Module6/Lesson1
Module 6: Two Dimensional Problems in Polar
Coordinate System
6.1.1 INTRODUCTION
I
n any elasticity problem the proper choice of the co-ordinate system is extremely
important since this choice establishes the complexity of the mathematical

Module2/Lesson3
Module 2: Analysis of Stress
2.3.1 GENERAL STATE OF STRESS IN THREE-DIMENSION IN
CYLINDRICAL CO-ORDINATE SYSTEM
Figure 2. 17 Stresses acting on the element
In the absence of body forces, the equilibrium equations for three-dimensional stat

Module3/Lesson1
Module 3 : Analysis of Strain
3.1.1 INTRODUCTION
o define normal strain, refer to the following Figure 3.1 where line AB of an axially
loaded member has suffered deformation to become AB .
T
Figure 3.1 Axially loaded bar
The length of AB i

Module3/Lesson2
Module 3: Analysis of Strain
3.2.1 MOHRS CIRCLE FOR STRAIN
The Mohrs circle for strain is drawn and that the construction technique does not differ from
that of Mohrs circle for stress. In Mohrs circle for strain, the normal strains are pl

Module4/Lesson1
Module : 4 Stress-Strain Relations
4.1.1 INTRODUCTION
the previous chapters, the state of stress at a point was defined in terms
six
In internal stresses andand inapplied forces. equilibrium equationswere independenttoofrelate
components o

Module4/Lesson2
Module 4: Stress-Strain Relations
4.2.1 ELASTIC STRAIN ENERGY FOR UNIAXIAL STRESS
(a)
(b)
Figure 4.1 Element subjected to a Normal stress
In mechanics, energy is defined as the capacity to do work, and work is the product of force
and the

Module1/Lesson1
Module 1: Elasticity
1.1.1 INTRODUCTION
If the external forces producing deformation do not exceed a certain limit, the deformation disappears
with the removal of the forces. Thus the elastic behavior implies the absence of any permanent
d

Module5/Lesson3
Module 5: Two Dimensional
Problems in Cartesian Coordinate System
5.3.1
SOLUTIONS OF TWO-DIMENSIONAL PROBLEMS BY THE USE
OF POLYNOMIALS
The equation given by
2
2
2 + 2
x
y
2f 2f
4f
4f
4f
2 + 2 = 4 +2 2 2 + 4 =0
x
x
x y
y
y
will

Module5/Lesson1
Module 5: Two Dimensional Problems in
Cartesian Coordinate System
5.1.1 INTRODUCTION
Plane Stress Problems
In many instances the stress situation is simpler than that illustrated in Figure 2.7. An
example of practical interest is that of a

Module5/Lesson2
Module 5: Two Dimensional Problems in
Cartesian Coordinate System
5.2.1 THE STRESS FUNCTION
For two-dimensional problems without considering the body forces, the equilibrium
equations are given by
s x t xy
+
=0
x
y
s y
y
+
t xy
x
=0
and th

Module6/Lesson2
Module 6: Two Dimensional Problems in Polar
Coordinate System
6.2.1 AXISYMMETRIC PROBLEMS
Many engineering problems involve solids of revolution subjected to axially symmetric
loading. The examples are a circular cylinder loaded by uniform

Module 8/Lesson 1
Module 8: Elastic Solutions and Applications
in Geomechanics
8.1.1 INTRODUCTION
of the elasticity problems in geomechanics were
later
Most but simply to answerthey were usually solved not forsolved in thetoelastic part of
nineteenth cent

Module 7/Lesson 2
Module: 7 Torsion of Prismatic Bars
7.2.1 TORSION OF ELLIPTICAL CROSS-SECTION
Let the warping function is given by
y = Axy
where A is a constant.
condition gives
(Ay - y)
or
dy
dx
- ( Ax + x)
=0
dS
dS
y (A-1)
dy
dx
- x( A + 1)
=0
dS
dS
i

Module7/Lesson1
Module: 7 Torsion of Prismatic Bars
7.1.1 INTRODUCTION
F
rom the study of elementary strength of materials, two important expressions related to
the torsion of circular bars were developed. They are
t=
and
Mtr
J
(7.1)
q=
M t dz
1
L GJ
L
(7

Module2/Lesson1
Module 2: Analysis of Stress
2.1.1 INTRODUCTION
body
undergoes distortion and the
this
Asystemunder the action ofatexternal forces,Figure body(a), inside theinternaleffect dueatoplane
of forces is transmitted throughout the
developing
forc