Final answer:
To determine the forces in members a, b, and c using the method of sections, one analyzes the equilibrium of one of the sections after cutting the truss through these members and then applies the sum of forces and moments to calculate whether each member is in tension or compression.
Step-by-step explanation:
The method of sections is a process used in statics, a branch of engineering mechanics, to determine the forces in members of a truss. When applying this method, we look at how a truss is held in equilibria under various forces, which means the sum of forces and moments equals zero. Each truss member can be in tension or compression. To determine the forces in members a, b, and c, one would cut the truss through these members and consider the equilibrium of one of the two resulting sections. In this scenario, we assume that the members are originally at a length L0 and when a force is applied, they either extend or contract by a length ΔL. Tension would cause elongation (ΔL is positive), while compression leads to shortening (ΔL is negative). The forces in the members are then calculated using equilibrium equations (ΣFx = 0, ΣFy = 0, ΣM = 0). Each force's nature, tension or compression, is inferred from the sign of the calculated force; a positive force suggests tension, and a negative force indicates compression. A comprehensive understanding of the concepts such as normal force, Hooke's law of elastic deformation, and static equilibrium is essential for solving such problems, along with the ability to use trigonometry to resolve forces into components.