Pushover analysis of a metallic structure

[centondollar]

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.

The calculation is made in static and the snow loading is applied using linear forces.

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.

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?

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.

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.