**Introduction**

This verification example studies a simple fork supported beam member with welded section equivalent to IPE360 (flanges: 170-12,7; web: 347-8) subjected to biaxial bending due to concentrated end moments and compression due to axial force. Second order deformations of the middle cross-section of the member are calculated by hand and by the ConSteel software using both 7DOF beam and shell finite elements and Superbeam function. In addition to the verification, the difference between modelling with 6DOF and 7DOF elements is demonstrated.

**Geometry**

**Calculation by hand**

The first order and the simple amplified (P-δ) deformations can be analitically calculated by the well known formulas. The calculation of the second order deformations considering true, three-dimensional behaviour of the beam is however so complicated that there are only approximate analitical formulas available for hand calculation. The formula below can be found in Chen, W. and Atsuta, T.: Theory of Beam-Columns, Vol. 2: Space behavior and design, McGRAW-HILL 1977, p. 192

**Computation by Consteel**

Version nr: Consteel 15 build 1722

**First order**

**Second order – 6DOF beam element**

The second order deformation of the member which was computed by the ConSteel software. It is visible that there is no torsion, only increments of the lateral displacements due to P-δ effect:

**Second order – 7DOF beam element**

The second order deformation of the member which was computed by the ConSteel software using the 7DOF beam finite element model (n=16). It is visible that there is torsion and further increment in the lateral displacement (Dy):

**Second order – Shell finite element**

The second order deformation of the member which was computed by the ConSteel software using the shell finite element model (δ=25mm):

**Second order – Superbeam**

The second order deformation of the member which was computed by the ConSteel software using the Superbeam model (δ=25mm):

## Introduction

As it is important to have a clear overview of the structural model, the visualization of the analysis results is also essential when it comes to effective design process. From Consteel 15 we use an advanced method for deformation representation which makes it smooth and realistic.

## Description

Civil engineering software in general use the traditional beam-type deformation representation where the section is shown on the deformation of the reference line. There are some consequences of this representation mode that can be disturbing for the users. The best example is an eccentric support, where the deformed shape is visualized as if the supported point would’ve moved. The reference line indeed moved but the supported point not – the representation can not show that.

With Consteel’s advanced deformation representation not only the position of the reference line points are calculated and the section is only shown automatically, but the positions of all the decorated points of the section are calculated during a post-process and so it is possible to represent the real deformations. As a consequence it is also visible that the supported points stay in position.

Civil engineering software in general use the traditional beam-type deformation representation where the section is shown on the deformation of the reference line. In Consteel 15 we use an advanced method for deformation representation which makes it smooth and realistic. The analysis results are the same, but with the improved visualisation the real 3D behavior of the structure can be better seen.

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