Calculate deflection, end moments, and reactions for fixed-fixed (fully restrained) beams under point and distributed loads.
Enter the span, Young's Modulus, and moment of inertia, then choose a load case: a point load at midspan, a uniformly distributed load, or a point load at any position. Both supports are fully restrained, so the beam develops hogging moments at the walls in addition to sagging at midspan.
For a center point load the fixed-end moments are PL/8 and the midspan deflection is PL³/192EI — one quarter of the simply supported value PL³/48EI. Under a UDL the end moments are wL²/12, twice the wL²/24 at midspan, and the deflection wL⁴/384EI is one fifth of the simply supported case.
For an off-center point load the end moments become Pab²/L² and Pa²b/L², and the largest sagging moment 2Pa²b²/L³ occurs at the load itself. The deflection shown is the closed-form value at the load point, Pa³b³/3EIL³, and is labeled accordingly since the true maximum sits slightly away from the load.
Four times for a midspan point load (PL³/192EI versus PL³/48EI) and five times under a uniform load (wL⁴/384EI versus 5wL⁴/384EI). End fixity forces the beam into double curvature, which sharply reduces deflection without changing the section.
At the supports. The fixed ends carry wL²/12 in hogging while midspan sees only wL²/24 in sagging — half as much. Capacity checks on a built-in beam therefore focus on the ends, the opposite of a simply supported beam.
The closed-form expression Pa³b³/3EIL³ gives the deflection exactly where the load acts. For an asymmetric load the true maximum lies slightly toward the longer segment, so the calculator labels the value as δ at the load point rather than overstating it as the absolute maximum.
They are the starting values for classical indeterminate methods such as moment distribution. The PL/8 and wL²/12 values this tool reports are the standard fixed-end moments, so you can feed them directly into a frame analysis or use them to cross-check hand calculations.