Fixed-Fixed Beam Deflection (UDL)
Fixed-Fixed Beam Deflection (UDL)
Fixing both ends of a beam stiffens it dramatically — the end moments resist rotation and cut the mid-span deflection.
For a fixed-fixed beam under a UDL the mid-span deflection is δ = wL⁴/(384EI). where w is the load per unit length, L the span, E Young’s modulus and I the second moment of area.
Inputs
w := 15 kN/m=15000 kg/s^2
L := 6 m=6 m
E := 200 GPa=200000 MPa
I := 1.2e8 mm^4=1.2e-04 m^4
Apply the fixed-fixed UDL deflection formula.
delta := w·L^4/(384·E·I)=2.11 mm
Results
This deflection is one-fifth of the simply supported value for the same load and span — the benefit of moment-resisting end connections.
Assumptions & limitations
- Both ends fully fixed (no rotation or settlement).
- Prismatic section, elastic behaviour.
- Shear deformation neglected.