STRESS & FATIGUE
Determine stress, strain and elongation or shortening of a uniform bar under an axial force.
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Theoretical result · verify applicability below
Schematic illustration · not to scale
Positive force means tension / elongation; negative means compression / shortening. Compression requires a separate buckling check.
Axial force creates uniform average normal stress. Hooke’s law relates stress to strain, and multiplying strain by original length gives elongation or shortening. A negative result indicates compression.
For F = 10 kN, L = 1 m, A = 400 mm² and E = 200 GPa: stress = 25 MPa, strain = 0.000125 and elongation = 0.125 mm. Reversing the force reverses all three signed results.
The initial inputs reproduce this example. Material values are illustrative inputs, not a material database or certified design values.
Straight uniform prismatic bar, concentric axial loading, homogeneous linear elastic material and small strain. Thermal strain, plasticity, stress concentrations and buckling are excluded. The material proportional limit must be checked independently.
No factor of safety or design-code allowance is applied unless explicitly stated. Read the engineering disclaimer before applying these results.
Confirm the load direction and units first. Check the schematic against your actual supports and geometry, then compare the worked example with your own independent calculation. A valid numerical result does not establish that the model is appropriate for a real component.
For background, consult the Air Force Stress Analysis Manual’s column analysis and MIT’s Mechanics of Materials learning modules. Use applicable design standards and certified material data for real designs.