Explanation Given information: The point load act at a center of the shaft is P . The moment of inertia of region BC is 2 I . The moment of inertia of region AB and CD is I . The modulus of elasticity is E . The length of the shaftis L . Calculation: Show the free body diagram of the moment area and tangent of the rod as in Figure 1. Refer to Figure 1. 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 − P = 0 R A + R B = P (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 × L ) − ( P × L 2 ) = 0 L R A − P L 2 = 0 L R B = P L 2 R B = P L 2 L R B = P 2 Substitute P 2 for R B in Equation (1). R A + P 2 = P R A = P − P 2 R A = P 2 The shaft is symmetry

10th Edition

ISBN: 9780134319650

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 12.4, Problem 12.57P

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The maximum deflection of the shaft (υmax).

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Chapter 12.4, Problem 12.56P

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The maximum deflection of the shaft ( υ max ) .

Solution Summary: The author explains how to determine the maximum deflection of the shaft by applying the equation of equilibrium: Sum of moments about point A is equal to 0.

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The maximum deflection of the shaft (υmax).

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