(a) Explanation Calculation: Show the free body diagram of the beam as in Figure 1. Calculate the reaction ( R A ) at point A by taking moment about B . ∑ M B = 0 M 0 − R A L = 0 R A L = M 0 R A = M 0 L Show the free body diagram of the beam section AC as in Figure 2. Calculate the moment ( M ) as below: ∑ M C = 0 M 0 − M 0 L x + M = 0 M = M 0 L ( x − L ) (1) Calculate the equation of the elastic curve ( y ) by integrating the equation (1). E I d 2 y d x 2 = M 0 L ( x − L ) E I d y d x = M 0 L ( x 2 2 − L x ) + C 1 (2) E I y = M 0 L ( x 3 6 − L x 2 2 ) + C 1 x + C 2 (3) Substitute 0 for x and 0 for y in Equation (3). E I ( 0 ) = M 0 L ( ( 0 ) 3 6 − L ( 0 ) 2 2 ) + C 1 ( 0 ) + C 2 0 = 0 − 0 + 0 + C 2 C 2 = 0 Substitute L for x 0 for C 2 and 0 for y in Equation (3). E I ( 0 ) = M 0 L ( L 3 6 − L ( L ) 2 2 ) + C 1 ( L ) + 0 C 1 ( L ) = 1 3 M 0 L 2 L C 1 = 1 3 M 0 L 2 L C 1 = M 0 L 2 3 Substitute M 0 L 2 3 and C 1 in Equation (3). E I y = M 0 L ( x 3 6 − L x 2 2 ) + M 0 L 2 3 x + 0 E I y = M 0 x 3 6 L − M 0 L x 2 2 L + M 0 L 2 x 3 y = M 0 E I L ( 1 6 x 3 − 1 2 L x 2 + 1 3 L 2 x ) (4) Calculate the slope equation as below; Substitute M 0 L 2 3 and C 1 in equation (2). E I d y d x = M 0 L ( x 2 2 − L x ) + M 0 L 2 3 E I d y d x = M 0 x 2 2 L − M 0 x L + M 0 L 2 3 d y d x = M 0 E I L ( 1 2 x 2 − L x + 1 3 L 2 ) (5) Calculate the location ( x m ) of maximum deflection: Set 0 for d y d x in Equation (5) (b) To determine The maximum allowable value of moment M 0 if the maximum deflection is not to exceed 1 mm .

7th Edition

ISBN: 9780100257061

Author: BEER

Publisher: YUZU

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Chapter 9, Problem 158RP

(a)

To determine

The location (xm) and magnitude (ym) of the maximum deflection of the beam AB.

(b)

To determine

The maximum allowable value of moment M0 if the maximum deflection is not to exceed 1 mm.

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Chapter 9, Problem 157RP

Chapter 9, Problem 159RP

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The location ( x m ) and magnitude ( y m ) of the maximum deflection of the beam AB .

Solution Summary: The author calculates the reaction (x_m) at point A by taking moment about B.