Explanation Given information: The allowable shear stress for aluminum is 12 ksi. The allowable shear stress for steel is 10 ksi. Calculation: Sketch the free body diagram of the shaft as shown in Figure 1. Apply Equilibrium equation. Sum of moments at x is equal to 0. Σ M x = 0 T A + T C − ( P ) ( 5 ft ) = 0 T A + T C = 5 P kip ⋅ ft (1) The angle of twist of the shaft is expressed as follows: ϕ = T L J G Here, T is the torque applied, L is the length of the shaft, J is the polar moment of inertia, and G is the shear modulus of elasticity of the material. Refer the properties of 6061-T6 aluminum and A992 steel. The value of shear modulus of elasticity of 6061-T6 aluminum and A992 steel are 3.7 × 10 3 ksi and 11 × 10 3 ksi . Apply compatibility condition. The angle of twist of B with respect to end A is equal to the angle of twist of B with respect to end C . ϕ B / A = ϕ B / C T A L J G al = T C L J G st Substitute 3.7 × 10 3 ksi for G al and 11 × 10 3 ksi for G st . T A L J ( 3.7 × 10 3 ksi ) = T C L J ( 11 × 10 3 ksi ) T A = 0.3364 T C (2) Substitute 0.3364 T C for T A in Equation (1). 0.3364 T C + T C = 5 P T C = 3.7414 P kip ⋅ ft Substitute 3.7414 P kip ⋅ ft for T C in Equation (2). T A = 0.3364 ( 3.7414 P ) = 1.259 P kip ⋅ ft The outer radius of the shaft is r . The radius value of the shaft is 2 in. The polar moment of inertia for a solid shaft of radius ( r ) is π 2 r 4 . The torsion formula for allowable shear stress in the region AB of the solid shaft ( τ A B ) allow is shown below: ( τ A B ) allow = T A c J Here, c is the outer radius of the shaft. Substitute r for c and π 2 r 4 for J

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382869

Author: HIBBELER

Publisher: PEARSON

See similar textbooks

Concept explainers

Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

Videos

Question

Chapter 10, Problem 7RP

To determine

Find the maximum allowable couple force that can be applied to the lever arm.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 10, Problem 6RP

Chapter 10, Problem 8RP

Students have asked these similar questions

Determine the smallest allowable diameter of the shaft which is subjected to the concentrated forces. The journal bearing at A and B only support vertical forces. The allowable bending stress is σallow= 160 MPa Bearing A only receives forces in the radial direction of the bearing. Bearing B is a steering bearing and also carries longitudinal loads on the shaft. F1= 10kN F2=23 kN L1=420 mm L2= 310mm L3=540mm

Determine the x-y and n-t components of the 13.0 kip force F acting on the simply supported beam. Assume a = 30 ft, b = 13 ft, 0 = 12°, and = 40° A 0 a Answers: C F b B n kips Fx = kips Fy= Fn = F₁ = Hi kips kips

8-27. The column is built up by gluing the two identical boards together. If the wood has an allowable normal stress of o allow 6 MPa, determine the maximum allowable || eccentric force P that can be applied to the column. 150 mm 250 mm 75 mm 150 mm 50 mm 300 mm Probs. 8–26/27

Chapter 10 Solutions

Statics and Mechanics of Materials (5th Edition)

Ch. 10.3 - Determine the internal torque at each section and...Ch. 10.3 - Determine the internal torque at each section and...Ch. 10.3 - Prob. 3PP Ch. 10.3 - Prob. 4PP Ch. 10.3 - Prob. 1FP Ch. 10.3 - The hollow circular shaft is subjected to an...Ch. 10.3 - Prob. 3FP Ch. 10.3 - Prob. 4FP Ch. 10.3 - Determine the maximum shear stress in the shaft at...Ch. 10.3 - Prob. 6FP

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.

Find the maximum allowable couple force that can be applied to the lever arm.

Solution Summary: The author calculates the maximum allowable couple force that can be applied to the lever arm.

Concept explainers

Videos

Find the maximum allowable couple force that can be applied to the lever arm.

Want to see the full answer?

Chapter 10 Solutions