Beam calculation examples
Every example below opens the calculator already set up for one standard beam problem: the supports, the load, the cross section and the material are pre-filled, so you can change only the numbers that matter to you.
They cover the cases that come up most often in practice — a cantilever arm, a beam on two supports, an eccentric load, a steel pipe, an I-beam, and the two statically indeterminate arrangements where the supports themselves share the load.
Cantilever beams
Beams fixed at one end and free at the other, loaded along the span or at the tip.
- Cantilever beam with a load at the free end A beam fixed at one end and loaded at the free end: deflection, slope and reactions, solved online.
- Cantilever beam with a load in the middle A beam fixed at one end and loaded at midspan: where the load sits changes the deflection, and this page shows by how much.
- Steel pipe as a cantilever A clamped steel pipe loaded at its free end: deflection and reactions for a hollow circular section.
- Aluminium cantilever arm An aluminium rod fixed at one end and loaded at the other: why aluminium arms sag, and how to size one that does not.
Simply supported beams
Beams on a pin and a roller, with central, eccentric, inclined or multiple loads.
- Simply supported beam with a load in the middle The classic pin-and-roller beam loaded at midspan: deflection, moment and reactions, solved online.
- Simply supported beam with an eccentric load A rectangular steel bar supported at both ends and loaded at the third point: where the load sits decides which support works harder.
- Simply supported beam with two point loads A steel tube on two supports carrying two equal loads: the middle section bends without shear, exactly like a four-point test.
- Simply supported beam with an inclined load A force pushing at an angle onto a supported beam: split it into bending and axial parts, and only the first one visibly bends the beam.
- Steel pipe loaded in the middle A steel pipe on two supports with a load at midspan: how much it bends, and which pipe dimensions actually matter.
- I-beam on two supports with a load at midspan An IPE 120 steel beam spanning 3 m and loaded at the centre: deflection, moment and reactions for an I-section.
Statically indeterminate beams
Beams where the supports share the load by stiffness: propped cantilevers and built-in beams.
- Propped cantilever with a load at midspan A beam clamped at one end and propped by a roller at the other: the classic first step beyond statically determinate beams.
- Beam fixed at both ends with a load at midspan A built-in beam clamped at both supports: the stiffest single-span arrangement, and the one with the highest end moments.