DESIGN OF STAIR CASE WITH CENTRAL STRINGER BEAM pkn Project name :Space available for staire case 5.20 Vetical distance of floor 3.60 1.40 width of stair case 0.16 Risers 0.25 Treads 4000 Live load 20 Conrete Mwt. 25000 415 Steel fy 25 Nominal cover 80 W est slab thickness 200 assume width of stringer beam
x
4.40 3600 1400 160 250
m
mtr mtr mtr
m mm
mm mm mm
2
N/m
m scbc
13.33 7
N/mm
Effective cover
230 30
N/mm mm
Bars Required Bars Required Sapcing c/c Sapcing c/c
4 2 250 90
Nos. Nos. mm mm
3
N/mm
sst mm mm mm
2 2
Reinforcement
20 10 10 10
Main Bars Anchor bars bars Waist slab bars Strirrups
mm F mm F mm F mm F
1.50
2.25
230
2-
1.45
10 mm anchore bars Bottom of waist 10 mm f @
1.50
250 mm c/c
stirrups 2 ldg. 10 mm F @
250
10 mm f @ 250 mm c/c Landing
160
90 mm c/c stirrups 2 ldg. 10 mm F @
80
180 180 mm c/c c/c mid span
8 mm F @
1.50
300 mm c/c
stirrups 2 ldg. 10 mm F @
L - section
90 mm c/c 10 mm f @
250 250 mm c/c c/c 1450 80
10 mm f @
2 - 10 mm f Anchor bars
90 mm c/c
10 mm F @ 180 mm c/c stirrups 2 ldg.
4
-20 mm f main bars
200
[email protected]
Cross section at mid span
mm
DESIGN OF STAIR CASE WITH CENTRAL STRINGER BEAM width of stair case Risers live load Conrete Nominal cover
1.40 0.16 4000 M- 20 25
1 D e s i g n C o n s t a n t s : - For HYSD Bars
sst = scbc =
= = =
m k= j=1-k/3 j=1-k/3 R=1/2xc x j x k
230
N/mm
2
7
N/mm
3
13.33 m*c
m*c+sst
=
= =
1 0.5
mtr 1400 1400 mm mtr 160 mm Treads 0.25 mtr 2 N/m 2 Steel fy- 415 N/mm mm Effective cover 30 mm Cocrete M =
20
wt. of concrete
13.33
x
13.33 x
7
-
0.289
/
3
x
7
x
0.904
7 +
250 mm
230
= 25000 N/mm
2
= 0.289 = 0.904
x 0.289 =
0.913
2 L o a d i n g o n w a i s t s l ab ab : - Assume waist slab thickness = 80 mm The weight of waist slab on the slope should should be multi plied plied by the factor 2 2 R +T where R= 160 mm and T = 250 mm T 2 2 = 160 + 250 = 1.19 to get the equivalent weight of horizontal plane . 250 Considered 1 m width of slab. Load per metre horizontal run will be as follows. Self weight Weight of steps Laoding of finishing Live load
x 25000 x 1.19 = 2380 N x 1 x #### = 2000 N 100 N L.S. = = 4000 N Total = 8480 N The loading on landing will be lasser : however , for simplicity , we will take the same loading throught. = = = =
0.08 0.5
x x
1 0.16
x
1 1
3 Design of waist slab:- the waist slab is supported on central stringer beam . Hence the worst condition may be when we considred concentrated live load of 4000 N to act to one side only. Dead weight = 2380 + 2000 + 100 = 4480 N Assume width of stringer beam = 200 mm 1.40 0.2 Projection of slab beyond the rib of beam = = 0.60 mtr 2 2 4480 x( 0.60 )2 wL B.M. due to dead load = = 806 N-m 2 2 2 4000 x( 0.60 )2 wL B.M. due to U.D. live load = = 720 N-m 2 2 B.M. due to concentreted live load = 4000 x 0.60 = 2400 N-m Max. B.M. M = 80 806 + 2400 = 3206 N-m 3206000 But BM Effective depth required = = = 60 mm 80 mm available= 0.913 x 1000 Rxb However , keep minimum total depth - 25 = 55 mm = 80 80 mm . Efective depth = BM x 1000 3206000 2 = Ast = = 280 mm sst x j x D 230 x 0.904 x 55 2 3.14 x 10 x 10 3.14xdia using 10 mm F bars A = = = 79 mm2 100 4 x100 4 x spacing of Bars = A*1000/Ast = x 1000 / 79 28 280 = 280 mm However , keep spacing = 250 mm , one bar per step Distribution reinforcement
=
1.2
x
80
=
96
mm
2
using
8
mm F bars
A
spacing of Bars = A*1000/Ast Maimu aimum m perm permis issi sibl ble e spac spacin ing g However , keep spacing
2 3.14 x 8 = 3.14xdia = 4 x100 4 x x 1000 / = 50 96 96 x 8 = 45 = 360 mm say = 300 mm, Maximum
4 Design of stringer beam :- The stringer beam will act as T- beam. Flight CD is longest, Hence we will design the stringer beam CD 0.2 1.45 Effective span = 1.50 + 2.25 + = 2 2
x 8 100 300
50
mm2
= 523 mm
mm
=
4.38 m
The loading on stringer beam will be as follows,
asssuming the web to be (a) W eight of rib /m run = 0.20 x (b) Load from waist slab = 8480 x
200 mm wide and 200 mm deep 1190 0.20 x #### x 1.19 = 1 x 1.50 = 12720 Total = 13910
N N N say
14000 N/m
Assuming partial fixidity at ends, 2 14000 x 4.38 2 x 1000 M = wL = = 26796875 26.8 x 10 6 N-mm 10 10 Taking lever arm = 0.9 x d , balance balance depth is given by by Eq. 2kcd - D where bf = flange width of isolated T-Beam given byEq. 0.45 bf. scbc. Df M = kc l0 where lo = L= 4.38 m ;b = actual width = 1.50 m bf bw, = + and bw = 0.20 m l0 + 4 b 4.38 bf = + 0.20 = 0.833 m = 833 mm 4.38 + 4 1.50 2x 0.289 d- 80 Hence, = 0.45 x 833 x 7 x 80 = 26796875 0.289 2 x 0.289 d80 209916 = 26796875 \ 0.289 80 2d = 127.66 \ 0.289 127.66 + 277.2 d = = 202.00 mm 2 Ve where tc max =1.8 N/mm2 for m-20 concrete Also, d = bw . Tc max T wL 14000 x 4.38 Ve = V+ 1.6 W here V = = = 30625 N bw 2 2 T = torsional moment, which will be induced due to live load acting only to one side of step. 4000 x 0.60 2 x 4.38 T = x 1000 = 1575000 N-mm 2 2 4.4 or T =( 4000 x 0.60 )x x 1000 = 5250000 N-mm 2 5250000 which ever is more = \ T 5250000 Ve = 30625 + 1.6 x = 72625 N 200 72625 Hence, d = = 227 mm However, keep total depth = 230 mm 200 x 1.6 using 20 mm main bars, 10 mm F ring and cover 25 mm 10 10 25 = 185 mm mm Net available d = 230 BM x 1000 26796875 2 Ast = = = 697 mm sst x j x D 230 x 0.904 x 185 2 3.14 x 20 x 20 3.14xdia using 20 mm F bars A = = = 314 mm2 100 4 x100 4 x Ast/A spacing of Bars = / 314 = Nos. Say 4 = 697 3 2 Actual Ast provided = 4 x 314 = 1256 mm Note:- the above reinforcement is for bending requirements only. there will be additional longitudinal reinforcement for torsion, as computed later.
Location of N.A. Assuming the N.A. falls within the flange, we have have 2 833 x n = = 13.33 x 1256 x( 185 n ) 2 2 33485 x = 6194718 n \ 833 n 2 7437 40.20 = n \ n 2 -7437 + 40.2 n = 0 \ n 29747 )0.5 40.2 + ( 1616 + n = \ 2*1 68.4 mm Hence the resultant falls inside the flanges y n = = 22.8 mm \ mm \ L.A. a = d - y = 185 - 22.8 = 162.2 26796875 M 2 Stress in steel = = = 132 230 Hence safe N/mm < Ast . A 1256 x 162 Corresponding stress in concrete is given by 68.4 txn 132 c = = x = 5.80 N/mm2 < 7 Hence safe m d-n 13.33 185 - 68.4 5 Design for torsion :- As computed earlier, T= 5250000 N-mm 30625 N 72625 N v = and ve = 72625 Ve 2 \ tve = = = 1.96 N/mm bw.d 200 x 185 x st 100 x 1256 = = 3.395 % hence from table 3.2 tc = 0.51 N/mm2 bxd 200 x 185 tve Since > tc shear reinforcemnt required ( a) a) L o n g i t u d i n a l r e i n f o r c e m e n t : -
M e1 = M + MT MT = T
\
(1+ D/bw) 1.7 26796875
Where M= =
5250000
6639706 = 33436581 = Ast = sst x j x D 230 x 162.18 Hence the provision of 4 bars of 20 mm f, Near Near the the col colum umn n D, take take the the bar bars s stra straig ight ht up. up. Pro Provi vide de 2Me1
=
Me1
+
26796875 1
+
230 / 200 1.7 33436581 N-mm =
=
6639705.9
N-mm
896 mm2
giving 1256 mm2 is O.K. 20 mm f bars at the lower face under the landing.
(b) Transvers e reinforc ement: -
Transverse reinforcement will be provided in the form of vertical stirrups. 25 mm clea clearr cov cover er all roun round d b1 = center to to center distence distence betwee between n corner bars in the the direction direction of width width = 200 2 x 25 10 = 140 mm d1 = center to to center distence distence betwee between n corner bars in the the direction direction of depth depth = 230 2 x 25 10 = 170 mm 2 mm F 3.14 x 10 x 10 using 10 A= 2x 3.14xdia = 2x = 157 mm2 stirrups bars 100 4 x100 4 x Vsv T.sv + now, Asv = = or b1d1ssv 2.5d1 ssv 5250000 30625 157 = + Sv 140 x 170 x 230 2.5 x 170 x 230 157 =( = ( 0.959 + 0.313 )S )Sv or S v = 157 / 1.27 or Sv = 123 mm However, the spacing should not exceed the least of x 1, (x1+y1)/4 and 300 mm 20 where x1= short diamension of stirrups = 140 + + 10 = 170 mm y1 = 170 + 20 20 + 10 10 = 200 mm (x1+y1)/4 =( 170 + 200 )/ 4 = 92.5 mm mm Hence Sv = 123.4 mm is not permis missib sible. Keep Sv = 90 mm c/c . Incas case the spac spaciing to 200 mm c/c in the mid span where both transverse shear as well as torsional shear are minimum. prov provid ide e 2 - 10 mm f hol holdi ding ng bars bars.. Kee Keep p the the same same seti setion on for for oth other er flig flight ht.. Let provide
[email protected]
1.50
2.25
230
2-
1.45
10 mm anchore bars Bottom of waist 10 mm f @
1.50
250 mm c/c
stirrups 2 ldg. 10 mm F @
250
10 mm f @ 250 mm c/c Landing
160
90 mm c/c stirrups 2 ldg. 10 mm F @
0
180 180 mm c/c c/c mid span
8 mm F @
1.50
300 mm c/c
stirrups 2 ldg. 10 mm F @
L - section 10 mm f @
90 mm c/c
250 250 mm c/c c/c 1450 80
10 mm f @
2 - 10 mm f Anchor bars bars
90 mm c/c
10 mm F @ 180 mm c/c stirrups 2 ldg.
4
-20 mm f main bars
200 Cross section at mid span
[email protected]
mm
VALUES OF DESIGN CONSTANTS Grade of concrete Modular Ratio
M-15 18.67
M-20 13.33
M-25 10.98
M-30 9.33
M-35 8.11
M-40 7.18
scbc N/mm2 m scbc
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
Rc
0.89 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
(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 100As bd
v
in concrete (IS : 456-2000)
Permissible shear stress in concrete tv N/mm M-15 M-20 M-25 M-30 M-35
2
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
Maximum shear stress tc.max c.max in concrete (IS : 456-2000) Grade of concrete
tc.max
M-15 1.6
M-20 1.8
M-25 1.9
M-30 2.2
M-35 2.3
M-40 2.5
Gra
t
table-3.2 Shear stress tc 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
M -2 0
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
Reiforcement % M -20
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
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 1.00 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
0.32 0.32 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
1.15 1.16 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
0.4 0.41 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
1.67 1.68 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
0.46 0.46 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
2.19 2.20 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
0.50 0.50 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
2.71 2.72 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 0.51 0.51
Permissible Bond stress Table de of conc bd
(N / mm
M-10 --
M-15 0.6
M-20 0.8
M-25 0.9
bd
in concrete (IS : 456-2000)
M-30 1
M-35 1.1
M-40 1.2
M-45 1.3
Development Development Length in tension Plain M.S. Bars
H.Y.S.D. Bars
Grade of concrete
tbd (N / mm2)
kd = Ld F
tbd (N / mm2)
M 15
0.6
58
0.96
60
M 20
0.8
44
1.28
45
M 25
0.9
39
1.44
40
M 30
1
35
1.6
36
M 35
1.1
32
1.76
33
M 40
1.2
29
1.92
30
M 45
1.3
27
2.08
28
M 50
1.4
25
2.24
26
kd = Ld
F
Permissible stress in concrete concrete (IS : 456-2000) 2 Permission stress in compression (N/mm ) Permissible stress in bond (Average) for Grade of 2 Bending acbc Direct (acc) plain bars in tention (N/mm ) concrete 2 2 2 (N/mm2) (N/mm2) (N/mm2) in kg/m Kg/m Kg/m --M 10 3.0 300 2.5 250 0.6 60 M 15 5.0 500 4.0 400 0 . 8 80 M 20 7.0 700 5.0 500 0.9 90 M 25 8.5 850 6.0 600 1.0 100 M 30 10.0 1000 8.0 800 1.1 110 M 35 11.5 1150 9.0 900 1.2 120 M 40 13.0 1300 10.0 1000 1 . 3 130 M 45 14.5 1450 11.0 1100 140 16.0 12.0 1.4 M 50 1600 1200
M-50 1.4
2.0
e r o t c a f n o i t a c i f i d o M
1.4 1.2 0.8 0.4
0.0
0.4 0.8 Percentage of tension reinforcement
1.2
1.6
2
2.4
2.8
