For a truss with a pin joint, what condition must be satisfied for equilibrium?

For a truss with a pin joint, what condition must be satisfied for equilibrium?

Step 1: Understand that a truss is a structure made of connected elements, and a pin joint is where two elements meet and can rotate.
Step 2: Recognize that for the pin joint to be stable and not move, it must be in a state of equilibrium.
Step 3: Identify the two directions we need to consider: the x-direction (horizontal) and the y-direction (vertical).
Step 4: For the pin joint to be in equilibrium, the total forces acting in the x-direction must balance out, meaning they should add up to zero.
Step 5: Similarly, the total forces acting in the y-direction must also balance out, adding up to zero.
Step 6: Therefore, the conditions for equilibrium at the pin joint are: Sum of forces in the x-direction = 0 and Sum of forces in the y-direction = 0.

Equilibrium of Forces – For a structure to be in equilibrium, the vector sum of all forces acting on it must be zero.
Truss Analysis – Understanding how forces are distributed in a truss system, particularly at pin joints.