Stress Points for Shear Stresses

Tips & Tricks

000616 30 July 2013

The stresses in the cross‑section of the member are calculated in the so‑called stress points. These points are set at locations in the cross‑section, at which the extreme values for the stresses due to the different loading can occur in the material.

To determine the stresses, the following parameters of the stress points are used:

• Coordinates relative to the centroid of the cross‑section (for normal stresses from axial force and bending moment)
• Statical moments (for shear stresses from shear forces)
• Thickness (for shear stresses from shear forces and torsional moment)
• Core area for closed cross‑sections (for shear stresses from torsional moment)

For thin‑walled cross‑sections, we can assume as a simplification that the shear stress runs parallel to the wall of the cross‑section. Therefore, the parts of the shear stresses resulting from both the components of the shear forces are added. The sign of the statical moments defines here, which parts are applied positively and which negatively.

The shear stress due to the torsional moment is to be considered differently for the total shear stress, depending on whether it is an open or a closed cross‑section. For an open cross‑section, the torsion shear stress is added with the sign to that sum from the individual shear stresses that results in the greatest absolute value of the sum.

For a closed cross‑section, on the other hand, the torsional shear stress is simply added to the sum from the individual shear stresses. Here, the signs for core area and statical moments are set in such a way that they correspond to the program-specific sign conventions of the shear stress that is dependent on the loading.

Stress points lying within the cross‑section do not permit the assumption mentioned above that the shear stress runs parallel to the wall of the cross‑section. Here, a special method with twin stress points is used that creates two stress points with identical coordinates in the cross‑section. The one stress point considers the statical moment about the y‑axis (parameter for the shear stress due to vertical shear force), the other considers the statical moment about the z‑axis (parameter for shear stress due to horizontal shear force). For these stress points, the complementary statical moment is zero, respectively.

It is possible to assign different thicknesses to the twin stress points that have an influence on the calculation of the shear stress. The shear stresses are considered as interdependent components acting perpendicular to each other: they are components of one stress state. For the determination of the total shear stress, both parts are quadratically added. The shear stress due to the torsional moment is not considered in these points.

The shear stresses of result combinations in the twin stress points may not be combined linearly. Therefore, the extreme values of both components are evaluated with the corresponding complementary shear stresses in order to determine the greatest total shear stress.