Mid-Span Deflection (Central Point Load)
Mid-Span Deflection (Central Point Load)
A central point load is a classic deflection check — the stiffest loading position and a common test arrangement.
The mid-span deflection is δ = FL³/(48EI). where F is the central load, L the span, E the modulus and I the second moment of area.
Inputs
F := 10 kN=10000 N
L := 4 m=4 m
E := 200 GPa=200000 MPa
I := 8.0e6 mm^4=8e-06 m^4
Apply the central point-load deflection formula.
delta := F·L^3/(48·E·I)=8.33 mm
Results
Compare against the span/deflection limit (often L/360). Deflection grows with the cube of span, so longer beams need disproportionately more stiffness.
Assumptions & limitations
- Simply supported, prismatic beam.
- Elastic, small deflections.
- Load at exact mid-span.