Cross-section
Second moment of area I = 6.67e+7 mm⁴ · Area = 20,000 mm²
Material / modulus
Supports
Point loads
Distributed loads
No distributed loads.
Applied moments
No applied moments.
Support reactions
This tool solves Euler–Bernoulli beam bending using the direct-stiffness finite element method, so it handles cantilevers, simply-supported, overhanging, continuous multi-span and statically indeterminate beams. Sign convention: downward loads are positive, bending moment is sagging-positive, and deflection is reported downward.
Supports
Pinned and roller supports restrain vertical movement; a fixed support also restrains rotation and develops a reaction moment.
Section
Pick a standard profile to compute I and the extreme-fibre distance automatically, or enter the second moment of area directly from a datasheet.
Bending stress
Bending stress σ = M·y/I is evaluated along the span and compared against the material's yield strength for a safety factor.
Worked example: Simply-supported 5 m beam with a central 10 kN point load
- Reactions: each support carries P/2 = 5 kN
- Max bending moment at mid-span M = PL/4 = 10 × 5 / 4 = 12.5 kN·m
- Max deflection δ = PL³/(48EI)
M_max = 12.5 kN·m at mid-span, with peak shear of 5 kN at the supports
What beam types can this calculator analyse?
It uses the finite element (direct stiffness) method, so it handles cantilevers, simply-supported, overhanging, propped and continuous multi-span beams, including statically indeterminate cases. Add any combination of pinned, roller and fixed supports.
Do I have to design the cross-section?
No. You can pick a standard profile (rectangle, circle, I-beam, hollow rectangle or tube) to compute the second moment of area automatically, or simply type in the second moment of area I from a datasheet and skip the geometry.
What sign conventions are used?
Downward loads and clockwise applied moments are positive, the bending moment is sagging-positive, positive shear is the net upward force on the segment to the left of a cut, and deflection is reported as positive downward.
How is the bending stress calculated?
Bending stress is σ = M·y/I, evaluated along the span using the local bending moment M and the distance y from the neutral axis to the extreme fibre. The peak stress is compared with the material's yield strength to give a safety factor.
What is free and what needs Pro?
Single-span beams (two supports) with point loads and uniform distributed loads, plus on-screen shear, moment and deflection diagrams, are free. Multi-span beams, applied moments, linearly varying loads, bending-stress utilisation, saving and branded PDF export are Pro features.