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# Online Calculator: Bending Stress

Elastic Bending Stress in Beams

This calculator is based on the elastic-stress formula; σ/y = M/I = E/R
and therefore assumes that none of the material undergoes plastic strain. Enter known properties:

Property: Input Data Output Data
stress @'y' (σ):
neutral axis to outermost layer (y):
bending moment (M):
second moment of area (I):
tensile modulus (E):
bend radius at neutral axis (R):

Plastic Bending Stress in Beams

This calculator determines the amount of plastic strain at any point along the length of a loaded beam.
It assumes that the force is applied in the middle of the beam's length (worst case scenario). Enter known properties:

Input: Data Output @ 'x': Data
distance to 'Mₓ' (x): distance from neutral axis (y):
applied load at '½L' (F): bending moment (M):
beam length (L): elastic bending moment (Mₑ):
beam thickness (t): plastic bending moment (Mₚ):
yield stress (σy): total [checking] moment (Mₜ):

## Help

These Bending Stress calculators are accessible from anywhere in the website using the shortcut key; "Alt" + "n".

### Stress

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

Stress outside the neutral axis is tensile, and stress inside the neutral axis is compressive.

### Elastic Calculator

This calculation method assumes that the entire thickness of the material deforms elastically and that the greatest stress occurs in the material plane furthest from the neutral axis; 'y'.

The elastic 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.

### Plastic Calculator

The plastic calculation identifies the yield stress plane ('y') through a beam when loaded at the middle of its length.
The bending moment (M), which occurs as a result of load (F) and distance (x), comprises an elastic component (Mₑ) and a plastic component (Mₚ) that together make the total moment (M).
If the [tensile and compressive] plastic stress zones touch (y=0) you will have created a plastic hinge, and if they overlap (y<0), you risk breaking your beam.

If 'y' is greater than 't/2', the entire beam section has been deformed elastically; no plastic deformation has occurred in your beam.