In this type of stair, the effective span is the horizontal distance between center to center of

support. Each step is design as spanning horizontally. Eachstep is considered equivalent to

horizontal beam of width b= R2+T

2measured parrallel to slope of stair , and an

effective depth D/2 , as shown in fig.1. Main reinforcement, provided in the direction of span,

The distribution reinforcement, provided inform of 6 mm diameter bars at 30 cm c/c is

normally adequate.

Horizontal Span of stair case 1.25 mtr 1250 mm

Risers 0.15 mtr 150 mm

Treads 0.25 mtr 250 mm

Conrete M- 20

Steel fy- 415

Nominal cover 25

Effective cover 30

Reinforcement

Main Top 16 mm F Bars Required= #REF! Nos.

Anchor bars (Bottom ) 8 mm F Bars Required= 2 Nos.

Strirrups 8 mm F spacing c/c #REF! mm

Nominal Cover 25 mm

Effective Cover 30 mm

DESIGN OF STAIR SPANNING HORIZONTALLY

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Horizontal Span of stair case 1.25 mtr 1250 mm

Risers 0.15 mtr 150 mm

Treads 0.25 250 mm

Conrete M- M- 20

Steel fy- fy- 415 N/mm2

Nominal cover 25 mm

Effective cover 30 mm

1 Design Constants:- For HYSD Bars = 20

sst = = 230 N/mm2

= 25000 N/mm2

scbc = = 7 N/mm3

m = 13.33

x

13.33 x 7 + 230

j=1-k/3 = 1 - 0.289 / 3 = 0.904

R=1/2xc x j x k = 0.5 x 7 x 0.904 x 0.289 =

2 Step dimension:-

R "= 150 mm T "= 250 mm

\ b = R2 +T

2= 150

2+ 250

2= 292 mm

Let us keep waist thicness = 80 mm \ D = 80 + RT / b =

150 x 250

= 208 / 2 = 104 1.25 mtr

3 Loading and B.M. Each step span horizontally:-

1 150 250

2 1000 1000

80 292

1000 1000

Total = N/M

250

1000

Total = N/M

M wL2 1873 x( 1.25

8

4 Design of section :-

0.913 x 292

230 x 0.904 x 104

using 8mm bars A = 3.14xdia2

= 3.14 x 8 x 8

4 x100 4 x

Nomber of Bars = Ast/A = 17 / 50 = 0.34 say = 1 No.

Hence Provided 8 = 300 mm (maximum)

DESIGN OF STAIR SPANNING HORIZONTALLY

=

Cocrete M

0.9130

0.289m*c+sst

wt. of concrete

k=m*c

=13.33

=D292

= 20880 +

7

N/m

mm

mm span L

Dead load of each step per meter= x x x 25000 = 469

Dead load of waist =

Laoding of finishing L.S. =

N/m

x x #### = 584

= 7503000 N/m2

70 N/m

1123

x

366000= =8

)2'=

Live load @ 3000 N/m

1873

=

N-mm

Effective depth

required == =

Rxb

366000

366 N-m or

mm

Hence the effective depth of equivalent beam =D/2

Ast = = 16.93 mm2

37 mmBut

available=104

= 50 mm2

mm F bar, @c/c

100

BM x 100

sst x j x D=

366000

wall

D

F

Main reinforcement

Section x x

1.25

DESIGN OF STAIR SPANNING HORIZONTALLY

Stringer Beam

DESIGN OF STAIR SPANNING HORIZONTALLY

M-15 M-20 M-25 M-30 M-35 M-40 Grade of concrete

18.67 13.33 10.98 9.33 8.11 7.18

5 7 8.5 10 11.5 13

93.33 93.33 93.33 93.33 93.33 93.33

kc 0.4 0.4 0.4 0.4 0.4 0.4

jc 0.867 0.867 0.867 0.867 0.867 0.867

Rc 0.867 1.214 1.474 1.734 1.994 2.254

Pc (%) 0.714 1 1.214 1.429 1.643 1.857

kc 0.329 0.329 0.329 0.329 0.329 0.329

jc 0.89 0.89 0.89 0.89 0.89 0.89

Rc 0.732 1.025 1.244 1.464 1.684 1.903

Pc (%) 0.433 0.606 0.736 0.866 0.997 1.127

kc 0.289 0.289 0.289 0.289 0.289 0.289

jc 0.904 0.904 0.904 0.904 0.904 0.904

Rc 0.653 0.914 1.11 1.306 1.502 1.698

Pc (%) 0.314 0.44 0.534 0.628 0.722 0.816

kc 0.253 0.253 0.253 0.253 0.253 0.253

jc 0.916 0.916 0.916 0.914 0.916 0.916

Rc 0.579 0.811 0.985 1.159 1.332 1.506

Pc (%) 0.23 0.322 0.391 0.46 0.53 0.599

M-15 M-20 M-25 M-30 M-35 M-40

0.18 0.18 0.19 0.2 0.2 0.2

0.22 0.22 0.23 0.23 0.23 0.23

0.29 0.30 0.31 0.31 0.31 0.32

0.34 0.35 0.36 0.37 0.37 0.38

0.37 0.39 0.40 0.41 0.42 0.42

0.40 0.42 0.44 0.45 0.45 0.46

0.42 0.45 0.46 0.48 0.49 0.49

0.44 0.47 0.49 0.50 0.52 0.52

0.44 0.49 0.51 0.53 0.54 0.55

0.44 0.51 0.53 0.55 0.56 0.57

0.44 0.51 0.55 0.57 0.58 0.60

0.44 0.51 0.56 0.58 0.60 0.62

0.44 0.51 0.57 0.6 0.62 0.63

M-15 M-20 M-25 M-30 M-35 M-40

1.6 1.8 1.9 2.2 2.3 2.5

VALUES OF DESIGN CONSTANTS

Grade of concrete

Modular Ratio

scbc N/mm2

m scbc

(a) sst =

140

N/mm2

(Fe 250)

(b) sst =

190

N/mm2

(c ) sst =

230

N/mm2

(Fe 415)

(d) sst =

275

N/mm2

(Fe 500)

Permissible shear stress Table tv in concrete (IS : 456-2000)

100As Permissible shear stress in concrete tv N/mm2

0.75

1.00

1.25

1.50

bd

< 0.15

0.25

0.50

tc.max

2.753.00 and above

Maximum shear stress tc.max in concrete (IS : 456-2000)

Grade of concrete

1.75

2.00

2.25

2.50

Grade of concrete M-10 M-15 M-20 M-25 M-30 M-35 M-40 M-45

tbd (N / mm2) -- 0.6 0.8 0.9 1 1.1 1.2 1.3

M 15

M 20

M 25

M 30

M 35

M 40

M 45

M 50

(N/mm2) Kg/m2 (N/mm2) Kg/m

2

M 10 3.0 300 2.5 250

M 15 5.0 500 4.0 400

M 20 7.0 700 5.0 500

M 25 8.5 850 6.0 600

M 30 10.0 1000 8.0 800

M 35 11.5 1150 9.0 900

M 40 13.0 1300 10.0 1000

M 45 14.5 1450 11.0 1100

M 50 16.0 1600 12.0 1200 1.4 140

1.2 120

1.3 130

0.9 90

1.0 100

1.1 110

Direct (acc)

-- --

0.6 60

0.8 80

Permissible Bond stress Table tbd in concrete (IS : 456-2000)

Grade of

concrete

Permission stress in compression (N/mm2) Permissible stress in bond (Average) for

plain bars in tention (N/mm2)

(N/mm2) in kg/m2

Bending acbc

Development Length in tension

Grade of

concrete

Plain M.S. Bars H.Y.S.D. Bars

tbd (N / mm2) kd = Ld F tbd (N / mm2) kd = Ld F

0.6 58 0.96 60

0.8 44 1.28 45

1 35 1.6 36

0.9 39 1.44 40

1.1 32 1.76

1.3 27 2.08 28

1.4 25 2.24 26

33

1.2 29 1.92 30

Permissible stress in concrete (IS : 456-2000)

M-50

1.4

Permissible Bond stress Table tbd in concrete (IS : 456-2000)

Development Length in tension