Beam deflection & stress calculator
The tool computes beam deflection and bending stress from static elastic beam theory, using the standard beam-table formula for the selected support/load case and section.
How to use
- Enter the calculation conditions
Enter the dimensions, loads, speeds or operating conditions requested by the form.
- Run the calculation
The tool applies the formulas shown on this page to the entered values.
- Review the result
Review the resulting specification and checks, then verify them against the cited source, current standard and real operating conditions before use.
Core formula
δ = P·L³/(48·E·I), M = P·L/4, σ = M/Z, Z = I/c
Example using default values
b40×h60 steel, L=1000, P=1000 N → I=720,000 mm⁴, δ=0.140 mm, σ=10.4 MPa
Source: Mechanics of Materials (Hibbeler / Gere); Roark's Formulas for Stress and Strain — standard single-span beam tables.
Frequently asked questions
Why does increasing section height help more than width?
Because the moment of inertia I of a rectangle scales with h³ but only linearly with b, and deflection is inversely proportional to I, so increasing the height (in the bending plane) reduces deflection far faster.
What deflection limit should I use?
It depends: machine frames typically use L/500 to L/1000, general support structures around L/250. The value is user-entered per your standard or required precision.
Does the result replace a full structural analysis?
No. It covers a single span, static, pure bending; stress concentration, shear, buckling, fatigue and dynamic loads are excluded. Multi-span or complex loading needs separate analysis against the applicable standard.
MINATA — minatavn.com