Inputs
Notes: For accuracy, confirm I is about the bending axis. Deflection limits provide a quick serviceability check only.
Results
| Load Case | Unit System | Span L | E | I | Load | Max Deflection | Units | Limit | Pass? |
|---|
Batch Compute
One row per case. Columns: loadCase,units,L,E,I,P,w,x,limit. Use dashes for unused fields.
Formulas Used
Symbols: \( L \) span, \( E \) elastic modulus, \( I \) second moment.
- Simply supported, point load at midspan: \( \delta_{max} = \dfrac{P L^3}{48 E I} \)
- Simply supported, uniform load: \( \delta_{max} = \dfrac{5 w L^4}{384 E I} \)
- Fixed–fixed, point load at midspan: \( \delta_{max} = \dfrac{P L^3}{192 E I} \)
- Fixed–fixed, uniform load: \( \delta_{max} = \dfrac{5 w L^4}{384 E I} \)
- Cantilever, point load at end: \( \delta_{max} = \dfrac{P L^3}{3 E I} \)
- Cantilever, uniform load: \( \delta_{max} = \dfrac{w L^4}{8 E I} \)
Deflection at a position \( x \) (simply supported, uniform load): \( \delta(x) = \dfrac{w\,x\left(L^3 - 2Lx^2 + x^3\right)}{24\,E\,I} \)
Assumes small deflection, linear elastic behavior, prismatic members.
How To Use This Calculator
- Select unit system, supports, and load case.
- Pick material and shape presets, or enter E and I.
- Enter span and either a point load or a uniform load.
- For SS UDL, optionally enter a position to evaluate.
- Set an allowable deflection limit if desired.
- Compute and export results; use batch for multiple cases.
- Save inputs locally or copy a shareable URL.
FAQs
Which load case should I choose?
Match supports and loading to the real member. Use simply supported for pinned ends, fixed–fixed for fully restrained ends, and cantilever when one end is fixed and the other free. Select point load or uniform load accordingly.
Why do results differ from my code check?
This tool computes elastic, small-deflection responses. Building codes may include serviceability modifiers, composite action, cracking, creep, or construction tolerances. Always verify with project specifications and governing standards before finalizing designs.
What values should I enter for E and I?
Use your material’s elastic modulus and the section’s second moment about the bending axis. You can pick presets for typical steel. For precise work, use manufacturer tables or section properties from your regional steel handbook.
How do I apply deflection limits like L/360?
Select a ratio under Allowable Deflection or enter a custom value. The calculator compares the computed maximum deflection with L divided by the chosen ratio and reports PASS or FAIL for a quick serviceability screening.
Can I check deflection at a specific position?
Yes. For a simply supported beam with uniform load, enter a position x and compute. The calculator displays deflection at x alongside the maximum. For other cases, only maximum deflection is currently reported.
Example Data
| Case | L | E | I | P | w | Units |
|---|---|---|---|---|---|---|
| ss_pt_mid | 6 | 200 | 12000 | 25 | - | SI |
| ss_udl | 8 | 200 | 20000 | - | 5 | SI |
| ff_pt_mid | 8 | 200 | 20000 | 40 | - | SI |
| ff_udl | 10 | 200 | 30000 | - | 8 | SI |
| cant_pt_end | 12 | 29000 | 500 | 8 | - | US |
| cant_udl | 10 | 29000 | 900 | - | 1.2 | US |
Tip: Click any example row to auto-fill the form.
Assumptions & Checks
- Elastic, isotropic steel material behavior.
- Limit check compares against user-selected L/ratio.
- No lateral-torsional buckling considered here.
- Loads are static; dynamic effects are excluded.
Unit Reference
SI: L m, E GPa, I cm⁴, P kN, w kN/m.
US: L ft, E ksi, I in⁴, P kips, w klf.
Serviceability Limits Cheat‑Sheet
| Limit Ratio | Typical Use | Comment |
|---|---|---|
| L/240 | Roof live load | Lenient, noticeable deflection possible. |
| L/300 | General floors | Balanced comfort and economy. |
| L/360 | Residential floors | Common comfort criterion. |
| L/480 | Ceilings/finishes | More stringent to protect finishes. |
| L/600 | Long-span beams | Visual control for sensitive spans. |
Material Elastic Modulus Reference
| Material | E (GPa) | E (ksi) |
|---|---|---|
| Carbon steel | 200–210 | 29,000–30,500 |
| Stainless steel | 190–200 | 27,500–29,000 |
| Aluminum (for comparison) | 68–72 | 9,860–10,440 |
Conversion Factors & Quick Notes
| Quantity | SI → US | US → SI |
|---|---|---|
| Length | 1 m = 3.28084 ft | 1 ft = 0.3048 m |
| Force | 1 kN = 0.224809 kips | 1 kip = 4.44822 kN |
| UDL | 1 kN/m = 0.0685218 klf | 1 klf = 14.5939 kN/m |
| Modulus | 1 GPa = 145.038 ksi | 1 ksi = 6.89476 MPa |
| Inertia | 1 cm⁴ = 0.02401 in⁴ | 1 in⁴ = 41.623 cm⁴ |
| Deflection | 1 mm = 0.03937 in | 1 in = 25.4 mm |