In a built up beam, actual bending compressive stress fbc is given by (where y is the distance of the edge of the beam from the neutral axis):

Explanation:
The equation for simple bending is given by:

\(\frac{M}{I} = \frac{σ}{Y} = \frac{E}{R}\)

where I = Moment of Inertia, E = Modulus of Elasticity, σ = Stress at any fibre at a distance of y from the neutral axis,

M = Bending moment and R = Radius of curvature.

In a built-up beam, the formula for the actual bending compressive stress f_bc is derived from the simple bending theory, which is:

\( f_{bc} = \frac{M \cdot y}{I_{xx}} \)

Where,

M is the bending moment,

y is the distance from the neutral axis to the point where the stress is being calculated,

I_xx  is the moment of inertia about the neutral axis.