Frame Analysis - Temperature Load

[Chris Lee]

I set up a 2D analysis to study the effect of thermal load on 2D frame.

Case 1 - with short column and 10 degree of uniform temperature
Case 2 - with long column and 10 degree of uniform temperature
My question is, why for case 1 horizontal reaction at point B is larger than point A?

I did another frame with 4 spans, the same temperature load.
The horizontal reaction at point B is smaller than point A in both short and long-column cases.

 

[rb1957]

the 4 bay is what I'd've expected (higher loads further from the CL)

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[Chris Lee]

In fact, when the temperature load increase to 250 degrees. Reaction at point B is larger than at point A too. I can't figure out the theory behind it.

 

[GeorgeTheCivilEngineer]

Can you show the deflected shapes?

 

[Chris Lee]

Sure. Below are deflection shape of case 1 and case 2

 

[SWComposites]

You have pinned connections at the base of the columns, right?
Reactions are probably a function of the relative stiffness of the frame members. Have you looked at the moment and forces in the frame members?

 

[rb1957]

why would the elongation (of the horizontal beam) be longer with short legs than long ones ?
I don't think it is .... just I don't think the two views use the same scale.

The frame legs are fixed at the top (no problem, just an observation) so "messing" with the beam deflections for the short legs.

If the extreme ends have the higher deflection (as you'd expect) why does the load peak at the inner support ?
Maybe it is relative stiffness ... something easy to check ... change I or E up/down by a factor of 100 (1000?).

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[SWComposites]

I suspect the deflection plots are scaled values, and not actual deflections.

The reaction at B is higher because the connection at the top of column B is stiffer than at the top of column A - two horizontal members to bend vs one.

 

[rb1957]

We should see that in the BM diagram of the beam.

it would be interesting to see if reversing the leg fixity (fix the base, pin at the beam) changes things.

it would be interesting to see the affect of varying the spans (so 1-2 is twice 2-3).

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[Newmark918]

The shorter the column, the higher the shear. Imagine infinitely short columns, and your shear is going to approach some form of PL/AE (A, E, and L for the beam). Stiffness attracts load is another way to think of this problem. Also, think of the curvature (induces bending and shear in this case) - your short columns move out the same amount so their curvature at the fixed joints will be higher.

Maybe. Idk.

 

[JStephen]

The end columns only have a beam framing in from one side, so that joint is more flexible than the one at the second column in, where it has beams framing in from each side.
So that's my interpretation for the difference.

On a side note- I've run into issues in the past, what assumptions ought to be made about the foundation/ground in that case? To what extent can temperature variations in the frame be applied to the foundation/ground also?