# Plastic steel bar

Content

## Concept

The plastic analysis of steel bars is available for any steel cross section. The material model of steel beam / column elements is linear elastic - perfectly plastic regarding the sigma normal stresses for both tension and compression, but the relationship between shear stress and shear strain remains linear elastic. The shear stresses in plasticity are excluded in Timoshenko beam theory regarding the limitation that a cross-section only has one equivalent shear strain value in finite element formulation.

## Theoretical background

The detailed theoretical background and the verification examples of plastic steel bar analysis can be found here: Plastic steel bar analysis

## Input

The plasticity of steel bars can be set individually for different limit states in the Beam / Column > Define > Default settings > General tab.

Due to the newly formulated stiffness matrix for plastic bars (see theoretical background), stiffness modifiers have no effect on the final results when the plastic behavior is set on a steel beam or column.

The plastic beam / column calculation is also available for variable cross-sections, but in the background of the finite element method, a bar with a variable cross-section is built-up by several sections with constant cross-section following the shape of the variable geometry.

## Analysis

In Calculations dialog (Analysis tab) select Load combinations then in Setup by load combinations dialog select for which load combination(s) the plastic analysis should be run.

Hints:

The finite element division number of the plastic bars plays an important role in the accuracy of the results. Based on our tests, the division number should be at least 20 for Fine elements and at least 40 for Standard elements. Apply the Minimum division number command (Finite elements tab) for the selected bars to be checked as plastic.

Convergence analysis is strongly recommended due to the nonlinearity of the calculation: the mesh size of the finite element should be reduced (e.g. with increasing number of divisions) and the effect on the results (e.g. displacements and internal forces) should be checked. It is used as the final division number when the difference between two adjacent calculations is quite small (about 5%).

## Results

Following results of the plastic beam/column analysis are available

• Translational displacement (with detailed results)
• Rotational displacement (with detailed results)
• Bar internal forces (with detailed results)
• Bar stresses (with detailed results)
• Plastic condition
• First unstable state displacement