Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Spring 2010
Strength of Materials (Torsion of Shafts)
Q.1.
For a solid or a hollow shaft subject to a twisting moment T, the torsional shearing stress t at a distance r
from the centre will be
(a) t = Tr/J
(b) t = Tr
(c) t = TJ/r
(d) none of these
where J is second m
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Spring 2010
Strength of Materials (Stresses and Strains)
Q.1. If all the dimensions of a prismatic bar of square cross section suspended freely from the ceiling of a roof are
doubled then the total elongation produced by its own weight will increase
(a) eight times
(
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Spring 2010
Strength of Materials (Torsion of Shafts)
Q.1.
A propeller shaft in a ship is 350 mm in diameter. the allowable working stress in shear is 50 MPa and the
allowable angle of twist is 1 degree in 15 diameters of length. If G = 85 GNm2, then the shaft can t
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Spring 2010
Strength of Materials Quiz (Stresses and Strains)
Q.1. A material having identical properties in all directions, is called
(a) elastic
(b) homogeneous
(c) isotropic
(d) all the above
Q.2. Match List I with List II and select the correct answer using the c
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Spring 2010
Strength of Materials (Practice Test)
1. Strain is defined as the ratio of
(a) change in volume to original volume
(b) change in length to original length
(c) change in crosssectional area to original crosssectional area
(d) any one of the above
(e) non
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Spring 2010
Strength of Materials (Torsion of Shafts)
Q.1.
Two steel shafts A and B are used for transmitting power. The ratio of revolutions of shafts i.e. NA/NB = 2.
The ratio of torques on shafts i.e. TA/TB = 1/2. The ratio of the horse power transmitted by the sh
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Spring 2010
Strength of Materials (Stresses & Strains)
Q.1. The work done on a unit volume of material, as simple tensile force is gradually increased from zero to a value
causing rupture, is called
(a) modulus of elasticity
(b) modulus of toughness
(c) modulus of re
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Spring 2010
Strength of Materials (Stresses in Beams)
Q.1.
(a)
(b)
(c)
(d)
Which of the following statements regarding assumptions in analysis of stressed beam is false
The material is homogeneous and isotropic, so that it has the same elastic properties in all direc
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Spring 2010
2.57 NanotoMacro Transport Processes Fall 2004 Lecture 8 In the last lecture, we have talked about the primitive unit cell. There is only one lattice point (equivalently speaking) per primitive unit cell. The smallest space formed by all the bisecting p
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Spring 2010
2.57 NanotoMacro Transport Processes Fall 2004 Lecture 9 3.4 Density of states (1) Electron in a quantum well ENERGY AND WAVEFUNCTION
U =
n= 3 n= 2
n= 1 x U=0 For electrons in a quantum well, the energy has discrete levels as h2 n2 E= (n=1,2,) 8m D 2 Fo
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Spring 2010
2.57 NanotoMacro Transport Processes Fall 2004 Lecture 10 Review on previous lectures
kz
k ky
kx
In above figure, we can find the volume of one state is V1 = (2 / L)3 . In the sphere, the number of states within k and k+dk is 4 k 2 k Vk 2 k N = = , (2 )
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Spring 2010
2.57 NanotoMacro Transport Processes Fall 2004 Lecture 11 4.1.1 Photons (continue) First let us continue the discussion of photons. We have 1 n = f ( , T ) = / kBT . e 1 The internal energy is
u = f ( , T ) =
kx ky kz
0
f ( , T ) D( )d ,
where the den
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Spring 2010
2.57 NanotoMacro Transport Processes Fall 2004 Lecture 12 5.1 Plane waves & their interface reflection (continue)
Transmission wave Reflection wave Incoming wave x
For the above problem, we have obtained i = Ae i (t k1x ) (incoming wave),
Energy barrier
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Spring 2010
2.57 NanotoMacro Transport Processes Fall 2004 Lecture 13 Review of previous lectures 1. Energy transport between two points Q1>2 1 Q2>1 x 2. Plane waves & their interface reflection We are interested in the wave energy at points 1 and 2 on two sides
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Winter 2015
BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE, PILANI
FIRST SEMESTER 201213
Assignment 1
Course No. ES C221
Course Title: Mechanics of Solids
Q1.
Q2. Three cylinders (I, II and III) are placed in a box as shown in Fig: Q.2. The weight and diameter
of the cylin
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Summer 2015
Rankine cycle questions
Determine the fractions of steam extracted from the turbine as well as the thermal
efficiency of the cycle.
utilization factor )
Net work output process heat delivered
Heat Supplied
The mass flowrate of steam through the boiler i
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Summer 2015
Applied Thermodynamics
ME F214/MF F214
BITS Pilani
Pilani Campus
Dr. M. S. Soni
Asst. Professor, Mechanical Engineering,
BITS Pilani
Pilani Campus
Vapour Power Cycles
1
Topics for Discussion
Simple Seam power cycle
Rankine Cycle and Actual vapour Cycle Pr
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Summer 2015
10/1/2015
BITS Pilani
Pilani Campus
Gas power cycles
Carnot Cycle
Two reversible isotherms and two reversible isentropics
make this cycle.
Efficiency = Work Done/heat supplied
= (Thigh Tlow)/ Thigh
It is the maximum possible efficiency for the conversion
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Summer 2015
Fundamentals of Thermal
Engineering
Dr. M. S. Soni
BITS Pilani
Pilani Campus
Asst. Professor, Mechanical Engineering,
3rd Sept., 2013
BITS Pilani
Pilani Campus
Fundamentals of Thermal
Engineering
1
Topics for Discussion
Basics of thermodynamics
Air standa
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Summer 2015
8/31/2015
BITS Pilani
Pilani Campus
Availability
and
Second Law Efficiency
Availability
For a given initial state of control mass,
which final state will give the maximum
reversible work?
For a given inlet condition of the flow
process, which exit state w
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Summer 2015
8/31/2015
BITS Pilani
Pilani Campus
FIRSTLAW ANALYSIS FOR A
CONTROL VOLUME
Conservation of mass and
Control Volume
Control volumes:
Mass can cross the boundaries, and so we must keep track
of the amount of mass entering and leaving the control
volume.
Co
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Summer 2015
8/31/2015
Mixing Chamber
In engineering applications, the
section where the mixing
process
takes
place
is
commonly referred to as a
mixing chamber
The Telbow of an ordinary shower serves as the mixing
chamber for the hot and the coldwater streams.
BITS
Birla Institute of Technology & Science, Pilani  Hyderabad
MECHANICS OF MATERIALS
ME 305

Summer 2015
BITS Pilani
Pilani Campus
Second law analysis for a control
volume
M. S. SONI
1
Second Law Analysis for
a Control Volume
We start with the second law expressed as change
of entropy for a control mass
dS C .M .
Q
S gen
dt
T
to which we will add mass flow