# Effect of tension on torsional stiffness

1. Oct 12, 2011

### Ma77h3w

So say I have a steel pipe under a torque and an axial load.
I want to know whether the axial load has any effect on the twist due to torque.

Have one calculation which (perhaps falsely) assumes the pipe is made of lots of axially running "wires" and calculates the torque due to this axial force on slightly twisted "wires". See the attachment.

However the simple Ansys model I've done shows absolutely no effect on torsional stiffness when an axial load is applied.

Thoughts?

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2. Oct 12, 2011

### AlephZero

If you run a linear (small displacement) FE model on a straight pipe, there will be no coupling between axial load and torsional stiffness, because the "twisted wire" effect is a second-order effect and is therefore left out of the model by definition of what "linear" means.

I'm not an Ansys user so I dont know what terminology it uses, but try running a "geometric nonlinear" or "large displacement, small strain" analysis. (Ignore material nonlinearity options like plasticity.)

Start with torque on its own, and increase the load till a plot of torque against twist in the pipe is not a straight line. Then try superimposing some axial loads - both tension and compression. (Note, the model will probably "blow up" if the applied loads would make the pipe buckle.)

3. Oct 13, 2011

### Ma77h3w

I'm only interested in loads where the material is performing in it's linear stress/strain region. I suppose this is a different thing than the FEA linear (small displacement) model?

Typically the shaft will twist a couple of degrees given a certain torque. If an axial load is applied in Ansys I only see a tiny change of twist for huge values of axial load, 100x greater than my hand calc. Perhaps the hand calculation is wrong. I'm using Ansys Workbench (we dont seem to have Classic) and there are a few non-linear options:- Force Convergence, Moment Convergence, Displacement Convergence, Rotation Convergence and Line Search. They can be switched on and have a Tolerance value in % etc.

The values my hand calc show a reduction in twist of 0.069% for an axial load of 220,000N on a shaft with 30000Nm Torque.
(OD 100, ID 70, Length 400mm, twist 1.16 deg)

Perhaps Ansys is correct and there is very little effect of tension on torsional stiffness, and the hand calc which assumes a pipe made of "wires" is not a good model?

4. Oct 13, 2011

### AlephZero

They are two different ideas. Linear material behavour means stress is proportional to strain, however big the stresses and strains are. In other words, the material never yields. A small displacement model assumes that the strains in the structure can be considered as linearized changes in the shape of the structure.

The "next level" of complexity (often called geometric nonlinearity) is to consider the strains are always small, but the displacements may not be. In your torsion situation, your shaft twists a couple of degrees for a certain torque. If the shaft was 100 times as long, it would twist 200 degrees (more than half a revolution) for the same torque, but the shear stress and strain would still be the same.

That is the type of situation where your ideas about "wires" begin to be important, because the straight "wire" is now wrapped into a helix when the structure deforms. If there is an axial stress in the pipe, you can think about what will happen in two different (but equivalent) ways. One way is to imagine that the "wire" is being stretched as its length increases, and therefore the tension will increase. The other way is to imagine that the "wire" will actually try to stay the same length as it wraps into a helix, therefore the length of the pipe must get shorter to compensate, and therefore work is done agaisnt the axial tension force applied to the pipe as the ends of the pipe are pulled closer together. Both ways of thinking lead to the same conclusion, that the torsional stiffness is increased in a nonlinear fashion. (And if you do the math correctly, they both lead to the same "formulas".)

This line of thinking also says that the ends of the pipe will not remain plane, because the amount of stretch in the "wires" depends on their distance from the center of the pipe. For a solid circular rod, the ends will bulge outwards in the center as you twist it.

For a small amount of twist (like 2 degrees), the axial force does not affect the torsional stiffness much, but as the twist increases the torsional stiffness will also increase if the pipe is in axial tension, or decrease if it is in axial compression.

NB to be sure your model can include this sort of effect, make a solid model of the pipe with 3D brick or tetrahedron elements. Don't use axisymmetric or beam elements, or special "pipework modelling" elements, because they might not include these effects in the element formulation.