Design and reinforcement detailing of doglegged staircase using IS 456: 2000

1. DESIGN OF STAIRCASE

2. Diagram showing support condition

4. Data and calculations
•Height between floor=2.79 m
•Tread=250 mm
•Riser=155 mm
•Width of staircase=1000 mm =1 m
•Number of riser =2790/155 =18 nos.

5. Continued…
•So giving
First flight: 8 tread and 9 riser
Second flight: 8 tread and 9 riser
•Height of landing = 9155 =1395 mm
=1.395m

6. Continued…
• Then effective span will be provided as =going span +x+y;
l=2+x+y
l=2+0.45+0.3675
l=2.82 m
(since: x<1m and y<1m.)

7. Based upon IS 456:2000 code
specification
• Minimum reinforcement for HYSD bar =0.12%
• For pt =0.12%.
• Modification factor for tension reinforcement =1.25
• Taking (span/depth) ratio 32.
• l/d =32.
• d=2820/32 =88.125 mm
• Clear cover = 15 mm;
• Steel diameter =10 mm.

8. Continued..
• Total depth of waist =88.125+15+10/2 =108.125 mm
• Provide total depth = 110 mm.
• B= 0.1552 + 0.252
= 0.294m

9. LOAD CALCULATION:
Load on landing:
Live load =3 KN/m2.
Finishing load=1 KN/m2.
Dead load =250.11=2.75 KN/m2
Total load on landing = 6.75 KN/m2.(not factored)
Load on going:
Live load =3 KN/m2.
Finishing load=1 KN/m2
Dead load = (WB+ 0.5RT)25/T ; (refer diag.)
=(0.1100.294+0.50.1550.25)25/0.25;
=5.1715 KN/m2;
Total load on going =9.1715 KN/m2 (not factored)

10. Loading diagram

11.  MB=0  RA2.82 - 10.1250.37(0.370.5+2.45) - 13.75721.45 -
10.1250.50.452=0
RA=18.0112 KN
RA+RB = 35.8165 KN
 RB=17.805 KN
MX=17.805X – 10.1250.37(X-0.370.5) -13.757(X-0.37)2 0.5
dM/dx =0
x=1.39166 m
hence MX=13.073 KNm/m
Mu/bd2 =(13.07106)/(1000852)=1.809

12. Using SP 16
From table 1; for M20 and fy=415 N/mm2
Pt =0.565 %
Pt =
𝐴 𝑆𝑡
𝑏𝑑
100 Ast =(0.565100085)/100 =480.25 mm2/m
Spacing = 160 mm
ASt min= 0.121000110/100=132 mm2/m
Take distribution bar: 8mm dia.
Spacing =(100064)/(4132) =380 mm

13. Primary bar spacing check:
Smax =3d (or) 300 mm
=255 mm
We have , spacing = 160 mm< 255 mm -ok
Secondary bar spacing check:
Smax =5d (or) 450 mm
=425 mm
So provide spacing = 380 mm

14. Detailing of staircase: