!"#"$%&'()*)$'+,-)*$.'/&0)*1&'!2'3)4%.'5)*&6)'72'8$99$*.':$*;'<2'<)%$-"1'
=&%1)%">&' !"#$%&'(()*"+ ,"#-(-&-"#-.+ ,"/0).).+1+2).-3%+ 4.#'&)%+456-$)7-"#80+ &-+9%0'7"8.+9:;+ 980)<$8()*"+&-+&8#%.++ ,"/0).).+"%=0)"-80-.+ >$%6'-.#8.+&-+&).-3%+ 9%7-"#8$)%.+?"80-.+ 4.#'&)%.+6$%(-.%+ ,@$8&-()7)-"#%.+
?"@1)6$@'A&6BC)@1&@'$A)*&DA&%A*)1&' !"#$%&'()*%(+,&-".'(/'#(0%.$'1'#(2%('&-,#(+,&3,.%.$%#( !"#$%&"'#(%#)"*#("*#$+,("*#-#
'JA)*&'K@1*CA1C*$,'
• • • •
</$'(:%#"#$%.+"'( 9=+>/( ?@+"/(2%(%.#'&-/':( 4@3"2,('/(&,.$':(
• • • •
456"2,( 7+,.8&"+,( 9*:'-/%( 4%#"#$%.$%('(;*%6,(
E' 311#+
F' 2.#+
./0#+
F'
E' 4+
=&6BC)@1&' G@"%)*H"$')%' B*&B")>$>)@I'
=&%A*)1&'
2.+
12.+
?"@1)6$@'A&6BC)@1&@'$A)*&DA&%A*)1&' !â&#x20AC;¯ G-"-?()%.+(%76$%<8&%.+-"+0%.+.).#-78.+&-+6).%+-"+.-(()*"+(%76'-.#8+ A80#8+$-.).#-"()8+1+7-"%$-.+&-.608F87)-"#%.B+
A8B+C)@8+(%76'-.#8+
A<B+D).#-78+0%.8(-$%+
A&B+,$78&'$8+(%76'-.#8+
A-B+C)@8+(%76'-.#8+(%"+#8(%"-.+ ++++++A#$*-(6":2%:B+
A(B+C)@8+(%76'-.#8+(%"+8<-$#'$8+$-E%$F8&8+-"+8078+
(&@"0,)@'A&%LHC*$A"&%)@'A&,C6%$@'A&6BC)@1$@'
a) SRC
b) Circular and Rectangular CFT
c) Combinations between SRC and CFT
M)%1$9$'NO'/PB">$'A&%@1*CAA"4%(
!,*:+%A(B':>.%CD4,&%:,E(FGGH(
I"%#$(%$('/JE(KLLM(
M)%1$9$'QO'/"H">)#'$>"A"&%$,(
Walter P. Moore
M)%1$9$'RO'($%>)&',&A$,'
9%76%.)#-+9%0'7"+ I-(#8"@'08$+9:;+ D#--0+H)$&-$.+
B':+,(+,.(+,/*&.'#(+,&3*%#$'#(./0( OP*-,(&%$@/"+,(Q!!(:%//%.,(+,.(+,.+:%$,R( N'.2%,(/,+'/(%.(+,/*&.'(2%(5.627( OP*-,(&%$@/"+,(Q!!(#".(:%//%.,R(
M)%1$9$'SO'=&%L%$6")%1&(
?'//'(%.(+,/*&.'(2%(.78.2607#
S,/*&.'#(./0(%.(3"/'#(2%(3*%.$%#( 4,%2%:(
/)@"@1)%A"$'>)',$'@)AA"4%'1*$%@-)*@$,'TJU?=.'QVVWXO'' /YH">&D(,P@ZA&'-@2'=&6B$Z0",">$>'>)'<)[&*6$A"&%)@' J=K/+'
2)8@$878+&-+!"#-$8(()*"+K+LMNOP+A!IQRR5STUPB+ ?VVWRX.)+AOSWY>8BU+AS,&%.$':",#+<T!SE(FGGUB+
=+:(\K?!+'
2)8@$878+&-+!"#-$8(()*"+;J6)(%+ +AS,&%.$':",#+<T!SE(FGGUB+
=$B$A">$>)@'B,P@ZA$@'>)'@)AA"&%)@' A&6BC)@1$@'?/='^'=7!'TJU?=.'QVVWX'
K[)A1&@'>)')@1$0",">$>' / PA
=&,C6%$@'=&6BC)@1$@'$'_)`&6B*)@"4%'TJU?=.'QVVWX' 1" !" #c!"
A
!"
Efectos de Estabilidad Capacidad ignorada
B
#b" 1"
/ MB
f (# , EI eff ) Pn $= = Po As Fy + Ar Fyr + " ! Ac f c '
9:"';+<#)=*#%*>'+?>+'=*#?"$@+%*>=*#,"#*",# ?"$+,%*#A?"$"#)=*#?",B%,?C",=)%*D#=E,F# =&6B,)9">$>)@')%'B*&A)@&@'A&%@1*CAZ-&@' – 9%%$&)"8()*"+-"#$-+08.+)"&'.#$)8.+&-+8(-$%+1+(%"($-#%+ – Z#$8.+(%760-[)&8&-.+-"+08+(%".#$'(()*"+++ A)U-U+.-('-"()8.+7%"#8[-\(%08&%B+ +
7$,1$'>)')@B)A"LA$A"&%)@')%',$@'%&*6$@' – ]8.+"%$78.+&-+&).-3%+8^"+"%+-.#/"+(%760-#8.+ – ]8.+-.6-()?(8()%"-.+"%+$-_-[8"+08.+`-"#8[8.+&-<)&%+80+ &-.(%"%()7)-"#%+-"+-0+(%76%$#87)-"#%+A7'1+6%(8+ )"`-.a@8()*"+-56-$)7-"#80+1+8"80Ja(8B+ – ]%.+2).-38&%$-.+"%+a-"-"+)"(-"a`%.+68$8+'.8$0%.+
Ejemplo 1: Resistencia flexocompresiรณn Secciรณn transversal CCFT20x0.375-25MPa 12000 NTC (2004) AISC (2005) 10000
EC-4 (2004) AIJ (2001) Anรกlisis de Fibras
(%'T;aX''
8000
9%768a<)0)&8&+&-+&-E%$78()%"-.+
6000
4000
HSS20x0.375
2000
9
!508
508
0 0
200
400
600
:%'T;aD6X'
800
1000
ON%:%'(V(W%8.E(FGGXR(
Ejemplo 2: Rigidez a flexión (EI) • =&%A*)1&+%+JA)*&O'''
,^"+(%7^"+-"+6$/(a(8b+c7'1+(%".-$`8&%$d+
• KAC$A"&%)@')6BY*"A$@O++
OY,:&'#(,(T.0%#>6'+",.%#R(
EI eff = ! s Es I s + ! c Ec I c
• J%P,"@"@'TL0*$@'&'),)6)%1&@'L%"1&@X+ Concrete mesh
HSS Section
Concrete
t
steel-concrete’s surfaces in contact (with adjustment zone)
D
?)AA"4%'A&%'),)6)%1&@'L0*$@+
Steel
Steel
J%P,"@"@'>)'),)62'L%"1&@+
K9)6B,&'RO'7$A1&*'A&6B&*1$6")%1&'@Y@6"A&' '
J?=Kb?KU'cDVW.'!$0,)NQDQDN' R (Q´) 'Cd (Q)
Sistema S-OMF (Steel – Ordinary Moment Frames):
3.5
3.0
RC-OMF (RC – Ordinary Moment Frames):
3.0
2.5
C-OMF (Composite – Ordinary Moment F):
3.0
2.5
F
$"
Fe
F
Fe/R
Moment Frame (OMF)
$e
Cd$e
$"
K9)6B,&'RO'7$A1&*'A&6B&*1$6")%1&'@Y@6"A&' a!=D?'QVVS'^':+='QVVd' '
e%+-.#/+(%".)&-$8&%+")"@^"+.).#-78+(%76'-.#%+ +?U?!K:J'K?!/\=!\/J3
+ Y8$(%.+&^(a0-.+&-+A&%A*)1&'*)[&*#$>&'AfV+O+*+SB Y8$(%.+&^(a0-.+&-+$A)*&+AfV+O+*+SB Y8$(%.+&-+$A)*&'&'A&%A*)1&'(%"+&'(a0)&8&+0)7)#8&8+AfV+P+*+QB 3&@$@'B,$%$@'.)"+7'$%.+%+(%"#$8`)-"#%. Y8$(%.+&-+$A)*&+(%"+(%"#$8`)-"#%.+-5(g"#$)(%. Y8$(%.+&-+$A)*&'&'A&%A*)1&'(%"+(%"#$8`)-"#%.+(%"(g"#$)(%. :C*&@+(%7<)"8&%.+(%"+78$(%.+&^(a0-.+&-+A&%A*)1&+AfV+OB :C*&@+(%7<)"8&%.+(%"+78$(%.+&-+A&%A*)1&+(%"+&'(a0)&8&+0)7)#8&8+AfV+P+*+QB :C*&@+&)8E$8@78 Y'$%.+6$6B&@1)*Y$+(%"?"8&8+6)-F8.+78()F8.+$-E'-$F%+h%$)F%"#80+%+78008 Y'$%.+6$6B&@1)*Y$+(%"?"8&8+$-E%$F8&8+(%"+78008 Y'$%.+6$6B&@1)*Y$+&-+6)-F8.+h'-(8.+(%"+$-E'-$F%+)"#-$)%$ Y'$%.+6$6B&@1)*Y$+i'-+"%+('7608"+-.6-()?(8()%"-.+7876%.#-$J8+(%"?"8&8
'<U?!+/?Uea' +RUROR+ +RUROR+ +RURPW+ +RURPW+ +RURQR+ +RURPW+ +RURPW+ +RURPR+ +RURRT+ +RURRW+ +RURRS+ +RURRQ+ +RURRPW+ ++
K9)6B,&'SO':]1&>&'<"*)A1&'>)'J%P,"@"@' T&3%:;%++"8.(2%(2%#3/,3&%A(
#(>"bjVP+
!(Z(Q([(UGG(
4k-(a`-+]-"@#h+
,(S':6'(.,2'/A(
Ni = 0.002Yi
#(>"bjVj+
2).#$)<'#-&+ >08.a()#1+,"801.).+
>$+
4"6"2%C(7/@#>+'(4%2*+"2'(
EI * = 0.8! b EI EA* = 0.8 EA
2)$-(#+,"801.).+
Y$+
f'g+`80%$-.+.%"+86$%6$8&%.+68$8+(%76'-.#%.K+++++4!l+V+RUMW+4!+m+
=&%1)%">&' !"#$%&'(()*"+ ,"#-(-&-"#-.+ ,"/0).).+1+2).-3%+ 4.#'&)%+456-$)7-"#80+ &-+9%0'7"8.+9:;+ 980)<$8()*"+&-+&8#%.++ ,"/0).).+"%=0)"-80-.+ >$%6'-.#8.+&-+&).-3%+ 9%7-"#8$)%.+?"80-.+ 4.#'&)%.+6$%(-.%+ ,@$8&-()7)-"#%.+
+09)Z-&@' • K@1C>"$*'),'A&6B&*1$6")%1&'$,'&01)%)*'^'B*&A)@$*',$' *)@BC)@1$')`B)*"6)%1$,O' 98$@8+($Ja(8+&-+68"&-%+AN+:B I)@)&-F+8+:0-5)*"+A7T%\B ;%$.)*"+A$-.).#-"()8+1+$)@)&-FB 4.#8&%.+0J7)#-
+2)8@$878.+&-+)"#-$8(()*"+NDB+ +>8"&-%+0%(80+A"/-B+ +9%".)&-$8()%"-.+80+(%08$+ +]%"@)#'&+8$a('08()*"+60/.a(8+AW3B+
• \Z,"#$*',&@'>$1&@'B*&A)@$>&@'B$*$'6)9&*$*'^b&'-)*"LA$*O' – Y%&-0%.+(%".a#'a`%.+&-+0%.+78#-$)80-.+ – Y%&-0%.+&-+40-7-"#%.+"%+0)"-80-.+
• (*&-))*'>)'*)A&6)%>$A"&%)@')%',$'A&%@1*CAA"4%.' $%P,"@"@.'^'),'>"@)f&'>)'A&,C6%$@'A&6BC)@1$@2'
(*C)0$@')`B)*"6)%1$,)@'B*)-"$@+
<$1&@'&01)%">&@'>)',$@'0$@)@'>)'>$1&@'A&6B",$>$@'B&*'3)4%')1'$,2.'QVVW'^'g&&>)')1'$,2.'QVVc' 2.5
Pexp/Po
NRcW'=7!'="*AC,$*)@'+ o pPQ+(%0'7"8.+ o STO+`)@8=(%0'7"8+
2.0
Pn/Po
>\>%+
AISC
chd'=7!'/)A1$%HC,$*+ o WQS+(%0'7"8.+ o QqS+`)@8=(%0'7"8+
1.5
1.0
0.5
0.0 0.00
0.50
1.00
1.50
2.00
2.50
3.00
%"
SS?P(+,/*&.(2'$'-'#%( 1.6
>\>%+
1.4
1.2
Pexp/Po
%nRUW+
1.4
>\>%+
Steel
1.2
Pexp/Po
RUWn%nP+
1.2
>\>%+ Pn%nPUW+
1.0
Steel
1.0
Pexp/Po Steel
0.8
1.0
0.8 0.8
0.6 0.6
0.6 0.4
0.4
0.2
0.2
0.0 0.00
0.25
0.50
0.75
1.00
1.25
0.4
0.2
0.0 1.50 0.00
Y\Y%+
0.25
0.50
0.75
1.00
0.0 1.25 0.00
Y\Y%+
SS?P(-%'&D+,/*&.(2'$'-'#%(
0.25
0.50
0.75
1.00
1.25
Y\Y%+
K@B)AY6)%)@'>"@)f$>&@O'
K@B)AY6)%)@'>)'B*C)0$+
+
Specimen
L
Steel section
Fy
fc’
D/t
name
(ft)
HSS D x t
(ksi)
(ksi)
1-C5-18-5
18
HSS5.563x0.134
42
5
45
2-C12-18-5
18
HSS12.75X0.25
42
5
55
3-C20-18-5
18
HSS20x0.25
42
5
86
4-Rw-18-5
18
HSS20x12x0.25
46
5
67
5-Rs-18-5
18
HSS20x12x0.25
46
5
67
6-C12-18-12
18
HSS12.75X0.25
42
12
55
7-C20-18-12
18
HSS20x0.25
42
12
86
8-Rw-18-12
18
HSS20x12x0.25
46
12
67
9-Rs-18-12
18
HSS20x12x0.25
46
12
67
10-C12-26-5
26
HSS12.75X0.25
42
5
55
11-C20-26-5
26
HSS20x0.25
42
5
86
12-Rw-26-5
26
HSS20x12x0.25
46
5
67
13-Rs-26-5
26
HSS20x12x0.25
46
5
67
14-C12-26-12
26
HSS12.75X0.25
42
12
55
15-C20-26-12
26
HSS20x0.25
42
12
86
16-Rw-26-12
26
HSS20x12x0.25
46
12
67
17-Rs-26-12
26
HSS20x12x0.25
46
12
67
18-C5-26-12
26
HSS5.563x0.134
42
12
45
=)**$*'-$AY&@'>)'>$1&@' • WE((#E(9[$E(;+]( :$`"6"#$*'A$B$A">$>'>),'3$0' • NC(Z(KHFG(^"3(Z(XGG(P,.( • _`Z_VZa[DKXbZa[DcGJX+&( • Kd]Z(UJU&(e(W(e(FX]Z(d&( • f$:'#(:%#$:"++",.%#(
:J?!'3$0'T\:aX+
U%@1*C6)%1$A"4%+ ArPQS+9h+s+P+tFb+PRUq4T+&8#%.\-.6-()7-"B+
• ?"@1)6$':J?!' • =),>$@'>)'A$*H$'TdX' • !)6B&@4%"A&@'TdX' • D#$8)"+@8'@-.+ArSRB+ • ]C2;.+APMB+ • D#$)"@+6%#.+APRB+ • ]42.+ASRB+ • C)&-%+(878$8.+AMB+ • 987-$8.+AMB+ • ;)7-=086.-+AQB+
U%@1*C6)%1$A"4%+ • ,(#'8&%$-.=9$'F+ • 9-0&8.+&-+(8$@8+AMB+ • ;-76%.*")(%.+AMB+ • ?1*$"%'H$CH)@'TiSVX' • ]C2;.+APMB+ • D#$)"@+6%#.+APRB+ • ]42.+ASRB+
Rosettes or cross gages
Gages at: 25’ 6”
Longitudinal strain gages
9’ 6” (3L/4)
Gages at:
12’ 0” (2L/3)
9’ 0” (L/2)
• C)&-%+(878$8.+AMB+ • 987-$8.+AMB+ • ;)7-=086.-+AQB+ 6’ 0” (L/3) 4’ 6” 3’ 6”
2’ 6” 1’ 6” 0’ 6”
13’ 0” (L/2)
RCFTs
CCFT12
6’ 6” (L/4)
3’ 6”
RCFTw
2’ 6”
CCFT20
1’ 6” 0’ 6”
Strain gages in 26 ft long CFTs
13’ 6” (3L/4)
Strain gages in 18 ft long CFTs
17’ 6”
U%@1*C6)%1$A"4%+ • ,(#'8&%$-.=9$'F+ • 9-0&8.+&-+(8$@8+AMB+ • ;-76%.*")(%.+AMB+ • D#$8)"+@8'@-.+ArSRB+ • 3M<!@'TNdX' • D#$)"@+6%#.+APRB+ • ]42.+ASRB+ • C)&-%+(878$8.+AMB+ • 987-$8.+AMB+ • ;)7-=086.-+AQB+
1 top LVDT set
6 LVDT sets
U%@1*C6)%1$A"4%+ • ,(#'8&%$-.=9$'F+ • 9-0&8.+&-+(8$@8+AMB+ • ;-76%.*")(%.+AMB+ • D#$8)"+@8'@-.+ArSRB+ • ]C2;.+APMB+ • ?1*"%H'B&1@'TNVX' • ]42.+ASRB+
String pots at:
22’ 0”
CCFT 18’ 0”
String pots at:
14’ 0”
12’ 0” (2L/3)
RCFTs
9’ 0” (L/2)
• C)&-%+(878$8.+AMB+ • 987-$8.+AMB+ • ;)7-=086.-+AQB+
6’ 0” (L/3)
RCFTw
String pots in 26 ft long CFTs
String pots in 18 ft long CFTs
13’ 6” (3L/4)
10’ 0”
6’ 0”
U%@1*C6)%1$A"4%+ • ,(#'8&%$-.=9$'F+ • 9-0&8.+&-+(8$@8+AMB+ • ;-76%.*")(%.+AMB+ • D#$8)"+@8'@-.+ArSRB+ • ]C2;.+APMB+ • D#$)"@+6%#.+APRB+ • 3K<@'TSVX' • C)&-%+(878$8.+AMB+ • 987-$8.+AMB+ • ;)7-=086.-+AQB+
U%@1*C6)%1$A"4%+ North strong wall
ca N m W er at ow er
ca m NE er at ow er
se ba
• M">)&'A$6$*$@'TdX' • =$6)*$@'TdX' • !"6)D,$B@)'TQX'
!
or at tu ac
Specimen
West strong wall
• ,(#'8&%$-.=9$'F+ • 9-0&8.+&-+(8$@8+AMB+ • ;-76%.*")(%.+AMB+ • D#$8)"+@8'@-.+ArSRB+ • ]C2;.+APMB+ • D#$)"@+6%#.+APRB+ • ]42.+ASRB+
A:%#%.\C)&-%.+r+P+;<B+
Y Y Crosshead projection ca m er a SW tow
er
tow a r me SE ca
X X
er
(*&1&A&,&'>)'A$*H$'jB"A&' !"
!z
P !
constant
!x
!
P
constant
!y
T
P
constant
P
constant
1+ 5+ 1+
1+
5+
5+
P
P!
]9PK++ 9%76$-.)*"+
M
P
F
constant
]9QK+ :0-5)*"+u")85)80+
Mx My
P
constant
]9OK+ :0-5)*"+G)85)80+
T
]9SK+ ;%$.)*"+
(*C)0$@')`B)*"6)%1$,)@'
K@B)A"6)%'N=WDNdDW'
K@B)A"6)%'Nd=WDQkDNQ'
(*C)0$@')`B)*"6)%1$,)@'
K@B)A"6)%'c=QVDNdDNQ'
K@B)A"6)%'Nk/lDQkDNQ'
K-$,C$A"4%'(&@16&*1)6'
(a) Local buckling deformation in steel
(d) Condition of the concrete in the external surface
(b) Close up to the local buckling in steel
(c) Close up to the concrete deformed shape inside the steel local buckling
(e) Condition of the concrete in the interior core
=&%1)%">&' !"#$%&'(()*"+ ,"#-(-&-"#-.+ ,"/0).).+1+2).-3%+ 4.#'&)%+456-$)7-"#80+ &-+9%0'7"8.+9:;+ 980)<$8()*"+&-+&8#%.++ ,"/0).).+"%=0)"-80-.+ >$%6'-.#8.+&-+&).-3%+ 9%7-"#8$)%.+?"80-.+ 4.#'&)%.+6$%(-.%+ ,@$8&-()7)-"#%.+
(*)@"4%'m">*&@1PZA$')%'/=7!@# & (µ&)" !" (x10-6) 700700
#T (ksi) 20.3
600600
17.4
500500
14.5
400400
11.6
300300
nQo'
200200
5.8
100100
2.9
0 0
0.0 0.5
1
1.5 Time (hrs) time (hours)
7K'J%P,"@"@O' &max ! 755 µ&" 'max !+QOUQ+X.)+ (max ! 0.19 in
8.7
Non-restrained Restrained
:)>"A"&%)@O'' &max ! 713 µ&" 'max !+QPUp+X.)+ (max ! 0.2 in
2
2.5
3
K[)A1&@'>)',$'"6B)*[)AA"4%')%'B,$A$@'>)0">$'' $',$'B*)@"4%'>),'A&%A*)1&')%')@1$>&'[*)@A&'
nNodI
ndI' p=I.=PM=PQb+(%"+$-E'-$F%+08#-$80+
'
S=Iv=PM=Wb+.)"+$-E'-$F%+08#-$80+-"+(%08&%+
/)A&6)%>$A"&%)@'B$*$'6"%"6"#$*',&@' )[)A1&@'>)'B*)@"4%'>),'A&%A*)1&'[*)@A&' !
1 " 5bc + 4hc # p $ hc 4 L = & % ' 3 32 ( bc + 4hc ) Es $ t 2000
!
" $ 2hc % p & hc 2 # ' ) ( * 2 Fy + bc + 4hc , t ' ( = max ' 2( . $ % ' 1 ) 3bc + 4hc * p & hc ( '/ 3 + bc + 4hc , t 2 (0
! max
! max
]J7)#-.+6'-&-"+('760)$.-+80K+ • !"($-7-"#8$+$+%$+$-&'()$+g[$U+ • I-&'()$+3+%+80#'$8.+&-+(%08&%+ • ,@$-@8"&%+$)@)&)F8&%$-.+ #-76%$80-.++ A7)"+q+&J8.b+'+MRw+&-+;+xB+ • 4.68()87)-"#%+n+-+%$+g( • ]%"@)#'&+$)@)&)F8&8+W\O+ • 4`)#8$+)"&'()$+E'-$F8.+ "%$780-.+%+&-E%$78()*"+80+ )"#-$)%$+&-0+#'<%+
D)+0%.+0J7)#-.+"%+.-+('760-"b+-0+#'<%+&-<-+.-$+(%".)&-$8&%+(%7%+.-(()*"+ -.<-0#8+&-<)&%+8+i'-+.-$/+.'.(-6a<0-+8+68"&-%+0%(80+#-76$8"%U+
=$*H$'3=N'p'=&6B*)@"4%'BC*$' 3000
!z !
?1$0","1^'Kr)A1@'
!"
D6-()7-"+Pq=I.=QT=PQ+
2500
('T;"BX'
2000
Cross-section Beam-column Experimental
1500 1000 500
P
P!
0
0
200
400 600 :'T;"BDqX'
800
1000
=&A")%1)@':%G@b:"'>)',&@'>$1&@'B*&A)@$>&@' !
Experimental
"
Euler curve +,)
P Po
Analytical
&
AISC (2010)
$
+,' "
"$!
*
(!
+,%
% ")! #! "(! ""!
+,#
"' "#!
)! "& '
"#
"+ "%
+
+
+,&
"
!
",&
#
#,&
$
=C*-$'$%$,YZA$'>)'A&,C6%$'==7!' 2000
Axial Force (kip)
!+,-./0/%&123)4((*
$$567% !"8%'(9 #"8%(:';;9 $%%8%<'%=/0 &'>%8%4%=/0
1500
!+,-./0/%&123)(((* !"#$%&'()(*
2)E-$-"()8.+&-<)&8+8K+ 9%"?"87)-"#%K++RUpW;+x++`.++;++x+ >8"&-%+]%(80K++"Wj(V+EA9[$B+ I)@)&-.+&-+:0-5)*"+A7T%\B+
" ( L ) = %o
1000 L #
# ! z $$ (( ) 2L * *
" ( z ) = % o '1 & cos ' )
500
0
0
10
20
30
40 50 60 Effective length KL (ft)
70
80
90
100
=$*H$'3=Q'p'7,)`&A&6B*)@"4%'C%"$`"$,' Y-#h%&%0%@J8+68$8+%<#-"-$+-0+&)8@$878+&-+)"#-$8(a%"+>=Y+-"+Q2+
F
P
!
P !"#!$!%"&' ()#*+!",
F
!"#$
%i
"
Po Pcr
&' (& $%
*'
PD !"
+*,+-+(*#$ ./,01+*2
!
"#
$% & '( &
!"i
P
C
PC
)
#$
M2
E
Pn
#)* #%&%'(
F
cross-section strength
%
M
L
A
"i
"
0
,!D9+D)760U+
D B Mo
M
P (kip)
P (kip)
M$,&*)@'(D:')`1*$Y>&@'>)'>$1&@')`B)*"6)%1)@' '"! 3000
!"& N([(N.(
>+AX)6B+
!"#-$7-&)%.+ %+n+PUW+
2500 2000 1500
M (kip-ft) 0 (a) Specimen 3-C20-18-5 -1000
+#! ,-
!"!
-500
0
500
1000
!"!7-C20-18-12 !"# !"$ (b) Specimen Y+AX=yB+
P (kip)
P (kip)
3000 2000
2500
N([(N.(
3500
2500
>+AX)6B+
!"$
,.
500
40.<-0#%.+ %+z+PUW+
()*+
!"#
1000
2000
1500
1000 500
500
-500
0
500
0 Y+AX=yB+ -1000
M (kip-ft)
'"!
!"%
!"&
'"!
'"#
'"!
'"#
Y\Y%+
!"& !"%
()*+
!"$
+'#
1500
1000
0
!"%
+#!
!"#
,!"! !"! -500
!"# 0
!"$ 500
!"% 1000
!"&
Y\Y%+
(*&BC)@1$O'KAC$A"&%)@'A&%j%C$@'B$*$'A$,AC,$*',&@'>"$H*$6$@' >)'"%1)*$AZ&%'(D:'>)'@)AA"&%)@'A&6BC)@1$@'=7!2' t
bc
!s
!c
t
Fc
Fy
t
t
hc/2-y
Dc/2-y
PNA +y
h
CL
"
+y
hc
2t
t
Dc/2
t
t
b
! hc " P ( y ) = $ # y % bc Fc # 4 ytFy &2 ' 1 M ( y ) = Z s ( y ) Fy + Z c ( y ) Fc 2
Fc = 0.85 fc '
Fy
D
CL
Dc
hc/2
PNA
D
P ( y ) = (! # " ) Ks + (! # sin ! ) Kc
1 M ( y ) = Z s ( y ) Fy + Z c ( y ) Fc 2 1.56 Fy " ! Fc = 0.85 f cc = 0.85 # f c '+ $ D / t % 2 & '
(*&BC)@1$O'<"$H*$6$@'>)'"%1)*$AZ&%'(D:'*)>CA">&@'B&*' )@1$0",">$>'B$*$''A&,C6%$@'A&6BC)@1$@'=7!2' !
P
0 A
Po
AISC (2005) functions P(y), Continuous M(y) Mimp+Mstb
1
2
PPc c Pn 0.75P
C
3
c
0.5P Pc/2c 0.25Pc
P, M!
B 9 10 Moo M
0 T -P Ps 12
-%'&D+,/*&.(
P4n, Mn 5 D 6
8
7 M Mbb M
M
11
P ( Pn " Pe ) M! = M " Mn Pn ( P " Pe )
-%'&D+,/*&.(
=$*H$'3=R'p'7,)`&A&6B*)@"4%'0"$`"$,' !y
15
5 00 -5 -10
10
10
Y Displacement (in)
10
Y Displacement (in)
5 00 -5 -10
-20 -20 -15 -10 -5
00
5
-20 ! 10 15 x 20 -20 -15 -10 -5
(a) Biaxial 8 probes (in) SpecimensX 2Displacement to 7
600
-5
-15
D6-()7-"+O=9QR=PM=Wb+>VWRRX+
Axial Load (kip)
MMoment Y (kip-ft) y (kip-ft)
00
00 5 10 15 !x20 -15 -10 -5 00 ! 5 10 x 15 (b) Biaxial probe with subprobes (c) Incremental biaxial (figure-eight) X Displacement (in) X Displacement Specimen 9 Specimens 8 and 10 to(in) 18
400
Mx
5
-10
-15
-15
P (kip)
!y
15
!y
15
Y Displacement (in)
!x
P
20
20
!y
200
0
2500
D6-()7-"+O=9QR=PM=W+ +>VPQWRX+
2000 1500 1000 500 0
-200
-500
My
500
-400
0 -500 -500
0 Moment X (kip-ft)
Mx (kip-ft)
500
Moment Y (kip-ft)
-500
0
M x (kip-
500
ft)
Moment X (kip-ft)
K`1*$AA"4%'>)'*"H">)#')[)AZ-$'),P@ZA$'>)'B*C)0$@'A&%'3=N' 1@%?C$%,#H2IJKLJM#
Axial force, P (kip)
Moment at the base, M (kip-ft)
Cross-section Beam-column Experimental
2000
1500
1000
500
0
0
200
400
600
Moment at the base, M (kip-ft)
2
EI test
# KL $ =% & " ' ! (
Po " log(0.658) log( Ptest / Po )
if
Ptest > 0.44 Po
Ptest / 0.877
if
Ptest ) 0.44 Po
Curvature at the base, #+APR=S\)"B+
EI test
Mb " Ma = !b " !a
K`1*$AA"4%'>)'*"H">)#')[)AZ-$'),P@ZA$'>)'B*C)0$@'A&%'3=Q'
exp
400
EI
200
-200
X
15 10 5 0 -5 -10 -15
-400
-20
exp
=18148225 kip-in 2
0
EI
Moment at the base, M (kip-ft)
600
20
Lateral force, F (kip)
=17696536 kip-in 2
6*@%?C$%,#H2IJKLJMN#:OPQQ#RC@#
-600
-6
-4
-2
0
2
4
6
8
10
-25 -4
-4
Curvature at the base, #+APR=S\)"B+
EI test
Mb " Ma = !b " !a
x 10
-2
0
2
4
6
Top displacement, $ (in)
" FL3 #" # 1 $=% &% & 3 EI 1 ' P / P test )( test e ) ( EI test
" Fb ' Fa =% ( $b ' $ a
2
# L3 " KL # & +% & Ptest )3 ( ! )
=$,"0*$A"4%')6BY*"A$'>)',$'*"H">)#'$'_)`"4%')[)AZ-$' '"#!
C3
'"#!
'"!!
'"!!
!"&!
!"&!
!"%!
!"#!
3=N+
EI eff = Es I s + C3 Ec I c
!"#!
)(
'!(
')(
% = As / A+!
9O+
#!(
!"%!
!"!!
'0%:'6%(
3=Q+ !"!
!"(
'"!
#+
'"(
!"! !"*! !")! !"(! !"'! !"&! !"%! !"$! !"#! !"!!
EI eff = Es I s + 0.40 Ec I c
!"&!
!"#!
3=N+
!"!! !(
!"$!
'0%:'6%(
!"$!
!"!!
'"!!
EI eff = Es I s + 0.80 Ec I c
!"%!
! " As C3 = min # 0.6 + 2 , 0.9 $ As + Ac % &
!"$!
C3
#"!
#"(
)"!
!")
9O+
'"!
'")
"#=+ As / A
#"!
#")
*"!
$"'
%"!
EI eff = 0.85 ( Es I s + 0.40Ec I c )
'0%:'6%(
3=R+ !"!
!"'
#"!
#+
#"'
$"!
K-&,CA"4%'>),'B$%>)&',&A$,'
=$,"0*$A"4%')6BY*"A$'>),'"%"A"&')%'),'B$%>)&',&A$,'' I9:;.+
99:;.+ $"
! lb = 0.09 R "2 !y
$!
! lb !y
7
23+%",4+5456"7
!"#"$%"&'()"#*+$(,$ !*-".'#/0"11")2$3454
/0#12)3#"3"425
! lb = 9 R "2 !y
6
6*7#7$'-$#8'7$9):1*%# $$$;<$$$$$$$$$;53$$$$$$$$$;34 $$$=:$&:%"&$(>%?&'-@
Data calibrated by Tort-Hajjar, 2010
5
Tests in this project
Rs
#"
5
! lb !y
54
#!
! lb = 0.214 R "1.41 !y
!#
5<
3 2
55 D E
3
Fy R= D# t Es
B
5A
$ !%
&
! lb = 3.14 R "1.48 !y
Rw
!"#$%&'(('#)*+,,-.
'
5C
!"#$%&'()$**$+,-./0/1
"
4
!( !" )
1
Fy R= h# t Es
0
! !
!%!"
!%#
!%#"
!%$
5
Non compact
Compact
3 2
!%&
E !r = 0.3 s Fy
4
" lb "y
!%$"
! p = 0.15
1
Es Fy
Slender
Fy R= D! t Es
0
0.5
1
1.5
2
4
" lb "y
!r = 3
3
! p = 2.12 2
Es Fy
0
0.1
0.2
0.3
0.4
0.5
3
3.5
Es Fy
Non compact
Compact
Slender
1 Fy R= h! t Es
0
0
2.5
0
1
2
3
4
(*)>"AA"4%'>)',&@'$%P,"@"@'
A)"-0/.a(%.b+&-+.-@'"&%+%$&-"b+608.a()&8&+&).#$)<')&8B+ 4.6-()7-"+SIv=PM=Wb+]9Q<+ 20
20 "2
Fy Es
# $ 18 ! lb = 9 % h Fy & Fy % t Es & Es ' ( 16
14
14
12
12
?(AX)6B+
?(AX)6B+
# $ 18 ! lb = 3.14 % h Fy & % t Es & ' ( 16
"1.48
10 8
10 8
6
6
4
4 Experiment Analysis
2 0
0
5
10
!+A)"B+
15
Experiment Analysis
2 0
0
5
10
!+A)"B+
15
(*)>"AA"4%'>)',&@'$%P,"@"@'
A)"-0/.a(%.b+&-+.-@'"&%+%$&-"b+608.a()&8&+&).#$)<')&8B+ 4.6-()7-"+PW9QR=QT=PQb+]9Q8+ 800
1+
600
1+
600
5+
400
5+
400
200
BF(O^"3DkR(
BF(O^"3DkR(
4.6-()7-"+O9QR=PM=Wb+]9O<+
0
-200 -400
200 0 -200 -400
Experiment Analysis
-600 -4
-2
0
2
&+A&-@B+
4
-600 -800 -3
Experiment Analysis -2
-1
0
1
&++A&-@B+
2
=&6B$*$Z-&'>)'*)@C,1$>&@')`B)*"6)%1$,)@'^'$%$,YZA&@' D6-()7-"+PP+{+]%8&+98.-+O8+
3&%H"1C>'>)',$'$*ZAC,$A"4%'B,P@ZA$' ! S" Lp = L $1 # % & Z' W(OkR(
T9PQ=PM=Wb+]9O(+
&%
)
&$
*
&# &" &!
% $ #
" ! !
!'!!!(
!'!!&
' (1/in)
!'!!&(
"$ "# "" "! &% &$ &# &" &! % $ # " !
W(OkR(
PR9PQ=PM=Wb+]9O<+ ( )
!
!'!!!"
!'!!!#
' (1/in)
!'!!!$
!'!!!%
K@1$>&@',Y6"1)' N(O^"3R(
?(O^"3R( !
yc
15
!
lb
?(O^"3R( !
!
cc ! lb
yt
!
cc
10
10
1000
!
!
yt
800
yc
5
5
0 0
-5
600
-10
400
-5
-15
!
lb
-20
-10
200
!
yc
-25
!
cc
0
0
100
200
300
400
500
600
M2 (k-ft) 4.6-()7-"+SIv=PM=Wb+]9P+
-30 -4
-2
0
2
4
6
! (in) 4.6-()7-"+O9QR=PM=Wb+]9Q8+
-15 -20
-10
!
yt
0
10
20
! (in) 4.6-()7-"+PW9QR=QT=PQb+]9Q8+
KAC$A"&%)@'A$,"0*$>$@')6BY*"A$6)%1)' B$*$'>)1)*6"%$*',$'*)@"@1)%A"$'^'*"H">)#'1&*@"&%$,' T
'
I9:;+.6-()7-".+ 500
1 Tn = Ts + Tc 4
400 300
T (kip-ft)
200 100 0 -100 -200
GJ eff
-300 -400 -500 -10
-5
0
*z (deg)
T
5
10
1 GJ s + GJ c 2 = 1 GJ s + GJ c 6
for CCFTs for RCFTs
=&%1)%">&' !"#$%&'(()*"+ ,"#-(-&-"#-.+ ,"/0).).+1+2).-3%+ 4.#'&)%+456-$)7-"#80+ &-+9%0'7"8.+9:;+ 980)<$8()*"+&-+&8#%.++ ,"/0).).+"%=0)"-80-.+ >$%6'-.#8.+&-+&).-3%+ 9%7-"#8$)%.+?"80-.+ 4.#'&)%.+6$%(-.%+ ,@$8&-()7)-"#%.+
U6B$A1&'^'A&%1*"0CA"&%)@' ! >$%@$878+)"#-@$80+-56-$)7-"#80+(%"+9:;.+ ! 4.6-()7-"-.+&-+-.(808+$-80+1+-.<-0#%.+ ! !".#$'7-"#8()*"+-5#-".)`8+ ! 9%760-[%+6$%#%(%0%+&-+(8$@8+ ! S':6'(+:5>+'(2%(3'.2%,( ! 9"'6:'&'#(2%(".$%:'++"8.(NDB( ! 70,/*+"8.(2%(/'(:"6"2%C(Ol%`"8.E($,:#"8.R( ! N'.2%,(/,+'/( ! W,.6"$*2(2%(/'(':>+*/'+"8.(3/@#>+'( ! 70'/*'+"8.(2%(/,#(%#$'2,#(/5&"$%( ! 45#-".)`%+6$%(-.87)-"#%+&-+&8#%.+-56-$)7-"#80-.+ ! ,"/0).).+68x+-`80'8$\(80)<$8$+$-.6'-.#8+-56-$)7-"#80+ ! H')8.+.)760)?(8&8.+&-+&).-3%+&-+-0-7-"#%.+9:;+
Estudios de investigación en proceso: " 98$8(#-$)F8()*"+1+(80)<$8()*"+8"80Ja(8+&-+08+$)@)&-F+7T%\+ " 980)<$8()*"+&-+08+7-#%&%0%@J8+&-+&).-3%+6$%6'-.#%++ AE'"()%"-.+(%"a"'8.+1+$-&'(()*"+&-+7%7-"#%+6%$+ -.#8<)0)&8&B+ " :8(#%$-.+&-+&-.-76-3%+.J.7)(%+Af\4E(mn[S2E(4[(B+&-+ &)E-$-"#-.+8$i'-a6%.+&-+78$(%.+(%76'-.#%.+A)U-U+9:;=DY:b+ 9:;=DG:b+DI9.b+-#(UB+ " 980)<$8()*"+&-0+2,Y+-"+78$(%.+-"+(%".#$'(()*"+(%76'-.#8+ " I-.).#-"()8+8+(%$#-+&-+-0-7-"#%.+(%76'-.#%.U+ " 4`80'8()*"+-56-$)7-"#80+8"&+8"80Ja(8+&-0+&-.0)F87)-"#%+ 8(-$%=(%"($-#%+-"+(%0'7"8.+(%76'-.#8.+ " >8"&-%+#%$.)%"80+1+_-5%#%$.)%"80+&-+7)-7<$%.+(%76'-.#%.+
Reconocimientos N:,V%+$,(o.'.+"'2,(3,:A((
T.#>$*+",.%#(3':>+"3'.$%#A((
9,.'+",.%#(2%A((
W'-,:'$,:",A((
<3,V':,.('/(3:%#%.$'2,:A((
Comentarios finales ! 7#$'(3:%#%.$'+"8.(&*%#$:'(:%#*/$'2,#(2%(*.(3:,V%+$,(2%( ".0%#>6'+"8.()*%(#%(g'(%#;,:C'2,(%.A( ! 2-.8$$%008$+"'-`%+(%"%()7-"#%+ ! 4`80'8$+1+8.)7)08$+-0+(%76%$#87)-"#%+&-+(%0'7"8.+ (%76'-.#8.+ ! 45#-"&-$+0%.+$8"@%.+-"+08.+`8$)8<0-.+&-+&).-3%+ ! >$%`--$+&-+&8#%.+68$8+E'#'$8.+(80)<$8()%"-.+ ! ,'7-"#8$+08+6$-().)*"+-"+08+6$-&)(()*"+&-+08+(868()&8&+1+ &-+08+$-.6'-.#8+&-+(%0'7"8.+(%76'-.#8.+9:;+ ! 7#3%:'&,#()*%(%#$'(3:%#%.$'+"8.(+,.$:"-*V'(%.(;,&%.$':(%/( *#,(2%(#"#$%&'#(+,&3*%#$,#(%.(/'(3:@+>+'(p( t'(*)HC%1$@'u'