Explanation Given information: The load act at the first pulley ( P 1 ) is 50 lb . The load act at the second pulley ( P 2 ) is 80 lb . The flexural rigidity of the shaft is E I . The length of the shaft ( L ) is 60 in . Calculation: Show the free body diagram of the shaft as in Figure 1. Refer to Figure 1. Calculate the support reactions A and B ( R A and R B ) : 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 − 50 − 80 = 0 R A + R B = 130 (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 × 48 ) − ( 80 × 24 ) + ( 50 × 12 ) = 0 48 R B − 1 , 320 = 0 48 R B = 1 , 320 R B = 1 , 320 48 R B = − 27.5 lb R B = 27.5 lb ( ↓ ) Substitute 27.5 lb for R B in Equation (1). R A + 27.5 = 130 R A = 130 − 27.5 R A = 102.5 lb Calculate the moment function with respect of the x distance M ( x ) : M ( x ) = − 50 ( x − 0 ) − ( − 102.5 ) ( x − 12 ) − 80 ( x − 36 ) = − 50 x + 102.5 ( x − 12 ) − 80 ( x − 36 ) Elastic Curve and slope is as follows: E I d 2 υ d x 2 = M ( x ) (2) Substitute [ − 50 x + 102.5 ( x − 12 ) − 80 ( x − 36 ) ] for M ( x ) in Equation (2). E I d 2 υ d x 2 = − 50 x + 102.5 ( x − 12 ) − 80 ( x − 36 ) (3) Integrate both sides of the Equation (3). E I d υ d x = − 50 x 2 2 + 102.5 2 ( x − 12 ) 2 − 80 2 ( x − 36 ) 2 + C 1 = − 25 x 2 + 102.5 2 ( x − 12 ) 2 − 40 ( x − 36 ) 2 + C 1 (4) Integrate both sides of the Equation (4). E I υ = − 25 x 3 3 + 102.5 3 ( x − 12 ) 3 − 40 3 ( x − 36 ) 3 + C 1 x + C 2 = [ − 25 3 x 3 + 102.5 6 ( x − 12 ) 3 − 40 3 ( x − 36 ) 3 + C 1 x + C 2 ] (5) Boundary conditions are as follows: υ = 0 at x = 12 in . υ = 0 at x = 60 in

10th Edition

ISBN: 9780134583228

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 12.3, Problem 12.42P

To determine

The slop at A(θA).

The slop at B(θB).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.3, Problem 12.41P

Chapter 12.3, Problem 12.43P

Students have asked these similar questions

The shaft supports the two pulley loads shown. Determine the slope of the shaft at A and B. The bearings exert only vertical reactions on the shaft. EI is constant.

this is in the section for statiCally inDeterminate Beams anD shafts—methoD of superposition

*11-84. Determine, to the nearest millimeter, the smallest allowable diameter of the shaft which is subjected to the concentrated forces. There is a journal bearing at A and a thrust bearing at B. The allowable bending stress is stm = 150 MPa. 0.5m- -0.4 m- a6 m 12 kN 20 kN

Chapter 12 Solutions

MECHANICS OF MATERIALS (LOOSE)-W/ACCESS

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...

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 slop at A ( θ A ) . The slop at B ( θ B ) .

Solution Summary: The author calculates the slop at A and B by applying the equation of equilibrium: Sum of moments about point A is equal to 0.

Concept explainers

The slop at A(θA).

The slop at B(θB).

Want to see the full answer?

Chapter 12 Solutions

The slop at A ( θ A ) . The slop at B ( θ B ) .

Solution Summary: The author calculates the slop at A and B by applying the equation of equilibrium: Sum of moments about point A is equal to 0.

Concept explainers

The slop at A(θA). The slop at B(θB).

Want to see the full answer?

Chapter 12 Solutions

The slop at A(θA).

The slop at B(θB).