C6: DESIGN OF STAIRCASE AS PER IS CODE

                                           DESIGN OF STAIRCASE

DATA:

Number of steps in flight = 11

                        Tread,    T = 300 mm

                         Rise,     R = 150 mm

Width of landing beams   = 300 mm

M20 grade concrete & Fe415 HYSD bars

EFFECTIVE SPAN:

Effective span               = (11*300) + 300 = 3.6 m

Thickness of waist slab = Span / 20  = 3600 / 20 = 180 mm

Adopt overall depth,  D = 180 mm

Effective depth,           d = 155 mm

LOADS:

Dead load of slab on slope, Ws = 0.18*1*25 = 4.5 KN/m

Dead load of slab on horizontal span is:

                           W = [ (Ws*√  R²+T² ) / T ]

                                = [ (4.5*√  150²+300² ) / 300 ]

                                     = 5.031 KN/m

 Dead load of one                     = 0.5*0.15*0.3*25   = 0.56 KN/m

Load of steps per metre length = (0.56*1000) / 300 = 1.86 KN/m

Finishes                  = 0.53 KN/m

Total dead load      = 4.5+1.86+0.53 = 6.89 KN/m

Service load           = 5 KN/m²

Total service load  = 6.89 + 5 = 11.89 KN/m²

Factored load, Wu = 1.5*12  = 17.835 KN/m

BENDING MOMENT:

Max BM, M = 0.125*Wu*L²

                     = 0.125*17.835*3.6²

                     = 28.89 KNm

CHECK FOR DEPTH OF WAIST SLAB:

       Mmax = 0.138* fck* b*d²

                                      28.89*10⁶ = 0.138*20*1000*d²

                                     d²  = (28.89*10⁶) / (0.138*20*1000)

           d = 102 mm

MAIN REINFORCEMENT:

                           Mu = 0.87*fy*Ast*d*[(1)-((Ast*fy) / (fck*b*d))]

                28.89*10⁶ = 0.87*415*Ast*155[(1)-((Ast*415) / (20*1000*155))]

               28.89*10⁶ = 55962.75*Ast*[(1)-((6.4516129*10^-6)*(Ast))]

               0.36105Ast²-55962.75Ast+(5.996*10⁶) = 0

                          Ast = 587 mm².

                       Use 12 mm dia bar.

                       Spacing = [((π*12²/4)*(1000))/(587)]

                                  s  = 192.6 mm

                      Provide 12 mm dia bars at 200 mm c/c (Ast = 565 mm²)

DISTRIBUTION REINFORCEMENT:

Distribution reinforcement = 0.12 %

                                            = 0.0012*1000*155

                                            = 186 mm²

Provide 8 mm dia bars @ 20 mm c/c ( Ast = 251 mm²)

DESIGN BY USING SP-16 DESIGN CHARTS:

Mu/bd² = (28.89*10⁶) / (1000*155²) = 1.25

Refer table sp-16,

          Pt = 0.376

        Ast = Pt*b*d / 100

               = (0.376*1000*155) / 100

               = 582.8 mm²