RAFT FOUNDATION DESIGN IN ACCORDANCE WITH BS8110:PART _FOR MULTISTOREY BUILDING (BS8110 : PART 1 : 1997)

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1 App'd by RAFT FOUNDATION DESIGN IN ACCORDANCE WITH BS8110:PART _FOR MULTISTOREY BUILDING (BS8110 : PART 1 : 1997) A sedgetop A sslabtop A sedgelink h slab h edge h hcoreslab h boot a edge A sslabbtm h hcorethick b boot b edge A sedgebtm Soil and raft definition Soil definition Allowable bearing pressure; q allow = 75.0 kn/m 2 Number of types of soil forming sub-soil; Two or more types Soil density; Firm to loose Depth of hardcore beneath slab; h hcoreslab = 200 mm; (Dispersal allowed for bearing pressure check) Depth of hardcore beneath thickenings; h hcorethick = 0 mm; (Dispersal allowed for bearing pressure check) Density of hardcore; γ hcore = 20.0 kn/m 3 Basic assumed diameter of local depression; φ depbasic = 3500mm Diameter under slab modified for hardcore; φ depslab = φ depbasic - h hcoreslab = 3300 mm Diameter under thickenings modified for hardcore; φ depthick = φ depbasic - h hcorethick = 3500 mm Raft slab definition Max dimension/max dimension between joints; l max = m Slab thickness; h slab = 250 mm Concrete strength; f cu = 35 N/mm 2 Poissons ratio of concrete; ν = 0.2 Slab mesh reinforcement strength; f yslab = 500 N/mm 2 Partial safety factor for steel reinforcement; γ s = 1.15 Page 1 of 14

2 App'd by From C&CA document Concrete ground floors Table 5 Minimum mesh required in top for shrinkage; A142; Actual mesh provided in top; A393 (A sslabtop = 393 mm 2 /m) Mesh provided in bottom; A393 (A sslabbtm = 393 mm 2 /m) Top mesh bar diameter; φ slabtop = 10 mm Bottom mesh bar diameter; φ slabbtm = 10 mm Cover to top reinforcement; c top = 20 mm Cover to bottom reinforcement; c btm = 40 mm Average effective depth of top reinforcement; d tslabav = h slab - c top - φ slabtop = 220 mm Average effective depth of bottom reinforcement; d bslabav = h slab - c btm - φ slabbtm = 200 mm Overall average effective depth; d slabav = (d tslabav + d bslabav)/2 = 210 mm Minimum effective depth of top reinforcement; d tslabmin = d tslabav - φ slabtop/2 = 215 mm Minimum effective depth of bottom reinforcement; d bslabmin = d bslabav - φ slabbtm/2 = 195 mm Edge beam definition Overall depth; h edge = 600 mm Width; b edge = 550 mm Depth of boot; h boot = 250 mm Width of boot; b boot = 250 mm Angle of chamfer to horizontal; α edge = 60 deg Strength of main bar reinforcement; f y = 500 N/mm 2 Strength of link reinforcement; f ys = 500 N/mm 2 Reinforcement provided in top; 3 H25 bars (A sedgetop = 1473 mm 2 ) Reinforcement provided in bottom; 3 H20 bars (A sedgebtm = 942 mm 2 ) Link reinforcement provided; 2 H12 legs at 250 ctrs (A sv/s v = mm) Bottom cover to links; c beam = 40 mm Effective depth of top reinforcement; d edgetop = h edge - c top - φ slabtop - φ edgelink - φ edgetop/2 = 546 mm Effective depth of bottom reinforcement; d edgebtm = h edge - c beam - φ edgelink - φ edgebtm/2 = 538 mm Boot main reinforcement; H8 bars at 250 ctrs (A sboot = 201 mm 2 /m) Effective depth of boot reinforcement; d boot = h boot - c beam - φ boot/2 = 206 mm Internal beam definition Page 2 of 14

3 App'd by A sintlink A sinttop A sslabtop h slab h int h hcoreslab a int A sslabbtm h hcorethick b int A sintbtm Overall depth; h int = 550 mm Width; b int = 500 mm Angle of chamfer to horizontal; α int = 60 deg Strength of main bar reinforcement; f y = 500 N/mm 2 Strength of link reinforcement; f ys = 500 N/mm 2 Reinforcement provided in top; 3 H25 bars (A sinttop = 1473 mm 2 ) Reinforcement provided in bottom; 3 H25 bars (A sintbtm = 1473 mm 2 ) Link reinforcement provided; 2 H12 legs at 225 ctrs (A sv/s v = mm) Effective depth of top reinforcement; d inttop = h int - c top - 2 φ slabtop - φ inttop/2 = 498 mm Effective depth of bottom reinforcement; d intbtm = h int - c beam - φ intlink - φ intbtm/2 = 486 mm Internal slab design checks Basic loading Slab self weight; w slab = 24 kn/m 3 h slab = 6.0 kn/m 2 Hardcore; w hcoreslab = γ hcore h hcoreslab = 4.0 kn/m 2 Applied loading Uniformly distributed dead load; w Dudl = 2.0 kn/m 2 Uniformly distributed live load; w Ludl = 2.5 kn/m 2 Slab load number 1 Page 3 of 14

4 Line load width; Line load w D1 = 3.0 kn/m w L1 = 2.0 kn/m w ult1 = 1.4 w D w L1 = 7.4 kn/m b 1 = 140 mm App'd by Internal slab bearing pressure check Total uniform load at formation level; w udl = w slab + w hcoreslab + w Dudl + w Ludl = 14.5 kn/m 2 Bearing pressure beneath load number 1 Net bearing pressure available to resist line load; q net = q allow - w udl = 60.5 kn/m 2 Net ultimate bearing pressure available; q netult = q net w ult1/(w D1 + w L1) = 89.5 kn/m 2 Loaded width required at formation; l req1 = w ult1/q netult = m Effective loaded width at u/side slab; l eff1 = max(b 1, l req1-2 h hcoreslab tan(30)) = m Effective net ult bearing pressure at u/side slab; q netulteff = q netult l req1/l eff1 = 52.9 kn/m 2 Cantilever bending moment; M cant1 = q netulteff [(l eff1 - b 1)/2] 2 /2 = 0.0 knm/m Reinforcement required in bottom Maximum cantilever moment; M cantmax = 0.0 knm/m K factor; K slabbp = M cantmax/(f cu d 2 bslabmin ) = z slabbp = d bslabmin min(0.95, ( K slabbp/0.9)) = mm Area of steel required; A sslabbpreq = M cantmax/((1.0/γ s) f yslab z slabbp) = 0 mm 2 /m PASS - A sslabbpreq <= A sslabbtm - Area of reinforcement provided to distribute the load is adequate The allowable bearing pressure will not be exceeded Internal slab bending and shear check Applied bending moments Span of slab; l slab = φ depslab + d tslabav = 3520 mm Ultimate self weight udl; w swult = 1.4 w slab = 8.4 kn/m 2 Self weight moment at centre; M csw = w swult l 2 slab (1 + ν) / 64 = 2.0 knm/m Self weight moment at edge; M esw = w swult l 2 slab / 32 = 3.3 knm/m Self weight shear force at edge; V sw = w swult l slab / 4 = 7.4 kn/m Moments due to applied uniformly distributed loads Ultimate applied udl; w udlult = 1.4 w Dudl w Ludl = 6.8 kn/m 2 Moment at centre; M cudl = w udlult l 2 slab (1 + ν) / 64 = 1.6 knm/m Moment at edge; M eudl = w udlult l 2 slab / 32 = 2.6 knm/m Shear force at edge; V udl = w udlult l slab / 4 = 6.0 kn/m Moment due to load number 1 Approximate equivalent udl; w udl1 = w ult1/(2 0.3 l slab) = 3.5 kn/m 2 Moment at centre; M c1 = w udl1 l 2 slab (1 + ν) / 64 = 0.8 knm/m Moment at edge; M e1 = w udl1 l 2 slab / 32 = 1.4 knm/m Shear force at edge; V 1 = w udl1 l slab / 4 = 3.1 kn/m Resultant moments and shears Total moment at edge; M Σe = 7.2 knm/m Page 4 of 14

5 Total moment at centre; Total shear force; M Σc = 4.3 knm/m V Σ = 16.5 kn/m App'd by Reinforcement required in top K factor; K slabtop = M Σe/(f cu d 2 tslabav ) = z slabtop = d tslabav min(0.95, ( K slabtop/0.9)) = mm Area of steel required for bending; A sslabtopbend = M Σe/((1.0/γ s) f yslab z slabtop) = 80 mm 2 /m Minimum area of steel required; A sslabmin = h slab = 325 mm 2 /m Area of steel required; A sslabtopreq = max(a sslabtopbend, A sslabmin) = 325 mm 2 /m PASS - A sslabtopreq <= A sslabtop - Area of reinforcement provided in top to span local depressions is adequate Reinforcement required in bottom K factor; K slabbtm = M Σc/(f cu d 2 bslabav ) = z slabbtm = d bslabav min(0.95, ( K slabbtm/0.9)) = mm Area of steel required for bending; A sslabbtmbend = M Σc/((1.0/γ s) f yslab z slabbtm) = 53 mm 2 /m Area of steel required; A sslabbtmreq = max(a sslabbtmbend, A sslabmin) = 325 mm 2 /m PASS - A sslabbtmreq <= A sslabbtm - Area of reinforcement provided in bottom to span local depressions is adequate Shear check Applied shear stress; v = V Σ /d tslabmin = N/mm 2 Tension steel ratio; ρ = 100 A sslabtop/d tslabmin = From BS8110-1: Table 3.8; Design concrete shear strength; v c = N/mm 2 PASS - v <= v c - Shear capacity of the slab is adequate Internal slab deflection check Basic allowable span to depth ratio; Ratio basic = 26.0 Moment factor; M factor = M Σc/d 2 bslabav = N/mm 2 Steel service stress; f s = 2/3 f yslab A sslabbtmbend/a sslabbtm = N/mm 2 Modification factor; MF slab = min(2.0, [(477N/mm 2 - f s)/(120 (0.9N/mm 2 + M factor))]) MF slab = Modified allowable span to depth ratio; Ratio allow = Ratio basic MF slab = Actual span to depth ratio; Ratio actual = l slab/ d bslabav = PASS - Ratio actual <= Ratio allow - Slab span to depth ratio is adequate Edge beam design checks Basic loading Hardcore; w hcorethick = γ hcore h hcorethick = 0.0 kn/m 2 Edge beam Rectangular beam element; w beam = 24 kn/m 3 h edge b edge = 7.9 kn/m Boot element; w boot = 24 kn/m 3 h boot b boot = 1.5 kn/m Chamfer element; w chamfer = 24 kn/m 3 (h edge - h slab) 2 /(2 tan(α edge)) = 0.8 kn/m Slab element; w slabelmt = 24 kn/m 3 h slab (h edge - h slab)/tan(α edge) = 1.2 kn/m Edge beam self weight; w edge = w beam + w boot + w chamfer + w slabelmt = 11.5 kn/m Page 5 of 14

6 App'd by Edge load number 1 Longitudinal line load width; Centroid of load from outside face of raft; Edge load number 2 Longitudinal line load width; Centroid of load from outside face of raft; Longitudinal line load w Dedge1 = 13.2 kn/m w Ledge1 = 0.0 kn/m w ultedge1 = 1.4 w Dedge w Ledge1 = 18.5 kn/m b edge1 = 102 mm x edge1 = 51 mm Longitudinal line load w Dedge2 = 16.1 kn/m w Ledge2 = 5.6 kn/m w ultedge2 = 1.4 w Dedge w Ledge2 = 31.5 kn/m b edge2 = 100 mm x edge2 = 230 mm Edge beam bearing pressure check Effective bearing width of edge beam; b bearing = b edge + b boot + (h edge - h slab)/tan(α edge) = 1002 mm Total uniform load at formation level; w udledge = w Dudl+w Ludl+w edge/b bearing+w hcorethick = 16.0 kn/m 2 Centroid of longitudinal and equivalent line loads from outside face of raft Load x distance for edge load 1; Moment 1 = w ultedge1 x edge1 = 0.9 kn Load x distance for edge load 2; Moment 2 = w ultedge2 x edge2 = 7.2 kn Sum of ultimate longitud l and equivalent line loads; ΣUDL = 50.0 kn/m Sum of load x distances; ΣMoment = 8.2 kn Centroid of loads; x bar = ΣMoment/ΣUDL = 164 mm Initially assume no moment transferred into slab due to load/reaction eccentricity Sum of unfactored longitud l and eff tive line loads; ΣUDLsls = 34.9 kn/m Allowable bearing width; b allow = 2 x bar + 2 h hcoreslab tan(30) = 559 mm Bearing pressure due to line/point loads; q linepoint = ΣUDLsls/ b allow = 62.5 kn/m 2 Total applied bearing pressure; q edge = q linepoint + w udledge = 78.4 kn/m 2 q edge > q allow - The slab is required to resist a moment due to eccentricity Now assume moment due to load/reaction eccentricity is resisted by slab Bearing width required; b req = ΣUDLsls/(q allow - w udledge) = 591 mm Effective bearing width at u/s of slab; b reqeff = b req - 2 h hcoreslab tan(30) = 360 mm Load/reaction eccentricity; e = b reqeff/2 - x bar = 16 mm Ultimate moment to be resisted by slab; M ecc = ΣUDL e = 0.8 knm/m From slab bending check Moment due to depression under slab (hogging); M Σe = 7.2 knm/m Total moment to be resisted by slab top steel; M slabtop = M ecc + M Σe = 8.1 knm/m K factor; K slab = M slabtop/(f cu d 2 tslabmin ) = z slab = d tslabmin min(0.95, ( K slab/0.9)) = 204 mm Area of steel required; A sslabreq = M slabtop/((1.0/γ s) 460 N/mm 2 z slab) = 99 mm 2 /m Page 6 of 14

7 App'd by PASS - A sslabreq <= A sslabtop - Area of reinforcement provided to transfer moment into slab is adequate The allowable bearing pressure under the edge beam will not be exceeded Edge beam bending check Divider for moments due to udl s; β udl = 12.0 Applied bending moments Span of edge beam; Ultimate self weight udl; Ultimate slab udl (approx); Self weight and slab bending moment; Self weight shear force; l edge = φ depthick + d edgetop = 4045 mm w edgeult = 1.4 w edge = 16.1 kn/m w edgeslab = max(0 kn/m,1.4 w slab ((φ depthick/2 3/4)-(b edge+(h edge-h slab)/tan(α edge)))) w edgeslab = 4.7 kn/m M edgesw = (w edgeult + w edgeslab) l 2 edge /β udl = 28.3 knm V edgesw = (w edgeult + w edgeslab) l edge/2 = 42.0 kn Moments due to applied uniformly distributed loads Ultimate udl (approx); Moment and shear due to load number 1 Moment and shear due to load number 2 w edgeudl = w udlult φ depthick/2 3/4 = 8.9 kn/m M edgeudl = w edgeudl l 2 edge /β udl = 12.2 knm V edgeudl = w edgeudl l edge/2 = 18.1 kn M edge1 = w ultedge1 l 2 edge /β udl = 25.2 knm V edge1 = w ultedge1 l edge/2 = 37.4 kn M edge2 = w ultedge2 l 2 edge /β udl = 43.0 knm V edge2 = w ultedge2 l edge/2 = 63.7 kn Resultant moments and shears Total moment (hogging and sagging); Maximum shear force; M Σedge = knm V Σedge = kn Reinforcement required in top Width of section in compression zone; b edgetop = b edge + b boot = 800 mm Average web width; b w = b edge + (h edge/tan(α edge))/2 = 723 mm K factor; K edgetop = M Σedge/(f cu b edgetop d 2 edgetop ) = z edgetop = d edgetop min(0.95, ( K edgetop/0.9)) = 518 mm Area of steel required for bending; A sedgetopbend = M Σedge/((1.0/γ s) f y z edgetop) = 482 mm 2 Minimum area of steel required; A sedgetopmin = b w h edge = 564 mm 2 Area of steel required; A sedgetopreq = max(a sedgetopbend, A sedgetopmin) = 564 mm 2 PASS - A sedgetopreq <= A sedgetop - Area of reinforcement provided in top of edge beams is adequate Reinforcement required in bottom Width of section in compression zone; b edgebtm = b edge + (h edge - h slab)/tan(α edge) l edge = 1157 mm K factor; K edgebtm = M Σedge/(f cu b edgebtm d 2 edgebtm ) = z edgebtm = d edgebtm min(0.95, ( K edgebtm/0.9)) = 511 mm Area of steel required for bending; A sedgebtmbend = M Σedge/((1.0/γ s) f y z edgebtm) = 489 mm 2 Minimum area of steel required; A sedgebtmmin = b w h edge = 564 mm 2 Page 7 of 14

8 App'd by Area of steel required; A sedgebtmreq = max(a sedgebtmbend, A sedgebtmmin) = 564 mm 2 PASS - A sedgebtmreq <= A sedgebtm - Area of reinforcement provided in bottom of edge beams is adequate Edge beam shear check Applied shear stress; v edge = V Σedge/(b w d edgetop) = N/mm 2 Tension steel ratio; ρ edge = 100 A sedgetop/(b w d edgetop) = From BS8110-1: Table 3.8 Design concrete shear strength; v cedge = N/mm 2 v edge <= v cedge + 0.4N/mm 2 - Therefore minimum links required Link area to spacing ratio required; A sv_upon_s vreqedge = 0.4N/mm 2 b w/((1.0/γ s) f ys) = mm Link area to spacing ratio provided; A sv_upon_s vprovedge = N edgelink π φ 2 edgelink /(4 s vedge) = mm PASS - A sv_upon_s vreqedge <= A sv_upon_s vprovedge - Shear reinforcement provided in edge beams is adequate Boot design check Effective cantilever span; l boot = b boot + d boot/2 = 353 mm Approximate ultimate bearing pressure; q ult = 1.55 q allow = kn/m 2 Cantilever moment; M boot = q ult l boot 2 /2 = 7.2 knm/m V boot = q ult l boot = 41.0 kn/m K factor; K boot = M boot/(f cu d boot 2 ) = z boot = d boot min(0.95, ( K boot/0.9)) = 196 mm Area of reinforcement required; A sbootreq = M boot/((1.0/γ s) f yboot z boot) = 85 mm 2 /m PASS - A sbootreq <= A sboot - Area of reinforcement provided in boot is adequate for bending Applied shear stress; v boot = V boot/d boot = N/mm 2 Tension steel ratio; ρ boot = 100 A sboot/d boot = From BS8110-1: Table 3.8 Design concrete shear strength; v cboot = N/mm 2 Corner design checks Basic loading Corner load number 1 PASS - v boot <= v cboot - Shear capacity of the boot is adequate Centroid of load from outside face of raft; Corner load number 2 Centroid of load from outside face of raft; Corner load number 3 Line load in x direction w Dcorner1 = 13.2 kn/m w Lcorner1 = 0.0 kn/m w ultcorner1 = 1.4 w Dcorner w Lcorner1 = 18.5 kn/m y corner1 = 51 mm Line load in x direction w Dcorner2 = 16.1 kn/m w Lcorner2 = 5.6 kn/m w ultcorner2 = 1.4 w Dcorner w Lcorner2 = 31.5 kn/m y corner2 = 230 mm Page 8 of 14

9 App'd by Centroid of load from outside face of raft; Corner load number 4 Centroid of load from outside face of raft; Corner load number 5 Centroid of load from outside face of raft; Line load in y direction w Dcorner3 = 14.3 kn/m w Lcorner3 = 0.0 kn/m w ultcorner3 = 1.4 w Dcorner w Lcorner3 = 20.0 kn/m x corner3 = 51 mm Line load in y direction w Dcorner4 = 11.7 kn/m w Lcorner4 = 0.0 kn/m w ultcorner4 = 1.4 w Dcorner w Lcorner4 = 16.4 kn/m x corner4 = 230 mm Line load in y direction w Dcorner5 = 15.0 kn/m w Lcorner5 = 0.0 kn/m w ultcorner5 = 1.4 w Dcorner w Lcorner5 = 21.0 kn/m x corner5 = 230 mm Corner bearing pressure check Total uniform load at formation level; w udlcorner = w Dudl+w Ludl+w edge/b bearing+w hcorethick = 16.0 kn/m 2 Net bearing press avail to resist line/point loads; q netcorner = q allow - w udlcorner = 59.0 kn/m 2 Total line/point loads Total unfactored line load in x direction; Total ultimate line load in x direction; Total unfactored line load in y direction; Total ultimate line load in y direction; Total unfactored point load; Total ultimate point load; Length of side of sq reqd to resist line/point loads; w Σlinex = 34.9 kn/m w Σultlinex =50.0 kn/m w Σliney = 41.0 kn/m w Σultliney = 57.4 kn/m w Σpoint = 0.0 kn w Σultpoint = 0.0 kn p corner =[w Σlinex+w Σliney+ ((w Σlinex+w Σliney) 2 +4 q netcorner w Σpoint)]/(2 q netcorner) p corner = 1286 mm Bending moment about x-axis due to load/reaction eccentricity Moment due to load 1 (x line); Moment due to load 2 (x line); Total moment about x axis; M x1 = max(0 knm, w ultcorner1 p corner (p corner/2 - y corner1)) = 14.1 knm M x2 = max(0 knm, w ultcorner2 p corner (p corner/2 - y corner2)) = 16.7 knm M Σx = 30.8 knm Bending moment about y-axis due to load/reaction eccentricity Moment due to load 3 (y line); Moment due to load 4 (y line); Moment due to load 5 (y line); Total moment about y axis; M y3 = max(0 knm, w ultcorner3 p corner (p corner/2 - x corner3)) = 15.2 knm M y4 = max(0 knm, w ultcorner4 p corner (p corner/2 - x corner4)) = 8.7 knm M y5 = max(0 knm, w ultcorner5 p corner (p corner/2 - x corner5)) = 11.1 knm M Σy = 35.1 knm Check top reinforcement in edge beams for load/reaction eccentric moment Max moment due to load/reaction eccentricity; M Σ = max(m Σx, M Σy) = 35.1 knm Page 9 of 14

10 App'd by Assume all of this moment is resisted by edge beam From edge beam design checks away from corners Moment due to edge beam spanning depression; M Σedge = knm Total moment to be resisted; M Σcornerbp = M Σ + M Σedge = knm Width of section in compression zone; b edgetop = b edge + b boot = 800 mm K factor; K cornerbp = M Σcornerbp/(f cu b edgetop d 2 edgetop ) = z cornerbp = d edgetop min(0.95, ( K cornerbp/0.9)) = 518 mm Total area of top steel required; A scornerbp = M Σcornerbp /((1.0/γ s) f y z cornerbp) = 638 mm 2 PASS - A scornerbp <= A sedgetop - Area of reinforcement provided to resist eccentric moment is adequate The allowable bearing pressure at the corner will not be exceeded Corner beam bending check Cantilever span of edge beam; Moment and shear due to self weight Ultimate self weight udl; Average ultimate slab udl (approx); Self weight and slab bending moment; Self weight and slab shear force; Moment and shear due to udls Maximum ultimate udl; l corner = φ depthick/ (2) + d edgetop/2 = 2748 mm w edgeult = 1.4 w edge = 16.1 kn/m w cornerslab = max(0 kn/m,1.4 w slab (φ depthick/( (2) 2)-(b edge+(h edge-h slab)/tan(α edge)))) w cornerslab = 4.1 kn/m M cornersw = (w edgeult + w cornerslab) l 2 corner /2 = 76.1 knm V cornersw = (w edgeult + w cornerslab) l corner = 55.4 kn w cornerudl = ((1.4 w Dudl)+(1.6 w Ludl)) φ depthick/ (2) = 16.8 kn/m M cornerudl = w cornerudl l 2 corner /6 = 21.2 knm V cornerudl = w cornerudl l corner/2 = 23.1 kn Moment and shear due to line loads in x direction M cornerlinex = w Σultlinex l 2 corner /2 = knm V cornerlinex = w Σultlinex l corner = kn Moment and shear due to line loads in y direction M cornerliney = w Σultliney l 2 corner /2 = knm V cornerliney = w Σultliney l corner = kn Total moments and shears due to point loads Bending moment about x axis; Bending moment about y axis; M cornerpointx = 0.0 knm M cornerpointy = 0.0 knm V cornerpoint = 0.0 kn Resultant moments and shears Total moment about x axis; M Σcornerx = M cornersw+ M cornerudl+ M cornerliney+ M cornerpointx = knm Total shear force about x axis; V Σcornerx = V cornersw+ V cornerudl+ V cornerliney + V cornerpoint = kn Total moment about y axis; M Σcornery = M cornersw+ M cornerudl+ M cornerlinex+ M cornerpointy = knm Total shear force about y axis; V Σcornery = V cornersw+ V cornerudl+ V cornerlinex + V cornerpoint = kn Deflection of both edge beams at corner will be the same therefore design for average of these moments and shears Design bending moment; M Σcorner = (M Σcornerx + M Σcornery)/2 = knm Page 10 of 14

11 Design shear force; V Σcorner = (V Σcornerx + V Σcornery)/2 = kn App'd by Reinforcement required in top of edge beam K factor; K corner = M Σcorner/(f cu b edgetop d 2 edgetop ) = z corner = d edgetop min(0.95, ( K corner/0.9)) = 518 mm Area of steel required for bending; A scornerbend = M Σcorner/((1.0/γ s) f y z corner) = 1331 mm 2 Minimum area of steel required; A scornermin = A sedgetopmin = 564 mm 2 Area of steel required; A scorner = max(a scornerbend, A scornermin) = 1331 mm 2 PASS - A scorner <= A sedgetop - Area of reinforcement provided in top of edge beams at corners is adequate Corner beam shear check Average web width; b w = b edge + (h edge/tan(α edge))/2 = 723 mm Applied shear stress; v corner = V Σcorner/(b w d edgetop) = N/mm 2 Tension steel ratio; ρ corner = 100 A sedgetop/(b w d edgetop) = From BS8110-1: Table 3.8 Design concrete shear strength; v ccorner = N/mm 2 v corner <= v ccorner + 0.4N/mm 2 - Therefore minimum links required Link area to spacing ratio required; A sv_upon_s vreqcorner = 0.4N/mm 2 b w/((1.0/γ s) f ys) = mm Link area to spacing ratio provided; A sv_upon_s vprovedge = N edgelink π φ 2 edgelink /(4 s vedge) = mm PASS - A sv_upon_s vreqcorner <= A sv_upon_s vprovedge - Shear reinforcement provided in edge beams at corners is adequate Corner beam deflection check Basic allowable span to depth ratio; Ratio basiccorner = 7.0 Moment factor; M factorcorner = M Σcorner/(b edgetop d 2 edgetop ) = N/mm 2 Steel service stress; f scorner = 2/3 f y A scornerbend/a sedgetop = N/mm 2 Modification factor; MF corner=min(2.0,0.55+[(477n/mm 2 -f scorner)/(120 (0.9N/mm 2 +M factorcorner))]) MF corner = Modified allowable span to depth ratio; Ratio allowcorner = Ratio basiccorner MF corner = Actual span to depth ratio; Ratio actualcorner = l corner/ d edgetop = PASS - Ratio actualcorner <= Ratio allowcorner - Edge beam span to depth ratio is adequate Internal beam design checks Basic loading Hardcore; w hcorethick = γ hcore h hcorethick = 0.0 kn/m 2 Internal beam self weight; Internal beam load number 1 Longitudinal line load width; Centroid of load from centreline of beam; w int=24 kn/m 3 [(h int b int)+(h int-h slab) 2 /tan(α int)+2 h slab (h int-h slab)/tan(α int)] w int = 9.9 kn/m Longitudinal line load w Dint1 = 15.0 kn/m w Lint1 = 5.3 kn/m w ultint1 = 1.4 w Dint w Lint1 = 29.5 kn/m b int1 = 140 mm x int1 = 0 mm Page 11 of 14

12 Internal beam load number 2 Transverse line load width; Full transverse line load; w Dint2 = 10.0 kn/m w Lint2 = 4.0 kn/m w ultint2 = 1.4 w Dint w Lint2 = 20.4 kn/m b int2 = 140 mm App'd by Internal beam bearing pressure check Total uniform load at formation level; w udlint = w Dudl+w Ludl+w hcorethick+24kn/m 3 h int = 17.7 kn/m 2 Effective point load due to transverse line/point loads Effective point load due to load 2 (Line load); W int2 = w ultint2 [b int + 2 (h int - h slab)/tan(α int)] = 17.3 kn Total effective point load; W int = 17.3 kn Minimum width of effective point load; b intmin = 140 mm Approximate longitudinal dispersal of effective point load Approx moment capacity of bottom steel; M intbtm = (1.0/γ s) f y 0.9 d intbtm A sintbtm = knm Max allow dispersal based on moment capacity; p intmom = [2 M intbtm + (4 M 2 intbtm +2 W int M intbtm b intmin)]/w int p intmom = mm Limiting max dispersal to say 5 x beam depth; p int = min(p intmom, 5 h int) = 2750 mm Total dispersal length of effective point load; l inteff = 2 p int + b intmin = 5640 mm Equivalent and total beam line loads Equivalent ultimate udl of internal load 2; w intudl2 = W int2/l inteff = 3.1 kn/m Equivalent unfactored udl of internal load 2; w intudl2sls = w intudl2 (w Dint2 + w Lint2)/w ultint2 = 2.1 kn/m Sum of factored longitud l and eff tive line loads; ΣUDL int = 32.5 kn/m Sum of unfactored longitud l and eff tive line loads; ΣUDLsls int = 22.4 kn/m Centroid of loads from centreline of internal beam Load x distance for internal load 1; Moment int1 = w ultint1 x int1 = 0.0 kn Sum of load x distances; ΣMoment int = 0.0 kn Centroid of loads; x barint = ΣMoment int/σudl int = 0.0 mm Moment due to eccentricity to be resisted by slab; M eccint = ΣUDL int abs(x barint) = 0.0 knm/m Assume moment due to eccentricity is resisted equally by top steel of slab on one side and bottom steel of slab on other From slab bending check Moment due to depression under slab (hogging); M Σe = 7.2 knm/m Total moment to be resisted by slab top steel; M slabtopint = M eccint/2 + M Σe = 7.2 knm/m K factor; K slabtopint = M slabtopint/(f cu d 2 tslabmin ) = z slabtopint = d tslabmin min(0.95, ( K slabtopint/0.9)) = 204 mm Area of steel required; A sslabtopintreq = M slabtopint/((1.0/γ s) f yslab z slabtopint) = 82 mm 2 /m PASS - A sslabtopintreq <= A sslabtop - Area of reinforcement in top of slab is adequate to transfer moment into slab Mt to be resisted by slab btm stl due to load ecc ty; M slabbtmint = M eccint/2 = 0.0 knm/m K factor; K slabbtmint = M slabbtmint/(f cu d 2 bslabmin ) = z slabbtmint = d bslabmin min(0.95, (0.25-K slabbtmint/0.9)) = 185 mm Area of steel required in bottom; A sslabbtmintreq = M slabbtmint/((1.0/γ s) f yslab z slabbtmint) = 0 mm 2 /m Page 12 of 14

13 App'd by PASS - A sslabbtmintreq <= A sslabbtm - Area of reinforcement in bottom of slab is adequate to transfer moment into slab Bearing pressure Initially check bearing pressure based on beam soffit/chamfer width only Allowable bearing width; b bearint = b int + 2 (h int - h slab)/tan(α int) = 846 mm Bearing pressure due to line/point loads; q linepointint = ΣUDLsls int/b bearint = 26.5 kn/m 2 Total applied bearing pressure; q int = q linepointint + w udlint = 44.2 kn/m 2 PASS - q int <= q allow - Allowable bearing pressure is not exceeded Internal beam bending check Divider for moments due to udl s; β udl = 12.0 Divider for moments due to point loads; β point = 7.0 Applied bending moments Span of internal beam; Ultimate self weight udl; Ultimate slab udl (approx); Self weight and slab bending moment; Self weight shear force; l int = φ depthick + d inttop = 3998 mm w intult = 1.4 w int = 13.9 kn/m w intslab = max(0 kn/m,1.4 w slab ((φ depthick 3/4)-(b int+2 (h int-h slab)/tan(α int)))) w intslab = 14.9 kn/m M intsw = (w intult + w intslab) l 2 int /β udl = 38.4 knm V intsw = (w intult + w intslab) l int/2 = 57.6 kn Moments due to applied uniformly distributed loads Ultimate udl (approx); Moment and shear due to load number 1 Moment and shear due to load number 2 Ultimate point load; w intudl = w udlult φ depthick 3/4 = 17.9 kn/m M intudl = w intudl l 2 int /β udl = 23.8 knm V intudl = w intudl l int/2 = 35.7 kn M int1 = w ultint1 l 2 int /β udl = 39.3 knm V int1 = w ultint1 l int/2 = 58.9 kn W int2 = w ultint2 φ depthick 3/4 = 53.6 kn M int2 = W int2 l int/β point = 30.6 knm V int2 = W int2 = 53.6 kn Resultant moments and shears Total moment (hogging and sagging); Maximum shear force; M Σint = knm V Σint = kn Reinforcement required in top Width of section in compression zone; b inttop = b int = 500 mm Average web width; b wint = b int + h int/tan(α int) = 818 mm K factor; K inttop = M Σint/(f cu b inttop d 2 inttop ) = z inttop = d inttop min(0.95, ( K inttop/0.9)) = 473 mm Area of steel required for bending; A sinttopbend = M Σint/((1.0/γ s) f y z inttop) = 642 mm 2 Minimum area of steel; A sinttopmin = b wint h int = 585 mm 2 Area of steel required; A sinttopreq = max(a sinttopbend, A sinttopmin) = 642 mm 2 Page 13 of 14

14 App'd by PASS - A sinttopreq <= A sinttop - Area of reinforcement provided in top of internal beams is adequate Reinforcement required in bottom Width of section in compression zone; b intbtm = b int + 2 (h int - h slab)/tan(α int) l int = 1646 mm K factor; K intbtm = M Σint/(f cu b intbtm d 2 intbtm ) = z intbtm = d intbtm min(0.95, ( K intbtm/0.9)) = 461 mm Area of steel required for bending; A sintbtmbend = M Σint/((1.0/γ s) f y z intbtm) = 658 mm 2 Minimum area of steel required; A sintbtmmin = b wint h int = 585 mm 2 Area of steel required; A sintbtmreq = max(a sintbtmbend, A sintbtmmin) = 658 mm 2 PASS - A sintbtmreq <= A sintbtm - Area of reinforcement provided in bottom of internal beams is adequate Internal beam shear check Applied shear stress; v int = V Σint/(b wint d inttop) = N/mm 2 Tension steel ratio; ρ int = 100 A sinttop/(b wint d inttop) = From BS8110-1: Table 3.8 Design concrete shear strength; v cint = N/mm 2 v int <= v cint + 0.4N/mm 2 - Therefore minimum links required Link area to spacing ratio required; A sv_upon_s vreqint = 0.4N/mm 2 b wint/((1.0/γ s) f ys) = mm Link area to spacing ratio provided; A sv_upon_s vprovint = N intlink π φ 2 intlink /(4 s vint) = mm PASS - A sv_upon_s vreqint <= A sv_upon_s vprovint - Shear reinforcement provided in internal beams is adequate Page 14 of 14