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.

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.

**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 hope you found this article helpful. In upcoming articles, I will solve some more PE exam practice problems and answer other questions from our subscribers. Pass the PE Exam videos will publish weekly, so be sure to click the subscribe button so you don’t miss something that could make a substantial difference in your exam result.

Lastly, I encourage you to ask questions in the comments of this video, or on this page and I’ll read and respond to them in future videos. So, if there’s a specific topic you want me to cover or answer, we have you covered.

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

Anthony Fasano, P.E.

Engineering Management Institute

Author of Engineer Your Own Success

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