# DESIGN OF STAIRCASE

DESIGN OF STAIRCASE
Rise of the stair =150 mm
Tread of the stair =300 mm
width of the landing = 1.2 m
Effective span  L=3.2+1.2+0.3/2
=4.5m
Thickness of waist slab
L/d =25
d = 4500/25
=180mm
d  ~200mm
D=220mm
self weight of slab
w =(0.25×25)√(1502+3002)/300
=6.98kN/m2
Self weight of step
=√T2+R2/1000×((D/2)×1×25/1000)
=√(1502+3002)/100×(3.55)
=1.19kN/m2
=1000/300   =4 nos

Surface weight of steps
=no of steps×weight of one step
=4×1.19
=4.76kN/m2
W1 =6.98+3+1+4.76
=15.74kN/m2
RA=(4×1.2)+(0.5×10×2.2)
=4.8+6.25
=11.05kN
M=[11.05×(0.6+2.2)]-(4×1.2×2.8)-(1.4×10×0.5×7.4)
=30.94-13.44-9.8
=13.78kNm
Vu =1.5×11.05
=16.58kN
Mu=1.5×13.78
=20.67kNm
CHECK FOR WEIGHT OF WAIST SLAB:
d=√Mu/0.138fckb
=√20.67/0.138×25×103
d=77.3mm
Hence safe.
REINFORCEMENT:
M =0.87fyAstd[1-(fyAst/fckbd)]
20.67×106=0.87×415×180×Ast[1-(415Ast/25×1000×180)]
Ast   =328mm2
Provide 10mm dia bars
Spacing=250
Adopt 10mm dia 250mm centre to centre spacing
Disk bars =0.12%bd
=(0.12/100)×1000×200
Ast=240mm2
Provide 10mm dia bars
Spacing =350
10 mm dia at 350 mm centre to centre spacing.
Number of steps=3.2/0.25
=12nos
BENDING MOMENTS AND SHEAR FORCES:
RA={(5.5×1.2)+(0.5×12×3.25)}
=26.1kN
Mmax  =(14.2×1.725)-(5.5×1.1×1.725)
=32.28kNm
RA = Vmax = 26.1
Factored moment Mu =30.28×1.5=48.43KNm
Vu =26.1×1.5=39.15
Check for depth of waist slab
D=    (Mu /0.138fchb)
=√(48.43×106 /.138×25×103)
D=118mm