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 p. ( U? . , p 
 
 MJlA^QsO Xb/t^ Axt^& AxCxOCXt/ 
 
 ^ 
 
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 vnx3 -ca^> OA^A- ^3Ut<yCHkx7^ix dc?e^s I +*j cL*. } >< 
 
 /V7ex ^^v^\A.jOc^vru(^tA) v\-\ xC-<a,c-vu 
 <3 ; /to -C^i-^x -jvtcvwe oK ^S'CM^vO^vt^ X ' 
 dsy, 'Wv/u^'V- ^u 
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 /IX/tx/e 
 
 ; 
 
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70 
 
 24-6 CASE ~VZI . 
 
 
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 cxx-vt^z/ x?> 
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 t c*^xv yVc^wl^> -c*; Vuj-^/e \sis>Xs /Oe/i/wv s /co/ N ^ 
 / M!^vw /t/ = /tt; ( ll. 1 - >VJ . J/vt >^vtt)/wvi-a M , -/(J'V XA^ux x*-C C 
 
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71 
 
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 N 
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 VVl 
 
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 ^.(N.N.-. 
 
 N 
 
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 x. 
 
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 J- ( N - I ) x^c 
 
 J 
 
 2 N S N (N-I) 
 
 ''b/M, ^WUCUV?>VW<31 xbl^C/ 
 
 y, u0 . d (? 
 
 d 
 
 /vw. 
 
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 s 
 
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 xx-w 
 
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STRESS. 
 
 ^ 10*. *<a. O) -p.. no 
 
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 tS-T^, J 
 
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 d-t) -WXVtvO -W ) 'V* 'VVtt /UVl/vMi- 
 
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 >t* '^^VLXlX X^T^LXL^XA/Wld ^O'T-t-Cx 'Q/Cx 
 
 j ,5 r 
 
 -C^vi^v( ^VvO 
 
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 90 
 
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 2. 5 
 
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 ^ 1 
 
 
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 vt ^a. 
 c-vtvoJu' 
 
 108 , 
 
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 OA 
 
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 SOLUTION. 
 
 Jx 
 
 8 . 
 
 
 
 ?J^ 
 
 /CtXTt^. 
 
 G, 
 
 2 A 
 
 ^ A. (,+ , 
 
 2A 
 
 2 A 
 V * + *** 
 
 2 A 
 
 '=.-+ 
 
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 2A 
 
 
 <H 
 
 .(2 A) 
 
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 A - A -. A . :; .'*.* : EC = 
 
 4 1 ~~ 
 
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 \i.\ ' z a 
 
 S : A :. EC^EO '. EC. 
 
 X 
 
 : EC +to : ED = 
 
7 4- 
 
 VUt^VK 
 
 V 
 
 
 T 
 
 
 "fl-T *-- 
 
 P' , 
 Sk V- i 
 
 P 
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 T ^ 
 
 2A 
 
 X ? H * A ' 5 A * A 
 
 rt r> 
 
 (7 u \-0 u i. i 'V 
 
 /VV^-^A 'WtC/V SW*QL l \\\st/ >**CL/)fc' /\^S\/W\s AAt r\A- Cs\\. 
 
 d fl 
 
 A_,v 
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 , +~A T 
 ^t^f _ A 
 
 A ^' P 
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 = 3A. 
 
 
 
 'K "u 
 
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 A| . A '& ; <vwu 
 ^A i ' j 
 
 '&xx*;ex, 
 
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 M . 
 
 O ^^^^ * 
 
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 A + A. 
 
 
75 
 
 15 
 
 EXACT SOLUT 
 
 IOM 
 
 
 A, 
 
 
 L 
 
 ^- j 
 
 
 c 
 
 
 
 B 
 
 
 i 
 
 
 P 
 
 
 N 
 
 1 
 
 
 
 
 
 
 
 M 
 
 j^L?^ 
 
 
 
 
 
 / 
 
 ^ 
 
 i 
 
 
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 D ^ 
 
 
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 LH = &. 
 
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 Z : A, :: i l ; PH 
 
 (A, + A l} 
 
 J-o >M0 C. OP- ^ . xi> A , + A x ^^.a 
 PS = PH 
 
 M 
 
 : OP 
 
 2 A 
 
 2 A 
 
 _ 
 
 34 " I 
 
 A. -^. ) A. - 
 
 2 A 
 
 LM = 
 
 =HO = 
 
 1 A 
 LO = L H + H - '*' + *Ts.+ 'N _ _ ( A t + A I 
 
 + . 
 
 2A 
 
 2A 
 
 HO, 10, 0$ 
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 2A 
 
 + A, 1^1 
 
 
 A 
 
 o''vua 
 
 'H^n. 
 
2.55 
 
 r-v 
 
 
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 'V 
 
 (Lo. 
 
 ; A/P 
 
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 'W. ^-A ^wwt> /ve^wvit-wv-v 
 
 
 
 >'^t t<M-Axwv<3 
 
 - / v^wvvo 
 
 
 + 2 A, A, 
 . 2 A 
 
 
 APPROXIMATE SOLUTION . $L - 
 
 v V 
 
 2 2A 
 
 A.+A,** 
 
 2.A 
 
 -2 A 
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 .#)' 
 
77 
 
 J-o 
 
 Jr/w 
 
 Ifa3 
 
 "M. + 'n. = 
 
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 9 r P i \ V 
 
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 K 
 
 
 A 
 
 Comjii-es sio^- 
 
 r-Sj 
 
 M O ^ ffj: 
 
 -zr. 
 
 Tension, fj 
 
 
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 ^x~ 2 
 Vt = vv 
 
 A,= vLl. = 
 
 A 
 
 
 
 M. 
 
 (A, + 1 A,) 
 
 / |v. 
 
 > 
 
 x-ce. 
 
 9 
 
 >v -+ 
 
 
 'M-cvi/ 
 
 o 
 
 --t< 
 
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 .(4.) 
 
 {C y' /" i & A 
 
 M ffe>- A z (^Ai + 4-A v -f* ^3 ) * 
 T- A a ^A, 
 
 ><xA>Mxe x?> A >. 
 
 ,z 
 
 -(f a _ ^ ) A ....(5.; 
 
7 S 
 
 = P 
 
 'u- . 
 
79 
 
 , VV ^ <aA^xx> xs*x* 
 
 iv: 
 
 LLJ 
 
 M - A* 
 
 .--.. 
 
 c- 
 
 v-w>\. 
 
 ^ xJtl*C^U ) X?> XVuS^t b 
 
 y 
 
 -Tvvc AV <x-a vvAf -ojf- 'Vvvxi "ue^Vvvx/ ( xtx-' Vvi. M't A/ Avvc-Yvo'vbvc'-vvoixC/ xtc 't/vve fovyo H.X ^ 
 x>cx<) /Ur <uvwx C^W^IAX f= ^f l 
 ,a 
 
 -^/u 
 /Ve/wcA'Wt, ^v J x<AA^. /vwi cJpvxXvixXC^ 
 
 /to - 
 
 ' - 
 
 ja. 
 
 ,- . 
 
 '/ . J 
 
 
 p 
 
 3T 
 
 V- 
 
 XVVCIA? V-cxww. 
 
 (u ) -CVK.W 
 
 ^Ka^-wv x>, IV '- x^> a 13 'to xi, W 
 /b^ui<vc) / t 
 
 t-vi. ^e' ^w e^c<x^'C- /v 
 = "o 
 
 ;Cxx3|/H/b 'Or %> 
 
 .... 
 
 /VWIA 
 
 -vi 
 
 i/ui 
 
 o> X>XX*CAA,), ^/ 
 
 'I 
 
 B ~ 
 AOI 
 
 W- /^B = 
 
 ^, ^ / 
 
 
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 [UITIVBRSITT] 
 
80 
 
 TT -vod -vu^ue 
 
 -il 
 
 13 = 
 
 w 
 
 8 = 
 
 
 W 
 
 i 
 
 L : 
 L : 
 
 /: W : ^ B : A w' 
 :: W : B : w' .... 
 
 (11.) 
 
 DISTRIBUTION OF SHEARING. STRESS IN Besms 
 
 a 3A: -VKX^ 'fc 
 
 T! 
 
 J-L...2 
 OMB 
 
 1 
 IX 
 
 H,-......-..-..H 
 
 H 
 
 I 
 
 1 
 1 
 
 SECTION 
 
 ! 
 
 3 3 
 
 -cx-^-O 
 
 -V 
 
 'wlxu 
 
 'wo 
 
 'UC. 
 
 ykuuvwC 
 
 ^ 
 
 <A 
 
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 > P i-P J 7 
 
 /Uu /o> /x^vt' ^J-^vtfx^A^o^ta 
 
 /nX^Uvuc .wtvo^-c 
 <o)t A^*x~x5 x Vuextvv 
 EF. 
 
 HFD pt. 
 
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 C-/wvO'vix)' 
 
 H F" ^ J/va AJfv4x CxX^ve 
 
 xu^HA. / 
 
 
 
 /wJk->^c-L-xw^> /Co Jr***v 
 ^nXtvuxC A^KO 
 
 'b 
 
 GitB. 3r /l>tv- 
 G E B ^ 
 vixC- --i?> 
 
 xVvt<Vv^e-4 -t>> 
 
 7i-<y- 
 
 
 >*o-xt. 
 
 
 
 b- 
 
 
 > x3T-t--<viA-vvd 
 
 -C--lx>voyxxCCx /CO xtKxX<> "VuO^HxJ -O-vubtVU -T 
 
 x?J^ /-tvufc ^vvuvvvc FE (a/ 
 
 d 
 
 .^VvCiVwfc re 
 
 7/- 
 
 ve 
 
 /t^vt^C^ 
 
 rxx 
 
 
 
 
 E . 
 
 f) 
 
 
8 I 
 
 ^OT ^^\^o^v^cjL ^>Vi^o^.^^\ 
 
 a = 
 
 9 -v P(? 
 
 /K^ >VC^L-& XXV ..(XS AX^3 /vtxX-V\t-< 
 
 j-0- P Pi? " u c 
 
 Z z 'l.^uc <- wCXn-'i -3-r -'V&^Vvvt. -CMT t j 
 
 
 
 ' 
 
 z = 
 
 <J 
 
 voxvw >v Zf 3 lG.o . 107 . = c: .'. 
 
 = fp cty: .'. = F 
 
 o " tf 
 
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 --b ; \za A i^u = '-:;rH 
 
 Jo ^ d 0' 
 
 3. 
 
 II 
 
 ifff-T.iA xtf-it. .-i-iJxv^uC FE- 
 
 ' 
 
 q z <i* = ^Cti. ^ . x otu ---- ................. ... (a.) 
 
 J*+ .'* 
 
 -n.2 ^ i,7 ois, ^..73 ^U).tf M = ^ I /. /p. = - u 
 
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 3lf 
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 TL 
 
 f 
 
 r/-^ at rn r? 
 
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 6~ 
 
 nr,iv,v, xwJ-vi Mlc* 
 3 "V ^4 
 
 "vn iw AJU* 
 
 -<xxW 
 
 r 
 
 A 
 
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 -T..... 
 
 A, A t 
 
 - 
 
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 *, + A\ 
 
 A, A, 
 
 "vnr 
 
 ^t 
 
 vftA 
 
 A, 
 
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 2> 
 
 J X 
 
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 + 
 
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 tO'Vvwt^xJ'W O' 
 
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 --8AA t + SA.A^zA^ 
 
83 
 
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 -4- 
 
 "/"~ ^ ---- 'JO 
 
 ^ J 
 
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 -Lo s 'WUJ'V^VC-viyt- 0-T /WVAiAxbt-<X- -QxC- <>vvC AvCn^vIx -tc'luM/e At-A(. . 
 
 ^-o ~ i >/ <> i/ -M. = M. ' 
 
 -Or /Mo^5-^ xa^C- x^^ux ytvO^wb -cv> C? /ct'Wo/ae' 
 J-VWL/ xt/Vve n^xMxy\>u?txL, xV^-t^4 >OO 1/j , 
 
 r L. ^7 r? /7 " 
 
 >= xM-o.e-v- /cut/ xJ^iA><xext = -^vua^. aaXxxx2/ ^jl* ^jv 
 
 L.* 
 
 OVM! XxiC-cX"x^7xv^ . 
 
 J - /vwoc^'uJl/tx^ -o> /K/vo<j> >3 "tXxC wO'T-'V'- = ^ 'to "3 "/ / 
 
 X/C-vvOlVVi- . 
 
 tC-VvU7-vv x-t i-VC-^H. M. = M.O , 
 
 > /to -tvul ^v c<xxt^e4A> xMx7-0' -<?i* /Dvv<i D e<Vwix 
 
 
 O*' 
 
 * 
 
 -c-ctvn/ 
 
 i>wJ'C.<VC OA 
 
 u?'vw -T^ix 
 
 .P P - P .(? 
 
 = -vva It- -cxJivc^t^e >. x^ /TH/ve/ 
 
 i r 
 
 >a 
 
 
 V = /vvt 
 
 t- = -vcvuxxi ^?j^ -c .^a-i: x^O'vwV -<?Ji q 
 
 
 
 ^ = " ., ^ . 
 
 <y t?, x^Mi ^txVUl -t>a<-t/WJ' -oj- 
 
 c 
 -Ma. aife ^^'T S 1^9 ^e / UuA?e i ^ = = ' f 
 
 t x 6 ) 
 
 vj -o4* ' 
 
 J'o-xoc *vvC(.tA^ A% -cXAvn-U.-ex) /to -a -UO^/M 
 \AS3 X^M^Ct/si, -O^t C/tviyj -H. AA /CO C^XO 
 
 p / 
 
 CAuvvKxe . 
 
 
 
 a. 
 
 
 /wAtf, VV*. 
 
 p ^ <, 
 
 | -toad 
 
 
 
 -U /u) 
 
 ;; -r : 
 
 M. - *- 
 
 C^ba -a" / vvC Co/nxj x-T 
 
 * 
 
 +'u. 
 
 -cu 
 
 JL = t - A 
 
 " ~ - 
 
 CD 
 
 . ^/ 
 
 I/ 
 
xb 
 
 84- 
 
 i -- _ ^k 
 
 u 
 
 e- 'vvci^c 1. = " * -4- 
 
 CVwi) 0*U4* I VIA A/C 
 
 d r 
 
 , t = t" WL. 
 
 T " 6 -" i " "- 1 
 
 o f - s f. c JL>> P *< 
 
 -c;f c<J vT* ' "Ttt 7, -cvwJ OMJ\JU i VIA AAsa XO /v/ttX/V -^r 
 J 1 d , I 
 
 xwue^vvb-c^i^ 
 
 /vO t 
 
 CUt^V- 
 
 d 
 
 C7,, I. ^v J 7 U 
 
 _? 6/PTZ'C . /C>w 'I- = -j~ : -M?'VtA> 
 
 -V 
 
 ^xvi^ 
 
 ^= ^ ' 
 ^>6 
 
 JP^.^ 
 
 
 
 foe,,; 
 
 ff- 
 
 
 n C 
 
 Ou(\\J, 'Or ^tnrVli. ^ A LCLX/ / Vt\^3 'OA CAA/Vl/CL'i'lA/V^ . ,T-^VO^VX 
 
 J^ ^ 
 
 ota i>tu 
 
 T = ^V 3 . J. _ ^y. 1 
 
 ^tv T ' ( \+ &U*' y/*- 
 
 -wiXvOtOxC^5 
 
 p. P w <iv ., JP 
 
 /V5 VC/MA y^VuA'VVC jf A/5 <V O/CAAA Xv/VWCXAA 
 
 -uP f 3 oo ^p i-j Q?.P 
 
 nJ&TA. \ A>SV\.O /VWOlAX ^T7i /TA^ixX WXMiU? ' /U<_7 'VOA.C/^t^' Cl'l 
 
 ^wiixX\ 
 
 
 
 
 Step 4 ~JL 
 
 j Slop^e 
 
 
 . (2 A) , u. 252 . 
 
 
211 
 169 
 
 ^"vuz q 
 
 C(Jt 
 
 ^ 
 
 _ _ 
 
 ?> /WvC 
 
 ' P 
 
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 y 
 
 )-cx-viM^.^/vvtxa 
 
 o 
 
 fo 
 
 C 
 -Vixa^ 
 
 'i'vvU 
 
 i* ^" 
 
 vvt 
 
 / VW 
 
 Wl 
 
 , y< -j_ 
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