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Compatibility supplies the missing reaction.
This is a first-degree indeterminate beam. The vertical prop reaction is selected so that the prop point has zero vertical movement; the remaining vertical reaction and fixed-end action then follow from equilibrium.
Implemented equations and signs
Let L be the fixed-end-to-prop span, P the downward point load, and a its distance from the fixed end, with 0 < a < L. Taking upward reactions as positive, the prop reaction is RB = Pa2(3L - a)/(2L3) and the fixed vertical reaction is RA = P - RB. The displayed fixed-end hogging magnitude is |MA| = Pa - RBL; the sagging moment at the load is M(a) = RB(L - a).
Classic load-case variants covered
The position parameter covers a point load anywhere strictly inside the span, including the common midspan case by setting a = L/2. It also covers an off-centre point load without assuming symmetry. P = 0 is accepted as a zero-load screen. The page does not represent a prop at the fixed end or exactly at the free/prop end because the implemented compatibility case requires 0 < a < L.
Keep it as an elastic load-case screen.
- The left support is perfectly fixed; the right support is a rigid vertical prop with no rotational restraint.
- The load is vertical, downward, and applied at one point; signs are represented by a non-negative P input and named hogging/sagging outputs.
- Constant EI, small deflection, zero settlement, continuous contact, and no prop flexibility or gap are assumed.
- Shear deformation, axial force, second-order effects, member strength, connection design, and serviceability criteria are not checked.