How to use this tool
- Choose the defined load/support arrangement.
- Enter span, central/end point load, rectangular width and depth, and Young's modulus.
- Review moment, stress and deflection curve.
- Check load combinations, buckling, shear deformation and material allowable stress outside the calculator.
Calculation method and formula
Rectangular second moment I = b h³/12. Simply supported center load: δmax = P L³/(48 E I), Mmax = P L/4. Cantilever end load: δmax = P L³/(3 E I), Mmax = P L.
WORKED EXAMPLE
A 1,000 mm simply supported rectangular beam, b = 20 mm, h = 40 mm, E = 200 GPa and a 100 N midpoint load has δmax ≈0.097656 mm and σmax ≈4.6875 MPa.
What the calculation does not cover
- Model excludes shear deflection, connections, lateral torsional buckling, dynamics and nonlinear yielding.
- The model warns when span/depth is low, where Euler–Bernoulli assumptions degrade.
- Not suitable for certifying a real bridge, structure or lifting system.
Common questions
Which support cases are included?
Simply supported beam with one midpoint point load and a cantilever with one free-end point load.
Does this calculate factor of safety?
No. It estimates elastic response; strength and safety factors require separate engineering evaluation.
Engineering use: This calculator is a transparent estimate for its defined model; confirm units, applicability, standards and engineering decisions independently.