Question

1.26 The scaffolding system, shown in Fig. 1.27, is used to carry a load of 10,000 lb. Assuming that the weights of the beams and the ropes are negligible, formulate the problem of determining the values of x1, x2, X3, and x4 to minimize the tension in ropes A and B while maintaining positive tensions in ropes C, D, E, and F.

Answer 1

TB We know ou 10-et-L₂-23 X, Ha Juk 16 TA + T8 = 10000.14 a soft fort minimita ratare and, TE + TF = 1000 Te Tp TF Телъ you minimum value, @ 9-10-26 - Kz -22 17 . TE = + 5000 lb TE TE 105 x 1 Te Ti = +5000 lb. - 10000.1b For . So equally distribute | Tet To =TE load, art . Tot To = 5000 lb Te =+2500lb & ID=42500lb. For the denoton to be equally, distributed [a= '10 - 2y = 2z = 42 2

О, 3 м)=0 : 5000 (0) - Te € 10-аа). -Tp C0 - 2 - 1 ) – Тех, = 0 50000 - 5000 (10-) - 500 Clo-z-z) - 2500 С, = 0, 50000 - 50000 + 5000 22 - 25000 + 45002, 250093 - 1500 х = 0 15 фра, + 2500 аз - 25фф х = 250 58, + 25х3 - 25 х = 25, = | За, + 3 = х = 10- 1,-2,