## Simple Three Sided Box - Trying to Understand Deformed Shape

## Simple Three Sided Box - Trying to Understand Deformed Shape

(OP)

So, I was trying to build a simple model of a three sided box in Etabs (with a membrane element, no rigid diaphragm assumption) and was expecting get a deformed shape like the following, (expected mostly shear deformation of the membrane element):

When I run my analysis, I get the following deformed shape:

Applied loading looks like the following:

A few notes:

The other interesting thing is that the axial load in the chords and collectors exactly matches what I would expect (red = compression, yellow = tension):

Questions:

Seems like the shear stresses in my diaphragm build up as you move page left (like you would typically calculate)

Only thing that maybe wrong with traditional assumptions is there seems to be some non-neglible axial stresses in my membrane element (see image showing compressive stress build up on front edge of diaphragm).

I've played with bringing down the axial stiffness but it makes my deformed shape look very odd.

Thoughts appreciated!

When I run my analysis, I get the following deformed shape:

Applied loading looks like the following:

A few notes:

- I am unsure why the free (right) edge of the diaphragm does not deflect in a smily face upward manner

- Floor is modeled as a membrane element

- Chords and Collectors are modeled as steel beams

- Self weight is turned off, only load applied is the lateral load shown above

The other interesting thing is that the axial load in the chords and collectors exactly matches what I would expect (red = compression, yellow = tension):

Questions:

- Do you agree with my anticipated deformed shape?

- Any ideas on why Etabs shows the deformed shape that it does? Maybe something in our hand methods for diaphragms that does not match what Etabs is doing?

Seems like the shear stresses in my diaphragm build up as you move page left (like you would typically calculate)

Only thing that maybe wrong with traditional assumptions is there seems to be some non-neglible axial stresses in my membrane element (see image showing compressive stress build up on front edge of diaphragm).

I've played with bringing down the axial stiffness but it makes my deformed shape look very odd.

Thoughts appreciated!

S&T

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

Open Source Structural Applications: https://github.com/buddyd16/Structural-Engineering

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

Releasing the shear in the out of plane direction at the top yields much the same deformed shape:

You can also see no reactions in the out of plane direction at the base of the wall:

I am having a hard time understanding why semi rigid action would create "reverse" curvature in my chords though. Mind explaining?

S&T

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

Still not sure if my intuition is correct on the deformed shape.

S&T

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

Mike McCann, PE, SE (WA)

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

My goal here is to try to understand why the model is behaving the way it is and potentially get it to mimic/match our assumed diaphragm deformed shape.

S&T

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

Try using super position. Apply a shear load at the main shear wall, see what it's deflected shape looks like (probably closer to what you originally assumed). Then apply equal and opposite shears to the other walls and see what that deflection looks like. Add the two loads together and then see what this combined deflection is. It should be pretty close to your original eccentric shear load.

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

Everything you mentioned in the first paragraph makes perfect sense... I guess my main question is the odd deformed shape of the diaphragm (cannot understand deflected shape at all).

I explored your super position idea:

Shear Load:

Shear Deflection:

Torsional Load:

Torsional Deflection:

Combined Deflection (shear and torsional case):

Again for reference (the original deflected shape with eccentrically applied load).

The combined superposition method you mentioned produces results more in line with what I would have anticipated (see smile face up at free edge).

The eccentric load method I orginally presented also results in more deflection which I would expect (both images have the same scale factor for deflected shape).

Still at a loss... might try this in another program and see if I get similar results to either of these models.

S&T

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

S&T

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

Open Source Structural Applications: https://github.com/buddyd16/Structural-Engineering

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

steel beam collectors are pinned ended members.

Celt, that graph is for vertical deflection, you can see the deflected shape of the diaphragm almost looks like a moment frame beam. Note that I have turned off out of plane stiffness in both models so I assume the deflection I am seeing is just compatibility deflection.

You bring up a good idea though, maybe axial stresses in the membrane element?

The image below is the axial stress from the etabs model (I do not think this is available to me in RAM SS).

This would explain the deformed shape I guess... not sure if it is reality though?

S&T

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

So I have added a moment at about mid cantilever to produce a 0 moment reaction at the fixed end, so left support only has a vertical reaction and the moment represents the couple formed by the walls.

Green line is the moment diagram

Purple line is the cross section slope, in the larger model that point moment becomes spread out so the peak would be more gradual

Grey line is the

centerlinedeflectionSame thing with a series of point moments to smooth out the slope:

Open Source Structural Applications: https://github.com/buddyd16/Structural-Engineering

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

Makes perfect sense that the end would curve back now.

These counter intuitive (at least for me) things are always a little fascinating to explore.

S&T

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

Open Source Structural Applications: https://github.com/buddyd16/Structural-Engineering

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

If you're still not comfortable, try making the semi-rigid diaphragm extremely rigid. Does that deflected shape of the rigid diaphragm make sense to you. If not, then there is something really weird going on.

If the rigid example makes sense, then try softening it a bit until you start to see the diaphragm deform a little. Does that extra diaphragm deformation make some sense? If you soften the diaphragm more and more, then it should lead to a deflection like you originally saw.

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

A three sided diaphragm is not a cantilever, but rather a simple span beam cut in half. So the deflected shape looks like the deflected shape of half of a simple span beam.

DaveAtkins

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

Thought a lot about it over weekend haha... things like this just eat at me. I am still not settled on my understanding of the deformed shape, may just need to accept it as the way it is.

Counter to your line of thinking (just throwing it out there, not sure how valid):

S&T

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

True, but the "moment" is contained in the two perpendicular shear walls, so I still think this acts like half of a simple span beam.

DaveAtkins

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

Open Source Structural Applications: https://github.com/buddyd16/Structural-Engineering

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

Also, let me know if you think the deflected shape changes if I move the left-right shearwalls all to one side.

I have the images, but don't want to taint the guesses

S&T

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

I am making an assumption this is an outdoor structure subject to wind loads. If not, if the loads on the "roof" are interior from a static mechanical load, the following doesn't apply.

Now: change the wind direction so it from the left side of the picture (into the sheer wall.) You should see two "new" shear walls, one bending wall flexing towards the right. The "roof" will twist more uniformly, but will have an oscillating (flapping) action as turbulence pushes up and pushes down irregularly (in the real world)This flappingf will be exaggerated by the curve of the roof in static flexing: So the curve amplifies the wind force up as it hits the static "flex" you see now, then down as the cantilever roof edge bends and sheds that vortex.

When the wind force is from the right, the whole 3-wall shape traps the wind and amplifies the right-side horizontal force (and all "static" motions you now see in the FEA model.) The deflections of all three walls to the left will be greater. The corners deflection of the roof will be greater.

When the flapping starts again, the corners of the roof will move more than in the "wind from left side" case.

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

That.

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

Seriously, though, that is a nice explanation of what is happening.

DaveAtkins

## RE: Simple Three Sided Box - Trying to Understand Deformed Shape

Deformed shape exactly match his assumption with the assigned point load at the end

Again truly appreciative of all that I have learned on this site.

I should free up tonight, I will be able to post the results of shifting the shearwalls all the way to one side, more counter intuitive stuff for me at least.

S&T