## Introduction

Real-world problems are complex and involve multiple forms of loading. Fortunately for us, we tend to still employ linear elastic materials in real-world applications, so we can exploit the principle of superposition in order to break down complex problems into more simple sub-problems. That is what this unit is all about. There are no new formulas to derive or displacement fields to visualize. It is all about breaking down complex problems into ones we already know how to solve.

So why to de have a whole unit dedicated to a topic that in essence is not teaching anything new? Well, so far we have focused on simple problems that were easy to visualize. Real-world problems can become more complex, and often involve a 3-D aspect to them. It takes practice to visualize such a complex problem and break it down into manageable components. So this unit is all about practice, practice, practice. Please do not skip this practice. Combined loading questions are an efficient way of testing multiple concepts in an exam, so you can be assured that many of the questions in the exam will contain a combined loading aspect.

## Learning Objectives

By the end of this unit, students should be able to…

• Break down complex 3-D, combined loading problems into more simple sub problems.
• Solve individual sub-problems using the concepts learned in the previous units.
• Recombine the results of sub-problems to evaluate the conditions of the main problem.