Steel pipes RS and SV each have a weight per unit length of

Steel pipes RS and SV each have a weight per unit length of 10 lbs/ft and are welded together at point S. The steel pipes are supported by three wires. Find the tension in each wire.

Solution

F_y = 0

Or, T_a + T_b +T_c + (-10x (9+4))x 9.8 x 0.453= 0                                                  [ 1 pound = 0.453 kg]

Or, T_a + T_b +T_c = 577.122 N…………………….i

Taking moments about S, T_a x 3+ Tc x (9-2)=0   or, Ta= -7T_c/3………………………….ii

Taking moments about R, Ta x 1 + T_b x 4 + T_c x7 = 0……………….iii   

Using ii and iii, we get, -7T_c/3 + 4T_b + 7T_c = 0    or, 4T_b + 14T_c/3= 0………………….iv

Using I and ii, we get -7T_c/3+ T_b + T_c = 577.122   or, -4T_c/3 + T_b = 577.122 or, 4T_b – 16T_c/3 = 577.122

Solving equations, we get T_c (14/3 + 16/3)= 0- 577.122 or, T_c =-577.122/10 = -57.712 N

Ta= -7 x -57.712/3 = 134.66 N and T_b = -14T_c/12 = -14 x -57.712 /12= 67.33 N