8/9/2019 Eccentrically Loaded Columns1

1/17

ECCENTRICALLY LOADED

COLUMNS

8/9/2019 Eccentrically Loaded Columns1

2/17

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*

8/9/2019 Eccentrically Loaded Columns1

3/17

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*

8/9/2019 Eccentrically Loaded Columns1

4/17

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*

8/9/2019 Eccentrically Loaded Columns1

5/17

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*

8/9/2019 Eccentrically Loaded Columns1

6/17

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!*

8/9/2019 Eccentrically Loaded Columns1

7/17

Eccentrically loa!e! columns6-en!in' in one !irection only

($en actual e 7 eb # compressioncontrols

8alues of eb6

8/9/2019 Eccentrically Loaded Columns1

8/17

Symmetrical tie! column Symmetrical spiralcolumn

s9uare section

!:

!:

Dst

tt

t

8/9/2019 Eccentrically Loaded Columns1

9/17

Symmetrical spiral column6 Unsymmetrical tie!column

Roun! section

!:

!

:

Ds D

;

Y

t

b

!: !

M

8/9/2019 Eccentrically Loaded Columns1

10/17

!

! ? 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*

8/9/2019 Eccentrically Loaded Columns1

11/17

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

8/9/2019 Eccentrically Loaded Columns1

12/17

8/9/2019 Eccentrically Loaded Columns1

13/17

T$ere are t%ocolumns

8/9/2019 Eccentrically Loaded Columns1

14/17

8/9/2019 Eccentrically Loaded Columns1

15/17

8/9/2019 Eccentrically Loaded Columns1

16/17

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

8/9/2019 Eccentrically Loaded Columns1

17/17

* 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*