Engineering structural analysis

Solutions of the fifteen governing equations of linear elasticity are not easy to develop for practical problems. Chapter 3 outlined the complexity of the problem and presented solutions to a few of the simpler practical problems that can be easily treated. These equations define what is commonly called the linearly elastic theory of solid mechanicsor more simply linear elasticitytheory. Engineers and mathematicians have studied these equations for more than two centuries, and their efforts to develop solutions have led to broad areas of applied mathematics. The range of useful analytical solutions, however, still remains quite limited, and the problems for which solutions are available are usually very simple.

To analyze practical structures that are generally more complicated, it is almost always necessary to make judicious simplifications that reduce the governing equations to a form that can be solved with modest effort. This approach is widely referred to as engineering structural analysisor more simply structural analysis. These efforts have produced a rich collection of solutions to practical problems, and structural analysis is an important part of many areas of engineering. The chapters that follow treat the subject of structural analysis, but the developments are based on the fundamental theory of solid mechanics presented in the first three chapters. This chapter introduces basic solution processes, and subsequent chapters extend them to a range of useful structural elements.