# Find the principal stresses in a shaft with torque applied

• Kyle Grayston
In summary, the conversation discusses the calculation of normal stress and shear stress using equations such as M = Fd, σ/y = M/I, and T/J = τ/r. The values for J and I are calculated to be 38.35e-9 m4 and 19.17e-9 m4, respectively. The maximum and minimum principal stresses are then determined using Mohrs circle, with values of 99.17 MPa and -17.01 MPa. The conversation also mentions the use of σalternating and σmean equations and the consideration of bending stress when determining a suitable factor of safety. There is some uncertainty about whether bending stress should be taken into account in the analysis.
Kyle Grayston

## Homework Equations

M = Fd
σ/y = M/I
T/J = τ/r
σalternating (σa) = σmax - σmin / 2
σmean (σm) = σmax + σmin / 2
soderberg: σa/σ'e + σm/σy = 1/FoS

## The Attempt at a Solution

I am still unsure whether my progress so far is correct but..
I have calculated J to be 38.35e-9 m4 and I to be 19.17e-9 m4. I then use these values in the shear stress and normal stress equations to find that:

σ = 82.16 MPa
τ = 41.07 MPa

I apply these values to a loading element diagram (am I right in thinking there is no force in the y direction??) and then used Mohrs circle to find that the maximum and minimum principal stresses are:

σmax = 99.17 MPa
σmin = -17.01 MPa

When applying these values to the σalternating and σmean equations, I am not sure whether it is expressed as:

σa = σmax - σmin / 2
σa = 99.17 - (-17.01) / 2 OR
σa = 99.17 - 17.01 / 2

After I get the correct σa and σm values and I need to find a suitable factor of safety, I'll have σa, σm, σy but I am not sure how I am to find the σ'e, or is there a different method to finding a suitable factor of safety?

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I'm not sure whether they really intended for you to be considering the bending of the shaft in addition to the torque. What do you think?

Chestermiller said:
I'm not sure whether they really intended for you to be considering the bending of the shaft in addition to the torque. What do you think?

I see what you're saying, I guess when I saw 'principal stresses' I thought about what we had learned in class and to draw mohrs circle. I am not sure how I would go about finding the maximum and minimum principal stresses without applying a bending stress? I have drawn the following loading element:

Im just unsure as to whether I am on the right track with this..

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## 1. What is the purpose of finding the principal stresses in a shaft with torque applied?

The purpose of finding the principal stresses in a shaft with torque applied is to determine the maximum stress that the shaft is experiencing, which is important for ensuring the safety and reliability of the shaft.

## 2. How is torque applied to a shaft?

Torque is typically applied to a shaft through the use of a rotating force, such as a motor or engine, which causes the shaft to twist. This twisting motion creates shear stress in the shaft.

## 3. What factors affect the principal stresses in a shaft?

The principal stresses in a shaft can be affected by various factors such as the magnitude of the applied torque, the dimensions and material properties of the shaft, and any external loads or forces acting on the shaft.

## 4. What is the difference between the maximum shear stress and the maximum normal stress in a shaft?

The maximum shear stress is a result of the torsional or twisting forces applied to the shaft, while the maximum normal stress is a result of the bending forces applied to the shaft. These two stresses are often present simultaneously and can contribute to failure in different ways.

## 5. How is the principal stress calculated in a shaft with torque applied?

The principal stress in a shaft with torque applied is typically calculated using the Mohr's circle method, which involves plotting the different stress components on a graph and finding the maximum and minimum values. This method takes into account both the normal and shear stresses in the shaft.

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