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GOVERNMENT POLYTECHNIC MUZAFFARPUR LAB MANUAL OF ENGINEERING MECHANICS SUBJECT CODE - 02108

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Page 1: GOVERNMENT POLYTECHNIC MUZAFFARPURgpmuz.bih.nic.in/docs/eml.pdfAPPARATUS: Apparatus consists of a circular aluminium disc graduated in 360 . Apparatus is provided with leveling screws,

GOVERNMENT POLYTECHNIC

MUZAFFARPUR

LAB MANUAL OF ENGINEERING MECHANICS

SUBJECT CODE - 02108

Page 2: GOVERNMENT POLYTECHNIC MUZAFFARPURgpmuz.bih.nic.in/docs/eml.pdfAPPARATUS: Apparatus consists of a circular aluminium disc graduated in 360 . Apparatus is provided with leveling screws,

Government Polytechnic Muzaffarpur

Name of the Lab: Engineering Mechanics

Subject Code: 02108

List of Experiments

Exp.

No.

Experiment Page No.

1

To find experimentally the reactions at the supports of a Simply

Supported Beam and verify the same with analytical values.

1-3

2

To verify Polygon law of forces with the help of Force Polygon

Apparatus

4-6

3

To determine the efficiency of Simple Wheel And Axle Apparatus

7-9

4

To determine the efficiency of Worm and Worm Wheel

Apparatus

10-12

5

To find out forces in Jib and tie with the help of Jib Crane

Apparatus

13-15

6

To determine the efficiency of Simple Screw Jack Apparatus

16-18

Page 3: GOVERNMENT POLYTECHNIC MUZAFFARPURgpmuz.bih.nic.in/docs/eml.pdfAPPARATUS: Apparatus consists of a circular aluminium disc graduated in 360 . Apparatus is provided with leveling screws,

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Government Polytechnic Muzaffarpur

Name of the Lab: Engineering Mechanics

Subject Code : 02108

EXPERIMENT NO. 1

Practical Name: Simply Supported Beam

AIM:-

To find experimentally the reactions at the supports of a simply supported beam and compare the results

with analytical values.

APPARATUS:-

Simply supported beam setup, hangers, and loads.

THEORY:-

Beam is a structural member usually horizontal and straight provided to carry loads that are vertical or

inclined to its axis. A simply supported beam is one whose ends are resting freely on the supports that

provide only vertical reactions. Simply supported beam becomes unstable if it is subjected to oblique or

inclined loads. When simply supported beam is subjected to only vertical loads, its FBD forms a system

of parallel forces in equilibrium. Conditions of equilibrium = 0 and ΣM=0 can be applied to determine

the support reactions analytically.

PROCEDURE:-

1. Place the beam of length L on simple supports. Note that below both the simple supports there is

a spring arrangement. On loading, the spring compresses due to the reaction force and this

compressive force is indicated on the dial.

2. Arrange the load hangers arbitrarily on the beam and set the left and right dial pointers to zero.

This will nullify the effect due to self-weight of the beam and the hangers.

3. Suspend the loads from the hangers. Note the load values W1 W2, and so on and their distances

X1, X2 and so on from the left support.

4. Note the left and right support dial readings.

Fig. Simply supported beam with two loads

Page 4: GOVERNMENT POLYTECHNIC MUZAFFARPURgpmuz.bih.nic.in/docs/eml.pdfAPPARATUS: Apparatus consists of a circular aluminium disc graduated in 360 . Apparatus is provided with leveling screws,

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5. Repeat the above steps 1 to 4 by changing the weights in the hangers and also the hanger position

for two more sets of observations.

6. Compare the experimental values with analytical values obtained by applying Conditions of

Equilibrium.

OBSERVATION TABLE:

Sr.

No.

W1

(Kg)

W2

(Kg)

X1

(mm)

X2

(mm)

Observed Reaction Analytical Reaction

(N) (N) (N) (N)

1.

2.

3.

Page 5: GOVERNMENT POLYTECHNIC MUZAFFARPURgpmuz.bih.nic.in/docs/eml.pdfAPPARATUS: Apparatus consists of a circular aluminium disc graduated in 360 . Apparatus is provided with leveling screws,

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RESULT:-

The support reactions obtained experimentally are nearly equal to the analytical values. The difference is

within the limits of experimental error. Hence the experiment is verified.

Page 6: GOVERNMENT POLYTECHNIC MUZAFFARPURgpmuz.bih.nic.in/docs/eml.pdfAPPARATUS: Apparatus consists of a circular aluminium disc graduated in 360 . Apparatus is provided with leveling screws,

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EXPERIMENT NO. 2

Practical Name: Force Polygon

THEORY:

If any number of force acting on a particle be presented in magnitude and direction by the sides of a

closed polygon, taken in order, they shall be in equilibrium. Converse of polygon law of forces states

that if any number of forces acting on a particle are in equilibrium, a close polygon can be drawn whose

sides represent these forces both in magnitude and direction. The converse of polygon law of forces is

true in the sense that if any number of co-planer forces acting at a point are in equilibrium and if sides

are drawn parallel and proportional to the forces then the sides will form only one closed polygon. But if

the sides are drawn only parallel and not proportional to the forces then they cannot be represented by

the sides of such a polygon as any number of such polygons can be drawn. Therefore the converse of

polygon law of forces is not true in the same way as the converse of triangle law of forces.

OBJECTIVE:

To verify the Polygon Law of Forces with the help of Force Polygon Apparatus.

APPARATUS:

Apparatus consists of a circular aluminium disc graduated in 360°. Apparatus is provided with leveling

screws, clamping device to fix the table at any desired angle, five sliding clamping pulleys and a central

ring. Apparatus is supplied complete with a set of weights.

PROCEDURE:

1. Make the graduated disc horizontal by adjusting the screws at its base. This can be tested with

the help of spirit level.

2. Put a white sheet on the force table.

3. One end of a string is fastened to small ring on the table while other end is fastened with hanger,

which is to carry weights hanging freely through a pulley. Connect other four strings in the

similar manner.

4. Place small weights in to the different hangers. In the last hanger, place weights in such a

quantity that the small ring comes at the centre of the table. Check that the ring is placed

symmetrically round the axis and does not touch the axis or the plane surface of the graduated

disc to avoid any reaction on the ring.

5. Note the position of one string on the disc and note also the relative positions of the other strings.

6. Mark the directions of the strings by drawing straight line on the paper. Note the weights applied

on each string in each direction.

7. Draw the scale diagram of forces (as shown in fig. a) acting at a point cutting the line of action of

each force proportional to the magnitude of the force.

8. Draw the stress diagram ABCDE and verify that the polygon ABCDE is completed. If the last

force ‘oe’ falls short or is greater than the side, which would complete the polygon, then measure

the side, which would complete the polygon.

9. Repeat the experiment three times by changing weights in hangers and angles between them.

Page 7: GOVERNMENT POLYTECHNIC MUZAFFARPURgpmuz.bih.nic.in/docs/eml.pdfAPPARATUS: Apparatus consists of a circular aluminium disc graduated in 360 . Apparatus is provided with leveling screws,

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SAMPLE DATA SHEET: Let 1 cm = gm

S.No. Weight Angle Last

Force E

(observed

)

Magnitude

of E from

polygon

(theoretical

)

%

error in

E

% error

between

angle

D’DE &

doe

A B C D

1.

2.

3.

Working out of result

1. Find % error between the force ‘oe’ and the force required to complete the polygon.

2. Measure the angle D’DE and the angle ‘doe’. If they are different, then find the % error between

these angles.

3. Find out mean % error taking all the reading at 1 & 2 above.

RESULT

Mean % error in apparatus while verifying polygon of forces is ……….

PRECAUTIONS:

Pulleys should be frictionless.

There should not be any knot in the string.

Directions of the string should be marked carefully.

Page 8: GOVERNMENT POLYTECHNIC MUZAFFARPURgpmuz.bih.nic.in/docs/eml.pdfAPPARATUS: Apparatus consists of a circular aluminium disc graduated in 360 . Apparatus is provided with leveling screws,

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Experiment no. 3

Practical Name: Simple Wheel and Axle

THEORY:

The most simple machine which is in use, since ages is the simple wheel and ale used for drawing up

water from well. It is used on the village wells even till date. Simple wheel and axle is used to lift loads.

Fig. Simple Wheel and Axle

Simple wheel and axle consists of an effort wheel and an axle of different diameters which are keyed to

same spindle. The diameter of the wheel is greater than the diameter of the axle to reduce the frictional

resistance.

A sting is wound on the axle, with one end fixed to it. The other end of this rope carries the load W,

which is to be lifted. A second string is wound around the wheel, in a direction opposite to that of the

rope on axle. One end of this rope is fixed to the wheel while to the other end effort P is applied. Since

the two strings are wound in opposite directions, therefore, a downward motion of P will lift the load W.

Let D = Diameter of the effort wheel,

d = Diameter of axle,

W = Load lifted and

P = Effort applied to lift the weight

Page 9: GOVERNMENT POLYTECHNIC MUZAFFARPURgpmuz.bih.nic.in/docs/eml.pdfAPPARATUS: Apparatus consists of a circular aluminium disc graduated in 360 . Apparatus is provided with leveling screws,

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Since the wheel and axle are mounted on the same spindle. In one revolution of the wheel, the axle will

also make one revolution.

Distance moved by load in one revolution = π d

Distance moved by effort in one revolution = π D

⸫ V.R. =

=

=

Now, Mechanical advantage = M.A. =

Efficiency = ղ =

=

× 100

=

× 100

OBJECTIVE:

To determine the mechanical advantage, velocity ratio and efficiency of simple wheel and axle.

APPARATTUS:

Simple wheel and axle apparatus consists of two grooved wooden wheels of different diameter which

are fixed rigidly together and are mounted on steel centers on wooden base. Apparatus requires strings, a

set of weight, scale pan and meter scale.

PROCEDURE:

1. Measure the diameter of the wheel as D by the help of outside caliper.

2. Measure the diameter of the axle as d by the help of outside caliper.

3. Wind one string on the effort wheel and attach scale pan to carry effort P.

4. Wind other string on the axle to hang load.

5. Put the weight in the load pan.

6. Now place the weight slowly in the effort pan unless and until the load Pan just starts to lift up.

7. Note the weight placed in the effort Pan.

8. Calculate M.A., V.R. and efficiency.

9. Repeat the above procedure by increasing the load in the load pan and note down the

corresponding effort.

Page 10: GOVERNMENT POLYTECHNIC MUZAFFARPURgpmuz.bih.nic.in/docs/eml.pdfAPPARATUS: Apparatus consists of a circular aluminium disc graduated in 360 . Apparatus is provided with leveling screws,

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SAMPLE DATA SHEET:

Diameter of wheel, D in cm =

Diameter of axle, d in cm =

V.R. =

Weight of load pan/hanger = a gm =

Weight of effort pan/hanger = b gm =

S.

No.

Load Effort M.A = W/P % ղ =

× 100

Wt. in

Pan, w1

(gm)

Total weight

W = a + w1

(gm)

Wt. in

Pan, w2

(gm)

Total weight

P = b + w2

(gm)

RESULT:

Mean efficiency of apparatus …………..

PRECAUTIONS:

1. There should not be any overlapping of the strings.

2. Weights in the pan/hanger should be placed very gently.

3. The string should be free from knot.

4. Do not increase the effort by throwing the weight on the pan. Increase the effort gently.

Page 11: GOVERNMENT POLYTECHNIC MUZAFFARPURgpmuz.bih.nic.in/docs/eml.pdfAPPARATUS: Apparatus consists of a circular aluminium disc graduated in 360 . Apparatus is provided with leveling screws,

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EXPERIMENT NO. 4

Practical Name: Worm and Worm Wheel

INTRODUCTION

Worm and worm wheel consists of a square threaded screw (known as worm) and a toothed wheel

(known as worm wheel) geared with each other. A wheel is attached to the worm, over which passes a

rope a load is securely mounted on the worm wheel.

FORMULA USED

Let L = Radius of the wheel

r = Radius of the load drum

W = Load lifted

P = Effort applied to lift the load

T = Number of teeth on the worm wheel

If the worm is single threaded (i.e., for one revolution of the wheel, the worm pushes the worm wheel

through one tooth) then for one revolution of the wheel the distance moved by the effort = 2πL

The load drum will move through = 1/ T revolution

Distance, through which the load will move = 2πr / T

V.R = (Distance moved by P) / (Distance moved by W) = (2πL / (2πr / T)) = LT / r

In general, if the worm is n threaded then, V.R = LT / nr

M.A = W / P

η = M.A / V.R

Figure - Worm and worm wheel

Page 12: GOVERNMENT POLYTECHNIC MUZAFFARPURgpmuz.bih.nic.in/docs/eml.pdfAPPARATUS: Apparatus consists of a circular aluminium disc graduated in 360 . Apparatus is provided with leveling screws,

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PROCEDURE:

1. Firstly stabilize the Single Start Worm and Worm Wheel machine and wrap the cord around the

load drum and the effort wheel.

2. Put some weight on the load drum. And add the some effort to the effort wheel via hanger.

3. Hit the machine with some material, thus you will see some kind of movement in the load drum

as well as in effort wheel.

4. Write down the reading in the observation table

5. After this apply the above procedure, four to five times with gradually increasing the Load as

well as Effort to the load drum and effort pulley respectively.

6. Write down the all reading in the given observation table.

7. Measure the radius of the load drum and the radius of the effort wheel.

8. Calculate the MA, VR and η of machine.

SAMPLE DATA SHEET:

Diameter of wheel, D in cm =

Diameter of axle, d in cm =

V.R. =

Weight of load pan/hanger = a gm =

Weight of effort pan/hanger = b gm =

S.

No.

Load Effort M.A = W/P % ղ =

× 100

Wt. in

Pan, w1

(gm)

Total weight

W = a + w1

(gm)

Wt. in

Pan, w2

(gm)

Total weight

P = b + w2

(gm)

RESULT:

Mean efficiency of apparatus …………..

Page 13: GOVERNMENT POLYTECHNIC MUZAFFARPURgpmuz.bih.nic.in/docs/eml.pdfAPPARATUS: Apparatus consists of a circular aluminium disc graduated in 360 . Apparatus is provided with leveling screws,

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PRECAUTIONS:

1. Lubricate the screw before starting the experiment.

2. Trapping should be done after adding the weight in the effort hanger.

3. Overlapping of string should not be there.

Page 14: GOVERNMENT POLYTECHNIC MUZAFFARPURgpmuz.bih.nic.in/docs/eml.pdfAPPARATUS: Apparatus consists of a circular aluminium disc graduated in 360 . Apparatus is provided with leveling screws,

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EXPERIMENT NO. 5

Practical Name: Jib Crane

AIM:

Study of Forces In The Members Of Jib Crane.

APPRATUS:

Apparatus of jib crane, hook, weights, scale, string.

OBJECTIVES:

a) To understand facts & concepts of mechanism of jib crane & nature of forces in members of jib

crane.

b) To find the relationship between forces in the members of jib crane & lengths of members of jib

crane.

Figure-Jib Crane

Page 15: GOVERNMENT POLYTECHNIC MUZAFFARPURgpmuz.bih.nic.in/docs/eml.pdfAPPARATUS: Apparatus consists of a circular aluminium disc graduated in 360 . Apparatus is provided with leveling screws,

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THEORY:

Triangle law of forces:

If three coplanar concurrent forces are in equilibrium be represented in magnitude & direction by three

sides of triangle taken in order then the first point of the first force coincides with the last point of last

force i.e. force triangle is closed.

Jib crane is used to lift heavy loads. When it lifts load then jib member is subjected to compression & tie

member is subjected to tension.

PROCEDURE:

1. Organise the physical set up of experiment & study it. Adjust the position of clamp on vertical

post.

2. Observe the initial readings in jib & tie & note them.

3. Apply load (W), say 10N.

4. Observe the final readings in tie & jib. Also measure the lengths of tie, post & jib in loaded

condition & note them.

5. Tabulate your observations.

6. Calculate forces in jib &tie by subtracting the initial readings from final readings.

7. Construct the scaled triangle for lengths of members of jib crane.

8. Considering the vertical side of triangle as the applied load (W) then find forces in jib &tie by

measuring the lengths of corresponding sides of triangle &multiplying it by scale.

9. Repeat the procedure from 2 to 8 for two more values of W for same position of clamp.

10. Change position of clamp & repeat the steps from 2 to 9.

OBSERVATIONS:

Initial readings of jib = -------------- N

Initial readings of tie = -------------- N

OBSERVATION TABLE:

Position

Of

clamp

Vertical

Load

(W) N

Observed forces N

Calculated forces N

Jib

Tie

Lengths of members Force

Final

reading

Force

in jib

Final

reading

Force

in tie

Post

cm

Jib

cm

Tie

cm

Jib

Tie

Page 16: GOVERNMENT POLYTECHNIC MUZAFFARPURgpmuz.bih.nic.in/docs/eml.pdfAPPARATUS: Apparatus consists of a circular aluminium disc graduated in 360 . Apparatus is provided with leveling screws,

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CALCULATIONS:

RESULT:

a) Force triangle closes / remains open.

b) Nature of forces in jib & crane.

c) Relationship between forces in members & their lengths.

Page 17: GOVERNMENT POLYTECHNIC MUZAFFARPURgpmuz.bih.nic.in/docs/eml.pdfAPPARATUS: Apparatus consists of a circular aluminium disc graduated in 360 . Apparatus is provided with leveling screws,

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EXPERIMENT NO. 6

Practical Name: Simple Screw Jack

AIM:

To find the Mechanical Advantage, Velocity Ratio and Efficiency of Simple Screw-Jack.

APPARATUS REQUIRED:

Simple screw jack, Load to be lifted (W), Weights or Effort to be applied (P), Vernier caliper, Pan,

Weight box.

THEORY:

Screw Jack

It is a device used for lifting heavy loads which are usually centrally loaded by applying smaller effort.

It works on the principle of inclined plane. The device consists of a nut and screw. The load is carried by

screw head. The body consisting of a nut is fixed and screw is rotated by means of a lever.

The axial distance moved by the screw when it makes one complete revolution is known as the Lead of

the screw. The distance between two consecutive threads is called Pitch of the screw. For single

threaded screw Lead = Pitch, and for double threaded screw L = 2p

Mechanical Advantage

It is the ratio of weight lifted to effort applied. M.A. = W/ P

Velocity Ratio

It is the ratio of distance moved by the effort (y) to the distance moved by the load (x). V.R. = y/ x

In one complete revolution of the lever by effort P:

Distance traveled by effort = 2 π R

Figure - Screw Jack

Page 18: GOVERNMENT POLYTECHNIC MUZAFFARPURgpmuz.bih.nic.in/docs/eml.pdfAPPARATUS: Apparatus consists of a circular aluminium disc graduated in 360 . Apparatus is provided with leveling screws,

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And, distance traveled by the load = p

Therefore, Velocity Ratio = 2 π R / p

Mechanical efficiency =

PROCEDURE:

1. Note down the pitch ‘p’ of the screw.

2. Measure the circumference of the flanged table with an inextensible thread and meter scale or

measure the diameter of flanged table with the help of outside caliper.

3. Wrap the string around the circumference of the flanged table and pass it over one pulley.

Similarly, wrap another string over the circumference of flanged table and take it over the second

pulley. The free ends of both the strings be tied to two pans/hanger in which the weights are

placed/hanged. 4. Place a load ‘W’ on the top of the flanged table and start adding weights on to the pans gradually

till the load starts lifting. P1 and P2are the weights (effort) in the pans.

5. Calculate M.A, V.R and % Efficiency.

6. Repeat the above procedure by increasing the load on flanged table and note down the

corresponding efforts applied.

OBSERVATIONS :

Let, Load Lifted = W

Effort Applied = P

Effort Wheel Diameter ( D) =

Diameter of the rope (d ) =

Pitch of the screw ( p ) =

No. of teeth on the gear ( N ) =

Weight of the Pan ( w ) =

Sr. No.

W (kg ) P( kg ) MA = W/P VR = 2 π R

/ p

η%=

M.A./V.R.

* 100

Page 19: GOVERNMENT POLYTECHNIC MUZAFFARPURgpmuz.bih.nic.in/docs/eml.pdfAPPARATUS: Apparatus consists of a circular aluminium disc graduated in 360 . Apparatus is provided with leveling screws,

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RESULT :

i. V.R. of machine =

ii. Efficiency of machine = M.A. /V.R.