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Job Title

XX

Material Properties

Characteristic strength of concrete, fcu (≤ 60N/mm2; HSC N/A) 25 N/mm2 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, ρc 24 kN/m3

Stair Structural Scheme

Stair structural scheme

Scheme 1 Stair spanning longitudinally simply supported with SDL on elevation over width b

Scheme 2 Stair spanning horizontally cantilever with SDL on elevation at free end

Scheme 3 Stair spanning horizontally simply supported without SDL on elevation

Insitu (landing starters) or precast (mid section shear connection) (applicable to scheme 1 only)

Breadth of supporting member at one end (applicable to scheme 1 only), lb,1 0.150 m

Breadth of supporting member at the other end (applicable to scheme 1 only), l 0.150 m

Stair Parameters

Bottom landing 150 mm thick

Top landing 150 mm thick

Point A 0 mm to the left

Point B 0 mm to the left

Use of stair

rmax gmin

Private stair 220 220 mm

Institutional and assembly stair 180 280 mm

Other stair 190 250 mm

Slope angle of stair, θ (<=42°) 32.5 degrees OK

Rise of stair, H 1.750 m

Number of risers, Nriser 10

Height of riser, r = H/Nriser (<=rmax) 175 mm OK

Number of goings, Ngoing = Nriser + No. of offset goings 12

Length of going, g = r/tanθ (>=gmin) 275 mm OK

Span of stair, L = Ngoing.g 3.300 m

Effective span of stair (applicable to scheme 1 only), Leff = L+0.5(MIN(lb1,1.8m)+MIN(l3.450 m

Stair flight L occupies at least 60% of stair effective span Leff (applicable to scheme 1 only) ?Yes

Parameter 2r+g (>=550mm, <=700mm) 625 mm OK

Slope length of stair, q = √(L2+H2) 3.735 m

Depth of waist, h 150 mm

Width of stair, b 1.200 m

Member Design - RC Staircase 19-08-15

Engineering Calculation Sheet Consulting Engineers jXXX 1

Member Design - Reinforced Concrete Staircase BS8110 v2015.01.xlsx

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L

Hr

gh

Structural Landing

Structural Landing

Point A

Point B

The start of a flight (firstrise) and the end of theprevious flight (lastgoing) may be set outstaggered by:-1. 0 going2. 1 going3. 2 goingsThis merely increases thestair flight span by theabove goings.


Job Title

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Cover to all reinforcement, cover (usually MAX(25, φ) internal; 40 external) 25 mm

Effective depth to sagging steel, ds 119 mm

Scheme 1 d s = h - cover - φ s /2 119 mm

Scheme 2 d s = (r.L/ q + h - cover - φ s /2)/2 N/A mm

Scheme 3 d s = (r.L/ q + h - cover - φ s /2)/2 N/A mm

Effective depth to hogging steel, dh 119 mm

Scheme 1 d h = h - cover - φ h /2 119 mm

Scheme 2 d h = h. q/L + r/2 - cover - φ h /2 N/A mm

Scheme 3 d h = h. q/L + r/2 - cover - φ h /2 N/A mm

Sagging steel reinforcement diameter, φs 12 mm

Sagging steel reinforcement pitch, ps 175 mm

Sagging steel area provided, As,prov,s = (π.φs2/4)/ps 646 mm2/m

Hogging steel reinforcement diameter, φh 12 mm

Hogging steel reinforcement pitch, ph 175 mm

Hogging steel area provided, As,prov,h = (π.φh2/4)/ph 646 mm2/m

Shear link diameter, φlink 0 mm

Number of links per metre, nlink 4 /m

Area provided by all links per metre, Asv,prov = nlink.π.φlink2/4 0 mm2/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.ρc + g.(H/2)/q.ρc 5.15 kPa

ULS stair loading (on slope) excluding SDLelev,stair, ωULS,stair,noSDLelev 15.13 kPa

ω 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 0.00 kN/m

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Member Design - Reinforced Concrete Staircase BS8110 v2015.01.xlsxMade by Date Chd.

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Job Title

XX

Utilisation Summary

Item UT Remark

Sag moment, Ms 79% OK

Hog moment, Mh 38% OK

% Min sag reinforcement 30% OK

% Min hog reinforcement 30% OK

Ultimate shear stress 5% OK

Shear design capacity 31% OK

Deflection utilisation 97% OK

Total utilisation 97% OK

Detailing requirements

% Sagging reinforcement 0.43 %

% Hogging reinforcement 0.43 %

Estimated steel reinforcement quantity (130 − 220kg/m3) 68 kg/m3

[ 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) 108 kg/m3 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)100 units/m2

ULS Loading on Supporting Structure

Line shear on supporting structure, RV = V 26 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, θ OK

Height of riser, r OK

Length of going, g OK

Parameter 2r+g OK

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Member Design - RC Staircase 19-08-15Made by Date Chd.

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Structural Analysis Stair

Sag moment, Msag 24 kNm/m

Scheme 1 M sag = 0.125(ω ULS,stair,noSDLelev+1.4SDL elev,stair /b).q.L eff 24 kNm/m

Scheme 2 M sag = 0.0 N/A kNm/m

Scheme 3 M sag = 0.125ω ULS,stair,noSDLelev .b2 N/A kNm/m

Hog moment, Mhog 12 kNm/m

Scheme 1 Insitu M hog = 0.0625(ω ULS,stair,noSDLelev+1.4SDL elev,stair 12 kNm/m

Precast M hog = 0.0 N/A kNm/m

Scheme 2 M hog = 0.5ω ULS,stair,noSDLelev .b2+1.4SDL elev,stair .b N/A kNm/m

Scheme 3 M hog = 0.0625ω ULS,stair,noSDLelev .b2 N/A kNm/m

Shear, V 26 kN/m

Scheme 1 V = 0.5(ω ULS,stair,noSDLelev+1.4SDL elev,stair /b).L eff 26 kN/m

Scheme 2 V = ω ULS,stair,noSDLelev .b+1.4SDL elev,stair N/A kN/m

Scheme 3 V = 0.5ω 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 13 kN/m

Scheme 1 A = ±0.5(ω ULS,stair,noSDLelev+1.4SDL elev,stair /b).H 13 kN/m

/scheme(h)) ]; No curtailment; No laps; Links ignored; Distribution steel ignored;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 24 kNm/m

Hog moment, Mhog 12 kNm/m

Ensure singly reinforced

K' K z As As,prov UT

Sag moment, Msag 0.156 0.069 109 511 646 79% OK

Hog moment, Mhog 0.156 0.034 113 247 646 38% OK

Note β 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) 0.43 %

Scheme 1 h = h 150 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 30% OK

% Min hog reinforcement (>= 0.0024bh G250; >= 0.0013bh G460) 0.43 %

Scheme 1 h = h 150 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 30% OK

Stair Shear Design

Ultimate shear stress, vult=V/bdh (< 0.8fcu0.5 & 5N/mm2) 0.22 N/mm2

Ultimate shear stress utilisation 5% OK

Design shear stress, vd=V/bdh 0.22 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,h 646 mm2/m

ρw = 100As,prov,h/bdh 0.54 %

vc = (0.79/1.25)(ρwfcu/25)1/3(400/dh)

1/4; ρw<3; fcu<40; (400/dh)1/4>0.67 0.70 N/mm2

Check vd < vc for no links VALID

Concrete shear capacity vc.(bdh) 83 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) 131 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 + v 83 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 31% OK

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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+φs, >100mm+φs if T40) 175 mm OK

Min hogging steel reinforcement pitch (>75mm+φh, >100mm+φh 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) 0.43 % OK

% Max hogging reinforcement (<= 0.04bh) 0.43 % OK

Sagging steel reinforcement diameter, φs (>=10mm) 12 mm OK

Hogging steel reinforcement diameter, φh (>=10mm) 12 mm OK

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Deflection Criteria

Span, l 3.450 m

Scheme 1 l = L eff 3.450 m

Scheme 2 l = b N/A m

Scheme 3 l = b N/A m

Span, l / effective depth, d ratio 29.0

Scheme 1 l/d = l/d s 29.0

Scheme 2 l/d = l/d h N/A

Scheme 3 l/d = l/d s N/A

Basic span / effective depth ratio criteria 20.0

Scheme 1 Basic l/d = 20 20.0

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 1.72 N/mm2

Scheme 1 M/bd2 = M sag /bd s

2 1.72 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

(βb=1.0) 243 N/mm2

Scheme 1 As,req/As,provsag 0.79

Scheme 2 As,req/As,provhog N/A

Scheme 3 As,req/As,provsag N/A

Modification 1.30

Modification factor for tension C3 = 1.15 if stair flight L occupies at least 60% of stair effective span Leff (applicable to scheme 1 only) 1.15

Modified span / effective depth ratio criteria 29.8

Deflection utilisation 97% 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. Thepitch should be no steeper than 42 degrees so the minimum going cannot be used with the maximumrise. 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 totwo rooms. The clear headroom of at least 2m should be provided. Handrails should be 900mmabove the pitch line minimum. Landings are required at the top and bottom of each flight. They shouldbe at least as wide and long as the stair width.


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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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