Trusses are commonly used to span distances between two walls. There are many truss designs, but one of the most common a Howe truss due to its simplicity and efficiency. Trusses usually need to carry both roof loads and ceiling loads. Both types of loads are modeled can be modeled as point loads at the truss joints.

What is known:

The width of the truss is 10 ft.

The roof incline angle, θ, is 40°.

There are loads at each joint as shown in the diagram at the left

Loads are shown in the diagram.

Problem Diagram
Howe Truss

Questions

Which member will have the largest tension force and the largest compression force? What is the magnitude of those member forces?

Approach

Use the method of joints to analyze each pin joint using the basic statics equations,

ΣF_{x} = 0 ΣF_{y} = 0

Each joint must be in equilibrium. Only two unknown member forces can be determined per joint. Each member is a two-force member.