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Determine the slope and displacement at point B. Assume the support at A is a pin and C is a roller. Account for the additional strain energy due to shear if the cross section is

Determine the slope and displacement at point B. Assume the support at A is a pin and C is a roller. Account for the additional strain energy due to shear if the cross section is

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 slope and displacement at point B. Assume the support at A is a pin and C is a roller. Account for the additional strain energy due to shear if the cross section is a wide flange. Take E=200Gpa, I=150(10^6)mm^4, G=75Gpa, and assume AC has a cross section web area of A=2.50(10^3)mm^2. Use the method of virtual work

### Engineering Mechanics: Beam Problems and Analysis #### Problem 8-34 Determine the slope and displacement at point \( B \). Assume the support at \( A \) is a pin and \( C \) is a roller. Given: - Modulus of Elasticity, \( E = 200 \, \text{GPa} \) - Moment of Inertia, \( I = 150 \times 10^6 \, \text{mm}^4 \) Use the method of virtual work. #### Problem 8-35 Solve Problem 8-34 using Castigliano’s theorem. #### Problem 8-36 Determine the slope and displacement at point \( B \). Assume the support at \( A \) is a pin and \( C \) is a roller. Consider additional strain energy due to shear if the cross-section is a wide flange. Given: - Modulus of Elasticity, \( E = 200 \, \text{GPa} \) - Moment of Inertia, \( I = 150 \times 10^6 \, \text{mm}^4 \) - Shear Modulus, \( G = 75 \, \text{GPa} \) - Cross-sectional web area, \( A = 2.5 \times 10^3 \, \text{mm}^2 \) Use the method of virtual work. --- #### Problem 8-39 Use the method of virtual work to find the displacement of point \( C \) of the beam. Given: - Modulus of Elasticity, \( E = 29 \times 10^6 \, \text{ksi} \) - Moment of Inertia, \( I = 245 \, \text{in}^4 \) #### Problem 8-40 Use the method of virtual work to find the slope at point \( A \) of the beam made of: - Moment of Inertia, \( I = 245 \, \text{in}^4 \) #### Problem 8-41 Solve Problem 8-40 using Castigliano’s theorem. --- ### Diagram Explanation In both diagrams: 1. **First Diagram:** - A simply supported beam \( AC \) is shown with a uniformly distributed load of \( 16 \, \text{kN/m} \). - Supports are located at \( A \) (pin)
Transcribed Image Text:### Engineering Mechanics: Beam Problems and Analysis #### Problem 8-34 Determine the slope and displacement at point \( B \). Assume the support at \( A \) is a pin and \( C \) is a roller. Given: - Modulus of Elasticity, \( E = 200 \, \text{GPa} \) - Moment of Inertia, \( I = 150 \times 10^6 \, \text{mm}^4 \) Use the method of virtual work. #### Problem 8-35 Solve Problem 8-34 using Castigliano’s theorem. #### Problem 8-36 Determine the slope and displacement at point \( B \). Assume the support at \( A \) is a pin and \( C \) is a roller. Consider additional strain energy due to shear if the cross-section is a wide flange. Given: - Modulus of Elasticity, \( E = 200 \, \text{GPa} \) - Moment of Inertia, \( I = 150 \times 10^6 \, \text{mm}^4 \) - Shear Modulus, \( G = 75 \, \text{GPa} \) - Cross-sectional web area, \( A = 2.5 \times 10^3 \, \text{mm}^2 \) Use the method of virtual work. --- #### Problem 8-39 Use the method of virtual work to find the displacement of point \( C \) of the beam. Given: - Modulus of Elasticity, \( E = 29 \times 10^6 \, \text{ksi} \) - Moment of Inertia, \( I = 245 \, \text{in}^4 \) #### Problem 8-40 Use the method of virtual work to find the slope at point \( A \) of the beam made of: - Moment of Inertia, \( I = 245 \, \text{in}^4 \) #### Problem 8-41 Solve Problem 8-40 using Castigliano’s theorem. --- ### Diagram Explanation In both diagrams: 1. **First Diagram:** - A simply supported beam \( AC \) is shown with a uniformly distributed load of \( 16 \, \text{kN/m} \). - Supports are located at \( A \) (pin)
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