Civil Engineering 16/05/2008

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1 1 App'd by RAFT FOUNDATION DESIGN (BS8110 : Part 1 : 1997) TEDDS calculation version ; Library item - Raft title A sedgetop A sslabtop A sedgelink h slab h edge h hcoreslab a edge A sslabbtm h hcorethick b edge A sedgebtm Soil and raft definition Soil definition Allowable bearing pressure; q allow = 50.0 kn/m 2 Number of types of soil forming sub-soil; Two or more types Soil density; Firm Depth of hardcore beneath slab; h hcoreslab = 150 mm; (Dispersal allowed for bearing pressure check) Depth of hardcore beneath thickenings; h hcorethick = 250 mm; (Dispersal allowed for bearing pressure check) Density of hardcore; hcore = 19.0 kn/m 3 Basic assumed diameter of local depression; depbasic = 2500mm Diameter under slab modified for hardcore; depslab = depbasic - h hcoreslab = 2350 mm Diameter under thickenings modified for hardcore; depthick = depbasic - h hcorethick = 2250 mm Raft slab definition Max dimension/max dimension between joints; l max = m Slab thickness; h slab = 250 mm Concrete strength; f cu = 40 N/mm 2 Poissons ratio of concrete; = 0.2 Slab mesh reinforcement strength; f yslab = 500 N/mm 2 Partial safety factor for steel reinforcement; s = 1.15 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; slabtop = 10 mm Bottom mesh bar diameter; slabbtm = 10 mm Cover to top reinforcement; c top = 50 mm Cover to bottom reinforcement; c btm = 75 mm Average effective depth of top reinforcement; d tslabav = h slab - c top - slabtop = 190 mm Average effective depth of bottom reinforcement; d bslabav = h slab - c btm - slabbtm = 165 mm Overall average effective depth; d slabav = (d tslabav + d bslabav)/2 = 178 mm Minimum effective depth of top reinforcement; d tslabmin = d tslabav - slabtop/2 = 185 mm Minimum effective depth of bottom reinforcement; d bslabmin = d bslabav - slabbtm/2 = 160 mm Edge beam definition Overall depth; h edge = 500 mm

2 2 App'd by Width; b edge = 500 mm Angle of chamfer to horizontal; 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; 2 T20 bars (A sedgetop = 628 mm 2 ) Reinforcement provided in bottom; 2 T20 bars (A sedgebtm = 628 mm 2 ) Link reinforcement provided; 2 T10 legs at 250 ctrs (A sv/s v = mm) Bottom cover to links; c beam = 35 mm Effective depth of top reinforcement; d edgetop = h edge - c top - slabtop - edgelink - edgetop/2 = 420 mm Effective depth of bottom reinforcement; d edgebtm = h edge - c beam - edgelink - edgebtm/2 = 445 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 = hcore h hcoreslab = 2.9 kn/m 2 Applied loading Uniformly distributed dead load; w Dudl = 0.0 kn/m 2 Uniformly distributed live load; w Ludl = 0.0 kn/m 2 Slab load number 1 Load type; Point load Dead load; w D1 = 0.0 kn Live load; w L1 = 75.0 kn Ultimate load; w ult1 = 1.4 w D w L1 = kn Load dimension 1; b 11 = 440 mm Load dimension 2; b 21 = 440 mm Internal slab bearing pressure check Total uniform load at formation level; w udl = w slab + w hcoreslab + w Dudl + w Ludl = 8.9 kn/m 2 Bearing pressure beneath load number 1 Net bearing pressure available to resist point load; q net = q allow - w udl = 41.2 kn/m 2 Net ultimate bearing pressure available; q netult = q net w ult1/(w D1 + w L1) = 65.8 kn/m 2 Loaded area required at formation; A req1 = w ult1/q netult = m 2 Length of cantilever projection at formation; p 1 = max(0 m, [-(b 11+b 21) + ((b 11+b 21) 2-4 (b 11 b 21 - A req1))]/4) p 1 = m Length of cantilever projection at u/side slab; p eff1 = max(0 m, p 1 - h hcoreslab tan(30)) = m Effective loaded area at u/side slab; A eff1 = (b p eff1) (b p eff1) = m 2 Effective net ult bearing pressure at u/side slab; q netulteff = q netult A req1/a eff1 = 86.6 kn/m 2 Cantilever bending moment; M cant1 = q netulteff p 2 eff1 /2 = 5.9 knm/m Reinforcement required in bottom Maximum cantilever moment; M cantmax = 5.9 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/ s) f yslab z slabbp) = 89 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

3 3 App'd by Internal slab bending and shear check Applied bending moments Span of slab; l slab = depslab + d tslabav = 2540 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 + ) / 64 = 1.0 knm/m Self weight moment at edge; M esw = w swult l 2 slab / 32 = 1.7 knm/m Self weight shear force at edge; V sw = w swult l slab / 4 = 5.3 kn/m Moments due to applied uniformly distributed loads Ultimate applied udl; w udlult = 1.4 w Dudl w Ludl = 0.0 kn/m 2 Moment at centre; M cudl = w udlult l 2 slab (1 + ) / 64 = 0.0 knm/m Moment at edge; M eudl = w udlult l 2 slab / 32 = 0.0 knm/m Shear force at edge; V udl = w udlult l slab / 4 = 0.0 kn/m Moment due to load number 1 Moment at centre; M c1 = w ult1/(4 ) (1+ ) ln(l slab/min(b 11, b 21)) = 20.1 knm/m Moment at edge; M e1 = w ult1/(4 ) = 9.5 knm/m Minimum dispersal width for shear; b v1 = min(b b 21, b b 11) = mm Approximate shear force; V 1 = w ult1 / b v1 = 90.9 kn/m Resultant moments and shears Total moment at edge; Total moment at centre; Total shear force; M e = 11.2 knm/m M c = 21.1 knm/m V = 96.2 kn/m Reinforcement required in top K factor; K slabtop = M e/(f cu d tslabav 2 ) = z slabtop = d tslabav min(0.95, ( K slabtop/0.9)) = mm Area of steel required for bending; A sslabtopbend = M e/((1.0/ s) f yslab z slabtop) = 143 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 c/(f cu d bslabav 2 ) = z slabbtm = d bslabav min(0.95, ( K slabbtm/0.9)) = mm Area of steel required for bending; A sslabbtmbend = M c/((1.0/ s) f yslab z slabbtm) = 310 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 /d tslabmin = N/mm 2 Tension steel ratio; = 100 A sslabtop/d tslabmin = From BS8110-1: Table 3.8; Design concrete shear strength; v c = N/mm 2 Internal slab deflection check Basic allowable span to depth ratio; Ratio basic = 26.0 Moment factor; M factor = M c/d bslabav 2 = N/mm 2 PASS - v <= v c - Shear capacity of the slab is adequate Steel service stress; f s = 2/3 f yslab A sslabbtmbend/a sslabbtm = N/mm 2

4 4 App'd by 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 = hcore h hcorethick = 4.8 kn/m 2 Edge beam Rectangular beam element; w beam = 24 kn/m 3 h edge b edge = 6.0 kn/m Chamfer element; w chamfer = 24 kn/m 3 (h edge - h slab) 2 /(2 tan( edge)) = 0.4 kn/m Slab element; w slabelmt = 24 kn/m 3 h slab (h edge - h slab)/tan( edge) = 0.9 kn/m Edge beam self weight; w edge = w beam + w chamfer + w slabelmt = 7.3 kn/m Edge load number 1 Load type; Longitudinal line load Dead load; w Dedge1 = 4.0 kn/m Live load; w Ledge1 = 0.0 kn/m Ultimate load; w ultedge1 = 1.4 w Dedge w Ledge1 = 5.6 kn/m Longitudinal line load width; b edge1 = 140 mm Centroid of load from outside face of raft; x edge1 = 0 mm Edge beam bearing pressure check Effective bearing width of edge beam; b bearing = b edge + (h edge - h slab)/tan( edge) = 644 mm Total uniform load at formation level; w udledge = w Dudl+w Ludl+w edge/b bearing+w hcorethick = 16.1 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 = 0.0 kn Sum of ultimate longitud l and equivalent line loads; UDL = 5.6 kn/m Sum of load x distances; Moment = 0.0 kn Centroid of loads; x bar = Moment/ UDL = 0 mm Initially assume no moment transferred into slab due to load/reaction eccentricity Sum of unfactored longitud l and eff tive line loads; UDLsls = 4.0 kn/m Allowable bearing width; b allow = 2 x bar + 2 h hcoreslab tan(30) = 173 mm Bearing pressure due to line/point loads; q linepoint = UDLsls/ b allow = 23.1 kn/m 2 Total applied bearing pressure; q edge = q linepoint + w udledge = 39.2 kn/m 2 PASS - q edge <= q allow - Allowable bearing pressure is not exceeded Edge beam bending check Divider for moments due to udl s; udl = 10.0 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 = depthick + d edgetop = 2670 mm w edgeult = 1.4 w edge = 10.2 kn/m w edgeslab = max(0 kn/m,1.4 w slab (( depthick/2 3/4)-(b edge+(h edge-h slab)/tan( edge)))) w edgeslab = 1.7 kn/m M edgesw = (w edgeult + w edgeslab) l 2 edge / udl = 8.5 knm V edgesw = (w edgeult + w edgeslab) l edge/2 = 15.9 kn

5 5 App'd by Moments due to applied uniformly distributed loads Ultimate udl (approx); w edgeudl = w udlult depthick/2 3/4 = 0.0 kn/m M edgeudl = w edgeudl l 2 edge / udl = 0.0 knm V edgeudl = w edgeudl l edge/2 = 0.0 kn Moment and shear due to load number 1 M edge1 = w ultedge1 l 2 edge / udl = 4.0 knm V edge1 = w ultedge1 l edge/2 = 7.5 kn Resultant moments and shears Total moment (hogging and sagging); Maximum shear force; M edge = 12.5 knm V edge = 23.4 kn Reinforcement required in top Width of section in compression zone; b edgetop = b edge = 500 mm Average web width; b w = b edge + (h edge/tan( edge))/2 = 644 mm K factor; K edgetop = M edge/(f cu b edgetop d 2 edgetop ) = z edgetop = d edgetop min(0.95, ( K edgetop/0.9)) = 399 mm Area of steel required for bending; A sedgetopbend = M edge/((1.0/ s) f y z edgetop) = 72 mm 2 Minimum area of steel required; A sedgetopmin = b w h edge = 419 mm 2 Area of steel required; A sedgetopreq = max(a sedgetopbend, A sedgetopmin) = 419 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( edge) l edge = 911 mm K factor; K edgebtm = M edge/(f cu b edgebtm d 2 edgebtm ) = z edgebtm = d edgebtm min(0.95, ( K edgebtm/0.9)) = 423 mm Area of steel required for bending; A sedgebtmbend = M edge/((1.0/ s) f y z edgebtm) = 68 mm 2 Minimum area of steel required; A sedgebtmmin = b w h edge = 419 mm 2 Area of steel required; A sedgebtmreq = max(a sedgebtmbend, A sedgebtmmin) = 419 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 edge/(b w d edgetop) = N/mm 2 Tension steel ratio; 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/ s) f ys) = mm Link area to spacing ratio provided; A sv_upon_s vprovedge = N edgelink 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 Corner design checks Basic loading Corner load number 1 Load type; Dead load; Live load; Ultimate load; Centroid of load from outside face of raft; Corner load number 2 Line load in x direction w Dcorner1 = 4.0 kn/m w Lcorner1 = 0.0 kn/m w ultcorner1 = 1.4 w Dcorner w Lcorner1 = 5.6 kn/m y corner1 = 0 mm

6 6 App'd by Load type; Dead load; Live load; Ultimate load; Centroid of load from outside face of raft; Line load in y direction w Dcorner2 = 4.0 kn/m w Lcorner2 = 0.0 kn/m w ultcorner2 = 1.4 w Dcorner w Lcorner2 = 5.6 kn/m x corner2 = 0 mm Corner bearing pressure check Total uniform load at formation level; w udlcorner = w Dudl+w Ludl+w edge/b bearing+w hcorethick = 16.1 kn/m 2 Net bearing press avail to resist line/point loads; q netcorner = q allow - w udlcorner = 33.9 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 linex = 4.0 kn/m w ultlinex =5.6 kn/m w liney = 4.0 kn/m w ultliney = 5.6 kn/m w point = 0.0 kn w ultpoint = 0.0 kn p corner =[w linex+w liney+ ((w linex+w liney) 2 +4 q netcorner w point)]/(2 q netcorner) p corner = 236 mm Bending moment about x-axis due to load/reaction eccentricity Moment due to load 1 (x line); Total moment about x axis; M x1 = w ultcorner1 p corner (p corner/2 - y corner1) = 0.2 knm M x = 0.2 knm Bending moment about y-axis due to load/reaction eccentricity Moment due to load 2 (y line); Total moment about y axis; M y2 = w ultcorner2 p corner (p corner/2 - x corner2) = 0.2 knm M y = 0.2 knm Check top reinforcement in edge beams for load/reaction eccentric moment Max moment due to load/reaction eccentricity; M = max(m x, M y) = 0.2 knm 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 edge = 12.5 knm Total moment to be resisted; M cornerbp = M + M edge = 12.6 knm Width of section in compression zone; b edgetop = b edge = 500 mm K factor; K cornerbp = M cornerbp/(f cu b edgetop d 2 edgetop ) = z cornerbp = d edgetop min(0.95, ( K cornerbp/0.9)) = 399 mm Total area of top steel required; A scornerbp = M cornerbp /((1.0/ s) f y z cornerbp) = 73 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; l corner = depthick/ (2) + d edgetop/2 = 1801 mm 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; w edgeult = 1.4 w edge = 10.2 kn/m w cornerslab = max(0 kn/m,1.4 w slab ( depthick/( (2) 2)-(b edge+(h edge-h slab)/tan( edge)))) w cornerslab = 1.3 kn/m M cornersw = (w edgeult + w cornerslab) l 2 corner /2 = 18.6 knm V cornersw = (w edgeult + w cornerslab) l corner = 20.7 kn

7 7 App'd by Moment and shear due to udls Maximum ultimate udl; w cornerudl = ((1.4 w Dudl)+(1.6 w Ludl)) depthick/ (2) = 0.0 kn/m M cornerudl = w cornerudl l corner 2 /6 = 0.0 knm V cornerudl = w cornerudl l corner/2 = 0.0 kn Moment and shear due to line loads in x direction M cornerlinex = w ultlinex l 2 corner /2 = 9.1 knm V cornerlinex = w ultlinex l corner = 10.1 kn Moment and shear due to line loads in y direction M cornerliney = w ultliney l 2 corner /2 = 9.1 knm V cornerliney = w ultliney l corner = 10.1 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 cornerx = M cornersw+ M cornerudl+ M cornerliney+ M cornerpointx = 27.7 knm Total shear force about x axis; V cornerx = V cornersw+ V cornerudl+ V cornerliney + V cornerpoint = 30.8 kn Total moment about y axis; M cornery = M cornersw+ M cornerudl+ M cornerlinex+ M cornerpointy = 27.7 knm Total shear force about y axis; V cornery = V cornersw+ V cornerudl+ V cornerlinex + V cornerpoint = 30.8 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 corner = (M cornerx + M cornery)/2 = 27.7 knm Design shear force; V corner = (V cornerx + V cornery)/2 = 30.8 kn Reinforcement required in top of edge beam K factor; K corner = M corner/(f cu b edgetop d 2 edgetop ) = z corner = d edgetop min(0.95, ( K corner/0.9)) = 399 mm Area of steel required for bending; A scornerbend = M corner/((1.0/ s) f y z corner) = 160 mm 2 Minimum area of steel required; A scornermin = A sedgetopmin = 419 mm 2 Area of steel required; A scorner = max(a scornerbend, A scornermin) = 419 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( edge))/2 = 644 mm Applied shear stress; v corner = V corner/(b w d edgetop) = N/mm 2 Tension steel ratio; 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/ s) f ys) = mm Link area to spacing ratio provided; A sv_upon_s vprovedge = N edgelink 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 corner/(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))])

8 8 App'd by 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

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

App'd by RAFT FOUNDATION DESIGN IN ACCORDANCE WITH BS8110:PART 1-1997_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