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CivilKits/Calculators/Structural/Loading analysis/Two-span point loads

structural / loading analysis

Two-span continuous beam with point loads.

Analyse one point load on each of two unequal spans, with optional unloaded spans, relative stiffness, continuous middle support, and support-reaction screening.

compatibility at support B

Capture the hogging moment that a simple-span model misses.

The outer supports are simple and the middle support is continuous with zero settlement. Each point load is located from the left end of its own span. The relative EI inputs allow a first comparison where the two spans do not have the same stiffness.

Three-moment method

The internal support moment is found from the three-moment theorem by combining the simply supported moment-area terms from the two point-load diagrams, with the stiffness weighting from EI1 and EI2. Once MB is known, each span is recovered by static equilibrium and the span sagging peak is located from the zero-shear position.

POINT-LOAD MOMENT DIAGRAMMss(x) = P a (L - x)/L for x ≥ a, with the symmetric left branch

Signed results use sagging positive and hogging negative. Negative support reactions indicate uplift in the idealised model.

Assumptions and limits

  • Two prismatic spans, simple outer supports, continuous middle support, and no support settlement.
  • One downward point load per span; a zero load is permitted.
  • Constant EI in each span, linear elastic response, small deflection, and no shear deformation.
  • No support width, redistribution, moving-load envelope, vibration, lateral stability, or member design is included.