# ANALYSIS OF STRUCTURAL MEMBER SYSTEMS

## ANALYSIS OF STRUCTURAL MEMBER SYSTEMS

With the development over the past decade of computer-based analysis
methods, the teaching of structural analysis subjects has been revolutionized.
The traditional division between structural analysis and structural mechanics

became no longer necessary, and instead of teaching a preponderance of solu-
tion details it is now possible to focus on the underlying theory.

What has been done here is to integrate analysis and mechanics in a sys-
tematic presentation which includes the mechanics of a member, the matrix

formulation of the equations for a system of members, and solution techniques.

The three fundamental steps in formulating a problem in solid mechanics—.
enforcing equilibrium, relating deformations and displacements, and relating
forces and deformations—form the basis of the development, and the central

theme is to establish the equations for each step and then discuss how the com-
plete set of equations is solved. In this way, a reader obtains a more unified

view of a problem, sees more clearly where the various simplifying assumptions

are introduced, and is better prepared to extend the theory

The chapters of Part I contain the relevant topics for an essential back-
ground in linear algebra, differential and matrix transformations.
Collecting this material in the first part of the book is convenient for the con-
tinuity of the mathematics presentation as well as for the continuity in the
following development.

Part II treats the analysis of an ideal truss. The governing equations for
small strain but arbitrary displacement are established and then cast into
matrix form. Next, we deduce the principles of virtual displacements and
virtual forces by manipulating the governing equations, introduce a criterion
for evaluating the stability of an equilibrium position, and interpret the gov-
erning equations as stationary requirements for certain variational principles.
These concepts are essential for an appreciation of the solution schemes de-

scribed in the following two chapters.

Part III is concerned with the behavior of an isolated member. For com-
pleteness, first are presented the governing equations for a deformable elastic
solid allowing for arbitrary displacements, the continuous form of the princi-
ples of virtual displacements and virtual forces, and the stability criterion.
Unrestrained torsion-flexure of a prismatic member is examined in detail and
then an approximate engineering theory is developed. We move on to re-
strained torsion-flexure of a prismatic member, discussing various approaches

for including warping restraint and illustrating its influence for thin-walled
open and closed sections. The concluding chapters treat the behavior of

planar and arbitrary curved members.