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

STANDALONE CODE MECHANICS OF MATERIALS-M

11th Edition

ISBN: 9780137605200

Author: HIBBELER

Publisher: PEARSON

See similar textbooks

Concept explainers

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 …

Question

Chapter 12.4, Problem 60P

To determine

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.4, Problem 59P

Chapter 12.4, Problem 61P

Students have asked these similar questions

Solve, use engineering economic tables

Chapter 12 Solutions

STANDALONE CODE MECHANICS OF MATERIALS-M

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...Ch. 12.2 - A torque wrench is used to tighten the nut on a...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

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

Concept explainers

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

Want to see the full answer?

Chapter 12 Solutions