# Solving Torsion Problems: Finding Torque & Rotation When Plastic

• morry
In summary, the question is asking for the torque and angular rotation that will be produced if the bar is deformed until it is fully plastic. They are given the yield stress and elastic modulus for this case, and the answer is that the torque and angular rotation are the same.
morry
Hi guys,

Just a quick question. I have been attempting some problems to do with torsion.

Most are pretty standard, you know, find the torque, angular rotation etc.

However I am stuck on this one. I have calculated the torque and rotation for a shaft that's at its proportional limit. But the next part asks me to find the same things, but this time the beam is fully plastic. How can I do this?? I have no idea.

Thanks guys.

Morry, it is most efficient to post the exact question.

Ok here it is:

What torque and angular rotation are produced if the bar is deformed until it is fully plastic? Assume perfectly elasto-plastic material behaviour.

I am given the yield stress and elastic modulus. Dont worry about giving me specific answers, just a quick understanding is all I am after.

Cheers.

Last edited:
At first thought, they may be asking you to use the ultimate yield stress as your failure criteria in stead of the yield stress. I am not quite sure what "perfectly elasto-plastic material behaviour" really means.

The trouble is, they don't give us anymore information about the Uts. I think its a weird question. Its good to see I am not the only one who thinks this way.

Are you familiar with analyses using rigid or ideal plastic plasticity descriptions? The first thing coming to mind in a question such as this one is that they'd want you to do a limit load / plastic collapse analysis. Usage of solely yield strength in this case implies probably that hardening in all forms is neglected.

Perennial, I suspect this is much simpler still, and yes, strain hardening must be neglected.

The stress-strain curve, I believe, looks as shown in the attachment. This is what I recall is referred to as "perfectly elastoplastic".

That said, I believe there is insufficient data to answer the second question : the angular rotation at failure. Clearly, the torque will be the same as in the elastic case.

#### Attachments

• elastoplast.JPG
5 KB · Views: 410
yeah, that looks familiar ... if I was to answer the question would do a collapse analysis with the material model ... which can be done with "ease" for a simple geometry such as a shaft - however, can be that they're after something much simpler (or complex) ... depending on the "degree" of answer they're after ...

Thanks for the replies guys. So you think that the ultimate tensile stress will be the same as the yield stress?

Its only for 2nd year solid mechanics so the answer shouldn't be too complicated. We didnt cover torsion in great detail, only the basics.

Thanks again.

In this case the UTS is the same as YS ... since you don't have info on the former (or course noting the obvious about the relationships of yield properties in shear versus tension). In these sorts of plasticity simplifications you often see people use either YS, UTS or mean of them ... and since you only got one it simplifies.

Well, i finally sorted it out. Turns out for shafts, that when they go beyond their proportional limit, the twisting moment turns out to be (4/3)*Ty, where Ty is the max moment at proportional limit.

So it was pretty simple. And of course, once you have this new torque, finding the angular rotation is easy.

Thanks for the help guys!

## 1. What is torsion and why is it important to solve torsion problems?

Torsion is the twisting force that occurs when a material is subjected to a torque. It is important to solve torsion problems because it can cause structural failure or deformation in a material, which can have serious consequences in various industries such as construction, engineering, and manufacturing.

## 2. How do you calculate torque in a torsion problem?

To calculate torque in a torsion problem, you can use the formula T = Fr, where T is the torque, F is the applied force, and r is the perpendicular distance between the applied force and the axis of rotation. This formula can be applied to both linear and rotational motion.

## 3. What is the relationship between torque and rotation in a torsion problem?

The relationship between torque and rotation in a torsion problem is directly proportional. This means that as the torque increases, the rotation also increases. Similarly, if the torque decreases, the rotation will also decrease. This relationship is described by the equation τ = kθ, where τ is the torque, θ is the rotation, and k is the torsional stiffness constant of the material.

## 4. How do you determine the amount of plastic deformation in a torsion problem?

The amount of plastic deformation in a torsion problem can be determined by finding the maximum shear stress (τmax) in the material. If the shear stress exceeds the yield strength of the material, then plastic deformation occurs. The amount of plastic deformation can be calculated using the formula δ = Lθ, where δ is the plastic deformation, L is the length of the material, and θ is the rotation.

## 5. What are some common methods used to solve torsion problems?

Some common methods used to solve torsion problems include the method of sections, Mohr's circle, and the principle of superposition. These methods involve breaking down the problem into smaller parts and applying the laws of mechanics and equations to solve for unknown variables such as torque, rotation, and deformation. Finite element analysis is also commonly used to solve more complex torsion problems.

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