Materials & Structures Calculators
Four calculators for how materials respond to load — stress, strain, stiffness and the reactions in a loaded beam.
Stress, strain and stiffness in one sentence
Stress is the load a material carries per unit area; strain is how much it deforms as a proportion of its original length; Young's modulus is the ratio between the two, and therefore the material's stiffness. Work them out with the Stress Calculator, the Strain Calculator and the Young's Modulus — and note that all three describe the elastic region only, before any permanent deformation begins.
Why strain has no units
Strain is a length divided by a length, so it cancels to a pure number — usually a very small one, which is why it is often quoted in microstrain (10⁻⁶) or as a percentage. Stress, by contrast, is force over area, in pascals, and structural values are large enough that MPa and GPa are the working units.
From a beam to a stress
The Beam Load gives support reactions and the maximum bending moment for a simply supported beam. That moment is the input to a bending-stress check — divide by the section modulus and you have the stress the material must survive, which is where the elastic tools above take over.
These are teaching tools, not design tools
Every calculator here uses idealised, simply supported, statically determinate cases with no safety factors, no buckling check and no fatigue. Real structural design is governed by codes such as the Eurocodes and must be signed off by a qualified engineer. Use these to understand and check, never to specify.
Choosing the section is usually the real problem
Once you know the bending moment, the question becomes which section can carry it. That depends on the section modulus, a purely geometric property: a deeper beam is dramatically stiffer than a wider one of the same area, because depth enters the second moment of area cubed while width enters it linearly. Doubling the depth of a rectangular section increases its bending resistance roughly fourfold and its stiffness eightfold, which is why joists stand on edge and why an I-beam puts almost all its material in the flanges. Deflection, not stress, is often the governing limit in floors — a beam can be comfortably within its material strength and still bounce enough to fail a serviceability check.
Frequently asked questions
Why does strain have no units?＋
It is a change in length divided by an original length, so the units cancel and what remains is a pure ratio. Because typical elastic strains are tiny, they are usually quoted as microstrain (parts per million) or as a percentage rather than as a bare decimal.
What is a typical Young’s modulus?＋
Steel is around 200 GPa, aluminium around 70 GPa, concrete around 30 GPa and most structural timbers around 10 GPa along the grain. If a calculation returns a modulus far outside the range for the material you are studying, the usual cause is a unit mismatch between the stress and the strain rather than an unusual material.
Does the beam calculator handle fixed or continuous beams?＋
No. It solves a simply supported, statically determinate span with pin and roller supports. Fixed ends, cantilever overhangs, continuous multi-span beams and any indeterminate arrangement need moment distribution or a stiffness method, and will give the wrong reactions here.
Can I use this to size a real beam?＋
No. There are no partial safety factors, no load combinations, no deflection or buckling checks and no material grade data. Real design is governed by codes such as the Eurocodes or AISC and must be carried out and signed off by a qualified engineer. Use these tools to understand the behaviour and to sanity-check a result you already have.