Free Web Tool

Multi-Span Reactions

Solve a continuous beam with the Three-Moment Theorem — support moments, reactions, and approximate Mmax.

Inputs

Set spans + UDL per span. Tool builds Three-Moment equations and solves continuous beam reactions/support moments. Pinned ends.
SpanL (m)w (kN/m)
Method — Three Moment Theorem
  • For UDL spans, three-moment eqn: M(i-1)·L(i-1) + 2·M(i)·(L(i-1)+L(i)) + M(i+1)·L(i) = -w(i-1)·L(i-1)³/4 − w(i)·L(i)³/4.
  • End moments at pinned supports = 0.
  • Solve linear system for interior support moments, then back out reactions.

Results

N spans
Support moments
Reactions
Mmax (interior)