SLAB TYPE RECTANGULAR COMBINED FOOTING INPUT DATA 1) LOAD ON COLUMN ON A = 2)LOAD ON COLUMN ON B = 3)CENTRE TO CENTRE DIST. (L3) = 4)DIST. OF CENTRE OF COLUMN A FROM PROPERTY LINE (L1) = 5)DIST. OF CENTRE OF COL. B = 5)SIZE OF COLUMN A d1 = b1 = 6)SIZE OF COLUMN B d2 = b2 = 7) BEARING CAPACITY OF SOIL = 8)STRENGTH OF CONCRETE fck = 9)STRENGTH OF STEEL fy = 10)WIDTH OF PEDESTRAL = LENGTH OF FOOTING = WIDTH OF FOOTING =
P1 = 670 Kn
KN KN m
0.3 0.3
m m
450 300
mm mm
450 300 100 20 415 300
mm mm KN/mm2 N/mm2 N/mm2 mm
8.6 1.65
m m
P2 = 670 Kn
B
A
L1 = 0.3 m
670 670 8
L3= 8 M 8.6
4.3 Page 1 of 45
L2 = 0.3 m
DESIGN :LENGTH AND WIDTH OF FOOTING:C.G. OF LOADS FROM PROPERTY LINE X =
4.3
m
WT. OF FOOTING & EARTH ABOVE (10%) =
67
KN
TOTAL LOAD ON EARTH = 670 + 670 + 67 =
1407
KN
FACTORED LOAD ON COL. A = 1.5 x 670 = FACTORED LOAD ON COL. A = 1.5 x 670 =
1005 1005
KN KN
NET UPWARD SOIL PRESSURE = (1005 + 1005) / (8.6 x 1.65) = =
142
KN/m2
NET UPWARD SOIL PRESSURE PER UNIT LENGTH = 142 x 1.65 = =
234.3
KN/m
B/2 C1
b1
C2 b2
B/2
d1
d2
L1
L2
1005 / 0.45 = 2233.34 KN/m.
L3
1005 / 0.45 = 2233.34 KN/m.
234.3 KN/m
A
B
C
D
E
Page 2 of 45
F
G
H
J
FACTORED SHEAR FORCE AT FOLLOWING POINTS:B=
234.3 x (0.3-0.225) =
17.57
DLEFT = 234.3 x 0.525 - 2233.34 x 0.45 = DRIGHT = F=
-1 x -881.993 = -881.993 + 234.3 x 7.55 =
KN -881.99 KN
881.99
KN
886.97
KN
HLEFT = 886.972 - 2233.34 x 0.45 + 234.3 x 0.45 = HRIGHT =
-1 x -12.593 =
12.59
-12.59 KN
SHEAR FORCE CHANGES SIGN AT C (BC) =
0.01
m.
SHEAR FORCE CHANGES SIGN AT E (DE) =
3.54
m.
SHEAR FORCE CHANGES SIGN AT G (FG) =
0.44
m.
THE DISTANCE OF FOLLOWING POINTS FROM LEFT EDGE,m B=
0.07
AB =
0.07
C=
0.08
BC =
0.01
D=
0.53
CD =
0.44
E=
4.07
DE =
3.54
F=
8.08
EF =
4.01
G=
8.52
FG =
0.44
H=
8.53
GH =
0.01
Page 3 of 45
KN
BENDING MOMENT AT VARIOUS POINTS :(NEGATIVE SIGN INDIACATES HOGGING MOMENTS)
B=
0.66
KN-m
B (ABS) =
0.659
C=
0.74
KN-m
C (ABS) =
0.736
D=
-193.84
KN-m
D (ABS) =
193.836
E=
-1848.02
KN-m
E (ABS) = 1848.017
F=
-175.04
KN-m
F (ABS) =
175.036
G=
21.71
KN-m
G (ABS) =
21.714
H=
0.66
KN-m
H (ABS) =
0.659
1848.017
KN-m
MAXI. DESIGN MOMENT,Mumax =
REQUIRED THICKNESS FOR FOOTING, WIDTH OF FOOTING b = 1650 Mumax = 0.138 fck b d2 1848.017 = 0.138 x 20 x 1650 x d^2 HENCE d= 700 CONSIDER EFFECTIVE COVER =
mm. 50
mm
OVERALL DEPTH D =
750
mm
MAIN NEGATIVE LONG. REINFORCEMENT (HOGGING MOMENTS):h
vw w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w wi
u 0.5 f fffffflf u 4.6M ffffffffffffffffffufffffm j 1 @t 1 @ k B bd Ast = ffffffffffffffck fy f ck b d
Ast =
8664.44
mm2
MINI.Ast = 0.85 x 1650 x 700 / 415
Page 4 of 45
% pt =
0.76
Ast (min) = 2365.66 HENCE Ast PROVIDED =
BAR DIA.
AREA
Ast reqd.
BAR
(mm)
(mm2)
(mm2)
REQD.
12 16 20
113.1 201.07 314.16
8664.44 8664.44 8664.44
76.61 43.1 27.58
8664.44
BAR
% pt =
mm2 mm2
PROVIDE SPACING UNIT WT
TOTAL
(mm) c/c 22 39 60
Kg/m
WT. (kg)
0.89 1.58 2.47
547.63 556.52 553.28
PROVIDE Ast (mm2)
77 44 28
0.21
8708.7 8847.08 8796.48
HENCE PROVIDE # 28 - 20 mm BAR ( SPACING = 60 mm c/c ) MAIN NEGATIVE LONG. REINFORCEMENT (SAGGING MOMENTS):DESIGN MOMENT UNDER COLUMN A / COLUMN B = Ast =
778.22
mm2
Ast min =
2365.67
mm2
HENCE Ast PROVIDED = BAR DIA.
AREA
Ast reqd.
BAR
(mm)
(mm )
(mm )
REQD.
12 16 20
113.1 201.07 314.16
2365.67 2365.67 2365.67
20.92 11.77 7.54
2
2
BAR
2365.67
mm2
PROVIDE SPACING UNIT WT
TOTAL
(mm) c/c 79 141 220
Kg/m
WT. (kg)
0.89 1.58 2.47
149.36 151.78 158.08
PROVIDE Ast (mm ) 2
21 12 8
193.836 KN-m
2375.1 2412.84 2513.28
HENCE PROVIDE # 8 - 20 mm BAR ( SPACING = 220 mm c/c )
Page 5 of 45
Page 6 of 45
SLAB AND BEAM TYPE RECTANGULAR COMBINED FOOTING INPUT DATA 1) LOAD ON COLUMN ON A = 2)LOAD ON COLUMN ON B = 3)CENTRE TO CENTRE DIST. (L3) = 4)DIST. OF CENTRE OF COL. A FROM PROPERTY LINE (L1) = 5)DIST. OF CENTRE OF COL. B = 5)SIZE OF COLUMN A d1 = b1 = 6)SIZE OF COLUMN B d2 = b2 = 7) BEARING CAPACITY OF SOIL = 8)STRENGTH OF CONCRETE fck = 9)STRENGTH OF STEEL fy = 10)WIDTH OF PEDESTRAL = 11)EFFECTIVE COVER = LENGTH OF FOOTING = WIDTH OF FOOTING =
1000 1000 3.5
KN KN m
0.3 0.3
m m
400 400
mm mm
400 400 190 20 415 300 75 5.6 2.1
mm mm KN/mm2 N/mm2 N/mm2 mm mm m m
DESIGN :LENGTH AND WIDTH OF FOOTING:C.G. OF LOADS FROM PROPERTY LINE X =
2.05
m
WT. OF FOOTING & EARTH ABOVE (10%) =
200
kN
TOTAL WORKING LOAD = 1000 + 1000 + 200 =
2200
kN
REQD. AREA OF FOOTING = Af = TOTAL LOAD / SBC = 2200 / 190 Af =
11.58
m2
LET THE WIDTH OF FOOTING Bf = 2.1 m. REQD. LENGTH OF FOOTING Lf = 11.58 / 2.1 Lf = 5.6 m HENCE PROVIDE FOOTING SIZE 5.6m X 2.1m, AREA Af = 11.76 sq.m FOR UNIFORM PRESSURE DISTRIBUTION THE C.G. OF THE FOOTING SHOULD COINCIDE WITH THE C.G. OF COLUMN LOADS. LET " x " BE THE DISTANCE OF C.G. FROM THE CENTRE LINE OF COLUMN A. THEN x = ( P2 x 3.5 ) / (P1 + P2) = (1000 x 3.5) / (1000 + 1000) x=
1.8
m. FROM COLUMN A
IF THE CANTILEVER PROJECTION OF FOOTING BEYOND COLUMN A IS 'a', THEN, (a + 1.8) = Lf / 2 = 5.6 / 2 HENCE a= 1 m Page 7 of 45
Page 8 of 45
SIMILARLY IF THE CANTILEVER PROJECTION OF FOOTING BEYOND B IS 'b' THEN,
b + (3.5 - 1.8 ) = Lf / 2 = 2.8 m.
HENCE
b=
1.1
m
THE DETAILS ARE SHOWN IN FIGURE,
P1 = 1000 kN
P2 = 1000 kN
B
A x
L1 = 1 m
L3= 3.5 m
L2 = 1.1 m
5.6
2.8 GENERAL ARRANGEMENT OF COMBINED FOOTING
RECTANGULAR FOOTING WITH CENTRAL BEAM :DESIGN OF BOTTOM SLAB:FACTORED LOAD ON COL. A = 1.5 x 1000 = FACTORED LOAD ON COL. A = 1.5 x 1000 =
1500 1500
NET UPWARD SOIL PRESSURE = (1500 + 1500) / (5.6 x 2.1) =
NET UPWARD SOIL PRESSURE PER UNIT LENGTH = 256 x 2.1 =
KN KN 256
KN/m2
537.6
KN/m
Page 9 of 45
B/2 C1
b1
C2 b2
B/2
d1
d2
L1
L2
L3
1500 / 0.4 = 3750 KN/m.
1500 / 0.4 = 3750 KN/m.
537.6 KN/m DESIGN OF SLAB :INTENSITY OF UPWARD PRESSURE = Wu =
256
KN/m2
CONSIDER ONE METER WIDTH IF THE SLAB (b = 1 m) LOAD PER m. RUN OF SLAB AT ULTIMATE = =
256 x 1 256 KN/m.
CANTILEVER PROJECTION OF THE SLAB (FOR SMALLER COLUMN) = 1050 - 400 / 2 = 850 mm MAXIMUM ULTIMATE MOMENT = 256 x 0.85 ^2 / 2 = 92.48
1.05 m.
KN-m.
Mu lim = 0.138 fck b d^2
STEEL ### ### ###
0.4 m. 185
HENCE DEPTH d =
0.85 m.
mm
SINCE THE SLAB IS IN CONTACT WITH THE SOIL CLEAR COVER OF 50 mm IS ASSUMED.
1m.
USING
20
mm DIAMETER BARS
pu = 256 KN/m2 REQD. TOTAL DEPTH D =
HENCE, EFF. DEPTH d =
300 240
mm mm
REINFORCEMENT IN SLAB:h
Ast
i vw w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w u 0.5 f ck l 4.6M u m u ffffffffffffffffffffffffff j 1 @t 1 @ k bd = fffffffffffffffffffff 2
fy
Ast =
0.5 f fffff Ast = ffffffffffffffck fy
f ck b d
1190.29
mm2
% pt =
0.5
Page 10 of 45
MINI.Ast = 0.85 x 1000 x 240 / 415 Ast (min) =
491.57
HENCE Ast PROVIDED = BAR DIA.
AREA
Ast reqd.
BAR
(mm)
(mm )
2
(mm )/m.
REQD.
PROVIDE
12 12 12
113.1 113.1 113.1
1190.29 1190.29 1190.29
10.53 10.53 10.53
11 11 11
2
BAR
% pt =
mm2 1190.29
0.21
mm2
PROVIDE SPACING UNIT WT
TOTAL
Ast (mm ) (mm) c/c
Kg/m
WT. (kg)
0.89 0.89 0.89
110.15 110.15 110.15
2
1244.1 1244.1 1244.1
95 95 95
HENCE PROVIDE # 59 - 12 mm BAR (SPACING = 95 c/c ) CHECK THE DEPTH FOR ONE-WAY SHEAR CONSIDERATIONS AT DISTANCE 'd' FROM FACE OF COLUMN:-
240 B/2 C1
b1
C2 b2
B/2 d1 L1
d2 L2
L3
DESIGN SHEAR FORCE = Vu = 256 x (0.85 - 0.24) HENCE Vu =
156.16
KN
NOMINAL SHEAR STRESS τv = Vu / b*d = 156160/ ( 1000 x 240) τv =
0.66
% pt = PERMISSIBLE SHEAR STRESS 0.52 HENCE FROM IS:456,TABLE-19, PERMISSIBLE SHEAR STRESS τc =
Mpa
0.49
Mpa k
VALUE OF 'k' FOR 300 mm THICK SLAB =
1
CAL.PERMISSIBLE SHEAR STRESS k*τc= 1 x 0.4864 =
0.49
N/mm2
HENCE REVISE CHECK FOR DEVELOPMENT LENGTH:AS PER IS:456, THE DEVELOPMENT LENGTH Ld IS GIVEN BY, φσ Ld = ffffffffffsffff 4τ bd
GRADE τbd
Page 11 of 45
DEVELOPMENT LENGTH Ld =
565
mm
AVAILABLE LENGTH OF BAR = 850 - 25 = 825 mm > 565 mm AND HENCE SAFE TRANSVERSE REINFORCEMENT:REQUIRED Ast = 0.12 x 1000 x 300 / 100 = BAR DIA.
AREA
Ast reqd.
BAR
BAR
(mm)
(mm2)
(mm2)/m.
REQD.
PROVIDE
10
78.54
360
4.59
5
360
mm2 / m.
PROVIDE SPACING UNIT WT
TOTAL
Ast (mm2) (mm) c/c
Kg/m
WT. (kg)
0.62
34.61
392.7
215
HENCE PROVIDE 10 mm BARS AT 215 mm c/c DESIGN OF LONGITUDINAL BEAM:LOAD FROM THE SLAB WILL BE TRANSFERRED TO THE BEAM. AS THE WIDTH IF THE FOOTING IS 2 m, THE NET UPWARD SOIL PRESSURE PER METER LENGTH OF THE BEAM Wu = 256 x 2.1 = 537.6 KN/m.
1500
KN
1500 3.5
C
1 m.
E
A
537.6
KN
m. KN/m.
D
B
1.1
SHEAR FORCE AND BENDING MOMENT S.F.@ AL = 537.6 KN POINT OF ZERO S.F. FROM LEFT END C, S.F.@ AR =
-962.4
KN
X1 = 1500 / 537.6 =
2.8
m.FROM C OR
S.F.@ BL =
919.2
KN
X2 = 1500 / 537.6 =
2.8
m.FROM D
S.F.@ BR =
-580.8 KN MAXIMUM B.M. OCCURS AT A DISTANCE OF 2.8 m.FROM D MuE = 537.6 x 2.8 ^2 / 2 - 1500 ( 2.8 - 1.1 ) = B.M. UNDER COLUMN A, MuA = 537.6 x 1 ^2 / 2 = B.M. UNDER COLUMN B, MuB = 537.6 x 1.1 ^2 / 2 =
-442.61 KN-m. 268.8
KN-m.
325.25 KN-m.
LET THE POINT OF CONTRA FLEXTURE BE AT A DISTANCE x FROM THE CENTRE OF COLUMN A THEN, Mx = 1500x - 537.6 (x + 1 )^2 / 2 = 0 THEREFORE x = 0.31 m. and 3.28 m. FROM COLUMN A i.e. 0.23 m. FROM B. DEPTH OF BEAM FROM B.M.:THE WIDTH OF BEAM IS KEPT EQUAL TO THE MAXI. WIDTH OF THE COLUMN i.e. 400 DETERMINE THE DEPTH OF THE BEAM WHERE T-BEAM ACTION IS NOT AVAILABLE.THE BEAM ACTS AS A RECTANGULAR SECTION IN THE CANTILEVER PORTION,
a= b= c= x1 = x2 =
Page 12 of 45
WHERE THE MAXIMUM POSITIVE MOMENT =
325.25
KN-m.
HENCE EFFECTIVE DEPTH OF BEAM deff =
545
mm
ASSUMING TWO ROWS OF BARS WITH EFFECTIVE COVER OF
75
mm
TOTAL DEPTH OF BEAM D = AND EFF. DEPTH d =
620 545
mm mm
800
THE HEAVIER COLUMN CAN PUNCH THROUGH THE FOOTING ONLY IF IT SHEARS AGAINST THE DEPTH OF THE BEAM ALONG ITS TWP OPPOSITE EDGES, AND ALONG THE DEPTH OF THE SLAB ON THE REMAINING TWO EDGES. THE CRITICAL S/C FOR TWO-WAY SHEAR IS TAKEN AT DIST, d/2 (i.e.545 / 2mm )FROM THE FACE OF THE COL. THEREFORE, THE CRITICAL S/C WILL BE TAKEN AT A DISTANCE HALF THE EFFE. DEPTH OF THE SLAB (ds/2) ON THE OTHER SIDE AS SHOWN IN FIG.
COLUMN DIMENSION b=
400
mm
BEAM & SLAB EFF. DEPTH db = BEAM 545 mm
d=
400
mm
SLAB
ds =
240
mm
AREA RESISTING TWO WAY SHEAR
= 2(b x db + ds x ds) + 2( D + db ) ds = 2 x (400 x 545 + 240 x 240 ) + 2 ( 400 + 545 ) x 240 AREA RESISTING TWO WAY SHEAR = 1004800 mm2
DESIGN SHEAR Pud = COLUMN LOAD - Wu x AREA AT CRITICAL SECTION Pud =
1500 - 256 x (b + ds) x (D + db ) = 1500 - 256 x (0.4 + 0.24) x ( 0.4 + 0.545) Pud = 1345.18 KN τv = Pud / b0 d = 1345.18 x 1000 / 1004800 τv =
1.34
Mpa
SHEAR STRESS RESISTED BY CONCRETE = τuc = τuc Ks τuc =
0.25 x ( fck )^ 0.5 = 0.25 x (20)^0.5 =
1.12
N/mm2
Page 13 of 45
Ks = 0.5 + b / D = 0.5 + 400 / 400 = HENCE, Ks = τuc =
1.12 x 1 =
>
1.5
1
1 1.12
N/mm2
----- REVISE THE DEPTH OF BEAM INCREASED DEPTH OF BEAM Db = AND EFF. DEPTH d =
800 725
mm mm
AREA RESISTING TWO WAY SHEAR = 2(b x db + ds x ds) + 2( D + db ) ds
= 2 x (400 x 725 + 240 x 240 ) + 2 ( 400 + 725 ) x 240 AREA RESISTING TWO WAY SHEAR= 1235200 mm2
DESIGN SHEAR Pud = 1500 - 256 x (0.4 + 0.24) x ( 0.4 + 0.725) Pud = 1315.68 KN τv =
1.09
Mpa
τuc =
1.12
Mpa ----- HENCE DEPTH IS SUFFICIENT
AREA OF STEEL : CANTILEVER PORTION BD:-
400
C
1000
400
3500
A
537.6
1100
B
D
KN/m
LENGTH OF CANTILEVER FROM THE FACE OF COLUMN = 1100 - 400 / 2 = 900 mm ULTIMATE MOMENT AT THE FACE OF THE COLUMN = 537.6 x 0.9 x 0.9 / 2 = 217.73 KN-m Mumax = 0.138 x 20 x 400 x 725 ^ 2 Mumax = HENCE
580.29 580.29 KN-m
KN-m >
217.73
KN-m Page 14 of 45
HENCE 580.29 KN-m > 217.73 KN-m S/C IS SINGLY REINFORCED Mu / bd2 =
1.1
HENCE % pt =
0.33
Ast =
948.3
N/mm2
mm2
MINI.Ast = 0.85 x 400 x 725 / 415 Ast (min) =
593.98
HENCE Ast PROVIDED = BAR DIA.
AREA
Ast reqd.
BAR
BAR
(mm)
(mm2)
(mm2)
REQD.
16
201.07
948.3
4.72
mm2 948.3
%pt =
0.21
mm2
PROVIDE UNIT WT
TOTAL
PROVIDE
Ast (mm2)
Kg/m
WT. (kg)
5
1005.35
1.58
HENCE PROVIDE # 5 - 16 mm BAR AT BOTTOM FACE CURTAILMENT:All bottom bars will be continued up to the end of cantilever. the bottom bars of 3 curtailed at a dist. d ( = 230 mm )from the point of contraflexure (λ = 230 mm ) in the portion ' BE ' with its distance from the centre of support equal to 460 mm from B.
CANTILEVER PORTION AC LENGTH OF CANTILEVER FROM THE FACE OF COLUMN = 1000 - 400 / 2 =
800
ULTIMATE MOMENT = 537.6 x 0.8 ^2 / 2 = 172.04 KN-m
BAR DIA.
Mu / bd2 =
0.9
HENCE % pt =
0.26
N/mm2
Ast =
765.6
mm2
Ast (min) =
593.98
mm2
HENCE Ast PROVIDED =
765.6
mm2
AREA
Ast reqd.
BAR
BAR
(mm)
(mm2)
(mm2)
REQD.
16
201.07
765.6
3.81
%pt =
0.21
PROVIDE UNIT WT
TOTAL
PROVIDE
Ast (mm2)
Kg/m
WT. (kg)
4
804.28
1.58
HENCE PROVIDE # 4 - 16 mm BAR AT BOTTOM FACE REGION AB BETWEEN POINTS OF CONTRAFLEXURES:Page 15 of 45
THE BEAM ACTS AS AN ISOLATED T-BEAM. bf = [L0 / (L0 / b + 4)] + bw
------CL.23.1.2 IS:456-2000
L0 =
3500 - 306 - 230 = b = ACTUAL WIDTH OF FLANGE = bw = WIDTH OF BEAM = bf =
2964 2100 400
mm mm mm
[2964 / ( 2964 / 2100 + 4 ) ] + 400
bf =
948 Df = DEPTH OF SLAB =
< 300 Mumax =
2100 mm mm 442.61 KN-m
MOMENT OF RESISTANCE Muf of A BEAM FOR Xu = Df is, Muf = [ 0.36 x 20 x 948 x 300 ( 725 - 0.42 x 300 )] / 1000000
Muf =
1226.56 KN-m
AREA
Ast reqd.
BAR
BAR
(mm)
(mm2)
(mm2)
REQD.
20
314.16
1788.3
5.7
BAR DIA.
> Mumax = 442.61 KN-m Therefore, Xu < Df Ast = 1788.3 mm2 PROVIDE UNIT WT
TOTAL
PROVIDE
Ast (mm2)
Kg/m
WT. (kg)
6
1884.96
2.47
HENCE PROVIDE # 6 - 20 mm BAR AT TOP FACE CURTAILMENT:CONSIDER THAT
3
20
mm ARE TO BE CURTAILED
Nos. OF BARS TO BE CONTINUED =
3
20
Ast =
942.48 mm2
MOMENT OF RESISTANCE OF CONTINUING BARS Mur =
( 0.87 x 415 x 942.48 x ( 725 - (415 x 942.48 ) / (20 x 400))) / 1000000
Mur = 230.07 KN-m LET THE THEOROTICAL POINT OF CONTRAFLEXURE BE AT A DISTANCE " X " FROM THE FREE END " C ". THEN, Muc = Mur, -537.6 X^2/2 + 1500( X - 1 ) = 230.07 X^2 - 5.59X +6.44 = 0 THEREFORE x = 3.97 m. OR
1.62
ACTUAL POINT OF CURTAILMENT = 3.967 + 0.23 =
a= b= c= x1 = x2 =
m. FROM C 4.2
m from C
or = 1.624 - 0.23 = 1.39 m from C Terminate 3 - 20 mm bars at a distance of 394 mm ( = 1394 - 1000 ) from the column A and Page 16 of 45
303 mm ( = 4500 - 4197 ) from column B. Remaining bars 3 - 20 shall be continued beyond the point of inflection for a distance of 230 mm from column A and up to the outer face of column B and continued in the cantilever portion. DESIGN OF SHEAR REINFORCEMENT:PORTION BETWEEN COLUMN i.e. AB In this case the crack due to diagonal tension will occur at the point of contra flexure because the distance of the point of contra flexure from the column is less than the effective depth d ( = 725 mm ) (i) Maximum Shear force at B, Vmax =
919.2
kN
SHEAR AT THE POINT OF CONTRAFLEXURE IS Vud = 919.2 - 537.6 x 0.23 Vud = τv =
795.55 kN
MAXIMUM SHEAR STRESS τcma
795552 / (400 x 725)
2.75 Mpa τcmax = < 2.8 AREA OF STEEL AVAILABLE 3 - 20 mm BARS
CONCRETE τcmax =
τv =
Ast = HENCE
942.48
mm2
τc =
Mpa
% pt = 0.4
0.33
Mpa
τv > τc HENCE DESIGN SHEAR REINFORCEMENT REQUIRED USING
10
mm DIA.
4
LEGGED STIRRUPS, 120
SPACING = [ 0.87 x 415 x ( 4 x 78.6)] / ( (2.75 - 0.3984 ) x 400)=
(ii) Maximum Shear force at A, Vmax =
962.4
mm c/c
kN
SHEAR AT THE POINT OF CONTRAFLEXURE IS Vud = 962.4 - 0.306 x 537.6 Vud = 797.89 kN τv = τv =
797894.4 / (400 x 725) 2.76 Mpa
<
τcmax =
% pt =
0.65
2.8
Mpa
AREA OF STEEL AVAILABLE 6 - 20 mm BARS Ast =
1884.96 mm2
HENCE
τc = 0.53 Mpa τv > τc HENCE DESIGN SHEAR REINFORCEMENT REQUIRED
Page 17 of 45
USING
10
mm DIA.
4
LEGGED STIRRUPS, 125
SPACING = [ 0.87 x 415 x ( 4 x 78.6)] / ( (2.76 - 0.528 ) x 400)=
mm c/c
FOR THE REMAINING CENTRAL PORTION PROVIDE MINI. SHEAR REINFORCEMENT.
(Cl.26.5.1.6 AS PER IS:456-2000) USING
8
mm DIA.
2
LEGGED STIRRUPS AT,
SPACING = [ 0.87 x 415 x ( 2 x 50.3)] / ( 0.4 x 400)=
220
mm c/c
HENCE PROVIDE 2 LEGGED 8 mm DIA. AT 220 mm C/C AS NOMINAL SHEAR R/F. CANTILEVER PORTION BD :Vumax = VuD = VuD = τv = τv = Ast =
τv
591.36
kN
591.36 - 537.6 ( 0.4 / 2 + 0.23 ) 360.2
kN
360200 / ( 400 x 725 )
1.25 Mpa 1005.35 mm2 &
< % pt =
HENCE
τc =
0.41
>
τc
AND
τv - τc
USING
8
mm DIA.
2
τcmax =
2.8
Mpa
0.35
Mpa
SPACING = [ 0.87 x 415 x ( 2 x 50.3)] / ( 0.4 x 400)=
>
0.4
LEGGED STIRRUPS AT, 220
mm c/c
HENCE PROVIDE 2 LEGGED 8 mm DIA. AT 220 mm C/C AS NOMINAL SHEAR R/F. CANTILEVER PORTION AC :PROVIDE 2 LEGGED 8 mm DIA. AT 220 mm C/C AS NOMINAL SHEAR R/F.
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2100 mm
5600 mm
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% pt 0 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
DESIGN SHEAR STRENGTH OF CONCRETE Τc N/mm2 M15 M20 M25 M30 M35 M40 & ABOVE 15 20 25 30 35 40 0.280 0.280 0.290 0.290 0.290 0.300 0.287 0.288 0.297 0.298 0.298 0.308 0.294 0.296 0.304 0.306 0.306 0.316 0.301 0.304 0.311 0.314 0.314 0.324 0.308 0.312 0.318 0.322 0.322 0.332 0.315 0.320 0.325 0.330 0.330 0.340 0.322 0.328 0.332 0.338 0.338 0.348 0.329 0.336 0.339 0.346 0.346 0.356 0.336 0.344 0.346 0.354 0.354 0.364 0.343 0.352 0.353 0.362 0.362 0.372 0.350 0.360 0.360 0.370 0.370 0.380 0.354 0.365 0.365 0.375 0.375 0.385 0.359 0.370 0.370 0.380 0.380 0.390 0.363 0.374 0.376 0.386 0.386 0.396 0.368 0.379 0.381 0.391 0.391 0.401 0.372 0.384 0.386 0.396 0.396 0.406 0.376 0.389 0.391 0.401 0.401 0.411 0.381 0.394 0.396 0.406 0.406 0.416 0.385 0.398 0.402 0.412 0.412 0.422 0.390 0.403 0.407 0.417 0.417 0.427 0.394 0.408 0.412 0.422 0.422 0.432 0.398 0.413 0.417 0.427 0.427 0.437 0.403 0.418 0.422 0.432 0.432 0.442 0.407 0.422 0.428 0.438 0.438 0.448 0.412 0.427 0.433 0.443 0.443 0.453 0.416 0.432 0.438 0.448 0.448 0.458 0.420 0.437 0.443 0.453 0.453 0.463 0.425 0.442 0.448 0.458 0.458 0.468 0.429 0.446 0.454 0.464 0.464 0.474 0.434 0.451 0.459 0.469 0.469 0.479 0.438 0.456 0.464 0.474 0.474 0.484 0.442 0.461 0.469 0.479 0.479 0.489 0.447 0.466 0.474 0.484 0.484 0.494 0.451 0.470 0.480 0.490 0.490 0.500 0.456 0.475 0.485 0.495 0.495 0.505 0.460 0.480 0.490 0.500 0.500 0.510 0.463 0.483 0.493 0.504 0.504 0.514 0.466 0.486 0.496 0.507 0.507 0.517 0.470 0.490 0.500 0.511 0.511 0.521 0.473 0.493 0.503 0.514 0.514 0.524 0.476 0.496 0.506 0.518 0.518 0.528 0.479 0.499 0.509 0.522 0.522 0.532 0.482 0.502 0.512 0.525 0.525 0.535 0.486 0.506 0.516 0.529 0.529 0.539 0.489 0.509 0.519 0.532 0.532 0.542
0.6 0.61 0.62 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 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09
0.492 0.495 0.498 0.502 0.505 0.508 0.511 0.514 0.518 0.521 0.524 0.527 0.530 0.534 0.537 0.540 0.542 0.545 0.547 0.550 0.552 0.554 0.557 0.559 0.562 0.564 0.566 0.569 0.571 0.574 0.576 0.578 0.581 0.583 0.586 0.588 0.590 0.593 0.595 0.598 0.600 0.602 0.603 0.605 0.606 0.608 0.610 0.611 0.613 0.614
0.512 0.515 0.518 0.522 0.525 0.528 0.531 0.534 0.538 0.541 0.544 0.547 0.550 0.554 0.557 0.560 0.562 0.565 0.567 0.570 0.572 0.574 0.577 0.579 0.582 0.584 0.586 0.589 0.591 0.594 0.596 0.598 0.601 0.603 0.606 0.608 0.610 0.613 0.615 0.618 0.620 0.622 0.624 0.626 0.628 0.630 0.632 0.634 0.636 0.638
0.522 0.525 0.528 0.532 0.535 0.538 0.541 0.544 0.548 0.551 0.554 0.557 0.560 0.564 0.567 0.570 0.573 0.576 0.578 0.581 0.584 0.587 0.590 0.592 0.595 0.598 0.601 0.604 0.606 0.609 0.612 0.615 0.618 0.620 0.623 0.626 0.629 0.632 0.634 0.637 0.640 0.642 0.645 0.647 0.650 0.652 0.654 0.657 0.659 0.662
0.536 0.540 0.543 0.547 0.550 0.554 0.558 0.561 0.565 0.568 0.572 0.576 0.579 0.583 0.586 0.590 0.593 0.596 0.598 0.601 0.604 0.607 0.610 0.612 0.615 0.618 0.621 0.624 0.626 0.629 0.632 0.635 0.638 0.640 0.643 0.646 0.649 0.652 0.654 0.657 0.660 0.662 0.664 0.666 0.668 0.670 0.672 0.674 0.676 0.678
0.536 0.540 0.543 0.547 0.550 0.554 0.558 0.561 0.565 0.568 0.572 0.576 0.579 0.583 0.586 0.590 0.593 0.596 0.600 0.603 0.606 0.609 0.612 0.616 0.619 0.622 0.625 0.628 0.632 0.635 0.638 0.641 0.644 0.648 0.651 0.654 0.657 0.660 0.664 0.667 0.670 0.672 0.675 0.677 0.680 0.682 0.684 0.687 0.689 0.692
0.546 0.550 0.553 0.557 0.560 0.564 0.568 0.571 0.575 0.578 0.582 0.586 0.589 0.593 0.596 0.600 0.603 0.606 0.610 0.613 0.616 0.619 0.622 0.626 0.629 0.632 0.635 0.638 0.642 0.645 0.648 0.651 0.654 0.658 0.661 0.664 0.667 0.670 0.674 0.677 0.680 0.682 0.685 0.687 0.690 0.692 0.694 0.697 0.699 0.702
1.1 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.2 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.3 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.4 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 1.5 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59
0.616 0.618 0.619 0.621 0.622 0.624 0.626 0.627 0.629 0.630 0.632 0.634 0.635 0.637 0.638 0.640 0.642 0.643 0.645 0.646 0.648 0.650 0.651 0.653 0.654 0.656 0.658 0.659 0.661 0.662 0.664 0.666 0.667 0.669 0.670 0.672 0.674 0.675 0.677 0.678 0.680 0.681 0.682 0.684 0.685 0.686 0.687 0.688 0.690 0.691
0.640 0.642 0.644 0.646 0.648 0.650 0.652 0.654 0.656 0.658 0.660 0.662 0.664 0.666 0.668 0.670 0.672 0.674 0.676 0.678 0.680 0.682 0.684 0.686 0.688 0.690 0.692 0.694 0.696 0.698 0.700 0.702 0.704 0.706 0.708 0.710 0.712 0.714 0.716 0.718 0.720 0.721 0.722 0.724 0.725 0.726 0.727 0.728 0.730 0.731
0.664 0.666 0.669 0.671 0.674 0.676 0.678 0.681 0.683 0.686 0.688 0.690 0.693 0.695 0.698 0.700 0.702 0.703 0.705 0.706 0.708 0.710 0.711 0.713 0.714 0.716 0.718 0.719 0.721 0.722 0.724 0.726 0.727 0.729 0.730 0.732 0.734 0.735 0.737 0.738 0.740 0.742 0.743 0.745 0.746 0.748 0.750 0.751 0.753 0.754
0.680 0.682 0.684 0.686 0.688 0.690 0.692 0.694 0.696 0.698 0.700 0.702 0.704 0.706 0.708 0.710 0.712 0.714 0.716 0.718 0.720 0.722 0.724 0.726 0.728 0.730 0.732 0.734 0.736 0.738 0.740 0.742 0.744 0.746 0.748 0.750 0.752 0.754 0.756 0.758 0.760 0.762 0.763 0.765 0.766 0.768 0.770 0.771 0.773 0.774
0.694 0.696 0.699 0.701 0.704 0.706 0.708 0.711 0.713 0.716 0.718 0.720 0.723 0.725 0.728 0.730 0.732 0.734 0.736 0.738 0.740 0.742 0.744 0.746 0.748 0.750 0.752 0.754 0.756 0.758 0.760 0.762 0.764 0.766 0.768 0.770 0.772 0.774 0.776 0.778 0.780 0.782 0.783 0.785 0.786 0.788 0.790 0.791 0.793 0.794
0.704 0.706 0.709 0.711 0.714 0.716 0.718 0.721 0.723 0.726 0.728 0.730 0.733 0.735 0.738 0.740 0.742 0.744 0.746 0.748 0.750 0.752 0.754 0.756 0.758 0.760 0.762 0.764 0.766 0.768 0.770 0.772 0.774 0.776 0.778 0.780 0.782 0.784 0.786 0.788 0.790 0.792 0.794 0.796 0.798 0.800 0.802 0.804 0.806 0.808
1.6 1.61 1.62 1.63 1.64 1.65 1.66 1.67 1.68 1.69 1.7 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79 1.8 1.81 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.9 1.91 1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99 2 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09
0.692 0.693 0.694 0.696 0.697 0.698 0.699 0.700 0.702 0.703 0.704 0.705 0.706 0.708 0.709 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710
0.732 0.733 0.734 0.736 0.737 0.738 0.739 0.740 0.742 0.743 0.744 0.745 0.746 0.748 0.749 0.750 0.752 0.753 0.755 0.756 0.758 0.760 0.761 0.763 0.764 0.766 0.768 0.769 0.771 0.772 0.774 0.776 0.777 0.779 0.780 0.782 0.784 0.785 0.787 0.788 0.790 0.791 0.792 0.792 0.793 0.794 0.795 0.796 0.796 0.797
0.756 0.758 0.759 0.761 0.762 0.764 0.766 0.767 0.769 0.770 0.772 0.774 0.775 0.777 0.778 0.780 0.782 0.783 0.785 0.786 0.788 0.790 0.791 0.793 0.794 0.796 0.798 0.799 0.801 0.802 0.804 0.806 0.807 0.809 0.810 0.812 0.814 0.815 0.817 0.818 0.820 0.821 0.822 0.824 0.825 0.826 0.827 0.828 0.830 0.831
0.776 0.778 0.779 0.781 0.782 0.784 0.786 0.787 0.789 0.790 0.792 0.794 0.795 0.797 0.798 0.800 0.802 0.803 0.805 0.806 0.808 0.810 0.811 0.813 0.814 0.816 0.818 0.819 0.821 0.822 0.824 0.826 0.827 0.829 0.830 0.832 0.834 0.835 0.837 0.838 0.840 0.842 0.843 0.845 0.846 0.848 0.850 0.851 0.853 0.854
0.796 0.798 0.799 0.801 0.802 0.804 0.806 0.807 0.809 0.810 0.812 0.814 0.815 0.817 0.818 0.820 0.822 0.823 0.825 0.826 0.828 0.830 0.831 0.833 0.834 0.836 0.838 0.839 0.841 0.842 0.844 0.846 0.847 0.849 0.850 0.852 0.854 0.855 0.857 0.858 0.860 0.862 0.863 0.865 0.866 0.868 0.870 0.871 0.873 0.874
0.810 0.812 0.814 0.816 0.818 0.820 0.822 0.824 0.826 0.828 0.830 0.832 0.834 0.836 0.838 0.840 0.842 0.843 0.845 0.846 0.848 0.850 0.851 0.853 0.854 0.856 0.858 0.859 0.861 0.862 0.864 0.866 0.867 0.869 0.870 0.872 0.874 0.875 0.877 0.878 0.880 0.882 0.883 0.885 0.886 0.888 0.890 0.891 0.893 0.894
2.1 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.2 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.3 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39 2.4 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.5 2.51 2.52 2.53 2.54 2.55 2.56 2.57 2.58 2.59
0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710
0.798 0.799 0.800 0.800 0.801 0.802 0.803 0.804 0.804 0.805 0.806 0.807 0.808 0.808 0.809 0.810 0.810 0.811 0.811 0.812 0.812 0.812 0.813 0.813 0.814 0.814 0.814 0.815 0.815 0.816 0.816 0.816 0.817 0.817 0.818 0.818 0.818 0.819 0.819 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820
0.832 0.833 0.834 0.836 0.837 0.838 0.839 0.840 0.842 0.843 0.844 0.845 0.846 0.848 0.849 0.850 0.851 0.852 0.854 0.855 0.856 0.857 0.858 0.860 0.861 0.862 0.863 0.864 0.866 0.867 0.868 0.869 0.870 0.872 0.873 0.874 0.875 0.876 0.878 0.879 0.880 0.881 0.882 0.882 0.883 0.884 0.885 0.886 0.886 0.887
0.856 0.858 0.859 0.861 0.862 0.864 0.866 0.867 0.869 0.870 0.872 0.874 0.875 0.877 0.878 0.880 0.881 0.882 0.884 0.885 0.886 0.887 0.888 0.890 0.891 0.892 0.893 0.894 0.896 0.897 0.898 0.899 0.900 0.902 0.903 0.904 0.905 0.906 0.908 0.909 0.910 0.911 0.912 0.914 0.915 0.916 0.917 0.918 0.920 0.921
0.876 0.878 0.879 0.881 0.882 0.884 0.886 0.887 0.889 0.890 0.892 0.894 0.895 0.897 0.898 0.900 0.901 0.902 0.904 0.905 0.906 0.907 0.908 0.910 0.911 0.912 0.913 0.914 0.916 0.917 0.918 0.919 0.920 0.922 0.923 0.924 0.925 0.926 0.928 0.929 0.930 0.931 0.932 0.934 0.935 0.936 0.937 0.938 0.940 0.941
0.896 0.898 0.899 0.901 0.902 0.904 0.906 0.907 0.909 0.910 0.912 0.914 0.915 0.917 0.918 0.920 0.921 0.922 0.924 0.925 0.926 0.927 0.928 0.930 0.931 0.932 0.933 0.934 0.936 0.937 0.938 0.939 0.940 0.942 0.943 0.944 0.945 0.946 0.948 0.949 0.950 0.951 0.952 0.954 0.955 0.956 0.957 0.958 0.960 0.961
2.6 2.61 2.62 2.63 2.64 2.65 2.66 2.67 2.68 2.69 2.7 2.71 2.72 2.73 2.74 2.75 2.76 2.77 2.78 2.79 2.8 2.81 2.82 2.83 2.84 2.85 2.86 2.87 2.88 2.89 2.9 2.91 2.92 2.93 2.94 2.95 2.96 2.97 2.98 2.99 3
0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710 0.710
0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820 0.820
0.888 0.889 0.890 0.890 0.891 0.892 0.893 0.894 0.894 0.895 0.896 0.897 0.898 0.898 0.899 0.900 0.901 0.902 0.902 0.903 0.904 0.905 0.906 0.906 0.907 0.908 0.909 0.910 0.910 0.911 0.912 0.913 0.914 0.914 0.915 0.916 0.917 0.918 0.918 0.919 0.920
0.922 0.923 0.924 0.926 0.927 0.928 0.929 0.930 0.932 0.933 0.934 0.935 0.936 0.938 0.939 0.940 0.941 0.942 0.942 0.943 0.944 0.945 0.946 0.946 0.947 0.948 0.949 0.950 0.950 0.951 0.952 0.953 0.954 0.954 0.955 0.956 0.957 0.958 0.958 0.959 0.960
0.942 0.943 0.944 0.946 0.947 0.948 0.949 0.950 0.952 0.953 0.954 0.955 0.956 0.958 0.959 0.960 0.961 0.962 0.964 0.965 0.966 0.967 0.968 0.970 0.971 0.972 0.973 0.974 0.976 0.977 0.978 0.979 0.980 0.982 0.983 0.984 0.985 0.986 0.988 0.989 0.990
0.962 0.963 0.964 0.966 0.967 0.968 0.969 0.970 0.972 0.973 0.974 0.975 0.976 0.978 0.979 0.980 0.981 0.982 0.984 0.985 0.986 0.987 0.988 0.990 0.991 0.992 0.993 0.994 0.996 0.997 0.998 0.999 1.000 1.002 1.003 1.004 1.005 1.006 1.008 1.009 1.010
Fck =
20
% pt =
0.52
Tc =
0.49
Fck =
20
% pt =
0.33
Tc =
0.4
Fck =
20
% pt =
0.65
Tc =
0.53
Fck =
20
% pt =
0.35
Tc =
0.41
% pt 0.15 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
DESIGN SHEAR STRENGTH OF CONCRETE Τc N/mm2 M15 M20 M25 M30 M35 M40 & ABOVE 15 20 25 30 35 40 0.280 0.280 0.290 0.290 0.290 0.300 0.350 0.360 0.360 0.370 0.370 0.380 0.460 0.480 0.490 0.500 0.500 0.510 0.540 0.560 0.570 0.590 0.590 0.600 0.600 0.620 0.640 0.660 0.670 0.680 0.640 0.670 0.700 0.710 0.730 0.740 0.680 0.720 0.740 0.760 0.780 0.790 0.710 0.750 0.780 0.800 0.820 0.840 0.710 0.790 0.820 0.840 0.860 0.880 0.710 0.810 0.850 0.880 0.900 0.920 0.710 0.820 0.880 0.910 0.930 0.950 0.710 0.820 0.900 0.940 0.960 0.980 0.710 0.820 0.920 0.960 0.990 1.010
Fy =
415
Mu/bd2 =
1.1
% pt =
0.33
Fy =
415
Mu/bd2 =
0.9
% pt =
0.26
TABLE 3 FLEXURE - REINFORCEMENT PERCENTAGE, pt FOR SINGLY REINFORCED SECTIONS Mu/bd2 N/mm2 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.02 2.04
Fy N/mm2 240 0.146 0.171 0.196 0.222 0.247 0.272 0.298 0.324 0.350 0.376 0.403 0.430 0.456 0.483 0.511 0.538 0.566 0.594 0.622 0.650 0.678 0.707 0.736 0.765 0.795 0.825 0.855 0.885 0.916 0.947 0.978 1.009 1.041 1.073 1.106 1.119 1.132
250 0.140 0.164 0.188 0.213 0.237 0.262 0.286 0.311 0.336 0.361 0.387 0.412 0.438 0.464 0.490 0.517 0.543 0.570 0.597 0.624 0.651 0.679 0.707 0.735 0.763 0.792 0.821 0.850 0.879 0.909 0.939 0.969 1.000 1.030 1.062 1.074 1.087
415 0.085 0.099 0.114 0.128 0.143 0.158 0.172 0.187 0.203 0.218 0.233 0.248 0.264 0.280 0.295 0.311 0.327 0.343 0.359 0.376 0.392 0.409 0.426 0.443 0.460 0.477 0.494 0.512 0.530 0.547 0.565 0.584 0.602 0.621 0.640 0.647 0.655
480 0.073 0.086 0.098 0.111 0.123 0.136 0.149 0.162 0.175 0.188 0.201 0.215 0.228 0.242 0.255 0.269 0.283 0.297 0.311 0.325 0.339 0.354 0.368 0.383 0.397 0.412 0.427 0.443 0.458 0.473 0.489 0.505 0.521 0.537 0.553 0.559 0.566
500 0.070 0.082 0.094 0.106 0.119 0.131 0.143 0.156 0.168 0.181 0.193 0.206 0.219 0.232 0.245 0.258 0.272 0.285 0.298 0.312 0.326 0.339 0.353 0.367 0.382 0.396 0.410 0.425 0.440 0.454 0.469 0.484 0.500 0.515 0.531 0.537 0.543
2.06 2.08 2.10 2.12 2.14 2.16 2.18 2.20 2.22 2.24 2.26 2.28 2.30 2.32 2.34 2.36 2.38 2.40 2.42 2.44 2.46 2.48 2.50 2.52 2.54 2.56 2.58 2.60 2.62 2.64 2.66 2.68 2.70 2.72 2.74 2.76 2.78 2.80 2.82 2.84 2.86 2.88 2.90 2.92 2.94 2.96 2.98
1.145 1.159 1.172 1.185 1.199 1.212 1.226 1.239 1.253 1.267 1.281 1.295 1.309 1.323 1.337 1.351 1.365 1.380 1.394 1.408 1.423 1.438 1.452 1.467 1.482 1.497 1.512 1.527 1.542 1.558 1.573 1.588 1.604 1.620 1.636 1.651 1.667 1.683 1.700 1.716 1.732 1.749 1.766 1.782 1.799 1.816 1.833
1.099 1.112 1.125 1.138 1.151 1.164 1.177 1.190 1.203 1.216 1.230 1.243 1.256 1.270 1.283 1.297 1.311 1.324 1.338 1.352 1.366 1.380 1.394 1.408 1.423 1.437 1.451 1.466 1.481 1.495 1.510 1.525 1.540 1.555 1.570 1.585 1.601 1.616 1.632 1.647 1.663 1.679 1.695 1.711 1.727 1.743 1.760
0.662 0.670 0.678 0.685 0.693 0.701 0.709 0.717 0.725 0.733 0.741 0.749 0.757 0.765 0.773 0.781 0.790 0.798 0.806 0.814 0.823 0.831 0.840 0.848 0.857 0.866 0.874 0.883 0.892 0.901 0.910 0.919 0.928 0.937 0.946 0.955 -
0.573 0.579 0.586 0.593 0.599 0.606 0.613 0.620 0.627 0.633 0.640 0.647 0.654 0.661 0.668 0.675 0.683 0.690 0.697 0.704 0.711 0.719 0.726 0.734 0.741 0.748 0.756 0.764 0.771 0.779 0.786 0.794 -
0.550 0.556 0.562 0.569 0.575 0.582 0.588 0.595 0.602 0.608 0.615 0.621 0.628 0.635 0.642 0.648 0.655 0.662 0.669 0.676 0.683 0.690 0.697 0.704 0.711 0.719 0.726 0.733 0.740 0.748 0.755 -
Fy =
415
Mu/bd2 =
1.1
% pt =
0.32
Fy =
415
Mu/bd2 =
0.9
% pt =
0.26
TABLE 3 FLEXURE - REINFORCEMENT PERCENTAGE, pt FOR SINGLY REINFORCED SECTIONS Mu/bd2 N/mm2 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10
Fy N/mm2 240 0.146 0.171 0.195 0.220 0.245 0.271 0.296 0.321 0.347 0.373 0.399 0.425 0.451 0.477 0.504 0.530 0.557 0.584 0.611 0.638 0.666 0.693 0.721 0.749 0.777 0.805 0.834 0.862 0.891 0.920 0.949 0.979 1.009 1.038 1.068 1.099 1.129
250 0.140 0.164 0.188 0.211 0.236 0.260 0.284 0.309 0.333 0.358 0.383 0.408 0.433 0.458 0.483 0.509 0.535 0.561 0.587 0.613 0.639 0.666 0.692 0.719 0.746 0.773 0.800 0.828 0.856 0.883 0.911 0.940 0.968 0.997 1.026 1.055 1.084
415 0.084 0.099 0.113 0.127 0.142 0.156 0.171 0.186 0.201 0.216 0.231 0.246 0.261 0.276 0.291 0.307 0.322 0.338 0.353 0.369 0.385 0.401 0.417 0.433 0.449 0.466 0.482 0.499 0.515 0.532 0.549 0.566 0.583 0.601 0.618 0.635 0.653
480 0.073 0.085 0.098 0.110 0.123 0.135 0.148 0.161 0.174 0.186 0.199 0.212 0.225 0.239 0.252 0.265 0.279 0.292 0.306 0.319 0.333 0.347 0.360 0.374 0.388 0.403 0.417 0.431 0.446 0.460 0.475 0.489 0.504 0.519 0.534 0.549 0.565
500 0.070 0.082 0.094 0.106 0.118 0.130 0.142 0.154 0.167 0.179 0.191 0.204 0.216 0.229 0.242 0.255 0.267 0.280 0.293 0.306 0.320 0.333 0.346 0.359 0.373 0.387 0.400 0.414 0.428 0.442 0.456 0.470 0.484 0.498 0.513 0.527 0.542
2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25 3.30 3.32 3.34 3.36 3.38 3.40 3.42 3.44 3.46 3.48 3.50 3.52 3.54 3.56 3.58 3.60 3.62 3.64 3.66 3.68 3.70 3.72 3.74
1.160 1.191 1.222 1.254 1.285 1.317 1.350 1.382 1.415 1.448 1.482 1.515 1.549 1.584 1.618 1.653 1.689 1.724 1.760 1.797 1.834 1.871 1.909 1.947 1.962 1.978 1.993 2.009 2.025 2.040 2.056 2.072 2.088 2.104 2.120 2.137 2.153 2.170 2.186 2.203 2.219 2.236 2.253 2.270 2.287 2.304
1.114 1.143 1.173 1.204 1.234 1.265 1.296 1.327 1.358 1.390 1.422 1.455 1.487 1.520 1.554 1.587 1.621 1.655 1.690 1.725 1.760 1.796 1.832 1.869 1.884 1.899 1.914 1.929 1.944 1.959 1.974 1.989 2.005 2.020 2.036 2.051 2.067 2.083 2.099 2.115 2.131 2.147 2.163 2.179 2.196 -
0.671 0.689 0.707 0.725 0.743 0.762 0.781 0.799 0.818 0.837 0.857 0.876 0.896 0.916 0.936 0.956 0.977 0.997 1.018 1.039 1.061 1.082 1.104 1.126 1.135 1.144 1.153 1.162 1.171 1.180 1.189 -
0.580 0.596 0.611 0.627 0.643 0.659 0.675 0.691 0.708 0.724 0.741 0.758 0.775 0.792 0.809 0.827 0.844 0.862 0.880 0.898 0.917 0.936 0.954 0.973 0.981 0.989 -
0.557 0.572 0.587 0.602 0.617 0.632 0.648 0.663 0.679 0.695 0.711 0.727 0.744 0.760 0.777 0.794 0.811 0.828 0.845 0.863 0.880 0.898 0.916 0.935 0.942 -
Fy =
415
Mu/bd2 =
1.1
% pt =
0.32
Fy =
415
Mu/bd2 =
0.9
% pt =
0.26
TABLE 3 FLEXURE - REINFORCEMENT PERCENTAGE, pt FOR SINGLY REINFORCED SECTIONS Mu/bd2 N/mm2 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10
Fy N/mm2 240 0.145 0.170 0.195 0.219 0.244 0.269 0.294 0.320 0.345 0.370 0.396 0.422 0.447 0.473 0.499 0.525 0.552 0.578 0.608 0.631 0.658 0.685 0.712 0.739 0.766 0.793 0.821 0.849 0.876 0.904 0.932 0.961 0.989 1.018 1.046 1.075 1.104
250 0.140 0.163 0.187 0.211 0.235 0.259 0.283 0.307 0.331 0.356 0.380 0.405 0.429 0.454 0.479 0.504 0.529 0.555 0.580 0.606 0.631 0.657 0.683 0.709 0.735 0.762 0.788 0.815 0.841 0.868 0.895 0.922 0.950 0.977 1.005 1.032 1.060
415 0.084 0.098 0.113 0.127 0.141 0.156 0.170 0.185 0.200 0.214 0.229 0.244 0.259 0.274 0.289 0.304 0.319 0.334 0.350 0.365 0.380 0.396 0.411 0.427 0.443 0.459 0.475 0.491 0.507 0.523 0.539 0.556 0.572 0.589 0.605 0.622 0.639
480 0.073 0.085 0.097 0.110 0.122 0.135 0.147 0.160 0.172 0.185 0.198 0.211 0.224 0.237 0.250 0.263 0.276 0.289 0.302 0.315 0.329 0.342 0.356 0.369 0.383 0.397 0.410 0.424 0.438 0.452 0.466 0.480 0.495 0.509 0.523 0.538 0.552
500 0.070 0.082 0.093 0.105 0.117 0.129 0.141 0.153 0.166 0.178 0.190 0.202 0.215 0.227 0.240 0.252 0.265 0.277 0.290 0.303 0.316 0.329 0.342 0.355 0.368 0.381 0.394 0.407 0.421 0.434 0.448 0.461 0.475 0.488 0.502 0.516 0.530
2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 3.50 3.55 3.60 3.65 3.70 3.75 3.80 3.85 3.90 3.95 4.00 4.05 4.10 4.15 4.20 4.25 4.30 4.35 4.40 4.45
1.134 1.163 1.192 1.222 1.252 1.282 1.312 1.343 1.374 1.404 1.435 1.467 1.498 1.530 1.562 1.594 1.626 1.659 1.691 1.725 1.758 1.791 1.825 1.859 1.893 1.928 1.963 1.998 2.034 2.069 2.105 2.142 2.178 2.215 2.253 2.291 2.329 2.367 2.406 2.445 2.485 2.525 2.566 2.607 2.648 2.690 2.733
1.088 1.116 1.145 1.173 1.202 1.231 1.260 1.289 1.319 1.348 1.378 1.408 1.438 1.469 1.499 1.530 1.561 1.592 1.624 1.656 1.687 1.720 1.752 1.785 1.818 1.851 1.884 1.918 1.952 1.986 2.021 2.056 2.091 2.127 2.163 2.199 2.236 2.273 2.310 2.348 2.386 2.424 2.463 2.502 2.542 2.583 2.623
0.656 0.630 0.690 0.707 0.724 0.742 0.759 0.777 0.794 0.812 0.830 0.848 0.866 0.885 0.903 0.922 0.940 0.959 0.978 0.997 1.017 1.036 1.055 1.075 1.095 1.115 1.135 1.156 1.176 1.197 1.218 1.239 1.260 1.281 1.303 1.325 1.347 1.369 1.391 1.414 -
0.567 0.581 0.596 0.611 0.626 0.641 0.656 0.671 0.687 0.702 0.718 0.733 0.749 0.765 0.781 0.797 0.813 0.829 0.846 0.862 0.879 0.896 0.913 0.930 0.947 0.964 0.981 0.999 1.017 1.035 1.053 1.071 1.089 1.108 1.126 1.145 1.164 1.184 -
0.544 0.558 0.572 0.587 0.601 0.615 0.630 0.645 0.659 0.674 0.689 0.707 0.719 0.734 0.750 0.765 0.781 0.796 0.812 0.828 0.844 0.860 0.876 0.892 0.909 0.925 0.942 0.959 0.976 0.993 1.011 1.028 1.046 1.063 1.081 1.099 1.118 -
