DESIGN OF COLUMNS
DESIGN OF COLUMNS
Grouping of columns:
Group-1
(Axial columns C6,C7,C10,C11)
Group-2
(Bi-axial columns C1,C4,C13,C16)
Group-3
(Uni-axial columns C2,C3,C5,C8,C9,C12,C14,C15)
Design of group-1 axial columns (internal
columns):
Size
of column = 450×450mm
Moment
at the interior support ‘M’ =
wd=14.53kN/m2 ; wL=
6.75Kn/m2
l2= 6.6m ; ln = 6.6-0.45 =
6.15m
stiffness
of column Kc =
=
1.13×106
stiffness
of slab Ksb =
=
0.62×106
MX=
=
52.88kNm
Since the slab around the column
have same dimensions in both directions,
MY = 52.88kN/m.
Total
load from slab and drop = 21.2805kN
Axial
load on ground floor = w×L1×L2 = 21.2805×6.6×6.6 = 926.97
KN.
Axial
load for 4storey = 926.97×5 = 4634089kN
Factored
self weight of column = 1.5×0.45×0.45
=
7.59 KN
Total
axial load = PU = 4642.48 KN
Slenderness ratio:
λ =
=
=
4.33<12 (hence designed as short column)
Effective length
(le) = 0.65×l = 1.95m
Eccentricity calculations: ey
= ex =
+
=
21>20.
From page 71 of IS-456: minimum eccentricity =
0.005D
=
0.005×450 = 22.5>21
Longitudinal reinforcement:
PU = 0.4fck Ag + (0.67fy- 0.4fck)Asc
4642.48×106 = 0.4× 20×( 450× 450) + (0.67×415 - 0.4×
20)Asc
Asc = 1119.29 mm2
Provide 14bars of 32mm diameter.
Spacing
in longitudinal direction: 450-40-40 =
370
=
92.55
Provide spacing of 92.55mm
in longitudinal direction
Spacing
in transverse direction: 450-40-40 = 370
=
123.33
Provide spacing of 123.33mm
in transverse direction
Lateral
reinforcement:
Spacing
as per code : pitch and diameter of lateral ties
1) Least
lateral dimension = 450mm
2) 16×ɸ = 16
=
512mm
3) 300mm
Size
of lateral ties =
=
=
8mm
Hence
provide lateral ties of 8mm diameter at 300mm c/c
Design of group-2 Bi-axail columns(corner
columns):
Size
of column = 450×450mm
Load
on ground floor = w×L1×L2 = 21.2805×3×3 = 191.52 KN.
Load
for 4-storey = 191.52×5 = 957.21KN
Factored
self weight of column = 1.5×0.45×0.45
=
7.59 KN
Total
bi-axial load (Pu) =
965.21KN
Moment
in X-direction ‘MUX’ = 75% of the total moment on column
from slab
= 0.75×189.972
= 142.479kNm
Moment
in Y-direction ‘MUY’ = 142.479kNm
Slenderness ratio:
λ =
=
=
4.33<12 (hence designed as short column)
Effective
length(le) = 0.65×l = 1.95m
Minimum
eccentricity as per code , ey min = ex min =
+
=
21>20
Minimum
eccentricities are less than the applied eccentricities no modification to MUX
, MUY is called for:
Trial section:
Longitudinal
reinforcement:
MU= 1.15
=
1.15
=
231.705KNm
Assuming
d1 (using 8mm
ties &25mm bars) = 40+
+8 = 60.5mm
=
=
0.134
0.15
S.F
ratio:
=
=
0.238
B.M
ratio:
=
= 0.127
Referring
to chart 45 of SP:16 :
=
0.105
Pt =
0.105×20 = 2.11>0.8 and <4.0
Ast =
=
4272.75mm2
Provide
12 bars of 25mm diameter.
Moment capacities: MUX1,
MUX2 [due to symmetry MUX1=MUX2]
=
0.238 (as calculated earlier)
P(provided) =
=
2.909
=
=
0.145
Assuming d1 (using 8mm
ties &25mm bars) = 40+
+8 = 60.5mm
=
=
0.134
0.15
Referring
to chart 45 of SP-16:
=
0.165
MUX1
= MUY1 = 0.165×20×4503 = 300.71kNm
Which
is greater than MUX, MUY = 142.479kNm
Values of PUZ &
:
PUZ = 0.45fck Ag +
(0.75fy – 0.45fck) ASC
= 3603.35 KN
=
=
0.267 (which is lies between 0.2 &0.8)
=
1.0 +
(2.0 – 1.0) = 1.11
Check safety under bi-axial loading:
+
=
+
= 0.8<1.0
Hence
the trail section is safe under the applied loading.
Lateral reinforcement:
The
minimum diameter and the maximum spacing of the lateral ties are specified by
the code [eq 13.9, 13.10]
=
greater of
& 6mm
Spacing as per code: pitch and diameter of
lateral ties
1) Least
lateral dimension = 450mm
2) 16×ɸ = 16
=
400mm
3) 300mm
Hence
provide 8mm
ties at 300 c/c
Arrangement
of bars: spacing = 450 – 40 – 40 =370
=
=
123.33mm
Spacing is same in both directions.
Design of group-3 Uni-axial columns
(exterior columns):
Size
of column = 450×450mm
Load
on ground floor = w×L1×L2 = 21.2805×3×6.6 = 421.344 KN.
Load
for 4-storey = 421.344×5 =
2106.72KN
Factored
self weight of column = 1.5×0.45×0.45
=
7.59 KN
Total
bi-axial load (Pu) =
2114.31KN
Moment
in X-direction = 212.543Kn/m
The
unbalanced moment in Y-direction = 441.346 – 315.135
=
126.211kN/m
Because
of unbalanced moment, uni- axial columns acts as bi-axial columns.
Slenderness ratio:
λ =
=
=
4.33<12 (hence designed as short column)
Effective
length(le) = 0.65×l = 1.95m
Minimum
eccentricity as per code , ey min = ex min =
+
=
21>20
Minimum
eccentricities are less than the applied eccentricities no modification to MUX
, MUY is called for:
Trial section:
Longitudinal
reinforcement:
MU = 1.15
=
1.15
=
284.26KNm
Assuming
d1(using 8mm
ties &25mm bars) = 40+
+8 = 60.5mm
=
=
0.134
0.15
S.F
ratio :
=
=
0.522
B.M
ratio:
=
= 0.155
Referring
to chart 45 of SP:16 :
=
0.135
Pt = 0.135×20 = 2.7 >0.8 and
<4.0
Ast =
=
5467.5mm2
Provide
4 bars of 32mm diameter and 8bars of 25mm diameter.
Moment capacities : MUX1
, MUX2 [due to symmetry MUX1=MUX2]
=
0.5220 ( as calculated earlier)
P(provided) =
=
3.17
=
=
0.158
Assuming d1(using 8mm
ties &25mm bars) = 40+
+8 = 60.5mm
=
=
0.134
0.15
Referring
to chart 45 of SP-16:
=
0.178
MUX1
= MUY1 = 0.178×20×4503 = 324.405kNm
Values of PUZ &
:
PUZ = 0.45fck Ag +
(0.75fy – 0.45fck) ASC
= 3767.15KN
= 0.56 (which is lies between 0.2
&0.8)
=
1.0 +
(2.0 – 1.0) = 1.6
Check safety under bi-axial loading:
+
=
+
=
0.72<1.0
Hence
the trail section is safe under the applied loading.
Lateral reinforcement:
The
minimum diameter and the maximum spacing of the lateral ties are specified by
the code [eq 13.9, 13.10]
= greater
of
& 6mm
Spacing
as per code: pitch and diameter of lateral ties
1) Least
lateral dimension = 450mm
2) 16×ɸ = 16
=
512mm
3) 300mm
Hence
provide 8mm
ties at 300 c/c
Arrangement
of bars: spacing = 450 – 40 – 40 =370
=
=
123.33mm
Spacing is same in both directions
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