We'll demonstrate this hierarchy by working backwards. We first combine the 2 equilibrium equations to eliminate V,
Next replace the moment resultant M with its definition in terms of the direct stress s,
Use the constitutive relation to eliminate s in favor of the strain e, and then use kinematics to replace e in favor of the normal displacement w,
As a final step, recognizing that the integral over y^{2} is the definition of the beam's area moment of inertia I,
allows us to arrive at the EulerBernoulli beam equation,
