Civil Engineering Reference
In-Depth Information
Basic mechanics
This chapter, and the following one, cover the basic methods for the analysis of stress
and strain using the Mohr circle constructions and the general features of material
behaviour. These techniques are essential for understanding soil behaviour and for
analysing soil structures and will be used extensively throughout the topic. The topics
should be covered in other courses on strength of materials, but here they are put into
the context of soil mechanics. Readers are advised to skim through these two chapters
and come back to them to work through the details as necessary.
2.1 Introduction
Mechanics is the study of forces and displacements, or stresses and strains, and there
are a number of branches of mechanics associated with particular materials or with
particular applications. The fundamental principles of mechanics are simply the appli-
cation of equilibrium and compatibility. For any body that is not accelerating the forces
and moments must be in equilibrium: this is simply Newton's first law. For any body,
or system of bodies, that is distorting or moving around the strains and displacements
must be compatible. This means that material does not vanish and gaps do not appear;
this is simply common sense. What we can do is to analyse states of stress (or strain) so
that we can calculate the stresses (or strains) on any plane at a point from the stresses
(or strains) on any other pair of planes.
2.2 Stresses and strains
I shall assume that readers have been introduced to the basic ideas of stress and strain
in other courses. A stress is basically an intensity of loading given by a force acting
on a unit area, while a strain is basically an intensity of deformation given by a dis-
placement over a unit gauge length. In geotechnical engineering there are two minor
differences from the definitions of stress and strain usually adopted for metals and
concrete, and these account for the particulate nature of soils. Firstly, the unit area or
gauge length must be large enough to include a representative number of soil grains
and, secondly, because uncemented soils cannot sustain tensile stresses compressive
stresses are positive.
Figure 2.1 shows stresses and strains in a cube of soil subjected to normal and shear
forces. The changes of normal stress
δσ
and normal strain
δε
due to a change of normal
