Determining the Force in Each Member of the Loaded Truss

What is the force in each member of the loaded truss?

Can symmetry help in determining the forces in the truss members?

Answer:

The force in each member of the loaded truss is 10 kN in tension.

When analyzing the loaded truss, it is essential to consider the symmetry of the structure and the loading to determine the forces in each member accurately. Symmetry plays a crucial role in simplifying the analysis process and reducing the number of calculations required.

In this case, the loaded truss has a symmetrical structure, and the loading is also symmetric. The two forces of 20 kN acting at the midpoint of the top chord create equal and opposite reactions at the bottom chord, resulting in vertical reactions of 20 kN at each support. Due to symmetry, the reactions at both supports can be considered identical.

Since there is no horizontal force or movement in the truss, the forces in each member are solely due to vertical loading. The truss has diagonal members inclined at 60 degrees with respect to the horizontal. By resolving the vertical forces at each joint, we can determine the force in each member.

Considering the left side of the truss, the vertical force equilibrium at the two bottom joints gives a force of 10 kN in both the inclined members and the bottom horizontal member. As the truss is symmetric, the force in the corresponding members of the right side will also be 10 kN. Therefore, the force in each member of the loaded truss is 10 kN in tension.