Bending moment

The bending moment is the force acting on a workpiece clamped on one or two sides. The bending stress at the clamping points increases with the distance to the point of application of the force due to the law of leverage.

The three deformation ranges of deformable materials

Deformable materials such as metals or various plastics have three areas in which they can absorb force.

• elastic range
• deformation range
• Elongation at break

Within the elastic range, the workpiece always springs back to its original state after relaxation. Permanent deformation does not take place within the elastic range at any applied stress. The forming area begins after the bending stress for the elastic area is exceeded. The workpiece reshapes in proportion to the applied stress. When the tension is released, it springs back again slightly. Therefore, slightly higher forces are always required to produce a desired bending radius. After exceeding the maximum bending moment, the workpiece breaks. This is the separating area.

Relationship between bending moment and moment of area

The required bending stress is calculated as the quotient of bending moment and section modulus. The section modulus is again the moment of area divided by the distance between the outer edge of a profile and the neutral fibre. The neutral fibre is an imaginary centre line along the workpiece.

Complex formulae are required to determine the moment of area (or moment of inertia). Therefore, tabular values are used for standard profiles.

Application of the bending moment

The bending stress at the point of maximum deformation is calculated from the bending moment. This can then be compared with the yield strength of the selected material. If the bending stress is below the yield point, the component will always spring back to its original state after stress relief. If the yield point is exceeded, permanent deformation occurs until the breaking point is reached. For all forces above this, the component breaks at the point of maximum bending stress. It is thus possible to calculate very precisely what force is required to achieve a certain effect.

Metal bending in practice

Bending machines and bending processes reshape a workpiece by exceeding the defined bending stress. Typical processing methods are as follows:

• Roller stretching
• Tensile bending
• Bending
• Roller and roll bending
• Deep drawing and pressing

In these processes, a bending stress is applied to a workpiece at a point or along a defined path. The result is a bending radius with a defined size. This can be only a few millimetres or extend over the entire length of the workpiece.