Engineering Mechanics Lab Manual(3)

Engineering Mechanics

Laboratory Manual

Structural Engineering Division Department of Civil Engineering National University of Computer and Emerging Sciences

Civil Engineering Department FAST-NU, Lahore Lah ore

Regd. No  Name  Section 

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Regd. No  Name  Section 

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Engineering Mechanics Lab E!periments

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"reface This Laboratory Manual is intended to provide undergraduate engineering students an understanding of basic concepts of Engineering Mechanics and apparatus covering all experiments related to the first year level of the B.Sc. Civil Engineering at FST!"#CE FST!"#CES. S. $n this text% related theory is discussed &ith the help of photographs of apparatus to 'uic(ly grasp the basic concepts. Blan( spaces are provided for observations and calculations. The manual also contains brief procedure for the experiments performed% precautions and blan( spaces for &riting results and finally comments on results. ny comments ) suggestions by teachers ) students &ill be highly appreciated.

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Civil Engineering Department FAST-NU, Lahore

#as$ No.% #o Study the Layout of Engineering Mechanics Laboratory %.%. &b'ective To have an idea about location and function of different machines.

%.(. Lay &ut The plan vie& is of any ob*ect that sho&s the position of various components. $n our case layout gives an idea about the position of various apparatus installed)place in laboratory.

%.). Layout of Laboratory

%.*. Details of Layout i. ii. iii. iv. v.

Hanging rope Apparatus eri!" Prin#iple o! $oment Apparatus Centre o! %ravit" Apparatus &i' #rane Apparatus Fl" (heel Apparatus

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vi. )eam Loa*ing Apparatus vii. Apparatus to +n* !ri#tion

%.+. Description of Laboratory Lay out %.+.% ,anging rope -pparatus

This apparatus is used to determine the tension in various parts of hanging rope loaded at different points.

%.+.( "rinciple of Moment -pparatus

Moment apparatus is used to find out the effects and to verify the la&s of moment via practical. This apparatus uses cloc(&ise forces and anti!cloc(&ise forces and tell us about the rotating factor of the force. $t tells us ho& the forces produce turning effects in a structure and ho& it is nullified.

%.+.) Centre of ravity -pparatus

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This apparatus is used to determine center of gravity +centroid, of an irregular shaped ob*ects using plumb line and compare the centroid of various ob*ects using experimental and analytical values.

%.+.* /ib crane -pparatus

-ib carne apparatus is used to find out the relation and effects of tension forces on the top and compression forces at bottom of a load lifting cranes. lso it explains the forces action in the hanging type parts of a structure.

%.+.+ 0ly 1heel -pparatus

This apparatus is used to determine the angular acceleration  ant to'ue of fly&heel. This apparatus is an introduction to the basic concepts of rotational dynamics.

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%.+.2 3eam -pparatus

Beam pparatus is used to study different situations and the effects of forces on a beam on different points. From this apparatus &e can find out ho& to distribute the load &hen different loads are sub*ect to a beam at different points.

%.+.4 -pparatus to find a friction

/esistance la& apparatus is used to find friction bet&een different surfaces and co!efficient of friction.

%.2. Comments

#as$ No.(

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#o determine the surface area and volume of 5ooden6concrete cube7 steel cabinet7 in CS7 M8S7 0"S and S9 units. -lso determine the area of the Engr. Mech. Lab. 9n cm (7 m(7 marla7 $anal7 acres and hectors (.%. &b'ective To understand concept of area% volume and different system of units and practical use of system unit along &ith their conversion from one system to another system.

(.(. -pparatus Measuring tape% &ooden)concrete cube% and steel cabinet. (.). "rocedure 0e measured the dimensions of a cube from its three faces and noted nine values% three from each face using steel tape. Then &e measured the dimensions of a steel cabinet% &e too( three readings from each side and calculated their mean value and finally the length and &idth of mechanics lab.

(.*. Conversion factors Length 1m 2 3.45 ft 1 yard 2 3 ft 1mile 2 1.61 (m 2 7458 ft 2 5 furlong

1 furlong 2 668 ft

-rea 1 m4 2 18.96: ft4 2 48 Marla

1 hector 2 188 m x 188 m 2 18%888 m 4

1 acre 2 5 (anal

1 (anal

1 Marla 2 494 ft4 +447 ft4 in Lahore, :olume 1 m3 2 37.311 ft 3 2 41;.;9 gallons #< 2 46:.19 gallons #S (.+. &bservations and calculations ;uantity Length +L, 0idth +0, =eight +=, rea of side  +Lx=, 9 | Page

Steel cabinet CS 0"S

S9

1ooden6Concrete Cube CS 0"S S9


rea of side B +=x0, rea of side C +Lx0, Surface rea >+?B?C,x4@ Aolume +Lx0x=,

Engr. Mech. Lab Length +L, 2 0idth +0, 2 rea Cm4

(.2. Comments

#as$ No.) 10 | P a g e

M4

Ft4

Marla

cres

=ectors


#o Determine the Reactions of Simply Supported 3eam by E!perimental &bservations uilibrium= ).%. &b'ective To understand different methods of reaction calculations.

).(. -pparatus Simply supported beam model% &eights% hangers% spring balances% meter rod

).). Related theory ).).%. #ypes of supports i. Roller support $t transmits the compressive force normal to the supporting face.

ii. 0i!ed Support $t can provide support to the structure against any type of force +vertical% horiontal and rotating,.

iii.

,inge Support $t is capable of transmitting both horiontal and vertical forces.

).).(. 3eam

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$t is a structural member sub*ected to shear force and bending moments under the influence of lateral and transverse load.  structural member is desired to resist the forces acting transverse to its longitudinal axis is called beam.

i.

Statically determinate beams Beam having three un(no&n are called statically determinate beam. E.g. cantilever and simply supported beam etc.

ii. Statically indeterminate beam Beams having more than three un(no&n reactions are called statically indeterminate beams. E.g. propped cantilever beam.

iii. 3uilt up beam Beams &hich are fabricated or constructed &ith t&o or more pieces of material to form a single beam are called built!up beams. E.g. $ sections.

iv. Composite beam Beams &hich are made up of more than one material are called composite beams. E.g. /.C.C.

v. "rismatic beam $f the beam has a uniform cross!sectional are throughout the length% its called prismatic beam.

vi. Non prismatic beam Beams having non uniform cross!sectional area throughout the length are (no&n as non prismatic beams.

).).). #ypes of beams

i. Simply supported beam 12 | P a g e


 beam in &hich a support is provided at the t&o ends of the beam is called simply supported beam. Three reactions +t&o vertical and one horiontal, are the minimum re'uirements for the stability.

ii. &ver hanging beam $n this case one or both the ends are freely extended over the supports and &hen the load is applied at the ends the maximum stress is at the middle of beam.

iii.

Cantilever beam  beam &hich is fixed only at one end and the other end is *ust in air &ithout any support.

).).*. #ypes of load i.

"oint load

$t is applied over a very small area as compared &ith the area of the ob*ect on &hich load is applied and is assumed to be applied at a single point +concentrated,.

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ii.

Uniformly distributed load

$t is uniformly distributed over the area of the ob*ect. Self &eight of the ob*ect is al&ays ta(en as #DL.

:arying distributed load This type of load is not uniformly distributed over the area of an ob*ect but it is not concentrated.

).).+. Conditions of e>uilibrium %st condition The sum of all forces exerted on the body is e'ual to ero.

i.e. ?0!@A% ?0y@A and ?0B@A

(nd condition The sum of all the moments acting on the body is e'ual to ero. i.e. ?M@A

1st condition

4nd condition

).*. "rocedure Set the apparatus as sho&n in the fig. ma(e sure that the beam is exactly horiontal. "ote the initial reading on the spring balance / 1 and / 4. =ang t&o e'ual &eights 0 1 and 04 &ith the beam at

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e'ual distances from both ends. lso note the distance bet&een the t&o &eights. "o& again note the readings of the spring balances% subtract the initial reading from the noted value to get the re'uired value. /epeat the experiment by varying &eights and distances.

/ a

/ b

Fy 2 8

/ a  / b 2 8

Ma 2 8

+/ b x l,!+G x a, 2 8

/ b2 G x a)l

M b 2 8

+/a x l,!+G x b, 2 8

/ a2 G x b)l

Total length of the rod 2 The reading sho&n by spring balance &ithout adding the &eight in hangers2 So the reading after putting &eight in hangers &ill be ta(en as2 +x! , lbs &here HxI is the reading ta(en &hile doing experiment.

).+. &bservations and calculations "o. of 0eight obs 01 15 | P a g e

0eight 04

 +in,

B +in,

/eaction / 1 +lbs,

/eaction /4 +lbs,


"

lbs

"

Lbs

Exp

nal JErr Exp

nal JErr

1 4 3 : J Error2 >+nal.  Exp,x 188@) nal.

).2. Comments

#as$ No.* #o 0ind the 0orces in the #ie and /ib Crane

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*.%. &b'ective To verify the forces in tie are tensile and forces in *ib are compressive.

*.(. -pparatus -ib crane% &eights% &eight hangers% spring balance% measuring steel tape)meter rod.

*.). Related theory *.).%. 0orce The action of one body on another is called force. $t is the agent &hich changes or tends to change the state of rest or motion of a body &hich is already in rest or motion.

*.).(. E>uilibrium  body is said to be in e'uilibrium if all the forces and moments applied on it are in balanced condition i.e. F28 and M28

*.).). Conditions of e>uilibrium There are three conditions of e'uilibrium. Fx28 Fy28 and M28

*.).*. #rigonometric rules Sine la5 a)sin+x, 2 b)sin+y, 2 c)sin+, Cosine la5 a4 2 b ? c! 4cos+x, +b,+c, *.).+. raphical method ,ead to tail rule Aectors can be added by *oining the head of 1st vector by the tail of 4 nd vector and so on. The resultant &ill be indicating by *oining the tail of 1 st vector &ith the head of 4 nd vector.

"arallelogram method $f &e have t&o components of a vector% dra& t&o parallel lines to them such that they ma(e a parallelogram% the resultant &ill be the main diagonal.

*.*. Cranes Cranes are machines used to lift heavy loads.

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#ypes -ib crane% over head crane% gantry crane% cra&ler crane% hydraulic crane etc.

*.*.%. /ib crane $t has horiontal load supporting beam fastened to a rotating vertical column% attached to &all.

*.*.(. &ver head crane $t is used inside the building li(e factories or loading labs or in outside storage yards .

*.*.).antry crane $t is used in ship yards.

*.*.*. Cra5ler crane $t is propelled crane that move on caterpillar treads.

*.*.+. #o5er crane $t is a common fixture at construction sites. The rise hundreds of feet into air% used to lift steel% concrete% generators and other building materials.

*.*.2. ,ydraulic cranes $t is used to raise multi to&er bridge beams on high&ay% heavy e'uipment in factories and even lift beach front houses. $ can lift thousands of pounds through fluid.

*.+. "rocedure • • • • •

Set the apparatus according to the specified conditions. "ote do&n the ero error of the spring balance. pply the loads. "ote do&n the final reading of the spring balance. Measure the length of tie and *ib.

*.2. "recautions • •

Find ero error of the spring balance. Find correct dimensions.

*.4. Comments

#as$ No.+ #o :erify the "rinciple of Moment

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*.%. &b'ective •

This apparatus is used to verify the principle of moment and second condition of

•

e'uilibrium +cloc(&ise moments 2 anti!cloc(&ise moments, This apparatus is also applicable to varignons theorem.

*.(. -pparatus Moment balancing apparatus% 0eights% balance% measuring tape.

*.). Related theory *.).%. Moment /otating tendency of a force is (no&n as moment. $t is also referred as tor'ue.

M @ 0d Moment is defined as the vector product of the perpendicular distance from line of action of force to the axis of rotation and the force applied. i.e.

M2r!0

0 xis of rotation

K r

*.).(. "rinciple of Moment $t states that sum of all the moments in cloc(&ise direction is e'ual to sum of all the moments in anticloc(&ise direction.

*.).). Scalar and vector approach s the cross product of t&o vectors% the moment is a vector M perpendicular to the plane of both force and the moment arm +r,.

M2r!0 The sense of M depends on the direction in &hich 0 tends to rotate the body. =ere &e use the /ight =and /ule. 0hich states that &hen the curl of finger of the right hand are in direction of rotation +from 1 st vector to 4 nd one, the erected thumb points in the direction of M.

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Considering the angle bet&een the t&o vectors% the perpendicular component is al&ays ta(en because it causes the moment. nd the magnitude if

M @ 0d
#S customary pound!feet +lb!ft,

*.).+. #heorems :arignons #heorem This theorem states that HThe moment of a force about a point is e'ual to the sum of the moments of the components of the force about the same point.I

Mo @ r ! 0 Let " and ; are non rectangular components of force 0.

0 @ "  ; 7 Mo @ r ! <"  ;=7

Mo @ r ! 0 @ r ! "  r ! ;

*.).2. "rocedure •

Gaste the graph paper on the rotating &heel of apparatus.

•

Gut &eight in hangers.

•

ttach the hangers &ith scre&s and attach them &ith apparatus by passing thread &ith the pulley.

•

0ait for a&hile until e'uilibrium is produced.

•

Calculate perpendicular distance from line of action of force to the center of moment.

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Civil Engineering Department FAST-NU, Lahore •

Direct the force in their respective direction.

•

Calculate the cloc(&ise and counter cloc(&ise moment. For the system of e'uilibrium% cloc(&ise and counter cloc( &ise moment must be e'ual.

*.).2. &bservations and calculations "o. of obs 1 4 3 : 7

pp. 0t +",

*.).4. Comments

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0t of hanger +",

Total &t +",

Moment rm +m,

Moment +"m,

/emar(s


#as$ No.2 #o Determine Centre of ravity of :arious &b'ects by -nalytical Solution and E!perimental &bservations

2.%. &b'ective To determine the center of gravity +centroid, of an irregularly shaped ob*ects using plumb line and compare the centroid of various ob*ects determined by experimental observation and analytical result.

2.(. -pparatus Center of gravity apparatus% b*ects of various shapes% Nraph Gaper% Cutter% Stationary

2.). Related #heory 2.).%. Centre of ravity The center of gravity of a distribution of mass in space is the uni'ue point &here the &eighted relative position of the distributed mass sums to ero.

2.).(. Centroid The Centroid can be said as the centre of area of the ob*ect +a geometric figure, or a point &here the distributed area e'uals to ero. $t is also (no&n as geometric center and barycenter.

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2.).). Centroid of eometric Shapes Follo&ing are the centroid of some of the geometric shapes.

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2.).*. Centroid of Composite -reas

0igure %

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Coordinates of the centroid is at +4.3:% 9.:9,. 0igure (

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Civil Engineering Department FAST-NU, Lahore answer

answer

0igure )

For the semicircle

For the shaded area

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answer

2.*. "rocedure •

Fix the graph paper on the given ob*ect of any shape.

•

=ang the figure through its hole in the center of gravity apparatus.

•

=ang plumb bob &ith nail and dra& line of action of the plumb bob.

•

=ang plumb bob at various positions and dra& all line of action

•

Common point &here all the line intersects is the center of gravity of given shape.

•

/epeat the same step to measure the center of gravity of various shape ob*ects.

2.+. &bservation and Calculation Measurement of Centroid by -nalytical Method

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Measurement of Centroid by raphical Method

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2.2.

"recaution

•

Gaste the ob*ect allo& the static state.

graph on the carefully and body to come in

•

Glumb line should be ta(en carefully and measure all the dimensions accurately.

2.4. Comments

#as$ No.4 #o 0ind out the Coefficients of 0riction bet5een Different Surfaces 4.% &b'ective The purpose of this apparatus is to find a friction bet&een different surfaces and coefficient of friction. 4.(. -pparatus Friction apparatus% 0eight% =angers% Stationary

4.). Related theory 4.).% 0riction 0hen t&o surface are in contact% longitudinal force% called frictional force% develop if one attempts to move one surface &.r.t another 4.).(. #ype of friction i.

Dry friction

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0hen t&o surface of different solid material ob*ect are attempted to move over one another% the frication produce b)& this surface is called dry friction. For example% dry friction b)& &ood and steel surface "ote dry friction is also (no&n as coulombs friction ii.

0luid friction $t develops b)& layers of fluid moving at different velocities e.g. the friction present b)& the different layer of fluid passing through pipes

4.).). 0actors affecting friction i.

Smoothness of contact surface Friction partly depends upon the smooth of the contact surface.  greater force is

being needed to move t&o surface past one another if they are rough then if they are smooth ii.

0orce holding t5o surfaces 0hen a body is moving on a horiontal surface% it presses do&n against the surface &ith a force e'ual to its &eight. $ncrease in &eight increasing the friction

4.).*. Coefficient of 0riction $t is a measure of amount of resistance that a surface exerts. µ = F / N

4.*. 0ormula

Component of load H0I parallel to the plane2 0sin K Component of load H0I perpendicular to the plane2 0cos K ?0! @ A

f!F!0sinK 2 8OOOOO..+1,

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F2f!0sinK ?0y @ A "20cosKOOOOOO.O +4,

From E'uation +1, and +4, Coefficient of friction% F µ = =( f −Wsinθ )/ Wcosθ N

4.+. "rocedure • • • • • •

ttach one end of a string &ith a hanger and other &ith a &ooden or metal mass. Glace it on the inclined surface. "ote the initial &eight of hanger and box. dd &eight in the box to increase the moment force. fter that add &eight in the hanger till box starts to slide. "ote the &eight applied and repeat the process for other t&o boxes.

4.2. &bservations and Calculations

$nclination

0eight Box

=anger 0eight "ormal Force

Friction

Material

K

"

"

0ood!0ood 0ood!Copper 0ood!Steel

4.4 "recautions • • • •

The plane should be clean and smooth. The guide pulley should move freel y. 0eight should be added gently in the hanger. Direction of thread should be parallel to the plane.

4.F. Comments

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"

"

F N

=


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#as$ No.F #o Determine the #ension in :arious "arts of ,anging Rope F.%. &b'ective To compare experimental and theoretical results and e'uilibrium of concurrent force system. F.(. -pparatus Flexible hanging rope% spring balance% &eights and hangers% meter rod% measuring tape. F.). Related theory F.).%. 0orce ction of one body on another body is called force. $ts S$ unit is ne&ton +",% and in FGS% are pounds +lb,.

F.).(. E>uilibrium  body is said to be in e'uilibrium if all the forces and moments applied on it are in a balanced condition.

) conditions of e'uilibrium are

G0! @ A

G0y @ A

GMB @ A

F.).). Concurrent force system The system of forces in &hich all the forces are passing through same point is called concurrent force system.

F.).*. Categories of e>uilibrium i. ii. iii.

E'uilibrium of collinear forces clearly re'uires only one force e'uation in the direction of force +x direction or y direction,% since all other e'uations are automatically satisfied. E'uilibrium of forces &hich lie in a plane +x!y plane, and are concurrent at point % re'uire the t&o force e'. only. Since the moment sum about  i.e. about !axis through  is ero. E'uilibrium of parallel forces in a plane re'uires the one force e'uation in the direction of force +x direction, and one moment e'. through an axis + axis, normal to the plane of the force.

Categories of e'uilibrium in t&o dimensions! i.

Collinear

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G0! @ A


ii.

Concurrent at a point

G0! @ A

G0y @ A

iii.

Garallel force system

G0! @ A

GMB @ A

G0! @ A T4 cosK4  T1 cosK1 2 8

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T4 2 T1 cosK1 ) cosK4


G0y @ A T1 sinK1 ? T4 sinK4 2 0

T1 sinK1 ? T1 cosK1 sinK4 ) cosK4 2 0

T1 +sinK1 ? cosK1 tanK4, 2 0 T1 2 0 ) +sinK1 ? cosK1 tanK4, F.*. "rocedure •

• • • • • • •

ttach a string of (no&n length to the t&o ha&(s nailed in &all of some height at (no&n distance. Find out ero error of both spring balances attached &ith the rope. pply &eight in the centre of the string to measure the tension. Measure the displaced height of rope from the height of hoo(s. "ote the readings of spring balance attached on both the ends of string. Subtract the ero error from the obtained value. /epeat the process by changing the &eights. Compare the experimental values &ith analytical values.

F.+. &bservations and calculations "o of obs. 1

0 "

lbs

4 3 :

F.2. Comments

#as$ No.AH 35 | P a g e

L1 +in,

L4 +in,

= +in,

P1

P4

Qero err T12lbs Exp

n.

Jdiff

Qero err T42lbs Exp

n.

Jdiff


#o determine the angular acceleration ue <#= of 0ly5heel H.%. &b'ective To determine the angular acceleration  and tor'ue R of fly&heel.

H.(. -pparatus Fly &heel% &eight hanger% slotted &eights% stop &atch% meter scale.

H.). Related theory The fly&heel consists of a heavy circular disc)massive &heel fitted &ith a strong axle pro*ecting on either side. The axle is mounted on ball bearings on t&o fixed supports. There is a small peg on the axle. ne end of a cord is loosely looped around the peg and its other end carries the &eight!hanger.

Let m be the mass of the &eight hanger and hanging rings +&eight assembly,.0hen the mass m descends through a height h% the loss in potential energy is

The resulting gain of (inetic energy in the rotating fly&heel assembly +fly&heel and axle, is

0here $ !moment of inertia of the fly&heel assembly !angular velocity at the instant the &eight assembly touches the ground.

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H.).%. #or>ue of a fly5heel Consider a body &hich can be rotated. 0hen &e rotate a body% &e are applying a turning force to it. The turning effect depends not only on the force but also on the place &here the force is applied. So &e can define the tor'ue as% Tor'ue2force x perpendicular distance from the axis to the line of action of force So for a fly&heel having radius of axle r and having mass m attached to it the tor'ue is given by

The tendency of a moving body to change its state of motion is called inertia. $f the inertia of fly&heel is high% considerable amount of tor'ue is needed to be applied. The property of inertia is applicable to every ob*ect since it is having mass. =o&ever the inertia of rotating body depends on the distribution of its mass as &ell as the amount of mass.

H.).(. -ngular acceleration of a fly5heel 0hen a tor'ue is applied to body the angular acceleration  is given by

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That is the angular acceleration depend not only on the tor'ue R but also on the moment of inertia $ of the body about the given axis &hich is determined by using the e'uation

0here% $ 2 Moment of inertia of the fly&heel assembly " 2 "umber of rotation of the fly&heel before it stopped m 2 mass of the rings n 2 "umber of &indings of the string on the axle g 2 cceleration due to gravity of the environment. h 2 =eight of the &eight assembly from the ground. r 2 /adius of the axle.

H.*. -pplications

Fly&heels can be used to store energy and used to produce very high electric po&er pulses for experiments% &here dra&ing the po&er from the public electric net&or( &ould produce unacceptable spi(es.  small motor can accelerate the fly&heel bet&een the pulses. The phenomenon of precession has to be considered &hen using fly&heels in moving vehicles.

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=o&ever in one modern application% a momentum &heel is a type of fly&heel useful in satellite pointing operations% in &hich the fly&heels are used to point the satelliteUs instruments in the correct directions &ithout the use of thrusters roc(ets. Fly&heels are used in punching machines and riveting machines. For internal combustion engine applications% the fly&heel is a heavy &heel mounted on the cran(shaft. The main function of a fly&heel is to maintain a near constant angular velocity of the cran(shaft.

H.+. "rocedure for doing Real Lab 1.

The length of the cord is carefully ad*usted% so that &hen the &eight!hanger *ust touches the ground% the loop slips off the peg. 4.  suitable &eight is placed in the &eight hanger 3.  chal( mar( is made on the rim so that it is against the pointer &hen the &eight hanger *ust touches the ground. :. The other end of the cord is loosely looped around the peg (eeping the &eight hanger *ust touching the ground. 7. The fly&heel is given a suitable number +n, of rotation so that the cord is &ound round the axle &ithout overlapping. 6. The height +h, of the &eight hanger from the ground is measured. 9. The fly&heel is released. 5. The &eight hanger descends and the fly&heel rotates. ;. The cord slips off from the peg &hen the &eight hanger *ust touches the ground. By this time the fly&heel &ould have made n rotations. 18.  stop cloc( is started *ust &hen the &eight hanger touches the ground. 11. The time ta(en by the fly&heel to come to a stop is determined as t seconds. 14. The number of rotations +", made by the fly&heel during this interval is counted. 13. The experiment is repeated by changing the value of n and m. 1:. From these values the moment of inertia of the fly&heel is calculated using e'uation

.

H.4. &bservations

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Mean value of moment of inertia% $ 2.........(gm 4

H.F. Result Moment of inertia of the fly &heel 2.........(gm 4

H.H. Comments

#as$ No.%A 40 | P a g e


-nalysis of 3eams and #russes by MDSolids Soft5are %A.%. &b'ective MD!Solids is an educational soft&are pac(age devoted to the introductory mechanics of materials course. MD!Solids &as developed &ith several ob*ectives in mind •

:ersatility MD!Solids has routines pertaining to all of the topics taught in a typical mechanics of materials course. These routines are grouped in modules% similar to typical textboo( chapters% and the modules can be accessed in any se'uence.

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Easeof9nput Ease!of!input is an essential aspect in the MD!Solids concept. Throughout MD!Solids% graphic cues are provided to guide users in entering data. The illustrations can be easily ad*usted so that the MD!Solids input screen loo(s very similar to the textboo( illustration. Aarious units +e.g.% stress units% length units, are available and internal conversion factors are present to ensure dimensional consistency.

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:isual Communication Each MD!Solids routine features a picture% s(etch% or plot that graphically depicts important aspects of the problem. S(etches are used to sho& the direction of internal stresses% applied loads% and reaction forces. Glots are given for a number of topics including critical buc(ling stress% beam deflections% and shaft shearing stress.

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#e!tbased E!planations Many of the MD!Solids modules provide extra explanations to describe in &ords ho& the calculations are performed. These explanations can help students develop the thought processes used in solving mechanics of materials problems.

%A.(. Soft5are MD!Solids :.1.8

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%A.). Related theory %A.).%. 0eatures of MDSolids Soft5are

%A.).(. #russ Module

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%A.).). Determinate 3eam Module

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Engineering Mechanics Lab Manual(3)

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