Worked Example: Truss Method of Joints

This worked example demonstrates the use of 2D static equilibrium to determine the axial force in a truss member using the Method of Joints.

1. Problem Statement

Consider a simple triangular truss supported by a pin at joint A and a roller at joint B, with a top joint C. The base AB is $3\text{ m}$ wide, and height is $4\text{ m}$ . A downward load of $10\text{ kN}$ is applied at C. Assume symmetry implies the vertical reactions at A and B are $5\text{ kN}$ each acting upwards. Find the force in member AC.

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2. Given Data

Reaction Force at A (R_A = F_y)

Height of Member AC (h)

Length of Member AC (L)

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3. Formula and Calculation

From the sum of vertical forces at Joint A, the vertical component of the force $F_{AC}$ must resist the reaction $R_A$ . Thus, $F_{AC,y} = F_y$ (pushing down on the joint). Using similar triangles (or trigonometric relations), the axial force is calculated as:

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Note: Because the force pushes into Joint A, member AC is in Compression.

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