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# Pushover analysis of a metallic structure

## Pushover analysis of a metallic structure

(OP)
I’m modeling a metallic structure whose roof collapsed under snow weight. I modeled this structure using beam elements and I specify that the roof elements are bolted together (no ball joint).
In small displacements, the code diverges while I have not reached the steel ultimate strength; I get the following error message: “The strain increment is so large that the program will not attempt the plasticity calculation at 171 points. The plasticity/creep/connector friction algorithm did not converge at 55 points.” I tried to increase the time period, to decrease the initial and minimum increment sizes, to increase AI or to reduce the size of the mesh… Nothing works! And in big displacements, the code diverges even earlier! As a result, I can’t perform risk analysis integrating imperfections.
I would appreciate a recommendation on how to improve convergence in small and big displacements?

### RE: Pushover analysis of a metallic structure

Sounds like you need larger Iy.
What's the frame look like?

Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

### RE: Pushover analysis of a metallic structure

what code are you using?
what material properties are you using? are they minimum properties, or realistic typical properties?
perhaps the joints in the model are more flexible than the real structure.(?)
if the roof collapsed, why do you expect your model to converge?

### RE: Pushover analysis of a metallic structure

(OP)
I'm using Abaqus.
I'm using an elasto-plastic law with next properties : E=210MPa,fy=294MPa,fu=432MPa and epseu=0.2.
I don’t necessarily expect my model to converge but the error message is not clear. I can’t know if the code is diverging because the structure collapses or because there’s a numerical convergence problem.

### RE: Pushover analysis of a metallic structure

Depth of the trusses looks too small.
Some dimensions would help.

Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

### RE: Pushover analysis of a metallic structure

If you lessen the loads will it run?
Software error messages that are 100% correct but totally useless are a fact of life.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, consulting work welcomed

### RE: Pushover analysis of a metallic structure

(OP)
I have a first step with only dead load that goes well.
The building is 54 m long, 45 m wide and 8.9 m high. You will find attached a description of one single roof frame element; the outside and inside diameters of the tubes are 48.30 mm and 42.5 mm respectively.

### RE: Pushover analysis of a metallic structure

Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

### RE: Pushover analysis of a metallic structure

The forces in the top and bottom chords will be very high.
I suspect they are failing with full load.

What loads are you using and
What is the material's yield strength?

1.9m depth of truss is probably half of what you will need to control deflection.

Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

### RE: Pushover analysis of a metallic structure

(OP)
I'm using line loads and the material's strength is 294 MPa.

### RE: Pushover analysis of a metallic structure

N/m^2 ?

Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

### RE: Pushover analysis of a metallic structure

Just did a very quick check of forces generated at midspan assuming one way action.
Using a very minimal total load of 500 N/m2 (10 psf), trusses fail generating 2 x Yield Stress.
If the roof acted as a rigid plate, lets say you can carry load in both directions, roughly dividing the stress by 2. So that system most likely fails with about a 500 N/m2 load.

Hope it doesn't snow. Its barely carrying its own weight.

Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

### RE: Pushover analysis of a metallic structure

(OP)
I'm using an elasto-plastic load with an ultimate strength equal to 432 MPa.

### RE: Pushover analysis of a metallic structure

Won't work.

Too much stress in the fibres.

Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

### RE: Pushover analysis of a metallic structure

N/m^2 is the definition of Pascal, not MPa. 294 MPa is about 42 ksi.

### RE: Pushover analysis of a metallic structure

Engineering Toolbox uses N/m2 for roof loads.
I use Pa for fluid pressure and stress.

The 500 N/m2 roof load produces 42ksi member stress.

Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

### RE: Pushover analysis of a metallic structure

I have never used 'Engineering Toolbox', but those of us who deal everyday in SI for structural purposes use kN loads, kPa distributed load, kN/m line loading, MPa stress. We rarely use N or Pa alone, but instead use the derived units. That's just the way we think.

### RE: Pushover analysis of a metallic structure

Right. But I think you calculate kM/m line load by multiplying N/m2 x C/C spacing and dividing by 1000? In the States its a floor or snow load in, psf, x C/C ft = lbs_force/ft /1000 for Kips_lineal l_ft.

Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

### RE: Pushover analysis of a metallic structure

#### Quote (Ossau56)

I modeled this structure using beam elements and I specify that the roof elements are bolted together (no ball joint).
First off, the figure shows a truss structure. Even if they are bolted (they are usually connected by welds), they will probably not develop rotational fixity and therefore act more like pin-jointed members than rigid-jointed members.

#### Quote (Ossau56)

What do you mean by "using linear forces"? Are you referring to a force-controlled analysis? Are you applying the load as a force in several steps or in one step?
Usually, one must apply the load as a displacement (incrementally or in one step) or use arc length method to model collapse.

#### Quote (Ossau56)

I tried to increase the time period, to decrease the initial and minimum increment sizes, to increase AI or to reduce the size of the mesh… Nothing works!
There is no "time" in a static analysis involving only material or geometric non-linearity. Are you referring to some type of numerical damping parameter?

#### Quote (Ossau56)

I would appreciate a recommendation on how to improve convergence in small and big displacements?
You may start by reading the ABAQUS documentation explaining the non-linear solvers it offers and then choose a solver suitable for your problem. ABAQUS should have no issues solving a beam problem with elasto-plastic material behavior and geometric non-linearity.

#### Quote (Ossau56)

I'm using an elasto-plastic law with next properties : E=210MPa,fy=294MPa,fu=432MPa and epseu=0.2.
I don’t necessarily expect my model to converge but the error message is not clear. I can’t know if the code is diverging because the structure collapses or because there’s a numerical convergence problem.
If you use a proper solver, the collapse will not cause issues with numerical convergence, and the full load-displacement diagram will be produced.

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