Method of Substitute Members in Trusses

The method of substitute members is commonly used in the analysis of complex trusses. Complex trusses are trusses that have more than three members meeting at any joint. This method is a simplification technique that allows engineers to replace a complex truss with a simpler truss for analysis purposes.

Explanation:

The method of substitute members involves replacing a group of members in a complex truss with a single member that has the same effect on the truss as the original group of members. This simplifies the truss and makes the analysis easier.

Procedure:

1. Identify the complex truss: Determine if the truss in question is complex, i.e., if it has more than three members meeting at any joint.

2. Select the group of members: Identify the group of members that can be replaced. This group of members should be in equilibrium and must not be part of any external forces or moments acting on the truss.

3. Replace the group of members: Replace the group of members with a single substitute member. The substitute member should have the same length and orientation as the original group of members. The point of intersection of the original members should be the same as the point of intersection of the substitute member.

4. Analyze the simplified truss: After replacing the group of members, the complex truss is now simplified into a simpler truss. This simplification makes it easier to analyze the forces and reactions in the truss.

5. Calculate the forces in the substitute member: Determine the forces acting on the substitute member using the principles of equilibrium. These forces can be calculated using methods such as the method of joints or the method of sections.

6. Determine the forces in the original members: Once the forces in the substitute member are known, the forces in the original members can be determined by considering the equilibrium of the substitute member and applying the appropriate equations.

Advantages:

- Simplifies the analysis of complex trusses by reducing them to simpler trusses.
- Reduces the number of unknowns in the truss, making it easier to solve for the forces in the members.
- Allows for a more efficient analysis of trusses with a large number of members and joints.

Conclusion:

The method of substitute members is used for the analysis of complex trusses. By replacing a group of members with a single substitute member, the truss is simplified, making it easier to determine the forces and reactions in the truss. This method is a valuable tool in structural analysis and design, particularly for trusses with multiple members meeting at a joint.