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H.W2 Determine the maximum deflection of the simply supported beam. E = 200 GPa and I = 39.9(10) m². 40 kN-m 10 kN-m 6 m H.W2

H.W2 Determine the maximum deflection of the simply supported beam. E = 200 GPa and I = 39.9(10) m². 40 kN-m 10 kN-m 6 m H.W2

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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Please explain how to find the value of x when precipitation has a maximum value Use the integration method
**Topic: Beam Deflection Analysis** **Example Problem H.W2:** Determine the maximum deflection of the simply supported beam. Given the modulus of elasticity \( E = 200 \) GPa and the moment of inertia \( I = 39.9 \times 10^{-6} \) m\(^4\). ### Diagram Description A simply supported beam is shown, with the following features: - Span length: 6 meters. - Left end (A) is supported by a pinned support, allowing rotation but no vertical or horizontal movement. - Right end (B) is supported by a roller support, allowing vertical movement and rotation but no horizontal movement. - A counter-clockwise moment of 40 kN·m is applied at the left support (A). - A clockwise moment of 10 kN·m is applied at the right support (B). ### Given Data: - Modulus of Elasticity, \( E = 200 \) GPa - Moment of Inertia, \( I = 39.9 \times 10^{-6} \) m\(^4\) ### Objective: To determine the maximum deflection of the beam under the given loading conditions. ### Method: Use the principles of structural analysis and beam theory to calculate deflections and bending moments. The solutions are often derived using integration methods, area-moment methods, or by using standard formulas for deflection of beams under known loading conditions. This problem involves calculating maximum deflection caused by moments at the supports of a simply supported beam, considering the beam’s flexural rigidity (\(EI\)) and the lengths involved. Ensure to refer to structural engineering texts and beam deflection tables for appropriate formulas and methods of solving such problems. Further steps would involve breaking down the beam's loading conditions and applying boundary conditions specific to simply supported beams with moment applications. **[Educational Link for Further Reading: Simply Supported Beam Deflection](#)**
Transcribed Image Text:**Topic: Beam Deflection Analysis** **Example Problem H.W2:** Determine the maximum deflection of the simply supported beam. Given the modulus of elasticity \( E = 200 \) GPa and the moment of inertia \( I = 39.9 \times 10^{-6} \) m\(^4\). ### Diagram Description A simply supported beam is shown, with the following features: - Span length: 6 meters. - Left end (A) is supported by a pinned support, allowing rotation but no vertical or horizontal movement. - Right end (B) is supported by a roller support, allowing vertical movement and rotation but no horizontal movement. - A counter-clockwise moment of 40 kN·m is applied at the left support (A). - A clockwise moment of 10 kN·m is applied at the right support (B). ### Given Data: - Modulus of Elasticity, \( E = 200 \) GPa - Moment of Inertia, \( I = 39.9 \times 10^{-6} \) m\(^4\) ### Objective: To determine the maximum deflection of the beam under the given loading conditions. ### Method: Use the principles of structural analysis and beam theory to calculate deflections and bending moments. The solutions are often derived using integration methods, area-moment methods, or by using standard formulas for deflection of beams under known loading conditions. This problem involves calculating maximum deflection caused by moments at the supports of a simply supported beam, considering the beam’s flexural rigidity (\(EI\)) and the lengths involved. Ensure to refer to structural engineering texts and beam deflection tables for appropriate formulas and methods of solving such problems. Further steps would involve breaking down the beam's loading conditions and applying boundary conditions specific to simply supported beams with moment applications. **[Educational Link for Further Reading: Simply Supported Beam Deflection](#)**
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