advanced structural design - lecture note 03

7/21/2019 Advanced Structural Design - Lecture Note 03

http://slidepdf.com/reader/full/advanced-structural-design-lecture-note-03 1/29

12/15/15

Prepared by: Eng. Chamil Duminda

Mahagamage B.Sc.Eng (Hons), C Eng,1

n"erna"ional College o# Business and$echnology

6102BEUG- Lecture Note:03

Design of CompositeColumns

Introduction

Steel-concrete composite columns are compression memers in t!e"orm o" concrete encase# $-sections or concrete-%lle# !ollo& sections' (pical cross sections o" some tpe o" composite columns are s!o&nelo&' (!e earl #e*elopment o" composite columns &as ase# on t!e nee#to pro*i#e e+ecti*e %re protection encasin, steel stanc!ions in

concrete' ncrease in stren,t! an# sti+ness #ue to concreteencasement &ere i,nore#. alt!ou,! it &as reco,nie# t!at t!euclin, resistances o" encase# columns &ere increase#' (!e a#*anta,es o" composite columns are: increase# resistance "or a ,i*en memer sie. lea#in, to economin t!e use o" t!e steel sections'

increase# sti+ness. lea#in, to re#uce# slen#erness an# increase#uclin, resistance' impro*e# connection e!a*iour &it! attac!ments ma#e *ia t!esteel sections ,oo# %re resistance ecellent corrosion protection o" encase# columns

en!ance# seismic resistance



12/15/15

Prepared by: Eng. Chamil Duminda

Mahagamage B.Sc.Eng (Hons), C Eng,2





12/15/15

Prepared by: Eng. Chamil Duminda Mahagamage B.Sc.Eng (Hons), C Eng,ME(S!)

4n"erna"ional College o# Business and$echnology


Design methods (&o met!o#s o" #esi,n "or isolate# composite columns in race# ornon-s&a "rames are ,i*en in E4-1-1. lause 6''

- ,eneral #esi,n met!o# "or composite columns applicale to ot!prismatic an# non-prismatic memers &it! eit!er smmetrical or non-smmetrical cross-sections'

- simpli%e# #esi,n met!o# speci%call #e*elope# "or prismaticcomposite columns &it! #oul smmetrical cross-sections'

%o"e&: 'hen "he limi"s o# applicabili"y o# simplied me"hod are no"sa"ised, "he general design me"hod should be used.

Fire resistancen ,eneral. composite columns possess muc! !i,!er %re resistancest!an t!e parent steel columns' omposite columns are usuall

#esi,ne# in t!e normal cool) state an# t!en c!ece# un#er %recon#itions'7esi,n ,ui#ance on t!e %re resistances o" composite columns ma e"oun# in E4-1-2'



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Simplied Design method (!e simpli%e# met!o# !as een #e*elope# speci%call "or prismaticcomposite columns &it! #oul smmetrical cross-sections &it! !ot

rolle#. col# "orme# or &el#e# steel sections' (o pre*ent local uclin,. t!e &i#t! to t!icness ratio o" *ariouselements in t!e steel sections in compression must satis" t!e"ollo&in, limits as ,i*en in (ale 6'3 o" E4-1-1'

8or "ull encase# sections. local uclin, in t!e steel sections is not

possile. an# !ence. *eri%cation "or local uclin, is not necessar'



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Compression resistance of cross-sections (!e plastic resistance o" a composite cross-section in compressionrepresents t!e maimum loa# t!at can e applie# to a s!ort column

&!ic! #oes not e!iit memer uclin,' t s!oul# e note# t!at. inconcrete-%lle# !ollo& sections. a !i,!er compression resistance isac!ie*e# in t!e concrete o&in, to t!e con%nement pro*i#e# t!e!ollo& section' 9oreo*er. "urt!er stren,t! en!ancement isac!ie*e# in concrete-%lle# circular !ollo& sections o&in, to t!e#e*elopment o" circum"erential action in t!e circular !ollo& section'

Concrete encased H-sections and concrete-lled rectangularhollow sections (!e plastic resistance o" a concrete-encase# $-section or a concrete-%lle# rectan,ular or suare !ollo& section in compression is ,i*en

t!e sum o" t!e resistances o" t!e components in compression. #e%ne#in E4-1-1. lause 6''3'2. as "ollo&s:



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Belo& %,ure s!o&s t!e i#ealise# stress #istriution &!ic! t!e ao*eeuation is ase#' ;n important #esi,n parameter is t!e steelcontriution ratio.< &!ic! is #e"ine# as "ollo&s' t is important to notet!at < s!oul# lie &it!in 0'2 an# 0'='



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>n"erna"ional College o# Business and$echnology


Concrete-lled circular hollow sections 8or composite columns &it! concrete-%lle# circular !ollo& sections.t!e increase# compression resistance o" t!e concrete #ue to t!econ%nement pro*i#e# t!e circular !ollo& section s!oul# e

inclu#e#' t s!oul# e note# t!at t!ese en!ancement e+ects #epen#on t!e slen#erness o" t!e columns. an# t!e are onl si,ni%cant instoc columns' n a##ition. t!e eccentricit. e. o" t!e applie# loa#s!oul# not ecee# 0'1d &!ere d is t!e outer #imension o" t!e circular!ollo& section' (!e plastic resistance o" concrete-%lle# circular !ollo& sections in

compression to E4-1-1 lause 6''3'26) is ,i*en :



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=n"erna"ional College o# Business and$echnology




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Bending resistances of cross-sections



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Shear resistance of cross-sections n ,eneral. t!e applie# s!ear "orce. @E#. ma e conser*ati*el

assume# to e resiste# entirel t!e steel section' No re#uction tot!e resistances o" t!e cross section in compression an# in en#in, arenee#e# &!en @E# is smaller t!an !al" o" t!e s!ear resistance o" t!e

steel section. i'e' 0'5@a.#

$o&e*er. &!en Ed A 0'5@a.#. t!e resistances o" t!e cross-section in

compression an# in en#in, s!oul# e e*aluate# accor#in, to are#uce# #esi,n stren,t! 1 - ) # yd in t!e s!ear area. ;* o" t!e steel

section in accor#ance &it! lause 6'2'2'42). an# is ,i*en :



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Resistances of cross-sections in combined compression andbending

(!e resistance o" composite cross-sections to comine# compression.N. an# uniaial en#in,. 9. an# t!e correspon#in, non-linear N-9interaction cur*e are e*aluate# accor#in, to rectan,ular stresslocs in *arious components o" t!e cross-sections't s!oul# e note# t!at in a tpical N-9 interaction cur*e o" a steelsection. its moment resistance un#er,oes an almost linear re#uction&it! increasin, aial loa#. as s!o&n in 8i,ure 23'4 a)' $o&e*er. ass!o&n in 8i,ure 23'4). a composite cross section ma e!iitsi,ni%cant increases in its moment resistance in t!e presence o" aialloa#' (!is is ecause. un#er some "a*ourale con#itions. t!ecompressi*e aial loa# &ill pre*ent concrete cracin,. an# enalet!e composite cross-section to e more e+ecti*e in resistin,moments'Suc! a non-linear N-9 interaction cur*e "or a composite cross-sectionma e rea#il simpli%e# into a multi-linear interaction cur*e &it!

3 to 5 e points. as s!o&n in 8i,ure 23'5' (!e coor#inates o" t!ese e points o" t!e multi-linear interaction

cur*e are #etermine# "rom t!e internal "orces an# moments. ase#on t!e rectan,ular stress locs o" t!e *arious elements o" t!e



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C Doint ; #e%nes t!e plastic compression resistance o" t!e cross-section: % * +% pl

C Doint B correspon#s to t!e plastic en#in, resistance o" t!e cross-section: MBM pl,d

C ;t Doint . t!e plastic resistances o" t!e cross-section incompression an# in en#in, are ,i*en respecti*el as "ollo&s:

%c %pm.#or %c.# ) ;c" c# Mc M pl,d

(!e epressions ma e otaine# cominin, t!e stress #istriutionso" t!e cross section at Doints B an# ' (!e compression area o" t!econcrete at Doint B is eual to t!e tension area o" t!e concrete at Doint' (!e moment resistance at Doint is eual to t!at at Doint B since t!e

stress resultants "rom t!e a##itionall compresse# parts nulli" eac!ot!er in t!e central re,ion o" t!e cross-section' t ma e s!o&n t!at t!ea##itionall compresse# re,ions create an internal aial "orce &!ic! iseual to t!e plastic resistance o" t!e concrete in compression. Npl.# or

%c,d.

C ;t Doint 7. t!e plastic neutral ais coinci#es &it! t!e centroi#al ais o"



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• n ,eneral. Doint 7 is less important t!an Doint in #esi,n' Doint Eis mi#-&a et&een Doints ; an# ' t is o"ten reuire# "or !i,!lnon-linear interaction cur*es. ut is ,enerall not nee#e# "or encase#

$-sections suFect to moments aout t!e maFor ais' t is important to note t!at t!e positions o" t!e neutral aes "or DointsB an# . hn can e #etermine# "rom t!e #i+erence in stresses at Doints B

an# ' (!e resultin, aial "orces. &!ic! are #epen#ent on t!e position o"t!e neutral ais o" t!e cross-section. h

n

, can e easil #etermine#. as

s!o&n in 8i,ure 23'' (!e sum o" t!ese "orces is eual to Npm.#' (!is

calculation enales t!e euation #e%nin, hn to e #etermine#. &!ic! is

#i+erent "or *arious tpes o" sections'



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6102BEUG- Lecture Note:03Bucling resistance of columns omposite columns ma "ail in uclin, #ue to t!e secon#-or#er or-P&- e+ects. an# it is possile to e*aluate t!eir memer resistances

t!rou,! t!e con*entional use o" uclin, cur*es' n t!is approac!. t!econ*entional column uclin, concept as ,i*en in BS E3-1-1 isa#opte#. an# t!e memer resistance o" a composite column #epen#son its relati*e slen#erness an# use o" an appropriate column uclin,cur*e' $ence. t!e uclin, resistance o" t!e composite column is#etermine# as a re#uction to t!e plastic resistance o" t!e composite

cross-section. accor#in, to its slen#erness'

Critical Bucling load

t is important to e*aluate t!e elastic critical uclin, loa#. %cr , o" t!ecomposite column &!ic! is #e%ne# in E4-1-1. lause 6''3'33). as"ollo&s:



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1>n"erna"ional College o# Business and$echnology


n ,eneral. t!e uclin, len,t!. l o" an isolate# non-s&a compositecolumn ma conser*ati*el e taen as its sstem len,t!. !.

;lternati*el. t!e uclin, len,t! ma e #etermine# usin, ;nne E o"E3-1-1'9oreo*er. "or slen#er composite columns un#er lon,-term loa#in,.creep an# s!rina,e o" concrete ma cause a re#uction in t!e e+ecti*eeural sti+ness o" t!e composite columns. t!ere re#ucin, itsuclin, resistance' n suc! cases. Ecm s!oul# e re#uce# multiplin,

t!e "ollo&in, "actor:

&!ere /i is t!e creep coeHcient . %Ed is t!e total #esi,n compression"orce. an# %0,Ed is t!e part o" %Ed t!at is permanent' ;s a simple rule.

t!e lon,-term e+ects s!oul# e consi#ere# in a composite column i" itsuclin, len,t!-to-#ept! ratio ecee#s 15'



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1=n"erna"ional College o# Business and$echnology




12/15/15






12/15/15

Prepared by: Eng. Chamil Duminda Mahagamage B.Sc.Eng (Hons), C Eng,

ME(S!)





12/15/15


ME(S!)



Resistance of members in combined compression and bendingUn#er comine# compression an# en#in,. slen#er composite columnsma "ail primaril in lateral uclin, un#er t!e secon# or#er. or -P&-e+ects' $ence. it is necessar to e*aluate t!e internal "orces an#moments o" slen#er columns accuratel'

Direc" e1alua"ion approach;ccor#in, to E4-1-1lause 6''3'5. structural a#euac o" a slen#ercomposite column to comine# compression an# en#in, ma e*eri%e# usin, secon#-or#er analsis &it! memer imper"ections' (!isapproac! ma e re"erre# to as t!e 7irect E*aluation ;pproac! in &!ic!structural a#euac o" a composite column is assesse# #irectcomparison o" its cross-section resistances a,ainst t!e applie# "orces an#moments at lar,e #e"ormations' n t!is met!o#. an initial ,eometricalimper"ection. io, is speci%e# "or t!e column accor#in, to (ale 6'5 o"

E4-1-1. or to (ale 23'2 "or #irect e*aluation o" t!e secon#-or#ermoment. <M un#er t!e applie# loa#. %Ed, i'e' 2Mi %ed io. as s!o&n in

8i,ure 23'=' (!is moment <Mi is comine# &it! t!e applie# moment

9E# "or #irect comparison a,ainst t!e en#in, resistance o" t!e

composite cross-section in t!e presence o" t!e applie# loa#. 9pl.N.#.

usin, t!e N-9 interaction cur*e o" t!e composite cross-section'n ,eneral. "or tpical structural "orms &it! &ell estalis!e# structural



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ME(S!)



7epen#in, on t!e slen#erness o" t!e column. ampli%cation "actors. k ,ma e applie# to t!ese I%rst-or#erI "orces an# moments to account "oran secon#-or#er e+ect as necessar'

$o&e*er. "or structures &it! irre,ular memer con%,urations an# *erslen#er columns an# eams. accurate internal "orces an# momentss!oul# e otaine# t!rou,! t!e use o" appropriate a#*ance#

structural analsis so"t&are inclu#in, ot! ,eometrical an# materialnon-linearities' n suc! cases. t!e important consi#erations are t!e initial,eometrical an# mec!anical imper"ections o" t!e memers. inter"acial

s!ear e!a*iour et&een steel sections an# concrete. crus!in, an#cracin, o" concrete. eural ri,i#ities o" t!e eam-column Foints an#column splices. an# t!e e!a*iour o" t!e concrete un#er lon, termloa#s'



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ME(S!)





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ME(S!)



6 02 G



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ME(S!)



Chec3 #or s"ruc"ural ade4uacy ;s s!o&n in 8i,ure 23'11. E4-1-1. lause 6''3'6 consi#ers t!at t!e#esi,n is a#euate &!en t!e "ollo&in, con#ition is satis%e#:

6102BEUG L t N t



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ME(S!)



6102BEUG L t N t



12/15/15


ME(S!)

2>n"erna"ional College o# Business and$echnology


esistances o" memers in comine# compression an# i-aialen#in,8or t!e #esi,n o" a composite column un#er comine# compression an# i-aial en#in,. t!e *alue o" 5d s!oul# e calculate# separatel "or eac!

ais' mper"ections s!oul# e consi#ere# onl in t!e plane in &!ic! "ailureis epecte# to occur' " it is not e*i#ent &!ic! plane is t!e more critical.c!ecs s!oul# e ma#e "or ot! planes';"ter t!e e*aluation o" t!e moment resistance ratios 5dy an# 5d6 "or

ot! aes. t!e interaction o" t!e moments s!oul# also e c!ece#

accor#in, to lause 6''3'2) at *arious positions alon, t!e memerlen,t! a,ainst t!e resistance o" t!e cross section in en#in, in t!epresence o" aial loa#. as "ollo&s:

6102BEUG L t N t



12/15/15

Prepared by: Eng. Chamil Duminda Mahagamage B.Sc.Eng (Hons), C Eng,2=n"erna"ional College o# Business and

$echnology


advanced structural design - lecture note 03

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