Continuous beam with UDLs over two to four spans.

multi-span response

Use one compatibility system for the whole beam line.

The outer supports are simple and the internal supports are continuous with zero settlement. Each span carries its own full-span UDL w_i. The solver forms the internal support moments from the three-moment theorem and then recovers reactions and positive span moments.

Three-moment equation

For adjacent spans i and i+1, the compatibility equation is written with the stiffness-weighted support moments:

For a full-span UDL, the simply supported moment diagram supplies the familiar area and centroid terms. CivilKits solves the resulting tridiagonal system and reports signed support moments, reactions, and local span sagging peaks.

Assumptions and limits

• Two to four prismatic spans, full-span downward UDL on each selected span, and constant EI per span.
• Simple outer supports, continuous internal supports, and zero support settlement.
• Linear elastic, first-order Euler-Bernoulli response; no shear deformation or plastic redistribution.
• No moving-load envelope, support width, load combinations, vibration, lateral stability, or code resistance checks.