Strength of materials
Oblique bending
- Introduction to oblique bending
- Definition and characteristics
- Projection of the bending moment onto the main central axes
- Components of the moment in the y and z axes
- Neutral axis in oblique bending
- Position of the neutral axis
- Geometric locus of zero stress points
- Normal stresses in oblique bending
- Normal stress equation
- Parameters of the formula
- Normal stress diagram
- Stress body
Introduction to oblique bending
Oblique bending is a type of bending in which the direction of the bending moment vector does not align with any of the principal axes of inertia of the cross-section. This means that the plane of action of the load is not parallel to any of these axes. By projecting the bending moment vector onto the main central axes of the system, we obtain the moment components (M) in the (y) and (z) axes.
Fig. 1. Oblique bending - projection of the moment onto the main central axes
From this course, you will learn:
- how to determine reactions and draw internal force diagrams,
- how to draw the distribution of normal stresses,
- how to determine the stress body,
- how to determine and draw the position of the neutral axis,
- how to dimension a beam subjected to oblique bending based on strength conditions,
- how to determine the allowable load value for a given specific cross-section.
The neutral axis in oblique bending
In general, the neutral axis does not coincide with the line of action of the bending moment vector, although it passes through the centroid of the cross-section. The neutral axis of bending is the geometric locus of points where the stresses are equal to zero.
Normal stresses in oblique bending
The equation for normal stress considering the effect of the bending moment in the direction of the two main central axes:
$$\sigma(x) = \frac{-M_y}{I_y} \cdot z - \frac{M_z}{I_z} \cdot y$$
where:
- \( \sigma \) is the normal stress,
- \( M_y, M_z \) are the bending moments,
- \( y, z \) are the distances from the centroid along the main central axes to the section point where we want to calculate the stresses,
- \( I_y, I_z \) are the main central moments of inertia of the cross-section.
Fig. 2. Example of a normal stress diagram - oblique bending
You have access to video courses and a wide database of problems with solutions for each type of bending separately.