Section Properties
Area, second moments, elastic and plastic section moduli, radii of gyration and the principal axes of angles for I, box, channel, angle, tee, pipe and custom shapes, with an AISC ASD 1989 stress check.
Composite sections are assembled by the parallel axis theorem, I = Σ(I_c + A·d²); the elastic modulus is W = I/c at the governing fibre and the plastic modulus is taken about the equal-area axis, which is not the centroid unless the section is symmetric about it. For an angle, whose leg axes are not principal, the product of inertia gives I_u, I_v and i_v. Catalogue sizes are read from EN 10365 and DIN 1026-1 rather than reconstructed, and the stress panel checks elastic service-load stresses in steel against AISC ASD 1989, giving no verdict where an element exceeds its width-thickness limit.
Shape and dimensions
Axes: x-x is horizontal and y-y vertical, as drawn. For the catalogue sections x-x is the major axis: EN 10365 calls it y-y (Iy, Wel,y, Wpl,y) and calls the minor axis z-z. Where x and y are not principal axes (an angle) the principal axes u-u (major) and v-v (minor) are printed as well, and the stress check uses them.
Material and internal forces
Section properties
Stress check
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| Stress check | MPa | Allowable | Utilisation | Governing |
|---|
Width-thickness limits: AISC ASD (1989) Table B5.1 and §F4
| Element | Ratio | Limit | Governing |
|---|
Section comparison
| Section | Dimensions | A cm² | Ix cm⁴ | Wx cm³ | Zx cm³ | Iy cm⁴ | kg/m | Utilisation | Remove row |
|---|
No sections yet: pick a section, then add it.
Units: dimensions in millimetres, forces in kN, moments in kN·m, stresses in MPa. Area is shown in cm², second moments in cm⁴ and section moduli in cm³ (the units the section tables use) to four significant figures. Everything is computed in millimetres and rounded only for display.
Questions engineers ask
Does this calculator check buckling?
Not as a member. It does not check lateral-torsional buckling, column buckling or torsion, so a section that passes here can still fail as a member. Local buckling is handled as a gate: whenever the loads can compress or shear it, each flange, web, stem, leg and wall is compared with its AISC ASD 1989 Table B5.1 noncompact limit (a web in uniform compression with the stricter compact limit), and the web with h/t_w ≤ 380/√F_y (ksi) for the 0.40F_y shear allowable. An element beyond its limit gets "No verdict" instead of a utilisation, because the Appendix B5 reduction and Eq. F4-2 are not implemented.
Where does the shear area A_v come from?
It is pre-filled from the shape and stays editable. For I and channel sections it is d·t_w per AISC 360-22 §G2.1 (the overall depth, not the clear web, which is the detail most often got wrong) and a tee likewise takes the overall depth times the stem thickness. A box takes 2(h − 2t)·t, both webs over the clear depth between the flanges; an angle a·t on its vertical leg; a tube A/2; a solid rectangle A/1.5 and a solid circle 3A/4, which give the peak shear stress. The basis is printed beside the field.
Why do the catalogue properties differ from the same dimensions drawn as rectangles?
The root fillets. The custom shapes have sharp corners, so a custom I-section with the dimensions of an IPE, HEA or HEB runs about 2–6% light on area and on the major-axis second moment. That is why a catalogue size is read from the EN 10365 or DIN 1026-1 table (its radii of gyration and mass are derived from the tabulated A and I) and the rectangles are used only to draw it.
Which allowable-stress code are the limits taken from?
The AISC 1989 ASD specification: 0.60F_y for tension (§D1) and for bending of a noncompact section (Chapter F), and 0.40F_y for shear (Eq. F4-1). Axial and bending stresses are added and compared with 0.60F_y, which is the ASD interaction when every allowable is 0.60F_y; compression is a cross-section check only, since F_a for a real length is lower and is not computed. The utilisation is the larger of the normal-stress and shear checks, and a von Mises value is shown for information only. ANSI/AISC 360-22 does not use allowable stresses, and the page has no concrete check.
Why does an angle show I_u and I_v, and a higher bending stress than M/W?
The axes parallel to the legs of an angle are not principal axes: its product of inertia I_xy is not zero. The page prints I_xy, the principal second moments I_u and I_v, their radii of gyration and the angle α from x-x to u-u, and computes the bending stress at every corner with I_xy included. That is unrestrained bending (roughly 20–35% above M/W about a leg axis for common sizes) and it is conservative if the angle is restrained to bend about that axis. i_v is the radius of gyration that governs buckling, which the page does not check.
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Structural design
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