A beam's free end does not always have zero shear force and bending moment. If a concentrated force or couple is applied at the free end, both shear force and bending moment will be non-zero. However, in the absence of any external loads at the free end, the shear force, bending moment, and curvature will indeed be zero. This distinction is crucial for accurately analyzing beam behavior under various loading conditions.
PREREQUISITESCivil engineers, structural engineers, and students studying mechanics of materials will benefit from this discussion, particularly those focusing on beam analysis and design.