## Beam Bending Moment and Deflection Analysis### Problem Statement:Based on the given equations for the bending moment \( M(x) \) applied to the shown beam, determine the vertical deflection of the beam at distances of 1 [m], 2 [m], 2.5 [m] and 3 [m] from the left support. Assume an elastic modulus of \( E = 200 \) GPa and the cross-sectional moment of inertia is \( I = 4.5 \times 10^{-6} \) m\(^4\).### Beam Diagram:The beam setup is described as follows:- Total length of beam: 4 m- Left section: 2 m (supported by a hinge support)- Middle section: 2 m with a uniform distributed load of 800 N/m (supported by a roller support at the end)### Shear Force Diagram (SFD):The graph labeled "Shear Diagram" illustrates the shear force distribution along the length of the beam. Key observations from the diagram:- The shear force starts from 400 N at the left support.- It linearly decreases due to the distributed load and drops to -1200 N at the roller support.### Bending Moment Diagram (BMD):The graph labeled "Moment Diagram" illustrates the moment distribution along the length of the beam:- Starts from 0 at the left hinge.- Peaks at 2.5 m with a value of 990 Nm.- Returns to 0 at the right roller support.### Bending Moment Equation:The bending moment is piecewise-linear, represented by the function \( M(x) \) and defined as follows:\[ M(x) = \begin{cases} 400x & \text{if } 0 \leq x < 2 \\-400x^2 + 2000x - 1600 & \text{if } 2 \leq x \leq 4 \end{cases} \]### Analysis Procedure:Using the given beam properties and boundary conditions, the deflection at specified points (1m, 2m, 2.5m, and 3m) along the beam length can be calculated through deflection formulas and integration methods specific to Euler-Bernoulli beam theory.### Additional Notes:The diagrams provided are essential tools in analyzing how loads affect beam structures in engineering. The Shear Force

Name: ## Beam Bending Moment and Deflection Analysis### Problem Statement:B
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Description: ## Beam Bending Moment and Deflection Analysis### Problem Statement:Based on the given equations for the bending moment \( M(x) \) applied to the shown beam, determine the vertical deflection of the beam at distances of 1 [m], 2 [m], 2.5 [m] and 3 [

To find: The vertical deflection of beam at distance of 1 m, 2 m, 2.5 m, 3 m. Given: The modulus of…

Engineering

Mechanical Engineering

Based on the given equations for the bending moment M(x) applied to the shown beam, determine the vertical deflection of the beam at distances of 1 [m], 2 [m], 2.5 [m] and 3 [m] from the left support. Assume an elastic modulus of E= 200 GPa and the cross-sectional moment of inertia is 1 = 4.5 x 10-6 m². Shear Force [N] Moment [Nm] 400 200 D -200 400 -600 -800 -1000 -1200 1000 800 0 600 400 200 0.5 0.5 2 m 1.5 1.5 Shear Diagram 2 Distance [m] Moment Diagram (2.5,900) 2 Distance (m) 800 N/m 2.5 2 m 2.6 3.5 3.5

Based on the given equations for the bending moment M(x) applied to the shown beam, determine the vertical deflection of the beam at distances of 1 [m], 2 [m], 2.5 [m] and 3 [m] from the left support. Assume an elastic modulus of E= 200 GPa and the cross-sectional moment of inertia is 1 = 4.5 x 10-6 m². Shear Force [N] Moment [Nm] 400 200 D -200 400 -600 -800 -1000 -1200 1000 800 0 600 400 200 0.5 0.5 2 m 1.5 1.5 Shear Diagram 2 Distance [m] Moment Diagram (2.5,900) 2 Distance (m) 800 N/m 2.5 2 m 2.6 3.5 3.5

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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