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ECCENTRICALLY LOADED
COLUMNS
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Impossible for a column to beperfectly aially loa!e! E"en if loa!s coul! be perfectly centere!
at one time# t$ey %oul! not stay in place
Columns may $a"e ot$er &a%s %it$ t$e
result t$at lateral ben!in' %ill occur (in! an! ot$er lateral loa!s
Cause columns to ben! an! columns in ri'i!frames are sub)ecte! to moments e"en
%$en t$e frame is supportin' 'ra"ity loa!salone*
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In actual construction
Columns an! beams + monolit$ic
Moments of "aryin' si,es are present in t$e )oints -ecause of frame action un!er bot$ applie! loa!s an!
!eformations in!uce! by temperature# s$rin.a'e an!settlement
Columns
Al%ays sub)ect to some ben!in' moments as %ell
as aial loa!s (ill ben! un!er t$e action of moments an! t$ose
moments %ill ten! to pro!uce compression on onesi!e an! tension on t$e ot$er si!e*
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Eccentrically loa!e! ($en a combination of aial loa! an! moment
are present
Eccentricity Represents t$e !istance t$e aial loa!
/01# %oul! $a"e to be o2 center of t$e
column to pro!uce M*
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Columns sub)ect to Loa! %it$ Lar'er
an! Lar'er /e1
Illustration Description
a*3 0n Lar'e aial loa! causes a crus$in'failure of t$e concrete %it$ all barsreac$in' t$eir yiel! point incompression*
b*3 e 0n Lar'e aial loa! an! small momentbut entire cross section incompression* 4ailure occurs bycrus$in' of t$e concrete# all bars incompression*
c*3 e 0n Lar'e aial loa!# moment lar'er in5b3# bars on far si!e in tension but$a"e not yiel!e!# failure occurs by
crus$in' of t$e concrete*
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Columns sub)ect to Loa! %it$Lar'er an! Lar'er /e1
Illustration Description
!*3 e0n
-alance loa!in' con!ition + bars ontensile si!e yiel! at t$e same timeconcrete on compression si!ecrus$es*
e*3 e0n
Lar'e moment# relati"ely small aialloa! failure initiate! by yiel!in' oftensile bars* If eccentricity is furt$erincrease!# failure %ill be initiate! byyiel!in' of tensile bars*
f*3Mn
Lar'e ben!in' moment# failure occursas in a beam* Lar'e moment %it$ noappreciable aial loa!*
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Eccentrically loa!e! columns6-en!in' in one !irection only
($en actual e 7 eb # compressioncontrols
8alues of eb6
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Symmetrical tie! column Symmetrical spiralcolumn
s9uare section
!:
!:
Dst
tt
t
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Symmetrical spiral column6 Unsymmetrical tie!column
Roun! section
!:
!
:
Ds D
;
Y
t
b
!: !
M
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!
! ? ratio of t$e area ofcompression reinforcement tot$e e2ecti"e area of concrete*
= ? ratio of area of tensionreinforcement to t$e e2ecti"e
area of concrete*
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Eccentrically Loa!e! Column6-en!in' in one !irection
Tie! Column
($en eb @ e# compression controls
eb? 5*B='m *3 5tF!3
Use interaction e9uation6
fa?actual aial stress
4a ? allo%able aial stress
fb?actual ben!in' stress4b? allo%able ben!in' stress
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T$ere are t%ocolumns
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Sample 0roblem6
A s$ort tie! column $as a crossF
section of GH mm GH mm %it$HFG mm !iameter bars place! atan eccentricity of H mm fromt$e center of t$e column section*fc?*J M0a# fy?GKJ*J Mpa# n ?H*
Determine t$e "alue of eb
Determine t$e moment of inertia of
t$e concrete composite section Determine t$e safe loa! t$at it coul!
carry
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* Determine t$e safe loa! t$at t$es$ort tie! column can carry if it $as across section of GH mm GH mm
%it$ HFG mm bars* T$e loa! isplace! at an eccentricity of H mmfrom center of t$e column section*
fc:?*J Mpa# fy ? GKJ*J Mpa# n ? H*