### Educational Resource on Beam Deflection#### IntroductionThis exercise involves determining the slope and deflection of cantilever beams using the area moment method. The tasks include analyzing both point loads and distributed loads separately, and then superimposing their effects.#### Problems1. **Problem F12-10:** - **Objective:** Determine the slope and deflection at point A of the cantilevered beam. - **Given:** Modulus of Elasticity \( E = 29 \times 10^6 \, \text{ksi} \), Moment of Inertia \( I = 245 \, \text{in}^4 \). - **Diagram Description:** - The beam is 6 ft long overall, with a 2 kip/ft uniform load over the left 3 ft and a 3 kip point load at the right end. - The diagram shows a beam labeled from B to A, with loads applied as specified.2. **Problem 12-6:** - **Objective:** Determine the elastic curve for a cantilevered beam subjected to a couple moment \( M_0 \). Calculate the maximum slope and deflection. - **Diagram Description:** - A beam is shown fixed at point A with a couple moment \( M_0 \) applied at the free end, point B. - The beam length is labeled as \( L \).3. **Problem 12-53:** - **Objective:** Determine the deflection of end B of the cantilever beam. - **Diagram Description:** - The beam is labeled from A to B, with two point loads \( P \) acting downward. The distances are equal (\( \frac{L}{2} \)) from the fixed end at A to the positions of the loads and from the loads to end B. - The beam is symmetrical with respect to the load placement.#### Analysis ApproachFor these problems, you would:- Use the area moment method to find slopes and deflections.- Separate the Moment of Inertia over modulus of elasticity (M/EI) diagram for both point and distributed loads.- Superimpose results from separate loads to get the cumulative effects for each problem.This exercise underscores the importance of understanding how different loading conditions affect the structural behavior of beams, which is essential for ensuring safety and performance in engineering design.

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1. Use area moment method for this problem: Separate M/EI diagram for the point load, and the uniformly distributed load. Then superimposed. F12-10, Determine the slope and deflection at A of the cantilevered beam. E-29(10) ksi, /-245 in. 3 kip 2 kip/t 3 ft -3t F12-10

1. Use area moment method for this problem: Separate M/EI diagram for the point load, and the uniformly distributed load. Then superimposed. F12-10, Determine the slope and deflection at A of the cantilevered beam. E-29(10) ksi, /-245 in. 3 kip 2 kip/t 3 ft -3t F12-10

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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