Section modulus

As a resistance torque derived from the shape and the size of the cross-sectional area size of a beam is known in the engineering mechanics. It is a measure of which is dependent on the cross-sectional resistivity of the formation in a loaded beam is opposite to internal stresses.

When the stresses bending and twisting (torsion) is spoken by the axial moment of resistance (or resistance to bending moment ) and the polar moment of resistance (or Torsionswiderstandsmoment ).

The section modulus of a cross section is in simple geometric relation to its area moment of inertia. Both sizes are a function of the typical length dimensions geometrically simple surfaces and standardized media profiles often contain (eg steel profiles) in general technical manuals in common tables. Wherein the cross-sectional design of a beam forming and voltages examined. The deformation is i.a. calculated using the area moment of inertia and compared with the application- specific permissible deformation. The voltages are determined by the extension to the modulus, and placed in relation to the tolerable by the material stresses.

Basics

With forces perpendicular to a reference axis which will force the body unless a lever provided to rotate said axis. If the turn is prevented by clamping, results in a bending or torsional moment. Moduli are always calculated with respect to the respective axis of moment.

Calculation of the area moments of inertia

The resistance factor is taken solely from the geometry of the cross-sectional area. In his determination, the position of the neutral fiber in cross section must be known. This is the line in the case of pure bending neither pressure nor tensile stresses (dashed center lines 1 and 2 in the figure ). From this line has the maximum perpendicular distance from the section edge and are thus intended to outer fiber, where the wanted maximum stresses / component loads occur. The section modulus is the ratio of the area moment of inertia and the distance of the extreme fiber from the neutral ( unstressed ) fiber:

With:

For symmetrical cross-sections, the section modulus equal in the peripheral fibers parallel to the axis of symmetry. Therefore, the stresses in these fibers are the same, when the bending forces perpendicularly to this axis of symmetry.

Application

The occurring in the extreme fibers of maximum stresses are determined for moments about the reference axis by:

Examples ( axial moment of resistance )

• Rectangle

• Square

Note: For non-circular cross-sections, the polar section modulus can be calculated. However, they have no practical significance, since the distribution of torsional stress for such cross sections is subject to completely different laws.

• Circle

• Annulus

• Trapeze

• Hollow section (square tube)