lab manual mechanics of solids ii b.tech i semester
TRANSCRIPT
LAB MANUAL
MECHANICS OF SOLIDS
II B.Tech I Semester
Department of Mechanical Engineering
DEPARTMENT OF MECHANICAL ENGINEERING
To excel in preparing mechanical engineering graduates with core knowledge, advanced
skills and professional ethics in order to meet the ever changing industrial demands and social
needs.
M1: To provide the students with the best of knowledge by imparting quality education in
the area of Mechanical Engineering and allied fields.
M2: To facilitate the students by providing the interaction with Mechanical Engineering
related companies to be part of technological advancements which enhances
employment opportunities.
M3: To inculcate self learning abilities, leadership qualities and professional ethics among
the students to serve the society.
DEPARTMENT VISION
OUR MISSION
PEO1: To make the graduates who are equipped with technical knowledge and engineering
skills through the program to achieve a successful career in the field of mechanical
engineering.
PEO2: To participate in ongoing developments of mechanical engineering to be strong with
the fundamentals and relate it with the present trends.
PEO3: To gain the practical knowledge through the program by identifying, formulating and
solving mechanical engineering related problems.
PROGRAM EDUCATIONAL OBJECTIVES
1. PO1: Engineering knowledge: Apply the knowledge of mathematics, science,
engineering Fundamentals and an engineering specialization to the solution of
complex engineering problems.
2. PO2: 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. PO3: 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. PO4: 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. PO5: 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. PO6: 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.
PROGRAM OUTCOMES
7. PO7: 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. PO8: Ethics: Apply ethical principles and commit to professional ethics and
responsibilities and norms of the engineering practice.
9. PO9: Individual and team work: Function effectively as an individual, and as a
member or leader in diverse teams, and in multidisciplinary settings.
10. PO10: 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. PO11: 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. PO12: 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 SPECIFIC OUTCOMES
PSO1: Identify and analyze the real time engineering problems in Manufacturing, Design
and Thermal domains.
PSO2: Execute the work professionally as an employee in industries by applying
manufacturing and management practices.
PSO3: Gain the knowledge of latest advancements in Mechanical Engineering using
Computer Aided Design and Manufacturing.
COURSE OUTCOMES
After completion of the course students will be able to
C207.1 Analyze the behaviour of the solid bodies subjected to various types of
loading.
C207.2 Apply knowledge of materials and structural elements to the analysis of
simple structures.
C207.3 Undertake problem identification, formulation and solution using a range of
analytical methods.
C207.4
Analyze and interpret laboratory data relating to behaviour of structures and
the materials they are made of, and undertake associated laboratory work
individually and in teams.
C207.5 Expectation and capacity to undertake lifelong learning.
CONTENTS
S.No. NAME OF THE EXPERIMENTS
1. DIRECT TENSION TEST
2. BENDING TEST ON SIMPLE SUPPORTED BEAM
3. BENDING TEST ON CANTILEVER BEAM
4. TORSION TEST
5. BRINELL HARDNESS TEST
6. ROCKWELL HARDNESS TEST
7. TEST ON SPRINGS
8. COMPRESSION TEST ON CUBE
9. IZOD IMPACT TEST
10. CHARPY IMPACT TEST
11. PUNCH SHEAR TEST
TENSILE TEST
Objective:
To conduct tension test on the given steel specimen for determining the
1. Stress at yield point.
2. Ultimate stress.
3. Nominal breaking stress.
4. Actual breaking stress.
5. Percentage elongation.
6. Percentage reduction in area.
7. Young's modulus.
Apparatus:
1. Universal testing machine with accessories
2. Vernier callipers.
3. Scale.
4. Dot punch.
5. Hammer.
6. Specimens as ISI
Theory:
The Tension test which is conducted on a universal testing machine at room temperature is a
Common method to evaluate strength and ductility under static load conditions. The tension
test is carried by loading a standard specimen gripped at both ends and measuring the
resultant elongation of the specimens at various increments of loads.
Procedure:
1. Measure the diameter of the given mild steel specimen at three different places with the
help of Vernier callipers and determine the average diameter of the specimen and gauge
length.
2. Mount the specimen in the grip of the movable and fixed cross head
3. Adjust the load stabilizer, start the machine and open the inlet valve slightly. When
the load pointer just kicks it, indicates that the load is held caught between the grips,
and then adjusts the pointer to read zero.
4. Apply the load at a steady uniform rate and until specimen breaks.
5. After some time the actual point returns slowly. At this stage, a neck is formed in
the specimen, which breaks. Note the position of actual pointer during breaking.
Record the maximum load as "Breaking load".
6. Press the freeze button and then print to get the graph between load verses
elongation.
7. Repeat the procedure for other specimen.
Observations:
Diameter of rod — Trial 1 = mm
Trial 2 = mm
Trial 3 = mm
Average diameter of rod (d0) = mm
Original length (Gauge length) of rod (Lo) = mm
Yield point load (Py) = KN
Ultimate load (Pu) = KN
Breaking Load (Pb) = KN
Calculations:
Original area of cross section (A0) = 2
4d
Area of cross section at neck (Af) = 224
fd
Stress at yield point = Yield load/Original area N/mm2
Ultimate stress = Ultimate load/Original area N/mm2
Actual breaking stress = Breaking load/Original area N/mm2
Percentage reduction area = 100
o
fo
A
AA
Percentage elongation = 100
o
fo
L
LL
Young’s modulus =
Original Length (L0 ) = mm
Final Length (Lf ) = mm
Ori
gin
al d
ia (
do)
mm
Nec
k d
ia (
df)
mm
Ori
gin
al l
ength
(Lo)
mm
Fin
al l
ength
(Lf)
m
m
Ori
gin
al a
rea
(Ao)
Mm
2
nec
k a
rea
(A
f)
Mm
2
Yie
ld s
tres
s N
/mm
2
Ult
imat
e st
ress
N/m
m2
Bre
akin
g s
tres
s
N/m
m2
Young’s
modulu
s
N/m
m2
% o
f el
ongat
ion
Graph: Print the graph between load [Y-Axis] and deflection [X- Axis] from the graph
calculate stresses.
Result: Stress from graph = ------------------------------
TORSION TEST
Objective:
To find out the shear stress and rigidity modulus orate given material using the torsion testing
machine.
Apparatus:
Torsion testing machine — Model TT-6. Vernier callipers, scale, specimens.
Specifications:
Max torque capacity : 60 N m
Torque ranges : 0- 60 Nm
No of divisions on dial : 600
Torsion speed : 1.5 RPM
Clearance between grips : 0- 420 mm
Grips for round bars : 4- 8 nun
Grips for flat bars (t) : 1-5 mm, 25 mm
Motor power : 0.5 HP
Accuracy of torque indication: +1% of true torque above 20% its range
Procedure:
1. Measure the diameter of the specimen and select the suitable grips for the specimen and
insert into the driving and driven chucks
2. Insert the specimen into the two chucks by holding driven chuck firmly.
3. Adjust torque range depending on the type of specimen (hard or soft) by turning a knob on
the right hand side of measuring panel.
4. Then adjust the zero of the angle-measuring disc.
5. Switch on the motor by pressing green button.
6. Switch off the motor after the specimen breaks.
7. Note down the torque shown by the red pointer in the dial and that is the maximum
capacity of specimen.
8. The angle of twist can be directly read on the angle-measuring disc.
9. Repeat the Same Procedure for different specimens of the same material.
2 TEST PROCEDURES:
Various types of grips are supplied to the customer depending upon their requirement. The
jaws inserts along with holders slide in the driving chuck. The sliding motion of the jaws
Inserts is achieved by rotating driving chuck by operating special shafts provided the taper
Portion of the holders ensures firm clamping are the specimen and easy take: Out of the
broken specimen.
The specimen is then held in the driving chuck and driven chuck with help of handles. Also
adjust the angle measuring dial at zero position, and black Pointer is to be adjusted at the
starting position and the pen in its required position. The red dummy pointer is to be brought
in line with the black pointer. The thread from the driving chuck pulley is to be taken over
small pulleys and should be wound over the graph PULLEY Groove.
Then machine is to be started a' now the specimen will be gripped, properly and it will be
subjected to TORSION.
This torque goes on increasing till the specimen breaks. Then red dummy pointer then
indicates the breaking Torque.
Observation table:
S.
No.
MATERIA
L
GAUGE
LENGT
H (L)
MM
DIAMETE
R (d) MM
TORQU
E (T) N-
M
TWIST
𝜽 RADS
SHEAR
STRES
S (τ)
N/MM2
GIGIDITY
MODULU
S (G)
N/MM2
Calculations:
Polar moment of inertia of rod (J) =32
4d
L
G
RJ
T
Slope=Tan =
Rigidity of modulus = G =J
LT
N/mm2
Shear stress (T) = J
rT N/mm2
Result: The maximum shear stress on the given material is ---------N/mm2
Rigidity modulus----------- N/mm2
IMPACT TEST (CHARPY)
Objective:
To determine the impact strength of the given specimen by conducting Charpy test.
Apparatus:
Charpy testing machine with accessories
Specimen
Vernier Callipers.
Theory:
The loads that are suddenly applied to a structure are known as impact loads. The
performance on engineering materials like strength, toughness etc. varies with rate of loading.
Materials exhibits poor performance tough Hess under dynamic or shock loads. Hence it is
required to know how the strength and toughness varies with impact or instant shock loads. In
the impact test, the impact strength (i.e. the resistance to shock loads) and the toughness of
material under dynamic load is determined.
The principle employed in all impact testing procedures is that a material absorbs a certain
amount of energy before it breaks or fractures. The quantity of energy thus absorbed is
characteristic of the physical nature of the materials. If it is brittle it breaks more readily, i.e.,
absorbs a lesser quantity of energy and if it is tough, it needs more energy for fracture.
The two important standard impact tests are (1) Izod Impact test and (2) Charpy impact test.
Description:
The machine consists of a swinging pendulum that has an arm and head. For this test the
dimensions of standard specimen are 55 mm x 10 mm x 10 mm. It is a simple supported
beam. Swinging Head strikes other side of the specimen notch. Pendulum falls from 1.457 m
height or from in angle of 140°. The weight swinging hammer is 20.932 kg or 250 N. The
specimen struck exactly at its centre i.e. 27.5 mm. The machine also has a pedal operated
brake, to stop the hammer after the specimen struck.
Specifications:
Maximum impact energy of pendulum : 300 Joules
Minimum value of scale graduation : 2 Joules
Distance between supports : 40 mm±0.mm
Angle of test piece supports : 78° to 80°
Angle of inclination of supports : 0
Radius of supports : 1 mm to 1.5 mm
Maximum width of striker : 10 — 18 mm
Angle of striking edge : 30°± 1°
Radius of curvature of striking edge : 2 mm to 2.5 mm
Weight of the machine : 415 kg (approx.)
Procedure:
1. Measure the dimensions of specimen by using Venire Callipers.
2. Raise the pendulum and keep it in position, fix the correct striking edges to the head
of the swinging pendulum.
3. Set the pointer of the scale to maximum energy value.
4. Calibrate the tester by releasing the clutch so that the pointer coincides with zero on
the scale with no specimen at the anvil
5. Re-clutch the hammer after calibration.
6. Place the specimen centrally over the supports such that the notch is opposite to
striking end.
7. Reset the pointer on. The scale at its maximum value
8. Release the pendulum by operating the two levers simultaneously. The striking edge
strike against the specimen and ruptures it. The specimen absorbs a part of the energy
due to fall of the pendulum.
9. Stop the free swinging or oscillations of pendulum by a pedestal brake.
10. Collect the broken pieces of specimen to observe the nature of fracture.
11. Read the scale reading as shown by the pointer as the toughness of the material in
Joules.
Observations:
Breadth:
S.NO Main scale reading
g MSG in mm
Vernier coincidence
VC in mm
MSR+(VC×LC) IN
MM
Avg. breadth = mm
Thickness:
S.NO Main scale reading
g MSG in mm
Vernier coincidence
VC in mm
MSR+(VC×LC) IN
MM
Avg.thickness=mm
Tabular form:
Calculations: Specific impact power = Energy absorbed / area of cross section at the notch.
Precautions:
1. Ensure no one is at the path of swinging hammer, before its every return case
2. The pointer should be at the bottom i.e. it should at maximum value of scale, prior to
the release of the hammer.
3. Ensure the right striking edge, and correct weight of the swinging head.
4. Swinging hammer should be clutched at the standard height depending upon the type
of testing.
Result:
Specific impact power of the given material =
Assessment Questions:
1. Differentiate between impact loads, gradually applied load and suddenly applied
load?
2. Define strength toughness, Brittleness
3. Which type of material absorbs more energy i.e, either brittle or ductile material?
S.No
Material of
the
specimen
Area of the
specimen at
the notch
mm×mm
Energy absorbed Energy
absorbed to
brake the
specimen J
Specific
impact
power
J/mm2 Initial final
IZOD TEST
Objective:
To determine the suitability of a material, which is expected to resist repeated shocks by
determining the energy required to break the material by conducting Izod test.
Apparatus:
1. Izod testing machine with Accessories
2. Specimen
3. Vernier callipers
Theory:
The loads that are suddenly applied to a structure are known as impact loads. The
performance on engineering materials like strength, toughness etc. varies with rate of loading.
Materials exhibits poor Performance under dynamic or shock loads. Hence it is required to
know how the strength and toughness varies with impact or instant shock loads. In the impact
test, the impact. Strength i.e. (the resistance to shock loads) and the toughness of material
under dynamic load are determined.
The principle employed in all impact testing procedures is that a material absorbs a certain
amount of energy before it breaks or fractures. The quantity of energy thus absorbed is
characteristic of the physical nature of the materials. If it is brittle it breaks more readily, i.e.,
absorbs a lesser quantity of 'energy and if it is tough, it needs more energy for fracture.
The two important standard impact tests are (1) Izod Impact test and (2) Charily impact test.
Description:
The machine consists of a swinging pendulum that has an arm and head. For this test, the
dimensions of standard specimen are 75 mm x 10 mm x 10 mm. It is a cantilever beam.
Swinging Head strikes face of the specimen notch. Pendulum falls from 0.758 m height or
from an angle of 84°. The weight swinging hammer is 21.79 kg or 214 N. The specimen
struck exactly at its centre i.e. 27.5mm. The machine also has a pedal operated brake, to stop
the hammer after the specimen is struck.
Procedure:
1. The specimen is of square cross section of 10 nun side of and its length is 75 mm. It is
notched at a distance of 28 mm from one side, the notch being 2mm deep and with an
inclined angle of 45°.
2. Rise the swinging pendulum. Pendulum and keep it in position, Fix the correct
striking edges to the head of the
3. See the pointer of the scale is positioned at the maximum energy value.
4. Calibrate the tester by releasing the clutch so that the pointer coincides with zero on
the scale with no specimen at the anvil
5. Re-clutch the hammer after calibration.
6. The specimen is firmly held in the vice and fastened to base of the machine.
7. Place the specimen centrally over the supports such that the notch is opposite to
striking end.
8. Reset the pointer on the scale at its maximum value
9. Release the pendulum by operating the two levers simultaneously. The striking edge
strike against the specimen and ruptures it. The specimen absorbs a part of the energy
due to fall of the pendulum.
10. Stop the free swinging or oscillations of pendulum by a pedestal brake.
11. Collect the broken pieces of specimen to observe the nature of fracture.
12. Read the scale reading as shown by the pointer as the toughness of material in Joules.
Observation:
Breadth
Avg.breadth = mm
Thickness:
S. No. Main scale reading g
MSG in mm
Vernier coincidence
VC in mm
MSR+(VC×LC) IN
MM
Avg. thickness= mm
Tabular form:
S.No. Main scale reading MSR
in mm
Vernier scale reading
VC in mm MSR+(VC+LC) in mm
S.No
Material of
the
specimen
Area of the
specimen at
the notch
mm×mm
Energy absorbed Energy
absorbed to
brake the
specimen J
Specific
impact
power
J/mm2 Initial final
Calculations:
Specific impact power = Energy absorbed / area of cross section at the notch
Precautions:
1. Ensure no one is at the path of swinging hammer, before its every return case
2. The pointer should be at the bottom i.e. it should at maximum value of scale, prior to
the release of the hammer.
3. Ensure the right striking edge, and correct weight of the swinging head.
4. Swinging hammer should be clutched at the standard height depending upon the type
of testing.
Result:
Specific impact power of the given material =
COMPRESSION TEST
Objective: -
1 to determine the ultimate crushing strength of concrete and wood.
Equipment & Materials Used:
Compression Testing Machine M/C (CTM).
Wooden block or Concrete block
Scale.
Theory:
Concrete and Wood are generally used in engineering constructions and it may be subjected
to compressive loads. To with stand the structural loads, it is necessary to determine the
compressive strength of concrete and wood.
Compressive test is conducted at room temperature to determine the ultimate compressive
strength of the given concrete and wooden block under static loading conditions. The external
faces of wooden block are made perfectly plane. The block is held between the lower and
upper cross head of C. T. M. Inter mutual loads are applied gradually on the specimen. The
concrete or wood undergoes compression. At a particular load the needle of the control unit
starts to rotate anti clock wise, which can be noted as ultimate crushing load.
Description of the Equipment:
Compression Testing Machine is operated hydraulically. Driving is performed with the help
of electric motor. Depending upon the size of the specimen the C. T. M. can be set into two
ranges C. T. M. consists of two units
(a) Loading & (b) Control Unit.
The specimen is tested upon the loading unit and the corresponding readings are taken from
the dial fitted to the control unit. Hydraulic cylinder is fitted in the center of the base and the
piston slides in the cylinder when the machine is in operated. A lower table is rigidly
connected to an upper crosshead by two straight columns. This assembly moves up and
down. Compression test is conducted by putting the specimen in between lower table and
upper crosshead.
The control panel consists the two valves one is at right side and the another one at left side.
These valves control the flow of oil in the hydraulic system. The right side valve is a pressure
flow control valve and left side valve is return valve to allow the oil from cylinder to go back
in to the tank. Control panel co ..,,t,.; of dynamometer., which measures and indicates the
load on the specimen
Procedure:
1. Prepare the concrete or wood specimen as per required dimensions.
a) In case of compression test of wood perpendicular to the grain, tests are made on
normal 50 x 50 x 150 mm.
b) In case of compression test of wood parallel to the grains the dimensions of the
specimen is 50 x 50 x 200 mm.
c) Incase of concrete block 150 x 150 x 150 mm
2. Measure the dimensions of the specimen with the help of scale.
3. Place the specimen in between the lower table and upper crosshead of C. T. M. in
such a way that the grains of the specimen are perpendicular to the direction of
application of the load.
4. Apply the compressive load on the specimen. The needle of the control unit rotates in
clockwise direction.
5. By applying the load the specimen crushes. At particular load the needle starts to
rotate in anti clockwise direction. The corresponding load is called ultimate crushing
load.
6. Repeat the same procedure by keeping the specimen in such a way that the grains are
along the axis of loading and take the ultimate crushing load.
Observations:
When the load is applied perpendicular to the grains of the specimen.
S. No. Area of cross section
in mm2 (A)
Ultimate crushing
load in N (Pc)
Ultimate crushing
stress
A
Pc
N/mm2
When the load is applied along the grains of the specimen.
S. No. Area of cross section
in mm2 (A)
Ultimate crushing
load in N (Pc)
Ultimate crushing
stress
A
Pc
N/mm2
Result:
Ultimate crushing strength of given concrete or wood specimen = When the load is applied
perpendicular to the grains of the specimen= When load acts along the grains
HARDNESS TEST ROCKWELL HARDNESS TEST
Aim:
To measure the Rockwell hardness number for the given material.
Apparatus:
Rockwell hardness testing machine with accessories, emery paper, Specimen.
Theory:
Hardness is the property exhibited b a material. It can be defined as the property' of a material
by virtue Of which it resists scratch, wear, abrasion or indentation.
Description:
Rockwell Hardness Testing consists of an anvil which can be changed depending up on the
shape of the specimen under test. Different anvils are available for different specimen. The
anvil can moved up or down. But turning the hand wheel, which is situated, at bottom of the
spindle a loading leaver is situated at the right hand side bottom position of the machine. The
loading mass also be applied by simple operating a handle leaver which is just below the
handle wheel.
The machine reading type. These are two scales B and C. B for soft material, C for hard
materials.
Procedure:
1. Remove all mill scales from the surface of the specimen by rubbing it with emery
paper
2. Based on the type of materials. Select the proportional load on the indenting tool for
very hard materials. Measure in Rock-well `C scale, 1500N proportional load and
diamond penetrator. For medium hard and soft materials measure in Rockwell 'E'
scale, 1000N proportional load and 1.58 mm dia. ball penetrator.
3. Insert indenter and fasten with a screw.
4. Keep the load required for the scale which we are using
5. Place the specimen on the anvil and turn the wheel to raise the elevating screw till the
small pointer on the dial reaches the set position. Now the s and also set the bi pointer
to zero. Preliminary load of 100N and also set the big pointer to zero.
6. Push forward the Loading handle to transmit the major load to the specimen.
7. When the penetration is complete (Give 5 to 6 seconds for hard material and 6 to 8
seconds for soft material) release the major load by pushing backward the loading
handle. Keep the initial 100N load still on the specimen.
8. Then directly read the Rockwell 'C' or Rockwell '8' hardness number on the dial
where the needle stopped and record it.
9. Then release the minor load of 100N by rotating the hand wheel and lowering the
screw.
10. Repeat the Experiments to obtain at least four different sets of observation for the
same material.
Observations:
Sl. No. Material Trail
NO
Minor
load in N
Major
load in
N
Indenter
used
Scale
used R.H.NO.
Average R.H.No. =
Result:
Rockwell hardness No. For the given material =---------------RC or RB
BRINNELS HARDNESS TEST
Objective:
To measure the brinnel hardness number for given material.
Apparatus:
Brinnel hardness testing machine with accessories, emery paper, microscope.
Theory:
Hardness is a property exhibited by a material .it can be defined as the property of material by
virtue of which it resists scratch, where abrasion or indentation.
Description:
For a number of engineering materials which are subjected to friction such as steel,castiron
etc. it is necessary to find out their resistance to wear and tear (hardness)of surface can be
increased by heat treatment or by the chemical treatment and finding out the hardness can
check the efficiency of the process the brinnel hardness test is carried out by forcing a
hardened steel ball of diameter D under load of P into a test specimen and measuring the
mean diameter d of the Indentation left on the surface after removal of the load normally for
hard materials a ball of 10mm diameter should be used for soft material 5mm,2.5mm,2mm
and 1mm are to be used depending upon the softness of the surface.
The British Standard Institution has recommended the following four different ratios for
different materials.
The hydraulic pump applies the load required for specified time. A Brinnel Microscope is
used to measure the Indentation.
BHN= 22
2
dDDD
P
Where,
P is the load adjusted in the machine in N
D is the diameter of indenter and d is the diameter of impression.
In Brunel’s Machine the surface area of the Indentation is calculated and is used as an index
of hardness of the metal.
The surface area of Indentation is dependent upon the depth of penetration. The load applied
(in kgf) divided by the spherical area of Indentation in square mm is taken as the Brinnel's
Hardness number.
Procedure:
1. Polish the surface with emery paper.
2. Place the specimen on the work table and raise it by turning the elevating screw till
the small pointer on the dial reaches the set position. Now the specimen is subjected
to the preliminary the load 10 kgf.
3. Adjust the diaphragm the required weight, that is, if the penetrate diameter is 25mm.
and P/D- ratio is 30, then the load to be adjusted to 187.5 Kg. If the diameter of
penetrator is 10 mm, then the load is 30 Kg (300N). Apply the load by operating the
lever arm.
4. Wait for 30 Sec for soft materials and 15 sec for hard material so as to make the load
reach the specimen fully. Wait till the pointer stops moving.
5. Remove the specimen and measure the diameter of the indentation correct to 0.1mm
with Brinnel microscope. To do this, keep the specimen at microscope adjusted
indentation to the scale of the microscope and measure the diameter of the
indentation.
6. Repeated the process to obtain at least 4 different sets of observation for the same
material.
7. Brinnel Hardness number BHN= 22
2
dDDD
P
Observations:
Diameter of the indenter = mm
Load = kgf
Tabular form:
S. No. material
Diameter
of
indenter
in mm
Diameter of impression Load P
in kgf B.H.N
Tail-1 Tail-2 Average
Calculations:
BHN= 22
2
dDDD
P
Result:
Brinnel hardness number of given material= --------------BHN.
FLEXURAL TEST ON SIMPLY SUPPORTED BEAM
Objective:
To determine the young's modulus and bending stress for the given steel beam by conducting
deflection test.
Apparatlts:
Two knife edge supports, Deflect meter, Callipers, Scale, load hanger, set of weights.
Theory:
A beam extremely supported at both ends and load applied normal to axis of beam is called
Simply supported beam. The maximum deflection occurs at middle of span, where the load is
applied at the Mid Point of the beam. The loads are placed in pan. The pan is adjusted to
exactly middle of the beam. Weights are slowly placed on the pan. The beam under goes
deflection. The deflection of the beam is measured with the help of dial gauge and with the
help of relation between deflection of beam and load system. The Modulus of elasticity of
material of the beam is obtained. For this purpose consider two cases loading & unloading.
Description:
The apparatus consists of beam testing on two simply supported knife edges. The load `W’ is
applied at centre and the maximum deflection is measured at centre. For this load condition
the deflection at centre is given by
Where
⸹ =
E
W
I
L
48
3
f =I
YM
E =
W
I
L
48
3
W=concentrated load at centre in N
E=Young's Modulus in N /mm2
L = Length of the beam in mm
f= bending stress N /mm2
⸹ = Deflection of the beam in mm
y = Distance of top fiber from Neutral axis
I = Moment of Inertia about Neutral axis
b= breadth of the beam in mm
M = Bending moment WL/4
t = Thickness of the beam in mm.
Procedure:
1. Adjust the knife-edge supports for the required span.
2. Measure the dimensions of the given beam.
3. Place test beam over the centre or supports.
4. Place the deflect meter under the beam where the deflection is to be measured.
5. Suspend the hanger at the point where the deflection of the beam is to be noted.
6. Note the initial reading, of the deflect meter.
7. Add the loads to the hanger art the rate of SOON, the load should be carefully applied
without causing any shock. Note the corresponding deflect meter reading for each
increasing load.
8. Observe five set of readings.
9. Remove the loads at the rate of 500 N
10. Note the corresponding deflect meter reading for each decreasing load.
11. Draw the graph load Vs deflection mm, taking deflection on X-axis and load on Y-
axis.
Observations:
Span of the beam (L) = mm
Width of the beam (b) = mm
Thickness of the beam (t) = mm
Least count of Deflectometer = mm
Observation:
Breadth:
Avg.breadth = mm
Thickness:
S.NO Main scale reading g
MSG in mm
Vernier coincidence
VC in mm
MSR+(VC×LC) IN
MM
Avg.thickness= mm
S.No Main scale reading MSR
in mm
Vernier scale reading
VC in mm MSR+(VC+LC) in mm
Tabular form:
S.No Load
W (N)
Deflect meter reading Deflection in, mm
(initial-final) Young’s
modulus
N/mm2
loading Un-loading loading
Un-
loading average
Initial final Initial final
Sample Calculations:
For a simply supported beam of span I with central load W and deflection is measured at mid
span
Deflection at centre ⸹ =W L3/48EI
Moment of inertia I = b t3/12
E= L3/48EI (W/⸹)
From the bending equation, M/I=F/Y
F = (M/I) ×Y
Graph:
Plot a graph between load and deflection from the graph corresponding to any convenient
points. Find the value of W/⸹ ratio and calculate E from expression
E= L3/48EI (W/⸹).
Result:
Young's modulus of beam materials is = ------------------- N/mm2
Young's modulus from Graph = ------------------- N/mm2.
Bending stress at the applied maximum toad is = ------------------- N/mm2.
Assessment question:
1. Define Young's modulus, what are its units?
2. What is moment of inertia?
3. Define Hooks Law?
4. Define Bending moment?
5. Area under stress — Strain curve is?
FLEXURAL TEST ON CANTILEVER BEAM
Objective:
To conduct bending test on simply Cantilever beam and verify the Maxwell’s reciprocal
theorem.
Apparatus:
Simply supported beam. Dial gauge to measure the deflection of the beam
Specification:
Type of beam used: MS flat
Width of beam: 4.64 cm
Depth of beam: 0.27 cm
Type of measuring of instrument: Dial test indicator.
Materials and equipment:
1. Deflection of beam apparatus
2. Weights
3. Beam of different cross-sections and materials
The specimen is to be tested in a rectangular steel beam. A weight holder with a sliding hook
and weights of 1 kg, 4 kg, 10 kg and 25 kg is given.
Description of apparatus:
Beam:
The beam, which is to be used, is of simply supported beam having width of the beam is
4.64 cm and the depth is 0.27 cm
Weights:
The weights are of 1kg, 4kg, 10kg, and 25kg.
Supports:
This supports or supporting mine, device is used to place beam and weights.
Theory:
The bending test apparatus consists of a long rectangular steel bar resting on stands at both
the ends on this horizontal steel bar. Two sliding supports rest vertically. A dial gauge with a
pointer on its head provided. This can be adjusted with the nut provided.
Maxwell reciprocal theorem:
The Maxwell reciprocal theorem states that the deflection of a beam at any intermediate
point. Due to the load at the point C will be same as the deflection at point c due to the load at
point D.
Tabular column:
S. No. Load applied
(kg)
Deflection at C in mm
loading Un-loading averages
Procedure:
1. Fix one end of the beam and other end is to be free.
2. Fix dial gauge at one point of the beam.
3. Fix loads at the other end of the beam
4. Note down the deflections of the beam by using dial gauge Repeat the experiment for
different loads Regut3tecisgrae procedure for the unloading also
Precautions:
1. Be sure that the distance marked on the beam is equal
2. Before applying load do not forget to set the dial gauge pointer to the initial point
end.
3. Make sure there is nothing placed on the table except the operators a smallest
pressure on the table can soil the experiment
4. Make sure that the beam and load are placed in the proper position.
Result:
From above the experiment the deflection of the beam at L/2nd and L/4th is increasing that is
deflection for cantilever increases from fixed end to free end.
DIRECT SHEAR TEST
Objective:
To determine the shearing strength of the soil using the direct shear apparatus.
Need and Scope:
In many engineering problems such as design of foundation, retaining walls. Slab bridges,
pipes, sheet piling, the value of the angle of internal friction and cohesion of the soil involved
are required for the design. Direct shear test is used to predict these parameters quickly. The
laboratory report covers the laboratory procedures for determining these values for cohesion
less soils.
Planning and Organization
Apparatus 1. Direct shear box apparatus
2. Loading frame (motor attached).
3. Dial gauge.
4. Proving ring.
5. Tamper.
6. Straight edge.
7. Balance to weigh up to 200 mg.
8. Aluminium container.
9. Spatula.
Knowledge of Equipment:
Strain controlled direct shear machine consists of shear box, soil container, loading unit,
proving ring, dial gauge to measure shear deformation and volume changes. A two piece
square shear box is one type of soil container used.
A proving ring is used to indicate the shear load taken by the soil initiated in the shearing
plane.
Procedure:
1. Check the inner dimension of the soil container.
2. Put the parts of the soil container together.
3. Calculate the volume of the container. Weigh the container.
4. Place the soil in smooth layers (approximately 10 mm thick). If a dense sample is
desired tamp the soil.
5. Weigh the soil container, the difference of these two is the weight of the soil.
Calculate the density of the
6. Make the surface of the soil plane.
7. Put the upper grating on stone and loading block on top of soil.
8. Measure the thickness of soil specimen.
9. Apply the desired normal load.
10. Remove the shear pin.
11. Attach the dial gauge which measures the change of volume.
12. Record the initial reading of the dial gauge and calibration values.
13. Before proceeding to test check all adjustments to see that there is no connection
between two parts except sand/soil.
14. Start the motor. Take the reading of the sheer force and record the reading
15. Take volume change readings till failure.
16. Add 5 kg normal stress 0.5 kg /cm' and continue the experiment till failure
17. Record carefully all the readings. Set the dial gauges zero, before starting the
experiment.
Data calculations sheet for direct shear test:
Normal stress 0.5 kg/cm2
L.C=........... P.R.C=.......
Hori
zonta
l gau
ge
read
ing(1
)
Ver
tica
l dia
l gau
ge
read
ing(2
)
Pro
vid
ing r
ing
read
ing(3
)
Hori
.dia
l gau
ge
read
ing i
nit
ial
read
ing d
ia.g
aug
e (4
)
Shea
r def
orm
atio
n
col.
(4)×
leas
t co
unt
of
dia
l (5
)
Ver
tica
l gau
ge
read
ing i
nit
ial
read
ing (
6)
Ver
tica
l def
orm
atio
n
=div
.in.c
ol.
6×
L.C
of
dia
l gau
ge
(7)
Pro
vid
ing r
eadin
g
init
ial
read
ing (
8)
Shea
r st
ress
div
.col.
(8)×
pro
vid
ing
ring
const
ant
area
of
the
spec
imen
(kg/c
m2)(
9)
0
25
50
75
100
Observation and Recording:
Proving Ring constant.................
Calibration factor.................
Least count of the dial.................
Leverage factor.................
Dimensions of shear box 60x60mm
Empty weight of shear box.................
Least count of dial Gauge.................
Volume change.................
Result:
S.No Normal load
(kg)
Normal stress
(kg/cm2)
Shear stress
proving ring
reading
×calibration/area
of container.
TEST ON SPR1NGS
Aim:
To determine the Stiffness of the spring while Tension and Compression loads are applied
and to determine in which case tension / compression the stiffness is more.
Apparatus Required:
Spring test machine, scale
Specifications:
Make : Tech track, Haryana, India
Mode of operation : Hand operator, Hydraulic pump.
Dia of spring coil : 4.6Cm
Number of turns of spring coil : 54
Dia of loading platform : 33.8 Cm
Max. Load capacity : 2000 Kg
CS canned Cam Scanner
Sketch:
Description of apparatus:
Pumping Handle: It is used to pump the hydraulic oil.
Loading unit:
It consists of a panel. The main hydraulic cylinder is fitted in the canter of the panel and
the piston slides in the cylinder. Special material used for cylinder and piston and there
careful precision machining including individual lapping have increase the accuracy of the
machine to great extent. The- Pump is a positive displacement type pump. This assures a
continuous pressure — non - palsating oil current for the smooth application of load on the
specimen. The pump is fitted to the tank cover from bottom, which makes it easily assessable.
Belt tightening or loosing can be achieved very easily and the motor can be looped at the
desired position by check nuts.
Valves:
Two valves on the control panel
One at the right side and the other at the bottom side
The right side valve is a return valve. This valve allows the oil from the cylinder to go back to
tank, thereby reducing the pressure gauge in the cylinder and then the working piston collies
down. If the returns valve is closed, oil delivered by the pump passes through the central
value to the cylinder and the piston goes up.
Pressure gauge:
Pressure gauge is a unit which measures the load on the specimen. The overall accuracy of
the machine depends mainly on the accuracy of the unit depends on pressure gauge. Consists
etc cylinder in which the piston reciprocates top is connected with the pressure gauge. So the
oil pressure under the work piston is transmitted to the pressure gauge. This pressure
represents the measurements of the load on the specimen.
The bottom valve is provided for the flow/pressure of oil for slow/fast adjust the value
according to the equipment
Measuring scale: The scale is used to measure the deflection and it is vertically fitted along the rod.
Theory:
Stiffness:
The resistance of a material to elastic deformation is called stiffness. A material which suffers
light deformation under load has high degree of stiffness
It is denoted by K
Thus stiffness K=load (P)/unit deflection (⸹l)
Where, load (P) is kg
Deflection (⸹l) in mm.
The change in length is given by kg/mm
Spring: The springs are resilient member and extensively used to absorb shocks.
There springs are of two types.
1. Helical spring and
2. Leaf or laminated spring
Procedure:
1. Insert the pumping rod into the rod holder of the hand-pumping unit.
2. Now create pressure, inside the unit by pumping air by moving_ the rod up and down
till the deflection starts.
3. Tight the release the valve so that the pressure inside the machine is locked.
4. Note down the dial gauge reading and the deflection on the scale in mm
5. Now change the load and not down the deflection.
6. Likewise take at least 3 readings.
7. After testing the spring for tension, change the spring to test for compression.
8. After changing the spring set up using the spanner apply load and measure the
deflection
By using following the equation.
K=P/SL N/mm
'Where K = stiffness of spring n/mm
P = applied load, n
⸹l = deflection of length mm
9. After taking the reading for bottom tension and compression calculate the deflection and
change in length and tabulate it.
Tabular column: compression
S.No Load applied P
kg×9081
Change in length
⸹l mm
Stiffness of spring K
N/mm
Tensile:
S.No Load applied P
kg×9.81
Change in length
⸹l mm
Stiffness of spring K
N/mm
Precautions:
1. Properly handle the pumping rod and prevent slipping from band
2. See that the release valve is fully tightened
3. Carefully change the spring as the spring used for compression is too heavy and little
slippery
4. Before starting cleaning of any arrangement the main should be put off.
5. The load when applied must be kept constant by tightening the knob provided for this
purpose.
Result:
Stiffness in Tension =
Stiffness in compression =
From the obtained table, we come to the conclusion that stiffness is more in compression.