consulting job no. sheet no. rev. e n g i n e e r s · member design - rc staircase 23/9/2017...
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Job No. Sheet No. Rev.
Job Title
XX
Material Properties
Characteristic strength of concrete, fcu (≤ 60N/mm2; HSC N/A) 30 N/mm
2 OK
Yield strength of longitudinal steel, fy 460 N/mm2
Yield strength of shear link steel, fyv 460 N/mm2
Type of concrete and density, rc 24 kN/m3
Stair Structural Scheme
Stair structural scheme
Scheme 1 Stair spanning longitudinally simply supported or semi-continuous with
SDL on elevation over width b
Note precast (mid section shear connection), insitu (landing starters);
Scheme 2 Stair spanning horizontally cantilever with SDL on elevation at free end
Scheme 3 Stair spanning horizontally simply supported without SDL on elevation
Breadth of landing at one end, lb,1 1.600 1.600 m Note
Breadth of landing at the other end, lb,2 1.000 1.000 m Note
Stair Parameters
Bottom landing 150 mm thick
Top landing 150 mm thick
Point A 90 mm to the right
Point B 90 mm to the right
Use of stair
r max g min
Private stair 220 220 mm
Institutional and assembly stair 180 280 mm
Other stair 190 250 mm
Slope angle of stair, q (<=42) 33.9 degrees OK
Rise of stair, H 1.714 m
Number of risers, Nriser 10
Height of riser, r = H/Nriser (<=rmax) 171 mm OK
Number of goings, Ngoing = Nriser + No. of offset goings 10
Length of going, g = r/tanq (>=gmin) 255 mm OK
Span of stair, L = Ngoing.g 2.550 m
Effective span of stair, Leff = L+(0%-100%)(lb1+lb2) 5.150 m Note
Stair flight L occupies ≥ 60% of stair effective span Leff ? No Note
Parameter 2r+g (>=550mm, <=700mm) 598 mm OK
Slope length of stair, q = √(L2+H
2) 3.073 m
Depth of waist, h 200 mm
Width of stair, b 1.250 m
Member Design - RC Staircase 23/9/2017
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L
H r
g h
Structural Landing
Structural Landing
Point A
Point B
The start of a flight (first
rise) and the end of the
previous flight (last
going) may be set out staggered by:-
1. 0 going
2. 1 going
3. 2 goings
This merely increases the
stair flight span by the
above goings.
Job No. Sheet No. Rev.
Job Title
XX
Cover to all reinforcement, cover (usually MAX(25, f) internal; 40 external) 25 mm
Effective depth to sagging steel, ds 167 mm
Scheme 1 d s = h - cover - f s /2 167 mm
Scheme 2 d s = (r.L/ q + h - cover - f s /2)/2 N/A mm
Scheme 3 d s = (r.L/ q + h - cover - f s /2)/2 N/A mm
Effective depth to hogging steel, dh 167 mm
Scheme 1 d h = h - cover - f h /2 167 mm
Scheme 2 d h = h. q/L + r/2 - cover - f h /2 N/A mm
Scheme 3 d h = h. q/L + r/2 - cover - f h /2 N/A mm
Sagging steel reinforcement diameter, fs 16 mm
Sagging steel reinforcement pitch, ps 175 mm
Sagging steel area provided, As,prov,s = (p.fs2/4)/ps 1149 mm
2/m
Hogging steel reinforcement diameter, fh 16 mm
Hogging steel reinforcement pitch, ph 175 mm
Hogging steel area provided, As,prov,h = (p.fh2/4)/ph 1149 mm
2/m
Shear link diameter, flink 0 mm
Number of links per metre, nlink 4 /m
Area provided by all links per metre, Asv,prov = nlink.p.flink2/4 0 mm
2/m
Pitch of links, S 200 mm
Stair Loading (Slope Loading)
Live load, LL 4.00 kPa
Superimposed dead load, SDL 1.20 kPa
Dead load of stair (on slope), DL = h.rc + g.(H/2)/q.rc 6.51 kPa
ULS stair loading (on slope) excluding SDLelev,stair, wULS,stair,noSDLelev 16.75 kPa
w ULS,stair,noSDLelev = 1.4(DL + SDL.(L, H or L+H)/q) + 1.6(LL.L/q)
Note that the loading above is in the vertical direction, however on and along the slope;
Stair Loading (Elevation Loading)
Superimposed dead load on stair (on slope), SDLelev,stair 24.20 kN/m
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Member Design - Reinforced Concrete Staircase BS8110 v2017.01.xlsx
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Job No. Sheet No. Rev.
Job Title
XX
Utilisation Summary
Item UT Remark
Sag moment, Ms 75% OK
Hog moment, Mh 75% OK
% Min sag reinforcement 23% OK
% Min hog reinforcement 23% OK
Ultimate shear stress 15% OK
Shear design capacity 92% OK
Deflection utilisation 108% NOT OK
Total utilisation 108% NOT OK
Detailing requirements
% Sagging reinforcement 0.57 %
% Hogging reinforcement 0.57 %
Estimated steel reinforcement quantity (130 - 220kg/m3) 90 kg/m
3
[ 7.850 . (A s,prov,s /scheme(h)+A s,prov,h /scheme(h)) ]; No curtailment; No laps; Links ignored; Distribution steel ignored;
Estimated steel reinforcement quantity (130 - 220kg/m3) 144 kg/m
3 IStructE
[ 12.5 . (A s,prov,s /scheme(h)+A s,prov,h /scheme(h)) ]; No curtailment; No laps; Links ignored; Distribution steel ignored;
[Note that steel quantity in kg/m3 can be obtained from 125.0 x % rebar];
Material cost: concrete, c 180 units/m3 steel, s 4500 units/tonne
Reinforced concrete material cost = [c+(est. rebar quant).s].scheme(h)165 units/m2
ULS Loading on Supporting Structure
Line shear on supporting structure, RV = V 113 kN/m
Line moment on supporting structure, RM = Mhog N/A kNm/m
Note that for scheme 1, R V is conservatively calculated based on L eff instead of L.
Geometrical Requirements
All geometrical requirements satisfied ? OK
Slope angle of stair, q OK
Height of riser, r OK
Length of going, g OK
Parameter 2r+g OK
Member Design - Reinforced Concrete Staircase BS8110 v2017.01.xlsx
Member Design - RC Staircase 23/9/2017
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Structural Analysis Stair
Sag moment, Msag 58 kNm/m
Scheme 1 Type A M sag = 0.1250( w ULS,stair,noSDLelev +1.4SDL elev,stair /b).q.L effN/A kNm/m
Type B M sag = 0.1250( w ULS,stair,noSDLelev +1.4SDL elev,stair /b).q.L effN/A kNm/m
Type C M sag = 0.0833( w ULS,stair,noSDLelev +1.4SDL elev,stair /b).q.L eff58 kNm/m
Type D M sag = 0.0500( w ULS,stair,noSDLelev +1.4SDL elev,stair /b).q.L effN/A kNm/m
Scheme 2 M sag = 0.0 N/A kNm/m
Scheme 3 M sag = 0.125 w ULS,stair,noSDLelev .b2 N/A kNm/m
Hog moment, Mhog 58 kNm/m
Scheme 1 Type A M hog = 0.0 N/A kNm/m
Type B M hog = 0.0625( w ULS,stair,noSDLelev +1.4SDL elev,stair /b).q.L effN/A kNm/m
Type C M hog = 0.0833( w ULS,stair,noSDLelev +1.4SDL elev,stair /b).q.L eff58 kNm/m
Type D M hog = 0.0833( w ULS,stair,noSDLelev +1.4SDL elev,stair /b).q.L effN/A kNm/m
Scheme 2 M hog = 0.5 w ULS,stair,noSDLelev .b2+1.4SDL elev,stair .b N/A kNm/m
Scheme 3 M hog = 0.0625 w ULS,stair,noSDLelev .b2 N/A kNm/m
Shear, V 113 kN/m
Scheme 1 V = 0.5( w ULS,stair,noSDLelev +1.4SDL elev,stair /b).L eff 113 kN/m
[ 12.5 . (A s,prov,s /scheme(h)+A s,prov,h /scheme(h)) ]; No curtailment; No laps; Links ignored; Distribution steel ignored;Scheme 2 V = w ULS,stair,noSDLelev .b+1.4SDL elev,stair N/A kN/m
Scheme 3 V = 0.5 w ULS,stair,noSDLelev .b N/A kN/m
Note that the effect of the axial force within the stair is ignored, the magnitude of which is presented below;
Axial force, A 38 kN/m
Scheme 1 A = ±0.5( w ULS,stair,noSDLelev +1.4SDL elev,stair /b).H 38 kN/m
Scheme 2 A = 0.0 N/A kN/m
Scheme 3 A = 0.0 N/A kN/m
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Stair Moment Design
Sag moment, Msag 58 kNm/m
Hog moment, Mhog 58 kNm/m
Ensure singly reinforced
K' K z As As,prov UT
Sag moment, Msag 0.156 0.069 153 865 1149 75% OK
Hog moment, Mhog 0.156 0.069 153 865 1149 75% OK
Note b b = 1.00 and K' = 0.156. If K > K', then UT = 999%.
Note that A s and A s,prov above are in units of mm2/m.
% Min sag reinforcement (>= 0.0024bh G250; >= 0.0013bh G460) 0.57 %
Scheme 1 h = h 200 mm
Scheme 2 h = (r.L/ q + h)/2 N/A mm
Scheme 3 h = (r.L/ q + h)/2 N/A mm
% Min sag reinforcement utilisation 23% OK
% Min hog reinforcement (>= 0.0024bh G250; >= 0.0013bh G460) 0.57 %
Scheme 1 h = h 200 mm
Scheme 2 h = h. q/L + r/2 N/A mm
Scheme 3 h = h. q/L + r/2 N/A mm
% Min hog reinforcement utilisation 23% OK
Stair Shear Design
Ultimate shear stress, vult=V/bdh (< 0.8fcu0.5
& 5N/mm2) 0.68 N/mm
2
Ultimate shear stress utilisation 15% OK
Design shear stress, vd=V/bdh 0.68 N/mm2
(Conservatively, shear capacity enhancement by either calculating v d at d from support and
comparing against unenhanced v c as clause 3.4.5.10 BS8110 or calculating v d at support and
comparing against enhanced v c within 2d of the support as clause 3.4.5.8 BS8110 ignored;)
Area of tensile steel reinforcement provided, As,prov,s/h 1149 mm2/m
Scheme 1 Type A A s,prov,s Type B, C or D A s,prov,h
Scheme 2 A s,prov,h
Scheme 3 A s,prov,h
rw = 100As,prov,s/h/bdh 0.69 %
vc = (0.79/1.25)(rwfcu/25)1/3
(400/dh)1/4
; rw<3; fcu<40; (400/dh)1/4
>0.67 0.74 N/mm2
Check vd < vc for no links VALID
Concrete shear capacity vc.(bdh) 123 kN/m
Check vc < vd < 0.4 + vc for nominal links N/A
Provide nominal links such that Asv / S > 0.4b/(0.95fyv) i.e. Asv / S > 0.92 mm2/mm/m
Concrete and nominal links shear capacity (0.4 + vc).(bdh) 190 kN/m
Check vd > 0.4 + vc for design links N/A
Provide shear links Asv / S > b(vd-vc)/(0.95fyv) i.e. Asv / S > 0.92 mm2/mm/m
Concrete and design links shear capacity (Asv,prov/S).(0.95fyv).dh + vc.(bdh)123 kN/m
Area provided by all links per metre, Asv,prov 0 mm2/m
Tried Asv,prov / S value 0.00 mm2/mm/m
Design shear resistance utilisation 92% OK
Member Design - Reinforced Concrete Staircase BS8110 v2017.01.xlsx
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Detailing Requirements
All detailing requirements met ? OK
Max sagging steel reinforcement pitch (<3ds, <750mm) 175 mm OK
Max hogging steel reinforcement pitch (<3dh, <750mm) 175 mm OK
Max sagging steel reinforcement pitch 175 mm OK
Max hogging steel reinforcement pitch 175 mm OK
Min sagging steel reinforcement pitch (>75mm+fs, >100mm+fs if T40) 175 mm OK
Min hogging steel reinforcement pitch (>75mm+fh, >100mm+fh if T40) 175 mm OK
Note an allowance has been made for laps in the min pitch by increasing the criteria by the bar diameter.
% Max sagging reinforcement (<= 0.04bh) 0.57 % OK
% Max hogging reinforcement (<= 0.04bh) 0.57 % OK
Sagging steel reinforcement diameter, fs (>=10mm) 16 mm OK
Hogging steel reinforcement diameter, fh (>=10mm) 16 mm OK
Member Design - Reinforced Concrete Staircase BS8110 v2017.01.xlsx
Member Design - RC Staircase 23/9/2017
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Deflection Criteria
Span, l 5.150 m
Scheme 1 l = L eff 5.150 m
Scheme 2 l = b N/A m
Scheme 3 l = b N/A m
Span, l / effective depth, d ratio 30.8
Scheme 1 l/d = l/d s 30.8
Scheme 2 l/d = l/d h N/A
Scheme 3 l/d = l/d s N/A
Basic span / effective depth ratio criteria 23.0
Scheme 1 Type A Basic l/d = 20 N/A
Type B Basic l/d = 20 N/A
Type C Basic l/d = 23 23.0
Type D Basic l/d = 26 N/A
Scheme 2 Basic l/d = 7 N/A
Scheme 3 Basic l/d = 20 N/A
Multiplier C1,span more or less than 10m 1.00
Modification factor for tension C2
M/bd2 2.07 N/mm
2
Scheme 1 M/bd2 = M sag /bd s
2 2.07 N/mm2
Scheme 2 M/bd2 = M hog /bd h
2 N/A N/mm2
Scheme 3 M/bd2 = M sag /bd s
2 N/A N/mm2
(bb=1.0) 231 N/mm2
Scheme 1 As,req/As,provsag 0.75
Scheme 2 As,req/As,provhog N/A
Scheme 3 As,req/As,provsag N/A
Modification 1.24
Modification factor for tension C3 = 1.15 if stair flight L occupies ≥ 60% of Leff 1.00 Note
Modified span / effective depth ratio criteria 28.5
Deflection utilisation 108% NOT OK
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Scheme Design
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Typical Initial Span / Effective Depth Ratios
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Standard Critical Dimensions Details
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The rise should not be more than 220mm and the going (tread less nosing) no less than 220mm. The
pitch should be no steeper than 42 degrees so the minimum going cannot be used with the maximum
rise. A good guide is that twice the rise plus the going (2R+G) should be between 550mm and 700mm.
The width of the stair should not be less than 600mm if leading to one room or 800mm if leading to two rooms. The clear headroom of at least 2m should be provided. Handrails should be 900mm
above the pitch line minimum. Landings are required at the top and bottom of each flight. They should
be at least as wide and long as the stair width.
Job No. Sheet No. Rev.
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Standard Insitu Concrete Staircase Reinforcement Details (Scheme 1)
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Standard Insitu Concrete Staircase Reinforcement Details (Scheme 2)
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Standard Insitu Concrete Staircase Details
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Standard Precast Concrete Staircase Details
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Standard Construction Method Details
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