User`s guide
125
This relationship between radius of curvature and the bending moment can be determined by
summing the moment due to the normal stresses on an arbitrary beam cross section and equating
it to the applied internal moment. This is the same as applying the moment equilibrium equation
about the neutral axis (NA).
Combining Eq.7 and Eq.8 gives
Note that the integral is the area moment of inertia, I, or the second moment of the area. Using
the area moment of inertia gives
Eq. 10 can be used again to eliminate ρ, giving,
Rearranging gives,
This equation gives the bending normal stress, and is also commonly called the flexure
formula. The y term is the distance from the neutral axis (up is positive). The I term is the
moment of inertia about the neutral axis.
Eq.6
Eq.7
Eq.8
Eq.9
Eq.10
Eq.11
Eq.12