HES1125
Mechanics of Structures
Lecturer Name Saravana Kannan Thangavelu Student Na Name/ ID ID Muaid Abdul Kareem Alnair !" !"2#$11"% Lab Date 21/1#/2##& Submi''i(n Date #5/11/2##& Lab )e*(rt !+ENDIN, ST)ESS IN A +EAM%
1. Objective 1-1 T( inve'tigate bending 'tre'' in a beam
2. Equipment 2-1 Te't .rame 2-2 L(ading rame and ST)0A L(ad ell 2- An inverted T3'ha*ed aluminum beam itted 4ith nine 'train gauge' re'ting (n t4( r(ller 'u**(rt2-" Digital (rce and 'train di'*la unit'
3. Theory
In thi' e6*eriment7 4e are g(ing t( u'e the bending m(ment a**aratu' a' 'h(4n in .igure 1- + u'ing ST)0A l(ad cell7 4e are able t( c(ntr(l the l(ad that 4e a**l t( the T beam re'ting (n the r(ller 'u**(rt'- + u'ing the 'train gauge' and digital 'train di'*la that i' c(nnected t( the 87 4e are able t( (btain the l(ad reading at nine dierent gauge *('iti(n'- .r(m the reading'7 4e are able t( (b'erve the bending m(ment and relati(n'hi* bet4een 'train and bending m(ment-
4. Experimental Procedure
"-1 En'ure the beam and L(ad ell are *r(*erl aligned- Turn the thumb4heel (n the L(ad ell t( a**l a !*('itive d(4n4ard% *rel(ad t( the beam ( ab(ut 1## N- 9er( the L(ad ell u'ing the c(ntr(l e:ui*ment *r(vided"-2 Ta;e the nine er( 'train reading' b ch(('ing the number 4ith the 'elect(r '4itch- .ill in Table 1 4ith er( (rce value'"- Increa'e the l(ad t( 1##N and n(te all nine ( 'train reading'- )e*eat the *r(cedure in 1##N t( 5##N- .inall< graduall relea'e the l(ad and *rel(ad"-" (rrect the 'train reading value' t( er( and c(nvert the l(ad t( a bending m(ment then ill in Table 2 "-5 .r(m (ur re'ult'7 *l(t a gra*h ( 'train again't bending m(ment (r all nine 'train gauge' !(n the 'ame gra*h%-
5 ata !heet The'e are the data (btained r(m the e6*eriment,auge 1 2 " 5 = $ 0 &
L(ad !N% # 1## 2## ## "## 315-# 3$$-5 31"5-" 321- 32#-= 3&-" 3"0-& 30&-= 31"=-" 321# 3$-$ 351- 3&0-& 315=- 321&-1 35-$ 3-5 31-2 3$-5 315-0 3#-" 1-& "-# 5-= $-2 3#-= #-" ="-$ &1-" 110-" 12-2 22-# &-5 5=- $#-= 0- "5-= "0-0 51-2 5- 1"-& 0 $#-0 1#"-" 1$-5 Table 1 )e'ult' (r e6*eriment !unc(rrected%
5## 3"2-0 320#-$ 320&-1 32-$ &-1 1"5- 00-0 5=-2 1$5-2
,auge 1 2 " 5 = $ 0 &
# # # # # # # # # #
L(ad !N% 1## 2## ## "## 3=2-5 31#-" 321=- 3#5-= 3&-5 30#-2 31$-# 32##-= 3"-= 3&1-2 31"0-= 3211-" 2-2 "-5 31-0 31#-1 2- "-" =-# $-= 1-# =5- &2-# 11&-# &-0 2$- ""-1 50-" $- "#-5 "2-& "5-# 2-1 55-& 0&-5 122-= Table 2 )e'ult' (r e6*eriment !c(rrected%
". #odel $alculation ra% &' and (# dia)ram!.
'i)ure 2 'ree body dia)ram o* the T beam
+'y,-
/y0(y 2 2 ,/y, (y
+#/,-
26-.35m6 26-.475m6 0 -.735m6(y,(y , -.4185m6-.735m6 (y, -.5 /y, -.5
&ection 19 M
- : x ; -.35
V
>/2
5## 3"#0-0 32$1- 3201-" 310 &-5 1"5-& $=-= "$-& 1=#-
x
?.@#7
@ >/2
?MNA@#7
M3 !>/2%!6%@# M@ !>6%/2
At 6@ #7
@ >/2 and M@#
At 6@#-5m
@ >/2 and M@ #-1$5 >
Secti(n 2 - .35 : x ; -.475
W/2
M x- 0.35m
0.35m x
V
>/2 ?.@#7
@ #
?MNA@#7
M3 !>/2%!6% B !>/2%!63#-5m% @# M@ !>6%/2 C !>6%/2 B #-1$5> M@ #-1$5>
At 6@ #-5m7
@ # and M@#-1$5>
At 6@#-"05m 7
@ # and M@ #-1$5 >
Secti(n - .475 : x ; -.735
W/2
W/2
M
0.35m
0.135m
x-0.485m
V
x
>/2 ?.@#7
@ 3>/2
?MNA@#7
M3 !>/2%!6% B !>/2%!63#-5m% B !>/2%!63#-"05m%@# M@ !>6%/2 C !>6%/2 B #-1$5> 3 !>6%/2 B #-2"25> M@ 3!>6%/2 B #-"1$5>
At 6@ #-"05m7
@ 3>/2 and M@ 3#-2"25> B #-"1$5> @ #-1$5>
At 6@#-05m 7
@ 3>/2 and M@ 3#-"1$5> B#-"1$5> @#
V (! W/2
0 -W/2
M m 0.175 W 0
.igure Shear .(rce and +ending M(ment Diagram
r('' 'ecti(n anal'i' ( the T beam
.igure " r('' 'ecti(n ( the T beam !dimen'i(n' are in millimeter'%
entr(id y @ ?iAi/ ?Ai @ !22-52#2-00%B!-22"-0"%Fmm/!2#2-00B2"-0"%mm2 @ 11-052mm Segment I
A !1-$%!=-"%mm2
22-5mm
d !22-25311-05%mm
I66@ bh/12 !=-"%!1-$%F/12
A-d2 !2#2-00mm2%!1#-"mm%2
@1#-"mm
@ 1-=&0&61#"mm"
@21-&"61#mm"
!-2311-05%mm
!0-1%!=-"%F/12
!2"-0"mm2%!30-=5mm%2
@ 30-=5mm
@02-#$2mm"
@10-261#mm"
@ 2#2-00mm2 II
!0-1%!=-"%mm2
-2mm
@ 2"-0"mm2
Table alculati(n table
M(ment ( inertia ab(ut the neutral a6i' I6(@ I I76( B I II76( @!1-=&0&61#" B 21-&"61#%mm"F B !02-#$2B10-261#%mm"F @ 50-#61# mm" @50-#61#3& m"
.igure 5 r('' 'ecti(n ( the T beam 4ith gauge *('iti(n !dimen'i(n' are in millimeter'%
y3di'tance bet4een neutral a6i' and gauge' y1 @ 0-1 C 11-05F mm @ 2=-25mm
y27 @ #-1 C 11-05F mm @ 10-25mm y"75 @ 15-13 11-05F mm @ -25mm y=7$ @ 11-05 C =-"F mm @ 5-"5mm y07& @11-05 mm .le6ure +ending .(rmula The bending 'tre'' at a cr('' 'ecti(n at an di'tance y r(m the neutral a6i' i' given a'G
4here7 M @ +ending m(ment @ +ending 'tre'' I @ Sec(nd m(ment ( area ab(ut the neutral a6i' Acc(rding t( H((;e' La47 @ E J 4hich lead' t(7
E <
<, #y =E (i) 4here7 J @ Strain E @ (ung' m(dulu' !(r aluminium7 E @ =&1#& 8a%
8. >e!ult! and i!cu!!ion ?au)e
(endin) #oment @m6
y po!ition m6
-
18.5
35
52.5
8-
78.5
1
#
31-="#=25
3-"2
35-=$$0$5
30-#22
31#-$1
#-#2=25
2
#
3#-$2#0$5
31-"==5
32-5##25
3-==#&5
3"-&51225
#-#1025
3
#
3#-$&5$
31-==""
32-$11&5
3-050#5
35-1555
#-#1025
4
#
#-##$15
#-#1"=25
3#-##505
3#-#2025
3#-#505
#-##25
5
#
#-##$"$5
#-#1"
#-#1&5
#-#2"$
#-##0$5
#-##25
"
#
#-1=0&5
#-55005
#-5#1"
#-="055
#-$&5155
#-##5"5
8
#
#-#5"1
#-1"0$05
#-2"#"5
#-1020
#-"1$"$
#-##5"5
7
#
#-""2##5
#-"$&&25
#-5#0=5
#-525
#-5=$=15
#-#1105
A
#
#-2$$5
#-==2"15
1-#=#5$5
1-"5201
1-0&&555
#-#1105
Table" "esu#ts for ex$eriment in terms of %en&in' moment (ith )-$osi*on inc#u&e&!
?au)e
(endin) #oment @m6 -
18.5
35
52.5
8-
78.5
&train 1
#
31-#$=12 61# 35
32-2"522 61# 35
3-$2"2" 61# 35
35-2=101 61# 35
3$-#0$ 61# 35
2
#
3-20$5 61# 3=
3=-=$"5$ 61# 3=
31-1"#1$ 61# 35
31-==&"$ 61# 35
32-25$& 61# 35
3
#
3-=205$ 61# 3=
3$-5&## 61# 3=
31-2=$1 61# 35
31-$5&= 61# 35
32-"1& 61# 35
4
#
5-0#="$ 61# 3&
1-10$=& 61# 30
3"-$5#$5 61# 3&
32-==5$ 61# 30
3"-$5#$ 61# 30
5
#
=-#$#" 61# 3&
1-1=12& 61# 30
1-5050 61# 30
2-##50$ 61# 30
2-5#$" 61# 30
"
#
2-##$& 61# 3$
"-0"=51 61# 3$
=-0201= 61# 3$
0-02#0 61# 3$
1-#020= 61# 3=
8
#
$-2$"0 61# 30
2-#2=10 61# 3$
-2$#= 61# 3$
"-"" 61# 3$
5-=051&E3#$
7
#
1-#0$& 61# 3=
1-"21#$ 61# 3=
1-5#520 61# 3=
1-5$0&= 61# 3=
1-=0#$2 61# 3=
A
#
0-1#55E3#$
1-&=1"2 61# 3=
-1"#0 61# 3=
"-#10 61# 3=
5-=2"=2 61# 3=
Table5 Strain in dierent gauge' 4ith vari(u' bending m(ment u'ing e:uati(n (i)
?au)e
(endin) #oment -
18.5
35
52.5
8-
78.5
&train 1
0
-1.07+12x10-5
-2.24522 x10-5
-3.72424 x10-5
-5.2+181 x10-5
-7.0387 x10-5
23
0
-3.457,+ x10-+
-7.1323 x10-+
-1.18844 x10-5
-1.71441 x10-5
-2.2,,, x10-5
45
0
5.,3844 x10-,
1.1744, x10-8
5.54254 x10-,
-3.2,,13 x10-,
-1.1217 x10-,
"8
0
1.51407 x10-7
3.43+35 x10-7
5.050+1 x10-7
+.58324 x10-7
8.25+88 x10-7
7A
0
1.05,++ x10-+
1.+,125 x10-+
2.32283 x10-+
2.,4038 x10-+
3.+52+7 x10-+
16 hat i! the relation!hip bet%een the bendin) moment and !train at the variou! po!ition!B
,ra*h1 +ending M(ment v' Strain
A' the m(ment increa'e' at dierent *('iti(n'7 the value ( the 'train al'( increa'e' !*r(*(rti(nal relati(n'hi*%-
26 hat do you notice about the !train )au)e readin) on the oppo!ite !ide! o* the !ectionB &hould they be identicalB Acc(rding t( the e6*eriment !reer t( table 2% and ater c(rrecting the value' 'till the (**('ite 'ide' are n(t identical- H(4ever acc(rding t( the the(r the (**('ite 'ide' 'h(uld be identical36 =* the readin)! are not identical )ive t%o rea!on! %hyB a% In the the(r 4e a''ume the di'tributi(n ( the l(ad i' uni(rm- H(4ever7 a' the (**('ite 'ide' have dierent reading' in the e6*eriment 4hich mean' the l(ad di'tributi(n i' n(t uni(rm a' it 'h(uld be b% Al'(7 the a**aratu' d(e' n(t give e6act and accurate reading- .(r e6am*le7 4hen the thumb4heel give' a reading ( 1##N the c(m*uter give' either 'lightl m(re (r le'' than 1##N and that 4ill eect negativel (n the mea'urement' and calculati(n'46 hat i! the value o* the !train readin) at neutral axi!B
The value ( the 'train i' er(56 $alculate the maximum !tre!! in the !ection by turnin) the !train! into !tre!! value! at maximum load6. $ompare thi! to theoretical value. Experimentally:
C, E< , "Ax1-A Pa6 8.-378 x1- 56 , 4.758 x1- " Pa Theoretically:
C, #y6= , 1-.831@m6 -.-2"25m6 57D1- A m46 , 4.758 x1- " Pa The e6*erimental value and the(retical value are the 'ame"6 oe! the bendin) equation accurately predict the !tre!! in the beamB e'7 the bending e:uati(n *redict' accuratel the 'tre'' in the beam-
8. Conclusion
The 'train i' directl *r(*(rti(nal t( the bending m(ment- A' the value ( the bending m(ment increa'e'7 the value ( the 'train al'( increa'e'The bending e:uati(n *redict' accuratel the 'tre'' in the beam-
