Copy of 06.02.2009-Combine Footing

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Page 2 of 45

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


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



Page 3 of 45

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 =



Page 4 of 45

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

wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwh

l j

i

mkB bd





Page 6 of 45



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





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:-



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



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

l j

i

mk bd



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



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



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



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



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


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




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




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



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



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



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 &





2100 mm

5600 mm









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



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



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



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



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

























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





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 =





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 - - - -



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 =





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 - - -

Documents

Copy of 06.02.2009-Combine Footing