Question

Ball joints connect the ends of each of the struts shown The resulting structure supports a force of 1375 N which is in the xz plane. The dimensions of this arrangement are a 8 cm b = 15 cm C 10 cm d-12 cm g=5 cm h 6 cm k = 14 cm Find the force in each strut Denote compressive forces with negative values and tonsite forces with positive values 02 FAB =

Answer 1

fisst assuming all the forces in each Stout is tensile, unit vector in the direction of CA Fein FA 2 | Ca kí +03+C-a), 1 , 24 ✓ K²+ (coaj? - CA = - 14ît2 r = -0.989 î+ 0.141 R 142+22 unit vector in the direction of D A DA= - Kit dŷ – ar 141 + 129-8k :-0.696?+0.5979 - 0,398K Vk²x d²+02 | 142+ 12²+ 82 . Unit vector in the direction of BA =-0.6352 -0.6819 - 0.368 BAZKî- bi-ak - - 147 15 7-8F- ✓ K²+6²+ a2 0 14215²782 G √ 9² Cath? vector i, & 24315 × 8 Leyath i tof - 1375 x gt (ath? t = -1395 x 5 î - 1375x14 F 15+142 1527142 = - 462.46î - 1294.89 k

80, vector addition of all the forces at A should be zero, Et Feat FA+F BATO » – 462,462-1294.89 Rt FCA (-0.989ît 0.14 & J + FA -0. 6961 +0.5979-0.398 Â J + FRA C -0.635Î-0.681 -0.363ť )=0 by comparing ?, ? Ř component to zero, -462.46 - 0.989 FCA -0. 696 FDA ~0.635FBAZO 0.597 FDA -0.681 FBA=0 - 1-294.89 +0:141 FCA -0.398 FDA-0363 FBAO solving above three equation. FCA = 1458.63N (Tensile) FDA 2-1520.78 N ( Compressive ) EBA= -1333. IGN (compressive)