A simply supported beam is loaded as shown. Using singularity functions, the shear, bending moment, slope, and displacement along the beam can be expressed by the following equations By definition, the singularity function can be expressed as follows r-a) when : > a when r a). *(z-a).^ n Note 2: Minimum/Maximum of a function occurs where its derivative is equal to zero 20 kips/ft 150 kip-ft 15 kips 5 2