Axial Stress and Elongation of a Rod
Axial Stress, Strain and Elongation of a Rod
When a straight member is pulled along its axis it stretches. This worksheet computes the normal stress, the elastic strain and the total elongation — the basis of every tension-member and tie-rod check.
The stress is σ = F/A, Hooke’s law gives the strain ε = σ/E, and the elongation is δ = FL/(AE).
Inputs
A circular rod of diameter d and length L pulled by an axial force F, made of a material of modulus E.
F := 50 kN=50000 N
d := 20 mm=20 mm
L := 1.5 m=1.5 m
E := 200 GPa=200000 MPa
Cross-section area
A := pi·d^2/4=3.14e-04 m^2
Stress, strain and elongation
sigma := F/A=159.15 MPa
strain := sigma/E=7.96e-04
delta := F·L/(A·E)=1.19 mm
Results
The axial stress must stay below the material’s allowable (for structural steel, well under the 250–355 MPa yield range). The strain is dimensionless and usually only a fraction of a percent in the elastic range; the elongation it produces is what matters for fit-up and pre-tension.
Assumptions & limitations
- Uniform stress over the cross-section (away from the ends).
- Linear-elastic behaviour — below the proportional limit.
- Prismatic bar, concentric load, no buckling (tension).