The maximum deflection (δ) at the free end of a cantilever beam with a uniform distributed load (w) is given by δ = 5wL^4 / 384EI, where E is the modulus of elasticity and I is the moment of inertia.

The reaction force at each support for a simply supported beam with a uniform load (w) is R = wL/2.

The Method of Joints is commonly used to determine the forces in the members of a truss structure by analyzing the equilibrium of each joint.

If a member in a truss is in tension, the force acting on it is pulling away from the joint.

Increasing the moment of inertia (I) of a beam decreases its deflection under a given load, as deflection is inversely proportional to I.

The deflection (δ) at the center of a simply supported beam under a central point load (P) is given by δ = PL^3 / 48EI.

The relationship is given by V = dM/dx, meaning the shear force is the derivative of the bending moment with respect to the position along the beam.

The shear force (V) at the supports of a simply supported beam with a point load (P) at the center is V = P/2.