Cracking Truss Forces: Mastering Method of Joints

In this article (and video above), we calculate the internal forces of trusses using the method of joints. This is a classic example that you might encounter in the static section of the FE Exam. This problem was created and solved by Mechatronical engineer, Chanté van der Spuy.

Question:

Consider the truss shown below. It is subjected to a horizontal load of 5 kN at joint D and a vertical load of 5 kN at joint C. The horizontal and vertical reaction forces at joint A are given as 2 kN and 4 kN, respectively. Determine the force in member BD.

Discussion and assumptions:

What is a truss?

A truss is a structural element that consists of long straight members connected at their ends. The members are connected by frictionless joints, typically forming triangular structures.

Modelling assumptions

The joints between members offer no resistance to moment and are frictionless
Truss members contain only axial forces. Each member is either in tension or compression.

Explanation:

1. Determine the reactions at support A

Draw the free-body diagram for joint A:

Sum forces in the x- and y-direction:

Solve for F_AC and F_AB:

Draw the free-body diagram for joint A

Sum the moments about A to find E_y

2. Determine the reactions at support E

Draw the free-body diagram for joint E:

Sum forces in the x- and y-direction:

Solve for F_DE and F_BE:

3. Determine the reactions at joint D

Draw the free-body diagram for joint D:

Sum forces in the x- and y-direction:

Solve for F_DE and F_BE:

Answer:

The correct answer is D.

Final remarks:

Pay attention to the sign conventions for forces (tension vs. compression).
Use free-body diagrams to visualize the forces acting on each joint.
Apply the equations of equilibrium (∑F_x=0, ∑F_y=0, ∑M=0) carefully.
Practice with different truss configurations and loading conditions.

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I’ll see you next week… on Pass the PE Exam

Anthony Fasano, P.E.
Engineering Management Institute
Author of Engineer Your Own Success