RAFT FOUNDATION DESIGN (BS8110 : Part 1 : 1997) - Advanced

RAFT FOUNDATION DESIGN (BS8110 : Part 1 : 1997) - Advanced

Project Job Ref. Section Sheet no./rev. Civil Engineering Calc. by Advanced Engineering Solutions Date Kevin Miller 1 Chk'd by 16/05/2008 D...

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Project

Job Ref.

Section

Sheet no./rev.

Civil Engineering Calc. by

Advanced Engineering Solutions

Date

Kevin Miller

1

Chk'd by

16/05/2008

Date

App'd by

Date

Kevin Miller

Ltd RAFT FOUNDATION DESIGN (BS8110 : Part 1 : 1997) TEDDS calculation version 1.0.02; Library item - Raft title

Asslabtop

A sedgetop

hslab

A sedgelink

hhcoreslab

hedge

aedge

A sslabbtm

hhcorethick

bedge

Asedgebtm

Soil and raft definition Soil definition 2

Allowable bearing pressure;

qallow = 50.0 kN/m

Number of types of soil forming sub-soil;

Two or more types

Soil density;

Firm

Depth of hardcore beneath slab;

hhcoreslab = 150 mm; (Dispersal allowed for bearing pressure check)

Depth of hardcore beneath thickenings;

hhcorethick = 250 mm; (Dispersal allowed for bearing pressure check)

Density of hardcore;

hcore = 19.0 kN/m

Basic assumed diameter of local depression;

depbasic = 2500mm

Diameter under slab modified for hardcore;

depslab = depbasic - hhcoreslab = 2350 mm

Diameter under thickenings modified for hardcore;

depthick = depbasic - hhcorethick = 2250 mm

3

Raft slab definition Max dimension/max dimension between joints;

lmax = 10.000 m

Slab thickness;

hslab = 250 mm

Concrete strength;

fcu = 40 N/mm

Poissons ratio of concrete;

 = 0.2

Slab mesh reinforcement strength;

fyslab = 500 N/mm

Partial safety factor for steel reinforcement;

s = 1.15

2

2

From C&CA document ‘Concrete ground floors’ Table 5 Minimum mesh required in top for shrinkage;

A142;

Actual mesh provided in top;

A393 (Asslabtop = 393 mm /m)

Mesh provided in bottom;

A393 (Asslabbtm = 393 mm /m)

Top mesh bar diameter;

slabtop = 10 mm

Bottom mesh bar diameter;

slabbtm = 10 mm

Cover to top reinforcement;

ctop = 50 mm

Cover to bottom reinforcement;

cbtm = 75 mm

Average effective depth of top reinforcement;

dtslabav = hslab - ctop - slabtop = 190 mm

Average effective depth of bottom reinforcement;

dbslabav = hslab - cbtm - slabbtm = 165 mm

Overall average effective depth;

dslabav = (dtslabav + dbslabav)/2 = 178 mm

Minimum effective depth of top reinforcement;

dtslabmin = dtslabav - slabtop/2 = 185 mm

Minimum effective depth of bottom reinforcement;

dbslabmin = dbslabav - slabbtm/2 = 160 mm

2

2

Edge beam definition Overall depth;

hedge = 500 mm

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bedge = 500 mm

Angle of chamfer to horizontal;

edge = 60 deg

Strength of main bar reinforcement;

fy = 500 N/mm

Strength of link reinforcement;

fys = 500 N/mm

Reinforcement provided in top;

2 T20 bars (Asedgetop = 628 mm )

Reinforcement provided in bottom;

2 T20 bars (Asedgebtm = 628 mm )

Link reinforcement provided;

2 T10 legs at 250 ctrs (Asv/sv = 0.628 mm)

Bottom cover to links;

cbeam = 35 mm

Effective depth of top reinforcement;

dedgetop = hedge - ctop - slabtop -edgelink - edgetop/2 = 420 mm

Effective depth of bottom reinforcement;

dedgebtm = hedge - cbeam - edgelink - edgebtm/2 = 445 mm

2 2 2

2

Internal slab design checks Basic loading Slab self weight;

wslab = 24 kN/m  hslab = 6.0 kN/m

Hardcore;

whcoreslab = hcore  hhcoreslab = 2.9 kN/m

3

2 2

Applied loading 2

Uniformly distributed dead load;

wDudl = 0.0 kN/m

Uniformly distributed live load;

wLudl = 0.0 kN/m

2

Slab load number 1 Load type;

Point load

Dead load;

wD1 = 0.0 kN

Live load;

wL1 = 75.0 kN

Ultimate load;

wult1 = 1.4  wD1 + 1.6  wL1 = 120.0 kN

Load dimension 1;

b11 = 440 mm

Load dimension 2;

b21 = 440 mm

Internal slab bearing pressure check Total uniform load at formation level;

wudl = wslab + whcoreslab + wDudl + wLudl = 8.9 kN/m

2

Bearing pressure beneath load number 1 2

Net bearing pressure available to resist point load;

qnet = qallow - wudl = 41.2 kN/m

Net ‘ultimate’ bearing pressure available;

qnetult = qnet  wult1/(wD1 + wL1) = 65.8 kN/m

Loaded area required at formation;

Areq1 = wult1/qnetult = 1.823 m

Length of cantilever projection at formation;

p1 = max(0 m, [-(b11+b21) + ((b11+b21) - 4(b11b21 - Areq1))]/4)

2

2 2

p1 = 0.455 m Length of cantilever projection at u/side slab;

peff1 = max(0 m, p1 - hhcoreslab  tan(30)) = 0.368 m

Effective loaded area at u/side slab;

Aeff1 = (b11 + 2  peff1)  (b21 + 2  peff1) = 1.385 m

Effective net ult bearing pressure at u/side slab;

qnetulteff = qnetult  Areq1/Aeff1 = 86.6 kN/m

Cantilever bending moment;

Mcant1 = qnetulteff  peff1 /2 = 5.9 kNm/m

2

2

2

Reinforcement required in bottom Maximum cantilever moment;

Mcantmax = 5.9 kNm/m

K factor;

Kslabbp = Mcantmax/(fcu  dbslabmin ) = 0.006

Lever arm;

zslabbp = dbslabmin  min(0.95, 0.5 + (0.25 - Kslabbp/0.9)) = 152.0 mm

Area of steel required;

Asslabbpreq = Mcantmax/((1.0/s)  fyslab  zslabbp) = 89 mm /m

2

2

PASS - Asslabbpreq <= Asslabbtm - Area of reinforcement provided to distribute the load is adequate The allowable bearing pressure will not be exceeded

Project

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Ltd Internal slab bending and shear check Applied bending moments Span of slab;

lslab = depslab + dtslabav = 2540 mm

Ultimate self weight udl;

wswult = 1.4  wslab = 8.4 kN/m

Self weight moment at centre;

Mcsw = wswult  lslab  (1 + ) / 64 = 1.0 kNm/m

Self weight moment at edge;

Mesw = wswult  lslab / 32 = 1.7 kNm/m

Self weight shear force at edge;

Vsw = wswult  lslab / 4 = 5.3 kN/m

2

2

2

Moments due to applied uniformly distributed loads Ultimate applied udl;

wudlult = 1.4  wDudl + 1.6  wLudl = 0.0 kN/m

Moment at centre;

Mcudl = wudlult 

Moment at edge;

Meudl = wudlult  lslab / 32 = 0.0 kNm/m

Shear force at edge;

Vudl = wudlult  lslab / 4 = 0.0 kN/m

2

2 lslab

 (1 + ) / 64 = 0.0 kNm/m

2

Moment due to load number 1 Moment at centre;

Mc1 = wult1/(4)  (1+)  ln(lslab/min(b11, b21)) = 20.1 kNm/m

Moment at edge;

Me1 = wult1/(4) = 9.5 kNm/m

Minimum dispersal width for shear;

bv1 = min(b11 + 2b21, b21 + 2b11) = 1320.0 mm

Approximate shear force;

V1 = wult1 / bv1 = 90.9 kN/m

Resultant moments and shears Total moment at edge;

Me = 11.2 kNm/m

Total moment at centre;

Mc = 21.1 kNm/m

Total shear force;

V = 96.2 kN/m

Reinforcement required in top K factor;

Kslabtop = Me/(fcu  dtslabav ) = 0.008

Lever arm;

zslabtop = dtslabav  min(0.95, 0.5 + (0.25 - Kslabtop/0.9)) = 180.5 mm

Area of steel required for bending;

Asslabtopbend = Me/((1.0/s)  fyslab  zslabtop) = 143 mm /m

Minimum area of steel required;

Asslabmin = 0.0013  hslab = 325 mm /m

Area of steel required;

Asslabtopreq = max(Asslabtopbend, Asslabmin) = 325 mm /m

2

2

2

2

PASS - Asslabtopreq <= Asslabtop - Area of reinforcement provided in top to span local depressions is adequate Reinforcement required in bottom K factor;

Kslabbtm = Mc/(fcu  dbslabav ) = 0.019

Lever arm;

zslabbtm = dbslabav  min(0.95, 0.5 + (0.25 - Kslabbtm/0.9)) = 156.7 mm

Area of steel required for bending;

Asslabbtmbend = Mc/((1.0/s)  fyslab  zslabbtm) = 310 mm /m

Area of steel required;

Asslabbtmreq = max(Asslabbtmbend, Asslabmin) = 325 mm /m

2

2

2

PASS - Asslabbtmreq <= Asslabbtm - Area of reinforcement provided in bottom to span local depressions is adequate Shear check 2

Applied shear stress;

v = V/dtslabmin = 0.520 N/mm

Tension steel ratio;

 = 100  Asslabtop/dtslabmin = 0.212

From BS8110-1:1997 - Table 3.8; Design concrete shear strength;

vc = 0.535 N/mm

2

PASS - v <= vc - Shear capacity of the slab is adequate Internal slab deflection check Basic allowable span to depth ratio;

Ratiobasic = 26.0

Moment factor;

Mfactor = Mc/dbslabav = 0.775 N/mm

Steel service stress;

fs = 2/3  fyslab  Asslabbtmbend/Asslabbtm = 262.667 N/mm

2

2 2

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Ltd Modification factor;

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MFslab = min(2.0, 0.55 + [(477N/mm - fs)/(120  (0.9N/mm + Mfactor))]) 2

2

MFslab = 1.616 Modified allowable span to depth ratio; Actual span to depth ratio;

Ratioallow = Ratiobasic  MFslab = 42.021 Ratioactual = lslab/ dbslabav = 15.394 PASS - Ratioactual <= Ratioallow - Slab span to depth ratio is adequate

Edge beam design checks Basic loading Hardcore;

whcorethick = hcore  hhcorethick = 4.8 kN/m

2

Edge beam Rectangular beam element;

wbeam = 24 kN/m  hedge  bedge = 6.0 kN/m

Chamfer element;

wchamfer = 24 kN/m  (hedge - hslab) /(2  tan(edge)) = 0.4 kN/m

Slab element;

wslabelmt = 24 kN/m  hslab  (hedge - hslab)/tan(edge) = 0.9 kN/m

Edge beam self weight;

wedge = wbeam + wchamfer + wslabelmt = 7.3 kN/m

3

3

2

3

Edge load number 1 Load type;

Longitudinal line load

Dead load;

wDedge1 = 4.0 kN/m

Live load;

wLedge1 = 0.0 kN/m

Ultimate load;

wultedge1 = 1.4  wDedge1 + 1.6  wLedge1 = 5.6 kN/m

Longitudinal line load width;

bedge1 = 140 mm

Centroid of load from outside face of raft;

xedge1 = 0 mm

Edge beam bearing pressure check Effective bearing width of edge beam;

bbearing = bedge + (hedge - hslab)/tan(edge) = 644 mm

Total uniform load at formation level;

wudledge = wDudl+wLudl+wedge/bbearing+whcorethick = 16.1 kN/m

2

Centroid of longitudinal and equivalent line loads from outside face of raft Load x distance for edge load 1;

Moment1 = wultedge1  xedge1 = 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;

xbar = 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;

ballow = 2  xbar + 2  hhcoreslab  tan(30) = 173 mm

Bearing pressure due to line/point loads;

qlinepoint = UDLsls/ ballow = 23.1 kN/m

Total applied bearing pressure;

qedge = qlinepoint + wudledge = 39.2 kN/m

2

2

PASS - qedge <= qallow - 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;

ledge = depthick + dedgetop = 2670 mm

Ultimate self weight udl;

wedgeult = 1.4  wedge = 10.2 kN/m

Ultimate slab udl (approx);

wedgeslab = max(0 kN/m,1.4wslab((depthick/23/4)-(bedge+(hedge-hslab)/tan(edge)))) wedgeslab = 1.7 kN/m

Self weight and slab bending moment;

Medgesw = (wedgeult + wedgeslab)  ledge /udl = 8.5 kNm

Self weight shear force;

Vedgesw = (wedgeult + wedgeslab)  ledge/2 = 15.9 kN

2

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Ltd Moments due to applied uniformly distributed loads Ultimate udl (approx);

wedgeudl = wudlult  depthick/2  3/4 = 0.0 kN/m

Bending moment;

Medgeudl = wedgeudl  ledge /udl = 0.0 kNm

Shear force;

Vedgeudl = wedgeudl  ledge/2 = 0.0 kN

2

Moment and shear due to load number 1 Bending moment;

Medge1 = wultedge1  ledge /udl = 4.0 kNm

Shear force;

Vedge1 = wultedge1  ledge/2 = 7.5 kN

2

Resultant moments and shears Total moment (hogging and sagging);

Medge = 12.5 kNm

Maximum shear force;

Vedge = 23.4 kN

Reinforcement required in top Width of section in compression zone;

bedgetop = bedge = 500 mm

Average web width;

bw = bedge + (hedge/tan(edge))/2 = 644 mm

K factor;

Kedgetop = Medge/(fcu  bedgetop  dedgetop ) = 0.004

Lever arm;

zedgetop = dedgetop  min(0.95, 0.5 + (0.25 - Kedgetop/0.9)) = 399 mm

Area of steel required for bending;

Asedgetopbend = Medge/((1.0/s)  fy  zedgetop) = 72 mm

Minimum area of steel required;

Asedgetopmin = 0.0013  1.0  bw  hedge = 419 mm

Area of steel required;

Asedgetopreq = max(Asedgetopbend, Asedgetopmin) = 419 mm

2

2

2 2

PASS - Asedgetopreq <= Asedgetop - Area of reinforcement provided in top of edge beams is adequate Reinforcement required in bottom Width of section in compression zone;

bedgebtm = bedge + (hedge - hslab)/tan(edge) + 0.1  ledge = 911 mm

K factor;

Kedgebtm = Medge/(fcu  bedgebtm  dedgebtm ) = 0.002

Lever arm;

zedgebtm = dedgebtm  min(0.95, 0.5 + (0.25 - Kedgebtm/0.9)) = 423 mm

Area of steel required for bending;

Asedgebtmbend = Medge/((1.0/s)  fy  zedgebtm) = 68 mm

Minimum area of steel required;

Asedgebtmmin = 0.0013  1.0  bw  hedge = 419 mm

Area of steel required;

Asedgebtmreq = max(Asedgebtmbend, Asedgebtmmin) = 419 mm

2

2

2 2

PASS - Asedgebtmreq <= Asedgebtm - Area of reinforcement provided in bottom of edge beams is adequate Edge beam shear check Applied shear stress;

vedge = Vedge/(bw  dedgetop) = 0.086 N/mm

Tension steel ratio;

edge = 100  Asedgetop/(bw  dedgetop) = 0.232

2

From BS8110-1:1997 - Table 3.8 Design concrete shear strength;

vcedge = 0.454 N/mm

2 2

vedge <= vcedge + 0.4N/mm - Therefore minimum links required Link area to spacing ratio required;

Asv_upon_svreqedge = 0.4N/mm  bw/((1.0/s)  fys) = 0.593 mm

Link area to spacing ratio provided;

Asv_upon_svprovedge = Nedgelinkedgelink /(4svedge) = 0.628 mm

2

2

PASS - Asv_upon_svreqedge <= Asv_upon_svprovedge - Shear reinforcement provided in edge beams is adequate Corner design checks Basic loading Corner load number 1 Load type;

Line load in x direction

Dead load;

wDcorner1 = 4.0 kN/m

Live load;

wLcorner1 = 0.0 kN/m

Ultimate load;

wultcorner1 = 1.4  wDcorner1 + 1.6  wLcorner1 = 5.6 kN/m

Centroid of load from outside face of raft;

ycorner1 = 0 mm

Corner load number 2

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Line load in y direction

Dead load;

wDcorner2 = 4.0 kN/m

Live load;

wLcorner2 = 0.0 kN/m

Ultimate load;

wultcorner2 = 1.4  wDcorner2 + 1.6  wLcorner2 = 5.6 kN/m

Centroid of load from outside face of raft;

xcorner2 = 0 mm

Corner bearing pressure check Total uniform load at formation level;

wudlcorner = wDudl+wLudl+wedge/bbearing+whcorethick = 16.1 kN/m

Net bearing press avail to resist line/point loads;

2

2

qnetcorner = qallow - wudlcorner = 33.9 kN/m

Total line/point loads Total unfactored line load in x direction;

wlinex = 4.0 kN/m

Total ultimate line load in x direction;

wultlinex =5.6 kN/m

Total unfactored line load in y direction;

wliney = 4.0 kN/m

Total ultimate line load in y direction;

wultliney = 5.6 kN/m

Total unfactored point load;

wpoint = 0.0 kN

Total ultimate point load;

wultpoint = 0.0 kN

Length of side of sq reqd to resist line/point loads;

pcorner =[wlinex+wliney+((wlinex+wliney) +4qnetcornerwpoint)]/(2qnetcorner) 2

pcorner = 236 mm Bending moment about x-axis due to load/reaction eccentricity Moment due to load 1 (x line);

Mx1 = wultcorner1  pcorner  (pcorner/2 - ycorner1) = 0.2 kNm

Total moment about x axis;

Mx = 0.2 kNm

Bending moment about y-axis due to load/reaction eccentricity Moment due to load 2 (y line);

My2 = wultcorner2  pcorner  (pcorner/2 - xcorner2) = 0.2 kNm

Total moment about y axis;

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;

bedgetop = bedge = 500 mm

K factor;

Kcornerbp = Mcornerbp/(fcu  bedgetop  dedgetop ) = 0.004

Lever arm;

zcornerbp = dedgetop  min(0.95, 0.5 + (0.25 - Kcornerbp/0.9)) = 399 mm

Total area of top steel required;

Ascornerbp = Mcornerbp /((1.0/s)  fy  zcornerbp) = 73 mm

2

2

PASS - Ascornerbp <= Asedgetop - 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;

lcorner = depthick/(2) + dedgetop/2 = 1801 mm

Moment and shear due to self weight Ultimate self weight udl; Average ultimate slab udl (approx);

wedgeult = 1.4  wedge = 10.2 kN/m wcornerslab = max(0 kN/m,1.4wslab(depthick/((2)2)-(bedge+(hedge-hslab)/tan(edge)))) wcornerslab = 1.3 kN/m

Self weight and slab bending moment;

Mcornersw = (wedgeult + wcornerslab)  lcorner /2 = 18.6 kNm

Self weight and slab shear force;

Vcornersw = (wedgeult + wcornerslab)  lcorner = 20.7 kN

2

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Ltd Moment and shear due to udls Maximum ultimate udl;

wcornerudl = ((1.4wDudl)+(1.6wLudl))  depthick/(2) = 0.0 kN/m

Bending moment;

Mcornerudl = wcornerudl  lcorner /6 = 0.0 kNm

Shear force;

Vcornerudl = wcornerudl  lcorner/2 = 0.0 kN

2

Moment and shear due to line loads in x direction Bending moment;

Mcornerlinex = wultlinex  lcorner /2 = 9.1 kNm

Shear force;

Vcornerlinex = wultlinex  lcorner = 10.1 kN

2

Moment and shear due to line loads in y direction Bending moment;

Mcornerliney = wultliney  lcorner /2 = 9.1 kNm

Shear force;

Vcornerliney = wultliney  lcorner = 10.1 kN

2

Total moments and shears due to point loads Bending moment about x axis;

Mcornerpointx = 0.0 kNm

Bending moment about y axis;

Mcornerpointy = 0.0 kNm

Shear force;

Vcornerpoint = 0.0 kN

Resultant moments and shears Total moment about x axis;

Mcornerx = Mcornersw+ Mcornerudl+ Mcornerliney+ Mcornerpointx = 27.7 kNm

Total shear force about x axis;

Vcornerx = Vcornersw+ Vcornerudl+ Vcornerliney + Vcornerpoint = 30.8 kN

Total moment about y axis;

Mcornery = Mcornersw+ Mcornerudl+ Mcornerlinex+ Mcornerpointy = 27.7 kNm

Total shear force about y axis;

Vcornery = Vcornersw+ Vcornerudl+ Vcornerlinex + Vcornerpoint = 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;

Kcorner = Mcorner/(fcu  bedgetop  dedgetop ) = 0.008

Lever arm;

zcorner = dedgetop  min(0.95, 0.5 + (0.25 - Kcorner/0.9)) = 399 mm

Area of steel required for bending;

Ascornerbend = Mcorner/((1.0/s)  fy  zcorner) = 160 mm

Minimum area of steel required;

Ascornermin = Asedgetopmin = 419 mm

Area of steel required;

Ascorner = max(Ascornerbend, Ascornermin) = 419 mm

2

2

2 2

PASS - Ascorner <= Asedgetop - Area of reinforcement provided in top of edge beams at corners is adequate Corner beam shear check Average web width;

bw = bedge + (hedge/tan(edge))/2 = 644 mm

Applied shear stress;

vcorner = Vcorner/(bw  dedgetop) = 0.114 N/mm

Tension steel ratio;

corner = 100  Asedgetop/(bw  dedgetop) = 0.232

2

From BS8110-1:1997 - Table 3.8 Design concrete shear strength;

vccorner = 0.449 N/mm

2 2

vcorner <= vccorner + 0.4N/mm - Therefore minimum links required Link area to spacing ratio required;

Asv_upon_svreqcorner = 0.4N/mm  bw/((1.0/s)  fys) = 0.593 mm

Link area to spacing ratio provided;

Asv_upon_svprovedge = Nedgelinkedgelink /(4svedge) = 0.628 mm

2

2

PASS - Asv_upon_svreqcorner <= Asv_upon_svprovedge - Shear reinforcement provided in edge beams at corners is adequate Corner beam deflection check Basic allowable span to depth ratio;

Ratiobasiccorner = 7.0

Moment factor;

Mfactorcorner = Mcorner/(bedgetop  dedgetop ) = 0.314 N/mm

Steel service stress;

fscorner = 2/3  fy  Ascornerbend/Asedgetop = 84.751 N/mm

Modification factor;

2

2

2

2 2

MF corner=min(2.0,0.55+[(477N/mm -fscorner)/(120(0.9N/mm +Mfactorcorner))])

Project

Job Ref.

Section

Sheet no./rev.

Civil Engineering Calc. by

Advanced Engineering Solutions

Kevin Miller

Ltd

Date

Chk'd by

16/05/2008

8 Date

App'd by

Date

Kevin Miller

MFcorner = 2.000

Modified allowable span to depth ratio;

Ratioallowcorner = Ratiobasiccorner  MFcorner = 14.000

Actual span to depth ratio;

Ratioactualcorner = lcorner/ dedgetop = 4.288 PASS - Ratioactualcorner <= Ratioallowcorner - Edge beam span to depth ratio is adequate