Mechanical Engineering: Lab Manual for Strength Of Materials

ME- 214-F STRENGTH OF MATERIAL-I LAB

L T P Sessional : 25 Marks

- - 2 Exam : 25 Marks

Total : 50 Marks

Duration of exam : 3 Hrs.

List of Experiments:

1. To study the Brinell hardness testing machine & perform the Brinell hardness test.

2. To study the Rockwell hardness testing machine & perform the Rockwell hardness test.

3. To study the Vickers hardness testing machine & perform the Vickers hardness test.

4. To study the Erichsen sheet metal testing machine & perform the Erichsen sheet metal test.

5. To study the Impact testing machine and perform the Impact tests (Izod & Charpy).

6. To study the Universal testing machine and perform the tensile test.

7. To perform compression & bending tests on UTM.

8. To perform the sheer test on UTM.

9. To study the torsion testing machine and perform the torsion test.

10. To draw shear Force, Bending Moment Diagrams for a simply Supported Beam under Point and Distributed Loads.

11. To determine Mechanical Advantage and Efficiency of Single and Double Purchase Winch Crab.

12. To determine Mechanical Advantage and Efficiency of Worm and Worm Gear of Single, Double and Triple start.

13. To determine Mechanical Advantage, Efficiency of Simple and Compound Screw Jack.

14. To find Moment of Inertia of a Fly Wheel.

Note:

1. At least ten experiments are to be performed in the semester.

2. At least eight experiments should be performed from the above list. Remaining two experiments may either be performed from the above list or designed & set by the concerned institute as per the scope of the syllabus.

EXPERIMENT No. 1

Aim:

To determine the M.A.,V and efficiency of a square thread screw jack and plot a graph between W and P and W and efficiency.

Apparatus used:

1. Screw Jack Apparatus

2. Slotted & Conical Weights

3. Nylon String

4. Meter Rod & Pan

Theory:

This machine is used for lifting heavy load with the application of a smaller effort. It may have different shapes but the principle is same I, e, it works on the principle of a screw. The screw head carries the load w. the nut is fixed and the screw is rotated by means of a lever. The effort p is applied at the screw is rotated by means of a lever. The effort p is applied at the end of the lever. Please see fig.

Now if the screw head revolves through n number of revolutions, the load w placed on the screw head will move by a distance p x n, where p is the pitch of the screw thread. The effort p will move a distance n x 2 R, where 2r is the circumference of the screw head over which P is coming.

There fore

V = Distance moved by the effort P

Distance moved by the load W

= n x 2 ∏R = 2∏R

n x p p

Procedure:

1. Wrap on string round the circumference of the screw head and take it over a small pulley . Effort p1 is tied to the free end of this string.

2. Wrap another string around the circumference of the screw head in the same direction in which the above string is wounded and take it over the other small pulley.

3. Place a load w on the screw head.

4. Suspend p1 and p2 to the free ends of both the strings coming over the two small pulleys. This load p1 and p2 should be increased gradually suitable to give a just upward motion to the load w placed on the screw head.

5. Note down w and p to determine the M.A. i.e w/p. in this case p1+p2 will be the value of p.

6. p1 and p2 should be noted down carefully.

7. Take in this way about 10 reading by increasing w and finding out the corresponding value of P(p1+p2).

8. Measure the circumference of the screw head.

9. Measure the pitch i.e. the distance between the two consecutive threads.

Observations

1. Circumference of the screw Head = 2∏R=

2. Pitch =

S. No.	Load Lifted Upward W	Effort P1	Effort P2	Total Effort P1+P2	M.A. = W/P	Velocity Ratio V	Percentage Efficiency
1. 2. 3. 4. 5.

Conclusion: Hence efficiency of the screw jack is determined as ___________.

EXPERIMENT No. 2

Aim: To study the UTM and perform the tensile test.

Apparatus: A UTM, mild steel specimen, vernier caliper/micrometer, dial gauge & graph paper.

Theory:

Various m/c and structure components are subjected to tensile loading in numerous application. For safe design of these components, there ultimate tensile strength and ductility one to be determine before actual use. Tensile test can be conducted on UTM. A material when subjected to a tensile load resists the applied load by developing internal resisting force. These resistances come due to atomic bonding between atoms of the material. The resisting force for unit normal cross-section area is known as stress. The value of stress in material goes on increasing with an increase in applied tensile load, but it has a certain maximum (finite) limit too. The minimum stress, at which a material fails, is called ultimate tensile strength. The end of elastic limit is indicated by the yield point (load). This can be seen during experiment as explained later in procedure with increase in loading beyond elastic limit original cross-section area (A_o) goes on decreasing and finally reduces to its minimum value when the specimen breaks.

Procedure:

Measure the diameter of the specimen at three different sections. Calculate the original diameter by taking average of three readings. The minimum overall length of the specimen shall be 20 times diameter plus 200 mm.
Mark the points over the grip length, with the punch such that the distance between two consecutive points is half the gauge length.
Select a suitable loading range depending on the diameter of specimen. Start the UTM and adjust the dead weight of movable heads and then set the load pointer to zero.
Fix the specimen bar between the grips of top and middle cross heads of loading frame.
Attach the extensometer on the bar at the central portion of the bar. The distance between upper and lower pivots of extensometer shall be equal to gauge length.
Switch on the machine and open the control valve so that the load is increased gradually and at the required rate.
Record the load at suitable interval from the digital display unit or the load dial.
Corresponding to loads, note the readings of extensometer.
For initial few observations, load and extension are in pace with each other. Record the yield point load by observing the hesitation of load pointer. The extension readings are faster at this moment.
Remove the extensometer; hence measure extension by divider or suitable scale
Record the maximum load. Observe the decrease in load and neck formation on the specimen.
Record the load at fracture and put off the machine.
Remove the specimen. Observe the cup and cone formation at the fracture point. Rejoin the two pieces, measure the final gauge length and the reduced diameter.

Observations:

Calculations:

EXPERIMENT No. 3

Aim: To Perform compression test on UTM.

Apparatus: A UTM or A compression testing m/c, cylindrical or cube shaped specimen of cast iron, Alumunium or mild steel, vernier caliper, liner scale, dial gauge (or compressometer).

Theory:

Several m/c and structure components such as columns and struts are subjected to compressive load in applications. These components are made of high compressive strength materials. Not all the materials are strong in compression. Several materials, which are good in tension, are poor in compression. Contrary to this, many materials poor in tension but very strong in compression. Cast iron is one such example. That is why determine of ultimate compressive strength is essential before using a material. This strength is determined by conduct of a compression test. Compression test is just opposite in nature to tensile test. Nature of deformation and fracture is quite different from that in tensile test. Compressive load tends to squeeze the specimen. Brittle materials are generally weak in tension but strong in compression. Hence this test is normally performed on cast iron, cement concrete etc. But ductile materials like aluminium and mild steel which are strong in tension, are also tested in compression.

Procedure:

1. Dimension of test piece is measured at three different places along its height/length to determine the average cross-section area.

2. Ends of the specimen should be plane for that the ends are tested on a bearing plate.

3. The specimen is placed centrally between the two compressions plates, such that the centre of moving head is vertically above the centre of specimen.

4. Load is applied on the specimen by moving the movable head.

5. The load and corresponding contraction are measured at different intervals. The load interval may be as 500 kg.

6. Load is applied until the specimen fails.

Observation:

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

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

S.No.	Applied load (P) in Newton	Recorded change in length (mm)

Calculations:

• Original cross-section area A_o = -----

• Final cross-section area A_f= --------

• Stress = -------

• Strain = -------

For compression test, we can

• Draw stress-strain (σ-ε) curve in compression,

• Determine Young’s modulus in compression,

• Determine ultimate (max.) compressive strength, and

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

Conclusion: The compressive strength of given specimen = -------N/mm2

EXPERIMENT No. 4

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: δ = WL3 / 48EI

Procedure:

1. Measure the length, width and thickness of test piece, by vernier caliper.

2. Place the bending fixture on the lower cross head of the testing m/c.

3. Place the test piece on the rollers of the bending fixture.

4. By loading the dial gauge in a stand, make its spindle knob the test piece.

5. Start the m/c and note down the load and dial gauge readings.

6. Plot the graph between load and deflection.

Observations:

1. Least count of vernier caliper = -----

2. Length of beam (L) = --------

3. Width of beam (b) = ------

4. Thickness of beam (t) = ------

S.No.	Load ‘W’ in Newton	Deflection ‘δ’ in mm.	Young’s Modulus ‘E’ N/mm2 N/mm2

Calculations:

• I = bt3 / 12

• δ = WL3 / 48EI

Conclusion: The compressive strength of given specimen = -------N/mm2

EXPERIMENT No. 5

Aim: To perform the shear 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:

The method for determining the shear strength consists of subjecting a suitable length of steel specimen in full cross-section to double shear, using a suitable test rig, in a testing m/c under a compressive load or tensile pull and recording the maximum load ‘F’ to fracture.

Observation:

• Applied compressive force (F) = ---------kgf.

• Diameter of specimen = ---------mm.

Calculations:

The shear strength shall be calculated from the following formulae :

τs = (F/2) / (πd2/4) = 2F / πd2

where ‘d’ is the actual diameter of the specimen

Conclusion: Shear strength of specimen = --------

EXPERIMENT No. 6

Aim: To determined impact strength of steel.

Apparatus used: Impact testing machine, steel specimen 75 mm X 10mm X 10mm

Theory: An impact test signifies toughness of material that is ability of material to absorb energy during plastic deformation. Static tension tests of unnotched specimens do not always reveal the susceptibility of a metal to brittle fracture. This important factor is determined by impact test. Toughness takes into account both the strength and ductility of the material. Several engineering materials have to withstand impact or suddenly applied loads while in service. Impact strengths are generally lower as compared to strengths achieved under slowly applied loads. Of all types of impact tests, the notch bar tests are most extensively used. Therefore, the impact test measures the energy necessary to fracture a standard notch bar by applying an impulse load. The test measures the notch toughness of material under shock loading. Values obtained from these tests are not of much utility to design problems directly and are highly arbitrary. Still it is important to note that it provides a good way of comparing toughness of various materials or toughness of the same material under different condition. This test can also be used to assess the ductile brittle transition temperature of the material occurring due to lowering of temperature.

Procedure: Izod test

1. With the striking hammer (pendulum) in safe test position, firmly hold the steel specimen in impact

testing machine’s vice in such a way that the notch face the hammer and is half inside and half above

the top surface of the vice.

2. Bring the striking hammer to its top most striking position unless it is already there, and lock it at that

position.

3. Bring indicator of the machine to zero, or follow the instructions of the operating manual supplied

with the machine.

4. Release the hammer. It will fall due to gravity and break the specimen through its momentum, The

total energy is not absorbed by the specimen. Then it continues to swing. At its topmost height after

breaking the specimen, the indicator stops moving, While the pendulum falls back. Note the indicator

at that topmost final position.

5. Again bring back the hammer to its idle position and back

Conclusion: Impact value = --------------N-m

EXPERIMENT No. 7

Aim: To determined impact strength of steel.

Apparatus used: Impact testing machine, steel specimen 55 mm X 10mm X 10mm

Procedure: Charpy Test

1. With the striking hammer (pendulum) in safe test position, firmly hold the steel specimen in impact testing machine’s vice in such a way that the notch face s the hammer and is half insider and half above the top surface of the vice.

2. Bring the striking hammer to its top most striking position unless it is already there, and lock it at that position.

3. Bring indicator of the machine to zero, or follow the instructions of the operating manual supplied with the

machine.

4. Release the hammer. It will fall due to gravity and break the specimen through its momentum, The total

energy is not absorbed by the specimen. Then it continues to swing. At its topmost height after breaking the specimen, the indicator stops moving, while the pendulum falls back. Note the indicator at that topmost final position.

5. The specimen is placed on supports or anvil so that the blow of hammer is opposite to the notch.

Conclusion: Impact value = --------------Nm

EXPERIMENT No. 8

Aim: To determine Mechanical Advantage, V.R. and Efficiency of worm and worm gear of single, double and triple start.

Apparatus: Worm and worm gear of single, double and triple start and weights.

Theory: As the pulley of the worm moves through n revolutions, n teeth of the wheel pass completely through the worm. If there are N teeth in the worm wheel, then N revolutions will have to be given to the pulley of the worm to rotate completely the worm wheel. So that if the effort applied at the pulley of the worm moves through N revolution the load is raised up by the a distance equal to the length of the circumference of the pulley of the worm wheel.

So that velocity ratio is

N x circumference of pulley of worm

Circumference of pulley of worm wheel

Procedure:

1. Wrap the string round the pulley of the worm the free end of which is to be tied to the effort.

2. Wrap another string to carry the load round the pulley the worm wheel in such a manner that as the effort is applied the load is lifted up.

3. Suspend a small weight (w) through the free end of the second string and suspend another weight (p) through the free end of the first string which should just move the load upward.

4. Note w and P, so that mechanical advantage is given by W/ P

5. Increase the load (w) gradually and increase the effort (p) correspondingly and take in this way about seven readings.

6. Measure the circumference of the pulley of the worm and also that of the worm wheel.

7. The percentage efficiency is given by W x 100 /PV

8. Plot a graph between w and p.

9. The same procedure can be followed for single, double and triple start worm and worm wheel.

Observations :

1. Circumference of pulley of the worm (2∏R₁) = _________ cm.

2. Circumference of pulley of the worm wheel (2∏R₂) =_________ cm.

3. No of teeth in the worm wheel (N)=

4. Velocity ratio for single start= (N x 2∏R₁)/((2∏R₂)*1)

5. Velocity ratio for double start= (N x 2∏R₁)/((2∏R₂)*2)

6. Velocity ratio for triple start= (N x 2∏R₁)/((2∏R₂)*3)

Observations Table for single start:

S. No.	Weight Lifted (W)	Effort Applied (P)	Mech. Adv. = W/P	Velocity Ratio	% Efficiency =W/PV x 100
1
2
3
4
5
6

Observations Table for double start:

S. No.	Weight Lifted (W)	Effort Applied (P)	Mech. Adv. = W/P	Velocity Ratio	% Efficiency =W/PV x 100
1
2
3
4
5
6

Observations Table for triple start:

S. No.	Weight Lifted (W)	Effort Applied (P)	Mech. Adv. = W/P	Velocity Ratio	% Efficiency =W/PV x 100
1
2
3
4
5
6

Conclusion: Hence the efficiency of single, double and triple worm and worm wheel is completed.

EXPERIMENT No. 9

Aim: To determine Mechanical Advantage and Efficiency of Single and Double Purchase Winch Crab.

Apparatus used: Winch crab apparatus, weights.

Theory: Winch crab is a kind of lifting m/c in which velocity ratio obtained by employing spur gears. This m/c. is basically used on boats ships to raise starboard or tightening rope and on bridges and dam to operate lockage. These are classified as:

1. Single purchase Winch crab.

2. Double purchase Winch Crab

Single Purchase Winch Crab :- It consists of two parallel spindles, upper one called effort spindle and lower one is called as load spindle. One effort spindle a small touched wheel pinion is mounted in such a way that pinion and a lever is attached to apply the effort. On load spindle, a large toothed wheel known as spur wheel is mounted in such a way that pinion meshes with it. The load spindle also carries a cylinder of dia ‘d’. Both the spindles are suitably mounted on a rigid frame. A rope is wound round the cylinder while load is attached on the other end,

Let,

P = Effort applied

W = load lifted

T_p= No. of teeth on pinion

T_w = No. of teeth on wheel

l = length of the lever arm

d = diameter of the cylinder

Suppose, lever arm is rotated by one revolution

Therefore distance moved by effort = 2πl

The pinion will also make one revolution and the spur wheel makes T_p/T_w rev.

Distance moved by load in T_p/T_w revolutions of spur wheel = πd * T_p/T_w

Velocity ratio = Distance moved by effort / Distance moved load.

= 2πl / πd * T_w / T_p

= 2l / d * T_w / T_p

M. A. = W / P

Double Purchase Winch Crab :- In this case to obtain velocity ratio compound gear train is used, because intermediately gears are compound wheel mounted on the same shaft. Other arrangements are similar to that of single purchase winch crab.

Let,

T1 & T3 = No. of teeth on pinion.

T2 & T4 = No. of teeth on the spur wheels.

l = Length of the lever

d = Dia.of the load spindle

W = Load lifted,

P = Effort applied to lift the load, at the end of the handle.

For one revolution of lever, distance moved by effort is 2πl,

No. of revolutions made by spur wheel of load spindle can be calculated by considering it a case of compound by train.

Therefore No. of revolutions made by the pinion-1 = 1

And no. of revolutions made by the wheel-2 = T1 / T2 = revolution of pinion-3

And no. of revolutions made by the wheel-4 = T1xT3/T2xT4

Distance moved by load = πd x T1xT3/T2xT4

V.R. = 2l / d * T2xT4 / T1xT3

Procedure:

Count the number of teeth of the pinion A and spur gear B.
Measure the circumference of pulley and of load drum with a string and meter rod or measure the diameter with an outside caliper.
Wrap the string round the effort pulley and the other free end of the string will carry the effort.
Wrap another string round the load drum to carry load W in such a manner so that as the effort is applied, the load is lifted up.
Suspend a load W on the string of the load drum and put the weights in the effort pan so that load start moving up gradually.
Note down the values of W and P and calculate the M.A., V.R. and efficiency.
Increase the load W and again find the value of P.
In this way take at least six reading at different values of load.
Plot the graph between W & P and W & Efficiency.
Take W along horizontal axis.
Repeat the same procedure for double winch crab.

Observation:

For single winch crab:

S.No.	Load (W) in Nt.	Effort (P) in Nt.	Distance moved by effort	Distance moved by load	V.R.	M.A.	Efficiency

For double winch crab:

S.No.	Load (W) in Nt.	Effort (P) in Nt.	Distance moved by effort	Distance moved by load	V.R.	M.A.	Efficiency

Calculations:

M.A. = W/P

V.R. =

Efficiency = M.A./V.R

Conclusion: Hence the winch crab is studied.

EXPERIMENT No. 10

Aim: To study the torsion testing machine and perform the torsion test.

Apparatus used: A torsion testing machine, twist meter for measuring angles of twist and a steel rule and calipers or micrometer.

Theory: A torsion test is quite instrumental in determining the value of modulus of rigidity of a metallic specimen. The value of modulus of rigidity can be found out thought observations made during the experiment by using the torsion equation.

EXPERIMENT No. 11

Aim : To study the Rockwell Hardness testing machine and perform the Rockwell hardness test.

Apparatus: Rockwell Hardness testing machine, specimen of mild steel or other material.

Theory: Hardness represents the resistance of material surface to abrasion, scratching and cutting, hardness after gives clear indication of strength. In all hardness tests, a define force is mechanically applied on the piece, varies in size and shape for different tests. Common indentors are made of hardened steel or diamond.

Rockwell hardness tester presents direct reading of hardness number on a dial provided with the m/c. principally this testing is similar to Brinell hardness testing. It differs only in diameter and material of the indentor and the applied force. Although there are many scales having different combinations of load and size of indentor but commonly ‘C’ scale is used and hardness is presented as HRC. Here the indentor has a diamond cone at the tip and applied force is of 150 kgf. Soft materials are often tested in ‘B’ scale with a 1.6mm dia. Steel indentor at 60kgf.

SPECIFICATION OF HARDNESS TESTING M/C AND INDENTORS:-

A hardness test can be conducted can be conducted on Brinell testing m/c, Rockwell hardness m/c or vicker testing m/c. the specimen may be a cylinder, cube, thick or thin metallic sheet. A Brinell-cum-Rocwell hardness testing m/c along with the specimen is shown in figure.

Various scales in Rockwell hardness test are given below:-

Scale	Type of indentor (Dimension)	Initial load (kgf)	Major load (kgf)	Pointer Position on dial	Kind of material
A	Cone, 120o	10	50	0	Much harder such as carburized steel, cemented carbides
B	Ball, 1.58mm	10	90	30	Soft steels, copper, aluminum,brass, grey cast iron.
C	Cone, 120o	10	140	0	Hard steels, Ti, W, Va, etc

Procedure:

1. Insert ball of dia. ‘D’ in ball holder of the m/c.

2. Make the specimen surface clean by removing dust, dirt, oil and grease etc.

3. Make contact between the specimen surface and the ball by rotating the jack adjusting wheel.

4. Push the required button for loading.

5. Pull the load release lever wait for minimum 15 second. The load will automatically apply gradually.

6. Remove the specimen from support table and locate the indentation so made.

7. Repeat the entire operation, 3-times.

Observation and Calculations: Following observation are recorded are from a test on steel specimen using a hardened steel ball as indentor.

• Test piece material =-----------

• HRA = 100-(t/0.002)

• HRB = 130-(t/0.002)

• HRC = 100-(t/0.002

Conclusion: Hence the Rockwell Hardness of the material is_________.

EXPERIMENT No. 12

Aim: To study the Brinell Hardness testing machine and the Brinell hardness test.

Apparatus: Brinell Hardness testing machine, specimen of mild steel / cast iron/ non ferrous metals and Brinell microscope.

Theory: Hardness represents the resistance of material surface to abrasion, scratching and cutting, hardness after gives clear identification of strength. In all hardness testes, a define force is mechanically applied on the test piece for about 15 seconds. The indentor, which transmits the load to the test piece, varies in size and shape for different tstes. Common indenters are made of hardened steel or diamond. In Brinell hardness testing, steel balls are used as indentor. Diameter of the indentor and the applied force depend upon the thickness of the test specimen, because for accurate results, depth of indentation should be less than 1/8th of the thickness of the test pieces. According to the thickness of the test piece increase, the diameter of the indentor and force are changed.

Specifications: A hardness test can be conducted on Brinell testing m/c, Rockwell hardness m/c or vicker testing m/c. the specimen may be a cylinder, cube, think or thin metallic sheet. A Brinell- cum-Rockwell hardness testing m/c along with the specimen is shown in figure. Its specification are as follows:

1. Ability to determine hardness upto 500BHN.

2. Diameter of ball (as indentor) used D = 2.5mm, 5mm, 10mm.

3. Maximum application load = 3000kgf.

4. Method of load application = Lever type

5. Capability of testing the lower hardness range = 1 BHN on application of 0.5D2 load.

Procedure:

1. Insert ball of dia ‘D’ in ball holder of the m/c.

2. Make the specimen surface clean by removing dust, dirt, oil and grease etc.

3. Make contact between the specimen surface and the ball by rotating the jack adjusting wheel.

4. Push the required button for loading.

5. Pull the load release level and wait for minimum 15 second. The load will automatically apply gradually.

6. Remove the specimen from support table and locate the indentation so made.

7. View the indentation through microscope and measure the diameter ‘d’ by micrometer fitted on microscope.

8. Repeat the entire operation, 3-times.

Observations and Calculations: Following observation are recorded from a test on steel specimen using a hardened steel ball as indentor.

Test piece material = ---------------

S.No.	Ball diameter ‘D’ in mm.	Load applied P in kgf.	Diameter of indentation ‘d’ (mm)	P/D2	BHN

BHN = Load Applied (kgf.)/ Spherical surface area indentation (in mm.)

= 2P/πD(D-√D2 – d2)

Conclusion: Hence the Brinell Hardness of the material is_________.

Tuesday, 20 December 2011

Lab Manual for Strength Of Materials