Rectangular ground water tank.xlsx

DESIGN OF REACTANGULAR GROUND WATER TANK Name of work :1 Tank size 2 Tank capacity

pkn L=

3

Saturated soil unit wt

4

Conrete

5

Steel

6 7

Nominal Cover Thickness

7

9

6.00

x

17.00

kN/m3

M

20

cbc

7

fy

B=

4.00 72000

x ltr

H=

17000 N/m3 concrete unit wt.

N/mm2

415

3.00

25000

m

N/m3

m

13

Tensile stress

115

N/mm2

9.80 0.22 0.10

kN/m3 m m

35

mm

Walls Bottom slab

100

mm

Water unit wt 220 mm 10 cm

Reinforcement Long wall In side near corner Horizont

20

mmbars

110

20 20

mmbars mmbars

110 220

mm c/c 1.00 m height above the base, near corners. mm c/c upto top mm c/c upto top

20 20 10 8

mmbars mmbars mmbars mmbars

110 220 230 250

mm c/c upto top mm c/c, upto top mm c/c vertical mm c/c in both direction

in side middle horizontal Out side middle horizontal Short wall In side near corner Horizont Out side middle horizontal Distribution Base C 20

mm

20 mm

110 mm c/c

110 mm c/c

20 mm

220 mm c/c 20 mm

A

20 mm

110 mm c/c

20 mm

220 mm c/c

20 mm

220 mm c/c (d)

10 mm 20 mm

20 mm 10 mm

220 mmc/c

220 mmc/c

230 mmc/c

230 mm c/c both side 110 mm c/c(d+e)

10 mm

20 mm

10 mm

110 mmc/c

220 mmc/c

110 mmc/c

20 mm

250 mmc/c

B Bars(c)

Section plan at depth of H/4 or 1 mt.

Section on CD

D

Bar(a)

20

mm 

220 mm c/c

20 mm

440 mm c/c

10 mm

230 mm c/c

Bar(b)

20

mm 

220 mm c/c

10 mm

230 mm c/c

Bar(c)

20

mm 

220 mm c/c

20 mm

220 mm c/c 8 mm

Bar(d)

20

mm 

220 mm c/c

Bar(e)

10

mm 

230 mm c/c

250 mm c/c both way Bar F

Section on AB

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DESIGN OF REACTANGULAR GROUND WATER TANK Name of work :- pkn 1 Tank size 2 Tank capacity 3 4

Conrete Steel

6 7

Nominal Cover Thickness

9

M

20

cbc

7

fy Walls Top roof Bottom slab

Reinforcement Long wall In side near corner Horizontal in side middle horizontal Out side middle horizontal Short wall In side near corner Horizontal Out side middle horizontal Distribution Base Main

6.00 17.00

Saturated soil unit wt

5

7

L=

x B= kN/m

3

4.00 72000

x ltr

17000

N/m3

H=

unit weight N/mm2

415

3.00

25000

m

N/m3

m

13

Tensile stress

115

N/mm2

9.80 0.22 0.20 0.10

kN/m3 m m m

35

mm

200 100

mm mm

Water unit wt 220 mm 20 cm 10 cm

20

mm

110

20 20

mm mm

110 220

mm c/c 1.00 m height above the base, near corners. mm c/c upto top mm c/c upto top

20 20 10 8

mm mm mm mm

110 220 230 250

mm c/c upto top mm c/c, upto top mm c/c vertical mm c/c in both direction

DESIGN OF REACTANGULAR GROUND WATER TANK Name of work :Tank size Tank capacity

pkn 6.00 x

Saturated soil unit wt

4.00 x

17.00 kN/m3

3.00 72000

m ltr

17000

N/m3

Conrete

M

20

unit weight

= 25000

Steel

fy cbc

415 N/mm2

Tensile stess

=

Nominal cover

7

N/mm2

unit wt. of water

1 Design Constants:- For HYSD Bars

st  cbc  k=

115 7 m*c

m*c+st j=1-k/3  1 R=1/2xc x j x k  0.5

N/mm

Cocrete M =

2

wt. of concrete =

N/mm2

m 

= x

115 N/mm2

m=

35 mm

x 7 13 = 13 x 7 + 115 0.442 / 3 = 7 x 0.853 x 0.442 =

N/m3

13

=

9.8 N/mm3

9800

20 25000

N/mm2

13 0.442 0.853 1.320

3 Determination of B.M. for horizontal bending :-L/B = 6.00 / 4.00 = 1.50 < 2 Hence Both long and short walls will bend horizontally for upper portion, upto poin D, where horizontal water pressure is p=w(H-h). Here h = H/4 or 1 m which ever is greater h = 1.00 m  Thus top 2.00 m height of walls will be bend horizontally while the bottom 1.00 m will bend as vertical cantilever . The bending moments for horizontal bending may be determined by moment distribution by considering tank as continuos frame of unit height at level of D. Water pressure p at point D is given by =p= w (H - h ) = 19600 9800 ( 3.00 1.00 )= N-m 2 2 PL P x 6.00 '= The Fixed end moments for long wall = = 3.00 P N-m 12 12 PB2 P x 4.00 2'= Fixed end moments for short wall = = 1.33 P N-m 12 12 Refer fig 1. Consider quarter frame FAE with joint A rigid. Taking clock wise moment as positive and anticlock wise moment as negative, the fixed end moment M AF for long wall will be + 3.00 P while the fixed end end moments MAF for short wall will be

- 1.33 P Considreing Area A and moment of inertia l for both the walls to be the same, the stiffness of walls will be inversely proportional to these length. Thus we have following table. Member Stiffness Relative stiffness Sum Distribution factor 2 1 1 AE x 6.00 = 2 = 0.4 5 3 3 5 3 1 1 AF x 6.00 = 3 = 0.6 2 2 5 The moment distribution is carried out in the following table. A Joint AE Member Distribution facvtor 0.4 Fixed end moments

+

p

-

Balancing moments

- 0.6667 p

-

+

-

Final moments

3.00

2.33

p

AF 0.6 1.33 p 1

p

2.33 p

Final moments

+

2.33

p

-

2.33 p

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2.33 x 19600 = 45733 N-m/m This support moment will cause tension at the water force.

Hence moment at supports, Mf=

p L2 19600 x 6.00 2 Mf "= 45733 8 8 This bending moment cause tension at outer face.

B.M. at the center long span =

p B2 19600 x 4.00 2 Mf "= 45733 8 8 This will cause tension at the water face.  Max. design B.M.

B.M. at the center short span =

3 Design of section :-

42467 N-m/m

=

-6533 N-m/m

=

42467 N-m/m

Considring bending effect alone,

Required depth Provide total depth T=

=

=

179

+

42467 x 1.320 x 35 =

1000 = 1000 220 mm

179

mm

185 mm

so that available d =

4 Determination pull :Direct tension on Long wall = PL = P x B/2 =

19600

x

4.00 /

2

=

Direct tension on short wall = PL = P x B/2 =

19600

x

6.00 /

2

=

39200 58800

N N

5 Cantilever Moment :-

Cantilever moment atb the base, per unit length . h2 9800 x 4.00 x 1.00 2 = wH x = 6533 N-m 6 6 This will cause tension at water face. 6 Reinforcement at corners of long walls.:The upper portion of long walls is subjected to both bending in horizontal direction as well as pull. The reinforcement for both will be in horizontal direction. Hence reinforcement has to be provided forr a net moment (M F - Px ), where Mf is the moment at ends (causing tension on water face). Similarly vertical section of unit height ( 1 m) of long wall, at its end, at the level of 1.00 m above the base , where reinforcement is provided at the water face. T 220 x=d= 179 = 69 mm 2 2 Mf - Pl x 45733 x 1000 ) - 39200 x 69 Ast for B.M. = = = 2371 mm2 st.j.d 115 x 0.853 x 185 PL 39200 Ast for pull = = = 341 mm2 115 s Total Ast = 2371 + 341 = 2712 mm2 per meter height. 3.14xdia2 3.14 x 20 x 20 = = 314 mm2 4 x100 4 x 100 Spacing of Bars = 1000 x 314 / 2712 = 116 say = 110 mm mm bar, @ 20 Hence Provided 110 mm c/c. The above reinforcement is to be provided at inner face, near the corners, and at a height 1.00 m above the base. For other height the above spacing may be varied, since bending moment will reduce. using 20

mm bars

A

=

7 Reinfocement at the middle of long wall. :Tension occurs at outer face. However, since distance of corner of steel from water face will be less than 225 mm, permissible stress will be 115 N/mm2 only. Design constants will be k = 0.4417 j = 0.853 R = 1.318 Design B.M. = 42467 N-m per meter height. Also PL = 39200 N M - Pl x 42467 x 1000 ) - 39200 x 69 Ast for B.M. = = = 2192 mm2 115 x 0.853 x 185 st.j.d

Ast for pull

=

Total Ast

=

PL

=

s

2192 +

39200 = 115 341 =

341

2533

mm2 mm2

per meter height.

3.14xdia 3.14 x 20 x 20 = = 314 mm2 4 x100 4 x 100 Spacing of Bars = 1000 x 314 / 2533 = 124 say = 120 mm This is very near to the reinforcement provided at ends.Hence provided 20 mm bars 110 mm 1.50 m form ends. c/c. Bend half the bars provided at ends, outwards.at distance L/4 = mm  bars provided @ 220 mm c/c. This reinforcement is to be provided at outer face. The additional 20 are continued upto the end. using 20

mm bars

A

8 Reinforcement for shorts walls.:B.M. at ends=Mf = Ast for B.M. =

M - PB x

st.j.d

=

Ast for pull

=

Total Ast

=

=

45733 45733 x 115 x PL

s

2

Direct pull pu =

N-m

1000 ) - 58800 x 0.853 x 185 58800 = = 511 115

2297 +

511

=

2808

69

58800 =

2297

N mm2

mm2 mm2

per meter height.

3.14xdia 3.14 x 20 x 20 = = 314 mm2 4 x100 4 x 100 Spacing of Bars = 1000 x 314 / 2808 = 112 say = 110 mm Hence provide 20 mm f bars @ 110 mm c/c at inner face near the ends of short span. The B.M. at the center of short walls cause tension at water face (unlikethat in the center of long walls where tension is produced at outer face ).since this B.M. is small, only nominal reinforcement is required. Similarlly, we have to provide nominal reinforcement at outer face,. Hence bend half bars outward at distance B/4= 1.00 m from each end, and continue remaning half tjrought. Thus at the center of span, the reinforcement on each face will consist of 20 mm bars @ 220 mm c/c. using 20

mm bars

A

=

2

9 Reinforcement for cantilever moment and distribution reinforcement.:max. cantilever moment= 6533 N-m 6533 x 1000 Ast = = 360 mm2 115 x 0.853 x 185 0.3 But minimum reinforcementin vertical direction = x( 220 x 1000 )= 660 mm2 100 Since half of this area of steel can reist cantilever momnt, we will provide = 330 mm2 steel area vertically on the inner face and remaining area i.e.= 330 mm2 vertically at outer face to serve as distribution reinforcment.  Area of steel on each face = 330 mm2. 3.14xdia2 3.14 x 10 x 10 = = 78.5 4 x100 4 x 100 Spacing of Bars = 1000 x 78.5 / 330 = 238 say = 230 mm 10 mm bar, @ Hence Provided 230 mm c/c on out side face, at bottom of long wall using 10

mm bars

A

=

mm2

10 Design of base slab:Since tank rest on ground, provide a 100 mm thick base slab. taking 1m length for calculation and 0.20 % of nominal reinforcement 0.20 x 1000 x 100 area of steel = = mm2 200 100 3.14xdia2 3.14 x 8 x 8 = = 50.2 4 x100 4 x 100 Spacing of Bars = 1000 x 50.2 / 200 = 251 say = 250 mm 8 mm bar, @ Hence Provided 250 mm c/c in both direction , at top and bottom of base slab. using 8

mm bars

A

=

mm2

11. Detail of reinforcement :shown in drawing.

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DESIGN OF REACTANGULAR GROUND WATER TANK

Name of work :- pkn Err:509

mm@ Err:509

Err:509 mm c/c mm@ Err:509 mm c/c Err:509 Roof

Err:509

mm @

Err:509 mm c/c

Err:509 Err:509 4.00

Err:509

Err:509 0.00 Err:509

Err:509

6.00 m

mm@ mm c/c

0

Err:509 mm@ mm@

Err:509

mm@ mm@

Err:509 Err:509

Err:509 Err:509

3.00

0.00

Err:509 Reinforcement detail for short wall, Roof and bottom slab

Err:509 mm @

Err:509 mm c/c Err:509 mm @

Err:509 mm

mm @

Err:509 mm

Err:509 3.00

Err:509 Err:509 Err:509

mm @ mm @

Err:509 mm c/c Err:509 mm c/c mm @ Err:509

Err:509 Err:509 mm

Reinforcement detail for short wall

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VALUES OF DESIGN CONSTANTS Grade of concrete Modular Ratio

M-15 18.67

cbc N/mm2 m cbc

5

7

8.5

10

11.5

13

93.33

93.33

93.33

93.33

93.33

93.33

kc

0.4

0.4

0.4

0.4

0.4

0.4

jc

0.867

0.867

0.867

0.867

0.867

0.867

Rc

0.867

1.214

1.474

1.734

1.994

2.254

Pc (%)

0.714

1

1.214

1.429

1.643

1.857

Grade of concrete

kc

0.329

0.329

0.329

0.329

0.329

0.329

M 15

jc

0.89 0.732

0.89

0.89

0.89

0.89

0.89

M 20

Rc

1.025

1.244

1.464

1.684

1.903

M 25

Pc (%)

0.433

0.606

0.736

0.866

0.997

1.127

M 30

kc

0.289

0.289

0.289

0.289

0.289

0.289

M 35

jc

0.904

0.904

0.904

0.904

0.904

0.904

M 40

Rc

0.653

0.914

1.11

1.306

1.502

1.698

M 45

Pc (%)

0.314

0.44

0.534

0.628

0.722

0.816

M 50

kc

0.253

0.253

0.253

0.253

0.253

0.253

jc

0.916

0.916

0.916

0.914

0.916

0.916

Rc

0.579

0.811

0.985

1.159

1.332

1.506

Pc (%)

0.23

0.322

0.391

0.46

0.53

0.599

(a) st = 140 N/mm2 (Fe 250) (b) st = 190 N/mm2 (c ) st = 230 N/mm2 (Fe 415) (d) st = 275 N/mm2 (Fe 500)

M-20 13.33

M-25 10.98

M-30 9.33

M-35 8.11

M-40 7.18

Grade of concrete bd (N / mm2)

Permissible shear stress Table  v in concrete (IS : 456-2000) 100As

Permis

Permissible shear stress in concrete tv N/mm2

bd

M-15

M-20

M-25

M-30

M-35

M-40

< 0.15

0.18

0.18

0.19

0.2

0.2

0.2

0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75

0.22 0.29 0.34 0.37 0.40 0.42 0.44 0.44 0.44 0.44 0.44 0.44

0.22 0.30 0.35 0.39 0.42 0.45 0.47 0.49 0.51 0.51 0.51 0.51

0.23 0.31 0.36 0.40 0.44 0.46 0.49 0.51 0.53 0.55 0.56 0.57

0.23 0.31 0.37 0.41 0.45 0.48 0.50 0.53 0.55 0.57 0.58 0.6

0.23 0.31 0.37 0.42 0.45 0.49 0.52 0.54 0.56 0.58 0.60 0.62

0.23 0.32 0.38 0.42 0.46 0.49 0.52 0.55 0.57 0.60 0.62 0.63

3.00 and above

Grade of concrete M M M M M M M M M

10 15 20 25 30 35 40 45 50

Maximum shear stress c.max in concrete (IS : 456-2000) Grade of concrete

c.max

Shear stress tc

M-15 1.6

M-20 1.8

Reiforcement %

M-25 1.9

M-30 2.2

M-35 2.3

Permissible d M-40 2.5

Grade of concrete

ct.max

100As bd 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62 0.63 0.64

M-20

M-20

0.18 0.18 0.18 0.19 0.19 0.19 0.2 0.2 0.2 0.21 0.21 0.21 0.22 0.22 0.22 0.23 0.23 0.24 0.24 0.24 0.25 0.25 0.25 0.26 0.26 0.26 0.27 0.27 0.27 0.28 0.28 0.28 0.29 0.29 0.29 0.30 0.30 0.30 0.30 0.30 0.31 0.31 0.31 0.31 0.31 0.32 0.32 0.32 0.32 0.32

0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.46 0.47 0.48 0.49 0.50 0.51

100As bd 0.15 0.18 0.21 0.24 0.27 0.3 0.32 0.35 0.38 0.41 0.44 0.47 0.5 0.55 0.6 0.65 0.7 0.75 0.82 0.88 0.94 1.00 1.08 1.16 1.25 1.33 1.41 1.50 1.63 1.64 1.75 1.88 2.00 2.13 2.25

Valu Degree 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 20.5 21 21.5 22 22.5 23 23.5 24 24.5 25 25.5

0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16

0.33 0.33 0.33 0.33 0.33 0.34 0.34 0.34 0.34 0.34 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.36 0.36 0.36 0.36 0.36 0.36 0.37 0.37 0.37 0.37 0.37 0.37 0.38 0.38 0.38 0.38 0.38 0.38 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.41

26 26.5 27 27.5 28 28.5 29 29.5 30 30.5 31 31.5 32 32.5 33 33.5 34 34.5 35 35.5 36 36.5 37 37.5 38 38.5 39 39.5 40 40.5 41 41.5 42 42.5 43 43.5 44 44.5 45 45.5 46 46.5 47 47.5 48 48.5 49 49.5 50 50.5 51 51.5

1.17 1.18 1.19 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.40 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 1.50 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.60 1.61 1.62 1.63 1.64 1.65 1.66 1.67 1.68

0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.46 0.46 0.46 0.46 0.46 0.46

52 52.5 53 53.5 54 54.5 55 55.5 56 56.5 57 57.5 58 58.5 59 59.5 60 60.5 61 61.5 62 62.5 63 63.5 64 64.5 65 65.5 66 66.5 67 67.5 68 68.5 69 69.5 70 70.5 71 71.5 72 72.5 73 73.5 74 74.5 75 75.5 76 76.5 77 77.5

1.69 1.70 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79 1.80 1.81 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.90 1.91 1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20

0.46 0.46 0.46 0.46 0.46 0.46 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50

78 78.5 79 79.5 80 80.5 81 81.5 82 82.5 83 83.5 84 84.5 85 85.5 86 86.5 87 87.5 88 88.5 89 89.5 90

2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.30 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39 2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50 2.51 2.52 2.53 2.54 2.55 2.56 2.57 2.58 2.59 2.60 2.61 2.62 2.63 2.64 2.65 2.66 2.67 2.68 2.69 2.70 2.71 2.72

0.50 0.50 0.50 0.50 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51

2.73 2.74 2.75 2.76 2.77 2.78 2.79 2.80 2.81 2.82 2.83 2.84 2.85 2.86 2.87 2.88 2.89 2.90 2.91 2.92 2.93 2.94 2.95 2.96 2.97 2.98 2.99 3.00 3.01 3.02 3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.10 3.11 3.12 3.13 3.14 3.15

0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51

Permissible Bond stress Table  bd in concrete (IS : 456-2000) M-10 --

M-15 0.6

M-20 0.8

M-25 0.9

M-30 1

M-35 1.1

M-40 1.2

M-45 1.3

Development Length in tension bd

Plain M.S. Bars (N / mm2) kd = Ld 

H.Y.S.D. Bars (N / mm2) kd = Ld 

bd

0.6

58

0.96

60

0.8

44

1.28

45

0.9

39

1.44

40

1

35

1.6

36

1.1

32

1.76

33

1.2

29

1.92

30

1.3

27

2.08

28

1.4

25

2.24

26

Permissible stress in concrete (IS : 456-2000) Permission stress in compression (N/mm2) Permissible stress in bond (Average) for plain bars in tention (N/mm2) Bending cbc Direct (cc) (N/mm2) 3.0 5.0 7.0 8.5 10.0 11.5 13.0 14.5 16.0

Kg/m2 300 500 700 850 1000 1150 1300 1450 1600

(N/mm2) 2.5 4.0 5.0 6.0 8.0 9.0 10.0 11.0 12.0

Kg/m2 250 400 500 600 800 900 1000 1100 1200

(N/mm2) -0.6 0.8 0.9 1.0 1.1 1.2 1.3 1.4

in kg/m2 -60 80 90 100 110 120 130 140

Permissible direct tensile stress in concrete (IS : 456-2000) Grade of concrete

ct.max

M-10 1.2

M-15 2.0

M-20 2.8

M-25 3.2

M-30 3.6

M-35 4.0

M-40 4.4

M-50 1.4

sin 0.017 0.026 0.035 0.044 0.052 0.061 0.070 0.078 0.087 0.096 0.104 0.113 0.122 0.131 0.139 0.148 0.156 0.165 0.174 0.182 0.191 0.199 0.208 0.819 0.225 0.233 0.242 0.250 0.259 0.259 0.276 0.284 0.292 0.301 0.309 0.317 0.326 0.334 0.342 0.350 0.358 0.367 0.375 0.383 0.391 0.399 0.407 0.415 0.422 0.431

Value of angle Degree cos 1 1.000 1.5 1.000 2 0.999 2.5 0.999 3 0.999 3.5 0.998 4 0.998 4.5 0.997 5 0.996 5.5 0.995 6 0.995 6.5 0.994 7 0.993 7.5 0.991 8 0.990 8.5 0.989 9 0.988 9.5 0.986 10 0.985 10.5 0.983 11 0.981 11.5 0.980 12 0.978 12.5 0.976 13 0.974 13.5 0.972 14 0.970 14.5 0.968 15 0.966 15.5 0.964 16 0.961 16.5 0.959 17 0.956 17.5 0.954 18 0.951 18.5 0.948 19 0.946 19.5 0.943 20 0.940 20.5 0.937 21 0.934 21.5 0.930 22 0.927 22.5 0.924 23 0.921 23.5 0.917 24 0.924 24.5 0.910 25 0.906 25.5 0.905

tan 0.017 0.262 0.035 0.044 0.052 0.061 0.070 0.079 0.087 0.096 0.105 0.114 0.123 0.132 0.140 0.149 0.158 0.168 0.176 0.185 0.194 0.203 0.213 0.839 0.231 0.240 0.249 0.259 0.268 0.269 0.287 0.296 0.306 0.315 0.325 0.335 0.344 0.354 0.364 0.374 0.384 0.394 0.404 0.414 0.424 0.435 0.440 0.456 0.466 0.476

cot 57.295 56.300 28.644 22.913 19.083 16.362 14.311 12.707 11.437 10.385 9.563 8.777 8.149 7.597 7.119 6.691 6.315 5.963 5.673 5.396 5.142 4.915 4.704 1.192 4.332 4.166 4.011 3.867 3.732 3.723 3.488 3.376 3.272 3.172 3.078 2.989 2.905 2.824 2.747 2.674 2.605 2.539 2.475 2.414 2.356 2.300 2.271 2.194 2.148 2.103

0.438 0.446 0.454 0.462 0.469 0.477 0.485 0.492 0.500 0.508 0.515 0.522 0.530 0.537 0.545 0.552 0.559 0.566 0.573 0.581 0.588 0.595 0.602 0.609 0.616 0.623 0.629 0.636 0.643 0.649 0.656 0.663 0.669 0.676 0.682 0.688 0.695 0.701 0.707 0.713 0.719 0.725 0.731 0.737 0.742 0.749 0.755 0.760 0.766 0.772 0.777 0.786

26 26.5 27 27.5 28 28.5 29 29.5 30 30.5 31 31.5 32 32.5 33 33.5 34 34.5 35 35.5 36 36.5 37 37.5 38 38.5 39 39.5 40 40.5 41 41.5 42 42.5 43 43.5 44 44.5 45 45.5 46 46.5 47 47.5 48 48.5 49 49.5 50 50.5 51 51.5

0.898 0.895 0.891 0.887 0.883 0.879 0.875 0.870 0.866 0.862 0.857 0.853 0.848 0.843 0.839 0.834 0.829 0.834 0.819 0.814 0.809 0.804 0.799 0.793 0.788 0.783 0.777 0.772 0.766 0.760 0.755 0.749 0.743 0.737 0.731 0.725 0.719 0.713 0.707 0.701 0.695 0.688 0.682 0.676 0.669 0.663 0.656 0.649 0.643 0.636 0.629 0.623

0.488 0.499 0.510 0.521 0.532 0.543 0.554 0.566 0.577 0.589 0.601 0.613 0.625 0.637 0.649 0.662 0.675 0.679 0.700 0.713 0.726 0.740 0.754 0.767 0.781 0.795 0.810 0.824 0.839 0.854 0.869 0.885 0.900 0.916 0.933 0.949 0.966 0.983 1.000 1.018 1.036 1.054 1.072 1.091 1.109 1.130 1.150 1.171 1.192 1.213 1.235 1.262

2.049 2.006 1.963 1.921 1.881 1.842 1.804 1.767 1.732 1.698 1.664 1.632 1.600 1.570 1.540 1.511 1.483 1.473 1.429 1.402 1.377 1.351 1.327 1.303 1.280 1.257 1.235 1.213 1.191 1.171 1.150 1.130 1.111 1.091 1.072 1.054 1.036 1.018 1.000 0.983 0.966 0.949 0.933 0.916 0.902 0.885 0.869 0.854 0.839 0.824 0.810 0.792

0.788 0.793 0.799 0.804 0.809 0.814 0.819 0.824 0.829 0.834 0.839 0.843 0.848 0.853 0.857 0.862 0.866 0.870 0.875 0.879 0.883 0.887 0.891 0.895 0.899 0.903 0.906 0.910 0.914 0.917 0.921 0.924 0.927 0.930 0.934 0.937 0.940 0.943 0.946 0.948 0.951 0.954 0.956 0.959 0.961 0.964 0.966 0.968 0.970 0.982 0.974 0.976

52 52.5 53 53.5 54 54.5 55 55.5 56 56.5 57 57.5 58 58.5 59 59.5 60 60.5 61 61.5 62 62.5 63 63.5 64 64.5 65 65.5 66 66.5 67 67.5 68 68.5 69 69.5 70 70.5 71 71.5 72 72.5 73 73.5 74 74.5 75 75.5 76 76.5 77 77.5

0.616 0.609 0.602 0.595 0.588 0.581 0.574 0.566 0.559 0.552 0.545 0.537 0.530 0.522 0.515 0.508 0.500 0.492 0.485 0.477 0.470 0.462 0.454 0.446 0.438 0.431 0.423 0.415 0.407 0.399 0.391 0.383 0.375 0.819 0.358 0.350 0.342 0.556 0.326 0.317 0.309 0.301 0.292 0.284 0.276 0.267 0.259 0.250 0.242 0.233 0.225 0.216

1.280 1.303 1.327 1.351 1.376 1.402 1.428 1.455 1.483 1.511 1.540 1.570 1.600 1.632 1.664 1.698 1.732 1.767 1.804 1.842 1.880 1.921 1.963 2.006 2.051 2.097 2.145 2.195 2.246 2.300 2.356 2.414 2.475 1.136 2.605 2.674 2.747 1.696 2.904 2.989 3.078 3.172 3.271 3.376 3.488 3.606 3.732 3.868 4.011 4.209 4.332 4.511

0.781 0.767 0.754 0.740 0.727 0.713 0.700 0.687 0.675 0.662 0.649 0.637 0.625 0.613 0.601 0.589 0.577 0.566 0.554 0.543 0.532 0.521 0.510 0.498 0.488 0.477 0.466 0.456 0.445 0.435 0.424 0.414 0.404 0.880 0.384 0.374 0.364 0.590 0.344 0.335 0.325 0.315 0.306 0.296 0.287 0.277 0.268 0.259 0.249 0.238 0.231 0.222

0.978 0.980 0.982 0.983 0.985 0.986 0.988 0.989 0.999 0.991 0.993 0.994 0.995 0.995 0.996 0.997 0.998 0.998 0.999 0.999 0.999 1.000 0.9998 0.9999 1.000

78 78.5 79 79.5 80 80.5 81 81.5 82 82.5 83 83.5 84 84.5 85 85.5 86 86.5 87 87.5 88 88.5 89 89.5 90

0.208 0.199 0.191 0.182 0.174 0.165 0.156 0.148 0.139 0.131 0.122 0.113 0.105 0.096 0.087 0.078 0.070 0.061 0.052 0.044 0.035 0.026 0.017 0.009 0.000

4.705 4.915 5.145 5.396 5.673 5.977 6.315 6.691 7.178 7.597 8.145 8.777 9.517 10.389 11.431 12.716 14.302 16.362 19.083 22.913 28.637 38.299 57.295 114.931 1.000

0.213 0.203 0.194 0.185 0.176 0.167 0.158 0.149 0.139 0.132 0.123 0.114 0.105 0.096 0.087 0.079 0.070 0.061 0.052 0.044 0.035 0.026 0.017 0.009 0.000