Differential Equation of the Elastic Curve for Beam Deflection in Strength of Materials
The differential equation of the elastic curve relates the curvature of a beam's deformed axis to its internal bending moment, expressed as EI(d²y/dx²) = M, where EI is the flexural rigidity. This is a core result in the strength-of-materials theory of beam deflection: successive integration of the moment, shear, and load forms of this equation (EI d²y/dx² = M, EI d³y/dx³ = −V, EI d⁴y/dx⁴ = −Q) yields the slope and deflection of the beam as functions of position, with integration constants fixed by static boundary conditions (on moment and shear) and kinematic boundary conditions (on slope and displacement) at the supports.
Differential Equation of the Elastic Curve for Beam Deflection in Strength of Materials
The differential equation of the elastic curve relates the curvature of a beam's deformed axis to its internal bending moment, expressed as EI(d²y/dx²) = M, where EI is the flexural rigidity. This is…