(a) Explanation Calculation: Use moment area method: Show the free body diagram of beam as in Figure 1. Draw the moment diagram of the above beam as in Figure 2. Calculate the moment ( M 1 ) using the formula: M 1 = − w L 2 8 Calculate the moment ( M 1 E I ) using the relation: Moment = M 1 E I Substitute − w L 2 8 for M 1 and 3 EI for EI . M 1 E I = − w L 2 8 3 E I = − w L 2 24 E I Calculate the moment ( M 2 ) using the relation: M 2 = − w L 2 8 Calculate the moment ( M 2 E I ) using the relation: Moment = M 2 E I Substitute − w L 2 8 for M 2 and EI for EI . M 2 E I = − w L 2 8 E I = − w L 2 8 E I Calculate the moment ( M 3 ) using the relation: M 2 = − w L 2 8 Calculate the moment ( M 3 E I ) using the relation: Moment = M 3 E I Substitute − w L 2 8 for M 3 and EI for EI . M 3 E I = − w L 2 8 E I = − w L 2 8 E I Show the moment diagram ( M E I ) of the beam as in Figure 3. Calculate the area ( A 1 ) using the formula: A 1 = 1 2 b 1 h 1 Here, b 1 is the width of the triangle in area ( A 1 ) and h 1 is the height of the triangle in area ( A 1 ) . Substitute L 2 for b 1 and − w L 2 24 E I for h 1 . A 1 = 1 2 × L 2 × ( − w L 2 24 E I ) = − w L 3 96 E I Calculate the area ( A 2 ) using the formula: A 2 = 1 2 b 2 h 2 Here, b 2 is the width of the triangle in area ( A 2 ) and h 2 is the height of the triangle in area ( A 2 ) . Substitute L 2 for b 2 and − w L 2 8 E I for h 2 (b) To determine Find the deflection ( y A ) at point A .

7th Edition

ISBN: 9780100257061

Author: BEER

Publisher: YUZU

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Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and af…

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Chapter 9.5, Problem 105P

(a)

To determine

Find the slope (θA) at point A.

(b)

To determine

Find the deflection (yA) at point A.

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Chapter 9.5, Problem 104P

Chapter 9.5, Problem 106P

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Find the slope ( θ A ) at point A .

Solution Summary: The author illustrates the moment area method by showing the free body diagram of beam as in Figure 1.