Job No. Sheet No. Rev. CONSULTING Engineering Calculation Sheet. Structure, Member Design - Geotechnics Pad, Strip and Raft XX

Transcription

1 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 ) 35 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 Factor of Safety Factor of safety (overall net (effective) bearing), FOS 1 (usually 2.5 to 3.0) 3.0 Factor of safety (overall sliding resistance), FOS 2 (usually 1.6) 1.6 Factor of safety (overall uplift resistance), FOS 3 (usually 1.0) 1.0 Factor of safety (overall overturning resistance), FOS 4 (usually 1.6) 1.6 Loading factor, K (between 1.40 and 1.60 depending on DL to LL ratio) 1.50 BS8110 Note loading factor K multiplies SLS loads for ULS loads for section (reinforcement) design; cl Soil Description Water unit weight, γ w = 9.81kN/m kn/m 3 Soil name Dry bulk unit weight, γ dry 18.0 kn/m 3 Saturated bulk unit weight, γ sat 20.5 kn/m 3 Undrained shear strength limit to adopt? Undrained shear strength (lower limit), S u,ll Undrained shear strength (upper limit), S u,ul Undrained shear strength limit adopted, S u = {S u,ll, (S u,ll +S u,ul )/2, S u,ul } Note that S u can be obtained from SPT (Stroud) values; kpa kpa kpa Tomlinson Effective cohesion, c' 0.0 kpa Effective angle of shear resistance, φ' 35.0 degrees Note that φ ' can be obtained from SPT (Peck) or CPT (Durgunoglu and Mitchell) values; Effective angle of friction on base, δ' 23.1 degrees Tomlinson Bearing capacity limit to adopt? Bearing capacity values from allowable bearing capacity, BC ll,a/ul,a values or SPT, N values? Factor for SPT, N value, K SPT 30.0 Bearing capacity (lower limit), FOS 1.BC ll,a kpa SPT (lower limit), N ll 4 Bearing capacity (upper limit), FOS 1.BC ul,a kpa SPT (upper limit), N ul 10 Note that FOS 1 is multipled onto the allowable bearing capacity, BC ll,a/ul,a at this stage because it will be refactored when the empirical overall net effective bearing capacity is calculated; Ground water level modification for bearing capacity, MOD BC 1.00 BS5975 Bearing capacity adopted, BC 300 kpa Note BC = MOD BC. [FOS 1.{BC ll,a, (BC ll,a +BC ul,a )/2, BC ul,a } or {K SPT.N ll, K SPT.(N ll +N ul )/2, K SPT.N ul }];

2 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 2 Analysis Method Undrained, drained or empirical analysis? For clays, perform undrained, drained and empirical analyses; For sands / gravels, perform drained and empirical analyses; For rocks, perform drained and empirical analyses; Evaluate overall uplift resistance? Note that overall uplift resistance (mid third) is conservative to overturning, thus may in certain instances be deemed to be overconservative and subsequently ignored; Foundation Dimensions 1 Foundation type D z u Depth of foundation founding level from ground level, D (>= 0.000m) m OK Depth of water table from ground level, z u m Note that the soil beneath the water table has an effective submerged unit weight of about half of the soil above the water table, thus reducing the drained overall net effective bearing capacity; Hence use the highest water table forseeable; Enter a negative z u value for water table above ground level, this representing a flood event or a bridge pier within a sea or river with the ground level being the sea or river bed; However, a water table above ground level may unconservatively decrease the overall (effective) bearing capacity utilisation, thus consider also the case when the water table is at ground level; Foundation Reinforcement Cover to all (bottom and side) reinforcement, cover 1 (usually 75) Cover to all (top) reinforcement, cover 2 (usually 45) 50 mm 25 mm Foundation SLS Loading Surcharge at surface, p surface 0 kpa Note that (unlike retaining walls) surface surcharging increases overall (effective) bearing capacity, thus consider the case when there is no surcharge unless it can be guaranteed; Consider reduction of working pressure due to surcharge above founding level, p 0 or p 0 ' in net (effective) working pressure, q wnet or q wnet '? Note that for the case where an excavation and backfill (embedded footing) takes place prior to application of working pressure at the founding level: - i. include additional soil (above footing) weight, F above,soil ii. do consider reduction of working pressure due to p 0 or p 0 ' in q wnet or q wnet ' Note that for the case where an excavation without backfill takes place prior to application of working pressure at the founding level: - i. do not include additional soil (above footing) weight, F above,soil ii. do consider reduction of working pressure due to p 0 or p 0 ' in q wnet or q wnet ' Note that for the case where an excavation had already taken place in the past prior to application of working pressure at the founding level: - i. do not include additional soil (above footing) weight, F above,soil ii. do not consider reduction of working pressure due to p 0 or p 0 ' in q wnet or q wnet '

3 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 3 Executive Summary Undrained overall net bearing capacity Drained overall net effective bearing capacity Empirical overall net effective bearing capacity 91% OK Overall sliding resistance capacity 0% OK Overall uplift resistance capacity Overall overturning resistance capacity 0% OK Pad Footing Sagging bending moment in plane of width 5% OK Sagging bending moment in plane of length 10% OK % Min sag reinforcement in plane of width 34% OK % Min sag reinforcement in plane of length 34% OK Punching shear at column base face 12% OK Punching shear at first shear perimeter 14% OK Punching shear at second shear perimeter 0% OK Ultimate shear stress for bending in plane of width 4% OK Shear design capacity for bending in plane of width 7% OK Ultimate shear stress for bending in plane of length 5% OK Shear design capacity for bending in plane of length 14% OK Detailing requirements NOT OK Strip Footing Sagging bending moment % Min sag reinforcement Ultimate shear stress Shear design capacity Detailing requirements Multi Column Footing Sagging bending moment in plane of width Sagging bending moment in plane of length Hogging bending moment in plane of length % Min sag reinforcement in plane of width % Min sag reinforcement in plane of length % Min hog reinforcement in plane of length Punching shear at column base face Punching shear at first shear perimeter Punching shear at second shear perimeter Ultimate shear stress for bending in plane of width Shear design capacity for bending in plane of width Ultimate shear stress for bending in plane of length Shear design capacity for bending in plane of length Detailing requirements

4 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 4 Combined Footing Sagging bending moment in plane of width Sagging bending moment in plane of length Hogging bending moment in plane of length % Min sag reinforcement in plane of width % Min sag reinforcement in plane of length % Min hog reinforcement in plane of length Punching shear at column base face Punching shear at first shear perimeter Punching shear at second shear perimeter Ultimate shear stress for bending in plane of width Shear design capacity for bending in plane of width Ultimate shear stress for bending in plane of length Shear design capacity for bending in plane of length Detailing requirements Strap Footing Sagging bending moment in plane of width of outer foo Hogging bending moment in beam % Min sag reinforcement in plane of width of outer foot % Min hog reinforcement in beam Punching shear at column base face Punching shear at first shear perimeter Punching shear at second shear perimeter Ultimate shear stress for bending in plane of width of o Shear design capacity for bending in plane of width of o Ultimate shear stress in beam Shear design capacity in beam Detailing requirements Raft Design reinforcement based on the combination of multi column footings, combined Overall utilisation summary 91% % Sagging reinforcement in plane of width 0.38 % % Sagging reinforcement in plane of length 0.38 % % Hogging reinforcement in plane of length (or in beam for strap footing) % Estimated steel reinforcement quantity (60 70kg/m 3 ) 59 kg/m 3 [Note that steel quantity in kg/m 3 can be obtained from 78.5 x % rebar]; Material cost: concrete, c 260 units/m 3 steel, s 3200 units/tonne Reinforced concrete material cost = c+(est. rebar quant).s 449 units/m 3

5 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 5 Relevant Foundation Parameters Relevant foundation type Pad Footing Overall (Effective) Bearing Capacity and Overall Sliding Resistance Capacity B (m) L (m) B' (m) L' (m) Pad Footing B pad L pad B pad ' L pad ' Strip Footing B strip infinity B strip ' infinity Multi Column Footin B multi L multi B multi L multi Combined Footing B com L com B com L com Strap Footing B strap,1 L strap,1 B strap,1 L strap,1 Raft B raft L raft B raft L raft B L B' L' Gross working pressure, q w Note q w above is q w,1 for strap footing; 102 kpa Overall Sliding Resistance Capacity Vertical Load (kn or kn/m) Horizont al Load (kn or kn/m) Overall Uplift Resistance Capacity e B (m) e B,limit (m) e L (m) Pad Footing F pad,v ' 43 F pad,h Strip Footing F strip,v ' F strip,h Multi Column Footin Combined Footing Strap Footing e L,limit (m) Raft F v ' 43 F h Overall Overturning Resistance Capacity M ot,b M rt,b M ot,l M rt,l (knm or (knm or (knm or (knm or knm/m) knm/m) knm/m) knm/m) Pad Footing Strip Footing Multi Column Footin Combined Footing Strap Footing Raft

6 E N G I N E E R S Consulting Engineers jxxx 6 Structure, Member Design - Geotechnics Pad, Strip and Raft XX Undrained Overall Net Bearing Capacity Total surcharge above founding level, p 0 Case when (z u D) >= MAX (B, L) p 0 = p surface +γ dry.d Case when 0 < (z u D) < MAX (B, L) p 0 = p surface +γ dry.d Case when (z u D) = 0 p 0 = p surface +γ dry.d Case when (z u D) < 0 and z u >= 0 p 0 = p surface +γ sat.(d-z u )+γ dry.z u Case when z u < 0 p 0 = p surface +γ sat.d+γ w.(-z u ) kpa kpa kpa kpa kpa kpa Net bearing capacity, q fnet = q f - p 0 kpa Gross bearing capacity, q f = s c.d c.n c,strip.s u + p 0 kpa Terzaghi Shape factor, EC7 Depth factor, d c = 1+(0.053D/B') 0.5 for D/B' <= 4.0 Bearing capacity factor, N c,strip Skempton Net working pressure, q wnet = q w - (p 0 or 0) kpa Gross working pressure, q w kpa Note a negative q wnet indicates an excavation, the following analysis ascertains the susceptibility of the system to base heave instability, conservatively however ignoring the contribution of the shearing resistance of the soil interface above the founding level and any wall embedment below the founding level; Undrained overall net bearing capacity (factored), q fnet / FOS 1 kpa Undrained overall net bearing capacity utilisation = ABS (q wnet ) / (q fnet / FOS 1 Note an absolute function is applied to the above to present the susceptibility to base heave instability as well as the overall net bearing capacity;

7 E N G I N E E R S Consulting Engineers jxxx 7 Drained Overall Net Effective Bearing Capacity Effective surcharge above founding level, p 0 ' kpa Unit weight, γ' kn/m 3 Case when (z u D) >= MAX (B, L) p 0 ' = p surface +γ dry.d kpa γ' = γ dry kn/m 3 Case when 0 < (z u D) < MAX (B, L) p 0 ' = p surface +γ dry.d kpa γ' = z u /MAX(B,L). [γ dry - (γ sat - γ w )] + (γ sat - γ w ) kn/m 3 Case when (z u D) = 0 p 0 ' = p surface +γ dry.d kpa γ' = γ sat - γ w kn/m 3 Case when (z u D) < 0 and z u >= 0 p 0 ' = p surface +(γ sat -γ w ).(D-z u )+γ dry.z u kpa γ' = γ sat - γ w kn/m 3 Case when z u < 0 p 0 ' = p surface +γ sat.d+γ w.(-z u )-γ w.(d+(-z u )) kpa Note that the above equation reduces to p 0 ' = p surface +( γ sat - γ w ).D; γ' = γ sat - γ w kn/m 3 Net effective bearing capacity, q fnet ' = q f ' p 0 ' kpa Gross effective bearing capacity, q f ' kpa Terzaghi = s c.d c.n c,strip.c' kpa + s q.d q.n q,strip.p 0 ' kpa + s γ.d γ.n γ,strip.b'/2.γ' kpa Equations for bearing capacity factors Cohesion Factors Shape factor, EC7 Depth factor, Note B in the above equation is B'; Bearing capacity factor, N c,strip Soils N c,strip = (N q,strip -1).cotφ' EC7 (Prandtl Rocks N c,strip Kulhawy and Goo

8 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 8 Surcharge Factors Shape factor, EC7 Depth factor, d q Bearing capacity factor, N q,strip Soils EC7 (Reissne Rocks N q,strip Kulhawy and Goo Self Weight Factors Shape factor, EC7 Depth factor, Bearing capacity factor, N q,strip Soils N γ,strip = 2.0(N q,strip -1).tanφ' EC7 (Hansen Rocks N γ,strip Kulhawy and Goo Net effective working pressure, q wnet ' = q w ' (p 0 ' or 0) kpa Gross working pressure, q w kpa Water pressure at founding level, u = γ w. MAX (D z u, 0) kpa Gross effective working pressure, q w ' = q w - u kpa Note a negative q wnet ' indicates an excavation, the following analysis ascertains the susceptibility of the system to base heave instability, conservatively however ignoring the contribution of the shearing resistance of the soil interface above the founding level and any wall embedment below the founding level; Drained overall net effective bearing capacity (factored), q fnet ' / FOS 1 kpa Drained overall net effective bearing capacity utilisation = ABS (q wnet ') / (q fnet Note an absolute function is applied to the above to present the susceptibility to base heave instability as well as the overall net effective bearing capacity; odman

9 CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 9 Empirical Overall Net Effective Bearing Capacity Effective surcharge above founding level, p 0 ' Case when (z u D) >= MAX (B, L) p 0 ' = p surface +γ dry.d Case when 0 < (z u D) < MAX (B, L) p 0 ' = p surface +γ dry.d Invalid Invalid r) Case when (z u D) = 0 Valid 12 kpa kpa kpa odman p 0 ' = p surface +γ dry.d 12 kpa Case when (z u D) < 0 and z u >= 0 Invalid p 0 ' = p surface +(γ sat -γ w ).(D-z u )+γ dry.z u kpa Case when z u < 0 Invalid p 0 ' = p surface +γ sat.d+γ w.(-z u )-γ w.(d+(-z u )) kpa n) Note that the above equation reduces to p 0 ' = p surface +( γ sat - γ w ).D; odman Net effective bearing capacity, q fnet ' = q f ' p 0 ' Gross effective bearing capacity, q f ' = BC + p 0 ' 300 kpa 312 kpa Net effective working pressure, q wnet ' = q w ' (p 0 ' or 0) 91 kpa Gross working pressure, q w 102 kpa Water pressure at founding level, u = γ w. MAX (D z u, 0) 0 kpa Gross effective working pressure, q w ' = q w - u 102 kpa Note a negative q wnet ' indicates an excavation, the following analysis ascertains the susceptibility of the system to base heave instability, conservatively however ignoring the contribution of the shearing resistance of the soil interface above the founding level and any wall embedment below the founding level; Empirical overall net effective bearing capacity (factored), q fnet ' / FOS kpa Empirical overall net effective bearing capacity utilisation = ABS (q wnet ') / (q fn 91% OK Note an absolute function is applied to the above to present the susceptibility to base heave instability as well as the overall net effective bearing capacity;

10 E N G I N E E R S Consulting Engineers jxxx 10 Structure, Member Design - Geotechnics Pad, Strip and Raft XX Overall Sliding Resistance Capacity Note for simplicity, only frictional resistance capacity considered, passive resistance of soil in an embedded foundation not considered, arguably rightly so, however reference should be made to retaining wall analysis should this additional capacity be required and can be guaranteed; Dead load component of SLS vertical (downward) load, k SLStoDL 0.60 Note that the dead load component is applied to reduce the SLS vertical (downward) load to the dead vertical (downward) load, this required as the live load component cannot be guaranteed; Total foundation dead vertical load, k SLStoDL.F v ' 26 kn or kn/m Total foundation SLS horizontal load, F h 0 kn or kn/m Overall sliding resistance capacity (factored), F s,cap 7 kn or kn/m Undrained Analysis F s,cap = (B'.L').S u / FOS 2 kn or kn/mtomlinson Drained Analysis F s,cap = k SLStoDL.F v '.tanδ' / FOS 2 kn or kn/mtomlinson Empirical Analysis F s,cap = k SLStoDL.F v '.tanδ' / FOS 2 7 kn or kn/mtomlinson Overall sliding resistance capacity utilisation = F h / F s,cap 0% OK

11 E N G I N E E R S Consulting Engineers jxxx 11 Structure, Member Design - Geotechnics Pad, Strip and Raft XX Overall Uplift Resistance Capacity Overall uplift in width resistance capacity utilisation = e B / e B,limit Overall uplift in length resistance capacity utilisation = e L / e L,limit Overall uplift resistance capacity utilisation = MAX (e B / e B,limit, e L / e L,limit )

12 E N G I N E E R S Consulting Engineers jxxx 12 Overall Overturning Resistance Capacity Overall overturning in width resistance capacity utilisation = M ot,b / M rt,b 0% OK Overall overturning in length resistance capacity utilisation = M ot,l / M rt,l 0% OK Overall overturning resistance capacity utilisation = MAX (M ot,b / M rt,b, M ot,l / M 0% OK

13 Cell References concrete grade longitudinal reinforcement steel grade shear link reinforcement steel grade type of concrete 1 Normal Weight Light Weight soil name 36 undrained shear strength limit to adopt 1 Lower Limit Middle Limit Upper Limit ignore effective cohesion 2 Include Exclude effective angle of friction ø' (Cast in Place Concrete - Soil Interface) ø' (Precast Concrete - Soil Interface) ø' (Timber - Soil Interface) ø' (Rough Corrugated Steel - Soil Interface) ø' (Insitu Concrete Active Zone - Soil Interface) ø' (Smooth Coated Steel - Soil Interface) ø' (Insitu Concrete Passive Zone - Soil Interface) 0.50

14 E N G I N E E R S Consulting Engineers jxxx 13 Pad Footing Foundation Dimensions Width, B pad (<=L pad ) m OK Length, L pad (>=B pad ) m OK Thickness beneath base slab, t 1,pad m Thickness of base slab, t 2,pad (if no base slab, then enter 0.000m) m Thickness of foundation, T pad = t 1,pad + t 2,pad m Column base section type (for punching shear only) Column base location (for punching shear only) Column base depth, h (rectangular) or diameter, D (circular) 230 mm Column base width, b (rectangular) or (circular) 230 mm Note where applicable, it is assumed that h is in same plane as L pad and that the column base is always interior and located in the centre of the pad footing B pad and L pad ; Pad Footing Foundation Reinforcement Sagging in length Sagging in width Sagging steel reinforcement diameter in width, φ sx Sagging steel reinforcement pitch for resistance in width, p sx 12 mm 150 mm Sagging steel area provided in width, A s,prov,x,s = (π.φ 2 sx /4)/p sx 754 mm 2 /m Sagging steel reinforcement diameter in length, φ sy 12 mm Sagging steel reinforcement pitch for resistance in length, p sy 150 mm Sagging steel area provided in length, A s,prov,y,s = (π.φ sy 2 /4)/p sy 754 mm 2 /m Shear link diameter for first shear perimeter, φ link,2 0 mm Number of link legs for first shear perimeter, n l,2 30 Area provided by all links for first shear perimeter, A sv,prov,2 = n l,2.π.φ 2 link,2 /4 0 mm 2 Shear link diameter for second shear perimeter, φ link,3 0 mm Number of link legs for second shear perimeter, n l,3 30 Area provided by all links for second shear perimeter, A sv,prov,3 = n l,3.π.φ 2 link,3 /4 0 mm 2 Shear link diameter for bending in width, φ link,x = φ link,2 0 mm Number of link legs per metre for bending in width, n link,x 4 /m Area provided by all links per metre for bending in width, A sv,prov,x = n link,x.π.φ l 0 mm 2 /m Pitch of links for bending in width, S x 150 mm Shear link diameter for bending in length, φ link,y = φ link,2 0 mm Number of link legs per metre for bending in length, n link,y 4 /m Area provided by all links per metre for bending in length, A sv,prov,y = n link,y.π.φ 0 mm 2 /m Pitch of links for bending in length, S y 150 mm Effective depth to sagging steel in width, d x,s = T pad - cover 1 - MAX (φ link,2, φ link Effective depth to sagging steel in length, d y,s = T pad - cover 1 - MAX (φ link,2, φ lin It is assumed that sagging steel in length is exterior to sagging steel in width; 132 mm 144 mm Estimated steel reinforcement quantity 59 kg/m 3 [ (A s,prov,x,s +A s,prov,y,s ) / T pad ]; No curtailment; No laps; Links ignored;

15 E N G I N E E R S Consulting Engineers jxxx 14 Pad Footing Foundation SLS Loading SLS vertical (downward) load from column and base slab (if suspended), F col,v 36 kn OK Eccentricity of F col,v from centroid in width, e m Eccentricity of F col,v from centroid in length, e m SLS horizontal load from column in width, F col,h1 (defined to add to e 1 eccentr 0 kn SLS horizontal load from column in length, F col,h2 (defined to add to e 2 eccent 0 kn SLS moment from column in plane of width, M col,1 (defined to add to e 1 eccen 0 knm SLS moment from column in plane of length, M col,2 (defined to add to e 2 eccen 0 knm Note F col,h1/h2 and M col,1/2 are defined to add to the corresponding eccentricities, thus enter positive values; Pad footing (projection beneath base slab) weight, F under,pad = B pad.l pad.t 1,pad.ρ Additional soil (above footing) weight, F above,soil = B pad.l pad.max(0, D-t 1,pad ).γ sa 4 kn Note additional soil above the footing is included for embedded footings whereby the top of the footing is below ground level and backfilled, for conservatism the saturated soil density is adopted, and ρ c γ sat ; 2 kn Note that this has a stabilizing effect on footings subject to destabilizing moments, thus both inclusive and exclusive cases should be considered; Water pressure at founding level, u = γ w. MAX (D z u, 0) Water uplift force at founding level, F water = u.b pad.l pad Total foundation SLS vertical (downward) load, F pad,v = F col,v + F under,pad + F abo Total foundation SLS effective vertical (downward) load, F pad,v ' = F pad,v - F water Total foundation SLS horizontal load, F pad,h = (F 2 col,h1 + F 2 col,h2 ) kpa 0 kn 43 kn 43 kn 0 kn Equivalent eccentricity in width, e B = ABS(F col,v.e 1 + M col,1 + F col,h1.t pad ) / F pad, Limiting eccentricity for no overall uplift (factored), e B,limit = (B pad / 6) / FOS 3 Equivalent eccentricity in length, e L = ABS(F col,v.e 2 + M col,2 + F col,h2.t pad ) / F pad Limiting eccentricity for no overall uplift (factored), e L,limit = (L pad / 6) / FOS 3 ( m m m m Overturning moment in width, M ot,b = M col,1 + F col,h1.t pad Restoring moment in width, M rt,b = [F col,v.(b pad /2-e 1 ) + (F under,pad +F above,soil -F wa Overturning moment in length, M ot,l = M col,2 + F col,h2.t pad Restoring moment in length, M rt,l = [F col,v.(l pad /2-e 2 ) + (F under,pad +F above,soil -F wa 0 knm 7 knm 0 knm 10 knm

16 E N G I N E E R S Consulting Engineers jxxx 15 Structure, Member Design - Geotechnics Pad, Strip and Raft XX Maximum gross working pressure in width, q w1,b = F pad,v /(B pad.l pad ) + 6.(F col,v Minimum gross working pressure in width, q w2,b = F pad,v /(B pad.l pad ) 6.(F col,v.e Maximum gross working pressure in length, q w1,l = F pad,v /(B pad.l pad ) + 6.(F col,v Minimum gross working pressure in length, q w2,l = F pad,v /(B pad.l pad ) 6.(F col,v. Maximum gross working pressure in width, q w1,b = 2F pad,v /[3L pad.(b pad /2-e B )] Minimum gross working pressure in width, q w2,b = 0.0 Maximum gross working pressure in length, q w1,l = 2F pad,v /[3B pad.(l pad /2-e L )] Minimum gross working pressure in length, q w2,l = kpa 75 kpa 95 kpa 95 kpa kpa kpa kpa kpa Equivalent width, B pad ' = B pad 2e B Equivalent length, L pad ' = L pad 2e L Gross working pressure, q w = F pad,v / (B pad '. L pad ') m m 102 kpa Pad Footing Foundation ULS Loading ULS vertical (downward) load from column and base slab (if suspended), F col, 59 kn Note it is assumed that the ULS load acts at the same eccentricity as the SLS load; Note that this enhancement is required to cater for the moment as an enhanced load in the ULS design;

17 E N G I N E E R S Consulting Engineers jxxx 16 Structure, Member Design - Geotechnics Pad, Strip and Raft XX Pad Footing Foundation Reinforcement Design Gross ULS Pressure Gross ULS pressure, q w,uls = F col,v,uls / (B pad. L pad ) 131 kpa Shear force diagram Bending moment diagram Sagging Bending Moment Design in Plane of Width Moment at column base face, M x = q w,uls. L pad. [(B pad -(b or D))/2] 2 / 2 Moment at column base face per metre, M x /L pad 2 knm 2 knm/m 2 Concrete moment capacity per metre, M u,x = 0.156f cu.1000.d x,s 95 knm/m Bending stress, [M/bd 2 ] x = (M x /L pad ) / [(1000).d 2 x,s ] 0.13 N/mm 2 Bending stress ratio, K x = [M/bd 2 ] x / f cu <= OK Lever arm, z x = d x,s. [0.5 + (0.25-K x /0.9) 0.5 ] <= 0.95d x,s 125 mm Area of tension steel required, A s,x = (M x /L pad ) / [(0.95f y ).z x ] 41 mm 2 /m Area of tensile steel reinforcement provided, A s,prov,x,s 754 mm 2 /m Sagging bending moment in plane of width utilisation = A s,x / A s,prov,x,s 5% OK Requirement to concentrate 2/3 rebar within 1.5d x,s fro No [Yes if L pad /2>3/4(h or D)+9/4d x,s ; No if not;] mm mm BS8110 Note that should the above requirement be applicable, it is not automatically reflected in the detailing considerations and as such should be specifically reconsidered; % Min sag reinforcement in plane of width (>= T pad G250; >= % % Min sag reinforcement in plane of width utilisation 34% OK Sagging Bending Moment Design in Plane of Length Moment at column base face, M y = q w,uls. B pad. [(L pad -(h or D))/2] 2 / 2 Moment at column base face per metre, M y /B pad 3 knm 4 knm/m 2 Concrete moment capacity per metre, M u,y = 0.156f cu.1000.d y,s 113 knm/m Bending stress, [M/bd 2 ] y = (M y /B pad ) / [(1000).d 2 y,s ] 0.21 N/mm 2 Bending stress ratio, K y = [M/bd 2 ] y / f cu <= OK Lever arm, z y = d y,s. [0.5 + (0.25-K y /0.9) 0.5 ] <= 0.95d y,s 137 mm Area of tension steel required, A s,y = (M y /B pad ) / [(0.95f y ).z y ] 74 mm 2 /m Area of tensile steel reinforcement provided, A s,prov,y,s 754 mm 2 /m Sagging bending moment in plane of length utilisation = A s,y / A s,prov,y,s 10% OK Requirement to concentrate 2/3 rebar within 1.5d y,s fro No [Yes if B pad /2>3/4(b or D)+9/4d y,s ; No if not;] mm mm BS8110 Note that should the above requirement be applicable, it is not automatically reflected in the detailing considerations and as such should be specifically reconsidered; % Min sag reinforcement in plane of length (>= T pad G250; >= 0.38 % % Min sag reinforcement in plane of length utilisation 34% OK

18 E N G I N E E R S Consulting Engineers jxxx 17 Punching Shear Design ULS vertical (downward) load from column and base slab (if suspended), F col, 59 kn Area of column base section, A c1 = b.h (rectangular) or πd 2 /4 (circular) mm 2 Average effective depth of both rebar layers, d = (d x,s + d y,s )/2 138 mm Area of tensile steel reinforcement provided, A s,prov,x,s 754 mm 2 /m Area of tensile steel reinforcement provided, A s,prov,y,s 754 mm 2 /m Average area of tensile steel reinforcement provided, A s,prov,s 754 mm 2 /m ρ w = 100A s,prov,s /(1000.d) 0.55 % ν c = (0.79/1.25)(ρ w f cu /25) 1/3 (400/d) 1/4 ; ρ w <3; f cu <40; (400/d) 1/4 > N/mm 2 Column Base Face Perimeter Shear force at column base face, V 1 = F col,v,uls - q w,uls.a c1 52 kn Effective shear force, V eff,1 = V 1 52 kn Note V eff,1 = V 1 because moment effects have been accounted for in the derivation of F col,v,uls ; Column base face perimeter, u 1 Rectangular Circular 690 mm Internal column: 2.(b+h) 920 π.d mm Edge column: 2b+h or 2h+b 690 3/4( π.d) mm Corner column: (b+h) 460 π.d/2 mm Shear stress at column base face perimeter, ν 1 = V eff,1 / u 1 d (< 0.8f cu 0.5 & 5N 0.55 N/mm 2 Ultimate shear stress utilisation 12% OK First Shear Perimeter Shear force 1.5d from column base face, V 2 = F col,v,uls - q w,uls.a c2 Rectangular 22 kn Internal column: (b+3d).(h+3d) 0.41 (D+3d) 2 m 2 Edge column: (b+1.5d).(h+3d) or (h+1.5d).(b+3d) 0.28 d).(d+3d) m 2 Corner column: (b+1.5d).(h+1.5d) 0.19 (D+1.5d) 2 m 2 Effective shear force, V eff,2 = V 2 22 kn Note V eff,2 = V 2 because moment effects have been accounted for in the derivation of F col,v,uls ; Column base first perimeter, u 2 Rectangular Circular Circular 1518 mm Internal column: 2.(b+h)+12d D+12d mm Edge column: 2b+h+6d or 2h+b+6d D+6d mm Corner column: (b+h)+3d 874 2D+3d mm Shear stress at column base first perimeter, ν 2 = V eff,2 / u 2 d 0.11 N/mm 2 (Shear capacity enhancement by calculating v d at 1.5d from "support" and comparing against unenhanced v c as clause BS8110 employed instead of calculating v d at "support" and comparing against enhanced v c within 1.5d of the "support" as clause BS8110;) Case ν 2 < ν c No links required. Case ν c < ν 2 < 1.6ν c VALID >= mm 2 Note >

19 E N G I N E E R S Consulting Engineers jxxx 18 Case 1.6ν c < ν 2 < 2.0ν c >= mm 2 Case ν 2 > 2.0ν c Note > First shear perimeter shear utilisation 14% OK Second Shear Perimeter Shear force 2.25d from column base face, V 3 = F col,v,uls - q w,uls.a c3 Rectangular -1 kn Internal column: (b+4.5d).(h+4.5d) 0.72 (D+4.5d) 2 m 2 Edge column: (b+2.25d).(h+4.5d) or (h+2.25d).(b+4.5d) 0.46 ).(D+4.5d) m 2 Corner column: (b+2.25d).(h+2.25d) 0.29 D+2.25d) 2 m 2 Effective shear force, V eff,3 = V 3-1 kn Note V eff,3 = V 3 because moment effects have been accounted for in the derivation of F col,v,uls ; Column base second perimeter, u 3 Rectangular Circular Circular 1932 mm Internal column: 2.(b+h)+18d D+18d mm Edge column: 2b+h+9d or 2h+b+9d D+9d mm Corner column: (b+h)+4.5d D+4.5d mm Shear stress at column base second perimeter, ν 3 = V eff,3 / u 3 d 0.00 N/mm 2 Case ν 3 < ν c No links required. Case ν c < ν 3 < 1.6ν c VALID >= mm 2 Note > Case 1.6ν c < ν 3 < 2.0ν c >= mm 2 Case ν 3 > 2.0ν c Note > Second shear perimeter shear utilisation 0% OK Note a negative shear stress ν 2 and/or ν 3 on a correctly specified column (wrt internal, edge or corner) indicates that the shear perimeter is beyond the physical extremes of the foundation and as such punching shear failure is not critical;

20 E N G I N E E R S Consulting Engineers jxxx 19 Structure, Member Design - Geotechnics Pad, Strip and Raft XX Shear Design for Bending in Plane of Width Shear force at column base face, V x,ult = q w,uls. L pad. [(B pad -(b or D))/2] Shear force at column base face per metre, V x,ult /L pad Shear force at 1.0d x,s from column base face, V x = q w,uls. L pad. [(B pad -(b or D Shear force at 1.0d x,s from column base face per metre, V x /L pad Note the above shear forces are for bending in plane of width; 18 kn 24 kn/m 5 kn 7 kn/m Ultimate shear stress for bending in plane of width, v ult,x =(V x,ult /L pad )/(1000.d 0.18 N/mm 2 Ultimate shear stress for bending in plane of width utilisation 4% OK Design shear stress for bending in plane of width, v d,x =(V x /L pad )/(1000.d x,s ) 0.05 N/mm 2 (Shear capacity enhancement by calculating v d at d from "support" and comparing against unenhanced v c as clause BS8110 employed instead of calculating v d at "support" and comparing against enhanced v c within 2d of the "support" as clause BS8110;) Area of tensile steel reinforcement provided, A s,prov,x,s 754 mm 2 /m ρ w = 100A s,prov,x,s /(1000.d x,s ) 0.57 % v c,x = (0.79/1.25)(ρ w f cu /25) 1/3 (400/d x,s ) 1/4 ; ρ w <3; f cu <40; (400/d x,s ) 1/4 > N/mm 2 Check v d,x < v c,x for no links Concrete shear capacity v c,x.(1000.d x,s ) VALID 102 kn/m Check v c,x < v d,x < v c,x for nominal links Provide nominal links such that A sv / S > 0.4.(1000)/(0.95f yv ) i.e. Concrete and nominal links shear capacity (0.4 + v c,x ).(1000.d x,s ) 0.92 mm 2 /mm/m 155 kn/m Check v d,x > v c,x for design links Provide shear links A sv / S > 1000.(v d,x -v c,x )/(0.95f yv ) i.e. A sv / S > Concrete and design links shear capacity (A sv,prov,x /S x ).(0.95f yv ).d x, 0.92 mm 2 /mm/m 102 kn/m Area provided by all links per metre, A sv,prov,x 0 mm 2 /m Tried A sv,prov,x / S x value 0.00 mm 2 /mm/m Design shear resistance for bending in plane of width utilisation 7% OK

21 E N G I N E E R S Consulting Engineers jxxx 20 Shear Design for Bending in Plane of Length Shear force at column base face, V y,ult = q w,uls. B pad. [(L pad -(h or D))/2] Shear force at column base face per metre, V y,ult /B pad Shear force at 1.0d y,s from column base face, V y = q w,uls. B pad. [(L pad -(h or D Shear force at 1.0d y,s from column base face per metre, V y /B pad Note the above shear forces are for bending in plane of length; 20 kn 34 kn/m 9 kn 15 kn/m Ultimate shear stress for bending in plane of length, v ult,y =(V y,ult /B pad )/(1000.d 0.24 N/mm 2 Ultimate shear stress for bending in plane of length utilisation 5% OK Design shear stress for bending in plane of length, v d,y =(V y /B pad )/(1000.d y,s ) 0.11 N/mm 2 (Shear capacity enhancement by calculating v d at d from "support" and comparing against unenhanced v c as clause BS8110 employed instead of calculating v d at "support" and comparing against enhanced v c within 2d of the "support" as clause BS8110;) Area of tensile steel reinforcement provided, A s,prov,y,s 754 mm 2 /m ρ w = 100A s,prov,y,s /(1000.d y,s ) 0.52 % v c,y = (0.79/1.25)(ρ w f cu /25) 1/3 (400/d y,s ) 1/4 ; ρ w <3; f cu <40; (400/d y,s ) 1/4 > N/mm 2 Check v d,y < v c,y for no links Concrete shear capacity v c,y.(1000.d y,s ) VALID 106 kn/m Check v c,y < v d,y < v c,y for nominal links Provide nominal links such that A sv / S > 0.4.(1000)/(0.95f yv ) i.e. Concrete and nominal links shear capacity (0.4 + v c,y ).(1000.d y,s ) 0.92 mm 2 /mm/m 164 kn/m Check v d,y > v c,y for design links Provide shear links A sv / S > 1000.(v d,y -v c,y )/(0.95f yv ) i.e. A sv / S > Concrete and design links shear capacity (A sv,prov,y /S y ).(0.95f yv ).d y, 0.92 mm 2 /mm/m 106 kn/m Area provided by all links per metre, A sv,prov,y 0 mm 2 /m Tried A sv,prov,y / S y value 0.00 mm 2 /mm/m Design shear resistance for bending in plane of length utilisation 14% OK

22 E N G I N E E R S Consulting Engineers jxxx 21 Detailing Requirements All detailing requirements met? NOT OK Max sagging steel reinforcement pitch in plane of width (<3d x,s, <750mm) 150 mm OK Max sagging steel reinforcement pitch in plane of length (<3d y,s, <750mm) 150 mm OK Max sagging steel reinforcement pitch in plane of width 150 mm OK Max sagging steel reinforcement pitch in plane of length 150 mm OK Min sagging steel reinforcement pitch in plane of width (>100mm) 150 mm OK Min sagging steel reinforcement pitch in plane of length (>100mm) 150 mm OK Note no allowance has been made for laps in the min pitch as not deemed to be required; % Max sagging reinforcement in plane of width (<= T pad ) 0.38 % OK % Max sagging reinforcement in plane of length (<= T pad ) 0.38 % OK Sagging steel reinforcement diameter in plane of width, φ sx (>=16mm) 12 mm NOT OK Sagging steel reinforcement diameter in plane of length, φ sy (>=16mm) 12 mm NOT OK

23 E N G I N E E R S Consulting Engineers jxxx 22 Standard Pad Footing Foundation Reinforcement Details

24 E N G I N E E R S Consulting Engineers jxxx 23

25 0.40ø' ø' ø' ø' ø' (No Friction Interface) 0.00 bearing capacity limit to adopt 3 Lower Limit Middle Limit Upper Limit bearing capacity values from allowable bearing capacity, BC ll,a/ul,a values or SPT 2 BC ll,a/ul,a N factor for SPT, N value 2 Undrained Soil: Drained Soil: ground water level modification for bearing capacity 1 2 GWL >= B GWL < Bth Flooding Cohesive Soil GWL >= B Non Cohesive Soil GWL < B Rock With Flooding method of analysis 3 Undrained Analysis Drained Analysis Empirical Analysis evaluate overall uplift resistance 2 Yes No foundation type 1 Pad Footing Strip Footing Multi Column Footing Combined Footing Strap Footing Raft consider surcharge above founding level in net (effective) working pressure 1 Yes No column base section type Rectangular Circular column base location Interior Edge for Span in Width Direction Edge for Span in Length Direction

26 E N G I N E E R S Consulting Engineers jxxx 24 Strip Footing Foundation Dimensions Width, B strip Thickness beneath base slab, t 1,strip Thickness of base slab, t 2,strip (if no base slab, then enter 0.000m) Thickness of foundation, T strip = t 1,strip + t 2,strip Wall width, b m m m m 400 mm Note where applicable, it is assumed that the wall is always interior and located in the centre of the strip footing B strip ; Strip Footing Foundation Reinforcement Sagging in width Sagging steel reinforcement diameter, φ s 20 mm Sagging steel reinforcement pitch, p s 200 mm Sagging steel area provided, A s,prov,s = (π.φ 2 s /4)/p s mm 2 /m Shear link diameter, φ link 10 mm Number of link legs per metre, n link 4 /m Area provided by all links per metre, A sv,prov = n link.π.φ 2 link /4 mm 2 /m Pitch of links, S 150 mm Effective depth to sagging steel, d s = T strip - cover 1 - φ link - φ s /2 mm Estimated steel reinforcement quantity kg/m 3 [ (A s,prov,s ) / T strip ]; No curtailment; No laps; Links ignored; Distribution steel ignored; Strip Footing Foundation SLS Loading SLS vertical (downward) load from wall and base slab (if suspended), F wall,v 1000 kn/m Eccentricity of F wall,v from centroid, e m SLS horizontal load from wall, F wall,h (defined to add to e eccentricity) 0 kn/m SLS moment from wall, M wall (defined to add to e eccentricity) 0 knm/m Note F wall,h and M wall are defined to add to the corresponding eccentricity, thus enter positive values; Strip footing (projection beneath base slab) weight, F under,strip = B strip.t 1,strip.ρ c kn/m Additional soil (above footing) weight, F above,soil = B strip.max(0, D-t 1,strip ).γ sat kn/m Note additional soil above the footing is included for embedded footings whereby the top of the footing is below ground level and backfilled, for conservatism the saturated soil density is adopted, and ρ c γ sat ; Note that this has a stabilizing effect on footings subject to destabilizing moments, thus both inclusive and exclusive cases should be considered; Water pressure at founding level, u = γ w. MAX (D z u, 0) Water uplift force at founding level, F water = u.b strip Total foundation SLS vertical (downward) load, F strip,v = F wall,v + F under,strip + F a Total foundation SLS effective vertical (downward) load, F strip,v ' = F strip,v - F wat Total foundation SLS horizontal load, F strip,h = F wall,h kpa kn/m kn/m kn/m kn/m

27 E N G I N E E R S Consulting Engineers jxxx 25 Equivalent eccentricity, e B = ABS(F wall,v.e + M wall + F wall,h.t strip ) / F strip,v ' Limiting eccentricity for no overall uplift (factored), e B,limit = (B strip / 6) / FOS 3 m m Overturning moment, M ot,b = M wall + F wall,h.t strip Restoring moment, M rt,b = [F wall,v.(b strip /2-e) + (F under,strip +F above,soil -F water ).B strip knm/m knm/m Maximum gross working pressure, q w1 = F strip,v /B strip + 6.(F wall,v.e + M wall + F w Minimum gross working pressure, q w2 = F strip,v /B strip 6.(F wall,v.e + M wall + F wal Maximum gross working pressure, q w1 = 2F strip,v /[3.(B strip /2-e B )] Minimum gross working pressure, q w2 = 0.0 kpa kpa kpa kpa Equivalent width, B strip ' = B strip 2e B Gross working pressure, q w = F strip,v / B strip ' m kpa Strip Footing Foundation ULS Loading ULS vertical (downward) load from wall and base slab (if suspended), F wall,v,uls kn/m Note it is assumed that the ULS load acts at the same eccentricity as the SLS load; Note that this enhancement is required to cater for the moment as an enhanced load in the ULS design;

28 E N G I N E E R S Consulting Engineers jxxx 26 Strip Footing Foundation Reinforcement Design Gross ULS Pressure Gross ULS pressure, q w,uls = F wall,v,uls / B strip kpa Shear force diagram Bending moment diagram Sagging Bending Moment Design Moment at wall face per metre, M = q w,uls. [(B strip -b)/2] 2 / 2 knm/m 2 Concrete moment capacity per metre, M u = 0.156f cu.1000.d s knm/m Bending stress, [M/bd 2 ] = M / [(1000).d 2 s ] N/mm 2 Bending stress ratio, K = [M/bd 2 ] / f cu <= Lever arm, z = d s. [0.5 + (0.25-K/0.9) 0.5 ] <= 0.95d s mm Area of tension steel required, A s = M / [(0.95f y ).z] mm 2 /m Area of tensile steel reinforcement provided, A s,prov,s mm 2 /m Sagging bending moment utilisation = A s / A s,prov,s % Min sag reinforcement (>= T strip G250; >= T strip % % Min sag reinforcement utilisation

29 E N G I N E E R S Consulting Engineers jxxx 27 Shear Design Shear force at wall face per metre, V ult = q w,uls. [(B strip -b)/2] Shear force at 1.0d s from wall face per metre, V = q w,uls. [(B strip -b)/2-d s ] kn/m kn/m Ultimate shear stress, v ult =V ult /(1000.d s ) (< 0.8f cu 0.5 & 5N/mm 2 ) N/mm 2 Ultimate shear stress utilisation Design shear stress, v d =V/(1000.d s ) N/mm 2 (Shear capacity enhancement by calculating v d at d from "support" and comparing against unenhanced v c as clause BS8110 employed instead of calculating v d at "support" and comparing against enhanced v c within 2d of the "support" as clause BS8110;) Area of tensile steel reinforcement provided, A s,prov,s mm 2 /m ρ w = 100A s,prov,s /(1000.d s ) % v c = (0.79/1.25)(ρ w f cu /25) 1/3 (400/d s ) 1/4 ; ρ w <3; f cu <40; (400/d s ) 1/4 >0.67 N/mm 2 Check v d < v c for no links Concrete shear capacity v c.(1000.d s ) kn/m Check v c < v d < v c for nominal links Provide nominal links such that A sv / S > 0.4.(1000)/(0.95f yv ) i.e. Concrete and nominal links shear capacity (0.4 + v c ).(1000.d s ) mm 2 /mm/m kn/m Check v d > v c for design links Provide shear links A sv / S > 1000.(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 s + mm 2 /mm/m kn/m Area provided by all links per metre, A sv,prov mm 2 /m Tried A sv,prov / S value mm 2 /mm/m Design shear resistance utilisation

30 E N G I N E E R S Consulting Engineers jxxx 28 Detailing Requirements All detailing requirements met? Max sagging steel reinforcement pitch (<3d s, <750mm) mm Max sagging steel reinforcement pitch mm Min sagging steel reinforcement pitch (>100mm) mm Note no allowance has been made for laps in the min pitch as not deemed to be required; % Max sagging reinforcement (<= T strip ) % Sagging steel reinforcement diameter, φ s (>=16mm) mm

31 E N G I N E E R S Consulting Engineers jxxx 29 Standard Strip Footing Foundation Reinforcement Details As per standard pad footing reinforcement details, but in width direction only;

32 E N G I N E E R S Consulting Engineers jxxx 30

33 E N G I N E E R S Consulting Engineers jxxx 31

34 E N G I N E E R S Consulting Engineers jxxx 32

35 E N G I N E E R S Consulting Engineers jxxx 33

36 E N G I N E E R S Consulting Engineers jxxx 34

37 Corner parallel or perpendicular to edge Parallel to Edge Perpendicular to Edge Perpendicular to Edge Parallel to Edge longitudinal sagging rebar diameter longitudinal hogging rebar diameter shear link diameter None soil above embedded footing Include Exclude equations for bearing capacity factors 1 Prandtl, Reissner and Hansen Equations for Soils Kulhawy and Goodman Equations for Rocks shear case for direction x shear case for direction y shear case 3

38 E N G I N E E R S Consulting Engineers jxxx 35 Multi Column Footing Foundation Dimensions Note that the multi column footing is used when a more efficient use of a footing is required than a conventional pad footing. A pad footing is subject to sagging moments akin to a cantilever beam or slab whilst a multi column footing is subject to both sagging and hogging moments akin to a continuous beam or slab; Width, B multi (<=L multi ) m Length (internal span), L multi (>=B multi ) m Thickness beneath base slab, t 1,multi Thickness of base slab, t 2,multi (if no base slab, then enter 0.000m) Thickness of foundation, T multi = t 1,multi + t 2,multi Column base section type (for punching shear only) Column base location (for punching shear only) Column base depth, h (rectangular) or diameter, D (circular) m m m 400 mm Column base width, b (rectangular) or (circular) 400 mm Note where applicable, it is assumed that h is in same plane as L multi and that the column base is always interior and located in the centre of the multi column footing B multi ; Multi Column Footing Foundation Reinforcement Sagging steel reinforcement diameter in width, φ sx Sagging steel reinforcement pitch for resistance in width, p sx Hogging in length Sagging in length Sagging in width 20 mm 200 mm Sagging steel area provided in width, A s,prov,x,s = (π.φ 2 sx /4)/p sx mm 2 /m Sagging steel reinforcement diameter in length, φ sy 20 mm Sagging steel reinforcement pitch for resistance in length, p sy 200 mm Sagging steel area provided in length, A s,prov,y,s = (π.φ 2 sy /4)/p sy mm 2 /m Hogging steel reinforcement diameter in length, φ hy 16 mm Hogging steel reinforcement pitch for resistance in length, p hy 200 mm Hogging steel area provided in length, A s,prov,y,h = (π.φ hy 2 /4)/p hy mm 2 /m Shear link diameter for first shear perimeter, φ link,2 0 mm Number of link legs for first shear perimeter, n l,2 30 Area provided by all links for first shear perimeter, A sv,prov,2 = n l,2.π.φ 2 link,2 /4 mm 2 Shear link diameter for second shear perimeter, φ link,3 0 mm Number of link legs for second shear perimeter, n l,3 30 Area provided by all links for second shear perimeter, A sv,prov,3 = n l,3.π.φ 2 link,3 /4 mm 2 Shear link diameter for bending in width, φ link,x = φ link,2 0 mm Number of link legs per metre for bending in width, n link,x 4 /m Area provided by all links per metre for bending in width, A sv,prov,x = n link,x.π.φ l mm 2 /m Pitch of links for bending in width, S x 150 mm Shear link diameter for bending in length, φ link,y = φ link,2 0 mm Number of link legs per metre for bending in length, n link,y 4 /m Area provided by all links per metre for bending in length, A sv,prov,y = n link,y.π.φ mm 2 /m Pitch of links for bending in length, S y 150 mm Effective depth to sagging steel in width, d x,s = T multi - cover 1 - MAX (φ link,2, φ lin Effective depth to sagging steel in length, d y,s = T multi - cover 1 - MAX (φ link,2, φ Effective depth to hogging steel in length, d y,h = T multi - cover 1 - φ hy /2 It is assumed that sagging steel in length is exterior to sagging steel in width; mm mm mm

39 E N G I N E E R S Consulting Engineers jxxx 36 Estimated steel reinforcement quantity kg/m 3 [ (A s,prov,x,s +A s,prov,y,s +A s,prov,y,h ) / T multi ]; No curtailment; No laps; Links ignored; Distribution steel ig Multi Column Footing Foundation SLS Loading SLS vertical (downward) load from column and base slab (if suspended), F col,v 1350 kn Multi column footing (projection beneath base slab) weight, F under,multi = B multi. kn Additional soil (above footing) weight, F above,soil = B multi.l multi.max(0, D-t 1,multi ). kn Note additional soil above the footing is included for embedded footings whereby the top of the footing is below ground level and backfilled, for conservatism the saturated soil density is adopted, and ρ c γ sat ; Total foundation SLS vertical (downward) load, F multi,v = F col,v + F under,multi + F a kn Gross working pressure, q w = F multi,v / (B multi. L multi ) kpa Multi Column Footing Foundation ULS Loading ULS vertical (downward) load from column and base slab (if suspended), F col, kn

40 E N G I N E E R S Consulting Engineers jxxx 37 Multi Column Footing Foundation Reinforcement Design Gross ULS Pressure gnored; Gross ULS pressure, q w,uls = F col,v,uls / (B multi. L multi ) kpa Shear force diagram Bending moment diagram Sagging Bending Moment Design in Plane of Width Moment at column base centreline, M x = q w,uls. L multi. (B multi /2) 2 / 2 Moment at column base centreline per metre, M x /L multi knm knm/m 2 Concrete moment capacity per metre, M u,x = 0.156f cu.1000.d x,s knm/m Bending stress, [M/bd 2 ] x = (M x /L multi ) / [(1000).d 2 x,s ] N/mm 2 Bending stress ratio, K x = [M/bd 2 ] x / f cu <= Lever arm, z x = d x,s. [0.5 + (0.25-K x /0.9) 0.5 ] <= 0.95d x,s mm Area of tension steel required, A s,x = (M x /L multi ) / [(0.95f y ).z x ] mm 2 /m Area of tensile steel reinforcement provided, A s,prov,x,s mm 2 /m Sagging bending moment in plane of width utilisation = A s,x / A s,prov,x,s Requirement to concentrate 2/3 rebar within 1.5d x,s fro [Yes if L multi /2>3/4(h or D)+9/4d x,s ; No if not;] mm mm BS8110 Note that should the above requirement be applicable, it is not automatically reflected in the detailing considerations and as such should be specifically reconsidered; % Min sag reinforcement in plane of width (>= T multi G250; >= % % Min sag reinforcement in plane of width utilisation Sagging Bending Moment Design in Plane of Length Moment at column base centreline, M y = q w,uls. B multi. L multi 2 Note moment coefficient based on internal span 0.08 instead of end span 0.11; Moment at column base centreline per metre, M y /B multi knm knm/m T.3.5 BS Concrete moment capacity per metre, M u,y = 0.156f cu.1000.d y,s knm/m Bending stress, [M/bd 2 ] y = (M y /B multi ) / [(1000).d 2 y,s ] N/mm 2 Bending stress ratio, K y = [M/bd 2 ] y / f cu <= Lever arm, z y = d y,s. [0.5 + (0.25-K y /0.9) 0.5 ] <= 0.95d y,s mm Area of tension steel required, A s,y = (M y /B multi ) / [(0.95f y ).z y ] mm 2 /m Area of tensile steel reinforcement provided, A s,prov,y,s mm 2 /m Sagging bending moment in plane of length utilisation = A s,y / A s,prov,y,s Requirement to concentrate 2/3 rebar within 1.5d y,s fro [Yes if B multi /2>3/4(b or D)+9/4d y,s ; No if not;] mm mm BS8110 Note that should the above requirement be applicable, it is not automatically reflected in the detailing considerations and as such should be specifically reconsidered; % Min sag reinforcement in plane of length (>= T multi G250; >= % % Min sag reinforcement in plane of length utilisation

41 E N G I N E E R S Consulting Engineers jxxx 38 Hogging Bending Moment Design in Plane of Length Moment, M y = q w,uls. B multi. L multi 2 Note moment coefficient based on internal span 0.07 instead of end span 0.09; Moment per metre, M y /B multi knm knm/m T.3.5 BS Concrete moment capacity per metre, M u,y = 0.156f cu.1000.d y,h knm/m Bending stress, [M/bd 2 ] y = (M y /B multi ) / [(1000).d 2 y,h ] N/mm 2 Bending stress ratio, K y = [M/bd 2 ] y / f cu <= Lever arm, z y = d y,h. [0.5 + (0.25-K y /0.9) 0.5 ] <= 0.95d y,h mm Area of tension steel required, A s,y = (M y /B multi ) / [(0.95f y ).z y ] mm 2 /m Area of tensile steel reinforcement provided, A s,prov,y,h mm 2 /m Hogging bending moment in plane of length utilisation = A s,y / A s,prov,y,h Requirement to concentrate 2/3 rebar within 1.5d y,h fro [Yes if B multi /2>3/4(b or D)+9/4d y,h ; No if not;] mm mm BS8110 Note that should the above requirement be applicable, it is not automatically reflected in the detailing considerations and as such should be specifically reconsidered; % Min hog reinforcement in plane of length (>= T multi G250; >= % % Min hog reinforcement in plane of length utilisation

42 E N G I N E E R S Consulting Engineers jxxx 39 Punching Shear Design ULS vertical (downward) load from column and base slab (if suspended), F col, kn Area of column base section, A c1 = b.h (rectangular) or πd 2 /4 (circular) mm 2 Average effective depth of both rebar layers, d = (d x,s + d y,s )/2 mm Area of tensile steel reinforcement provided, A s,prov,x,s mm 2 /m Area of tensile steel reinforcement provided, A s,prov,y,s mm 2 /m Average area of tensile steel reinforcement provided, A s,prov,s mm 2 /m ρ w = 100A s,prov,s /(1000.d) % ν c = (0.79/1.25)(ρ w f cu /25) 1/3 (400/d) 1/4 ; ρ w <3; f cu <40; (400/d) 1/4 >0.67 N/mm 2 Column Base Face Perimeter Shear force at column base face, V 1 = F col,v,uls - q w,uls.a c1 kn Effective shear force, V eff,1 = V 1 kn Note V eff,1 = V 1 because no moment effects assumed ; Column base face perimeter, u 1 mm Rectangular Circular Internal column: 2.(b+h) π.d mm Edge column: 2b+h or 2h+b 3/4( π.d) mm Corner column: (b+h) π.d/2 mm Shear stress at column base face perimeter, ν 1 = V eff,1 / u 1 d (< 0.8f 0.5 cu & 5N N/mm 2 Ultimate shear stress utilisation First Shear Perimeter Shear force 1.5d from column base face, V 2 = F col,v,uls - q w,uls.a c2 Rectangular kn Internal column: (b+3d).(h+3d) (D+3d) 2 m 2 Edge column: (b+1.5d).(h+3d) or (h+1.5d).(b+3d) d).(d+3d) m 2 Corner column: (b+1.5d).(h+1.5d) (D+1.5d) 2 m 2 Effective shear force, V eff,2 = V 2 kn Note V eff,2 = V 2 because no moment effects assumed; Column base first perimeter, u 2 Rectangular Circular Circular mm Internal column: 2.(b+h)+12d 4 D+12d mm Edge column: 2b+h+6d or 2h+b+6d 3D+6d mm Corner column: (b+h)+3d 2D+3d mm Shear stress at column base first perimeter, ν 2 = V eff,2 / u 2 d N/mm 2 (Shear capacity enhancement by calculating v d at 1.5d from "support" and comparing against unenhanced v c as clause BS8110 employed instead of calculating v d at "support" and comparing against enhanced v c within 1.5d of the "support" as clause BS8110;) Case ν 2 < ν c No links required. Case ν c < ν 2 < 1.6ν c >= mm 2 Note >

43 E N G I N E E R S Consulting Engineers jxxx 40 Case 1.6ν c < ν 2 < 2.0ν c >= mm 2 Case ν 2 > 2.0ν c Note > First shear perimeter shear utilisation Second Shear Perimeter Shear force 2.25d from column base face, V 3 = F col,v,uls - q w,uls.a c3 Rectangular kn Internal column: (b+4.5d).(h+4.5d) (D+4.5d) 2 m 2 Edge column: (b+2.25d).(h+4.5d) or (h+2.25d).(b+4.5d) ).(D+4.5d) m 2 Corner column: (b+2.25d).(h+2.25d) D+2.25d) 2 m 2 Effective shear force, V eff,3 = V 3 kn Note V eff,3 = V 3 because no moment effects assumed; Column base second perimeter, u 3 Rectangular Circular Circular mm Internal column: 2.(b+h)+18d 4 D+18d mm Edge column: 2b+h+9d or 2h+b+9d 3D+9d mm Corner column: (b+h)+4.5d 2D+4.5d mm Shear stress at column base second perimeter, ν 3 = V eff,3 / u 3 d N/mm 2 Case ν 3 < ν c No links required. Case ν c < ν 3 < 1.6ν c >= mm 2 Note > Case 1.6ν c < ν 3 < 2.0ν c >= mm 2 Case ν 3 > 2.0ν c Note > Second shear perimeter shear utilisation Note a negative shear stress ν 2 and/or ν 3 on a correctly specified column (wrt internal, edge or corner) indicates that the shear perimeter is beyond the physical extremes of the foundation and as such punching shear failure is not critical;

44 E N G I N E E R S Consulting Engineers jxxx 41 Shear Design for Bending in Plane of Width Shear force at column base centreline, V x,ult = q w,uls. L multi. B multi /2 Shear force at column base centreline per metre, V x,ult /L multi Shear force at 1.0d x,s from column base centreline, V x = q w,uls. L multi. (B multi / Shear force at 1.0d x,s from column base centreline per metre, V x /L multi Note the above shear forces are for bending in plane of width; kn kn/m kn kn/m Ultimate shear stress for bending in plane of width, v ult,x =(V x,ult /L multi )/(1000.d N/mm 2 Ultimate shear stress for bending in plane of width utilisation Design shear stress for bending in plane of width, v d,x =(V x /L multi )/(1000.d x,s ) N/mm 2 (Shear capacity enhancement by calculating v d at d from "support" and comparing against unenhanced v c as clause BS8110 employed instead of calculating v d at "support" and comparing against enhanced v c within 2d of the "support" as clause BS8110;) Area of tensile steel reinforcement provided, A s,prov,x,s mm 2 /m ρ w = 100A s,prov,x,s /(1000.d x,s ) % v c,x = (0.79/1.25)(ρ w f cu /25) 1/3 (400/d x,s ) 1/4 ; ρ w <3; f cu <40; (400/d x,s ) 1/4 >0.67 N/mm 2 Check v d,x < v c,x for no links Concrete shear capacity v c,x.(1000.d x,s ) kn/m Check v c,x < v d,x < v c,x for nominal links Provide nominal links such that A sv / S > 0.4.(1000)/(0.95f yv ) i.e. Concrete and nominal links shear capacity (0.4 + v c,x ).(1000.d x,s ) mm 2 /mm/m kn/m Check v d,x > v c,x for design links Provide shear links A sv / S > 1000.(v d,x -v c,x )/(0.95f yv ) i.e. A sv / S > Concrete and design links shear capacity (A sv,prov,x /S x ).(0.95f yv ).d x, mm 2 /mm/m kn/m Area provided by all links per metre, A sv,prov,x mm 2 /m Tried A sv,prov,x / S x value mm 2 /mm/m Design shear resistance for bending in plane of width utilisation

45 E N G I N E E R S Consulting Engineers jxxx 42 Shear Design for Bending in Plane of Length Shear force at column base centreline, V y,ult = q w,uls. B multi. (0.55.L multi ) kn T.3.5 Note shear coefficient based on internal span 0.55 instead of end span 0.6; BS8110 Shear force at column base centreline per metre, V y,ult /B multi kn/m Shear force at 1.0d y,s from column base centreline, V y = V y,ult - q w,uls. B multi. kn Shear force at 1.0d y,s from column base centreline per metre, V y /B multi kn/m Note the above shear forces are for bending in plane of length; Ultimate shear stress for bending in plane of length, v ult,y =(V y,ult /B multi )/(1000 N/mm 2 Ultimate shear stress for bending in plane of length utilisation Design shear stress for bending in plane of length, v d,y =(V y /B multi )/(1000.d y,s ) N/mm 2 (Shear capacity enhancement by calculating v d at d from "support" and comparing against unenhanced v c as clause BS8110 employed instead of calculating v d at "support" and comparing against enhanced v c within 2d of the "support" as clause BS8110;) Area of tensile steel reinforcement provided, A s,prov,y,s mm 2 /m ρ w = 100A s,prov,y,s /(1000.d y,s ) % v c,y = (0.79/1.25)(ρ w f cu /25) 1/3 (400/d y,s ) 1/4 ; ρ w <3; f cu <40; (400/d y,s ) 1/4 >0.67 N/mm 2 Check v d,y < v c,y for no links Concrete shear capacity v c,y.(1000.d y,s ) kn/m Check v c,y < v d,y < v c,y for nominal links Provide nominal links such that A sv / S > 0.4.(1000)/(0.95f yv ) i.e. Concrete and nominal links shear capacity (0.4 + v c,y ).(1000.d y,s ) mm 2 /mm/m kn/m Check v d,y > v c,y for design links Provide shear links A sv / S > 1000.(v d,y -v c,y )/(0.95f yv ) i.e. A sv / S > Concrete and design links shear capacity (A sv,prov,y /S y ).(0.95f yv ).d y, mm 2 /mm/m kn/m Area provided by all links per metre, A sv,prov,y mm 2 /m Tried A sv,prov,y / S y value mm 2 /mm/m Design shear resistance for bending in plane of length utilisation

46 E N G I N E E R S Consulting Engineers jxxx 43 Detailing Requirements All detailing requirements met? Max sagging steel reinforcement pitch in plane of width (<3d x,s, <750mm) mm Max sagging steel reinforcement pitch in plane of length (<3d y,s, <750mm) mm Max hogging steel reinforcement pitch in plane of length (<3d y,h, <750mm) mm Max sagging steel reinforcement pitch in plane of width mm Max sagging steel reinforcement pitch in plane of length mm Max hogging steel reinforcement pitch in plane of length mm Min sagging steel reinforcement pitch in plane of width (>100mm+φ sx ) mm Min sagging steel reinforcement pitch in plane of length (>100mm+φ sy ) mm Min hogging steel reinforcement pitch in plane of length (>100mm+φ hy ) mm Note an allowance has been made for laps in the min pitch by increasing the criteria by the bar diameter. % Max sagging reinforcement in plane of width (<= T multi ) % % Max sagging reinforcement in plane of length (<= T multi ) % % Max hogging reinforcement in plane of length (<= T multi ) % Sagging steel reinforcement diameter in plane of width, φ sx (>=16mm) mm Sagging steel reinforcement diameter in plane of length, φ sy (>=16mm) mm Hogging steel reinforcement diameter in plane of length, φ hy (>=16mm) mm

47 E N G I N E E R S Consulting Engineers jxxx 44 Standard Multi Column Footing Foundation Reinforcement Details

48 E N G I N E E R S Consulting Engineers jxxx 45

49

50 E N G I N E E R S Consulting Engineers jxxx 46 Combined Footing Foundation Dimensions Note that the combined footing is used when a more efficient use of a footing is required than a conventional pad footing. It is also used when a column is too close to the site boundary to allow the employment of a conventional pad footing with no eccentricity. A pad footing is subject to sagging moments akin to a cantilever beam or slab whilst a combined footing is subject to both sagging and hogging moments akin to a continuous beam or slab. A combined footing differs from a multi column footing in the fact that the column loads are not uniform, and thus require that the dimensions of the combined footing be such that the resultant load passes through the centroid of the base area; Width, B com (<=L com ) m Length, L com (>=B com ) m Length internal span, L com,3 (<L com ) m Centroid, y c = (F col,v,2.l com,3 )/(F col,v,1 +F col,v,2 ) m Length external span, L com,1 = L com /2-y c (>0.000) m Length external span, L com,2 = L com /2-(L com,3 -y c ) (>0.000) m Note the combined footing is centred on the centroid, which is a function of the loads; Should the relative loads vary greatly, the effectiveness of the combined footing reduces; L com y c B com Column 1 Column 2 L com,1 L com,3 Thickness beneath base slab, t 1,com Thickness of base slab, t 2,com (if no base slab, then enter 0.000m) Thickness of foundation, T com = t 1,com + t 2,com Column base section type (for punching shear only) L com, m m m Column base location (for punching shear only) Column 1 base depth, h 1 (rectangular) or diameter, D 1 (circular) 300 mm Column 1 base width, b 1 (rectangular) or (circular) 300 mm Column 2 base depth, h 2 (rectangular) or diameter, D 2 (circular) 400 mm Column 2 base width, b 2 (rectangular) or (circular) 400 mm Note where applicable, it is assumed that h 1 and h 2 are in same plane as L com and that the column base is always interior and located in the centre of the combined footing B com, although not L com ; Combined Footing Foundation Reinforcement Hogging in length Sagging in length Sagging in width Sagging steel reinforcement diameter in width, φ sx Sagging steel reinforcement pitch for resistance in width, p sx 20 mm 200 mm Sagging steel area provided in width, A s,prov,x,s = (π.φ 2 sx /4)/p sx mm 2 /m Sagging steel reinforcement diameter in length, φ sy 20 mm Sagging steel reinforcement pitch for resistance in length, p sy 200 mm Sagging steel area provided in length, A s,prov,y,s = (π.φ 2 sy /4)/p sy mm 2 /m Hogging steel reinforcement diameter in length, φ hy 16 mm Hogging steel reinforcement pitch for resistance in length, p hy 200 mm Hogging steel area provided in length, A s,prov,y,h = (π.φ hy 2 /4)/p hy mm 2 /m

51 E N G I N E E R S Consulting Engineers jxxx 47 Shear link diameter for first shear perimeter, φ link,2 0 mm Number of link legs for first shear perimeter, n l,2 30 Area provided by all links for first shear perimeter, A sv,prov,2 = n l,2.π.φ 2 link,2 /4 mm 2 Shear link diameter for second shear perimeter, φ link,3 0 mm Number of link legs for second shear perimeter, n l,3 30 Area provided by all links for second shear perimeter, A sv,prov,3 = n l,3.π.φ 2 link,3 /4 mm 2 Shear link diameter for bending in width, φ link,x = φ link,2 0 mm Number of link legs per metre for bending in width, n link,x 4 /m Area provided by all links per metre for bending in width, A sv,prov,x = n link,x.π.φ l mm 2 /m Pitch of links for bending in width, S x 150 mm Shear link diameter for bending in length, φ link,y = φ link,2 0 mm Number of link legs per metre for bending in length, n link,y 4 /m Area provided by all links per metre for bending in length, A sv,prov,y = n link,y.π.φ mm 2 /m Pitch of links for bending in length, S y 150 mm Effective depth to sagging steel in width, d x,s = T com - cover 1 - MAX (φ link,2, φ lin Effective depth to sagging steel in length, d y,s = T com - cover 1 - MAX (φ link,2, φ li Effective depth to hogging steel in length, d y,h = T com - cover 1 - φ hy /2 It is assumed that sagging steel in length is exterior to sagging steel in width; mm mm mm Estimated steel reinforcement quantity kg/m 3 [ (A s,prov,x,s +A s,prov,y,s +A s,prov,y,h ) / T com ]; No curtailment; No laps; Links ignored; Distribution steel ig Combined Footing Foundation SLS Loading SLS vertical (downward) load from column 1 and base slab (if suspended), F c 1200 kn SLS vertical (downward) load from column 2 and base slab (if suspended), F c 1650 kn Combined footing (projection beneath base slab) weight, F under,com = B com.l com kn Additional soil (above footing) weight, F above,soil = B com.l com.max(0, D-t 1,com ).γ s kn Note additional soil above the footing is included for embedded footings whereby the top of the footing is below ground level and backfilled, for conservatism the saturated soil density is adopted, and ρ c γ sat ; Total foundation SLS vertical (downward) load, F com,v = F col,v,1 + F col,v,2 + F unde kn Gross working pressure, q w = F com,v / (B com. L com ) kpa Combined Footing Foundation ULS Loading ULS vertical (downward) load from column 1 and base slab (if suspended), F c ULS vertical (downward) load from column 2 and base slab (if suspended), F c kn kn

52 E N G I N E E R S Consulting Engineers jxxx 48 Combined Footing Foundation Reinforcement Design Gross ULS Pressure Gross ULS pressure, q w,uls = (F col,v,1,uls + F col,v,2,uls ) / (B com. L com ) kpa Shear force diagram Bending moment diagram Sagging Bending Moment Design in Plane of Width Moment at column base centreline, M x = q w,uls. L com. (B com /2) 2 / 2 Moment at column base centreline per metre, M x /L com knm knm/m 2 Concrete moment capacity per metre, M u,x = 0.156f cu.1000.d x,s knm/m Bending stress, [M/bd 2 ] x = (M x /L com ) / [(1000).d 2 x,s ] N/mm 2 Bending stress ratio, K x = [M/bd 2 ] x / f cu <= Lever arm, z x = d x,s. [0.5 + (0.25-K x /0.9) 0.5 ] <= 0.95d x,s mm Area of tension steel required, A s,x = (M x /L com ) / [(0.95f y ).z x ] mm 2 /m Area of tensile steel reinforcement provided, A s,prov,x,s mm 2 /m Sagging bending moment in plane of width utilisation = A s,x / A s,prov,x,s Requirement to concentrate 2/3 rebar within 1.5d x,s fro [Yes if max(l com,1, L com,2, L com,3 /2)>3/4min(h 1 or D 1 mm mm BS8110 Note that should the above requirement be applicable, it is not automatically reflected in the detailing considerations and as such should be specifically reconsidered; % Min sag reinforcement in plane of width (>= T com G250; >= % % Min sag reinforcement in plane of width utilisation Sagging Bending Moment Design in Plane of Length Moment at column base face, M y = q w,uls. B com. [max(l com,1 -h 1 /2, L com,2 -h 2 /2 Moment at column base face per metre, M y /B com knm knm/m 2 Concrete moment capacity per metre, M u,y = 0.156f cu.1000.d y,s knm/m Bending stress, [M/bd 2 ] y = (M y /B com ) / [(1000).d 2 y,s ] N/mm 2 Bending stress ratio, K y = [M/bd 2 ] y / f cu <= Lever arm, z y = d y,s. [0.5 + (0.25-K y /0.9) 0.5 ] <= 0.95d y,s mm Area of tension steel required, A s,y = (M y /B com ) / [(0.95f y ).z y ] mm 2 /m Area of tensile steel reinforcement provided, A s,prov,y,s mm 2 /m Sagging bending moment in plane of length utilisation = A s,y / A s,prov,y,s Requirement to concentrate 2/3 rebar within 1.5d y,s fro [Yes if B com /2>3/4min(b 1 or D 1, b 2 or D 2 )+9/4d y,s ; mm mm BS8110 Note that should the above requirement be applicable, it is not automatically reflected in the detailing considerations and as such should be specifically reconsidered; % Min sag reinforcement in plane of length (>= T com G250; >= % % Min sag reinforcement in plane of length utilisation

53 E N G I N E E R S Consulting Engineers jxxx 49 Hogging Bending Moment Design in Plane of Length Distance to zero shear force from column 1, L com,4 = (F col,v,1,uls -q w,uls.b com.l com Moment, M y = F col,v,1,uls. L com,4 - q w,uls. B com. (L com,1 +L com,4 ) 2 / 2 Moment per metre, M y /B com m knm knm/m 2 Concrete moment capacity per metre, M u,y = 0.156f cu.1000.d y,h knm/m Bending stress, [M/bd 2 ] y = (M y /B com ) / [(1000).d 2 y,h ] N/mm 2 Bending stress ratio, K y = [M/bd 2 ] y / f cu <= Lever arm, z y = d y,h. [0.5 + (0.25-K y /0.9) 0.5 ] <= 0.95d y,h mm Area of tension steel required, A s,y = (M y /B com ) / [(0.95f y ).z y ] mm 2 /m Area of tensile steel reinforcement provided, A s,prov,y,h mm 2 /m Hogging bending moment in plane of length utilisation = A s,y / A s,prov,y,h Requirement to concentrate 2/3 rebar within 1.5d y,h fro [Yes if B com /2>3/4min(b 1 or D 1, b 2 or D 2 )+9/4d y,h ; mm mm BS8110 Note that should the above requirement be applicable, it is not automatically reflected in the detailing considerations and as such should be specifically reconsidered; % Min hog reinforcement in plane of length (>= T com G250; >= % % Min hog reinforcement in plane of length utilisation

54 E N G I N E E R S Consulting Engineers jxxx 50 Punching Shear Design Critical column 1 or 2 i.e. MAX(F col,v,1,uls /(b 1.h 1 ), F col,v,2,uls /(b 2.h 2 )) or MAX(F col,v ULS vertical (downward) load from relevant column and base slab (if suspend Relevant column base depth, h (rectangular) or diameter, D (circular) Relevant column base width, b (rectangular) or (circular) kn mm mm Area of column base section, A c1 = b.h (rectangular) or πd 2 /4 (circular) mm 2 Average effective depth of both rebar layers, d = (d x,s + d y,s )/2 mm Area of tensile steel reinforcement provided, A s,prov,x,s mm 2 /m Area of tensile steel reinforcement provided, A s,prov,y,s mm 2 /m Average area of tensile steel reinforcement provided, A s,prov,s mm 2 /m ρ w = 100A s,prov,s /(1000.d) % ν c = (0.79/1.25)(ρ w f cu /25) 1/3 (400/d) 1/4 ; ρ w <3; f cu <40; (400/d) 1/4 >0.67 N/mm 2 Column Base Face Perimeter Shear force at column base face, V 1 = F col,v,uls - q w,uls.a c1 kn Effective shear force, V eff,1 = V 1 kn Note V eff,1 = V 1 because no moment effects assumed ; Column base face perimeter, u 1 mm Rectangular Circular Internal column: 2.(b+h) π.d mm Edge column: 2b+h or 2h+b 3/4( π.d) mm Corner column: (b+h) π.d/2 mm Shear stress at column base face perimeter, ν 1 = V eff,1 / u 1 d (< 0.8f 0.5 cu & 5N N/mm 2 Ultimate shear stress utilisation First Shear Perimeter Shear force 1.5d from column base face, V 2 = F col,v,uls - q w,uls.a c2 Rectangular kn Internal column: (b+3d).(h+3d) (D+3d) 2 m 2 Edge column: (b+1.5d).(h+3d) or (h+1.5d).(b+3d) d).(d+3d) m 2 Corner column: (b+1.5d).(h+1.5d) (D+1.5d) 2 m 2 Effective shear force, V eff,2 = V 2 kn Note V eff,2 = V 2 because no moment effects assumed; Column base first perimeter, u 2 Rectangular Circular Circular mm Internal column: 2.(b+h)+12d 4 D+12d mm Edge column: 2b+h+6d or 2h+b+6d 3D+6d mm Corner column: (b+h)+3d 2D+3d mm Shear stress at column base first perimeter, ν 2 = V eff,2 / u 2 d N/mm 2 (Shear capacity enhancement by calculating v d at 1.5d from "support" and comparing against unenhanced v c as clause BS8110 employed instead of calculating v d at "support" and comparing against enhanced v c within 1.5d of the "support" as clause BS8110;) Case ν 2 < ν c No links required. Case ν c < ν 2 < 1.6ν c >= mm 2 Note >

55 E N G I N E E R S Consulting Engineers jxxx 51 Case 1.6ν c < ν 2 < 2.0ν c >= mm 2 Case ν 2 > 2.0ν c Note > First shear perimeter shear utilisation Second Shear Perimeter Shear force 2.25d from column base face, V 3 = F col,v,uls - q w,uls.a c3 Rectangular kn Internal column: (b+4.5d).(h+4.5d) (D+4.5d) 2 m 2 Edge column: (b+2.25d).(h+4.5d) or (h+2.25d).(b+4.5d) ).(D+4.5d) m 2 Corner column: (b+2.25d).(h+2.25d) D+2.25d) 2 m 2 Effective shear force, V eff,3 = V 3 kn Note V eff,3 = V 3 because no moment effects assumed; Column base second perimeter, u 3 Rectangular Circular Circular mm Internal column: 2.(b+h)+18d 4 D+18d mm Edge column: 2b+h+9d or 2h+b+9d 3D+9d mm Corner column: (b+h)+4.5d 2D+4.5d mm Shear stress at column base second perimeter, ν 3 = V eff,3 / u 3 d N/mm 2 Case ν 3 < ν c No links required. Case ν c < ν 3 < 1.6ν c >= mm 2 Note > Case 1.6ν c < ν 3 < 2.0ν c >= mm 2 Case ν 3 > 2.0ν c Note > Second shear perimeter shear utilisation Note a negative shear stress ν 2 and/or ν 3 on a correctly specified column (wrt internal, edge or corner) indicates that the shear perimeter is beyond the physical extremes of the foundation and as such punching shear failure is not critical;

56 E N G I N E E R S Consulting Engineers jxxx 52 Shear Design for Bending in Plane of Width Shear force at column base centreline, V x,ult = q w,uls. L com. B com /2 Shear force at column base centreline per metre, V x,ult /L com Shear force at 1.0d x,s from column base centreline, V x = q w,uls. L com. (B com /2 Shear force at 1.0d x,s from column base centreline per metre, V x /L com Note the above shear forces are for bending in plane of width; kn kn/m kn kn/m Ultimate shear stress for bending in plane of width, v ult,x =(V x,ult /L com )/(1000.d N/mm 2 Ultimate shear stress for bending in plane of width utilisation Design shear stress for bending in plane of width, v d,x =(V x /L com )/(1000.d x,s ) N/mm 2 (Shear capacity enhancement by calculating v d at d from "support" and comparing against unenhanced v c as clause BS8110 employed instead of calculating v d at "support" and comparing against enhanced v c within 2d of the "support" as clause BS8110;) Area of tensile steel reinforcement provided, A s,prov,x,s mm 2 /m ρ w = 100A s,prov,x,s /(1000.d x,s ) % v c,x = (0.79/1.25)(ρ w f cu /25) 1/3 (400/d x,s ) 1/4 ; ρ w <3; f cu <40; (400/d x,s ) 1/4 >0.67 N/mm 2 Check v d,x < v c,x for no links Concrete shear capacity v c,x.(1000.d x,s ) kn/m Check v c,x < v d,x < v c,x for nominal links Provide nominal links such that A sv / S > 0.4.(1000)/(0.95f yv ) i.e. Concrete and nominal links shear capacity (0.4 + v c,x ).(1000.d x,s ) mm 2 /mm/m kn/m Check v d,x > v c,x for design links Provide shear links A sv / S > 1000.(v d,x -v c,x )/(0.95f yv ) i.e. A sv / S > Concrete and design links shear capacity (A sv,prov,x /S x ).(0.95f yv ).d x, mm 2 /mm/m kn/m Area provided by all links per metre, A sv,prov,x mm 2 /m Tried A sv,prov,x / S x value mm 2 /mm/m Design shear resistance for bending in plane of width utilisation

57 E N G I N E E R S Consulting Engineers jxxx 53 Shear Design for Bending in Plane of Length Shear force at column 1 base left face, V y,1 = q w,uls. B com. (L com,1 -h 1 /2) Shear force at column 1 base right face, V y,2 = F col,v,1,uls - q w,uls. B com. (L com,1 Shear force at column 2 base left face, V y,3 = F col,v,2,uls - q w,uls. B com. (L com,2 + Shear force at column 2 base right face, V y,4 = q w,uls. B com. (L com,2 -h 2 /2) Shear force at critical column base face, V y,ult = MAX(V y,1, V y,2, V y,3, V y,4 ) Shear force at critical column base face per metre, V y,ult /B com Shear force at 1.0d y,s from critical column base face, V y = V y,ult - q w,uls. B com Shear force at 1.0d y,s from critical column base face per metre, V y /B com Note the above shear forces are for bending in plane of length; kn kn kn kn kn kn/m kn kn/m Ultimate shear stress for bending in plane of length, v ult,y =(V y,ult /B com )/(1000. N/mm 2 Ultimate shear stress for bending in plane of length utilisation Design shear stress in plane of length, v d,y =(V y /B com )/(1000.d y,s ) N/mm 2 (Shear capacity enhancement by calculating v d at d from "support" and comparing against unenhanced v c as clause BS8110 employed instead of calculating v d at "support" and comparing against enhanced v c within 2d of the "support" as clause BS8110;) Area of tensile steel reinforcement provided, A s,prov,y,s mm 2 /m ρ w = 100A s,prov,y,s /(1000.d y,s ) % v c,y = (0.79/1.25)(ρ w f cu /25) 1/3 (400/d y,s ) 1/4 ; ρ w <3; f cu <40; (400/d y,s ) 1/4 >0.67 N/mm 2 Check v d,y < v c,y for no links Concrete shear capacity v c,y.(1000.d y,s ) kn/m Check v c,y < v d,y < v c,y for nominal links Provide nominal links such that A sv / S > 0.4.(1000)/(0.95f yv ) i.e. Concrete and nominal links shear capacity (0.4 + v c,y ).(1000.d y,s ) mm 2 /mm/m kn/m Check v d,y > v c,y for design links Provide shear links A sv / S > 1000.(v d,y -v c,y )/(0.95f yv ) i.e. A sv / S > Concrete and design links shear capacity (A sv,prov,y /S y ).(0.95f yv ).d y, mm 2 /mm/m kn/m Area provided by all links per metre, A sv,prov,y mm 2 /m Tried A sv,prov,y / S y value mm 2 /mm/m Design shear resistance for bending in plane of length utilisation

58 E N G I N E E R S Consulting Engineers jxxx 54 Detailing Requirements All detailing requirements met? Max sagging steel reinforcement pitch in plane of width (<3d x,s, <750mm) mm Max sagging steel reinforcement pitch in plane of length (<3d y,s, <750mm) mm Max hogging steel reinforcement pitch in plane of length (<3d y,h, <750mm) mm Max sagging steel reinforcement pitch in plane of width mm Max sagging steel reinforcement pitch in plane of length mm Max hogging steel reinforcement pitch in plane of length mm Min sagging steel reinforcement pitch in plane of width (>100mm+φ sx ) mm Min sagging steel reinforcement pitch in plane of length (>100mm+φ sy ) mm Min hogging steel reinforcement pitch in plane of length (>100mm+φ hy ) mm Note an allowance has been made for laps in the min pitch by increasing the criteria by the bar diameter. % Max sagging reinforcement in plane of width (<= T com ) % % Max sagging reinforcement in plane of length (<= T com ) % % Max hogging reinforcement in plane of length (<= T com ) % Sagging steel reinforcement diameter in plane of width, φ sx (>=16mm) mm Sagging steel reinforcement diameter in plane of length, φ sy (>=16mm) mm Hogging steel reinforcement diameter in plane of length, φ hy (>=16mm) mm

59 E N G I N E E R S Consulting Engineers jxxx 55 Standard Combined Footing Foundation Reinforcement Details As per standard multi column footing reinforcement details;

60 E N G I N E E R S Consulting Engineers jxxx 56

61

62 E N G I N E E R S Consulting Engineers jxxx 57 Strap Footing Foundation Dimensions Note that the strap footing is used when a column is too close to the site boundary to allow the employment of a conventional pad footing with no eccentricity. The strap beam effectively restrains the overturning force due to the eccentric load on the outer footing. A strap footing differs from a combined footing in the fact that the proximity of the outer footing to the boundary is even more dramatic; Width and length of inner footing, B strap, m Length of outer footing, L strap, m Length internal span, L strap m Centroid, y c = (F col,v,2.l strap )/(F col,v,1 +F col,v,2 ) m Width of outer footing, B strap,1 = (B 2 strap,2.l strap -y c.b 2 strap,2 )/(y c.l strap,1 -L strap,1.(l s m Note the strap footing is centred on the centroid, which is a function of the loads; Should the relative loads vary greatly, the effectiveness of the strap footing reduces; L strap,1 B strap,2 y c Inner footing to be designed as a conventional pad footing; B strap,1 B strap,2 L strap Column 1 Column 2 Note the subsequent design concerns the design of the outer footing since the inner footing can be designed conventionally as a pad footing with the loads F col,v,2 and dimensions B strap,2, t 1,strap and t 2,strap defined herein; Thickness beneath base slab, t 1,strap Thickness of base slab, t 2,strap (if no base slab, then enter 0.000m) Thickness of foundation, T strap = t 1,strap + t 2,strap Column base section type (for punching shear only) Column base location (for punching shear only) Column 1 base depth, h (rectangular) or diameter, D (circular) m m m 300 mm Column 1 base width, b (rectangular) or (circular) 300 mm Note where applicable, it is assumed that h is in same plane as L strap,1 and that the column base is always interior and located in the centre of the strap footing B strap,1, although not L strap,1 ; Depth of beam, h beam m Width of beam, b beam m Note that the strap beam must not bear on the soil, compressible void former to be specified; Strap Footing Foundation Reinforcement Sagging steel reinforcement diameter in width of outer footing, φ sx Sagging steel reinforcement pitch for resistance in width of outer footing, p sx Hogging in length Sagging in width 20 mm 200 mm Sagging steel area provided in width of outer footing, A s,prov,x,s = (π.φ 2 sx /4)/p sx mm 2 /m Hogging steel reinforcement diameter in beam, φ hy 16 mm Hogging steel reinforcement number in beam, n hy 5 Hogging steel area provided in beam, A s,prov,y,h = n hy.π.φ hy 2 /4 mm 2

63 E N G I N E E R S Consulting Engineers jxxx 58 Shear link diameter for first shear perimeter of outer footing, φ link,2 0 mm Number of link legs for first shear perimeter of outer footing, n l,2 30 Area provided by all links for first shear perimeter of outer footing, A sv,prov,2 = mm 2 Shear link diameter for second shear perimeter of outer footing, φ link,3 0 mm Number of link legs for second shear perimeter of outer footing, n l,3 30 Area provided by all links for second shear perimeter of outer footing, A sv,prov, mm 2 Shear link diameter for bending in width of outer footing, φ link,x = φ link,2 0 mm Number of link legs per metre for bending in width of outer footing, n link,x 4 /m Area provided by all links per metre for bending in width of outer footing, A sv mm 2 /m Pitch of links for bending in width of outer footing, S x 150 mm Shear link diameter in beam, φ link,y 12 mm Number of links in a cross section in beam, i.e. number of legs, n link,y 2 Area provided by all links in a cross-section in beam, A sv,prov,y = π.φ 2 link,y /4.n link mm 2 Pitch of links in beam, S y 150 mm Effective depth to sagging steel in width of outer footing, d x,s = T strap - cover 1 Effective depth to hogging steel in beam, d y,h = h beam - cover 1 - φ link,y - φ hy /2 mm mm Estimated steel reinforcement quantity kg/m 3 [ (A s,prov,x,s ) / T strap (A s,prov,y,h ) / b beam h beam ]; No curtailment; No laps; Links ignored; Distr Strap Footing Foundation SLS Loading SLS vertical (downward) load from column 1 and base slab (if suspended), F c 650 kn SLS vertical (downward) load from column 2 and base slab (if suspended), F c 1000 kn Strap footing (projection beneath base slab) weight of outer footing, F under,stra kn Additional soil (above footing) weight, F above,soil,1 = B strap,1.l strap,1.max(0, D-t 1,s kn Note additional soil above the footing is included for embedded footings whereby the top of the footing is below ground level and backfilled, for conservatism the saturated soil density is adopted, and ρ c γ sat ; Strap footing (projection beneath base slab) weight of inner footing, F under,stra kn Additional soil (above footing) weight, F above,soil,2 = B 2 strap,2.max(0, D-t 1,strap ).γ s kn Note additional soil above the footing is included for embedded footings whereby the top of the footing is below ground level and backfilled, for conservatism the saturated soil density is adopted, and ρ c γ sat ; Strap beam weight, F beam,strap = b beam.h beam.ρ c.l strap kn Total foundation SLS vertical (downward) load of outer footing, F strap,v,1 kn Note F strap,v,1 = [F col,v,1.l strap + F beam,strap.l strap /2 + (F under,strap,1 +F above,soil,1 ).(L strap +h/2-l strap,1 /2)] / (L strap +h/2-l strap,1 /2); Note the value of F strap,v,1 is calculated by taking moments about the inner footing and solving for the reaction beneath the outer footing. This is essentially the sls reaction beneath the outer footing; Total foundation SLS vertical (downward) load of inner footing, F strap,v,2 kn Note F strap,v,2 = F col,v,1 + F col,v,2 + F beam,strap + F under,strap,1 + F above,soil,1 + F under,strap,2 + F above,soil,2 - F strap,v,1 ; Note the value of F strap,v,2 is calculated by resolving vertical loads; F strap,v,2 will be less than F col,v,2 ; This is essentially the sls reaction beneath the inner footing and must not be negative; Gross working pressure under outer footing, q w,1 = F strap,v,1 / (B strap,1. L strap,1 ) Gross working pressure under inner footing, q w,2 = F strap,v,2 / B strap,2 2 kpa kpa Strap Footing Foundation ULS Loading ULS vertical (downward) load from column 1 and base slab (if suspended), F c ULS vertical (downward) load from column 2 and base slab (if suspended), F c kn kn

64 E N G I N E E R S Consulting Engineers jxxx 59 Strap Footing Foundation Reinforcement Design Gross ULS Pressure Total foundation ULS vertical (downward) load of outer footing, F strap,v,1,uls kn Note F strap,v,1,uls = [F col,v,1,uls.l strap + 1.4F beam,strap.l strap /2] / (L strap +h/2-l strap,1 /2); Note the value of F strap,v,1,uls is calculated by taking moments about the inner footing and solving for the reaction beneath the outer footing. This is essentially the uls reaction beneath the outer footing; Gross ULS pressure under outer footing, q w,uls,1 = F strap,v,1,uls / (B strap,1. L strap,1 kpa Total foundation ULS vertical (downward) load of inner footing, F strap,v,2,uls Note F strap,v,2,uls = F col,v,1,uls + F col,v,2,uls + 1.4F beam,strap - F strap,v,1,uls ; kn Note the value of F strap,v,2,uls is calculated by resolving vertical loads; F strap,v,2,uls will be less than F col,v,2,uls ; This is essentially the uls reaction beneath the inner footing and must not be negative; Gross ULS pressure under inner footing, q w,uls,2 = F strap,v,2,uls / B strap,2 2 kpa F col,v,1,uls.r-q w,uls,1.b strap,1.(r+h/2) 2 /2 (F col,v,2,uls -F strap,v,2,uls ).B strap,2 /2 F col,v,2,uls -q w,uls,2.b strap,2.b strap,2 /2 Shear force diagram r F strap,v,1,uls -F col,v,1,uls Bending moment diagram ibution steel F col,v,1,uls ignored; -q w,uls,1.b strap,1.h/2 q w,uls,2.b strap,2.b strap,2 /2 Sagging Bending Moment Design in Plane of Width of Outer Footing Moment at column base face, M x = q w,uls,1. L strap,1. [(B strap,1 -(b or D))/2] 2 / 2 Moment at column base face per metre, M x /L strap,1 knm knm/m 2 Concrete moment capacity per metre, M u,x = 0.156f cu.1000.d x,s knm/m Bending stress, [M/bd 2 ] x = (M x /L strap,1 ) / [(1000).d 2 x,s ] N/mm 2 Bending stress ratio, K x = [M/bd 2 ] x / f cu <= Lever arm, z x = d x,s. [0.5 + (0.25-K x /0.9) 0.5 ] <= 0.95d x,s mm Area of tension steel required, A s,x = (M x /L strap,1 ) / [(0.95f y ).z x ] mm 2 /m Area of tensile steel reinforcement provided, A s,prov,x,s mm 2 /m Sagging bending moment in plane of width of outer footing utilisation = A s,x / Requirement to concentrate 2/3 rebar within 1.5d x,s fro [Yes if (L strap,1 -(h or D)/2)>3/4(h or D)+9/4d x,s ; No if mm mm BS8110 Note that should the above requirement be applicable, it is not automatically reflected in the detailing considerations and as such should be specifically reconsidered; % Min sag reinforcement in plane of width of outer footing (>= % % Min sag reinforcement in plane of width of outer footing utilisation

65 E N G I N E E R S Consulting Engineers jxxx 60 Hogging Bending Moment Design in Beam Distance to zero shear force from column 1, r = F col,v,1,uls /(q w,uls,1.b strap,1 ) - h/ Moment, M y = F col,v,1,uls. r - q w,uls,1. B strap,1. (r+h/2) 2 / 2 m knm 2 Concrete moment capacity, M u,y = 0.156f cu.b beam.d y,h knm Bending stress, [M/bd 2 ] y = M y / [b beam.d 2 y,h ] N/mm 2 Bending stress ratio, K y = [M/bd 2 ] y / f cu <= Lever arm, z y = d y,h. [0.5 + (0.25-K y /0.9) 0.5 ] <= 0.95d y,h mm Area of tension steel required, A s,y = M y / [(0.95f y ).z y ] mm 2 Area of tensile steel reinforcement provided, A s,prov,y,h mm 2 /m Hogging bending moment utilisation = A s,y / A s,prov,y,h % Min hog reinforcement in beam (>= b beam.h beam G250; >= % % Min hog reinforcement in beam utilisation

66 E N G I N E E R S Consulting Engineers jxxx 61 Punching Shear Design ULS vertical (downward) load from column and base slab (if suspended), F col, kn Area of column base section, A c1 = b.h (rectangular) or πd 2 /4 (circular) mm 2 Average effective depth of rebar layer, d = d x,s mm Area of tensile steel reinforcement provided, A s,prov,x,s mm 2 /m Average area of tensile steel reinforcement provided, A s,prov,s mm 2 /m ρ w = 100A s,prov,s /(1000.d) % ν c = (0.79/1.25)(ρ w f cu /25) 1/3 (400/d) 1/4 ; ρ w <3; f cu <40; (400/d) 1/4 >0.67 N/mm 2 Column Base Face Perimeter Shear force at column base face, V 1 = F col,v,1,uls - q w,uls,1.a c1 kn Effective shear force, V eff,1 = V 1 kn Note V eff,1 = V 1 because no moment effects assumed; Column base face perimeter, u 1 mm Rectangular Circular Internal column: 2.(b+h) π.d mm Edge column: 2b+h or 2h+b 3/4( π.d) mm Corner column: (b+h) π.d/2 mm Shear stress at column base face perimeter, ν 1 = V eff,1 / u 1 d (< 0.8f 0.5 cu & 5N N/mm 2 Ultimate shear stress utilisation First Shear Perimeter Shear force 1.5d from column base face, V 2 = F col,v,1,uls - q w,uls,1.a c2 Rectangular kn Internal column: (b+3d).(h+3d) (D+3d) 2 m 2 Edge column: (b+1.5d).(h+3d) or (h+1.5d).(b+3d) d).(d+3d) m 2 Corner column: (b+1.5d).(h+1.5d) (D+1.5d) 2 m 2 Effective shear force, V eff,2 = V 2 kn Note V eff,2 = V 2 because no moment effects assumed; Column base first perimeter, u 2 Rectangular Circular Circular mm Internal column: 2.(b+h)+12d 4 D+12d mm Edge column: 2b+h+6d or 2h+b+6d 3D+6d mm Corner column: (b+h)+3d 2D+3d mm Shear stress at column base first perimeter, ν 2 = V eff,2 / u 2 d N/mm 2 (Shear capacity enhancement by calculating v d at 1.5d from "support" and comparing against unenhanced v c as clause BS8110 employed instead of calculating v d at "support" and comparing against enhanced v c within 1.5d of the "support" as clause BS8110;) Case ν 2 < ν c No links required. Case ν c < ν 2 < 1.6ν c >= mm 2 Note >

67 E N G I N E E R S Consulting Engineers jxxx 62 Case 1.6ν c < ν 2 < 2.0ν c >= mm 2 Case ν 2 > 2.0ν c Note > First shear perimeter shear utilisation Second Shear Perimeter Shear force 2.25d from column base face, V 3 = F col,v,1,uls - q w,uls,1.a c3 Rectangular kn Internal column: (b+4.5d).(h+4.5d) (D+4.5d) 2 m 2 Edge column: (b+2.25d).(h+4.5d) or (h+2.25d).(b+4.5d) ).(D+4.5d) m 2 Corner column: (b+2.25d).(h+2.25d) D+2.25d) 2 m 2 Effective shear force, V eff,3 = V 3 kn Note V eff,3 = V 3 because no moment effects assumed; Column base second perimeter, u 3 Rectangular Circular Circular mm Internal column: 2.(b+h)+18d 4 D+18d mm Edge column: 2b+h+9d or 2h+b+9d 3D+9d mm Corner column: (b+h)+4.5d 2D+4.5d mm Shear stress at column base second perimeter, ν 3 = V eff,3 / u 3 d N/mm 2 Case ν 3 < ν c No links required. Case ν c < ν 3 < 1.6ν c >= mm 2 Note > Case 1.6ν c < ν 3 < 2.0ν c >= mm 2 Case ν 3 > 2.0ν c Note > Second shear perimeter shear utilisation Note a negative shear stress ν 2 and/or ν 3 on a correctly specified column (wrt internal, edge or corner) indicates that the shear perimeter is beyond the physical extremes of the foundation and as such punching shear failure is not critical;

68 E N G I N E E R S Consulting Engineers jxxx 63 Shear Design for Bending in Plane of Width of Outer Footing Shear force at column base face, V x,ult = q w,uls,1. L strap,1. [(B strap,1 -(b or D))/2 Shear force at column base face per metre, V x,ult /L strap,1 Shear force at 1.0d x,s from column base face, V x = q w,uls,1. L strap,1. [(B strap,1 -( Shear force at 1.0d x,s from column base face per metre, V x /L strap,1 Note the above shear forces are for bending in plane of width of outer footing; kn kn/m kn kn/m Ultimate shear stress for bending in plane of width, v ult,x =(V x,ult /L strap,1 )/(1000 N/mm 2 Ultimate shear stress for bending in plane of width utilisation Design shear stress for bending in plane of width, v d,x =(V x /L strap,1 )/(1000.d x,s ) N/mm 2 (Shear capacity enhancement by calculating v d at d from "support" and comparing against unenhanced v c as clause BS8110 employed instead of calculating v d at "support" and comparing against enhanced v c within 2d of the "support" as clause BS8110;) Area of tensile steel reinforcement provided, A s,prov,x,s mm 2 /m ρ w = 100A s,prov,x,s /(1000.d x,s ) % v c,x = (0.79/1.25)(ρ w f cu /25) 1/3 (400/d x,s ) 1/4 ; ρ w <3; f cu <40; (400/d x,s ) 1/4 >0.67 N/mm 2 Check v d,x < v c,x for no links Concrete shear capacity v c,x.(1000.d x,s ) kn/m Check v c,x < v d,x < v c,x for nominal links Provide nominal links such that A sv / S > 0.4.(1000)/(0.95f yv ) i.e. Concrete and nominal links shear capacity (0.4 + v c,x ).(1000.d x,s ) mm 2 /mm/m kn/m Check v d,x > v c,x for design links Provide shear links A sv / S > 1000.(v d,x -v c,x )/(0.95f yv ) i.e. A sv / S > Concrete and design links shear capacity (A sv,prov,x /S x ).(0.95f yv ).d x, mm 2 /mm/m kn/m Area provided by all links per metre, A sv,prov,x mm 2 /m Tried A sv,prov,x / S x value mm 2 /mm/m Design shear resistance for bending in plane of width of outer footing utilisati

69 E N G I N E E R S Consulting Engineers jxxx 64 Shear Design in Beam Shear force at column 1 base right centreline, V y,1 = F col,v,1,uls - q w,uls,1. B strap Shear force at outer footing right face, V y,2 = F strap,v,1,uls - F col,v,1,uls Shear force at column 2 base left centreline, V y,3 = F col,v,2,uls -q w,uls,2.b strap,2.b st Shear force at column 2 base right centreline, V y,4 = q w,uls,2.b strap,2.b strap,2 /2 Shear force at critical location, V y = MAX(V y,1, V y,2, V y,3, V y,4 ) kn kn kn kn kn Ultimate shear stress in beam, v ult,y =V y /(b beam.d y,h ) (< 0.8f cu 0.5 & 5N/mm 2 ) N/mm 2 Ultimate shear stress in beam utilisation Design shear stress in beam, v d,y =V y /(b beam.d y,h ) N/mm 2 (Conservatively, shear capacity enhancement by either calculating v d at d from support and comparing against unenhanced v c as clause BS8110 or calculating v d at support and comparing against enhanced v c within 2d of the support as clause BS8110 ignored;) Area of tensile steel reinforcement provided, A s,prov,y,h mm 2 Note it is assumed that A s,prov,y,h provided where critical shear force occurs; ρ w = 100A s,prov,y,h /(b beam.d y,h ) % v c,y = (0.79/1.25)(ρ w f cu /25) 1/3 (400/d y,h ) 1/4 ; ρ w <3; f cu <40; (400/d y,h ) 1/4 >0.67 N/mm 2 Check v d,y < 0.5v c,y for no links Concrete shear capacity v c,y.(b beam.d y,h ) kn Check 0.5v c,y < v d,y < v c,y for nominal links Provide nominal links such that A sv / S > 0.4b beam /(0.95f yv ) i.e. A sv Concrete and nominal links shear capacity (0.4 + v c,y ).(b beam d y,h ) mm 2 /mm kn Check v d,y > v c,y for design links Provide shear links A sv / S > b beam (v d,y -v c,y )/(0.95f yv ) i.e. A sv / S > Concrete and design links shear capacity (A sv,prov,y /S y ).(0.95f yv ).d y, mm 2 /mm kn Area provided by all links in a cross-section, A sv,prov,y mm 2 Tried A sv,prov,y / S y value mm 2 /mm Design shear resistance in beam utilisation

70 E N G I N E E R S Consulting Engineers jxxx 65 Detailing Requirements All detailing requirements met? Max sagging steel reinforcement pitch in plane of width of outer footing (<3d mm Max hogging steel reinforcement pitch in beam (<3d y,h, <750mm) mm Max sagging steel reinforcement pitch in plane of width of outer footing mm Max hogging steel reinforcement pitch in beam mm Min sagging steel reinforcement pitch in plane of width of outer footing (>100 mm Min hogging steel reinforcement pitch in beam (>100mm+φ sy ) mm Note an allowance has been made for laps in the min pitch by increasing the criteria by the bar diameter. Sagging steel reinforcement diameter in plane of width of outer footing, φ sx (> mm Hogging steel reinforcement diameter in beam, φ sy (>=16mm) mm % Max sagging reinforcement in plane of width of outer footing (<= % % Max hogging reinforcement in beam (<= 0.04.b beam.h beam ) % Min link diameter, φ link,y (>=8mm) mm Link pitch, S y (<=0.75d y,h, <=300mm, >=MAX(100mm, n link,y ) mm A sv,prov,y / (b beam.s y ) (>0.10% G460; >0.17% G250) % Note that only single layer of reinforcement assumed for beams in calculation of pitch;

71 E N G I N E E R S Consulting Engineers jxxx 66 Standard Strap Footing Foundation Reinforcement Details As per standard multi column footing reinforcement details;

72 E N G I N E E R S Consulting Engineers jxxx 67

73

74 E N G I N E E R S Consulting Engineers jxxx 68 Raft Foundation Dimensions Note that the raft is the two-dimensional version of the combination of multi column footings, combined footings and strap footings. These two-dimensional multi-column, combined and strap footings combinations can effectively be analysed and designed as an inverted flat slab in the case of a solid raft, or as an inverted one- or two-way spanning slab in the case of a stripped raft; Width, B raft (<=L raft ) m Length, L raft (>=B raft ) m Thickness of foundation, T raft m Raft Foundation SLS Loading SLS vertical (downward) load from selected building area, F bdarea kn Note that DL of base slab is to be included and is the DL of the raft; Note a selected building area may for instance refer to either the highly loaded core area or the normally loaded regular floor plate area, as they should be analysed and designed separately; Additional soil (above footing) weight, F above,soil = B raft.l raft.max(0, D-T raft ).γ sat kn Note additional soil above the footing is included for embedded footings whereby the top of the footing is below ground level and backfilled, for conservatism the saturated soil density is adopted, and ρ c γ sat ; Total foundation SLS vertical (downward) load, F raft,v = F bdarea + F above,soil kn Gross working pressure, q w = F raft,v / (B raft. L raft ) kpa Raft Foundation (Inverted) ULS Loading SLS vertical (downward) load from selected building area minus raft DL, F raft,v kn ULS vertical (downward) load from selected building area minus raft DL, F raft,v kn ULS vertical (downward) pressure from selected building area minus raft DL, kpa Note the above ULS vertical (downward) pressure can be applied on an inverted flat, one- or two-way spanning slab analysis as the ULS pressure for the determination of effects for the design of the solid or stripped raft foundation;

75 E N G I N E E R S Consulting Engineers jxxx 69 Raft Foundation Reinforcement Design Design reinforcement based on the combination of multi column footings, combined footings and strap footings reinforcement designs, culminating in the reinforcement design of a two-dimensional inverted flat, one- or two-way spanning slab as the raft foundation;

76 E N G I N E E R S Consulting Engineers jxxx 70 Standard Raft Foundation Reinforcement Details Design reinforcement based on the combination of standard multi column footing, standard combined footing and standard strap footing reinforcement details, culminating in the standard reinforcement detailing of a two-dimensional inverted flat, one- or two-way spanning slab as the raft foundation;

77 E N G I N E E R S Consulting Engineers jxxx 71

78 E N G I N E E R S Consulting Engineers jxxx 72

79 E N G I N E E R S Consulting Engineers jxxx 73

80 E N G I N E E R S Consulting Engineers jxxx 74

81 E N G I N E E R S Consulting Engineers jxxx 75

82 E N G I N E E R S Consulting Engineers jxxx 76

83 E N G I N E E R S Consulting Engineers jxxx 77

84 E N G I N E E R S Consulting Engineers jxxx 78

85

86 E N G I N E E R S Consulting Engineers jxxx 79 Building Regulations Minimum Dimensions Minimum Width Stepped Foundations Piers and Chimneys

87 E N G I N E E R S Consulting Engineers jxxx 80 Minimum Thickness

88 E N G I N E E R S Consulting Engineers jxxx 81 Minimum Depth (Frost Heave in Granular or Cohesive Soils) Minimum depth is 450mm to avoid frost heave, but this is often exceeded due to other Minimum Depth (Volume Change in Cohesive Soils Without Trees) This is applicable to cohesive soils only, not granular soils. For there to be no influence from trees, the following minimum distance must be satisfied (NHBC, 2002):- Low water demand trees = 0.2 x mature height Moderate water demand trees = 0.5 x mature height High water demand trees = 1.25 x mature height Minimum depth to avoid seasonal volume changes due to wetting and drying of expandable and shrinkable clays are as follows (NHBC, 2002):- Low plasticity index (10-20%) = 750mm Medium plasticity index (10-40%) = 900mm High plasticity index (>40%) = 1000mm

89 E N G I N E E R S Consulting Engineers jxxx 82 Minimum Depth (Volume Change in Cohesive Soils With Trees)

90 E N G I N E E R S Consulting Engineers jxxx 83

91 E N G I N E E R S Consulting Engineers jxxx 84