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Chapter S4, Problem S4/060 The pyramidal truss section BCDEF is symmetric about the vertical x-z plane as shown. Cables AE, AF, and AB support a 6.9-kN load. Determine the force in member BE. The force is positive if in tension, negative if in compression. 360 mm mm C 300 mm 300 mm 330 mm 330 mm 390 mm Y6.9 kN kN Answer: BE = the tolerance +/-2% Click if you would like to Show Work for this question: Open Show Work

Answer 1

Codnates of vavious poits at e jonts wit respect to the given coôldinate axeS (360,0,) A = 20) 20, 0, Mm 050) mm о, Зоо, -300, lo50 б, —. mmm 30) -300, rnm F = о, Зо0, 390) Conider a AF AB AE 6.9KN

Face vecto AE AE (360,0,0) -A (0, -Зо0, 390) AE AE 7-Z A - 0) +(390-0)k (0-369+( -300 (o-360-300-0)t (390 -360i -300 390k 609. 62 -0.59i - 0.492j f0-639k AE-o.5 AE - .

Face vezt8 AF AF A360,0,p) Flo,300, 390) AF AF (o-36of+(300-0) +(390-0)R V (36+(300) (39o - - 0.540.492j to 639 0-637R) (-0-599 AF -AF -AB Folle vezt -AB A 360,0 D) 20, 0,4 20) B -AB -AB

Frо -30/7 + о+to t -АВ у Y у 360 D 20 А о.ч447 toо-894 АВ (oчи + 874k) АВ 69кN -Pace Ps Paralle| to the t- axfs. FE (а +о- 61) KN. 2F АЕ + AF t AB AE-059049 +0-6392) AF fos toча:5 +o639) loч 165 089) +of +j -6R_ AB t о-ччаА8) 1+-о-ч92-АЁ +0492-4F) -0 59AE-059 AF +0 +(о-(39-Е +0-639-4ғ +o894-A8 - 69) к —о.

aot Re hree £quatons of alt biun We 0 o59 AF O Sq AF to.44AB-o Eo -o.492 AE + 0.492AF o.639 AF0.639 AF 0.B94-AB - 69 0 -om uatio n AF -AE = w riten Equation can be as, 0 444 AB =6 -18AE O44 AB AF -AF = 0-3482(AB) -AE =AF

Then atfon O becomes; 639(0-3+88) AB f o 639(0.318B) -AB D 0.89y A6 1. 3181 -AB 6.9 O - 6.9 AB 318 -AB 5.0l KN 5olo-44400894R) -AB KM 2231 AB +D +4.4 KN. (bth in BA 39 .4498); KN. Conder t joint BC BD BE BA

večto (BE Bc F3Ice B(420,0, 120) c(o, 300, 1oSo) Bc Bc (300-0) +loSo -t20) (o-t20) + Y (-20)+ (300) +(330)" 0.85 0.354 to-389 BC (-08st +035 - 0387R) BC Fale vectosD) Bo - t20) 420, 0, Dlo,-300, lo SD) (20)300 30R - BD (20)-300)t 330 050.354+o 389

.382) o(-o.8sA -035 to BB F81e vect8BE BE Bt20, 0,20) E o,-300, 39oj york (-20)-300)-3s0) -330R 300J BE Y Y Y - 354 -0.381A -0-6sf sel-o.8s-0.354-o 38) BE BE F81ce vet (BE B F B(20, 0,120) FL0,3 0, 370) +300 330k BF -20) r(300) + (-330) 0.85 t0354 , 354-0.388) 0.3612 Br-o.85t to

SF = 0 ニ0 BD + BE + BF + BA -0.85BC-0.85BD -o.85BE-0.8S BF .39-- o.354 Bc -0-354 BD -o354 BE +035y BF)- o.389 BC 03898D o.389 BE b 389BF 4.449 K X マ-339 = .E5BD0858E - o 85BE -0.85BC Y 03SY BE-BF) 0-35y Bc 0.35Y BD 0354Be BD) o35BE-BF) pc- Ba=(BE-BF)

Bc- BD& BE BF From immetiy 2.239 BE - Bc BE 2.239 B - oj o. 8 Bc 0t18 BE 4.49 we Q. RKN BC BE 3.53 KN shce negaive sin incates Hat BE member s & Compresslo7 3.53 KN (C) BE