Transverse bending

Introduction to transverse bending

Transverse bending refers to situations where a structural element, such as a beam, is subjected to loads acting perpendicular to its longitudinal axis. A key aspect of the analysis of transverse bending involves determining shear stresses (also known as tangential or shear stresses). Shear forces arise parallel to the transverse load and cause tangential stresses in the material.

Shear stresses in transverse bending

In transverse bending, shear stresses can be expressed by the formula (we provide two variants, depending on the direction of the transverse force – of course, it can act in both planes at once):

$$\tau_{xz} = \frac{-Q_z \cdot S_y}{I_y \cdot b}$$ $$\tau_{xy} = \frac{-Q_y \cdot S_z}{I_z \cdot h}$$

where:

• \( \tau \) is the shear stress,
• \( Q \) is the shear force at the given cross-section,
• \( S \) is the static moment of the section above the point where the shear stress is calculated (\( S_y \) – moment about the y-axis, \( S_z \) – about the z-axis),
• \( I \) is the moment of inertia of the entire cross-section,
• \( b/h \) is the width/height of the cross-section at the point where the stress is calculated.

Fig. 1. Shear stress diagram for a rectangular cross-section

Maximum shear stresses and reduced stresses

Maximum shear stresses typically occur at the neutral axis of the beam's cross-section.

Having calculated normal stresses (simple bending) and shear stresses (transverse bending), one can address further issues, including calculating reduced stresses from strength hypotheses – most commonly according to the Huber-Mises-Hencky hypothesis or Tresca-Guest. One can also draw a stress cube for a given point in the cross-section and calculate minimum and maximum stresses for that point.

You have access to video courses and a wide database of problems with solutions for each type of bending separately.