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# Modelling thermal expansion

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## Modelling thermal expansion

(OP)
I've modelled a stainless 12 ga SS304 duct for a kiln where the temperature goes between ambient room and 120 degrees C. Currently, the duct is proposed to be built with fixed ends. In my RISA model, I end up with 44 kips/ft force along the perimeter of the ends of the duct. The numbers correspond with my hand calculations.

The thing is, this intuitively doesn't seem right. For this 8' by 8' duct we're talking about 1400 kips of force acting at the ends. I've noticed that the RISA model shows no deflection in the steel. Wouldn't the plate deflect/buckle under the loads?

Any help would be greatly appreciated.

Mike

### RE: Modelling thermal expansion

RISA 3D only makes elastic analyses. Hence anything above the proportional limit is not going to be well analyzed nor represented. This is not to say the tool can't be used to other purposes but it must be within the understandign of what at hand.

Now the question is, if the material was elastic and of your properties the duct would sustain such big forces. Big forces appear quite typically with full restraint. Now you need to see what happens... is the pipe yielding? Does overall bend buckling develop?

In any case the solution to these full restraint problems are expansion joints, many times C or S shapes formed in the duct, or other proper devices that allow almost unrestrained expansion.

### RE: Modelling thermal expansion

Forces due to restrained thermal expansion/contraction are usually very large - 44kips/ft and 1400kips is a not insignificant 642kN/m and 6230kN in my language!

It's impractical and uneconomic to restrain such forces.  Consequently expansion joints are a ubiquitous feature in all the ducting I've ever seen.

What is your Client's reason for requiring that the ducting be fixed at each end?

### RE: Modelling thermal expansion

(OP)

I agree about the expansion joint. It was my intuition from the start. But it's one of those "we've always done it that way" things.

I'm still curious as to whether or not steel would buckle. I'm exceeding the yield stress in the model, but not getting any deflection. Is this due to the elastic analysis ishvaaag is referring to, or is this realistice to expect in real life?

Cheers,

MIke

### RE: Modelling thermal expansion

It is a device of the way and tool of analysis you are using. Even by the mere fact of the section being overall yielded you know that the pipe is failed.

You can use even a elastic analysis program such RISA to ascertain some of the effects of anelasticity, bout to this you need to model geometrical anelasticity and material anelasticity. The first you more easily introduce in your model by assuming initial imperfections, both maybe for the overall member and out of circularity for the pipe. Once you have such more "realistic" model in place, and say modelled through plates, you will asign to every plate a modulus of elasticity reduced as pertain to the axial stress present in the plate, say by a CRC formulation.

This thing you do by iterations and enabling P-Delta Analysis in RISA 3D you will see something closer to reality than what you presently have.

Even with a nonlinear program you may end with a straight shape if you do not model the initial imperfections, directly or through equivalent called notional loads. It will assume the structure will show the compression concomitant with the restrained expansion, and then see the pipe yielded for further increases of temperature. The more significant thing that the nonlinear program will do better than RISA 3D (other than having proper algorithms for the more complex analyses required for geometrical nonlinearity) is to hold a proper material model, that is, the nonlinear stress-strain law for the material will be built-in in the program.

Normally this woul

### RE: Modelling thermal expansion

(OP)
Thanks Ishavaaag,

I've re-run the model with a 0.05 ft offset for the middle of my member. Now when I run it with the thermal load, I get a deflection of over 1 inch. Your help was invaluable. I'll definitely have to learn how to use a stronger finite element program soon.

Cheers,
Mike

### RE: Modelling thermal expansion

Just in order to complete what said, the "notional" modulus of Young to use to model material anelasticity when the concurrent axial stress becomes the yield strength is 0.

Hence you wouldn't see a lateral deflection of over 1", but to the purpose of calculation infinite... or just very big, as you were suspecting when placing your initial question.

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