Mechanics of Material Lab6

8/9/2019 Mechanics of Material Lab6

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An-Najah National University

Engineering College

Civil Engineering Department

Strength of Material

Laboratory Manual

Prepare by!

Dr" #sam $araneh Eng" %amees &ubeileh

'(()


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An- Najah National University

Civil Engineering Department

Me*hani*s of Material Laboratory

+bje*tivesThe primary objectives of this laboratory are as followed:

1- To learn how the main properties and parameters of the materials

can be measured.

2- To investigate and apply a group of the mechanics of material

principles studies in its course.

3- To connect theory with practice.

4- To practice on the laboratory devices.

Course ,eferen*e- aboratory manual and handouts.

Eperiments!n this laboratory the following e"periments will be performed:

1- #$uilibrium of forces.

2- #$uilibrium of beams.

3- %ember forces in a truss.

4- &heer in rubber test.

'- Tensile strength test.

(- #"tension of wires.

)- &imple suspension bridge.

*- Torsion test.

+- ,eflection of beams.

.raeseports: 2'

/resentation and participation 10

%idterm e"am 2'inal e"am 40

ote: to pass the laboratory the student has to attend *).' of the

e"periments ) e"periments5 and to do all the e"ams.


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,eport /ormat

aboratory reports should be type written. eports are due to one wee6

from the completion of the e"periment. The laboratory reports should

include the following topics in the given order.

0- &itle page! 1234

a5 7ourse name and number

b5 umber and title of the e"periment

c5 ames of students

d5 ,ate of the e"periment

'- +bje*tives! 1234

!t includes a brief and clear statement of the purpose of the e"periment.

5- &heory! 10(34

Theoretical analysis of the e"periment approach and the basics e$uations

needed for the calculations.

6- Eperimental Apparatus an pro*eure! 10(34

,escription of the apparatus and the e"perimental procedure that you

used in performing the e"periment to collect the re$uired data.

2- ,esults an Dis*ussions! 17(34

/resentation of the obtained e"perimental results in tabular or graphical

form. ,iscussion of the results and comparison with the theoretical

analysis. !t also includes a discussion of the reliability of the results and

the possible sources of errors.

7- Con*lusions! 1234

7ollect all the important results and interpretations in clear summary

form.

8- ,eferen*es! 1234

!nclude the references cited in the te"t. !n general the references should

be the laboratory manuals and the te"t boo6s of the theoretical materials.


4/36

E9uilibrium of /or*es

+bje*t!

The purpose of this e"periment is to study the e$uilibrium of a set of forces acting in avertical plane.

!n the first part the case of concurrent forces is to be investigated and chec6ed by the

graphical solution of triangle of forces three forces5 or a close polygon for more than

three forces.

The second part deals with non-concurrent forces and the use of a lin6 polygon.

&heory

8 *on*urrentforce system is a system of two or more forces whose lines of action all

intersect at a common point. 9owever all of the individual vectors might not actually

be in contact with the common point. These are the most simple force systems to

resolve with any one of many graphical or algebraic options.

The other system is a non-*on*urrent system. This consists of a number of vectors

that do not meet at a single point. These systems are essentially a jumble of forces and

ta6e considerable care to resolve.

8lmost any system of 6nown forces can be resolved into a single force called a

resultant force or simply a esultant. The resultantis a representative force which

has the same effect on the body as the group of forces it replaces.. This is one way to

save time with the tedious boo66eeping involved with a large number of individual

forces. esultants can be determined both graphically and algebraically.


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Pro*eure!

;ith a clean sheet drawing paper in place ta6e the cord ring and attach three or four

or five load cord assemblies. /lace the cord ring temporarily on the center peg. ,rape

the load cord over the pulleys and add a load hanger to each free end. 8dd loads to the

hanger and gently lift the cord ring off the center peg and allow the ring to find itsposition of e$uilibrium. 8dd loads to hangers noting how the cord ring moves to a

new e$uilibrium position each time an e"tra load is added. or any e$uilibrium state

thought interesting use the line mar6er to transfer onto the drawing paper two points

on each of the cords radiating from the ring.

7arefully remove the sheet of drawing paper from the force board for further wor6 as

described later in results.

,esults

,ecide a scale for the force vectors for e"ample 1cm


6/36

E9uilibrium of :eams

#N&,+DUC+N!

=ne common e"ample of parallel forces in e$uilibrium is that of a beam because in

most cases the forces are vertical weights due to gravity. 9ence the beam supportswill develop vertical reactions to carry the weights on the beam and the self weight

of the beam itself.

or a beam on two supports there will be the two un6nown reactions so two

e$uations of e$uilibrium must be set up. !t is necessary to start by ta6ing moments

about a convenient point? if this point is at a reaction then there is only one un6nown

force the other reaction5 in the e$uation. The second reaction can then be found from

vertical e$uilibrium.

8n alternative type of beam which projects from a support into mid-air is called acantilever. 9ere the two un6nown reaction are a fi"ing moment and a force which

can be calculated independently of each other.

E;PE,#MEN&

+:$EC&

The purpose of the e"periment is to verify the use of conditions of e$uilibrium in

calculating the reactions of a simply supported beam or a cantilever.

P,+CEDU,E

Part0 < :eam rea*tions

1. i" the reaction balance in the test frame with the 6nife edges 1 m apart.

2. est the channel section beam over the 6nife edge supports with the @ero of the

scale lined up with the left hand support.

3. 8dd a stirrup and load hanger at mid span.

4. Ase the @ero adjustment on the balances to bring the pointer to @ero. This is an

artificial way to nullifying the self weight of the beam stirrup and load hanger so

that the balance will read only the reaction for any added load.

'. 8dd a succession of weights up to (0 to the mid span load hanger and record

the two reaction values for each case. Because of the symmetry the reactionsshould be e$ual and therefore each will be half of the load to satisfy vertical

e$uilibrium. !n these simple cases the e"periment is used to chec6 the obvious.

ecord the results in table 1.

(. ow move the stirrup and load hanger to the $uarter span position and using a

40 load record the reactions. epeat this for two or three more positions

measured from the left hand reaction tabulating the results.

). inally use the three stirrups and load hanger at pre selected positions. 8dd a

set of three loads one at a time to these hangers recording the reactions as each

load is applied.


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&able 0,ea*tion for a simply supporte beam

:eam span = 0m

Loa an position from left

en

left en rea*tion ,ight en rea*tion

Ept" &heory Ept" &heory1N4 1mm4 1gm4 1N4 1N4 1gm4 1N4 1N4

0( 2((

'( 2((

5( 2((

6( 2((

6( '2(

6( 82(

Part ## < Cantilever beam rea*tions

1. 8ttach the spring balance assembly mid way between the reaction balance and

move the channel section beam to the right so that the threaded tie rod of the spring

balance passes through the hole in the top of the beam by the @ero on the beam scale.

The beam will e"tend through the right hand side of the test frame and it should be

leveled by adjusting the tie-rod. The beam cantilevers to the right of the upward

reaction balance while the spring balance provides a downward reaction. 8ny initial

readings will be those due to the self weight of the cantilever.

2. /osition a stirrup and load hanger on the end of the cantilever 2(( mm from the

reaction balance and adjust the @ero of the reaction balance.3. 8dd a succession of 2 loads on the hanger. or each loading adjust the length of

the spring balance tie rod to re-level the cantilever. ote weather the spring balance

reading changes while this is being done.5 ecord the readings in table 2.

4. 7hange the position of the spring balance by moving it closer say by '((mm5 to

the reaction balance. eposition the stirrup and load hanger so that it is the same

distance of 2((mm from the reaction balance as above. >ero the balance. 8dd a

succession of 2 loads on the hanger. e-level the cantilever and record the balance

reading for each load.

&able ',ea*tions for a 2(( mm *antilever

Enloa

Support,ea*tion

Spring ,ea*tion Distan*e:et?een

,ea*tions

/iingmoment

Support,ea*tion

minus

loa

1N4 Ept" &heory Ept" &heory 1mm4 1N"m4 1N4

1gm4 1N4 1N4 1N4 1N4

2

0(

02


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,ESUL&S

Tabulate the readings for part 1 and add the calculated theoretical reactions. 8 suitable

table is given for single loads.

or part 2 theoretical values are calculated by using conditions of e$uilibrium. The

wall fi"ing moment is the product of the spring balance reading and the distancebetween the balances.

+:SE,@A+NS

9ow well the e"perimental and theoretical results compare try stating the differences

as a percentage of the true values5>


9/36

Member /or*es in a &russ

+bje*t!The truss is to be used to compare the forces measured in the members with the values

found by resolution at the joints.

.eneral &heory!Before the advent of computers the analysis of structures was typically based on

simplifying assumptions to minimi@e the calculations. 8 good e"ample of this was the

assumption that for ordinary plane trusses the joints could be treated as if they were

frictionless pins. The ne"t step was to construct the truss and design the supports so

that the force in each member could be determined using the three condition of

e$uilibrium. This leads to a rule for calculating the number of memberCs mand joints j

fora so-called perfect or statically determinate5 truss in the form.

M= 2j - 38lthough truss joints are either welded or bolted the assumption wor6s sufficiently

well because the members are long compared to their cross sectional si@e. 9ence

fle"ural bending5 stresses are small say 235 compared to the direct compression

or tension5 stresses.

9owever this e"periment uses a model truss specially designed with pinned joints to

be correctly representative of the mathematical model. 9ence there should be good

correlation between the e"perimental results and the simple theory of resolution at the

joints. This method providing two e$uations of e$uilibrium of forces in mutually

perpendicular directions. e$uires a systematic joint by joint approach. =nly two

un6nowns can be resolved so one wor6s across the truss from the load or the supportreaction until every member forces has been determined.

Apparatus

The truss is a 62triangulated frame made from /erspe" members of 2'0 mm2cross

sectional area. 9ori@ontal and vertical members are 6((mmlong. ;hile the diagonal

ones are 272"8 mm. !n order to preserve symmetry in the plane of the frame each

member consists of a pair of /erspe" bars spaced apart either (< 0(< '(or 5( mm. The

joints have turned and fitted pins in reamed holes. !n its normal configuration the truss

springs from two side brac6ets fastened to the side of the 9&T.1 frame.


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!n the first instance the truss should be assembled on a hori@ontal surface. &pacing

discs are provided to fill in at joints where less than four members meet. The side

brac6ets should be attached to the truss with threaded holes to the rear. The whole

truss can now be lifted into the 9&T.1 frame and clamped by the brac6ets whose pins

should be 6((mm a part.
http://www.hi-techedu.com/products/structures/level1/hst1-0_win.htm


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Shear of ,ubber&est

.ENE,AL &%E+,B!

ubber has always been an interesting engineering material. !ts elasticity isremar6able while its use in vehicle tyres re$uires other properties. 8lthough

originally a natural product rubber became so important and in such demand that

synthetic rubber was developed with the possibility of having special properties to suit

the application.

This e"periment concentrates on the shear characteristics of rubber which are used in

anti -vibration mountings for machinery and sprung suspension of railway carriage.

ubber can withstand large shear deformation especially in medium and soft grades

of the material which helps to absorb shoc6 loading.

APPA,A&US

8 bloc6 of medium rubber 1'0 " )' " 2'5 mm si@e has aluminum alloystripes bonded to the two long edges. =ne strip has two fi"ing holes enabling this

assembly to be fi"ed to a rigid vertical surface. The bottom end of the other strip is

drilled for a load hanger while a small dial gauge indicates the position of the top end.

E;PE,#MEN&

+bje*t! The purpose of the e"periment is to measure the shear deformation of the

rubber bloc6 and hence determine the modulus of rigidity.

P,+CEDU,E The apparatus must be fi"ed to a convenient vertical surface.

1. /lace the load hanger in position and read the dial gauge.

2. 8dd load to the hanger in 10 increments reading the dial gauge at each load

until the travel of the gauge is e"ceeded. 8s the load increases observe if any

creep occurs.

3. ecord the reading in table 1.

;hen the load is removed note whether the rubber fully recovers it may be necessaryto have 10 or 20 on the hanger to get a dial gauge reading5.

Loa 1 N 4 Dial .auge ,eaing

1("(04

Defle*tion 1 mm 4 Shear Stress

1Mpa4

+

0(

'(

5(

6(

2(


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7(

8(

(

)(

0((00(

0'(

,ESUL&S!n the first place plot a graph of deflection against load and draw a best-fit straight

line through the points. This implies a linear load- deformation relationship in the

vertical plane.

ow the definition of the modulus of rigidity or shear modulus5 is:

. =Shear stress / Shear strain = F

!n this e"periment the shear stress is simply

= Load / Area = W / A = W / (150 * 25)

But the strain angle is ta6en as:

F 1raians4 = defletion / !lo" #idth = G b = G 82

This is amathmatical appro"imation with an error increasing with the angle F "

$he relationshi% !et#een the &ra%h of the res'lt and and the mod'l's of ri&idit is

therefor deried as

+ = W/ 3,50 * ,5/ = ,5/ 3,50 * &ra%h &radient 1Nmm'4

=bservation;ere the results linear> ;ould greater or lesser deflection improve linearity>

&ensile Strength &est


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This is most important as damage to the e"tensometer will occur if it is in place

during fracture.

(. emove the specimen for study of fractured area. it the two pieces together

and measure the final length between the e"tensometer mar6s and the diameter in

the nec6 .

). 7alculate values for stress and strain plot against each other.*. ,etermine values for EoungCs %odulus #5 from the graph.

+. 7alculate values for /ercentage reduction in area and elongation.

10. epeat for another specimen.

Data!

ength:

7ross - sectional area: FFFFF..

%aterial :

/ 1loa4

JN

Etension

1ial4 1mm4

Stress

Nmm'Strain

HLL


15/36

Con*lusions!

7ompare your values of EoungCs modulus Eield strength Altimate strength

#longation and /ercentage reduction in the cross-sectional area with the values

e"pected for the specimen material.

7omment on the manner in which the e"periment was carried out and suggests ways

in which you feel the efficiency of the e"periment could be improved.


16/36

Etension of Kires

#ntrou*tion!

The tensile behavior of materials is a very important aspect of design.

early all-engineering materials have a linear elastic range wherein e"tension is

proportional to load. 9oo6Cs law defines the modulus of elasticity Eas

E = Stress Strain = PA L L

Khere

P = loa

A = *ross se*tional area

L = length

L= etension

8s the stress increases most materials have a limit to the linear elasticity above which

the e"tension increases more rapidly for e$ual increments of load. 9owever the

graphs showing this are plotted as stress load5 against strain e"tension5 so the typical

curves are li6e those shown here.

!t is also necessary to understand that the physical condition of the material being

tested may affect the loadGe"tension readings .;ire is produced by drawing pulling5

rod through a tapered hole in a die .8s the diameter is reduced the material is being

cold wor6ed hardened5and this causes an increase in the proof stress and elastic

range. !f the wire is needed for an easy bending operation li6e the copper wire

windings in an electric motor the drawn wire has to be softened annealed5 by heat

treatment.


17/36

8nnealed wire stretches plastically when it is loaded in tension for the first time. =n

unloading and then reloading the wire will have become elastic up to the initial load.

Because the wire used in this e"periment is continually re-loaded it will behave

elastically although its original condition may have been annealed. The term CCstrain

hardenedCC describes this modified condition.

Apparatus

8 wire test specimen about 2m active length is suspended from a brac6et

fi"ed to a wall around 2.'m above floor level. 8t the lower end of the wire is clamped

a load hanger lin6 which slides in the guides of the bottom brac6et also fi"ed to the

wall. There is a vernier on the hanger lin6 which reads the wire e"tension to 0.1mm

against a )cm scale on the bottom brac6et.

The wire can be gripped top and bottom either by winding it round a stud or by

threading it through a hole in the stud and then using washers and nuts to clamp it.

The set of wires includes three si@es of a hard drawn brass and four wires of one si@e

but different materials namely brass steel copper and commercially pure aluminum.

E;PE,#MEN&

+bje*t

The two objects are to verify that the modulus of elasticity is independent of

wire si@e and that it depends on the material from which the wire is made.

Pro*eure

!t is essential that the brac6ets have been fi"ed to the wall and that a

ladder or other means5 is available to reach the top brac6et. 8 plump line should be

used when fi"ing the brac6ets to the wall. The copper and aluminum wires should be

hung up as they will be straight and soft. The brass and steel wires are springy and

self-coiling.

Three test specimens of 1( 1* and 20 swg hard drawn brass wire are provided.

emove the clamping nuts and washers from the top and bottom fi"tures. ;ind the 1(

wire cloc6wise round the top suspension and clamp it with a washer and nut. 9old

the load hanger lin6 with the venire near @ero and wind the bottom end of the wire

round the studH and then clamp it. 9ang the load hanger from the lin6 and chec6 that

the venire is near the start of the scale. %easure the length of the wire between theclamp and the average diameter of the wire.

;hen loading the wires add the load gently as suddenly applied load is

instantaneously doubled. This may brea6 the aluminum or copper wires.

/re-load the wires with the ma"imum load shown in the following schedule. Anload

the wires adjust the venire if necessary5 and enter the scale reading against @ero load

in the table 1 and commence loading the wires by increment as shown below to the

ma"imum load ta6ing the scale reading of e"tension at each load unload and record

the @ero load reading before removing the wires.


18/36


19/36

Loaing S*heule for the ?ires

Material Sie

1mm4

Ma" Loa

1N4

#n*rements

1N4

Brass 0.+ *0 10

Brass 1.( 100 10

Brass 1.* 2.0 200 20

&teel 1.* 2'0 30

7opper 1.* 1*0 20

8luminum 1.* *0 10

,ESUL&S!

/lot the load on E a"is against e"tension on " a"is 8lthough this is not

the normal plotting of effect against cause it is the accepted practice for tensile tests5.

,raw the best fit straight lines through each set of points and determine thegradients. Then enter the e"perimental data in the formula for the modulus of

elasticity:

E = Stress Strain = PA LL

= L A graient

;here A< cross sectional area of wire

7ompare the values of #.

8nother possibility is to test and compare different materials of the same si@e.

+:SE,@A+NS!

,escribe the effect of lac6 of straightness of wire at @ero load.

To what e"tent did the results conform to 9oo6Cs law>


20/36

Simple Suspension :rige

The suspension bridge is defined as a bridge that has a roadway supported by cables

that are anchored at both ends.

,ange of Eperiment 1obje*tives415 7omparison of simplified theory with e"perimental results for a uniformly

distributed load

25 &tudy of the effect of a point load

Des*ription8 rigid bridge dec6 is carried each side by hangers of different lengths such that the

fle"ible steel cables from which they hang are constrained to a parabolic curve. The

twin suspension cables pass over pulleys each end of the 0 mspan and terminate inyo6es carrying load hangers. 8djustable stops prevent the yo6es moving upward and

mar6 the correct length from the cables. &teel bars are provided to simulate a

uniformly distributed load and a special point load is supplied.

&heory!The main concept used in this test is the e$uilibrium e$uation. The tension in each

cable is e$ual to:

TG2I TG2 < weight added on each hanger

&o &= Keight ae

Theoretically the tension in each cable is e$ual to the reaction on the supports. orthe distributed load w5 the tension is e$ual:


21/36

&= KL'7ompare the stress in the cable with the allowable stress. Dnowing that the stress in

each cable is e$ual to:

O = /A = 1&'A4

8ccording to the data in the lab fill the following table:

Loa

1Nm4

Keight Ae

1N4

&ep1N4

&theory1N4

Stress

1Nmm'4

2'

'0

)'

100

Point loa! at loa '(N< & 1N4 = --------------------

+bservation!,raw the relation with the load 5 with the e"perimental value of the tension 5.

7ompare the effect of a point load e$ual to 20 with a similar value of a distributed

load. 7omment on the results.


22/36

&orsion &est

/eatures

Tor$ue capacity up to 30m 300lbf in5 ,irect readings of tor$ue and strain

,igital tor$ue meter

&uitable for specimen testing to destruction

8ccommodates specimens up to )'0mm long

&pecimens gripped by standard he"agonal drive soc6ets

;ide range of standard test specimens

&%2 Torsi meter available for accurate strain measurement

Des*ription

The &%1 %6!! Torsion Testing %achine has the same basic features as its well 6nown

predecessor but has been improved by introducing a digital tor$ue measurement

system and e"tending the length of the unit to allow tests on longer specimens if

re$uired. 8 rigid s$uare aluminum tube is supported at each end by cast aluminum

feet and carries a straining head at one end and a tor$ue measuring system at the

other. The straining head consists of a (0:1 worm drive reduction gear bo" mounted

on a special e"truded aluminum platform which slides long the s$uare tube and can be

loc6ed in any position. The output shaft is free to slide on a 6eyway in the gear bo" to

accommodate any change in length of the specimen during testing and to enable

insertion of specimens. eaction to the tor$ue applied to the specimen is supplied by

the torsion shaft which is supported at each end by self aligning bearings. Testspecimens are held at each end by he"agonal drive soc6ets which fit on the gearbo"

output and torsion shafts. 8n arm is fitted to each end of the torsion shaft the one at

the far end being located by a turnbuc6le and hand wheel for adjusting the angular

position of the torsion shaft. The arm at the inner end bears on a dial gauge and can be

adjusted using the turnbuc6le to maintain one end of the specimen in a fi"ed position

during tests. 8 linear potentiometer is fitted between the two arms and provides an

output proportional to the angle of twist of the torsion shaft.

The potentiometer is connected to a digital meter which reads directly in m and lbf

in. 8 calibration arm weight hanger and weights are supplied for chec6ing or

recalibrating the meter if re$uired. &train of the specimen is measured by protractorscales on the gearbo" input and output shafts these scales being loc6ed in position by


23/36

6nurled thumbnuts. 8 reset table digital revolution counter is also fitted to the gearbo"

input shaft to provide a record of total input revolutions in any test. %easurements of

specimen strain can be obtained when the torsion shaft is adjusted during a test to

maintain one end of the specimen in a fi"ed position. 8 Torsiometer &%2 can be

supplied as an e"tra if re$uired for greater accuracy in measuring strain for e"ample

in determining modulus of rigidity.

,ange of Eperiments 1obje*tives4

1. Jerification of the elastic torsion e$uation.

2. ,etermination of modulus of rigidity and yield shear stress.

3. ,etermination of upper and lower yield stresses for normali@ed steel specimens.

&heoryAse the general torsion theory for a circular specimen:

&$ = .

L= Q

Khere!-

T< 8pplied Tor$ue m or !bf

K < /olar second moment of area mm5 or in5

L < %odulus of igidity GmmM or !bfGinM

< 8ngle of twist over length5 radians

< Lauge length mm5 or in5

N < &hear stress at radius O GmmM or !bfGinM

O < adius mm or in

Eperimental pro*eure1. %easure the overall length and diameter of the test section of the specimen.

2. ,raw a line down the length of the test section of the specimen with a mar6er?

3. i" the test specimen at each end by he"agonal drive soc6ets which fit on the

gearbo" output and torsion shafts. 8n arm is fitted to each end of the torsion

shaft the one at the far end being located by a turnbuc6le and hand wheel for

adjusting the angular position of the torsion shaft. The arm at the inner end bears

on a dial gauge and can be adjusted using the turnbuc6le to maintain one end ofthe specimen in a fi"ed position during tests. 8 linear potentiometer is fitted

between the two arms and provides an output proportional to the angle of twist of

the torsion shaft.

4. ound the arm which ma6e torsion on the sample.

'. ecord the values of torsion and the angle of twist from the apparatus.

,esults


24/36

&or9ue

1N"m4

Angle of &?ist

1egree4

Angle of t?ist

1raian4


25/36

rom the upper e$uation a relation between torsion T m5 on the y-a"is5 vs.

angle of twists on the "-a"is5 is drawn. ind gradient of the linear range then

determine the modulus of rigidity?


26/36

.= 1&L41$

4=r

.= 1graient L4$

rom the graph obtain the upper yield point T yield5 then calculate the yield shearstress?

Q


27/36

/eatures

#"tensive range of e"periments

&imply supported and cantilever beam tests on up to four supports with any

loading

Three load cells measure reactions or act as rigid sin6ing supports

Three dial gauges for deflection measurements

/oint loads applied by four weight hangers and cast iron weights

ive different test beams supplied with each rig

&%104a set of 10 special test beams available as an e"tra

Des*ription

This is a much improved version of the &%104 Beam 8pparatus with many new

features which e"tend the range of e"periments to cover virtually all course

re$uirements relating to bending of beams. The basic unit provides facilities for

supporting beams on simple built in and sin6ing supports? applying point loads andmeasuring support reactions and beam deflections. ive different test beams are

supplied as standard and a special pac6 of 10 additional specimen beams is available

as an e"tra for further e"periments.

The Beam 8pparatus can be used for an almost limitless number of e"periments

ranging from determination of the #lastic %odulus for beams of different materials

through to studies of continuous beams with any loading. Lreat care has been ta6en at

the design stage to ensure the ma"imum fle"ibility and ease of use.

The main frame of the apparatus consists of an upper cross member carrying

graduated scales and two lower members bolted to tee-legs to form a rigid assembly.The three load cells and cantilever support pillar slide along the lower members and

can be clamped firmly in any position. The load cells are direct readings and each is

fitted with a hardened steel 6nife edge which can be adjusted by a thumb nut to set the

initial level or to simulate a sin6ing support. 8 lead screw in the base of each load cell

can be screwed upwards to support the 6nife edge and thus convert it to a rigid

support when re$uired.

The cantilever support consists of a rigid pillar with a sturdy clamping arrangement to

hold the beams when built-in end conditions are re$uired. our weight hangers and a

set of cast iron weights are supplied for applying static loads. 8ll beam deflections are

measured by three dial gauges mounted on magnetic carriers which slide along the

upper cross member. The dial gauge carriers load cells and weight hangers are all


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fitted with cursors which register on the scale located on the upper cross member thus

ensuring easy accurate positioning.

The standard test beams are in three thic6nesses and include three different materials.

They are suitable for the complete range of e"periments covering different loading

and support configurations. The optional &%104a &pecimen Beams provide fore"periments on different types of beam including compound channel and non-

uniform beams of various materials.

+bje*t!

To measure the deflection of simply supported beam and compare e"perimental and

theoretical results.

&heory of the efle*tion of simply supporte beams!

!t can be shown that the deflection of a bean supported to direct loading can always be

e"pressed in the form:

P< aH ;35G #!5

;here:

P: is the deflection

a: is a constant whose value depends upon the type of loading and supports

;: is the load acing on the beam

: is the span length

#: %odulus of elasticity

!: moment of inertia

This is the relation investigated in the e"periment.

Pro*eure!

15 /lace the beam in position with 1G4 span overhang at both ends.

25 /lace the hanger at mid span so that the loading point in the center-line of the

beam.

35 /lace a dial gauge at mid span. 8djust the dial to read @ero and loc6 the be@el.

45 8pply a load to the hanger and record the beam deflection on the dial gauge.

'5 !ncrease the load to the hanger and record the new dial reading. ,o this at least

4 times.(5 /lot a graph of deflection against load. ,etermine the gradient of the graph.


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)5 7hange the position of the hangers and repeat from 3 to (

*5 ,o the test for different types of beams.

:eam 0

Material --------------- length----------------

Kith ------------------ epth ---------------

Moulus of elasti*ity---------------------

Loa

1N4

Dial reaing efle*tion

1mm4

:eam '

Material --------------- length----------------

Kith ------------------ epth ---------------


Loa

1N4


1mm4

,esults

The graphs of deflection vs. load are straight lines the transverse stiffness of the

beams can be determined from the slope where

Stiffness = 1K efle*tion4

Theoretically the stiffness of a beam is proportional to thic6ness5 3.

7ompare e"perimental and theoretical values. 7omment on the results.

Appeni! forms

E9uilibrium of beams


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04 Simply Supporte :eam

:eam span= 0mLoa an

position fromleft

Left En ,ea*tion ,ight En ,ea*tion Error

in left

Error

inrightEperimentally &heory Eperimentally &heory

1N4 1mm4 1gm4 1N4 1N4 1gm4 1N4 1N4 3 3

0( 2((

'( 2((

5( 2((

6( 2((

6( '2(

6( 82(

'4 Cantilever :eam

En

loa

Support rea*tion Spring rea*tion Distan*e

bet?een

balan*es

/iing

moment

Support

rea*tion

minus loaEperiment &heory Eperiment &heory

1N4 1gm4 1N4 1N4 1N4 1N4 1mm4 1N"m4 1N4

2 2((

0( 2((

02 2((

Sheer in ,ubber &est


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Loa

1N4

Dial ,eaing Deformation

1mm4

Sheer Stress

1Nmm'4

(

0(

'(

5(

6(

2(

7(

8(

(

)(

0((

00(

0'(

&ensile &est

Loa Dial Etension Stress Strain


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1JN4 ,eaing HL 1mm4 O 1Nmm'4 14

&orsion &est


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&or9ue

1N"m4

Angle of &?ist

1egree4

Angle of t?ist

1raian4

&able 0Loa etension of ?ires


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Material! --------------- Diam" 1mm4! ---------------

&est length L 1m4

Loa 1P4

N

S*ale reaing

1mm4

Etension HL

1mm4

&able '

Loa etension of ?ires

Material! --------------- Diam" 1mm4! ---------------&est length L 1m4

Loa 1P4

N

S*ale reaing

1mm4

Etension HL

1mm4

&able 5

Loa etension of ?ires

Material! --------------- Diam" 1mm4! ---------------

&est length L 1m4

Loa 1P4

N

S*ale reaing

1mm4

Etension HL

1mm4

Simple Suspension :rige


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04 Distribute Loa

D" loa 1Nm4 '2 2( 82 0((

&1ep"41N4

& 1theory41N4

Stress 1Nm'4

Comment

'4 Point loa! at loa '(N< & 1N4 = --------------------


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Defle*tion in :eams

:eam 0

Material --------------- length----------------

Kith ------------------ epth ---------------


Loa

1N4


1mm4

:eam '

Material --------------- length----------------

Kith ------------------ epth ---------------Moulus of elasti*ity---------------------

Loa

1N4


1mm4

Mechanics of Material Lab6

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Transcript of Mechanics of Material Lab6