Structural design of staircase

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Staircase design using eurocode 2

Waist          = 150 mm
Rise            = 150 mm
Treads        = 250 mm
Finishes      = 1 kN/mm2
Span          = 3.3 m
Live Load  = 4 kN/mm2
Cover        = 25 mm
Concrete    = 25 N/mm2

Load Calculation

Total Dead Load  = 5.625 kN/m2

Variable load        = 4 kN/m2

Ultimate load        = 1.25*5.625 + 1.5*4

                            = 13.03 kN/m2

Moment               = W*l²/8

                            = 13.03*(3.3^2)/8
                  
                            = 17.74 kNm

d                          = 150-25-12/2

                            = 119 mm

k                          = M / (b*d^2*fck)

                            = 17.74*10^6/ (1000*119^2*25)

                            = 0.05

z                          = (d/2)[1+(1-3.53k)^0.5]  ≤ 0.95d

                           =   (d/2)[1+(1-3.53*0.05)^0.5] ≤ 0.95d

                           = 0.954d  ≥ 0.95d

Hence

z                          = 0.95d

                           = 0.95*119

                           = 113.05

As                       = M/ (fyd* z)

                           = 17.74*10^6 / (500*113.05)

                           = 313.84 mm2

Proved T10 @ 150mm c/c

Deflection Check