Column design Name of work:-
pkn 1000
1 Exte Extern rnal al + sel selff load load 2 Con Concre crete
Mscbc
3 Steel
fy
kN
Height of column
21
Grade
6
N/mm
415
N/mm
Unit weight concrete
2
m
2
3.00
3 25000 N/m
13.33
Tensile stress
190
Effective cover
50
4 Nomi Nomina nall cove cover r
40
mm
5 Reinfo Reinforce rceme ment nt Main Main vertic vertical al
20
mm F
5
6 2 - lgd. lgd. Stri Strirr rrup ups s
10
mm F
320
mm c/c
280
mtr
7 Rectangular Coloumn Size
width
420
mtr
depth
5 Nos.
20
Nos bars
mm f bars
420 280 10 mm f 2 ldg strirrup 320 320 m c/c c/c 420
280 3.00
Ractangular column
Foundation pad
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mtr
N/mm mm
2
Column design 1 External + self load 2 Concrete
1000 kN/m M 21 N/mm 6 cbc
3 Steel 4 Nominal cover
fy
415 N/mm 40 mm
1 D e s i g n C o n s t a n t s : - For HYSD Bars
m*c
k=
=
m*c+sst j=1-k/3 j=1-k/3 = 1 R=1/2xc x j x k = 0.5 x
2
Tensile st stess = Effective cover =
Cocrete M =
2 = 190 N/mm 3 N/mm = 6 = 13.33
sst = scbc = m
Height of column 3.00 mt mtr = 3 Unit weight concrete = 25000 N/m m = 13.33
x
13.33 x
6
0. 0.296
3
/
6 x
6 +
0.90 x
mm
2
21
wt. of concrete
13.33
190 N/mm 50 mm
3000
= 25000 N/mm
=
0.296
=
0.901
0.296 =
0.8010
190
2
2 Design of section:- Minimum steel = 0.80% Let us use = 1 %steel Design column as a short columns The load carring capacity of short column is p = scbc . Ac +sst. Asc =scbc(Ag - pAs)+ sst.pAs From which A g
p
=
scbc (1-p) +p. sst
Size of square column Area of columns columns = 360
= ( x
126743 360
1000
=
=
6
Hef
=
Hence
Hef b
=
Cr
=
Reduction factore =
3000 x 3000 = 360 1.25
-
=
1
-
0.5
)
356 = 129600 mm2
3 Check column whatever short or long. Effective hieght of column H ef Here,
x(
x
1000
0.01 )+ mm
0.01 x
Provide =
190
0.01
=
360 x
126743 2
mm
360 mm
= Height Height of column column x Effective Effective height height factor factor
1
=
8.333
<
Hef = 48 b 1000
3000 mm mm 12 1.25
b
=
mm
360
short column Hence O.K. -
3000 48 x 360 925926 N
1.08
1000 x = 1.08 The load carring capacity of short column is p = scbc . Ac +sst. Asc = scbc(Ag - pAs)+ sst.pAs Revised Load P 1
Revised Ag
p
=
scbc (1-p) +p. sst
=
925926 6
x(
1
-
0.01 )+
0.01 x
190
280
say
=
117354 2
mm
Revised Ractangular column
Size
=
1.50
x2=
280
x
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2
117354
or x
=
420
Area
=
78236
x
117600 mm2
=
(b =
280 mm
1.5 d Assume)
4 L o n g i t u d i n a l R e i n fo r c e m e n t : - Asc =pA = using 20
mm bars
0.01 x
5
having, Ast Keeping
3.14xdia 4 x100 = 1267 / =
2
1267
=
2
A
Nomber of Bars = Ast/A Hence Provided
126743
= 314 =
mm 3.14 x 20 4 x 4.04 say
bars of
20 mm F bar,
= =
x 314 = 1570.00 mm mm nominal side cover
5 40
x 20 = 314 100 = 5 No.
2
5 Design of ties:- minimum 6 mm.
Diameter of ties should be 1/4 of the diameter of longitudinal reinforcement subject to However use 10 mm f bars of ties.
The spacing of the ties should not exceed least of the following.
(I) Least lateral diamension. (II) 16 x Diameter of main bars
= 16
x
20
=
360 320 480
mm mm
(III) 48 x dia of ties 48 x 10 = mm Hence provided the ties @ = 320 mm c/c. The ties will be square in shape in two size as shown in fig. using them alternately, so that longitudinal bars pass through the corners of ties. Keep pitch of each set of ties at = 320 mm
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2
mm
Column design Name of work:-
pkn 420 20 mm f 5 Nos bars 280
40 mm cover Square column
280 420
3.00 mtr
Foundation pad
[email protected]
Length effect coefficient
lef = 0.65L
Height
case 1
lef = 0.80L
case 2
lef = 1.00L
case 3
lef = 1.2L
case 4
lef =1.5L
case 5
lef = 2L
case 6
lef =2L
case 7.
case no. Degree of end restraint of compression member
1 Effectively held in position and restrained against rotation at both ends 2 Effectively held in position at both ends, restrained regainst rotation atone ends. 3 Effectivly held in position at both ends, buy notrestrained regainst rotation . 4 Effectively held in position, restrained regainst rotation atone ends. And at the other restrained against rotation but not held in position 5 Effectively held in position, restrained regainst rotation atone ends. And at the other partialy restrained against rotation but not held in position 6 Effectively held in position, at one ends but not restrained against rotation,. And at the other end restrained against rotation but not held in position 7 Effectively held in position, and restrained against rotation at one endbut not held in position nor restrained against rotation at the other end.
VALUES OF DESIGN CONSTANTS Grade of concrete Modular Ratio
M-15 18.67
M-20 13.33
M-25 10.98
M-30 9.33
M-35 8.11
M-40 7.18
scbc N/mm2 m scbc
5
7
8.5
10
11.5
13
93.33
93.33
93.33
93.33
93.33
93.33
kc
0.4
0.4
0.4
0.4
0.4
0.4
jc
0.867
0.867
0.867
0.867
0.867
0.867
Rc
0.867
1.214
1.474
1.734
1.994
2.254
Pc (%)
0.714
1
1.214
1.429
1.643
1.857
kc
0.329
0.329
0.329
0.329
0.329
0.329
jc
0.89
0.89
0.89
0.89
0.89
Rc
0.89 0.732
1.025
1.244
1.464
1.684
1.903
Pc (%)
0.433
0.606
0.736
0.866
0.997
1.127
kc
0.289
0.289
0.289
0.289
0.289
0.289
jc
0.904
0.904
0.904
0.904
0.904
0.904
R
0 653
0 914
1 11
1 306
1 502
1 698
(a) sst = 140 N/mm2 (Fe 250) (b) sst = 190 N/mm2 (c ) sst = 230 N/mm2
Gra t
VALUES OF DESIGN CONSTANTS Grade of concrete Modular Ratio
M-15 18.67
M-20 13.33
M-25 10.98
M-30 9.33
M-35 8.11
M-40 7.18
scbc N/mm2 m scbc
5
7
8.5
10
11.5
13
93.33
93.33
93.33
93.33
93.33
93.33
kc
0.4
0.4
0.4
0.4
0.4
0.4
jc
0.867
0.867
0.867
0.867
0.867
0.867
Rc
0.867
1.214
1.474
1.734
1.994
2.254
Pc (%)
0.714
1
1.214
1.429
1.643
1.857
kc
0.329
0.329
0.329
0.329
0.329
0.329
jc
0.89
0.89
0.89
0.89
0.89
Rc
0.89 0.732
1.025
1.244
1.464
1.684
1.903
Pc (%)
0.433
0.606
0.736
0.866
0.997
1.127
kc
0.289
0.289
0.289
0.289
0.289
0.289
jc
0.904
0.904
0.904
0.904
0.904
0.904
Rc
0.653
0.914
1.11
1.306
1.502
1.698
Pc (%)
0.314
0.44
0.534
0.628
0.722
0.816
kc
0.253
0.253
0.253
0.253
0.253
0.253
jc
0.916
0.916
0.916
0.914
0.916
0.916
Rc
0.579
0.811
0.985
1.159
1.332
1.506
Pc (%)
0.23
0.322
0.391
0.46
0.53
0.599
(a) sst = 140 N/mm2 (Fe 250) (b) sst = 190 N/mm2 (c ) sst = 230 N/mm2 (Fe 415) (d) sst = 275 N/mm2 (Fe 500)
Permissible shear stress Table 100As bd
v
in concrete (IS : 456-2000)
Permissible shear stress in concrete tv N/mm M-15 M-20 M-25 M-30 M-35
2
M-40
< 0.15
0.18
0.18
0.19
0.2
0.2
0.2
0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75
0.22 0.29 0.34 0.37 0.40 0.42 0.44 0.44 0.44 0.44 0.44 0.44
0.22 0.30 0.35 0.39 0.42 0.45 0.47 0.49 0.51 0.51 0.51 0.51
0.23 0.31 0.36 0.40 0.44 0.46 0.49 0.51 0.53 0.55 0.56 0.57
0.23 0.31 0.37 0.41 0.45 0.48 0.50 0.53 0.55 0.57 0.58 0.6
0.23 0.31 0.37 0.42 0.45 0.49 0.52 0.54 0.56 0.58 0.60 0.62
0.23 0.32 0.38 0.42 0.46 0.49 0.52 0.55 0.57 0.60 0.62 0.63
3.00 and above
Maximum shear stress tc.max in concrete (IS : 456-2000) Grade of concrete
tc.max
M-15 1.6
M-20 1.8
M-25 1.9
M-30 2.2
M-35 2.3
M-40 2.5
Gra t
Shear stress tc 100As bd
0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62
M-20
0.18 0.18 0.18 0.19 0.19 0.19 0.2 0.2 0.2 0.21 0.21 0.21 0.22 0.22 0.22 0.23 0.23 0.24 0.24 0.24 0.25 0.25 0.25 0.26 0.26 0.26 0.27 0.27 0.27 0.28 0.28 0.28 0.29 0.29 0.29 0.30 0.30 0.30 0.30 0.30 0.31 0.31 0.31 0.31 0.31 0.32 0.32 0.32
Reiforcement % M-20
0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.46 0.47 0.48 0.49 0.50 0.51
100As bd
0.15 0.18 0.21 0.24 0.27 0.3 0.32 0.35 0.38 0.41 0.44 0.47 0.5 0.55 0.6 0.65 0.7 0.75 0.82 0.88 0.94 1.00 1.08 1.16 1.25 1.33 1.41 1.50 1.63 1.64 1.75 1.88 2.00 2.13 2.25
0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14
0.32 0.32 0.33 0.33 0.33 0.33 0.33 0.34 0.34 0.34 0.34 0.34 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.36 0.36 0.36 0.36 0.36 0.36 0.37 0.37 0.37 0.37 0.37 0.37 0.38 0.38 0.38 0.38 0.38 0.38 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.4 0.4 0.4 0.4 0.4 0.4 0.4
1.15 1.16 1.17 1.18 1.19 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.40 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 1.50 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.60 1.61 1.62 1.63 1.64 1.65 1.66
0.4 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.46 0.46 0.46 0.46
1.67 1.68 1.69 1.70 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79 1.80 1.81 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.90 1.91 1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18
0.46 0.46 0.46 0.46 0.46 0.46 0.46 0.46 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.50 0.50 0.50 0.50 0.50 0.50
2.19 2.20 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.30 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39 2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50 2.51 2.52 2.53 2.54 2.55 2.56 2.57 2.58 2.59 2.60 2.61 2.62 2.63 2.64 2.65 2.66 2.67 2.68 2.69 2.70
0.50 0.50 0.50 0.50 0.50 0.50 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51
2.71 2.72 2.73 2.74 2.75 2.76 2.77 2.78 2.79 2.80 2.81 2.82 2.83 2.84 2.85 2.86 2.87 2.88 2.89 2.90 2.91 2.92 2.93 2.94 2.95 2.96 2.97 2.98 2.99 3.00 3.01 3.02 3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.10 3.11 3.12 3.13 3.14 3.15
0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51
Permissible Bond stress Table de of conc bd
(N / mm
M-10 --
M-15 0.6
M-20 0.8
M-25 0.9
bd
in concrete (IS : 456-2000)
M-30 1
M-35 1.1
M-40 1.2
M-45 1.3
Development Length in tension Plain M.S. Bars
H.Y.S.D. Bars
Grade of concrete
tbd (N / mm2)
kd = Ld F
tbd (N / mm2)
kd = Ld F
M 15
0.6
58
0.96
60
M 20
0.8
44
1.28
45
M 25
0.9
39
1.44
40
M 30
1
35
1.6
36
M 35
1.1
32
1.76
33
M 40
1.2
29
1.92
30
M 45
1.3
27
2.08
28
M 50
1.4
25
2.24
26
Permissible stress in concrete (IS : 456-2000) 2 Permission stress in compression (N/mm ) Permissible stress in bond (Average) for Grade of 2 Bending acbc Direct (acc) plain bars in tention (N/mm ) concrete 2 2 2 (N/mm2) (N/mm2) (N/mm2) in kg/m Kg/m Kg/m --M 10 3.0 300 2.5 250 0.6 60 M 15 5.0 500 4.0 400 0.8 80 M 20 7.0 700 5.0 500 0.9 90 M 25 8.5 850 6.0 600 1.0 100 M 30 10.0 1000 8.0 800 1.1 110 M 35 11.5 1150 9.0 900 1.2 120 M 40 13.0 1300 10.0 1000 1.3 130 M 45 14.5 1450 11.0 1100 140 16.0 12.0 1.4 M 50 1600 1200
M-50 1.4
2.0
e r o t c a f n o i t a c i f i d o M
1.4 1.2 0.8 0.4
0.0
0.4 0.8 Percentage of tension reinforcement
1.2
1.6
2
2.4
2.8
