10. Trusses and Structure Analysis

Simple Trusses

A truss is an assembly of beams or other elements that creates a rigid structure.

Assumptions for Design

  1. All the loadings are applied at the joints
  2. The members are joined together by smooth pins. ( no friction force between the pin and the beam)


  • If the force tends to elongate the member, it is a tensile force.
  • If the force tends to compress the member, it is a compressive force.

Method of Joints for Trusses

This method is based on the fact that if the entire truss is in equilibrium, then each of its joints is also in equilibrium.

Note: Sum of forces about x-axis and y-axis is Zero.

Note: The sense of the unknown force can be assumed via inspection otherwise it is safe to assume it to be tensile force.

Tip: Pick the joint where there are 2 unknowns and 1 known.

Zero force member

If two non-linear members form a truss joint and no external load or support reaction is applied to the joint, the two members must be Zero-force members.

Zero Force members will have no force in them.

Note: “If 3 members form a truss joint for which two of the members are collinear, the third member is a zero-force member provided no external force or support reaction is applied to the joint.”

Method of Sections

it is based on the principle that if a truss is in equilibrium then any segment of the truss is also in equilibrium.

Note: Trusses have only 2 force member

Frame and Machines

Frames and machines have at least 1 multi-force member (members that are subject to more than two forces)

Steps for Analysis of a frame or machine

  1. Identify any 2-force member.
  2. Forces on contacting surfaces are equal and opposite.
  3. For a joint with more than two force member/external force draw FBD
The method of section has the basic advantage that the force in almost any desired member may be found directly from an analysis of a section that has cut the member. In choosing a section of the truss, in general, not more than three members whose forces are unknown may be cut, since there are only three available equilibrium equations which are independent. The method of joints utilizes the force equations of equilibrium for each joint. Analysis normally begins at a point where at least one force is known and not more than two forces are unknown for plane trusses (or not more than three forces are unknown for space trusses)

For better understanding of the topic please visit my previous lecture.