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Fixed-fixed beam with central point load.

Check the equal support reactions, restraint moments, balanced midspan moment, and elastic movement caused by one point load at the beam centre.

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Use symmetry to expose the restraint actions.

A central point load gives equal vertical reactions, but a fixed-fixed beam also develops hogging moments at both ends. The positive midspan moment has the same magnitude in this symmetric load case.

Governing equations

For a central point load P, RA = RB = P/2. Internal end moments are -PL/8 and the positive midspan moment is PL/8. The maximum elastic deflection is PL3/(192EI) directly under the load.

Why location matters

The compact coefficients on this page rely on exact midspan placement and symmetry. Moving the load requires piecewise continuity and compatibility equations; do not use this page as an arbitrary point-load calculator.

Keep it as an elastic load-case screen.

  • Both ends must restrain rotation and vertical translation.
  • The point load is vertical, downward, and exactly at L/2.
  • Support settlement, cracking, shear deformation, stability, stress, and code limits are not checked.
  • This is elastic analysis, not member or connection design.