Question

Statics

Given: A truss is loaded as shown Drawing is to scale SOOON 47.67 3000N using method of sections Find Forces in elements 34

Answer 1

Free Body Diagram of the given truss is 2m (4m R5 5000N 3000N Taking Equilibrium equation's - summation of all horizontal forces is equal to zero Ex=0 3) Summation of vertical forces is equal to zero. Ev so take itve t-ve Forom figure R-5000 - 3000 + R5 = 0 3) 0 : Ri+ Rs = 80000 > 0 Summation of all moments with respect to is EM, zo Take ove Dve 5000 X8 + 3000 x12 - Rs x16 = 0 40000 + 56000 – R5x16 = 0

R5 = 76000 16 : Rg = 47.50 N By substituting 'Ro in equation 0 we get Rx +4750 = 8000 Ri= 8000 -4750 (Ri= 3250 Now, Cut the truss in such a way that the : section should not pass through more than 3 · members. OL Taking Right hand side section Again taking equilibrium R5= 4750N equations 67 + sin 45° + 39 Os 26.56 = 0 ->

Ev=0 R5 - Cos 45° + sin 26.56° = 0 4750 – 6s 45° + son 26.56° = 0 -> Taking moments about Cw..to) Eme=0 67 x 4 - R$*4 =0 - X it = 4750x4 67 = 19000 6 = 4750 N) Substituting in equation 2. we get 4750 + 47 sin 45 + cos 26-56 =0 Solving eq ® and op n c 4750 -67 845 + 4 Sin 26-56 = 0 4750 + sin 45 + 34 Cos 26:56=0 @ 9500 + 34 (sin 26-56.+ cos 26.56) =0. 34 = - 9500 sin 26:56 + cos 26.56 34 = -7081.09 N

. By Substituting y value in equation ® we get.. 4750 + 47 sin. 45 + 67081.09) cos 26:56 =0 a sin 45 = Fogi:09) cas 26:56 -- 4750 CD sin 45 = 1583.79 1583.79 sin 4-5 16 = 2239.82 N 'the forces in the elements 34, 47,67 are -7081-09N , 2239.82N, 4750 N respectively