# 11.1 Introduction

All of the methods that have been covered in this book are suitable for analysis of determinate and indeterminate civil engineering structures by hand. These methods are useful for performing quick calculations for simple structures and were the only methods available to civil engineers prior to the widespread adoption of personal computers.

For structures that are more complex than those having less that three degrees of indeterminacy (using the force method) or less than three degrees of freedom (using the slope-deflection method), only the moment distribution method covered in the previous chapter is suitable. Even then, for a moderately complex frame analysis such as the one previously shown in Figure 10.1, the moment distribution method would need many iterations of calculations before the error in the final moments become small enough for the results to be useful.

In modern engineering practice, such structures of medium to high complexity are typically analysed using *matrix structural analysis*. The advantage of matrix structural analysis is that it can easily be programmed to be solved using a computer. The use of this method with a computer allows the analysis of complex structures that would have been impossible previously.

Matrix structural analysis usually uses a stiffness-type method for analysis. In this way, it is similar to the slope-deflection and moment-distribution methods from the previous two chapters. Both of these methods required the calculation of member *stiffness* parameters to conduct the analysis by distributing moments according to stiffness. In the moment-distribution method, the stiffness parameters were explicitly determined in order to calculate the distribution factors. In the slope-deflection method, the slope-deflection equations represented the stiffness of each element (by relating the deflections/rotations directly to the associated end moments).

These are in contrast to force-type methods such as the force method, which require the calculation of *flexibility* parameters to conduct the analysis by determining deflections and rotations based on forces and moments.

Matrix structural analysis is usually performed in practice using commercial software packages (although free alternatives do also exist). These software packages can often appear to act as 'black-boxes,' accepting geometry and forces as input and returning the internal moments, shears and structural deflections to the user; however, this can be dangerous if the user does not understand the behaviour of structures on a conceptual level (as provided by this book), or if the user does not understand how the underlying matrix structural analysis works. It is the responsibility of an engineer to understand her tools.

This chapter will provide a basic explanation of matrix structural analysis for a very simple structural system consisting of one-dimensional truss elements (the simplest possible type of structural system); however, prior to using matrix structural analysis for design, the reader is strongly advised to pursue a full course in matrix structural analysis that will build upon the concepts in this book. Such courses are often titled 'Structural Analysis 2' or 'Matrix Structural Analysis.'