Safety Factor of Shaft :Machine Design

It may be helpful to use Mohr's circle to determine the principal stresses present in the shaft under this loading. This will give you a more accurate safety factor calculation. In summary, a solid bar of Class 40 cast iron with dimensions of 8" long and 2.5" diameter is subjected to a torque of 75,000 lbf-in and an axial compressive load of 165,000 lbf. With these loads increasing at a constant ratio, the safety factor is calculated to be 4.1667. To get a more accurate calculation, it is recommended to use Mohr's circle to determine the principal stresses present in the shaft.
  • #1
speedy21cvb
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Homework Statement


An 8” long, 2.5” diameter, solid bar of Class 40 cast iron is subjected to both a torque of 75,000 lbf-in and an axial compressive load of 165,000 lbf. If these two loads can increase at a constant ratio, calculate the safety factor.

Homework Equations


[tex]\sigma[/tex]x=F/A
[tex]\tau[/tex]xy=Tr/J
nf= Allowed/Actual
For class 40 cast iron:
Sut=42.5 kpsi
Suc=140 kpsi

The Attempt at a Solution


[tex]\sigma[/tex]x=165000/4.91=33.6 kpsi
[tex]\tau[/tex]xy=75000*1.25/([tex]\pi[/tex]*2.54/32=24.5 kpsi

Take the higher stress of 33.6 kpsi.
nf=140kpsi/33.6kpsi= 4.1667I did it this way, however afterwards I thought about the principal stresses. Would I need to solve for the principal stresses present in the shaft under this loading? We used mohrs circle in class, does this apply? This is my first post, I'm finally going to stop being proud and ask for help :) Please let me know if my formatting is incorrect.

-Chris Van Buren, Mechanical Engineer Student, Georgia Tech
 
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  • #2
speedy21cvb wrote: "Would I need to solve for the principal stresses present in the shaft under this loading? Does this apply?"

speedy21cvb: That sounds like a good plan.
 
  • #3
Hi Chris,

First of all, great job on your attempt at solving this problem! Your method and calculations are correct. However, you do not need to consider principal stresses in this case. The safety factor is simply a ratio of the allowable stress to the actual stress, and you have already calculated the actual stress using the maximum value between axial and torsional stresses.

In cases where multiple stresses are acting on a component, you would need to calculate the principal stresses and then compare them to the allowable stress to determine the safety factor. Mohr's circle can be used to find the principal stresses, but it is not necessary in this case since you only have two primary stresses to consider.

Keep up the good work and don't hesitate to ask for help when needed. it is important to collaborate and seek input from others in order to advance knowledge and understanding. Good luck with your studies!
 

Related to Safety Factor of Shaft :Machine Design

1. What is the safety factor of a shaft in machine design?

The safety factor of a shaft refers to the ratio between the maximum stress the shaft can withstand and the maximum stress it is expected to encounter during operation. It is a measure of the shaft's strength and reliability, and is typically calculated by dividing the ultimate stress of the material by the maximum stress the shaft is expected to encounter.

2. Why is the safety factor important in machine design?

The safety factor is important in machine design because it ensures that the shaft is strong enough to withstand the expected stress and load during operation. A higher safety factor means that the shaft is less likely to fail or break, providing a margin of safety and reducing the risk of accidents or damage to the machine.

3. How is the safety factor determined for a shaft?

The safety factor for a shaft is determined by considering various factors such as the material properties, expected load and stress, and the required reliability of the machine. Engineers use mathematical equations and calculations to determine the appropriate safety factor for a specific shaft design.

4. What is a safe safety factor for a shaft in machine design?

The safe safety factor for a shaft in machine design can vary depending on the industry, application, and specific requirements of the machine. However, a commonly used safety factor for shafts is 1.5 to 2. This means that the shaft is designed to withstand 1.5 to 2 times the maximum stress it is expected to encounter during operation.

5. Can the safety factor be too high for a shaft in machine design?

Yes, the safety factor can be too high for a shaft in machine design. While a higher safety factor provides a greater margin of safety, it can also result in a heavier and more expensive shaft. In some cases, an excessively high safety factor can also cause the shaft to be less flexible, leading to reduced performance or efficiency of the machine. Engineers must carefully consider all factors and find a balance between safety, cost, and performance when determining the appropriate safety factor for a shaft.

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