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Simply supported beam with triangular load.

Screen the support reactions, critical sagging moment, and elastic deflection for a full-span load that increases linearly toward the right support.

read the result

Turn a varying load into a traceable elastic check.

This load case represents a linearly varying downward load, zero at the left support and q0 at the right. Reactions come from equilibrium; the deflection curve follows the constant-EI Euler-Bernoulli beam equation.

Governing equations

For q(x) = q0x/L, RA = q0L/6 and RB = q0L/3. The positive moment maximum is q0L2/(9√3) at x = L/√3. The maximum deflection occurs at x = L√(1 - 2√30/15), using the elastic curve shown by the calculator.

Orientation is part of the load case.

If the triangle is reversed, the reactions and result locations mirror about midspan. Do not reuse the rising-right formulas without swapping the orientation.

Keep it as an elastic load-case screen.

  • Use positive L, E, I, and peak intensity values; all loads are vertical and downward.
  • Peak intensity q0 is not the same as total load: W = q0L/2.
  • Shear deformation, cracking, self-weight unless entered, stability, stress, and code limits are not checked.
  • This is elastic analysis, not member or connection design. Confirm the actual support and load arrangement before using the result.