Beam Deflection due to temperature

[5234185]

I am a Geotechnical Engineer and need some guidance.
A 40 foot long steel beam (415) is fixed at one end and other end is simply supported. Will there be any deflection (vertical) in the beam due to change in temperature. The beam is allowed to move at one end. I have a dial gauge with precision of 1000th of an inch.
I think beam will deflect under its own weight. How about deflection with temperature. Will there be any deflection I should be concern about?

 

[dik]

If it is unrestrained, then any deflection due to normal temperatures will be minimal.

If subjected to higher temperatures, then the Young's modulus will diminish and the yield strength will also be reduced and deflection can increase substantially. By higher temperatures, I thinking in the magnitude of several hundred degrees.

Dik

 

[rb1957]

for normal changes in temp, i won't think so; 'cause the beam is free to extend axially. now if you heat it up so much that you affect E, then you'll change either the bending stiffness and it'll change the deflections (due to the weight of the beam).

 

[SteelPE]

What is the temperature of the beam?

Under normal conditions you shouldn't get any deflection due to a change in temperature... However, the beam length will change... but as long as it is free to move at one end it should not deflect except under it's own weight.

Now if the beam is at an extremely high temperature then you will get a decrease in the material properties, which would have an effect on your self-weight deflection.

 

[Lion06]

If one end really can move laterally, then you shouldn't have additional deflection due to normal temperature changes. If it can't slide, however, then you will have additional deflection, even due to normal temperature changes.

 

[InDepth]

Based on your precision there could be effects. Where are you located and what is the expected temperature differential? Are all sides exposed to the sun or environment? Is the beam exposed to wind? Is any portion of it shaded?

 

[5234185]

Thank You all for your prompt responses.

What if the temperature difference be about 25 degrees over a period of 24 hours. Also, if top flange of W10 by 40 steel beam is exposed to sun and bottom flange not, is it going to make any difference. Please advise

 

[Wrenchbender]

A uniform temperature fluctuation of 25° F, independent of time, should not appreciable affect the modulus (and stiffness) of the beam, but you may want to run some numbers. E = 29.5 Msi and 28.8 Msi, at 70° F and 200° F, respectively.
Reference

http://www.engineeringtoolbox.com/young-modulus-d_773.html

On the other hand, I think a vertical temperature gradient should make the beam want to bow, concave-cold. I get a rude & crude change in arc length of a fraction of an inch, top to bottom, unrestrained, 100-deg delta. You can model it, superimposing its own weight. Coef of thermal expansion, like E, is a function of temperature, but you can treat it as a constant; for steel its pretty flat in this range.

 

[dik]

Bestwench... thanks for the added info... I've been involved in a few structure fires and the beams become spaghetti that's why the comment about heat <G>

Dik

 

[InDepth]

5234185, can you tell us what is your application and reason for a 40 ft beam. is the 1/1000th measurement super critical or is there a different level of accuracy you are looking for....1/16 inch level or 1/4 inch level, etc...

 

[ishvaaag]

Self equilibrated thermal stresses for a differential temperature across the section appear, and cause both bending on both axis (if the temperature differential is not applied symmetrically) and stresses. I did a Mathcad worksheet some years ago on this and is still freely available in the Collaboratory for Mathcad 2000. I followed a paper, doing it.

On the papers I was reading by then and at bridges (don't know the scale of such bridges) I think to remember that a spanish civil engineer stated that these stresses meant in practical terms around 15 to 20 MPa of actual top values of additional stresses appearing. For a proper analysis of bridges, these self equilibrated thermal stresses should be included as a thermal hypothesis for combinations.

 

[rb1957]

IMHO, if you heat one flange then it'll strain and the unheated one won't and the beam will deflect; actually it should deflect less (as the thermal deflection opposes the deflection due to weight. the OP left us all, i think, considering thermal soak. now, as other posters note, the change will be roughly 1/4 of a gnat ...

 

[msquared48]

I think the temperature will heve to get in the range of 800 to 1000 degrees Farenheight before significant additional vertical deflection is seen.

Mike McCann
MMC Engineering

 

[csd72]

rb1957

That "a gnats ..." thank you very much.

It is a measurement only slightly more primative than feet and inches

I agree with the thermal gradient causing bending.

 

[rb1957]

there's another sacle for samll measurments; i forget the name for now, but there's (so i'm told) a black one and a white one too, and apparently you need to be a coal miner ...

 

[IRstuff]

5234185,

You are asking a VERY general question, and the responses you've gotten reflect the lack of information about your concerns. Would a 1 micron deflection cause a problem? Would 10, or 100? Until you can clearly define your area of concern, you're going to get a vast range in answers.


TTFN

FAQ731-376

 

[BAretired]

If the beam is fixed at one end and roller supported at the other, it is indeterminate to the first degree. Heating the top flange will cause deflection throughout the beam, moment at the fixed end and an upward reaction at the roller.

BA

 

[Ron]

It all depends on the restraint conditions and the magnitude of the self weight. If you have no self-weight and the ends are unrestrained, if you apply to heat to the top flange it will cause cambering. That's generally how camber is put into beams in the shop. If you have self-weight, it might or might not deflect depending on the restraint. If restrained, yes you're like to get a small deflection, likely insignificant. If not restrained, you simply get an increase in length of the beam. As Mike said, you will have to get very high temperatures in a restrained condition to get appreciable deflection with only self-weight.

 

[msquared48]

Sorry, but that was FARENHEIT. Never could spell that correctly.

Mike McCann
MMC Engineering

 

[hokie66]

One more h. Fahrenheit. Now you've got it.