## Abstract

Mechanics of materials is one of the sciences underlying the design of any device that must support loads, from the simplest machines and tools to complex vehicles and structures. Three fundamental questions are examined. *Will an object or structure support the loads acting on it?* Answering this question requires introducing the state of stress, which describes the forces within a material. The state of stress must be determined at each point of a structure to ensure that it does not exceed the capacities of the materials used. *What is the change in shape, or deformation, of an object subjected to loads?* Design engineers must be concerned with how objects change shape due to the loads acting on them. *What can be done if the external loads on an object cannot be determined by using the equilibrium equations?* Supplementing the equilibrium equations with the relationships between the loads acting on an object and its deformation makes it possible to determine unknown reactions. The quantities used to analyze problems in mechanics of materials are expressed in terms of two types of units, the International System, or SI system of units, and the U.S. Customary system of units. The *base units* of the SI system are length in meters (abbreviated m), mass in kilograms (kg) and time in seconds (s). The base units of the U.S. Customary system are length in feet (ft), force in pounds (lb) and time in seconds. Studying mechanics of materials requires familiarity with the fundamentals of statics, including the concept of equilibrium, the equilibrium equations, methods for analyzing truss and frame structures, centroids of areas and distributed forces. Suppose that an object is subjected to two systems of forces and couples. If the sums of the forces in each system are equal and the sums of the moments about a point are equal, the systems are said to be *equivalent*.