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Online Calculator: Bending Stress

The bending moments calculator allows you to calculate the elastic/plastic stress in a section of material bent at a specified radius.

Enter known properties:

yield stress (σ):
neutral axis to stress (y):
bending moment (M):
second moment of area (I):
tensile modulus (E):
bend radius at neutral axis (R):

bending stress in beams
Bending Stress in Beams


yield stress (σ):
neutral axis to stress (y):
bending moment (M):
second moment of area (I):
tensile modulus (E):
bend radius at neutral axis (R):


Help

This Bending Stress calculator is accessible from anywhere in the website using the shortcut key; "Alt" + "t".

Calculation

The above calculation comprises three property groups according to colour: stress, section, & shape.
You need both properties of one group and one of any other to calculate the unknown group property.
You will be notified if you have provided insufficient data for a calculation.

Stress

A straight beam (or plate) that has been bent as described in the above image will develop a neutral axis at its centre of [cross-sectional] area.
Stress along this neutral axis is [in theory] zero if no axial tension or compression, or torsion is applied to the beam.

Stress outside the neutral axis is tensile. Stress inside the neutral axis is compressive.
If the bend radius is such that the stress exceeds yield within the beam thickness, the material beyond these radii (R+y and R-y) will have deformed plastically. The material between these radii will have been deformed elastically.

If all the material had been deformed elastically when the [bending] load was released, the beam will return to its original shape and remain in a relaxed state.
If, on the other hand, the outer edges of the beam material were plastically deformed when the bending load was released, the outer edges will attempt to remain in their deformed shape, whilst the elastically deformed section will try to recover its original shape.
These two layers will induce competing tensile and compressive residual stress in the material. The beam will therefore remain in [reduced] bent condition; settling at a larger but definite bend radius.

Downloadable Version

A full, downloadable version of this calculator is available from this website at; Engineering Basics.

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