**Did you know that you could use Consteel to perform dual analysis with 7DOF beam and/or shell elements?**

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**Did you know that you could use Consteel to** **calculate effective cross-section properties for Class 4 sections?**

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**Introduction**

This verification example studies a simple fork supported beam member with welded section (flanges: 200-12 and 100-12; web: 400-8) subjected to bending about major axis. Constant bending moment due to concentrated end moments and triangular moment distribution from concentrated transverse force is examined for both orientations of the I-section. Critical moment and force of the member is calculated by hand and by the Consteel software using both 7 DOF beam finite element model and Superbeam function.

**Geometry**

**Normal orientation – wide flange in compression**

Constant bending moment distribution

Triangular bending moment distribution – load on upper flange

Triangular bending moment distribution – load on bottom flange

**Reverse orientation – narrow flange in compression**

Constant bending moment distribution

Triangular bending moment distribution – load on upper flange

Triangular bending moment distribution – load on bottom flange

**Calculation by hand**

Factors to be used for analitical approximation formulae of elastic critical moment are taken from *G. Sedlacek, J. Naumes: Excerpt from the Background Document to EN 1993-1-1 Flexural buckling and lateral buckling on a common basis: Stability assessments according to Eurocode 3 CEN / TC250 / SC3 / N1639E – rev2*

**Normal orientation – wide flange in compression**

Constant bending moment distribution

**Reverse orientation – narrow flange in compression**

**Computation by Consteel**

Version nr: Consteel 15 build 1722

**Normal orientation – wide flange in compression**

Constant bending moment distribution

**7 DOF beam element**

First buckling eigenvalue of the member which was computed by the Consteel software using the 7 DOF beam finite element model (n=25). The eigenshape shows lateral torsional buckling.

**Superbeam**

First buckling eigenvalue of the member which was computed by the Consteel software using the Superbeam function (δ=25).

**Introduction**

This verification example studies a simple fork supported beam member with welded section (flanges: 200-12; web: 400-8) subjected to bending about major axis. Constant bending moment due to concentrated end moments and triangular moment dsitribution from concentrated transverse force is examined. Critical moment and force of the member is calculated by hand and by the Consteel software using both 7 DOF beam finite element model and Superbeam function.

**Geometry**

Constant bending moment distribution

Triangular bending moment distribution – load on upper flange

Triangular bending moment distribution – load on bottom flange

**Calculation by hand**

Constant bending moment distribution

Triangular bending moment distribution

**Computation by Consteel**

Version nr: Consteel 15 build 1722

Constant bending moment distribution

**7 DOF beam element**

First buckling eigenvalue of the member which was computed by the Consteel software using the 7 DOF beam finite element model (n=16). The eigenshape shows lateral torsional buckling.

**Superbeam**

First buckling eigenvalue of the member which was computed by the Consteel software using the Superbeam function (δ=25).

Triangular bending moment distribution – load on upper flange

**7 DOF beam element**

First buckling eigenvalue of the member which was computed by the Consteel software using the 7 DOF beam finite element model (n=16).

**Superbeam**

First buckling eigenvalue of the member which was computed by the Consteel software using the Superbeam function (δ=25).

Triangular bending moment distribution – load on bottom flange

(more…)**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**

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.

**Geometry**

**Calculation by hand**

**Computation by Consteel**

Version nr: Consteel 15 build 1488

**7DOF beam element** The second order bending moment diagram of the member which was computed by the Consteel software using the 7DOF beam finite element model:

Normal stress in the middle cross-section:

(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.

**Geometry**

**Calculation by hand**

**Computation by Consteel**

Version nr: Consteel 15 build 1488

**7DOF beam element**

Deformation of the member with the numerical value of the maximum rotation (self-weight is neglected):

## 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.

## Geometry

## Calculation by hand

## Computation by Consteel

Version nr: Consteel 15 build 1488

**7DOF beam element**

Deformation of the member due to concentrated twist moment:

Bimoment of the member due to concentrated twist moment:

Warping normal stress in the middle cross-section:

**Shell FE model**

Maximum deformation of the middle cross-section:

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.

gateClick the button bellow to download and read the full article at page 187-195.

In this paper a numerical study is presented which examines a steel frame with two different finite element programs. Stability failure is more frequent in a lot of cases than strength failure hence it is important to focus on these failure modes: global, in-plane-, out-of-plane -, lateral-torsional- and local buckling. Three models were used with different elements such as shell elements and 7 DOF beam elements. 7 DOF beam elements were used in the first model, shell elements were used in the other two. The first of the shell models gave too much local buckling shapes therefore it was improved with local constraints and that is the third model where global buckling shapes can be examined. There are three different procedures to calculate the resistance: (i) the general method, (ii) the method of the reduction factors, and (iii) the simulation. The analysis results of the different programs and design methods were compared to each other and to the manual calculation based on the Eurocode 3 standards.

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