tugas as i (kentank)
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Soal 1
Sebuah balok dengan ukuran dan pembebanan seperti tergambar, hitung dan
lukislah luas bidang momen (M) dan bidang gaya lintang (D) nya dengan cara:a. Clapeyron
b. Cross
A3,! m
" C#,!! m
$D
%# & !,' tm
%' & !,! tm' & 3,! t
3 & ',! t# & #,! t
',! $*#,!! $*',! $*
3,! m ',! m ',! m',! m
enyelesaian
A Metode Clapeyron
Momen pada kantile+er
MD & 3. -& ',! . #, & 3 tm
Menghitung putaran sudut akibat beban luar (
o
)/itik A & oA"
oA" & EIEIEI
Lq 0,!,3.!,!.
#-
'..
#-
'33
' ==
/itik " & o"A1 o
"C
o"A & oA" & EI
0,!
o
"C '
##
#'#
#
#
#
3
##
#
.
)(.
2
')#3(.
..2 LEI
bLbPdxxLxLx
LEI
q b
a
++
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&.
)!,'(!,'.!,3.
2
')!'(.
..2 '
##,3
!
#3
#
#
EIdxxxx
EI
q ++
&EI
xxx
EI
00,'
#
!
3
'
-.
!2#,!,3
!
#3-
+
+
&[ ]
EIEI
00,'#,3!2#,2'',3.
!2#,!++
& EIEIEI
2-4,'000,'24,'=+
o" & EIEIEI
#-3,#!2-4,'00,!
=+
/itik C & oC"1 o
CD
oC" & #
##
#'3#
#
#
.
)(.
2
')(.
..2 LEI
aLaPdxxxL
LEI
q b
a
+
&.
)!,'(,3.',!.
2
')(.
..2
',! ##,3
!
3#
EIdxxx
EI
+
& EI
xx
EI
'00,!
-#
'#,'3!2#,!,3
!
-#
+
& EIEIEI
-#-,'00,!##,=+
oCD & 3
##
3#
.
)(.
2
'
LEI
bLbP
&3.
)!,'3(!,'.!,#.
2
' ##
EI
& EI
-3,4
o
C & EIEIEI
42','-3,4-#-,=+
Menghitung putaran sudut akibat Momen (')
/itik A & 'A"
'A" & EI
LM
EI
LM BA
2
.
3
. '' +& EI
M
EI
M BA
2
,-.
3
,-.+
& EI
M
EI
M BA 4,!,' +
/itik " & '"A1 '
"C
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'"A & EI
LM
EI
LM BA
3
.
2
. '' +& EI
M
EI
M BA
3
,-.
2
,-.+
& EI
M
EI
M BA ,'4,! +
'"C & EI
LM
EI
LM CB
2
.
3
. ## +& EI
M
EI
M CB
2
,.
3
,.+
& EI
M
EI
M CB -'2,!433,! +
'" & EI
M
EI
M
EI
M
EI
M CBBA -'2,!433,!,'4,! +++
& EIM
EIM
EIM CBA -'2,!43,#4,! ++
/itik C & 'C"1 '
CD
'C" & EI
LM
EI
LM CB
3
.
2
. ## +& EI
M
EI
M CB
3
.
2
.+
& EI
M
EI
M CB 433,!-'2,! +
'CD & EI
LM
EI
LM DC
2
.
3
. 33 +& EI
M
EI
M DC
2
3.
3
3.+
& EIEI
M
EIEI
M CC !,'22,!
2
3.322,! +=+
'C & EIEI
M
EI
M
EI
M CCB !,'22,!433,!-'2,! +++
& EIEI
M
EI
M CB !,','-'2,! ++
Menentukan persamaan '& !
'A & !A
& EIEIM
EIM BA 0,!4,!,' =+
& ', MA1 !,4 M"& !,0 (pers *)
'" & !"
& EIEI
M
EI
M
EI
M CBA #-3,#!433,!43,#4,! =++
& !,4 MA1 #,43 M"1 !,433 MC& #!,#-3 (pers **)
'C & !C
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& EIEIEI
M
EI
M CB 42','!,','-'2,! =++
& !,-'2 M"1 ', MC1 ',! & ',42' (pers ***)
ersamaan * dan **
', MA 1 !,4 M" & !,0 5 #,43
!,4 MA 1 #,43 M" 1 !,-'2 MC & #!,#-3 5 !,4
-,#! MA 1 #,#2! M" & ',32
!,2 MA 1 #,#2! M" 1 !,32- MC & ','#
3, MA 1 !,32- MC & 6'2,'2 (ers *7)
ersamaan ** dan ***
!,4 MA 1 #,43 M" 1 !,-'2 MC & #!,#-3 5 !,-'2
!,-'2 M" 1 ', MC & '-,42' 5 #,43
!,32- MA 1 ',!- M" 1 !,'3 MC & 4,#-'
',!- M" 1 3,4- MC & 34,34
!,32- MA 8 3,!' MC & -2,434 (ers 7)
ersamaan *7 dan 7
3, MA 1 !,32- MC & 6'2,'2 5 !,32-
!,32- MA 8 3,!' MC & -2,434 5 3,
',32 MA 1 !,'3# MC & 6,444
',32 MA 8 '3,44'MC & ',2-#'3,-0 MC & '4',3
MC & 6'3,#!3 tm
Masukkan MC ke persamaan ***
!,-'2 M" 1 ', MC & '-,42'
!,-'2 M" 1 ', (6'3,#!3) & '-,42'
!,-'2 M" & -,0--
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M" &
-'2,!
0--,-
& '',433 tm
Masukkan M" ke persamaan *
', MA 1 !,4 M" & !,0
', MA 1 !,4 ('',433) & !,0
', MA & 60,4!#
MA & 6,2!' tm
Momen pada cantile+er
MD & 3 . l-
& ', . #,!
& 3 tm
9adi besar momen clapeyronnya
MA & 6,2!' tm
M" & '',443 tm
MC & 6'3,#!3 tm
MD & 3 tm
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B. Metode Cross
I. Stiffness Factor (SF)
A"& "A&,3'
EILEI =
& !,-#4 $*
"C& C"
EI
L
EI=
& !,- $*
CD& DC&33
EI
L
EI=
& !, $*
"A: "C& !,-#4 : !,-
C": CD& !,- : !,
II. Distribute Factor (DF)
M"A&4#4,!
-#4,!
& !,'2
M"C&4#4,!
-,!
& !,-43
MC"&0,!
-,!
& !,---
MCD&0,!
,!
& !,2
III. Momen-momen primer aibat beban luar
%' & !,! t(m
',! $*
3,! mA "
"atang A 6 "
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MA" & '#
,3!,!
'#
##
'' = l
& !,'!- tm
M"A & 6 MA"& 6!,'!- tm
3,! m"
%# & !,' t(m
#,!! $*
"atang " 6 C
M"C
#-3##
#)(
-
')(
3
#)(
#
'
l
Pabaalal
l
q+
+
#-3##
#
!,',3!,3),3(
-
'),3(
3
#),3(
#
'
',! +
+
& !,!!2 ;'3,'# 8 '-#,0# 1 3,'< 1 ','!#
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& ',30-3 tm
MC" & 6#
#-3
#)(
-
')(3
'
l
bPaaall
q
& 6#
#-3
#
!,',3),3(
-
'),3(
3
'
',! +
& 6 !,!##2 ;#!,-'2 8 3,'< 8 3,2
C D
)# & #,! t
',! m ',! m
& 6!,342 8 3,2 & 6 -!2' tm
"atang C 6 D
MCD
#
l
Pab
#
3
!,'!,'!,#
& !,03 tm
MDC
#
l
bPa
#
3
!,'!,'!,#
& 6!,03 tm
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D $
)3 & ',! t
#,!! m
"atang D 6 $
MD$ &lP 3 & ',! . # & 3 tm
/itik A " C D
"atang A" "A "C C" CD DC D$
D= & 6 M ! 6!,'2 6!,-4- 6!,--- 6!,2 6' 6
M primer !,'!- 6!,'!- ',30-3 6!,-!2' !,03 6!,03 3
6!,#
6!,!'
6!,'-
6!,!3
!,'''
6!,-4'4
!,!240
6!,!333
!,##3
6!,#-!0
!,'34
6!,!'22
6',!3'3
!,#0
6!,!20-
!,'#
6!,#'
6#,!2#
!,'340
6!,'340
!,!423
6!,!423
9umlah !,#3 6',!00 ',!02 6!,3!#4 !,3!'0 63,!! 3,!!
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*7. enggambaran bidang momen (M)
"atang A 6 "
>A& >"'& #
!,!,3
& !,4 t
Mma?&
#
4
'lg
&
#,3!,!
4
'
& !,22 tm
3,! m" C
%# & !,' t(m
)' & 3,! t
',! m
"atang " 8 C
>"#&
!,3,'
,3,3',! +
& ',-' t
>C'&
!,3,'
,',3',! +
& ',#3- t
Mma? &
#
##
'xqxRB
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&
#',!#
'-',' xx
& ',-'? 8 !,!?#
Mma?!=
dx
dMx
',-' ? 8 !,! ?#
',-' 8 !,' ? & !
? & ',!
-','
& 0,-- m
M ma? 0,--dari titik "
Mma? & ',-'? 8 !,!?#
& ',-' (-,--) 8 !,! (0,--)#
& 2,20# tm
C D
)# & #,! t
',! m ',! m
"atang CD
>C#& 3
!,'!,#
& ',# t
>D'& 3
!,'!,#
& ',# t
Mma?& >C#. ',!
& ',# . ',! & ',4 t
"atang D$
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D $
3 & ',! t
#,!! m
MD$ &lP 3 & ',! . # & 3 tm
7. enggambaran bidang gaya lintang
>A& >A'1
+
'l
MM BAAB
& !,4 1
,3
!0,'#3',!
& !,22 t
>"kr& >"'6 & !,4 6
,3
!0,'#3',!
& ',!0- t
>"kn& >"#1
+
#l
MM CBBC
& ',-' 1
3!#4,!!02,'
& #,-' t
>A& >"kr1 >"kn& ',!0# 1 #,-' & 3,!4 t
>Ckr& >C'6 & ',#3- 6
3!#4,!!02,'
& !,#3 t
>Ckn& >C#1
+
3l
MM DCCD
& ',# 1
3
!!,33!'0,!
& !,# t
>C& >Ckr1 >Ckn& !,#3 8 !,# & 6! 3' t
>Dkr& >D'8
+
3l
MM DCCD
& ',# 8
3
!!,33!'0,!
& ',0-4' t
>Dkn& 3& ',! t
>D& >Dkr1 >Dkn& ',0-4' 1 ',! & 3,--4' t
+
'lMM BAAB
+
#l
MM CBBC
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%# & !,' t(m%' & !,! t(m
)' & 3,! t)3 & ', t
',!! $*#,!! $*',! $*
)# & #,! t
',!m',!m3,!m ',! m #,!! m3,!m
#,#0
2,20#
',4
6,2!'
'',44 3
6'3,#!3
3
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!,22
',!0-
#,-'
,#
!,#3
!,#
',0-4'
',
!,#3
',
',0-4'
!,#
%# & !,' t(m%' & !,! t(m
)' & 3,! t)3 & ', t
',!!$*#,!!$*',!$*
)# & #,! t
',! m',! m3,!m ',! m #,!! m3,! m
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D
C"
A
-,# m
-,# m
-,# m
3 & ', t
@
4, m
' & , t
%' & !, tm
$
', m
, m
# & #, t
onstruksi portal dengan ukuran dan pembebanan seperti tergambar. itung dan
lukislah bidang momen lengkung (M) bidang gaya lintang (D) dan bidang normal
(B) dengan cara :
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a. clapeyron
b. cross
enyelesaian
A. metode clapeyron
menghitung putaran sudut (!) akibat beban luar
/itik "
!"&
( )] ( ) ( )hEI
hP
lEI
blbP
EI
xllxxq
+
+
2
#,-#,-
2,'#2
##
'3
'
##
''
#,-
!
##3-
-'
&
( )] ( ),'#2
,4,'#,4,
,2
,'#,'#,! ###,-
!
##3-
-'
++
EIEI
xxx
( ),42
#,-,4#,-,' ##
EI
&
( )EIEIEI
0!#,'0',
,2
#,-,'##,-,'##,-,! ##3--'
++
& EIEIEI
0!#,'0',00','0+
& EI
#4,2
/itik C
!C&
( ) ( )] #,-!
-
-'##
#'
##
'
2xxlq
lEI
alaP+
&
( ) ( ),'#2
#,-#,-,'#,!
,'#2
#,-,'##,-,-
-'##
#'##
+
EIEI
& EIEI
030,'3'#,--+
& EI
-22,
/itik DoD& !
Menghitung putaran sudut akibat momen (')
/itik "
'"&EI
lM
EI
lM
EI
hM
h
CBBCBA
233
'''
'
+++
& EI
M
EI
M
EI
M CBBCBA
2
,'#
3
,'#
3
,4
,4+++
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& EI
M
EI
M
EI
M CBBCBA '#,##,-433,#''2,! +++
& #,443 M"A1 -,# M"C1 #,'# MC"8 !,''2 $*
/itik C
'C& #
##''
2332 hEI
hM
EI
hM
EI
lM
EI
lM DCCDCBBC ++
& ,2
,
3
,
3
,'#
2
,'# ++
EI
M
EI
M
EI
M
EI
M DCCDCBBC
&
'4',!0'2,!433,'#,-'#,#
++EI
M
EI
M
EI
M
EI
M DCCDCBBC
/itik D
'D& hEI
hM
EI
hM DCCD ++32
##
& ,3
,
2
, ++
EI
M
EI
M DCCD
&'4',!
033,'0'2,!++
EI
M
EI
M DCCD
Menentukan persamaan
(
'
&
!
) #,433 M"A1 -,# M"C1 #,'# MC"8 !,''2 $*& 2,#4
(pers ')
#,'# MCD 1 -,# M"C 1 ',433 MDC 8 !,0'2 MC" 8 !,'4' $* &
,-22 (pers #)
!,0'2 MCD 1 ',433 MDC 1 !,'4' $*& !
(pers 3)
Dititik C berlaku
MC"& MCD1 MC$MC$& #, . ', & -,3 tm
MC"& MCD1 -,3
(pers -)
Dititik D berlaku
M"A& 6 M"CM"C& 6 M"A
(pers )
& !
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!,4
#,-
,,,4
3 =
++ PMMM DCCDBA
!,''2 M"A8 !,'4' MCD1 !,'4' MDC1 #, & ! (pers 2)
ersamaan 2
M"A & ''2,!
,#'4',!'4',! DCCD MM
& ',30 MCD8 ',30 MDC8 #3,34- (pers )
ersamaan ' dan
#,433 M"A1 -,# 6 M"A1 #,'# MC"8 !,''2 $* & 2,#4
6',-' M"A1 #,'# MC"8 !,''2 $* & 2,#4
(pers 4)
ersamaan - dan 4
6',-' M"A1 #,'# (MCD1 -,3) 8 !,''2 $* & 2,#4
6',-' M"A1 #,'# MCD8 !,''2 $* & ,043
(pers 0)
ersamaan dan 0
6',-' (',30 MCD8 ',30 MDC8 #3,34-) 1 #,'# MCD8 !,''2 $* & ,043
6#,'4 MCD1 #,'4 MDC1 33,'3 1 #,'# MCD8 !,''2 $* & ,043
6!,! MCD1 #,'4 MDC8 !,''2 $* & 0',''4
(pers '!)
ersamaan - dan #
#,'# MCD 1 -,# M"C1 ',433 MDC6 !,0'2 (MCD1 -,3) 6 !,'4' $* &
,-22
',#!0 MCD 1 -,# M"C1 ',433 MDC8 !,'4' $* & 2',-
(pers '')
ersamaan 3 dan''
-,# M"C1 ',#!0 MCD 1 ',433 MDC8 !,'4' $* & 2',-
!,0'2 MCD 1 ',433 MDC1 !,'4' $* & !
-,# M"C1 ',!# MCD 1 3,222 MDC& 2',-
(pers '#)
ersamaan dan '#
-,# (6M"A) 1 ',!# MCD 1 3,222 MDC& 2',-
(pers '3)
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ersamaan 0 dan 3
6',-' M"A1 #,'# MCD8 !,''2 $* & ,043 5 !,'4' !,0'2 MCD 1 ',433 MDC1 !,'4' $* & ! 5 !,''2
6!,#2 M"A1 !,34- MCD8 !,!#'# $* & '!,-0
6!,'! MCD 1 !,#' MDC1 !,!#'# $* & ! (1)
6!,#2 M"A1 !,# MCD 1 !,#' MDC & '!,-0
(pers '-)
ersamaan dan '3
-,# (',30 MCD8 ',30 MDC8 #3,34-) 1 ',!# MCD 1 3,222 MDC& 2',-
62,- MCD1 2,- MDC1 00,34# 1 ',!# MCD 1 3,222 MDC& 2',-
6,!34 MCD1 '!,#!2 MDC& 63,2#4
(pers ')
ersamaan dan '-
6!,#2 (',30 MCD8 ',30 MDC8 #3,34-) 1 !,# MCD 1 !,#' MDC& '!,-0
6!,30- MCD1 !,30- MDC1 ,042 1 !,# MCD 1 !,#' MDC& '!,-0
6!,'' MCD1 !,2!0 MDC& '!,-0
(pers '2)
ersamaan ' dan '2
6,!34 MCD1 '!,#!2 MDC & 63,2#4 5 !,''
6!,'' MCD1 !,2!0 MDC & '!,-0 5 ,!34
6!,40 MCD1 ','0- MDC & -,-!#
6!,40 MCD1 3,!24 MDC & #,4-
6',4- MDC & 6-4,-#
MDC & #,42 tm
ersamaan '
6,!34 MCD1 '!,#!2 (#,42) & 63,2#4
MCD& 0,422 tm
ersamaan '3
6-,# M"A1 ',!# (0,422)1 3,222 (#,42) & 2',-
6-,# M"A& 6'##,04
M"A& #4,03 tm
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ersamaan 3
!,0'2 (0,422) 1 ',433 (#,42) 1 !,'4'.'!!!. & !
&2,!
'4'
#-,'!#=
ersamaan
M"C& 6 M"A& 6#4,03 tm
ersamaan -
MC"& MCD1 -,3
& 0,422 1 -,3& 2-,#-' tm
esimpulan
MA"& !
M"A& #4,03 tm
M"C& 6#4,03 tm
MC"& 2-,#-' tm
MC$& -,3 tm
MCD& 0,422 tm
MDC & #,42 tm
Metode Cross
I. Stiffness Factor (SF)
A"& "A&,4-
3
-
3
' = EI
L
EI
& !,!44# $*
"C& C"& ,'#
EI
L
EI=
& !,!4- $*
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CD& DC&
,
EI
L
EI=
& !,'4'4 $*"A: "C& !,!44# : !,!4-
C": CD& !,!4- : !,'4'4
II. Distribute Factor (DF)
M"A&'2'2,!
!,!44#
& !,#0
M"C&'2'2,!
!4-,!
& !,-'
MC"& #2!#,!
!4-,!
& !,3!'
MCD!#,!
'4'4,!
& !,200
III. Momen primer
"atang A"
M"A &
( )#
##
#l
alPab
&
( )#
##
,4#
#,-,4#,-#,-,'
& 6'',43 tm
"atang "C
M"C
#-3##
#)(
-
')(
3
#)(
#
'
l
Pabaalal
l
q+
+
&
#
#-3##
# ,'#
,4#,-,)#,-(
-
')#,-(,'#
3
#)#,-(,'#
#
'
,'#
,! +
+
&
[ ]4',23-2#,!4'-24,'-#,'#
,!#
+1 '!,344
& -,#234 1 '!,344 & '-,2'4 tm
MC" & 6
+
#
#-3
#)(
-
')(
3 l
bPaaa
l
l
q
& 6
#
#-3
#,'#
,4#,-,)#,-(
-
')#,-(
3
,'#
,'#
,! +
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& 6 ','#40 1 ,'0-- & -,!2 tm
MD$ & ,'#P & #, . ', & -,3 tm
!er"itun#an ta"ap I diasumsian seba#ai portal ta ber#oyan#
I$. !"ase I (dipasan# pendel)
" C D
"A "C C" CD DC D$
6!,#0 6!,-' 6!,3!' 6 6!,200 6
6'',43 '-,2'4 -,!2 -,3 6 6
6!,4!42
6!,!#426!,!!!'
6',#!3
6!,'00!,!-'
6!,!#-
!,!!'0
6!,!!!4
6#,-!2
6!,300!,'!43
6!,!'#
!,!!34
6!,!!!-
6,4000
!,#'2!,!!44
6#,0-00
!,'#4!,!!--
6'#,20!3 '#,20'- ',#2- -,3 6,230 6#,4'0
$. !"ase II pendel dilepas%portal diberi pergoyangan yang menyebabkan
adanya momen primer
dd" C $$*
A
$*h'
D
$*h#
M"A &
#
'
3
h
EI
diasumsikan $* & '!!!
,4
.'!!!.3
& -',##
MCD& MDC
#
2
h
EI
,
.'!!!.2
& '04,3-
/abel perhitungan
" C D
"A "C C" CD DC D$
6!,#0 6!,-' 6!,3!' 6 !,200 6
-',## '04,3- '04,3-
-
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62,'3
6!,#'4
6!,!!
6#0,4'
6,-0
!,-'36!,'0-
!,!'-
6!,!!2
60,!#
6#,-4
!,4#6!,!0
!,!#0
6!,!!3
6'34,2--
6',0#'
!,!24
620,3##
!,02!
!,!3-
3,'#- 63,'#' 62',242 2',20# '3!,!'0
" $C
A
)3 & ', t
3,'#-6 '#,20!3
@
D
6#,4'0'3!,!'0
2',20#6,230
%' & !, t(m
)' & , t
)# & #, t
& !
,4
#,-,'
,
4'0,#!'0,'3!
,
230,20#,2'
,4
'#20!3'#-,3
+
+
34,044 & 3,0!2
& !,'!!
$I. &asil momen a"ir
"A "C C" CD DC D$
6'#,20!3
3,'#-
'#,20'-
63,'#'
',#2-
62,'242
-,3
6
6,230
2,'20#
6#,4'0
'3,!!'0
60,'0 0,'03 6-,0!-2 -,3 !,#0 '!,'4##
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$II. !en##ambaran bidan# momenerhatikan =ree body masing6masing batang akibat beban luar, momen6
momen simpul diabaikan
batan# BC (batan# "orisontal)
-,# m
"4, m
%' & !, t(m
)' & , t
', m
C
)# & #, t
>"'& ,'#
,42#,'!#,- '+ Pq
& 2,3#3 t
>C'& ,'#
'#,##,-#,- +p
& #,32 t
Mma?!=
dx
dMx
Mma? &
#
#
'xqxRB
,!3#3,2 xx
dx
dMx
& 6!, ? 1 2,3#3 & !
? & ,!
3#3,2
& 4,-3 dari "
Mma?& 2,3#3 (4,-3) 8 !,3 (4,-3)#
& #2,2 tm
batan# AB (batan# 'ertial)
Ah'& ,4
#,-3P
& ,4
#,-,'
& !,4 t
"h'& 38 Ah'
& ', 8 !,4 & !,4 t
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M@ & Ah'. -,#
& !,4 . -,# & 3,'4 tm
$III. !en##ambaran bidan D
easi 'ertial
>" & >"'1 L
MM CBBC+
& 2,3#3 1 ,'#
!2,-2'4,'- +
& ,0' t
>C'& >C'8 #l
MM CBBC+
>C#& #& #, t
& #,32 8 ,'#
!2,-2'4,'- +
& !,40 t
>C & >C'1 >C#
& !,40 1 #,
& 3,30 t
Check
>"
1 >C& % (-,#) 1 '1 #
,0' 1 3,30 & !, (-,#) 1 , 1 #,
'','44 & '','4
'','44 & '','44 E
easi "orisontal
Ah & Ah'1 'h
MBA
& !,4 1 ,4
'0,0
& 6!,#!- ton
"h & "h'8 'h
MBA
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& !,4 8
,4
'0,0
& ',0- ton
Dh & #h
MM DCCD+
& ,
'4##,'!#0,! +
& ',0- ton
Check
& !
Ah 1 Dh & 3
6!,#!- 1 ',0- & ',
',-3 & ', E
I. !en##ambaran bidan# *
Faya normal "atang A"
&>"
& >"'1 L
MM CBBC+
& 2,3#3 1 ,'#
!2,-2'4,'- +
& ,0' t
Faya normal "atang CD
& >C& >C'1 >C#
>C'& >C'
8 #l
MM CBBC+
>C#& #& #, t
& #,32 8 ,'#
!2,-2'4,'- +
& !,40 t
>C& !,40 1 #,
& 3,30 t
Faya normal "atang "C
& Dh
& ',0- t
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A-,!! m
"#,! m
C',! m
$D
%# & !,# tm
%' & !, tm' & t
3 & #, t# & - t
',! m 3,! m
',!! $*',! $*',!! $*
#,! m
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