OJEBCTIVE- Study of tensile properties of a material

22 Department of Mechanical Engineering Mechanics of Solids

Mechanics of Solid

Mr. Sunil Pandey

Department

of

Mechanical Engineering

itm

University

An ISO 9001:2000 Certified InstitutionS.No.ContentPage No.

General Instructions3

1. To perform the tensile test on UTM8

2. To perform the compression test on UTM19

3. To perform the bending test on UTM24

4. To perform the shearing test on UTM29

5. To perform the tensional test on Torsion testing machine33

6. To perform hardness test on hardness test machine40

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

Content

General InstructionsTo 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.

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.

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.

(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

PREFACE

There was a long felt demand by faculty and students for a comprehensive lab manual on Mechanics of solids, studied in engineering branch at itm university. 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.

Twelve 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 Mechanics of solid subject of itm University Gurgaon. 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.

Authors express gratitude to Governing body of itm university for their continuous encouragement for the successfully completion of this difficult task.

We also express very thankful to those people who, directly or indirectly was involved in this task.

Authors

ITM, Gurgaon

June, 2010

Experiment No. 1Name__________________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 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. 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 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 gear- box 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.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

=

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.

Graph:-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

4. What is modulus of toughness

5. What is modulus of resistance

6. What is proportional limit

7. What is elastic limit

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

13. How does a mild steel fail?

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

15. What is gauge length?Experiment No. 2Name_________________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

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.GRAPH:-RESULT:-CONCLUSION:-QUESTIONS :-Q.No. 1 Compression tests are generally performed on brittles materials-why

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 ?

Experiment No. 3Name__________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:

PROCEDURE:-1. Least count of vernier caliper

= 2. Length of beam (L)

=

3. Width of beam (b)

=

4. Thickness of beam (t) `

=

STEPSGRAPH:-CALCULATION :-

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 ?

What is moment of inertia ?

What is young modulus

Write Eulers formula

How many types of column?Experiment No. 4Name_________________RollNo._________Group/BatchNo._________

Date___________Marks/Grade_____FacultysSignature_____________AIM:- To perform the shearing test on UTM APPARATUS USED :- A UTM, Specimen, shearing attachment, vernier caliper etcTHEORY :-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 strengthPROCEDURE :-

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 specimenGRAPH:-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?

What is single & double shear?

What is find in shear test?What is unit of shear strength?Experiment No. 5Name_________________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.

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

OBSERVATION:

Diameter of test piece =_____________________________mm

Length of the test piece = ____________________________mm

OBSERVATION TABLE:

SNoTorque

(Kgfm)Torque

(Nmm)Angle of twist

(Degree)Angle of twist

(Radian)Shear strength

(N/ mm2)

CALCUTATIONS:-RESULT:

Ultimate shear strength=

Modulus of rigidity

=

Modulus of rupture

=

PRECAUTIONS:

QUESTIONS:

1. What is the purpose of the torsion test?

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?Experiment No. 6Name_________________RollNo._________Group/BatchNo._________Date__________Marks/Grade____FacultysSignature_______________

AIM: To perform hardness test on hardness test mcahineEQUIPMENT 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

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.

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 TEST2. ROCKWELL HARDNESS TEST

OBSERVATIONS:ROCKWELL HARDNESS TESTS.No.Material of specimenScale usedRockwell Hardness Number

1.

2.

3.

4.

5.

BRINELL HARDNESS TEST

S. No.Material of specimen Applied load Diameter of ballDiameter of indentationBrinell Hardness Number

1.

2.

3.

4.

5.

CALCULATIONS:

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 :

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?

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?

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

9. How is machine checked for accuracy?

Experiment No. 7Name____________________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.

EMBED PBrush 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 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

OBSERVATION:

1.Izod Test

Dimensions of specimen

Length=

Breadth=

Notch angle and its depth= S.No.Type of materialTotal energy

JLoss of energy JResultant energy

J

1.

2.

3.

2.Charpy Test

Dimensions of specimen

Length=

Breadth=

Notch angle and its depth= S.No.Type of materialTotal energy

JLoss of energy JResultant energy

J

1.

2.

3.

RESULT:

DISCUSSION:

PRECAUTIONS:

QUESTIONS:

1. What is influence of increase in strain rate?

2. What is an impact load?

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?

7. Define notch sensitivity?

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

9. What is transition temperature?

Experiment No. 8Name___________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 spannerTHEORY: 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.

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:-

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:-

QUESTION:-

1. What is fatigue?

2. Explain factor effecting fatigue

3. Explain endurance limit.

4. What is infinite number of cycle?

Experiment No. 9Name___________Roll No._________Group/Batch No._______________

Date________Marks/Grade______FacultysSignature_______________

AIM: To perform cupping test on cupping test machine.EQUIPMENT REQUIRED: Erichsen cupping testing machine, sheet to be tested, Steel rule.

EMBED PBrush 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 .

PROCEDURE:

OBSERVATION:

S.No.Type of metalThickness of sheet

(mm)Initial reading of dial gaugeFinal reading of dial gaugeCupping umber

(from table)

CALCULATIONS:

RESULT:

cupping value of the specimen No._______________ =

cupping value of the specimen No._______________ =

cupping value of the specimen No._______________ =

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

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.SHORT QUESTIONS:

1. What is cupping number?

2. What is importance of cupping test?

3. What is drawing and deep drawing?

4. Give some example of other forming operations?CUPPING NUMBER TABLE

MINIMUM ERICHSEN VALUES OF SHEET

THICKNESS IN mmCUPPING DEPTH IN mm (min)

TYPE DTYPE DDTYPE EDD

0.508.348.809.20

0.558.408.949.36

0.608.569.109.50

0.658.729.229.64

0.708.989.389.78

0.759.049.519.92

0.809.209.669.04

0.859.349.809.20

0.909.509.949.32

0.959.6210.069.48

1.009.8010.2010.58

1.059.9410.3210.70

1.1010.0810.4610.84

1.1510.2010.5810.95

1.2010.3510.7011.06

1.2510.4410.8211.15

1.3010.5810.9411.25

1.3510.7011.0311.35

1.4010.8011.1211.44

1.4510.9011.2211.53

1.5011.0011.3011.64

1.5511.0811.3511.72

1.6011.1411.4011.80

1.6511.1811.4611.88

1.7011.2411.5211.94

1.7511.2611.5712.02

1.8011.3011.6212.08

1.8511.3011.6612.14

1.9011.3011.7212.20

1.9511.2911.7612.26

2.0011.2811.8012.3

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

Date__________Marks/Grade____FacultysSignature_______________

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

APPARATUS :

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 steelI = Least moment of inertia of column section

1e = Effective length of columnP = Critical or buckling load

Depending on support conditions, four cases may arise. The effective length for each of which are given as underBoth ends are fixed

One end is fixed and other is pinned

Both ends are pinned

One end is fixed and other is free

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

Sl.

NoEnd conditionsEulers

Buckling load (kg)Effective

Length (mm)

TheoreticalObservedTheoreticalObserved

1.

2.

3.

4Both ends fixed

One end fixed and the

Other pinned

Both ends pinned

One end fixed and the

other free.

PROCEDURE:-CALCULATION:-Results and Comments:

Questions:

1. What is equivalent length?2. Define buckling and crushing.Experiment No. 11Name________________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 APPARATUS:-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 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 thediagram between the two points about the point at which the deflection is required.Slope at

Since the tangent at C is horizontal due to symmetry,

Slope at

Displacement at B with respect to tangent at C

(y1 + y2)=

=

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 106Steps:-Sl. No.Load at each

hanger (kg)Central

Deflection y1

(cm)Deflection at

free end y2(cm)Slope at B

Deflection at C

(y1) cm = &

Deflection at B

(y2) cm =

Results and Discussions:

1. Calculate the slope at B as (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. 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:

Results and Comments:

Questions:

1. State moment area theorem2. Where moment area theorem can be appliedExperiment No. 12Name___________Roll No._________Group/Batch No._______________

Date________Marks/Grade______FacultysSignature_______________

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, 1

Where,

a = length of overhang on each side

W = load applied at the free ends

L = main span

E = modulus of elasticity of the material of the beam

I = moment of inertia of cross section of the beam

2

Also it is known that EI for beam =

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 106Sl. 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 )

Results and Discussions:

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.

Figures:

Calculations:

Results and Comments:

Questions:

What is flexural stiffness?

What is the value of EI for any beam?

NAME -------------------------------------------------------------------

ROLL NO.---------------------------------------------------------------

BRANCH----------------------------------------------------------------

BATCH-------------------------------------------------------------------

TENSILE TEST SPECIMEN

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