load calculation+staircase design

DESIGN OF STAIR- CASE (Limit State Method as per IS 456-2000) 1.

Geometry of staircase

Riser of each step (Rise)

160.00 mm

Tread of each Step (Tread)

250.00 mm

Width of the Step (Width)

1.10 m

Length from Beam to the Start of the Flight

Span (L1)

1.12 m

Length from End of the Flight to the Midlanding Beam

Span(L2)

2.00 m

Span (L3)

1.24 m

=

4.36 m

Horizontal Length of the Flight Portion Total length of span

(L1+L2+L3)

Material Properties

2.

Grade of concrete

(Fck)

=

20 Mpa

Grade of steel

(Fy)

=

500 Mpa

Unit Weight of materials Reinforced concrete

=

Screed

=

Cement plaster

=

marble

=

3.

25 KN/m3 22 KN/m3 20.4 KN/m3 27 KN/m3

Load Calculation thickness of structural waist slab Thickness of screed

=

137.5 mm

=

Thickness of cement plaster

=

0.025 m 0.0125 m

Thickness of marble

=

0.02 m

(assuming)

Dead load of Flights(going) Dead Load of structural staircase waist slab on slope Factor for slope

=

3.4375 KN/m2

=

1.18727

Dead load of structural inclined staircase slab on plan

=

4.08123 KN/m2

Dead Load of screed

=

0.55 KN/m2

Dead Load of cement plaster

=

0.255 KN/m2

Dead Load of marble

=

0.54 KN/m2

Dead load of steps

=

2 KN/m2

Dead load of Flights(going)

=

7.42623 KN/m2

Dead Load of structural landing slab

=

3.4375 KN/m2

Dead Load of screed

=

0.55 KN/m2

Dead Load of cement plaster

=

0.255 KN/m2

Dead Load of marble

Dead load of Landing

=

0.54 KN/m2

Dead load on landings

=

4.7825 KN/m2

Live load in staircase

=

3 KN/m2

Detailed Design of Stairs Loading on Spans L1 and or L3 per metre run (Landing Portion) : Factored Wl1 = Wl3 = 1.5(dead load +live load)

=

11.67 kN/m

=

15.64 kN/m

Loading on Span L2 per metre run (Flight Portion) Factored Wl2 = 1.5(dead load +live load)

Load here given in factored (i.e. multiplied with 1.5) 11.67

15.64

11.67

A

1.12

2.00

1.24

Ra

L1

L2

L3

29.50 58.77 KN

Taking moments of all forces about B Ra X

Ra

4.36

=

=

128.47

29.50 kN

Reaction at the support A

=

29.50 kN

Rb

=

29.27 kN

=

29.27

Maximum BM Occurs at the point 'x' where SF is Zero or Changes its sign. Point of Maximum Moment = Max factored BM:

=

2.17

34.32

m kNm

Required Effective Depth from Bending Point of View:

Rb 29.27

Reactions Ra and Rb Ra+Rb=

B

2 0.1338 fck bd

Mu limit = d (reqd) =

113.249 mm

However Provide an Effective depth of

117.5 mm

Provide an overall depth of

138 mm

Factor Mu/bd2 (R)=

2.49 Mpa

Required percentage of steel (pt)

=

Area of Steel Required =

811.70 mm2/m

However provided steel = %Ast prov =

0.691 %

16# @

use 16mm dia @ 100 mm c/c

Ast Provided =

247.706

mm c/c 2010.62 mm2/m

1.711 %

Provide 8 mm minimum distribution steel @ 0.12% of gross area =

150 mm2/m

reqn area of 8# @

300 mm c/c

335.1

mm c/c

provide 8#@ =

check for serviciebility requirement The effective depth provided (deff) basic L/d ratio= actual (L/d)= modification factor required steel stress at service load (fs) % of reinforcement (pt) required modification factor permissible (L/d)= dmin (mm)

117.5 mm 20 37.06 1.853 117.07 0.691 % 1.99 39.87 SAFE in Deflection 109.2 SAFE

Load here given in factored (i.e. multiplied with 1.5) 7.17

11.14

7.17

A

1.12

2.00

1.24

Ra

L1

L2

L3

19.70

Load here given in factored (i.e. multiplied with 1.5)

B Rb 19.47

4.50

4.50

4.50

A

1.12

2.00

1.24

Ra

L1

L2

L3

9.80

End reaction for Live Load

Reactions Ra and Rb

Reactions Ra and Rb

Ra+Rb=

Ra+Rb=

Taking moments of all forces about B Ra X

Ra

4.36 =

=

Rb 9.80

End reaction for Dead Load

39.17 KN

B

19.60 KN

Taking moments of all forces about B

85.79

Ra X

19.70 kN

Ra

4.36

=

=

42.67

9.80 kN

Reaction at the support A

=

19.70 kN

Reaction at the support A

=

9.80 kN

Rb

=

19.47 kN

Rb

=

9.80 kN

=

19.47

=

9.80