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P8.2. For the truss in Figure P8.1, compute the vertical displacement of joint A and the horizontal displacement of joint C. Assume all member properties are the same except the areas of AE, ED, BD, and BC are 8 in.².

P8.2. For the truss in Figure P8.1, compute the vertical displacement of joint A and the horizontal displacement of joint C. Assume all member properties are the same except the areas of AE, ED, BD, and BC are 8 in.².

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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### Engineering Mechanics: Structural Analysis #### Introduction to Maxwell-Betti Law of Reciprocal Deflections In Section 8.9, we introduce the Maxwell-Betti law of reciprocal deflections. This law will be useful when we set up the terms for the symmetric matrices required to solve indeterminate structures using the flexibility method in Chapter 9. ### Problems #### *P8.1.* For the truss in Figure P8.1, compute the horizontal and vertical components of displacement of joint B produced by the 100-kip load. The area of all bars \( A = 4 \, \text{in}^2 \), and \( E = 24,000 \, \text{kips/in}^2 \). #### Explanation of Figure P8.1 The figure illustrates a truss with the following characteristics: - Joint A is located at the bottom left. - Joint E is located directly to the right of Joint A, 20 feet apart horizontally. - Joint D is directly above Joint E, 15 feet vertically. - Joint C is directly above Joint B, similarly 15 feet vertically. - Joint B is 20 feet horizontally to the right of Joint C. A 100-kip load is applied horizontally to the right at Joint C. #### *P8.2.* For the truss in Figure P8.1, compute the vertical displacement of joint A and the horizontal displacement of joint C. Assume all member properties are the same except the areas of AE, ED, BD, and BC are \( 8 \, \text{in}^2 \). ### Explanation of Graphs/Diagrams In Figure P8.1, the truss diagram is provided. It showcases the geometric layout and loading conditions of the truss: - The lengths and heights of individual members are specified (20 feet horizontal, 15 feet vertical). - The critical joints and members are labeled (A, B, C, D, E). - The applied load of 100 kips is shown pointing horizontally at joint C. This figure is essential for solving the given problem by applying principles of structural analysis to determine the displacements at specific joints.
Transcribed Image Text:### Engineering Mechanics: Structural Analysis #### Introduction to Maxwell-Betti Law of Reciprocal Deflections In Section 8.9, we introduce the Maxwell-Betti law of reciprocal deflections. This law will be useful when we set up the terms for the symmetric matrices required to solve indeterminate structures using the flexibility method in Chapter 9. ### Problems #### *P8.1.* For the truss in Figure P8.1, compute the horizontal and vertical components of displacement of joint B produced by the 100-kip load. The area of all bars \( A = 4 \, \text{in}^2 \), and \( E = 24,000 \, \text{kips/in}^2 \). #### Explanation of Figure P8.1 The figure illustrates a truss with the following characteristics: - Joint A is located at the bottom left. - Joint E is located directly to the right of Joint A, 20 feet apart horizontally. - Joint D is directly above Joint E, 15 feet vertically. - Joint C is directly above Joint B, similarly 15 feet vertically. - Joint B is 20 feet horizontally to the right of Joint C. A 100-kip load is applied horizontally to the right at Joint C. #### *P8.2.* For the truss in Figure P8.1, compute the vertical displacement of joint A and the horizontal displacement of joint C. Assume all member properties are the same except the areas of AE, ED, BD, and BC are \( 8 \, \text{in}^2 \). ### Explanation of Graphs/Diagrams In Figure P8.1, the truss diagram is provided. It showcases the geometric layout and loading conditions of the truss: - The lengths and heights of individual members are specified (20 feet horizontal, 15 feet vertical). - The critical joints and members are labeled (A, B, C, D, E). - The applied load of 100 kips is shown pointing horizontally at joint C. This figure is essential for solving the given problem by applying principles of structural analysis to determine the displacements at specific joints.
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