Sectional characteristics
2013.0
General
The definition of cross sections is an essential part of structural analysis. Not only does the crosssection 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, crosssection property calculation is determined in 2 steps:
Standardized crosssection properties part I (biaxial bending and axial force)
 area
 centre of gravity
 angle of principal axis system
 principal moments of inertia
Standardized crosssection properties part II (torsion)
 shear centre
 torsion constant
 warping constant
 standardized warping ordinate
If we apply this to SCIA Engineer:
Standardized crosssection properties part I
Standardized crosssection properties part II
SCIA Engineer 2013 improvements
Rearranging 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 rearranged and extended the section properties functionality.
Calculation of the "Part I" properties
We have implemented a new method for the determination of crosssection properties in version 2013 which is valid for ALL crosssection types. This method discretizes the crosssection 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 crosssection 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 crosssections.
Another new feature calculates plastic moments for every type of crosssection shape and can generate fibres even in openings in the crosssection.
To conclude, we now also calculate and display the radii of gyration and the shear area for every crosssection .
Calculation of the "Part II" properties
In the calculation of section properties related to torsion, the general theory distinguishes 3 types of cross sections:
 Thinwalled open cross sections: analytical solutions are widely available
 Thinwalled closed crosssections: analytical solutions are available for single opening crosssections. In case of multiple openings the system becomes statically indeterminate
 Arbitrary thickwalled crosssections: analytical solutions exist only for some basic shapes
For thinwalled, open crosssections the properties are easily determined using the wellknown analytical solutions. The torsion related properties of arbitrary thickwalled crosssections are obtained using 2D FEM analysis in SCIA Engineer.
Thinwalled closed crosssections 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 crosssections.
What is a Thinwalled cross section
In essence, any crosssection which can be represented by means of centrelines, is called "thinwalled"
The new 1D Finite Element approach is only valid for this kind of thinwalled sections.
Main advantages of this approach are:
 valid for any thinwalled OPEN section
 valid for any thinwalled CLOSED section, even with multiple openings

valid for any thinwalled section that is a combination of both open and closed parts
 fully transparent approach
Calculation stepbystep
 Discretization into nodes and elements (centrelinebased)
Elements are defined with a beginnode "a", endnode "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 crosssection 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 thinwalled sections
 New organization of the 2D FEM group , including colour coding
 New dialogue with tabs.
 Calculation of monosymmetry constants for the calculation of Mcr for LTB
 New crosssection 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 crosssections.
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)
Testcases 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 crosssection 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 socalled closed formulas in SCIA Engineer which override certain calculated crosssection properties. A typical example is the shear area of a rectangle which is hardcoded 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 Isections, 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 crosssection.
General approach for the calculation of the crosssection properties
The following flowchart shows the different steps in the calculation of the crosssections:
Stefan Belmans
15/05/2013