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

Mechanics of Materials Plus Mastering Engineering with Pearson eText - Access Card Package (10th Edition)

10th Edition

ISBN: 9780134518121

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 frame shown is fitted with three 50 cm diameter frictionless pulleys. A force of F = 630 N is applied to the rope at an angle ◊ 43°. Member ABCD is attached to the wall by a fixed support at A. Find the forces indicated below. Note: The rope is tangent to the pully (D) and not secured at the 3 o'clock position. a b •C *су G E e d BY NC SA 2013 Michael Swanbom Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 81 cm b 50 cm с 59 cm d 155 cm For all answers, take x as positive to the right and positive upward. At point A, the fixed support exerts a force of: A = + ĴN and a reaction couple of: →> ΜΑ Member CG is in Select an answer magnitude У as k N-m. and carries a force of N.

The lower jaw AB [Purple 1] and the upper jaw-handle AD [Yellow 2] exert vertical clamping forces on the object at R. The hand squeezes the upper jaw-handle AD [2] and the lower handle BC [Orane 4] with forces F. (Member CD [Red 3] acts as if it is pinned at D, but, in a real vise-grips, its position is actually adjustable.) The clamping force, R, depends on the geometry and on the squeezing force F applied to the handles. Determine the proportionality between the clamping force, R, and the squeezing force F for the dimensions given. d3 d4 R 1 B d1 2 d2 D... d5 F 4 F Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value d1 65 mm d2 156 mm d3 50 mm 45 d4 d5 113 mm 30 mm R = F

Chapter 12 Solutions

Mechanics of Materials Plus Mastering Engineering with Pearson eText - Access Card Package (10th Edition)

Ch. 12.2 - In each case, determine the internal bending...Ch. 12.2 - Determine the slope and deflection of end A of the...Ch. 12.2 - Determine the slope and deflection of end A of the...Ch. 12.2 - Determine the slope of end A of the cantilevered...Ch. 12.2 - Determine the maximum deflection of the simply...Ch. 12.2 - Determine the maximum deflection of the simply...Ch. 12.2 - Determine the slope of the simply supported beam...Ch. 12.2 - An L2 steel strap having a thickness of 0.125 in....Ch. 12.2 - The L2 steel blade of the band saw wraps around...Ch. 12.2 - A picture is taken of a man performing a pole...

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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