Simply supported beam calculator

Inputs

Span

Central point load

kip

Uniform load

kip/ft

Elastic modulus, E

ksi

Moment of inertia, I

in⁴

Results

Left reaction: —
Right reaction: —
Maximum shear: —
Maximum moment: —
Maximum deflection: —

How it works

Results are superposed from standard simply supported, elastic beam cases.

R_A=R_B=\frac{P+wL}{2}

M_{max}=\frac{PL}{4}+\frac{wL^2}{8}

\Delta_{max}=\frac{PL^3}{48EI}+\frac{5wL^4}{384EI}

Assumptions and limitations

The beam is simply supported, prismatic, linearly elastic, and has a centered point load plus a full-span uniform load. Shear deformation, self-weight, lateral stability, load combinations, local effects, strength, vibration, and code checks are not included.

Worked example

For a 10 ft span with a 2 kip center load, 1 kip/ft uniform load, E = 29,000 ksi, and I = 100 in⁴, each reaction is 6.00 kip, maximum moment is 17.50 kip-ft, and calculated elastic deflection is approximately 0.102 in.

Frequently asked questions

Can I use this for an off-center load?: No. This version only evaluates a central point load and a full-span uniform load.
Does this size the beam?: No. It reports elastic actions and deflection only; design checks require project-specific engineering.

Important disclaimer

For estimation and education, verify with a licensed engineer.