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AX\ALLY LOADED RC COLUMNS
ACI (^) /NSCP (^) Code (^) Requremems )For (^) moin (^) lorgittia (^) Reinorcig ars
(a) o.o1 0.
(b)
Pa
min. n0. OF ES six (^) (o) For (^) circular (^) arangentert FOUr (4) (^) For (^) rectglar (^) ariargemt three (^) (3) For (^) triangular (^) arrBrgement (c) min. (^) clear (^) distance betueen (^) jogitinal bars
(Sc)
For lateral Ties
concrete cover : 40 mn( minimum )
(a) minimum size
- Pms
L40 mm
(b) maximum size
Po
(c) (^) maximum spaing oF (^) barr (^) (eTC)
megnitude oF usoe column AxYl Lad Stmg
(a) Tied Column
JDmm
12 rmg
Ieast column dimension
Pu 0.80 p o8sft (Ag-As) +Asf
(b) Spiral Column
p O-05 ;tso.1h (perpendicular)
0.85fé( A9- As) + AsfY
b pure axial capacity
Pu 0.52 o-esf (Ag AS) + Asfy
Pu 85 o85f (Ag-As) *Agy |
smY)l ecentricity
Pu 0-w375 0.85f (Ag-As)+AfYJ
i circular buj hed cpacing :
1- 4.5 % Cco nomical
ucually more
eiclen (0)
steel
iF So 50, dect case pma
raho
(odd or even )
by 2 , by +(quale)
honer tnan beaM S bar oF Cegiegation (honeycom)
9) Spiralsodd or Gven)
(a) min size IOmm
(b) max s1ze lon
(c) ciear pocing oF pilas,
min (^) 2Gnn (^) fdagg t (^) sp
(a) mnimum spra teel rano
Prmin 0.
(e) min spoBùng (theo. compar ) s) 4ASPDe - psp)
AS Ag
2 De fsmin ’ Area oF Suel Gros Area oF Column gross stcel raio
AC Area oF Core
,0.C
De = Core Diameter
De = Dg - 2(cc)
Asp Cross- sectional Arca of spral ar
PROBLEM 1. Design the Q P 9o KN. Ute fC
lomn laterol tier
pg Ag
AS
AS
445
Pg A
A : 02 Ag
445
S 48 OLT
syuare hcd colum to camYy seryicC axial load
- MPa, fy 414 MP, T 219GMP•, Po > 2
leat dim.
Pudes 2D +-6L
:. S 400 mm
2000 xI Ag
Pudes : 2000 KN
Puder Pucap Pu
Pu
= 12(J00)^ +).o/800)
s Ag sAg
0-80 o-85t^ (Ag-^ As)^ +^ Afy^ 0-b 6-80(0-b5)0-8s (21)(A9 - 0-02A9) + (0-02A9) (414)|
AS 0-02Ag
0.02 (445)(445) Ac =3900.5^ mm^2
3900-
T (25)
n25 8.
minimum spacing oF Lateral Ties
l(25)
use |2 -25mm p
raurd up by 5 (design , exan)
S 440. 450mm Say 445 mm
4
S- 2CC 20Lt nme
okay!
445- 2(4o)- 2(1o)
Sc 8).0Mm
Should be ymmeti^ cal^ (by^ 4)^4 peride
1-5(25) >^ 37.5^ /
40
Detas
+(25)
4 45
445
Lyuse
C-
Po lotN 25mm d ma
445 x445 mm |2-25mn man Bar
use l0mn LateralTies
1@ SOmm, rest 40Dmn
194,00|. 4744 mm 2 A
R cOLUMN^ VBUECTED^ To^ AXAL^
BENDING MOMENT
Mp ML
ML
PE
Frame A (FA)
P ME PE
"Eceyicitby, e
F(ame 1 (F-1)
Benavior OF Column
f balanced
MOF-A
rension cotiecl Compresion contraled
mF-A
mudes
Mudes @x-•xis
Pu des
MO F-
ME F-
" Mudes @y-oxis
Col. int oF
grids A 1
col. @int oF
gids A
Pudes >(>F-A t Pp4) 102d combination
Column
M =Pe
Bending Moment
AbDUt y- xis
Kung ano mag-gogoven sa
Po
Bendne amen t
About Xaxis
DL+ LL + EL per rame Y
A-
DF-A (^) pop-t
cno0sSe tne max or greatest bton Fame A Reme 1 (bigget value)
gogamitin sa load com bination
N.A.
Actual e < ebal
Balanced Condition (fs *f9) Compression Controls
Tension Contro)S
PIastic Centroid
fe 20. mpa
fy= 44 Mpa
Bi 0.
4- 28mnd
4- 28mm
350
similar o centric
(rectangular, regular shape)
PROBLEM 1. Determin the nomnal axial capcity , Pn ,
@balanced cordition.
T- Ce -Cs t Pn
Pn =^ 0-8sft^ ab
Pn
AS -
yF# >0^ (@^ FOrce^ Diagram)
d-d'
Pa epal
(ExIo) tbal +
G00(drc)
a
e< eal
G00(530-c)
a
bal 452.^448 mm
e
Asfy - 0-95feab^ -^ Asfy^ +^ Pn^ o
C 313.ol mm cl
(@ Force magiam)
co.
: 0"85^ (20)^ A(3s0)^ y^
D-
530- 7O
eb•l
2a. So8mm A
784T
0 85{
Force Dig am
As fy
T ASfy
As fr
ASfY
)- cs (d-d') - ce (a-)
Pn
Ce C1 0.85fcab
Cr :C
Ccor Ci
fi
ASfy or A[fS
ASOT f9)
and ecenttricity, e,
(@ center of a
As (ps orf9)
balanced eebal
As fY As >AS
aoo(c -d)
Goo(D-0)
- Asfy (d-d')^ -^ 08sfiab(d-)^ o
Comp. steel yiedr
- (A847)(414)(50-0)^ -^ 085(20-*)D()(530^ -
PROBLEM 3. Same / poolem 2 t Coctua So0mm
AS : 24-03Ol mm 2 AS =
fy
p
- ol mm 2 20¬ MPa 414 MPa
ebal 452. 44B nn D)
Pn -Cs - Ce +T
Pn - Asfy -0-85ft qb +
Compreucion Contros
Pn = loi9%86.|4 + 5234.5125C
Afe
Asfy
a(0-)
C = 302. 122 m c
Pn - z409.01( **) - o8s(o1) (0.85c) (30) +2443-0|I
Pn 2230- I|9 kN
Bc
Pn (tac t) -cs ( drd') - Co (d-)
(30 t
d530mn
B (530-)
E(530-)
d' 70mn
fn (eaet
n o00mm
6co(
1477800 (530 rc)
) -(820-7o)^ - (Dc{^50 -^ )^ -o
+)-A[fy (d-d') - o.8sfiab (d-) o
INTERACTION DIAGRAM
PROBLEM 1. using^ the^ iteraction^ diagram^ ,^
determine tne^ value^ oF^ Pn^ Fr^ te^ dort
tied column^ Shoan^ pr:
(a) ecemcity^ along^ yraxis (0) eccenicity^ along^ yaxis
fc 20. MPa fy =^ 43.^70 MPa d =534.5 mm
b 3 5Oom
(o)
(o)
02.5 mn
Pg
X 0.792 A
Po
O. o.
490
As Ag
AS
200 (
495
475
X
(1949- 25)(2)
SEES
(356) (900)
0-
(847.25)(2 ider) (3s0)(o)
200 mn
interpolYto
e44.2s
X 0-
X 2-83 MPa
X -0-
0-90- 0.
Ag
0-05 PO
3D (uco)
20- 3
X
Pn
AQ
o 48
35D(0)
X
plot g(let)^ (ngn)
he value on the
X axjs
X-0. o-55- 0-4gksi
Pn 1 484.503 kN
X = 3.45 NPa p
20-7 MPa 3 kui
Po - 2U34. 206 KN
SLENDER OR^ LONG^ COLUMNS
Conditons @wich^ sleerness^ cFrects^ may^
be neylectad^ (NCP^ 2o5)
por columns^ braced^
agsint sideay
Klu
- por^ columns^ rot^ braced^ 8ganst
Where
KLu 2 22
Por
K erFective^ lengtn^ Factor
KLu3 eFFeCtive length
Lu unsupported^ jengtn^ oF^ the^
column
Magni ied Moment i(Mo)
Mo M
1
34 4 12
: radus^ oF^ gyration
" Case^ I.^ Frames Cm
rectargular ciraul ar
(ET) eFF -
Pu 0.75 Per
+ Magnipled mament
Cm 0.b0^ 0.^ o
(Kiu)*
pin fo pin
Mi
1.2D Mp Mu
Larger OF^ the^ nd^ moments
Moment magnification Factor
0.40E, Ig
pn to ixed
()
Braced AgainstSderway
Pu ultmate Facorod Loat
Per Citiçal Buckling Load
K 1.
and
cidesoay
K 0.
r0.30h
efrecive value OF EI
k 05
klu
Single Curvatue m - (egative)
Me M2ns
Double cufvoure
" case I. Frames not Braced Aqaist SidenaN
(a) Ss
() Ss=
(o) Ss
m2ns (DL) larger erd Fatorecd
moment (o sway)
(positive)
m2s (E^ tW)^ larer^ end^ Factored
perpercicular to tre
axir of bendirg
t s M2s
2Pu Ao Vule
Pu
O.75fer
yPU 0 15 Pcr
Le CTcs
Vu Stoey cnear
Ao 1t order
rlative dertection
2På = Um of all ctual FoTes of •ll e
columns in tne ctorey aralye
2Per = um o all ciical loac oF tne
Columns ln tne storey analyzd
nc 518. 083 KN-m
D (9%)
S D 2949
4040
0.15Pcr
Pu
Cm
1
Pr: 81 49. 90oKNC
(Ku)e
(ET)erf
Po 1900 kN
fy 400 MP•
:1 (fixed)
2
dergn,
(EJ )err: 29.727,293.^58 xlo
o.40 (470Bo)
0.40EcIg
j9% 2(90)
A0-
Mu
1-2mD
AIGNMENTCHART
(EJ)err
W-(single curvoture)
" )+-2(90 1-6(00)
(pinned)
pd
Cm 1
pd
Pu 4D4 kN
Pu -2Pp +1.oPL
theCalculate magnpiecdmonent
1.PROBLEMhe column ishna memeroFa Frame bracec gaint y.
z(4)
: joint rigidity
theoreical,
JAC kroN MORE LAND
