# Math Help - Truss and frame analysis

1. ## Truss and frame analysis

Determine the member forces for all members in each truss shown using the method of joints. Remember to list each member force as either tention or compression.

2. Originally Posted by Celia
Determine the member forces for all members in each truss shown using the method of joints. Remember to list each member force as either tention or compression.
The first thing you must do is draw a free body diagram of the whole structure, replacing the boundary conditions with reaction forces. The support at A is a roller, and hence it exerts only a NORMAL force on the frame, $H_A$. The support at G, however, exerts both a horizontal and vertical force, $H_G$ and $V_G$ respectively.

Now, you must get values for these reaction forces before you can analyse each joint. Do this by applying the equilibrium conditions to the whole structure. I would suggest you start by taking moments about point G, as the lines of action of 2 unknowns run through G, leaving only 1 unknown in your equation. Then apply the conditions that $\sum F_x = 0$ and $\sum F_y = 0$ to acquire the other unknowns.

After that, pick any node G or A, and analyse it. At these poinst you will have less than 2 unknowns, which is good because you only have 2 equations to work with using the method of joints. When you solve for the unknown at A and G, you can move onto another node which has 2 or less unknowns. Continue in this fashion until you have covered every member of the structure. You will have to use trigonometry to find the various angles of the members which are not horizontal or vertical.

Remember, when you draw your free body diagrams, just make a random guess as to what the direction of the force is (tension or compression). If you guess that the force is compressive, and your working gives you a negative answer, then this indicates that your guess was wrong, and that the force was actually tensile, and vice versa. If your working gives you a positive answer, your guess was correct.