Engineering task and calculation objective
The BIEG module supplies moments of inertia, section moduli and geometry data of standardized hot-rolled sections: T-sections to DIN 1024, I-sections to DIN 1025, U-channels to DIN 1026, L-sections to DIN 1027, and angle steels to DIN 1028 and DIN 1029. If you want to calculate or look up the moment of inertia of a steel section, you select the designation and size and obtain the complete cross-sectional properties for both principal axes.
In vessel engineering and structural steelwork these values are needed constantly: for support rings and ring girders, bracket substructures, pipe bridges, reinforcing sections and skirt stiffeners. Besides moment of inertia and section modulus, the module outputs the cross-sectional area, weight per length and radius of gyration — the latter being the characteristic quantity for buckling checks of members in compression.
The basis is the dimensional and property data of the DIN standards listed; the module works as a verified section database and avoids error-prone manual transfer from printed tables.
Standard and calculation basis: DIN Normen
Calculation workflow
- Choose the section family: The new-selection input defines the section family: T-, I-, U- or L-section, or equal-leg or unequal-leg angle steel. The designation (e.g. IPB, U, L) identifies the standard series.
- Specify the size: Within the series, the nominal size is chosen; for angles, additionally the leg thickness s = t. This uniquely identifies the table entry.
- Output the cross-sectional properties: The module returns the cross-sectional area and weight per length as well as, for both principal axes, the moment of inertia, section modulus and radius of gyration.
- Transfer the values into the strength verification: The cross-sectional properties enter bending, deflection and buckling verifications, for example for support structures per the AD 2000 S 3 series of the German AD 2000 code or in the structural steel verification of substructures.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| New selection (1 = yes) | ) | – |
| Abbreviation | Kurzzeichen | – |
| Dimension | h | mm |
| Dimension | s | mm |
| Cross-sectional area | A | mm² |
| Weight / Length | G | kg/m |
| Dimension | b | mm |
| Dimension | ex | mm |
| Moment of inertia | Jx | mm^4 |
| Section modulus | Wx | mm³ |
| Radius of gyration | ix | mm |
| Moment of inertia | Jy | mm^4 |
| Section modulus | Wy | mm³ |
| Radius of gyration | iy | mm |
| Dimension | ey | mm |
| Dimension | t | mm |
| Dimension | a | mm |
Frequently asked questions
What is the difference between moment of inertia and section modulus?
The moment of inertia I describes the stiffness of the cross-section against bending and governs the deflection; the section modulus W = I/z (z = distance to the extreme fiber) links the bending moment to the extreme-fiber stress sigma = M/W and thus governs the strength utilization. For the stress check you need W, for the deformation check I.
What is the radius of gyration needed for?
The radius of gyration i = sqrt(I/A) enters the slenderness ratio lambda = Lk/i of the buckling verification. For columns and struts in compression, the weak axis with the smaller i always governs — for angle sections often even the inclined principal axis, which must be observed when applying the tabulated values.
Why are the values output for two axes?
Rolled sections are generally not rotationally symmetric: I- and U-sections have a strong and a weak axis with moments of inertia that can differ by an order of magnitude. For biaxial bending, lateral-torsional buckling checks and buckling about the weak axis, both sets of values must be available.
Are the old DIN section series still available?
The classic series (e.g. IPE, HEA/HEB as IPBl/IPB per DIN 1025, U-channels per DIN 1026) are still commercially available; many dimensional standards were transferred in substance into European standards (such as DIN EN 10365 for hot-rolled sections). The cross-sectional properties themselves do not change as long as the dimensions have remained identical.