Deflection, maximum bending moment, and maximum shear force for a simply-supported or cantilever beam under a point load or uniformly distributed load. Classical Euler-Bernoulli beam theory — linear elastic, small-deflection.
Standard method — stated scope limits apply
Beam & Load
Section & Material
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Enter beam, load and section properties.
About This Calculation
Beam deflection, bending moment and shear force are the starting point of any beam design check — before you can verify a section against a code (AISC, IS 800, Eurocode), you need the actual mechanics result for the load case you have. This calculator uses classical Euler-Bernoulli beam theory, the same equations in every mechanics-of-materials textbook, for the four most common cases: simply-supported or cantilever, under a point load or a uniformly distributed load. It gives you the mechanics answer; verifying that answer against deflection limits, allowable stress, and code-specific safety factors is the next step, done separately.
Frequently Asked Questions
Why does deflection formula have 48 in the denominator for a point load but 384/5 for a UDL?
Both come from integrating the same bending-moment equation twice along the beam — the different load distributions (a single point load vs. a load spread evenly along the whole span) integrate to different constants. Both are standard, independently verifiable results, not approximations of each other.
Does this account for the beam’s own self-weight?
No — self-weight is not automatically added. If it’s significant relative to the applied load, add it into your UDL input as an additional distributed load before calculating.
What is the difference between a simply-supported and a cantilever beam here?
A simply-supported beam is free to rotate at both ends (like a beam resting on two supports) — its maximum deflection and moment occur at midspan. A cantilever is fixed at one end and free at the other — both occur at the free end for deflection, and at the fixed support for moment, which is why a cantilever of the same span typically deflects far more under the same load.
Is this result enough to check the beam is safe?
No — this gives you the deflection, moment and shear for the load case. A real design check still needs the section’s actual capacity (from a code-compliant stress or deflection-limit check), load and resistance factors, and confirmation the assumed support conditions match reality.