The question asks us to identify the method among the given options that is NOT used for analyzing trusses.

Truss Analysis Methods

Trusses are structural elements composed of slender members connected at their ends by frictionless pins to form a stable framework. The primary goal of truss analysis is to determine the forces in each member of the truss.

Commonly used methods for analyzing trusses include:

• Method of Joints: This method analyzes the equilibrium of each joint in the truss. By considering the forces acting at a joint, which must sum to zero in both horizontal and vertical directions, the unknown forces in the members connected to that joint can be determined.
• Method of Sections: This method involves cutting the truss into two sections by passing an imaginary cutting plane through the members whose forces are to be determined. The equilibrium of either section is then considered to find the unknown forces. This is particularly useful when forces in only a few specific members are required.
• Graphical Method: This involves drawing the force polygons for each joint to scale, or using graphical techniques like the Maxwell-Bowmore diagram. These methods allow for the determination of member forces through graphical representation rather than algebraic calculations.

Macaulay's Method Explained

Macaulay's method, also known as the method of singularity functions, is a technique primarily used in structural analysis to determine the slope and deflection of beams subjected to various types of loads (concentrated loads, uniformly distributed loads, bending moments). It uses singularity functions to write a single equation for the bending moment or shear force along the entire length of the beam, making integration simpler and avoiding the need for multiple equations for different segments of the beam.

This method is specifically designed for the analysis of beams, which behave differently from trusses (beams resist bending moments and shear forces internally, while truss members are assumed to carry only axial forces).

Identifying the Non-Truss Method

Comparing the methods, we see that:

• Method of Sections is used for truss analysis.
• Method of Joints is used for truss analysis.
• Graphical Method is used for truss analysis.
• Macaulay's Method is used for beam analysis (specifically for slope and deflection), not for determining forces in truss members.

Therefore, Macaulay's Method is the one that is NOT used for analyzing trusses.