This overview delves into Consteel’s solution, offering an alternative approach to calculating effective cross-sectional properties and reshaping conventional methodologies in structural analysis and design.
Determine the strength utilization of a double symmetric welded I cross-section with 384×4 web and 300×8 flanges, if the internal forces on the cross-section are NEd=500kN compressive force and My,Ed=100kNm bending moment. The material grade of the cross section is S235.
Calculation of cross-sectional properties
First, take the cross-section data (symmetric welded I-section), from which the Consteel software generates the EPS (and GSS) (see Online Manual/10.1.1 The EPS model) cross-section model (Fig. 1).
If the cross-section is class 4, the effective model is determined by the assumed normal stress distribution. According to EC3-1-1, the EPS model of a class 4 cross-section can be defined in two ways :
– method A: based on pure stress conditions,
– method B: based on complex stress condition.
In order to compare the results, the cross-section properties will be calculated by method A at first and then by method B.
Cross-sectional properties by method A
- pure compression NEd (Fig. 2):
Aeff=4720mm2
- pure bending My,Ed (Fig. 3):
Weff,y,min=864080mm3
ez=14.5mm
Cross-sectional properties by method B
GATEIn Consteel, the calculation of cross sectional interaction resistance for Class 3 and 4 sections is executed with the modified Formula 6.2 of EN 1993-1-1 with the consideration of warping and altering signs of component resistances. Let’s see how…
Application of EN 1993-1-1 formula 6.2
For calculation of the resistance of a cross section subjected to combination of internal forces and bending moments, EN 1993-1-1 allows the usage -as a conservative approximation- a linear summation of the utilization ratios for each stress resultant, specified in formula 6.2.
$$\frac{N_{Ed}}{N_{Rd}}+\frac{M_{y,Ed}}{M_{y,Rd}}+\frac{M_{z,Ed}}{M_{z,Rd}}\leq 1$$
As Consteel uses the 7DOF finite element and so it is capable of calulcating bimoment, an extended form of the formula is used for interaction resistance calculation to consider the additional effect.
$$\frac{N_{Ed}}{N_{Rd}}+\frac{M_{y,Ed}}{M_{y,Rd}}+\frac{M_{z,Ed}}{M_{z,Rd}}+\frac{B_{Ed}}{B_{Rd}}\leq 1$$
Formula 6.2 ignores the fact that not every component results the highest stress at the same critical point of the cross-section.
In order to moderate this conservatism of the formula, Consteel applies a modified method for class 3 and 4 sections. Instead of calculating the maximal ratio for every force component using the minimal section moduli (W), Consteel finds the most critical point of the cross-section first (based on the sum of different normal stress components) and calculates the component ratios using the W values determined for this critical point. Summation is done with considering the sign of the stresses caused by the components corresponding to the sign of the dominant stress in the critical point.
(For class 1 and 2 sections, the complex plastic stress distribution cannot be determined by the software. The Formula 6.2 is used with the extension of bimoments to calculate interaction resistance, but no modification with altering signs is applied)
Example
Let’s see an example for better explanation.
GATEDid you know that you could use Consteel to perform local and distortional buckling checks for cold-formed members?
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Did you know that you could use Consteel to calculate effective cross-section properties for Class 4 sections?
Download the example model and try it!
Download modelIf you haven’t tried Consteel yet, request a trial for free!
Try Consteel for free
Did you know that you could use Consteel to draw a user-defined cross section and calculate its section properties?
Download the example model and try it!
Download modelIf you haven’t tried Consteel yet, request a trial for free!
Try Consteel for free
Did you know that you could use Consteel to include in your model a wide range of cold-formed macro sections?
Download the example model and try it!
Download modelIf you haven’t tried Consteel yet, request a trial for free!
Try Consteel for free
Introduction
It is essential for the effective work of the design engineers to have a model which is easy to overview. In Consteel there are several functions to achieve that such as layers and portions, and also Member coloring by cross-section.
How it works
The color of the displayed objects is now determined by the object style settings in Options.
Layer color can overwrite these settings if the Layer style cell is checked on Layers dialog.
In the case of beam type members, it is also possible to set the color of the object according to the section it has defined. Coloring by member can be set with Object color setting dialog in the right bottom corner:
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