Explanation Given information: The yield strength of steel is σ Y = 45 ksi . The magnitude of load is P = 60 kips . The diameter of the shaft AB is d = 1.5 in . . Calculation: Apply maximum distortion energy criterion as shown below. σ a 2 − σ a σ b + σ b 2 = σ Y σ a 2 − σ a σ b + σ b 2 = σ Y 2 (1) Calculate the area of the shaft ( A ) as shown below. A = π d 2 4 Substitute 1.5 in . for d . A = π × 1.5 2 4 = 1.7671 in . 2 Calculate the axial stress ( σ x ) as shown below. σ x = − P A Substitute 60 kips for P and 1.7671 in . 2 for A . σ x = − 60 1.7671 = − 33.954 ksi 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 − 33.954 ksi for σ x and 0 for σ y . σ avg = − 33.954 + 0 2 = − 16.977 ksi Calculate the value of τ x y as shown below. R = ( σ x − σ y 2 ) 2 + τ x y 2 Substitute − 33.954 ksi for σ x and 0 for σ y . R = ( − 33.954 − 0 2 ) 2 + τ x y 2 = 288.2185 + τ x y 2 Calculate principal stresses ( σ max and σ min ) as shown below. σ max , min = σ avg ± R Substitute − 16.977 ksi for σ avg and 288.2185 + τ x y 2 for R . σ a , b = − 16.977 ± 288.2185 + τ x y 2 σ a = − 16.977 + 288.2185 + τ x y 2 σ b = − 16.977 − 288.2185 + τ x y 2 Calculate the value of τ x y as shown below. Substitute − 16

7th Edition

ISBN: 9780100257061

Author: BEER

Publisher: YUZU

See similar textbooks

Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial…

Videos

Question

Chapter 7.5, Problem 88P

To determine

The magnitude of the torque T using maximum distortion energy criterion.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7.5, Problem 87P

Chapter 7.5, Problem 89P

Students have asked these similar questions

In direct calorimetry, a person is placed in a large, water-insulated chamber. The chamber is kept at a constant temperature. While in the chamber, the subject is asked to perform a number of normal activities, such as eating, sleeping, and exercising. The rate of heat released from the subject’s body can be measured by the rate of heat gain by the water bath. Would direct calorimetry be a practical way to measure metabolic rate? Why or why not?A person is placed inside a calorimetric chamber for 24 hours. During this time, the 660-gallon water bath heats up by 3.2°F. What is the subject’s metabolic rate during this period? Report your answer in kcal/day. Assume that there is no heat loss from the water to the surroundings.

Upon reentry into the Earth’s atmosphere, the bottom of a space shuttle heats up to dangerous levels as the craft slows for landing. If the velocity of the shuttle is 28,500 km/hr at the beginning of reentry and 370 km/hr just prior to landing, how much energy is lost as heat? The shuttle has a mass of 90,000 kg. Assume that the change in potential energy is negligible compared to the change in kinetic energy.

of the basket of the balloon at point A, and their other ends are staked to the ground. The hook is located in the geometric center of the basket. The balloon and the air inside it have a combined mass of 3000 kg. You want to determine the resultant of the tension forces in the four cables acting on the hook at point A. It is known that the magnitudes of the tension in the cables are as follows: TAB = 207 N; TAC = 355 N; TAD = 250 N; and TAE = 486 N. B E 2.5 m C E 5.5 m D 2.5 m 3.5 m 1.5 m Using the information provided in the problem, express the force on the hook at point A by cable AC in rectangular component form. The force on the hook at point A by cable AC in rectangular component form is given below. T AC N) i+ N) + N) R

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 using maximum distortion energy criterion.

Solution Summary: The author explains the magnitude of the torque T using maximum distortion energy criterion.

Concept explainers

Videos

The magnitude of the torque T using maximum distortion energy criterion.

Want to see the full answer?

Chapter 7 Solutions