Elastic Axial Deformation
Calculate extension or shortening of a uniform elastic bar.
Try this formula
Calculate signed axial deformation or choose another supported quantity.
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Try this formula
Calculate signed axial deformation or choose another supported quantity.
Use decimals or scientific notation, such as 1.2e3. Calculations update as you type.
Signed axial deformation
Enter the known values to see the result.
Use small strains and a homogeneous, linearly elastic material. Loads are static or slowly applied; remain below the proportional limit. Force, area, and modulus are constant along the bar; otherwise integrate F/(AE) along its length.
Difficulty
Intermediate
Read time
5 min
Prerequisites
Basic algebra, mechanics, and consistent SI units
Source
Donney Fan — MECH 360 — Mechanics of MaterialsReference equation: Axial Load — Elastic deformation under axial loading. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Definition
An axial member stretches more when it is longer or more heavily loaded. A larger area or elastic modulus makes it stiffer, reducing the displacement.
Variables & Units
| Symbol | Meaning | Units |
|---|---|---|
| Signed axial deformation | ||
| Signed axial force | ||
| Bar length | ||
| Cross-sectional area | ||
| Young’s modulus |
Real-World Applications
Tie-rod extension
Estimate extension under a known tensile load.
Axial stiffness
Compare materials and member dimensions.
Worked Example
Problem
A 2 m steel bar with area 0.0004 m² and modulus 200 GPa carries 20,000 N in tension. Find its extension.
Given
Solution
Final Answer
Contents
Info
Tools
Source & review
Reference equation: Axial Load — Elastic deformation under axial loading. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Assumptions
- • Use small strains and a homogeneous, linearly elastic material.
- • Loads are static or slowly applied; remain below the proportional limit.
- • Force, area, and modulus are constant along the bar; otherwise integrate F/(AE) along its length.
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