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El is constant for the beam shown in Figure 4. • Compute the rotation of the beam at B. • Compute the vertical deflection at B. 8 ft. 13 k/ft. B Figure 4 12 ft. 19k с + 12 ft.

El is constant for the beam shown in Figure 4. • Compute the rotation of the beam at B. • Compute the vertical deflection at B. 8 ft. 13 k/ft. B Figure 4 12 ft. 19k с + 12 ft.

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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Use the method of virtual work, for example, virtual integration, and principle of superposition , handwritten work only don’t forget FBDs and ensure neatness pls.
### Beam Deflection and Rotation **Objective:** 1. Compute the rotation of the beam at B. 2. Compute the vertical deflection at B. **Given:** - EI is constant for the beam shown in **Figure 4**. **Figure 4:** Description of the Beam The figure illustrates a beam supported at three points: - Point A: A simple support on the far left. - Point B: A support with a uniformly distributed load of 3 k/ft over an 8-foot length, starting from A to B. - Point C: A point load of 9 k applied 12 feet from B. - Point D: A simple support 12 feet from C. **Beam Details:** - Distance AB: 8 ft - Distance BC: 12 ft - Distance CD: 12 ft **Loading:** - Uniform Load: 3 k/ft from A to B - Point Load: 9 k at point C ### Tasks: 1. **To Compute the Rotation at Point B:** - Using the principles of beam deflection and rotation, we can determine the rotation at point B by integrating the moment equation derived from the loading conditions. 2. **To Compute the Vertical Deflection at Point B:** - The vertical deflection at B can be found by double integration of the moment-curvature relation, applying boundary conditions for the supports at A, B, C, and D. Use the given boundary conditions and the provided load diagram to solve for the beam's response at the specified points.
Transcribed Image Text:### Beam Deflection and Rotation **Objective:** 1. Compute the rotation of the beam at B. 2. Compute the vertical deflection at B. **Given:** - EI is constant for the beam shown in **Figure 4**. **Figure 4:** Description of the Beam The figure illustrates a beam supported at three points: - Point A: A simple support on the far left. - Point B: A support with a uniformly distributed load of 3 k/ft over an 8-foot length, starting from A to B. - Point C: A point load of 9 k applied 12 feet from B. - Point D: A simple support 12 feet from C. **Beam Details:** - Distance AB: 8 ft - Distance BC: 12 ft - Distance CD: 12 ft **Loading:** - Uniform Load: 3 k/ft from A to B - Point Load: 9 k at point C ### Tasks: 1. **To Compute the Rotation at Point B:** - Using the principles of beam deflection and rotation, we can determine the rotation at point B by integrating the moment equation derived from the loading conditions. 2. **To Compute the Vertical Deflection at Point B:** - The vertical deflection at B can be found by double integration of the moment-curvature relation, applying boundary conditions for the supports at A, B, C, and D. Use the given boundary conditions and the provided load diagram to solve for the beam's response at the specified points.
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