Question

Homework Problem H22.B Given: Consider the truss shown below with the loading on joints D, E, I and N, in addition to the loading due to the weight W of the block that is supported by the cable-pulley system shown, where W = 2P. Find: Determine the load carried by members 1, 2 and 3. Identify each member as either being in tension, in compression or carrying zero load. Leave your answers in terms of P. N NA cable radii of pulleys at K and M:r all horizontal members of length: 4d all vertical members of length: 3d AP

Answer 1

P w/2 = 2P/2 =P 2P cable 8d+r 2P 4d - r radii of pulleys at K and M:r all horizontal members of length: 4d all vertical members of length: 3d Ad WWWP

Use EFY = 0 ; {Fx = 0 {M CA =0 Moment equilibrium about A EM@ A =0 (2 tre] [ 2P x3d] + [ AP x6d] + [Px9d] + P x 12 d] - [ By x 4 d] + [ P(4d-r)] + [P(ed) + [(P) (8d+r)] ? -O Solve I + S 56 Pd + 12 pd + g Pd + 12 Pd + 4Pd - Pr + 8 pd. + 8 Pd + Pri = . 59 Pd = 4 By . d

EFx = 0 Ax - = 2P + 2P + P + P . Ax = GPL Efy = o p = Ay + By = P + P + P . AY = 3P - 14.75 P AY = -11.75 P P :: AY = 11.75 P .75P Joints Method Joint of A FAD EFY = 0 - FAB FAD = 11.75P Tension AK = GP - AY = 11.75 P Ex = 0 T FAB = 6P - Tension

Toint - FBO B V FBC = 36.870 = tant (3d) 14d/ EFx=0 .: 6P = FBD cos 36.87 FBD = 7.5P compression Efy = 0 FBD sino + FBC = 14.75P FBC = 10.25 p compression

Joint c e & FCH ots FBC = 10.25 P = 10.25 P compression - Answer EFx = 0 FED = Tero force member Joint D FDE A FOH Etro tre. oo (FDH Cosa + 2P) FBD = 7.5P - 37.5 cos = 11.75P FDH = 5 p Tension I Answer EFY = 0 (1 = 4 FDE + FDH sino &7.5P sino = 11.75P JEDE = 4.25P Tension

Joint E I FEI 2P * FEH FDE = 4.25P £fy = 0 . FEI = 4.25P Tension Answer " Final Answers force 4.25 P Member [ EI Nature T Member 2 DH 5.00P I Member 3 CH 10.25 P c