Question 1

How do I calculate beam deflection?

Accepted Answer

Deflection depends on the support case, the load, the span and the bending stiffness EI. For a simply supported beam with a central point load P the maximum deflection is δ = P·L³ / (48·E·I), where E is the elastic modulus and I is the section moment of inertia. A cantilever with an end load P gives δ = P·L³ / (3·E·I). This tool applies the standard formula for the case you choose.

Question 2

What is the difference between a cantilever and a simply supported beam?

Accepted Answer

A cantilever is fixed at one end and free at the other, so it deflects much more for the same load and span. A simply supported beam rests on a support at each end. For an equal point load the cantilever end-load deflection (P·L³/3EI) is sixteen times larger than the simply supported central case (P·L³/48EI).

Question 3

How is the section moment of inertia I calculated?

Accepted Answer

For a rectangle of width b and height h, I = b·h³ / 12. For a solid round bar of diameter d, I = π·d⁴ / 64. For a round pipe of outer diameter OD and wall thickness t, the inner diameter is id = OD − 2t and I = π·(OD⁴ − id⁴) / 64. The larger I is, the stiffer and stronger the beam in bending.

Question 4

What does the maximum bending stress tell me?

Accepted Answer

Maximum bending stress is σmax = Mmax·c / I, where Mmax is the maximum bending moment and c is the distance from the neutral axis to the outermost fibre. Compare σmax with the material's yield strength (with a safety factor) to judge whether the beam is strong enough — deflection alone is not enough.

Question 5

What are the assumptions and limits of this calculator?

Accepted Answer

The results assume linear-elastic material, small deflections, a prismatic (constant) cross-section and that self-weight is ignored. Shear deflection and buckling are not considered. Treat the numbers as a theoretical first estimate for design guidance, not a substitute for verified engineering analysis.

Beam DeflectionCalculator

Beam Deflection
Calculator