🌉 Continuous Beam Moments

Written and maintained by the PhDino author · Last reviewed 21 September 2026 · Checked against 4 independent reference calculations · how PhDino checks its numbers

Related standards: AISC 360

Estimating support and span moments for a two-span continuous beam under uniform load.

A beam continuous over an interior support (rather than two separate simple spans) redistributes moment: the interior support develops a negative (hogging) moment, which reduces the positive (sagging) moment within each span compared to treating the spans as simply supported. The classical hand method for this is moment distribution (Hardy Cross), which iteratively balances unbalanced moments at each joint until they converge.

For two spans that share the same stiffness (EI) and rest on simple supports at both ends, the interior support moment has an exact closed form from the three-moment equation, so this calculator uses that rather than iterating. Hardy Cross moment distribution converges to the same answer for this case.

Key formula

Support moment: M_B = −(w_A·L_A³ + w_B·L_B³) / (8·(L_A + L_B))
Outer reaction of a span: R = wL/2 − |M_B|/L
Largest sagging moment in that span: M = R² / (2w)
Equal spans and loads: M_B = −wL²/8, span moment = 9wL²/128

Variables

w

uniform load on that span

L

span length

M_B

bending moment over the interior support (negative = hogging, tension on top)

Notes & limitations

• Two equal spans under the same load give a support moment of wL²/8 — the moment of a span that is fixed at the middle support and pinned at its far end — and a largest span moment of 9wL²/128, about 44% less than the wL²/8 a single simple span would carry. That reduction is the benefit of continuity.
• This assumes constant EI along both spans, simple supports at the outer ends, and uniform loads only. Point loads, pattern loading (live load on one span at a time) and unequal stiffness need a full analysis, and a beam with three or more spans needs software or a full moment-distribution / stiffness-method calculation.