# Structural Mechanics Modelling and Analysis of Frames and Trusses

## Structural Mechanics Modelling and Analysis of Frames and Trusses

Structural mechanics is the branch of physics that describes how different materials, which
have been shaped and joined together to structures, carry their loads. Knowledge on the modes
of action of these structures can be used in different contexts and for different purposes. The
Roman architect and engineer Vitruvius, who lived during the first century BC summarises
in the work De architectura libri decem (‘Ten books on architecture’) the art of building
with the three classical notions of firmitas, utilitas and venustas (strength, functionality and

beauty). Engineering of our time has basically the same goal. It is about utilising the knowl-
edge and practices of our time in a creative process where sustainable and efficient, functional

and expressive buildings are designed.
At an early design stage a structural engineer needs to be trained to see how to efficiently
use material and shape to provide the construction with stability, stiffness and strength. Using
simple models, structural behaviour can be evaluated and cross-section sizes estimated.

structures are presented, and tools for analysis and simulation are provided. The book has
been limited to treating trusses and frames in two and three dimensions. To demonstrate
the generality of the methodology the book also has a chapter, ‘Flows in Networks’, that
addresses other areas of applied mechanics, including thermal conduction and electrical flow.
The method used in this textbook to formulate computational models is characterised by the
use of matrices. The different quantities – load, section force, stiffness and displacement – are
separated and gathered into groups of numbers. All load values are gathered in a load matrix
and all stiffnesses in a stiffness matrix. This is one of the primary strengths of the method. With
a matrix formulation, the formulae describing the relations between quantities are compact and
easy to view. Physical mechanisms and underlying principles become clear. We begin with a

short summary of the matrix algebra and the notations that are used.