Mathcad - culee1

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Button:=Caracteristicile straturilor:

Strat 1: Strat 2: Strat 3:

h2 6.6m:=h

1

4.8 m⋅:= h

3

1.00 m⋅:=

γ2 17.1kN

m3

:=γ1 18.1

kN

m3

:= γ3 17kN

m3

:=

c1 3.1kPa:= c2 19.5kPa:= c3 2.1kPa:=

ϕ1 19.7deg:= ϕ2 15deg:= ϕ3 11deg:=

Eforturi de calcul:

Nd 2000 kN⋅:=

Td 300kN:=

Vg 1400kN:=

Vc 600kN:=

He 0.9m:=

q0 He γ1⋅ 16.29mkN

m3

⋅=:= (suprasarcina de calcul)

Lcarosabil 7 m⋅:= Bcheson 3.00 m⋅:=

L

zidintors

0.3 m⋅:= H

cheson

0.8 m⋅ h

2

+ h

3

+ 8.4m=:=

Lcheson 7.00 m⋅:=

Coeficienti partiali de siguranta:

γG.stb 0.9:=- actiuni permanente: - favorabile

- nefavorabile γG.dst 1.1:=

- actiuni variabile: - favorabile γQ.std 0:=

- nefavorabile γQ.dst 1.5:=

γG 1:=- pentru actiuni sau efectul actiunilor: - actiuni permanente nefavorabile:

γQ 1.3:=- actiuni variabile nefavorabile:

- parametrii geotehnici: -unghi de frecare interna efectiv γϕ1 1.25:=



-coeziunea efectiva γc1 1.25:=

γγ1 1.00:=-greutatea volumica

Valorile de calcul pentru caracterisiticile straturilor:Stratul 1: Stratul 2: Stratul 3:

γ1d

γ1

γγ1

18.1kN

m3

⋅=:= γ2d

γ2

γγ1

17.1kN

m3

⋅=:= γ3d

γ3

γγ1

17kN

m3

⋅=:=

c1d

c1

γc1

2.48 kPa⋅=:= c2d

c2

γc1

15.6 kPa⋅=:= c3d

c3

γc1

1.68 kPa⋅=:=

ϕ1d

ϕ1

γϕ1

15.76 deg⋅=:= ϕ2d

ϕ2

γϕ1

12 deg⋅=:= ϕ3d

ϕ3

γϕ1

8.8 deg⋅=:=

Calculul greutatii:

γbeton 25kN

m3

:=A1 3.195m

2:=

G1 A1 γbeton⋅ m⋅ 7⋅ 559.125 kN⋅=:=

A2 1.8m2

:=

G2 A2 γbeton⋅ m⋅ 7⋅ 315 kN⋅=:=

G3 3.18m

2

2⋅

7⋅

m γbeton⋅

18.56m

2

6.2⋅

m γbeton⋅+

3.99 10

3×

kN⋅=:=

A4 1.2 m2

⋅:=

G4 A4 γbeton⋅ 0.5⋅ m 2⋅ 30 kN⋅=:=

Coeficientii de presiuni active:

β 0deg:= δ1 0.5 ϕ1d⋅ 7.88 deg⋅=:= α1 0deg:=

k

a1

cos ϕ1d α1−( )

cos α1( )2

cos α1 δ1+( )⋅ 1sin ϕ1d δ1+( ) sin ϕ1d β−( )⋅

cos α1 ϕ1d+( ) cos β α1−( )⋅

+

2

⋅

0.544=:=

δ2 0.5 ϕ2d⋅ 6 deg⋅=:= β 0deg:= α2 0deg:=



k a2

cos ϕ2d α2−( )

cos α2( )2


cos α2 ϕ2d+( ) cos β α2−( )⋅

+

2

⋅

0.623=:=

δ3 0.5 ϕ3d⋅ 4.4 deg⋅=:= β 0deg:= α3 0deg:=

k a3

cos ϕ3d α3−( )

cos α3( )2


cos α3 ϕ3d+( ) cos β α3−( )⋅

+

2

⋅

0.702=:=

Coeficientii de presiuni pasive:

δ1 0.5 ϕ1d⋅ 7.88 deg⋅=:= β 0deg:= δ1 0.5 ϕ1d⋅ 7.88 deg⋅=:= α1 0deg:=

k p1

cos ϕ1d α1+( )2

cos α1( )2

cos α1 δ1−( )⋅ 1sin ϕ1d δ1+( ) sin ϕ1d β−( )⋅

cos α1 δ1+( ) cos α1 β−( )⋅

−

22.093=:=

δ2

0.5 ϕ2d

⋅ 6 deg⋅=:= β 0deg:= α2 0deg:=

k p2

cos ϕ2d α2+( )2

cos α2( )2


cos δ2 α2+( ) cos α2 β−( )⋅

−

2

⋅

1.729=:=

δ3 0.5 ϕ3d⋅ 4.4 deg⋅=:= β 0deg:= α3 0deg:=

k p3

cos ϕ3d α3+( )2

cos α3( )2


cos δ3 α3+( ) cos α3 β−( )⋅

−

2

⋅

1.483=:=



Ipoteza I (G1+G2+G3+G4):

Verificarea la sectiuni periculoase

xG.1 0.78m:=

xG.4 0.5m:=

V1 G1 G4+ 589.125 kN⋅=:=

M1 G1 xG.1⋅ G4 xG.4⋅− 421.118 kN m⋅⋅=:=

W1Bcheson Lcheson

2⋅

624.5 m

3⋅=:=

σmax

V1

Bcheson Lcheson⋅

M1

W1+ 45.242

kN

m2

⋅=:=

σmin

V1

Bcheson Lcheson⋅

M1

W1− 10.865

kN

m2

⋅=:=

Rezistenta betonului la compresiune

Aleg Beton C50/60

αcc 1:= γc 1.5:=f ck 50

N

mm2

:=

f cdαcc f ck ⋅

γc

3.333 104

×kN

m2

⋅=:=

σmax f cd≤ 1=

Rezistenta la intindere a betonului

f ct.k 5.3MPa:= f ct.k 5.3N

mm2

⋅=

αct 1:=f ctd

αct f ct.k ⋅

γc

3.533 103

×kN

m2

⋅=:=

σmin f ctd≤ 1=

NU NECESITA ARMATURA DE LEGATURA INTRE ELEVATIE SI RADIER CULEE



Verificarea la rasturnare:

Sectiunea a-a:

- brate:

xG.1 0.78m:= xG.4 0.5m:=

- momente:

M1stb G1 xG.1⋅ G4 xG.4⋅+ 451.118 kN m⋅⋅=:=

M1dst 0kN m⋅:=

M1stb M1dst>

Sectiunea b-b:

- brate:

xG.1. 2.48m:= xG.4. 3.5m:= xG.2 1.5m:=

- momente:

M1stb. G1 xG.1⋅ G4 xG.4⋅+ G2 xG.2⋅+ 923.617 kN m⋅⋅=:=

M1dst. 0kN m⋅:=

M1stb M1dst>

Verificare la capacitate portanta:

Va G1 G2+ G4+ 904.125 kN⋅=:=

- brate:

xG1. 0.98m:= xG2. 0m:= xG4 2m:=

Ma G1 xG1.⋅ G2 xG2.⋅+ G4 xG4⋅+ 607.942 kN m⋅⋅=:=

ea

Ma

Va

0.672m=:=

B1 Bcheson 2 ea⋅− 1.655m=:=

L1 Lcheson:=

-aria efectiva: Aa B1 L1⋅ 11.586 m2

=:=



Pef

Vc

Aa

5.179 104

× Pa=:=

- Factorii adimensionali pt calculul presiunii terenului de fundare:

-factori care tin de capaciatatea portanta:

Nq eπ tan ϕ3d( )⋅

tan 45degϕ3d

2+

2

⋅ 2.214=:=

Nc Nq 1−( )1

tan ϕ3d( )⋅ 7.841=:=

Nγ 2 Nq 1−( ) tan ϕ3d( )⋅ 0.376=:=

-factori care tin de inclinarea bazie fundatiei: ε 0:=

bq 1 ε tan ϕ3d( )⋅−( )2

1=:=

bγ bq:=

bc bq

1 bq−

Nc tan ϕ3d( )⋅

− 1=:=

-forma fundatiei:

sq 1B1

L1

sin ϕ3d( )⋅+ 1.036=:=

sγ 1 0.3B1

L1

⋅− 0.929=:=

sc

sq Nq⋅ 1−

Nq 1−

1.066=:=

-inclinarea incarcarii



Hd 0kN:= (actiuni verticale).

m1

2B1−

L1

+

1B1−

L1

+

2.31=:=

iq 1Hd

Va A1 c3d⋅ 1tan ϕ3d deg⋅( )

⋅+

−

m1

1=:=

iγ 1Hd

Vg A1 c3d⋅1

tan ϕ3d deg⋅( )⋅+

−

m1 1+

1=:=

ic iq

1 iq−( )N

ctan ϕ

3d( )⋅

− 1=:=

Calculul suprasarcinii:

γmed

γ1 γ2+ γ3+( )3

17.4kN

m3

⋅=:=

Df h1 h2+ h3+ 12.4m=:=

Q1 Df γmed⋅ 215.76kN

m2

⋅=:=

Rd

A1

c3d Nc⋅ bc⋅ sc⋅ ic⋅ Q1 Nq⋅ bq⋅ sq⋅ iq⋅+ 0.5 γ3d⋅ m Nγ⋅ bγ⋅ sγ⋅ iγ⋅+ 511.951 kPa⋅=:=

Rd

A1

Vc Rd<

Ipoteza II (G1+G2+G4+Pa+Pp):


Impingerea activa:

qk 0kN

m3

:=

pab1.0 γQ.dst qk ⋅ k a1⋅ 2 γG.dst⋅ c1d⋅ k a1⋅− 2.968−1

m2

kN⋅=:=





Pab3H Pab3 cos2

3ϕ3d

⋅ 156.937 kN⋅=:=

Pab3V Pab3 sin2

3ϕ3d

⋅ 16.126 kN⋅=:=

zab3

h3 2 pab3.0⋅ pab3.1+( )⋅

pab3.0 pab3.1+

30.493m=:=

Impingerea pasiva:

h1' 2.2 m⋅:=

ppb1.0 γQ.dst qk ⋅ k p1⋅ 2 γG.dst⋅ c1d⋅ k p1⋅− 7.893−

1

m2 kN⋅=:=

ppb1.1 γQ.dst qk ⋅ γG.dst γ1d⋅ h1'⋅+( ) k p1⋅ 2 γG.dst⋅ c1d⋅ k p1⋅− 83.781

m2

kN⋅=:=

ppb2.0 γQ.dst qk ⋅ γG.dst γ1d⋅ h1'⋅+( ) k p2⋅ 2 γG.dst⋅ c2d⋅ k p2⋅− 30.621

m2

kN⋅=:=

ppb2.1 γQ.dst qk ⋅ γG.dst γ1d⋅ h1'⋅+ γG.dst γ2d⋅ h2⋅+( ) k p2⋅ 2 γG.dst⋅ c2d k p2⋅− 245.3281

m2

kN⋅=:=

ppb3.0 γQ.dst qk ⋅ γG.dst γ1d⋅ h1'⋅+ γG.dst γ2d⋅ h2⋅+( ) k p3⋅ 2 γG.dst⋅ c3d⋅ k p3⋅− 244.4921

m2

kN⋅=:=

ppb3.1 γQ qk ⋅ γG.dst γ1d⋅ h1'⋅+ γG.dst γ2d⋅ h2⋅+ γG.dst γ3d⋅ h3⋅+( ) k p3⋅ 2 γG.dst⋅ c3d⋅ k p3⋅−:=

ppb3.1 272.216 kN1

m2

⋅⋅=

Descompunerea impingerii dupa orizontala si verticala:

hc 0.21m:=

P

pb1

p

pb1.1

p

pb1.0

+

( )

h1

2

⋅ m⋅ 182.129 kN⋅=:=

Ppb1H Ppb1 cos2

3ϕ1d

⋅ 179.075 kN⋅=:=

Ppb1V Ppb1 sin2

3ϕ1d

⋅ 33.211 kN⋅=:=



zpc11

3h1' hc−( ) 0.663m=:=

Ppb2 m ppb2.1 ppb2.0+( )h2

2⋅

⋅ 910.629 kN⋅=:=

Ppb2H Ppb2 cos2

3ϕ2d

⋅ 901.767 kN⋅=:=

Ppb2V Ppb2 sin2

3ϕ2d

⋅ 126.735 kN⋅=:=

zpb2

h2 2 ppb2.0⋅ ppb2.1+( )⋅

ppb2.0 ppb2.1+

32.444m=:=

Ppb3 m ppb3.1 ppb3.0+( )h

32

⋅

⋅ 258.354 kN⋅=:=

Ppb3H Ppb3 cos2

3ϕ3d

⋅ 257.001 kN⋅=:=

Ppb3V Ppb3 sin2

3ϕ3d

⋅ 26.407 kN⋅=:=

zpb3

h3 2 ppb3.0⋅ ppb3.1+( )⋅

ppb3.0 ppb3.1+

30.491m=:=

Verificarea la rasturnare

Sectiunea a-a

- brate:

xG1 0.78 m⋅:= xab1 13 m⋅:= xT 2.9m:=

xG4. 1.80 m⋅:= yab1 0.09 m⋅:=

- momente:

M2stb G1 xG1⋅ G4 xG4.⋅+ Pab1V xab1⋅+ 746.123 kN m⋅⋅=:=

M2dstb Pab1H yab1⋅ 9.557 kN m⋅⋅=:=

M2dst M2stb<



Sectiunea b-b

- brate:

xG1.. 2.48 m⋅:= xab1. 3 m⋅:= xpb1. 0 m⋅:= yab1. 9 m⋅:= ypb1. 8.14 m⋅:=

xG2.. 1.5m:= xab2. 3 m⋅:= xpb2. 0 m⋅:= yab2. 3.71 m⋅:= ypb2. 3.43 m⋅:=

xG3. 1.5 m⋅:= xab3. 3 m⋅:= xpb3. 0 m⋅:= yab3. 0.49 m⋅:= ypb3. 0.49 m⋅:=

xG4.. 3.5 m⋅:= xT. 11.81 m⋅:=

- momente:

M2stb. G1 xG1..⋅ G2 xG2..⋅+ G3 xG3.⋅+ G4 xG4.⋅+ Pab1V xab1.⋅+ Pab2V xab2.⋅+ Pab3V xab3.⋅+:=

M2stb. 8.201 103

× kN m⋅⋅=

M2dstb. Pab1H yab1.⋅ Pab2H yab2.⋅+ Pab3H yab3.⋅+ Td xT.⋅+ Ppb1H ypb1.⋅−( )Ppb2H− ypb2.⋅ Ppb3H ypb3.⋅−( )+

...:=

M2dstb. 1.624 103

× kN m⋅⋅=

M2dsb. M2stb<

Verificarea la capacitate portanta

Impingerea activa:

pab1.0. γQ qk ⋅

k a1⋅

2 γG⋅

c1d⋅

k a1⋅−

3.658−

1

m2 kN

⋅=:=

pab1.1. γQ qk ⋅ γG γ1d⋅ h1⋅+( ) k a1⋅ 2 γG⋅ c1d⋅ k a1⋅− 43.6051

m2

kN⋅=:=

pab2.0. γQ qk ⋅ γG γ1d⋅ h1⋅+( ) k a2⋅ 2 γG⋅ c2d⋅ k a2⋅− 29.5121

m2

kN⋅=:=

pab2.1. γQ qk ⋅ γG γ1d⋅ h1⋅+ γG γ2d⋅ h2⋅+( ) k a2⋅ 2 γG⋅ c2d k a2⋅− 99.8441

m2

kN⋅=:=

pab3.0. γQ qk ⋅ γG γ1d⋅ h1⋅+ γG γ2d⋅ h2⋅+( ) k a3⋅ 2 γG⋅ c3d⋅ k a3⋅− 137.4521

m2

kN⋅=:=

pab3.1. γQ qk ⋅ γG γ1d⋅ h1⋅+ γG γ2d⋅ h2⋅+ γG γ3d⋅ h3⋅+( ) k a3⋅ 2 γG⋅ c3d⋅ k a3⋅− 149.3911

m2

kN⋅=:=


hc. 0.3m:=



Pab1. pab1.1. pab1.0.+( )h1

2⋅

m⋅ 95.872 kN⋅=:=

Pab1H. Pab1. cos2

3

ϕ1d

⋅ 94.265 kN⋅=:=

Pab1V. Pab1. sin2

3ϕ1d

⋅ 17.482 kN⋅=:=

zab1.1

3h1 hc.−( )⋅ 1.5m=:=

Pab2. m pab2.1. pab2.0.+( )h2

2⋅

⋅ 426.873 kN⋅=:=

Pab2H. Pab2. cos2

3

ϕ2d

⋅ 422.719 kN⋅=:=

Pab2V. Pab2. sin2

3ϕ2d

⋅ 59.409 kN⋅=:=

zab2.

h2 2 pab2.0.⋅ pab2.1.+( )⋅

pab2.0. pab2.1.+

32.702m=:=

Pab3. m pab3.1. pab3.0.+( )h3

2⋅

⋅ 143.421 kN⋅=:=

Pab3H.

Pab3.

cos2

3ϕ

3d

⋅ 142.67 kN⋅=:=

Pab3V. Pab3. sin2

3ϕ3d

⋅ 14.66 kN⋅=:=

zab3.

h3 2 pab3.0.⋅ pab3.1.+( )⋅

pab3.0. pab3.1.+

30.493m=:=

Impingerea pasiva:

ppb1.0. 2− γG⋅ c1d⋅ k p1⋅ 7.176−1

m2

kN⋅=:=

ppb1.1. γG γ1d⋅ h1'⋅( ) k p1⋅ 2 γG⋅ c1d⋅ k p1⋅− 76.1641

m2

kN⋅=:=



ppb2.0. γG γ1d⋅ h1'⋅( ) k p2⋅ 2 γG⋅ c2d⋅ k p2⋅− 27.8371

m2

kN⋅=:=

ppb2.1. γG γ1d⋅ h1'⋅ γG γ2d⋅ h2⋅+( ) k p2⋅ 2 γG⋅ c2d k p2⋅− 223.0251

m

2kN⋅=:=

ppb3.0. γG γ1d⋅ h1'⋅ γG γ2d⋅ h2⋅+( ) k p3⋅ 2 γG⋅ c3d⋅ k p3⋅− 222.2661

m2

kN⋅=:=

ppb3.1. γG γ1d⋅ h1'⋅ γG γ2d⋅ h2⋅+ γG γ3d⋅ h3⋅+( ) k p3⋅ 2 γG⋅ c3d⋅ k p3⋅− 247.4691

m2

kN⋅=:=


hc. 0.21m:=

P

pb1.

p

pb1.1.

p

pb1.0.

+

( )

h1

2

⋅ m⋅ 165.572 kN⋅=:=

Ppb1H. Ppb1. cos2

3ϕ1d

⋅ 162.796 kN⋅=:=

Ppb1V. Ppb1. sin2

3ϕ1d

⋅ 30.192 kN⋅=:=

zpb1.1

3h1' hc.−( )⋅ 0.663m=:=

Ppb2. m ppb2.1. ppb2.0.+( )h2

2⋅

⋅ 827.844 kN⋅=:=

Ppb2H. Ppb2. cos2

3ϕ2d

⋅ 819.788 kN⋅=:=

Ppb2V. Ppb2. sin2

3ϕ2d

⋅ 115.214 kN⋅=:=

zpb2.

h2 2 ppb2.0.⋅ ppb2.1.+( )⋅

ppb2.0. ppb2.1.+

32.444m=:=

Ppb3. m ppb3.1. ppb3.0.+( )h3

2⋅

⋅ 234.868 kN⋅=:=

Ppb3H. Ppb3. cos2

3ϕ3d

⋅ 233.637 kN⋅=:=

Ppb3V. Ppb3. sin2

3ϕ3d

⋅ 24.007 kN⋅=:=



zpb3.

h3 2 ppb3.0.⋅ ppb3.1.+( )⋅

ppb3.0. ppb3.1.+

30.491m=:=

- brate:

xG1. 0.98 m⋅:= xab1.. 1.5 m⋅:= xpb1.. 1.5 m⋅:= yab1.. 9.01 m⋅:= ypb1.. 8.17 m⋅:=

xG4.. 2 m⋅:= xab2.. 1.5 m⋅:= xpb2.. 1.5 m⋅:= yab2.. 3.71 m⋅:= ypb2.. 3.43 m⋅:=

xG2. 0m:= xab3.. 1.5 m⋅:= xpb3.. 1.5 m⋅:= yab3.. 0.49 m⋅:= ypb3.. 0.49 m⋅:=

xG3 0m:= xT. 11.81 m⋅:=

Mb G1 xG1.⋅ G4 xG4.⋅+ Pab1V xab1..⋅+ Pab2V xab2..⋅+ Pab3V xab3..⋅+ Ppb1V xpb1..⋅−( )Ppb2V− xpb2..⋅ Ppb3V xpb3..⋅− Pab1H yab1..⋅− Pab2H yab2..⋅−( )+

...

Pab3H− yab3..⋅ Ppb1H ypb1..⋅+ Ppb2H ypb2..⋅+ Ppb2H ypb3..⋅+ Td xT.⋅−( )+

...:=

Mb 829.59− kN m⋅⋅=

Vb G1 G2+ G3+ G4+ Pab1V+ Pab2V+ Pab3V+ Ppb1V+ Ppb2V+ Ppb3V+ 5.181 103

× kN⋅=:=

-excentricitatea:

eb

Mb

Vb0.16− m=:=

B1b Bcheson 2 eb⋅− 3.32 m=:=

L1 Lcheson:=

-aria efectiva: Ab B1b L1⋅ 23.242 m2

=:=

Pef

Vb

Ab

222.939 kPa⋅=:=



Nq. eπ tan ϕ3d( )⋅

tan 45degϕ3d

2+

2

⋅ 2.214=:=



Nc. Nq. 1−( )1

tan ϕ3d( )⋅ 7.841=:=

Nγ. 2 Nq. 1−( ) tan ϕ3d( )⋅ 0.376=:=


bq. 1 ε tan ϕ3d( )⋅−( )2

1=:=

bγ. bq.:=

bc. bq

1 bq.−

Nc tan ϕ3d( )⋅

− 1=:=

-forma fundatiei:

sq. 1B1b

L1

sin ϕ3d( )⋅+ 1.073=:=

sγ. 1 0.3B1b

L1

⋅− 0.858=:=

sc.

sq. Nq.⋅ 1−

Nq. 1−

1.132=:=


-daca H actioneaza pe directia lui B'=>m1.

2 B1−

L1

+

1B1−

L1

+

2.31=:=

Hd. Pab1H Pab2H+ Pab3H+ Ppb1H− Ppb2H− Ppb3H− Td+ 309.732− kN⋅=:=.

iq. 1Hd.

Vb Ab c3d⋅

1


−

m1.

1.037=:=

iγ. 1Hd

Vb Ab c3d⋅1


−

m1. 1+

1=:=



ic. iq.

1 iq.−( )Nc. tan ϕ3d( )⋅

− 1.067=:=


γmed.

γ1 γ2+ γ3+( )3

17.4kN

m3

⋅=:=

Df. h1 h2+ h3+ 12.4 m=:=

Q1. Df γmed⋅ 215.76kN

m2

⋅=:=

Rd

Ab

c3d Nc.⋅ bc.⋅ sc.⋅ ic.⋅ Q1 Nq.⋅ bq.⋅ sq. iq.⋅+ 0.5 γ3d⋅ m Nγ.⋅ bγ.⋅ sγ.⋅ iγ.⋅+ 549.726 kPa⋅=:=

Rd

Ab

Vb Rd< - verifica

Verificarea la sectiuni periculoase:

Sectiune A-A

xG.1 0.78m:=

xG.4 0.5m:=

P1 3.31m 0.5⋅ m 31.03⋅kN

m2

51.355 kN⋅=:=

P1H P1 cos α1 δ1+( )⋅ 50.87 kN⋅=:=

P1V P1 sin α1 δ1+( )⋅ 7.041 kN⋅=:=

P2 0.8m 0.5⋅ m 25.44⋅kN

m2

10.176 kN⋅=:=

P2H P2 cos α1 δ1+( )⋅ 10.08 kN⋅=:=

P2V P2 sin α1 δ1+( )⋅ 1.395 kN⋅=:=



V2 G1 G4+ P1V+ P2V+ 597.561 kN⋅=:=

M2 G1 xG1⋅ G4 xG.4⋅− P1H 1.13⋅ m+ P2V 1.25⋅ m+ P2H 0.2667⋅ m− P1V 0⋅ m− 477.656 kN m⋅⋅=:=

W2Bcheson Lcheson

2⋅

624.5 m

3⋅=:=

σmax

V2

Bcheson Lcheson⋅

M2

W2+ 47.951

kN

m2

⋅=:=

σmin

V2

Bcheson Lcheson⋅

M2

W2− 8.959

kN

m2

⋅=:=


Aleg Beton C50/60

f ck 50N

mm2

:=αcc 1:= γc 1.5:=

f cd

αcc f ck ⋅

γc

3.333 104

×kN

m2

⋅=:=

σmax f cd≤ 1=



mm2

⋅=

αct 1:=f ctd

αct f ct.k ⋅

γc

3.533 103

×kN

m2

⋅=:=

σmin f ctd≤ 1=


Ipoteza III (G1+G2+G4+Pa+Pp+q+Vg):


Impingerea activa:



pac1.0 γQ.dst q0⋅ k a1⋅ 2 γG.dst⋅ c1d⋅ k a1⋅− 9.2691

m2

kN⋅=:=

pac1.1 γQ.dst q0⋅ γG.dst γ1d⋅ h1⋅+( ) k a1⋅ 2 γG.dst⋅ c1d⋅ k a1⋅− 61.2581

m2

kN⋅=:=

pac2.0 γQ.dst q0⋅ γG.dst γ1d⋅ h1⋅+( ) k a2⋅ 2 γG.dst⋅ c2d⋅ k a2⋅− 47.691

m2

kN⋅=:=

pac2.1 γQ.dst q0⋅ γG.dst γ1d⋅ h1⋅+ γG.dst γ2d⋅ h2⋅+( ) k a2⋅ 2 γG.dst⋅ c2d k a2⋅− 125.0551

m2

kN⋅=:=

pac3.0 γQ.dst q0⋅ γG.dst γ1d⋅ h1⋅+ γG.dst γ2d⋅ h2⋅+( ) k a3⋅ 2 γG.dst⋅ c3d⋅ k a3⋅− 168.3571

m2

kN⋅=:=

pac3.1 γQ.dst q0⋅ γG.dst γ1d⋅ h1⋅+ γG.dst γ2d⋅ h2⋅+ γG.dst γ3d⋅ h3⋅+( ) k a3⋅ 2 γG.dst⋅ c3d⋅ k a3⋅−:=

pac3.1 181.489 kN1

m2

⋅⋅=


Pac1 pac1.1 pac1.0+( )h1

2⋅

m⋅ 169.265 kN⋅=:=

Pac1H Pac1 cos2

3ϕ1d

⋅ 166.427 kN⋅=:=

Pac1V Pac1 sin

2

3 ϕ1d

⋅

30.865 kN⋅=:=

zac1

h1 2 pac1.0⋅ pac1.1+( )⋅

pac1.0 pac1.1+

31.81m=:=

Pac2 m pac2.1 pac2.0+( )h2

2⋅

⋅ 570.061 kN⋅=:=

Pac2H Pac2 cos 23

ϕ2d

⋅ 564.513 kN⋅=:=

Pac2V Pac2 sin2

3ϕ2d

⋅ 79.337 kN⋅=:=



zac2

h2 2 pac2.0⋅ pac2.1+( )⋅

pac2.0 pac2.1+

32.807m=:=

Pac3 m pac3.1 pac3.0+( ) h32

⋅

⋅ 174.923 kN⋅=:=

Pac3H Pac3 cos2

3ϕ3d

⋅ 174.007 kN⋅=:=

Pac3V Pac3 sin2

3ϕ3d

⋅ 17.88 kN⋅=:=

zac3

h3 2 pac3.0⋅ pac3.1+( )⋅

pac3.0 pac3.1+

30.494m=:=

Impingerea pasiva:

h1.' 2.2 m⋅:=

ppc1.0 γQ.dst q0⋅ k p1⋅ 2 γG.dst⋅ c1d⋅ k p1⋅− 43.2471

m2

kN⋅=:=

ppc1.1 γQ.dst q0⋅ γG.dst γ1d⋅ h1'⋅+( ) k p1⋅ 2 γG.dst⋅ c1d⋅ k p1⋅− 134.921

m2

kN⋅=:=

ppc2.0

γQ.dst

q0

⋅ γG.dst

γ1d

⋅ h1'

⋅+

( )k

p2⋅ 2 γ

G.dst⋅ c

2d⋅ k

p2⋅− 72.88

1

m2

kN⋅=:=

ppc2.1 γQ.dst q0⋅ γG.dst γ1d⋅ h1'⋅+ γG.dst γ2d⋅ h2⋅+( ) k p2⋅ 2 γG.dst⋅ c2d k p2⋅− 287.5871

m2

kN⋅=:=

ppc3.0 γQ.dst q0⋅ γG.dst γ1d⋅ h1'⋅+ γG.dst γ2d⋅ h2⋅+( ) k p3⋅ 2 γG.dst⋅ c3d⋅ k p3⋅− 280.7191

m2

kN⋅=:=

ppc3.1 γQ.dst q0⋅ γG.dst γ1d⋅ h1'⋅+ γG.dst γ2d⋅ h2⋅+ γG.dst γ3d⋅ h3⋅+( ) k p3⋅ 2 γG.dst⋅ c3d⋅ k p3⋅−:=

ppc3.1 308.442 kN1

m2

⋅⋅=


Ppc1 ppc1.1 ppc1.0+( )h1

2⋅ m⋅ 427.602 kN⋅=:=



Ppc1H Ppc1 cos2

3ϕ1d

⋅ 420.432 kN⋅=:=

Ppc1V Ppc1 sin2

3ϕ1d

⋅ 77.973 kN⋅=:=

zpc1.

h1' 2 ppc1.0⋅ ppc1.1+( )⋅

ppc1.0 ppc1.1+

30.911m=:=

Ppc2 m ppc2.1 ppc2.0+( )h2

2⋅

⋅ 1.19 10

3× kN⋅=:=

Ppc2H Ppc2 cos2

3ϕ2d

⋅ 1.178 103

× kN⋅=:=

Ppc2V Ppc2 sin 23

ϕ2d ⋅ 165.552 kN⋅=:=

zpc2

h2 2 ppc2.0⋅ ppc2.1+( )⋅

ppc2.0 ppc2.1+

32.645m=:=

Ppc3 m ppc3.1 ppc3.0+( )h3

2⋅

⋅ 294.581 kN⋅=:=

Ppc3H Ppc3 cos2

3

ϕ3d

⋅ 293.038 kN⋅=:=

Ppc3V Ppc3 sin2

3ϕ3d

⋅ 30.11 kN⋅=:=

zpc3

h3 2 ppc3.0⋅ ppc3.1+( )⋅

ppc3.0 ppc3.1+

30.492m=:=

Sectiunea a-a

- brate:

xG1 0.78 m⋅:= xac1 1.3 m⋅:= xpc1 0 m⋅:= xVg 0.75m:=

xG4 1.80 m⋅:= yac1 0.41 m⋅:= ypc1 0 m⋅:=



- momente:

M3stb G1 xG1⋅ G4 xG4⋅+ Pac1V xac1⋅+ Ppc1V xpc1⋅− Vg xVg⋅+ 1.58 103

× kN m⋅⋅=:=

M3dstb Pac1H yac1⋅

Ppc1H ypc1⋅−

68.235 kN m⋅⋅=:=

M3dst M3stb< - verifica

Sectiunea b-b

- brate:

xG1. 2.48 m⋅:= xac1. 3 m⋅:= xpc1. 0 m⋅:= yac1. 9.32 m⋅:= ypc1. 8.42 m⋅:=

xG2. 1.5m:= xac2. 3 m⋅:= xpc2. 0 m⋅:= yac2. 3.77 m⋅:= ypc2. 3.63 m⋅:=

xG3. 1.5 m⋅:= xac3. 3 m⋅:= xpc3. 0 m⋅:= yac3. 0.49 m⋅:= ypc3. 0.49 m⋅:=

xG4. 3.5 m⋅:=xVg. 2.45 m⋅:=

- momente:

M3stb. G1 xG1.⋅ G2 xG2.⋅+ G3 xG3.⋅+ G4 xG4.⋅+ Pac1V xac1.⋅+ Pac2V xac2.⋅+ Pac3V xac3.⋅+

Ppc1V− xpc1.⋅ Ppc2V xpc2.⋅− Ppc3V xpc3.⋅−( ) Vg xVg.⋅++

...:=

M3stb. 1.176 104

× kN m⋅⋅=

M3dstb. Pac1H yac1.⋅

Pac2H yac2.⋅+

Pac3H yac3.⋅+

Ppc1H ypc1.⋅−

Ppc2H ypc2.⋅−

Ppc3H ypc3.⋅−:=

M3dstb. 4.195− 103

× kN m⋅⋅=

M3dst. M3stb.< - verifica

Verificarea la capacitate portanta:

Impingerea activa:

pac1.0. γQ q0⋅ k a1⋅ 2 γG⋅ c1d⋅ k a1⋅− 7.8621

m2

kN⋅=:=

pac1.1. γQ q0⋅ γG γ1d⋅ h1⋅+( ) k a1⋅ 2 γG⋅ c1d⋅ k a1⋅− 55.1261

m2

kN⋅=:=

pac2.0. γQ q0⋅ γG γ1d⋅ h1⋅+( ) k a2⋅ 2 γG⋅ c2d⋅ k a2⋅− 42.7091

m2

kN⋅=:=



pac2.1. γQ q0⋅ γG γ1d⋅ h1⋅+ γG γ2d⋅ h2⋅+( ) k a2⋅ 2 γG⋅ c2d k a2⋅− 113.0411

m2

kN⋅=:=

pac3.0. γQ q0⋅ γG γ1d⋅ h1⋅+ γG γ2d⋅ h2⋅+( ) k a3⋅ 2 γG⋅ c3d⋅ k a3⋅− 152.3241

m

2kN⋅=:=

pac3.1. γQ q0⋅ γG γ1d⋅ h1⋅+ γG γ2d⋅ h2⋅+ γG γ3d⋅ h3⋅+( ) k a3⋅ 2 γG⋅ c3d⋅ k a3⋅− 164.2621

m2

kN⋅=:=


Pac1. pac1.1. pac1.0.+( )h1

2⋅

m⋅ 151.17 kN⋅=:=

Pac1H. Pac1. cos2

3ϕ1d

⋅ 148.636 kN⋅=:=

Pac1V. Pac1. sin2

3ϕ1d

⋅ 27.566 kN⋅=:=

zac1.

h1 2 pac1.0.⋅ pac1.1.+( )⋅

pac1.0. pac1.1.+

31.8m=:=

Pac2. m pac2.1. pac2.0.+( )h2

2⋅

⋅ 513.974 kN⋅=:=

Pac2H. Pac2. cos 2

3ϕ2d

⋅ 508.972 kN⋅=:=

Pac2V. Pac2. sin2

3ϕ2d

⋅ 71.531 kN⋅=:=

zac2.

h2 2 pac2.0.⋅ pac2.1.+( )⋅

pac2.0. pac2.1.+

32.803m=:=

Pac3. m pac3.1. pac3.0.+( )h

32

⋅

⋅ 158.293 kN⋅=:=

Pac3H. Pac3. cos2

3ϕ3d

⋅ 157.464 kN⋅=:=

Pac3V. Pac3. sin2

3ϕ3d

⋅ 16.18 kN⋅=:=



zac3.

h3 2 pac3.0.⋅ pac3.1.+( )⋅

pac3.0. pac3.1.+

30.494m=:=

Impingerea pasiva:

ppc1.0. γQ.dst q0⋅ k p1⋅ 2 γG⋅ c1d⋅ k p1⋅− 43.9651

m2

kN⋅=:=

ppc1.1. γQ.dst q0⋅ γG γ1d⋅ h1'⋅+( ) k p1⋅ 2 γG⋅ c1d⋅ k p1⋅− 127.3041

m2

kN⋅=:=

ppc2.0. γQ.dst q0⋅ γG γ1d⋅ h1'⋅+( ) k p2⋅ 2 γG⋅ c2d⋅ k p2⋅− 70.0961

m2

kN⋅=:=

ppc2.1. γQ.dst q0⋅

γG γ1d⋅

h1'⋅+

γG γ2d⋅

h2⋅+

( ) k p2⋅

2 γG⋅

c2d k p2⋅−

265.285

1

m2 kN

⋅=:=

ppc3.0. γQ.dst q0⋅ γG γ1d⋅ h1'⋅+ γG γ2d⋅ h2⋅+( ) k p3⋅ 2 γG⋅ c3d⋅ k p3⋅− 258.4921

m2

kN⋅=:=

ppc3.1. γQ.dst q0⋅ γG γ1d⋅ h1'⋅+ γG γ2d⋅ h2⋅+ γG γ3d⋅ h3⋅+( ) k p3⋅ 2 γG⋅ c3d⋅ k p3⋅− 283.6961

m2

k ⋅=:=


Ppc1. ppc1.1. ppc1.0.+( )h1

2⋅ m⋅ 411.044 kN⋅=:=

Ppc1H. Ppc1. cos 23

ϕ1d

⋅ 404.153 kN⋅=:=

Ppc1V. Ppc1. sin2

3ϕ1d

⋅ 74.954 kN⋅=:=

zp.c1.

h1' 2 ppc1.0.⋅ ppc1.1.+( )⋅

ppc1.0. ppc1.1.+

30.922m=:=

Ppc2. m ppc2.1. ppc2.0.+( )h2

2⋅

⋅ 1.107 10

3× kN⋅=:=

Ppc2H. Ppc2. cos2

3ϕ2d

⋅ 1.096 103

× kN⋅=:=



Ppc2V. Ppc2. sin2

3ϕ2d

⋅ 154.031 kN⋅=:=

zpc2.

h2 2 ppc2.0.⋅ ppc2.1.+( )⋅

ppc2.0. ppc2.1.+

32.66 m=:=

Ppc3. m ppc3.1. ppc3.0.+( )h3

2⋅

⋅ 271.094 kN⋅=:=

Ppc3H. Ppc3. cos2

3ϕ3d

⋅ 269.674 kN⋅=:=

Ppc3V. Ppc3. sin2

3ϕ3d

⋅ 27.71 kN⋅=:=

zpc3.

h3

2 ppc3.0.

⋅ ppc3.1.

+

( )⋅

ppc3.0. ppc3.1.+

30.492m=:=

- brate:

xG1.. 0.98 m⋅:= xac1.. 1.5 m⋅:= xpc1.. 1.5 m⋅:= yac1.. 9.32 m⋅:= ypc1.. 8.43 m⋅:=

xG4.. 2 m⋅:= xac2.. 1.5 m⋅:= xpc2.. 1.5 m⋅:= yac2.. 3.81 m⋅:= ypc2.. 3.65 m⋅:=

xac3.. 1.5 m⋅:= xpc3.. 1.5 m⋅:= yac3.. 0.49 m⋅:= ypc3.. 0.49 m⋅:=xVg.. 0.95 m⋅:=

Mc G1 xG1..⋅ G4 xG4..⋅+ Pac1V xac1..⋅+ Pac2V xac2..⋅+ Pac3V xac3..⋅+ Ppc1V xpc1..⋅−

Ppc2V xpc2..⋅ Ppc3V xpc3..⋅− Pac1H yac1..⋅− Pac2H yac2..⋅− Pac3H yac3..⋅−( )+

...

Ppc1H ypc1..⋅ Ppc2H ypc2..⋅+ Ppc2H ypc3..⋅+ Vg xVg..⋅++

...

:=

Mc 6.85 103

× kN m⋅⋅=

Vc. Vg G1+ G2+ G3+ G4+ Pac1V Pac2V+ Pac3V+ Ppc1V+ Ppc2V++ Ppc3V+ 6.696 103

× ⋅=:=

-excentricitatea:

ec

Mc

Vc.1.023m=:=

B1c Bcheson 2 ec⋅− 0.954m=:=

L1 Lcheson:=



-aria efectiva: Ac B1c L1⋅ 6.677m2

=:=

Pef

Vc.

Ac

1.003 103

× kPa⋅=:=



Nq.. eπ tan ϕ3d( )⋅

tan 45degϕ3d

2+

2

⋅ 2.214=:=

Nc.. Nq.. 1−( )1

tan ϕ3d( )⋅ 7.841=:=

Nγ.. 2 Nq.. 1−( ) tan ϕ3d( )⋅ 0.376=:=


bq.. 1 ε tan ϕ3d( )⋅−( )2

1=:=

bγ.. bq..:=

bc.. bq

1 bq..−

Nc.. tan ϕ3d( )⋅

− 1=:=

-forma fundatiei:

sq.. 1B1c

L1

sin ϕ3d( )⋅+ 1.021=:=

sγ.. 1 0.3B1c

L1

⋅− 0.959=:=

s

c..

sq Nq⋅ 1−

Nq 1−

1.066=:=



:=


-daca H actioneaza pe directia lui B'=>m1..

2B1−

L1

+

1 B1−

L1

+

2.31=:=

Hd.. Pac1H Pac2H+ Pac3H+ Ppc1H− Ppc2H− Ppc3H− Td+ 686.489− kN⋅=:=.

iq.. 1Hd

Vg Ac c3d⋅1


−

m1

1=:=

iγ.. 1Hd

Vg Ac c3d⋅1


−

m1 1+

1=:=

ic.. iq

1 iq−( )Nc tan ϕ3d( )⋅

− 1=:=


γmed..

γ1 γ2+ γ3+( )3

17.4kN

m3

⋅=:=

Df.. h1 h2+ h3+ 12.4 m=:=

Q1.. Df γmed⋅ 215.76kN

m2

⋅=:=

Rd

Ac

c3d Nc⋅ bc⋅ sc⋅ ic⋅ Q1 Nq⋅ bq⋅ sq⋅ iq⋅+ 0.5 γ3d⋅ m Nγ⋅ bγ⋅ sγ⋅ iγ⋅+ 511.951 kPa⋅=:=

Rd

Ac

Vc Rd< - verifica

Verificarea la Sectiuni periculoase:



xG.1 0.78m:=

xG.4 0.5m:=

P1

3.31m 0.5⋅ m 51.03⋅kN

m2

84.455 kN⋅=:=

P1H P1 cos α1 δ1+( )⋅ 83.657 kN⋅=:=

P1V P1 sin α1 δ1+( )⋅ 11.579 kN⋅=:=

P2 0.8m 0.5⋅ m 45.44⋅kN

m2

18.176 kN⋅=:=

P2H P2 cos α1 δ1+( )⋅ 18.004 kN⋅=:=

P2V P2 sin α1 δ1+( )⋅ 2.492 kN⋅=:= :=

V3 G1 G4+ P1V+ P2V+ 603.196 kN⋅=:=

M3 G1 xG1⋅ G4 xG.4⋅− P1H 1.13⋅ m+ P2V 1.25⋅ m+ P2H 0.2667⋅ m− P1V 0⋅ m− Vg 0.55⋅ m+ 1.284 1×=:=

W3Bcheson Lcheson

2⋅

624.5 m

3⋅=:=

σmax

V3

Bcheson Lcheson⋅

M3

W2+ 81.13

kN

m2

⋅=:=

σmin

V3

Bcheson Lcheson⋅

M3

W3− 23.683−

kN

m2

⋅=:=


Aleg Beton C50/60

f ck 50N

mm2

:=αcc 1:= γc 1.5:=

f cd

αcc f ck ⋅

γc

3.333 104

×kN

m2

⋅=:=

σmax f cd≤ 1=





mm2

⋅=

αct 1:=

f ctd

αct f ct.k ⋅

γc 3.533 10

3×

kN

m2

⋅=:=

σmin f ctd≤ 1=


Ipoteza IV (G1+G2+G3+G4+Pa+Pp+Vc+Vg+Td):


Impingerea activa:

qk. 0kN

m3

:=

pad1.0 γQ.dst qk ⋅ k a1⋅ 2 γG.dst⋅ c1d⋅ k a1⋅− 4.024−1

m2

kN⋅=:=

pad1.1 γQ.dst qk ⋅ γG.dst γ1d⋅ h1⋅+( ) k a1⋅ 2 γG.dst⋅ c1d⋅ k a1⋅− 47.9661

m2

kN⋅=:=

pad2.0 γQ.dst qk ⋅

γG.dst γ1d⋅

h1⋅+

( ) k a2⋅

2 γG.dst⋅

c2d⋅

k a2⋅−

32.463

1

m2 kN

⋅=:=

pad2.1 γQ.dst qk ⋅ γG.dst γ1d⋅ h1⋅+ γG.dst γ2d⋅ h2⋅+( ) k a2⋅ 2 γG.dst⋅ c2d k a2⋅− 109.8281

m2

kN⋅=:=

pad3.0 γQ.dst qk ⋅ γG.dst γ1d⋅ h1⋅+ γG.dst γ2d⋅ h2⋅+( ) k a3⋅ 2 γG.dst⋅ c3d⋅ k a3⋅− 151.1981

m2

kN⋅=:=

pad3.1 γQ.dst qk ⋅ γG.dst γ1d⋅ h1⋅+ γG.dst γ2d⋅ h2⋅+ γG.dst γ3d⋅ h3⋅+( ) k a3⋅ 2 γG.dst⋅ c3d⋅ k a3⋅−:=

pad3.1 164.33 kN1

m2

⋅⋅=


hc'. 0.32m:=

Pad1 pad1.1 pad1.0+( )h1

2⋅

m⋅ 105.459 kN⋅=:=



Pad1H Pad1 cos2

3ϕ1d

⋅ 103.691 kN⋅=:=

Pad1V Pad1 sin2

3

ϕ1d

⋅ 19.231 kN⋅=:=

zad11

3h1 hc'−( )⋅ 1.493m=:=

Pad2 m pad2.1 pad2.0+( )h2

2⋅

⋅ 469.56 kN⋅=:=

Pad2H Pab2 cos2

3ϕ2d

⋅ 464.991 kN⋅=:=

Pad2V Pab2 sin2

3ϕ2d

⋅ 65.35 kN⋅=:=

zad2

h2 2 pad2.0⋅ pad2.1+( )⋅

pad2.0 pad2.1+

32.702m=:=

Pad3 m pad3.1 pad3.0+( )h3

2⋅

⋅ 157.764 kN⋅=:=

Pad3H

Pad3

cos2

3ϕ

3d

⋅ 156.937 kN⋅=:=

Pad3V Pad3 sin2

3ϕ3d

⋅ 16.126 kN⋅=:=

zad3

h3 2 pad3.0⋅ pad3.1+( )⋅

pad3.0 pad3.1+

30.493m=:=

Impingerea pasiva:

h.1.' 2.2 m⋅:=

ppd1.0 γQ.dst qk ⋅ k p1⋅ 2 γG.dst⋅ c1d⋅ k p1⋅− 7.893−1

m2

kN⋅=:=

ppd1.1 γQ.dst qk ⋅ γG.dst γ1d⋅ h1'⋅+( ) k p1⋅ 2 γG.dst⋅ c1d⋅ k p1⋅− 83.781

m2

kN⋅=:=



ppd2.0 γQ.dst qk ⋅ γG.dst γ1d⋅ h1'⋅+( ) k p2⋅ 2 γG.dst⋅ c2d⋅ k p2⋅− 30.621

m2

kN⋅=:=

ppd2.1 γQ.dst qk ⋅ γG.dst γ1d⋅ h1'⋅+ γG.dst γ2d⋅ h2⋅+( ) k p2⋅ 2 γG.dst⋅ c2d k p2⋅− 245.3281

m

2kN⋅=:=

ppd3.0 γQ.dst qk ⋅ γG.dst γ1d⋅ h1'⋅+ γG.dst γ2d⋅ h2⋅+( ) k p3⋅ 2 γG.dst⋅ c3d⋅ k p3⋅− 244.4921

m2

kN⋅=:=

ppd3.1 γQ qk ⋅ γG.dst γ1d⋅ h1'⋅+ γG.dst γ2d⋅ h2⋅+ γG.dst γ3d⋅ h3⋅+( ) k p3⋅ 2 γG.dst⋅ c3d⋅ k p3⋅−:=

ppd3.1 272.216 kN1

m2

⋅⋅=


h'c. 0.21m:=

Ppd1 ppd1.1 ppd1.0+( )h1

2⋅ m⋅ 182.129 kN⋅=:=

Ppd1H Ppd1 cos2

3ϕ1d

⋅ 179.075 kN⋅=:=

Ppd1V Ppd1 sin2

3ϕ1d

⋅ 33.211 kN⋅=:=

zpd11

3h1' hc−( ) 0.663m=:=

Ppd2 m ppd2.1 ppd2.0+( )h2

2⋅

⋅ 910.629 kN⋅=:=

Ppd2H Ppd2 cos2

3ϕ2d

⋅ 901.767 kN⋅=:=

Ppd2V Ppb2 sin2

3ϕ2d

⋅ 126.735 kN⋅=:=

z

pd2

h2 2 ppd2.0⋅ ppd2.1+( )⋅

ppd2.0 ppd2.1+

3

2.444m=:=

Ppd3 m ppd3.1 ppd3.0+( )h3

2⋅

⋅ 258.354 kN⋅=:=

Ppd3H Ppd3 cos2

3ϕ3d

⋅ 257.001 kN⋅=:=



Ppd3V Ppd3 sin2

3ϕ3d

⋅ 26.407 kN⋅=:=

zpd3

h3 2 ppd3.0⋅ ppd3.1+( )⋅

ppd3.0 ppd3.1+

30.491m=:=

Sectiunea a-a

- brate:

xG..1 0.78 m⋅:= xad.1 13 m⋅:= xT.. 2.9m:=

xG..4. 1.80 m⋅:= yad.1 0.09 m⋅:= xN 0.75m:=

- momente:

M4stb G1 xG1⋅ G4 xG4.⋅+ Pad1V xad.1⋅+ Nd xN⋅+ 2.291 103

× kN m⋅⋅=:=

M4dstb Pad1H yad.1⋅ Td xT⋅+ 879.332 kN m⋅⋅=:=


Sectiunea b-b

- brate:

xG.1.. 2.48 m⋅:= xad1. 3 m⋅:= xpd1. 0 m⋅:= yad1. 9 m⋅:= ypd1. 8.14 m⋅:=

xG.2.. 1.5m:= xad2. 3 m⋅:= xpd2. 0 m⋅:= yad2. 3.71 m⋅:= ypd2. 3.43 m⋅:=

xG.3. 1.5 m⋅:= xad3. 3 m⋅:= xpd3. 0 m⋅:= yad3. 0.49 m⋅:= ypd3. 0.49 m⋅:=

xG.4.. 3.5 m⋅:=

xT... 11.81 m⋅:= xN. 2.45m:=

- momente:

M4stb. G1 xG1..⋅ G2 xG2..⋅+ G3 xG3.⋅+ G4 xG4.⋅+ Pad1V xad1.⋅+ Pad2V xad2.⋅+ Pad3V xad3.⋅+ N+:=

M4stb. 8.912 10

3

× kN m⋅⋅=

M4dstb. Pad1H yad1.⋅ Pad2H yad2.⋅+ Pad3H yad3.⋅+ Td xT.⋅+ Ppd1H ypd1.⋅− Ppd2H ypd2.⋅−

Ppd3H ypd3.⋅ 1−⋅( )+

...:=



M4dstb. 1.602 103

× kN m⋅⋅=


Verificarea la capacitate portanta

Impingerea activa:

pad1.0. γQ qk ⋅ k a1⋅ 2 γG⋅ c1d⋅ k a1⋅− 3.658−1

m2

kN⋅=:=

pad1.1. γQ qk ⋅ γG γ1d⋅ h1⋅+( ) k a1⋅ 2 γG⋅ c1d⋅ k a1⋅− 43.6051

m2

kN⋅=:=

pad2.0. γQ qk ⋅ γG γ1d⋅ h1⋅+( ) k a2⋅ 2 γG⋅ c2d⋅ k a2⋅− 29.5121

m2

kN⋅=:=

pad2.1. γQ qk ⋅ γG γ1d⋅ h1⋅+ γG γ2d⋅ h2⋅+( ) k a2⋅ 2 γG⋅ c2d k a2⋅− 99.8441

m2

kN⋅=:=

pad3.0. γQ qk ⋅ γG γ1d⋅ h1⋅+ γG γ2d⋅ h2⋅+( ) k a3⋅ 2 γG⋅ c3d⋅ k a3⋅− 137.4521

m2

kN⋅=:=

pad3.1. γQ qk ⋅ γG γ1d⋅ h1⋅+ γG γ2d⋅ h2⋅+ γG γ3d⋅ h3⋅+( ) k a3⋅ 2 γG⋅ c3d⋅ k a3⋅− 149.3911

m2

kN⋅=:=


hc.. 0.3m:=

Pad1. pad1.1. pad1.0.+( )h1

2⋅

m⋅ 95.872 kN⋅=:=

Pad1H. Pad1. cos2

3ϕ1d

⋅ 94.265 kN⋅=:=

Pad1V. Pad1. sin2

3ϕ1d

⋅ 17.482 kN⋅=:=

zad1.1

3h1 hc.−( )⋅ 1.53 m=:=

Pad2. m pad2.1. pad2.0.+( )

h2

2⋅

⋅ 426.873 kN⋅=:=

Pad2H. Pad2. cos2

3ϕ2d

⋅ 422.719 kN⋅=:=

Pad2V. Pad2. sin2

3ϕ2d

⋅ 59.409 kN⋅=:=



zad2.

h2 2 pad2.0.⋅ pad2.1.+( )⋅

pad2.0. pad2.1.+

32.702m=:=

Pad3. m pad3.1. pad3.0.+( ) h32

⋅

⋅ 143.421 kN⋅=:=

Pad3H. Pad3. cos2

3ϕ3d

⋅ 142.67 kN⋅=:=

Pad3V. Pad3. sin2

3ϕ3d

⋅ 14.66 kN⋅=:=

zad3.

h3 2 pad3.0.⋅ pad3.1.+( )⋅

pad3.0. pad3.1.+

30.493m=:=

Impingerea pasiva:

ppd1.0. 2− γG⋅ c1d⋅ k p1⋅ 7.176−1

m2

kN⋅=:=

ppd1.1. γG γ1d⋅ h1'⋅( ) k p1⋅ 2 γG⋅ c1d⋅ k p1⋅− 76.1641

m2

kN⋅=:=

ppd2.0. γG γ1d⋅ h1'⋅( ) k p2⋅ 2 γG⋅ c2d⋅ k p2⋅− 27.8371

m2

kN⋅=:=

ppd2.1. γG γ1d⋅ h1'⋅ γG γ2d⋅ h2⋅+( ) k p2⋅ 2 γG⋅ c2d k p2⋅− 223.0251

m2

kN⋅=:=

ppd3.0. γG γ1d⋅ h1'⋅ γG γ2d⋅ h2⋅+( ) k p3⋅ 2 γG⋅ c3d⋅ k p3⋅− 222.2661

m2

kN⋅=:=

ppd3.1. γG γ1d⋅ h1'⋅ γG γ2d⋅ h2⋅+ γG γ3d⋅ h3⋅+( ) k p3⋅ 2 γG⋅ c3d⋅ k p3⋅− 247.4691

m2

kN⋅=:=


h.c. 0.21m:=

Ppd1. ppd1.1. ppd1.0.+( )

h1

2⋅ m⋅ 165.572 kN⋅=:=

Ppd1H. Ppd1. cos2

3ϕ1d

⋅ 162.796 kN⋅=:=

Ppd1V. Ppd1. sin2

3ϕ1d

⋅ 30.192 kN⋅=:=



zpd1.1

3h1' hc.−( )⋅ 0.663m=:=

Ppd2. m ppd2.1. ppd2.0.+( )h2

2

⋅

⋅ 827.844 kN⋅=:=

Ppd2H. Ppd2. cos2

3ϕ2d

⋅ 819.788 kN⋅=:=

Ppd2V. Ppd2. sin2

3ϕ2d

⋅ 115.214 kN⋅=:=

zpd2.

h2 2 ppd2.0.⋅ ppd2.1.+( )⋅

ppd2.0. ppd2.1.+

32.444m=:=

Ppd3. m ppd3.1. ppd3.0.+( )

h3

2⋅

⋅ 234.868 kN⋅=:=

Ppd3H. Ppd3. cos2

3ϕ3d

⋅ 233.637 kN⋅=:=

Ppd3V. Ppd3. sin2

3ϕ3d

⋅ 24.007 kN⋅=:=

zpd3.

h3 2 ppd3.0.⋅ ppd3.1.+( )⋅

ppd3.0. ppd3.1.+

30.491m=:=

- brate:

xG.1. 0.98 m⋅:= xad1.. 1.5 m⋅:= xpd1.. 1.5 m⋅:= yad1.. 9.01 m⋅:= ypd1.. 8.17 m⋅:=

xG.4.. 2 m⋅:= xad2.. 1.5 m⋅:= xpd2.. 1.5 m⋅:= yad2.. 3.71 m⋅:= ypd2.. 3.43 m⋅:=

xG2. 0m:= xad3.. 1.5 m⋅:= xpd3.. 1.5 m⋅:= yad3.. 0.49 m⋅:= ypd3.. 0.49 m⋅:=

xG3 0m:= x.T.. 11.81 m⋅:= xN.. 0.95m:=

Md G1 xG1.⋅ G4 xG4.⋅+ Pad1V xad1..⋅+ Pad2V xad2..⋅+ Pad3V xad3..⋅+ Ppd1V xpd1..⋅−

Ppd2V− xpd2..⋅ Ppd3V xpd3..⋅− Pad1H yad1..⋅− Pad2H yad2..⋅− Pad3H yad3..⋅−( )+

...

Ppd1H ypd1..⋅ Ppd2H ypd2..⋅+ Ppd2H ypd3..⋅+ Td xT.⋅− Nd xN.⋅++

...

:=

Md 4.982 103

× kN m⋅⋅=



Vd G1 G2+ G3+ G4+ Pad1V+ Pad2V+ Pad3V+ Ppd1V+ Ppd2V+ Ppd3V+ Nd+ 7.181 103

× k ⋅=:=

-excentricitatea:

edMdVd

0.694m=:=

B1d Bcheson 2 eb⋅− 3.32 m=:=

L1 Lcheson:=

-aria efectiva: Ad B1d L1⋅ 23.242 m2

=:=

Pef

Vd

Ad

308.972 kPa⋅=:=



N.q. eπ tan ϕ3d( )⋅

tan 45degϕ3d

2+

2

⋅ 2.214=:=

N.c. Nq. 1−( )1

tan ϕ3d( )⋅ 7.841=:=

N.γ.

2 Nq.

1−

( )tan ϕ

3d( )⋅ 0.376=:=


b.q. 1 ε tan ϕ3d( )⋅−( )2

1=:=

b.γ. bq.:=

b.c. bq

1 bq.−

Nc tan ϕ3d( )⋅

− 1=:=

-forma fundatiei:

s.q. 1B1d

L1

sin ϕ3d( )⋅+ 1.073=:=



s.γ. 1 0.3B1d

L1

⋅− 0.858=:=

s.c.

sq. Nq.⋅ 1−

Nq. 1−

1.132=:=


-daca H actioneaza pe directia lui B'=>m.1.

2B1−

L1

+

1B1−

L1

+

2.31=:=

H.d. Pad1H Pad2H+ Pad3H+ Ppd1H− Ppd2H− Ppd3H− Td+ 312.224− kN⋅=:=.

i.q. 1 H.d.

Vb Ad c3d⋅1


−

m1.

1.037=:=

i.γ. 1H.d.

Vb Ad c3d⋅1


−

m1. 1+

1.053=:=

i.c. iq.

1 iq.−( )Nc. tan ϕ3d( )⋅

− 1.067=:=


γ.med

γ1 γ2+ γ3+( )3

17.4kN

m3

⋅=:=

D.f h1 h2+ h3+ 12.4 m=:=

Q.1 Df γmed⋅

215.76

kN

m2

⋅=:=

Rd

Ad

c3d Nc.⋅ bc.⋅ sc.⋅ ic.⋅ Q1 Nq.⋅ bq.⋅ sq. iq.⋅+ 0.5 γ3d⋅ m Nγ.⋅ bγ.⋅ sγ.⋅ iγ.⋅+ 549.726 kPa⋅=:=

Rd

Ad



Vd Rd< - verifica

Verificare sectiuni periculoase:

xG1 51.68cm 0.517m=:=

xG4 50cm 0.5m=:=

P1 3.4m 0.5⋅ m 51.27⋅kN

m2

87.159 kN⋅=:= P1H P1 cos α1 δ1+( )⋅ 86.336 kN⋅=:=

P1V P1 sin α1 δ1+( )⋅ 11.949 kN⋅=:=

P2 0.8m 0.5⋅ m 25.44⋅

kN

m2 10.176 kN⋅=:=

P2H P2 cos α1 δ1+( )⋅ 10.08 kN⋅=:=

P2V P2 sin α1 δ1+( )⋅ 1.395 kN⋅=:=

V4b G1 G4+ P1V+ P2V+ Vg+ Vc+ 2.602 103

× kN⋅=:=

M4b G1 xG1⋅ G4 xG4⋅− P1H 1.13⋅ m+ P2V 1.25⋅ m+ P2H 0.2667⋅ m−

P1V 0⋅ m 0.55m Vg Vc+( )⋅+ Td 2.77⋅ m++

...:=

M4b 2.302 103× kN m⋅⋅=

M'4b G1 xG1⋅ G4 xG4⋅+ Ppd3V. 1.13⋅ m− Ppd3V. 1.25⋅ m+ Ppd1V. 0.2667⋅ m+

Ppd3V. 0⋅ m 0.75m Vg Vc+( )⋅+ Td 2.90⋅ m−+

...:=

M'4b 944.889 kN m⋅⋅=

W4bBcheson Lcheson

2⋅

624.5 m

3⋅=:=

σmax

V4b

Bcheson Lcheson⋅

M4b

W4b+ 217.869

kN

m2

⋅=:=



σmax1

V4b

Bcheson Lcheson⋅

M'4b

W4b+ 162.494

kN

m2

⋅=:=

σmin

V4b

Bcheson Lcheson⋅

M4b

W4b− 29.985 kN

m2

⋅=:=

σmin1

V4b

Bcheson Lcheson⋅

M'4b

W4b− 85.36

kN

m2

⋅=:=


Aleg Beton C50/60

f ck 50 N

mm2

:=αcc 1:= γc 1.5:=

f cd

αcc f ck ⋅

γc

3.333 104

×kN

m2

⋅=:=

σmax f cd≤ 1=σmax1 f cd≤ 1=



mm2

⋅=

αct 1:=f ctd

αct f ct.k ⋅

γc

3.533 103

×kN

m2

⋅=:=

σmin f ctd≤ 1= σmin1 f ctd≤ 1=






3kN m⋅⋅



xN⋅

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