At the end of this section you should be able to:

1. Use singularity function (Macaulay bracket) to create internal moment equation

2. Use double-integral method to find slope and deflection across span of beam

3. Find the slope and deflection of a statically-determinate or indeterminate beam at an arbitrary location

4. Find location and value of maximum deflection and slope

Elasticity focuses on beam slope and deflection, using the elastic curve to connect loading to deformation. You will build internal bending moment equations with singularity functions (Macaulay brackets), apply the double integration method to obtain slope and deflection across the span, and evaluate deflection at any location for both statically determinate and statically indeterminate beams. You will also find the location and value of maximum slope and maximum deflection, and you can use beam deflection tables and superposition as an efficient alternative for common boundary conditions and load cases. The page includes ready-to-use computational resources (Python, MATLAB, and Mathematica) for deflection plots and equation solving.