The shaft shown consists of a steel tube (1) bonded to a brass core (2). The shear modulus of steel is 11,400 ksi and the shear modulus of brass is 5,200 ksi. A torque is applied at A. The radius of the brass core is 0.5 in. The outer radius of the steel tube is 1 in. a) Write the equilibrium and compatibility equation(s) needed to solve the problem along with supporting sketches. b) Use your equilibrium and compatibility equations two develop two new equations. The first will be a symbolic relationship between the applied torque, T, and the internal torque in the steel (Tsteel). The second will be a symbolic relationship between the applied torque, T, and the internal torque in the brass (Tbrass). [Ans. to Check: Tsteel = 0.97T and Tbrass = 0.0295T] c) Assume the allowable shear stress in the steel tube is 2,000 psi. Calculate the maximum allowable torque you could apply to the steel (Tsteel) in k-in. Then, use the equation from part (b) to compute how much torque you could have in the system in k-in. [Ans. to Check: Tmax=3.04 kip]
The shaft shown consists of a steel tube (1) bonded to a brass core (2). The shear modulus of steel is 11,400 ksi and the shear modulus of brass is 5,200 ksi. A torque is applied at A. The radius of the brass core is 0.5 in. The outer radius of the steel tube is 1 in. a) Write the equilibrium and compatibility equation(s) needed to solve the problem along with supporting sketches. b) Use your equilibrium and compatibility equations two develop two new equations. The first will be a symbolic relationship between the applied torque, T, and the internal torque in the steel (Tsteel). The second will be a symbolic relationship between the applied torque, T, and the internal torque in the brass (Tbrass). [Ans. to Check: Tsteel = 0.97T and Tbrass = 0.0295T] c) Assume the allowable shear stress in the steel tube is 2,000 psi. Calculate the maximum allowable torque you could apply to the steel (Tsteel) in k-in. Then, use the equation from part (b) to compute how much torque you could have in the system in k-in. [Ans. to Check: Tmax=3.04 kip]
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Question
![**Problem Description:**
The problem involves a shaft consisting of a steel tube (1) bonded to a brass core (2). A torque is applied at point A. Here are the given parameters:
- Shear modulus of steel: 11,400 ksi
- Shear modulus of brass: 5,200 ksi
- Radius of the brass core: 0.5 in
- Outer radius of the steel tube: 1 in
- A torque is applied at A
**Questions:**
a) **Equilibrium and Compatibility Equations:**
- Write the necessary equations and provide supporting sketches to solve the problem.
b) **Symbolic Relationships:**
- Develop two equations:
1. A symbolic relationship between applied torque \( T \) and internal torque in the steel (\( T_{\text{steel}} \)).
2. A symbolic relationship between applied torque \( T \) and internal torque in the brass (\( T_{\text{brass}} \)).
- [Answers to Check: \( T_{\text{steel}} = 0.97T \) and \( T_{\text{brass}} = 0.0295T \)]
c) **Torque in Steel:**
- Assume the allowable shear stress in the steel tube is 2,000 psi.
- Calculate the maximum allowable torque for the steel (\( T_{\text{steel}} \)) in k-in.
- Use the equation from part (b) to compute total allowable torque in the system.
- [Answer to Check: \( T_{\max} = 3.04 \text{ kip} \)]
d) **Torque in Brass:**
- Assume the allowable shear stress in the brass core is 450 psi.
- Calculate the maximum torque for the brass (\( T_{\text{brass}} \)) in k-in.
- Use the equation from part (b) to compute how much torque the system can handle.
- [Answer to Check: \( T_{\max} = 3.00 \text{ kip} \)]
e) **Factor of Safety:**
- Use a factor of safety (FOS) of 2.
- Determine the maximum torque (in k-in) applicable to the system.
**Diagram Explanation:**
The diagram shows the shaft with a steel tube around a brass core. The core has a radius of 0.5 inches, and](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F830a9ab4-0f8d-4f12-b221-b9e6e16cfd86%2Fa15ac8b0-3ff5-4a22-88d7-e645d3038758%2F2u2m9hr_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
The problem involves a shaft consisting of a steel tube (1) bonded to a brass core (2). A torque is applied at point A. Here are the given parameters:
- Shear modulus of steel: 11,400 ksi
- Shear modulus of brass: 5,200 ksi
- Radius of the brass core: 0.5 in
- Outer radius of the steel tube: 1 in
- A torque is applied at A
**Questions:**
a) **Equilibrium and Compatibility Equations:**
- Write the necessary equations and provide supporting sketches to solve the problem.
b) **Symbolic Relationships:**
- Develop two equations:
1. A symbolic relationship between applied torque \( T \) and internal torque in the steel (\( T_{\text{steel}} \)).
2. A symbolic relationship between applied torque \( T \) and internal torque in the brass (\( T_{\text{brass}} \)).
- [Answers to Check: \( T_{\text{steel}} = 0.97T \) and \( T_{\text{brass}} = 0.0295T \)]
c) **Torque in Steel:**
- Assume the allowable shear stress in the steel tube is 2,000 psi.
- Calculate the maximum allowable torque for the steel (\( T_{\text{steel}} \)) in k-in.
- Use the equation from part (b) to compute total allowable torque in the system.
- [Answer to Check: \( T_{\max} = 3.04 \text{ kip} \)]
d) **Torque in Brass:**
- Assume the allowable shear stress in the brass core is 450 psi.
- Calculate the maximum torque for the brass (\( T_{\text{brass}} \)) in k-in.
- Use the equation from part (b) to compute how much torque the system can handle.
- [Answer to Check: \( T_{\max} = 3.00 \text{ kip} \)]
e) **Factor of Safety:**
- Use a factor of safety (FOS) of 2.
- Determine the maximum torque (in k-in) applicable to the system.
**Diagram Explanation:**
The diagram shows the shaft with a steel tube around a brass core. The core has a radius of 0.5 inches, and
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