The definition of cross sections is an essential part of structural analysis. Not only does the cross-section shape determine, partially, the model shape, but it also influences the check methodology by affecting the design parts of norms to be used during the design.
In general, cross-section property calculation is determined in 2 steps:
Standardized cross-section properties part I (bi-axial bending and axial force)
- centre of gravity
- angle of principal axis system
- principal moments of inertia
Standardized cross-section properties part II (torsion)
- shear centre
- torsion constant
- warping constant
- standardized warping ordinate
If we apply this to SCIA Engineer:
Standardized cross-section properties part I
Standardized cross-section properties part II
SCIA Engineer 2013 improvements
Re-arranging the properties
In previous versions, the properties were not in the most logical order possible, which made it difficult to derive one section property from another.
In SCIA Engineer 2013, we have re-arranged and extended the section properties functionality.
Calculation of the "Part I" properties
We have implemented a new method for the determination of cross-section properties in version 2013 which is valid for ALL cross-section types. This method discretizes the cross-section into 'n'-parts and performs a numerical integration of the well known properties (A, Iy, Iz,...) . Even though simplified formulas are available for certain shapes, by using the described approach we handle all possible cross-section shapes in the same way.
In addition, we provided a clear description for each property using tooltips
Another new feature is the calculation of the circumference (AL) and the Drying Surface (AD), which we can now calculate also for general cross-sections.
Another new feature calculates plastic moments for every type of cross-section shape and can generate fibres even in openings in the cross-section.
To conclude, we now also calculate and display the radii of gyration and the shear area for every cross-section .
Calculation of the "Part II" properties
In the calculation of section properties related to torsion, the general theory distinguishes 3 types of cross sections:
- Thin-walled open cross sections: analytical solutions are widely available
- Thin-walled closed cross-sections: analytical solutions are available for single opening cross-sections. In case of multiple openings the system becomes statically indeterminate
- Arbitrary thick-walled cross-sections: analytical solutions exist only for some basic shapes
For thin-walled, open cross-sections the properties are easily determined using the well-known analytical solutions. The torsion related properties of arbitrary thick-walled cross-sections are obtained using 2D FEM analysis in SCIA Engineer.
Thin-walled closed cross-sections with more than one opening, however, do present a challenge. In general, it is possible to use the 2D FEM solution in SCIA Engineer to calculate section properties related to torsion, but this would be overkill. That's why we have implemented a new 1D FEM analysis solution in SCIA Engineer 2013 for this type of cross-sections.
What is a Thin-walled cross -section
In essence, any cross-section which can be represented by means of centrelines, is called "thin-walled"
The new 1D Finite Element approach is only valid for this kind of thin-walled sections.
Main advantages of this approach are:
- valid for any thin-walled OPEN section
- valid for any thin-walled CLOSED section, even with multiple openings
valid for any thin-walled section that is a combination of both open and closed parts
- fully transparent approach
- Discretization into nodes and elements (centreline-based)
Elements are defined with a begin-node "a", end-node "b"and thickness "t"
- Finite element analysis is carried out using the following steps
- Step 1: calculation of the warping ordinate w
- Step 2: position of the shear centre and standardization of the warping ordinate
- Step 3: calculation of the cross-section properties Iw and It
- Step 4: calculation of the shear deformation due to shear force and secondary torsion
- Step 5: calculation of the shear stresses
- Step 1: calculation of the warping ordinate w
Other improvements in the Part II calculation
- The curve division algorithm, used for dividing a curve into parts, has been improved. For arcs we now also generate a centre fibre.
- Graphical indication of the shear centre
- 2D FEM method can now also be used for thin-walled sections
- New organization of the 2D FEM group , including colour coding
- New dialogue with tabs.
- Calculation of mono-symmetry constants for the calculation of Mcr for LTB
- New cross-section setup
- Visual display of the new axis system of the effective shape.
In addition to that, an improved algorithm has been included for the determination of the angle between the principal axes and the original coordinate system.
- FEM cache
The first calculation will not change anything. The 2D FEM cache needs to be populated at least one time.
In previous versions any modification to the structure or to the project in general removed this 2D FEM results for the cross-sections.
By keeping the CSS FEM results in the cache we ensure faster runtime when restarting the analysis.
Even when the basic results are cleared and the project has to be recalculated, the CSS 2D FEM results are kept (unless you clean them intentionally)
Test-cases showed decreased calculation time up to around 80 %
- Numerical output table of the centreline with typology
A new output table is provided in the Detailed Additional otx, showing the centreline data as well as the type of each centreline element.
- Editable properties
In the cross-section properties dialogue option "Properties editable" can be found. This allows the user to override the part II properties as well as shear areas. The editable properties are highlighted in 'cyan' to visually inform the user about the affected values.
- Improved "Closed formulas"
As mentioned above, for a large number of "standard" profiles analytical solutions are widely available. As an extension we have implemented a number of so-called closed formulas in SCIA Engineer which override certain calculated cross-section properties. A typical example is the shear area of a rectangle which is hard-coded to 5/6 A. Version 2013 contains a number of improvements to these formulas. For a rectangle e.g. the torsional stiffness was calculated in previous versions using an interpolated "gamma"-coefficient, which depended on the height and width of the rectangle. In version 2013 we use a closed formula for "gamma" and as such an exact formula for It
In the case of rolled I-sections, the centreline analysis for torsional stiffness does not take into account the rounding in the section. This can lead to a significant underestimation of the torsional stiffness. By using the more exact closed formula, we now do take rounding into account.
- Improved export
All the improvements (order of properties, calculation of new properties, centreline data,...) have been added to the export functionality of the cross-section.
General approach for the calculation of the cross-section properties
The following flowchart shows the different steps in the calculation of the cross-sections: