The moment of inertia for a beam can be calculated using the formula I = (bh^3)/12, where b is the base width of the beam and h is the height of the beam.
The bending moment for a beam can be calculated using the formula M = wL^2/8, where w is the distributed load and L is the length of the beam.
The maximum deflection of a beam can be calculated using the formula δmax = (5wL^4)/(384EI), where w is the distributed load, L is the length of the beam, E is the elastic modulus of the material, and I is the moment of inertia.
A simply supported beam is supported at both ends and can only resist vertical forces, while a cantilever beam is supported at one end and can resist both vertical and horizontal forces.
The shear force and bending moment diagrams for a beam can be determined by analyzing the loads and supports acting on the beam and calculating the reactions, then plotting the values along the length of the beam.