Normal Stress and Strain Calculator

What is normal stress?

A force pulling or pushing a bar along its axis spreads over the cross section as an internal force per unit area. This is the normal stress, σ = F / A. With force in newtons and area in square millimetres the result is in N/mm², which is the same as MPa. Tension is taken as positive and compression as negative.

Strain and Hooke's law

Under load the bar stretches slightly. Strain is the change in length divided by the original length: ε = ΔL / L. It has no unit and is usually written as a percentage, per mille or microstrain (µε).

Below the proportional limit stress and strain are proportional: σ = E × ε. E is the elastic modulus, a measure of how stiff the material is. Combining the two relations gives the elongation of the bar: ΔL = F × L / (E × A).

Example

A bar of 400 mm² section and 2 m length carries 50 kN in tension. The stress is 50 000 / 400 = 125 MPa. With an elastic modulus of 200 GPa the elongation is 50 000 × 2000 / (200 000 × 400) = 1.25 mm. The strain is 1.25 / 2000 = 0.000625, or 0.0625 percent.

What each tab does

• Stress: σ from force and section. Enter the area directly or let the tool work it out from circle, tube or rectangle dimensions.
• Strain: ε from a measured change in length.
• Hooke's law: any one of stress, strain and elastic modulus from the other two.
• Bar elongation: ΔL from force, length, section and material.
• Required area: the smallest section for a given force and allowable stress.

Limits

The result is the average stress over the section. Around holes and notches the local stress is much higher. In compression members buckling can govern even when the stress is low. The elongation formula holds only in the elastic range.