Calculator
Example data table
These examples show typical inputs and expected deflection scales. Use them to sanity-check units.
| Case | Span | E | Section | Loads | Approx. max deflection |
|---|---|---|---|---|---|
| Center point load | 4 m | 200 GPa | Rect 0.05×0.20 m | P=10 kN at 2 m | ≈ 2.0 mm |
| Full-span UDL | 4 m | 200 GPa | Rect 0.05×0.20 m | w=2 kN/m from 0–4 m | ≈ 1.0 mm |
| Two point loads | 3 m | 69 GPa | Solid d=0.10 m | P=3 kN at 1 m, P=3 kN at 2 m | Order of 0.1–1 mm |
Formula used
The calculator uses the Euler–Bernoulli beam model for small deflections. The governing relation is:
E I \; \dfrac{d^2 y}{dx^2} = -M(x)
- M(x) is the internal bending moment from reactions and applied loads.
- E is Young’s modulus and I is the second moment of area.
- The solver enforces simply supported conditions: y(0)=0 and y(L)=0.
For combined loads, the code builds M(x) from point loads and uniform segments, then integrates curvature numerically (trapezoidal rule) to get slope and deflection.
How to use this calculator
- Enter the span L and choose its unit.
- Enter E and pick the material unit (GPa, MPa, Pa, or psi).
- Select a section mode: direct I or a common shape.
- Choose force units, then add point loads and/or uniform load segments.
- Optionally set xq to read deflection at a specific position.
- Press Compute deflection to see results above the form.
- Use the CSV/PDF buttons to export the latest calculation.
Tip: If results look too large or too small, re-check units for geometry and loads first.