Explanation Given information: The diameter of the shaft ( d ) is 50 mm . The shaft is made of A-36 steel. The modulus of elasticity of the shaft ( E ) is 200 GPa The moment of inertia of the shaft is I The load act at first pulley of the shaft ( P 1 ) is 600 N . The load act at second pulley of the shaft ( P 2 ) is 1200 N . The length of the shaft ( L ) is 2500 mm . Calculation: Show the free body diagram of the shaft 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 − 600 − 1 , 200 = 0 R A + R B − 1 , 800 = 0 R A + R B = 1 , 800 (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 × 2 , 500 ) − ( 1 , 200 × 1 , 300 ) − ( 600 × 500 ) = 0 2 , 500 R A − 186 × 10 4 = 0 2 , 500 R A = 186 × 10 4 R B = 186 × 10 4 2 , 500 R B = 744 N Substitute 744 N for R B in Equation (1). R A + 744 = 0 R A = 1800 − 744 R A = 1056 N Show the moment area diagram of the shaft as in Figure 2. Refer to Figure 2. Show the bending monument calculation follows: Calculate the bending moment at A : M A = ( 744 × 2.5 ) − ( 1200 × 1.3 ) − ( 600 × 0.5 ) = 0 Calculate the bending moment at C : M C = ( 744 × 2 ) − ( 1200 × 0.8 ) = 528 N ⋅ m Calculate the bending moment at D : M D = ( 744 × 1.2 ) − ( 1200 × 0 ) = 892.8 N ⋅ m Calculate the bending moment at x : M x = 744 ( 2 − x ) − 1200 ( 0.8 − x ) = 1488 − 744 x − 960 + 1200 x = 528 + 456 x N ⋅ m Show the deflected shape of the shaft as in Figure 3. Refer to Figure 2. Calculate the vertical distance between the tangent at a point B and A ( t B / A ) : t B / A = { [ 1 2 × 892.8 E I × 1.2 × 0.8 ] + [ 1 2 × 364.8 E I × 0.8 × 1.4667 ] + [ 528 E I × 0.8 × 1.6 ] + [ 1 2 × 528 E I × 0.5 × 2.1667 ] } = − 428.544 E I + 214.020864 E I + 675.84 E I + 286.0044 E I = 1 , 604.4 E I N ⋅ m 3 Calculate the vertical distance between the tangent at a point A and B ( t A / B ) : t A / B = { [ 1 2 × 892

10th Edition

ISBN: 9780134319650

Author: Russell C. Hibbeler

Publisher: PEARSON

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Design of Shafts and Shaft Components

The shaft is basically defined as the machine element that rotates, is in circular cross-section, it is majorly used to transfer the power from one part of the system to another, or from a power generating machine to a power absorbing machine. The shaft …

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Chapter 12.4, Problem 12.60P

To determine

The slope of the shaft at the journal bearings at A and B (θA and θB).

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Chapter 12.4, Problem 12.59P

Chapter 12.4, Problem 12.61P

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The slope of the shaft at the journal bearings at A and B ( θ A and θ B ) .

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The slope of the shaft at the journal bearings at A and B (θA and θB).

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Chapter 12 Solutions