Birla Institute of Technology & Science, Pilani  Hyderabad
Mechanics of solids
AMME 2301

Spring 2013
Stresses in Bending
DR PRAVIN SINGRU
INTRODUCTION
IN ORDER TO MAINTAIN EQUILIBRIUM, A SHEAR FORCE
,V & BENDING MOMENT, M HAVE TO ACT ON THE
CROSS SECTION.
GEOMETRY OF DEFORMATION OF A
SYMMETRICAL BEA
Birla Institute of Technology & Science, Pilani  Hyderabad
Mechanics of solids
AMME 2301

Spring 2013
Chapter 2
Introduction to Mechanics
of deformable bodies
Analysis of deformable bodies
1. Identification of a system
2. Simplification of this system
3. To develop model which can be analyzed
Steps to
Birla Institute of Technology & Science, Pilani  Hyderabad
Mechanics of solids
AMME 2301

Spring 2013
Chapter: 1
Fundamental Principles of
Mechanics
Mechanics of Solids
Vikas Cahudhari
1
Mechanics
Study of Force & Motion
Mechanics of Solids
Vikas Cahudhari
2
Mechanics
Study of Force & Motion
Gross/Ove
Birla Institute of Technology & Science, Pilani  Hyderabad
Mechanics of solids
AMME 2301

Spring 2013
Chapter 5
Suitability of a structure or machine may
depend on the deformations in the structure as
well as the stresses induced under loading.
Sometimes structures must be designed to
accommodate or p
Birla Institute of Technology & Science, Pilani  Hyderabad
Mechanics of solids
AMME 2301

Spring 2013
CHAPTER 4
STRESS AND STRAIN
Objectives
STRESS
To know state of stress at a point
To solve for plane stress condition
applications
STRAIN
To know state of stress at a point
To solve for plane stres
Birla Institute of Technology & Science, Pilani  Hyderabad
Mechanics of solids
AMME 2301

Spring 2013
Chapter 3
Forces and Moments
Transmitted by Slender
Members
Contents:
Slender members
Determination of Forces and moments under
point loads
Sign conventions for shear force and Bending
moment
Shear fo
Birla Institute of Technology & Science, Pilani  Hyderabad
Mechanics of solids
AMME 2301

Spring 2013
AMME2301/AMME5301
Combined Loadings
Lecturer: Dr Li Chang
Room s503, Building J07
Tel: 93515572
email: [email protected]
State of Stresses Caused by Combined Loadings
Loading Types
Stresses
Birla Institute of Technology & Science, Pilani  Hyderabad
Mechanics of solids
AMME 2301

Spring 2013
AMME2301/AMME5301
Torsion
Lecturer: Dr Li Chang
Room s503, Building J07
Tel: 93515572
email: [email protected]
Torsion of Circular Section: Maximum Shear Stress
Engineer's Theory of Torsion
Birla Institute of Technology & Science, Pilani  Hyderabad
Mechanics of solids
AMME 2301

Spring 2013
Week 6 Discussion Handout
Strain compatibility conditions for a simply connected body
At every point in the current conguration C, which is a simply connected domain,
curl curl = 0.
(1)
In some Cartes
Birla Institute of Technology & Science, Pilani  Hyderabad
Mechanics of solids
AMME 2301

Spring 2013
Week 4 Discussion Handout
Denitions
Let f , v and A be a scalar, a vector and a second order tensor elds, respectively, dened on an open domain
U of V and continuously dierentiable on U . Let c V be x
Birla Institute of Technology & Science, Pilani  Hyderabad
Mechanics of solids
AMME 2301

Spring 2013
Let V be the three dimensional Euclidean vector space and L be the set of all linear maps
from V to V . The set of real numbers is denoted by R. Let E be the three dimensional Euclidean
point space. I
Birla Institute of Technology & Science, Pilani  Hyderabad
Mechanics of solids
AMME 2301

Spring 2013
Week 2 Discussion Handout
V is the three dimensional Euclidean space, which is a three dimensional vector space equipped with the
Euclidean inner product x y = xi yi , where x, y V and z = zi ei is th
Birla Institute of Technology & Science, Pilani  Hyderabad
Mechanics of solids
AMME 2301

Spring 2013
Let V be the three dimensional Euclidean vector space and L be the set of all linear maps
from V to V . The set of real numbers is denoted by R. The identity element in L is denoted
by I.
Two theorems
Birla Institute of Technology & Science, Pilani  Hyderabad
Mechanics of solids
AMME 2301

Spring 2013
AMME2301/AMME5301
Energy Methods Castiglianos
Second Theorem
Lecturer: Dr Li Chang
Room s503, Building J07
Tel: 93515572
email: [email protected]
Energy Methods Strain Energy
y
Internal Wor
Birla Institute of Technology & Science, Pilani  Hyderabad
Mechanics of solids
AMME 2301

Spring 2013
Quiz 3: ME 321 (Total 10 Marks)
Name: Roll Number:
Problem 1 (2): Investigate what problem is solved by the stress function ¢ = ——§§wy2(3d — 23/) applied to a region
included in y = 0, y = d, m = 0, o
Birla Institute of Technology & Science, Pilani  Hyderabad
Mechanics of solids
AMME 2301

Spring 2013
Chapter 14
THERMOELASTICITY
Most materials tend to expand iftheir temperature rises and, to a first approximation,
the expansion is proportional to the temperature change. If the expansion is unre
st
Birla Institute of Technology & Science, Pilani  Hyderabad
Mechanics of solids
AMME 2301

Spring 2013
/ Quiz 5: ME 321 (Total 10 Marks)
Name: Roll Number:
Problem 1 (3): Prove that 15% : a’  (13, i = 1,.,3, where ('1; = a x d.;, d; = 9 x di, and Q = midi. [Hintz
b><c><g=(bg)ci[b'c)gl '
Ln’ = to a
Birla Institute of Technology & Science, Pilani  Hyderabad
Mechanics of solids
AMME 2301

Spring 2013
Quiz 1 Makeup: ME 321 (Total 10 Marks) C S OLUT (0N)
Name: Roll Number:
Problem 1 (2): Show that if A  B 2 0 is true for every tensor B then tensor A = 0.
Mam 2
E Can/n bu. My. (3. (dims.
*3
WG
Birla Institute of Technology & Science, Pilani  Hyderabad
Mechanics of solids
AMME 2301

Spring 2013
Quiz 1: ME 321 (Total 10 Marks) ( S 0 L U T' W")
Name: Roll Number:
Let u, v, and W be arbitrary vectors.
Problem 1 (2): Show that det(u (8 v) = 0.
AJ(961)= [wager (Q®!)é;_ @Cg‘ilgzl (41%” M'm'h'm)
=
Birla Institute of Technology & Science, Pilani  Hyderabad
Mechanics of solids
AMME 2301

Spring 2013
Q. 1. An axisymmetric composite cylinder is composed of a solid inner shaft, of radius a shear
modulus 1 , and an outer sleeve of outer radius b and shear modulus 2 . The shaft and sleeve
are ideally
Birla Institute of Technology & Science, Pilani  Hyderabad
Mechanics of solids
AMME 2301

Spring 2013
Problem 1.
Figure 1:
A curved beam, as shown in Fig. 1, is xed at one end and subjected to a radial force (per unit
thickness of the beam) of magnitude P at the free end ( = 0). The inner and outer ra