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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