The differential equation for the deflection curve of a beam is:
$\frac{d^2y}{dx^2} = \frac{M}{EI}$
Where:
- y is the deflection of the beam at a point x along its length.
- x is the distance along the longitudinal axis of the beam.
- M is the bending moment at the point x.
- E is the modulus of elasticity of the beam material (Young's modulus).
- I is the area moment of inertia of the beam's cross-section about the neutral axis.
- EI is the flexural rigidity of the beam.
This equation relates the second derivative of the deflection curve to the bending moment, providing a basis for calculating beam deflections under various loading conditions. Solving this differential equation, along with appropriate boundary conditions, yields the equation of the deflection curve, y(x).
