Dr. T.

THIMMAIAH INSTITUTE OF TECHNOLOGY

(Affiliated to Visvesvaraya Technological University)
Oorgaum, K.G.F- 563120

DEPARTMENT OF MECHANICAL ENGINEERING

VII Semester
DESIGN LAB
Subject Code: 18MEL77

Name of the Student:

Reg No of the Student:

 Dr .T. THIMMAIAH INSTITUTE OF TECHNOLOGY
(Estd. 1986) Oorgaum, Kolar Gold Fields, Karnataka –
563120 (AffiliatedtoVTU,Belgaum,ApprovedbyAICTE -
NewDelhi) NAAC Accredited ‘A’ Grade

DEPARTMENTOFMECHANICALENGINEERING

VII SEMESTER

Design Lab

18MEL77

ACADEMICYEAR2023-2024

LABORATORYMANUAL

NAMEOF THESTUDENT:

BRANCH:

USN:

SEMESTER:

BATCH:

Head of theDepartment 40

StaffIn-charge
Vision

To transform students into technically competent Mechanical Engineers nurturing

them in learning sustainable and innovative technology with professional ethics and
social concern.

Mission

Striving to empower students with fundamentals in the field of

M1:
Mechanical Engineering with innovative, managerial and professional
skills.
To create an environment for progressive learning through industry–
M2:
institute partnership.

Imparting quality technical education stressing on new technology with

M3: professional ethics for the benefit of the society.

Program Outcomes(PO)
Graduates will be able to:

1. Engineering knowledge: Apply the knowledge of mathematics, science,

engineering fundamentals, and an engineering specialization to the
solution of complex engineering problems.
2. Problem analysis: Identify, formulate, review research literature, and
analyze complex engineering problems reaching substantiated
conclusions using first principles of mathematics, natural sciences, and
engineering sciences.
3. Design/development of solutions: Design solutions for complex
engineering problems and design system components or processes that
meet the specified needs with appropriate consideration for the public
health and safety, and the cultural, societal, and environmental
considerations.
4. Conduct investigations of complex problems: Use research-based
knowledge and research methods including design of experiments,
analysis and interpretation of data, and synthesis of the information to
provide valid conclusions.
5. Modern tool usage: Create, select, and apply appropriate techniques,
resources, and modern engineering and IT tools including prediction and
modelling to complex engineering activities with an understanding of the
limitations.
6. The engineer and society: Apply reasoning informed by the contextual
knowledge to assess societal, health, safety, legal and cultural issues and
the consequent responsibilities relevant to the professional engineering
practice.
7. Environment and sustainability: Understand the impact of the
professional engineering solutions in societal and environmental
contexts, and demonstrate the knowledge of, and need for sustainable
development.
8. Ethics: Apply ethical principles and commit to professional ethics and
responsibilities and norms of the engineering practice.
 9. Individual and team work: Function effectively as an individual, and as
a member or leader in diverse teams, and in multidisciplinary settings.
10. Communication: Communicate effectively on complex engineering
activities with the engineering community and with society at large,
such as, being able to comprehend and write effective reports and
design documentation, make effective presentations, and give and
receive clear instructions.
11. Project management and finance: Demonstrate knowledge and
understanding of the engineering and management principles and
apply these to one’s own work, as a member and leader in a team, to
manage projects and in multidisciplinary environments.
12. Life-long learning: Recognize the need for and have the preparation
and ability to engage in independent and life-long learning in the
broadest context of technological change.

Program Educational Objectives (PEOs)

Graduates shall have successful career in Mechanical Engineering with

PEO1:
sound fundamental knowledge in science and engineering practice.

Graduates shall be professional in applying Mechanical engineering

PEO2: principles with a focus on innovation, research and having awareness
of societal impact.

Graduates shall have ability to work in a team with professional ethics,

PEO3: good communication skills to achieve lifelong learning.

Program Specific Outcomes(PSOs)

1. Have the ability to apply principles of Mathematics, Basic science and

Engineering technology to solve Mechanical Engineering problems.
2. Ability to design components or processes in the areas of Mechanical
Engineering.
3. Graduates will have the ability to perform thermal analysis and
implement mechanical systems in domain specific industries.
Objectives

 To demonstrate the concepts discussed in Design of Machine Elements, Mechanical

Vibrations & Dynamics of Machines courses.
 To visualize and understand the development of stresses in structural members and
experimental determination of stresses in members utilizing the optical method of
reflected photo-elasticity
Course Outcome
At the end of the course the students will be able to

To practically relate to concepts discussed in Design of Machine Elements, Mechanical

CO1 Vibrations & Dynamics of Machines courses.
To measure strain in various machine elements using strain gauges and determine strain
CO2
induced in a structural member using the principle of photo-elasticity.

CO – PO MAPPING

PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12
CO1 2 1 1 1
CO2 21 1 1 1

CO – PSO MAPPING

PSO1 PSO2 PSO3

CO1 1 2
CO2 1 2
Slight (Low) = 1 Moderate (Medium) = 2 Substantial (High) = 3
 DESIGN LABORATORY

PART – A

1. Determination of natural frequency, logarithmic decrement, damping ratio and

Damping coefficient in a single degree of freedom vibrating systems (longitudinal and
torsional)
2. Balancing of rotating masses.
3. Determination of critical speed of a rotating shaft.
4. Determination of Fringe constant of Photoelastic material using.
a) Circular disc subjected to diametral compression.
b) Pure bending specimen (four point bending )
5. Determination of stress concentration using Photo elasticity for simple components like
plate with a hole under tension or bending, circular disk with circular hole under
compression, 2D Crane hook.

PART – B
6. Determination of equilibrium speed, sensitiveness, power and effort of Porter / Prowel
/ Hartnel Governor. (Only one or more)
7. Determination of Pressure distribution in Journal bearing.
8. Determination of Principal Stresses and strains in a member subjected to
combined loading using Strain rosettes.
9. Determination of stresses in Curved beam using strain gauge.
10. Experiments on Gyroscope (Demonstration only)
 ASSESMENT SHEET
Sl. Experiment Conduction
Name of the Experiment Page No
No Date Marks (12)

10

11

12

13

14

Average Conduction Marks ( )

Record ( )

Test & Viva ( )

Total Marks Obtained ( )

Faculty In-Charge
Design Laboratory 18MEL77

Experiment No - 01 Date:

SPRING MASS SYSTEM

1. UNDAMPED FREE LONGITUDINAL VIBRATIONS

Aim: To study the longitudinal vibration of the spring mass system and determine
the natural frequency.

Apparatus Required: Vibration Testing equipment, spring, weights.

Theory: Components in a vibrating system have three properties of interest. They are:
mass (weight), elasticity (springiness) and damping (dissipation). The property of mass
(weight) causes an object to resist acceleration. It also enables an object to store energy, in
the form of velocity (kinetic) or height (potential). The property of elasticity enables an
object to store energy in the form of deflection (example is a spring, but any piece of metal
has the property of elasticity). The size of the deflection depends on the size of the applied
force and the dimensions and properties of the piece of metal. The amount of deflection
caused by a specific force determines the "spring rate" of the metal piece. The property of
damping enables an object to dissipate energy, usually by conversion of kinetic (motion)
energy into heat energy. The resonant frequency of an object (or system) is the frequency
at which the amplitude of vibration is maximum.

Procedure:
1. Measure the free length of the spring.
2. Attach a known weight to the bottom end of the shaft.
3. Measure the final length of the spring.
4. Gently pull the system and note the time taken for 10 vibrations.
5. Carry out the same procedure for different weights added.
6. Calculate the natural frequency of the spring mass system and compare with the
theoretical natural frequency.
7. Find the percentage of error.

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Observation:
1. Free length of the spring, L1 =............mm
2. Final length of the spring after a known massis attached, L2 =.............mm
3. Type of spring : Undamped
4. Accessories: Undamped spring, Weight hangers, Weights, Stop watch.

Tabular Column:
Static Stiffness of Time taken Theoretical Experimental
Sl. Load deflection ‘Δ’ Spring for 10 natural natural %
No. W (N) (L2-L1) in ‘K’ oscillations frequency frequency error
(m) (N/m) ‘t’ in (sec) ‘fn(the)’ in (Hz) ‘fn(exp)’ in (Hz)

Formulae:
1g
1. Theoretical natural frequency, fn (the)= Hz.
2Π

Where g= acceleration due to gravity = 9.81m/s2

Δ = static deflection of spring in meter = L2 - L1
Forcein Newton mg
2. Spring Stiffness= K=  N/m
Static deflection 
3. Determination of Experimental natural frequency
1
Hz
Experimental natural frequency (exp) =
fn tp

Time period tp = T/10

Calculations:

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Result: The theoretical and experimental Natural Frequency of the spring mass system is
as tabulated

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Experiment No - 02 Date:

TORSIONAL VIBRATION OF A SINGLE ROTOR SYSTEM

Aim: To study the torsional vibration and determine the natural frequency of the single
rotor system.

Apparatus Required: Vibration equipment, shaft, disc, etc.

Theory: When the particle of the shaft (or) disc moves in a circle about the axis of the shaft,
then the vibrations are known as Torsional vibration. In Torsional vibrations the shaft is
twisted and untwisted alternately and Torsional shear stresses are induced in the shaft.
In a single rotor system a shaft is fixed at one end and carries a rotor at the free end. The
amplitude of Torsional vibration is maximum at the free end. The point at which the
amplitude is zero is known as the node.

Procedure:
1. Measure the length of the shaft.
2. Attach a known weight to the bottom end of the shaft.
3. Give twisting movement to a shaft to induce vibration and obtain the time
required for 3 oscillations of the disc.
4. Calculate the natural frequency of the system and compare with the
theoretical natural frequency.
5. Find the percentage of error

Fig: Torsional one-degree of freedom system

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Specifications:
Rigidity modulus of the shaft material, G = 8.6x109 N/m2
Diameter of Disc, D =180 mm
Mass of the Disc, m =1.725 Kg (W = 16.92 N)
Wire (shaft) diameter, d =3.08 mm
Length between rotors, L = 935 mm

Tabular Column:
Theoretical Experimental
Mass Time for 3
Length ‘L’ natural natural %
Sl.No. added Oscillations ‘t’
in (m) frequency frequency error
‘m’in (Kg) in (sec) ‘fn(th)’ in (Hz) ‘fn(exp)’ in (Hz)

Formulae:
1G J
1.
Theoretical natural frequency, fn (the)= 2ΠI L Hz
d 4

Polar moment of inertia of shaft: J  in m4

32 2
Mass moment of inertia of rotor: I  mk 2 D
m 
2
Torsional Stiffness K   2 
GJ N-m
L m D2
I=mass moment of inertia of Disc, = ½ mk2 = in Kg-m2
8
2.
Determination of Experimental natural frequency.
Experimental natural frequency fn (exp) = Hz, Where
1 t
 t
t p
p
3
fth ~ fexp
3.
Percentage of error = *100
f th

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Calculations:

Results: The theoretical and experimental Natural Frequency of single rotor is as tabulated

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Experiment No - 03 Date:

TORSIONAL VIBRATION OF TWO ROTOR SYSTEM

Aim: To study the torsional vibration and determine the natural frequency of the
two rotor system.

Apparatus Required: Vibration equipment, shaft, disc, etc.

Theory: When the particle of the shaft (or) disc moves in a circle about the axis of the shaft,
then the vibrations are known as Torsional vibration. In Torsional vibrations the shaft is
twisted and untwisted alternately and Torsional shear stresses are induced in the shaft.
In a two rotor system a shaft at its two ends carries a two rotors or disc of varying size.
Both the discs are twisted and untwisted simultaneously to measure the vibration level for
a given time and actual frequency is noted down.
1GJ
fn t

2I AlA
Procedure:
1. Fix the two discs on the shaft.
2. Attach a known weight to the bottom end of the shaft.
3. Give twisting movement to a shaft to induce vibration and obtain the time
required for 3 oscillations of the disc.
4. Calculate the natural frequency of the system and compare with the
theoretical natural frequency.
5. Find the percentage of error

Specifications:

Length between two discs, L = 935 mm

Diameter of smaller Disc, Ds =180 mm
Diameter of bigger Disc, Db =180 mm
Mass of the smaller Disc, ms =1.725 Kg
Mass of the bigger Disc, mb =2.433 Kg
Wire (shaft) diameter, d =3.08 mm

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Design Laboratory 18MEL77

Tabular Column:-
Theoretical Experimental
Mass Weight Time for 3
natural natural %
Sl.No. added added Oscillations
frequency frequency error
‘m’ in (Kg) ‘W’ in ‘t’ in (sec)
‘fn(th)’ in(Hz) ‘fn(exp)’ in Hz)
(N)

Formulae:
1
1.
Theoretical natural frequency, fn (th) = 𝐺𝐽
2𝜋 Hz
𝐼𝑠𝐿𝑠
d 4
Polar moment of inertia of J in m4
shaft: 32
Mass moment of inertia of smaller rotor: 𝐼 𝑊𝑠+𝑊 𝐷2
𝑠 = 𝑔 8
�

Mass moment of inertia of bigger rotor: 𝐼 𝑊𝑏 𝐷2

𝑏 = 𝑔 8

Distance between the smaller disc from nodal point: 𝐿𝑠 = 𝐼𝑏 ∗𝐿

𝐼𝑠+𝐼𝑏

2.
Determination of Experimental natural frequency.
1
Experimental natural frequency (exp) = Hz
fn
t p

Where t  3
p
t
~ fexp
3.
Percentage of error = *100
fth f th

Calculations:

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Design Laboratory 18MEL77

Results: The theoretical and experimental Natural Frequency of single rotor is as tabulated

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Design Laboratory 18MEL77

Experiment No - 04 Date:

PERFORMANCE OF PORTER GOVERNOR

Aim: - To determine the magnitude of the frictional force acting on the sleeve of porter
governor.

Apparatus Required: -Universal Governor, weights.

Theory:- A governor is a device used to control or maintain the speed within the
prescribed limit for varying load conditions. Governors are generally classified into
centrifugal governors and inertia governors. Porter governors are centrifugal type
governors. As the load on the engine shaft increased the speed of the shaft decreases and
this is transmitted into the spindle by using a bevel gear. As the spindle speed decreases
and hence ball moves inwards which in turn increases the fuel supply to the engine thereby
the speed is brought to a constant.
When the load on the engine decreases the engine speed increases and also the spindle
speed. Due to this increase in speed the centrifugal force on the governor increases which
makes the fly balls more outward and the fuel supply to the engine is decreased thereby
the speed is brought to a constant.
The Porter governor is a modification of a watt’s governor, with central load attached to the
sleeve. The load moves up and down the central spindle. This additional downward force
increases the speed of revolution required to enable the balls to rise to any pre-determined
level.

Procedure:-
1. Select the chosen rotating weights, where applicable to the governor
mechanism under test and insert into the drive unit.
2. Add extra weights (w) over sleeve assembly.
3. Fix Links, Arms and masses properly to the governor.
4. Connect power cord to electrical supply and switch ON. Power supply.
5. Adjust the variable transformer (Dimmer) to the required speed so that the
sleeve starts lifting.

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6. Note down the speed and scale readings.

7. Repeat the experiment for different speeds and note down the corresponding lifts.
8. Tabulate the readings in tabular column and find magnitude of the frictional
force and calculate sensitiveness, effort and power of the governor.
9. Plot the results on graph as Governor Speed Vs Sleeve position
and Controlling force Vs Radius of rotation.

Fig: Porter governor with central load and with unequal arm (i.e. α ≠ β)

lsin 2d-
r

Fig. For when arm and link lengths are equal. Hence α=β and k=1

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Tabular Column:

1. Sleeve moving upwards: -

Sleeve Speed of Height of the
governor Frictional
Sl No. Lift governor
Force F (N)
X (m) N (rpm) H (m)

2. Sleeve moving downwards: -

Sleeve Speed of Height of
governor Frictional
Sl No. Lift the
Force F (N)
X (m) N (rpm) governor
H (m)

Observations:-
1. Length of each link, l = 0.125m
2. Weight of Governor ball, w = 3.6N.
3. Initial height of Governor, h0 = …… m
4. Weight of sleeve assembly, W = 22.1N
5. For equal arm length, k=1 and α=β=θ
6. Distance between the arm pivot to the axis of rotation= 0.5 m

Formulae :
Angular velocity:  = 2𝜋𝑁 rad/sec
60

Distance h, = 𝑋
𝑕𝑜 −
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2

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Radius of rotation: r = (S + 0.5) m

S  l 2 C 2
Controlling Force = Fc = m2r in N
Height of the governor h = r tan  in
m
sin= C/l
𝑚𝑔 +(𝑀𝑔±𝐹)
𝑕= 𝑚𝜔 2

Frictional Force (Going Up)

F=(hm2-mg-Mg) N

Frictional Force (Going Down)

F= - (hm2-mg-Mg) N

Tabular column to find effort and power of governor

Change of speed % Change Sleeve Effort Power

(rpm) of speed lift (m) (N) (N.m)

Specimen Calculations:

Change of speed: N1-N2

N -N
2 1
Speed factor, c =
N1
Sleeve lift, x= x1-x2
Effort = c
(mgMg) Power =
effort *(x)
Draw the characteristic curves: Height vs. Speed, Lift vs. Speed and Controlling force
diagram (Radius of rotation vs. controlling force)

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Calculations:

Results:

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Experiment No.:05 Date:

PERFORMANCE OF HARTNELL GOVERNOR

Aim: To determine the magnitude of the frictional force acting on the sleeve of hartnell
governor.

Apparatus Required: Hartnell governor, tachometer, etc.

Theory: The Hartnell governor is illustrated in Figure. The two bell crank leners have been
provided that can have rotating motion around fulcrums O and O′. One ending of each bell crank
lever carries a ball at one ending of one arm and a roller at the ending of other arm. The rollers
make contact along the sleeve. The frame is associated to the spindle. A helical spring is mounted
around the spindle among frame and sleeve. With the rotation of the spindle, all of these parts
rotate. Along the increase of speed, the radius of rotation of the balls enhanced and the rollers lift
the sleeve against the spring force. Along the decrease in speed, the sleeve moves downwards. The
movements of the sleeve are transferred to the throttle of the engine through linkages.

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Procedure:

1. Switch on the main power supply and operate the dimmer stat such that the
sleeve lift and governor will lift by ‘h’ cm.
2. Measure the speed of the governor for sleeve lift h.
3. Repeat the above procedure for different sleeve lift gradually reducing speed
of governor and note down the corresponding sleeve rate.
4. Calculate the centrifugal force Fc and weight balanced by the balls.

Tabular Column

Sl. Sleeve lift h Speed N Centrifugal Force balanced by Frictional

No. In (m) In (rpm) force Fc in (N) balls Fb in (N) force F in (N)

Specifications:

1. Weight of sleeve assembly, W = 22.1N

2. Stiffness of spring, K=1230N/m
3. Length of vertical arm, a=0.07m
4. Length of horizontal arm, b=0.11m
5. Initial radius of rotation, r1=0.153m
6. Mass of balls, m=0.369kg

Formulae:
𝑏
Sleeve lift, 𝑕 = 𝑟 − 𝑟
m
2 1 𝑎𝑕
𝑎
Final radius of rotation, 𝑟2 = 𝑏 + 𝑟1 m

Spring force, S=hK N

Centrifugal force, 𝐹𝑐 = 𝑚𝜔2𝑟 N

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Design Laboratory 18MEL77

Total force balanced by balls, 𝑊+𝑆

𝑏
𝐹𝑏 = × 𝑎N
2

Frictional force, F = Fc- Fb N

Tabular column to find effort and power of governor

Change of speed % of Change Sleeve Effort Power

(rpm) of speed lift (m) (N) (kW)

Specimen Calculations:

Change of speed: N1-N2

N -N
2 1
Speed factor, c =
N1
Sleeve lift, x= x1-x2
Effort = c
(mgMg) Power =
effort *(x)
Draw the characteristic curves: Height vs. Speed, Lift vs. Speed and Controlling force
diagram (Radius of rotation vs. controlling force)

Calculations:

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Results:

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Experiment No.:06 Date:

JOURNAL BEARING

Aim: - To conduct experiment on journal bearing and to plot radial distribution (pressure)
across the clearance of a journal bearing.

Apparatus Required: Journal bearing setup, Tacho meter, weights and lubricating oil.

Theory- A Journal bearing supports a shaft and permits rotary motion this causes wear of
surfaces due to friction between the contact surfaces and heat is generated, resulting in loss
of power. To minimize this, lubricating oil is introduced in the clearance between the
journal and bearing. Pressure developed in the oil film due to viscous force while the
journal is rotating and this separates the contact surfaces (lift the journal). The study of
pressure distribution and variables associated with the bearing and can be used for design
purposes. The operating characteristics such as load carrying capacity and coefficient of
friction of a full journal bearing will be discussed.

Experimental setup: It consists of a Journal and bearing assembly connected to a D.C.

motor the motor is fixed on a rigid support. The bearing carries a hook on which weights
can be placed. Lubricating oil (SAE 40) is supplied to the bearing through the tubes from
the oil tank, which is placed above the bearing. The bearing has 16 tapping, 12 for radial
and 5 (including one radial tap, which is also in axial direction) for axial pressure
distribution. These tapping are connected to flexible tubes, which are supported vertically.
These tubes form manometers for reading the pressure. Each of the tubes is provided with
an adjacent scale for measuring the head of the oil.

Procedure:
1. Fill the oil tank with lubricating oil (SAE 40).
2. Note down the initial manometer reading.
3. Check and ensure that the dimmerstat is at zero position.
4. Load the bearing by adding weight on the weight hanger.
5. Rotate the dimmerstat knob gradually till the desired speed is reached.

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6. Run the setup at this speed, till the oil levels in all the manometer tubes are
in steady state.
7. Note down the pressure of oil in all the manometer tubes and tabulate them.
8. Bring down the speed to zero and switch off the motor and the main supply.
9. The difference in manometer pressure at each tapping is plotted.
Specifications:
1. Diameter of the journal d = 22 mm
2. Inside diameter of bearing D = 23 mm
3. Bearing width l =100 mm
4. Speed of the journal N = rpm
5. Speed of the journal n =N/60=rps
6. Lubricating Oil used = SAE 40
7. Viscosity of the oil around 400 = = 150 x 10-3
8. Self weight of the bearing W1 = 3.0 kg
9. Load on the shaft after applying a load Wa W2 = W1+Wa

Specimen calculations:

Unit Load or Pressure P = Load w = N/m2


Pr ojected Area Ld

Diametral Clearance =   c  D  d 
d d
2  n   1 
Petroffs equation for Coefficient of friction:   2  p   =
  
Tabular column:
With Load Condition
Initial Final
Angle in Final – Initial
Sl No Pressure Pressure
degrees Reading
Reading Pi Reading Pf
01

02

03

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04

05

06

07

08

09

10

11

12

Without Load Condition

Initial Final
Sl No Angle in Final – Initial
Pressure Pressure
degrees Reading
Reading Pi Reading Pf
01

02

03

04

05

06

07

08

09

10

11

12

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Graph: Graph to be plotted for pressure distribution (Cm) in radial direction at intervals
of 300.Graph to be drawn for pressure in axial direction (tube No v/s Pressure (p).

Steps for plotting the graph:

1. Select a suitable scale to plot the pressure distribution curve
2. With the initial pressure head as the radius draw a circle.
3. Divide the circle in to 8 equal divisions to represent the location of the
pressure tapping on the bearing along the circumference.
4. Draw radial lines from the center of the circle along these 12 points, starting
from the tube 1.
5. Mark the pressure heads along these radial lines corresponding to the tapping.
6. Join these points with a smooth curve.
7. Mark the direction of rotation of the journal on the fig.

Calculations:

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Results:

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Experiment No.:07 Date:

STRAIN ROSETTES

Aim: To determine the magnitude of principle stress using strain gauge rosette.
Apparatus Used: Experimental setup, which includes strain gauges, mounted on the
specimen, weights and strain indicator.
Theory: Applications: Electrical resistance strain gauges are widely used because of its
negligible mass, their Small size and faithful response to rapidly fluctuating strains. As the
output is electrical, remote observation is possible. The output can be displayed, recorded
or processed as required.
Electrical resistance strain gauges are widely used in
1. Experimental study of stresses in transports vehicles, Aircraft, Ships, Automobiles
and Trucks.
2. Experimental analysis of stresses in structures and machines, Apartment
buildings, Pressure vessels, Bridges, Dams, Transmission towers, Steam and Gas
turbines.
3. Experimental verification of theoretical analysis
4. Assist failure analysis.
5. As a sensing element in Transducers for measurement of force, load,
pressure, displacement and Torque.
Strain gauges are very sensitive to temperature. The error in strain measurement due to
temperature variation can be reduced to a minimum either through the use of suitable
compensate gauge or by using self compensated gauges.
Strain gauges can be used for the measurement of strains on the free surface of any
member. In electrical strain resistance gauge a change in length or strain produces a
change in resistance. It is necessary to measure 3 strains at a point ( x,y,xy) to completely

define either the strain or stress field. To determine Principal strains ( 1 and 2) and the

direction  of 1 relative to the X-axis. It is necessary to employ multiple element strain

gauges and they can be arranged in combination to get three-element rectangular rosette
or three-element delta rosette four-element rectangular rosette etc.
For Three element rectangular rosette with gauges A, B and C with angles of A,B andC
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respectively, the strains induced are

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A = xcos2 A + ysin2A +XY cosA .sinA  (1)

B = xcos2 B + ysin2B +XY cosB .sinB  (2)
C = xcos2 C + ysin2C +XY cosC .sinC  (3)
At a point on the member, the strain gauge B is mounted along the axis of the shaft and the
strain gauges A and C are mounted 450 the strain gauge B clock wise and anticlock wise
respectively.
Hence A= -450,B = 00 and C= 450

Substituting these values in the equations (1), (2) and (3), We can get the values of x, y
and xy.

x = B, y = (A + C - B) and XY = C - A

Principal Strains:  A C 1 2BAC

    2  CA
  2
1  2 2

 A  1 2BAC
    2  CA
  2
2  2
C
2

Principal Stresses: E
    2 
1 
1 2
1
E
 
2
1 
2   1 
2

Principal Directions: 1   C  A 
1
  tan  

2  2B  A C 
  xy 
tan 2    
 x y
 
Procedure:
1. Connect the apparatus to strain indicator and switch on the power supply..
2. Set initial reading on the indicator to zero.
3. Apply the load in X and Y directions by adding weights on the weight hanger.
4. Note down the readings for three strain gauges A, B and C and find the direction
of Principal stresses and strains.
5. Repeat the above procedure and tabulate the results.
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Tabular Column:

Strain Indicator Principal Principal Principle

Load (F)
Sl No. Reading Strains Stresses direction in
(N)
() () (Mpa) degree

X Y A B C 1 2 1 2

Specifications:
Young’s modulus of aluminium EAl= 68.9x103 Mpa.
Poisons ratio  =0.3

Calculations:

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Results:

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Experiment No.:08 Date:

STRESS CONCENTRATION FACTOR

Aim: To determine the stress concentration factor for a plate having a circular hole
subjected to an axial load using strain gauges.
Apparatus Used: Strain indicator, strain gauges, loads, weight hanger.
Theory: A stress concentration (often called stress raisers or stress risers) is a location in an
object where stress is concentrated. An object is strongest when force is evenly distributed over its
area, so a reduction in area, caused by a crack, results in a localized increase in stress. A material
can fail, via a propagating crack, when a concentrated stress exceeds the material's theoretical
cohesive strength. The real fracture strength of a material is always lower than the theoretical value
because most materials contain small cracks or contaminants (foreign particles) that concentrate
stress. Fatigue cracks always start at stress raisers, so removing such defects increases the fatigue
strength. When inner forces go around holes or notches, they will concentrate near such obstacles.
Stress concentrators are areas that tend to magnify the stress level within a part. Stress that is high
in one area than it is in surrounding regions can cause the part to fail. If the radius of curvature in
the notch tip is very small or if there is no radius (crack), the stress level is very high. Sharp corners
are especially critical.

There are experimental methods for measuring stress concentration factors

including photoelastic stress analysis, brittle coatings or strain gauges. While all these
approaches have been successful, and also have experimental, environmental, accuracy
and/or measurement disadvantage. During the design phase, there are multiple
approaches to estimating stress concentration factors.

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Procedure:
1. Connect the strain indicator to the experimental setup using appropriate wires.
2. Switch on the main power supply and calibrate the strain indicator to read
zero initially.
3. Load the member by adding weights to the weight hanger.
4. Note the strain indicator readings.
5. Find the maximum and minimum nominal stress and hence the stress conc. factor.
6. Repeat the process for different loads.
7. Plot a graph of ςmax Vs ςnom.
Tabular Column
Sl. Load in Strain gauge readings ςmax ςnom SCF
No. (N) St1 x 10-6 St2 x 10-6 (N/m2) (N/m2) Kt = ςmax/ ςnom

Specifications:
Young’s modulus of aluminium EAl= x103 Mpa.

Formulae:

Maximum stress = 𝐸 𝑋 𝑆𝑡1

4 N/m
= 2
𝜎𝑚𝑎𝑥
Nominal stress =
=
𝐸𝑋 N/m2
𝜎𝑛𝑜𝑚 𝑆𝑡2
4
𝜎𝑚𝑎𝑥
Stress concentration factor = Kt =
𝜎𝑛𝑜𝑚

Calculations:

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Results:

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Experiment No.:09 Date:

WHIRLING OF SHAFT

Aim: To determine the critical speed of shafts and hence to study whirling of shaft.

Theory: Rotating shafts tend to vibrate violently at certain speeds called critical or
whirling speed. When the gears or pulleys are mounted on a shaft the center of gravity of
the mounted element does not coincide with the center line of the bearing (or) axis of the
shaft, due to this the shaft is subjected to a centrifugal force. This further increases the
distance of center of gravity from the axis of rotation and hence the centrifugal force
increases. This effect is commutative and ultimately the shaft fails. At critical speed the
shaft deflection becomes excessive and may cause permanent de-formation or structural
damage. Hence a machine should not be operated close to the critical speed. To determine
critical speed of a shaft, which may be subjected to point, loads, UDL or a combination of
both, since the frequency of transverse vibration is equal to critical speed in RPS, determine
the frequency of transverse vibration. The Dunkerley’s method may be used to calculate
the frequency of transverse vibration. Therefore, natural frequency fn is given by:
1 1 1
1  ..... 
2
F 2 Fn2 2 Fns 2
Fn n1

Procedure:
1. Fix the desired shaft to the driving end,
2. Fix the bearing block with chuck at the other end for supporting the shaft.
3. Start the motor connected to the dimmerstat, which is at the minimum position.
4. Adjust the dimmerstat slowly. Until a state is reached when the shaft begins
to vibrate.

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5. Slowly adjust the speed till the point, where maximum amplitude of vibration
is attained.
6. Note down the speed.
7. Find out the deflection and frequencies for different diameters of shaft

Specifications:
Length of the shaft L= 750mm=0.750m
Youngs modulus E= 210 GPa
Density of mild steel ρ= 7806 kg/m3

Tabular column:

Critical Natural Critical

Sl. No. Diameter of
speed frequency speed Error % Error
shafts d (m)
Nexp rpm) Fn (Hz) Ntheo (rpm)

Formulae:

Weight of Shaft W= Density x Volume = ρ d

x 2 xLN
 4 4
Moment of Inertia I  D m4
64
  WL3
Deflection of shaft under self weight: s m
EI

1g 2
Natural Frequency of shaft: Fn  Hz
2
Theoretical speed=Fn.60 rpm
Nthe  Nexp
% of error = X 100
Nthe

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Calculations:

Results:

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Experiment No.: 10 Date:

PHOTOELASTICITY (CIRCULAR DISC)

Aim: To determine the difference in principle stress at the centre at a point of interest in
a circular disc subjected to diametrical compression.
Apparatus Required: Circular disc of photoelastic material (Epoxy resin), Universal
loading frame, and 12” diffused light transmission polariscope.
Theory - Photoelasticity is an experimental technique for stress and strain analysis that is
particularly useful for members having complicated geometry, complicated loading
conditions, or both. For such cases, analytical methods (that is, strictly mathematical
methods) may be cumbersome or impossible, and analysis by an experimental approach
maybe more appropriate.
While the virtues of experimental solution of static, elastic, two-dimensional problems are
now largely overshadowed by analytical methods, problems involving three-dimensional
geometry, multiple-component assemblies, dynamic loading and inelastic material
behavior are usually more amenable to experimental analysis.
The name photoelasticity reflects the nature of this experimental method: photo implies the
use of light rays and optical techniques, while elasticity depicts the study of stresses and
deformations in elastic bodies. Through the photoelastic-coating technique, its domain has
extended to inelastic bodies, too.
Photoelastic Behavior -The photoelastic method is based upon a unique property of some
transparent materials, in particular, certain plastics. Consider a model of some structural
part made from a photoelastic material. When the model is stressed and a ray of light
enters along one of the directions of principal stress, a remarkable thing happens. The light
is divided into two component waves, each with its plane of vibration (plane of
polarization) parallel to one of the remaining two principal planes (planes on which shear
stress is zero). Furthermore, the light travels along these two paths with different
velocities, which depend upon the magnitudes of the remaining two principal stresses in
the material.
The incident light is resolved into components having planes of vibration parallel to the
directions of the principal stresses s1 and s2. Since these waves traverse the body with

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different velocities, the waves emerge with a new phase relationship, or relative
retardation.2 specifically, the relative retardation is the difference between the numberof
wave cycles experienced by the two rays traveling inside the body.
Isoclinics are the locus of the points in the specimen along which the principal stresses are
in the same direction. It is locus of the point at which the principal plane is inclined to the
same extent with respect to reference direction.
Isochromatics are the locus of the points along which the difference in the first and second
principal stress remains the same. Thus they are the lines which join the points with equal
maximum shear stress magnitude.

Effects of a stressed model in a plane Polariscope

It has been established that the principal stress difference can be determined in a two
dimensional model if N is measured at each point in the model. Also, it was stated that the
optical axes of the model coincide with the principal –stress directions. These two facts can
be effectively utilized once a method to measure the optical properties of a stressed model
has been established.
Consider first the case of the plane – stressed model inserted into the field of a plane
polariscope with its normal coincident with the axis of the polariscope, as illustrated in the
figure. Note that the principal- stress direction at the point under consideration in the
model makes an angle with the axis of polarization of the polarizer.

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Polarizer Analyzer

Photoelastic model

Source  41  2
-Q14 wave plate -Q2
Quarter wave plateQuarter

Fig:DIFFUSED LIGHT REASERCH POLARISCOPE

Circular disc under diametrical

compression (calibration model)

Tarday’s Method
This method is used for measuring fractional order by compensation at any desired point.
There is every possibility that your point of interest may not be exactly on a integral fringe.
In such case fractional fringe order may be found out by this method.

Determination of principle stress difference at a point:

This can be found by using the relation

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Nf
σ1 σ2  σ
h
Where, ς1=Major principal stress
ς2=Minor principal stress

N=Fringe order at a point

fς =Material fringe value

h= Thickness of photoelastic model

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Procedure:
1. Load the circular disc in universal loading frame, under diametrical compression
as shown in experimental setup.
2. Apply light load on plain polariscope (D-D) arrangement.
3. Observe the isoclinic fringe pattern and note the isoclinic reading at the center
of the disc which is automatically zero.
4. Switch ‘ON’ the sodium lamp (monochromatic) 10 mins before conducting the test.
5. Load the specimen gradually and set to circular polariscope (M-M) position.
6. Use white light and Observe the isoclinic fringe pattern at the center of the disc.
7. Use Tardy’s method, if required, to find fractional fringe order at the center of the
disc. This can be done by rotating the analyser either clock wise or anticlock wise to
enable the coinciding at the center from lower or higher fringe order.
8. Determine the average fringe order.
9. Repeat the above procedure for different loads.
10. Plot the graph between Load v/s Fringe order.
Observation:
1. Specimen dimensions: Diameter d = 50mm, Thickness h = 6.5mm
2. Distance from the fulcrum to the Applied load, X = mm
3. Distance from fulcrum to the centre of the specimen, Y = mm
4. Actual load F = 5W N

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Tabular Column:

Actual Load on
Load applied specimen in Fringe Order
𝜎1 − 𝜎2 𝑡𝑒𝑜 𝜎1 − 𝜎2 𝑒𝑥𝑝
‘W’ in (N) F = W(X/Y) or N
5W (N)

Formulae:

Material Fringe constant

8F
f  N/mm
8𝐹
dN
𝜎1 − 𝜎2 𝑡𝑒𝑜 = 𝐌𝐩𝐚
𝜋𝑑𝑕
𝑓𝜎 𝑁
𝜎1 − 𝜎2 𝑒𝑥𝑝 = 𝐌𝐩𝐚
𝑕

Calculation:

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Results - The material and model fringe value for the given photoelastic material is
founded to be ……….

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Experiment No.: 11 Date:

PHOTOELASTICITY (CIRCULAR DISC)

Aim: To determine the difference in principle stress at a point 10 mm from the centre along
a horizontal axis of a circular disc subjected to diametrical compression.
Apparatus Required: Circular disc of photoelastic material (Epoxy resin), Universal
loading frame, and 12” diffused light transmission polariscope.
Theory: Same as in previous experiment
Procedure:
1. Mark x=10mm from the centre of the disc, where the stresses has to be calculated
2. Load the circular disc in universal loading frame, under diametrical compression
as shown in experimental setup.
3. Apply light load on plain polariscope (D-D) arrangement.
4. Observe the isoclinic fringe pattern and note the isoclinic reading at the center
of the disc which is automatically zero.
5. Switch ‘ON’ the sodium lamp (monochromatic) 10 mins before conducting the test.
6. Load the specimen gradually and set to circular polariscope (M-M) position.
7. Use white light and Observe the isoclinic fringe pattern at the center of the disc.
8. Use Tardy’s method, if required, to find fractional fringe order at the center of the
disc. This can be done by rotating the analyser either clock wise or anticlock wise to
enable the coinciding at the center from lower or higher fringe order.
9. Determine the average fringe order.
10. Repeat the above procedure for different loads.
11. Plot the graph between Load v/s Fringe order.

Observation:
1. Diameter of specimen, d = 50mm
2. Thickness, h = 6.5mm
3. Distance from the centre, x=10mm
4. Distance from the fulcrum to the Applied load, X = mm
5. Distance from fulcrum to the centre of the specimen, Y = mm

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Formulae:
(ς - ς ) =
𝐹8 𝑑4 −4𝑑2 𝑋 2
Mpa
1 2 the
𝜋𝑑 𝑕𝑑2 −4𝑋 2 2
𝑓𝜎 𝑁
(ς1- ς2)exp = Mpa
𝑕

Tabular Column:
Actual load on the
Sl. Load W in Fringe order (ς1- ς2)exp (ς1- ς2)the
specimen F=
No. (N) N In (Mpa) In (Mpa)
W(X/Y) in (N)

Calculations:

Result:

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Experiment No.: 12 Date:

SIMPLE PENDULUM

Aim: To determine the natural frequency of the simple pendulum.

Apparatus Required: universal vibration apparatus, nylon ropes, chuck and pendulum
bob.
Theory: when no external force acts on a body after giving it an initial displacement, then
the body is said to be under free or natural condition. The frequency of the vibration is
called free or natural frequency vibrations. The natural frequency of vibration of a simple
pendulum is inversely proportional to time period. Hence by determining the time period
experimentally and comparing it with its theoretical values, the natural frequency can be
determined.
Procedure:
1. Fix the ball with nylon ropes, into the gripping chuck provided at the top beam of
the frame.
2. Adjust the balls to suitable length and measure the length of the pendulum.
3. Oscillate the pendulum and note down the time required for 10 oscillations.
4. Repeat the process by changing the ball and length of the rope.
5. Plot a graph for natural frequency v/s length.

Observation:
1. Radius of small ball, r1 = 0.0278 m
2. Radius of big ball, r2 = 0.0395 m
Tabular Column:
Rope Time for one Time for 10
Sl Radius of ball Fn (theo) Fn (Exp)
length oscillations oscillations
No. r (m) in Hz in Hz
L(m) T (sec) T (sec)

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Formulae: (for small and big ball)

1. Length of the rope to the centre of pendulum, L = x + r (m)
2. Time period, T = t/10 (sec)
3. Acceleration due to gravity, g = (4π2L)/T2 (m/s2)
4. Theoretical Frequency, Fn(theo) = (1/2π)(g/L)1/2 (Hz)
5. Experimental Frequency, Fn(exp) = 1/T (Hz)

Calculations:

Result:

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Experiment No.: 13 Date:

COMPOUND PENDULUM
Aim: To find the acceleration due to gravity and moment of inertial of the rod using
compound pendulum.
Apparatus Required:
Theory:

Procedure:
1. First hang the pendulum horizontally and move it until it reaches equilibrium so
you can find the center of mass and mark it.
2. Secondly hang it vertically inserting the tip of the knife in the first hole from
the center of mass. Then set it oscillating through a small angle.
3. Measure the time needed for 20 oscillations and the corresponding h.
4. Repeat steps 2 and 3 for the other holes.
5. Record your measurements in a table.
Nature of Graph:

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Tabular Column:

M=

One side of C.M Other side of C.M

h (m) 20T (sec) T(sec) h (m) 20T (sec) T(sec)

From the graph:

h2 K= g=
T h 1 average L=h1+h2 IG =MK2
average (h1h2)1/2 (4π2L)/T2
(sec) (m) (m) (kg-m2)
(m) (m) (m/s2)

Calculations:

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Result:

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