BIZOMAT MAKEOS · Engineering
Axial Stress and Extension
What elastic stress and length change follow from this axial force?
Calculate nominal stress, strain, extension or shortening and strain energy for a uniform member under concentric axial load.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Signed axial force | N | Concentric force: tension positive, compression negative. |
| Uniform cross-sectional area | mm² | Uniform load-carrying area normal to force, with any justified net-area reduction. |
| Member length | mm | Uniform length between the displacement reference points. |
| Young’s modulus | MPa | Young’s modulus for the actual material, temperature and elastic loading direction. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Signed axial force
- What it is
- The load acting along the member’s axis through the centroid of its section: positive for tension (pulling), negative for compression (pushing).
- Units and format
- Enter a number in N: newtons. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Stress, strain and length change are directly proportional to force.
- Get it right
- Watch the sign: a compressive load must be entered as negative. Kilonewtons need multiplying by 1000.
What this means: Uniform cross-sectional area
- What it is
- The cross-sectional area of the member that carries the load, cut at right angles to the force, constant along its length.
- Units and format
- Enter a number in mm²: square millimetres. The form accepts 0.000001 mm² or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 mm² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Stress and length change are inversely proportional to area.
- Get it right
- Use the net area where holes reduce the section, if that is justified for the check.
What this means: Member length
- What it is
- The length of the uniform member between the two points whose relative movement you want.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 100000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Length change is directly proportional to length; stress does not change.
- Get it right
- Measure between the actual load or displacement points, not the overall part length.
What this means: Young’s modulus
- What it is
- The elastic (Young’s) modulus of the member material: the ratio of stress to strain in the elastic range, from material data for the actual temperature.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.001 MPa or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200000 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Strain and length change are inversely proportional to the modulus.
- Get it right
- Enter MPa, not GPa: 1 GPa is 1000 MPa.
Method and formulas
- Stress = force/area in N/mm² (MPa); strain = stress/E; extension = strain × length.
- Energy in joules = force² × length/(2 × area × E × 1000), for elastic loading from zero.
- Example: 10,000 N, 200 mm², 1000 mm and 200,000 MPa gives 50 MPa, strain 0.00025, extension 0.25 mm and 1.25 J.
Limitations
- Small-strain linear elasticity, uniform area and concentric static load are assumed. Yielding, joints, thermal effects and concentrations are excluded.
- Compression may buckle before nominal stress becomes high; column stability is not calculated.
- No allowable load or structural compliance is established.
- Default values are worked examples, not recommended settings or material properties.
Typical uses
- axial deformation
- tensile stress
- elastic strain
Who it is for
- Mechanical designers
- Project engineers
What you get
- Signed nominal stress and strain
- Extension or shortening
- Elastic strain energy
Interpreting the result
- Compare with independently established material, stability and serviceability criteria.
- Check load introduction and joint compliance when comparing measured displacement.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 199–202. Topic reference; implementation and examples are original, and no source tables are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Stress, strain and why steel springs back
In Strain Gauges and Load Cells by the Numbers
What it covers: Why a metal behaves as a spring, how stress, strain, Young's modulus and Poisson's ratio are related, and why a load cell concentrates strain into a small spring element.
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