Finding diameter of torsion shaft

AI Thread Summary
The discussion centers on calculating the required diameter of a brass torsion shaft subjected to a torque of 25 kNm, with given shear stress and modulus of elasticity. The participant initially calculated a diameter of 7mm but was informed that this answer is incorrect. Key equations for shear strain and stress are referenced, emphasizing the need to understand how these vary with distance along the shaft and radial location. A correction in the algebra for the polar moment of inertia (J) is highlighted, indicating that it should be calculated using the formula J = TL / Gθ. Accurate calculations and understanding of the equations are essential for determining the correct diameter.
Mechanical94
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Homework Statement



The solid shaft is made from brass that has an allowable shear stress
= 100 MPa and a shear modulus of elasticity G = 39 GPa. The length of the shaft is L = 2 m, and over the length of the shaft the allowable angle of twist is θ = 0.10 rad.the shaft is subjected to a torque of T = 25 kNm, what is the required diameter of the shaft

Homework Equations



T/J=t/r=Gθ/L
 
Last edited:
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Mechanical94 said:

Homework Statement



The solid shaft is made from brass that has an allowable shear stress
= 100 MPa and a shear modulus of elasticity G = 39 GPa. The length of the shaft is L = 2 m, and over the length of the shaft the allowable angle of twist is θ = 0.10 rad.the shaft is subjected to a torque of T = 25 kNm, what is the required diameter of the shaft

Homework Equations



T/J=t/r=Gθ/L

Hi Mechanical94. Welcome to Physics Forums.

In this situation, what is the equation for the local shear strain as a function of how θ is varying with distance along the shaft, and as a function of radial distance r from the axis of the shaft? Does the shear strain vary with axial location? Does the shear strain vary with radial location? What is the equation for the local shear stress?

Chet
 
this is all the information given to me i have attached a picture to this post hopefully it can answer your questions
 

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Those are questions which you, Mechanical94, have to answer. After all, it is your problem to solve. In case you missed it when you read the Terms & Conditions, PF is not a homework service.
 
As SteamKing said, you already have enough information to answer all my questions. I already know the answers to these questions. Now, it's up to you.

Chet
 
i understand about this not being a homework service however this is my workings out and i got a diameter of 7mm, apparently my answer is not correct can anyone spot my error or can anyone help me to get the correct answer??
 

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  • picture023.jpg
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Last edited:
Mechanical94 said:
i understand about this not being a homework service however this is my workings out and i got a diameter of 7mm, apparently my answer is not correct can anyone spot my error or can anyone help me to get the correct answer??

In the right hand side of the equation in picture 1, the algebra is incorrect. It should be:

J=\frac{TL}{Gθ}

Chet
 

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