Estudio analítico y experimental de columnas compuestas esbeltas del tipo de tubo de acero relleno

!"#"$%&'()*)$'+,-)*$.'/&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'