S4 Column Design

7/26/2019 S4 Column Design

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I.C.E., IV, 2015-2016 Steel Industrial Building-Design Project

Stage 4 Column Design

4.1. Design values

in combinations N,

M,V- min/max

max

EdN cor

EdV cor

EdM

corespunzator

EdN max

EdV cor

EdM

cor

EdN cor

EdV max

EdM

4.2. Critical lengts o! te column

Static sce!e ado"ted#- in te trans$ersal %ra!e "lane te colu!n is &'ed in te %oundation and inged atte to"( )uc*ling a)out +-+#

Lcr,y= 0.7hc

- in te longitudinal direction te colu!n is dou)l+ inged at te e'tre!ities()uc*ling a)out -#Lcr,z= hc

Still, as tese $alues do not corres"ond entirel+ it te real conditions o%

restraining in te "lane o% te %ra!e trans$ersall+/ and nor!al to te "lane o% te

%ra!e, in te longitudinal direction o% te structure, tre !a+ )e a "aralel "ossi)ilit+

to e$aluate te critical lengts.

Buckling about y-y

se te relationsi"s %or a rigurous a""roac it te el" o% te oods cur$es#

1

4.1. "ctions an# combinations !or #esign

4.2. Critical lengts o! te column4.$. Si%ing te cross section4.4. Veri&cations in '.(.S. combinations4.4.

1.

Classi&cation o% te cross section

4.4.

2.

Veri&cations %or strengt under co!)ined state o%

stresses2.4.

$.

Veri&cations %or sta)ilit+


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2


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Buckling about z-z:

3


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4erestraining conditions at 2, 3 due to te second order structure tat

sustain te alling s+ste! joists/ are considered dou)l+ "inned.

4.$. Si%ing te cross sectionCoose a ot rolled uni$ersal section %or colu!ns, li*e 7E8,7EB,7E9Esti!ate a trial section it a sel%eigt deter!ined it#

gc,k = (0.15..0.20)[kN/m]hc [m]

ere cis te lengt o% te colu!n %ro! te )ase "late u" to te ca"ital le$el

)eometric caracteristics Sectional

caracteristics

....h mm=

2.....A mm=

...b mm=

4.....yI mm=

...wt mm=

4....

zI mm=

...ft mm=

4......tI mm=

...r mm= 3, .....pl yW mm=

2

, ......V ZA mm=

Sizing the sectin !r the c"#mn

1/ 9Ed : 9"l,+,;d li!+


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3/ @o to ta)elsand coose section?/ Veri%+#

0 0

max,

,

0.7

cor

y EdEd

y y

pl y

M M

MN

f fA W

+

Ai

0 0

max

,

,

0.7cor

y EdEd

y y

pl y

M M

MN

f fA W

+

4.4. Veri&cations in '.(.S. combinations?.?.1. Classi&cation o% te cross sectionClass 1 S; E 13-1-1#2006, ta). 5.2

e)#

2 2 ;c d h t r t t wf= = =

max1

12

Ed

w y

N

c t f

= +

5


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langes#

6


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4.4.2. Veri&cations !or strengt un#er combine# state o! stresses9e!)ers in )ending in te "resence o% a'ial an sear %orces, co!)ined 9--V

stresses S; E 13-1-1, "ct. 6.2..1/.4e eFect o% a'ial %orce u"on te reistent )ending !o!ent a)out te rele$ant a'is

o% te s+!!etric class 1 sections, li*e I and 7 ill )e cec*ed i%#

Ed G 0.15="l,;d and Ed G 0.5t%+,dSo#

,Ed N RdM M

ere# $%& = $m',%& $N,& = $N,y,&

, , , ,

1

1 0, 5N y Rd pl y Rd

nM M

a

=

,

2, 0,5

corfEd

pl Rd

A b tNn a dar a

N A

= =

;esistance to sear S; E 13 1-1-, "ct. 6.2.6/

, ,,

1 ( )Ed c Rd pl Rd c Rd

VV V in absenta rasucirii

V =

,max,

0

( / 3)v z yEd Ed pl Rd

M

A fV V si V

= =

,v zA

- sear area in te - "lane

%or I and 7 sections#

, 2 (2 )v z f f wA A bt t r t= + +

4e eFect o% sear u"on te "lastic resistant )ending !o!ent S; E 13-1-1, "ct. 6.2.H/

!ai )e neglected i%#

max,

,

0,5Ed

pl Rd

Vse neglieaz!

V

I%#

max,

, ,

,

0,5Ed

y V Rd

pl Rd

Vse calculeaza M

V

>

2

2,

, ,0 , ,

4 21

wy pl

w Edy V Rd w w w

M z pl Rd

AW

t VM cu A h t si

V

= = =

And the verification is :


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, ,Ed y V RdM M

4.4.$. Veri&cations o! stabilit* o! te column un#er com+ression an#

ben#ing about y-yS N 1$-1-1, +ct. 0.$.$

,

, , , ,

1y EdEd

yy

b y Rd b y Rd

MN"

N M+

,

, , , ,

1y EdEd

zyb z Rd b y Rd

MN"

N M+

ere#

,,Ed y EdN M

- design $alues o% te internal a'ial %orces and !o!ents in te

rele$ant co!)ination o% actions(

, ,

1

y

b y Rd y

M

A fN

=

(

, ,

1

y

b z Rd z

M

A fN

=

(

,

, ,

1

y pl y

b y Rd #$

M

W fM

=

,y z

- reducing %actors o% )+c*ling a)out +-+ and -(

#$

- reducing %actor %or Je'ural torsional )uc*ling o"en sections/(

,yy zy" "

- interaction %actors 8nne' B, S; E 13-1-1/

- )uc*ling cur$es#

- i!"er%ections %actors#

H


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*#ck"ing '+#t yy-

,cr y

y

y

#

i =

(

1

; 1!3.!

y y

y

= = =

20.5 1 ( 0.2)y y y y

= + +

2 2

1y

y y y

=

+

, ,1

yb y Rd y

M

A fN

=

*#ck"ing '+#t zz

,cr zz

z

#

i =

,

1

zz

=

20.5 1 ( 0.2)z z z z = + +

2 2

1

1z

z z z

= +

, ,1

yb z Rd z

M

A fN

=

"e#r'" trsin'" +#ck"ing-


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1

,

0.252

,1

,

/

/1

1 20 /

#$#$

cr z z #$

cr z z

# i

# i

% h tf

=

= +

8legerea cur)ei de Ja!)aj#

, 0.34

, 0.4!

#$

#$

curba b cu

curba c cu

=

=

,0 0.4#$ =

0.75=

2,00.5 1 ( )#$ #$ #$ #$ #$

= + +

2 2

1#$

#$ #$ #$

=

+

,

, ,

1

y pl y

b y Rd #$

M

W fM

=

nteraction !actors #etermine# accor#ing to te s*m+li&e# meto#,

"nexa 3, S N 1$-1-12550

10


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11


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4.6. Ca+ital o! te column

;@K - truss reaction

1/ca" "late

tc


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or te gusset i% necessar+/

15tt mm=

tb #=

4.0.1"ncor bolt ol# #o7n bolt

4e colu!n is gi'ed in te %oundation it ? ancor )olts. 4e dia!eter o% te )olt

is deter!ined %ro! te condition to resist to traction tension stresses !a+ )e

de$elo"ed under te )ase "late due to te eFect o% te )ending !o!ent/.

, ,2,

max2 0.! 4,

, 2 2

0.! 42,

2

( (t Ed t Rd ( Mt EdAscorM N f Ay Ed Ed sub( dst Ed h t

f dsAsA fs ub(t RdM

=

=

=

0.$!0.$!

dsd d ds

4.0.2. 3ase +late sub8ecte# to com+ression

4e design is )ased on te teoretical !odel "resented in S; E 13-1-H# te

Je'i)le )ase "late is re"laced )+ an eMui$alent rigid "late, tis one )eing o)tained

%ro! te "rint o% te colu!n cross section to ic a stri"e it te di!ension c is

added on te "eri!eter o% te colu!n section, ere#

13


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3 0

fyc tp

f Md

,

fd

- resistance o% te grout la+er )eteen te )ase "late and

te %oundation.

4e caracteristic $alues o% te resistance o% )ot te grout and te concrete areconsidered

Class o! resistance o! te concrete

C202

5

C2530 C303

C35?

5

C?050

2/f N mmcd

13 16, 20 23,3 26,

2/f N mmd

13 16, 20 23,3 26,

I% te "ressure under te eMui$alent sur%ace o% te )ase "late is considered as

e$enl+ distir)uted te reistance to co!"ression is#

,( f Ac Rd d eff =

8nd te $eri&cation to co!"ression is#max

,N (Ed c Rd

4.0.4. 3ase +late un#er axial !orce an# ben#ing moment

C"S 1

e'centricit+ one $eri&cation ;esistant !o!ent in te

connection

1?


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%

Ed

Ed

M #e

N=

Bot le%t and rigt are

acti$e in co!"ression

max, ,M My Ed Rd

e%istence o! te con+resse# area in te connection,c Rd

(

4e resistance is gi$en )+ te loest $alue )eteen te resistance o% te colu!n

Jange and te "art o% te e) in co!"ression and te resistance to co!"ression o%

te )ase "late as te su! )eteen te acti$e "arts in co!"ression/#

( )min ;, , , , ,( ( (c Rd c fc Rd c pl Rd =

,,, ,

MM pl Rdc Rd(c fc Rd h t h t f f

= =

, ,

2 ; 2 ; 2

( f Ac pl Rd d eff

A b l b c t l c beff eff eff eff f eff

=

= = + = +

, , , , ,( ( (c l Rd c r Rd c Rd = =

z h tf=

, ,2 2

c l c r

th fz z= =

e


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C"S 2

e'centricit+ one $eri&cation ;esistant !o!ent in te

connection

%

Ed

Ed

M #e

N= >

e%t side in tnesion and

rigt side in

co!"ression re$ersi)le

in s+!!etric situations/

max, ,M My Ed Rd

,2 2

f% r

thz =

, 022

$ r

hz d= +

, 022

f$ r

tz h d= +

esistance o! te %one in com+ression -, ,(c r Rd

It ill )e deter!ined as te loest $alue %ro! te resistances o% te co!"onents o%

te connection under co!"ression %orces( )min ;, , , , ,( ( (c Rd c fc Rd c pl Rd =

,,, ,

MM pl Rdc Rd(c fc Rd h t h t f f

= =

, ,

; 2 ; 2

( f Ac pl Rd d eff

A b l b c t l c beff eff eff eff f eff

=

= = + = +

esistance o! te %one in tension - ,",&min( ; ), , , , ,( ( ($ Rd t pl Rd t wc Rd =

, ,(t pl Rd

- resistance o% te one o% te )ase "late o)tained %ro! a nu!)er o%

eMui$alent 4-stu)s, ic de"end on te t+"e o% %ailure !ecanis!s de$elo"ed#min( ; ), , ,1 2, ,3,( ( (t pl Rd $ Rd $ Rd =

16


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$&e 12 cm"ete "'stic !'i"#re mech'nism ! the +'se "'te-2 ,1 , ,

,1 2,

l Meff y pl Rd ($ Rd m

=

$&e 3 !'i"#re mech'nism ! +r'king the 'nchr +"ts in tensin

0.!2,3, ,

2

A fs ub( ($ Rd t Rd M

= =

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S4 Column Design