member design reinforced concrete staircase bs8110 v2015 01

7/23/2019 Member Design Reinforced Concrete Staircase Bs8110 v2015 01

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Job No. Sheet No. Rev.

Job Title

XX

Material Properties

Characteristic strength of concrete, fcu( 60N/mm2

; HSC N/A) 25 N/mm2

OKYield strength of longitudinal steel, fy 460 N/mm

2

Yield strength of shear link steel, fyv 460 N/mm2

Type of concrete and density, c 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 mBreadth of supporting member at the other end (applicable to scheme 1 only) 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 g min

Private stair 220 220 mm

Institutional and assembly stair 180 280 mm

Other stair 190 250 mm

Slope angle of stair, (=550mm,


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Cover to all reinforcement, cover (usually MAX(25, ) internal; 40 external) 25 mmEffective depth to sagging steel, ds 119 mm

Scheme 1 ds = h - cover - s/2 119 mm

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

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

Effective depth to hogging steel, dh 119 mm

Scheme 1 dh = h - cover - h/2 119 mm

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

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

Sagging steel reinforcement diameter, s 12 mm

Sagging steel reinforcement pitch, ps 175 mm

Sagging steel area provided, As,prov,s= (.s2

/4)/ps 646 mm2

/mHogging steel reinforcement diameter, h 12 mm

Hogging steel reinforcement pitch, ph 175 mm

Hogging steel area provided, As,prov,h= (.h2/4)/ph 646 mm

2/m

Shear link diameter, link 0 mm

Number of links per metre, nlink 4/m

Area provided by all links per metre, Asv,prov= nlink..link2/4 0 mm2/m

Pitch of links, S 200 mm

Stair Loading (Slope Loading)

Live load, LL 4.00 kPaSuperimposed dead load, SDL 1.20 kPa

Dead load of stair (on slope), DL = h.c+ g.(H/2)/q.c 5.15 kPa

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

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 - RC Staircase

Engineering Calculation SheetConsulting Engineers

19-08-15

Member Design - Reinforced Concrete Staircase BS811Made by Date Chd.

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Job Title

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Utilisation Summary

Item UT RemarkSag 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)+As,prov,h/scheme(h)) ]; No curtailment; No laps; Links ignored; Distrib

Estimated steel reinforcement quantity (130 220kg/m3) 108 kg/m3 IStructE

[ 12.5 . (A s,prov,s/scheme(h)+As,prov,h/scheme(h)) ]; No curtailment; No laps; Links ignored; Distrib

[Note that steel quantity in kg/m3can 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].sche 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/mNote that for scheme 1, R Vis conservatively calculated based on L effinstead of L.

Geometrical Requirements

All geometrical requirements satisfied ? OK

Slope angle of stair, OK

Height of riser, r OK

Length of going, g OK

Parameter 2r+g OK

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Engineering Calculation SheetConsulting Engineers jXXX 3

OK

Member Design - Reinforced Concrete Staircase BS811

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

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Structural Analysis Stair

Sag moment, Msag 24 kNm/mScheme 1 Msag = 0.125(ULS,stair,noSDLelev+1.4SDL elev,stair/b).q.L eff 24 kNm/m

Scheme 2 Msag = 0.0 N/A kNm/m

Scheme 3 Msag = 0.125ULS,stair,noSDLelev.b2 N/A kNm/m

Hog moment, Mhog 12 kNm/m

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

Precast Mhog = 0.0 N/A kNm/m

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

Scheme 3 Mhog = 0.0625ULS,stair,noSDLelev.b2 N/A kNm/m

Shear, V 26 kN/m

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

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

Scheme 3 V = 0.5ULS,stair,noSDLelev.b N/A kN/mNote 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(ULS,stair,noSDLelev+1.4SDL elev,stair/b).H 13 kN/m

tion steel iScheme 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/mHog 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 b = 1.00 and K' = 0.156. If K > K', then UT = 999%.

Note that A s and A s,provabove 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 eithercalculating vdat d from support and

comparing against unenhanced vcas clause 3.4.5.10 BS8110 orcalculating vdat support and

comparing against enhanced vcwithin 2d of the support as clause 3.4.5.8 BS8110 ignored;)

Area of tensile steel reinforcement provided, As,prov,h 646 mm2/m

w= 100As,prov,h/bdh 0.54 %

vc= (0.79/1.25)(wfcu/25)1/3(400/dh)

1/4; w 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 + vcfor 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+ 83 kN/m

Area provided by all links per metre, Asv,prov 0 mm2/m

Tried Asv,prov/ S value 0.00 mm2/mm/mDesign shear resistance utilisation 31% OK

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Detailing Requirements

All detailing requirements met ? OK

Max sagging steel reinforcement pitch (100mm+hif 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 (=10mm) 12 mm OK

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Deflection Criteria

Span, l 3.450 mScheme 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/ds 29.0

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

Scheme 3 l/d = l/ds 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/AMultiplier C1,span more or less than 10m 1.00

Modification factor for tension C2

M/bd2 1.72 N/mm2

Scheme 1 M/bd2= Msag/bds

2 1.72 N/mm2

Scheme 2 M/bd2= Mhog/bdh

2 N/A N/mm2

Scheme 3 M/bd2= Msag/bds

2 N/A N/mm2

(b=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% 1.15

Modified span / effective depth ratio criteria 29.8

Deflection utilisation 97% OK

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Engineering Calculation SheetConsulting Engineers jXXX



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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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Theriseshould not be more than 220mm and the going(tread less nosing) no less than 220mm. Thepitchshould 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 stairshould not be less than 600mm if leading to one room or 800mm if leading to

two rooms. The clear headroomof at least 2m should be provided. Handrailsshould be 900mmabove the pitch line minimum. Landingsare 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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19-08-15Member Design - RC Staircase

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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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Job Title

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Standard Precast Concrete Staircase Details

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XXMember Design - RC Staircase 19-08-15


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CONSULTING

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Standard Construction Method Details

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member design reinforced concrete staircase bs8110 v2015 01

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