Calculator · Structural Mechanics
Axial Deformation Calculator
How much a prismatic bar stretches or shortens under a constant internal axial force. The stiffness of the bar is AE/L, so the deformation grows with load and length and falls with area and modulus.
Inputs
Positive is tension, negative is compression.
N is the internal axial force from the right free body, N(x) = Σ Fx for every load beyond the cut. N > 0 is tension, N < 0 is compression.
Results
| Internal axial force N | 25000 N |
|---|---|
| Axial stiffness AE/L | 5.0000e+7 N/m |
| Normal stress σ = N/A | 50 MPa |
| Normal strain ε = σ/E | 250 µε |
| Deformation δ = NL/(AE) | 0.5 mm |
| Sense | tension |
| Implied reaction at the fixed end | -25000 N |
Assumptions
- · Linear-elastic material and small strains.
- · Uniform stress over each cross-section (Saint-Venant away from load introduction).
- · The left end (x = xStart) is the restrained reference; its reaction is implied, not solved.
Open in the Lab
The Lab carries this bar over as a single segment and lets you add material changes and interior loads.
Technical reference
δ = N L / (A E)
σ = N / A
ε = σ / E
k = A E / L
- N
- internal axial force, constant along the member, tension positive[N]
- L
- original member length[m]
- A
- cross-sectional area[m²]
- E
- Young's modulus[Pa]
- δ
- change in length, positive when the member lengthens[m]
- k
- axial stiffness of the member[N/m]
This form assumes N, A and E are all constant over the length. When any of them changes — a stepped bar, a material change, an interior load — the member must be split and the contributions summed: δ = Σ NᵢLᵢ/(AᵢEᵢ). The Axial Members Lab does exactly that.
The reported reaction is the force the support must supply to hold the member; the engine states it rather than inventing a support condition.
Self-weight is not included. For a heavy vertical member the internal force varies along the length and this single-interval form understates the deformation.