BASIC CONCEPTS

1.1 INTRODUCTION

The primary function of a structure is to receive loads (usually known as service loads) at certain points and transmit them safely to some other points. For instance, a building frame receives occupancy loads of the building besides the self-weight of the structural components of the building and transfers them safely to the foundations. Similarly, a highway bridge has to support the live load due to the traffic and the dead load of the bridge itself besides several other loads. The structural system of the bridge has to be designed so as to transmit these loads safely through the supporting piers and abutments to the foundations. In performing this primary function of receiving service loads at certain points and transferring them safely to some other points, the structure develops internal forces in its component members known as structural elements.
It is the responsibility of the structural engineer to design all the structural elements of a structural system in such a way that they perform their functions adequately. The inadequacy of one or more structural elements may lead to the malfunctioning or even collapse of the entire structure. The object of structural analysis is to determine the internal forces and the corresponding displacements of all the structural elements as well as those of the entire structural system.
The safety and proper functioning of the structure can be ensured only through a thorough structural analysis. The importance of a correct structural analysis for the proper functioning and safety of the structure cannot, therefore, be over-emphasized. A systematic analysis of structural systems can be carried out by using matrices. The matrix approach for the solution of structural problems is also eminently suitable for a solution using modern digital computers. Hence, the advantage of using the matrix approach for large structural problems is evident.