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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.

elastic bending stress in beams

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).

plastic bending stress in beams

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):


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


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.

Downloadable Version

Full downloadable versions of these calculators are available from this website at; Engineering Basics & Plastic Stress.

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