Design of Concrete Stairs

Concrete and reinforcing steel bar properties

Concrete unit weight gC = 23.6 kN / m3

Concrete strength f'C = 28 MPa

Steel yield strength fy = 276 MPa

Moment reduction factor f m = 0.9

Main bar diameter fbm = 16 mm

Temperature bar diameter fbt = 10 mm

Concrete stair properties

Rise length r = 0.18 m

Tread length t = 0.30 m

Number of steps n = 10

Concrete slab properties

Slab thickness ts = 0.125 m

Concrete cover c = 20 mm

Effective depth d = tS - c - (fbm / 2) 97 mm

Weight of slab wS = gC tS (r2 + t

2)1/2

/ t 3.44 kPa

Weight of riser and tread wrt = gC r / 2 2.12 kPa

Total dead load wD = wS + wrt 5.56 kPa

Live load of stairs wL = 4.80 kPa

Total load per meter width wU = 1.4wD + 1.7wL 15.95 kN/m

Horizontal span L = nt 3.00 m

Maximum moment MU = wU L2 / 8 17.94 kN-m

Main bar reinforcement

m = 1.7 f'c / fy 0.17

n = m MU / (f m fy b d2) 0.00118

Check for rmax = 0.75 * 0.85 * (f'c / fy)*[600 / (600 + fy)] rmax = 0.04430

Solve for rR using the formula rR2 - mrR + n = 0 rR = 0.00712

Check for rmin = 1.4 / fy rmin = 0.00507 Use 0.00712

As = r b d 690.47 mm2

Main bar space sb = 1000 (p/4) fbm2 / As

291.20 say 200 mm

Temperature bar reinforcement

As = 0.002 b t 250.00 mm2

Temperature bar space sb = 1000 (p/4) fbt2 / As

314.16 say 300 mm

Provide 16-mm main reinforcement bars @ 200mm o.c.

Provide 10-mm main temperature bars @ 300mm o.c.

Shear rections from concrete stairs

Shear dead load VD = wD L / 2 8.35 kN/m (unfactored)

Shear live load VL = wL L / 2 7.20 kN/m (unfactored)