Copy of 06.02.2009-Combine Footing
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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 = 1005 KN
FACTORED LOAD ON COL. A = 1.5 x 670 = 1005 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
1005 / 0.45 = 1005 / 0.45 =
2233.34 KN/m. 2233.34 KN/m.
234.3 KN/m
b1
d1
C1 C2b2
d2
B/2
B/2
L1 L2 L3
A B C D E F G H J
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FACTORED SHEAR FORCE AT FOLLOWING POINTS:-
B = 234.3 x (0.3-0.225) = 17.57 KN
234.3 x 0.525 - 2233.34 x 0.45 = -881.99 KN
-1 x -881.993 = 881.99 KN
F = -881.993 + 234.3 x 7.55 = 886.97 KN
886.972 - 2233.34 x 0.45 + 234.3 x 0.45 = -12.59 KN
-1 x -12.593 = 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
DLEFT
=
DRIGHT
=
HLEFT
=
HRIGHT =
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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
MAXI. DESIGN MOMENT,Mumax = 1848.017 KN-m
REQUIRED THICKNESS FOR FOOTING,
WIDTH OF FOOTING b = 1650Mumax
1848.017 = 0.138 x 20 x 1650 x d^2
HENCE d = 700 mm.
CONSIDER EFFECTIVE COVER = 50 mm
OVERALL DEPTH D = 750 mm
MAIN NEGATIVE LONG. REINFORCEMENT (HOGGING MOMENTS):-
Ast = 8664.44 0.76
MINI.Ast = 0.85 x 1650 x 700 / 415
= 0.138 fck b d2
mm2 % pt=
A st =
0.5 f ck
fy
fffffffffffffffffffff1@ 1@
4.6 M u f
ck b d
fffffffffffffffffffffff
vuut
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SLAB AND BEAM TYPE RECTANGULAR COMBINED FOOTING
INPUT DATA
1) LOAD ON COLUMN ON A = 1000 KN
2)LOAD ON COLUMN ON B = 1000 KN
3)CENTRE TO CENTRE DIST. (L3) = 3.5 m
4)DIST. OF CENTRE OF COL. AFROM PROPERTY LINE (L1) = 0.3 m
5)DIST. OF CENTRE OF COL. B = 0.3 m
5)SIZE OF COLUMN A
d1 = 400 mm
b1 = 400 mm
6)SIZE OF COLUMN B
d2 = 400 mm
b2 = 400 mm
7) BEARING CAPACITY OF SOIL = 190 KN/mm2
8)STRENGTH OF CONCRETE fck = 20 N/mm29)STRENGTH OF STEEL fy = 415 N/mm2
10)WIDTH OF PEDESTRAL = 300 mm
11)EFFECTIVE COVER = 75 mm
LENGTH OF FOOTING = 5.6 m
WIDTH OF FOOTING = 2.1 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
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
m2
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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
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 = 1500 KN
FACTORED LOAD ON COL. A = 1.5 x 1000 = 1500 KN
NET UPWARD SOIL PRESSURE = (1500 + 1500) / (5.6 x 2.1) = 256 KN/m2
NET UPWARD SOIL PRESSURE PER UNIT LENGTH = 256 x 2.1 = 537.6 KN/m
A B
x
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1500 / 0.4 = 1500 / 0.4 =
3750 KN/m. 3750 KN/m.
537.6 KN/m
DESIGN OF SLAB :-
INTENSITY OF UPWARD PRESSURE = Wu = 256
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 KN-m.
1.05 m. Mu lim = 0.138 fck b d^2
0.4 m.
HENCE DEPTH d = 185 mm
0.85 m. SINCE THE SLAB IS IN CONTACT WITH THE SOIL
CLEAR COVER OF 50 mm IS ASSUMED.
USING 20 mm DIAMETER BARS
pu = 256 KN/m2
REQD. TOTAL DEPTH D = 300 mm
HENCE, EFF. DEPTH d = 240 mm
REINFORCEMENT IN SLAB:-
KN/m2
b1
d1
C1 C2
b2
d2
B/2
B/2
L1 L2 L3
1m.
A st =
0.5 f ck
fyfffffffffffffffffffff 1@ [email protected] M
u
f ck b d
2ffffffffffffffffffffffffff
vuut
wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwh
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MINI.Ast = 0.85 x 1000 x 240 / 415
Ast (min) = 491.57 0.21
HENCE Ast PROVIDED = 1190.29
BAR DIA. AREA Ast reqd. BAR BAR PROVIDE SPACING UNIT WT TOTAL
(mm) REQD. PROVIDE (mm) c/c Kg/m WT. (kg)
12 113.1 1190.29 10.53 11 1244.1 95 0.89 110.15
12 113.1 1190.29 10.53 11 1244.1 95 0.89 110.15
12 113.1 1190.29 10.53 11 1244.1 95 0.89 110.15
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
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 Mpa
PERMISSIBLE SHEAR STRESS 0.52HENCE FROM IS:456,TABLE-19,
PERMISSIBLE SHEAR STRESS τc = 0.49 Mpa
VALUE OF 'k' FOR 300 mm THICK SLAB = 1
CAL.PERMISSIBLE SHEAR STRESS k*τc= 1 x 0.4864 = 0.49
HENCE REVISE
CHECK FOR DEVELOPMENT LENGTH:-
GR
mm2 % pt=
mm2
(mm2) (mm2)/m. Ast (mm2)
% pt =
N/mm2
AS PER IS:456, THE DEVELOPMENT LENGTH Ld IS GIVEN BY,
τb
B/2
B/2
L1 L2 L3
C2
b2
d2
b1
d1
C1
φσffffffffffffff
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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 = 360
BAR DIA. AREA Ast reqd. BAR BAR PROVIDE SPACING UNIT WT TOTAL
(mm) REQD. PROVIDE (mm) c/c Kg/m WT. (kg)
10 78.54 360 4.59 5 392.7 215 0.62 34.61
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 PRESSUREPER METER LENGTH OF THE BEAM Wu = 256 x 2.1 = 537.6 KN/m.
1500 KN 1500 KN
3.5 m.
1 m. 537.6 KN/m. 1.1
SHEAR FORCE AND BENDING MOMENT537.6 KN POINT OF ZERO S.F. FROM LEFT END C,
-962.4 KN X1 = 1500 / 537.6 = 2.8 m.FROM C OR
919.2 KN X2 = 1500 / 537.6 = 2.8 m.FROM D
-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 ) = -442.61 KN-m.
B.M. UNDER COLUMN A, MuA = 537.6 x 1 ^2 / 2 = 268.8 KN-m.
B.M. UNDER COLUMN B, MuB = 537.6 x 1.1 ^2 / 2 = 325.25 KN-m.
a
LET THE POINT OF CONTRA FLEXTURE BE AT A DISTANCE x FROM b
THE CENTRE OF COLUMN A THEN, c
Mx = 1500x - 537.6 (x + 1 )^2 / 2 = 0
THEREFORE x = 0.31 m. and 3.28 m. FROM COLUMN A x1
i.e. 0.23 m. FROM B. x2
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 BEAMWHERE T-BEAM ACTION IS NOT AVAILABLE.THE BEAM ACTS AS A
RECTANGULAR SECTION IN THE CANTILEVER PORTION
mm2 / m.
(mm2) (mm2)/m. Ast (mm2)
S.F.@ AL
=
S.F.@ AR
=
S.F.@ BL
=
S.F.@ BR
=
E BAC D
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WHERE THE MAXIMUM POSITIVE MOMENT = 325.25 KN-m.
545 mm
ASSUMING TWO ROWS OF BARS WITH EFFECTIVE COVER OF 75 mm
TOTAL DEPTH OF BEAM D = 620 mm 800
AND EFF. DEPTH d = 545 mm
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 BEAM & SLAB EFF. DEPTH
b = 400 mm BEAM 545 mm
d = 400 mm SLAB 240 mm
AREA RESISTING TWO WAY SHEAR
= 2 x (400 x 545 + 240 x 240 ) + 2 ( 400 + 545 ) x 240
AREA RESISTING TWO WAY SHEAR = 1004800
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
1345.18 x 1000 / 1004800
τv = 1.34 Mpa
0.25 x ( fck )^ 0.5 = 0.25 x (20)^0.5 = 1.12
HENCE EFFECTIVE DEPTH OF BEAM deff
=
d b
=
ds =
= 2(b x d b
+ dsx d
s) + 2( D + d
b) d
s
mm2
DESIGN SHEAR Pud
= COLUMN LOAD - Wu
x AREA AT CRITICAL SECTION
τv = Pud
/ b0
d =
SHEAR STRESS RESISTED BY CONCRETE = τuc
= τuc
K s
τuc
= N/mm2
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Ks = 0.5 + b / D = 0.5 + 400 / 400 = 1.5 > 1
HENCE, Ks = 1
1.12 x 1 = 1.12
----- REVISE THE DEPTH OF BEAM
INCREASED DEPTH OF BEAM Db = 800 mm
AND EFF. DEPTH d = 725 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
DESIGN SHEAR Pud = 1500 - 256 x (0.4 + 0.24) x ( 0.4 + 0.725)
Pud = 1315.68 KN
τv = 1.09 Mpa
1.12 Mpa
----- HENCE DEPTH IS SUFFICIENT
AREA OF STEEL : CANTILEVER PORTION BD:-
400 400
1000 3500 1100
537.6 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 = 580.29 KN-m
τuc
= N/mm2
mm2
τuc
=
C A B D
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HENCE 580.29 KN-m > 217.73 KN-m S/C IS SINGLY REINFORCED
1.1
HENCE % pt = 0.33
Ast = 948.3
MINI.Ast = 0.85 x 400 x 725 / 415
Ast (min) = 593.98 %pt = 0.21
HENCE Ast PROVIDED = 948.3
BAR DIA. AREA Ast reqd. BAR BAR PROVIDE UNIT WT TOTAL
(mm) REQD. PROVIDE Kg/m WT. (kg)
16 201.07 948.3 4.72 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
0.9
HENCE % pt = 0.26
Ast = 765.6
Ast (min) = 593.98 %pt = 0.21
HENCE Ast PROVIDED = 765.6
BAR DIA. AREA Ast reqd. BAR BAR PROVIDE UNIT WT TOTAL
(mm) REQD. PROVIDE Kg/m WT. (kg)
16 201.07 765.6 3.81 4 804.28 1.58
HENCE PROVIDE # 4 - 16 mm BAR AT BOTTOM FACE
Mu / bd2 = N/mm2
mm2
mm2
mm2
(mm2) (mm2) Ast (mm2)
Mu / bd2 = N/mm2
mm2
mm2
mm2
(mm2) (mm2) Ast (mm2)
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THE BEAM ACTS AS AN ISOLATED T-BEAM.
------CL.23.1.2 IS:456-2000
3500 - 306 - 230 = 2964 mm
b = ACTUAL WIDTH OF FLANGE = 2100 mm
bw = WIDTH OF BEAM = 400 mm
[2964 / ( 2964 / 2100 + 4 ) ] + 400
948 < 2100 mm
Df = DEPTH OF SLAB = 300 mm
Mumax = 442.61 KN-m
[ 0.36 x 20 x 948 x 300 ( 725 - 0.42 x 300 )] / 1000000
1226.56 KN-m > Mumax = 442.61 KN-m
Therefore, Xu < Df
Ast = 1788.3
BAR DIA. AREA Ast reqd. BAR BAR PROVIDE UNIT WT TOTAL
(mm) REQD. PROVIDE Kg/m WT. (kg)
20 314.16 1788.3 5.7 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
MOMENT OF RESISTANCE OF CONTINUING BARS
Mur = ( 0.87 x 415 x 942.48 x ( 725 - (415 x 942.48 ) / (20 x 400))) / 1000000
a
Mur = 230.07 KN-m b
LET THE THEOROTICAL POINT OF CONTRAFLEXURE BE AT A DISTANCE " X " FROM c
THE FREE END " C ".
THEN, Muc = Mur, x1
-537.6 X^2/2 + 1500( X - 1 ) = 230.07 x2
X^2 - 5.59X +6.44 = 0
THEREFORE x = 3.97 m. OR 1.62 m. FROM C
ACTUAL POINT OF CURTAILMENT = 3.967 + 0.23 = 4.2 m from C
bf = [L
0/ (L
0/ b + 4)] + b
w
L0
=
bf =
bf =
MOMENT OF RESISTANCE Muf
of A BEAM FOR Xu
= Df
is,
Muf
=
Muf
=
mm2
(mm2) (mm2) Ast (mm2)
mm2
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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. ABIn 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 = 795.55 kN
τv = 795552 / (400 x 725)
τv = 2.75 Mpa
< 2.8 Mpa
AREA OF STEEL AVAILABLE 3 - 20 mm BARS
Ast = 942.48 % pt = 0.33
HENCE τc = 0.4 Mpa
τv > τc
HENCE DESIGN SHEAR REINFORCEMENT REQUIRED
USING 10 mm DIA. 4 LEGGED STIRRUPS,
SPACING = [ 0.87 x 415 x ( 4 x 78.6)] / ( (2.75 - 0.3984 ) x 400)= 120 mm c/c
(ii) Maximum Shear force at A, Vmax = 962.4 kN
SHEAR AT THE POINT OF CONTRAFLEXURE IS
Vud = 962.4 - 0.306 x 537.6Vud = 797.89 kN
τv = 797894.4 / (400 x 725)
τv = 2.76 Mpa < 2.8 Mpa
AREA OF STEEL AVAILABLE 6 - 20 mm BARS
Ast = 1884.96 % pt = 0.65
HENCE τc = 0.53 Mpaτv > τc
HENCE DESIGN SHEAR REINFORCEMENT REQUIRED
τcmax
=
mm2
τcmax
=
mm2
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USING 10 mm DIA. 4 LEGGED STIRRUPS,
SPACING = [ 0.87 x 415 x ( 4 x 78.6)] / ( (2.76 - 0.528 ) x 400)= 125 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 = 591.36 kN
591.36 - 537.6 ( 0.4 / 2 + 0.23 )
360.2 kN
τv = 360200 / ( 400 x 725 )
τv = 1.25 Mpa < 2.8 Mpa
Ast = 1005.35 % pt = 0.35
HENCE τc = 0.41 Mpa
τv > τc AND τv - τc > 0.4
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 AC :-
PROVIDE 2 LEGGED 8 mm DIA. AT 220 mm C/C AS NOMINAL SHEAR R/F.
VuD
=
VuD
=
τcmax
=
mm2 &
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2100 mm
5600 mm
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1.1 0.616 0.640 0.664 0.680 0.694 0.704
1.11 0.618 0.642 0.666 0.682 0.696 0.706
1.12 0.619 0.644 0.669 0.684 0.699 0.709
1.13 0.621 0.646 0.671 0.686 0.701 0.711
1.14 0.622 0.648 0.674 0.688 0.704 0.714
1.15 0.624 0.650 0.676 0.690 0.706 0.716
1.16 0.626 0.652 0.678 0.692 0.708 0.7181.17 0.627 0.654 0.681 0.694 0.711 0.721
1.18 0.629 0.656 0.683 0.696 0.713 0.723
1.19 0.630 0.658 0.686 0.698 0.716 0.726
1.2 0.632 0.660 0.688 0.700 0.718 0.728
1.21 0.634 0.662 0.690 0.702 0.720 0.730
1.22 0.635 0.664 0.693 0.704 0.723 0.733
1.23 0.637 0.666 0.695 0.706 0.725 0.735
1.24 0.638 0.668 0.698 0.708 0.728 0.738
1.25 0.640 0.670 0.700 0.710 0.730 0.740
1.26 0.642 0.672 0.702 0.712 0.732 0.742
1.27 0.643 0.674 0.703 0.714 0.734 0.744
1.28 0.645 0.676 0.705 0.716 0.736 0.7461.29 0.646 0.678 0.706 0.718 0.738 0.748
1.3 0.648 0.680 0.708 0.720 0.740 0.750
1.31 0.650 0.682 0.710 0.722 0.742 0.752
1.32 0.651 0.684 0.711 0.724 0.744 0.754
1.33 0.653 0.686 0.713 0.726 0.746 0.756
1.34 0.654 0.688 0.714 0.728 0.748 0.758
1.35 0.656 0.690 0.716 0.730 0.750 0.760
1.36 0.658 0.692 0.718 0.732 0.752 0.762
1.37 0.659 0.694 0.719 0.734 0.754 0.764
1.38 0.661 0.696 0.721 0.736 0.756 0.766
1.39 0.662 0.698 0.722 0.738 0.758 0.768
1.4 0.664 0.700 0.724 0.740 0.760 0.7701.41 0.666 0.702 0.726 0.742 0.762 0.772
1.42 0.667 0.704 0.727 0.744 0.764 0.774
1.43 0.669 0.706 0.729 0.746 0.766 0.776
1.44 0.670 0.708 0.730 0.748 0.768 0.778
1.45 0.672 0.710 0.732 0.750 0.770 0.780
1.46 0.674 0.712 0.734 0.752 0.772 0.782
1.47 0.675 0.714 0.735 0.754 0.774 0.784
1.48 0.677 0.716 0.737 0.756 0.776 0.786
1.49 0.678 0.718 0.738 0.758 0.778 0.788
1.5 0.680 0.720 0.740 0.760 0.780 0.790
1.51 0.681 0.721 0.742 0.762 0.782 0.792
1.52 0.682 0.722 0.743 0.763 0.783 0.7941.53 0.684 0.724 0.745 0.765 0.785 0.796
1.54 0.685 0.725 0.746 0.766 0.786 0.798
1.55 0.686 0.726 0.748 0.768 0.788 0.800
1.56 0.687 0.727 0.750 0.770 0.790 0.802
1.57 0.688 0.728 0.751 0.771 0.791 0.804
1.58 0.690 0.730 0.753 0.773 0.793 0.806
1.59 0.691 0.731 0.754 0.774 0.794 0.808
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1.6 0.692 0.732 0.756 0.776 0.796 0.810
1.61 0.693 0.733 0.758 0.778 0.798 0.812
1.62 0.694 0.734 0.759 0.779 0.799 0.814
1.63 0.696 0.736 0.761 0.781 0.801 0.816
1.64 0.697 0.737 0.762 0.782 0.802 0.818
1.65 0.698 0.738 0.764 0.784 0.804 0.820
1.66 0.699 0.739 0.766 0.786 0.806 0.8221.67 0.700 0.740 0.767 0.787 0.807 0.824
1.68 0.702 0.742 0.769 0.789 0.809 0.826
1.69 0.703 0.743 0.770 0.790 0.810 0.828
1.7 0.704 0.744 0.772 0.792 0.812 0.830
1.71 0.705 0.745 0.774 0.794 0.814 0.832
1.72 0.706 0.746 0.775 0.795 0.815 0.834
1.73 0.708 0.748 0.777 0.797 0.817 0.836
1.74 0.709 0.749 0.778 0.798 0.818 0.838
1.75 0.710 0.750 0.780 0.800 0.820 0.840
1.76 0.710 0.752 0.782 0.802 0.822 0.842
1.77 0.710 0.753 0.783 0.803 0.823 0.843
1.78 0.710 0.755 0.785 0.805 0.825 0.8451.79 0.710 0.756 0.786 0.806 0.826 0.846
1.8 0.710 0.758 0.788 0.808 0.828 0.848
1.81 0.710 0.760 0.790 0.810 0.830 0.850
1.82 0.710 0.761 0.791 0.811 0.831 0.851
1.83 0.710 0.763 0.793 0.813 0.833 0.853
1.84 0.710 0.764 0.794 0.814 0.834 0.854
1.85 0.710 0.766 0.796 0.816 0.836 0.856
1.86 0.710 0.768 0.798 0.818 0.838 0.858
1.87 0.710 0.769 0.799 0.819 0.839 0.859
1.88 0.710 0.771 0.801 0.821 0.841 0.861
1.89 0.710 0.772 0.802 0.822 0.842 0.862
1.9 0.710 0.774 0.804 0.824 0.844 0.8641.91 0.710 0.776 0.806 0.826 0.846 0.866
1.92 0.710 0.777 0.807 0.827 0.847 0.867
1.93 0.710 0.779 0.809 0.829 0.849 0.869
1.94 0.710 0.780 0.810 0.830 0.850 0.870
1.95 0.710 0.782 0.812 0.832 0.852 0.872
1.96 0.710 0.784 0.814 0.834 0.854 0.874
1.97 0.710 0.785 0.815 0.835 0.855 0.875
1.98 0.710 0.787 0.817 0.837 0.857 0.877
1.99 0.710 0.788 0.818 0.838 0.858 0.878
2 0.710 0.790 0.820 0.840 0.860 0.880
2.01 0.710 0.791 0.821 0.842 0.862 0.882
2.02 0.710 0.792 0.822 0.843 0.863 0.8832.03 0.710 0.792 0.824 0.845 0.865 0.885
2.04 0.710 0.793 0.825 0.846 0.866 0.886
2.05 0.710 0.794 0.826 0.848 0.868 0.888
2.06 0.710 0.795 0.827 0.850 0.870 0.890
2.07 0.710 0.796 0.828 0.851 0.871 0.891
2.08 0.710 0.796 0.830 0.853 0.873 0.893
2.09 0.710 0.797 0.831 0.854 0.874 0.894
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2.1 0.710 0.798 0.832 0.856 0.876 0.896
2.11 0.710 0.799 0.833 0.858 0.878 0.898
2.12 0.710 0.800 0.834 0.859 0.879 0.899
2.13 0.710 0.800 0.836 0.861 0.881 0.901
2.14 0.710 0.801 0.837 0.862 0.882 0.902
2.15 0.710 0.802 0.838 0.864 0.884 0.904
2.16 0.710 0.803 0.839 0.866 0.886 0.9062.17 0.710 0.804 0.840 0.867 0.887 0.907
2.18 0.710 0.804 0.842 0.869 0.889 0.909
2.19 0.710 0.805 0.843 0.870 0.890 0.910
2.2 0.710 0.806 0.844 0.872 0.892 0.912
2.21 0.710 0.807 0.845 0.874 0.894 0.914
2.22 0.710 0.808 0.846 0.875 0.895 0.915
2.23 0.710 0.808 0.848 0.877 0.897 0.917
2.24 0.710 0.809 0.849 0.878 0.898 0.918
2.25 0.710 0.810 0.850 0.880 0.900 0.920
2.26 0.710 0.810 0.851 0.881 0.901 0.921
2.27 0.710 0.811 0.852 0.882 0.902 0.922
2.28 0.710 0.811 0.854 0.884 0.904 0.9242.29 0.710 0.812 0.855 0.885 0.905 0.925
2.3 0.710 0.812 0.856 0.886 0.906 0.926
2.31 0.710 0.812 0.857 0.887 0.907 0.927
2.32 0.710 0.813 0.858 0.888 0.908 0.928
2.33 0.710 0.813 0.860 0.890 0.910 0.930
2.34 0.710 0.814 0.861 0.891 0.911 0.931
2.35 0.710 0.814 0.862 0.892 0.912 0.932
2.36 0.710 0.814 0.863 0.893 0.913 0.933
2.37 0.710 0.815 0.864 0.894 0.914 0.934
2.38 0.710 0.815 0.866 0.896 0.916 0.936
2.39 0.710 0.816 0.867 0.897 0.917 0.937
2.4 0.710 0.816 0.868 0.898 0.918 0.9382.41 0.710 0.816 0.869 0.899 0.919 0.939
2.42 0.710 0.817 0.870 0.900 0.920 0.940
2.43 0.710 0.817 0.872 0.902 0.922 0.942
2.44 0.710 0.818 0.873 0.903 0.923 0.943
2.45 0.710 0.818 0.874 0.904 0.924 0.944
2.46 0.710 0.818 0.875 0.905 0.925 0.945
2.47 0.710 0.819 0.876 0.906 0.926 0.946
2.48 0.710 0.819 0.878 0.908 0.928 0.948
2.49 0.710 0.820 0.879 0.909 0.929 0.949
2.5 0.710 0.820 0.880 0.910 0.930 0.950
2.51 0.710 0.820 0.881 0.911 0.931 0.951
2.52 0.710 0.820 0.882 0.912 0.932 0.9522.53 0.710 0.820 0.882 0.914 0.934 0.954
2.54 0.710 0.820 0.883 0.915 0.935 0.955
2.55 0.710 0.820 0.884 0.916 0.936 0.956
2.56 0.710 0.820 0.885 0.917 0.937 0.957
2.57 0.710 0.820 0.886 0.918 0.938 0.958
2.58 0.710 0.820 0.886 0.920 0.940 0.960
2.59 0.710 0.820 0.887 0.921 0.941 0.961
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2.6 0.710 0.820 0.888 0.922 0.942 0.962
2.61 0.710 0.820 0.889 0.923 0.943 0.963
2.62 0.710 0.820 0.890 0.924 0.944 0.964
2.63 0.710 0.820 0.890 0.926 0.946 0.966
2.64 0.710 0.820 0.891 0.927 0.947 0.967
2.65 0.710 0.820 0.892 0.928 0.948 0.968
2.66 0.710 0.820 0.893 0.929 0.949 0.9692.67 0.710 0.820 0.894 0.930 0.950 0.970
2.68 0.710 0.820 0.894 0.932 0.952 0.972
2.69 0.710 0.820 0.895 0.933 0.953 0.973
2.7 0.710 0.820 0.896 0.934 0.954 0.974
2.71 0.710 0.820 0.897 0.935 0.955 0.975
2.72 0.710 0.820 0.898 0.936 0.956 0.976
2.73 0.710 0.820 0.898 0.938 0.958 0.978
2.74 0.710 0.820 0.899 0.939 0.959 0.979
2.75 0.710 0.820 0.900 0.940 0.960 0.980
2.76 0.710 0.820 0.901 0.941 0.961 0.981
2.77 0.710 0.820 0.902 0.942 0.962 0.982
2.78 0.710 0.820 0.902 0.942 0.964 0.9842.79 0.710 0.820 0.903 0.943 0.965 0.985
2.8 0.710 0.820 0.904 0.944 0.966 0.986
2.81 0.710 0.820 0.905 0.945 0.967 0.987
2.82 0.710 0.820 0.906 0.946 0.968 0.988
2.83 0.710 0.820 0.906 0.946 0.970 0.990
2.84 0.710 0.820 0.907 0.947 0.971 0.991
2.85 0.710 0.820 0.908 0.948 0.972 0.992
2.86 0.710 0.820 0.909 0.949 0.973 0.993
2.87 0.710 0.820 0.910 0.950 0.974 0.994
2.88 0.710 0.820 0.910 0.950 0.976 0.996
2.89 0.710 0.820 0.911 0.951 0.977 0.997
2.9 0.710 0.820 0.912 0.952 0.978 0.9982.91 0.710 0.820 0.913 0.953 0.979 0.999
2.92 0.710 0.820 0.914 0.954 0.980 1.000
2.93 0.710 0.820 0.914 0.954 0.982 1.002
2.94 0.710 0.820 0.915 0.955 0.983 1.003
2.95 0.710 0.820 0.916 0.956 0.984 1.004
2.96 0.710 0.820 0.917 0.957 0.985 1.005
2.97 0.710 0.820 0.918 0.958 0.986 1.006
2.98 0.710 0.820 0.918 0.958 0.988 1.008
2.99 0.710 0.820 0.919 0.959 0.989 1.009
3 0.710 0.820 0.920 0.960 0.990 1.010
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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
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Fy = 415 1.1 % pt = 0.33
Fy = 415 0.9 % pt = 0.26
TABLE 3
240 250 415 480 500
0.30 0.146 0.140 0.085 0.073 0.070
0.35 0.171 0.164 0.099 0.086 0.082
0.40 0.196 0.188 0.114 0.098 0.094
0.45 0.222 0.213 0.128 0.111 0.106
0.50 0.247 0.237 0.143 0.123 0.1190.55 0.272 0.262 0.158 0.136 0.131
0.60 0.298 0.286 0.172 0.149 0.143
0.65 0.324 0.311 0.187 0.162 0.156
0.70 0.350 0.336 0.203 0.175 0.168
0.75 0.376 0.361 0.218 0.188 0.181
0.80 0.403 0.387 0.233 0.201 0.193
0.85 0.430 0.412 0.248 0.215 0.206
0.90 0.456 0.438 0.264 0.228 0.219
0.95 0.483 0.464 0.280 0.242 0.232
1.00 0.511 0.490 0.295 0.255 0.245
1.05 0.538 0.517 0.311 0.269 0.258
1.10 0.566 0.543 0.327 0.283 0.272
1.15 0.594 0.570 0.343 0.297 0.285
1.20 0.622 0.597 0.359 0.311 0.298
1.25 0.650 0.624 0.376 0.325 0.312
1.30 0.678 0.651 0.392 0.339 0.326
1.35 0.707 0.679 0.409 0.354 0.339
1.40 0.736 0.707 0.426 0.368 0.353
1.45 0.765 0.735 0.443 0.383 0.367
1.50 0.795 0.763 0.460 0.397 0.382
1.55 0.825 0.792 0.477 0.412 0.396
1.60 0.855 0.821 0.494 0.427 0.410
1.65 0.885 0.850 0.512 0.443 0.425
1.70 0.916 0.879 0.530 0.458 0.440
1.75 0.947 0.909 0.547 0.473 0.454
1.80 0.978 0.939 0.565 0.489 0.469
1.85 1.009 0.969 0.584 0.505 0.484
1.90 1.041 1.000 0.602 0.521 0.500
1.95 1.073 1.030 0.621 0.537 0.515
2.00 1.106 1.062 0.640 0.553 0.531
2.02 1.119 1.074 0.647 0.559 0.537
2.04 1.132 1.087 0.655 0.566 0.543
Mu/bd2 =
Mu/bd2 =
FLEXURE - REINFORCEMENT PERCENTAGE,pt FOR SINGLY REINFORCED SECTIONS
Mu/bd2 N/mm2 Fy N/mm2
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Fy = 415 1.1 % pt = 0.32
Fy = 415 0.9 % pt = 0.26
TABLE 3
240 250 415 480 500
0.30 0.146 0.140 0.084 0.073 0.070
0.35 0.171 0.164 0.099 0.085 0.082
0.40 0.195 0.188 0.113 0.098 0.094
0.45 0.220 0.211 0.127 0.110 0.106
0.50 0.245 0.236 0.142 0.123 0.1180.55 0.271 0.260 0.156 0.135 0.130
0.60 0.296 0.284 0.171 0.148 0.142
0.65 0.321 0.309 0.186 0.161 0.154
0.70 0.347 0.333 0.201 0.174 0.167
0.75 0.373 0.358 0.216 0.186 0.179
0.80 0.399 0.383 0.231 0.199 0.191
0.85 0.425 0.408 0.246 0.212 0.204
0.90 0.451 0.433 0.261 0.225 0.216
0.95 0.477 0.458 0.276 0.239 0.229
1.00 0.504 0.483 0.291 0.252 0.242
1.05 0.530 0.509 0.307 0.265 0.255
1.10 0.557 0.535 0.322 0.279 0.267
1.15 0.584 0.561 0.338 0.292 0.280
1.20 0.611 0.587 0.353 0.306 0.293
1.25 0.638 0.613 0.369 0.319 0.306
1.30 0.666 0.639 0.385 0.333 0.320
1.35 0.693 0.666 0.401 0.347 0.333
1.40 0.721 0.692 0.417 0.360 0.346
1.45 0.749 0.719 0.433 0.374 0.359
1.50 0.777 0.746 0.449 0.388 0.373
1.55 0.805 0.773 0.466 0.403 0.387
1.60 0.834 0.800 0.482 0.417 0.400
1.65 0.862 0.828 0.499 0.431 0.414
1.70 0.891 0.856 0.515 0.446 0.428
1.75 0.920 0.883 0.532 0.460 0.442
1.80 0.949 0.911 0.549 0.475 0.456
1.85 0.979 0.940 0.566 0.489 0.470
1.90 1.009 0.968 0.583 0.504 0.484
1.95 1.038 0.997 0.601 0.519 0.498
2.00 1.068 1.026 0.618 0.534 0.513
2.05 1.099 1.055 0.635 0.549 0.527
2.10 1.129 1.084 0.653 0.565 0.542
Mu/bd2 =
Mu/bd2 =
FLEXURE - REINFORCEMENT PERCENTAGE,pt FOR SINGLY REINFORCED SECTIONS
Mu/bd2 N/mm2 Fy N/mm2
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2.15 1.160 1.114 0.671 0.580 0.557
2.20 1.191 1.143 0.689 0.596 0.572
2.25 1.222 1.173 0.707 0.611 0.587
2.30 1.254 1.204 0.725 0.627 0.602
2.35 1.285 1.234 0.743 0.643 0.617
2.40 1.317 1.265 0.762 0.659 0.632
2.45 1.350 1.296 0.781 0.675 0.6482.50 1.382 1.327 0.799 0.691 0.663
2.55 1.415 1.358 0.818 0.708 0.679
2.60 1.448 1.390 0.837 0.724 0.695
2.65 1.482 1.422 0.857 0.741 0.711
2.70 1.515 1.455 0.876 0.758 0.727
2.75 1.549 1.487 0.896 0.775 0.744
2.80 1.584 1.520 0.916 0.792 0.760
2.85 1.618 1.554 0.936 0.809 0.777
2.90 1.653 1.587 0.956 0.827 0.794
2.95 1.689 1.621 0.977 0.844 0.811
3.00 1.724 1.655 0.997 0.862 0.828
3.05 1.760 1.690 1.018 0.880 0.8453.10 1.797 1.725 1.039 0.898 0.863
3.15 1.834 1.760 1.061 0.917 0.880
3.20 1.871 1.796 1.082 0.936 0.898
3.25 1.909 1.832 1.104 0.954 0.916
3.30 1.947 1.869 1.126 0.973 0.935
3.32 1.962 1.884 1.135 0.981 0.942
3.34 1.978 1.899 1.144 0.989 -
3.36 1.993 1.914 1.153 - -
3.38 2.009 1.929 1.162 - -
3.40 2.025 1.944 1.171 - -
3.42 2.040 1.959 1.180 - -
3.44 2.056 1.974 1.189 - -3.46 2.072 1.989 - - -
3.48 2.088 2.005 - - -
3.50 2.104 2.020 - - -
3.52 2.120 2.036 - - -
3.54 2.137 2.051 - - -
3.56 2.153 2.067 - - -
3.58 2.170 2.083 - - -
3.60 2.186 2.099 - - -
3.62 2.203 2.115 - - -
3.64 2.219 2.131 - - -
3.66 2.236 2.147 - - -
3.68 2.253 2.163 - - -3.70 2.270 2.179 - - -
3.72 2.287 2.196 - - -
3.74 2.304 - - - -
8/6/2019 Copy of 06.02.2009-Combine Footing
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Fy = 415 1.1 % pt = 0.32
Fy = 415 0.9 % pt = 0.26
TABLE 3
240 250 415 480 500
0.30 0.145 0.140 0.084 0.073 0.070
0.35 0.170 0.163 0.098 0.085 0.082
0.40 0.195 0.187 0.113 0.097 0.093
0.45 0.219 0.211 0.127 0.110 0.105
0.50 0.244 0.235 0.141 0.122 0.1170.55 0.269 0.259 0.156 0.135 0.129
0.60 0.294 0.283 0.170 0.147 0.141
0.65 0.320 0.307 0.185 0.160 0.153
0.70 0.345 0.331 0.200 0.172 0.166
0.75 0.370 0.356 0.214 0.185 0.178
0.80 0.396 0.380 0.229 0.198 0.190
0.85 0.422 0.405 0.244 0.211 0.202
0.90 0.447 0.429 0.259 0.224 0.215
0.95 0.473 0.454 0.274 0.237 0.227
1.00 0.499 0.479 0.289 0.250 0.240
1.05 0.525 0.504 0.304 0.263 0.252
1.10 0.552 0.529 0.319 0.276 0.265
1.15 0.578 0.555 0.334 0.289 0.277
1.20 0.608 0.580 0.350 0.302 0.290
1.25 0.631 0.606 0.365 0.315 0.303
1.30 0.658 0.631 0.380 0.329 0.316
1.35 0.685 0.657 0.396 0.342 0.329
1.40 0.712 0.683 0.411 0.356 0.342
1.45 0.739 0.709 0.427 0.369 0.355
1.50 0.766 0.735 0.443 0.383 0.368
1.55 0.793 0.762 0.459 0.397 0.381
1.60 0.821 0.788 0.475 0.410 0.394
1.65 0.849 0.815 0.491 0.424 0.407
1.70 0.876 0.841 0.507 0.438 0.421
1.75 0.904 0.868 0.523 0.452 0.434
1.80 0.932 0.895 0.539 0.466 0.448
1.85 0.961 0.922 0.556 0.480 0.461
1.90 0.989 0.950 0.572 0.495 0.475
1.95 1.018 0.977 0.589 0.509 0.488
2.00 1.046 1.005 0.605 0.523 0.502
2.05 1.075 1.032 0.622 0.538 0.516
2.10 1.104 1.060 0.639 0.552 0.530
Mu/bd2 =
Mu/bd2 =
FLEXURE - REINFORCEMENT PERCENTAGE,pt FOR SINGLY REINFORCED SECTIONS
Mu/bd2 N/mm2 Fy N/mm2
8/6/2019 Copy of 06.02.2009-Combine Footing
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2.15 1.134 1.088 0.656 0.567 0.544
2.20 1.163 1.116 0.630 0.581 0.558
2.25 1.192 1.145 0.690 0.596 0.572
2.30 1.222 1.173 0.707 0.611 0.587
2.35 1.252 1.202 0.724 0.626 0.601
2.40 1.282 1.231 0.742 0.641 0.615
2.45 1.312 1.260 0.759 0.656 0.6302.50 1.343 1.289 0.777 0.671 0.645
2.55 1.374 1.319 0.794 0.687 0.659
2.60 1.404 1.348 0.812 0.702 0.674
2.65 1.435 1.378 0.830 0.718 0.689
2.70 1.467 1.408 0.848 0.733 0.707
2.75 1.498 1.438 0.866 0.749 0.719
2.80 1.530 1.469 0.885 0.765 0.734
2.85 1.562 1.499 0.903 0.781 0.750
2.90 1.594 1.530 0.922 0.797 0.765
2.95 1.626 1.561 0.940 0.813 0.781
3.00 1.659 1.592 0.959 0.829 0.796
3.05 1.691 1.624 0.978 0.846 0.8123.10 1.725 1.656 0.997 0.862 0.828
3.15 1.758 1.687 1.017 0.879 0.844
3.20 1.791 1.720 1.036 0.896 0.860
3.25 1.825 1.752 1.055 0.913 0.876
3.30 1.859 1.785 1.075 0.930 0.892
3.35 1.893 1.818 1.095 0.947 0.909
3.40 1.928 1.851 1.115 0.964 0.925
3.45 1.963 1.884 1.135 0.981 0.942
3.50 1.998 1.918 1.156 0.999 0.959
3.55 2.034 1.952 1.176 1.017 0.976
3.60 2.069 1.986 1.197 1.035 0.993
3.65 2.105 2.021 1.218 1.053 1.0113.70 2.142 2.056 1.239 1.071 1.028
3.75 2.178 2.091 1.260 1.089 1.046
3.80 2.215 2.127 1.281 1.108 1.063
3.85 2.253 2.163 1.303 1.126 1.081
3.90 2.291 2.199 1.325 1.145 1.099
3.95 2.329 2.236 1.347 1.164 1.118
4.00 2.367 2.273 1.369 1.184 -
4.05 2.406 2.310 1.391 - -
4.10 2.445 2.348 1.414 - -
4.15 2.485 2.386 - - -
4.20 2.525 2.424 - - -
4.25 2.566 2.463 - - -4.30 2.607 2.502 - - -
4.35 2.648 2.542 - - -
4.40 2.690 2.583 - - -
4.45 2.733 2.623 - - -