SOM Lab Manual

Department of Mechanical Engineering Strength of Materials

1

Strength of Materials

Mr. Sunil Pandey

Department

of Mechanical Engineering

ECHELON INSTITUTE OF TECHNOLOGY

NAME ------------------------------------------------------------------- ROLL NO.--------------------------------------------------------------- BRANCH---------------------------------------------------------------- BATCH-------------------------------------------------------------------


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Content

S.No. Content Page No.

General Instructions 3

1. To perform the tensile test on UTM 8

2. To perform the compression test on UTM 19

3. To perform the bending test on UTM 24

4. To perform the shearing test on UTM 29

5. To perform the tensional test on Torsion testing machine 33

6. To perform hardness test on hardness test machine 40

7. to perform toughness test on toughness test machine. 49

8. To perform fatigue test on fatigue test machine. 56

9. To perform cupping test on cupping test machine. 60

10. To study the behavior of column with various end

conditions.

71

11. To verify the moment area theorem regarding the slopes and deflections of the beam

77

12. To determine the elastic properties of beam. 77


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General Instructions

To make laboratory experiments safe and effective, each student should follow the given

instructions.

SAFETY

1. High voltage source in the laboratory should be handled properly under the

guidance of lab assistant, as it may cause a serious accident.

2. Avoid loose clothes, shirts should be properly tucked, skirts with extra flares

should be avoided, slippers are not allowed, shoes with rubber soles are

recommended for mechanical work laboratories.

3. Make sure that all power sources are off during set-up of machines.

4. Keep safe distance from moving parts of machines.

5. Follow the instruction given by the instructor

6. Failure to obey instructions may result in being expelled from the lab

7. Be careful not to damage any machine or instrument. Care must be taken in

handling all instrument

8. Do not start any machine or operate it without the permission from instructor.

9. Lubrication should be checked before starting the machine if required.

10. The application or removal of the load should be gradual.

11. Any unusual behavior or noise of the machine must be reported immediately

reported to the instructor and investigated

ATTENDANCE

1. All students are required to attend and contribute adequately while

performing experiments in the group.

2. The punctuality in attendance in the laboratory is essential. The student

should not leave the lab without permission

3. All students must write satisfactory report for each lab experiments.


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4. Failure to be present for an experiment will result in losing entire marks

for the corresponding lab.

5. All students are supposed to attend only their group of experiment

assigned at the beginning of the lab.

PREPARATION OF LAB REPORT

1. Before coming to the laboratory, each student must read and review

appropriate experiment to be conducted on the subsequent turn.

2. Record your experiment observations and sample calculations carefully.

3. Each student is required to write a neat and clean report for the experiment

conducted.

4. Every student should bring his own set of drawing instruments logbooks,

slide rule etc

5. Student should get the necessary apparatus issued against their names

before starting the experiment should carefully inspect the apparatus and

returned it well to the lab in charge after finishing the work

6. Reports are due one week after the completion of the experiment.

7. Each report shall be submitted with all necessary instructions, sample

calculations, graphs, and discussion over data and graph.

8. Observations should be recorded in tabular form and in a proper order

9. Sample calculations should be done on a set of most important data. The

calculations should be complete, leading from observed quantities to final

results

10. Results within the scope of the object should be given, with graphical

representation wherever possible.

11. Sources of error should be reported properly. It provides a limit for

admissible inaccuracy in the results.

12. Discussion over results should be analyzed properly and compared with

the manufactures rating.


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13. A brief criticism of the test procedure and apparatus used with concrete

suggestions, if any, for improvement should be explained. Any unusual

occurrence observed during the test should be reported.

1. Discussion should reflect the opinion of the writer. It should not be a

collection of merely the self-evident facts.

2. Questions give at the end of each experiment have to be answered

appropriately with in the space provided in the manual.

3. Students should remain prepare for the viva-voce on any turn.

HOW TO PLOT A GRAPH

1. Before drawing a graph between two observed variables it is necessary to

know the nature of expected theoretical graph.

2. Decide which parameter to be considered on X axis and which one on the

Y-axis.( parameter which is under the control of the student is generally

kept over X axis)

3. Selection of appropriate scales for the two variables should be chosen such

that it appears as square graph.

4. The following procedure should be observed in drawing the graphs.

(i) A curve should first be drawn freehand in pencil. It should then be

faired, preferably in black ink, with proper instruments.

(ii) Unless otherwise specified, the independent variables should be

plotted on the abscissa.

(iii) The axes should be well defined and bold.

(iv) The scales should be chosen for easy reading with due regard to the

accuracy of the observed quantities so that variations are neither

concealed nor exaggerated. Too large a scale should not be chosen

simply to fill a curve sheet. Some times the scale of abscissa may be

taken larger than ordinate to make the curves clear.


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(v) The scale for the axes may or may not start from zero; but scale for the

curves of efficiency, economy rate, capacity, etc should always start

from zero.

(vi) When several curve are drawn over the same abscissa, care must be

taken in choosing the ordinates of the scales such that the curves do

not overlap confusingly.

5. Different indent points should identify each curve separately.

6. Points plotted should be joined such that it appears smooth and near to the

theoretical nature of the curve. It is not necessary to join all points on the

graph. Average graph is always advisable, instead of point


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PREFACE

There was a long felt demand by faculty and students for a comprehensive lab manual on

Strength of Materials, studied in engineering branch affiliated to M.D. University Rohtak.

This increasing demand encouraged the authors to come up with an illustrative write up

of the experiments.

All necessary guidelines have been given in this manual although on the time basis each

and every necessary step will be told to students at the time of performing a particular

experiment.

Ten selected experiments have been presented in the well suitable manner and are

expected to be student friendly.

This manual looks for the betterment of students and will be amended on the time basis.

This manual aims the practical performed for the strength of material subject of echelon

institute of technology Faridabad. Teachers copy of the experimental results and answer

for the question are available in the lab as sample guidelines.

We hope that this manual would be a great help for students of Mechanical Engineering

branch . Any suggestion, constructive criticism for further improvement of manual will

be accepted wholeheartly.

Author express gratitude to Management of Echelon Institute of Technology, Faridabad

for their continuous encouragement for the successfully completion of this difficult task.

I also express very thankful to those people who, directly or indirectly was involved in

this task.

Author

Sunil Pandey

June, 2012


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Experiment No. 1 Name__________________RollNo._________Group/BatchNo.____________

Date ________Marks/Grade__________Facultys Signature______________

AIM: - To perform the tensile test on UTM EQUIPMENT REQUIRED: Tensile testing machine, steel rule, specimen

THEORY- When a specimen is axially pulled under static loading conditions, the specimen

elongates and finally breaks. The elongation per unit length is called strain and the load acting

per unit cross- sectional area is called stress. The corresponding stress is called proportional

limit and the slope of straight line is called modulus of elasticity. Up to a particular load the

specimen regains its original dimensions upon removal of load. Beyond that load some

permanent deformations remains. The corresponding stress is called elastic limit. The

elongation less than that corresponding to the elastic limit is called elastic deformation,

elongation greater than that corresponding to the elastic limit is called plastic deformation.

After a particular load, the material elongates even when the load is kept constant. Since the

strain rate is low, the load has to be decreased to effect the elongation. The stress

corresponding to initial load is called upper yield point and that corresponding to decreased

constant load is called lower yield point and the phenomenon of elongation at constant load

corresponding to lower yield point is called yielding. After a particular load the specimen

undergoes localized deformation leading to sudden decrease in cross-sectional area and large

increase in elongation . The specimen breaks. The material which are weak in shear fail along a

plane of 45 degree to the axis - where the shear stresses are maximum .The materials which are


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weak in tension fail along a plane 90 degree to the axis, where the tensile stresses are

maximum. The energy absorbed per unit volume during the elastic deformation is called

modulus of resilience and is given by E2

2 . The energy absorbed per unit volume up to

rupture is given by the area under the curve and is called modulus of toughness. Materials

with strain less than 5% at fracture are regarded as brittle and those having strain more than 5%

at fracture are regarded as ductile. For materials which do not show yielding, a tangent to the

curve is drawn at the origin and is offset by 0.2% strain. The stress corresponding to the point

of intersection of the offset tangent with the curve is called proof stress. The strain

corresponding to the UTS is called maximum uniform strain. The percentage of elongation,

percentage of reduction in area and maximum uniform strain is used for comparing ductility of

materials. The ratio of load to original Cross-sectional area is called engineering stress and

ratio of load to current area is called proof stress. Similarly true strain is defined as summation

of incremental strains over the- entire load range. Some materials show increase in yield

strength when loaded to plastic range, unloaded and then reloaded. This phenomenon is called

strain hardening.

REQUIREMENTS- An arrangement to hold a specimen and pull it axially at a uniform preset

rate. An arrangement to measure the load acting on the specimen. An arrangement to measure

the elongation of the specimen.

DESCRIPTION OF APPARATUS - Three load scales for indicating the load acting on the

specimen. Three counter weights for use in different combinations corresponding to each of the


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three load scales Each load scale is for different range of loads and selection of any particular

scale for an experiment depends on the expected load range for the particular specimen used in

the experiment. A linear displacement measuring scale for indicating the elongation of the

specimen. A motor gearbox assembly with belt and pulley arrangement for obtaining

different speeds. A screw attached to the motor foundation for loosening and tightening the

belts so that the desired pulley combination is achieved. A vertical bolt is connected to the

gearbox output shaft. A nut on the vertical bolt. A cross slide welded to the nut at the center

and which slides on two vertical shafts at the ends. A lower grip attached to the cross slide. An

upper grip attached to a lever mechanism, which causes a shaft to rotate when load acts

downwards. Counter weights fixed to a pendulum, which swings when shaft rotates. A push

rod with a rack and pinion arrangement to actuate the load scale needle when the push rod is

pressed is by the swinging pendulum. A dashpot to dampen the movement of pendulum. A

rider needle which moves with the load scale needle when the load increases but remains the

last position when the load decreases. A lever with each grip to open and close the vice sothat

the specimen may be inserted into the grip and locked. Two limit switches to cut -off the motor

when the cross slides moves too close to either the base or the upper grip .One push button

each for moving the cross slide up and down and to stop the cross slide. When the motor runs ,

the vertical bolt rotates as a result of which nut moves up or down the bolt. The lower grip also

moves up or down because it is attached to the nut which in turn is welded to the cross slide .

The fixed between the upper and lower grips thus gets loaded or unloaded depending on

whether the lower grip is moving up or down respectively .The lever attached to the upper grip

gets operated due to the load transmission to the upper grip from the lower grip through the

specimen .


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DESCRIPTION OF THE SPECIMEN: Straight piece of uniform cross -section over the test

length . Enlarged ends which can be held . The gauge length to the cross-sectional area is

because % of elongation is not a unique quantity for a material but varies with the gauge length

For this reason gauge length is standardized so that comparison of ductility between two

materials may be made consistently length. Measure the dimensions of the specimen. Press the

lever to open the vice of the upper grip and insert the specimen inside the vice - Then release

the lever to lock the specimen. Move the lower grip up and when the bottom end of the

specimen enters into

PROCEDURE

OBSERVATIONS-

Initial reading on linear scale = Initial reading on load scale = Initial gauge length = Initial dimensions of specimen = Initial area of cross section =


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Department of Mechanical Engineering Mechanics of Solid

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PRECAUTIONS-

1. Switch on the machine craftily.

2. Fix the specimen at proper position in the machine.

3. Check the specimen should be marked with punch before fix it. 4. Note down the reading of both scales carefully.

5. Switch off the machine after performing the experiment.

TENSILE TEST SPECIMEN


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Graph:-


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RESULT

% OF ELONGATION = % OF REDUCTION IN AREA = TENSILE STRENGTH =

MODULUS OF ELASTICITY =

QUESTIONS:

1. What is engineering stress

2. What is engineering strain 3. What is modulus of rigidity


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4. What is modulus of toughness

5. What is modulus of resistance

6. What is proportional limit

7. What is elastic limit


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8. What is yield point

9. What is proof stress

10. What is ultimate tensile strength

11. What is percentage of reduction and percentage of elongation

12. What is ductility and malleability


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13. How does a mild steel fail?

14. Which instrument is used for measuring elongation within yield point?

15. What is gauge length?


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Experiment No. 2 Name_________________RollNo.________Group/BatchNo.__________

Date_______Marks/Grade__________FacultysSignature____________

Aim:- To perform the compression test on UTM

Theory: - A compression test can be performed on UTM by keeping the test-piece on

base block and moving down the central grip to apply load. It can also be performed on a

compression testing machine. A compression testing machine shown in fig. it has two

compression plates/heads. The upper head moveable while the lower head is stationary.

One of the two heads is equipped with a hemispherical bearing to obtain Uniform

distribution of load over the test-piece ends. A load gauge is fitted for recording the

applied load.

SPECIMEN: - In cylindrical specimen, it is essential to keep h/d = 2 to avoid lateral

instability due to bucking action. Specimen size = h = 2d


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PROCEDURE :-

OBSERVATION :-

1. Initial length or height of specimen h = ------mm

2. Initial diameter of specimen do = -------------mm.

CALCULATION :-

Original cross-section area Ao =

Final cross-section area Af =

Stress =

Strain =

Determine percentage reduction in length (or height) to the specimen

Determine ultimate (max.) compressive strength,

Determine Youngs modulus in compression

PRECAUTIONS:-

The specimen should be prepared in proper dimensions.

The specimen should be properly to get between the compression plates.

Take reading carefully.

After failed specimen stop to m/c.


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Graph


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RESULT:-

CONCLUSION:-

QUESTIONS :-

Q.No. 1 Compression tests are generally performed on brittles materials-why


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Q.No. 2 Which will have a higher strength: a small specimen or a full size member made

of the same material?

Q.No. 3 What is column action? How does the h/d ratio of specimen affect the test result?

Q.No.4 How do ductile and brittle materials in their behavior in compression test ?


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Experiment No. 3

Name__________RollNo._______________Group/BatchNo.__________

Date_______Marks/Grade________FacultysSignature______________

AIM: -To perform the bending test on UTM

APPARATUS USED: - UTM or Beam apparatus, Bending fixture, vernier caliper, meter

rod, test piece & dial gauge

THEORY :- Bending test is perform on beam by using the three point loading system.

The bending fixture is supported on the platform of hydraulic cylinder of the UTM. The

loading is held in the middle cross head. At a particular load the deflection at the center of

the beam is determined by using a dial gauge. The deflection at the beam center is given

by:

EIWLd48

2

PROCEDURE:-

1. Least count of vernier caliper =

2. Length of beam (L) =

3. Width of beam (b) =

4. Thickness of beam (t) ` =

STEPS


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Graph:-


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CALCULATION :-

12

3btI

EIWLd48

2

PRECAUTIONS :-

1. Test piece should be properly touch the fixture

2. Test piece should be straight

3. Take reading carefully

4. Elastic limit of the beam should not be exceeded

RESULT :-

CONCLUSION :-

VIVA-QUESTIONS :-

What is deflection ? how will define ?


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What is moment of inertia?

What is young modulus?

Write Eulers formula


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How many types of column?


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Experiment No. 4

Name_________________RollNo._________Group/BatchNo._________

Date___________Marks/Grade_____FacultysSignature_____________

Aim:- To perform the shearing test on UTM

APPARATUS USED :- A UTM, Specimen, shearing attachment, vernier caliper etc

THEORY :- A type of force which causes or tends to cause two contiguous parts of the

body to slide relative to each other in a direction parallel to their plane of contact is called

the shear force. The stress required to produce fracture in the plane of cross-section, acted

on by the shear force is called shear strength

PROCEDURE :-

OBSERVATION :-

Applied compressive force (F) =

Diameter of specimen =

CALCULATION :-

The shear strength shall be calculated from the following formulae

T= (F/2)/ (pd/4) = 2F/pd

where d is the actual diameter of the specimen


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Graph:-


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PRECAUTIONS :-

1. The specimen should be all place equal dia.

2. Measure the diameter of specimen carefully

3. The specimen should be properly grip between the test rig

4. Take reading more carefully

5. After shearing specimen stop to m/c.

RESULT: - Shear strength of specimen =

CONCLUSION:-

VIVA-QUESTIONS:-

Does the shear failure in wood occur along the 45 shear plane?


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What is single & double shear?

What is find in shear test?

What is unit of shear strength?


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Experiment No. 5

Name_________________RollNo._________Group/BatchNo._________

Date___________Marks/Grade_____FacultysSignature_____________

Aim:- To perform the tensional test on Torsion testing machine

EQUIPMENT REQUIRED - Torsion testing machine, steel rule, micrometer, test piece.


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FIG 2: TORSION TEST SPECIMEN (BEFORE AND AFTER TEST)


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THEORY: A torsion test is performed to determine the modulus of rigidity, torsional yield strength, and modulus of rupture in torsion. The modulus of rupture is equal to the nominal surface stress corresponding to the maximum torque. Now, the torsion formula is given by:

T/J= / R=G/L Where, = Modulus of rupture T == Maximum twisting moment R = Original outer radius of test piece J = Polar moment of inertia = D4 /32, Angle of twist D == Diameter of test piece L = Parallel length of test piece G = Modulus of rigidity Therefore, G=(T/) (L/J) = T x R/ J PROCEDURE


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OBSERVATION:

Diameter of test piece =_____________________________mm Length of the test piece = ____________________________mm

OBSERVATION TABLE:

SNo Torque (Kgfm)

Torque (Nmm)

Angle of twist

(Degree)

Angle of twist

(Radian)

Shear strength (N/ mm2)


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T O R Q U E V S A N G L E O F T W IS T C U R V E

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0

A N G L E O F T W IS T

TOR

QU

E


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CALCUTATIONS:-

RESULT: Ultimate shear strength = Modulus of rigidity = Modulus of rupture =

PRECAUTIONS: QUESTIONS: 1. What is the purpose of the torsion test?


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2. Define modulus of rigidity? 3. On what factors does the torsional strength of the test piece depends? 4. Under which conditions mild steel and cast iron fails? 5. How wire torsion testing is different from rod testing? 6. Give torsion formula and explain?


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Experiment No. 6 Name_________________RollNo._________Group/BatchNo._________Date__________Marks/Grade____FacultysSignature_______________ AIM: To perform hardness test on hardness test mcahine

EQUIPMENT REQUIRED: Rockwell hardness testing machine, diamond indenter,

Allen key set, specimen to be tested, Brinell attachment.

THEORY: The property of hardness is defined as resistance to indentation or

scratching. Based upon the method of measurement, it can be categorized as follows:

1. Scratch hardness

2. Indentation hardness


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1. BRINELL HARDNESS A steel ball is pressed upon a surface whose hardness to be

measured. This results in an indentation on the surface. The ratio of load, which caused

the indentation to the area of indented surface, is defined as Brinell Hardness Number. If

P = Applied load in kgf

D = Diameter of ball in mm

d = Diameter of indentation in mm

Then

BHN = P / ( D / 2) (D - D2 d2)) kgf / mm2

At any other load the ratio d / D must be constant which requires that P / D2 must be

constant. An anomaly may arise in measurement of diameter of indentation due to

localized deformation of metal in region of indentation. To arrive at the true value of d

the indenter is often coated by a dye before making the indentation. The diameter then

can be measured on the colored ring. To avoid interference between an indentation and

any edge of the specimen, or between two indentations, it is advisable that the center to

edge or center to center distance be at least 1.5 D. Similarly the thickness of plate must be

at least equal to D so that the plastically deformed zone below the indentation does

interfere with the back surface.

2. ROCKWELL HARDNESS In this method two types of indenters are commonly

used.


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1. An indenter in the form of 120o diamond cone

2. Steel balls of 1 / 16- inch and 1/ 8-inch diameters

Rockwell Hardness is measured on an arbitrary scale on which hardness number is

inversely proportionally to depth of indentation. A minor load is applied on the specimen

through the indenter so that the specimen sits properly and tendency for localized

deformation in region of deformation is reduced. Then a major load is applied and the

depth of indentation is automatically recorded as hardness number on a dial gauge. One

combination of load and indenter will not be able to produce a wide range of hardness.

Therefore three loads with three indenters are used in different combinations to provide

wide range to measure hardness of several materials.

The thickness of plate specimen must be at least ten times the depth of indentation

to avoid any effect of indentation to pass through the thickness. The distance between

two adjacent impressions should be at least three times the size of indentation. The

hardness read from indenting the curved surface should be corrected for curvature. The

surface on which indentation is made must be clean and smooth and it should be well

seated upon a clean plate form.

PROCEDURE:

1. BRINELL HARDNESS TEST


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2. ROCKWELL HARDNESS TEST

OBSERVATIONS: ROCKWELL HARDNESS TEST

BRINELL HARDNESS TEST

S.No. Material of specimen Scale used Rockwell Hardness Number

1. 2. 3. 4. 5.


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CALCULATIONS:

S. No. Material of specimen

Applied load

Diameter of ball

Diameter of indentation

Brinell Hardness Number

1. 2. 3. 4. 5.


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RESULT: R.H.N. of material _________________ = R.H.N. of material _________________= R.H.N. of material _________________= B.H.N. of material _________________= B.H.N. of material _________________ = B.H.N. of material _________________ =

PRECAUTIONS:

1. Place the lever at proper position.

2. Clean the surface of specimen with emery paper.

3. Fix the indenter at its position by taking care of diamond tip.

4. Apply and release the major and minor load slowly.

DISCUSSION :


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QUESTIONS:

1. Define hardness? What are the types of hardness tests?

2. What are the ways of conducting indentation tests?

3. What is practical application of hardness test?


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4. What is Brinell hardness number and give value of P and D in Brinell test?

5. What should be the rate of load application in Brinell test and how much time the load be maintained in Brinell test?

6. What is Rockwell Hardness Number and give the standard scales?

7. What is minor load and why it is applied?


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8. What is relation between penetration and reading on scale?

9. How is machine checked for accuracy?


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Experiment No. 7

Name____________________RollNo.______Group/BatchNo._________

Date_________Marks/Grade______FacultysSignature_____________

AIM: To perform toughness test on toughness test machine.

EQUIPMENT REQUIRED: Impact testing machine, specimen to be tested, izod and charpy hammers, steel rule, Leveler.


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THEORY:Brittle fracture tendency in materials like steel develops due to

1. A tri-axial state of stress

2. Low temperature

3. High strain rate.

Stress calculation at the tip of a notch under impact load is extremely difficult, due to

which the results of impact tests are not presented in the form of a stress. The property

that is measured in the impact test is the energy absorbed in fracturing the specimen of

standard dimensions and standard notch. This property measured in Joules is called

impact toughness. Impact toughness is property of specimen and is a good qualitative

index of behavior of material in presence of notch at low temperature. Such an index is

not possible to obtain from any static test; therefore this property is largely used in

selection of material and for development of material for specific purposes of inhibiting

the tendency of brittle fracture. The energy absorbed in fracture decreases as temperature


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decreases. In a particular temperature range the impact toughness decreases sharply with

decrease in temperature. Below this range material behaves in a brittle fashion.

PROCEDURE:

1. Charpy impact test

2.Izod impact test


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OBSERVATION: 1.Izod Test Dimensions of specimen Length = Breadth =

Notch angle and its depth = 2.Charpy Test Dimensions of specimen Length = Breadth = Notch angle and its depth =

S.No. Type of material Total energy J

Loss of energy J

Resultant energy J

1. 2. 3.

S.No. Type of material Total energy J

Loss of energy J

Resultant energy J

1.

2. 3.


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RESULT:

DISCUSSION:

PRECAUTIONS:

QUESTIONS:

1. What is influence of increase in strain rate?

2. What is an impact load?


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3. What property is measured in impact test?

4. What is the principal of impact test energy measurement?

5. Give differences between Izod and Charpy test?

6. What is the purpose of notch in the specimen?


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7. Define notch sensitivity?

8. Describe the surface in brittle failure and ductile failure?

9. What is transition temperature?


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Experiment No. 8 Name___________Roll No._________Group/Batch No._______________

Date________Marks/Grade______FacultysSignature_______________

AIM: To perform fatigue test on fatigue test machine.

EQUIPMENT REQUIRED: Fatigue testing machine, steel rule, micrometer, specimen to be tested, and adjustable spanner THEORY: On repeated application of load for a large number of time, a material fails even if the associate stress is less then the UTS of the material. Even though the load that are imposed upon machine parts and structures in the service may be random the nature, laboratory test are generally performed under sinusoidal stress for convenience. Techniques have been developed to use these result for application under actual service condition. The maximum value of stress is called max . the minimum value of stressis called min . The average value of stress is called m. The amplitude is given by half of the difference between maxand min. When max is zero then the loading is called repeated. When m is zero then the loading is called fully reversed. The ratio of maxand min is called stress ratio. The stress that are applied upon the fatigue test specimen can be axial, banding, torsion or there combination. The minimum value of stress beyond which specimen requires infinite number of cycle to fail is called ENDURANCE LIMIT.


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The fatigue behavior depends upon various factors

1. Frequency:- At high frequency ( above 1000 cycle per mim) , there is improvement in

life because less time is available during a load cycle to extend a crack. Below 200 cycle

per min. fatigue limit tends to become less with lower frequencies. Between 200 to 1000

cycle per min. there is generally no influence on fatigue behavior.

2. Surface condition:- better surface finish, better the fatigue behavior. Surface treatment

also increase fatigue life.

3. Stress concentration:- the fatigue strength decrease in presence of stress

concentration.

PROCEDURE:-


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OBSERVATION:- Weight used (W) =

Distance between fixed end and the end to witch weight is suspend (free

end) =

Diameter of rod first portion of specimen (d) =

Diameter of end portion of specimen (D) =

Moment of force (M) = W x L =

Stress (S) =

Number of cycle (N) =

CONCULATION:- RESULT:-


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QUESTION:- 1. What is fatigue? 2. Explain factor effecting fatigue 3. Explain endurance limit. 4. What is infinite number of cycle?


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AIM: To perform cupping test on cupping test machine.

EQUIPMENT REQUIRED: Erichsen cupping testing machine, sheet to be tested, Steel

rule.

THEORY:

The test consists of clamping a metal test piece under controlled pressure between

a retaining ring and pressing the test piece into the die by means of a ball or penetrater

having a spherical head until ruptures commences .The depth of penetration thereby

obtained is measured and provides an indication of the stretch forming capacity of the

sheet or strip within the limits imposed by the conditions of the test .


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PROCEDURE:

OBSERVATION:

S.No.

Type of metal

Thickness of sheet (mm)

Initial reading of dial gauge

Final reading of dial gauge

Cupping umber

(from table)


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CALCULATIONS:

RESULT:

cupping value of the specimen No._______________ =



PRECAUTIONS:

1. The test piece should be flat and thickness should not be more than 2 mm.


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2. The grease should be applied at the point of contact on the specimen.

3. The force should be applied slowly and constantly on the lever.

4. The reading of dial gauge should be taken carefully.

5.

SHORT QUESTIONS:

1. What is cupping number?

2. What is importance of cupping test?

3. What is drawing and deep drawing?


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4. Give some example of other forming operations?


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CUPPING NUMBER TABLE

MINIMUM ERICHSEN VALUES OF SHEET

THICKNESS IN mm CUPPING DEPTH IN mm (min)

TYPE D TYPE DD TYPE EDD 0.50 8.34 8.80 9.20 0.55 8.40 8.94 9.36 0.60 8.56 9.10 9.50 0.65 8.72 9.22 9.64 0.70 8.98 9.38 9.78 0.75 9.04 9.51 9.92 0.80 9.20 9.66 9.04 0.85 9.34 9.80 9.20 0.90 9.50 9.94 9.32 0.95 9.62 10.06 9.48 1.00 9.80 10.20 10.58 1.05 9.94 10.32 10.70 1.10 10.08 10.46 10.84 1.15 10.20 10.58 10.95 1.20 10.35 10.70 11.06 1.25 10.44 10.82 11.15 1.30 10.58 10.94 11.25 1.35 10.70 11.03 11.35 1.40 10.80 11.12 11.44 1.45 10.90 11.22 11.53 1.50 11.00 11.30 11.64 1.55 11.08 11.35 11.72 1.60 11.14 11.40 11.80 1.65 11.18 11.46 11.88 1.70 11.24 11.52 11.94 1.75 11.26 11.57 12.02 1.80 11.30 11.62 12.08 1.85 11.30 11.66 12.14 1.90 11.30 11.72 12.20 1.95 11.29 11.76 12.26 2.00 11.28 11.80 12.3


66

Experiment No. 10 Name_______________RollNo._________Group/Batch No.__________

Date__________Marks/Grade____FacultysSignature_______________

Aim: To study the behavior of column with various end conditions.

Apparatus Equipment:

Column buckling apparatus, weights, vernier calliper, screw gauge, weight container, etc.

Theory:

If compressive load is applied on a column, the member may fail either by crushing or by

buckling, depending upon its material, cross section and length. If member is

considerably long in comparison to its lateral dimensions, it will fail by bucking. If a

member shows signs of buckling, the member leads to failure with small increase in load.

The load at which the member just buckles is called buckling or critical load. For a

slender column, buckling load is less than the crushing load. The buckling load, as given

by Euler, can be found by using following expression:

Where E = Modulus of elasticity = 2.0 x 105 N/mm2 for steel

I = Least moment of inertia of column section

1e = Effective length of column

P = Critical or buckling load

Depending on support conditions, four cases may arise. The effective length for each of

which are given as under

Both ends are fixed

2Lle

One end is fixed and other is pinned

2Lle


67

Both ends are pinned

Lle

One end is fixed and other is free

Lle 2


68

Apparatus consists of four spring steel columns, which are put along a vertical wooden

board. These four columns have different end conditions as below:

Both ends fixed

One end fixed and the other pinned

Both ends pinned

One end fixed and other end free

Suggested Experimental Work:

Step1: Pin a graph paper on the wooden board behind the column.

Step2: Apply the load at the top of columns increasing the gradually. At certain stage of

loading the columns shows abnormal deflections and the gives the buckling load.

Step3: Note the buckling load for each of the four columns.

Step4: Trace the deflected shapes of the columns over the paper. Mark the points of

change of curvature of the curves and measure the effective length for each case

separately.

Step5: Also calculate the theoretical effective lengths and thus buckling loads by the

expressions given above and compare them with the observed values.

Results and Discussions:

1) Calculate the Euler's buckling load for each case.

2) Also calculate the theoretical effective lengths and thus buckling loads by the

expressions given above and compare them with the observed values.

Sample Data Sheet:

Width of strip (mm) b=

Thickness of strip (mm) t=

Length of strip (mm) L=

Least moment of inertia 12

3btI


69

PROCEDURE:-

CALCULATION:-

Sl.

No

End conditions Eulers

Buckling load (kg)

Effective

Length (mm)

Theoretical Observed Theoretical Observed

1.

2.

3.

4

Both ends fixed

One end fixed and the

Other pinned

Both ends pinned

One end fixed and the

other free.


70

Results and Comments:

Questions:

1. What is equivalent length

2. Define buckling and Crushing.


71

Experiment No. 11 Name________________Roll No.________Group/Batch No.__________

Date _________Marks/Grade____Facultys Signature_______________

Aim:- To verify the moment area theorem regarding the slopes and deflections of the

beam

Equipment required

Apparatus of Elastic properties of beam, weights, dial gauge, meter scale, etc.

Theory:

According to moment area theorem:

1. The change of slope of the tangents of the elastic curve between any two points of the

deflected beam is equal to the area of EIM diagram between these two points.

2. The deflection of any point relative to tangent at any other point is equal to the moment

of the area of theEIM diagram between the two points about the point at which the

deflection is required.

Slope at bYB 2

Since the tangent at C is horizontal due to symmetry,

Slope at EI

B area shaded

aLWaWa

EI 221 2

Displacement at B with respect to tangent at C


72

(y1 + y2)= EI

Babout area shaded ofMoment

=

42232

21 LabaLWaabaWa

EI

Procedure:

Length of main span, L (cm) =

Length of overhang on each side, a (cm) =

Modulus of elasticity, E (kg/cm2) calculated = 2.1 x 106

Steps:-


73

Sl. No. Load

at each

hanger

(kg)

Central

Deflection y1

(cm)

Deflection at

free end y2

(cm)

Slope at B

by2

Deflection at C

(y1) cm = &

Deflection at B

(y2) cm =


1. Calculate the slope at B as by2 (measured value).

2. Compute slope and deflection at B theoretically from B. M. D. and compare with

experimental values.

3. Deflection at C = y1 (Measured value)

4. Deflection at C = Average calculated value

Comments:

The moment area theorems may often be used more conveniently in the computation of

slopes and

Deflection of beams and frames, practically when concentrated rather than distributed

loads cause the deformation. These theorems are based on a consideration of the

geometry of the elastic curve of the beam and the relation between the rate of change of

slope and the bending moment at a point on the elastic curve.


74

Precautions:

Apply the concentration loads without jerks.

Measures the deflection only when the beam attains equilibrium.

Measure deflection very carefully and accurately.

Check the accuracy and least count of dial gauges used for measuring deflections.

Figures:

Calculations:


75


Questions:

1. State moment area theorem


76

2. Where moment area theorem can be applied


77



Aim: To determine the elastic properties of beam.

Equipment required:

Apparatus of Elastic properties of beam, weights, dial gauge, meter scale, etc.

Theory:

For the beam with two equal overhangs and subjected to two concentrated loads W each

at the free

ends, the maximum deflection y at the centre is given by

Central upward deflection, EILawy

8.. 2

1

Where,

a = length of overhang on each side

W = load applied at the free ends


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L = main span

E = modulus of elasticity of the material of the beam

I = moment of inertia of cross section of the beam

yLawEI

8.. 2

2

Also it is known that EI for beam = 12 bd3 x E

3

where, b = width of beam

d = depth of bean

Procedure:

Observation Table:

Length of main span, L (cm) =

Length of overhang on each side, a (cm) =

Width of beam, b (cm) =

Depth of beam, d (cm ) =

Modulus of elasticity, E (kg/cm2) = 2.1 x 106


79


1. Calculate the experimental value of EI by Eq. (2).

2. Compare the experimental value of EI with theoretical values.

Average values of EI from observation = ---------- kg. sq.cm

Average values of EI from calculation = ------------ kg.sq. cm

Comments:

Precaution:

Measure the central deflection y very accurately.

Ensure that the beam is devoid of initial curvature.

Loading should be within the elastic limit of the materials.

Sl. No. Equal loads at

the two ends

(kg)

Dial gauge reading at

the midspan of

beam(cm)

EI fromEq. (3)

(Kg.Sq. cm)

EI fromEq.(2)

(Kg. Sq. cm )


80

Figures:

Calculations:


81


Questions:

What is flexural stiffness?

What is the value of EI for any beam?

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