Analysis of a Truss

The analysis of a truss involves determining the reaction at the supports and the stresses induced in the members due to applied loads. Assumptions made for truss analysis are

1. All the members comprising the truss are rigid and lie in one plane if it is a plane truss.
2. The members are slender.
3. Each member is of uniform cross-section.
4. The members are subjected to pure axial forces and cannot develop moments at the ends.
5. The external loads and reactions act at the joints only.
6. The self-weight of the members is neglected.
7. The forces are transmitted from one member to another through frictionless pins fitting perfectly in the members.

Method of Joints

One way to determine the force in each member of a truss is to use the method of joints.

This method is based on the fact that if the entire truss is in equilibrium, then every joint is in equilibrium.

Therefore, if the free body diagram of each joint is drawn, the force equilibrium equations ΣFx = 0 and ΣFy = 0, can be used to determine the force on each joint. The steps involved in analyzing a truss using the method of joints are

• Draw the free body diagram of entire truss and find the support reaction using three equilibrium equations that are ΣFx = 0, ΣFy = 0 and ΣM = 0.
• Draw the free body diagram of a joint having atleast one known force and at most two unknown forces.
• Assume a certain direction of unknown force acting on the joint.
• Orient the x and y axes such that the forces on the free body diagram can be easily resolved into their x and y components and then solve for the two unknown forces. If the magnitude of a particular force comes out to be positive, then the assumption of force direction is correct, and if the magnitude of the force comes out to be negative, then the actual direction of the force is reversed.
• Using the calculated results, continue to analyze each of the other joints.

Note:

If the member pulls the joint to which it is connected, then it is subjected to tensile force whereas if the member pushes the joint to which it is connected, then it is subjected to compression force. A member under tension is called a tie, and a member under compression is called a strut.