CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 1 Material Properties Characteristic strength of concrete, f cu ( 60N/mm 2 ; HSC N/A) 25 N/mm 2 OK Yield strength of longitudinal steel, f y 460 N/mm 2 Yield strength of shear link steel, f yv 460 N/mm 2 Type of concrete and density, ρ c 24 kn/m 3 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), l b,1 0.150 m Breadth of supporting member at the other end (applicable to scheme 1 only) 0.150 m Stair Parameters Bottom landing Top landing Point A Point B Structural Landing 150 mm thick 150 mm thick 0 mm to the left 0 mm to the left g h r Point A L Point B Structural Landing H 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. 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, θ (<=42 ) 32.5 degrees OK Rise of stair, H 1.750 m Number of risers, N riser 10 Height of riser, r = H/N riser (<=r max ) 175 mm OK Number of goings, N going = N riser + No. of offset goings 12 Length of going, g = r/tanθ (>=g min ) 275 mm OK Span of stair, L = N going.g 3.300 m Effective span of stair (applicable to scheme 1 only), L eff = L+0.5(MIN(l b1,1.8m 3.450 m Stair flight L occupies at least 60% of stair effective span L eff (applicable to sch Yes Parameter 2r+g (>=550mm, <=700mm) 625 mm OK Slope length of stair, q = (L 2 +H 2 ) 3.735 m Depth of waist, h 150 mm Width of stair, b 1.200 m
E N G I N E E R S Consulting Engineers jxxx 2 Member Design - RC Staircase XX 19-08-15 Cover to all reinforcement, cover (usually MAX(25, φ) internal; 40 external) Effective depth to sagging steel, d s Scheme 1 d s = h - cover - φ s /2 Scheme 2 d s = (r.l/ q + h - cover - φ s /2)/2 Scheme 3 d s = (r.l/ q + h - cover - φ s /2)/2 Effective depth to hogging steel, d h Scheme 1 d h = h - cover - φ h /2 Scheme 2 d h = h. q/l + r/2 - cover - φ h /2 Scheme 3 d h = h. q/l + r/2 - cover - φ h /2 25 mm 119 mm 119 mm N/A mm N/A mm 119 mm 119 mm N/A mm N/A mm Sagging steel reinforcement diameter, φ s Sagging steel reinforcement pitch, p s 12 mm 175 mm Sagging steel area provided, A s,prov,s = (π.φ 2 s /4)/p s 646 mm 2 /m Hogging steel reinforcement diameter, φ h 12 mm Hogging steel reinforcement pitch, p h 175 mm Hogging steel area provided, A s,prov,h = (π.φ h 2 /4)/p h 646 mm 2 /m Shear link diameter, φ link 0 mm Number of links per metre, n link 4 /m Area provided by all links per metre, A sv,prov = n link.π.φ 2 link /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.ρ c + g.(h/2)/q.ρ c 5.15 kpa ULS stair loading (on slope) excluding SDL elev,stair, ω ULS,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), SDL elev,stair 0.00 kn/m
CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 3 Utilisation Summary Item UT Remark Sag moment, M s 79% OK Hog moment, M h 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 OK % Sagging reinforcement 0.43 % % Hogging reinforcement 0.43 % Estimated steel reinforcement quantity (130 220kg/m 3 ) 68 kg/m 3 [ 7.850. (A s,prov,s /scheme(h)+a s,prov,h /scheme(h)) ]; No curtailment; No laps; Links ignored; Distrib Estimated steel reinforcement quantity (130 220kg/m 3 ) 108 kg/m 3 IStructE [ 12.5. (A s,prov,s /scheme(h)+a s,prov,h /scheme(h)) ]; No curtailment; No laps; Links ignored; Distribu [Note that steel quantity in kg/m 3 can be obtained from 125.0 x % rebar]; Material cost: concrete, c 180 units/m 3 steel, s 4500 units/tonne Reinforced concrete material cost = [c+(est. rebar quant).s].schem 100 units/m 2 ULS Loading on Supporting Structure Line shear on supporting structure, R V = V 26 kn/m Line moment on supporting structure, R M = M hog 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 Height of riser, r Length of going, g Parameter 2r+g OK OK OK OK
CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 4 Structural Analysis Stair Sag moment, M sag 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 = 0.125 ω ULS,stair,noSDLelev.b 2 N/A knm/m Hog moment, M hog 12 knm/m Scheme 1 Insitu M hog = 0.0625( ω ULS,stair,noSDLelev +1.4SDL elev,s 12 knm/m Precast M hog = 0.0 N/A knm/m Scheme 2 M hog = 0.5 ω ULS,stair,noSDLelev.b 2 +1.4SDL elev,stair.b N/A knm/m Scheme 3 M hog = 0.0625 ω ULS,stair,noSDLelev.b 2 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 = 0.5 ω 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 ution steel igscheme 2 A = 0.0 N/A kn/m Scheme 3 A = 0.0 N/A kn/m
E N G I N E E R S Consulting Engineers jxxx 5 Stair Moment Design Sag moment, M sag Hog moment, M hog 24 knm/m 12 knm/m Ensure singly reinforced z <=0.95d K' K z A s A s,prov UT Sag moment, M sag 0.156 0.069 109 511 646 79% OK Hog moment, M hog 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 mm 2 /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, v ult =V/bd h (< 0.8f cu 0.5 & 5N/mm 2 ) 0.22 N/mm 2 Ultimate shear stress utilisation 5% OK Design shear stress, v d =V/bd h 0.22 N/mm 2 (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, A s,prov,h 646 mm 2 /m ρ w = 100A s,prov,h /bd h 0.54 % v c = (0.79/1.25)(ρ w f cu /25) 1/3 (400/d h ) 1/4 ; ρ w <3; f cu <40; (400/d h ) 1/4 >0.67 0.70 N/mm 2 Check v d < v c for no links Concrete shear capacity v c.(bd h ) VALID 83 kn/m Check v c < v d < 0.4 + v c for nominal links Provide nominal links such that A sv / S > 0.4b/(0.95f yv ) i.e. A sv / S Concrete and nominal links shear capacity (0.4 + v c ).(bd h ) N/A 0.92 mm 2 /mm/m 131 kn/m Check v d > 0.4 + v c for design links Provide shear links A sv / S > b(v d -v c )/(0.95f yv ) i.e. A sv / S > Concrete and design links shear capacity (A sv,prov /S).(0.95f yv ).d h + N/A 0.92 mm 2 /mm/m 83 kn/m Area provided by all links per metre, A sv,prov 0 mm 2 /m Tried A sv,prov / S value 0.00 mm 2 /mm/m Design shear resistance utilisation 31% OK
CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 6 Detailing Requirements All detailing requirements met? OK Max sagging steel reinforcement pitch (<3d s, <750mm) 175 mm OK Max hogging steel reinforcement pitch (<3d h, <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+φ s, >100mm+φ s if T40) 175 mm OK Min hogging steel reinforcement pitch (>75mm+φ h, >100mm+φ h 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, φ s (>=10mm) 12 mm OK Hogging steel reinforcement diameter, φ h (>=10mm) 12 mm OK
CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 7 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 C 1,span more or less than 10m 1.00 Modification factor for tension C 2 M/bd 2 1.72 N/mm 2 Scheme 1 M/bd 2 2 = M sag /bd s 1.72 N/mm 2 Scheme 2 M/bd 2 2 = M hog /bd h N/A N/mm 2 Scheme 3 M/bd 2 2 = M sag /bd s N/A N/mm 2 (β b =1.0) 243 N/mm 2 Scheme 1 A s,req /A s,prov sag 0.79 Scheme 2 A s,req /A s,prov hog N/A Scheme 3 A s,req /A s,prov sag N/A Modification 1.30 Modification factor for tension C 3 = 1.15 if stair flight L occupies at least 60% 1.15 Modified span / effective depth ratio criteria 29.8 Deflection utilisation 97% OK
E N G I N E E R S Consulting Engineers jxxx 8 Scheme Design
CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 9 Typical Initial Span / Effective Depth Ratios
E N G I N E E R S Consulting Engineers jxxx 10 Standard Critical Dimensions Details 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.
E N G I N E E R S Consulting Engineers jxxx 11 Member Design - RC Staircase XX 19-08-15
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E N G I N E E R S Consulting Engineers jxxx 13 Standard Insitu Concrete Staircase Reinforcement Details (Scheme 1)
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E N G I N E E R S Consulting Engineers jxxx 15 Member Design - RC Staircase XX 19-08-15 Standard Insitu Concrete Staircase Reinforcement Details (Scheme 2)
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E N G I N E E R S Consulting Engineers jxxx 17 Standard Insitu Concrete Staircase Details
E N G I N E E R S Consulting Engineers jxxx 18 Member Design - RC Staircase XX 19-08-15
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E N G I N E E R S Consulting Engineers jxxx 21 Standard Precast Concrete Staircase Details
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E N G I N E E R S Consulting Engineers jxxx 27 Standard Construction Method Details