Chapter 1
Introduction
This course builds upon the concepts learned in the course Mechanics of
Materials" also known as Strength of Materials". In the Mechanics of Materials"
course one would have learnt two new concepts stress" and strain"
in addition to revisiting the concept of a force" and displacement" that
one would have mastered in a rst course in mechanics, namely Engineering
Mechanics". Also one might have been exposed to four equations connecting
these four concepts, namely strain-displacement equation, constitutive
equation, equilibrium equation and compatibility equation. Figure 1.1 pictorially
depicts the concepts that these equations relate. Thus, the strain
displacement relation allows one to compute the strain given a displacement;
constitutive relation gives the value of stress for a known value of the strain
or vice versa; equilibrium equation, crudely, relates the stresses developed in
the body to the forces and moment applied on it; and nally compatibility
equation places restrictions on how the strains can vary over the body so
that a continuous displacement eld could be found for the assumed strain
eld.
In this course too we shall be studying the same four concepts and four
equations. While in the mechanics of materials" course, one was introduced
to the various components of the stress and strain, namely the normal and
shear, in the problems that was solved not more than one component of the
stress or strain occurred simultaneously. Here we shall be studying these
problems in which more than one component of the stress or strain occurs
simultaneously. Thus, in this course we shall be generalizing these concepts
and equations to facilitate three dimensional analysis of structures.
Before venturing into the generalization of these concepts and equations,
Chapter 1IntroductionThis course builds upon the concepts learned in the course Mechanics ofMaterials" also known as Strength of Materials". In the Mechanics of Materials"course one would have learnt two new concepts stress" and strain"in addition to revisiting the concept of a force" and displacement" thatone would have mastered in a rst course in mechanics, namely EngineeringMechanics". Also one might have been exposed to four equations connectingthese four concepts, namely strain-displacement equation, constitutiveequation, equilibrium equation and compatibility equation. Figure 1.1 pictoriallydepicts the concepts that these equations relate. Thus, the straindisplacement relation allows one to compute the strain given a displacement;constitutive relation gives the value of stress for a known value of the strainor vice versa; equilibrium equation, crudely, relates the stresses developed inthe body to the forces and moment applied on it; and nally compatibilityequation places restrictions on how the strains can vary over the body sothat a continuous displacement eld could be found for the assumed strain eld.In this course too we shall be studying the same four concepts and fourequations. While in the mechanics of materials" course, one was introducedto the various components of the stress and strain, namely the normal andshear, in the problems that was solved not more than one component of thestress or strain occurred simultaneously. Here we shall be studying theseproblems in which more than one component of the stress or strain occurssimultaneously. Thus, in this course we shall be generalizing these conceptsand equations to facilitate three dimensional analysis of structures.Before venturing into the generalization of these concepts and equations,
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