Isolate Footing Design to EC2v1.07

Isolated Footing by EC2 Ref: BA element Simple EC2 (1) & Projet BA Thonier 1986 (2) & 2011 (3)

A= 2.20 Inputs Soil bearing capacity in ELU=

3.00 bars

fck= fyk= Column Dimension: Load in ton (t) G= 104.20 t a (a
2

ELU

Design

0.20 0.80

m m

0.04

m

Results

Proposed dim: dimension diret. X=

2.20 2.80

ELS

1.20

1.25

B=

2.80

Asx

ELS

ELU

Asy

a

H=h= 0.70

0.00 0.00 t fcd= 1667 t/m2 1.35*G+1.5*Q= 163.17 119.2 t 5.96 t fyd= 4.35 t/cm2 (Ned+1.35G0)/simga ELU= 5.44 2.44 m Sqrt(S)= 2.33

A=

h mini=

B= 4.53 4.77 dimension direct. Y= 5.44 5.96 S=A*B= (Ned+1.35G0)/simga ELU= 6.16 OK OK S= area of footing= 0.50 m d= effective height= Rebars calculated Ax= Ned*(A-0.70*a)^2/(8*0.9*d*A*fyd)= 15.23 cm2 Ay= Ned*(B-0.70*b)^2/(8*0.9*d*B*fyd)= 14.59 cm2

4

Mpa Mpa

self-weigth=

G0= Ned= S=A*B= A=B=

3

25 500

b

1

d+e=

H=h= choice= d= h-e=

0.54

(1) DTU: (2) NF P94-261:

choice:

bars bars

2.00 0.00

bars

m

0.70 m 0.66

1

2.00 1.80

OK

m

Rebar in place 11 HA20 35cm2 @25cm 9 HA20 28cm2 @24cm

ULS

SLS

S= 163.17

119.20

A=

2.20

2.20

B=

2.47

2.71

Asmin=

0.0013

*b*d

Asmin=

0.0013

*b*d

Asminx=

24.65

cm2

Asminy=

19.37

cm2

Puching - ref: projet BA Thonier 1986 Gp= 104.20 t (equal to G by default) Qp= 15.00 t (equal to Q by default) 1.35*G+1.5*Q= 163.17 t

Puching Load Ned= Puching verification

x (0 à 2d) 0 1 2 3 4 5 6 7 8 9 10

vEd/vRd=

0.374 <1? OK

1.32 u* Ac** ΔVEd (MN) VEd,red (MN) 0m 2.00 0.160 0.04 1.59 0.13 2.83 0.479 0.13 1.50 0.26 3.66 0.907 0.24 1.39 0.40 4.49 1.445 0.38 1.25 0.53 5.32 2.092 0.55 1.08 0.66 6.15 2.848 0.75 0.88 0.79 6.98 3.715 0.98 0.65 0.92 7.81 4.690 1.24 0.39 1.06 8.64 5.775 1.53 0.10 1.19 9.46 6.970 1.85 -0.21 1.32 10.29 8.274 2.19 -0.56 u=2a+2b+2*pi*x *Ac=a*(b+2x)+b*(a+2x)-a*b+pi*x^2

Starter Bars 3.75 cm2 3.20 cm2 3.75 cm2 As= 8 HA12 9.05 cm2 As in place a*b*fcd+As*fyd= 306 ton NRd= Starter bars must be at least 15*Dia or 20cm anchorage As=

bars // A

bars // B

d= px= py= p= k= (1) (2) vRd=

0.1*N / fyd= 0.002*a*b= max(0.1*N/fd, 0.002*a*b)=

α2=1-0.15*(30/D-1)= σs=fyd*As real / As th = fbd= Lbd=α2 * Dia /4 * σs / fbd= A/4= α2=1-0.15*(30/D-1)= σs=fyd*As real / As th = fbd= Lbd=α2 * Dia /4 * σs / fbd= B/4=

0.925 191.66 2.69 0.33 0.55 0.925 224.43 2.69 0.39 0.7

OK OK

>=0.7 and <1

Mpa Mpa m m

0.66 (dx+dy)/2= 0.001 Ax/(A*d)= 0.001 Ay/(B*d)= 0.001 sqrt(px*py)= 1.550 min(2,1+sqrt(0.2/d))= 0.245 Mpa 0.12*k*(100p*fck)^(1/3)= 0.338 Mpa 0.035*k^1.5*fck^0.5= max(1,2)*2d/x= voir tableux vEd (MPa) 1.20 0.81 0.58 0.42 0.31 0.22 0.14 0.08 0.02 -0.03 -0.08

vRd (Mpa) vEd/vRd<1 3.38 0.24 1.69 0.34 1.13 0.37 0.84 0.36 0.68 0.32 0.56 0.25 0.48 0.16 0.42 0.04 0.38 -0.09 0.34 -0.24 0.37 must <1

Quantity Concrete: 2.20 x 2.80 x 0.70 = Formwork: 2.20 x 2.80 = Steel: 11 HA20 2.50 9 HA20 3.10 d=

NO Hoock*

>=0.7 and <1

Mpa Mpa m m

NO Hoock*

* in practice we always hoock!

4.312 m3 10 m2 67.82 kg 68.8 kg 31.7 kg/m3

EC2 OK OK

Isolated Footing - EC2 NF Ref: Maitrise BAEL91

1

Inputs Soil bearing capacity in ELU=

12.50 bars

(σelu=1.5*σels) (1bar=0.1Mpa) (1bar=10 t/m2)

fct ULS fct SLS

2

1.35 1.35

S=A*B= A=B=

3

9.11 336 33.6 e=Med/Ned= 0.10 (Ned+1.35G0)/simga ELU= 2.71 Sqrt(S)= 1.65

6.75 240.0 12 0.05 2.88 1.70

self-weigth= 0.00 0.00 (e+e).N=

0.30 0.30

m m

0.05

fcd= fyd=

1667 4.35

t/m2 t/cm2

1.80

h mini=

d+e=

0.48

m

B= 1.65 dimension direct. Y= S=A*B= area required= 2.71 3.60 OK S= area of footing= 0.43 m d= effective height= Rebars calculated 0.2 m 2e=

1.70

H=h= d=

choice=

0.75

h-e=

0.70

m m

A/2+0.35a=

Mu= Vu= Vu2= Ax= Ay=

Pu*(A-0.70a)^2/(8*(A-2e))= σsol*A*(d0-d/2)= 0.2*fcj/(2ϒb)*a2*d2=

1.105 74.76 62.5 116.67

m t.m t t

Asy

B 1.80 =

H=h= 0.75

t t t.m m t m

ELS

2.00 1.80

a

2.00

Asx

1.85

Proposed dim: dimension diret. X=

A=

m

ELU

Results A=

4

cover e=

ELS

1.50 1.50

1.00 1.00 0.00

Mpa Mpa

m

ELU

Design G0= Ned= Med=

1.35 1.50 0.00

25 500

b

Moment in direction A

G= 160.00 t Mg= 8.00 t.m Q= 80.00 t Mq= 4.00 t.m t Mq= 0.00 t.m W= 0.00 Additional excentric e2= 0.03 ea= 0.02 m taking into account SW in dimensionnement 1 SW= 0) No, 1) Yes Load

fck= fyk= Column: a (a
2.88 OK

Heigth check

OK

fctm=

u= 0.050859 z= 0.681722 m cm2 As= 25.22

-1.68

2.56

Mpa

Asmin=

0.0013

*b*d

Asmin=

0.0013

*b*d

Asminx=

16.81

cm2

Asminy=

18.67

cm2

Shear check

7 8

25.22 cm2 Ned*(B-0.70*b)^2/(8*0.9*d*B*fyd)= 22.17 cm2 Ned*(A-0.70*a)^2/(8*0.9*d*A*fyd)=

Rebar in place HA20 22cm2 @25cm HA20 25cm2 @24cm

OK

Puching (not include effect of moment) Gp= 160.00 t (equal to G by default) Qp= 80.00 t (equal to Q by default) 336 t 1.35*G+1.5*Q=

Puching Load Ned= Puching verification

x (0 à 2d) 0 1 2 3 4 5 6 7 8 9 10

vEd/vRd=

0.793 <1? OK

1.4 u* Ac** ΔVEd (MN) VEd,red (MN) 0m 1.20 0.090 0.08 3.28 0.14 2.08 0.320 0.30 3.06 0.28 2.96 0.672 0.63 2.73 0.42 3.84 1.148 1.07 2.29 0.56 4.72 1.747 1.63 1.73 0.70 5.60 2.469 2.30 1.06 0.84 6.48 3.315 3.09 0.27 0.98 7.36 4.283 4.00 -0.64 1.12 8.24 5.375 5.02 -1.66 1.26 9.12 6.590 6.15 -2.79 1.40 10.00 7.928 7.40 -4.04 u=2a+2b+2*pi*x *Ac=a*(b+2x)+b*(a+2x)-a*b+pi*x^2

Starter Bars 7.73 cm2 1.80 cm2 7.73 cm2 As= 8 HA12 9.05 cm2 As in place a*b*fcd+As*fyd= 189.34 ton NRd= Starter bars must be at least 15*Dia or 20cm anchorage As=

bars // A

0.1*N / fyd= 0.002*a*b= max(0.1*N/fd, 0.002*a*b)=

α2=1-0.15*(30/D-1)= σs=fyd*As real / As th = fbd= Lbd=α2 * Dia /4 * σs / fbd=

OK NON

0.925 >=0.7 and <1 498.69 Mpa 2.69 Mpa 0.86 m

d= px= py= p= k= (1) (2) vRd=

0.70 (dx+dy)/2= 0.002 Ax/(A*d)= 0.002 Ay/(B*d)= 0.002 sqrt(px*py)= 1.535 min(2,1+sqrt(0.2/d))= 0.303 Mpa 0.12*k*(100p*fck)^(1/3)= 0.333 Mpa 0.035*k^1.5*fck^0.5= max(1,2)*2d/x= voir tableux vEd (MPa) 3.90 2.10 1.32 0.85 0.52 0.27 0.06 -0.12 -0.29 -0.44 -0.58

vRd (Mpa) vEd/vRd<1 3.33 0.63 1.66 0.79 1.11 0.77 0.83 0.63 0.67 0.40 0.55 0.11 0.48 -0.26 0.42 -0.69 0.37 -1.18 0.33 -1.74 0.79 must <1

Quantity Concrete: 2.00 x 1.80 x 0.75 = Formwork: 2.00 x 1.80 = Steel: 7 HA20 2.30 8 HA20 2.10 d=

2.7 m3 7.6 m2 39.71 kg 41.4 kg 30.1 kg/m3

bars // B

A/4= α2=1-0.15*(30/D-1)= σs=fyd*As real / As th = fbd= Lbd=α2 * Dia /4 * σs / fbd= B/4=

0.5 0.925 383.51 2.69 0.66 0.45

m

Hoock

>=0.7 and <1

Mpa Mpa m m

Hoock

* in practice we always hoock!

Elastic Settlement Calculation Method 1: s= q*(1-v^2)/E*B*Cf= 6.5 Where Load= 2.00 E= 15 v= 0.5 L= 3.20 B= 1.10 q= 0.083 Cf=f= 1.409

Ref: Roger F. et Ph Method 2: s=(q'-σ'v0)/kv= where

mm MN (SLS) Mpa

(Coef Poisson of soil equal to 0.3 to 0.5) m (length of foundation L>=B) m (width of foudation) Mpa (stress applied on foundation: uniform or moyen) (Coef depend on form of foudation)

Elastic Settlement Calculation of a sigle pile Bored or driven=

1 0.7 sref= (0.003,0.01)*B= 0.010 sref= (0.008,0.012)*B= 0.012 sref= 7.0 Diameter pile B=

α= E= v= Eoe= EM=

1) Bored, 2) driven m *B (bored pile) *B (driven pile) mm

0.5 (see table below) 36.3 Mpa 0.30 (Coef Poisson= 0.3) 48.9 24.4

G= 700 kN (applied load/pile) Q= 300 kN (applied load/pile) Qs= 655 kN (frotement limit) Qp= 430 kN (poin load limit) G+Q= 1000 kN Gs+Qp= 1085 kN qs= 298 kPa (frotement limit) qp= 1117 kPa (poin load limit)

Soil fins:

Qs+Qp= sum of s= max s= Soil granulat

Mpa (E'*(1-v)/((1+v')*(1-2v')) Mpa (α*Eoe)

Soil fins: Kt=2*EM/B= 69808 kpa/m Kp=11*EM/B= ### kpa/m

Soil granulaire Kt=0.8*EM/B= 27923 kPa/m Kp=4.8*EM/B= ### kPa/m

Elastic Settlement Calculation of a group of piles Soil fins or granulat: 1 1) Fins, 2) Granulat number of pile in group: 2 distance btw axes S: 2.1 m (3*B as normal) length of pile D= 15 m (length of pile) s1=su 0.018 mm/kN (settlement unitaire) sG=s1*Load*X= 38.4 mm

Qs+Qp= sum of s= max s=

G= 2000 kN (applied load Group) Q= 0 kN (applied load Group) G+Q= 2000 kN

α=α(S) α(√2S) α(√2S/2)

no. pile X=(1+sum(α)) 1+α= 2 1+3α= 3 1+α+α+α(√2S)= 4 1+4α(√2S/2)= 5 1+3α+2α(√2S)= 6 1+4α+4α(√2S)= 9

X 1.07 1.21 1.24 1.28 1.41 1.68

0.07

0.10

0.07 (read table)

K=Ep/E= 849

B/S= 0.333 0.471 0.236 D/B= 21.43 v= 0.30

350 300 250 200

6 5 4 100 3 50 2 1 0 0 5 150

Ref: Roger F. et Philipponnat s=(q'-σ'v0)/kv= kw= g= kv=

8.8 25.0 0.557 9.501

Soil fins: ps= 0 ss= 0 pp= 0 sp= 0 Qs+Qp= sum of s= 0.0 max s= 17.9 su= 0.018 Soil granulat ps= 0 ss= 0 pp= 0 sp= 0 Qs+Qp= sum of s= 0.0 max s= 43.3 su= 0.043

350

mm Mpa/m =pi()/(4.f) Mpa/m (g.kv.75/(B*100))

1 2 3 4 5 6 7 8 9 10 29.78 59.57 89.35 119 149 179 208 238 268 298 kPa 0.43 0.85 1.28 1.71 2.13 4.27 6.40 8.53 10.67 12.80 mm 112 223 335 447 559 670 782 894 1006 1117 kPa 0.29 0.58 0.87 1.16 1.46 2.91 4.37 5.82 7.28 8.73 mm 108.5 217 325.5 434 542.5 651 759.5 868 976.5 1085 0.7 1.4 2.2 2.9 3.6 7.2 10.8 14.4 17.9 0.0 mm mm DON'T PASS!!! mm/kN (settlement unitaire) 1 2 3 4 5 6 7 8 9 10 29.78 59.57 89.35 119 149 179 208 238 268 298 kPa 1.07 2.13 3.20 4.27 5.33 10.67 16.00 21.33 26.67 32.00 m 112 223 335 447 559 670 782 894 1006 1117 kPa 0.67 1.33 2.00 2.67 3.33 6.67 10.00 13.34 16.67 20.01 m 108.5 217 325.5 434 542.5 651 759.5 868 976.5 1085 1.7 3.5 5.2 6.9 8.7 17.3 26.0 34.7 43.3 0.0 mm mm DON'T PASS!!! mm/kN (settlement unitaire)

ss soil fin 11

300 250

10 9 8

1200

sp soil fin

11 10

1000

9 8

350

ss soil fin 11

300

10

200

6 5 4 100 3 50 2 1 0 0 2

8 7

150

350

4

6

8

14

7

6 600 5 4 400 3 200 2 1 0 0 1 2

3

1200

11 10 8

800

7

150

10

15

20

25

4

30

35

6 600 5 4 400 3 200 2 1 0 0 5

5

6

7

sp granulat

8

9 10

11

10

1000

9

250 6 5 4 100 3 50 2 1 0 0 5

12

9 8

800

ss-granula

300

200

10

11 10

1000

9

250

sp soil fin

1200

9 8 7

10

15

20

25

Isolate Footing Design to EC2v1.07

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