Explanation Given information: The flexural rigidity of the beam is E I . The length of the beam ( L ) is 24 ft . Calculation: Show the free body diagram of the beam as in Figure 1. Refer to Figure 1. Calculate the support reactions A and B ( R A and R B ) : Calculate the vertical forces by applying the equation of equilibrium: Sum of vertical forces is equal to 0. ∑ F y = 0 R A + R B − 4 = 0 R A + R B = 4 (1) Calculate the moment about point A by applying the equation of equilibrium: Sum of moments about point A is equal to 0. ∑ M A = 0 ( R B × 24 ) − 6 − 6 − ( 4 × 24 ) = 0 24 R B − 108 = 0 24 R B = 108 R B = 108 24 R B = 4.5 kip Substitute 4.5 kip for R B in Equation (1). R A + 4.5 = 4 R A = 4 − 4.5 R A = − 0.5 kip R A = 0.5 kip ( ↓ ) Calculate the moment function with respect of the x distance M ( x ) : M ( x ) = − 0.5 ( x − 0 ) − ( − 6 ) ( x − 8 ) 0 − ( − 6 ) ( x − 16 ) 0 = − 0.5 x + 6 ( x − 8 ) 0 + 6 ( x − 16 ) 0 Elastic Curve and slope is as follows: E I d 2 υ d x 2 = M ( x ) (2) Substitute [ − 0.5 x + 6 ( x − 8 ) 0 + 6 ( x − 16 ) 0 ] for M ( x ) in Equation (2). E I d 2 υ d x 2 = − 0.5 x + 6 ( x − 8 ) 0 + 6 ( x − 16 ) 0 (3) Integrate both sides of the Equation (3). E I d υ d x = − 0.5 x 2 2 + 6 ( x − 8 ) + 6 ( x − 16 ) + C 1 = − 0.25 x 2 + 6 ( x − 8 ) + 6 ( x − 16 ) + C 1 (4) Integrate both sides of the Equation (4). E I υ = − 0

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ISBN: 2810014920922

Author: HIBBELER

Publisher: PEARSON

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Chapter 12.3, Problem 12.43P

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The equation of the elastic curve ( υ ) .

Solution Summary: The author calculates the flexural rigidity of the beam by applying the equation of equilibrium.

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