Truss Analysis

Why This Matters

Trusses are frameworks composed of straight members joined at their endpoints. They are highly efficient structures used globally in roofs, bridges, and cranes. Because they form stable triangular units, trusses carry heavy loads across long spans using significantly less material than solid beams.

What It Means

In an idealized truss analysis, we assume that all members are perfectly straight, all joints are frictionless pins, and all loads are applied directly at the joints. Because of these assumptions, the members cannot bend; they can only stretch or compress. Therefore, every member in an idealized truss acts as a two-force member carrying only pure axial tension or pure axial compression.

Theory and Methods

To analyze a truss, we use the principles of 2D static equilibrium. The entire truss must be in equilibrium, and every individual joint within it must also be in equilibrium.

The Method of Joints

This method involves isolating a single joint and drawing a Free Body Diagram (FBD) of all the forces acting on it. Because the joint is a single point, all forces are concurrent, meaning there is no bending moment. We simply apply:

$\sum F_x = 0$ $\sum F_y = 0$

Strategy: Start at a joint with a known external force and no more than two unknown member forces. Solve for those two unknowns, and then proceed to the next joint.

Worked Example

A detailed interactive calculation example for truss analysis using the method of joints can be found at Worked Example: Truss Method of Joints.

Engineering Meaning

• Tension vs Compression: Members in tension pull away from the joints and tend to snap. Members in compression push into the joints and tend to buckle. Engineers must explicitly design compression members to be thick enough to resist buckling.
• Zero-Force Members: Sometimes the analysis shows that a member carries zero force. These are still necessary! They provide stability, resist secondary unexpected loads, and prevent adjacent long compression members from buckling.

Common Mistakes

• Assuming members can carry moments: Idealized truss members carry ONLY axial force. If a load is applied to the middle of a member instead of at a joint, it becomes a beam-column and the basic truss analysis rules are violated.
• Incorrectly determining tension or compression: Drawing the unknown force vector pointing away from the joint assumes tension. If the math results in a negative number, the assumption was wrong, and the member is actually in compression.