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Determine the force in member AD for the truss shown using the method of joints. D B 120 kN -4 m 60 kN 2m

Determine the force in member AD for the truss shown using the method of joints. D B 120 kN -4 m 60 kN 2m

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Determine the force in member AD for the truss shown using the method of joints.

**Determine the Force in Member AD for the Truss Using the Method of Joints** In this problem, we are required to determine the force in member AD of the truss shown using the method of joints. #### Illustration of the Truss: - The truss is a simple triangular configuration supported at points A and C. - The span between points A and B is 4 meters, and the span between points B and C is also 4 meters, making the total length 8 meters. - Point D is located vertically below point B. - The truss is subjected to two external loads at joint D: a vertical load of 60 kN acting upwards and a vertical load of 120 kN acting downwards. #### Forces to be Determined: The forces in the members of the truss, specifically in member AD, need to be found out. ### Multiple Choice Answers: a. 168.75 kN tension b. 93.75 kN compression c. 77.31 kN tension d. 77.31 kN compression ### Method of Joints Explanation: The method of joints involves looking at each joint of the truss separately to ensure that the sum of forces in both the x and y directions is zero. 1. **Identify the external reactions at points A and C.** 2. **Use equilibrium equations to solve for unknown forces.** 3. **Use trigonometric relationships if necessary to resolve forces in triangular configurations.** #### Step-by-Step Calculation (Outline): 1. **Analyzing Joint A:** - Considering summation of moments around point C to find reaction at A. - Sum of vertical forces to find reaction at C. 2. **Analyzing Joint D:** - Using vertical and horizontal equilibrium (
Transcribed Image Text:**Determine the Force in Member AD for the Truss Using the Method of Joints** In this problem, we are required to determine the force in member AD of the truss shown using the method of joints. #### Illustration of the Truss: - The truss is a simple triangular configuration supported at points A and C. - The span between points A and B is 4 meters, and the span between points B and C is also 4 meters, making the total length 8 meters. - Point D is located vertically below point B. - The truss is subjected to two external loads at joint D: a vertical load of 60 kN acting upwards and a vertical load of 120 kN acting downwards. #### Forces to be Determined: The forces in the members of the truss, specifically in member AD, need to be found out. ### Multiple Choice Answers: a. 168.75 kN tension b. 93.75 kN compression c. 77.31 kN tension d. 77.31 kN compression ### Method of Joints Explanation: The method of joints involves looking at each joint of the truss separately to ensure that the sum of forces in both the x and y directions is zero. 1. **Identify the external reactions at points A and C.** 2. **Use equilibrium equations to solve for unknown forces.** 3. **Use trigonometric relationships if necessary to resolve forces in triangular configurations.** #### Step-by-Step Calculation (Outline): 1. **Analyzing Joint A:** - Considering summation of moments around point C to find reaction at A. - Sum of vertical forces to find reaction at C. 2. **Analyzing Joint D:** - Using vertical and horizontal equilibrium (
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