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7/23/2019 60302536 Unit 14 Design of Slender Columns
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
UNIT 14
DESIGN OF SLENDER COLUMNS
GENERAL OBJECTIVE
To be able to identify te b!a"ed #lende! "ol$%n# de#i&n '!in"i'le# a""o!din& to
B( )110 !e*$i!e%ent#+
At te end of ti# $nit yo$ ,ill be able to "al"$late-
1+ te %ini%$% e""ent!i"ity.%in
e +
+ te defle"tion . ua $#in& e*$ation 3
3+ te !ed$"tion fa"to!. $#in& e*$ation 33
4+ te additional %o%ent $#in& e*$ation 3
+ te initial end %o%ent# $#in& e*$ation 32
2+ te a!ea of lon&it$dinal !einfo!"e%ent+
+ te #ie and #'a"in& of late!al !einfo!"e%ent 5tie#6+
)+ #7et" te !einfo!"e%ent# detail# in #lende! "ol$%n#+
1
OBJECTIVES
(8ECI9IC OBJECTIVE(
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
14+1 Slender Columns
A b!a"ed #lende! "ol$%n i# defined a# a "ol$%n in ,i" te effe"ti:e
ei&t/de't !atio i# &!eate! tan 1+ Te #t!en&t of #lende! "ol$%n# i#
#i&nifi"antly !ed$"ed by t!an#:e!#e defle"tion#+ Te #lende!ne## effe"t !ed$"e# it#
load;"a!!yin& "a'a"ity+ If te "ol$%n i# #o!t. te defle"tion i# #%all and en"e
te additional %o%ent i# ne&li&ible. "o%'a!ed ,it te initial %o%ent+ If te
"ol$%n i# #lende!. te defle"tion i# no lon&e! #%all. ten te additional %o%ent
be"o%e# #i&nifi"ant "o%'a!ed to te initial %o%ent+ Te additional %o%ent
#o$ld ten be "on#ide!ed if te effe"ti:e ei&t/de't !atio i# &!eate! tan 1+ If
te "ol$%n i# :e!y #lende!. te "ol$%n ,ill *$i"7ly "olla'#e and #$" a fail$!e i#
"alled in#tability fail$!e+
Te additional %o%ent. add M i# "a$#ed by te defle"tion of #lende! "ol$%n+
<en"e te de#i&n %o%ent ,ill be &!eate! tan te initial %o%ent obtained f!o%
te #t!$"t$!al analy#i#+ Te de#i&n %o%ent# fo! b!a"ed and $nb!a"ed #lende!
"ol$%n# a!e diffe!ent+ T$#. tei! de#i&n %o%ent# ,ill al#o be diffe!ent o,e:e!
te "al"$lation fo! add M i# #i%ila!+
IN8UT 1
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
Now do !e "ollow#n$%
14+1 A b!a"ed #lende! "ol$%n i# a "ol$%n in ,en bot te !atio#h
l ex andb
l ey
a!e &!eate! tan ===========================+
14+ An $nb!a"ed #lende! "ol$%n i# one in ,i" bot !atio# h
l ex
and b
l ey
i#
&!eate! tan =========================+
14+3 Te #t!en&t of a #lende! "ol$%n i# !ed$"ed by =====================+
14+4 Te defle"tion of #lende! "ol$%n i# #i&nifi"ant "o%'a!ed ,it te
======================== %o%ent+
14+ 9o! #lende! "ol$%n#. ================= #o$ld be "on#ide!ed+
14+2 Te additional %o%ent of #lende! "ol$%n i# "a$#ed by te "ol$%n
========================+
3
ACTIVIT& 14'
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
Now (!e() *our 'nswers%
14%1 1
14%+ 10
14%, t!an#:e!#e defle"tion
14%4 initial %o%ent
14%- additional %o%ent
14%. defle"tion+
I" 'll *our 'nswers 're (orre(/ 0le'se 0ro(eed% O!erw#se 0le'se $o '() o
!e IN2UT #n !#s se(#on 'nd do !e '(#3#*%
4
FEEDBAC 14'
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
14%5 Add##on'l Momen/ add M
Con#ide! a "ol$%n a"ted by a>ial load N and an end %o%ent ?i a# #o,n belo,@
Te additional %o%ent. add M i# "al"$lated a# follo,#@
N
a$
IN2UT +
N
9i&$!e 14+1- efle"tion of a !e"tan&$la! "ol$%n+
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
uadd Na M =
e!e. N te $lti%ate a>ial load
ua "ol$%n defle"tion at $lti%ate li%it+
ua i# "al"$lated $#in& e*$ation 3 of te "ode &i:en belo, @
And Da i# "al"$lated $#in& e*$ation 34 a# follo,#@
Da "an al#o be obtained f!o% Table 3+3 of B( )110. ,i" in de'endent on te
!atioE
b
l e ,e!e e
l i# te effe"ti:e ei&t of "ol$%n in te 'lane "on#ide!ed and
bb =E . i# te di%en#ion of te #%alle! "ol$%n+
2
Kha au β =
/
E/000
1
=
b
l e
aβ
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
<o,e:e!. a""o!din& to "la$#e 3+)+3+2 fo! "ol$%n# in bia>ial bendin&. ,e!e
add M a!e '!e#ent in bot a>e#. > and y. te :al$eE
b
l e i# e*$al to
h
l ex and
b
l ey +
i# te !ed$"tion fa"to! to "o!!e"t te defle"tion and to ta7e into "on#ide!ation
te effe"t of a>ial load+ "an be "al"$lated $#in& e*$ation 33 of te "ode+ Ti# i#
#o,n belo,-
e!e. sc yccuuz A f A f N )+04+0 += and bd f N cubal /+0=
5$#ed fo! #y%%et!i"al !einfo!"ed "on"!ete "ol$%n#6+
Te!efo!e. add M "an be !e,!itten a#@
uz N de'end# on sc A b$t sc
A i# not yet 7no,n. i# ten ta7en a# 1+0+ Te
ite!ation '!o"e## i# to be "ontin$ed $ntil te :al$e obtained i# e*$al to o!
a''!o>i%ately e*$al to te :al$e a##$%ed ea!lie!+
1≤−−=
bal uz
uz
N N N N K
K b
l Nh M e
add
/
E/000
=
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
Now do !e "ollow#n$ e6er(#se% F#ll #n !e l'n)s%
14+ Te additional %o%ent. add M i# "al"$lated $#in& e*$ation
=========================+
14+) Te defle"tion. a$ i# "al"$lated $#in& e*$ation ================+
14+F aβ "an be obtained f!o% Table ==================of te "ode+
14+10 ================== i# te !ed$"tion fa"to! to "o!!e"t defle"tion+
14+11 Te !ed$"tion fa"to! "an be "al"$lated $#in& e*$ation
========================+
14+1 en 1/E =
b
l e . aβ i# e*$al to =====================+
14+13 en 20E =
b
l e . aβ i# e*$al to ======================+
14+14 en 00 %%. 1+0. aβ ======================+
14+1 en ua 00%% and N 3000 7N. te additional %o%ent i# e*$al to
========= 7N+
14+12 A "ol$%n of di%en#ion 300%% > 400%% i# !einfo!"ed ,it 4T3 ba!#+ If
f "$ 40 N/%% and f y 420 N/%%. "al"$late uz N +
)
ACTIVIT& 14
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
14+1 Cal"$late bal N fo! te "ol$%n #e"tion &i:en belo, $#in& f "$ a# 40 N/%%+
14+1) Cal"$late te !ed$"tion fa"to!. if uz N 3007N. bal N 3000 7N and
N 3100 7N+
0 %%
400%%
F
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
<e!e a!e te an#,e!#+
14+ uadd Na M =
14+) Khaau
β =
14+F Table 3+3
14+10 Red$"tion 9a"to!.
14+11 1≤−−
=bal uz
uz
N N
N N K
14+1 0+0
14+13 1+)0
14+14 mm//000+1/+0 =××
14+1 200 7N%
14+12 sc yccuuz A f A f N )+04+0 +=
3103/12420)+0400300404+0 −×××+×××
344 7N
14+1 bd f N cubal /+0=
10
FEEDBAC 14
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
310040040/+0
−××××
00 7N
14+1) bal uz
uz
N N
N N
K −
−
=
3000300
3100300
−−
00
400
0+) 1≤
11
IN2UT ,
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
14%17 Slender Br'(ed Columns
Con#ide! a "ol$%n e>'e!ien"in& an ea!lie! e""ent!i"ity of a>ial load a# #o,n
belo,@
Te total %o%ent i# add it M M M += + Te initial %o%ent ?i to be $#ed i# #i%'ly
te initial %o%ent at an end of te "ol$%n+ B()110 !e"o%%end# tat ?i be ta7en
a#-
1/ 4+02+0 M M M i += 5? bein& te la!&e!6 fo! #y%%et!i"al bendin&
N
e a$
1
9i&$!e14+- efle"tion of (lende! B!a"ed Col$%n
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
And. 1/ 4+02+0 M M M i −= /4+0 M ≥ b$t not le## tan /4+0 M fo!
a##y%%et!i"al bendin& i+e+ bendin& in do$ble "$!:at$!e+ Ti# i# #o,n in
9i& 3+0. B( )110+
Te t,o e*$ation# "an be "o%bined a# follo,#-
e!e.
?i i# te #%alle! initial end %o%ent 5ta7en a# ne&ati:e if te "ol$%n i#
bent in do$ble "$!:at$!e6 and ? i# te la!&e! initial end %o%ent. ,i" i# al,ay#
ta7en a# 'o#iti:e+
B()110 i%'o#e# a f$!te! "ondition tat add t M M M /
11 +≥
A "ol$%n in any "a#e i# de#i&ned fo! a %o%ent of at lea#t Ne%in+ <en"e ,e a:e
f$!te! "ondition tat %in Ne M t ≥
e%in i# te de#i&n %ini%$% e""ent!i"ity and i# ta7en a# 0+0 o! 0 %%.
,i"e:e! i# le##e!+
13
/1 2+04+0 M M M i +=/4+0 M ≥
ACTIVIT& 14(
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
Now do !e "ollow#n$ e6er(#se%
9ill in te blan7#+
14+1F =================== i# e*$al to te #$% of initial %o%ent. i M and
te additional %o%ent add M
14+0 9o! #y%%et!i"al bendin&. te initial %o%ent i# e*$al to
============================+
14+1 9o! ================= bendin&. 1/ 4+02+0 M M M i −=
14+ ====================== i# bendin& in do$ble "$!:at$!e+
14+3 A #lende! "ol$%n i# de#i&ned fo! a %ini%$% %o%ent of
==========================+
14+4 Te de#i&n %ini%$% e""ent!i"ity i# ta7en a# =========== o! 0 %%
,i"e:e! i# le##+
14+ 8i"7 fo$! 546 f!o% te follo,in& "!ite!ia in dete!%inin& te %a>i%$%
de#i&n %o%ent @
14
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
a6 / M
b6 14+0 M
"6 /2+0 M
d6 add i M M +
e6/
1add
M M +
f6 /4+0 M
&6 /1 2+04+0 M M +
6 N e%in
14+2 9o! te #lende! "ol$%n e>'e!ien"in& initial %o%ent# at bot end# 5#o,n
belo,6. dete!%ine te :al$e# of 1 M and / M a##$%in& do$ble "$!:at$!e+
14+ Cal"$late i M of te "ol$%n in $e#tion ) a##$%in& #in&le "$!:at$!e+
14+) Cal"$late te de#i&n %ini%$% e""ent!i"ity fo! te "ol$%n #e"tion #o,n
belo,@
100 7N%
007N%
1
9i&$!e 14+3- End ?o%ent# in (lende! Col$%n
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
14+F Cal"$late te %ini%$% %o%ent of te "ol$%n in $e#tion 10. if
N 4000 7N+
14+30 9!o% te follo,in& info!%ation. dete!%ine te %a>i%$% de#i&n %o%ent
of te "ol$%n-
? 00 7N%
?i 420 7N%
?add 3 7N%
Ne%in 100 7N%
?1 )00 7N%
30%%
00%%
12
FEEDBAC 14(
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
Ho$! an#,e!# #o$ld be a# follo,#@
14+1F Total %o%ent. ?t
14+0 #y%%et!i"al bendin&
14+1 #y%%et!i"al
14+ A##y%%et!i"al bendin&
14+3 Ne%in
14+4 0+0
14+ ? . ?i ?add ./
1add
M M + and e%in N
14+2 kNm M 1001 =
kNm M /00/ =
14+ /1 2+04+0 M M M i +=
( ) ( )/002+01004+0 +−
)0 7N%
14+) he 0+0%in =
300+0 ×
1+ %%
1
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
B$t. %ine #o$ld not be le## tan 0 %%+
Te!efo!e. te %ini%$% e""ent!i"ity i# 0 %%+
14+F %in Ne M =
310/04000
−××
)0 7N%
14+30 ?a>i%$% de#i&n i# ta7en a# te &!eate#t :al$e de!i:ed f!o% ?. ?i.
?add . Ne%in and ?1 + Te!efo!e. te %a>i%$% de#i&n %o%ent i# )00
7N%+
1)
IN2UT 4
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
14%,1 Des#$n E6'm0le
A b!a"ed #lende! "ol$%n of di%en#ion# 300 %% > 40 %% "a!!y an a>ial load of
100 7N and end %o%ent# of 0 7N% and 10 7N% at $lti%ate li%it #tate+ Ti#
load and %o%ent# ind$"ed a do$ble "$!:at$!e abo$t >;a>i# a# #o,n belo,+ Te
effe"ti:e ei&t# a!e le> 2+% and ley )+0 % + Te "a!a"te!i#ti" #t!en&t of
%ate!ial# a!e f "$ 30 N/%% and f y 420 N/%%+
Solu#on
(lende!ne## !atio-
1+//3+0
+2>==
h
l ex
1)+14+0
0+)>==
b
l ey
Ti# #o,# tat te "ol$%n i# #lende! and ,ill be de#i&ned a# #$"-
at te ti%e ,en do$ble "$!:at$!e o""$!# ,e a:e.
?1 ; 10 7N%
and
1/ 4+02+0 M M M i +=
63052+061054+0 +−
1F
(ECTION
14+4-Initial End ?o%ent#
?110 7N%
?
0 7N% b 40
d 40
300
d 20
6 x
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
3) 7N%
te!efo!e i M i# &!eate! tan /4+0 M
Additional %o%ent '!od$"ed by "ol$%n defle"tion i#.
K b
l Nh M e
add
/
E/000
=
3
/
100+1300
20
/000
300100××
×
1F 7N%
it 1+0 a# te initial t!ial :al$e. te total %o%ent i#.
add it M M M +=
3) 1F
12 7N%
30040
10100 3
××
=bh
N
2
1/
+0
/
2
/30040
1012
××
=bh
M
0
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
4+1
9!o% te Col$%n e#i&n Ca!t No+.
/+3100
=bh
A sc
and
2+0= K
No,. fo! te #e"ond t!ial ,e #all $#e 0+2. and !e"al"$late ?t. ,e a:e-
add it M M M +=
3) )3+F1
11+F1 7N%
9!o% Ca!t No+.
100
/+/ bh A
sc =
10
30040/+/ ××
F0 %%
No, "e"7 te final :al$e of f!o% te de#i&n "a!t.
bd f N cubal /+0=
1
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
5 /404030/+0 ××× 6 > 10 ;3 7N
)10 7N
sc ycuuz A f bh f N )+04+0 +=
5 /F0420)+030040304+0 ××+××× 6 > 10 ;3 7N
3011 7N
No,. "al"$late te !ed$"tion fa"to! a# follo,#@
1≤−−
=bal uz
uz
N N
N N K
)103011
1003011
−−
0+2
Ti# i# e*$al to te final :al$e in "ol$%n tab$lated belo,@
516 6 536 546 56
?t
/bh
M
bh
A sc100
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
1+0 12 4+1 3+ 0+2
0+2 1 3+0 0+2
Te ite!ation #to'# ,en :al$e in "ol$%n 516 i# a''!o>i%ately e*$al to :al$e in
"ol$%n 56+ Te!efo!e te a!ea of !einfo!"e%ent !e*$i!ed i# F0 %%+
<en"e. '!o:ide 4 T 3 5A#" 31) %% 6
T#es8
?ini%$% #ie 3/4
1× ) %%
?a>i%$% #'a"in& 1 > 3 3)4 %% "ent!e#+
U#e R) at 3 "ent!e#+
etail# of te !einfo!"e%ent# a!e #o,n belo,@
3
Table 14+1- Ite!ation 8!o"e## of K Val$e
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
Ti# $nit #o$ld a:e enabled yo$ to de#i&n a !einfo!"ed "on"!ete b!a"ed #lende!
"ol$%n a""o!din& to B( )110 !e*$i!e%ent#+ Te B( )110K# de#i&n '!o"ed$!e fo!
de#i&nin& ti# "ol$%n i# #$%%a!i#ed belo,-
(te' 1-
T3
T3
T3
R) 3
4
SUMMAR&
14+- Re"tan&$la! Col$%n#
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
Cal"$late te effe"ti:e ei&t. el
(te' -
Cal"$late te total %o%ent abo$t a %ino! a>i# fo! N and ?t
?t i# ta7en a# te &!eate#t a%on& te follo,in& 5i6 to 5i:6@
5i6 add it M M M +=
5ii6 / M M t =
5iii6 add t M M M
/
11 +=
5i:6 %in Ne M t =
(te' 3-
Cal"$late te total bendin& %o%ent on a %aMo! a>i# fo! N and ? t if te
!atio of te len&t of te lon&e! #ide to tat len&t of te #o!te! #ide i# le##
tan 3. and if /0≤h
l e +
(te' 4-
9o! bia>ial bendin& "al"$late te follo,in&@
a6 ?ty 5total %o%ent abo$t te %ino! a>i# 6
b6 ?t> 5total %o%ent abo$t te %aMo! a>i# 6
"6 de#i&n fo! N. ?ty and ?t>
(te' -
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
Cal"$late te !ed$"tion fa"to! $#in& te e*$ation &i:en belo, @
1≤−−
=bal uz
uz
N N
N N K
O! "an be !ead;off f!o% B( )110 8a!t 3 Col$%n e#i&n Ca!t#+
Con$r'ul'#ons9
Ho$ a:e no,
"o%'leted Unit 14
T$!n ba"7 to 'a&e 1
of ti# $nit+ <a:e
yo$ a"ie:ed te#e obMe"ti:e# #$""e##f$lly If yo$! an#,e! i# &ES. do te (elf;
A##e##%ent+ If yo$! an#,e! i# NO. &o t!o$& Unit 14 a&ain+
Read and an#,e! ti# *$e#tion+
2
SELF:ASSESSMENT
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
e#i&n te lon&it$dinal !einfo!"e%ent fo! te b!a"ed #lende! "ol$%n in 9i&$!e
#o,n belo, fo! bendin& abo$t te %ino! a>i#. if N 00 7N. ? 1y 100 7N%.
?y 10 7N%. f "$ 40 N/%% and fy 420 N/%%+ A##$%e tat te "o:e!. "
0 %% and t!y T40 ba!# fo! e#ti%atin& te effe"ti:e de't+
Now (!e() *our 'nswers%
52+ %6
N
400
00>>
y
y
(lende! "ol$%n
FEEDBAC ON SELF:ASSESSMENT
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
9o! bendin& abo$t a %ino! a>i#. "al"$late ?i and ?add -
a6 /1 2+04+0 M M M i +=
50+4651006 0+25?6
11 7N%
b6 /+12400
200
E ==
b
l e
"6 13+0=aβ
d6 1+0
Re%e%be! tat. i# te de't in te 'lane of bendin&. i+e+ 400 %%+
64+06516513+065/005=add M
130 7N%
add it M M M +=
11 130
4 7N%
?t ? 10 7N%
add t M M M /11 +=
61305/
1100 +
12 7N%
)
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
%in Ne M t = ,e!e. mme /06400650+05%in ==
500650+06
0 7N%
Ta7in& te &!eate#t :al$e@
?t 4 7N%
No,.
f "$ 40 N/%%
f y 420 N/%%
and )2+000
/0000=
−−=
h
d +
Te!efo!e $#e e#i&n Ca!t No+ 3) 5ta7in& d/ 0+)6+
4000061065/005 3
×=
bh
N
1+ N/%%
/
2
/ 40000
61065/4/5
×=
bh
M t
3+03 N/%%
9!o% te de#i&n "a!t.
A#" 1+0 5000 %%6
F
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
8!o:ide 4 #ie 3 ba!# 5312 %% 6
T#es8
Ho$ #o$ld "al"$late te %ini%$% #ie and #'a"in& of te tie# a# follo,#@
?ini%$% #ie 4
1> 3 ) %%
?a>i%$% #'a"in& 1 > 3 3)4 %%
U#e R) at 3 "ent!e#+
Te !einfo!"e%ent detail# a!e a# follo,#@
30
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
&OU S;OULD SCORE <=> OR MORE TO 2ASS T;IS UNIT% IF &OUR
SCORE IS LESS T;AN <=>/ &OU S;OULD ?OR T;ROUG; T;IS
UNIT OR 2ARTS OF T;IS UNIT AGAIN% GOOD LUC9
@T!e 0ower o" wor) 'nd !e 0ower o" (re'#3#* ('n e *our s'l3'#on
NICOLE IDMAN #n ?'s!#n$on 2os
END OF UNIT 14
R) ; 3
T3
T3
400
00
31
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REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/
GLOSSAR&
ENGLIS; MALA&
e""ent!i"ally loaded "ol$%n tian& dibebani #i'i
$nia>ial bendin& lent$!an #at$ 'a7#i
bia>ial bendin& lent$!an d,i;'a7#i
t!an#:e!#e !einfo!"e%ent tet$lan& %e%b$M$!
!e"tan&$la! #e"tion 7e!atan #e&ie%'at
b$M$!
#*$a!e "ol$%n tian& #e&ie%'at #a%a
tie# tet$lan& 'e%a$t
enan"e %o%ent %o%en te!ta%ba
%aMo! a>i# 'a7#i $ta%a
%ino! a>i# 'a7#i 7ed$a
#y%%et!y #i%et!i
b!a"ed be!e%bat
$nb!a"ed ta7 be!e%bat
#lende! "ol$%n tian& lan&#in&
!ed$"tion fa"to! fa"to! 'en&$!an&an
3