170 feet. The Washinf^ton approaeh 
 consists of twehe senucircular reinforced concrete 
 arch spans of GO feet elear length, and ."i.'jO feet of 
 end)ankiuent. wliile the Arlington approach has fif- 
 teen similar sji, iis and I.IJ.IO feet of enihanknient. 
 The entire e.xi.iior surface is shown faced with 
 granite '1 i; • fiu-e rings for main spans are T) feet (i 
 inches di i .ii tlie crown and 9 feet inches at th(! 
 .springs. Each main span has five eonerete-steel 
 arch ribs .U) inches ileep at the crown and 7 feet )} 
 inches at the springs, supporting a system of in- 
 terior steel columns carrying the tioor beams. Span- 
 drel curtain walls with expansion joints rest upon 
 the arch rings and are faced with granite. The 
 design shows asphalt road and granolithic walks 
 laid on concrete floor arches between the steel floor 
 beams. The estinmted cost is $3,080,000. William 
 II. Burr, engineer; E. P. Casey, architect. 
 

 i 
 
 I' 
 
 In. 
 
 it 
 
 
 
 :£ 
 a 
 
 
 :k 
 

 
 RISIX FORCED COXCRETE ARC I BRIDGES. 161 
 
 Jamestown Exposition Bridge. 
 
 This l)ri(lov was built in 1007 by the rnited States 
 (ioyerninent to conneet the outer ends of two j)i('i-s. 
 It is of reinforeed eonerete and has a eh-ar span 
 of lol feet, with a 20-foot rise. It is 36 feet wide 
 and is for pedestrians only. The aseent of the road- 
 way is made l)y means of a series of steps and land- 
 ings. It has two reinforeed eonerete areh ribs ear- 
 rying the roachvay on four lonjjitudinal walls. The 
 abutments are eored out and rest on piles. Then- 
 are 26 phunb piles and 12(i l)atter piles under eaeh 
 al)utmenf. It was designed and built by the Seo- 
 lield Company of Philadelphia. 
 
 Franklin Bridge, Forest Park, St. Louis. 
 
 ^^)rest Park has a very interesting eonerete 
 bridge of the Melaii type, known as Franklin 
 Uridge. It has a sj)an of 60 feet, a total width of 
 3:? feet, and a rise of If) feet. It has a 24-foot road- 
 way and one 6-fo()t sidewalk, with a total length of 
 !>2 feet. The areh ring is three-eentered and varies 
 in thiekness from 11 inches at the erown to ^O 
 inehes at the springs. At the four corners there 
 are ornamental iron lampposts not shown in the 
 illuslralion. lis total cost was .+r).(;00. The Geisel 
 Construction Company were the contractors and 
 John Dean, Engineer for the Park Department. 
 
 Jefferson Street Bridge, South Bend, Ind. 
 
 The bridge across the St. Joseph River with 
 tour elliptical arches of 110-foot si)an each. The 
 l>icrs are cpiite elaborate in design, being carried 
 

 \ii 
 
 ' I 
 
 4 
 
 
 7 I 
 
 a t- 
 
 e^ * 
 
 iti2 
 
REIXFORCED COXCRETE ARCH BLIDGES. I6;i 
 
 
 V. 
 
 
 
 up to support retreats at the sidewalk, and there 
 IS a heavy nioidded eorni.-e suniidunted with an 
 artistie railing. At the ends are steps leading down 
 from the roadway to the river. The lines of tlie 
 structure are true to a design in concrete, and tliere 
 has been no elfort made to imitate stone. The 
 Concrete Steel Engineering Company of Xew Yoi-k, 
 were engineers, and James 0. Ileyworth of Chi- 
 t-ago. contractor. A. J. Ilannnond, City Engineer 
 of South Bend. 
 
 Gary, Indiana, Bridge. 
 
 Gary is the home of the new steel companies 
 where an entirely new town is being built. The 
 l)ridge shoAvn is quite ornamental, and illustrates 
 some possibilities for single spans. The face of 
 arch and sj)anrlrcis are i)ineled. and the wings are 
 curved to facilitate approach. At either end of the 
 arch are pilasters extending up to the cornice and 
 forming in the balustrade, pedestals for future lamp 
 standards. The bridge spans the CaluuK 1 TJivcr 
 and was built in 1908 by Rudolph S. Bknne ^^- Co.. 
 <<f Chicago. 
 
 Como Park Foot Bridge, St Paul. 
 
 The Como i'aik liridge w.is ])uilt in the year 
 1003 for the Twin City Rapid Transit Conipany to 
 carry traffic entering Conio Park, over t!i. tracks 
 '»f the street railway company. The bridge has a 
 clear span of .30 fed. a roadway oi l.") feet and is 
 built on the ?,lelan system As a large luunber of 
 passengers leave the cars at the bridge, it Avas 
 
 n 
 
t I 
 
 \ii 
 
 
 u 
 
 lli 
 
 i-ii'-ff-k 
 
 b, ^ 
 
 w 
 
< 
 /: 
 
 SIC ^ 
 
 ue 
 
i ' 
 
 •(1 
 
 ! ' i 
 
 1 f 
 
 t ( 
 
 I J 
 
 ! I 
 
 I 
 
 I f 
 
 ii 
 
 " » !: 
 
 HI 
 lb 
 
 1| 
 
 166 
 
 COXCRETI-: BRIIH;i,s AM) crLnmTS. 
 
 <l.'s.rable that tho slruct.nv sl,u„M lunc a n.-at an- 
 poaraneo. T„ order to avoid for,,, ,„ark.s on the 
 exposed surfaces the forms wore covered with metal 
 iath and neatly plastered hefor,- plneing the eon- 
 erete. The length between centers of abutment 
 piers ,s 8:} feet, and the total wi.lth of arch is 17 
 feet 2 niches. It has a rise <,f 12 f,.,.t fi im-hes. and 
 IS 10 inches thick at the -rown. The length of span 
 openings over spandrels and abutments is 12 feet 
 and the thickness of the skewback piers is 2 feet' 
 There are five latticed steel Melan arch ribs in the 
 concrete. It was built by >Villia„. S. Hewitt & Co 
 of Muineapolis. George L. Wilson was consulting 
 engineer. ° 
 
 Boulder-Paced Bridge, Washington. 
 
 In a park at Washington. 1). (<.. there is a boulder- 
 faced arch of rustic design ,na<le to confor,n with 
 the surr(,undings. It has a span of SO feet a rise 
 of 1.) leet. and a clear widil, of roa.lwav between 
 parapets of 2:3 feet. The entire arch ring'is built of 
 concrete, but the soffit is darkened witli lampblack 
 to harinon.ze with the boulder facing. The boulders 
 ot the arch ring extend down below the sotlit .sev- 
 eral indies, and partly obscure the concrete arch 
 
 W T n T '!"'" '" ^-'^'^ "* ^ ''''' ^f -^17,500. 
 vV. J. Douglas, Engineer. 
 
 Grand Rapids Arch Bridge. 
 
 This is a good exa„,ple of the best American 
 practice ,n reinforced concrete arch bridge design 
 It has five spans, the center on. l,,ing S7 tVet th.^ 
 
 ^ 
 

REINFORCED COXCRETE ARCH BRIDGES. 169 
 
 two adjoining ones 83 feet, and the two end spans 
 79 feet. It has a clear width between railings of 
 64 feet. The piers have moulded concrete cornices 
 at the springs, and there is a continuous cornice 
 .supported on brackets at the floor level. There 
 iu-e retreats in the .sidewalk above the piers, and 
 •A heavy open balustrade with seven heavy railing 
 posts in each span. It was designed by William F. 
 Tubesing under the direction of L. W, Anderson, 
 rity Engineer, and was built in 1904 by J. P. 
 Ivusehe, contractor, of Grand Rapids, ilich. 
 
 Bridge at Venice, California. 
 
 At the little town of Venice in loiver ^VV! rnia, 
 laid out with numerous canals in imitnt- -;; of Ital- 
 ian Venice, are a number of bridges mostly built 
 of concrete with features of unusual design. The 
 town being on the sea coast, in a region where 
 flowers and foliage abound, has probably suggested 
 the ornamentation. The faces of the arch are elab- 
 orately decorated with festoons, and on the ends of 
 the balustrade are grotes(iue figures of sea animals 
 in concrete, the size of which may be estimated by 
 comparison with the people on the bridge. 
 
 Garfield Park Bridge, Chicago. 
 
 ITae illustration shows an attractive park bridge 
 I'uili in the year 1S93 in (jarfield Park. The open 
 l)alustradH with the heavy circular piers together 
 with the combination of rough and smooth finis'ii 
 unite to produce a pleasing appearance. 'Medal- 
 lions on the piers have monograms with thf-- park 
 
II 
 
 Hi 
 
 
 O 
 
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 X 
 
 V. 
 
 C 
 
 C 
 
 ^ a<* 
 
 > 
 
 z 
 
 < 
 as 
 U 
 
 > 
 
 c 
 
 b.' 
 
 
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 u 
 
 H 
 
 •< 
 
 U 
 
 o 
 
 a 
 
 X 
 
 n 
 
 d 
 
MICROCOPY RESOLUTION TEST CHART 
 
 (ANSI and ISO TEST CHART No. 2) 
 
 ■- IIIM 
 
 ■ 50 ™'= 
 
 2.5 
 2.2 
 
 ZO 
 1.8 
 
 ^ APPLIED IIVMGE 
 
 1653 East Wain Slreet 
 
 Rcchester, Ne« Yorn 14609 USA 
 
 (716) 482 - 0300 - Phone 
 
 (7!6) 288 - 5989 - Fox 
 
REIXPORCnn COXCRP.TP. ARCH BRIDGES. 173 
 
 
 c 
 o 
 < 
 o 
 
 s: 
 u 
 
 . o 
 M a 
 
 ^ PS 
 
 n 
 < 
 
 s 
 
 M 
 
 iiiilials, and tlie spaiidrt'ls arc paiu'lcd. The balus- 
 trade posts are mounted with ornamental urns. The 
 design is one Avhieh can well 1)e reproduced in con- 
 crete with either cut stone or moulded concrete 
 facing. 
 
 Stein- Teuf en Bridge, Switzerland. 
 
 The longest concrete; arcli span completed is at 
 Stein, Swit/ciland. Its total length is 5r)0 feet, and 
 the roadway, ;>2 feet wide, is 210 feet above the 
 Sitter River. The central span is 2.")!) feet, with two 
 approach spans '-V^^'-^ feet long at the Teufen end, 
 and four at the otlier end. The central piers are 
 ticavily reinforced to resist unbalanced thrusts from 
 the adjoining arches. The main arch rings are 21 ^j 
 feet wide and 4 feet t' ick at the crown, increasing 
 to the springs, raid reinforced with lVs-i"t'h round 
 bars from 10 to \S inches apart. It has a Telford 
 pavement and 2-foot walks on ct)nerete slabs sup- 
 ported on stringers and spandrel columns. The con- 
 crete balustrade has openings '.\ feet wide, guarded 
 Avith embeilded bars. It was designed by Professor 
 -Alorsch, and cost $80,000. 
 
ih 
 
 1 1 
 
 :t 
 
 ■ i.\> 
 
 m 
 
 174 COX CRETE BRIDGES AXD CULVERTS. 
 
 TABLt III 
 
 LIST OF REINFORCED CONCRETE BRIDGES 
 
 ri.Aci:, 
 
 C»V.T. 
 
 B 
 
 X. 
 
 J Stein, .Switzerland sitter Kivcr , 
 
 I- oKanis-Kronstatlt, Hunuary 
 
 T Decize, i-rance ' 
 
 > I'yrimont, Trance 
 
 ■r. ^ 
 
 _• ' c 
 
 
 -=■ 
 
 
 
 
 s 
 
 
 
 
 s 
 
 
 
 
 V 
 
 
 
 
 
 .c 
 
 
 % 
 
 a 
 
 TT 
 
 
 
 
 
 
 — 
 
 H 
 
 ?: 
 
 K ; 
 
 
 
 
 
 
 i 
 
 Loire River 
 
 Ulione Kiver. . 
 
 1 I 259 
 6 33.5 
 
 ...i 197 
 
 2 184 
 2 177 
 
 Bornjida. Italy 
 
 C'hatellerault, France. . 
 
 Painesville, Ohio 
 
 9 
 10 
 11' ^ 
 
 12 Jamo.stiiwn, Virginia. 
 
 I.'i I'layadel Kev, tal 
 
 Wakenian, Ohid 
 
 Uiiul' \Vaiiili()len, .\iistria. . . 
 
 ■Steyr, .\ii.stria 
 
 liranth HrcHiJt I'ark, Newark 
 
 To|)eka, Kansas 
 
 \ ienne River . . 
 Grand River 
 
 14 
 
 1.5 
 Hi 
 17 
 
 IS 
 
 19 
 20 
 21 
 22 
 2.i 
 24; 
 25' 
 2ii 
 
 r, 
 
 2s 
 29 
 30' 
 
 3i; 
 
 32 
 33 i 
 34, 
 
 35 
 
 3li 
 
 37,1 
 
 ■AS 
 
 3.» 
 
 4(1 
 
 41 
 
 42 
 
 4.': 
 
 \crmillion River . 
 
 Kansas River. 
 
 Route WililcKK, .Switzerland 
 
 ■ielliiwstiine I'ark 
 
 I'orto l{i(0 
 
 Lansini;, M'chiiran 
 
 Lake I'ark, .Milwaukee 
 
 I'lirtucal 
 
 Third St., iMvlun, Ohio 
 
 .\vranelie. i ranre. . . 
 Hoiilevard, St. Paul. 
 Circen Island 
 
 Vellow.stonc River 
 
 Jaea:|uas Kiver.. . 
 
 Orand River 
 Ravine. . . 
 1 ena River. 
 .Miami River 
 
 .feffersun St., South Benii 
 
 Knitricli.sville, Ind 
 
 Morris St., Indianapolis.. 
 
 I.aihaeh, .Vu.^tria 
 
 Huntincton, Indiana.... 
 Buda Pesth. .\ustria 
 
 Canal Dover, Ohio 
 
 .■^ia-ara River . 
 
 St. .loseph River . 
 White River. . . 
 
 Danube River 
 
 Tus{-arawas River . 
 
 I li 
 
 i} 
 
 ! 2 
 
 \ 1 
 
 ' 2 
 
 1 
 
 '1! 
 
 1 ! 
 1 ■ 
 1 i 
 
 2 I 
 
 2 I 
 
 1 ! 
 
 1 
 
 1 
 
 2 
 1 
 1 
 5 
 1 
 2 
 2 
 2 
 1 
 
 i 
 
 2 
 4 
 3 
 5 
 1 
 2 
 1 
 2 
 3 
 
 175 
 167 
 164 
 131 
 160 
 70 
 151 
 146 
 145 
 144 
 139 
 132 
 125 
 110 
 97 5 
 122 
 120 
 120 
 100 
 120 
 
 lis 
 
 114 
 
 110 i 
 100 
 90 
 80 
 110 
 110 
 110 
 
 100 ; 
 
 110 
 110 
 90-110 
 108 I 
 104 
 in.*! ! 
 
 96 I 
 107 ' 
 
 87 
 15 
 
 i.5' 
 
 550 22 
 
 " 1" 
 
 ....!.... 
 
 .... 34 
 612 12 
 
 21ti 
 
 4.< 
 14 
 
 25 
 16.7 
 
 "»l '•• 
 
 15.7 
 13.2 
 71 
 
 26" 
 
 443 20 
 
 401 68 
 
 ....'36 
 205 19 
 219 21 
 
 1 
 
 22 
 90 
 
 Sett. 
 
 18 
 
 
 
 33.5 
 
 36 
 
 
 8.5 
 16.2 
 18.9 
 16.3 
 14.6 
 1 1 i 
 
 165 19.7 
 244 74 
 693 40 
 
 " i" 
 
 1(1 o 
 
 19 
 24 
 32 
 
 Sen. 
 
 15 
 12 
 11.4 
 23 
 18 
 14 4 
 9 6 
 11 3 
 
 13 3 
 
 14 3 
 23.5 
 40 
 11.5 
 10 
 
 14.6 
 14 
 14 4 
 9 5 
 11 7 
 
 12.8. 
 160 17 
 404 20 
 
 ** *t 
 
 . . . . 64 
 214 54 
 . . 11.8 
 710 12 
 
 . ... 10.5 
 222 40 
 371 41 
 
 43 
 
 39 
 
 25 
 
 30 
 
 3 I'. 
 
 170 50 
 240 16 
 
 ..._. 45 
 
 .522'.55 
 
 50 
 16 
 
 25 3C. 
 21 
 
 30 
 
REINFORCED COS'CRETE ARCH BRIDGES. 175 
 
 TABLE III— Continued 
 
 LIST OF REINFORCED CONCRETE BRIDGES 
 
 4.'i 
 14 
 
 SeK. 
 
 u 
 
 S 
 
 M 
 
 I 
 
 1! 
 
 c 
 
 1 
 
 1 
 
 
 
 X 
 
 ■0 
 c 
 
 OQ 
 
 6 
 
 Kngineer. 
 
 References. 
 
 E.C., Eng..C m. 
 X.. " Xews 
 H.. " Reccird 
 
 
 i 
 
 is 
 
 
 1 
 
 1 'll 
 
 10 
 8 
 
 ISOU 
 
 u. 
 
 $80,000 
 
 Morech 
 
 X \ua. 5. '09 
 
 
 
 1 
 
 A 
 
 
 
 
 
 
 
 
 1 
 
 4 
 5 
 
 6 
 
 7 
 
 
 
 
 
 
 
 
 
 
 18 
 
 
 
 
 H. 
 H. 
 
 H. 
 H. 
 
 
 
 
 
 
 
 
 
 
 1907 
 
 *4 
 
 190? 
 
 $42,400 
 
 Ue Mollius 
 
 N.. Apr. 2. '08... 
 
 Rib. 
 
 
 $5.50 
 
 
 
 
 ?1 
 
 
 
 
 
 
 
 
 
 ?? 
 
 
 
 1899 
 
 4i 
 
 1908 
 
 1907 
 1906 
 1908 
 
 35,000 
 
 
 N., Apr. 10. '02.. 
 
 Rib. 
 
 
 3.05 
 
 8 
 g 
 
 1H 
 
 
 
 
 S7 
 
 
 
 R. R. 
 
 
 Leffler 
 
 R., Apr. 24. '09 
 
 
 
 
 10 
 11 
 12 
 13 
 14 
 15 
 16 
 
 54 
 
 
 
 
 
 
 
 
 
 Scofield Eng. Co 
 
 
 Rib. 
 Rib. 
 Rib. 
 Rib. 
 
 
 
 ?4 
 
 
 
 
 DePalo 
 
 Watson 
 
 N.. July 26, '06. 
 E.C., Feb. 24, '09 
 
 
 
 
 
 
 H. 
 H. 
 H. 
 H. 
 H. 
 
 16,870 
 
 3H. 
 3H 
 
 3.66 
 
 n 
 
 
 36 
 36 
 36 
 
 '24' 
 30 
 
 1897 
 1895 
 1897 
 
 
 
 
 
 84,000 
 150,000 
 
 Reynolds, 
 
 Keepers & Thacher 
 
 R., Aug. 12, 05. 
 
 
 
 4.6,5 
 5.40 
 
 ]7 
 
 20 
 
 it 
 
 a 
 ,2 
 
 R.. Apr. 16, '98.. 
 N.. Apr. 2 '96. 
 
 
 
 18 
 19 
 20 
 21 
 
 19 
 
 
 
 
 
 
 
 
 7 ... . ! 
 
 1890 
 1904 
 1901 
 
 190? 
 
 H. 
 H. 
 H. 
 
 H. 
 H 
 
 
 
 
 
 
 
 24 1 
 
 59,440 
 
 Crittenden 
 
 N., Jan. 14. '04 
 
 
 
 
 •)•> 
 
 2S 
 
 *.?'♦ 
 
 R., Aug. 3. '01 . 
 
 
 
 7.40 
 
 ?'< 
 
 ?l 
 
 
 N., Aug. 1, '01 . 
 E.C., Mar. 17 '09 
 
 
 
 24 
 
 
 31.000 
 
 
 25 
 
 ! 
 
 
 1904 
 
 Newton Eng. Co. 
 
 R., Nov. 25, '05 
 
 Rib. 
 
 
 
 26 
 
 
 
 190l'E. K. 
 
 
 
 
 ■'7 
 
 26 
 
 32 
 
 1906 
 
 H. 
 
 1* 
 
 184.000 
 
 Turner 
 
 R.. Mar. 4, '06.. 
 
 
 
 4.18 
 
 28 
 ?'t 
 
 " t 
 
 
 
 
 ..!.... 
 
 
 cO 
 
 •> 
 
 
 
 31 
 
 
 
 
 
 Rib. 
 
 
 
 1? 
 
 
 
 1909 
 1900 
 
 H. 
 H. 
 
 18.800 
 102.070 
 
 C..\. P.Turner. 
 
 R.. Apr. 3, '09 
 X., Dec. 6, '00 
 
 
 2.12 
 
 6.60 
 
 33 
 
 4(1 
 
 e.i'?* 
 
 36 
 
 
 34 
 
 38 
 
 R Feb Ifi '01 
 
 
 ■?") 
 
 
 . E. R. 
 
 
 Hammond 
 
 
 
 
 
 36 
 
 1 
 
 
 H. 
 H. 
 H. 
 H. 
 U. 
 
 
 
 
 
 
 V 
 
 
 
 
 
 
 
 
 
 
 
 
 38 
 
 20 
 
 "h" 
 
 42 
 
 12 
 
 1901 
 1907 
 1900 
 
 32,000 
 
 Melan | 
 
 N.. July 16. '03 
 
 
 
 3.77 
 
 39 
 
 21 
 
 
 
 
 40 
 
 20 
 
 
 
 41 
 42 
 43 
 
 24 
 
 
 
 
 
 
 
 
 24 
 
 lU 
 
 12 
 
 1905 
 
 H. 
 
 105,000 
 
 Thacher R., Feb. 9, '07 
 
 
 
 ?'= !*¥.'"'-«;>•■ '' 
 
 iT9B?r?^>- 
 
176 COXCRLTE BlUDGLS AXD CULVERTS. 
 
 i 
 
 I 
 
 ll 
 
 ^1 
 
 (: 
 
 W 
 
 i 
 
 'I 
 
 [! 
 
 'IN 
 
 TABLE III— Continued 
 
 LIST OF REINFORCED CONCRETE BRIDGES 
 
 E 
 
 3 
 
 H 
 
 45 
 46 
 47 
 48 
 4U 
 50 
 51 
 
 52 
 
 53 
 
 54 
 
 55 
 
 56! 
 
 57 
 
 58 
 
 59 
 
 60 
 
 61 
 
 62 
 
 63 
 
 64 
 
 65 
 
 66 
 
 67 
 
 68 
 
 69, 
 
 70: 
 
 71 
 
 72 
 
 73 
 
 74 
 
 "I 
 
 78' 
 
 77, 
 
 78' 
 79 
 80 
 81 
 82 
 
 PLACK. 
 
 Over. 
 
 
 I usi-arawas Kivtr 
 I luster Hay 
 
 Canal Dover, Ohio 
 
 Felham 
 
 Draw .Span 
 
 Paterson Xew Jersey Passaie River. 
 
 " ayne ^t., Peru. Indiana ... i A\ abash Hiver . 
 
 Sixth Ave., Dea Moines, Iowa lies Moint > 
 
 Stocl'^^rIdKe, Mass. . 
 Decatur, iUinois 
 
 Hoosatonic River . 
 
 l^anf^amon River . 
 
 Yorkton, Indiana. .... .. ' 
 
 Cartersburg, Indiana 
 
 W ashington St., Dayton Miami River ..'.'.'. 
 
 WateryiUe, Ohio ::;;:: j Maumee River. 
 
 Main fetreet, Dayton I .Miami River. 
 
 Paterson, >;ew Jersey.' .' . , Passaic River.' 
 Grand Rapids, .Mich Grand River . . 
 
 Seeley St., Broolilyn.' 
 New Goshen, Ohio. . . 
 
 Sarajero, Bosnia 
 
 Decori!,, Iowa 
 
 \\'ashington, D. C. . , 
 
 Prospect .\venue 
 
 MilJEclia 
 
 Rock Creek 
 
 Soissons France. Aisne River. 
 
 tolfax Ave., South Bend 
 
 Cedar Rapids, Iowa 
 
 I'ollasky California '.'.'.'.'.'. Sanjoaquin Kivor 
 
 i^resno, Galicia, . I . 
 
 Hyde Park-on-Hudaon.' .' .' .' .' .' ' . j Crum Elbow Creek 
 
 1 
 
 2 
 
 2 
 
 2 
 
 12 
 
 1 
 
 o 
 
 2 
 2 
 o 
 1 
 2 
 
 5 
 1 
 2 
 1 
 
 3 
 1 
 
 8 
 10 
 1 
 2 
 1 
 
 70 
 lO.-i 
 
 1)2 
 108 
 100 
 
 9.5 
 
 80 
 
 100 
 
 100 
 100 
 93 
 95 
 90 
 90 
 8B 
 80 
 74 
 
 75-90 
 88 
 S3 
 76 
 63 
 88 
 87 
 83 
 79 
 85 
 
 83.5 
 81 
 81 
 80 
 
 80 
 77 
 
 75 
 
 75 
 75 
 73 
 75 
 
 J 
 
 10 
 Hi ,i 
 
 12 
 15 
 
 13 
 
 c 
 
 •= 5 ^ C 
 
 2 — .^ > 
 
 "c := *S , ^ 
 
 522 55 
 
 807 ..-.a 
 
 360 40 
 
 6St ;-,o 
 
 ,23.9 36042.7 
 120. 
 
 124 7.5 
 
 640 28 i 
 
 10 
 30 
 
 11 .. il8 
 15.7: 21222 
 115, 62054 
 
 10 I '■ r 
 
 9.3 " 1" 
 
 8 i '• " 
 
 22-25 120016 
 
 5}5t 56 
 
 30 
 30 
 
 El.' 
 
 20 
 
 28 
 
 !'.'•. 
 
 (i 
 
 
 24 
 
 
 32 
 
 3C. 
 
 15 
 
 60 
 
 
 26 
 30 
 
 
 «» 
 
 
 ** 
 
 
 45 
 
 
 9.5 317 30 
 
 49£ C4 
 
 8 
 
 II I "j- 
 
 8.5 144,53 
 
 8.2 494 16 
 
 8 I 10;'S6 
 
 9.7; 18726 
 13t'27 
 
 8 
 7 
 
 7 
 11 
 
 30 I 3 C. 
 
 18 
 30 
 
 30545 30 
 
 14.7 
 
 ....;42 
 
 780;19.5 
 
 257:... 
 
 .. 20 
 
 18 
 21 
 
 5C. 
 Seg. 
 
 Seg. 
 Seg. 
 
 3C. 
 
 5C. 
 
 -J w!m 
 
REINFORCED CONCRETE ARCH BRIDGES. 177 
 
 TABLE III— Continued 
 
 LIST OF REINFORCED CONCRETE BRIDGES 
 
 El. 
 3 C. 
 
 3C. 
 
 If. 
 
 
 c 
 o 
 
 .a 
 
 CO 
 
 
 M 
 
 Engineer. 
 
 Reference*. 
 
 C, Cement 
 N., Eng. News 
 R.. •' Record 
 
 l.i lU [18 J1905. 
 24 Frame ' 36 190b H. 
 
 Thaoher. . . . 
 Lindenttul. 
 
 R., Feb. 9, '07. 
 R., Oct. 31, '08. 
 
 28 
 25 
 
 21 
 
 21 
 
 9 
 45 , 
 
 21 
 20 
 11 
 7 
 17 
 24 
 20 
 
 19 
 27 
 18 
 12 
 18 
 17 
 
 12 
 
 16 
 
 IS 
 
 1« 
 
 1 i 24 ,1907i H. 
 ^ I 6 1 1905; H. 
 
 i ' ' " 
 
 " ■ 12 i •' : " 
 
 ! I ! 
 ...1901 H. 
 
 " ^ I i 
 7 I I 2S 1895 F. B. 
 
 1 ' 12 1907 R. R. 
 
 l.i 10 I 
 
 1. lU 
 
 1'4 
 
 37,200 Wise. . . . 
 36,900 Luten. ... 
 
 R., Mar. 7, '08. 
 X., Mar. 29, '06 
 
 
 C, July, '02. . 
 
 1,475 I Von Empereer . 
 117,000 i Cunningham . . 
 
 V, Nov. 7, '95 
 N., Mar. 21, '07 
 
 . 1905 .. 
 6 1907 E. R 
 3t) VMa H. 
 
 1908 E. R. 
 . 1903 H. 
 
 j Luten. . 
 
 Luten. .. 
 
 122,000 Turner.. 
 
 36 i ;; 
 
 3t) 1897 
 30 1904 
 
 i 8 1903 
 
 ' 18 1906: 
 
 , 24 18971 
 
 i 12 1906; 
 
 \ 33 :1901 
 
 77,000 
 140,000 
 
 Walker. 
 Turner. . 
 
 Thaoher. . . . 
 TubesinR. . . 
 
 .\., May 11, '05 
 
 R.. Mar. 2. '07 
 
 R., Xvif, 8, '03 
 N., May 19. '04 
 
 N.. Mar. 16, '99 
 N., Dec. 1, '04 
 
 '1903 R. R. 
 ,1901 H. 
 
 21,803 
 16,500 
 17,500 
 
 Fort. . . . 
 Murray. . 
 Wunsch . 
 Luten. . . 
 Douglas . 
 
 Riboud. . 
 
 N, Deo. 31, '03 
 R., Mar. 30. "07 
 
 R., \u<r. 16, '02 
 .v., kMK. 14. '02 
 
 i .36 '1906 
 
 H I . . . 1905 
 
 1897i H. 
 
 » 
 
 Rib. 
 Rib. 
 
 1.80 
 
 1.58 
 6.50 
 
 3.60 
 
 4 00 
 4.30 
 
 12.90 
 
 4.65 
 4.30 
 
 4.95: 
 
 • . •• ■ Marsh Bridire Co. 
 4S,000 I Li-'.iiard 
 
 Conrrete Steel Co. 
 
 R., Feb. 24. '06 
 
 3.15 
 
 
 ::::i:;;: 
 
 44 
 
 45 
 
 46 
 47 
 
 48 
 *i 
 50 
 51 
 
 52 
 
 53 
 54 
 55 
 56 
 67 
 58 
 59 
 60 
 61 
 62 
 63 
 64 
 65 
 66 
 67 
 68 
 
 6a 
 
 70 
 71 
 72 
 73 
 74 
 75 
 
 76 
 77 
 
 78 
 79 
 80 
 81 
 
 (-2 
 
 i 
 
178 
 
 ; 
 
 i 
 
 I i 
 
 »H 
 
 si ; ! 
 
 \ t 
 
 '-\iU 
 
 
 i ii 
 il 
 
 coxcRinn BRinGHs axd culverts. 
 TABLE III— Continued 
 
 LIST OF REINFORCED CONCRETE BRIDGES 
 
 near Tcrre 
 
 S3, "Bin Koiir 
 
 I Haute. 
 
 S4| Wabash Indiana ;:.;.' Chariey' Creek, 
 
 N.) Mission Ave., Spokane. . j ' ^- 
 
 m Olive .\ve., Spokane. . 
 
 S7 Meridian St., Indianapolis. . 
 
 KS Illinois St. 
 
 S9 Northwestern .\ve.,Indianapo| 
 
 90 Derby, t'onn 
 
 91 Waterloo, Iowa 
 
 9? 
 %i 
 94 
 95 
 9fi 
 97 
 9S 
 93 
 100 
 101 
 102 
 WA 
 lO-l 
 10.-) 
 lOf) 
 107 
 108 
 109 
 110 
 111 
 112 
 113 
 114 
 ll.i 
 
 nr> 
 
 117 
 
 lis 
 
 119 
 120 
 121 
 122 
 
 i^pokane River. 
 Fall Creek 
 
 Kdcr. Park, Cincinnati 
 
 LoKan.sport, Indiana 
 
 -Austell, Georeia 
 
 Trinidad, Colorado ' . ' . 
 
 \\ abash, Indiana 
 
 Seventeenth .St., Boulder, Ci)l . 
 
 lola, Kansas 
 
 I'orto Hi™ 
 
 Howlcvard Brid-e, Philadelphia 
 .lack.sonville, Florida.... 
 Herkimer, N. Y 
 
 Sandv Hill. N. yV ■.'■:' ; 
 Iranklin Bridge, St. Louis... 
 
 Lima, Ohio 
 
 Plainwell, Michiian 
 
 Maryl)or(>usth, Queensland. . . . 
 
 Como Park, St. Paul 
 
 AtlanticHi^hlands, N. J... . 
 
 (ilendoin, Cal 
 
 Fore,st Park, St. Louis '.'. 
 
 London, Ohio 
 
 FarkTrive. 
 1 ine t reek. . 
 
 Miners Ford. . 
 (iuaya River. 
 
 R. R. Trark-s 
 
 W. Canada Creek 
 
 Hud.son River. . . . 
 I ark Stream 
 
 C'uftSt., Indianapolis 
 
 Oconomowoe, Wisron in 
 
 Columbia Park, Lafavette 
 
 Interlaken Bridse, Minneapolis 
 Plainfield, Indiana 
 
 Kalamazoo Ri\er 
 
 Mary River 
 
 Tracks 
 
 firand .Ave 
 
 San (labriil Ri\er 
 River I es 1 ercs . 
 
 1. 
 
 Chicapi.C. & E. L Ry^ 
 
 Trim Creek. 
 
 II 
 
 : 3 
 
 3 
 
 ! 7 
 
 1 
 2 
 4 
 2 
 2 
 I 
 3 
 3 
 1 
 11 
 
 I? 
 
 15 
 
 I 
 
 2 
 
 7 
 11 
 
 1 
 
 1 
 IS 
 
 1 
 I 
 
 2 
 I 
 I 
 1 
 1 
 1 
 2 
 2 
 1 
 
 7.5 
 7.i 
 70 
 9,5 
 74 
 74 
 74 
 72 
 72 
 
 70 
 70 
 70 
 70 
 70 
 70 
 70 
 70 
 69 
 66 
 66 
 62 
 60 
 60 
 
 59 
 
 54 
 
 50 
 
 50 
 
 50 
 
 50 
 
 45 
 
 45 
 
 40 
 
 43 
 
 42 
 
 40 
 
 38 
 
 42 
 
 39 
 35 
 38 
 
 i 
 
 
 
 -CI 
 
 
 » 
 
 t- 
 
 Vi 
 
 s| 6 
 
 ■~"~~ ~ 
 
 
 
 
 
 18 
 
 24(1 
 
 32 
 
 24 
 
 Par 
 ^1- 
 
 '2. 
 
 5a5 
 
 •■ifi ■ 
 
 26 
 
 « 5 
 
 284 
 
 70 
 
 18 
 
 3C 
 
 96 
 
 284 
 
 eo 
 
 18 
 
 3C. 
 
 
 
 54 
 
 
 
 7.2, 
 
 1 
 
 586 
 
 46 
 
 20 
 
 C. 
 
 10 1 
 
 
 33 
 
 
 r 
 
 14 
 
 163 
 
 16 
 
 1» j 
 
 
 20 
 
 300 
 
 26 
 
 45 1 
 
 5C. 
 
 7 
 18 
 10 5 
 
 9 
 
 7 
 
 201 
 240 
 89 
 242 
 270 
 
 7 845 
 14 755 
 12 
 
 8.5 1025 
 15 
 
 8 
 
 8 
 
 64 
 32 
 24 
 14 
 20 
 
 52 
 
 li 3 C. 
 24 i Par. 
 
 13 i. 
 
 14 i. 
 20 I 3 C. 
 
 35 
 
 4 
 
 12. 
 11 
 
 12 
 6.2 
 5.7 
 8.5 
 6.8 
 4 
 
 7.6 
 
 7 2: 
 
 6.51 
 
 9233 
 
 16l!l6 
 
 446 23 
 
 613;23 
 
 8317 
 
 . . i25 
 
 101926 
 
 65 45 
 
 150,16 
 
 53 '20 
 
 ....|15 
 56 6 
 82 63 
 
 216 16 
 
 48 
 
 30 
 
 ..... 
 
 32-4C 
 
 jSeB. 
 
 24 
 
 
 
 3C. 
 
 18 
 
 , 
 
 22 
 
 SeK. 
 
 22 
 
 SeK. 
 
 
 C. 
 
 22 
 
 
 12 
 
 
 11 
 
 
 17 
 
 s\ 
 
REIXVOKCED COXCRETE ARCH BRIDGES. 179 
 
 TABLE III— Continued 
 
 LIST OF REINFORCED CONCRETE BRIDGES 
 
 I 
 ■f i 
 
 i 
 
 N 
 
 ■7. 
 
 I ' 
 
 ^ 1 i 
 
 -=. & -^ 
 
 1 
 
 55.000 
 
 54.400 
 50,900 
 
 54.000 
 
 
 
 KnKincrr. 
 Duane 
 
 I 
 
 References. 
 
 K.C, Eng.-Con. 
 
 N.. •• Nc«s 
 
 , R., " Rccon 
 
 1 
 
 1 
 
 1 1 
 
 ■I 
 
 
 3 X i 
 
 .' 'r.r 
 
 24 , H. 
 
 1 ( 
 
 83 
 
 IS 
 
 Hiltv 
 
 
 
 Mclntyre 
 
 RaUton 
 
 Jcup 
 
 Jcup 
 
 Concrete i*tecl Co. . 
 
 Concrete Steel Co. 
 
 Von EmperRer. . . 
 Lutcn 
 
 X.. Dec. 6, '07 
 
 .\., Apr.ii.'Ol 
 N.. Apr. 11, 01 
 
 
 71 
 
 
 
 H. 
 H. 
 
 14 
 (* 
 
 b6 
 
 2.65 87 
 
 2.90 S8 
 J.9 
 
 Ifi 
 II) 
 
 10" I 
 10" 1 
 
 36 1900 
 36 |1900 
 
 
 E.C., Mar. 17, 07 
 R.. Feb. 13. 04 
 N'.. Oct. 3, 95 
 
 (in 
 
 14 
 
 15 
 14 
 
 2'2X'i 
 9" I 
 
 v: 
 
 1', 
 
 3x1 
 
 i" 1902 
 
 3e 1895 
 12 1905 
 
 
 .. 2.00 91 
 
 .. 93 
 
 94 
 
 95 
 
 40 
 14 
 IH 
 
 12 
 
 r; 
 
 J4 
 '.2 
 
 1905 R. v.. 
 1905 H. 
 
 Wells 
 
 Hibbard 
 
 Kahn 
 
 National RridceCo. 
 Lulen 
 
 R., .Sept. 22. '06.. 
 R.. Feb. 10. 06 
 
 
 14 
 1» 
 
 190« H. 
 
 25.680 
 
 
 
 
 97 
 98 
 00 
 
 
 4x 
 
 Ju son.... 
 
 N., Auk. 1. '01 
 R.. Apr. 20. '06 
 
 E.C.. Sept. 2, 'OS 
 
 1 4 75 
 
 
 ■•^U, -^: 
 
 
 
 ' lf.O 
 
 18 
 21 
 
 H. 
 
 K. a. 
 
 " 
 
 14J,900 
 
 Con Crete Steel Co. . 
 Osborn 
 
 
 . 13. 40101 
 ..... 1C2 
 
 103 
 
 2.1SJC4 
 
 1.84105 
 
 !K6 
 
 
 
 19061 H. 
 1897^ " 
 1907 E. R. 
 
 77,000 
 5,040 
 
 1 J.900 
 75,000 
 
 12.600 
 
 Burr 
 
 Dean 
 
 Lutcn 
 
 N, May 9, '07 
 
 R.. Dec. 10, '98 
 
 
 11 
 
 20 
 
 8" 1 
 
 4'^ 
 Frame 
 
 36 
 
 8 
 
 
 18 
 18 
 
 21 1903 H. 
 24 1896 •• 
 
 CourtriRht. ... 
 Brady 
 
 N.. Mav 12. '04 
 
 R.. Nov.17,'00 
 N., Apr. 6, '05 
 
 . i 1 96107 
 . S.:01C8 
 
 10 
 
 
 1904 F. B. 
 1896i H. 
 
 
 Il09 
 
 10 
 
 fi" 1 
 
 T 
 
 36 
 
 Mclan Con. Co . . . . 
 
 
 110 
 
 
 . .1 . E. R. 
 
 6 1902 ... 
 12 1907 E._R. 
 
 12 1905 H. 
 
 Mercereau 
 
 
 
 
 111 
 
 112 
 
 
 
 
 .. 1 4.31 
 
 17 
 
 Luten 
 
 
 . ' .. 113 
 
 14 
 
 
 
 114 
 
 9 
 
 
 Luten. ... ' 
 
 
 1 
 
 115 
 
 
 
 N., Oct. 19. '99 
 
 
 
 
 116 
 
 10 
 
 5"'l 
 
 12 i;k)2 H. 
 
 ... IJOO 
 
 4 , . . i H. 
 
 « 
 
 
 
 IJ7 
 
 
 Hewctt. 1 
 
 
 
 118 
 
 15 
 
 Luten 
 
 1 
 
 
 
 1t» 
 
 14 
 
 i 
 
 
 
 liO 
 
 1.3 
 
 8 
 
 
 
 ■•■:;:::••■::;:::. i 
 
 
 
 1?1 
 
 26 
 
 1905 U. R. 
 
 12,000, 
 
 
 E.C., Sept. 2, 'OS 
 
 6.53 
 
 122 
 
 
 
 ! 
 
 
 
 
 
 
 1 
 
 I 
 
 ^ 
 
r I 
 
 "I 
 
 Ir 
 
 h .. 
 
 If! 
 
 t 
 
 m 
 
 m 
 
 at 
 
 it 
 s 
 
 ^ X 
 
 S ^ 
 
 X 
 
 at 
 X 
 
 1m) 
 
 It 
 
X 
 
 I 
 
 IffOS 
 
 PART III. 
 
 Highway Beam Bridges. 
 Comparison of Arch and Beam. I'iio advj 
 <«r arch Itridjrcs havo already boon described in 
 Part I (.i* this l)ook, and original formulae have 
 bc«'ii jjiven from which the approximate cost of 
 eonerete bridfjes may be determined. One of tlie 
 chief merits of arch liridges i.s that Avhen properly 
 desijrncd, Ihey may be made beautiful in outline. 
 
 Some of the advantages of beam bridge.s are as 
 follows:— (1) It is possible in a beam bridge to 
 locate the grade of the bridge floor much lower and 
 nearer to the high water level or other clearance 
 line than can be done when an arch is used; (2) 
 foundations for beam bridges may be built on soil 
 tliat is more or less yielding, which cannot be done 
 with arch l)ridges. unless liinges are used at the 
 ••enter and spring The lateral thrust of arches on 
 soft foundations is liable to cause serious injury to 
 the structure, while the corresponding amount of 
 settlement inider the abutments of beam bridges 
 produces no injurious effect. 
 
 A fre(juent objection to the use of beam bridges 
 is that they are not susceptible to artistic treatment. 
 It will be seen, however, by referring to '"igures 37, 
 38 and 39, that beam bridges may be designed that 
 are equally piea;-" ig in appearance to arch bridges, 
 and for many locations are more suitable. 
 
 In making a sc-lecti.r.n between an arch and a 
 beam design, the chief consideration will generally 
 
 181 
 

 ib' 
 
 a. 
 
 V. 
 
 X /J 
 
 y. 
 
 
IIIGIUVAY HI. AM KlDGliS. 
 
 183 
 
 l)t' tln'ir. n'lativf 
 
 1 
 
 cost. Tlic ('(tst of (•(uicrpto arcli 
 
 l»ri<lir.'s 1ms filrcjidy hccii jjivoii l>y tlic fornuil} 
 n-t'crn'd t<> }|Im»vc. uvA for the purpose of cniupHr- 
 isuii. ilic costs of concrete hciiiii lirM 
 fjin^riiij: from 4 to 40 feet in lrii<' 
 
 p's. Ill spans 
 arc ffiven in 
 
 t'n- fiihics (III Figures :!S niiil .W) i'lie estiniatetl 
 ••osls of these Ix-ain hridjres ineludo \\\c filling,', pave- 
 ment and two lines of railinj;. hut (lo not include 
 lamps or other purely ornamental features. On 
 l''i<;ur.' ;;s is <;iv. , ,ds.i a tahh- of approximate eosts 
 for concrete ahiitments of various heights, which 
 ••slimates also include railing and pav<uient to- 
 gether with earth excavation an<l hack filling in th.« 
 ahiitments. These estimates will enahle the de- 
 signer to eompare the relative cost of nrch an 1 
 beam liridges. and to seleet the form which he finds 
 iiiosl . conomical. 
 
 TABLE IV 
 
 SlMW 
 
 l.i-nKth 
 
 ABrTMKNT* 
 
 Crvit 
 
 HelKht 
 
 Beam Bridges. Concrete beam 
 built in spans up to 70 feet in le 
 not generally economical for len 
 feet, for above this length arch 
 the least. 
 
 ♦ -. 
 
 4 
 
 t 380 
 
 nc 
 
 
 3tll 
 
 150 
 
 
 410 
 
 aw 
 
 
 5111 
 
 250 
 
 « 
 
 «5II 
 
 810 
 
 9 
 
 770 
 
 370 
 
 10 
 
 HNO 
 
 4 to 
 
 11 
 
 io:«i 
 
 510 
 
 12 
 
 lliX) 
 
 ('"«t 
 
 bridges have been 
 ngth, but they are 
 gths exceeding 35 
 
 bridges will cost 
 
3- 
 M 
 
 Ii-h'' 
 
 i • 1 M • 
 
 :| 
 
 I ■ 1 i 
 
 L 
 
 184 
 
 c 
 
 & 
 
 et 
 
 en 
 
 Z 
 
 c 
 u 
 
 s 
 < 
 
 n a. 
 
 ^ >- 
 as 
 
 e 
 
 > 
 
 < 
 
 B 
 
 H 
 
 O 
 
 u 
 
tllGHlVAY BEAM BRIDGES. 
 
 185 
 
 The economical lengths and forms for concrete 
 beam bridges are as follows: Simple slabs are eco- 
 noniieal for spans up to 12 feet. Beam bridges 
 similar to Figures 37 and 39, supported on parallel 
 longitudinal beams, are economical for spans from 
 12 to 25 feet in length, while above 2~) feet it is 
 economy to use two lines of heavy side beams carry- 
 ing light cross beams supporting the floor slab. 
 
 To determine the economic span length to use in 
 a long bridge containing several intermediate piers, 
 
 TABLE V 
 
 
 Side Beam 
 
 Center Benin 
 
 Kntiniate 
 
 Span 
 
 Cone. 
 
 Rods 
 Ft. In.Sq. 
 
 Cone. 
 
 Rods 
 Ft. lu. S.J. 
 
 Cone. 
 
 Steel 
 
 Cost 
 
 Ft. 
 
 
 
 Cu. Yds. 
 
 Lbs. 
 
 
 8 
 
 12x30 
 
 2- ?.i 
 
 12x16 
 
 3 - 'i' 
 
 3.8 
 
 656 
 
 $ 164 
 
 10 
 
 12x-.i0 
 
 2- \ 
 
 12x18 
 
 3- '4 
 
 4.9 
 
 850 
 
 207 
 
 Vi 
 
 12x20 
 
 3- 'a 
 
 12x20 
 
 *- ?4 
 
 6.1 
 
 1160 
 
 256 
 
 14 
 
 12x20 
 
 3- % 
 
 12x23 
 
 4- »4 
 
 7.3 
 
 1360 
 
 304 
 
 16 
 
 12X21 
 
 3-1 
 
 12x27 
 
 4- ', 
 
 8.9 
 
 1780 
 
 360 
 
 18 
 
 14x22 
 
 3-1 
 
 14x28 
 
 4- \ 
 
 11.2 
 
 2()(K) 
 
 420 
 
 20 
 
 14x25 
 
 3-l'„ 
 
 14X112 
 
 4-1 
 
 13.3 
 
 2550 
 
 490 
 
 22 
 
 14x28 
 
 3-1'a 
 
 14x35 
 
 4-1 
 
 15.5 
 
 2800 
 
 645 
 
 'ii 
 
 14x31 
 
 4-1 
 
 14x39 
 
 4-l'« 
 
 16.2 
 
 3350 
 
 603 
 
 26 
 
 14x34 
 
 4-1 
 
 14x42 
 
 4-l'„ 
 
 20,7 
 
 3620 
 
 682 
 
 28 
 
 14x37 
 
 5-1 
 
 14x46 
 
 6-1 
 
 23.8 
 
 4460 
 
 775 
 
 30 
 
 16x38 
 
 5-1 
 
 16x46 
 
 6-1 
 
 28.2 
 
 4770 
 
 865 
 
 32 
 
 16x41 
 
 6-1 
 
 16X.W 
 
 6 - 1'8 
 
 32.0 
 
 5800 
 
 960 
 
 34 
 
 16x44 
 
 6-1 
 
 16x54 
 
 6-l'8 
 
 35.7 
 
 6200 
 
 1090 
 
 36 
 
 16x48 
 
 7-1 
 
 16x57 
 
 8-1 
 
 39.8 
 
 7000 
 
 1140 
 
 38 
 
 16x52 
 
 7-1 
 
 18x58 
 
 8-1 
 
 45.5 
 
 7450 
 
 1244 
 
 40 
 
 16x56 
 
 7-l'« 
 
 18x62 
 
 8.1'8 
 
 61.2 
 
 9400 
 
 1400 
 
 the nile is to select such a span length that the cost 
 of one span will be approximately equal to the cost 
 of a pier. 
 
 Methods of Design. Single span concrete bridges 
 of either slab or beam design must be considered 
 non-continuous, but for a series of spans the effect 
 of continuity in the beams may be considered. To 
 provide for this continuity, it is customary to pro- 
 
18C 
 
 co.xch'jru: bridges .i\n ciut.rts. 
 
 11 , 
 
 I :i I ' 
 
 I)(>rti()n the boains for only 80^^ of the maximum 
 hciulins moment. Tlie floor slabs must be pro- 
 tected from injury by a sufficient depth of earth 
 i'illing, M-hieh is shown 12 inehes on Fii,'ures ;18 and 
 ■)!). This provides depth enouf,'h for beddinjr ties 
 of street railway tracks. A suitable pavement or 
 wearing surface may be laid on this earth fillin},' 
 which may be renewed as recpiired. 
 
 It is permissible and good practice in designing 
 small concrete beams which are united by slabs, to 
 consider the effect of a i)ortion of the floor slal) 
 and to projjortion the beams as T beams. Large 
 longitudinal beams carrying floor loads directly to 
 the piers, should be proportioncnl as simple beams 
 without considering the effect of the adjintiingslab. 
 They will then have additional strength due to the 
 l)resence of such slab. 
 
 The bridges shown in Figures .18 and 3f) are de- 
 signed for total loads of from 400 to 500 pounds 
 per S(|uare foot of floor surface. It is customary 
 to provide for impact either by adding a percentag'^ 
 to the live load or by using a factor of 2 for dead 
 load stresses, and a corresponding factor of 4 for 
 live load stresses. 
 
 It has been proven by numerous experiments that 
 the adhesion of concrete to metal is sufficiently 
 great so no additional bond is required, but as 
 voids in the concrete are liable to occur and it is 
 difficult to always secure the highest grade of work- 
 manship, it is desirable to use rough bars with 
 mechanical bond. As provision mast also be made 
 
 f'^3r"-m 
 
niGinVAV BEAM BRIDGES. 
 
 187 
 
 fur shear by the iiso of inclinoil or bent rods and 
 stirrup irons, it is desirable in all large beams, to 
 nsc reinforeing bars whidi have the inclined stir- 
 rups or shear members rigidly connected to the 
 main tension metal. 
 
 Til all bridges where appearance is any consider- 
 ation, the railing should be designed Avitli care so 
 the design may properly harmonize with the rest 
 of the structure. CJenerally speaking, the balus- 
 trade that presents the best appearance on a con- 
 ciM'te bridge is one composed of either natural or 
 artificial stone, but it is also evident (Figure 39) 
 that an cfpially artistic eflTect may be secured with 
 ail ornamental metal railing and stone or concrete 
 ])osts and pedestals. Open balustrades are usually 
 l)i-('ferable to solid ones, not only because they are 
 susceptible to more artistic treatment, but also be- 
 cause their light and open design emphasize by con- 
 trast the solidity and strength of the supporting 
 structure ])eneath them. Solid balustrades are per- 
 missible chiefly for through bridges, where the con- 
 crete side girders standing above the roadway form 
 a sufficient protection. The exposed girder surface 
 may then be paneled or otherwise ornamented. 
 
 r»it'!!^^« 
 
I n[i| 
 f l> i 
 
 
 !i 
 
 [J 
 
 1 
 
 ■ i : ! 
 
 lan 
 
 <^^m^^ 
 
 iM>it&.- 
 

 X 
 
 > 
 
 5 
 
 ' s 
 
 •■r. 
 
 u 
 
 u 
 
 as 
 '■J 
 z 
 
 PART IV 
 
 Concrete Culverts and Trestles. 
 
 Since the iiitroduetioii of reinforced eoi -rete as a 
 building material, nii,.iy railroad companies are re- 
 buildinj? their permanent bridges and culverts in 
 concrete, either plain or reinforced. The use of re- 
 inforced concrete for culvert construction has be- 
 come almost general with the railioad companies, 
 while the building of trestles in this material i:s grad- 
 ually raming into favor. :Many old wooden struc- 
 tures, both of the open and tl:c gravel deck types, 
 are being replaced by better ones of concrete ma- 
 sonry. Amor.^' the railroad companies that are 
 using reinforced concrete extensively for the con- 
 struction of trestles may be mentioned the Illinois 
 Central, the Cleveland. Cincinnati. Chicago & St. 
 Louis (Big Four), and other branches of the New 
 York Central Railroac' system. A notable concrete 
 trestle or viaduct that has attracted much attention 
 is the one recently built at Richmond. Virginia, for 
 the Richmond & Chesapeake Bay T?ailroad Com- 
 pany. This viaduct is 2,800 feet ir length, and 
 varies in height from 18 feet at the ends to 70 feet 
 near the middle, and is shown in Figure 40. At At- 
 lanta, Georgia, there is a reinforced concrete viaduct 
 carrying Nelson street over the tracks of the South- 
 ern Railroad. It contains 10 spans of various 
 lengths from 20 to l:^ fo,>t. has a total length of 480 
 feet, and is shown in Figure 41. The main line of 
 the Big Four Railroad is carried for a distance of 
 
 188 
 

 '■ \ 
 
 II! ^ 
 
 i 
 
 If 
 
 
 100 
 
 COXCRLIL BRWGl.S AXD CLLl'LKTS. 
 
 1.200 foot across the Lawrenceville Bottoms on a 
 rciiiforeo'l ooneroto trestle 20 feet in height. This 
 entire rcfifion is pcriodii-ally Hooded Avith baekwatci- 
 i'fniii the Ohio and Miami rivers, making it neees- 
 
 FlK. 41. 
 .NKLSO.N STKKKT VIAUUCT, ATL.ANTA, GKORGU. 
 
 siiry to bnild. not only this road, but all others in 
 tile vii-iiiily at an cb'vation of ;}0 feet above h»w- 
 Avater level of the Oliio River. 
 
 On tli( following pages are designs and estimates 
 for about 1.000 railroad culverts and trestles, and 
 
CONCKETli CLLlliUIS IXP TKES Fl.LS. 
 
 191 
 
 the cstunatetl costs are given on charts shown in 
 Figures 4G, 47 and 66. 
 
 Tt will be seen tha the trestle designs are equally 
 suitable for culverts, and may he adapted for that 
 purpose l)y iiuTcasing their width to correspond 
 with the depth of structure hclow the base of rail, 
 or to confonn to the depth of the enibaidanent. 
 When used as culverts, abutnu'ut wing walls must 
 l)e added and the nature of the f(>undation soil » my 
 be such as to reipiire culvert pavement. These 
 nu)difications in the trestle estimates may easily be 
 made either for one or more openings, and adapted 
 for either ingle or double box culverts. 
 
 The culvert designs are shown with a minimum 
 depth of filling of not less than 3 feet above the con- 
 crete top. This depth is desirable not only for the 
 purpose of distributing the live load from the engine 
 and train wheels, but also for the pnipose of form- 
 ing a cushion to absorb and distribute the shock 
 and impact from rapidly moving trains. Trestle de- 
 signs G and II, Figures 64-65, are shown with a 
 :?-foot depth of filling. It freiiuently occurs, how- 
 ever, that thin floors are necessary and only suf- 
 ficient depth can be secured for the usual 1.') inches 
 of ballast. This arrangement has been shown in 
 trestle designs A to F inclusive. (Fig\u-es r)S to 6:}.) 
 
 Required Size of Culvert Opening. 
 
 The nu)st important consideration effecting the 
 final cost of a culvert is the selection of its form 
 and size. It freciuently occurs that structures of 
 
 i L-».MHliJUL ' . 
 
 . ' B W' MJil l W t ii'illi* 
 
I' 
 
 i 1 
 
 "ini 
 
 192 CO-y CRETE BRIDGES .IXD CULVERTS. 
 
 too large a size and oxeossive cost are specified, 
 when smaller ones would be ample to carry off the 
 greatest rainfall. 
 
 The selection of the proper size of cnlvert is of 
 much greater importance than any consideration of 
 design. If a culvert costing .tlO,0()0 be specified, 
 where a snuiUer one costing only iji.l.OOO would be 
 sufficient, the loss by such an error would evidently 
 be $r),000. On the other hand, if the size of struc- 
 ture as specified be used, the engineer may by care- 
 ful estimating, select a form with the required wa- 
 terway, and with a cost of only .^8,000. The saving 
 in this case is only .'i;2.000. whereas, if greater care 
 had been given to the selection of the proper size, 
 there might have been a saving, not only of this 
 $2,000, but of ^:).{)00 additional. It will be seen, 
 therefore, that the one consideration outweighing all 
 others in efTecting the final cost is the selection of 
 a structure with the necessary waterway. 
 
 In the State of Wyoming there are four bridges 
 within a short listance of each other, carrying a 
 road over the same stream. The last of these 
 bridges to be built has two spans G.') feet in length, 
 or V.\() feet extreme. The second bridge has two 40- 
 foot spans, and is SO feet in length. The third has 
 a single GO-foot span, Mhile the fourth is an old 30- 
 foot wooden truss, which has for fifty years proved 
 itself sufficient to meet even flood conditions. There 
 are, therefore, in clo.se proximity to each other four 
 bridges over the same stream, the longest of which 
 is four times greater than the shortest, and the long- 
 
CONCRETE CULVERTS AND TRESTLES. 193 
 
 est one was the last one built. After selecting a 
 length of structure four times greater than required, 
 it is possible that the engineer may have spent con- 
 siderable time and thought in his endeavor to build 
 tliis bridge at the least possible cost, and may have 
 succeeded in saving a few hundred dollars on his 
 original estimate. • 
 
 A bridge 130 feet in length would cost approxi- 
 mately .$7,000, while a 30-f()ot bridge would not ex- 
 ceed $1,500. This saving is, therefore, only a frac- 
 tion of the saving that might have been effected, 
 had a 30-foot bridge been used, which length had 
 proved sufficient for half a century. 
 
 The most reliable data on which to base the size 
 of a prospective structure is the high-water level of 
 previous years. It is Trequcntly possible to obtain 
 such data from local records, or to determine the 
 size from that of other bridges passing the same 
 tlow of water in the near vicinity. In the case re- 
 ferred to above, if the engineer, before building the 
 130-foot bridge, had made sufficient inquiry, he 
 could easily have learned that a 30-foot span had 
 carried the entire stream discharge for fifty years, 
 and was therefore large enough for the raintVill of 
 the future. 
 
 It is not economy to provide openings of sufficient 
 size to carry the rainfall of freshets or cloudbursts 
 that may not occur oftener than once in a century. 
 For such unusual occurrences it is better to make 
 occasional repairs than to invest additional money 
 in larger structures than may ever be required, 
 
r 
 
 m 
 
 194 LOXCRETE BRIDGES JXD CiLrEKTS. 
 
 when Hiicli iiioiicy niiglit bo drawing iiitorost to 
 cover the cost ol" an occasional repair. 
 
 Where reliable data in reference to the niaxinniin 
 rainfall cannot be obtained, it is customary for the 
 railroads to build temporary wooden trestles at the 
 proposed bridge or culvert site, and to make thes.; 
 trestles unnecessarily long, so there will be no doubt 
 whatever of the openings being large enough. These 
 temporary bridges will last from six to ten years, 
 and during this period careful observations of the 
 water flow may be made, and other data secured 
 from which to determine the necessary culvert area. 
 As the cost of these temporary trestles will not ex- 
 ceed !f<10 per lineal foot their entire cost may easily 
 be saved by selecting the minimum reciuired size for 
 the permanent structure. 
 
 "Where no reliable data in reference to the volume 
 of water is obtaiiud)le, the culvert area may be coir.- 
 puted approximately by a empirical rule known as 
 >Ioyer's Formula, which is as follows: — The Re- 
 quired Culvert Area— ^ Drainage area in acres X F, 
 
 where F is a eoeifieient varying from unity for tiat 
 country, to 4 for rolling or mountainous country, 
 from which rainfall is discharged at a greater ve- 
 locity. The proper value for this coefficient for any 
 particular loention must be selected entirely by the 
 judgment of the engineer. 
 
 Reinforced Concrete Box Culverts. 
 
 The following series of designs for single and 
 double box, reinforced concrete railroad culverts, in- 
 
1 
 
 COXCRBTE CUWERTS ASD TRESTLES. 195 
 
 .'ludos between 800 atnl 000 separate estimates, and 
 is therefore.' very comprehensive and complete. Tlu« 
 charts of eomparative eosts, Fif?nres 46 and 47. show 
 these to be more economieal than any other form <>f 
 culvert, excepting perhaps reinforced concrete oval 
 culverts of the form shown in Fifrure 57. While arch 
 culverts of this latter form may contain less ma- 
 terial than box culverts of equal area, they are more 
 (lilTicult to build because of their curvature, even 
 though collapsible centers be used. Several large 
 railroad systems in America are now usiii;,' arch cul- 
 verts of this general form, in place of the old seg- 
 m"Mtal or semicircular types, which contain more 
 masonry in the abutments than in the arch wing. 
 
 Loads. There is much uncertainty in refen (<"» 
 to the amount of load carried by the cover of a rail- 
 road culvert. The amount of this load depends to 
 a great extent on the depth of the culvert top l)clow 
 the base of rail. The greatest load occurs when the 
 depth of filling above it is a nMnimum. for then the 
 culvert top is siibjected to the entire load from the 
 locomotive wheels and their impact. On the con- 
 trary, when the culvert is buried beneath a deep 
 embankment, the live load and impact is so distrib- 
 uted and dispersed that only a part of this loid goes 
 direclly to the culv rt. Various writers have en- 
 deavored to show that these loads are distributed 
 crosswise of the embankment, and slope outward 
 from the railroad ties at the rate of one foot hori- 
 zontal for every two feet vertical. The pressure on 
 the base of these triangles varies from zero at the 
 
\' i 
 
 196 COSCRLTE BRIDGES ASD CULVERTS. 
 
 outer point to a maxiinum uiulor the ond of tie. This 
 nssnniption is otily an approximation, though a rea- 
 sonable one. T'nfortunatcly, however, the author of 
 this liypothesis assumes that the earth pressures 
 slope outward at each side, hut makes lu) provision 
 for similar distribution lengthwise of the embank- 
 ment. It is (juite evident that whatever distribution 
 of loads does oeeur, nuist oeeur e(|ually in all direc- 
 tions, and the assumption referred to above is there- 
 fore incorrect. 
 
 "Where a culvert has a small depth of filling above 
 it, the entire weight of such filling is then suj)- 
 ported by the culvert, but if located at the bottotix 
 of a high embankment, the culvert then carries only 
 a portion of the live load above it, supporting also 
 a i»ortion only of the earth embankment. The 
 amount of this portion depends upon the nature of 
 the embankment material. If this material is ce- 
 mented wi'll together, it will then tend to support 
 itself by acting either as an arch or beam, and there- 
 by relieving the culvert of much superimposed load. 
 The uKist reasonable assumption is to consider that 
 the culvert carries the weight of a triangular sec- 
 tion of the embankment, the sides of which slope 
 outward from the vertical in the ratio of one foot 
 horizontal to two feet vertical. If the embankment 
 material is composed of clean sand, a larger propor- 
 tion of the imposed nuitcrial will then be borne by 
 the structure. In view of the uncertainty of various 
 conditions efl'ecting the amount of load on culvert 
 tops, it has been deternnned that these loads can 
 
CONCRETli CVI.ILKIS J.V/» TRESTLES. 197 
 
 never cxcood the values oeeurririff uiidor a miniiniim 
 depth of earth filling. 
 
 An assumed live load on oaeli traek eriuivalent 
 ♦o Cooper's eni^ine load K. ."»(). spread <»ut l)y the ties, 
 calls and l)allast, produces a distributed load on the 
 eulvert top of 1,100 pounds per scpiare foot. To 
 this has been ad«led impact, amounting to 50% 
 of the live load, or '^'yO pounds per sfjuare foot. 
 Adding to these the ^veight of ties, rails, ballast, 
 earth filling and eonerete in the culvert top, pro- 
 duces a total load of from 2,100 pounds per square 
 foot for small culverts with thin slabs, to 2.400 
 pcmnds per scpiare foot for larger spans with a 
 greater thickness of concrete. The following box 
 culvert tops are therefore proportioned for total 
 loads of from 2.100 to 2,400 pounds per square foot. 
 
 From the theory of horizontal earth pressure, it 
 is known that the thrust per s(iuare foot on an em- 
 bedded vertical surface is v pial to one-third of the 
 corresponding horizontal pressure on a unit •'* area 
 at the same level. This condition exists when the 
 einbankmcnt is comi)osed of clean, dry sand with an 
 angle of repose of about HO degrees. The proper 
 amount of pressure to assutiK on the culvert side is 
 therefore from 700 to 800 pounds per scpiare foot, 
 or one-third of the corresponding roof loads. As 
 the sides are, however, subjected to vertical loading 
 and impact from moving trains, th" .assumed side 
 pressure has been taken at one-half of the vertical, 
 or from 1,050 to 1,200 pounds pci upiare foot. 
 
 On account of the liberal provision for impact, 
 
 mm. 
 
 '■ ^" ■ ^BB ? 
 
f( 
 
 198 
 
 COXCRETl- BKIDGIiS AXD CTU'ERTS. 
 
 amounting to 50% of the live load, high 
 ^vorking values have been used for concrete and 
 metal reinforcement. A reasonably rich concrete 
 mixture, such as 1-:}-"), lias an ultimate crushing 
 value of 2,800 pounds per s(|uare inch. One-f<mrth 
 this amount, or TOO ponnds per stpiare inch, is there- 
 fore assumed as a working unit for concrete, ami 
 12.000 pounds per square inch as a working unit 
 for reinforcing steel. 
 
 Economic Length for Slabs and Beams. There is 
 evidently a limit where economy ce;ises in the use 
 of flat slalxs for supporting loads in bending, and 
 above that limit the economical construction is a 
 eombiiuition of Ix-ams and shibs. For the purpose 
 of determining tliese economic lengths, a slab tal)le 
 (Tai)le No. VI i lias been prepared, giving the amount 
 of concrete and steel and the estimated cost per 
 s(iuarc foot for spans varying in length from -4 lo 
 24 feet, and total imposed loads of from 2,100 to 
 2.400 i)ounds i)er scjuare foot. 
 
 TABLE VI 
 
 REINFORCED CONCRETE SLABS— SIMPLE SPANS 
 TOTAL LOADS 2100 TO 2400 LBS. PER SQUARE FOOT. 
 
 
 Kff.Ttivo 
 
 T<.l,il 
 
 
 
 pan. 
 
 Depth. 
 6 
 
 Dcptli. 
 
 1 . .*> 
 
 
 s,,. n 
 
 4 
 
 
 ;'4 ill. 7 1 J 
 
 6 
 
 9 
 
 11) .-> 
 
 
 ' s 1 
 
 8 
 
 12 
 
 1 :t :. 
 
 
 \ " .-.1.^ 
 
 10 
 
 1.5 
 
 17 
 
 
 " ."ll.l 
 
 12 
 
 18 
 
 JO 
 
 
 " 4'.". 
 
 14 
 
 21 
 
 J.-j (1 
 
 
 • 4 " 
 
 16 
 
 24 
 
 Jl) (1 
 
 
 <i •• .-.1.; 
 
 IS 
 
 28 
 
 :«) :> 
 
 
 U " 4 '.", 
 
 20 
 
 .^t 
 
 .>•»..» 
 
 
 U ' 4 ■ 
 
 ■>•! 
 
 :n 
 
 ;t7(i 
 
 
 + " ;{'V 
 
 jj 
 
 .{7 
 
 M) t) 
 
 
 4 •• ;{'. 
 
 in apart. 
 
 Cost 
 
 prr 
 
 sciuaro ft. 
 
 (Viits. 
 
 :<() 
 
 « 
 
 4.{ 
 
 f) 
 
 :.6 
 
 
 
 71 
 
 I) 
 
 S."i 
 
 ■" 
 
 97 
 
 t 
 
 110 
 
 •> 
 
 i:n 
 
 .1 
 
 140 
 
 .) 
 
 159 
 
 
 
 170 
 
 
 
1 
 
 CONCRETE Cr EVERTS AXD TRESTEES. 199 
 
 A corresponding set of ten tables was made giv- 
 iiij,' the anionnt of material and the estimated costs 
 pi'r scfuare foot for a combination of beam and slab 
 coiistrnction, Avith spans varying from 6 to 30 feet 
 ill length, and beams spaced from 6 to 18 feet apart, 
 on centers. The cost results from these ten tables 
 are given on the chart, Figure 42. The thickness 
 oF slabs and beams are proportioned so the stress 
 iit the outer edge will not exceed 700 pounds per 
 sijuare inch from dead, live and impact loads. The 
 thicknesses Avere determined from the "writer's orig- 
 ii:al formula 
 
 M 
 
 K 
 
 d^ 
 
 V. licrc ]\I. is the bending moment in inch pounds, 
 
 d the distance from slab top to center of ten- 
 sion bar. and 
 K a variable factt>r. 
 
 It is advisabk' to neglect the effect of continuity 
 ill proi)ortioning sla])s, even though a considerable 
 .•I mount doul)tless exists, whicli wovdd reduce the 
 shib thickness by about 2(V/( . Slab thicknesses are, 
 llii'refore, given, as re<[uii'ed for non-continuous 
 licains. From the comparative cost chart, Figure 
 42. the following conclusions are obtained. For 
 loads of from 2,100 to 2.400 i)ounds per sciuare 
 foot :— 
 
 Simple slabs are ccoiioiuical for clear spans up to 
 7 feet in length. 
 
 Sljibs with beams (5 fcot apart wn^ ccononiic.Ml for 
 spans from 7 to 14 feet in length. 
 
n 
 
 i I 
 i 
 
 III! 
 
 i :| 
 
 200 CONCRETE BRfDGES AND CULVERTS. 
 
 P 
 
 ?: 
 
 :i 
 
 Comparative Cost per Sq. Ft. 
 
 Combination of Slabs and Beams for 
 
 Various Beam Spacing also Cost 
 
 of Simple Slabs. 
 
 Total loads 210O to 2100 lbs. sq. ft. 
 
 S Pans. 
 
 i'lg. 42. 
 
 26- 
 
 So 
 
 3o 
 
CONCRETE CrU'ERTS AXD TRESTLES. 201 
 
 Slabs with beams 7 feet apart are economical for 
 spans from 14 to 20 feet in length. 
 
 Slabs with beams 8 feet apart are economical for 
 spans from 20 to 30 feet in length. 
 
 The comparative cost chart, Fignre 42, was ob- 
 tained from 130 separate estimates, and the conclu- 
 sion from it is that slabs for the above loads are not 
 economical for greater lengths than 8 feet or greater 
 thicknesses than 12 inches. 
 
 Figures 43, 44 and 45 are typical drawings for 
 single and double box railroad culverts for both 
 slab, and a combination of beam and slab construc- 
 tion, and Tables VII, VIII, IX and X give the cor- 
 responding sizes, (luantities and costs for culverts 
 varying in area from 4 to 480 square feet. These 
 tables give separately the rjuantities and cost for 
 the two portals and for the culvert barrel per foot 
 of length, and also the lengths and total costs of 
 culverts for six different heights of embankment, 
 varying from 10 to 50 feet. 
 
 The single and double slab culvert tables contain 
 34 different sizes each, varying from 2 feet by 2 
 feet to 12 feet by 12 feet for each opening, while the 
 combined beam and slab culverts contain 30 corre- 
 sponding sizes each, varying from 8 to 20 feet in 
 width, and from 4 to 12 feet in height. The esti- 
 mated costs of these culverts for banks 20, 30, 40 
 and 50 feet in height are shown in Figure 46. These 
 <Mivves represent the cost of the economic forms, 
 which generally have openings of a greater height 
 than width, such as 4 feet wide by 6 feet high, either 
 
 miiiiii 
 

 1 
 
 I 
 
 I I 
 
 \ff;?i;ijSs^s^:^MKB^m ^:-h^4^gs^'k*viBc^ 
 
 ■^'lAjrtt 
 
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2 
 
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 h 
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 X 
 
 H 
 
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 7 &< H 
 
 X 
 
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 7. 
 
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 5 
 
 
 Q 
 
 
 k 
 
 
 k 
 
 
 
 
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 '«1 
 
 4- -l 
 
 ^N 
 
 
 V 
 
 
 c> 
 
 
 k 
 
 Hn 
 
 
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 1 
 
 -; 
 
 _-.^.-L»...x 
 
 '' 
 
 
 
 i 
 
 ^ 
 
 IB 
 
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 f 
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 1 
 
 -1 
 
 
 + 
 
 i 
 
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 f, 
 
 4 
 
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 1 
 
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 t' 
 
 
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 s 
 
 
 
 
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 -3 
 
 h 
 
 
 a 
 
 CI 
 
 
 A 
 
 
 
 
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 g 
 
 £ 
 
 
 4 
 
 X 
 
 
 
 
 
 
 
 
 k 
 
 ^ 
 
 
 — '" 
 
 
 
 r: X 
 
 
 
 
 \r. 
 
 
 t- z 
 
 
 
 '— !< 
 
 C 
 
 
 
 5 
 
 
 
 s -• 
 
 
 
 
 
 
 z. ^ 
 
 
 f =" 
 
 
 
 
 
 
 
 
 s 
 
 3 J 
 
 S 11 
 
 o 
 
 0.3 
 
 l^i 
 
 « 
 
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 c « 
 
 
 it !- 
 
 "Z -a 
 
 4> 
 
 •5 5 
 
 a a 
 
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 c = 
 c — 
 
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 f, "j 
 
 1 i 
 
 v: "S » 
 
 a* ;3 
 
 
 ic „s 
 
 
 
 
 •2 u 
 
 u 
 
 
 £l 
 
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 ah 
 
 X 
 
 < 
 
 
 
 
 /HtH^Htm-rrr 
 
 |-|-i-.-;-r-r 
 
 ■!~;-!-i-i-h-i-; 
 
 ■ I I I I I ■ , I , 
 
 I , M I I * ' I ) ' I ' I I 
 
 5 
 
 
 
 k 
 
 M 
 
 203 
 
M 
 
 Vt 
 
 204 
 
 (•o.vcA'/{77: liRinciis ./.\7> ci-i.rnRTs. 
 
 TABLE VII 
 
 TO ACCOMPANY FIGURE 43 
 
 'T..pan,l H„tt.,„,' Si,l,.s. Onantitie»,M'rlin.f, 
 
 S: i 
 
 2 r.irlals. 
 
 i iT Siiuarc Hdils. 
 
 :- r r.c, 
 
 •c|iiarfl((Mls T- I ^' 
 
 :s '= -• 
 
 1 
 
 2 
 3 
 4 
 5 
 6 
 1 
 8' 
 9 
 10 
 
 11; 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 19 
 
 20 
 
 21 
 
 22' 
 
 23! 
 
 2 
 3 
 2 
 3 
 4 
 
 4 
 G 
 6 
 9 
 12 
 
 8 -^ —9 
 
 5 15 
 
 2 8' 
 
 9^'— 7'. 
 
 3 
 
 4' 
 
 12 " 
 16 " 
 " 5 20 " 
 " 6' 24 •■ ' 
 
 5 3 1510' 
 "i 4 20 " • 
 "i 5 25 " , ' 
 "' 6 30 '■ • 
 "i 8' 40 •■ " 
 
 6 4' 2412" 
 
 s 
 
 
 
 " 6 3(3 •■ 
 " 8 48 " 
 " 10 00 " 
 8 4 3214 
 " C 48 " 
 " 8 64 " 
 24! " 10 80 " 
 2510 4 4017 
 
 26 " 6 60 " •' 
 
 27 " 8, 80 " " 
 
 28 "10100 " •' 
 
 29 " 12 120 " •' 
 3012 4 4820 I 
 31 i " 6, 72 '■ ■ 
 32; " S 96 ■ ■' 
 33 "10120 " " 
 34' "12144 " " 
 
 1 —51. 
 
 41. 
 
 8 
 9 
 10 
 s 
 9 
 10 
 10 
 12 
 10' 
 10 
 12 
 14 
 12 
 12 ■ 
 12 • 
 14 • 
 15 
 15 
 15 
 
 IS 
 18 
 IS 
 IS 
 18 
 20 
 20 
 
 1 
 
 " -12 
 10 
 — 18 
 15 
 12 
 10 
 18 
 15 
 12 
 10 
 8 
 15 
 12 
 10 
 
 s 
 (> 
 
 12 
 10 
 
 8 
 
 12 
 10 
 s 
 6 
 -15 
 12 
 12 
 10 
 S 
 15 
 12 
 12 
 10 
 8 
 
 .19 
 
 .23; 
 
 .28 
 
 .36 
 .42 
 .50 
 .59 
 .69 
 . 55 
 .64 
 .74 
 
 22: 
 
 ;26; 
 
 35 
 
 § 
 
 62 
 58 
 55 
 65 
 75 
 92 
 66 
 75 
 86 
 
 2.43 
 
 2 91 
 
 3 69 
 4.50 
 
 5 . 39 
 
 6 , 55 
 5.25 
 
 1.7s 
 3.40 
 
 3 . 55 
 4.00; 
 
 4 . 5o: 
 
 6.00 
 3.85 
 
 5.60 4.30 
 
 6.66 
 7.75 
 9.26 
 7.06 
 8.10 
 
 9 42 
 
 5 . 50 
 6.8O; 
 8.70 
 5 . 00 
 6.70| 
 8 . 50 
 
 14 
 
 . ... I 27 
 .... 2S 
 ... 32 
 2(M) 44 
 250 58 
 ... j 40 
 . ..|34 
 250 54 
 300 66 
 
 500 
 500 
 600 65 
 800' 84 
 
 89 
 72 
 
 79101 10. .i7 10. 40 1000107 
 0U32j 13.6013.00 1600136 
 831131 11.2210.00) 900116 
 12. 97 12.40' 1200147 
 16 3013. 70 1S00173 
 20. 60 15. '0 2200208 
 15.0012.00l 900132 
 18. 00 22. 00! 1800248 
 
 .96134 
 .20168 
 .4 216, 
 .18 139 
 .33185 
 .47215| 
 . 76 265; 
 .712411 
 .84 2661 
 .07282i 
 .503241 
 ,88381' 
 33327' 
 56362; 
 7s;j78 
 00412 
 40466 
 
 20.4030.00' 2200328 
 24.7043.00 3200472 
 23.3018.00 1400200 
 25.4028.00 2200312 
 27.9037.00 3200424 
 32.9046.00 4000528 
 38.3057.00 5000656 
 31.8023.00 1800256 
 34 9037.00: 2.S(K) 378 
 37.3052.00:4000576 
 40.4068.00 5000744 
 45.8082.00 6500916 
 
 
CONCRETE CULVERTS AND TRErTI.ES. 205 
 
 TABLE VII— Continued 
 
 REINFORCED CONCRETE, SINGLE BOX, RAILROAD 
 
 CULVERTS— SLAB CONSTRUCTION 
 
 TO ACCOMPANY FIGURE 43 
 
 10 ft. Hank, j 15 ft. Bank. \ 20 ft. Bank. | 30 ft. Bank. \ 40 ft. Bank. 1 .50 ft. Bank, 
 
 2S 348 
 
 2.') 365 
 
 31 366 
 
 2.^) 470 
 
 30 .')82 
 
 30 900 
 
 29 1166 
 
 39 
 
 106 
 
 36 
 
 122 
 
 39 
 
 172 
 
 35 
 
 189 
 
 32 
 
 216 
 
 29 
 
 248 
 
 3S 
 
 230 
 
 35 
 
 230 
 
 32 
 
 26' 
 
 29 
 
 291 
 
 2() 
 
 330 
 
 34 
 '11 
 
 312 
 
 11 K 
 
 54 145 
 51, 175 
 54 228 
 50i 257 
 47 296 
 44' 346 
 52' 318 
 50 314 
 47, 366 
 44' 407 
 41 467 
 49 417 
 46, 427 
 43: 489 
 40 532 
 34; 598 
 46 631 
 40 662 
 34 725 
 28' 783 
 45 807 
 40 968 
 34 1020 
 28 1157 
 45 1250 
 39 1297 
 33 1339 
 27 1413 
 
 44 i656 
 
 38 1698 
 
 32 1766 
 
 26 1794 
 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 10 
 
 59 2126 
 
 53, 22 IS 
 47 2326 
 41 2394 
 351 2516 
 
 79i 1206 
 91 1136 
 85] 1247 
 1453 
 1708 
 1482 
 1778 
 1938 
 2262 
 2300 
 2442 
 2594 
 2888 
 3176 
 3076 
 3278 
 3436 
 7i: 3804 
 65; 3886 
 
 400 
 479 
 611 
 727 
 859 
 1033 
 861 
 1004 
 1064 
 1216 
 143911 
 1162|12 
 129513 
 1484 14 
 1607 15 
 201616 
 1816,17 
 2017118 
 2433|19 
 2928 20 
 2382'2I 
 2848,22 
 3148:23 
 3732 24 
 3700 25 
 3962,26 
 424427 
 484928 
 5456 29 
 4978130 
 5348 31 
 6676 '32 
 6024 j33 
 6636 34 
 
20f. coxchT/in BRinclis .wn cn.i'nRTS. 
 TABLE VIII 
 
 REINFORCED CONCRETE, DOUBLE BOX, RAILROAD 
 
 CULVERTS -SLAB CONSTRUCTION 
 
 TO ACCOMPANY FIGURE 44 
 
 r :? 
 
 1 
 
 1 .J 
 
 
 Top aTiil Bnttom 
 
 t J, 
 
 iilrs. (Juantifics per ft. 2 J'ortals. 
 
 
 
 ■/- 
 
 J Kjiiarc Kdil 
 
 1 - ■"' 
 
 1 > >■ 
 
 
 U) 
 
 
 1 ^ 
 
 (• 
 
 
 c. ('. i ? 1 i '*. I i * 
 
 it 1 lis 
 
 l|2;2 8 
 
 6 
 
 6 ' j" 
 
 6" 
 
 6'. 
 
 "—12" 
 
 .32 
 
 51' 4.60 2 6 2:) 
 
 2 "1 \i 12 
 
 j 
 
 ** " 
 
 " 
 
 () " 
 
 10 
 
 .38 
 
 43 4.72 3 9 31 
 
 3 :{ \i IS 
 
 9 
 
 !? V " 
 
 ~9 
 
 ru 
 
 -15 
 
 .61 
 
 76 7 94 4.9 39 
 
 4' " 
 
 4, 24 
 
 " 
 
 
 ** 
 
 X " 
 
 12 
 
 .72 
 
 89 9.30 5.3; 200 50 
 
 •V 
 
 5 30 
 
 "i 
 
 " " 
 
 *' 
 
 9 " 
 
 10 
 
 .8410410.85| 7.0| 250 66 
 
 fij 4' ;j: 24 
 
 12 
 
 ?'-,' 
 
 -"':; 
 
 7 " 
 
 15 
 
 .82,10110 52! 5 5, 44 
 
 7i "j 4 32 
 
 J 
 
 
 " 
 
 8 " 
 
 12 
 
 .9411412.05 
 
 6 6: 250 62 
 
 S; ;'i 5| 40 
 
 1 
 
 tt ii 
 
 " 
 
 9 " 
 
 10 '1.06:129 13.65 
 
 8 
 
 300 76 
 
 9 "j 6 48 
 
 t 
 
 " *' 
 
 " 
 
 10 " 
 
 8 il.l9;i5215.6010 
 
 500 UK) 
 
 10! r,' 3 30 
 
 12 
 
 10 y 
 
 -7 
 
 8 " 
 
 15 
 
 1.0612313.50 
 
 6 7 
 
 60()j 77 
 
 li; ", 4 40 
 
 "j 
 
 
 '* 
 
 9 " 
 
 12 
 
 1.21 
 
 13515.10 
 
 8 2 
 
 700! 89 
 
 12, ", 5 50 
 
 *' 
 
 It •( 
 
 t< 
 
 10 " 
 
 10 
 
 1.35 
 
 15116.81, 
 
 9 7 
 
 80010i> 
 
 13 " e; 60 
 
 '* 
 
 " " 
 
 1 
 
 11 ' 
 
 8 
 
 1.51 
 
 1 7419. 02 12. 61000 140 
 
 14 " 8, 80 
 
 '* 
 
 " " 
 
 
 12 " 
 
 6 
 
 1.79 
 
 23223.6515.01600184 
 
 15 6 4 48 
 
 12 
 
 12 "s 
 
 ~7 
 
 10 "s 
 
 12 
 
 1.6220621.1011.01 900124 
 
 16 " 6 72 
 
 " 
 
 it ti 
 
 " 
 
 11 " 
 
 10 
 
 1 . 89|23924 . 50 18 . O1200 192 
 
 17 ". 8* 96 
 
 " 
 
 '* ** 
 
 " 
 
 12 " 
 
 8 
 
 I 20 285 29 . 0024 . 1800264 
 
 IS "10120 
 
 ** 
 
 i* u 
 
 " 
 
 14 " 
 
 6 
 
 2 . 62353 35 . 50 30 . 0:2400 336 
 
 19 8 4, 64 
 
 15 
 
 14-s- 
 
 -5'. 
 
 12 " 
 
 12 
 
 2. 35:306 30. 901 4. d 900148 
 2 6533833 . 7020 . 02000246 
 
 2J " 6: 96 
 
 " 
 
 " " 
 
 " 
 
 12 " 
 
 10 
 
 21 ": 8128 
 
 " 
 
 " " 
 
 " 
 
 12 " 
 
 8 
 
 2 95384 38 . 9027 . 02700304 
 
 22 "10160 
 
 " 
 
 " '* 
 
 " 
 
 14 • 
 
 6 
 
 3 . 3645745 . 3037 .03200424 
 
 2310 4 80 
 
 15 
 
 17 1 
 
 -.") ' ') 
 
 15 1 
 
 -15 3 . 36|46245 . 50 15 . o! 1400 176 
 
 24 " 6120 
 
 " 
 
 *' '* 
 
 '• 
 
 15 " 
 
 12 
 
 ■} . 75498 49 . 6025 . 0:2200288 
 
 25 "i 8160 
 
 ** 
 
 " *' 
 
 " 
 
 15 " 
 
 12 
 
 4 . 1 1 522,53 . 5037 . 03200424 
 
 26 " 10200 
 
 *' 
 
 " " 
 
 *' 
 
 18 " 
 
 10 : 
 
 t . 70577,60 . 5047 . 04000536 
 
 27 "12240 
 
 (t 
 
 " '• 
 
 " 
 
 IS " 
 
 8 
 
 > . 1066066 . 8062 . 5000696 
 
 2812 4| 96 
 
 IS 
 
 21) 1 
 
 41.; 
 
 18 " 
 
 15 4.6264762.8020.01800232 
 
 29 " 6144 
 
 *' i 
 
 
 " 
 
 IS " 
 
 12 5 . OS GS5 67 . 60 35 . 2S00 392 
 
 30 ") 8192' 
 
 «• 
 
 *' " 
 
 " 
 
 S " 
 
 12 5.50 
 
 70871.7045.04000520 
 
 31 "10240 
 
 *' 
 
 " " 
 
 *' ' 
 
 >() " 
 
 10 6.02 
 
 759 78. 00 62. 050C J 696 
 
 32 "122881 
 
 1 
 
 
 
 >0 " 
 
 8 6 . 55 838 85 . 00 75 . 6500 860 
 
 , . I ^ 
 
COXCRIiTR CVIA'RRTS ASD TRUST I. ES. 207 
 
 TABLE VIII— Continued 
 
 REINFORCED CONCRETE, DOUBLE BOX, RAILROAD 
 
 CULVERTS— SLAB COKsIRUCTION 
 
 TO ACCOMPANY FIGURE 44 
 
 10 II.H k 1.5 ft. Hank, a) ft. Hank. :«» fl. Hank. 40 ft. Hank. .V) ft. Hank. 
 
 B 
 
 1 
 
 200 
 
 
 I 
 
 5 
 
 1 
 
 s 
 
 J 
 
 "' 
 
 ^ 
 
 5 
 
 J 
 
 
 \ 
 
 54 
 
 269 
 
 66 
 
 335 
 
 99 
 
 w 
 
 - 
 
 610 
 
 l.-)9 
 
 7.50 
 
 
 m 
 
 475 
 
 I.i9 
 
 1 
 
 m 
 
 201 
 
 51 
 
 272 
 
 66 
 
 341 
 
 96 
 
 482 
 
 126 
 
 623 
 
 156 
 
 763 
 
 2 
 
 Wh 
 
 3 IT) 
 
 50 
 
 434 
 
 65 
 
 551 
 
 95 
 
 789 
 
 125 
 
 1029 
 
 155 
 
 1269 
 
 3 
 
 32 
 
 347 
 
 47 
 
 486 
 
 62 
 
 625 
 
 92 
 
 905 
 
 122 
 
 1180 
 
 152 
 
 1470 
 
 4 
 
 29 
 
 3cSl 
 
 44 
 
 542 
 
 59 
 
 706 
 
 89 
 
 1031 
 
 119 
 
 1356 
 
 149 
 
 1686 
 
 5 
 
 ;i') 
 
 414 
 
 50 
 
 569 
 
 65 
 
 729 
 
 95 
 
 1064 
 
 125 
 
 1384 
 
 155 
 
 1674 
 
 (> 
 
 32 
 
 447 
 
 47 
 
 627 
 
 62 
 
 807 
 
 92 
 
 1172 
 
 122, 
 
 1522 
 
 152 
 
 1882 
 
 7 
 
 29 
 
 471 
 
 44 
 
 676 
 
 59 
 
 881 
 
 89 
 
 1286 
 
 119 
 
 1696 
 
 149 
 
 2106 
 
 8 
 
 2« 
 
 505 
 
 41 
 
 740 
 
 56 
 
 970 
 
 86 
 
 1440 
 
 116 
 
 1900 
 
 146 
 
 2370 
 
 9 
 
 :}4 
 
 535 
 
 49 
 
 729 
 
 64 
 
 939 
 
 94 
 
 1337 
 
 124 
 
 1747 
 
 154 
 
 2147 
 
 10 
 
 :n 
 
 555 
 
 46 
 
 780 
 
 61 
 
 1009 
 
 91 
 
 1459 
 
 121 
 
 1909 
 
 151 
 
 235!t 
 
 11 
 
 '_'S 
 
 579 
 
 44 
 
 849 
 
 58 
 
 1079 
 
 88 
 
 1589 
 
 118 
 
 2089 
 
 148 
 
 2579 
 
 12 
 
 2:) 
 
 (i22 
 
 40 
 
 906 
 
 55| 
 
 1196 
 
 85 
 
 1766 
 
 115 
 
 2316 
 
 145 
 
 2906 
 
 13 
 
 
 
 34 
 h6 
 
 984 
 1094 
 
 49 
 61 
 
 1344 
 1414 
 
 79 
 91 
 
 2044 
 2044 
 
 109 
 121 
 
 2754 
 2684 
 
 139 
 151 
 
 3465 
 3324 
 
 14 
 
 :n 
 
 779 
 
 15 
 
 25 
 
 802 
 
 40 
 
 1172 
 
 55 
 
 1532 
 
 85 
 
 2262 
 
 115 
 
 2992 
 
 145 
 
 3712 
 
 16 
 
 
 
 34 
 
 1244 
 
 49 
 
 1684 
 
 79 
 
 2544 
 
 109 
 
 3414 
 
 1.39 
 
 4264 
 
 17 
 
 
 
 28 
 
 1326 
 
 43 
 
 1856 
 
 73 
 
 2916 
 
 103 
 
 4086 
 
 133 
 
 5036 
 
 18 
 
 lioiOTU 
 
 45 
 
 1528 
 
 60 
 
 1998 
 
 90 
 
 2918 
 
 120 
 
 3848 
 
 150 
 
 4768 
 
 19 
 
 
 
 40 
 
 1586 
 
 55 
 
 2096 
 
 85 
 
 3106 
 
 115 
 
 4116 
 
 145 
 
 5096 
 
 20 
 
 
 
 34 
 
 1624 
 
 49 
 
 2204 
 
 79 
 
 3364 
 
 109 
 
 4.544 
 
 139 
 
 5654 
 
 21 
 
 
 
 28 
 
 1684 
 
 43 
 
 2364 
 
 73 
 
 3724 
 
 103 
 
 5074 
 
 133 
 
 6424 
 
 22 
 
 :joi-):i6 
 
 45 
 
 2226 
 
 60 
 
 2896 
 
 90 
 
 4276 
 
 120 
 
 5596 
 
 150 
 
 6976 
 
 23 
 
 
 
 39 
 
 2218 
 
 54 
 
 2968 
 
 84 
 
 4458 
 
 114 
 
 5i»38 
 
 144 
 
 740S 
 
 24 
 
 
 
 33 
 
 2184 
 
 48 
 
 2984 
 
 78 
 
 4584 
 
 108 
 
 6174 
 
 138 
 
 7774 
 
 25 
 
 
 
 27 
 
 2166 
 
 42 
 
 3066 
 
 72 
 
 4886 
 
 102 
 
 6786 
 
 132 
 
 8536 
 
 26 
 
 
 
 
 
 36 
 
 3096 
 
 66 
 
 5096 
 
 96 
 
 7098 
 
 126 
 
 9096 
 
 27 
 
 2920.-12 
 
 44 
 
 2982 
 
 59 
 
 3932 
 
 89 
 
 .5812 
 
 119 
 
 7882 
 
 149 
 
 9532 
 
 28 
 
 
 
 38 
 
 2950 
 
 53 
 
 3960 
 
 83 
 
 5992 
 
 113 
 
 7990 
 
 143 
 
 10040 
 
 29 
 
 
 
 Z2 
 26 
 
 2800 
 2716 
 
 47 
 
 3920 
 3896 
 
 77 
 71 
 
 6020 
 6216 
 
 107 
 101 
 
 8170 
 8596 
 
 137 
 131 
 
 10320 
 10896 
 
 30 
 
 
 
 31 
 
 
 
 
 
 35 
 
 3830 
 
 65 
 
 6370 
 
 96 
 
 8960 
 
 125 
 
 11460 
 
 32 
 
 
 
 
 
 
 
/y 
 
 I i 
 
 t 
 
 I 
 
 208 COXCRI-.TI'. liRIDGHS ,1X1) CULVllRTS. 
 
 TABLE IX 
 
 REINFORCED CONCRETE, SINGLE BOX, RAILROAD 
 
 CULVERTS— BEAM AND SLAB CONSTRUCTION 
 
 TO ACCOMPANY FIGURE 45 
 
 
 \€ 
 
 - 1^ 
 
 ■.~ IE: 
 
 lop and Ituttom 
 
 I Si|uarc 
 KuIh. 
 
 S<iuare 
 I Kwla. 
 
 I>r Lineal ft. 
 
 ■3 
 
 2 Portak 
 
 "■-a" 
 
 I- *. I 
 
 J3 
 
 J III 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17i 
 
 18 
 
 19 
 
 20 
 
 21 
 
 22 
 
 23 
 
 24 
 
 25i 
 
 26! 
 
 27 
 
 28 
 
 29 
 
 30 
 
 8 4 
 " 6 
 
 " 8 
 
 3212314 
 
 48 •' "•• 
 64 " "•' 
 " 10 80 " 'V 
 10 4 4014364 
 
 60 " 'V 
 80 " "," 
 
 V 
 
 1', 
 
 •' 6 
 
 "10100 
 "12120 
 12 4 4816404 
 
 "6 72 " "i" 
 " 8 96 " ";• 
 "10120 " ",' 
 "12144 " "i" 
 M 6 8418505 
 "-8112 ", "i" 
 "10140 " ■"' 
 "12168' " "i" 
 16 6)' 9620546 
 "• 8128 "i "i" 
 "10160 " "i" 
 " 12192 " " " 
 18 6 108 22 587- 
 "! 8144 ", "i" 
 "10180 " "I" 
 "il2216' "i "i" 
 20 6 12024 028- 
 "I 8160 "I "i" 
 "10200 " "," 
 " 12240: "I "i" 
 
 -1' 
 
 — 1' 
 
 12123 
 "174 
 "224 
 " 274 
 14133 
 "164 
 "214 
 "264 
 "304 
 16143 
 " 154 
 "194 
 "244 
 "294- 
 18194 
 " I "214 
 "264- 
 " I "315 
 I's 20204 
 " , "204 
 " ! "254- 
 " "295 
 l's22204 
 " "204- 
 " "244— 
 " "285 
 I ,, 24204 - 
 " i "204 
 " ! "234 
 " i "275— 
 
 1 
 
 - Jsl 
 -1 1 
 
 - ="4! 
 
 - -'41 
 
 - ^1 
 -1 1 
 
 - ^41 
 
 - ^1 
 
 - ".1 
 -1 2 
 
 -l's2 
 
 - Js2 
 1 12 
 
 -11^2 
 -1'm3 
 
 ■ J«2 
 
 I |2 
 l'^3. 
 
 II s3, 
 
 ■ J«3. 
 1 |3 
 1'.3 
 l's4 
 
 s3. 
 1 14. 
 lVs4, 
 13-8 4. 
 
 .9817714 
 
 .1020616 
 
 .2724019 
 
 .4827822 
 
 .2622319 
 
 .3726021 
 
 .5629624 
 
 .7833627 
 
 00:?8131 
 
 SI 23 
 
 .0. >1926 
 
 .88 35729 
 
 .1040332 
 
 .3745237 
 
 .3538834 
 
 .5545638 
 
 8450442 
 
 .0855946 
 
 .8249142 
 
 .9854044 
 
 2558948. 
 
 5064753 
 
 3257249. 
 
 4762452 
 
 7467756 
 
 02 74561 
 
 8866258. 
 
 0572461. 
 
 3077665. 
 
 6084270. 
 
 .6 9.4 1250 125 
 
 .9 15.7 2060 206 
 
 .7 23.2 3050 305 
 
 .9 32.0 4220 432 
 
 1 13.5 1800 LSO 
 .3 21.2 2800 280 
 
 3 30.6 4050 405 
 .6 41.5 5500 550 
 .1 53.5: 7100 710 
 .8, 16.5 2200 220 
 
 2 25 8 3400 340 
 2; 36 . 5 4800 485 
 
 .9 52.5: 7000 700 
 .1 64 0: 8500 850 
 .3i 40.0, 5300 530 
 .5^ 55.0 7200 730 
 .8 72.0 9600 960 
 9 91.0121001210 
 2, 49 0| 6500 650 
 . 4! 64 0- 8500 850 
 .4 84.0111001110 
 7106.0140001400 
 4j 60.0, 8000, 800 
 8 66.0 8800 880 
 99.0131001310 
 8122.0162001620 
 71 71.0 9400 940 
 2! 93.0123001230 
 4117.0155001550 
 2144.0191601910 
 
 \iL^i 
 
 **feti^.^aasP!R-=!5£ffiit^^r •''-swi^as- 
 
COSCRFTF. CVWERTS AND TRESTLES. 209 
 
 TABLE IX— Continued 
 
 REINFORCED CONCRETE, SINGLE BOX, RAILROAD 
 
 CULVERTS-BEAM AND SLAB CONSTRUCTION 
 
 TO ACCOMPANY FIGURE 45 
 
 10 ft. Rank 15 ft. Dsnk.l^O ft. Rank.'so ft. Rank.! 40 ft. Rank. 
 
 M ^ Jl 
 
 s * s „• 
 
 ? S S I 
 
 Ji i Js c 
 
 c 
 
 
 6 'i 
 
 27 535 
 
 2.^ 656 
 
 25 820 
 
 42 735 
 36 816 
 
 30 895 
 
 ! 
 
 40 940 
 ' 34 1005 
 ! 28 1085 
 
 i 
 
 . .'■ 
 
 40 1170 
 34 1230 
 28 1300 
 
 31 1590 
 25 1690 
 
 \'\ '" 
 
 30 
 28 
 28 
 
 ....1 
 1920 
 
 .... 
 
 2i80 
 
 25S0 
 
 57 
 51 
 
 973 87 
 1066 81 
 45 1190; 75 
 39 1317 69 
 55 1230 85! 
 49 1320! 79 
 43 145.., /3 
 
 37 1570 
 
 31 1675 
 
 55 1530 
 
 49 1620 
 
 43 1735 
 
 67 
 61 
 85 
 79| 
 73 
 
 37 1910 67 
 31 2000| 61 
 46 2110 76, 
 40; 2270 70 
 34 2420 
 28 2520 
 45 2550 
 39 2570 
 33 2700 
 27, 2850 
 43 2920 
 37: 2830 
 31 3050 
 25 3160 
 43 3460 
 37 3500 
 3i; 3570 
 251 3660 
 
 64; 
 
 58; 
 
 75 
 
 69 
 
 63 
 
 57, 
 
 73 
 
 67 
 
 61 
 
 55; 
 
 73i 
 
 67 
 
 61 
 
 55 
 
 «» 
 
 A 
 
 » 
 
 
 Xi 
 
 
 1 
 
 a 
 
 s 
 
 o 
 
 1403 
 
 1566 
 
 1775 
 
 2002; 
 
 1800| 
 
 1960 
 
 2175 
 
 2400 
 
 2610 
 
 2240 
 
 2500 
 
 2605 
 
 2900 
 
 3110 
 
 3130i 
 
 3430; 
 
 3710 
 
 3920I 
 
 3810 
 
 3900J 
 
 4080 
 
 4450J 
 
 4400 
 
 4410 
 
 4720! 
 
 £020| 
 
 520O1 
 
 5330I 
 
 55361 
 
 576(^ 
 
 50 ft. Rank. 
 
 147 2283 1 
 141 2576 2 
 135: 2955 3 
 129 3372 4 
 145 2940 .'> 
 139 3230, 6 
 133| 3625 7 
 127; 4050 8 
 121 4510! 9 
 145 367010 
 139; 398011 
 133 435512 
 127: 485013 
 121, 535014 
 136 5180,15 
 13f .-,73016 
 124 626017 
 118j 671018 
 135 6350:19 
 129, 6550,20 
 123 703021 
 117i 7650122 
 133| 7350;23 
 1271 •'530,24 
 1211 806025 
 115i 872026 
 1331 8740:27 
 127 8980,'28 
 121, 945029 
 85 78601 115 991030 
 
 117 1843 
 111 2076 
 
 105 2365 
 99 2692 
 
 115 2360 
 
 109: 2600 
 
 103; 2905 
 
 97] 3220 
 
 91 3530 
 
 115 2950 
 
 109 3190 
 
 103 3485 
 
 97 3870 
 
 91 4210 
 
 106 4150 
 100 4580 
 
 94 5000 
 
 88 5310 
 
 105 5070 
 
 99 5250 
 
 93 
 
 5610 
 
 87' 
 
 6050 
 
 103! 
 
 5850 
 
 97 
 
 5980 
 
 91 
 
 6410 
 
 85 
 
 6870 
 
 103 
 
 6950 
 
 97 
 
 7180 
 
 91 
 
 7450 
 
f 
 
 i^ 
 
 :io 
 
 coxcREiii HRinci.s .i\n cii.rnRis. 
 
 TABLE X 
 
 REINFORCED CONCRETE, DOUBLE BOX, RAILROAD 
 
 CULVERTS BEAM AND SLAB CONSTRUCTION 
 
 TO ACCOMPANY FIGURE 45 
 
 H 
 
 It 
 
 1' i'S 
 
 
 1 
 
 1 ^.1 
 
 T"|) iimI Hottom 
 
 __ 
 
 -5 [ 
 
 ■J- r - ^ 
 
 1 ' i ¥' 
 
 
 1(..,|.. 
 
 1 
 
 s 
 
 4 M 15 
 
 12 
 
 2!M 1" 
 
 2 
 
 •■ 
 
 !)0 " 
 
 " 
 
 *• " 
 
 :i 
 
 " 
 
 s 12s •• 
 
 " 
 
 •' •• •' 
 
 4 
 
 " 
 
 10 100 " 
 
 " 
 
 .. .1 n 
 
 
 10 
 
 4 SO 15 
 120 " 
 
 14 
 
 .TU Ps 
 
 7 
 
 S 
 
 -. 
 
 S 100 •' 
 
 10 2;)o " 
 
 
 
 
 
 
 " 
 
 >2 240 • 
 
 " 
 
 " " " 
 
 1(1 
 
 12 
 
 4 00 IS 
 
 10 
 
 ;{T 4 r , 
 
 11 
 
 " 
 
 144; •• 
 
 
 " " " 
 
 1-2 
 
 *' 
 
 S 102, " 
 
 " 
 
 " " *' 
 
 U 
 
 " 
 
 10 240; " 
 
 
 .. .. .1 
 
 14 
 
 " 
 
 12 2SS| " 
 
 
 " '* " 
 
 1.-. 
 
 14 
 
 () 1()S' IS 
 
 IS 
 
 475 1', 
 
 10 
 
 •■ 
 
 S 2241 " 
 
 
 
 17 
 
 " 
 
 10 2S0 " 
 
 
 
 IS 
 
 '* 
 
 12 ;';{« " 
 
 ** 
 
 " " " 
 
 19 
 
 10 
 
 1"? 20 
 
 20 
 
 500 l\ 
 
 20 
 
 1 
 
 S 2.) "^ 
 
 " 
 
 *' " " 
 
 21 
 
 "i 
 
 10 :{2() " 
 
 " 
 
 t( it a 
 
 22 
 
 tt ' 
 
 12 ;JS4 " 
 
 ** 
 
 ** " " 
 
 24 
 
 IS 
 
 210 22 
 
 22 
 
 54 7 -I's 
 
 24 
 
 "1 
 
 S 2SS " 
 
 " 
 
 " " " 
 
 25 
 
 "' 
 
 10 soo •' 
 
 " 
 
 " " " 
 
 26 
 
 " 
 
 12 482 " 
 
 11 
 
 t< •< ti 
 
 27 
 
 20 
 
 240 24 
 
 24 
 
 5SS— 1'^ 
 
 2S 
 
 
 S ;i20 • 
 
 
 
 29 
 
 " 
 
 10 400 •• 
 
 *' 
 
 •• '* *' 
 
 .SO 
 
 " 
 
 12 4S0 " 
 
 
 *' " " 
 
 Silk'.'*. 
 
 IVr l.iti. I'. 
 
 12 
 
 H 
 
 20 
 
 K0.IS. 
 
 10 14.{— 
 
 IS 
 
 12:i 
 
 
 '." 
 
 1 so 
 
 S20 20 S 
 
 174 
 
 — 
 
 
 , 2.05 
 
 .S4S .SO S 
 
 224 
 
 _ 
 
 ' H 
 
 2.S2 
 
 .sss s.s 
 
 27 4 
 
 -1 
 
 
 2 01 
 
 4SS S7 9 
 
 i:{;{ 
 
 - 
 
 '4 
 
 2.0.S 
 
 405 SS (» 
 
 104- 
 
 _ 
 
 .'» 
 
 2.SS 
 
 440 SO S 
 
 214 
 
 _ 
 
 s 
 
 2.02 
 
 4S9 40 1 
 
 20 4 
 
 
 
 2.91 
 
 5S7! 44 4 
 
 SO 4 
 
 - 1 
 
 H 
 
 S.42 
 
 .■)S7| .50 S 
 
 14. S- 
 
 _ 
 
 ',' 
 
 S . (K) 
 
 510 -14 < 
 
 15 4- 
 
 — • 
 
 ;,' 
 
 :i . 25 
 
 /)55, IS 
 
 19 4 
 
 ^. 
 
 .s 
 
 :i.52 
 
 601 .52 2 
 
 214 
 
 
 
 S . SO 
 
 0,50 .57 2 
 
 2<> 4 - 
 
 -1 
 
 s 
 
 4,21 
 
 710 020 
 
 194- 
 
 — 
 
 s 
 
 4 . .SS 
 
 767 65 . 5 
 
 214 
 
 -1 
 
 
 4 71 
 
 S25 70.0 
 
 21 i 4 
 
 1 
 
 i 
 
 5 . (K) 
 
 SSI 75.0 
 
 .SI 5 
 
 1 
 
 H 
 
 5 . SS 
 
 940 SO 7 
 
 20 4 
 
 - 
 
 s 
 
 .'J.2S 
 
 911 7S 2 
 
 20 4 
 
 
 
 5.51 
 
 90S S2.1 
 
 254 
 
 
 H 
 
 5.90 
 
 1024 SS.O 
 
 29 5 
 
 1' 
 
 H 
 
 6 . SO 
 
 loss 94.0 
 
 204 
 
 _ 1 
 
 S 
 
 6.25 
 
 1069: 9S.0 
 
 204- 
 
 -1 
 
 
 6 . 55 
 
 11. SO 97 
 
 24 4- 
 
 -11 
 
 S 
 
 6.95 
 
 1195102 5 
 
 28 5- 
 
 -1' 
 
 ^ 
 8 
 
 7..SS 
 
 126S 109.2 
 
 204- 
 
 _ ' 
 
 s 
 
 7.40 
 
 1251 109 
 
 204- 
 
 -1 
 
 
 7.70 
 
 iS2-.' 114.0 
 
 2S4- 
 
 -1 ' 
 
 s 
 
 S.IO 
 
 1S95119 5 
 
 27 .5- 
 
 -1' 
 
 s 
 
 8 . 50 
 
 1467126 5 
 
 24 204— 
 
cosch'i/n: cri.riiNTS .i\n r rustles. 
 
 •11 
 
 TABLE X— Continued 
 
 REINFORCED CONCRETE, DOUBLE BOX, RAILROAD 
 
 CULVERTS -BEAM AND SLAB CONSTRUCTION 
 
 TO ACCOMPANY FIGURE 45 
 
 :' r.irtiii. 
 
 'lOft.Bank.'l.Wt. 
 
 RHiik. 
 
 20 ft. HBiik. nofl. Rank. 40 ft. Unnk.-V) ft. Hank. 
 
 ••■=•••£ 
 
 ■' ^ .5 ' — c — 
 
 ^ *► — '-^ — 
 
 14 :< HMO 
 •_'.> (1 ;{(MK) 
 
 ;i2 4 4;UK) 
 
 l:! oTCK) 
 
 .'(1 4 2720 
 
 ;il .-) 42(K) 
 
 4:{ 2 .')72() 
 
 .-,:{ .-) 7 UK) 
 
 72 ».")(«) 
 
 •Jii :U.")0 
 
 :{,s c. '>1(M» 
 
 .Mr:. 7 KM) 
 
 7;{ () !»7(M) 
 .S7 11»)0 
 .-.4 (t 7200 
 71 94(h) 
 !t| (112100 
 111 ()147(M) 
 
 I 72 (I \nm). 
 
 5 02 012200 
 117.015:)00| 
 14H 0190001 
 
 91 012100j 
 10.-) 013900 
 145 019200J 
 Ho 023200 
 
 9S. 013000; 
 142 018800 
 17(i 023400 
 211.028100 
 
 101 
 
 3(K) 
 
 430 
 
 r)70 
 
 272 
 
 420 
 
 572 
 
 710 
 
 950 
 
 345 
 
 510 
 
 710 
 
 970 
 
 lUi 
 
 720 
 
 940 
 
 1210 
 
 1470 
 
 960 
 
 1220 
 
 1550 
 
 19(K); 
 
 1210 
 
 1390 
 
 1920 
 
 2320 
 
 1300' 
 
 18S0 
 
 2340 
 
 2810, 
 
 27 915 
 
 1(H) I 
 
 251450 
 
 42 
 
 3() 
 30 
 
 40 
 34 
 
 28 
 
 40 
 34 
 
 28 
 
 1350 
 1380 
 1440 
 
 1590 
 l(>(i() 
 1(592 
 
 2075 
 2140 
 2170 
 
 31 
 
 2750 
 2700 
 
 57 
 51 
 45 
 39 
 55 
 49 
 43, 
 37i 
 31! 
 55 
 49 
 43 
 37 
 31 
 4() 
 40i 
 34 
 
 1720 87 
 18701 81 
 1940 75 
 20401 69 
 
 30 3310 
 
 28 3810 
 
 2S 4350 
 
 28 
 45 
 39 
 33 
 27 
 43 
 37 
 31 
 25 
 43 
 37 
 31 
 25 
 
 2082 
 2200 
 2292 
 2340 
 2520 
 2785 
 
 2 !»()()' 
 
 2950, 
 
 3090 
 
 30701 
 
 3720! 
 
 3760i 
 
 3760| 
 
 3720! 
 
 4480' 
 
 4420, 
 
 4450! 
 
 4430 
 
 5210 
 
 4960 
 
 5100 
 
 5050 
 
 6000 
 
 6090} 
 
 6040 
 
 85: 
 
 79 
 73 
 67j 
 61 
 85 
 79 
 73 
 67 
 61 
 76 
 70 
 64 
 58 
 75 
 69 
 63 
 57 
 73 
 67 
 61 
 55 
 73 
 67 
 61 
 
 2530 117| 
 2750111 
 2940,105 
 3180 99 
 3072115; 
 3280109 
 34921031 
 
 36(50 
 4020 
 
 59701 55 
 
 4105115 
 4310109 
 4510103 
 4790J 97 
 49201 91 
 5(580106 
 5890100 
 60101 94 
 6120' 88 
 6860 105 
 6S70 99 
 7050: 93 
 7250 87 
 8010 103 
 7890 97 
 8170 91 
 8320 85 
 9250103 
 9480 97 
 9590 91 
 9760 85 
 
 4140 
 
 45(>0 
 
 4940 
 
 5490 
 
 5022 
 
 5470 
 
 5892 
 
 (5310 
 
 7050 
 
 674510 
 
 71(5011 
 
 7(5(5012 
 
 817013 
 
 8(5(5014 
 
 962015 
 
 3330147 
 
 3(550141 
 
 3940135 
 
 4320129 
 
 4040 145 
 
 1370139 
 
 4692133 
 
 .5010127 
 
 5550121 
 
 5445 145 
 
 57601391 
 
 6060 133J 
 
 6480 127i 
 
 67(50 121| 
 
 7640136 
 
 80001301014016 
 
 82301241051017 
 
 8520118 1092018 
 
 92101351156019 
 
 9321)1291182020 
 
 97001231235021 
 100501171290022 
 108101331351023 
 107901271369024 
 113201211432025 
 116201151482026 
 1250013315X0027 
 129801271638028 
 132401211674029 
 135101151731030 
 
:| 
 
 I J 
 
 ^ 
 
 I 
 
 mi:, 
 
 £ 
 
 S 
 
 35 
 
 
 ^ £1 
 
 a s 
 
 
 T T, 
 
 a a 
 
 i i 
 
 I g 
 
 f i 
 
 
 if 
 
 — L. 
 
 I 3 
 
 
 2 
 
 O 
 
 U 
 
 X 
 
 y. 
 
 
 
 5f ^ 
 
 
 
 
 
 ■rf^sfSfivi.: :«^..-yr a.*!*!? ^'^ ■ s^.^; ;:^!§^i£*% 
 
COS-CRRTi: CrUl-RTS JXD TRESTLES. 213 
 
 X 
 
 r. 
 
 Cost of Reinforced Concrete R. R. Culverts. 
 
 Singli' Track Banks. 
 
 For-i- kvctaijgiUar Box. 
 
 BrtHf Pricfx. 
 
 ('i)iicrfte ill place $H.OO cr yd. 
 Steel in place 4c per lb. 
 
 Jo' too I So 
 
 Fig. 46. 
 
j^"i'- 
 
 til 
 
 i.i 
 
 I:'': 
 
 ^■i 
 
 i 
 
 ll'llil 
 
 I: i 
 
 lU 
 
 COXCRETIi BRIDGES .WD CriAT.RTS 
 
 (lonhio or singlo. Culverts of these forms cost less 
 for ixny given area than if made with ,vi(ler ami 
 shallower openings. The reason for this is due to 
 the fact that for wider openings the thiekness of 
 .•()V(>r slabs increase more rai.idly than the thickness 
 of side walls. 
 
 From the comparative cost chart. Figure 4fi. the 
 follov.ing conclusions are deduced: 
 
 Single box slab culverts are economical for areas 
 up to 50 sfpiare feet. 
 
 Double box slab culverts are economical for areas 
 up to 7") s(|uare feet. 
 
 Single box beam and slal) culverts are ecoiu.mical 
 for areas up to 12.") .s(|uare feet. 
 
 Doul)le box beam and slab culverts are economical 
 for areas above 125 square feet. 
 
 Wide, flat culverts cost somewhat more than nar- 
 row and higher ones of the same area, but they are 
 nu>re effective ami offer less resistance to the free 
 flow of water. For a bank of any given height, the 
 loAv culvert will have a longer barrel than a higher 
 one. though this will be offset to sonu' extent by the 
 sh(nner length of wing walls. There is little or no 
 economy in reducing the length of culvert barrel by 
 using high end parapet retaining walls, as material 
 thus used might better be employed in increasing 
 the length of culvtit barrel, thereby causing shorter 
 wing walls. 
 
 Tn proportioning the thickness of wing walls, 
 M h( n these wings are placed at a considerable angle 
 to the culvert face, the stability of the wing wall is 
 
 "^1% 
 
 mjsmm^'^-^'^ssm^ 
 
COXCRL E CULILRTS AXU I RUSTLES. 215 
 
 11u'rel)y jjrcatly iiKToasod. and it is fronorally safe to 
 make tlie l)a.se thickness of the ■\viiigs near their 
 ('((iiiieetion to the tnient from 20/^ to 2y/( of 
 
 the Aving wall heijrht. Towards the ends wiiere 
 the wings reeeive no support from the eiilveit 
 sides, the width or thickness of wing wall base 
 should then be 40% of the unsupported height. 
 
 The size of beams and slal)s given in Tables VIF, 
 \'1II, IX and X are for culvert barrels sul)jected to 
 the loads specified, which occurs at and near the 
 eenter of the embaidiment. For long culverts, thest; 
 sizes may be rediu-ed towards the ends where the 
 loads are somewhat less than at the middle. 
 
 ^Vhere the nature of the soil will permit, some 
 economy nujy result by omitting the reinforced con- 
 crete pavement slab, and r.ubstituting ot^'set foot-' 
 ings under the side walls, as shown on the concrete 
 trestle plans. Figures aS to (io inclusive, using • 
 cobble stone pavement, if recpiired. 
 
 There is less probability of debris and drift col- 
 lecting when the culvert bottom is curved or disheil 
 out at the center, than when built flat or horizontal 
 bctAveen the two side walls. Hox culvert corners 
 should be l)ra('ed with straight or ciu-ved c(»rn(>r 
 fillets, reinforced with diagonal rods, as shown on 
 tile tyjiical drawings. 
 
 Tt is unnecessary to increase the thickness of side 
 walls from the top to the bottom, excepting perhaps 
 for high culverts, and eveii tlicn '^inep tlic condition 
 of earth pressure on the side walls is uncertain, any 
 efTort at ultra-refinement is unnecessary. 
 
216 
 
 COX'CRIiTE HRimmS AM) CCLIHRTS. 
 
 "Walorproofiiij,' slioiild be used on the exterioi' 
 surfaces of the roof mid sides to provont drainage 
 ■water from soakinjjj into the eoiierete. Tlie ad 
 hosion of eoncrete to steel is decreased about IOC 
 when the eoncri'te is eontinnously water soaked, 
 and this decrease can l)e avoided by finisliing the 
 outer surfac(> of the top and sides with a coating of 
 neat cement or otlier waterproof material. 
 
 Comparative Costs of Culverts of Various Forms, 
 Figure 47 shows the comparalive costs of reiid'orced 
 eoncrete box railroad culverts compared Avith corre- 
 sponding costs of culverts of other forms. The 
 chart gives the total cost of culverts for an end)ank- 
 ment 20 feet in heiglit. and for cross-sectional areas 
 varying from .") to 200 s((nare feet. 
 
 The new reinforced concrete l)ox culverts, the co-it 
 of which are shown by the heavy line nund)er 10, 
 are more economical than any other jx-rmanent cul- 
 verts, and cost but little more than wooden l)ox 
 culverts. They rangi- in cost from 'M) to oO cents 
 l)er s(|nare foot of sectional area. 
 
 The various culverts, the costs of whicli ai-e shown 
 in Figure 47 by lines. ar(> as follows: — 
 
 Xo. 1 srives the cost of standard cast iron pipe 
 culverts, which are suitable only for small oi)enings, 
 and while they can l)e quickly placed, and some- 
 times inserted inside of Avorn-out temporary wooden 
 box culverts, they are not economical. 
 
 Xo. 2 are reinforced concrete box culverts with 
 bottoms, similar to those in use on the rnion Pacific 
 and Southern Pacific railroads. 
 
 W^^^^*^ 
 
 'a.:.*,^ 
 
 '«i^i,a*«....,i;'#-*-: 
 
 '■■'■^^■: 
 
coxCREiE cn.rr.RTS .ixn ihT.srij-s. 217 
 
 Comparative Costs of Culverts. 
 
 STNGLK TRACK RAILROAD. IIKIGIIT OK HANK 20 IKKT. 
 
 , 1 Cast iron pipe. 
 
 2 Reinforced concrete box, witli bottoms. 
 
 H Kali top concrete box. 
 
 4 Reinforced concrete iirch. 
 
 5 Solid concrete arch. 
 
 6 Stone arch, Baker's standard. 
 
 7 Reinforced concrete box, no bottoms. 
 H Rubble stone box. 
 
 9 \V<M)d box. 
 It) Reinforced concrete box, new standard. 
 
 
 
 t 
 
 
 : yzzz: 
 
 J 
 
 T" y 
 
 1 '' &■■! 
 
 - i ^^ A^ - 
 
 ,,^. -- ^Cl^ - 
 
 .^ <>.*.-^»^ 
 
 /_ _^^^^^' : 
 
 /- .2^i^___ _ 
 
 /. 4* ^* _ . 
 
 - -^/L ^i.^,.^.it. 
 
 ^ tf.^,^^ ^ r- 
 
 y ^■i^ti ^ ° ' 
 
 /^-^^^ ,^ 5 : 
 
 /i-"'^^^^'' < 
 
 l^^l<7% ^y.,***. 
 
 y^ <-y ,A J-*%°^ 
 
 -^b^^^,^-,,. — __ "i?" 
 
 // ^ >'' y / ^^p." 
 
 222", ^"1?" *•'' :~_: 
 
 _ : iz^? ;^^3r_ ?T _ __ : 
 
 
 iS ^^' ^' 
 
 / d\i rf ^ 
 
 vf" ^ y 4. 
 
 --7--7^7-i^ ^- -p M^r 
 
 --?-7?2^'=--3'' 4- ''^^ 
 
 _3" :i^_~:z ~ ' 1 "ii: 
 
 _[ -^"^ i^?-t - - -- 
 
 -.^t^ At-- - - 
 
 / yiJnJn^ 
 
 i^Um- - - - 
 
 *^7.2" ' 
 
 _i^- _ ii": :. 
 
 
 
 Tor St. A^m/t 00 Wifrg/rwitY. 
 
 Fig. 47. 
 
 /So* 
 
 ZOO 
 
 Ain- . "iti'S'-:-- - W'-'^ "■■■ 
 
i I 
 
 ' I i 
 
 Ml 
 
 M 
 
 
 11 
 
 il, 
 
 21^ coxch'i-.Tn BRincis .ixn cri.rr.RTs. 
 
 \(). ;5 iifc coiicrctf rail lop <mi1 verts lijiviii«r slabs 
 J.") 1(» IS iiiclics thick, find reinforced with rails 
 spaced IS inches apart for a O-foot span. 10 inches 
 apart for an S-foot span, and C> inches apart for a 
 lO-foot span. 
 
 Xo. 4 are reinforced concrete arches, similar to 
 lliose in iis<' on tin' ahove named railroads. 
 
 Xo. T) are concrete arches withont reinforcement. 
 
 Xo. f) are se<;mental stone arcli culverts as pro- 
 posed by Mr. IJalvcr in his book on ^NFa.sonry Con- 
 stiMiction. 
 
 Xo. 7 are reinforced concrete box culverts, similar 
 to Xo. 2. exceptinjr that they are without bottoms 
 
 
 2:— Portals 
 
 (JoiiiTrtf 72 yds. ii ♦«.()()- $576 
 Steel a450 lbs. (</ ,01 \w 
 
 »714 
 Barrel per Un. ft. 
 Concrete itiMyda. iii( <;s.(M)- ♦ll'i 
 Steel 45»»lbs. (i( .04 IKO 
 
 ♦.''SI 
 Length for 20 ft. bank - 32. 
 Area -^ 180 aq. ft. Cost |i24a0. 
 
 t'lg. 4tt. 
 
CONCRETE CCI.rERTS .l.\l> TRESTLES. 219 
 
 and cost proportionately loss. They have offset 
 footings under the side walls. 
 
 No. 8 are rubble stone box eulverts, the kind most 
 eonnnoidy used by the railroads until recently, for 
 small openings. 
 
 No. are wooden box culverts, and while they are 
 not permanent, they have the merit of being the 
 least expensive of all. 
 
 No. 10 are the new standard reinforced concrete 
 box culverts, as shown in Figures 43, 44 and 45, 
 Ihe quantities and cost of which are given in Tables 
 YII, VIII, IX and X. 
 
 An actual cost record for building a 4-foot con- 
 crete arch culvert under a railroad embankment in 
 Idaho, during the tliirty days from June oth to July 
 J 1th, 1003, is as follows:— 
 
 Foundations contain 111 yards, and cost $5.00 per yd. 
 
 Upper part contains 137 yards, and cost 7.00 per yd. 
 
 Average cost about G.OO per yd. 
 
 Cost of whole culvert per cu. yard of concrete. 10.00 per yd. 
 
 Portland Cement used, 272 barrels. Cost 2.70 per bbl. 
 
 Foreman paid $150.00 per month. 
 
 1 Finisher paid 3.00 per day 
 
 Laborers paid 2.00 per day 
 
 4 Carpenters paid 3.00 per day 
 
 Labor cost $1723.00 
 
 Alaterial cost 830.00 
 
 Total $2553.00 
 
 Concrete made entirely from sand and gravel at rail- 
 road company's pit, without any broken stone. 
 
 Other Common Culvert Forms. Figures 48 to 57 
 inclusive, show other forms of culverts, and Table 
 
 
II '. 
 
 ■ 
 
 \ \ 
 
 
 lii 
 
 220 
 
 COXCRETE BRIDGES ASD CilA'ERTS 
 
 XI contains their ostiniated quantities and costs. 
 For the purpose of comparing these with others, the 
 costs have been estimated for lengths re(iuired 
 under a 20-foot embankment, and these costs are 
 given in Figure 47, together with their correspond- 
 ing numbers. They vary in cost from 2G to 36 cents 
 per scjuare foot of section area, for each lineal foot 
 of culvert. 
 
 Figure 48 is a reinforced concrete boxcidvertl2 
 feet high and 15 feet wide, v'th rod reinforcement, 
 similar to the new single box slab culvert. For so 
 large a section area, the slab typj is not economical. 
 
 Figure 49 is a reinforced concrete box culvert of 
 combined beam and slab construction. 12 feet high 
 
 1 ^ ''t- i 
 
 2 Portals:— 
 Concrete 74 yd8.(i?*8 (X) 
 Steel 472U lb». <tt .04 -- 
 
 Biirrelperft. 
 Concrete 5 . K yds. (ft $H.(in 
 Steel 615 Ibs.fe .04-^ 
 
 'Dgthfor 20 ft. bank 
 Area -230 square 
 CdRt = $2<)3(). 
 
 -1592 
 
 = 188 
 
 »780 
 
 $4r4 
 
 = 20.6 
 
 *67.6 
 = 32 ft. 
 feet. 
 
 Fig. rj. 
 
CONCRETE CrU'ERTS .IXD TRESTLES. 221 
 
 and 20 feet wide. For an area of this size a more 
 C'cononiieal form is secured by using a double box 
 of the same general tvpe. 
 
 Figure 50 is a beam top culvert, 12 feet high and 
 1.') feel wide. The culvert top is arched 3 feet and 
 tlie arch strength is f'onsidered when proportioning 
 
 'mm. 
 
 2 Piirfals:— 
 Concrete 88 yds. ^ $8.00 f;704 
 
 Barrel per lln ft. 
 Concretee. 1 yds. (& $8.0O=- 148.8 
 Steel 240 1bB.fe .04^ 9.6 
 t68.4 
 
 Length for 20 ft. Bank^-32 feet. 
 
 Area 161 sq. ft. Co8t = |2570. 
 
 FIk- 5lt. 
 
 tlie thickness of the culvert top. Culverts similar to 
 this have been used by the Illinois Central Railway 
 Company. 
 
 Figure 51 is a concrete box culvert with rod rein- 
 forcement similar to Figure 58, excepting that in 
 it offset footings and cobble stone pavement are 
 used instead of a reinforced concrete pavement slab. 
 
1 1 
 
 
 I 
 
 i(>Xii\'fiii: liRiinns .r:i> crirnRTs. 
 
 
 t Ourwvfn 
 
 i ro^ 
 
 ■1 Forliils: - 
 Concrete 88 yd*. ^ |S.00 *704 
 
 Barrel per lln. ft. 
 Coneretee.ayrlH. (fi »s (X) ♦49.0 
 Steel 150 Ihn. lit ,04 ti6 
 ♦•Vi 6 
 
 If foandntinn l>t depresneil in 
 own dotted, then area — 173 
 iiare feet. 
 
 Leritflh for 20 ft. bank=3a(t. 
 St |24»'U. 
 
 Fljf. r.i. 
 
 Fi<ji:ui"(' r)2 is a roint'orced coneroto box enlvort of 
 ht'iim and slab oonstruetiuii, 12 feet high and 20 feet 
 wide. For so largo an area, a donble box of the 
 same type "vvill be more eeonomical. 
 
 Figure 53 is a culvert of the same dimensions as 
 Figure 52, Avith solid conerete side walls, l)ottoni 
 cobblestone pavement, and roof reinforced with dou- 
 ble lines of 60-pound track rails,united with %-inch. 
 
 Figure 54 is a reinforced concrete arch culvert 
 with buttressed sitlo walls and slab pavement. 
 Structures similar to this are used by the Northern 
 Pacific Railroad. 
 
cnxcRFTi: criiTRTs .\\n tri-stiis. 
 
 (Jl ANJITIKS 
 
 (;i.iiiri>tHn3y>l-.»» IS.IXI IW"* 
 Steel 14500 \\>*. <« .04 SW" 
 $11M4 
 Uiirrel per lln. ft. 
 ('i.n<T(,tB4.«yd»."<»s.0O fM.H 
 StffI 7("l Ibx. (c( 04 'J8 
 
 LeiiKlli for 20 ft. biink- 'rifl. 
 Areu ■J40«(i. ft Oost*3100. 
 
 Fi<riir(> .").") is ii l)ciuii top culvrt 12 feet liigli iiiitl 
 Hi) i'tH'l wide, similar to Fit^iin- .')(). It will !»»' sceii 
 that neither of these types are eoononiieal. 
 
 Fijjure .")() is a paral 'die aicii culvert. 
 
 l'M<rure ill is a icinroreed eouerete areii culvert 
 possessiiifr jjreater merit than any other form of 
 arch culvert now in use. It contains the least 
 amount of material, the saving; hein«; chiefly in the 
 sides. :\ias(»nry arch culverts of the old type, 
 whetlier huilt of st(.ne or concrete, have the greater 
 l)art of their material in the side walls or ahutmcnts. 
 Fi<:;ure 'u is designed similar to a tunnel center, or 
 a sewer arch, and its form and light eonstruetiou 
 
w: 
 
 lii 
 
 
 llit! 
 
 i I 
 
 2l'» 
 
 loxck'inr. lih'/nar.s .ixn cn.rr.RTS. 
 
 art' possible (tiily liccause (»f tln' ((rcsoiifc (tf roin- 
 forciiij? metal in the areli riri^f. Culverts of this 
 p'lieral form are heiiij; used hy several of the rail- 
 road companies antl are eeononiical. They have n 
 disatlvaiitafre. however, in re(|uirin}; th(> use of 
 enrved forms, hut this is overcome to some extent 
 l)y iisinj? colla{)sil)le centers. 
 
 A jHodification of tliis form of culvert using a 
 semicircular top. is also sliown in Fijrure '>'. 
 
 Mr. Luten's rules for proportionin<; such arches 
 under railroad baidis. in spans of .lO feet or less, 
 and with a depth of earth filliuf; above of not less 
 than 10 feet, are as follows: — 
 
 fVowu TiPcluu'ss 0=.''^""'+.',. 
 
 :5() 
 
 2PortaN 
 CotKT' H- SH yds. «<( I8.1H) 1701 
 
 lliirrf 1 jx-r Ilii. ft. 
 Ciincrete H yds. (ii HH.dn f6».(Ht 
 Moel 1015 lbs. fa .015 ir>. •.>•.' 
 
 etiRth fur 20 ft. liiiiik 30 ft. 
 Area 'Jr.o si|. ft. diHt I30MI. 
 
 FiK. y-i. 
 
coxcRi Ti: Lr/.iiiuTs .ixn ii<i:siLiis. 225 
 
 ,, HpHll 
 hi =-rr - . 
 
 10 
 
 Fiiick (if iiliiitiiictits hnttcr (mm' in four. 
 Till' mimluT iif sijiijiii' iiiclu's of s\vv\ f(»r oiio 
 t'«I<,'<' I»<'i" litM'iil foot of jircli is 
 
 }{ L 
 
 40(».iM)(tl). 
 
 li is tlif live load in pounds lluil ciin Ik- fonccn- 
 tratcd on the half anli for on«' track. 
 
 
 ■J PiirtalH:— 
 
 (Concrete 47 yilo. »i IH.OO 
 Steel 1600 Ibx. <>( .(M 
 
 Harrel p»'r ft. 
 
 ''(>ncret»3.1y(ls. (fi $H.(Hi 
 Steel ITli 11)8. ^ .ot^ : 
 
 .\reii 92 sq. ft. I,f'ii»rth for 
 bank 4'.' ft. i^n^l for 
 hank, »17H0. 
 
 ♦376 
 _fi4 
 $140 
 
 I-J4.8 
 _6^« 
 
 131.6 
 
 20 ft. 
 20 ft. 
 
 ±7-0^ 
 
 Fig. 54. 
 

 Illlll 
 
 22fi coNCRiirn BRincEs Axn culverts. 
 
 2 Portals:- 
 Concrete 68 yds. *< iH.Od t7()4 
 
 Biirrel per ft. 
 Cc>ncrete7.2.") yds*. »/ $8.00 ^$58.0 
 Steel 4fiO lbs. *( .04 18.4 
 
 LeriKth for 20 ft. bank =-32 ft 
 Area •21.'-. 8<i. It. Cost »3150. 
 
 -....;.». ^.,..J^ _\l 2 Portals:— 
 
 U-V-V-ii-T-VH^^ -5f, Concrete 4;<.4 yds. *»t8.r) I t3«7.'.' 
 f.'. .'-'::; -irrl;—! — 4- steel 2fi7(iib».r« .u4 lofi.s 
 
 t:.: ;:::;-,».Ti =3= =4. '""'■•■i i">r ft. 
 
 tT'j-T.ii'fi". -r- ^"" f^onorete 3.3 yds. *( |8.(KI |26.4 
 Steel 230 lbs. *( .04 '^:l 
 
 Are* 12« scj. ft. I/enKth for 
 20 ft. bank :t'.tft. (^ost for '20 ft. 
 blink, tl8(4. 
 
 FlK. :,(,, 
 
/' 
 
 COXCRETE CULVERTS .IXP TRESTLES. 2L'7 
 
 R is the hoiijlit in feet, ami 1) tlic crown tliieknoss 
 in iiichos. 
 
 Fig. 57. 
 
 TABLE XI 
 
 CULVERT DATA, FIGURES 48 TO 66 
 
 
 
 
 
 Harrpl, iirr ft. 
 
 2 
 
 Portals 
 
 
 20 ft 
 
 . Bank 
 
 
 
 
 
 ^ 
 
 
 r. 
 
 
 
 •f. 
 
 
 ,1 
 
 
 L 
 
 
 
 
 
 ^ 
 
 2 
 
 
 ^ 
 
 ■~. 
 
 
 
 
 t, -^ 
 
 c 
 u 
 
 S 
 
 3 
 
 
 
 t 
 
 
 t.i "* 
 
 -r 
 
 
 
 *f> 
 
 it "^ 
 
 "^ 
 
 
 S 
 
 -< 
 
 4.7 
 
 ■A 
 
 — 
 
 C C^" 
 
 •/. 
 
 
 *. 
 
 
 
 is 
 
 1.-. 
 
 12 
 
 ISO 
 
 4.-.0 
 
 .■>:. . 4 
 
 72 
 
 34.-.0 
 
 714 
 
 32 
 
 24S6 
 
 30 ,S 
 
 •!<» 
 
 20 
 
 11 
 
 2:50 
 
 ."i.S 
 
 ..1.-. 
 
 67.0 
 
 74 
 
 4720 
 
 7S() 
 
 32 
 
 2924 
 
 WW 1 
 
 :>(! 
 
 l.-) 
 
 11 
 
 161 
 
 6 1 
 
 210 
 
 .is. 4 
 
 HH 
 
 
 704 
 
 32 
 
 2.'>72 
 
 36 4 
 
 51 
 
 i:. 
 
 11 
 
 172 
 
 6.2 
 
 l.M) 
 
 .V).6 
 
 HS 
 
 
 704 
 
 32 
 
 24S3 
 
 3' 4 
 
 :>2 
 
 20 
 
 12 
 
 2 10 
 
 4,6 
 
 700 
 
 64. S 
 
 113 
 
 14,'.(K) 
 
 14S4 
 
 2."> 
 
 3104 
 
 27.0 
 
 .l.'l 
 
 ■M 
 
 12 
 
 ■JAI 
 
 f(.U 
 
 101:. 
 
 79.1 
 
 8,S 
 
 
 704 
 
 .«) 
 
 .1077 
 
 31 8 
 
 .y\ 
 
 10 
 
 10 
 
 92 
 
 :m 
 
 170 
 
 31.6 
 
 47 
 
 16(K) 
 
 440 
 
 4'.! 
 
 17S4 
 
 31 4 
 
 O.I 
 
 20 
 
 11 
 
 215 
 
 7.2 
 
 460 
 
 76.4 
 
 SS . 
 
 
 704 
 
 32 
 
 3148 
 
 3:> . .') 
 
 M 
 
 lU 
 
 10 
 
 128 
 
 ■A.i 
 
 230 
 
 ,'ir>.6 
 
 43 
 
 2670 
 
 4.-,4 
 
 3<> 
 
 1S44 
 
 27.8 
 
 ;.l.""'.-' 
 
 "!^^ 
 
t\ 
 
 
 II f 
 
 228 COXCRETE BRIDGES JXD CULVERTS. 
 
 CONCRETE RAILROAD TRESTLES. 
 
 Figurt's ."58, 59 and 61 to (io inclusive sliow five 
 different types of reinforced concrete railroad tres- 
 tles. In connection with these and for the purpose 
 of comparison, a diaj,'rain and table of dimensions is 
 j^iyen in Fij,'ure 60, for double track steel beam 
 bridfjes, a type jrencrally in use by the railroad com- 
 panies for short spans. The drawings for these dif- 
 ferent types of concrete trestl(>s show double-track 
 structures, 28 feet wide Avith 1.") inches of filling, 
 suflficient only for the usual depth of ballast. When 
 headroom or other conditions will permit, additional 
 space for earth filling beneath the ballast shoidd be 
 provided, making *. mininnnn depth from base of 
 rail to concrete of not less than :] feet. \n many 
 bridges this depth has been exceeded. The arch 
 viaduct over the Santa Aiui Kiver at Riverside. Cali- 
 fornia, has a depth of ,1 feet from the base of rail to 
 the extrados at the crown. 
 
 These trestle designs marked A to 11 inclusive are 
 of the following types: 
 Double Track Structures. 
 
 A. Kailtops. Loads carried entirely by rails in 
 ])ending. 
 
 H. Beamtops. Loads carried entirely by beams 
 in bendijig. 
 
 r, Standard steel beam bridges. Open decks 
 
 D. Reajjitops. j.eams for reinforcing only. 
 
 E. Reinforced concrete. Slab type. Ii(>d rein- 
 forcement. 
 
COXCRllTE CVIJl-.KTS .IXD I RnSTI.liS. 229 
 
 F. Kciiiforcpil ('(Uicroto. lioain and slab type. 
 IJod I'cinf'orfeinent. 
 
 SINGLE TRACK STRUCTURES. 
 
 (i. Reinforced concrete. Slab type. Kod rein 
 fdreenient. 
 
 11. Keiid'oreed eoncrele. IJeain and slab type. 
 Uod reinforeeinent. 
 
 These standard trestles were desijjfiied by the au- 
 thor, ^vithont special reference to the standard cul- 
 verts, ami also under a sonunvhat different si)ecifiea- 
 lioii. Instead of making an impact alknvancc 
 amounting to '^O^/r of the live load aiul using 
 a 7!>()-i)ound concrete working unit, as in designing 
 tiie concrete cidverts. the stamlard trestles are de- 
 signed -with no impact addition and with a working 
 nnit of 500 pounds per scuuire inch for concrete in 
 iMMtiprcssion. The assiuued engin(> load is Cooper's 
 1-) .")(), Avhich is e<|uivalent Avhen distributed by the 
 ties, rails and ballast to a i>uiform live load of 1,100 
 |)ouiids per s(|uare foot. To this is added the weight 
 nf track, filling ami coiuu-ete, nmking the total loads 
 fro; . l..")00 to 1.700 pounds per scpiare foot, as par- 
 ■ . 'y noted on the various ngiu'es. The founda- 
 • are of sufficient width so the bearing pressur*^ 
 ( e soil will not exce(>d three tons per scjuare 
 
 foot. For the i)urposc. however, of making the esti- 
 mates lil)eral. the pier (putntities in all cases include 
 l)iles. It will ])(' scM'n that on each plate is a table 
 giving the length of span, thickm'ss of concrete, 
 size of metal, and the (juantitios of concrete, steel 
 and ballast, together with the estimated costs for 
 
 •W 
 
if 
 I! 
 
 iiiil 
 
 2;!0 COXCRIiTIi BRUKiliS .1X1) ClLlllRTS. 
 
 tlu. various spnns. In .....uuvtiu,, with .I.sifrns |} 
 •>. K juul (J. th.-n. i,.v als., tahLvs jrivin- tl„. sizes 
 ;i'"'"ftH-s and ,.osts for ,,i,M-s of various heights 
 "'" I"<''-s vary fron, 2 t.. ;5 f.vf i„ thiHou-ss at the 
 "!'• 'I-P«'n.lu>- o„ their hei^^ht, an.l thev have si,!.- 
 '•'tt-rs^ of 1 i„ 24. AVhen piers have a'less height 
 
 '''"l-> f-t. Ih.re is only a single fooling eourse Hi 
 
 <'"• l>Hs<.. 1,ut for heights greater than i:. fe,.t there 
 
 ■'•••' 2 tooting eonrses. This is neeessary to prevent 
 
 I'" load on the soil ...xeeeding :{ tons j.er square 
 
 root. 
 
 Economic Span Lengths. The designs are made 
 ••'•spans up 1o :.4 feet in length and piers up to 
 •^" /!'•'♦ '" l"M^d.f. and are suitable f,,,- struefures 
 "•■th.n these li.nifs. TIh> eeonon.ie span length to 
 iise tor any given heiirht of tn-stl.. is that one where 
 tlH" eost ol the span i. approxin.afely equal to th.' 
 -stofp.er. Th,. ,.ost of pi.r f.,, the given trestle 
 l'"'jrl.t n.ay he taken direetly from the pier tables 
 and tn.m the .'orrespon.ling table giving the eost of 
 ■si>an, a length nu.y be sele.-ted. the eost of whieh is 
 ;'PIH-oxnnately e.pud to the eost of the pier ir,v 
 H.g thus d.-tennine.l the eeonon.ie span length ihe 
 various sizes may i>e tak.Mi Jireetly from th.. tables. 
 
 Description of Various Trestle Designs. 
 
 The following are brief deseriplions of the various 
 trestle d.'signs referred to ai)()ve — 
 
 Design A Figure 58. This is a type that has 
 »>.-.>n extensively used for small spans up to 12 feet 
 
 ' «&" 'HUV^'tMMt '?-)kIl&r«^' 
 
j: 
 
 ."5 
 
 9 
 
 1- 
 
 
 s 
 
 g^ 
 
 ^ 
 
 13 
 
 i 
 
 
 o 
 
 s 
 
 X 
 X 
 
 w 
 
 
 
 
 
 
 
 
 
 ** » 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 X >^ 
 
 ■^ 
 
 CC 
 
 
 ^ 
 
 ?» 
 
 *♦< 
 
 CO 
 
 T 
 
 
 
 
 
 
 
 
 
 
 
 X 
 
 c» 
 
 c 
 
 CI 
 
 w 
 
 -f 
 
 Ift 
 
 •* 
 
 «c 
 
 
 
 
 
 
 
 
 
 u"C 
 
 
 
 
 L.>- 
 
 » 
 
 t- 
 
 t- 
 
 -«• 
 
 t- 
 
 •^ 
 
 •c 
 
 wm 
 
 5 . 
 
 t- 
 
 X 
 
 a 
 
 o 
 
 FN 
 
 ■?! 
 
 « 
 
 ■^ 
 
 XI « 
 
 o 
 
 T 
 
 X 
 
 9 
 
 ^ 
 
 c 
 
 o 
 
 9 
 
 fl 
 
 <c 
 
 H 
 
 "2 
 ^1 
 
 
 
 ii' 
 
 3 
 
 $ 
 
 
 
 
 
 i-< 
 
 
 ri 
 
 
 ■n 
 
 
 
 
 
 
 
 
 
 
 "^ 
 
 
 
 
 
 
 
 
 
 c « 
 
 M 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 •a 
 
 3 
 
 a 
 
 2 
 
 If: 
 
 s 
 
 
 ? 
 
 ? 
 
 X "* 
 
 ^ 
 
 • 
 
 1 
 
 1 
 
 1 
 
 1 
 
 
 
 
 to 
 
 
 1 
 
 ? 
 
 X 
 
 
 X 
 t- 
 
 s 
 
 1 
 
 X 
 
 t- 
 
 X 
 
 n 
 
 _ 
 
 „ 
 
 n 
 
 
 
 
 
 
 1^ 
 
 ^ 
 
 *"■ 
 
 
 X 
 H 
 
 !1D 
 
 
 H 
 
 U 
 
 '■J 
 
 
 » 
 
 
 
 K- 
 
 •m 
 
 
 B. 
 
 
 
 7^- 
 
 > 
 
 
 X 
 
 
 
 ^?.? 
 
 3 
 
 
 .7 
 
 
 
 i-, * ■ 
 
 
 
 
 
 
 n* 
 
 1 
 
 
 s i 
 
 
 
 
 
 
 s z 
 
 
 "~ 
 
 
 i; i 
 
 ■C 
 
 
 — = 
 
 
 
 
 
 0. 
 
 c 
 
 o 
 
 ^ "x 
 
 
 
 
 
 
 1 
 
 — * •* 
 
 OD 
 
 '^ 
 
 - __ 
 
 
 
 
 i 
 
 3-5 
 
 « 
 
 5 
 
 
 ■ - 
 
 
 
 '■J 
 
 I 
 
 2 c 
 
 X 
 
 1- 
 
 1 
 
 _J 
 
 ocl 
 
 ot 
 
 1^ 
 
 
 •4 
 
 
 u 
 
 
 4i« 
 
 ■'Ml 
 
 
 
 s 
 
 
 
 
 e 
 
 WKeHb.-!!^ 
 
/. 
 
 i! 
 
 hIip 
 
 n 
 
 ;{| i 
 
 232 
 
 COXCRETE BRIDGES AND CULVEkTF. 
 
 m length, tliough usually restricted to a length of 
 8 feet. The loads are carried entirely by the bend- 
 ing resistance of the rails. Railr-^'ad companies 
 usually have a large stock of old track rails on 
 hand, which they are willing to sell to their con- 
 struction department at a price of from $20 to $30 
 per ton. They are estimated in the table accom- 
 panying Figure 58, to c.»st $40 per ton. or 2 cents 
 per pound, placed in position. Only a sufficient 
 thickness of concrete is used, to completely embed 
 the rails and hold them securely in position. The 
 strength of the concrete is considered onlv by allow- 
 ing a flange stress of 10,000 pounds per scpiare inch 
 on the metal, which is 20 per cent, greater than 
 would be permitted, if the concrete filling were ab- 
 sent. This type of bridge is going out of favor, not 
 only because it is not economical, but also because 
 there is no provision for resisting shearing stresses. 
 Bridge decks so constructed have excessive deflec- 
 tion, and the concrete frequently cracks and 'jlls 
 away from the rails, leaving the steel exposed. 
 
 If loads were carried by the bending resistance of 
 the concrete and rails used only for the purpose of 
 reinforcement, these rails would then be spaced 
 from 2 to 3 feet apart. The best modern practice 
 in the use of railtop trestles and culverts is to adopt 
 a mean between these two extremes, and use slabs of 
 concrete IS inches in thickness, reinforced with old 
 60-pound rails spaced as follows : 
 
 For 6- foot span, place rails 18 inches apart on cen- 
 ters. 
 
 ^ V 
 
(' - 
 
 
 I 
 
 11 
 
 <1 ' 
 
 
 ra. 
 
 = i-icx*iexxr)tooc« 
 5 3>a?iii5i»t-xS»3x 
 CI ri « » ♦ w t- X » »- n « ^ 
 
 a 
 
 S8SaSsSSiSS35 
 
 2 »' 
 
 5^* 
 
 SSS555SS|Sg|S 
 
 H 
 
 ■^.^rim-fujxt^xaSSs 
 n Ti (N !N « c» r'l ri ci li Vi^^ ji 
 
 gS3 «=*SSSSSg?!S8S8 
 
 
 f «* 
 
 
 
 1.- 
 
 ocit«g»«4>ci^i-4^^xt:*ia 
 
 
 rH i-i i-< F^ ^ FN CI CI CT C-4 CI « OC 
 
 < 
 
 EC 
 
 i4 
 6^ 
 
 ^cai-HXO>o?5xcci-^x« 1 
 -^ o ^ ci **" ^ u; 00 t-^ lo -^ ^ «* 
 
 i-«f-CICIClCc55'*-*«»OWt- 
 
 3: -J 
 
 
 
 Q 
 
 i.'!iexXXrtK-(.-«ffl«D'CO 
 
 
 2 
 
 9 fri251bB. 
 
 10 - 25 
 12-31.5 
 12-31.5 
 12-35 
 16-42 
 15-50 
 18-55 
 18-60 
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 Icrs. 
 
 Design B. Figure 59. Tn Ihis design beams arc 
 placed 1.") inches apart on oonters, and are snf- 
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 stress on the metal of 12.000 pounds per sijuare incli 
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 disintegrating the concrete. 
 
 Design C. Figure 60. There is no conerete 
 whatever in connection with this design. It is one 
 of the conunon forms of sh()rt-si)an railroad bridges. 
 aM<l the table of sizes, weights and estimated costs 
 
 is given for comparison Mith tlu st of reinforced 
 
 concrete designs. The tyi)e of bridg(> is inferior to 
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 nent roadway. Tf a train is derailed on a solid deck 
 liridge, the chance of injury either to the train or 
 structure is less than wlien derailment occurs on an 
 open deck bridge. 
 
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 on.t.. tr..stb. (b-sio.,,, hotb span an.l pi.-rs havi..- rod 
 r.-int..r<...monl I„ tb.. two pr.'vious ' , ,l,.sij?ns 
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 stnir-tion. witb a 10-in.-b slab f.)r t;-fo.)t span, ii- 
 croasinjr to 3(; Jnclics f.)r a 24-foot span. 
 
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 track nn.I l.Mllj.st. TIh- si.I,. beams aiv oacli 2 feet 
 III Avidfli. while tlie center l)ea.n is 4 feet. The load 
 IXT lineal f<M,t ..n llie side beams varies from 8 ofV) 
 pounds for a lO-foot span to n.:JOO pounds for a 24- 
 ioot span. 
 
 Designs G and H. Figures 64, 65. Th,-se a.v 
 
 dcs.jrns for sin^de track trestles, similar to E and 
 
 ' already .lescribed. They differ, however, in that 
 
 .nn.I II have a ;{-foot depth <.f earth and ballast 
 
 nil 111 <r. 
 
 Comparative Trestle Costs. 
 
 The comparativ." eosts for the foregointr trestl- 
 spans for both sin-le and double track structures 
 IS fiivrn un the eharl. Fijr,,,,. ,;,;. The horizontal 
 ordinatcs represent clear spans in feet, while the 
 vertical ordinates give the eosts in dollars for a 
 ••""iplete span, not including piers. This chart 
 '•I«'arly sho^s that r-inforced concrete trestles of 
 the types marked E and F with rod reinforcement 
 are more ■•conomical than any other form of pernui- 
 i.ont trestle, with solid roadway. The chart shows 
 turther that reinforced con-rete railroad trestle 
 spans of slab constructions are economical fc -ingle 
 track in spans up to M feet, and for double track 
 HI spans up to 20 f,.,.t. Above these lengths the 
 •H'onomic form of span is a combination of beam 
 and slab. 
 
 m§ 
 
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 m^ 
 
 n ■'■!'''M 
 
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 'immdm.wmmii-M!MmmwMsm^ssFmi.mbK-:i:a^,'fi 
 
Comparative Cost of Short Span Bridges. 
 
 e 
 
 ZS Ci.eif/* J/'/tj\i 
 
 ZS' Cie*-t J^0^ 
 
 I 
 
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IXDEX. 
 
 Pago 
 
 Abutments ,'.">, .", 148 
 
 Movements of 10 
 
 lianklne's Rules fo*- 58 
 
 Tiautwine's Rules lor 55 
 
 Ahiitment Piers 11, 54, 70 
 
 Tiautwine's Rules lor 55 
 
 Adda River Bridge 80 
 
 Adhesion, Concrete to Steel 
 
 108, 114. 116. l::6. 1N6 
 
 Advantages of Masonry 1 
 
 Aisne River Bridge 176 
 
 Almendares, Cuba Bridge... 97 
 
 Augustus, Bridge of 3, 75, 7ti 
 
 Anthony Kill Bridge 97 
 
 Anderson. L. W IHtt 
 
 Approximate Computations. . 32 
 
 Aqueduct of Vejus Kiii 
 
 Aicade — Spandrels 19 
 
 Arch Ring. Thickness of. 50, 51 
 
 Architectural Design liio 
 
 Area of Arch Ring, Required ti9 
 Atlantic Highlands Bridge.. 17< 
 Atlanta. Georgia. Viaduct .. .189 
 Auckland. N e w Zealand, 
 
 Bridge 80 
 
 Austell. Georgia, Bridge 17S 
 
 Austrian Experiments 105 
 
 Avranche, Fiance, Bridge.. 174 
 
 Hacking '2 
 
 Tiakei's Musonry Constiuc- 
 
 tion ,',9. :;is 
 
 balustrade 1S7 
 
 lUitter of Piers l.^.i) 
 
 lUaring Power of Soils .Mt 
 
 I'.cllefiold Bridge, I'ittsburg. IS 
 Ho.im Bridges ISl, IS.'] 
 
 Advatitages of is:! 
 
 Cost of 1S5 
 
 ppsign of i,K5 
 
 landing Monnrits 13:!.1.'!5 
 
 Middle. Col. John S9 
 
 Hinnie 96 
 
 I'.ig Muddy ItiviT Bridge 
 
 17, 60, S!t, 116 
 
 i:if>me. Rudolph S Ifi3 
 
 r.lock Structures 7 
 
 Hond. Mechanical lOS 
 
 Con ti'a dors' 157 
 
 liiiHton. nridsre.s in fi.'i 
 
 I'.orrodale Bridge 95 
 
 liotmida Bridge. Italy 174 
 
 Biisnla 176 
 
 lioulder, Col 17S 
 
 24,'> 
 
 Page 
 
 Moulder Fared Bridge. 166. 168 
 Brookslde Park, Cleveland.. 97 
 
 Brick Arches 1 
 
 Brick, Strength of 34 
 
 Brooklyn, Seeley St. Bridge. 176 
 
 Brunei 30 
 
 Brown, Wm. H 98 
 
 Building Lintels 5 
 
 Burr, Wm. H...80, 147. 1.59. 179 
 
 Bush. Lincoln 96, 98 
 
 Buda Pesth 176 
 
 Cain, Prof. Wm 128 
 
 Carriage Travel Loads 123 
 
 Cantilever, Action of 5 
 
 Concrete 10 
 
 Caius Flavlus, Bridge Built 
 
 by 74 
 
 Casey. E. P., Architect. .87, 159 
 
 Canada Creek 178 
 
 Carter 98 
 
 Cartersburg, Ind 176 
 
 Canal Dover. Ohio 176 
 
 Cedar Rapids, Iowa 176 
 
 Centers 7 
 
 Chester Bay 176 
 
 Charley Creek 178 
 
 Chicago Park Bridge 169, 172 
 
 Chatellerault, France, 
 
 Bridge 174 
 
 Church. Prof. L P 42 
 
 Cincinnati Park Bridge 104 
 
 Cleveland, Rockv River 
 
 SI, Sli, 83, 84, 95 
 
 Colfax Ave.. So. Bend 176 
 
 Columbia Park Lafayette. . .178 
 
 Courtwright, P. A 179 
 
 Composition of Arclies 1 
 
 Concrete 120 
 
 Cost of Solid Concrete 
 
 Bridges 63 
 
 Re-Concrete 150 
 
 Slab Bridges 183 
 
 Beam 185 
 
 Piers 1S3 
 
 Conciete Steel Engineering 
 
 Co 163 
 
 Ccmo Park, St. Paul 
 
 F.I ICa, ICT, 17S 
 
 Con.iugate Pressures. . .4, si, 67 
 
 Continuity of Arch 7 
 
 Colonnade Spandrels 19 
 
 Compulations, Approximate., 32 
 
246 
 
 II^'DEX 
 
 Page 
 
 i\\ 
 
 Cooper'8 Engine Loading. 
 Connecticut' Av4; "Bridge .\^"' ""' 
 
 Com^etiu:ei3.JgAiS**"-^%-;^ 
 CorruKateil nn- *"'"« 101 
 
 Bar 
 Bridge/ 
 
 -orrugated 
 Craclis . . , 
 Cruft St. 
 
 olis 
 
 TrlV." ^'^"'^ <-''PPk 
 ( rittenden, H. M 
 
 Crown Tlirust . . .'.V " aV 
 Crown rvf A 1. ••••••'^•'> 
 
 118 
 
 i- 107 
 
 Ind anap- 
 
 ITS 
 
 1 7.S 
 
 ...IT.-. 
 
 40. 43 
 
 -Arcli., Rise and 
 
 Crown of 
 
 Fall 
 
 Thickness . 
 
 Radius 
 
 Killing Depth'oif!!!;:""i«" 
 
 Cut^'lvn^f of Arch Block.s/33" ... 
 £"* ^^ater on Piers..... 'ir, 
 
 Cunningham, A. O -- 
 
 Culverts ...... ■'' 
 
 Req uired open i ngs ' for .■.*;; 
 
 Tables of .'.*.*.V'i,-,' " -mit' ' 'wio" 
 Cost r'hnnt • -''• -*'•>' 
 
 Side 
 
 10 
 U 
 ].'. 
 67 
 34 
 
 .i;.i 
 
 .19!. 
 
 Chart ;;:.■;•. ::v;.:''r:ii] 
 
 <'hart. 
 •'orni.s of. 
 
 I'l; 
 1-16 
 217 
 219 
 S 
 
 Walls .... 
 Comparative Co.-t 
 tomparntive Co.«t 
 Other Common 
 
 Curves for 
 
 Cu.shinn, Filling as. . . ^l 
 
 Cup Bars ...::::; i}^ 
 
 Danville Bridge . -o' „- 
 
 iJanuhe Hiver Bridges.*." ' ""' o-. 
 
 iJayton, Ohio V-Vi?;' 
 
 l^es Moines Bri.lg... " "" V-" -« 
 
 &')":?: I^'-'Jeerciev'e-''' 
 
 Cost of" ".'■".■.■ si' ■s'."8V'oV ^i 
 
 ""iife"'...".' -"c^'i : 
 
 Design. Ultra Refinement " " " 
 
 Decatur m., Bridge.:... •'kb 
 
 Decorah. Iowa, IJri,|g4 ]-c 
 
 Derby. Ponn., Bridge i-« 
 
 De Mollins, M s^ ^'^ 
 
 De Palo. Michael."."."""" 
 Dock, Kind of . . 
 D-'ck Bridfies, I'refei-ciu' 
 Diversity of Design... i. 
 
 Diamond Bars . ,]^ 
 
 V, 
 
 17,-. 
 
 1 3.S 
 
 e for.lfis 
 
 Douglas. W. J....S], 
 Drainage of Arches. 
 
 ■ lis 
 
 89, IGG, 177 
 
 Pa 
 
 104, 1 
 
 1 
 
 1 
 
 Duane. W. M gs 
 
 Earth Slopes " " ' 
 
 Eads Bridge. St." " "louIs." ." " " 
 Koonomic Span Leiigtbs.. 
 Edmonson Ave. Bridge 
 Eden Park. Cincinnati " 
 Kla.stic Theorv 
 Electric Car Loads .".■.", 
 
 Ellip.xe 
 
 'I o Draw 
 
 raiiptical Intra(l"os i 
 
 Emperor Augustu.s "." i 
 
 Embankments, Loads from.. 
 
 '^^Tmperger," "von '."."."."iui " iVf'' J 
 i'^mpirical Rules . ' ' \i 
 
 Emerlchsville {: 
 
 Kngine Loading— ' 
 
 Cooper's E-50 . . ., 
 
 E.otimating . J 
 
 European Praeti'ce ■.".■." ,' 
 
 External Loads and Forces' '4 2 
 r.xpan.«inn . x-un.es », i 
 
 Expan.sion Joints".' i? 
 
 Expanded Metal .. \\ 
 
 Kyach River Bridge. .'."." I 
 
 Felgate, a.. M.." ,:• 
 
 Filling-Crown . , ""'• 
 
 Load froMi 
 
 g;;^'p[j^Eiiipticai "aVcVics." : : ; : 
 
 Finish, Siirf;-ce 
 
 i ive Centered Ar(h,"""To 
 
 Draw 
 
 Merits of 
 
 11 
 
 17! 
 
 9t 
 
 If 
 
 30 
 32 
 32 
 
 60 
 
 22 
 
 F.re Insurance" ." .".".■."." \\i 
 
 Hoor Renewals 9 
 
 Huid Pres.sure t 
 
 ?,'-\V^'"^"^«---::::::::::::::io? 
 Fieischmani-Eaward::::;::::;?^ 
 
 Forms ^ ' ° 
 
 ^!!l7l'I'" o' ^^Io«t Suitable. 27 
 
 Cost 
 
 P'orees 
 
 of 
 
 .].-,4 
 
 External on 
 
 Polygon of ■ ■ ■ QQ 
 
 Foundations . ro 
 
 .17 
 
 .■is 
 
 tions 
 '•"crt, E. J 
 
 Fort .snelling, Concrete iV^. 
 
 sign o,, ,-, 
 
 Frankfort Creelc iiridge."." ' 97 
 
 Iranklin Brid;,'e. F(.re.«ti'a'rk 
 
 Funicular ' i-olyg :n' '^!'^:. .^.'^,-; . ^l] 
 
Page 
 9S. 179 
 
 tjuis.'.';;;n5 
 
 ?tlis i'30 
 
 'S«^ 93 
 
 't'--104, 178 
 U'S 
 
 m 
 
 8 
 
 20 
 
 145 
 
 ••;■ •■.4. 76 
 I from. . 
 
 5, 30 
 
 Ji. 177, 179 
 
 139 
 
 174 
 
 49 
 
 1.-.4 
 
 10 
 
 orces 4, 29 
 
 60 
 
 148 
 
 118 
 
 97 
 
 of — n 
 
 178 
 
 C5, 90 
 
 16 
 
 30 
 
 DS 32 
 
 32 
 
 60 
 
 I, To 
 
 22 
 
 Ho 
 
 137 
 
 2 
 
 8 
 
 107 
 
 107 
 
 fl8 
 
 178 
 
 8 
 
 20 
 
 table. 27 
 
 1.-4 
 
 29 
 
 39 
 
 58 
 
 177 
 
 .SO. 153 
 
 97 
 
 33 
 
 i'» rk 
 Ifi-'. 178 
 67 
 
 fXDEX. 
 
 247 
 
 Pago 
 
 i.alicia Uridg.. iTc 
 
 •.iirliHd K-,,k Hii.lij... ' ('•iVi- 
 
 '"•KO J,;,; .-., 
 
 ':-n.-i;il Ouiliiif s 
 
 <;t iinantowii Hiidgf j; , 
 
 I Itiivial Design of Ke-Con'<i'. " 
 
 Bndg.'s ].,,; 
 
 i.iis.l Coiistniciion Co ici 
 
 i.'uslatic Aicli, To DraW ] ! ! 
 
 < ;l.n(ioiii. r'al!.' iVridgV ' " '*'i -v 
 ';"l<i«ii (Jale Park Uii.ii-i.;; ." 
 
 • • fi], ]ii4 
 
 •.lanitf. Strength of.... m 
 
 'ir.'.ri Island. Niagara ... .tiV ' 174 
 
 i.iiicnwald Rn n\ 
 
 <;nind Hapids Hiiig..'.;.'.'. ' '^"' 
 
 • •• • 106, ](!!), irb' 'i-,; 
 
 Hrand Hlvor i-.' ,-« 
 
 'Iiaiid Tower. IW... '.'.[" an n\ 
 'J'Ti'I Ave.. Milwaukee." • 
 
 „ 119, ij(! ■] r, 
 
 Orern. Prof. Clins K ,-s 
 
 <U\:\\n Kivir . 1-. 
 
 Gwyiins liiver '.'.'.'.'.'. yc 
 
 Hawgood. Henrv ... 01 09 
 
 aiutuond. .\. j ::;■, .:i;.;{ 
 
 ainsl.uig HiiilKi. .,- 
 
 H.-iglit of Hii.K'.^.s ■ ■■ ■ ','. 
 
 H.adn.om Iiider Hridg,'s: ] ] ^7; 
 H'ywonh. .; (I.. I,-.. ; 
 
 ;i"^y:it. w >* ...:::::::iw:\:^ * 
 
 lI'rKinier, X. V . i-u 
 
 HiMtje.s '4 
 
 ni"K<'d .\r( lu's V.'ln'.'].'!).' ]i;o"],o 
 istory of Cniierete Bridges' Kc' 
 
 Kiu'li Tension St., | . . ,,7 
 
 ighway n.am HridK. s. ..■."; .1 si 
 
 ' ' ' " .^' 1 - Q 
 
 Hihhard. M. s... j-., 
 
 Iliinliigton. ind i-'i 
 
 Undsen M( morial iiri'dge," ,' .' .' ' 
 
 !'nd^s:^,, Kiv'.r Hri.ige, Sanily '_ ' 
 
 Ily,'rostati'o".\iell."ii,jw"lo'"' 
 I iraw n o,' o- 
 
 I'yle I'ark on liuaaoiir.!." !'i76 
 
 |;]ahn. -nridge in ,9 
 
 '"• <"^"t. i:. 1:. liridKis.::.' 
 
 Piandard Culverts •..,, 
 
 :;|'h;.s Uiver nridge. i;'nvi:{jh 
 
 I'ier River Bridge....... •).-, , i ' 
 
 'i'lnaii. Bavaria ''''r,- I 
 
 iMerlakcn, MinncapoiiV!; [liVs , 
 
 I age 
 Interme.liate I'jir.s .. g, 
 
 Iiiger.soll. CM S^ 
 
 Intrado.s Form . .' ] 1,^ 
 
 Inzigliofen Bridge ,;'■; 
 
 ln-lianapoli.s. Moiri.s hi.' '.""\Yi 
 Meridian St. . ' ' i-w 
 Illinois St -J 
 
 • ■iiiit St ; jij 
 
 Northwestern Ave its 
 
 lola. Kan.sa.s . . \-'^ 
 
 lrrig.',ii,,n Canal, 'in "idaVio; ! u 
 Isur liivtr Bridge 35 
 
 Jark.oonville. Florida. BrIdgP ITS 
 Jaea.iuas Uiv.r Hridjj,. '^ 'i-, 
 Jannstown E x p o s i t Ion 
 
 T „ '^'i'lge .9. Hill 
 
 J. ffer.v-on St., South 
 
 J^'liP. B. J T..... 
 Jouit.<. i:.\|>ansion 
 
 Ti ii.sirin in 
 
 Judaun 
 
 ii;i. 
 
 Bend. . 
 161, lfi4, 
 
 174 
 
 174 
 
 179 
 
 148 
 
 7 
 
 Kahn, Julins 179 
 
 Kansas Kiv;:..-.. '■'■''^'>^' \^'! 
 
 l.alaniazoo River . 17s 
 
 Keepers ... ,i? 
 
 Kenipten Bridge ' '. " '. '. .." r.' JVl' 
 
 Key West. Horida. . . . . '07 
 
 Ki.sHinger Bridge ''.'.".' 140 
 
 97 
 
 Kirehlieini Bridgt 
 
 Krcsno. (Jalicia ..,....'. . 
 
 Taibaeh, Austria 
 
 I ake J'ark. ililw.VuKi'e' ' 
 
 law uf I, ever. . . 
 
 1 aiiiner Av.... l-ittsiuug 
 
 l.awreiieehurg Trestle ' -iq,') 
 
 Kansing, Mich -■ 
 
 l-antra.li. Cermatiy n-, 
 
 J-<fner. B. K iT-, 
 
 Leonard, John B. . . "1-7 
 
 T.englh of .Span. KeononuVaY 
 
 lea. A. B 
 
 1.1 ihlirand. Max . 
 l-iiidenthal Custav 
 
 lima. Ohio 
 
 1 i<|iiid Pressure . . 
 
 lintels r 
 
 line of Ifesistane-. IndViinii'.' 7 
 I iet( rinination of ■•(; 
 
 I'osition (.f \ ;,;, 
 
 Fi'r Filiform T.onil j" 
 
 lor I'aiMal Load :.-," ' ^^>^<^ 
 
 Linear Anii ^^ ..vj 
 
 Limestone. Strength 1 f . . ' Tu 
 Liability Insiiranee 1-7 
 
 I>ogar.sport. ind. its 
 
 London, (Jliio 178 
 
 W 
 
 176 
 
 174 
 171 
 
 i:;i 
 97 
 
 ];? 
 
 ! S 
 ITT 
 ITS 
 
I 
 
 [I 
 
 ft 1. 
 
 1 
 
 m I 
 
 2-18 
 
 IXDEX. 
 
 _ ' Vnifo 
 
 Loire River i-i 
 
 Loral l.abor '. M 
 
 Loads ]' J .jf 
 
 Load. Contour UtduVtVl 41 
 
 Adjustini-nt to Form ' "' ]■) 
 
 Kxternal ' ' ' .iIi 
 
 rnp\pn .' ,"o 
 
 On t'ulvcrts .A'.K, 
 
 LonK Koy Viaduct... 0: 
 
 '•'"<'"• f). li K.".. ■iV7,'lV:t 
 
 'i'r u.s.s 
 
 .lis 
 
 T.utf>n".s Kiiipirical Kornvilii -'I 
 
 Luxemburg j,o, ill 
 
 Mary RIvpr 17s 
 
 MaryborouKh l?ridK'- ITS 
 
 Maumee Rivor Uridgc... "iji; 
 
 Marsii Bridge Co j;; 
 
 Maintenance •» 
 
 Ma.sonry. Strength of.'.','." g 
 
 Matliriiiatlcal Theory of 
 
 Arcli ^2 
 
 Materials. Strength of... ^A 
 
 Maracliina River, Ilalv 76 
 
 M:iin River ", 117 
 
 Main Street Rridpc, bavioii'l'Tf; 
 Mclntyre. Ch;irlf.« ... ' ];') 
 
 Melon. I'rnf. j 1113 "17:, 
 
 Merit.s of Concrete Uridgis!. 
 
 ]07_ ](U 
 
 Metal Reinforcement 1 1 1 
 
 Medium Steel "m 
 
 Meyer's Formula ]'.i\ 
 
 Mechanicsville Bridge ' !)7 
 
 Mercereau 17;) 
 
 Milwaukee Viaduct '. . . .]]'.i 
 
 Milteriliurg (('7 
 
 Missi.«.sippi River '.'.'.'." it; 
 
 Middle Third of Arch Ring.. ;!:! 
 
 Miners Ford 17s 
 
 Mis.sion Ave., Spokane. ...!' ITS 
 
 Miami 151 vor 174 ]7(; 
 
 Monroe St. Bridge, Spokane 7> 
 
 Mois.seiff, T<. S so 
 
 Morsch. Prof. ,j si !n; 
 
 Morrl.son. fleorge S so' in; 
 
 Monier, .lean 'lo:! 
 
 Morris St.. Indian;'polis. ..'."!] 71 
 
 Monolith Frame ^s 
 
 Murray. Paul R 177 
 
 Miiltl-<^enter Curve 9 
 
 To Draw 21'. '"i 
 
 Municipal Art League ' fs 
 
 Mundt'i'kingt n 15 
 
 Navier's Prlnci. :. 04 
 
 National Zonlogical Park!!..' fil 
 
 New York Riidges 7; 
 
 New Zealand. Longest Mi- 
 sonry Span 80 
 
 I'agi 
 
 Neckar River gi 
 
 Bridge ' 3 
 
 Nelson St. Viaduct. A'tian'ta!l!s! 
 
 Newark, N. J n 
 
 New (jushen, Ohio 171 
 
 Newton, Ralph K !!i7. 
 
 Neckarhausen, Germanv t 
 
 Niagara Falls, Green Islati.i.. 
 
 ... til, 171 
 
 .Min<s, Aiiiiedu'^t. Krance. . .]ii; 
 
 Noi.^e, Absence of 11,7 
 
 Northern Pacific R. R. Cul- 
 verts "•10 
 
 Nobel, Alfred !!!!!!!!!! "os 
 
 Oconomowoo, ■\:^'fs i7<j 
 
 Olive Ave. Bridge, Spokan'e'.!l7s 
 
 <^>pen Spandrels i; 
 
 Ornamental Bridges !!!! '>C 
 
 O.xhcirn. Frank c "l7'' 
 
 Outline, General ...luij 
 
 Parkhiirst, H. W ni H 
 
 Park Bridge Design ' <i'\ 
 
 Pantheon, Rome !!inii 
 
 Painting • 
 
 Painting Reinforcing Steei!!ii6 
 Parabolic Arch, To Draw 
 
 „ • -■!, l!l. 117 
 
 Pavement jt; 
 
 I'avement Slabs !!!!'''l.", 
 
 Paveinent Tics '"-,«! 
 
 Paulins Kill 07 
 
 Painsville. Ohio ']',4 
 
 Palerson. N. J KU 
 
 Plainwell. Michigan !!"l7s 
 
 Passaic FSiv er 17(5 
 
 J'arlial Load. Line of i'ress- 
 
 U'e i.-,, 6s 
 
 Peoria Bridge 140 
 
 I'elham I'.ridg' !! "i7fi 
 
 J'eru. liid.. Bridge I7i; 
 
 Pena River 174 
 
 Philadelphia 8."), 86, S7 9.". 
 
 Philadelphia, Tacoiiy Creek. !i7 
 
 I'iney Creek 18, !<; 
 
 Piers. Thickness of..i;6 IP 
 
 c. St of ' 
 
 - hutment li, .-4 
 
 Intermediate '. 53 
 
 I'ier Thrust. To Balance....' 14 
 
 J'me Creek 17s 
 
 Pittsburg. Pa 07 
 
 Piles. Batter and Plum-,! ! 5:1 
 
 l.iiad on 
 
 Pla.va Del Riv.. 
 Plaintield. Ind. . 
 Pl.Tuon. Germanv ... sii 
 I'otoniac MeiiKnial Bridge !'. 
 117, I." 
 
 112 
 
 l.-ii 
 
 .IS! 
 
 711 
 
 61) 
 
 .->9 
 .171 
 
 .178 
 
 8" 
 
 iri9 
 
 Ri\er 87 
 
 
ixnr.x. 
 
 240 
 
 r'agp 
 
 85 
 
 !):. 
 
 Ulanta.1.v<» 
 m 
 
 iTi; 
 
 17.-. 
 
 ii.v .... H.") 
 slaiiil. . 
 
 ...til, 171 
 lllcr. . . iiir, 
 
 107 
 
 t. Ciil- 
 
 17.S 
 
 )kanf'..17s 
 
 17 
 
 no 
 
 17:' 
 
 lull 
 
 ni, H 
 
 !i:i 
 
 in.i 
 
 3tori.'.'ll6 
 iw. . . . 
 . lU, 1(7 
 
 16 
 
 2\:> 
 
 .'.6 
 
 07 
 
 IVJ 
 
 I7ii 
 
 17S 
 
 176 
 
 'rcss- 
 ...1.'.. 6.S 
 
 140 
 
 176 
 
 176 
 
 174 
 
 6, S7, 9.'i 
 
 rook. !t7 
 
 , !'7. 142 
 
 II v. l.-.ii 
 
 IS;! 
 
 I, .■>4. 711 
 ...53, 6n 
 
 !e 14 
 
 17S 
 
 . . 97 
 ...... 5!t 
 
 59 
 
 i;4 
 
 178 
 
 ..SU, 8'. 
 
 !:•:;, 1.-.9 
 87 
 
 Pajjo 
 
 I'ortland. Pa., Bridge '■>:> 
 
 I'oilo Uk'o 174, 17.S 
 
 I'urtugul 174 
 
 I'ollii.sKy. Cal 176 
 
 I'uiit l>u tJard lo,') 
 
 I'oiitf ItDtUt. Uuiiit' ;>, ',o, 74 
 
 I'oiis AciMllius 74 
 
 ralalimis 74 
 
 La|iiilt'iis 74 
 
 rolynon, Koicf ;t9 
 
 I'ulo 39. 67 
 
 Ui.stanc'f 4;{ 
 
 roiiil of Uiiptui-f .".0 
 
 I'lt's.suif Curve, To Deter- 
 mine ofi 
 
 ProKKuie of Liquid 5 
 
 Sand 5 
 
 Pressure on Surface.s, 'I'o 
 
 Find 4.' 
 
 Prlees, Ksti^natlng 17,:, 
 
 I'leservation of Steel 114 
 
 I'yriniont. France 174 
 
 Quitnliy, Honry M S7, 9S 
 
 Quantities. Approximate 1.'.8 
 
 Railing 187 
 
 Halslun, J. (' 179 
 
 Uankine's lUiles for Crown 
 'l"liicl<ne.ss 14 
 
 Pier 'Pliickno.5s .").'!. 66 
 
 Rankine's Motliod of Draw- 
 ing H.\drostatic Curve.. 
 26. 27 
 
 Rules for \butment Thick- 
 ness 58 
 
 Railroad Bridges 2. ,1 
 
 Roiiifoiced Concrete ,\rc'ies, 
 
 ^os^s 1,",0 
 
 Tal.le of 
 
 ..174, 175. 17i;, 177. 17S, 17H 
 
 Part II 1(10 
 
 A<l\antUBes of Iu6 
 
 Reynolds 175 
 
 Reduced Load Contour 41 
 
 Reilly and Riddle 87 
 
 Reinffrring Stool 101, 111 
 
 Rein'orcing Systems 117 
 
 fietaining Wails 122 
 
 Rlione JUver 174 
 
 Riverside, Cal, 91, 92, 93, 94. 97 
 
 lllboud 177 
 
 Ricluiiond, Va., Trestle 154. ISS 
 
 Rise of Arch 8. 40. 66 
 
 Rise and Span 12 
 
 Rihbed Arch 129. 142 
 
 Ro^k vllle .Stone Arch 61 
 
 Roxhorongh. Pa 87 
 
 Rocky River Bridge. Cost of 
 
 64. 9.5, 80, 81, 82. 83, 84 
 
 Rotation of Arch Blocks.. 33 
 
 Page 
 
 Rock Skewbacks 2!> 
 
 Rock Creek S7, 176 
 
 Rome, Ponle Kolto....3. 73, 74 
 
 Roman Arches 8 
 
 Length of Spans 
 
 13, i3, i4, to, 76 
 
 Rusche, J. 1' 16H 
 
 Rupture, Point of 5u 
 
 Santa Ana iiiidge. Cal 
 
 55, 91, 92, 93, 94. 97 
 
 Sun Uubriel River Hridge..l7s 
 
 San Joaquim Kiver 176 
 
 San Francisco Bridges 61 
 
 Sangamon River 176 
 
 Sandy Hill, X. Y 153, 178 
 
 Sarajero, Bosnia 176 
 
 St, I'aul Bridges 174 
 
 St. Josepli Kiver 174 
 
 St. Louis, Kads Bridge 145 
 
 Sand I'ressure 5 
 
 Sandstone. Strenglli of 34 
 
 Scolleld Engineering Co.... 
 
 161, 175 
 
 Sdiillinger Bros 85 
 
 Seeley St. Bridge, Brooklyn. 176 
 
 Schenley Park Bridge 18 
 
 Schefflers Theoroni 32 
 
 Semi-Circular Arch 8 
 
 Senators' Bridge 74 
 
 Segmental Arches f» 
 
 Culvert Arches 14 
 
 Selection of Most Suitable 
 
 Form 27 
 
 Sewer Arch 32 
 
 Simpson and Wilson, Engi- 
 neers 96 
 
 Sitter River 81 
 
 Skew-back, Rock 28 
 
 Slab Table for Culverts 198 
 
 Slabs, Cost of 200 
 
 Slab Reinforcing 118 
 
 Slab Arches 129 
 
 Slab Bridges, Table with 
 
 Costs 183 
 
 Slab and Beam Bridges 198 
 
 Slopes, Earth 5 
 
 Sliding of Blocks 33 
 
 South Bend. Ind 174 
 
 S' issoins. France 176 
 
 Solid Arches, Tables of 
 
 95. 96. 97, 98 
 
 Soil, Bearing Power of 59 
 
 Spokane, Mission Ave 178 
 
 Olive Ave 17s 
 
 Kiver 178 
 
 Monroe St 79, 72, 97 
 
 Spandrels 147, 16, 17 
 
 Spandrel Columns 138 
 
 
2:.o 
 
 ixnr.x. 
 
 ■ 
 
 »p1 
 
 Hi: If 
 
 
 
 VlVr 
 
 Col- 
 
 a; 
 M 
 !t:. 
 
 Spancinls. Arcade or 
 
 'iiiiiadf 
 
 Spi.iirifi Killing .....!!! 28 
 
 S|). iiiKs. l.ovv 
 
 I'lisiii.iri of 
 
 Kpari 
 
 Spirylrn Idivvn' CreH< ' ' '.TS. 
 Stii; y Cruok Uridgc. l;„.s- 
 
 ^. '"" fi.'i 
 
 M '•>!•. Austria n,-,_ 174 
 
 Slahillly ItciiniicltlfntH. .as' 13(i 
 
 Sti.ckliridKc Mass ' 176 
 
 Stt ln-'r.iif<n UridKi- 17;; 
 
 Stc<>l UcihliircijH lit ,.101 in 
 Strt'iiBth of !{<•-( '(incrtto 
 
 „,, '^'•'•'"•s 10: 
 
 Stirrups 117 
 
 Siir\«y for MiidKc .'.'.'.'.■.■.'■ ■i.-,7 
 
 Siirfacf Kiiiisli ' (•,„ 
 
 Switzerland Hridgc ..'.'.'.'.'.[ m 
 
 Tafony rit-ek 07 
 
 TeltiilKinf at nridgc .'.".'.' i-,7 
 
 Terr.- Haiito .... [is 
 
 Test Loads 1 
 
 Tf-nsion in Joints 7 
 
 Tension in CoiKietf. . 114 
 
 Teiifen Uridij... Switzerland 1T:1 
 I enipeialllle Stresses 
 Tliickliess of .\r<li 
 'J'iiehps Mrldge . . 
 
 Tliaiiies Hiver liiidKe 'i", 
 
 Ttiaeher. Kdwiii Is, ll'i "177 
 
 I haeher Har.s ' us 
 
 Three fentered Aieli ' ' 'I'o 
 
 I 'raw oi, 
 
 Merits of '.'.'.'.u:, 
 
 Theory, Matlieina t leal ' n- 
 
 I lieory of .Arches.,,. ' 1% 
 
 Thrust on piers. Tnhai- 
 anced -•> 
 
 Ties on Bridge KInor.s, , ' 107 
 
 Ties. Pavement -<; 
 
 Tiher River, itonie 74 
 
 Topelja Bridge, 10, .li, H9']7i 
 
 Trestles , , 
 
 Eennnniir Spans 
 Rail Tops,. 
 Ream 'r,,p>t 
 
 Str..| R.nill 
 
 Riiiiii Tops 
 
 ^ ' Reiiiforei 
 
 ll'i, 
 lilnyr,,. 
 
 ir.u 
 r;.". 
 
 Ill 
 
 . 2.10. 
 ks','.' 
 
 ,T'!1, 
 
 22.S 
 
 Slabs, Rod 
 
 Rod 
 
 2:! I, 2:;:. 
 ■;<;. 23S 
 •iiii'iit. 
 
 n.'inis. Rod U.iiiforee- 
 
 nient o-'s o.>9 
 
 foniparativp Costs ' 'm'-"' 
 
 Chart ..,.■.■. ■.■.L'lS 
 
 T^rtiporarv , , , . 4s 
 
 Trinidad, Col. i-u 
 
 Trim Creek '.'.'.'.'.'.'.'.'.'.l^S 
 
 Truss System . . , 
 Ttautwines ijulc 
 Thifkness . . 
 Aliiitliieni I'iers 
 Travertine. IscU 
 Trial Metliod of 
 'i'uliesing, w |.- 
 
 Til sea I a was Uiver 
 
 for Crown 
 
 in UoiiK 
 iHsign , , , 
 I«:i, 
 
 .1; 
 
 I II 
 
 Turner. K. Al . . 
 'I'uriier. ('. A I' 
 Tunnel Areh .', 
 
 Twisted Rods , 
 
 Twist, d Lug IJars ,'.'.'■.' 
 
 T^V'-'ll. II. n.. Coneiet.' 
 
 .11 
 17 
 1: 
 17 
 17 
 
 11 
 11; 
 
 HrldK 
 
 ii; 
 
 u 
 
 3:i 
 
 designed hy 
 
 _ Is. (JJ.' Mil 
 
 T.vrrell, M. K.. Designs 
 
 '•> I,s.'. is 
 
 rUra-Reflnement in Design 
 
 '.innate Values " ,. 
 
 1 Im, (Jernianv , , , 9" 
 
 Ijieertalnty o"f Masonrj "4 ' r.^ 
 I nit I'lessiires ' " 
 
 On Surface. To ' Fi'n.l 
 
 >\ orkitig 
 
 ritiniaic an j' WoVking. .' .' p";, 
 T nit Reinforcing l-Yame, . , , Us 
 
 l.iiev.ri Ijia.ling ,'s 
 
 «-Jlsyninu!i i( al Alcli ...... l'i\i 
 
 y.nrloiis Po-ms. To Draw., "(i 
 
 \ allies, ritilliate , •;( 
 
 \ar.Mn^ Span Lengths 13 
 
 \aiixliall, London ,.. «(", 
 
 \ein,iiii„„ jjiv. Bridge' 
 
 Wakeinan 9. .jo, 174 
 
 \ •rmillion Riv. Bridge, nnji- 
 
 ville 72 97 
 
 Vo.fns. Aqueduct of .. "int'i 
 
 \enice. Cal i,;9 \-] 
 
 Viaducts over Yards ']:! 6fi 
 
 \iIiiation. Absence of. 107 
 
 \ iiime Rixer 174 
 
 Von K'inperger , ..104, 177, "179 
 ■V^'.nshington, n. C. Rock 
 
 ,, ''••'••■k I7fi 
 
 ( onneclicut Avi>, 
 
 „. ■• S7, SS, ]i:(i,']fiS 
 
 \Jnsliington St.. Davtnn. . . .17t; 
 Waleilfxi, Iowa .,..". 17S 
 
 A\ahnslK Ind i 40. ns 
 
 Mat.'rvllle, Ohio ... 17(; 
 
 Wavne St.. Peru. Ind. .'.■.'.■.■ J 7f. 
 \\ alker j — 
 
 Wakemen. Ohio' '.'.■.'.'.'.■9"^o' 'lU 
 \^n,.*. Thickness of Span- 
 
 <lrel J 3 
 
 Loads on .... 09 
 
 Waterproofing '.'.^'.'.52,' '2I6 
 
 " f:! 
 
j.\i)i:.\. 
 
 •2ol 
 
 PttK- 
 
 ^ 
 
 • Crown 
 
 n 
 
 Uonif. 7) 
 ^iKi". ...in; 
 . ..Ui;i, 177 
 
 174 
 
 ■•IT.-', J 77 
 ...lU. 17.-. 
 
 ilng. . .11'.-, 
 
 mo n^ 
 
 IIS 
 
 13i' 
 
 raw... 2<i 
 
 ,". t 
 
 13 
 
 ;i.", 
 
 Jrklge, 
 >. .10, 174 
 
 I'nji- 
 
 .. .72. 97 
 
 106 
 
 .1«9, 171 
 ...1.'?. 66 
 
 107 
 
 174 
 
 177, 179 
 
 Rock 
 176 
 
 ii';(i."'i6,s 
 
 n 176 
 
 .... 17S 
 110. 17S 
 
 176 
 
 176 
 
 177 
 
 P.O. 174 
 !pan- 
 
 19 
 
 29 
 
 .52, 216 
 
 Page 
 
 Watersoaklng no U.'. 
 
 Waterway. Width of &G 
 
 Walnut l.ane Uridge, Sur- 
 
 faco Kiniitli 60 
 
 Co.st of 64. 14J, SO, 85, 97. 
 
 Warren. Whitney. Arehltect. S" 
 
 Wat.son. Wllber J s,',, 17.-, 
 
 Waldhofen 174 
 
 Wells. W. H 179 
 
 WehBter. George S,,85, 96. 9s 
 
 Whited, Willis 9H 
 
 WlldegK. Switzerland 174 
 
 Wise, C. H 177 
 
 Wilson, George I, 179 
 
 Wideniug Concrete Bridges. 3 
 
 Page 
 Window Arches, Load on... 6 
 
 Wire Net Heinforcement 118 
 
 Width ul Deik 138 
 
 Wing Walls 149 
 
 Wlssahiclton Creek 95 
 
 Wurknianslilp 7, no 
 
 Working Units 35, 106 
 
 Wood Bridges, Competition 
 
 with 102 
 
 Wunsch. Professor 116, 177 
 
 Wyoming Ave., Philadel- 
 phia 97 
 
 Yellowstone Park Bridge... 174 
 Zeslgtir, A. W 98 
 
 
 A 
 
 ■^AVv^'xrjk-vjwwr. 
 

 'I 
 
 11 I 
 
 
 Koehring Mixers 
 
 are built in all sizes and styles 
 with any kind of power. 
 
 Writo for Spocial Cit.tlos^ue Xo 4. 
 
 KOEHRING MACHINE CO. 
 
 MILWAIKKK :: WISCONSIN 
 
 ^v 
 
m^m: 
 
 "CHICAGO AA " 
 
 1,000,000 
 
 Barrels Annaal 
 
 Production. 
 
 Factory at 
 
 Ogeltby near 
 
 La Salle. III. 
 
 Highest Quality 
 Portland Cement 
 
 1. ■).()()() Harnls Used in 
 
 CHICAGO'S NEW CITY HALL AND 
 COOK COUNTY CO^RT HOUSE 
 
 S])Cfiti(.'(l 1)/ llir li .1. ,\it'l)it(H'ts, 
 ICiij^nnc'crsainl Contr. . l(.-> 'or all work 
 requiring a stiictly lii.u'i .uradc and 
 al>s()lut('l\' iniif(i'!n Portland. 
 
 "WE MAKE ONE BRAND ONLY 
 
 THE BEST THAT CAN BE MADE." 
 
 CHICAGO PORTLAND CEMENT CO. 
 
 108 La Salle Street, CHICAGO, ILL. 
 
 (Instinctive Booklets on Request.) 
 
 \ 
 
 •z3te3yaca,^iag a < ^g< i g t» m | iag1i*^ ^ 
 
 A 
 
EUREKA MIXERS 
 
 A Purtabk- Mixer of (lood Capacity 
 K(ir Particular Work. 
 
 ASK I- OR catal(x;up: "c." 
 HLRHKA MACHINE CO. LANSING. MICH. 
 
 I)i:SfRIl'TI().\ OF 
 
 Till' L()iij,'i-st Sini]>li'-Truss Briilyt- Span 
 
 in I'^xistonii', 
 
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 II . (i TV R R ELL, Civ I i. E s g i x e e r 
 
 I OR SALI- BY 
 
 'J II E E X (; I X E E R I X G X E W S 
 
 m:\v York city 
 
 L'4Pa^'es. .") Illustrations. (ixH inclu's. Pajjer Covers. 
 Price, 50 Cents. 
 
:h. 
 
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 What is 
 Engineering-Contracting? 
 
 Enjjinecrinji-Contractin^^ is a weekly journal for civil 
 entrineers and contractors, edited by Halbert P. Gillette, M. 
 Am. Soc. C. I''., aiitiior of the " Handbook of Cost Data" 
 and other books for Kngineers and Contractors. lingineer- 
 in<x-Contracting might be termed a serial sequel to this 
 "H.uidbook," for no issue is printed that does not contain 
 valuable cost data. This feature alone makes the paper one 
 that no civil engineer or contractor can afford to be without. 
 Mr. Gillette has just completed his appraisal of all the rail- 
 ways in the State of Washington, acting as Chief Engineer 
 for the Railroad Commission. Data of cost of all kinds of 
 railway structures, secured from the original records of rail- 
 ways, are now being i)rinted in Kngineering-Contracting. 
 The ".Methods and Cost" ariiclesth.it are appearing cover 
 so wide a r.inge that e\ery engineer and contractor should 
 read e;icii issue. Mr. Daniel J. Hauer has recently become 
 one of our associate iditors. Mr. H.iuer is well known as an 
 authority on eartli and rock e\ca\ati(Hi. The other asso- 
 ciate editors include: Mr. Charles S. Hill, joint author with 
 Mr. A. \V. lUiel of "Reinforced Concrete, ' and for eigh- 
 teen years on the I'xiitorial staff of I^ngineering News; Mr. 
 C. r. Murray, for many years editor ui the construction 
 news department of I'ngineering News; Mr. F. A. Smith, 
 author of " Railway Curves," "Maintenance of Way Stan- 
 dards" and "Standard Turnouts." The entire staff includes 
 fourteen persor.s formerly with other leading engineering 
 journ.ils thus pi. icing every department in charge of experi- 
 enced and competent men. 
 
 Engineering-Contracting is published every Wednes- 
 day and Costs only ?2.')0 for the 52 issues. 
 
 SAMPLE COPIES FREE. 
 
 ENQINEERINQ-CONTRACTINQ 
 
 355 Dearborn Street, Chicago. 
 
 /! 
 
'/■ 
 
 ifi 
 
 is ' 
 
 I W 
 
 Concrete Construction 
 Methods and Costs 
 
 Hy HALBERT P. GILLETTB 
 
 and 
 
 CHARLES S. lUuL. 
 
 This book is unique among all the books on 
 concrete. It is devoted exclusively to the 
 methods and costs of concrete construction, and 
 it gives detailed information regarding every 
 phase of that work. It tells what an engineer 
 or contractor needs in estimating the cost and 
 in reducing the cost of concrete work, both 
 plain and reinforced. The various designs of 
 forms and centers and the layout of plant for 
 mixing, conveying and j)lacing concrete, receive 
 the most complete treatment ever given to 
 these important subjects. 
 
 The book should he purchased hy evory enn- 
 triictor and hy every eoncrete I'uretnan an<l su])er- 
 intcndeut, for it is the liest "eorresjiondenci' school" 
 on ])ractical concrete construction that has ever 
 appeared in ])rint. 
 
 ICi-page circular FRRIi 
 
 Cloth. 6x9 inchuN . 700 pa)!i-s ; .^06 illustrations ; 
 price Sa.Olt net, postpaid. 
 
 THE MYRON C.CLARK PUBLISHING CO. 
 
 :>•").") Dearborn Street, Chicago 
 
X 
 
 Concrete 
 
 and 
 
 Reinforced Concrete 
 
 Construction 
 
 By 
 HOMER A. REID, Assoc. M. Am. Soc. C. E. 
 
 Tliis is tlic most cmipk-lc and coniprcliciisivo 
 liook cscr written or. this suiijcct. It is, in fact, a 
 combination of several booi<s in one — all original, 
 carefully written and iip-to-diUe. It has 200 workin.:; 
 drawings of bridges, bridge piers .ind enlverts; 60 
 working drawings of sewers, water mains and rcser 
 voirs; 30 working drawings each of 'etaining w.ills 
 and dams; 200 working drawings of buildings and 
 foundations, including shops, roundhouses, etc 
 
 It li.is iiuirc ttxt I'.igis, nunc ilrawinus ami nuv.o tahlts of test 
 ilat.i on ciMuri tc iml riiiifoiicil iDiuriMc rnn-.tnictmi\ tlian an) 
 other bniik cvir iuiI>lislRil. No ullur hook on (.omrili' rontains 
 otic titith so much of thv very latest data on U sts, thtoiy ami 
 praeticc. 
 
 90G pa^es, 71.'i illustrations. 
 70 tables; S»5.00 net. postpaid. 
 
 16-pag5 Table of Contents free. 
 
 The Myron C. Clark Publishinfl Co. 
 
 335 Dearborn St., Chicago 
 
 I 
 
I 
 
 ■ i- r 
 
 ^li i 
 
 Theory and Design 
 
 OF 
 
 Reinforced Concrete Arches 
 
 A Treatise for Eni^inecrs and Technical 
 Students. 
 
 hy ARVID REUTERDAHL, Sc. Ii...\. M 
 
 Chief of Briiigc Depart iTiiMit , Bn^inccrinR fX.parlmciit, 
 
 City i)f Spcikiiiic, Wash. 
 
 The books wbicli li;ive heretofore been 
 pubhshed on this subject are either so 
 niathematicLilly abstruse or leave s'> 
 much to the reader to demonstrate for 
 liimself, that they are of little value to 
 the general practitioner or to the tech- 
 nical student whose mathematical abilit v 
 is not of exceptional order. TJiesc objcc= 
 tions have been overcon e in this book. 
 Every principle is explained thoroughly 
 there are no missing steps in (he niathe= 
 matics. 
 
 Till- book shnuM l)e in the hainl^df cvcrv (i;,i;iiircr 
 wild ha.sconcrrtt' liri(ii,'es to fit-siLin .iiul of r\ cr\- sluilciit 
 of the theory and practice of concrete brid.^c .lesiv.r. 
 
 Cloth, 6x0 inches ; 1,52 pases ; numerous di.'mraiii> and lalilv, : 
 
 price f2AH) net, |>ostp;iid. 
 
 THE /MYRON C. CLARK PUBLISHING CO. 
 
 .').').") Dearborn Street. ('hica<'<i 
 
Reinforced Concrete 
 
 A Manual of Practice 
 
 By ERNEST McCLLLOUGH, C. E. 
 
 This book was written for the ])ractical concrete 
 worker — the man on the job — who has not the re- 
 quirements of statics and the theories of the mathe- 
 matician at his tonj,'ue's tip but who desires, in 
 plain words, the fundamentals of correct dcsijjn and 
 the practice of sound and economical construction 
 work. 
 
 Cloth, 5x7} inches; \36 pages; illustrated; 
 price $1.50 net, postpaid. 
 
 Field System 
 
 Hy FRANK IV OILT?RETH 
 
 This bonk was written by one of the largest 
 jjeniTal contr letors in the world, and contains nearly 
 L'(t!' paj;es of rules and instruction,, for the guidance 
 of his foremen and superintendents. It is the out- 
 growth of over twenty years of experience in the 
 contracting business, and embodies scores of sug- 
 gestions for i'conomizing and for increasing the ou'- 
 T>ut of the m.n on the job. Mr. (iilbreth is the con- 
 tractor who made the "("ost-plus-a-fixed-sum-con- 
 tr:ut" famous; in doing so. he has likewi.^e tnade 
 famous Gilbreth's "Fitld Systeni," only a few ex- 
 i'er]>ts from which have hrriic.forc appeared in print. 
 
 thousand lOpvf- 
 
 One 
 
 davs 
 
 In making pnbln. >us 
 \ , pi rforniing a sei \ U i 
 parabU- w Uh the ;u ti- 
 
 re sold in the first ten 
 
 Field S\ ,tem" Mr. (Iilbreth 
 
 I. the pul)lic that is com- 
 
 '\ a physician in disclosing 
 
 the svtut (if his sv\\ V v >>, in curing a disease. The 
 
 dtHcaso that Gilbreth s "Field Sv--tem" aims to cure 
 
 is the hit 'V miss methoil ot doing contract work. 
 
 Svstem supplants slo\ i-nliness, and makes sloth an 
 
 ilisolute iinpo-isibiht v 
 
 200 pages »UI| i)lust<'atn^Aa'- bound in leather; 
 iH^ke $.\.(B m%, postpaid. 
 
 TH!: MYRON C. CI ARK PIBLISHINQ CO. 
 
 ;"'"> 1>',iiIh !ii Sti\-<-l, i'hicago 
 
' ■ If 
 
 H. a TYRRELL 
 
 CIVIL ENGINEER 
 
 Chicago, Illinois 
 Evanston, Illinois 
 
 DESIGNER AND ENGINEER 
 FOR ALL KINDS OF 
 
 Bridges and 
 
 Structures 
 
 Special Attention to Selection 
 of Economic Types 
 
l4 
 
 I 
 
 3 
 1 
 
 5 
 
 
«'';1 
 
 ^