8/11/2019 load calculation+staircase design
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1. Geometry of staircase
160.00 mm
250.00 mm
1 .1 0 m
Length from Beam to the Start of the Flight Span (L1) 1 .1 2
m
Length from End of the Flight to the Midlanding Beam Span(L2) 2
.0 0 m
Span (L3) 1 .2 4 m
(L1+L2+L3) = 4 .3 6 m
2. Material Properties
(Fck) = 20 Mpa
(Fy) = 500 Mpa
Unit Weight of materials
= 25 KN/m3
= 22 KN/m3
= 20.4 KN/m3
= 27 KN/m3
3. Load Calculation
thickness of structural waist slab = 137.5 mm (assuming)
Thickness of screed = 0.025 m
Thickness of cement plaster = 0.0125 m
Thickness of marble = 0.02 m
Dead load of Flights(going)
Dead Load of structural staircase waist slab on 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 Landing
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 = 0.54 KN/m2
Dead load on landings = 4.7825 KN/m2
Live load in staircase = 3 KN/m2
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
Loading on Span L2 per metre run (Flight Portion)
Factored Wl2 = 1.5(dead load +live load) = 15.64 kN/m
Load here given in factored (i.e. m ultiplied with 1.5)
11.67 15.64 11.67
A 1.12 2.00 1.24 B
Ra L1 L2 L3 Rb
29.50 29.27
Reactions Ra and Rb
Ra+Rb= 58.77 KN
Taking moments of all forces about B
Ra X 4.36 = 128.47
Ra = 29.50 kN
Reaction at the support A = 29.50 kN
Rb = 29.27 = 29.27 kN
Maximum BM Occurs at the point 'x' where SF is Zero or Changes
its sign.
Point of Maximum Moment = 2.17 m
Max factored BM: = 34.32 kNm
Required Effective Depth from Bending Point of View:
Grade of steel
Detailed Design of Stairs
DESIGN OF STAIR- CASE
(Limit State Method as per IS 456-2000)
Riser of each step (Rise)
Tread of each Step (Tread)
Width of the Step (Width)
Reinforced concrete
Horizontal Length of the Flight Portion
Total length of span
Grade of concrete
Screed
Cement plaster
marble
Factor for slope
8/11/2019 load calculation+staircase design
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Mu lim it = 0.1 338 fckbd2
d ( re qd ) = 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) = 0.691 %
Area of Steel Required = 811.70 mm2/m use 16mm dia @ 247.706 mm
c/c
Ho wever provided steel = 16# @ 100 mm c/c Ast Provided =
2010.62 mm2/m
1.711 %
Provide 8 mm minimum distribution steel @ 0.12% of gross area =
150 mm2/mreqn area of 8# @ 335.1 mm c/c provide 8#@ = 300 m m
c/c
check for serviciebility requirement
The effect ive depth provided (def 117.5 mm
basic L/d ratio= 20
actual (L/d)= 37.06
modification factor required 1.853
steel stress at service load (fs) 117.07
% of re info rc ement (p t) requir ed 0 .691 %
modification factor 1.99
permissible (L/d)= 39.87 SAFE in Deflection
109.2 SAFE
%Ast prov =
dmin (mm)
8/11/2019 load calculation+staircase design
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Load here given in factored (i.e. multiplied with 1.5) Load here
given in factored (i.e. multiplied with 1.5)
7.17 11.14 7.17 4.50 4.50 4.50
A 1.12 2.00 1.24 B A 1.12 2.00 1.24 B
Ra L1 L2 L3 Rb Ra L1 L2 L3 Rb
19.70 19.47 9.80 9.80
End reaction for Dead Load End reaction for Live Load
Reactions Ra and Rb Reactions Ra and Rb
Ra+Rb= 39.17 KN Ra+Rb= 19.60 KN
Taking moments of all forces about B Taking moments of all
forces about B
Ra X 4.36 = 85.79 Ra X 4.36 = 42.67
Ra = 19.70 kN Ra = 9.80 kN
Reaction at the support A = 19.70 kN Reaction at the support A =
9.80 kN
Rb = 19.47 = 19.47 kN Rb = 9.80 = 9.80 kN
