I need to calculate the local stiffness of a cantilever beam with and without crack.

For the stiffness of the intact beam(without crack) I am using the following expression:

Kc=(3EI/L^3)

For the stiffness of the cracked beam I am using this expression:

Ko=EI/(6*pi*(1-v^2)*h*J); where J is an alpha function ( being alpha the crack ratio).

The problem is that using these two expressions I am getting higher Stiffness when the beam is cracked. Does anyone know how to fix this? Or if I am using the wrong expressions?

Thank you very much.