**Introduction**

This verification example studies a simple fork supported beam member with IPE 360 section subjected to axial force and bending about the minor axis due to lateral, distributed force. The second order bending moment and the maximum axial compressive stress of the member is calculated by hand and by the Consteel software using the 7DOF beam finite elements.

(more…)**Introduction**

Our verification examples are created to be able to compare hand calculation results with Consteel anaysis results with using either 7DOF beam or shell finite elements. This example is a member of mono-symmetric I- section loaded with transverse concentrated load.

GATE## Introduction

Our verification examples are created to be able to compare hand calculation results with Consteel anaysis results with using either 7DOF beam or shell finite elements including Superbeam function. This example is a member in torsion loaded with concentrated torque.

Gate**Introduction of Consteel Superbeam**

In general, Consteel uses 7 DOF beam elements for finite element analysis of steel structures which are adequate for most everyday design situations. It is also capable of using shell elements in order to get more precise results in cases where beam finite elements are not sufficient enough. With the new Superbeam function it is now possible to examine structural parts with the accuracy of shell elements but with the ease of using a beam element concerning definition, modification, model handling, etc. In practice, it means that 7DOF beams can be switched to shell elements (and back) at any stage of the design process.

**Validation**

The validation program aims to verify the full mechanical behavior of the Superbeam switched to and analyzed as shell elements within a structural model composed of 7DOF beam elements. The validation of the analysis of the shell finite elements was done before and it is clear that in the case of correctly set boundary conditions the results are the same as the beam model provided that the local web buckling effect is avoided because it can not be modeled with beam-theory. Therefore the accuracy of the mechanical behavior of the Superbeam basically depends on two major factors:

**1. the automatic shell modeling and mesh of the Superbeam**- When transforming a beam model in the structural analysis to shell model, several automatic transformations are done with the model objects (loads, supports, connected elements etc.) in order to yield a consistent mechanical model.

**2. the mechanical consistency of the connections of Superbeam at the boundary to 7DOF nodes**- To satisfy the mechanical consistency at the connecting nodes the Superbeam uses automatically set constraint elements at both ends. They ensure the compatibility of the complete displacement field (translations, rotations, and warping) with the adjacent 7DOF beam finite element node or with the 7DOF point support.

The validation studies prove that the beam analysis model is mechanically equivalent to the shell analysis model within the Superbeam by comparing the results of the two models. It is shown that

- in the case of models where the local plate-like specific behavior is not relevant (thick plates in the cross-secions) the results are the same
- in the case of models where the local plate-like specific behavior is relevant (thin plates in the cross-secions) the results can be different only because of this plate-like behavior (local buckling, cross-section distortion) while the isolated beam-like behavior is the same

**Part 1**

In this first part of the validation, we examined simply supported beams of welded I-sections with several different profile geometries. The full length of the beams was changed to Superbeam shell and so the consistency of results of both the shell elements and the constraints could be analyzed.

### Structural models and analysis

In every case, the beam was first calculated with 7 DOF beam finite elements, after with Superbeam shell elements, and finally also as a full shell model with the same finite element sizes as the Superbeam shell. In full shell models, we applied rigid bodies along the edge of the web.

Linear buckling analysis was executed in order to compare the first buckling eigenvalues.

Our expectation was that the two kinds of shell models would produce very similar results which are by nature somewhat less favorable than the 7 DOF beam results, meaning that alfa critical values should be lower when using shell elements. To be able to compare the results related to global (lateral-torsional) buckling, the effect of local buckling of the web was to be avoided as much as possible so the examples were chosen accordingly.

### Geometry

### Loading

Two loading scenarios were considered on every section

Uniform moment:

Linear moment:

### Result tables

First global buckling eigenvalue – α_{crit}

Consteel version CS15.1095

**Conclusion**

As expected, the critical load parameters of beam models are always higher than the ones from the shell models. The difference between the results of the beam and shell models increases when the difference between the top and bottom flanges becomes more and more significant. It is because the straightness of the web starts to deviate (section distortion) which is already outside of beam theory, and so it is impossible to model with beam finite elements.

Despite the very different modeling techniques, the α_{crit} parameters of the two types of shell models are very similar – differences are within +/-3% which proves the applicability of the Suprerbeam as an alternative to the usual 7DOF beam finite elements for structural analysis. The use of Superbeam is recommended in cases where a more accurate analysis is desired by the designer.