Leaf Spring
Compute bending stress and free-end deflection of a cantilever leaf (flat) spring under end load for rectangular section.
Inputs
Formula
σ = 6WL/(bt²); δ = 4WL³/(Ebt³)
Cantilever end-load model; use correction factor for trapezoidal/triangular profiles.
Fundamentals
Leaf springs stack curved plates; bending deflection cushions load — widely used in vehicle suspension.
Approximating an equal-strength beam, deflection $\delta$ grows with load $F$; total stiffness is roughly the sum of leaf stiffnesses, the master leaf taking the main moment.
History
The leaf spring is the oldest vehicle suspension (carriage era); the multi-leaf stack was the main early-automotive spring.
Engineering applications
Used for load distribution and stiffness in commercial vehicles, rail vehicles and leaf-sprung suspension.
Glossary
| Master leaf | Longest leaf, carrying the largest moment. |
| Equal-strength beam | Tapered section keeps stresses near-uniform. |
| Deflection $\delta$ | Vertical deformation under load. |
How to use
- Fill in Load W, Free length L, Width b, Thickness t, Young's mod. E in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Bending stress σ, Deflection δ in the results area.
Formula notesSemi-elliptic leaf spring: deflection δ = P·L³/(4·E·n·b·t³); stress σ = 3·P·L/(2·n·b·t²).
Formula · Worked Example · Knowledge
Formula
Cantilever leaf spring end load: bending stress $\sigma=6WL/(bt^2)$, free-end deflection $\delta=4WL^3/(Ebt^3)$ (rectangular section).
Worked Example
W=500 N, L=300, b=30, t=5, E=200 GPa → σ≈120 MPa, δ≈3.6 mm.
Key Points
- Thickness t dominates deflection (cube law).
- Multi-leaf stacks cut stress and thickness.
- Trapezoidal/triangular leaves need a shape factor.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Load W (N) | W | N | 500 |
| Free length L (mm) | L | mm | 300 |
| Width b (mm) | b | mm | 30 |
| Thickness t (mm) | t | mm | 5 |
| Young's mod. E (GPa) | E | GPa | 200 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Bending stress σ | sigma | MPa |
| Deflection δ | delta | mm |
Applications
- Common engineering use cases
FAQ
What formula does this tool use?
This tool computes per ISO / AGMA / ASME standard formulas: σ = 6WL/(bt²); δ = 4WL³/(Ebt³)
How accurate are the results?
Results match input precision, based on SI units and common engineering approximations; for critical duty re-check with a safety factor.
Where is it used?
Common engineering use cases