Virtual work principles

The concept of mechanical work is fundamental to the study of mechanics. The mechanical work done by a force is defined as the scalar product of that force by the displacement through which it acts: work is a scalar quantity, in contrast with forces and displacements, which are vector quantities characterized by magnitudes and directions. Consequently, work quantities are simpler to manipulate than forces and displacements, and this simplification makes work based formulations of mechanics very attractive.

Newtonian mechanics is based on the concepts of forces and moments, which are vector quantities. The equilibrium conditions stated by Newton's law are expressed in their most general form as vector equations, and vector algebra is required for most practical applications. While it is customary to make a distinction between externally applied loads, internal forces and reaction forces, Newton's condition for equilibrium states that the sum of all forces must vanish,without making any distinction between them. It follows that all forces explicitly appear in the equilibrium equations of the problem and the solution process involves the determination of all forces, including internal and reaction forces. Newton's approach effectively determines forces and displacements, but it becomes increasingly difficult and tedious for problems of increasing complexity.