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AXIAL COMPRESSION

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In members which sustain chiefly or exclusivelyaxial compression loads, such as building

columns, it is economical to make the concretecarry most of the load. Still, some steelreinforcement is always provided for variousreasons. For one, very few members are trulyaxially loaded; steel is essential for resisting anybending that may exist; For another, if part of thetotal load is carried by steel with its much greaterstrength, the crosssectional dimensions of themember can be reduced, the more so the larger

the amount of reinforcement. !he two chief forms of reinforcedconcretecolumns are shown in Fig. ".#

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Fig. 8.5 $einforced concrete columns% &'( longitudinal rods

and spiral hooping; &)( * longitudinal rods and lateral ties; &+( *

structural steel.

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!here are also composite compression members &+(reinforced longitudinally with structuralsteel shapes,pipe or tubing, with or without additional longitudinal

bars. !ypes &'( and &)( are by far the most common, and

most of the discussion will refer to them. In the suare column, the four longitudinal bars

serve as main reinforcement. !hey are held in place by

transverse small diameter steel ties, which preventdisplacement of the main bars during constructionoperations and counteract any tendency of thecompressionloaded bars to buckle out of the concreteby bursting the thin outer cover. -n the left is shown around column with eight main reinforcing bars. !hese aresurrounded by a closely spaced spiral, which serves thesame purpose as the more widely spaced ties, but alsoacts to confine the concrete within it, thereby increasingits resistance to axial compression.

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!he maority of compression members carry a

portion of their load in bending. !his may be due

to the load not beingapplied at the centroid of

the member &i.e. load is applied eccentrically(,

as illustrated in Fig. ".'.a. /lternatively, bending

moments in a compression member may resultfrom unbalanced moments in the members

connected to its ends. !he results of such

bending moments in axially loaded members are

to reduce the range of axial force, which themember can safely carry.

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For this reason, it isessential that the effects

of bending in axiallyloaded members beconsidered.

$einforced concrete

members can beeccentrically loaded in asymmetrical plane&uniaxial bending( orsimultaneously subected

to bending about two&usually perpendicular(axes &biaxial bending(.

Fig. 8.10olumn subected to axial load and moment

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8.1. Behavior under load

!he behavior is dependent by the initial

eccentricity value, given by , and by the

value of axial force 1, respectively, Fig. ".)

a( b( c(

Fig. 8.!Failure of member subected to compression plus bending.

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For eccentrically compression, the dominantloading influences the behavior of the members.

For instance the limit shortening of compressedconcrete for an axial force is 2,)3, but forbending it is 2,+#3. For eccentricallycompression, the deformations will be smaller if

the bending will be secondary load reported tothe axial force, or will be near the maximumdeformation &2,+#3( if bending is principal. !hedeformation of the tension steel will be in plasticdomain, if bending moment is dominant and thesteel percentage does not exceed the maximumvalue or they can be under the yielding level, ifbending moment is secondary.

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If the failure takes place with plastic deformationin the tension reinforcement, followed by thecrushing of compressed concrete one considers

that is the 'st case of eccentrically compression. If the reinforcement has only compressionstresses or, being tensioned it is elastic domain,the failure takes place by the crushing of

compressed concrete that is the IInd case. In Fig. ".)a, it results the failure in case I, and inFig. ".)b and c, the failure in case II.

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In Fig. ".+ the interaction diagram

41 is presented.

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Colu"n rein#or$ed %i&h

longi&udinal 'ar

and &ie ( &ied $olu"n )

5hen axial load is applied, the

compression strain is the same over theentire cross section and in view of thebonding between concrete and steel, isthe same in two materials.

/t low stresses, the concrete is seen tobehave nearly elastically; i.e., stressesand strain are uite closely proportional.

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1 6 7b&/bnet 8 n/a(

N

bRc aRa

N

Aa

Ab

N < Nr

Nb

Na

Fig. 8.*/xial compressed member

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!he term /bnet8/a can be interpreted as thearea of a fictitious concrete cross section, thesocalled transformed area &or ideal area( whichwhen subected to the particular concrete stress7b results in the same axial load 1 as the actualsection composed of both steel and concrete.!his transformed concrete area is seen to

consist of the actual area plus ntimes the areaof the reinforcement. It can be visualised asshown in Fig. "9. In Fig. ".9b the three barsalong each of the two faces are thought of asbeing removed and replaced, at the same

distance from the axis of the sections, withadded areas of fictitious concrete of total amountnAa.

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)

/a )

/n a

)

/('n& a

Actual Section Transformed Section

Abi= Abnet + nAa

Transformed Section

Abi= Ab+ (n-1)Aa

a) ') $)Fig. 8.+ !ransformed section in axial compression

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/t failure%

1 6 /b$c 8 /a$a

&$c is fcd and $a is fyd according tonew standard(

/t this load the concrete fails bycrushing and shearing outward

along inclined planes, and thelongitudinal steel by bucklingoutward between ties, Fig. ".".

Fig. 8.8Failure of tied column

S i l i # d l

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S,iral - rein#or$ed $olu"n

Aial $o",reion

!his type of columns is reinforced withlongitudinal rods and spiral hooping. In

view of this close spacing, the presence of

a spiral affects both the ultimate load andthe type of failure compared with an

otherwise identical tied column.

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Failure occurs only when the spiral steel yields, whichgreatly reduces its confining effect, or when it fractures.It has been found that in the form of a spiral a given

amount of steel per unit length of column is at least twiceas effective in adding to the carrying capacity as thesame amount of steel used in the form of longitudinalbars. In a spiralreinforced column, when the failure loadis reached, the longitudinal steel and concrete within the

core are prevented from outward failing by the spiral.!he concrete in the outer shell, however, not being soconfined, does fail; i.e., the outer shell spalls off whenthe failure load is reached. It is at this stage that theconfining action of the spiral takes effect, and if si:eable

spiral steel is provided, the load which will ultimately failthe column by causing the spiral to yield or burst can besignificantly larger than that at which the shell spalled off.

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!he carrying capacity of this type of column is

given by%

1 6 1b 8 1al 8 1atrwhere% 1b 6 /bs$c

/bs is the core concrete area;

ds 6 )&a8

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If%

It results% 1 6 /bs &$c 8 =a$a 8 ).#=fs$as(

where% $as * is the spiral yield strength !ests have shown that failure occurs when the spiral yields

and it does not confine anymore the concrete within the

core; at this stage the concrete core is broken bycompression and longitudinal steel yields.

It follows that two concentrically loaded columns, one tiedand one with spiral but otherwise identical, will fail at aboutthe same load, the former in a sudden and brittle manner,

the latter gradually with prior shell spalling and with moreductile behaviour. !his advantage of the spiral column ismuch less pronounced if the load is applied with significanteccentricity or when bending from other sources is presentsimultaneously with axial load.

bs

a

aA

A=

bs

as

fs/

/=

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where% /s is the area of spiral steel;

s * is the step of the spiral steel;

Since spiral steel is at least twice as effective as

longitudinal steel, one has, conservatively,

strength contribution of spiral 6 ).# /as$as

!he longitudinal rods are reali:ed from high

strength steel and spiral is reali:ed from soft

steel, and so% 1 6 /bs$c 8 /a$a 8).#/as$s

4

A2s

s

=

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8.!. Slender/hor& $olu"n

5hen an unbalanced moment or a moment due

to eccentric loading, Fig. ".', is applied to a

column, the member responds by bending.

5hether a column is short or slender is normallydefined by a slenderness ratio, which is function

of the parameters which determine the lateral

deflection of the column. !he slenderness ratio

is defined by%

r

lfo =

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5here%

lf is the effective length of the member

r * is the radius of gyration

A

Ir=

I * is the second moment of the section area

/ * is the crosssectional area

o

f 2!"#

l==

for rectangular section &".)(5here h% side of the section on the direction of the force 1

eccentricity.

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Function of slenderness ratio we have% for &short columns(, the secondorder

moments can be ignored for &slender columns(, it is necessary

to consider the secondorder moments for &very slender columns( the failure of

columns, under an continuous increasing of theaxial force will take place by loosing the stability&buckling(.

!he basic information on the behavior of

straight, concentrically loaded slender columnswas developed by >uler more than )22 yearsago. In generali:ed form, it states that memberwill fail by buckling at the critical load.

1"

$"1"

IInd order moment, determined on the deformed structure.

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5hen the members are

computed considering the IInd order

calculus and for bars it can consider the

following relation for the rigidity modulus%

!12!1

M

M

IEp

EI ld

bb

conv

+

+

= 1

)1(1!"

)(

@sually, preliminary one can consider%

bbcon I%$!")%I(

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For structures to which the importance of

secondorder moments is reduced,

it is accepted that the coefficient ? to be

determined with the following relation%

2!1

NcrN

=1

1

for rectangular, circular and ringshape section

2

f

con2

cr

l

)%I(N

=where%

!he secondorder moments can be neglected &? 6 '( in the

following situations%any shape sections with $"

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rectangular section 1"

circular section *!

d

lf =

!he influence of secondorder moments is considered in the

computation by multiplying the eccentricityoce

by coefficient ?%

aaooc eN

Meee +=+=

where%

=mm

hea2"

$"

1

ma+

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E0ROCOE ! 2133+

/rea of total reinforcement is obtainedfrom relation%

,d

cdctottot!s

f

fAA =

where /c is the concrete section

/c6 r) for circular section

/c6r)A'&riBr()C for ring shape section

0oefficient tot is obtained from interaction diagrams 4d

* 1d from Fig ' and ) depending on dand dand also on

dlBh for circular section and riBr and dB&rir( 62.# for ring

shape section.

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fcd&$c( is the design value of concrete

compressive strength

fcd6fckBc

andfck is given

cdc

dd

cdc

dd

#fA

'and

fA

N==

!he coefficient tot for circular section also can be

calculated with relation%

2d1tot -- +=

coefficients D' and D) from Fig.+

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Re$&angular e$&ion@sually, the columns are symmetrically reinforced% 21 ss AA =

!he total steel% 121 2 ssstot AAAA =+=

is determined on the basis of values%

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@sing the diagram from standard, Fig.+.E

cd

Ed

fhb

M

=

2

cd

Ed

fhb

Nv

=

h

d

h

d 21 =

ydcdtotstot ffhbA &=

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!he total reinforcement can be placed on

two or four faces, the diagram which is

used depends on the ratio d'Bh %

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For columns subected to axial force NEdandbending moment MEd when the moment actson another plan than symmetrical one, thecolumns are subected to biaxial bending.

For spatial statically computation of structuresthe results for columns are given as bendingmoments on two principal directions of the

crosssection MEdy and MEdz, Fig.. !he designing of columns can be made

separately on the two directions of the crosssection, as was presented upper and the section

is verified to biaxial bending with the followingrelation%

( ) ( ) 1&& + nn RdzEdzRdyEdy MMMM

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5here% and are the design bending

moments on two direction and are the capable bending moments ontwo direction, computed in the hypothesis of thesimple eccentric compression, under the action of 1>d

EdyM EdzM

RdyM RdzM

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is a coefficient given in !able....

function of the design value of axial

compression force 1>d and capable axialforce to centric compression, 1$d%

n

ydstotcdRd fAbhfN +=

!able... alues of coefficient n

n

N%d

& NRd

".1 "./ 1."

1!" 1! 2!"

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!he steel design also can be done withthe diagrams of interaction fromFig....function the type of reinforcing%

Steel in corners

Steel on four sides

Steel on two sides

!he coefficients , and arecomputed.

If% G then for the first two types of

reinforcing it must consider and .

In the other case% and

d Edy Edz

Edy Edz

=1 Edy=2 Edz

=1 Edz =2 Edy

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In the case of reinforcing on two sides%

=1 Edy

=2 Edz

From diagrams it can obtain tot

used for determining the steel area.

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4enerali&ie

0olumns can be classified%

* monolith columns

* poured in the site * precast columns

!he cross section of columns% rectangular, circular, ringshape, polygonal, !, H, &fig. 9.))(.

Fig.9.)). 0ross section of columns

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+.3.1. Proviion #or $olu"n

4inimum si:es of columns are established

from the flexibility condition%

14"if

=

For ordinary concrete

/"i

f =

For lightwight concrete

$if =

For spiral columns

where f

the effective length of the member , and iJ is

the radius of gyration

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4inimum si:es of transversal sections are )#2 mmfor monolith columns and )22 mm for

prefabricated columnsFor spiral columns, the exterior diameter must be at

least )22 mm and the concrete core diameter atleast )#2 mm.

!he ratio of si:es hBbK),#.

!he reinforcing is reali:ed with longitudinal bars andtranversal steel.

a( Longitudinal steel

In fig.9.)+ are presented some reinforcing types ofcolumns

Mini"u" ,er$en&ageof reinforcing for theentire longitudinal steel is obtained%

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cyd

Ed

s

Af

NA ""2."

1"."

min!

=

where% 1ed is axial force

fyd is the yielding limit

/c is the area of transversal section of

concrete

For seismic area the minimum steel area

must respect function the ductility class thefollowing conditions%

high &L( /sminM2.2'/c

medium &4( /sminM2.22"/c

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Hongitudinal bars are distributed at sides%For polygonal section, in each corner one bar and

in seismic area at least one bar between corners.For circular section at least N bars, but is

recommended E.

Mai"u" &eel ,er$en&ageis considered N3

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Fig.9.)+ 0olumns reinforcing

!he bars diameters and distances among bars aregiven in tabel 9.+.

!abel 9 + iameter of longitudinal bars to columns

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!abel 9.+ iameter of longitudinal bars to columns

!he free distance among bars must respect% beM #2 mm,and interax distance must not exceed )#2 mm.

!he reinforcing with four bars in the corners of the

section is admitted in the following situations% 0olumn is from / group with si:es O +#2 mm;

0olumns is from group P and 0 with si:es O N22 mm;

T,0e of column'inimum diameter! mm 'inimum diameter! mm

*"! 2 3$/ *"! 2 3$/

Structural column 12 14 2 5 ordinar, concrete

olumn included inmasonr,

1" 12

22 5 li6#t7ei6#t concrete

Non-structural column 1"

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!he following limits must be respected%

* !he total maximum steel percentage in the case of

lapping bars isO"3

* !he total minimum steel percentage according to

tabel 9.N

* !he minimum steel percentage on each si:e is 2,)3

!he lapping of bars can be reali:ed as in &fig.9.)Na.(acQ dimensiunile la douQ niveluri succesive sunt

diferite, panta maximQ admisQ pentru devierea

barelor este de 'BE, &fig 9.)Nb(.acQ panta nu poate fi

asiguratQ, innQdirea se reali:ea:Q cu bare

suplimentare care trec prin nod, &fig 9.)Nc(.

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$einforcing of lamellar columns

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/rmare stRlpi lamelari i diafragme

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') Transversal reinforcement!here are two :ones on column length

central :onewith stirrups at a distance aefrom

conditions%

Fig.9.)N Happing longitudinal bars

{ )8sia$""mm(6ru0)96ru0aA(mm2""!d1a e &9.+#(

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where dJ is diameter of longitudinal bars.

* !he :one with stirrups at a reduced distance,

ae,r%

* wherehJ is the big si:e of the column.

* istance ae,r is met%* on the length of plastic potential :ones, group /, &fig.

9.)#a(.

* -n the entire length of the column having LsBh &short

columns(, where Ls is the free length of column, andh is the maximum si:e of the crosssection.

* on lapping length of longitudinal bars

* on the bigger length between ls and lp.

8d:a r!e 5ith condition mm1""a r!e >

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4inimum steel percentage for transversal

reinforcing with stirrups is%

For highdu$&ili&class &L(%2.#3 in critical :one of columns at the column

base at first level;

2.2+# in other critical :one. for $la&4(%

2.2+#3 in critical :one of columns at the column

base at first level;

2.2)# in other critical :one.

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i&an$e a"ong &irru, function ductility class

will not exceed%

Ligh &L(

4edium &4(

where dbl is minimum diameter of longitudinal bars

mm

b

d

s o

bl

cl

12

$&

*

ma+!

mm

b

d

s o

bl

cl

1/(

2$&

ma+!

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bo este minimum si:e of effective section

depth placed inside the perimetral stirrup.

!o columns with reduced loads and also forcolumns outside the critical :ones, distance

between transversal stirrups &scl,max( will

not exceed the smallest value between% )2 times the minimum diameter of

longitudinal bars;

the smallest si:e of transversal section N22 mm

@pper distances for columns with reduced

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@pper distances for columns with reduced

loads can be diminished with the factor 2.E in

following cases%

in sections placed over and under a beam or

a slab, on a depth eual with maximum si:e of

cross section of the column;

on :ones where oints are reali:ed by

superposing bars if the bars diameter is

smaller than 'N mm.

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4inimum diameter of stirrups is chosen%

iameter for stirrups, loops or spiral must

respect%

for class &L(

5here% dblis maximum diameter oflongitudinal bars;

for class &4(

mm8*mm994&1: dde

ydwydlblbw ffdd &4."

mm

hdd

bl

bw

*

&

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Circular Sections are reinforced with

individual circular stirrups or spiral.

-n the depth of oint with a beam or a slabthe stirrups from the column are placed at

the same distances as at the ends of the

adacent columns. Stirrups must be reali:ed with hooks and

straight length at least #d or '2d for

columns for seismic structures

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0ritical length can be%

for high ductility class &L(

For medium &4(

Fig. 9.)#istances among stirrups

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Sections of spiral columnscan be circular,ring shape, polygonal &fig. 9.)9(.

Fig.9.)E Interior stirrups of columns

Fig. 9.)9 Sections of spiral columns

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!he spiral must respect the conditions

/s &/a( at least )23 /sl;

TsGE mm

Steel percentage of longitudinal bars function

the core area is%

p8ps 6 min '.#3 Hongitudinal bars must be at least in a number

of E, &fig. 9.)"(.

Tmin ') mm pt. U0 'N mm pt. -P +9

Tmax % )" mm

mm"s"

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Fig. 9.)" StVlp fretat