Beam Deflections



Length (m) L
Flexural rigidity (Pa m4) EI

Reactions and boundary conditions Point loads Distributed loads Point moments
Position, xR (m) Type v or dv/dx Reaction
xW (m) W (N)
xl (m) xr (m) wl (N m-1) wr (N m-1)
xC (m) C (N m)

This will calculate the reactions in the table above and the deflections and internal loads in the table below.
Where there is a discontinuity (of S or M) it will give the value on the positive side only.
Units of m and N can be replaced by general units as long as force and length units are consistent.

Deflections and internal loads

x (m) v (m) dv/dx S (N) M (N m)

Shape (-v)


Shear force (S)


Bending moment (M)