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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:
Consteel 14 is a powerful analysis and design software for structural engineers. Watch our video how to get started with Consteel.
Contents
- Set analysis parameters
- Perform first and second order analysis
- Perform buckling analysis
- Analysis results in graphics and in tables
- Results: deformation, internal forces, reactions