Explanation Given information: The flexural rigidity of the shaft is D:\nes . The moment act at L 3 distance from each end of the shaft is M 0 . The length of the shaft is L . Calculation: Show the free body diagram of the shaft as in Figure 1. Refer to Figure 1. Calculate the support reactions at A and B ( A y and B y ) : Calculate the vertical forces by applying the equation of equilibrium: Sum of vertical forces is equal to 0. ∑ F y = 0 A y + B y = 0 (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 ( B y × L ) + M 0 − M 0 = 0 B y L + 0 = 0 B y = 0 Substitute 0 for B y in Equation (1). A y + 0 = 0 A y = 0 Show the moment area diagram of the shaft as in Figure 2. Refer to Figure 2. Calculate the bending moment at A : M A = − ( 0 × L ) + M 0 − M 0 = 0 Calculate the bending moment at B : M B = − ( 0 × 0 ) = 0 Calculate the bending moment at C : M C = − ( 0 × L 2 ) + M 0 = M 0 Calculate the bending moment at D : M D = − ( 0 × 2 L 3 ) + M 0 = M 0 Calculate the bending moment at E : M E = − ( 0 × L 3 ) + M 0 = M 0 Show the deflected shape of the shaft as in Figure 3. Refer to Figure 3. The section is symmetrical. Therefore, the slope at mid span of the shaft ( θ C ) is 0

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ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 12.4, Problem 12.73P

To determine

The slope at A (θA) .

The maximum deflection of the shaft (Δmax) .

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Chapter 12.4, Problem 12.72P

Chapter 12.4, Problem 12.74P

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The slope at A ( θ A ) . The maximum deflection of the shaft ( Δ max ) .

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The slope at A (θA) . The maximum deflection of the shaft (Δmax) .

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Chapter 12 Solutions

The slope at A (θA) .

The maximum deflection of the shaft (Δmax) .