Stress & Strain Calculator - Young's Modulus

Stress, strain and Young's modulus

Stress (σ), Strain (ε) and Young's Modulus (E) modes

σ

engineering stress: force over the original area (N ÷ mm² = MPa)

F

axial force; negative is compression

A

cross-sectional area, at right angles to the force

ε

engineering strain

ΔL

change in length

L₀

original length

E

Young's modulus, in GPa

E = σ ÷ ε holds only below yield, where stress and strain are proportional. It is withheld when stress and strain have opposite signs.

Source: Standard formulas; no single publisher.

Safety factor

When a material or yield strength is set

SF

safety factor against yield

Sy

yield strength of the material

σ

applied stress

SAFE

SF at or above your target (1.5 unless you change it)

MARGINAL

SF from 1 up to the target: below yield, short of the margin

UNSAFE

SF below 1: past yield

Compression uses the magnitude, and buckling is not checked. Against a typical yield, the factor reads higher than against the minimum a part is bought to.

Source: Standard formula; no single publisher. The 1.5 default and the three bands are CalcTrail's own; no publisher.

Companion figures

With a material chosen

ν

the material's Poisson ratio

u

elastic strain energy per volume, withheld past yield

τmax

the largest shear, on planes at 45° to the load

E

the material's table modulus

These use the material's table modulus, not one measured from your ΔL. The member's mass is area × length × the material's density.

Source: Standard formulas; no single publisher.

True stress and strain

Every mode

σ

engineering stress

ε

engineering strain

They assume the volume stays the same and the bar stretches evenly, so they stop holding once it necks.

Source: Standard formulas; no single publisher.

Material values

With a material chosen

ASTM A36

yield 250, ultimate 400 MPa, taken as the grade's minimums (ASTM A36 was not read here); E 200 GPa

AISI 4140, 304 stainless

typical values

6061-T6, 7075-T6

typical; above MIL-HDBK-5J's A-basis design values (6061-T6 sheet 241 to 248 MPa yield)

Ti-6Al-4V

typical; MIL-HDBK-5J gives a Poisson ratio of 0.31 against this table's 0.342

C11000 copper

typical, annealed (OS050): yield 69, ultimate 220 MPa; E 117 GPa

C36000 brass

typical, annealed (O61): yield 125, ultimate 340 MPa; E 97 GPa

Room-temperature figures for one product form. Strength changes with temper, thickness and form.

Source: Steel's modulus is IS 456's 200 kN/mm² [1]. The copper and brass rows are the Copper Development Association's typical values [2] [3]. The aluminum and titanium moduli and densities, and the aluminum Poisson ratios, match MIL-HDBK-5J [4]; the Ti-6Al-4V Poisson ratio does not (row above). The A36, 4140 and 304 strengths are CalcTrail's own figures; no single publisher.