REESE LIBRARY or Tin: UNIVERSITY OF CALIFORNIA. 'cessions No. o9 v 6 / . Class A "^'Lv. THE DESIGNING OF DRAW-SPANS, BY CHARLES H. WRIGHT, M. AM. Soc. C. E., Chief of Detail and Drafting Department* Edge Moor Bridge Works. Author, with Prof. Wing, of ^ A Manual of Bridge Drafting." FIRST EDITION. FIRST THOUSAND. NEW YORK : JOHN WILEY & SONS LONDON: CHAPMAN & HALL, LIMITED. 1897. yright, 1897, BY CHARLES H. WRIGHT. ROBERT DRUMMOND, ELHCTROTYPKR AND PRINTER, NEW YORK. CONTENTS. PAGES MOMENTS AND REACTIONS .. 2-19 WEB-STRESSES 19-23 DEFLECTION 23-28 MACHINERY 28- 5 TABLES AND GENERAL DATA -. . 46-69 CUTS OF DRAW-SPANS SHOWING MACHINERY, ETC 70-84 DESIGNING OF DRAW-SPANS. PART FIRST. PLATE-GIRDER DRAW-SPANS. THE following pages aim to give a clear and simple expla- nation of the methods used in the determination of the stresses, sections required, and of the deflections produced by the various conditions of loading assumed. The machinery necessary for operating the draw is also considered, and the designing of wedging machinery for raising the ends, latching devices for preserving perfect alignment when the draw is closed, methods of raising the rails for clearance when the draw is opened, and the designing of gears, shafting, andi bearings are considered in detail. Each point as taken up is illustrated by examples, as fully as necessary to make the applications clear. The aim has been to use the simplest methods, rules, and tables that will give the desired results. Where formulae derived from the higher mathematics have been used, full and complete explanations of how they are used and applied are given.* It is believed the work may be * The reader is referred to the works of Professor Releaux and Unwin, from which notes have been taken. The author is also indebted for valu- able information to Professor Malverd A. Howe of Rose Polytechnic Insti- tute; the Edge Moor Bridge Works, and to the Pencoyd Bridge Works. 2 DESIGNING OF DRAW-SPANS,, readily followed and understood by those not having a full knowledge of the higher mathematics, and that it will prove of value to any one wishing a practical knowledge ef draw- spans and their machinery. PLATE- GIRDER DRAWS. For spans up to about one hundred and fifty feet the deck plate girder makes the most satisfactory bridge, and is the type in most general use. The conditions under whioh the draw-span works are much more severe than with fixed spans, and the bridge should be correspondingly heavy and rigid. Through plate-girder or lattice spans are unsatisfactory for draw-spans, owing to the small depth usually available below the floor for the introduction of diagonal bracing necessary to resist the twisting force produced in turning the draw, and especially in suddenly stopping or starting. This force is well illustrated by taking a piece of artist's rubber in the fingers and twisting. The rubber may be turned through a consid- erable angle and still a cross-section at any point will be a perfect rectangle as at first. This shows that any bracing introduced to resist this twisting action must run diagonally as in Fig. I and I A . Brace-frames at right angles to the girders do little good to resist such a force, and the same is true of bracing in the planes of the chords. An eighty-five-foot deck plate girder (Fig. i) will be used as an example to illustrate the methods pursued with girder draws in general. There are four conditions to be considered, 1st. The span swinging or in position to open, the end wedges being drawn and all the dead loads being carried by the centre, no live load acting. 2d. The draw closed and each arm considered as an independent span for live load; the dead load not being considered for the present. 3d. The bridge PLATE-GIRDER DR considered as two continuous spans for the live load; and 4th, considered as two continuous spans for the dead load onlv Cases I and 2 might occur at the same time; also I and 3 or 3 and 4. The one of these combinations giving the 4 DESIGNING OF DRAW-SPANS. greatest strains is to be used in determining the sections, required. If the end wedges are just driven to a bearing but not hard enough to raise the ends, the dead load would still be carried by the centre, and the span is still swinging so far as the dead load is concerned. If both arms were now loaded equally, the bridge is then a continuous girder of two spans so far as the live load is concerned. This is not true, however, if a live load comes on one arm only, unless the other arm be held down so that it does not raise up off the end support as the dectd load moves over the first arm. Instead of holding the unloaded arm down, it may be raised so high by the end wedges that the deflection produced in the loaded arm will not be sufficient to raise the unloaded end off the support. Unless one or the other of these plans is followed there will be what is called ' hammer ' in the draw. That is, as the load comes on one end and moves over the bridge, first one end and then the other will rise off the supports and drop back again to a bearing. This movement is very noticeable in some draws, and especially so where the rails are cut just at the clearance line and a small space left between the ends. To make sure the rails will clear as the draw turns, this space may needs be three-eighths or one-half inch. This method, or lac-k of method, of providing for the continuity of the rails is now almost entirely superseded by devices which do not require this clearance. Some of the methods used wi.l be described later. The amount it is necessary to raise the ends by means of the wedges or some similar device will be explained under the deflection of draws. To determine the strains produced by the dead load swing- ing, we will assume the weight of the floor (including ties, guards, rails, bolts, etc.) to be 400 Ibs. per linear foot, and the weight of the span itself to be 650 Ibs. per linear foot. 400 -f- 650 = 1050 Ibs. = 525 Ibs. for each girder. Only one arm need be considered if the two arms are equal. If the PLA TE-GIRDER DRA WS. two arms are not equal, the shorter one is counterweighted until they balance, but the strains would have to be consid- ered separately. The moments may be determined by assuming the dead load as concentrated at several points; thus for the moment over the pier we may assume the load on one arm as concentrated at its centre of gravity, which is at the centre of the arm (see Fig. 2). * 4275 H Arms for Dead-load Moments. Taking moments at A, we have the dead load of one arm, 525 X 42.5 = 22,310. Assuming this as concentrated at a, the moment is 22,310 X 21.25 = 474 IO ft.-lbs. This moment is balanced by forces represented by the arrows and acting in the flanges of the girder. One force is tension and the other compression. The depth of the girder at the centre is 7 feet and the moment 474,100 -r- 7 = 67,750, which is the tension in the upper flange and the compression in the lower. The depth assumed (7') should be the depth between the centres of gravity of the flanges. For the moment at B we have the load 525 X 31.86 (the distance from the end to E] = 16,730. This multiplied by the distance of the centre of this load from B, 15.93 feet, = 266,500. Dividing by the depth at this point, 6.25 feet, we have 266,500-7- 6.25 = 42,800. At the moment == 525 X 21.25 X 10.62 = 118,470. At D the moment = 525 X 10.62 X 5-3 1 = 29,600. It is not 6 DESIGNING OF DRA W-SPANS. necessary to find the chord stresses at each point now. The moments may be combined with others for live load, and the areas required for both found at one operation. The moment at any point for dead load may also be found by means of a parabola drawn as follows (Fig. 3). Lay off the horizontal 42 ;5 J NOTE: DOTTED LINE'IS FOR UNIFORM LOAD SWINGING METHOD OF DRAWING PARABOLA line BB' equal to twice the length of one arm of the draw. From the centre of this line draw a vertical line equal to> twice the moment at the pier* (in this case 474,000). Any convenient scale may be used, and the same scale need not necessarily be used for the horizontal and the vertical lines. Draw the inclined lines B 12 and B' 12, and divide each of them into any number of equal parts (12 in the figure). Con- nect the points i-i, 2-2, 3-3, etc., and the lines so drawn will be tangents to the required curve, which is now readily drawn. Only one half the curve is used, as shown by the figure. The curve being drawn, the moment at any point is * To find the centre of gravity of any number of loads from any point (as one of the end loads), multiply each load by its distance from the point, add the results, and divide by the sum of all the loads. The result will be the distance of the centre of gravity from the point assumed. Note that if there is a load at the point from which we start, this load must be in- cluded in getting the sum of all the loads. PLATE-GIRDER DRAWS. found simply by scaling the ordinate between the line B' B and the dotted curve. Having thus shown two methods for determining the dead-load moments with the draw swinging, Fig. 4 Curve of Moments, Dead Load Swinging. 525 Ibs. per lin. ft. we will now consider the case of the draw closed and each arm acting as a single span for live load.* For the live-load moments, each arm acting as a single span, we should so arrange the loads as to get as many loads as possible on the span, and the heavier ones as near the centre as may be. Placing the loads as in Fig. 5, we find the centre of gravity to be 18.7 feet from wheel No. I, and the wheels are shifted if need be until the ceritre of the span is half-way between the centre of gravity and load No. 4. We now lay off the load line AB, Fig. 5 A , assume a distance HO = 100,000 on a horizontal line drawn from any point in AB, and draw the lines AO, BO, etc., connecting the points found by laying off the loads on AB with the point O. This figure (5 A ) is called the force polygon. Next, starting from A' (any point in a vertical line through A) draw the line A' a' parallel to AO in the force polygon, and from a' draw the line a'b' parallel to %-O, from b' the line b'c' parallel to 4-O, and so on until the last \m& f f B f is drawn parallel to BO. * In drawing the parabola it will be noticed that the moment over the pier must first be figured. This moment for the load uniformly distributed is \ivL, L being the length of the arm, and w the dead load of one arm. (See first method of finding the dead-load moments.) 8 DESIGNING OF DRA W-SPANS. The line A'a'b'c'-f'B' meeting the vertical lines through A and B at A' and B' is called the equilibrium polygon. If the line OR be drawn in the force polygon parallel to A'B' of the equilibrium polygon, it will divide the load line AB into Diagram for One Arm as Single Span. Moment at any point as CC = CC X HO CC X 100. the two parts AR and RB which represent the reactions at A and B. Having the equilibrium polygon drawn, the moment at any point is found by multiplying the ordinate between the closing line A' B' and the line A'a'b'c' , etc., by the distance OH m the force polygon. HO being 100,000, the moment at b, for example, will be bb' multiplied by 100,000. The distance HO is made 100,000 for conveni- ence. It should be made of such length as will give a good PLATE-GIRDER DRAWS. 9 depth to the equilibrium curve, so that the ordinates may be accurately scaled. The distance HO must be measured to the same scale as the load line AB was laid off, and the ordinates in the equilibrium polygon must be measured to the scale used in laying off the half-length of the span (see Fig. 5). It is not necessary that the two figures be drawn to the same scale. The moments at as many points as nec- essary can now be determined. These moments are given in column 4 of the table of strains. In Fig. 5 the curved line A 'D and the line A ' B' give the dead-load moments with the span swinging, A 1 D being a parabola and the ordinate B' D being the moment at the centre support di- vided by the distance HO (= 100,000). The signs of the moments are determined as follows: The loads acting to the left of the centre support tend to revolve the span downward in a direction opposite to the movement of the hands of a clock. These moments are called minus ( ). Considering the same arm as a single span, the reaction at the left support tends to revolve the span upward or in the direction of clock motion. These moments are called plus (+). It is immaterial which are called plus, provided all moments tending to pro- duce rotation in the same direction are given the same sign. The total moment then at any point, as e 1 ', under the two conditions, dead load swinging and live load discontinuous, on one arm, would be the ordinate ee' ee* = e*e' multiplied by the pole distance HO. It might be found that slightly greater moments would be obtained by placing the loads so that the centre of the span would be between the centre of gravity and load number 3, instead of between the centre of gravity and load number 4 (see Fig. 6). Both positions should be tried. Having shown how to determine the moments for the span swinging, and for the condition of one arm acting as a single span supported at the ends, with live load only acting, we will now consider the span as a contin- uous girder under the action of both dead and live load. It UNIVERSITY CALIFORH\* 10 DESIGNING OF DRA W- SPANS. will be noted that in the case of dead load swinging only one arm was considered. This is sometimes confusing and the question is asked, * Why can one arm be neglected ? They must surely both produce strains over the centre.' It is the old problem of two men pulling at the ends of a rope; each man pulls one hundred pounds, but the strain on the rope is not two hundred pounds. One man cannot pull one hundred pounds unless there is a resistance of this amount opposing his pull. It makes no difference whether the resistance is given by a man or by a post at the other end of the line. In the same way an arm of the draw when open is balanced by the other arm. And the moment at the centre is the moment produced by one arm. When the span rests on three or more supports or the loads are not balanced we can no longer consider one arm only. If a load is placed at any point on the span, a greater pro- portion of this load will be carried to the centre support than would be the case if the arm on which the load is placed were considered as a single span resting on two supports. Just how much more of the load is carried to the centre is given by the diagram Fig. 9. The figures at the bottom under the line ' values of k ' are the distances from the left-hand support to the loaded point, in terms of the length, and the figures in the line marked ' values of D* give the per cent of the load going to the left-hand support. Suppose there is a load at three tenths of the length of the arm from the left support. From the figure 0.3 in line k l we move up until this line inteisects the curve marked ' 5, loads in first arm ' ; from the point where the line through 0.3 intersects this curve we go over to the left until we reach the line D v , which is at 0.63. 63 per cent of the load then goes to the left sup- port. If we wish for the bending moment at this point, we move up the line through 0.3 in k^ until we meet the curve marked ' M y loads in first or second arm.' We intersect PLATE-GIRDER DRAWS. II this curve on the horizontal line 0.685,* an d so for any other point in the span. We will now place the engine-loads on the span in two or three positions and see which position will -. -12.8 --*]- S.O^-O- - -7.fr - - 8.1- - ' 18. 18. 20. 18 10J2510|25 k]j.2511>25 8". 18. 18. 2b. 18. O (flafe 6) (5) FIRST ARM. k. c. CPL. 7.1 -5-42.5 = 12. = I6. 3 2O.7 33-5 = 38.5 Moment CPL .167 .282 .384 .487 .788 .906 .0405 .0645 .0819 .0927 .0745 .0400 30,980 49.340 69,610 70,900 32,450 17,420 270,700 279.385 550,085 SECOND ARM. SECOND ARM k. c. CPL. 6.7 -r-42.5 = .0156 .0380 29,608 n. i = .261 .0605 51,450 15-4 = .362 .0785 60,030 20.3 = -477 .0920 70,380 28.4 = .668 .0925 31,350 35-9 = -845 .0600 28,680 40-9 = .962 .0165 7.887 279.385 Diagram for Two Spans Continuous. Scales, 20 and 50. 0.685 is the value of C in formula M CPL = moment at any point* 12 DESIGNING OF DRA W-SPANS. give us the greatest moment over the pier. Arranging the loads as in Fig. 6, we first find the values of k\ thus for loads i i 18. 10.26 ID 10.25 11.25 llj.25 (troT (?) 6.6 I 8.1 | 4.9 | 4.3 | 4.4 12.8 j 3.6 i 5.5 5.0 7.5 8.1 4.9 4.3 1 3.6 20. FIRST ARM. >&. c. CPL. 6.6 14.7 19.6 23-9 28.3 41.1 Moment -5- 42.5 = .155 = -346 = .461 = .562 = .666 = .967 = CPL .0380 .0756 .0910 .0963 .0927 .0150 12,929 57,815 69,605 81,850 70,905 6,525 299,629 233,331 532,960 SECOND ARM. k. c. CPL. 3.6-^-42 5 = -084 .0215 18,274 7-9 = .186 .0450 34,422 12.8 = .301 .0685 52,395 20.9 = -492 0933 31,720 28.4 = .668 .0927 44,760 33-4 = .786 .0750 35,862 38.9 = -9J5 .0365 15,898 233.331 Diagram for Two Spans Continuous. Scales, 20 and 50, PLATE-GIRDER DRAWS. 1 I, 2, 3, 4, 5, and 6 we divide the distances from the left by the half-span 42.5', and for loads 7, 8, 9, 10, 11, 12, and 1 3 we divide the distances of the^ loads from the right-hand abut- Fig. 8 A Diagram for Uniform Load Continuous. 1000 Ibs. at each eighth point assumed load in diagram. ment by the half-span 42.5. The values are given in the table: .167, .282, etc., for first arm and .0156, .261, etc., for the second arm. From diagram Fig. 9 we now find the values of C corresponding. The vertical through k 167 meets the curve of moments on the horizontal line .0405, and for k = .788 on the line .0745. The values of k for the: second arm are given from the right abutment, so we find C exactly as in the first arm. If the distances had been given from the centre pier, we could have found C in the same manner, only using the line marked k* in the diagram instead of line k' \ for example, if a load is .8 the length of the half- span from the right abutment, it is .2 the half-arm from the centre pier. o. ik' is over k* = 0.9. It is perhaps a little simpler to use the line k' all the time, and give the distances of the loads from the abutments in each case. All values of C have the same sign. Multiplying each value of C by the load at that point, and by the length of the half-span, gives us the moment over the centre pier for that load. CPL = moment over pier for load P at any point. The values of 14 DESIGNING OF DRAW-SPANS. these moments for each of the wheel-loads with the engine placed in the two positions given in Figs. 6 and 7 are given Fig. 9 in the tables under the figures. Two or three trials will show how the engine should be placed to give the greatest PLATE-GIRDER DRAWS. 1 5 moments. By referring to the diagram Fig. 9 it will be seen that C is greatest for loads near the centre of each arm, and a little nearer the centre pier than the abutments. The heavier wheels should then be placed as near these positions as possible to give the maximum moments. Adding to- gether the moments produced by all the loads, we have the total moment. In the two cases given these total moments are 550,085 and 522,960. It is possible that the uniform train load might give a greater moment at the pier than the engines, and this moment should be found. Before considering the uniform load we will take one more example of moment from concentrated load to make the method just described perfectly plain. Suppose we take wheel No. 1 1 in Fig. 7. The distance of this wheel from the right abutment is 12. 8. k = 12. 8-^-42. 5 .301. C for k = .301 is .0685, and CPL, the moment, = 52,395. P = iSand L = 425. Considering now the case of uniform load, span continu- ous, the Reading loading diagram gives 4000 Ibs. per linear foot, or 2000 Ibs. on one girder. 2000 X 42.5 = 85,000 = the load on one arm. The formula for the moment at centre support with uniform load is \wl* w = tne load per foot, and / = the length of one arm of the span In this case w = 2000, /= 42.5, wl = 85,000, \wr = 451-562. This is con- siderably less than the moment from the wheel-loads, which was 550,085 for one pusition of the loads. It will be noticed that the moment over the pier, \wr, is just the same as the moment at the centre of a single span of length equal to one arm of the draw and covered with the same uniform load; and is also just one fourth as much as it would be over the centre support were the draw swinging and covered with the same load. Note that in moment \wr, wl is load on one arm. A convenient method of finding tnese moments for uniform load is to assume a load one pound or one thousand pounds per foot, find the moments for this loading, and then 1 6 DESIGNING OF DRA W-SPANS. multiply the results by the ratio of the actual loads to the one assumed. To make us a little more familiar with the force and equilibrium polygons, we will divide each arm into, eight parts and assume a load of 1000 Ibs. at each of these points and one half load at the ends. The loads at the ends, coming directly over the supports, may be neglected in the computation. We lay off then on the vertical line AB, Fig. 8 A , seven spaces representing 1000 Ibs. each. Any scale may be used, say one-half inch equals 1000 Ibs. Next assume the point O distant from AB 5000 to the same scale. Note that the point O may be anywhere in a vertical line which is dis- tant 5000 from the vertical line AB, and also remember that we assumed the distance 5000; any convenient distance may be used. We next connect the point O with each of the points laid off on AB. Now going to Fig. 8, at any point on a vertical through A we draw the line A' a' parallel to AO in Fig. 8 A , and from a' the line a'b' parallel to the next line in the force polygon, and so on until finally g'B is drawn parallel to BO in the force polygon. Now connect A' and B' with a straight line. From B' in Fig. 8 scale off the distance B'-B* equal to the moment at the centre support divided by the dis- tance HO 5000 in Fig. 8 A . The distance B ' B' must be laid off to the same scale as Fig. 8 is drawn to. The moment at the centre is of course found for the same loading (1000 Ibs. at each eighth point = Jw/ 2 ). By the diagram Fig. 9 the values of C for k i, f, f, f, f, f, and -J are: A' = i = .125 C=.03oS; P = 1000, L 42.5; CPL 1309.00- A'- = .250 C=.0586; " " =249050 A" =g = .375 C=.o8o6; " " =342550 A' ==.500 "=.0938; " " " =3986.50- A' = = .625 =.0952; " =4046.00 A' = = .750 C =.0820; " " =3485.00 A'=f = .875 =.0513; " " " =2180.25 .49 2 3 20922 25 The moment \wi, for the same load uniformly distributed (8000 Ibs. on each arm) is 42,500. The difference by the two PLATE-GIRDER DRAWS* I/ methods is 655.75 or J f P er cent which shows that the method is practically correct, and it is merely a question of reading the diagram correctly to obtain accurate results. Making a table of the moments (see p. 18), we have first the column of moments for dead load swinging, the moments being found by methods shown in Fig. 2 or 4. These moments are 474,000, 350,000, etc. Next we make the column of moments for dead load continuous, as shown by Fig. 8, remembering that the moment at any point is equal to the moment for the same load, considering the arm as a single span supported at the ends, less the negative moment at this point, and that this negative moment is represented by the ordinate between the lines A'B' and A'B* multiplied by the pole distance HO ; the ordinate B l E i being the moment over pier divided by the pole distance HO. Thus the moment at D equals ordinate dd' minus ordinate dd* (Fig. 8) multiplied by HO (HO = 5000). Having the moments tabulated, we now see which com- binations will give the largest totals. The dead load swing- ing and live load continuous, case A, give the largest moment over the centre support, 1,024,000. The same combination also gives the greatest moment at the -J point. At the quarter point the dead load swinging and case A live continuous give a minus moment of 318,000, and live load discontinuous with. dead load swinging give a plus moment of 187,000, and so at each of the points f, f, etc., we obtain the results given in column 8. Dividing these results by the depth of girder (centre to centre of gravity of flanges), we obtain the results given in column 10. Dividing these results by the unit stresses as allowed by the specifications (in this case 8000 Ibs.), we have the areas required (column 12).* In Fig. I E the areas required at the several points are laid off to scale, and the lengths of the cover-plates required readily determined. * Where the flange-areas are determined for tension, the areas after deducting rivet-holes must be used. iS DESIGNING OF DRA W-SPANS. d a oo M' in co 00 N co M r" 1! II II II II II II II II 1- = I,,, .-.-,,, | c 2 o ooo o o o o o OO O O W OO M O O O a S Q . co xn oo O co xn co >>! 1 00 N M M CO CO M N COO CO W Tf ** O O oco--< xn co O O xn co II + + + + + Dead Load Swinging. CN r^ \r> o oo c*! o w M -f co a -. M 1 1 1 1 1 1 1 1 i !ll - oo co co co co co co CU WEB-STRAINS. 1$ The plates should extend about two feet beyond the points so determined. The web is not considered as taking any flange-stress, and the area in top flange is made up by two 5" X 3%" X -fa" angles and two 12 X i plates. One of the plates will be too long to get in one length, and a splice-plate is added to make up the section at the splice. In the bottom flange two -f " plates are used. WEB-STRAINS. We will next consider the shearing stresses in the web. The greatest shear at the abutments will be obtained by con- sidering one arm as a single span for live load and dead load swinging, no dead reaction at abutment, as the condition of dead load continuous and live load discontinuous cannot occur. See combination of strains made. From a table of '* shears and bending moments ' for this engine we have the end shear for a span 42. 5 72,650 Ibs. That is, 72, 650 Ibs. is the upward force exerted by the support at the abutment. Say the specifications allow 6000 Ibs. per square inch shearing on webs; then 72,650 -=- 6000 = 12.1 sq. in. required; 48 Xf- inch web plate gives 18 sq. in. At the quarter point the upward shear is 46,500 Ibs. From this is to be taken the dead load between the abutment and this point. This load equals 525 X 10.62 = 5600 Ibs. 42,500 5600 = 36,900 Ibs. Note that in finding the greatest live-load shears the heavy wheel at the front of the engine is placed at the point where the shear is required, and that there is no live load on the span between the abutment and the point whose shear is being determined. At the centre of the arm the live shear is 22,700 upward, and the dead-load shear downward is 11,200. 22,700 11,200= 10,500. The greatest shear at the pier will be with dead load swinging (all dead load carried to the 20 DESIGNING OF DRA W-SPANS. pier) and with live either continuous or discontinuous. For discontinuous live load we have the same maximum shear at the pier as at the abutment, the engine simply headed the ! I-H i i I I 1 I i i i i 2.7 5.6 5.0 7.5 LOADl 8.1 14.750 4.9 4.3 4.4 12.8 CE nj E 5.0 5.6 5.0 9.0 i 5.1 Tig. 10 Span. 1 DI Load. -s\ 2.7 425 0.06 0-93 10,250 9.740 8.3 0.19 0.76 11,250 7.780 13.3 0.31 0.62 11,250 6,975 20.8 0.49 0.41 8,000 3,280 28.9 0.68 0.23 18,000 4,140 33-8 0.79 0.14 18,000 2,520 38.1 0.89 0.06 20,000 0,120 42.5 1.00 o.oo 18,000 0,000 34,355 D, 12.8 17.8 425 0.30 0.42 O.oSg 0.096 10,250 10,250 912 984 23-4 28.4 0.54 0.68 0.091 0.071 11,250 11,250 1,024 782 37-4 0.88 0.024 20,000 481 42.5 1. 00 0.0 000 4,183 114,750 - (34,355 - 4183) = 84,580 . Shear at Centre, Girder Continuous, other way. We have then the upward shear live = 72,650 4- the dead weight of one arm 22,300. 72,650 -f- 22,300 = 94,950. Considering now the case of live load continuous: it is clear that a load in any position (as the centre) on one arm WEB-STRAINS. 21 tends, by causing this arm to deflect, to raise the other arm off its abutment or end support. This support then has less to do or the shear is reduced at this point by the load on the other arm ; it follows therefore that, as all the load on the span must be carried by the abutments and the pier, if some load is taken from the abutment it must be added to the load on the pier, A greater proportion of the load is carried by the centre pier considering the two arms as continuous than by considering them as independent spans. And in determining the shear at any point the loads on both arms must be con- sidered. By means of diagram Fig. 9 the reactions caused by loads at any point in either arm are readily determined. Arranging the loads as in Fig. 10, and finding the values of k k and Z\, DV we get for the shear just to the left of the pier 84,580; this added to the dead-load shear gives a total of 84,580 -f- 22,300 = 106,880. The area of 84 X I web = 31.5 sq. in., against 106,880-^6000= 17.8 required. Stif- feners should be at intervals of about the depth of the web apart, with 6 ft. as a maximum. 22 DESIGNING OF DRA W-SPANS. LATERAL BRACING. The laterals should be figured for a wind-load of, say, 6oc Ibs. per lineal foot, the point being to get sections heavy enough to render the span stiff laterally. Cross-frames should be used at intervals of ten to fifteen feet. Note that lateral bracing should be figured to carry strains to the centre, and that this force, equalling at least 300 Ibs. per foot = 25,500 Ibs. for both arms, should be considered in designing centre pivot and anchorage. CROSS-GIRDERS. When the draw is closed and ready for the passage of trains the girders are supported at the centre by wedges, so the cross-girders carry only the dead weight of the span. This amounts to 44,600 at each side; as there are two cross- girders, the moment on each is 22,300 X 42 in. = 936,600 in. -Ibs. Using 2O-in. 64-lb. beams, with a moment of resistance of 114, gives a fibre-stress of 8200, allowing an ample margin. CENTRE-POST. The load on the centre-post is about 90,000 Ibs. The. base of the post should be large enough to distribute this well over the masonry and to give the post stability. There should be anchor- bolts built into the masonry, and their area should be sufficient to resist the shear from wind-forces, as- suming for this purpose a wind-pressure of 300 Ibs. per lineal foot of bridge, and neglecting the friction of the base-plate on the masonry. This gives a force of 300 X 85 25,500 Ibs. Four ij-in. bolts at 7300 Ibs. each would be ample. A wrought-steel post is preferable to one of cast iron, as it is much less liable to break if the bearing on masonry becomes unequally distributed. The post should be made high enough DEFLECTION. to throw the point of suspension into the upper half of the web ; the girders will then hang better and turn more easily, as there will be less weight thrown on the trailing-wheels. DEFLECTION. Deflection Formulae. NOTE. These formulae are applicable to spans of any length if the propor- tions are approximately as given below r 4.704 WD D for uniform loao = - - ........ (0 D for load at end = -, ........ (2) '=58*. *"T?* + K? i.i66WL* D for uniform load = - ~i ........ (3) D for load at end = ". ........ (4) . , I.3I for uniform load - - ~^i ....... (5) 4.248PZ 9 for load at end = - -r~ - ..... (6) 2 4 DESIGNING OF DRA W-SPANS^ D = deflection ; h v = height at centre ; h = height for any distance x ; L = length in inches ; x = distance from left end in inches ; P = load at end ; PF= totol load uniformly distributed. A 'B / 1C ;D , ! 70 ' 1 > 1- | 700 ; 1^ 1 i \ r / 2-6"x 6*L' z III o f Fig. 14. Fig. 15 The amount the girders will deflect under the various loads depends upon the length, the depth, and the arrange- ment of the material in the girders. If the flanges are parallel and their area of cross-section remain the same or nearly so DEFLECTION. 2$ throughout their length, the formula for deflection for con- stant section may be used ; thus for uniform load wr D = deflection, W ' = the load on the girder, /= the length in inches, E = 29,000,000, and 7= the moment of inertia. For a load at the end pr If the flanges are parallel, but the cover-plates are of several lengths and the girder have about the proportions shown in Fig. 13, the deflection for uniform load will be ^_ 4.704^ (I) Eh* W = total load on arm, and h = depth of girder back to back of flange-angles. For load at end Eh: Number I is equal to wr 195,500,0007* and number 2 may be written - 68,900,0007- ' ' W = total load on one arm in each case, and 7 = the moment of inertia at the centre support. For girders having approxi- mately the proportions shown in Fig. 14, which is the span 26 DESIGNING OF DRA W-SPANS. taken as the example in considering strains, etc., we have for uniform load 1. 16607* , , *>=- ...... (3) Wl* .... (3*) i6i,5oo,ooo7 and for load at end 3-377^/ 3 pr .... (44 55,700,0007* Where the girders have the proportions as given in Fig. 15, for uniform load (5) 132,000,0007 and for a load at end wr , . . . . (5*) 4O,8oo,ooo7* W and 7 as given above. Some one of the formulae would be applicable to any case likely to occur. Considering first the case of uniform load : the girder we have been considering is composed of 84" X i" web, four 5"X Si" X TV" angles, and (neglecting the short splice-plate), two 12" X i" plates in top flange and two 12" X f" in bottom flange. To simplify the calculations, we will for the present consider all cover-plates as \ in. ; if this is not done, we should first find the centre of gravity of the section, and then the moment of inertia about this axis. Usually the flange-plates DEFLECTION. 2f are the same, and we will obtain nearly correct results by so- considering them. The moment of inertia of the web about its centre is equal to -^bk\ (b f , and h = 84.) -fab/i* = T V X f X 84" = 18,522. The moment of inertia of the cover-plates and angles about the centre of the web is found by multiply- ing the area of each by the square of the distance between its centre of gravity and the centre of the web. Thus the area of the four -in. plates = 24 sq. in., and the square of the distance from the centre of web to their centre is (42 -|- J) 2 . 24 X (42.5)' = 43,350. By referring to Carnegie's Pocket- book we see that the centre of gravity of the 5 X 3i angles is about i in. from the back of the angle, and that the area of the four angles is 17.88 sq. in. The half-depth 42 in. I in. gives 41 in. as the distance from the centre of the web to- the centre of gravity of the angles. 17.88 X (41)' = 3^^6. To the moments of inertia thus obtained we add the moments of inertia of the cover-plates, and the angles about their own centres of gravity; for the cover-plates ^bh* = T V X 12 X i in. = i for each flange, and for the angles we have from the Pocket-book 4.2 for each angle (see page 103, edition of 1893). 4.2 X 4 16.8 + 2 18.8, amount to add for plates and angles. The total moment is then 18,522+43,350 + 30,056 + 18.8 = 91,946.8. It will be noticed that the moments of inertia of the plates and angles about their own axis is very small, and might be neglected without seriously affecting the result. Using our formula No. $a, we have _ wr 161,500,0007* W = 22,300, as previously found, L = 42.5 ft., and I 91,946.8. 22,300 X 132,651,000 D = - * -2-5- = o. IQ inch = A inch. 161,500,000 X 91,946.8 48 DESIGNING OF DRA W-SPANS. If each arm is given a camber, this must be considered in determining the end deflection. Suppose the top chord be lengthened by adding i in. at a web-splice near the centre of the arm. If the girder be 5 ft. 6 in. deep at this point, and the distance to the end be 21 ft., the end will drop i -r- 5.6 X 21 = .94, say f| in. Adding o. 19 + -94 = J -i3 in - i Jin., end deflection. MACHINERY. For Turning. The forces to be overcome in turning the draw are, first, the inertia of the span itself. That is, there is a certain mass which has to be revolved through a quarter of a circle or 90 of an arc in a certain time. Second, there is the friction on the centre pivot or rollers. Third, the friction of the trailing-wheels due to the overturning force of the wind, and the friction on the vertical surface of the pivot due to the wind-pressure. Fourth, there is the friction of the trailing-wheels due to any unbalanced load there may be. Fifth, the friction of the shaft-bearings, etc. Item four might be considerably increased by the rails on which the wheels bear being out of level, rough, and with wide openings at the joints. It is sometimes assumed that the draw shall turn against a wind-force acting on one arm only of the span. While this might possibly happen in the case of a long span, it could hardly occur in the short 85-foot span we are con- sidering, and this condition will not therefore be treated at present. Force required to Overcome Inertia. For convenience we replace the mass of the bridge by an equivalent mass act- ing at the rack-circle. This mass is found as follows: Mul- tiply the weight of the span by the square of half the length plus the square of half the width, and divide by 96.6 times the square of the radius of the rack-circle. Putting this in the form of an equation, MA CHINEX Y. 29 W(* + ff) M = 9 6.6R> ' where W = weight of sgan ; a = half-length of span ; b = half-width of span ; R = radius of rack-circle; M = equivalent mass at rack-circle. The weight of our span is 89,200 Ibs. = W. a, the half- length, = 42.5 ft.; b y the half-width, = 3.5 ft.; and R, the radius of the rack, = 7.85 ft. We have therefore 89,200 X (42. 5' +3-5') M= ~ 9 6.6 X 7-85^ - 2 If we assume that the draw shall open in two minutes, the average velocity will be one fourth the circumference of rack divided by 120 sec. = ^' 3 = 0.103 ft. per second. But 4 X 120 the velocity is not uniform; it increases during the first half of the turning, and then reduces to o again at the end. The maximum velocity at the end of 60 seconds is then twice the average, or 0.206 ft. per second. The rate of increase is 0.206 -r- 60 = .0034. The force necessary to give a mass of 27,224 Ibs. a con- stantly increasing velocity of .0034 ft. per second = 27,224 X 0.0034 92.5 Ibs. We will call this Fm. Force to Overcome Friction on Centre Bearing. A Sellers centre is used so the friction from load will be rolling friction; a coefficient of .003 may be used, and this multi- plied by the load gives 89,200 X .003 = 267.6 Ibs. This acts at the centre of the length of the roller, or with a lever- age of 8 in. or .62 ft. 267.6 X .62 -r- 7.85 =21.1 Ibs. the force required at rack to overcome it. This force we desig- nate F p . Friction on Side of Pivot or End of Rollers for Wind- pressure. Assuming a wind-load of 300 Ibs. per lineal foot. 30 DESIGNING OF DRAW-SPANS. there results a total horizontal force of 300 X 85 = 25,500 Ibs. This, whether acting against the ends of the rollers or on the side of a pivot, will produce sliding friction. Using a coefficient of o. I, this gives 25,500 X o. i =2550 Ibs. acting at the end of roller or at circumference of pivot (acting on vertical surface). Let the radius of end of roller be 9^ in. or .8 ft., then 2550 X .8 -f- 7.85 = 259.8 Ibs. at rack. We will denote this by Fw. Force required to Overcome an Unbalanced Condition of the Draw. Suppose that from snow or some other cause there is an unbalanced load on one arm, acting at a point 15 ft. from the centre pivot. The force at the wheel-circle required to balance this is 15-7-7 (the radius of the wheel- circle) 2.143 times the load. Assume the load to be 2000 Ibs.; this multiplied by 2.143 gives 4286 as the pressure on the balance-wheel. The friction caused by this pressure will be rolling friction and equal to 4286 X .003 = 13 Ibs. Thir- teen pounds at the wheel-circle will require 13X7-7- 7.85 = n.6 at the rack to overcome it (7 and 7.85 being the radii of the two circles). This force we will call Fu. The centre of the surface exposed to the wind, including ties and guard-rails, is almost exactly in line with the bottom of the cross-girders, so that the moment of the wind-force tending to revolve the girders about the centre casting as a fulcrum is in this case slight and may be neglected. Suppose the centre of wind-pressure had been one foot above the point of support for cross-girders, the overturning moment would then have been 25,500 X i = 25,500 Ibs. ; this divided by the horizontal distance from the centre support to the centre of the trail ing- wheel, 7 ft., gives the vertical force acting at wheel to resist overturning. 25,500 -~- 7 = 3643 Ibs. Using coeffi- cient of friction .003 gives 10.9 Ibs. 10.9 X 7 -5-7.85 =, say, 9.7, force at rack necessary to overcome it. This will show how to proceed in cases where this overturning force of the wind is too great to be neglected. MACHINERY. 31 Force required to Overcome the Friction of the Shaft. There will be only one shaft required in the turning arrangement. Assuming one man is able to turn the draw, and that he exerts a pressure of 75 Ibs. horizontally against the top of the shaft ; assuming for the present also that he works at the end of a five-foot lever, and that a pinion 8 in. in diameter can be used in rack, we have a horizontal pressure at foot of shaft of 75 X 60-^4 = 1125 Ibs. 1125 + 75 = 1200 Ibs., total pressure on shaft-bearings. The friction caused by this will be sliding friction, for which the coefficient is 0.05 to o.i. Multiplying 1200 X o. I = 120 Ibs. as the frictional force acting at the circumference of the shaft. This we will call Fs. We have then forces to be overcome as follows: Fm = 92.5, Fp = 21. ij Fw = 259.8, Fu = 1 1.6, and Fs = 120 Ibs. First we will see how much power is consumed in over- coming Fs. The radius of the shaft will be assumed as i in. for the present, then 120 X i H- 60 = 2.5, the power required at end of turning-lever to balance it. This leaves us 75 2.5 72.5 Ibs. as available against the other forces which all act at rack-circle. These equal 92.5 + 21.1 -f- 259.8 -4-11.6 = 384.9 Ibs. Dividing 384.9 by 72.5 gives 5.3, which is the number of times the power must be multiplied between the turning-lever and the pinion, or by the two. We see at once that our power will be greatly in excess of the amount required. It will multiply as many times as the radius of the pinion is contained in the length of the turning- lever, 60 -r- 4 = 15 (using an 8-in. pinion). We might use a six-inch pinion and four-foot turning-lever. It is well, how- ever, to have a good excess of power, as machinery may get out of adjustment, the track become rough, and with gaps at the joints, the span may become badly unbalanced, etc. Time for Turning. The man turning the draw will walk at an average velocity of, say, 3 ft. per second. If he be moving at the end of a five-foot lever, he will move in a 32 DESIGNING OF DRA W-SPANS. circle of 31.6 ft. circumference. It will require 31.6 -j- 3 = 10.5 seconds for him to make one complete revolution. The pinion of course makes one revolution in the same time. Using a pinion of 25 in. circumference on the pitch-line, and a rack of 49.3 ft. circumference, the pinion must make 501.6 in. . . c ,, , - = 5.0 revolutions in moving over one fourth of 4 X 25 the circumference of the rack, which would be necessary to open the draw. If one revolution is made in 10.5 seconds, 10.5 X 5.9 = 62 seconds as the time required to open or close the draw. Size of Turning-shaft. The man moving at the end of the turning-lever produces a twisting moment on the shaft of 75 X 60 = 4500 in.-lbs. In addition to this twisting there is the ben-ding produced by the force acting on the pinion. Fig. 1 6 Assuming an 8-in. pinion, this force equals 1125 Ibs. ; and assuming that the lower corner of the tooth is acting, and that the distance from this corner up to, say, I J in. inside the journal-bearing equals 6 in., then the bending moment will be 1125 X 6J = 7312 in.-lbs. By referring to the notes on shafting we find that the strength of a shaft to resist both bending and twisting is given by the formula M= bending moment, and T= twisting moment. 7" = 7312 + 1/53465344+20250000 = 7312 + 8585 = 15897. MACHINERY. 33 Adding 50 per cent to this to allow for contingencies, we have 23,846 in.-lbs., requiring a 2-f-in. diam. shaft. Note that the shaft is weakened by the keyways and the shoulders for turning-lever. Proportions of T railing-wheels. The face of the wheel should be about 4 in., to make sure it always has bearing on the rail and to keep the bearing back from the edge. Letting w = width of face, the other proportions would be about as follows: Thickness of rim = .^W\ thickness of solid web = .2$w; stiffening-ribs, six in number, thickness = ,2w\ length of hub, not less than i.$w\ diameter of hub, 1.85 times the size of axle required. The side bearings should not be less than the diameter of the axle, giving total bearing of 2D or more. In figuring the size of axle required, if a length from the centre of the wheel to the centre of bearing be used, the unit stress in bending might be assumed at 30,000 Ibs. per square inch. The reason for this is that the bearings and hub prac- tically fix the axle so that it cannot bend until it leaves the hub or the bearings. Strength of Teeth in Rack and Pinion. Referring to the tables and notes on the strength of teeth, we find the formula for the safe load on cast-iron teeth P = 375/ a . This formula is for the strength of tooth considering the load as applied at one corner. We found the pressure on the tooth to be 1125 Ibs.; then P = 1 125 = 375*''. f- 3, and / = 1.73. (See table of cast-iron teeth.) We find also from the table that the width of face must be 2\ in. to give the same strength, assuming the load as uniformly spread over the length of face. As the speed is slow, we use the value of P l for 100 ft. per minute or under. It is common practice to make the breadth of the tooth not less than two to three times the pitch. Steel Rollers in Centre Bearing. Making the rollers hard steel on hard-steel bearing-plates, we can allow a pres- 34 DESIGNING OF DRA W-SPANS. sure per lineal inch of roller of 1750 Vd\ d being the average diameter of roller. Calling this average diameter 2.J>", we have 2765 Ibs. allowed pressure per lineal inch. The weight of the span is 89,200 Ibs., and this divided by 2765 gives 32.2 lineal inches required. There are 15 rollers, 3 in. long, giving 45 in. actual. If a centre-pin is not used, care should be taken to give the ends of the rollers an even bearing to resist the lateral pressure as explained above. The plates or rings between which the rollers move should be thick enough to distribute the pressure evenly and so that there will be no give or spring as the span revolves. For three-inch rollers the plates should not be less than 2f to 3 in. thick. If a pivot with flat disks had been used (see details of this form of centre), the coefficient of friction would have been about o. I (see table of allowed bearing on disks of steel and bronze). The centre of pressure on pivots is at two thirds the radius from the centre. Wedging Arrangement at Centre and Ends. The cen- tre roller-bearing is supposed to carry dead load only. To support the span under live load, wedges or some equivalent device are used under the girders at the centre and at the ends. The supports at the centre should be driven just hard enough to bring them to a full solid bearing, but not hard enough to take the dead load off the centre pivot or rollers. The amount the end wedges should drive is determined by the amount of deflection it is found necessary to take out of the girder so that there shall be no raising of the ends off the supports as the load passes over one arm. The gears or levers moving the wedges are easily arranged to give any desired amount of motion to either set. The amount it is necessary to raise the ends of the girder will now be consid- ered. Placing the engine on one arm with the heavier wheels at the centre, we find the reaction at the end of unloaded arm to be 7070 Ibs. (see Fig. 9.) This means that MACHINERY. a force of 7070 Ibs. must be applied at the end of unloaded arm to prevent its raising off the support. This force may be obtained by driving the wedges under the ends of the girder, and giving it an upward deflection until it is strained sufficiently to give the reaction required. Our formula for the deflection from an end load and girder of varying section is, from page 26, No. 4*2, . 55,700,0007 We have ^=7070 Ibs., 7=42.5 ft. = 510 in., / = 91,946.8. 7070X132,615,100 ' . nch> 55,700,000 X 91,946.8 Our wedge must then have a vertical movement of some- thing over T 3 ^ in. If we make the slope of the wedge I in 5, a horizontal throw of 12 in. will give us ample clearance for turning. The horizontal force necessary to drive the wedge will be 7 y (fa being the slope of the wedge) plus the friction of the top and bottom surfaces of the wedge on their bearings. This friction we will assume as 236 Ibs. Then 70 6 70 -f- 236= 1414, which is the horizontal force to be applied. The coefficient of friction might be as high as o. 10. At this value we have JLQ B 15 -+ 77 + 77 = 2 59 2 Iks. as against the 1414 Ibs. we are now using. It will be noticed that the friction is an important element in determining the actual power to be derived from the wedge. The centre wedges should not be driven hard enough to lift the span off the centre support, but just to a solid bearing. We will assume, however, for the present that all six wedges are driven with a force of 1414 Ibs. each. This will give us an excess of power of about 50 per cent. One man, it was assumed, could exert a force of 75 Ibs. The power must then be multiplied between the man and the wedges. 1414 X 6 = 8484 -T- 75 = 113.2 times. Using a 6o-inch lever and 36 DESIGNING OF DRA W-SPANS. the worm-screw arrangement as shown in Fig. 46, in one revolution of the shaft the man moves 120 X 3.14 = 376.8 ft. The pitch of the screw is, say, 2\ in., or there is a vertical motion of 2j in. Dividing 376.8 by 2| gives 150.7 as the multiplication of power, against 113.2 required. We do not then need to increase the power further, and all arms on the shafts may be of the same length. If the rods connect- ing centre and end shafts are on one side of the bridge only, that is, if one set only are used (sometimes one and sometimes two are employed ; if the bridge is wide, there should be a set on each side), these rods will carry a strain of 1414 X 2 2828 Ibs. each. Rods f or f in. round will be ample. The worm-shaft has a twisting moment of 75 X 60 = 4500 in. -Ibs. ; by the table on shafting we see that this requires a shaft of, say, I T \ in. diameter. In order to make a suitable thread for the worm, the shaft ought not to be less than 5^ or 5} in. diameter. So in this case the worm would determine the size of shaft to use. The angle of repose for steel on cast iron is, say, 1 1. The thread of the worm should then have a slope not exceeding 10 or 12. If the pitch is 2-J in., the thread rises \\ in. in one half-revolution, and the angle is found by dividing this rise (ij- in.) by the diameter of screw on the pitch-line. Assuming this to be 5.8, we have 1.25 -=- 5.8 = .21 = tangent of 12. Rather than use a shaft of this diameter, it would be better to make the worm in the form of a sleeve, and key it to a 2j or 2^ in. shaft. Or a shaft 3^ or 3! in. in diameter might be used with a worm of ij or ij in. pitch. The objection to this arrangement for such a light span is that the time required to operate the machinery is made unnecessarily great. We will assume that the worm is made in the form of a sleeve and has a diameter at the centre of the thread (or pitch-line) of 5.8 in. Horizontal Shafts. We found that we multiplied our power between the end of the turning-lever and the sliding- MA CHINE K Y. 37 or worm-nut on the vertical shaft 150 times. The force exerted by one man at the end of the turning-lever was assumed as 75 Ibs. Then 75 X 150 = 11,250 would be the force exerted upon the sliding-nut, were not a portion of this used in overcoming the friction of the various parts. We will first determine what these frictional forces are, up to the point where the nut-lever acts on the horizontal shaft. These forces being found and subtracted from 11,250 will give us the force that the horizontal shaft must carry on to the wedges. We have, first, the friction of the bearings of the vertical shaft; second, the friction on the collars from the thrust of the vertical shaft; third, the friction of the sliding-nut in its guides; and fourth, the friction of the sliding-nut on the thread of the worm-shaft. These are all sliding frictions for which the coefficient would be between 0.05 and o. I, depending upon the smooth- ness of the surfaces and the amount and character of the lubrication. We will use 0.06. The horizontal pressure on the journals is the 75 Ibs. exerted by the man at the lever increased by the leverage due to the bearing being some distance below the lever. Suppose the lever to be 42 in. above the box, and that the play in the box is sufficient so that the lower box might be assumed as resisting this bending; then we have 75 X 42 -r- 70 45, as bearing on lower box. There is also the horizontal pres- sure from the worm-nut in its guides. This is equal to 75 X 60 -r- 8 562.5 Ibs. (Eight inches being the distance from the centre of the shaft to the centre of bearing of the nut on 38 DESIGNING OF DRA W-SPANS. its guides.) Forces causing friction on the bearings are then 120 + 45 + 562.5 = 727.5 Ibs. If we use a 2^-in. shaft, 727.5 X .06 X 1.25 -5-60= .91, . . . (i) the force at end of lever to overcome this friction (1.25 being the radius of the shaft, and 60 the length of the hand- lever). Friction of the Collars. The vertical thrust on the shaft we found to be 11,250 Ibs. This acts on the collars with a leverage (the distance to the centre of gravity of the ring) of, say, 1} in. ; then 11,250 X .06 X If -5- 60 = 19.7, the force at end of hand-lever. This is excessive, and the friction should be reduced by using a ball bearing in the collars (see detail of this arrangement in cuts). This reduces the friction to rolling instead of sliding friction, and the coefficient to .003 ; we have then 11,250 X .003 X 2 ^- 60 1. 12. ... (2) Friction of Worm-nut Sliding in its Guides. The hori- zontal pressure of the nut we found to be 75 X 60 -~- 8 == 562.5. Then 562.5 X .06 -:- 150 = 0.22 (3) (The number 150 is the number of times the power is multi- plied between the hand-lever and the nut.) Friction on the Worm -thread. The vertical pressure is 11,250; and if the slope of the thread is 12, this gives a force in the direction perpendicular to the screw-thread of 11,250 -r- 1.022 = I 1, 008. I 1, 008 X .06 = 660.48. We will assume that the force at end of hand-lever neces- sary to overcome this friction is 4.4 Ibs. This force is equal to the friction multiplied by the radius of the worm-thread, divided by the length of the hand-lever. In some cases the friction may reduce the efficiency of the worm 40 to 50 per cent. (See page 86.) MA CHINER Y. 39 The sum of these frictions is .91 -\- 1.12 -f- 0.22 + 4.4 = 6.65 Ibs. Subtracting this from 75 gives 75 6.65 = 68.35, the available power at hand-lever. 68.35 X 150 (the number of times power multiplies) = 10,253, tne power transferred by worm-nut to the arms on the horizontal shaft. The horizontal shafts have, in addition to the twisting moment, the bending due to the distances between the bear- ings and the various levers which are keyed to the shafts. On the centre shaft we have the levers or arms working the struts which draw the centre wedges, the arms driving the rods to the end wedges, and the arms working into the worm- nut. On the end shaft we have the arms working the end wedges, arms worked by long rods running to centre, and the cranks which work the rail-lifts. The twisting moment ex- tends nearly uniformly through the centre shaft if the centre wedges are only driven to a bearing, and there are rods run- ning to the end shafts on each side of the bridge. If the rods are on one side only, the moments of the twisting force will be greatest between the worm-nut lever and the end of shaft carrying the rod-arms. In the end shaft, with one set of driving-rods, the moment is greatest between the arms driven by the long rods and the strut driving the end wedge. Then it is reduced by the amount of the moment on the wedge strut-arm. It is again reduced by the amount of rail-lift moment when this point has been passed, and so on to the other end. With two sets of the driving-rods the moment at the centre would be o, and increase each way to the ends. For the bending moments the portion of shaft between bearings will be considered as a single span, and the bending moments in each portion combined with the twisting moment (see table and formulae for shafts). The distance from one arm or prong of the lever working in the worm-nut to the nearest bearing is, say, 8 in., and as 40 DESIGNING OF DRA W-SPANS. each prong carries half the load, the bending moment will be 10,253 ~- 2 X 8 in. = 41,012 in.-lbs. The twisting moment is, if there are driving-rods on each side, 5126.5 X n = 56,391 in.-lbs. (n being the length of the arm or prong from the centre of the shaft), If the driving-rods are on one side only of the bridge and run from the centre to the end on opposite sides, for opposite ends as in Fig. 19, the moments ROD 8 SJ K . O D 1-g 1 s. . 1! 1! .5 cfl t/) j oo o S . u H 1 ^ N 0\ 3 Z oo *n ** H < * 1 8 > ** aa rt be 8 u *tr\ o" "*- c - 2fc " g > II "3 . - J 1 || Is! TEETH. |i| 111 C u " >S 'S l| i L MINUTE. W O 1 & n I" 8 * 4 If K OH h v 5 IT w o "S o g 8 g mm fe n ts a N fe M g K^, STRENG1 lies of /*! and i ted over the fa ocity in feet p ioo Feet or under. II VELOCITY >! * k ,v 1 is : Js Hm a II II II II II ^ 3 S T rON O^O^O ^t-^M ^00 IO fO W m * 10 10VO t-^00 O ^ O M N ro -*- iovo t^oo o> o - w -3- ooo o ff> m t^ o \o ONNVO O\N lAiow moo w H i c NVOOO c>^)oO roi'iO^O mt** O\ - ff, u-ioo O M 10 t^ (N TJ-VO - M N HMMMmMMAfil | O CN) ONNO -^- ^ OO 10 CNI ONVC CO vo oo O M ro 10 t^oo O P) ro 10 t^ MMMI-M^-C^CJCNIMCN "C lOt^ONONM CNI TflOt^ONON*- CNI QlOO^iHNO-NOMMD-I^N ^ w roo ot^ioO t^rroo tot^roO M- CO w ONOO ti. 10 - t- ON - CNI -^-vo 00 O CNI * 10 t^ ON 1 c N t^roON^t-O IOMVO CNIOO roON IN CM m ro ^- io iovo NO t^ t>-oo oo S t( c JCSMOOOOCN!wCN)ONOw OOONOOOOOOONQO Cj rovo oo N Tf\c 1^ P) 1 c OMMOOO^WMMOO^ ^QVO CNIOO M-QNO CNIOO **-QNC CNI CO CO TC TT IOVO NO -- t^OO 0\ ON J S c OO 1000 ONIOONO O fOO OVO N O t^OO ON M CO TTVO hs O* O ^ CO 222-^??; ^Sr&JoS c 00 rotxO VOONM-ON rooo M vo O lONOO IOM t^-rfO t^roOvO ro CNI rO CO Tt- 10 IONO tv t^OO ON ON O eet or ier. ^ * \O CNI IOIOM IOM ^t^M r^oo <*) ON CN! ^t VO ON *" ^*-NO OO "- m IOOO oo - rn jo K o w ^-NO ON - ri\o fc a 8 3 c ONtx-^-OOO OfOO t^lOt^OOVC NO n o P*cr> 5 K * 5 v * o t^. M en < - < 8,R,8SS.8 co ^oo H joco rn jooj^^j . 3 * DESIGNING OF DRA W-SPANS. For a pitch t, face b, length of teeth /, and base thickness of tooth /z, we have for a tooth-oressure / and fibre-stress S the general formula and for proportions of teeth given, h being assumed at (See Table, page 5 I *-,*4 P=*. j ID. o In any case the breadth of face should not be made less, than i/, and is generally made from 2t to 3/. It is found that the breadth of face of the tooth should increase with the increase of /. As the wear on the tooth depends on the breadth, the tooth should be proportioned so that -r should not exceed a given amount. For iron r =. not more than 28,000. n = number of revolutions per minute. For small forces this constant may be made as low as, 12000 or 6000 without obtaining inconvenient dimensions. For Hoisting Gears, linear velocity at pitch-circle not exceeding 100 ft. per minute, 5 may be taken at 42,000. For Transmission Gears, velocity exceeding 100 ft. per 9600000 minute, take o from table on page 5 I, m which o = ^- for cast iron. For steel .S may be taken ^S for cast iron. v = lineal velocity in feet per minute. Arms of Gears. A good proportion for the arms is ob- tained when their number A is made as follows: * Fig. 27*1 Fig. 271 * From Releaux. TABLES AND GENERAL DATA. 53 = o. 53 \/~Z V 7; A = 0.73 Z = number of teeth ; t = pitch. A = 3 4 $ 6 7 8 10 12 -$o 53 83 119 162 211 330 475 23 36 52 93 146 209 Width of arm // = 2 to 2.5*. For thickness = '7]-{j} TABLE OF GEAR-WHEEL ARMS. h Value of when o t z ~A = 7 9 12 16 20 25 3 35 40 1.50 0.20 0.28 0.37 0.50 0.62 0.78 0-93 1. 08 1.24 1-75 0.16 0.21 0.27 0-37 0.46 0.57 0.69 0.80 0.91 2.OO 0. 12 o. 16 O.2I 0.28 0-35 0.44 0.53 0.61 0.70 2.25 o. ro 0.12 0.17 0.22 0.28 0.35 0.41 0.48 0-55 2.50 0.08 O. IO 0.13 0.18 0.22 0.28 0.34 0-39 o.45 2-75 0.06 0.08 O. II 0.15 0.18 0.23 0.28 0.32 0-37 3.00 0.05 0.07 0.09 0.12 0.16 0.19 0.23 0.27 0.31 WEIGHT OF GEARS. The approximate weight G of gear-wheels proportioned according to the preceding rules may be obtained from the following: G = 0.0357^(6.25^ + Q.04Z 2 ). The following table will facilitate the application of the G formula, as it gives the value of -j-^ for the number of teeth which may be given, and the weight can at once be found by multiplying the value in the table by bf. 54 DESIGNING OF DRA W-SPANS. z c 4 6 8 " 20 5.04 5.60 6.18 6.77 7.38 30 7.99 8.61 9.24 9.89 10.52 40 11.09 1.90 12.59 13-30 14.02 50 14.74 15.43 16.23 17.00 17-77 & qj 60 18.55 19-35 20.15 20.97 21. 80 6 70 22.65 23-50 24.36 25.24 26.12 H 80 27.02 27-93 28.85 29.79 30.73 0<{ go 31.69 32.66 33.63 34-62 35.63 -i 432 8 ii 15 18 22 7-5 'i 11,602 9 14 19 23 28 7-9 2 14,080 ii 17 23 28 34 8.2 *f 16,892 14 21 27 34 42 86 2 T 20,048 16 24 33 41 48 8.9 2f 23,580 19 29 38 48 58 9.2 2l 27,500 22 33 45 55 66 9.6 2| 36,603 24 36 48 60 72 10.2 3 47,520 39 58 77 96 116 10.8 3x 60,417 49 74 98 123 148 11.4 3| 75,46o 61 92 123 153 184 12.0 3i 92,812 75 H3 151 188 226 12.5 4 112,640 9i 137 183 228 274 I3.I DESIGNING OF DRA W-SPANS. Shafts having Both Bending and Twisting. M= bending moment in inch-pounds; T= twisting moments in inch-pounds; T' = a new twisting moment which, substituted for T in equations g to k, will give the desired proportions for the shaft. Factor of Divisor in Formulae. Safety. (j) for Iron. (A) for Steel. M . 3 T or less 4 1 1760 22OO M 6T " " c je7O Io6o M T " " 5! 1430 I7QO 6 I^IO 1640 Formula for Horse-power. V " = revolutions per minute; = 396,000 inch-pounds per minute. 1 = 63,057 HP 36 HP V 396,000 V Deflection of Shafting. I :=V873^ 2 for bare shafts; (/) /= i/1^5^ 2 for shafts carrying pulleys, etc. ; . (r) which would be the maximum distance in feet between bear- ings for continuous shafting subjected to bending stress alone. If the length is fixed and we desire the diameter of the shaft, we have = Y873 for bare shafting ; (s) TABLES AND GENERAL DATA, 59 d / I* = A / -- for shafting carrying pulleys, etc. Working Formula. 8 Ao HP d = \l for bare shafts ; d= * /70H P for shafts carrying pulleys, etc. ; (v) for bare shafts; 1= tyi^pd* for shafts carrying pulleys, etc. . Shafting- keys. k = o. 1 6 -f- \d\ k' = o. 16 + ^^ Taper of key, .04 in. to .08 in. in 4 in. w - (*) Shaft 1/2" 5/8" 3/4" i" if 2" a f 3" 3i" 4" 4i" 5 D Keys/32" 1/8" 5/32'' 7/32" 5/16" 7/16" 1/2" 9/16" 9/'6" 5/8" 3/4" 7/8" From Releaux. f Fig- 35 j If we call the diameter of the shaft D, the breadth of the. key 5, and the middle depth of the key S', we have: <)O DESIGNING OF DRA W-SPANS. For draft keys, 5 = 0.24" + ^-; S' = 0.16" + . /? D For torsion keys, 5 = o. 16" + : - ; 5 ' = o. 16" + . 5 I0 The taper of such keys is made about T ^. For the more commonly occurring diameters we have the following proportions: D = i 2 3 4 56 789 10 FOR DRAFT KEYS. S = 3/8" 1/2" 5/8" 13/16" i" if ij" if" if" if" ^' = 1/4" 5/16" 7/16" 1/2" 9/16" 5/8" 3/4" 13/16" 7/8" i" FOR TORSION KEYS. S = 3/8" 9/i6" 3/4" i" I T Y' if" ift" if" 2" 2 f" ^'= 1/4" 3/8" 1/2" 9/16" 11/16" 3/4" 7/8" i" I T V IT'S" For shafts of less diameter than I in. we may make c_^ c,_^ = r s If several keys are used, they may be made the same dimensions as single keys. For hubs which have been forced on, and hence would be secure without any key, the dimen- sions for draft-keys may be used. BEARINGS AND PIVOTS, SPRINGS, CAMS, ETC. Bearings. The bearings for shafts should be placed as near the points of loading as possible, and for low speeds and small loads the length of bearing should be once and one half to twice the diameter of the shaft. Where the load is heavy or speed great, the bearings are given a length of twice to four times the diameter. Where the bearing simply carries the weight of shaft, a length of once to once and one quarter the diameter is sufficient. Bearings of brass or a composition TABLES AND GENERAL DATA. 6} of metals are used at important points. A bushing of Babbitt metal is found to give excellent results. The friction is low and the wearing properties of this metal are good. Two bearings made in this manner are shown in the cuts. As the speed increases, the length of the bearing should be increased about in the ratio given in table below. N = 100 150 200 250 400 750 1000 l+d = 1.25 1.5 1.75 2.0 2.5 3-5 4-o N = number of revolutions per minute; / = the length of bearing in inches; d = diameter of shaft in inches. Ample provision should be made for keeping the bearing well oiled, and all oil-holes should be easy of access. To aid in spreading the oil over the whole bearing-surface small grooves are often cut spirally around the bearing. For thickness of metal and proportion of the various parts see cuts 39 and 40. Load on Rollers. Setter's Centre. The rotating load per lineal inch on steel roller should not exceed that given by the following formula for steel rollers on steel plates: P pressure per lineal inch of roller; d = mean diameter of roller in inches. Load on Wheels. The load per lineal inch of face of wheel, while span is turning, should not exceed that given by the following formulae, viz. : p 705 Vd for a cast-iron wheel on a cast-iron track; P= 900 Vd " " P" " " wrought-iron track. For steel wheels use the following formulae as to limit of pressure per lineal inch of wheel-face while the span is turn- ing, viz. : P= 1905 Vd for a steel wheel on a cast-iron track; P i$i$Vd " " " " wrought-iron track; P= i 7 $oVd " " " " steel track. * It is often specified that the load shall not exceed P = 1750 Vd. 62 DESIGNING OF DRA W-SPANS. In which formulae P = allowed pressure per lineal inch of face of wheel ; d = diameter of wheel in inches. Pivots. TABLE OF SAFE LOAD FOR STEEL ON BRONZE. FORMULAE FOR PIVOTS. Wrought Iron or Steel on Bronze. ( j* TA22 d. 0.035 ^/P Slow. 0.05 \ r P. Under iso.fi. Over iso/?. Slow-moving pivots -j ^ ~ * * , ^ Load. Load. Load. t jj _ 7OO I 816 398 204 n or < 150 } ,~ ' A/~B 1.25 i,275 622 319 i a 0.05 y f . 1.50 1,836 895 459 ( a = 75. 1.75 2,500 1,219 625 | ^ __ Q^ QQ ^ |// > n 2.00 3,265 1 '59 2 816 2.25 4,132 2,016 1,033 Ca.tf /r0 Bronze. 2.5O 5,102 2,488 1,275 2-75 6,173 3,on 1,543 Slow-moving pivots ^ ~~ ' , 3.OO 3-25 7,347 8,622 3,494 4,205 1,836 2,155 f * -3 CQ 3.50 10,000 4,877 2,500 w = r < 150 Y d =0 , 07 yp. 3-75 n,479 5,599 2,869 4.00 13,061 6,370 3,265 ( a = 75 4-25 M,745 7,192 3,686 C d = 0.006 yPn. 4-50 16 53P 8,063 4,132 Iron or Steel on Lignum Vita. 4-75 5.00 18,418 20,498 8,983 9-954 4,604 5,102 Slow-moving pivots \* '~ 2 44 . ( d = 0.017 y T 1 . 5-25 5-50 5-75 22,140 24,694 26,990 10,974 12,044 13,164 5,535 6,673 6,747 = or < 150 \* = I422 ' - {z "> ico -1 ^ :i::: I '^ 22 ' 6-75 37,190 18,220 9,298 ( rf = 0.035 v^. 7.00 41,690 19,600 10,000 The above table is made from the formula P= 8i6= 15.714-^-. The most generally preferred ratio for size is D = $d, where D = outside diameter of coil. It is customary to make the static load about one half the solid load. 64 DESIGNING OF DRAW-SPANS. Helical Springs. By D. K. CLARK. A - - for round steel; . . . (2) 3 fait v d D=z*/'- - for square steel. ... (3) E = compression or extension of one coil, in inches; d = diameter from centre to centre of steel bar composing the spring, in inches; w =. the weight applied, in pounds; D = the diameter, or the side of square, of the steel bar of which the spring is made, in sixteenths of an inch; C a constant which, from experiments made, may be taken as 22 for round steel and 30 for square steel. ECCENTRICS. Eccentrics. An eccentric is nothing more than a crank in which (if the crank-arm is R and the shaft diameter D) the crank-pin diameter d' is made so great that it exceeds D -\- 2R y or is greater than the shaft and twice the throw. The sim- pler forms of eccentric construction are shown in the illustra- tions. The most practical of these is that shown in Fig. 37^, the flanges on the strap, as shown in the section, serving to retain the oil and insure good lubrication. The breadth of the eccentric is \\d to 3<^, the same as that of the equivalent overhung journal subjected to the same pressure. For the depth of flange a we have a 1.5* = 0.07/4- 0.2 From which the other dimensions can be determined as in the illustrations TABLES AND GENERAL DATA. Nf Fig. 37 b Fig-37 c - 37 Hooks. Formulas prepared by the YALE & TOWNE MANUFACTURING Co. A = capacity of hook in tons of 2000 Ibs. D = .$4-\-i.2$ G.^D-, = .644+ i. 60 O= .363/4 + .66; F= .33J + .85; Q = H = i.oSA; L= u /= 1.33^4 ; M . J=i.2oA\ N=.%$B 16 Fig. 38 Capacity of hook iiiii234568io tons. Dimension A I H I *& T i J $ J t 2 2 i 2 \ 2 s 3i '" OF THB UNIVEBSITY 66 DESIGNING OF DRA W-SPANS. Fig 39 Fig. 39 a - SHAFT-BEARING. TABLES AND GENERAL DATA. 6 7 DRILL HOLES FOR %'TURNED BOLTS CUP OUT FOfU BABBITT $1"DEEP %STUD BOLTS 3& LONG BABBITTED FOR 3*ie'8HAFT [CORED Pig. 40. SHAFT-BEARING. 68 DESIGNING OF DRA W-SPANS. At middle of At point of 3 JF c support = >. '3 At middle of WL beam = . 8 At centre of WL* span = . 31.9^7 At middle support = \WY. 2. At middle of WL support = -. o ..StsZ O 4) II II o o B S II II 6 . II Q At end of WL beam= rr At end of WL* At middle of WL* K.S At point of support = W. At point of support = W. At point of W At point of support = WZ-. At point of WL support = At middle of WL beam = . TABLES AND GENERAL DATA. DRAW-SPAN MOMENTS AND SHEARS. (See Fig. n.) COEFFICIENTS C' FOR LOADS IN FIRST ARM AND COEFFICIENTS AND Z> FOR LOADS IN SECOND ARM. Number or Panels in Half- J B' C C' D D' E E' f F' G G' H H' 7 I' Totals. span. 4 .0586 .0938 .0820 2344 5 .048 .084 .096 .072 .300 6 7 .0406 .0350 .0740 .0656 0937 .0875 .0925 .0962 .0637 .0875 .0568 3645 .4285 8 .0308 .0586 .0806 .0938 .0952 .0820 0513 4923 9 .0274 .0527 .0740 .0891 0960 .0925 .0767 .0466 5550 COEFFICIENTS D' FOR LOADS IN FIRST ARM. 4 .691 .406 .168 1.265 5 752 .516 304 .128 1.700 6 .792 S9 2 .406 .241 .103 2-134 7 .822 .649 .484 332 .198 .086 2-57 1 8 -844 .691 544 .406 .280 .168 .074 3.007 9 .861 725 592 .466 .348 .241 .146 .065 3-444 VALUES OF E' FOR LOADS IN FIRST ARM. 4 .810 .842 .goo 5 .807 .827 .862 .916 6 -805 .818 .842 .879 .929 1 -803 .803 :SII .830 .824 .856 .842 893 .868 943 .900 943 9 .801 .809 .820 .832 .852 .879 .910 95 LOADS FOR MAXIMUM NEGATIVE MOMENTS-FIRST ARM. 4 I B C For maximum at F 7 B C D E " G 8 B C D E F " " H 9 B c D E F G u / All loads on second arm in each case. All loads cause negative moments over pier. LOADS FOR MAXIMUM POSITIVE MOMENTS-FIRST ARM. Max. at 4 B C D B to D B C D E B to E 6 B C D E F B to E 6 D E F F 7 B C D E F G B to F 7 F G G 8 B C D E F G H B toG 8 G H H 9 B C D E F G H I Bto H H I I SHEARS: All loads on second arm cause negative shear in first arm. Loads moving A towards Z cause negative shear in first arm Loads moving Z towards A cause positive shear in first arm. PI = any load in first arm. PI = any load in second arm. St = reaction at .<4 from PI or /> a . 7J/2 = moment at pier from P or />. X = distance from A to point of zero moment in first arm. L = length of half-span. WEB-STRESSES: Max. stress in any -j m A ?^'' J- Max. stress in any \ ;' [ tQ piece jn M- = L or C*PL. or Z>/V . E'L. When ' ad CXtendS tromA DESIGNING OF DRA W-SPANS. I I 1 GENERAL DATA DETAILS, ETC. Fig. 44- Fig. 45- END MACHINERY. 72 DESIGNING OF DRA W-SPANS. Fig. 46. CENTRE MACHINERY. Fig. 47- CENTRE MACHINERY GENERAL DATA DETAILS, ETC. 73 Fig. 48. Fig. 49. Fig. 50. BALL-BEARING CENTRE. PIVOT CENTRE. ADJUSTABLE END WEDGE. Fig- 5'- SHAFT BALL-BEARING. Fig- 52. CENTRE ON CONICAL ROLLERS. 74 DESIGNING OF DRA W-SPANS. G2- *a. SAILS IV 'All. 25.000 IB $ W/GffT 01VAlS. Fig. 53- /3-STEEL 20-3AUS MYALLS. 54- Fig. 55- BALL-BEARINGS. GENERAL DATA DETAILS, ETC. 75 Fig, 56. CENTRE PIVOT. Pivot 33" diam. to be forged in steel. Friction disks turned and ground spherically to a 36" radius. Upper part steel. Lower part phosphor-bronze. Base of cast iron, to be faced top and bottom, turned inside. WRCIRCLe. &/-AIUSMtt V-D/AM. WX.WM 125 GROSS 7WS. \ 23 25 ZJ'S PR ffALL '. Fig. 57- BALL-BEARING. DESIGNING OF DRA W-SPANS. Fig. 5 8. CENTRE FOR SMALL DRAW. Fig- 59 SELLERS COUPLING FOR SHAFTING. GENERAL DATA DETAILS, ETC. 77 End Elevation Sectional Plan Details of End Lifting Machinery Fig. 60. Section- Shovi Screw; Section Kail Lift teA Segment ;ftack Pinion Details of Turn Table. Fig. 6z. DESIGNING OF DRA W-SPANS. Fig. 62. END SUPPORTS, LATCH, ETC. Fig. 63. END LIFT, LATCH MACHINERY, ETC, GENERAL DATA DETAILS, ETC. 79 Fig. 6 5 b. Fig. 65. END LIFT. Fig. 6Sa. When draw is closed and ends are raised the middle pins of toggle-joint Stand \" inside of vertical line through top and bottom pins to prevent the toggle from opening In above position castings bear against each other. 8o DESIGNING OF DRA W- SPANS. JSLEMTION Fig. 66. WEDGING GEAR. 'ELEVATION Fig. 67. TURNING GEAR. 0W 16 Fig. 68. PIVOT CENTRE. GENERAL DATA DETAILS, ETC. 81 Fig. 70. LATCHING DEVICES. Fig. 71. SLEEVE FOR CLAMPING RAILS. OF THB UNIVERSITY 82 DESIGNING OF DRA IV-SPANS. Fig. 72. Fig. 73- MACHINERY FOR OPERATING SAFETY-SIGNALS. GENERAL DATA DETAILS, ETC. 83 VIEWS SHOWING PLATE-GIRDER DRAW IN PROCESS OF CON- STRUCTION. Balance-wheel and Centre Wedge. End Wedges and Portion of Machinery in Position. 84 DESIGNING OP DRAW-SPANS. VIEWS SHOWING PLATE-GIRDER DRAW IN PROCESS OF CON- STRUCTION. End Wedging Arrangement. Portion of Machinery at Centre. EXPLANATORY NOTES. Where the term " moment of resistance" and the letter R designating the same have been employed in this work, they are used as indicating the moment of resistance for a fibre- stress of i ; or the term indicates the " section modulus" as given by some authors. 2. In Case 5, page 68, for continuous beams on three supports, note that the moments are obtained by scaling the ordinates between the curve and the inclined line, and not by scaling between the curve and the horizontal line as in the other cases. 3. On page 16 it will be noticed t-hat the centre moments have been given for the loads on one arm only. The moments for the loads on the other arm are the same, and have been included in obtaining the total moment. 85 86 DESIGNING OF DRA W- SPANS. Friction of Worm-thread. (See page 38.) The efficiency of the worm is very much reduced by the friction. In many cases a coefficient as high as o. 15 would be nearer correct than o. 10. The formula for the available vertical force is W - , where W = vertical force, r = radius of 6.28 turning lever, F force at end of turning lever to overcome the vertical force W, F 1 = force at end of turning lever to overcome the friction produced by W, P= pitch of the worm- thread, D = the distance from centre of shaft to the centre of the worm-thread, c = the coefficient of friction. A force of i Ib. at the end of a 6-ft. lever gives an available vertical force on the worm-nut, after deducting the friction of the thread and of the guides, as follows : Diameter of Shaft. Pitch. Size of Thread. W, in Pounds. f *K" J*" iH" k" M irrsq. So 161 182 207 242 WORKING VALUES FOR WORM-SHAFTS. SQUARE THREAD EMERY THREAD A ,5 ' C Area of A. Area of C. Safe Tensile Strain Iron at 10.000. Safe Tensile Strain Steel at 12,500. D D' W W i^ 6 .167 1.284 1.767 i .'230 12,300 1 5-375 .696 .708 91.7 90.5 i6 5% .182 1.389 2.073 1.496 14,960 18,700 754 767 84.5 83-2 i% 5 .2OO i 491 2.405 1 750 1 7*, 5o 21,875 .810 .825 78.3 77.1 *% 5 .200 1.616 2.761 2.OOO 20,000 25,000 -8 73 .888 73-7 72.7 2 4^*2 222 1.712 3 MI 2.300 23.000 28,750 .928 944 68.8 67.8 2*4 4^ 222 1.962 3-976 2 990 29,900 37,375 1-053 1.070 62.1 61.3 2 %2 4 .250 2 . 176 4.908 3 640 36,400 45,5oo i ..169 1. 188 55-8 55-o 2% 4 .250 2.426 5-939 4.806 48,060 60,070 1.294 1 3 T 3 50.7 \y Ig .286 .286 2 629 2.879 7 068 8.295 5-4II 6.491 54,"o 64.910 67.638 81,137 1.407 1.420 I -554 4 6 - 8 43 6 46.2 42.6 3% 3/4 .308 3-100 9.621 7.080 70,800 88.500 i 650 1-673 40 5 40.0 3% 3 333 3.317 11.044 8.395 83,950 104,930 1.767 1.792 37 7 37-3 4 3 333 3-S67 12.566 9.970 99,700 124.620 i 892 1.917 35-6 35-2 4?4 2% 348 3 798 14.186 11.144 111,440 139,300 2.012 2.038 33 S 33-2 4^ 2% 364 4.028 15.904 12.567 125,670 157,080 2.132 2 I5Q 3i 8 Number ot threads per inch on above bolts is the number given in the Sellers System. A = external diameter ; B number ol threads per inch, C = diameter at root of thread; D, D' = radius of centre of thread ; W (for v thread), W (for square thread; = the weight which can be raised by a force of i Ib. with a leverage of i foot. Coefficient of friction = .15. INDEX. PAGE Anchor-bolts 22 Areas of flanges 17 Arms of gears 49, 52 Beams, deflection of 68 moments in . . . . 68 Bearings of shafts 40, 60 Bevel-gears 48 Bracing, lateral 22 Camber 28 Care of draw-spans 45 Centre-post 22 Collar-friction 55 Conditions of loading 2 Cover-plates, length of 17 Cross-girder 22 Deflection, formulae for 23 upward 4> 35 Diagram for moments and shear 14 Elbow- joint 42 example of 43 Eccentrics 64 Explanatory notes 85 Force to overcome friction of centre. 29 shafts 31, 40 trailing-wheel 30 worm-nut 38 inertia 28 total 31 unbalanced condition of draw 30 87 88 INDEX. PAGE Formulae for strength of shafts 56 Friction of collars 38, 55 shafts 55 Gears, breadth of face 52 mitre 48 proportions of , 46, 47 strength of 50 arms 52 table of strength 51 weight of 53 Hammer at ends of draw 4 Horse-power 58 Hooks 65 Keys 4 2 for shafting 59 Key ways 42 Latch 44 Lateral bracing 22 Length of cover-plates 17 Levers, strength of 41 Load on rollers 61 wheels , 61 Loading, conditions of 2 Machinery 28 for turning 28 latching 44 wedging 36 Mitre-gears 48 Moment of inertia 27 Moments, bending, in beams 68, 69 maximum ... 9, 1 1 signs of 9 Parabola, to draw 6 Pivot 34 load on 62 table of safe load on 62 wind-pressure on 29 Polygon, equilibrium 8 force 8 INDEX. 89 PAGE Rack 47 Rail-lift ?i, 79 -splice 44 Reactions 10, 14, 19 Rollers 33, 61 Set-screws . . 45 Shaft, horizontal 36 moments in 39 worm 35 Shafting, bending and twisting 58 deflection of 58 friction of 55 general formulae 56 horse-power of 58 keys 59 strength of 54 table of 57 Signals 44 Shear at pier, dead load 19 in web 19 Shearing forces, table of 69 Shears at end from live load 20 centre from live load 20 combination of 21 Springs. 63 Steel rollers 33 Stiff eners 21 Strains, combination of 17 dead load continuous 16 swinging 4 live load as single span 7 continuous 9 uniform 15 position of load for maximum 15 Stresses, unit 17 Strength of levers 41 teeth 33 Type of draw most satisfactory 2 Twisting force in draw 2 how best resisted 2 Teeth, strength of 33, 50 table, strength of 51 Time for turning 31 QO INDEX. PACK Trailing-wheels 33 Turning-shaft, size of . 32 Web-stresses 19 Wedging arrangement 35 Wedges 70 Weight of gears 53 Wheels, load on 61 Worm-shaft , 35 Worms 36 SHORT-TITLE CATALOGUE OF THE PUBLICATIONS OF JOHN WILEY & SONS, NEW YORK, LONDON: CHAPMAN & HALL, LIMITED. ARRANGED UNDER SUBJECTS. Descriptive circulars sent on application. Books marked with an asterisk are sold at net prices only. All books are bound in cloth unless otherwise stated. AGRICULTURE. CATTLE FEEDING DAIBY PRACTICE DISEASES OF ANIMALS GARDENING, ETC. Arrnsby's Manual of Cattle Feeding, 12mo, $1 75 Downing's Fruit and Fruit Trees 8vo, 5 00 Grotenfelt's The Principles of Modern Dairy Practice. (Woll.) 12mo, 2 00 Kemp's Landscape Gardening 12mo, 2 50 Lloyd's Science of Agriculture 8vo, 4 00 London's Gardening for Ladies. (Downing.) 12mo, 1 50 Steel's Treatise on the Diseases of the Dog 8vo, 3 50 " Treatise on the Diseases of the Ox 8vo, 6 00 Stockbridge's Rocks and Soils ... .8vo, 2 50 Woll's Handbook for Farmers and Dairymen , . . . ,12mo, 1 50 ARCHITECTURE. BUILDING CARPENTRY STAIRS VENTILATION, ETC. Berg's Buildings and Structures of American Railroads 4to, 7 50 Birkmire's American Theatres Planning and Construction. 8vo, 3 00 " Architectural Iron and Steel 8vo, 350 Birkmire's Compound Riveted Girders 8vo, 2 00 " Skeleton Construction in Buildings 8vo, 3 00 1 Carpenter's Heating aud Ventilating of Buildings 8vo, $3 00 Downing, Cottages 8vo, 2 50 and Wightwick's Hints to Architects. .8vo, 2 00 Freitag's Architectural Engineering 8vo, 2 50 Gerhard's Sanitary House Inspection 16mo, 1 00 Theatre Fires and Panics 12mo, 1 50 Hatfield's American House Carpenter 8vo, 5 00 Holly's Carpenter and Joiner , ,18mo, 75 Kidder's Architect and Builder's Pocket-book Morocco flap, 4 00 Merrill's Stoues for Building and Decoration 8vo, 5 00 Monckton's Stair Building Wood, Iron, and Stone 4to, 4 00 Stevens' House Painting , . 18mo, 75 "Worcester's Small Hospitals Establishment and Maintenance, including Atkinson's Suggestions for Hospital Archi- tecture 12ino, 1 25 World's Columbian Exposition of 1893 4to, 2 50 ARMY, NAVY, Etc. MILITARY ENGINEERING ORDNANCE PORT CHARGES, ETC. Bourne's Screw Propellers 4to, 5 00 Bruff's Ordnance and Gunnery. 8vo, 6 00 Bucknill's Submarine Mines and Torpedoes 8vo, 4 00 Chase's Screw Propellers 8vo, 3 00 Cooke's Naval Ordnance 8vo, 12 50 Cronkhite's Gunnery for Non-com. Officers 18mo, morocco, 2 00 De Brack's Cavalry Outpost Duties. (Carr.). .. .18mo, morocco, 200 Dietz's Soldier's First Aid 12mo, morocco, 1 25 * Dredge's Modern French Artillery 4to, half morocco, 20 00 Record of the Transportation Exhibits Building, World's Columbian Exposition of 1893.. 4to, half morocco, 15 00 Dyer's Light Artillery 12mo, 3 00 Hoff's Naval Tactics 8vo, 1 50 Hunter's Port Charges 8vo, half morocco, 13 00 Ingalls's Ballistic Tables 8vo, 1 50 " Handbook of Problems in Direct Fire 8vo, 4 00 Muhau's Advanced Guard 18mo, 1 50 " Permanent Fortifications. (Mercur.).8vo, half morocco, 750 Mercur's Attack of Fortified Places 12mo, $2 00 Elements of the Art of War 8vo, 4 00 Metcalfe's Ordnance and Gunnery 12ino, with Atlas, 5 00 Phelps's Practical Marine Surveying 8vo, 2 50 Powell's Army Officer's Examiner 12mo, 4 00 Reed's Signal Service 50 Sharpe's Subsisting Armies 18mo, morocco, 1 50 Strauss and Alger's Naval Ordnance and Gunnery Todd and Whall's Practical' Seamanship 8vo, 7 50 Very's Navies of the World 8vo, half morocco, 3 50 Wheeler's Siege Operations 8vo, 2 00 Winthrop's Abridgment of Military Law 12mo, 2 50 Woodhull's Notes on Military Hygiene 12rno, morocco, 2 50 Young's Simple Elements of Navigation.. 12mo, morocco flaps, 2 50 ASSAYING. SMELTING ORE DRESSING ALLOYS, ETC. Fletcher's Quant. Assaying with the Blowpipe.. 12mo, morocco, 1 50 Furman's Practical Assaying .- 8vo, 3 00 Kunhardt's Ore Dressing 8vo, 1 50 * Mitchell's Practical Assaying. (Crookes.) 8vo, 10 00 O'Driscoll's Treatment of Gold Ores 8vo, 2 CO Ricketts and Miller's Notes on Assaying 8vo, 3 00 Thurstou's Alloys, Brasses, and Bronzes 8vo, 2 50 Wilson's Cyanide Processes 12mo, 1 50 ASTRONOMY. PRACTICAL, THEORETICAL, AND DESCRIPTIVE. Craig's Azimuth 4to, 3 50 Doolittle's Practical Astronomy 8vo, 4 00 Gore's Elements of Geodesy 8vo, 2 50 Michie and Harlow's Practical Astronomy 8vo, 3 00 White's Theoretical and Descriptive Astronomy 12mo, 2 00 BOTANY. GARDENING FOR LADIES, ETC. Baldwin's Orchids of New England 8vo, $1 50 London's Gardening for Ladies. (Downing.) 12mo, 1 50 3 Thome's Structural Botany 18mo, $2 25 Westermaier's General Botany. (Schneider.) Svo, 2 00 BRIDGES, ROOFS, Etc. CANTILEVER DRAW HIGHWAY SUSPENSION. (See also ENGINEERING, p. 6.) Boiler's Highway Bridges 8vo, 2 00 * " The Thames River Bridge ; 4to, paper, 5 00 Burr's Stresses in Bridges. ... 8vo, 3 50 Crehore's Mechanics of the Girder Svo, 5 00 Dredge's Thames Bridges 7 parts, Du Bois's Stresses in Framed Structures 4to, 10 00 Foster's Wooden Trestle Bridges 4to, 5 00 Greene's Arches in Wood, etc Svo, 2 50 Bridge Trusses 8vo, 250 " RoofTrusses 8vo, 125 Howe's Treatise on Arches 8vo, Johnson's Modern Framed Structures ... .4to, 10 00 Merrimau & Jacoby's Text-book of Roofs and Bridges. Part L, Stresses ...8vo, 250 Merriman & Jacoby's Text-book of Roofs and Bridges. Part II., Graphic Statics 8vo, 2 50 Merrimau & Jacoby's Text-book of Roofs and Bridges. Part III., Bridge Design Svo, 5 00 Merriman & Jacoby's Text-book of Roofs and Bridges. Part IV., Continuous, Draw, Cantilever, Suspension, and Arched Bridges (In preparation). * Morison's The Memphis Bridge Oblong 4to, 10 00 Waddell's Iron Highway Bridges 8vo, 4 00 Wood's Construction of Bridges and Roofs Svo, 2 00 Wright's Designing of Draw Spans Svo, 2 50 CHEMISTRY. QUALITATIVE QUANTITATIVE ORGANIC INORGANIC, ETC. Adriance's Laboratory Calculations 12mo, 1 25 Allen's Tables for Iron Analysis Svo, 3 00 Ausleu's Notes for Chemical Students 12mo, 1 50 Bolton's Student's Guide in Quantitative Analysis. Svo, 1 50 Classen's Analysis by Electrolysis. (Herrick.) 8vo, $3 00 Crafts'sQualilative Analysis. (Schaeffer.) 12mo, 1 50 Drechsel's Chemical Reactions. (Merrill.) 12mo, 1 25 Fresenius's Quantitative Chemical Analysis. (Allen.) 8vo, 6 00 Qualitative Chemical Analysis. (Johnson.) 8vo, 400 Gill's Gas and Fuel Analysis 12mo, 1 25 Hammarsten's Physiological Chemistry (Maudel.) 8vo, 4 00 Kolbe's Inorganic Chemistry 12mo, 1 50 Mandel's Bio-chemical Laboratory 12mo, 1 50 Mason's Water Supply 8vo, 5 00 Miller's Chemical Physics .' 8vo, 2 00 Mixter's Elementary Text-book of Chemistry 12mo, 1 50 Morgan's Principles of Mathematical Chemistry 12mo, 1 50 " The Theory of Solutions and its Results 12rno, 1 00 Nichols's "Water Supply (Chemical and Sanitary) 8vo, 2 50 O'Brine's Laboratory Guide to Chemical Analysis 8vo, 2 00 Perkins's Qualitative Analysis 12mo, 1 00 Pinner's Organic Chemistry. (Austen.) 12mo, 1 50 Ricketts and Russell's Notes on Inorganic Chemistry (Non- metallic) Oblong 8vo, morocco, 75 Schimpf s Volumetric Analysis 12mo, 2 50 Spencer's Sugar Manufacturer's Handbook . 12mo, morocco flaps, 2 00 Stockbridge's Rocks and Soils , 8vo, 2 50 Troilius's Chemistry of Iron , 8vo, 2 00 Wiechmann's Chemical Lecture Notes 13ino, 3 00 " Sugar Analysis 8vo, 250 Wulling's Inorganic Phar. and Med. Chemistry 12mo, 2 00 DRAWING. ELEMENTARY GEOMETRICAL TOPOGRAPHICAL. Hill's Shades and Shadows and Perspective 8vo, 2 00 MacCord's Descriptive Geometry 8vo, 3 00 " Kinematics ' - -8vo, 5 00 Mechanical Drawing 8vo, 400 Mahan's Industrial Drawing. (Thompson.) 2 vols., 8vo, 3 50 Reed's Topographical Drawing. (H. A.) 4to, 5 00 Smith's Topographical Drawing. (Macmillan.) 8vo, 2 50 Warren's Descriptive Geometry 2 vols., 8vo, 3 50 Warren's Drafting Instruments 12mo, 1 25 Free-hand Drawing 12rno, $1 00 " Higher Linear Perspective 8vo, 3 50 " Linear Perspective 12mo, 1 00 " Machine Construction 2 vols., 8vo, 7 50 " Plane Problems , 12mo, 125 " Primary Geometry 12mo, 75 " Problems and Theorems 8vo, 250 " Projection Drawing 12mo, 150 " Shades and Shadows : 8vo, 300 ' Stereotomy Stone Cutting. 8vo, 250 Whelpley's Letter Engraving 12mo, 2 Oft ELECTRICITY AND MAGNETISM. ILLUMINATION BATTERIES PHYSICS. Anthony and Brackett's Text-book of Physics (Magie). . . .8vo, 4 00 Barker's Deep-sea Soundings 8vo, 2 00 Benjamin's Voltaic Cell 8vo, 3 00 Cosmic Law of Thermal Repulsion ISnio, 75 Crehore and Squier's Experiments with a New Polarizing Photo- Chronograph 8vo, 3 00 * Dredge's Electric Illuminations 2 vols., 4to, half morocco, 25 00 Vol.11 4to, 750 Gilbert's De magnete. (Mottelay.) 8vo, 2 50 Hoi man's Precision of Measurements 8vo, 2 00 Michie's Wave Motion Relating to Sound and Light 8vo, 4 00 Morgan's, The Theory of Solutions and its Results 12mo, Niaudet's Electric Batteries. (Fishback.) 12mo, 2 50 Reagan's Steam and Electrical Locomotives 12rao 2 00 Thurston's Stationary Steam Engines for Electric Lighting Pur- poses 12mo, 1 50 Tillman's Heat 8vo, 1 50 ENGINEERING. CIVIL MECHANICAL SANITARY, ETC. (See also BRIDGES, p. 4 ; HYDRAULICS, p. 8 ; MATERIALS OF EN- GINEERING, p. 9 ; MECHANICS AND MACHINERY, p. 11 ; STEAM ENGINES AND BOILERS, p. 14.) Baker's Masonry Construction 8vo, 5 00 6 Baker's Surveying Instruments 12mo, 3 00 Black's U. S. Public Works 4to, $5 00 Butts's Engineer's Field-book 12mo, morocco, 2 50 Byrne's Highway Construction 8vo, 5 00 Carpenter's Experimental Engineering 8vo, 6 00 Church's Mechanics of Engineering Solids'and Fluids 8vo, 6 00 " Notes and Examples in Mechanics 8vo, 2 00 Oandall's Earthwork Tables , 8vo, 1 50 Crandall's The Transition Curve 12mo, morocco, 1 50 * Dredge's Penu. Railroad Construction, etc. . . Folio, half mor., 20 00 * Drinker's Tunnelling 4to, half morocco, 25 00 Eissler's Explosives Nitroglycerine and Dynamite 8vo, 4 00 Gerhard's Sanitaiy House Inspection 16mo, 1 00 Godwin's Railroad Engineer's Field-book. 12mo,pocket-bk. form, 2 50 Gore's Elements of Goodesy 8vo, 2 50 Howard's Transition Curve Field-book 12mo, morocco flap, 1 50 Howe's Retaining Walls (New Edition.) 12mo, 1 25 - Hudson's Excavation Tables. Vol. II 8vo, 1 00 Button's Mechanical Engineering of Power Plants Svo, 5 00 Johnson's Materials of Construction Svo, 6 00 Johnson's Stadia Reduction Diagram .. Sheet ; 22 X 28A inches, 50 " Theory and Practice of Surveying Svo, 4 00 Kent's Mechanical Engineer's Pocket-book 12mo, morocco, 5 00 Kiersted's Sewage Disposal 12nio, 1 25 Kirkwood's Lead Pipe for Service Pipe Svo, 1 50 Msihan's Civil Engineering. (Wood.). Svo, 5 00 Merriman and Brook's Handbook for Surveyors 12mo, mor., 2 00 Merriman's Geodetic Surveying Svo, 2 00 Retaining Walls and Masonry Dams Svo, 2 00 Mosely's Mechanical Engineering. (Mahan.) 8vo, 5 00 Nagle's Manual for Railroad Engineers .12mo, morocco, Patton's Civil Engineering. Svo, 7 50 " Foundations Svo, 500 Rockwell's Roads and Pavements in France 12mo, 1 25 Ruffner's Non-tidal Rivers : Svo, 1 25 Searles's Field Engineering 12mo, morocco flaps, 3 00 Searles's Railroad Spiral 12mo, morocco flaps, 1 50 7 Siebert and Biggin's Modern Stone Cutting and Masonry. . .8vo, 1 50 Smith's Cable Tramways 4to, $2 50 " Wire Manufacture and Uses 4to, 3 00 Spalding's Roads and Pavements 12mo, 2 00 " Hydraulic Cement 12mo, Thurston's Materials of Construction 8vo, 5 00 * Trautwiue's Civil Engineer's Pocket-book. ..12m o, rnor. flaps, 5 00 * " Cross-section , Sheet, 25 Excavations and Embankments 8 vo, 2 00 * " Laying Out Curves 12mo, morocco, 2 50 Warren's Stereotomy Stone Cutting 8vo, 2 50 Webb's Engineering Instruments 12mo, morocco, 1 00 Wegmanu's Construction of Masonry Dams 4to, 5 00 Wellington's Location of Railways. . , 8vo, 5 00 Wheeler's Civil Engineering 8vo, 4 00 Wolff's Windmill as a Prime Mover 8vo, 3 00 HYDRAULICS. WATER-WHEELS WINDMILLS SERVICE PIPE DRAINAGE, ETC. (See also ENGINEERING, p. 6. ) Bazin's Experiments upon the Contraction of the Liquid Vein (Trautwine) 8vo, 2 00 Bovey's Treatise on Hydraulics 8vo, 4 00 Coffin's Graphical Solution of Hydraulic Problems. 12mo, mor., Ferrel's Treatise on the Winds, Cyclones, and Tornadoes. . .8vo, 4 00 Ganguillet & Kutter'sFlow of Water. (Bering & Trautwine ).8vo, 4 00 Hazen's Filtration of Public Water Supply 8vo, 2 00 Kiersted's Sewage Disposal 12mo, 1 25 Kirkwood's Lead Pipe for Service Pipe 8vo, 1 50 Mason's Water Supply 8vo, 5 00 Merriman's Treatise on Hydraulics , Svo, 4 00 Nichols's Water Supply (Chemical and Sanitary) Svo, 2 50 Ruffner's Improvement for Non-tidal Rivers Svo, 1 25 Wegmann's Water Supply of the City of New York 4to, 10 00 Weisbach's Hydraulics. (Du Bois.) Svo, 5 00 Wilson's Irrigation Engineering, ... Svo, 4 00 Wolff's Windmill as a Prime Mover Svo, 3 CO Wood's Theory of Turbines Svo, 250 8 MANUFACTURES. ANILINE BOILERS EXPLOSIVES IRON SUGAR WATCHES WOOLLENS, ETC. Allen's Tables for Iron Analysis 8vo, $3 00 Beaumont's Woollen and Worsted Manufacture 12rno, 1 50 Bollaud's Encyclopaedia of Founding Terms .... 12mo, 3 00 " The Iron Founder 12mo, 250 Supplement 12mo, 250 Booth's Clock and Watch Maker's Manual 12mo, 2 00 Bouviers Handbook on Oil Painting 12mo, 2 00 Eissler's Explosives, Nitroglycerine and Dynamite 8vo, 4 00 Ford's Boiler Making for Boiler Makers 18mo, 1 00 Metcalfe's Cost of Manufactures ' 8vo, 5 00 Metcalf 's Steel A Manual for Steel Users 12mo, 2 00 Reimann's Aniline Colors. (Crookes.). ... 8vo, 2 50 * Reisig's Guide to Piece Dyeing 8vo, 25 00 Spencer's Sugar Manufacturer's Handbook 12mo, inor. flap, 2 00 Svedelius's Handbook for Charcoal Burners 12mo, 1 50 The Lathe and Its Uses 8vo, 600 Thurston's Manual of Steam Boilers 8vo, 5 00 West's American Foundry Practice 12mo, 2 50 " Moulder's Text-book 12mo, 2 50 Wiechrnarm's Sugar Analysis 8vo, 2 50 Woodbury's Fire Protection of Mills 8vo, 2 50 MATERIALS OF ENGINEERING. STRENGTH ELASTICITY RESISTANCE, ETC. (See also ENGINEERING, p. 6.) Baker's Masonry Construction 8vo, 5 00 T3eardslee and Kent's Strength of Wrought Iron 8vo, 1 50 Bovey's Strength of Materials 8vo, 7 50 Burr's Elasticity and Resistance of Materials 8vo, 5 00 Byrne's Highway Construction 8vo, 5 00 Carpenter's Testing Machines and Methods of Testing Materials Church's Mechanic's of Engineering Solids and Fluids 8vo, 6 00 Du Bois's Stresses in Framed Structures 4to, 10 00 Hatfield's Transverse Strains 8vo, 5 00 Johnson's Materials of Construction 8vo, 6 00 9 Lanza's Applied Mechanics 8vo, $7 50 " Strength of Wooden Columns 8vo, paper, 50 Merrill's Stones for Building and Decoration 8vo, 5 00 Merriman's Mechanics of Materials 8vo, 4 00 Pattou's Treatise on Foundations 8vo, 5 00 Rockwell's Roads and Pavements in France 12mo, 1 25 Spaldiug's Roads and Pavements 12mo, 2 00 " Hydraulic Cement 12mo, Thurston's Materials of Construction , 8vo, 5 00 Thurston's Materials of Engineering 3 vols., 8vo, 8 00 Vol. I., Non-metallic 8vo, 2 00 Vol. II., Iron and Steel 8vo, 3 50 Vol. III., Alloys, Brasses, and Bronzes , 8vo, 2 50 Weyrauch's Strength of Iron and Steel. (Du Bois.) 8vo, 1 50 Wood's Resistance of Materials 8vo, 2 00 MATHEMATICS. CALCULUS GEOMETRY TRIGONOMETRY, ETC. Baker's Elliptic Functions 8vo, 1 50 Ballard's Pyramid Problem 8vo, 1 50 Barnard's Pyramid Problem 8vo, 1 50 Bass's Differential Calculus 12mo, 4 00 Brigg's Plane Analytical Geometry 12mo, 1 00 Chapman's Theory of Equations 12mo, 1 50 Chessin's Elements of the Theory of Functions Compton's Logarithmic Computations 12mo, 1 50 Craig's Linear Differential Equations 8vo, 5 00 Davis's Introduction to the Logic of Algebra 8vo, 1 50 Halsted's Elements of Geometry , . .8vo, 1 75 " Synthetic Geometry 8vo, 150 Johnson's Curve Tracing 12mo, 1 00 " Differential Equations Ordinary and Partial 8vo, 350 Integral Calculus 12mo, 150 " Least Squares , 12mo, 150 Ludlow's Logarithmic and Other Tables. (Bass.) 8vo, 2 00 Trigonometry with Tables. (Bass.) 8vo, 300 Mahan's Descriptive Geometry (Stone Cutting). 8vo, 1 50 Merriman and Woodward's Higher Mathematics 8vo, 5 00 Merriman's Method of Least Squares 8vo, 2 00> 10 Parker's Quadrature of the Circle 8vo, $2 50 Rice and Johnson's Differential and Integral Calculus, 2 vols. inl, 12mo, 2 50 " Differential Calculus 8vo, 350 " Abridgment of Differential Calculus 8vo, 1 50 Searles's Elements of Geometry 8vo, 1 50 Totten's Metrology 8vo, 2 50 Warren's Descriptive Geometry 2 vols., 8vo, 3 50 ' * Drafting Instruments 12mo, 1 25 " Free-hand Drawing 12mo, 1 00 " Higher Linear Perspective 8vo, 3 50 " Linear Perspective 12mo, 1 00 " Primary Geometry 12mo, 75 Plane Problems 12mo, 1 25 Plane Problems 12mo, 125 " Problems and Theorems 8vo, 2 50 " Projection Drawing 12mo, 1 50 Wood's Co-ordinate Geometry 8vo, 2 00 " Trigonometry 12mo, 1 00 Woolf's Descriptive Geometry Royal 8vo, 3 00 MECHANICS-MACHINERY. TEXT-BOOKS AND PRACTICAL WORKS. (See also ENGINEERING, p. 6.) Baldwin's Steam Heating for Buildings 12mo, 2 50- Benjamin's Wrinkles and Recipes 12mo, 2 00 Carpenter's Testing Machines and Methods of Testing Materials 8vo, Chordal's Letters to Mechanics 12mo, 2 Oft Church's Mechanics of Engineering. ... 8vo, 6 00 " Notes and Examples in Mechanics 8vo, 2 00 ; Crehore's Mechanics of the Girder 8vo, 5 00 Cromwell's Belts and Pulleys -12mo, 1 50 Toothed Gearing 12mo, 1 50> Compton's First Lessons in Metal Working 12mo, 1 50 Dana's Elementary Mechanics 12mo, 1 50 Dingey's Machinery Pattern Making 12mo, 2 OO 11 Dredge's Trans. Exhibits Building, World Exposition, 4to, half morocco,$15 00 Du Bois's Mechanics. Vol. I., Kinematics , 8vo, 3 50 " Vol.11., Statics 8vo, 400 Vol. III., Kinetics 8vo, 350 Fitzgerald's Boston Machinist 1 8m o, 1 00 Flather's Dynamometers 12mo, 2 00 " Rope Driving 12mo, 200 Hall's Car Lubrication 12mo, 1 00 Holly's Saw Filing 18mo, 75 Lanza's Applied Mechanics 8vo, 7 50 MacCord's Kinematics 8vo, 5 00 Merriman's Mechanics of Materials 8vo, 4 00 Metcalfe's Cost of Manufactures 8vo, 5 00 Michie's Analytical Mechanics 8vo, 4 00 Mosely's Mechanical Engineering. (Mahau.) 8vo, 5 00 Richards's Compressed Air 12mo, 1 50 Robinson's Principles of Mechanism 8vo, 3 00 Smith's Press- working of Metals 8vo, 8 00 The Lathe and Its Uses . 8vo, 6 00 Thurston's Friction and Lost Work 8vo, 3 00 " The Animal as a Machine 12mo, 1 00 Warren's Machine Construction 2 vols., 8vo, 7 50 Weisbach's Hydraulics and Hydraulic Motors. (Du Bois.)..8vo, 5 00 Mechanics of Engineering. Vol. III., Part I., Sec. I. (Klein.) 8vo, 500 Weisbach's Mechanics of Engineering. Vol. III., Part I., Sec. II. (Klein.). 8vo, 5 00 Weisbach's Steam Engines. (Du Bois.). < Svo, 5 00 "Wood's Analytical Mechanics Svo, 3 00 " Elementary Mechanics 12mo, 125 Supplement and Key 1 25 METALLURGY. IKON GOLD SILVER ALLOYS, ETS. Allen's Tables for Iron Analysis , 8vo, 3 00 Egleston's Gold and Mercury Svo, 7 50 12 Eglestou's Metallurgy of Silver 8vo, $7 50 * Kerl's Metallurgy Copper and Iron 8vo, 15 00 * ' Steel, Fuel, etc 8vo, 1500 Kunbardt's Ore Dressing in Europe 8vo, 1 50 Metcalf Steel A Manual for Steel Users 12mo, 2 00 O'Driscoll's Treatment of Gold Ores 8vo, 2 00 Thurston's Iron and Steel 8vo, 3 50 Alloys 8vo, 250 Wilson's Cyanide Processes 12mo, 1 50 MINERALOGY AND MINING. MINE ACCIDENTS VENTILATION ORE DRESSING, ETC. Beard's Ventilation of Mines 12mo, 2 50 Boyd's Resources of Soutb Western Virginia Svo, 3 00 Map of South Western Virginia Pocket-book form, 2 00 Brush and Penfield's Determinative Mineralogy Svo, 3 50 Chester's Catalogue of Minerals 8vo, 1 25 Dictionary of the Names of Minerals.. Svo, 3 00 Dana's American Localities of Minerals Svo, 1 00 " Descriptive Mineralogy. (E. S.) Svo, half morocco, 1250 " Mineralogy and Petrography. (J. D.) 12mo, 200 " Minerals aud How to Study Them. (E. S.)., 12uio, 1 50 " Text-book of Mineralogy. (E. S.) Svo, 3 50 *Drinker's Tunnelling, Explosives, Compounds, and Rock Drills. 4to, half morocco, 25 00 Eglestou's Catalogue of Minerals and Synonyms Svo, 2 50 Eissler's Explosives Nitroglycerine and Dynamite Svo, 4 00 Goodyear 's Coal Mines of the Western Coast. 12mo, 2 50 Hussak's Rock- forming Minerals. (Smith.) Svo, 2 00 Ihlseng's Manual of Mining . . Svo, 4 00 Kunbardt's Ore Dressing in Europe , Svo, 1 50 O'Driscoll's Treatment of Gold Ores Svo, 2 00 Rosenbusch's Microscopical Physiography of Minerals aud Rocks. (Iddings.) 8vo, 500 V 5 ) Sawyer's Accidents in Mines 8vo, 7 00 StDokbridge's Rocks and Soils 8vo, 2 50 13 Williams's Lithology 8vo, $3 00 Wilson's Mine Ventilation 16mo, 1 25 STEAM AND ELECTRICAL ENGINES, BOILERS, Etc. STATIONARY MARINE LOCOMOTIVE GAS ENGINES, ETC. (See also ENGINEERING, p. 6.) Baldwin's Steam Heating for Buildings 12mo, 2 50 Clerk's Gas Engine t 12mo, 400 Ford's Boiler Making for Boiler Makers 18mo, 1 00 Hemenway 's Indicator Practice 12mo, 2 00 Hoadley's Warm-blast Furnace 8vo, 1 50 Kneass's Practice and Theory of the Injector 8vo, 1 50 MacCord's Slide Valve 8vo, * Maw's Marine Engines Folio, half morocco, 18 00 Meyer's Modern Locomotive Construction 4to, 10 00 Peabody and Miller's Steam Boilers Svo, Peabody's Tables of Saturated Steam Svo, 1 00 " Thermodynamics of the Steam Engine 8vo, 5 00 Valve Gears for the Steam-Engine 8vo, 2 50 Pray's Twenty Years with the Indicator Royal Svo, 2 50 Pupin and Osterberg's Thermodynamics 12mo, 1 25 Reagan's Steam and Electrical Locomotives. 12rno, 2 00 RSntgen's Thermodynamics. (Du Bois.) Svo, 5 00 Sinclair's Locomotive Running 12mo, 2 00 Thurston's Boiler Explosion 12mo, 1 50 " Engine and Boiler Trials Svo, 500 " Manual of the Steam Engine. Part I., Structure and Theory, Svo, 7 50 " Manual of the Steam Engine. Part II., Design, Construction, and Operation Svo, 7 50 2 parts, 12 00 " Philosophy of the Steam Engine 12mo, 75 " Reflection on the Motive Power of Heat. (Caruot.) 12mo, 2 00 " Stationary Steam Engines 12mo, 1 50 " Steam-boiler Construction and Operation Svo, 500 14 Spaugler's Valve Gears 8vo, $2 50 Trowbridge's Stationary Steam Engines 4to, boards, 2 50 Weisbach's Steam Engine. (Du Bois.) 8vo, 5 00 Whitham's Constructive Steam Engineering 8vo, 10 00 ' ' Steam-engine Design ... 8vo, 6 00 Wilson's Steam Boilers. (Fluther.) 12mo, 2 50 Wood's Thermodynamics, Heat Motors, etc 8vo, 4 00 TABLES, WEIGHTS, AND MEASURES. FOR ACTUARIES, CHEMISTS, ENGINEERS, MECHANICS METRIC TABLES, ETC. Adriance's Laboratory Calculations 12mo, 1 25 Allen's Tables for Iron Analysis 8vo, 3 00 Bixby's Graphical Computing Tables Sheet, 25 Compton's Logarithms 12mo, 1 50 Crandall's Railway and Earthwork Tables 8vo, 1 50 Egleston's Weights and Measures 18mo, 75 Fisher's Table of Cubic Yards Cardboard, 25 Hudson's Excavation Tables. Vol. II 8vo, 1 00 Johnson's Stadia and Earthwork Tables , .8vo, 1 25 Ludlow's Logarithmic and Other Tables. (Bass.) 12mo, 2 00 Thurston's Conversion Tables 8vo, 1 00 Totten's Metrology 8vo, 2 50 VENTILATION. STEAM HEATING HOUSE INSPECTION MINE VENTILATION. Baldwin's Steam Heating 12mo, . 2 50 Beard's Ventilation of Mines 12mo, 2 50 Carpenter's Heating and Ventilating of Buildings 8vo, 3 00 Gerhard's Sanitary House Inspection Square 16mo, 1 00 Mott's The Air We Breathe, and Ventilation 16mo, 1 00 Reid's Ventilation of American Dwellings 12mo, 1 50 Wilson's Mine Ventilation 16mo, 1 25 niSCELLANEOUS PUBLICATIONS. Alcott's Gems, Sentiment, Language Gilt edges, 5 00 Bailey's The New Tale of a Tub , 8vo, 75 15 Ballard's Solution of the Pyramid Problem 8vo, $1 50 Barnard's The Metrological System of the Great Pyramid. .8vo, 1 50 Enimou's Geological Guide-book of the Rocky Mountains. .8vo, 1 50 Ferrel' s Treatise on the Winds 8vo, 4 00 Mott's The Fallacy of the Present Theory of Sound. .Sq. IGnio, 1 00 Perkins's Cornell University Oblong 4to, 1 50 Ricketts's History of Rensselaer Polytechnic Institute 8vo, 3 00 Rotherham's The New Testament Critical^ Emphathized. 12ino, 1 50 Totteu's An Important Question in Metrology 8vo, 2 50 Whitehouse's Lake Moeris Paper, 25 * Wiley's Yosemite, Alaska, and Yellowstone 4to, 3 00 HEBREW AND CHALDEE TEXT=BOOKS. FOR SCHOOLS AND THEOLOGICAL, SEMINARIES. Gesenius's Hebrew and Chaldee Lexicon to Old Testament. (Tregelles.) Small 4to, half morocco, 5 00 Green's Elementary Hebrew Grammar 12mo, 1 25 " Grammar of the Hebrew Language (New Edition). 8 vo, 3 00 " Hebrew Chrestomathy 8vo, 2 00 Letteris's Hebrew Bible (Massoretic Notes in English). 8vo, arabesque, 2 25 Luzzato's Grammar of the Biblical Chaldaic Language and the Talmud Babli Idioms 12mo, 1 50 MEDICAL. Bull's Maternal Management in Health and Disease 12mo, 1 00 Hammarsten's Physiological Chemistry. (Maudel.) 8vo, 4 00 Mott's Composition, Digestibility, and Nutritive Value of Food. Large mounted chart, 1 25 Steel's Treatise on the Diseases of the Ox 8vo, 6 00 " Treatise on the Diseases of the Dog 8vo, 3 50 Worcester's Small Hospitals Establishment and Maintenance, including Atkinson's Suggestions for Hospital Archi- tecture 12mo, 1 25