In this method, an equation for the beam's internal bending moment is derived. This equation is then integrated, yielding the equation for slope. Next, the slope equation is integrated to give the equation for the beam deflection.
Equations for the slope and deflection of a beam can be derived from equations describing the beam loading, shear force, or bending moment. Although there are a couple of methods and variations, we will focus here on the basic double-integration method.
A constant of integration will arise with each integration. To complete the slope and deflection equations, these constants of integration must be evaluated for the specific beam and loading.