1: Fundamental Concepts

1.1: Introduction

To perform a structural analysis means to determine all of the forces and displacements that act on and within a structural assembly such as a building frame or a truss. In reality, of course, the structural engineer creates a mathematical model that approximates a real structure, and performs an analysis of that model.

The act of creating the model is very important, but is largely beyond the scope of this course – left for the time when a student has a better grasp of material behaviour and construction techniques. In this course, we will largely provide you with models, without comment.

To have the ability to perform a structural analysis requires that you have a very good grasp of the following sets of concepts:

• Equilibrium
• Boundary Conditions: Constraints and Internal Conditions
• Elasticity (force/displacement relationships)
• Compatibility (of displacements)

All structures must satisfy all the requirements implied in the above, so these are a set of mathematical tools we can use to determine initially unknown quantities in our models. In fact, this list is sometimes reduced to three concepts:

• Equilibrium, which says something about the required relationships within a set of forces;
• Compatibility, which says something about the required relationships within a set of displacements; and
• Elasticity, which relates forces to displacements.

We will explicitly include boundary conditions as a part of compatibility and will discuss the four areas separately. We note here that we do not always have to use all tools for all structures – that will be clear later.

In addition, there are a small set of other tools that we use to assist us in our mathematics, and that are also fundamental:

• Free Body Diagrams
• Small Displacement Theory (both rigid body and elastic)

We will cover these in the order that we encounter their need as we progress through different kinds of problems, starting with equilibrium (next page).