Explanation Given information: The load P = 26 kN . The diameter of the shaft AB is d = 32 mm . The uniaxial tension for the aluminum alloy is σ U T = 60 MPa . The uniaxial compression for the aluminum alloy is σ U C = 120 MPa . Calculation: Calculate the area of the shaft ( A ) as shown below. A = π d 2 4 Substitute 32 mm for d . A = π × 32 2 4 = 804.2477 mm 2 Calculate the axial stress ( σ x ) as shown below. σ x = P A Substitute 26 kN for P and 804.2477 mm 2 for A . σ x = 26 kN × 1 , 000 N 1 kN 804.2477 mm 2 = 32.328 N / mm 2 × 1 MPa 1 N / mm 2 = 32.328 MPa The stress along y axis σ y = 0 . Calculate the average normal stress ( σ avg ) as shown below. σ avg = σ x + σ y 2 Substitute 32.328 MPa for σ x and 0 for σ y . σ avg = 32.328 + 0 2 = 16.164 MPa Calculate the value of R as shown below. R = ( σ x − σ y 2 ) 2 + τ x y 2 Substitute 32.328 MPa for σ x and 0 for σ y . R = ( 32.328 − 0 2 ) 2 + τ x y 2 = 261.2749 + τ x y 2 Calculate principal stresses ( σ max and σ min ) as shown below. σ max , min = σ avg ± R Substitute 16.164 MPa for σ avg and 261.2749 + τ x y 2 for R . σ a , b = 16.164 ± 261.2749 + τ x y 2 σ a = 16.164 + 261.2749 + τ x y 2 σ b = 16.164 − 261.2749 + τ x y 2 Here, | σ avg | < R

7th Edition

ISBN: 9780100257061

Author: BEER

Publisher: YUZU

See similar textbooks

Videos

Question

Chapter 7.5, Problem 96P

To determine

The magnitude of the torque T for which the failure should be expected using Mohr’s criterion.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7.5, Problem 95P

Chapter 7.5, Problem 97P

Students have asked these similar questions

Using Tall = 8.7 ksi and knowing that G= 5.6 × 106 psi, determine for each of the cold-rolled yellow brass bars shown the largest torque T that can be applied and the corresponding angle of twist at end B. Refer to Table 3.1. B 2 in.- T 2 in. B 2.8 in. 1.4 in. 16 in. The torque for the brass bar (a) is The angle of twist for the brass bar (a) is The torque for the brass bar (b) is The angle of twist for the brass bar (b) is kip-in. kip-in. 0

The solid circular drill rod AB is made of a steel that is assumed to be elastoplastic with TY = 22 ksi and G = 11.2 x 106 psi. Knowing that a torque T = 73 kip-in. is applied to the rod and then removed, determine the permanent angle of twist of the rod. The permanent angle of twist of the rod is

The solid circular drill rod AB is made of a steel that is assumed to be elastoplastic with ry= 22 ksi and G= 11.2 × 106 psi. Knowing that a torque T = 73 kip·in. is applied to the rod and then removed, determine the maximum residual shearing stress in the rod. 35 ft 4 1.2 in. The maximum residual shearing stress in the rod is ksi.

Chapter 7 Solutions

EBK MECHANICS OF MATERIALS

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 magnitude of the torque T for which the failure should be expected using Mohr’s criterion.

Solution Summary: The author calculates the magnitude of the torque T for which the failure should be expected using Mohr’s criterion.

Videos

The magnitude of the torque T for which the failure should be expected using Mohr’s criterion.

Want to see the full answer?

Chapter 7 Solutions