mathcad - fundatii

Etapele proiectarii unui zid de sprijin - beton simplu 1. Predimensionare - caracteristici geometrice (catalog I.P.T.A.N.A.)H1 3.75m:= qk 13

kN

m2:= 7.4deg:=

-strat 1 h1 2.8m:= -strat 2 h'2 10m:=

k1 18kN

m3:= k2 18.5

kN

m3:=

'k1 12deg:= 'k2 17.7deg:=

c'k1 13.8kN

m2:= c'k2 15.6

kN

m2:=

Dimensiuni zid de sprijin a 0.70m:= Df 1.40m:=

b 1.30m:= B 2.80m:=

f 0.80m:= B5

0.56 m=

d 0.80m:=

Ht Df H1+B5

+ 0.50m+ 6.21 m=:=

h2 Ht h1- 3.41 m=:=

2. Verificarea zidului de sprijin la lunecareCP 1.1 (A1+B1+R1)

- Coeficienti partiali pentru actiuni : permanente G.fav 1.00:=

G.nef 1.35:=

variabile Q.fav 0.00:=

Q.nef 1.50:=

- Coeficienti partiali pentru parametrii geotehnici' 1.00:=

c' 1.00:=

1.00:=

- Rezistenta totoala a pamantului Rh 1.00:=

Rv 1.00:=

Valorile de calcul ale parametrilor geotehnici

- strat 1 d1k1

18kN

m3=:=

'd1 12deg:=

c'd1c'k1c'

13.8kN

m2=:=

- strat 2 d2k2

18.5kN

m3=:=

'd2 17.7deg:=

c'd2c'k2c'

15.6kN

m2=:=

Evaluarea presiunilor active si a impingerii pamantului 0deg:=

s112'd1 6 deg=:=

s212'd2 8.85 deg=:=

7.4 deg=

ka1cos 'd1 -( )

2

cos ( )2 cos s1+( ) 1 sin 'd1 s1+( )sin 'd1 -( )

cos s1+( ) cos -( )+

2

0.717=:=

ka2cos 'd2 -( )

2

cos ( )2 cos s2+( ) 1 sin 'd2 s2+( )sin 'd2 -( )

cos s2+( ) cos -( )+

2

0.556=:=

Calculul presiunilor activepa10 Q.nef qk ka1 G.nef 2 c'd1 ka1- 17.568-

kN

m2=:=

pa11 pa10 G.nef d1 h1 ka1+ 31.202kN

m2=:=

pa20 Q.nef qk ka2 G.nef d1 h1 ka2 2 c'd2 ka2-( )+ 17.25 kNm2

=:=

pa21 pa20 G.nef d2 h2 ka2+ 64.579kN

m2=:=

Impingerea activa pe fiecare strat x 1.79m:=

pa1 pa11x2

27.926kNm

=:=

p'a2 pa20h22

29.411kNm

=:=

p''a2 pa21 pa20-( )h23

53.798kNm

=:=

Descompunerea impingerii active dupa H si V

pa1h pa1 cos s1+( ) 27.773kNm

=:=

pa1v pa1 sin s1+( ) 2.919kNm

=:=

p'a2h p'a2 cos s2+( ) 29.061kNm

=:=

p'a2v p'a2 sin s2+( ) 4.525kNm

=:=

p''a2h p''a2 cos s2+( ) 53.157kNm

=:=

p''a2v p''a2 sin s2+( ) 8.277kNm

=:=

Calculul actiunii orizontaleHd G.nef pa1h p'a2h+ p''a2h+( ) 148.488

kNm

=:=

Calculul actiunii verticaledren 19

kN

m3:= Gdren 2.625m

2dren 49.875

kNm

=:=

beton 24kN

m3:= Gbeton 11.90m

2beton 285.6

kNm

=:=

Vd G.fav Gdren Gbeton+( ) G.nef pa1v p'a2v+ p''a2v+( )+ 356.698kNm

=:=

Proiectiile fortelor dupa planul de lunecare al ziduluil 11deg:=

V'd Vd cos l( ) Hd sin l( )+ 378.477kNm

=:=

H'd Hd cos l( ) Vd sin l( )- 77.698kNm

=:=

Rezistenta la lunecare'cvd

23'd2 11.8 deg=:=

R'd V'dtan 'cvd( )

Rh 79.068

kNm

=:=

Verifiacarea la lunecare : H'd R'd

3. Verificarea la capacitate portanta a ziduluiz1 1.75m:= g1 2.625m

2:= G1 z1 g1 beton 110.25 kN=:=

z2 1.00m:= g2 3.00m2

:= G2 z2 g2 beton 72 kN=:=

z3 0.17m:= g3 2.76m2

:= G3 z3 g3 beton 11.261 kN=:=

z4 1.35m:= g4 0.75m2

:= G4 z4 g4 beton 24.3 kN=:=

z5 1.73m:= g5 0.35m2

:= G5 z5 g5 beton 14.532 kN=:=

z6 0.10m:= g6 4.20m2

:= G6 z6 g6 beton 10.08 kN=:=

z7 0.53m:= g7 0.84m2

:= G7 z7 g7 beton 10.685 kN=:=

y1 4.03m:= x1 1.40m:= p1 pa1h y1 111.923 kN=:=

y2 1.43m:= x2 2.01m:= p2 p'a2h y2 41.557 kN=:=

y3 0.86m:= x3 1.81m:= p3 p''a2h y3 45.715 kN=:=

p'1 pa1v x1 4.087 kN=:=

p'2 p'a2v x2 9.095 kN=:=

p'3 p''a2v x3 14.981 kN=:=

Med G.nef p1 p2+ p3+( ) G.fav G1 G2+ G3+ G4+G5 G6+ G7++

...

-

G.nef- p'1 p'2+ p'3+( ) +

...

1 m 22.212- kN m=:=

Vdc Vd 1 m 356.698 kN=:=

eBMedVdc

0.062- m=:=B6

0.467 m= eBB6

B' B 2 eB- 2.925 m=:= L' 1m:= A' B' L' 2.925 m2

=:=

Calculul capacitatii portante

Nq e tan 'd2( ) tan 45deg 'd2+( )

2 10.23=:=

Nc Nq 1-( )1

tan 'd2( ) 28.923=:=

N 2 Nq 1-( ) tan 'd2( ) 5.892=:= 'd2

2

1 11deg 0.192 rad=:=

bq 1 1 tan 'd2( )-( )2 0.881=:= b bq:=

bc bq1 bq-( )

Nc tan 'd2( )( )- 0.868=:=

sq 1B'L'

sin 'd2( )+ 1.889=:=

s 1 0.3B'L'

- 0.123=:=

scsq Nq 1-( )

Nq 1-( )1.985=:=

Hd actioneaza pe directia B' mB2

B'L'

+

1B'L'

+

1.255=:=

iq 1Hd 1 m

Vdc A' c'd2 cot 'd2( )+( )-

mB

0.642=:=

i 1Hd 1 m

Vdc A' c'd2 cot 'd2( )+( )-

mB 1+

0.452=:=

ic iq1 iq-( )

Nc tan 'd2( )( )- 0.604=:=

q' Df d2 25.9kN

m2=:=

Rd c'd2 Nc bc sc ic q' Nq bq sq iq+ 0.5d2 B' N b s i+ 760.755kN

m2=:=

VdA'

121.9671m

kN

m2= Rd 760.755

kN

m2=

Verificarea la capacitate portantaVdA'

Rd

4. Verificarea la rasturnareStabilirea coeficientilor partiali de siguranta pentru starea limita EQU

Actiuni : -permanente G.stb 0.9:=

G.dst 1.1:=

-variabile Q.stb 0:=

Q.dst 1.5:=

-parametrii gotehnici 'r 1.25:=

c'r 1.25:=

r 1.00:=

Valorile de calcul ale parametrilor geotehnici

d1 18kN

m3= d2 18.5

kN

m3=

'd1r atantan 'k1( )'r

9.651 deg=:= 'd2r atantan 'k2( )'r

14.322 deg=:=

c'd1rc'k1c'r

11.04kN

m2=:= c'd2r

c'k2c'r

12.48kN

m2=:=

s1r12'd1r 4.825 deg=:= s2r

12'd2r 7.161 deg=:=

ka1rcos 'd1r -( )

2

cos ( )2 cos s1r+( ) 1 sin 'd1r s1r+( )sin 'd1r -( )

cos s1r+( ) cos -( )+

2

0.807=:=

ka2rcos 'd2r -( )

2

cos ( )2 cos s2r+( ) 1 sin 'd2r s2r+( )sin 'd2r -( )

cos s2r+( ) cos -( )+

2

0.644=:=

Calculul presiunilor activepa10r Q.dst qk ka1r G.dst 2 c'd1r ka1r- 6.085-

kN

m2=:=

pa11r pa10r G.dst d1 h1 ka1r+ 38.631kN

m2=:=

pa20r Q.dst qk ka2r G.dst d1 h1 ka2r 2 c'd2r ka2r-( )+ 26.247 kNm2

=:=

pa21r pa20r G.dst d2 h2 ka2r+ 70.96kN

m2=:=

Impingerea activa pe fiecare strat xr 2.42m:=

pa1r pa11rxr2

46.744kNm

=:=

p'a2r pa20rh22

44.752kNm

=:=

p''a2r pa21r pa20r-( )h23

50.823kNm

=:=

Descompunerea impingerii active dupa H si V

pa1hr pa1r cos s1r+( ) 46.578kNm

=:=

pa1vr pa1r sin s1r+( ) 3.932kNm

=:=

p'a2hr p'a2r cos s2r+( ) 44.403kNm

=:=

p'a2vr p'a2r sin s2r+( ) 5.579kNm

=:=

p''a2hr p''a2r cos s2r+( ) 50.427kNm

=:=

p''a2vr p''a2r sin s2r+( ) 6.336kNm

=:=

Momentul destabilizatory1r 4.06m:= y2r 1.15m:= y3r 0.58m:=

Mdst.d G.dst pa1hr y1r p'a2hr y2r+ p''a2hr y3r+( ) 1 m 296.359 kN m=:=

zr1 3.15m:= gr1 2.625m2

:= Gr1 zr1 gr1 beton 198.45 kN=:=

zr2 2.40m:= gr2 3.00m2

:= Gr2 zr2 gr2 beton 172.8 kN=:=

zr3 1.53m:= gr3 2.76m2

:= Gr3 zr3 gr3 beton 101.347 kN=:=

zr4 2.75m:= gr4 0.75m2


zr5 3.17m:= gr5 0.35m2

:= Gr5 zr5 gr5 beton 26.628 kN=:=

zr6 1.50m:= gr6 4.20m2


zr7 1.93m:= gr7 0.84m2

:= Gr7 zr7 gr7 beton 38.909 kN=:=

xr1 2.80m:= xr2 3.41m:= xr3 3.21m:=

p'1r pa1vr xr1 11.009 kN=:= p'3r p''a2vr xr3 20.338 kN=:=

p'2r p'a2vr xr2 19.024 kN=:=

Mstb.d G.dst p'1r p'2r+ p'3r+( ) G.stb Gr1 Gr2+ Gr3+ Gr4+Gr5 Gr6+ Gr7++

...

+

1 m 720.358 kN m=:=

Verificarea la rasturnare Mdst.d Mstb.d

5. Verificarea in sectiuni periculoase

gs1 2.15m2

:=

gs2 3.00m2

:=

gzid gs1 gs2+ 5.15 m2

=:=

Gtot gzid beton 1 m 123.6 kN=:=

Vds G.fav Gtot 123.6 kN=:=

zs1 0.21- m:= y 1.85m:=

zs2 0.57m:=

pa1hs 27.926kNm

:=

Meds G.nef pa1hs y 1 m G.fav gs1 zs1 1 m gs2 zs2 1 m+( ) beton+ 99.949 kN m=:=

ba 1.95m:=

eBsMedsVds

0.809 m=:=

pmaxVdsL' ba

16 eBs

ba+

221.095kN

m2=:=

pminVdsL' ba

16 eBs

ba-

94.326-kN

m2=:=

Folosesc beton C12/15 fcd 8 103

kN

m2:= fctd 867

kN

m2:=

Verificare pmax fcd

pmin fctd

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