(a) Explanation Calculation: Use moment area method: Show the free body diagram of the beam as in Figure 1. Determine the reaction of the support by taking the vertical equilibrium condition: ∑ F y = 0 R A = R E = P 2 Show the shear force ( V ) diagram for the loading beam as in Figure 2. Show the moment ( M E I ) diagram for the loading beam as in Figure 3. Due to symmetric beam with symmetric loading, consider the left side of the beam. Calculate the moment ( M 1 ) using the formula: M 1 = R A × L 4 Substitute P 2 for R A . M 1 = P 2 × L 4 = P L 8 Calculate the ratio of M 1 E I : Ratio = M 1 E I Substitute P L 8 for M 1 . M 1 E I = P L 8 E I Since both the triangles are equal, then the moments M 1 and M 2 are equal. M 1 = M 2 = P L 8 E I Calculate the area ( A 1 ) due to the moment ( M 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 4 for b 1 and P L 8 E I for h 1 . A 1 = 1 2 × L 4 × ( P L 8 E I ) = P L 2 64 E I Since both the triangles are equal, then the area A 1 and A 2 are equal (b) To determine Find the deflection ( y C ) at point C .

7th Edition

ISBN: 8220100257063

Author: BEER

Publisher: YUZU

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Chapter 9.5, Problem 111P

(a)

To determine

Find the slope (θA) at end A.

(b)

To determine

Find the deflection (yC) at point C.

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Chapter 9.5, Problem 110P

Chapter 9.5, Problem 112P

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Find the slope ( θ A ) at end A .

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