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Simply supported beam with central triangular load.

Calculate the symmetric reactions and midspan moment for a full-span tent-shaped load that is zero at both supports and peaks at the centre.

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A symmetric triangle is not a one-way triangle.

The load rises linearly from zero at the left support to q0 at midspan, then falls linearly to zero at the right support. Symmetry makes the reactions equal, but its moment coefficient differs from a uniform load and from a triangle that rises toward one end.

Governing equations

The total distributed load is W = q0L/2. Therefore RA = RB = q0L/4. The maximum positive moment occurs at x = L/2 and is Mmax = q0L2/12.

Classic variant covered

This page covers the full-span symmetric, tent-shaped triangular load. It does not cover a triangle with its peak at one support; use the one-way triangular-load page for that orientation.

Keep it as a statics load-case screen.

  • Use positive L and a non-negative midspan peak q0.
  • The load must be zero at both supports and linearly varying on each half.
  • Deflection, stress, self-weight unless entered, load factors, stability, and code limits are not checked.
  • This is elastic-load analysis terminology, not member or connection design.