EXPERIMENT 1: REACTION OF A CONTINUOUS BEAM
INTRODUCTION Several methods had been used to solve the reactions of statically indeterminate beam. For theory, students are advised to use Virtual Work Method, Slope deflection Method or Moment Distribution Method to find reactions of a continuous beam
OBJECTIVE To determine determine at the reaction of a two span continuous beam
APPARATUS The apparatus comprise of . ". #. %. '. (.
! suppo upport rt fram framee # nos. nos. rea react ctio ion n supp suppor ortt pier pier " nos nos.. loa load d han han$e $ers rs &eam &eam spec specim imen en ! mete meterr ruler ruler to meas measure ure the the span span of the the beam beam ! set of of wei wei$h $htt
THEORY Moment Distribution Method) a* +reate +reated d by rof rof -ardy -ardy +ros +ros at #". #". b* !dvanta$es of this method) method) i. /ot /ot usi usin$ n$ e0ua e0uati tion on in solu soluti tion on.. ii. More More mecha mechanic nical al proc process ess and can be chec checked ked easily easily and 0uick 0uickly ly.. iii. The accuracy accuracy depends depends on on the the e0uilib e0uilibrium rium and distribu distribution tion process process that has been done. done.
Distribut Distribution ion Factor, Factor, F! 1
I / L I Σ ( ) L
F2 1 345 60uilibrium Moment, M 1 M ! 7 M& 7 M+ M-T 8point load* 1 549
PROCEDURES . The display display unit is switche switched d on to warm warm up the unit. unit. ". The reaction reaction piers piers are clamped clamped to the the support support frame frame usin$ the the place and and bolt suppli supplied ed with the the apparatus and at predetermine distant between the supports. #. The beam specimen specimen is placed placed between between the two cylindr cylindrical ical pieces pieces of each support support.. The two screws screws are ti$htened at the top of each support with your fin$er. %. The load load han$er han$er is fi:ed fi:ed at the the position position where where the the beam is to to be loaded. loaded. '. The load cell cell from the support support pier is connecte connected d to the display display unit each load load cell occupyin occupyin$ $ one terminal on the display (. &e$innin$ &e$innin$ with with channel channel the the initial initial readin readin$ $ for each each channel channel is recorded recorded.. ;. ! suitab suitable le load is placed placed on the han$er han$er and the readin$ readin$ of each load cell cell is noted. noted. This represent representss the reaction at each pier. 9. The load load on the load han$e han$err is increased increased at suitabl suitablee increments increments and and for each incremen incrementt record record the pier reaction.
DATA / TABLE Table )
Load on LR (N)
' "= "' #= #'
' "= "' #= #'
S!! S!!o" o"## R$a% R$a%#& #&on on E'!$ E'!$"& "& $n# $n# R&+# (N) '.== (.(9 9.#( .% .'%
M&dd,$ (N) ;.9( "#.9( ".(9 #'.;( %.;(
L$-# (N) %.9 (.(( 9.#( ." .'(
S!! S!!o" o"## R$a% R$a%#& #&on on T T$o $o"* "* R&+# (N) %.( (."' ;.9 .#; =.%
M&dd,$ (N) "=.(" ";.'= #%.#9 %."( %9."
L$-# (N) %.( (."' ;.9 .#; =.%
DATA DATA ANALYSIS ANALYSIS / C.P C. P / RAPH RAP H +alculations and ive all important important dimensio dimensions. ns.
?5
?<
5oad on 55
5oad on 5<
55
5<
". Derive Derive the the react reaction ionss at the the supp support orts. s. 6:ample calculation for 6:periment )
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3 I / 1600 0 + 3 I / 1600 1 3 I / 1600 3 I 3 I ( + ) 1 1600 1600
3 I / 1600 9600 I / 2360000
1 =.'
Mo$n Hn+ T$"&0a# (MHT):
MHT AB
MHT BA
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PL 1 8 1
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15 ( 400 ) 1 B;'=/mm 8
15 ( 400 ) 1 ;'=/mm 8
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+& 34%==A#4% 1 #34(==
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MHT BC
MHT CB
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1 = /mm
M BA
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M BC
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#. Gsin Gsin$ $ the the tabu tabula late ted d data data)) i. lot lot the the $raph $raph of reacti reaction on a$ains a$ainstt load load for each each supp support ort.. ii. ii. Draw Draw the the bes bestt fit fit curv curvee thro throu$ u$h h the the plot plotte ted d poin points ts.. iii. Gsin$ the slope slope of the the $raph, $raph, calculate calculate the percenta$e percenta$e error between between the e:periment e:perimental al and and the theoretical reaction.
R$a%#&on a# R&+# 2!!o"#
Graph of Reaction at Right support verses Load 14
12 f(x) = 0.33x + 0.13 R² ==10.31x + 0 f(x) 10
R² = 1
experimental
8
Linear (experimental) Reaction at Right support (N)
theory Linear (theory)
6
4
2
0 10 15 20 25 30 35 40 Load (N)
slopetheory− slopeexp ercenta$e error
1
slopetheory
0.3124 − 0.3268
1
0.3124
1 B %.( H
: ==
: ==
R$a%#&on a# M&dd,$ 2!!o"#
Graph of Reaction Reaction at Middle support verses v erses Load 60
50 f(x) = 1.38x 0 R² = 1 40
f(x) = 1.1!x 0.0" R² = 1 experimental Linear (experimental)
30
Reaction at Middle support (N)
theory Linear (theory)
20
10
0 10 15 20 25 30 35 40
Load (N)
slopetheory− slopeexp ercenta$e error
1
slopetheory
1.3752 −1.1940
1
1.3752
1 #.9 H
: ==
: ==
R$a%#&on a# L$-# 2!!o"#
Graph of Reaction at Left support verses Load 14
12 f(x) = 0.33x + 0.0! R² ==10.31x + 0 f(x) 10
R² = 1
experimental
8
Linear (experimental) Reaction at Left Left support (N)
theory Linear (theory)
6
4
2
0 10 15 20 25 30 35 40 Load (N)
slopetheory− slopeexp ercenta$e error
1
slopetheory
: ==
0.3124 −0.3284
1
0.3124
: ==
1 B '." H
RESULTS OF EXPERIMENT 5eftBhand span of beam, 55
1 %== mm
1 %== mm
Dist Distan ance ce of loa load d fro from m lef leftt han hand d sup suppo port rt,, ?5 ?5
1 "== "== mm
Distan Distance ce of of load load from from ri$h ri$htt hand hand suppo support, rt, ?<
1 "== "== mm
DISCUSSIONS . 3f the material material of the the beam is chan$ed chan$ed from from steel steel to aluminum aluminum,, how does this this effect effect the suppor supportt reactionI >ive reasons for your answer. 3f the material of the beam is chan$ed from steel to aluminum, the support reaction will increase. This is because the aluminum is milder than the steel. So, the more loadin$ that is put to the beam will make it overloaded and fail. ". 3f a thinner beam beam is used, how does does this effect effect the support support reaction reactionII >ive reasons reasons for your answer answer.. 3f the thinner beam is used, the support reaction will also increase. This is because the thinner beam is not stron$er like thicker beam. So, the more loadin$ that is put to the beam will make it bendin$ and fail. #. -ow does does the the e:perimen e:perimental tal reactio reaction n compare compare with with theoret theoreticalI icalI &ased on the percenta$e error that has been calculated, the e:perimental reaction for the ri$ht and left support is over than the theoretical reaction. !t the middle support, the e:perimental reaction is less than the theoretical reaction. This mi$ht happen because of the error in the apparatus or the mistake that we have made durin$ the e:periment. %. Stat Statee the the poss possib ible le fact factor orss that that mi$h mi$htt have have infl influe uenc nced ed your your resu result ltss and and poss possib ible le mean meanss of overcomin$ it. ossible factors) i.
The load load at at the the left left and and ri$ht ri$ht is is not not been been plac placed ed at at the the same same time time..
ii. iii. iii. iv. iv. v.
The indic indicato atorr read readin$ in$ is not not Jero Jero when when plac placin$ in$ the the load load.. The load load han$ han$er er and and the beam beam are are not not fi:ed fi:ed and can movin$ movin$.. The meas measurem urement ent of of distan distance ce betwe between en the the load load and the the suppo support rt is not not corre correct. ct. The indic indicato atorr read readin$ in$ is not not stati staticc when when readin readin$ $ is taken taken..
ossible means) i. ii. iii. iii. iv. iv. v.
ut ut the the loa load d at at the the left left and and ri$ ri$ht ht at the the same same time time.. !lways !lways press press the the tare tare butto button n if the indicator indicator readin$ readin$ is is not not Jero Jero before before placin$ placin$ the the load. load. Ti$ht Ti$hten en the the scre screw w ti$ht ti$htly ly at all the suppor supportt and the load load han$e han$er. r. Take Take the the measure measurement ment carefully carefully and correctly correctly to avoid avoid the error in the the e:perim e:periment ent data. data. Take Take the the readin readin$ $ only only if if the the indicato indicatorr readin$ readin$ is stabl stablee and not chan$e chan$e anymore. anymore.
CONCLUSION &ased on the e:periment that we have conducted, we can conclude that the value of the reaction at the ri$ht and the left support is the same and the value of the reaction at the middle is the bi$$est. This shows that the middle support will support more loadin$ compared to the left and ri$ht support and the total load that supported by the beam is e0ual to the total reaction at the three supports since the continuous beam is in e0uilibrium.
RECOMMENDATIONS RECOMMENDATIONS / COMMENTS i. ii. iii. iii. iv. iv. v. vi.
Make sure sure that that all all the screws screws are ti$htened ti$htened properly properly to avoid avoid the the beam beam and and the the load han$er han$er from from movin$. Take Take the the readin$ readin$ at at the indicator indicator only when the indic indicator ator is is stop stop or the readin readin$ $ is stable. stable. The dist distanc ancee of the the load load and the the suppo support rt must must be at at the corr correct ect measu measurem rement ent.. The load load should should be on on the the static static state state duri durin$ n$ the the read readin$ in$ is take taken. n. The readin readin$ $ on the the indicato indicatorr should should alway alwayss be Jero Jero before before placi placin$ n$ any load on the the beam so that that it will not affect the value of the data. ut the the loads loads slow slowly ly at the the load load han$e han$err to preve prevent nt the the dama$e dama$e to to the indi indicat cator or..
REFERENCE / ATTACHMENT <6F6<6/+6 M.2. -urst. 99.
!nalysis Structure Module. Stren$th of Materials and Structure Module. Desi$n of +oncrete and
!TT!+-M6/T
+ontinuous &eam
