Explanation Given information: The moment acting at points C and D of the shaft is M = 50 lb ⋅ ft . The flexural rigidity of the shaft is EI . The length of the shaft ( L ) is 8 ft. Calculation: Show the free body diagram of the shaft as in Figure 1. Refer Figure 1. Calculate the support reactions A and B ( A y and B y ) : 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 = 0 (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 × 8 ) − 50 + 50 = 0 8 B y − 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 Figure 2. Bending moment calculation: Calculate the bending moment at A : M A = − ( 0 × 8 ) − 50 + 50 = 0 Calculate the bending moment at B : M B = − ( 0 × 0 ) = 0 Calculate the bending moment at C : M C = − ( 0 × 6 ) − 50 = − 50 lb ⋅ ft Calculate the bending moment at D : M D = − ( 0 × 2 ) − 50 = − 50 lb ⋅ ft 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 ( θ E ) is 0. Calculate the slope between the point E and A ( θ E / A ) : θ E / A = − M L A B E I (2) Substitute 50 lb ⋅ ft for M and 2 ft for L A B in Equation (2). θ E / A = 50 × 2 E I = 100 E I lb ⋅ ft 2 Calculate the vertical distance between the tangent at point E and A ( t E / A ) : t E / A = 1 × M L A B E I (3) Substitute 50 lb ⋅ ft for M and 2 ft for L A B in Equation (3)

9th Edition

ISBN: 9789810694364

Author: Russell C Hibbeler

Publisher: Pearson Education

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Chapter 12.4, Problem 12.56P

To determine

The slope of the shaft at A (θA) .

The maximum deflection of the shaft (υmax) .

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Chapter 12.4, Problem 12.55P

Chapter 12.4, Problem 12.57P

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

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

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Chapter 12 Solutions

The slope of the shaft at A (θA) .

The maximum deflection of the shaft (υmax) .