Explanation Given information: The point load act at a first and second pulley of the shaft is P . The flexural rigidity of the shaft is EI . The length of the shaft ( L ) is 2 a . Calculation: Show the free body diagram of the shaft as in Figure 1. Refer to Figure 1. Calculate the vertical reactions by applying the equation of equilibrium: Sum of vertical forces is equal to zero. ∑ F y = 0 A y + B y − P − P = 0 A y + B y − 2 P = 0 A y + B y = 2 P (1) Calculate the moment about point A by applying the equation of equilibrium: Sum of moments about point A is equal to zero. ∑ M A = 0 ( B y × 2 a ) − ( P × 3 a 2 ) − ( P × a 2 ) = 0 2 a B y − 3 a 2 P − a 2 P = 0 2 a B y − 2 a P = 0 2 a B y = 2 a P B y = 2 a P 2 a B y = P Substitute P for B y in Equation (1). A y + P = 2 P A y = 2 P − P A y = P Show the moment area diagram of the shaft as in Figure 2. Refer Figure 2. Bending moment calculation: Calculate the bending moment at A : M A = ( P × 2 a ) − ( P × 3 a 2 ) − ( P × a 2 ) = 0 Calculate the bending moment at B : M B = ( P × 0 ) = 0 Calculate the bending moment at C : M C = ( P × a ) − ( P ×

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ISBN: 2810014920922

Author: HIBBELER

Publisher: PEARSON

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Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial…

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Chapter 12.4, Problem 12.57P

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The maximum deflection of the shaft (Δmax) .

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The maximum deflection of the shaft ( Δ max ) .

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The maximum deflection of the shaft (Δmax) .

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Chapter 12 Solutions