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Simply supported span with prescribed end moments.

Find reactions and the moment envelope when the internal end moments are supplied as signed boundary actions alongside a full-span UDL and optional point load.

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Use boundary actions without pretending to solve the frame.

This parameterised span accepts a full-span UDL, an optional downward point load, and prescribed internal end moments. It is useful for checking a member action envelope after a frame or joint analysis has supplied the boundary moments.

Governing equations

With sagging positive, RA = [MB - MA + wL2/2 + P(L - a)]/L and RB = wL + P - RA. For a section after the point load, M(x) = MA + RAx - wx2/2 - P(x - a). Candidate extrema occur at the ends, the point-load position, and any zero-shear positions.

Classic variants covered

Set P = 0 for a UDL with prescribed end moments, set w = 0 for end moments plus one point load, or use both for a combined boundary-action case. This is not a fixed-fixed calculation: the end moments are inputs.

Keep it as a boundary-action statics screen.

  • Use positive L; keep the optional point position a between 0 and L.
  • Use non-negative w and P for downward loads. Enter MA and MB as signed internal moments.
  • No joint stiffness, frame equilibrium, deflection, stress, stability, or code design is calculated.
  • Check that the prescribed end actions came from a compatible structural model before relying on the envelope.