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: 9780134319650

Author: Russell C. 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

Q4/ A compressor is driven motor by mean of a flat belt of thickness 10 mm and a width of 250 mm. The motor pulley is 300 mm diameter and run at 900 rpm and the compressor pulley is 1500 mm diameter. The shaft center distance is 1.5 m. The angle of contact of the smaller pulley is 220° and on the larger pulley is 270°. The coefficient of friction between the belt and the small pulley is 0.3, and between the belt and the large pulley is 0.25. The maximum allowable belt stress is 2 MPa and the belt density is 970 kg/m³. (a) What is the power capacity of the drive and (b) If the small pulley replaced by V-grooved pulley of diameter 300 mm, grooved angle of 34° and the coefficient of friction between belt and grooved pulley is 0.35. What will be the power capacity in this case, assuming that the diameter of the large pulley remain the same of 1500 mm.

You are tasked with designing a power drive system to transmit power between a motor and a conveyor belt in a manufacturing facility as illustrated in figure. The design must ensure efficient power transmission, reliability, and safety. Given the following specifications and constraints, design drive system for this application: Specifications: Motor Power: The electric motor provides 10 kW of power at 1,500 RPM. Output Speed: The output shaft should rotate at 150 rpm. Design Decisions: Transmission ratio: Determine the necessary drive ratio for the system. Shaft Diameter: Design the shafts for both the motor and the conveyor end. Material Selection: Choose appropriate materials for the gears, shafts. Bearings: Select suitable rolling element bearings. Constraints: Space Limitation: The available space for the gear drive system is limited to a 1-meter-long section. Attribute 4 of CEP Depth of knowledge required Fundamentals-based, first principles analytical approach…

- | العنوان In non-continuous dieless drawing process for copper tube as shown in Fig. (1), take the following data: Do-20mm, to=3mm, D=12mm, ti/to=0.6 and v.-15mm/s. Calculate: (1) area reduction RA, (2) drawing velocity v. Knowing that: ti: final thickness V. Fig. (1) ofthre

Chapter 12 Solutions

Mechanics of Materials (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...

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).