DESIGN OF STAIRCASE

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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
Loads:                              
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
Number of steps   =1000/tread
                             =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
Adopted effective depth=180mm
                                      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.
          Total load=8 kN/m2
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
Adopted effective depth=200mm
                                      Hence safe.
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