Answer to Question #241010 in Civil and Environmental Engineering for John Prats

Question

From the given loaded cantilever truss. Compute the following: (a) the external reaction at D. (b) the stress of member BC and the stress of member DE.

Answer 1

To calculate the external reactions at D and E, the analysis for a cantilever truss could begin with the joint at the loaded end. However, this truss will be analyzed completely, so the first step will be to compute the external forces at D and E from the free-body diagram of the truss as a whole. The equations of equilibrium give

$∑M E ​ =0]$

we have fbd showing the forces acting on each of the connecting pins. The correctness of the assigned directions of the forces is verified when each joint is considered in sequence. There should be no question about the correct direction of the forces on joint A. Equilibrium requires

$[∑F y ​ =0]$

$[∑F _x ​ =0]$

Note that the weights of the truss members have been neglected in comparison with the external loads.

Helpful Hint

1)It should be stressed that the tension/ compression designation refers to the member, not the joint. Note that we draw the force arrow on the same side of the joint as the member which exerts the force. In this way tension (arrow away from the joint) is distinguished from compression (arrow toward the joint).