BEAMS & DEFLECTION
Find reactions, bending stress and maximum deflection for a rectangular beam under a central point load.
Values are calculated locally in your browser.
Theoretical result · verify applicability below
Schematic illustration · not to scale
A centered point load splits equally between two simple supports. The largest bending moment and downward deflection occur at midspan. Section height is measured in the bending direction; doubling it increases stiffness by a factor of eight.
P = 1,000 N, L = 2 m, E = 200 GPa, b = 50 mm and h = 100 mm give I = 4.16667 × 10⁶ mm⁴, each reaction = 500 N, Mmax = 500 N·m, stress = 6 MPa and deflection = 0.2 mm.
The initial inputs reproduce this example. Material values are illustrative inputs, not a material database or certified design values.
Prismatic rectangular beam, ideal pin and roller supports, linear elasticity and small deflections under a static central load. Self-weight, shear deformation, lateral torsional buckling and stress concentrations are excluded.
No factor of safety or design-code allowance is applied unless explicitly stated. Read the engineering disclaimer before applying these results.
Confirm the load direction and units first. Check the schematic against your actual supports and geometry, then compare the worked example with your own independent calculation. A valid numerical result does not establish that the model is appropriate for a real component.
For background, consult the Air Force Stress Analysis Manual’s column analysis and MIT’s Mechanics of Materials learning modules. Use applicable design standards and certified material data for real designs.