Proiect Poduri Metalice - Badulecu Gabriel

8/12/2019 Proiect Poduri Metalice - Badulecu Gabriel

1/38

** Numarul de ordine: n 22:=

** Date initiale:

--Schema statica: grinda simplu rezemata

--Deschiderea: L 41.20m 0.50n m+ 52.20m=:=

--Dimensiunile sectiunii grinzilor principale:

tbf

bbf

hw

tuf

tw

buf

h'w 2500mm 12n mm+ 2764 mm=:= ==> hw 2800mm:=

tw 18mm:=

buf 500mm 5n mm+ 610 mm=:=

tuf 20mm:=

bbf 650mm 5n mm+ 760 mm=:=

tbf 50mm:=

200

25

800

25

200

15--Dimensiunile sectiunii antretoazelor de capat:

200

2

5

600

25

200

15

--Dimensiunile sectiunilor antretoazelor curente:

--Grosimea placii de beton: ht 250mm:=

--Materiale: otel S355; beton C35/45; otel beton BSt 500S (B)

--Clasa de incarare: -trafic international greu

-grupa 1a (LM1 + pietoni pe trotuare 3 kN/m^2)

Qi 1:= qi 1:= qr 1:=

--Convoi de calcul pentru oboseala: LMO3

** Evaluarea greutatilor permanente (pentru o grinda):

--Greutatea proprie a scheletului metalic:

lm - deschiderea tablierului, in metri lm 52.20:=

b - latimea dalei de beton, in metri b 11.20:=

g'sm 100

20 lm

0.6 0.035 b++

N

m2 1.152

kN

m2=:=

gk_sm g'smb 1 m 12.907kN

m=:=


2/38

2.1010

55

55

5.29/2

25

57

61

Ac 25

5.35--Greutatea dalei de beton:

ba 25kN

m3

:=

Ac 1.41m2

:=

gk_dala Acba 35.25 kN

m=:=

--Greutatea betonului de panta:

10

390140

25Abp

b 24kN

m3

:=

Abp 0.283m2

:=

gk_bp Abpb 6.792 kN

m

=:=

--Greutatea hidroizolatiei:

hidr 12kN

m3

:=

hhidr 1cm:= bhidr 5.50m:=

gk_hidr hhidrb hidr hidr 0.66 kN

m=:=

--Greutatea sapei de protectie:

hsapa 5cm:= bsapa 5.35m:=

gk_sapa hsapabsapa ba 6.688 kN

m=:=

--Greutatea stratelor caii:

asfalt 22kN

m3

:=

hsc 8cm:= bsc 3.90m:=

gk_sc hscbsc asfalt 6.864 kN

m=:=

--Greutatea trotuarului+borduri:

htb 25cm:= btb 1.45m:=

gk_tb htbbtb b 8.7 kN

m=:=

--Greutatea parapetilor: gp 1kN

m:=


3/38

** Calculul deformatiei specifice din contractie la t=:

cs cd ca+=

cs - deformatia totala de contractie

cd - deformatia datorata contractiei de uscare

ca - deformatia datorata contractiei endogeneCiment de tip N: ds1 4:= ds2 0.12:=

Beton C35/45: fck 35MPa:= fcm 43MPa:= fcm0 10MPa:= Ecm 34GPa:=

RH 0.80:= RH0 1:=

RH 1.55 1RH

RH0

3

0.756=:=

cd_0 0 .85 220 110 ds1+( ) eds2

fcm

fcm0

10

6 RH 0.0002533=:=

u 5.83m:= Ac 1.41 m

2

= h0

2 Ac

u 483.705 mm=:= ==> kh 0.7041:=

cd_ kh cd_0 0.0001783=:=

ca_ 2.5fck

1MPa10

10

6 0.0000625=:=

cs cd_ ca_+ 0.0002408=:=

** Calculul actiuinilor din contractia dalei de beton in centul de greutate al sectiunii mixte la t= :

Y

610x20

760x50

2800x18

5640

50

Ac 1.41 m2

= Ecm 34 GPa=

Es 210GPa:=

- Coeficientul de echivalenta pentru actiuni se scurta durata n0

n0

Es

Ecm

6.176=:=

- Calculul coeficientului de echivalenta pentru actiuni din contractie nL

135

fcm

1MPa

0.7

:= 235

fcm

1MPa

0.2

:=

RH 1

1 RH

0.10

3h0

1mm

1+

2 1.171=:=

fcm16.8

fcm

1MPa

2.562=:=

t0 1:=

t01

0.1 t00.2

+

0.909=:=

0 RHfcm t0 2.728=:=

t.t0 0:=

L 0.55:= nL n0 1 Lt.t0+( ) 15.444=:=


4/38

- Centrul de greutate al sectiunii mixte la t=

zg

5640 250

nL

125 610 20( )310+ 2800 18( )1710+ 760 50( ) 3135+

5640 250

nL

610 20+ 2800 18+ 760 50+

1 mm 1.149m=:=

- Modulul de elasticitate al betonului la t=

Ec_Ecm

1 L t.t0+ 13.597 GPa=:=

- Actiuni

zN zg

ht

2 1.024m=:=

Ncs AcEc_ cs 4617.459 kN=:=

Mcs NcszN 4728.745 kN m=:=

** Repartitia transversala a actiunilor din trafic:

BANDA1 L=3.00m

.

BANDA2 L=3.00m

.

ZONA RAMASA

L=1.80m

TROTUAR

L=1m

TROTUAR

L=1m

0.9

0 0.4

0

R1=1

R2=0

INCARCARE LINIE DE INFLUENTA A REACTIUNILOR REPARTITIEI TRANSVERSALE CU CONVOI TS / LMO3

Q1k / QLMO3 Q2k

1.50 3.00 3.30

0.9

0 0.4

0

R1=1

R2=0

q1k q2k qrkqpk

0.50 0.50 1.50 1.50 1.50 1.50 0.45 0.45

1.00 3.00 3.00 0.90

INCARCARE LINIE DE INFLUENTA A REACTIUNILOR REPARTITIEI TRANSVERSALE CU CONVOI UDL

SI PIETONI PE TROTUARE

1.3

1 0.

08

Q1k 300:= Q2k 200:= QLMO3 120:=

q1k 9:= q2k 2.5:= qrk 2.5:= qpk 3:=

-Valoare incarcarii pe osie a convoiului TS pentru incarcarea liniilor de influenta longitudinale :

Pk_TS 0.90 Q1k 0.4 Q2k+( )kN 350 kN=:=-Valoare incarcarii distribuite a convoiului UDL pentru incarcarea liniilor de influenta longitudinale :

pk_UDL 3 0.90 q1k 3 0.4 q2k+ 0.9 0.08 qrk+( )kN

m27.48

kN

m=:=

-Valoare incarcarii distribuite a pietonilor pentru incarcarea liniilor de influenta longitudinale :

pk_Pietoni 1 1.31 qpk( )kN

m3.93

kN

m=:=

-Valoare incarcarii pe osie a convoiului LMO3 pentru incarcarea liniilor de influenta longitudinale :

PLMO3 0.90 QLMO3( )kN 108 kN=:=


5/38

** Diagrame de eforturi sectionale, comform etapelor de executie - valori caracteristice

--Etapa 1: Montajul scheletului metalic pe reazemele provizorii - Incarcare cu greutatea proprie a scheletului metalic

SCHEMA STATICA

DIAGAMA M [kN*m]

DIAGRAMA V [kN]

--Etapa 2: Turmarea dalei de beton - Incarcare cu greutatea dalei de beton

SCHEMA STATICA

DIAGRAMA M [kN*m]

DIAGRAMA V [kN]


6/38

--Etapa 3: Incarcare cu actiuni din contractia betonului

SCHEMA STATICA

DIAGRAMA M [kN*m]

DIAGRAMA V [kN]

--Etapa 4: Coborarea tablierului cu sectiune mixta otel-beton pe reazermele definitive - Incarcare in sens gravitational

cu suma reactiunilor din etapele anterioare

SCHEMA STATICA

DIAGRAMA M [kN*m]

DIAGRAMA V [kN]


7/38

--Etapa 5: Executia caii si montajul echipamentelor tablierului - Incarcare cu suma greutatilor hidroizolatiei, betonului de

panta, stratelor caii, sapei de protectie, bordurilor, trotuarului si a parapetilor

SCHEMA STATICA

DIAGRAMA M [kN*m]

DIAGRAMA V [kN]

--Etapa 5: Darea in folosinta

- Incarcare cu convoi TS

SCHEMA STATICA

INFASURATOAREA M [kN*m]

INFASURATOAREA V [kN]


8/38

- Incarcare cu convoi UDL

SCHEMA STATICA



- Incarcare cu pietoni pe trotuare

SCHEMA STATICA




9/38

- Incarcare cu convoi LMO3

SCHEMA STATICA



** Predimensionarea grinzilor metalice principale:

Predimensionarea grinzilor metalice se face considerand indeplinita conditia de verificare la SLO, admitand ca actiunile

care produc oboseala sunt preluate numai de sectiunea de otel a grinzilor principale.

-Factorul echivalent de vatamare, :

1 2 3 4= < max

1 2.55 0.7

L

1m10

70 2.128=:=

Qm1 300kN:= Qm0 480kN:= Nobs 1 106

:= N0 0.5 106

:=

2

Qm1

Qm0

Nobs

N0

1

5

0.718=:=

tLd 100:=

3

tLd

100

1

5

1=:=

4 1:=

1 2 3 4 1.528=:= < max 2:=

-Modulul de rezistenta necesar intregii sectiuni, wncs:

Ff 1:= Mf 1.35:=

MLMO3 4878.7kN m:=

c 80N

mm2

:=


10/38

wncs

Ff Mf MLMO3

c

1.258 108

mm3

=:=

-Inaltimea optima a grinzii de otel:

MF1 766.3kN m:= ( momentul in faza1 - sectiune otel )

MF2 35371kN m:= ( momentul in faza2 - sectiune mixta otel-beton )

M

F1MF2

0.022=:=

0

0

0.1

0.2

0.3

0.4

0.5

:= 0

0.97

0.965

0.952

0.941

0.929

0.918

:= k0

1.9

2.1

2.2

2.3

2.4

2.5

:=

linterp 0 0, ,( ) 0.969=:=k linterp 0 k0, ,( ) 1.943=:=

hw.optim 5 3

wncs 2427 mm=:= Adopt hw 2500mm:=

-Aria sectiunii grinzii de otel:

Aok

hw

wncs 97771 mm2

=:=

buf

tbf

bbf

hw

tuf

tw

-Grosimile necesare componentelor grinzii de otel :

tw 0.40

Ao

hw 16 mm=:= Adopt tw 18mm:= ==> fyw 345

N

mm2:=

tbf 0.45Ao

bbf

58 mm=:= Adopt tbf 60mm:= ==> fybf 335 N

mm2

:=

tuf 0.15Ao

buf

24 mm=:= Adopt tuf 25mm:= ==> fyuf 345 N

mm2

:=

b0b1 b2

ev

ev

eD

D

s

e

btf

ttf

b0be1 be2

Ac

30002600

250

150

**Dispunerea preliminara a conectorilor

dconector 19mm:=

eD.max 9tuf235MPa

fyuf

186 mm=:=

eD.min 25mm:=

ev.min 50mm:=

Adopt ev 100mm:= ==> eD ev

dconector

2+ 110 mm=:=

emin 2.5 dconector 47.5 mm=:=

smax min 22tuf235MPa

fyuf

4 ht, 800mm,

454 mm=:=

smin 5 dconector 95 mm=:=


11/38

**Latimea activa de placa:

*In mijlocul deschiderii

b0 buf 2.eD 391 mm=:=

b1 2600mmb0

2 2404.5 mm=:=

b2 3000mmb0

2 2804.5 mm=:=

be1 min b1L

8,

2404.5 mm=:=

be2 min b2L

8,

2804.5 mm=:=

b'eff b0 be1+ be2+ 5600 mm=:=

Ac.eff 1320549mm2

:=

beff

Ac.eff

ht 5282 mm=:=Pentru o grosime constanta a placii de 250mm ==>

*Pe reazem:

1 0.55 0.025L

be1

+ 1.093=:= ==> 1 1:=

2 0.55 0.025L

be2

+ 1.015=:= ==> 2 1:=

b'eff.r b0 1b e1+ 2b e2+ 5600 mm=:=

Ac.eff.r 1320549mm2

:=

Pentru o grosime constanta a placii de 250mm ==> beff.r

Ac.eff.r

ht

5282 mm=:=

**Determinarea clasei sectiunii mixte otel beton in mijlocul deschiderii:

Intrucat talpa superioara a grinzii metalice conlucreaza cu placa de beton prin intermediul conectorilor si nu exista

pericolul aparitiei fenomenului de flambaj lateral pentru nici o situatie de incarcare a podului, admitem ca talpa este in CLASA1.

Talpa inferioara este intinsa in orice situatie de incarcare, deci ea se afla in CLASA1

Pe aceste considerente, clasa inimii va determina si clasa sectiunii

M0

1.00:= c

1.5:=

Fb 0.85fck

c

beff ht 26190.888 kN=:=

Fuf

fyuf

M0

buf tuf 5261.25 kN=:=

Fw

fyw

M0

hw tw 15525 kN=:=

Fbf

fybf

M0

bbf tbf 15276 kN=:=

Fb Fuf Fw+ Fbf+ 1===> Axa neutra plastica este situata in talpa superioara a grinzii metalice

la distanta z fata de fibra exterioara a talpii Intrucat toata inima este

intinsa sectiunea este in CLASA1

Fb Fuf+ Fw Fbf+ 1=


12/38

beff

t

50 z

Fc

Fuf2

Fw

Fbf

zFbf Fw+ Fuf+ Fb

2 buffyuf

M0

23.453 mm=:=

Fuf2fyuf

M0

buf z 4935.681 kN=:=

Fuf1

fyuf

M0

buf tuf z( ) 325.569 kN=:=

**Verificarea la SLUR moment incovoieror - in mijlocul deschiderii:

**Analiza plastica, MEd>MRd:

ME1.k 434kN m:=

ME2.k 332.3kN m:=

ME3.k 921.6 kN m:=

ME4.k 20957.3kN m:=

ME5.k 10456.6kN m:=

MTS.k

8925kN m:=

MUDL.k 9359.8kN m:=

MPietoni.k 1336.6kN m:=

MEd 1.35 ME1.k ME2.k+ ME5.k+( ) 1ME3.k+ 0.6 1.35 0.4 1+( ) ME4.k+1.35 0.75MTS.k 0.40MUDL.k+ 0.40MPietoni.k+( )+

... 54400.266 kN m=:=

zFb z 50mm+ht

2+ 198.453 mm=:=

zFuf2

z

211.726 mm=:=

zFuf1

tuf z

20.774 mm=:=

zFw tuf zhw

2+ 1251.547 mm=:=

zFbf tuf z hw+tbf

2+ 2531.547 mm=:=

MRd FbzFb Fuf2zFuf2+ Fuf1zFuf1+ FwzFw+ Fbf zFbf+ 63357.97 kN m=:=

MRd MEd> 1= ( se verifica )


13/38

buf

tbf

bbf

hw

tuf

tw

z'

y'

z

y

z'g

zg

**Analiza elastica, max


14/38

z'g.m.gp

1

nLld

beff htht

2

Aoe'o+

1

nLld

beff ht( ) Ao+1151.14 mm=:=

eo e'o z'g.m.gp 793.391 mm=:=

Am.gp

Ao

1

nLld

beff

ht

+ 187691.079 mm2

=:=

Iy.m.gp Iy.o Aoe o2

+ 1

nLld

beff

ht3

12 beff ht z'g.m.gp

ht

2

2

+

+ 2.59 10

11 mm

4=:=

zo1.gp hw tuf+ tbf+ 50mm+ ht+ z'g.m.gp 1733.86 mm=:=

zo2.gp z'g.m.gp ht 50mm 851.14 mm=:=

zb1.gp zo2.gp 50mm+ 901.14 mm=:=

zb2.gp z'g.m.gp 1151.14 mm=:=

-Sectiunea grinzii mixte --> pentru actiuni de scurta durata:

Y'eff

t

50

e'o

ANO

z'g

zg

Yz

'gms

d

zgms

d

ANM

eo

zo

1s

d

zo

2s

d

zb1s

d

zb2s

d

e'o z'g 50mm+ ht+ 1944.531 mm=:=

z'g.m.sd

1

n0

beff htht

2

Aoe'o+

1

n0

beff ht( ) Ao+727.52 mm=:=

eo e'o z'g.m.sd 1217.011 mm=:=

Am.sd Ao1

n0

beff ht+ 319653.171 mm2

=:=

Iy.m.sd Iy.o Aoeo2

+ 1

n0

beff

ht3

12 beff ht z'g.m.sd

ht

2

2

+

+ 3.413 10

11 mm

4=:=

zo1.sd hw tuf+ tbf+ 50mm+ ht+ z'g.m.sd 2157.48 mm=:=

zo2.sd z'g.m.sd ht 50mm 427.52 mm=:=

zb1.sd zo2.sd 50mm+ 477.52 mm=:=

zb2.sd z'g.m.sd 727.52 mm=:=

*Eforturi unitare pe etape de incarcare:

-Etapa 1:o1.E1

1.35ME1.k

Iy.o

zg 5.208 N

mm2

=:=

o2.E1

1.35ME1.k

Iy.o

z'g 9.107 N

mm2

=:=

-Etapa 2:

o1.E2

1.35ME2.k

Iy.o

zg 3.987 N

mm2

=:=

o2.E2

1.35ME2.k

Iy.o z'g 6.973

N

mm2=:=

-Etapa 3:

b1.E3

Ncs

beff ht

1

nLc

Ncs

Am.c

1 ME3.k

Iy.m.c

zb1.c+

2.134

N

mm2

=:=


15/38

b2.E3

Ncs

beff ht

1

nLc

Ncs

Am.c

1 ME3.k

Iy.m.c

zb2.c+

2.191

N

mm2

=:=

o1.E3

Ncs

Am.c

1 ME3.k

Iy.m.c

zo1.c+ 30.279 N

mm2

=:=

o2.E3

Ncs

Am.c

1 ME3.k

Iy.m.c

zo2.c

21.215 N

mm2

=:=

-Etapa 4:

b1.E41

nLld

0.6 1.35 0.4 1+( ) ME4.k

0.6Iy.m.gp 0.4 Iy.m.c+ 0.6zb1.gp 0.4 zb1.c+( ) 5.388

N

mm2

=:=

b2.E41

nLld

0.6 1.35 0.4 1+( ) ME4.k

0.6Iy.m.gp 0.4 Iy.m.c+ 0.6zb2.gp 0.4 zb2.c+( ) 6.896

N

mm2

=:=

o1.E4

0.6 1.35 0.4 1+( ) ME4.k

0.6Iy.m.gp 0.4 Iy.m.c+ 0.6zo1.gp 0.4 zo1.c+( ) 169.51N

mm2=:=

o2.E4

0.6 1.35 0.4 1+( ) ME4.k

0.6Iy.m.gp 0.4 Iy.m.c+ 0.6zo2.gp 0.4 zo2.c+( ) 82.071

N

mm2

=:=

-Etapa 5:

b1.E51

nLld

1.35 ME5.k

Iy.m.gp

zb1.gp 3.043 N

mm2

=:=

b2.E51

nLld

1.35 ME5.k

Iy.m.gp

zb2.gp 3.888 N

mm2

=:=

o1.E5

1.35 ME5.k

Iy.m.gp

zo1.gp 94.488N

mm2

=:=

o2.E5

1.35 ME5.k

Iy.m.gp

zo2.gp 46.384 N

mm2

=:=

-Grupa 1a:

b1.1a1

n0

1.35 0.75MTS.k 0.40MUDL.k+ 0.40MPietoni.k+( )

Iy.m.sd

zb1.sd 3.355 N

mm

2=:=

b2.1a1

n0

1.35 0.75MTS.k 0.40MUDL.k+ 0.40MPietoni.k+( )

Iy.m.sd

zb2.sd 5.112 N

mm2

=:=

o1.1a

1.35 0.75MTS.k 0.40MUDL.k+ 0.40MPietoni.k+( )Iy.m.sd

zo1.sd 93.632N

mm2

=:=

o2.1a

1.35 0.75MTS.k 0.40MUDL.k+ 0.40MPietoni.k+( )Iy.m.sd

zo2.sd 18.554 N

mm2

=:=

*Eforturi unitare in gruparea fundamentala:

b1 b1.E3 b1.E4+ b1.E5+ b1.1a+ 9.652 N

mm2

=:=

b2 b2.E3 b2.E4+ b2.E5+ b2.1a+ 13.705 N

mm2

=:=


16/38

o1 o1.E1 o1.E2+ o1.E3+ o1.E4+ o1.E5+ o1.1a+ 336.547 N

mm2

=:=

o2 o2.E1 o2.E2+ o2.E3+ o2.E4+ o2.E5+ o2.1a+ 184.303 N

mm2

=:=

50

b2

b1

o1

o2 b2

fck

c

< 1=

o1

fybf

M0

25mm).

Pentru stabilirea punctelor de variatie, mai intai, se determina care din SLUR si SLO este mai defavorabila pentru

structura.

c.var 90 N

mm2:=

tbf1 50mm:= fybf1 335 N

mm2

:= ks125mm

tbf1

0.2

0.871=:=

c1.red ks1 c.var 78.35 N

mm2

=:=

tbf2 40mm:= fybf2 345 N

mm2

:= ks225mm

tbf2

0.2

0.91=:=

c2.red ks2 c.var 81.925 Nmm

2=:=

Intrucat categoria de detaliu din mijlocul deschiderii, corespunzatoare sudurii rigidizarii inimii de talpa inferioara, este

mai defavorabila decat cea pentru variatia grosimii talpilor inferioare, pentru determinarea punctelor de variatie consider ca in

dreptul acestora detaliul este cel dintai.


17/38

cSLUR.Pl

MEd

MRd

0.859=:=

cSLUR.El

o1

fybf

1=:=

cSLO

Ff E2

c

Mf

0.795=:=

==> SLUR ( analiza elastica ) este cea mai defavorabila pentru structura

Presupunand ca factorul de siguranta cSLUR.Pl, al analizei plastice din sectiunea de la jumatatea

deschiderii, asigura verificarea in domeniul elastic si in sectiunile de variatie a grosimii talpii inferioare, momentul MEdin punctele de variatie se va stabili functie de MRd: MEd.i cSLUR.PlMRd=

*Stabilirea punctului de variatie 1 ( de la 60mm la 50mm ):

M0 1.00:= c 1.5:=

Fb 0.85fck

c

beff ht 26190.888 kN=:=

Fuf

fyuf

M0

buf tuf 5261.25 kN=:=

Fw

fyw

M0

hw tw 15525 kN=:=

Fbf.1

fybf1

M0

bbf tbf1 12730 kN=:=

Fb Fuf Fw+ Fbf.1+ 1= Axa neutra plastica este situata in talpa superioara a grinzii metalice ladistanta z fata de fibra exterioara a talpii

Intrucat toata inima este intinsa sectiunea este in CLASA1

==>

Fb

Fuf

+ Fw

Fbf.1

+ 1=

beff

t

50 z

Fc

Fuf2

Fw

Fbf

z1

Fbf.1 Fw+ Fuf+ Fb

2 buffyuf

M0

17.404 mm=:=

Fuf2.1

fyuf

M0

buf z1 3662.681 kN=:=

Fuf1.1

fyuf

M0

buf tuf z1( ) 1598.569 kN=:=

zFb.1 z1 50mm+ht

2+ 192.404 mm=:=

zFuf2.1

z1

28.702 mm=:=

zFuf1.1

tuf z1

23.798 mm=:=

zFw.1 tuf z1hw

2+ 1257.596 mm=:=

zFbf.1 tuf z1 hw+tbf1

2+ 2532.596 mm=:=

MRd.1 Fbz Fb.1 Fuf2zFuf2.1+ Fuf1zFuf1.1+ FwzFw.1+ Fbf.1zFbf.1+ 56847.544 kN m=:=

M'Ed.1 cSLUR.PlMRd.1 48810.3 kN m=:=


18/38

- Momente incovoietoare in punctul x=14.75m

ME1.k.1 156.3kN m:= ME2.k.1 307.3 kN m:= ME3.k.1 134.2 kN m:=

ME4.k.1 18036.7kN m:= ME5.k.1 8482.6kN m:=

MTS.k.1 7292.5kN m:= MUDL.k.1 7592.7kN m:= MPietoni.k.1 1085.9kN m:=

MEd.1 1.35 ME1.k.1 ME2.k.1+ ME5.k.1+( ) 1ME3.k.1+ 0.6 1.35 0.4 1+( ) ME4.k.1+1.35 0.75MTS.k.1 0.40MUDL.k.1+ 0.40MPietoni.k.1+( )+

... 45007.967 kN=:=

M'Ed.1 MEd.1> 1= ( se verifica ) ==> Primul punct de variatie estex=14.75m

*Stabilirea punctului de variatie 2 ( de la 50mm la 40mm ):

Fb 0.85fck

c

beff ht 26190.888 kN=:=

Fuf 5261.25 kN= Fw 15525 kN=

Fbf.2

fybf2

M0

bbf tbf2 10488 kN=:=

Fb

Fuf

Fw

+ Fbf.2

+ 1===> Axa neutra plastica este situata in talpa superioara a grinzii metalice la

distanta z fata de fibra exterioara a talpii

Intrucat toata inima este intinsa sectiunea este in CLASA1

Fb Fuf+ Fw Fbf.2+ 1=

beff

t

50 z

Fc

Fuf2

Fw

Fbf

z2

Fbf.2 Fw+ Fuf+ Fb

2 buffyuf

M0

12.077 mm=:=

Fuf2.2

fyuf

M0

buf z2 2541.681 kN=:=

Fuf1.2fyuf

M0

buf tuf z2( ) 2719.569 kN=:=

zFb.2 z2 50mm+ht

2+ 187.077 mm=:=

zFuf2.2

z2

26.039 mm=:=

zFuf1.2

tuf z2

26.461 mm=:=

z

Fw.2

t

uf

z

2

hw

2

+ 1262.923 mm=:=

zFbf.2 tuf z2 hw+tbf2

2+ 2532.923 mm=:=

MRd.2 Fbz Fb.2 Fuf2zFuf2.2+ Fuf1zFuf1.2+ FwzFw.2+ Fbf.2zFbf.2+ 51103.798 kN m=:=

M'Ed.2 cSLUR.PlMRd.2 43878.619 kN m=:=

- Momente incovoietoare in punctul x=11.5m

ME1.k.2 346.6kN m:= ME2.k.2 424.6kN m:= ME3.k.2 946.5 kN m:=

ME4.k.2 14028.6kN m:= ME5.k.2 7175.6kN m:=

MTS.k.2 6176kN m:= MUDL.k.2 6422.6kN m:= MPietoni.k.2 918.5kN m:=MEd.2 1.35 ME1.k.2 ME2.k.2+ ME5.k.2+( ) 1ME3.k.2+ 0.6 1.35 0.4 1+( ) ME4.k.2+

1.35 0.75MTS.k.2 0.4MUDL.k.2+ 0.4MPietoni.k.2+( )+... 38866.68 kN m=:=

M'Ed.2 MEd.2> 1= ( se verifica ) ==> Punctul de variatie 2estex=11.5m


19/38

buf

bf.1

bbf

w

uf

tw

z'

y'

z

y

z'g

.1

zg

.1

**Verificarea la SLUR moment incovoieror - in sectiunea x= 14.75m:

tbf1 50 mm=

*Caracteristici geometrice ale sectiunilor grinzilor principale:

-Sectiunea grinzii metalice:

Ao.1 hwtw bbf tbf1+ buf tuf+ 98250 mm2

=:=

z'g.1

buf tuftuf

2 hwtw tuf

hw

2+

+ bbf tbf1 tuf hw+

tbf1

2+

+

Ao.1

:=

z'g.1 1572.169 mm= zg.1 hw tuf+ tbf1+ z'g.1 1002.831 mm=:=

Iy.o.1

twhw3

12twhw

hw

2z'g.1

2

+bbf tbf1

3

12+

bbf tbf1 zg.1 tbf1( )2

buf tuf3

12+ buf tuf z'g.1 tuf( )2

++

... 9.912 1010

mm4

=:=

-Sectiunea grinzii mixte --> pentru actiuni din contractia betonului:

Y'eff

t

50

e'o

.1

ANO

z'g

.1

zg

.1

Yz

'gmc

.1

zgmc

.1

ANM

eo

.1

zo

1c

.1

zo

2c

.1

zb1c

.1

zb2c

.1e'o.1 z'g.1 50mm+ ht+ 1872.169 mm=:=

z'g.m.c.1

1

nLc

beff htht

2

Ao.1e'o.1+

1

nLc

beff ht( ) Ao.1+1059.179 mm=:=

eo.1 e'o.1 z'g.m.c.1 812.99 mm=:=

Am.c.1 Ao.11

nLc

beff ht+ 183754.232 mm2

=:=

Iy.m.c.1 Iy.o.1 Ao.1eo.12

+ 1

nLc

beff

ht3

12 beff ht z'g.m.c.1

ht

2

2

+

+ 2.391 10

11 mm

4=:=

zo1.c.1 hw tuf+ tbf1+ 50mm+ ht+ z'g.m.c.1 1815.821 mm=:=

zo2.c.1 z'g.m.c.1 ht 50mm 759.179 mm=:=

zb1.c.1 zo2.c.1 50mm+ 809.179 mm=:=

zb2.c.1 z'g.m.c.1 1059.179 mm=:=

-Sectiunea grinzii mixte --> pentru actiuni din greutati permanente:

Y'eff

t

50

e'o

.1

ANO

z'g

.1

zg

.1

Yz

'gmgp

.1

zgmgp.

1

ANM

eo

.1

zo

1gp.1

zo

2gp

.1

zb1gp

.1

zb2gp

.1

e'o.1 z'g.1 50mm+ ht+ 1872.169 mm=:=

z'g.m.gp.1

1

nLldbeff ht

ht

2

Ao.1e'o.1+

1

nLld

beff ht( ) Ao.1+1078.181 mm=:=


20/38

eo.1 e'o.1 z'g.m.gp.1 793.988 mm=:=

Am.gp.1 Ao.11

nLld

beff ht+ 180091.079 mm2

=:=

Iy.m.gp.1 Iy.o.1 Ao.1eo.12

+ 1

nLld

beff

ht3

12 beff ht z'g.m.gp.1

ht

2

2

+

+ 2.358 10

11 mm

4=:=

zo1.gp.1 hw tuf+ tbf1+ 50mm+ ht+ z'g.m.gp.1 1796.819 mm=:=

zo2.gp.1 z'g.m.gp.1 ht 50mm 778.181 mm=:=

zb1.gp.1 zo2.gp.1 50mm+ 828.181 mm=:=

zb2.gp.1 z'g.m.gp.1 1078.181 mm=:=


Y'eff

t

50

e'o

.1

ANO

z'g

.1

zg

.1

Yz

'gms

d.1

zgms

d.1

ANM

eo

.1

zo

1s

d.1

zo

2sd

.1

zb1sd

.1

zb2s

d.1

e'o.1 z'g.1 50mm+ ht+ 1872.169 mm=:=

z'g.m.sd.1

1

n0

beff htht

2

Ao.1e'o.1+

1

n0

beff ht( ) Ao.1+675.097 mm=:=

eo.1 e'o.1 z'g.m.sd.1 1197.073 mm=:=

Am.sd.1 Ao.11

n0

beff ht+ 312053.171 mm2

=:=

Iy.m.sd.1 Iy.o.1 Ao.1eo.12

+

1

n0beff

ht3

12 beff ht z'g.m.sd.1

ht

2

2

+

+ 3.057 1011

mm4

=:=

zo1.sd.1 hw tuf+ tbf1+ 50mm+ ht+ z'g.m.sd.1 2199.903 mm=:=

zo2.sd.1 z'g.m.sd.1 ht 50mm 375.097 mm=:=

zb1.sd.1 zo2.sd.1 50mm+ 425.097 mm=:=

zb2.sd.1 z'g.m.sd.1 675.097 mm=:=


-Etapa 1:

o1.E1.1

1.35ME1.k.1

Iy.o.1

zg.1 2.135 N

mm2

=:=

o2.E1.1

1.35ME1.k.1

Iy.o.1

z'g.1 3.347 N

mm2

=:=

-Etapa 2:

o1.E2.1

1.35ME2.k.1

Iy.o.1

zg.1 4.197 N

mm2

=:=

o2.E2.1

1.35ME2.k.1

Iy.o.1 z'g.1 6.58

N

mm2=:=

-Etapa 3:

b1.E3.1

Ncs

beff ht

1

nLc

Ncs

Am.c.1

1 ME3.k.1

Iy.m.c.1

zb1.c.1+

1.899

N

mm2

=:=


21/38

b2.E3.1

Ncs

beff ht

1

nLc

Ncs

Am.c.1

1 ME3.k.1

Iy.m.c.1

zb2.c.1+

1.908

N

mm2

=:=

o1.E3.1

Ncs

Am.c.1

1 ME3.k.1

Iy.m.c.1

zo1.c.1+ 26.148 N

mm2

=:=

o2.E3.1

Ncs

Am.c.1

1 ME3.k.1

Iy.m.c.1

z

o2.c.1

24.702 N

mm2

=:=

-Etapa 4:

b1.E4.11

nLld

0.6 1.35 0.4 1+( ) ME4.k.1

0.6Iy.m.gp.1 0.4 Iy.m.c.1+ 0.6zb1.gp.1 0.4 zb1.c.1+( ) 4.68

N

mm2

=:=

b2.E4.11

nLld

0.6 1.35 0.4 1+( ) ME4.k.1


N

mm2

=:=

o1.E4.1

0.6 1.35 0.4 1+( ) ME4.k.1

0.6Iy.m.gp.1 0.4 Iy.m.c.1+ 0.6zo1.gp.1 0.4 zo1.c.1+( ) 166.053

N

mm

2=:=

o2.E4.1

0.6 1.35 0.4 1+( ) ME4.k.1


N

mm2

=:=

-Etapa 5:

b1.E5.11

nLld

1.35 ME5.k.1

Iy.m.gp.1

zb1.gp.1 2.492 N

mm2

=:=

b2.E5.11

nLld

1.35 ME5.k.1

Iy.m.gp.1

zb2.gp.1 3.245 N

mm2

=:=

o1.E5.1

1.35 ME5.k.1

Iy.m.gp.1

zo1.gp.1 87.246N

mm2

=:=

o2.E5.1

1.35 ME5.k.1

Iy.m.gp.1

zo2.gp.1 37.785 N

mm2

=:=

-Grupa 1a:

b1.1a.11

n0

1.35 0.75MTS.k.1 0.4MUDL.k.1+ 0.4MPietoni.k.1+( )

Iy.m.sd.1

zb1.sd.1 2.717 N

mm2

=:=

b2.1a.11

n0

0.75MTS.k.1 0.4MUDL.k.1+ 0.4MPietoni.k.1+Iy.m.sd.1

zb2.sd.1 3.196 N

mm2

=:=

o1.1a.1

1.35 0.75MTS.k.1 0.4MUDL.k.1+ 0.4MPietoni.k.1+( )Iy.m.sd.1

zo1.sd.1 86.853N

mm2

=:=

o2.1a.1

1.35 0.75MTS.k.1 0.4MUDL.k.1+ 0.4MPietoni.k.1+( )Iy.m.sd.1

zo2.sd.1 14.809 N

mm2

=:=


b1.1 b1.E3.1 b1.E4.1+ b1.E5.1+ b1.1a.1+ 7.99 N

mm2

=:=

b2.1 b2.E3.1 b2.E4.1+ b2.E5.1+ b2.1a.1+ 10.639 N

mm2

=:=


22/38

o1.1 o1.E1.1 o1.E2.1+ o1.E3.1+ o1.E4.1+ o1.E5.1+ o1.1a.1+ 311.942 N

mm2

=:=

o2.1 o2.E1.1 o2.E2.1+ o2.E3.1+ o2.E4.1+ o2.E5.1+ o2.1a.1+ 144.977 N

mm2

=:=

50

b2

b1

o1

o2

b2.1

fck

c

< 1= ( se verifica )

o1.1

fybf1

M0


**Verificarea la SLUR moment incovoieror - in sectiunea x= 11.5m:buf

tbf2

bbf

hw

tuf

tw

z'

y'

z

y

z'g

.2

zg

.2

tbf2

40 mm= beff2

5282mm:=

*Caracteristici geometrice ale sectiunilor grinzilor principale:

-Sectiunea grinzii metalice:

Ao.2 hwtw bbf tbf2+ buf tuf+ 90650 mm2

=:=

z'g.2

buf tuftuf

2 hwtw tuf

hw

2+

+ bbf tbf2 tuf hw+

tbf2

2+

+

Ao.2

:=

z'g.2 1488.512 mm= zg.2 hw tuf+ tbf1+ z'g.2 1086.488 mm=:=

Iy.o.2

twhw3

12twhw

hw

2z'g.2

2

+bbf tbf2

3

12+

bbf tbf2 zg.2 tbf2( )2

buf tuf

3

12+ buf tuf z'g.2 tuf( )

2++

... 9.196 1010

mm4

=:=

-Sectiunea grinzii mixte --> pentru actiuni din contractia betonului:

Y'eff2

t

50

e'o

.2

ANO

z'g

.2

zg

.2

Yz'g

mc

.2

zgmc

.2

ANM

eo

.2

zo

1c

.2

zo2c

.2

zb1c

.2

zb2c

.2

nLc 15.444=

e'o.2 z'g.2 50mm+ ht+ 1788.512 mm=:=

z'g.m.c.2

1

nLc

beff2htht

2

Ao.2e'o.2+

1

nLc

beff2ht( ) Ao.2+981.069 mm=:=

eo.2 e'o.2 z'g.m.c.2 807.444 mm=:=

Am.c.2 Ao.21

nLc

beff2 ht+ 176151.06 mm2

=:=

Iy.m.c.2 Iy.o.2 Ao.2eo.22+ 1

nLc

beff2

ht

3

12 beff2ht z'g.m.c.2

ht

2

2

+

+ 2.142 1011 mm4=:=

zo1.c.2 hw tuf+ tbf2+ 50mm+ ht+ z'g.m.c.2 1883.931 mm=:=

zo2.c.2 z'g.m.c.2 ht 50mm 681.069 mm=:=


23/38

zb1.c.2 zo2.c.2 50mm+ 731.069 mm=:=

zb2.c.2 z'g.m.c.2 981.069 mm=:=

-Sectiunea grinzii mixte --> pentru actiuni din greutati permanente:

Y'eff2

t

50

e'o

.2

ANO

z'g

.2

zg

.2

Yz

'gmg

p.2

zgmgp

.2

ANM

eo

.2

zo

1gp

.2

zo

2gp.

2

zb1gp.

2

zb2gp

.2

nLld 16.136=

e'o.2 z'g.2 50mm+ ht+ 1788.512 mm=:=

z'g.m.gp.2

1

nLld

beff2htht

2

Ao.2e'o.2+

1

nLld

beff2ht( ) Ao.2+999.248 mm=:=

eo.2 e'o.2 z'g.m.gp.2 789.264 mm=:=

Am.gp.2 Ao.21

nLld

beff2 ht+ 172488.043 mm2

=:=

Iy.m.gp.2 Iy.o.2 Ao.2eo.22

+ 1

nLld

beff2

ht3

12 beff2ht z'g.m.gp.2

ht

2

2

+

+ 2.114 10

11 mm

4=:=

zo1.gp.2 hw tuf+ tbf2+ 50mm+ ht+ z'g.m.gp.2 1865.752 mm=:=

zo2.gp.2 z'g.m.gp.2 ht 50mm 699.248 mm=:=

z

b1.gp.2

z

o2.gp.2

50mm+ 749.248 mm=:=

zb2.gp.2 z'g.m.gp.2 999.248 mm=:=


Y'eff2

t

50

e'o

.2

ANO

z'g

.2

zg

.2

Yz

'gms

d.2

zgms

d.2

ANM

eo

.2

zo

1s

d.2

zo

2s

d.2

zb1s

d.2

zb2s

d.2

e'o.2 z'g.2 50mm+ ht+ 1788.512 mm=:=

z'g.m.sd.2

1

n0

beff2h tht

2

Ao.2e'o.2+

1n0

beff2ht( ) Ao.2+

620.319 mm=:=

eo.2 e'o.2 z'g.m.sd.2 1168.194 mm=:=

Am.sd.2 Ao.21

n0

beff2 ht+ 304445.238 mm2

=:=

Iy.m.sd.2 Iy.o.2 Ao.2eo.22

+ 1

n0

beff2

ht3

12 beff2ht z'g.m.sd.2

ht

2

2

+

+ 2.692 10

11 mm

4=:=

zo1.sd.2 hw tuf+ tbf2+ 50mm+ ht+ z'g.m.sd.2 2244.681 mm=:=

zo2.sd.2 z'g.m.sd.2 ht 50mm 320.319 mm=:=

zb1.sd.2 zo2.sd.2 50mm+ 370.319 mm=:=

zb2.sd.2 z'g.m.sd.2 620.319 mm=:=


24/38


-Etapa 1:

o1.E1.2

1.35ME1.k.2

Iy.o.2

zg.2 5.528 N

mm2

=:=

o2.E1.2

1.35ME1.k.2

I

y.o.2

z'g.2 7.574 N

mm

2=:=

-Etapa 2:

o1.E2.2

1.35ME2.k.2

Iy.o.2

zg.2 6.773 N

mm2

=:=

o2.E2.2

1.35ME2.k.2

Iy.o.2

z'g.2 9.278 N

mm2

=:=

-Etapa 3:

b1.E3.2

Ncs

beff ht

1

nLc

Ncs

Am.c.2

1 ME3.k.2

Iy.m.c.2

z

b1.c.2

+

1.59 N

mm2

=:=

b2.E3.2

Ncs

beff ht

1

nLc

Ncs

Am.c.2

1 ME3.k.2

Iy.m.c.2

zb2.c.2+

1.519

N

mm2

=:=

o1.E3.2

Ncs

Am.c.2

1 ME3.k.2

Iy.m.c.2

zo1.c.2+ 17.887 N

mm2

=:=

o2.E3.2

Ncs

Am.c.2

1 ME3.k.2

Iy.m.c.2

zo2.c.2 29.223 N

mm2

=:=

-Etapa 4:

b1.E4.21

nLld

0.6 1.35 0.4 1+( ) ME4.k.2


N

mm2

=:=

b2.E4.21

nLld

0.6 1.35 0.4 1+( ) ME4.k.2


N

mm2

=:=

o1.E4.2

0.6 1.35 0.4 1+( ) ME4.k.2


N

mm2

=:=

o2.E4.20.6 1.35 0.4 1+( ) ME4.k.2

0.6Iy.m.gp.2 0.4 Iy.m.c.2+ 0.6zo2.gp.2 0.4 zo2.c.2+( ) 55.274 N

mm2

=:=

-Etapa 5:

b1.E5.21

nLld

1.35 ME5.k.2

Iy.m.gp.2

zb1.gp.2 2.128 N

mm2

=:=

b2.E5.21

nLld

1.35 ME5.k.2

Iy.m.gp.2

zb2.gp.2 2.838 N

mm2

=:=

o1.E5.2

1.35 M

E5.k.2

Iy.m.gp.2zo1.gp.2 85.494 N

mm2=:=

o2.E5.2

1.35 ME5.k.2

Iy.m.gp.2

zo2.gp.2 32.041 N

mm2

=:=


25/38

-Grupa 1a:

b1.1a.21

n0

1.35 0.75 MTS.k.2 0.40MUDL.k.2+ 0.40MPietoni.k.2+( )

Iy.m.sd.2

zb1.sd.2 2.055 N

mm2

=:=

b2.1a.21

n0

1.35 0.75 MTS.k.2 0.40MUDL.k.2+ 0.40MPietoni.k.2+( )

Iy.m.sd.2

zb2.sd.2 3.442 N

mm2

=:=

o1.1a.2

1.35 0.75 MTS.k.2

0.40MUDL.k.2

+ 0.40MPietoni.k.2

+

( )

Iy.m.sd.2

zo1.sd.2 76.923 N

mm2

=:=

o2.1a.2

1.35 0.75 MTS.k.2 0.40MUDL.k.2+ 0.40MPietoni.k.2+( )Iy.m.sd.2

zo2.sd.2 10.977 N

mm2

=:=


b1.2 b1.E3.2 b1.E4.2+ b1.E5.2+ b1.1a.2+ 6.265 N

mm2

=:=

b2.2

b2.E3.2

b2.E4.2

+ b2.E5.2

+ b2.1a.2

+ 9.672 N

mm2=:=

o1.2 o1.E1.2 o1.E2.2+ o1.E3.2+ o1.E4.2+ o1.E5.2+ o1.1a.2+ 306.444N

mm2

=:=

o2.2 o2.E1.2 o2.E2.2+ o2.E3.2+ o2.E4.2+ o2.E5.2+ o2.1a.2+ 144.368 N

mm2

=:=

50

b2

b1

o1

o2

b2.2

fck

c


o1.2

fybf

M0


**Verificarea la SLO - in sectiunile de variatie a grosimii talpii inferioare:

*Sectiunea x=14.75m:

MLMO3.1 4322.1kN m:=

p.1

MLMO3.1

Iy.m.sd.1

zo1.sd.1 31.101N

mm2

=:=

E2.1 p.1 47.515N

mm2

=:=

Ff E2.1 47.515N

mm2

=c1.red

Mf

58.037N

mm2

= Ff E2.1c1.red

Mf

1= ( se verifica )

*Sectiunea x=11.5m:

MLMO3.2 3469.4kN m:=

p.2

MLMO3.2

Iy.m.sd.2

zo1.sd.2 28.926N

mm2

=:=

E2.2 p.2 44.192N

mm2

=:=

Ff E2.2 44.192N

mm2

=c2.red

Mf

60.685N

mm2

= Ff E2.1c1.red

Mf

1= ( se verifica )


26/38


27/38

w w0.83

1=

Axa neutra plastica este situata in placa de betonla distanta z1 fata de fibra exterioara a placii==>

z1

Fbf Fuf+

0.85fck

c

beff

196.034 mm=:=

z1Fc

z1

298.017 mm=:=

z1Fuf ht z1 50mm+tuf

2+ 116.466 mm=:=

z1Fbf ht z1 50mm+ tuf+ hw+tbf

2+ 2658.966 mm=:=

Mf.Rd Fbz1Fc Fuf z1Fuf+ Fbf z1Fbf+ 43798.271 kN m=:=

c a 0.251.6 bbf tbf

2 fyw

twhw2

fyw

+

1444.56 mm=:=

Vbf.Rd

bbf tbf2

fyw

c M1 1

MEd

Mf.Rd

2

MEd Mf.Rd


28/38

**Verificarea la SLUR forta taietoare - pe reazem:

VE1.k 105.9kN:= VE2.k 239.3kN:= VE3.k 329.5 kN:=

VE4.k 1222kN:= VE5.k 801.3kN:=

VTS.k 691.9kN:= VUDL.k 717kN:= VPietoni.k 102.5kN:=

VEd 1.35 VE1.k VE2.k+ VE5.k+( ) 1VE3.k+ 0.6 1.35 0.4 1+( ) VE4.k+1.35 0.75V

TS.k 0.4V

UDL.k+ 0.4V

Pietoni.k+

( )+

... 3839.974 kN=:=

*Verificarea la forfecare simpla:

235MPa

fyw

0.825=:=

1.2 f yw 460MPaif

1 otherwise

:=

1.2=

Av h w tw 54000 mm2

=:=

Vpl.Rd

Avfyw

3

M0

10756.036 kN=:=

Vpl.Rd VEd> 1= ( se verifica )

*Verificarea la voalare din forfecare:

a 6100mm:=

Isl 0mm4

:= ( nu sunt prevazite rigidizari longitudinale )

ksl max 9hw

a

2 4Isl

tw3

hw

2.1

tw

1mm

3Isl

1mm4

hw

1mm

,

0=:=

k 5.34 4hw

a

2

+ ksl+

a

hw

1if

4 5.34hw

a

2

+ ksl+

otherwise

:=

k 6.012=

hw

tw

138.889= 31

k 52.277=

hw

tw

31

k> 1= ( se verifica ) ==> Este necesara verificarea la voalare din forfecare

-Contributia inimii Vbw.Rd:

E 190000tw

hw

2

N

mm2

9.85 N

mm2

=:=

cr kE 59.214 N

mm2

=:=


29/38

w 0.76fyw

cr

1.834=:=

w w0.83

1=

Axa neutra plastica este situata in placa de beton

la distanta z1 fata de fibra exter ioara a placii==>

z1.r

Fbf.2 Fuf+

0.85fck

c

beff.r

150.331 mm=:=

z1Fc.r

z1.r

275.166 mm=:=

z1Fuf.r ht z1.r 50mm+tuf

2+ 162.169 mm=:=

z1Fbf.r ht z1.r 50mm+ tuf+ hw+tbf2

2+ 2694.669 mm=:=

Mf.Rd.r Fb.rz1Fc.r Fuf z1Fuf.r+ Fbf.2z1Fbf.r+ 31083.55 kN m=:=

c a 0.25

1.6 bbf tbf22

fyw

twhw2

fyw+

1630.495 mm=:=

Vbf.Rd

bbf tbf22

fyw

c M1 1

MEd.r

1Ncs

buf tuf fyuf bbf tbf2 fybf+

M0

Mf.Rd.r

2

MEd.r Mf.Rd


30/38

*Valoarea de calcul a rezistentei la forfecare:

VRd min Vpl.Rd Vb.Rd,( ) 4628.613 kN=:=

VEd

VRd

0.83=

VEd

VRd

1< 1= ( se verifica )

**Calculul elastic al conectorilor ( cf etapelor de incarcare ):

250

50

35

>40

35

dh

dc

hc

35

hsc

*Dimensiunile conectorilor :

d 19mm:=

hmin 35 40+( )mm 75 mm=:=

hmax 50 250+ 35 20( )mm 245 mm=:=

Adopt hhmin hmax+

2160 mm=:=

d'c

1.5d 28.5 mm=:= Adopt dc

30mm:=

h'c 0.4d 7.6 mm=:= Adopt hc 10mm:=

hsc h hc+ 170 mm=:=

*Resistenta de calcul a unui conector:

fu 500 N

mm2

:=

v 1.25:=

0.2hsc

d1+

3

hsc

d 4if

1hsc

d4>if

:=

1=

PRd min

0.8fu d

2

4

v

0.29 d2

fckEcm

v

,

90.729 kN=:=

*Calculul numarului de conectori pe zona "a1: 0m-8.20m" :

VE3.k 329.5 kN:= VE4.k 1222kN:= VE5.k 801.3kN:=

VTS.k 691.9kN:= VUDL.k 717kN:= VPietoni.k 102.5kN:=

-Etapa 3 + Etapa 4 + Etapa 5:

VEd.a1.gp 1.35 VE3.k VE4.k+ VE5.k+( ):=

Y'

Z'

eff.a1

t

50

Z

e'o

ANO

z'g

.2

zg

.2

Yz'g

mgp

.a1

zgmgp

.a1

ANM

eo

VEd.a1.gp 2286.63 kN=

nLld 16.136=

a1 8200mm:=

beff.a1 beff.r 5282 mm=:=

e'o z'g.2 50mm+ ht+ 1788.512 mm=:=

z'g.m.gp.a1

1

nLld

beff.a1htht

2

Ao.2e'o+

1

nLld

beff.a1ht( ) Ao.2+999.233 mm=:=


31/38

eo e'o z'g.m.gp.a1 789.279 mm=:=

Iy.m.gp.a1 Iy.o.2 Ao.2eo2

+ 1

nLld

beff.a1

ht3

12 beff.a1h t z'g.m.gp.a1

ht

2

2

+

+ 2.114 10

11 mm

4=:=

Sy.b.gp.a1

beff.a1

nLld

ht z'g.m.gp.a1

ht

2

7.155 10

7 mm

3=:=

qa1.gp

VEd.a1.gpSy.b.gp.a1

Iy.m.gp.a1

773.888kN

m=:=

Qa1.gp qa1.gpa1 6345.883 kN=:=

na1.gp

Qa1.gp

PRd

69.943=:=

-Grupa 1a:

VEd.a1.sd 1.35 0.75VTS.k 0.4VUDL.k+ 0.4VPietoni.k+( ):=

Y'

Z'

beff.a1

t

50

Z

e'o

ANO

z'g

.2

zg

.2

Yz'g

msd

.a1

zgmsd

.a1

ANM

eo

VEd.a1.sd 1143.079 kN=

n0 6.176=

e'o z'g.2 50mm+ ht+ 1788.512 mm=:=

z'g.m.sd.a1

1

n0

beff.a1htht

2

Ao.2e'o+

1

n0

beff.a1

ht

( ) A

o.2+

620.306 mm=:=

eo e'o z'g.m.sd.a1 1168.206 mm=:=

Iy.m.sd.a1 Iy.o.2 Ao.2eo2

+ 1

n0

beff.a1

ht3

12 beff.a1h t z'g.m.sd.a1

ht

2

2

+

+ 2.692 10

11 mm

4=:=

Sy.b.sd.a1

beff.a1

n0

ht z'g.m.sd.a1

ht

2

1.059 10

8 mm

3=:=

qa1.sd

VEd.a1.sdSy.b.sd.a1

Iy.m.sd.a1449.608

kN

m=:=

Qa1.sd qa1.sda1 3686.783 kN=:=

na1.sd

Qa1.sd

PRd

40.635=:=

==> Numarul de conectori necesar pentru zona "a1": n'a1 na1.gp na1.sd+ 110.578=:=

*Calculul numarului de conectori pe zona "a2: 8.2m-17.15m" :

VE3.k 329.5 kN:= VE4.k 1222kN:= VE5.k 549.5kN:=

VTS.k

581.9kN:= VUDL.k

509.4kN:= VPietoni.k

72.9kN:=


VEd.a2.gp 1.35 VE3.k VE4.k+ VE5.k+( ):=VEd.a2.gp 1946.7 kN=


32/38

Y'

Z'

eff.a2

t

50

Z

e'o

ANO

z'g

.2

zg

.2

Yz'g

mgp

.a2

zgm

gp

.a2

ANM

eo

nLld 16.136=

a2 8950mm:=

beff.a2 beff:=

e'o z'g.2 50mm+ ht+ 1788.512 mm=:=

z'g.m.gp.a2

1

n

Lld

beff.a2htht

2

Ao.2e'o+

1

nLld

beff.a2ht( ) Ao.2+999.233 mm=:=

eo e'o z'g.m.gp.a2 789.279 mm=:=

Iy.m.gp.a2 Iy.o.2 Ao.2eo2

+ 1

nLld

beff.a2

ht3

12 beff.a2h t z'g.m.gp.a2

ht

2

2

+

+ 2.114 10

11 mm

4=:=

Sy.b.gp.a2

beff.a2

nLld

ht z'g.m.gp.a2

ht

2

7.155 10

7 mm

3=:=

qa2.gp

VEd.a2.gpSy.b.gp.a2

Iy.m.gp.a2

658.842 kN

m=:=

Qa2.gp qa2.gpa2 5896.637 kN=:=

na2.gp

Qa2.gp

PRd

64.992=:=

-Grupa 1a:

VEd.a2.sd 1.35 0.75VTS.k 0.40VUDL.k+ 0.40VPietoni.k+( ):=

Y'

Z'

beff.a2

t

50

Z

e'o

ANO

z'g

.2

zg

.2

Yz'g

ms

d.a

2

zgms

d.a

2

ANM

eo

VEd.a2.sd 903.616 kN=

n0 6.176=

e'o z'g.2 50mm+ ht+ 1788.512 mm=:=

z'g.m.sd.a2

1

n0

beff.a2htht

2

Ao.2e'o+

1

n0

beff.a2ht( ) Ao.2+620.306 mm=:=

eo

e'o

z'g.m.sd.a2

1168.206 mm=:=

Iy.m.sd.a2 Iy.o.2 Ao.2eo2

+ 1

n0

beff.a2

ht3

12 beff.a2h t z'g.m.sd.a2

ht

2

2

+

+ 2.692 10

11 mm

4=:=

Sy.b.sd.a2

beff.a2

n0

ht z'g.m.sd.a2

ht

2

1.059 10

8 mm

3=:=

qa2.sd

VEd.a2.sdSy.b.sd.a2

Iy.m.sd.a2

355.42 kN

m=:=

Qa2.sd qa2.sda2 3181.005 kN=:=

na2.sd

Qa2.sd

PRd

35.06=:=



33/38

*Calculul numarului de conectori pe zona "a3: 17.15m-26.10m" :

VE3.k 0kN:= VE4.k 0kN:= VE5.k 274.8kN:=

VTS.k 449.9kN:= VUDL.k 320.6kN:= VPietoni.k 47.8kN:=


VEd.a3.gp 1.35 VE3.k VE4.k+ VE5.k+( ):=

VEd.a3.gp 370.98 kN=a3 8950mm:=

beff.a3 beff 5282 mm=:=

Iy.m.gp.a3 Iy.m.gp 2.59 1011

mm4

=:=

Sy.b.gp.a3

beff.a3

n0

ht z'g.m.gp

ht

2

2.194 10

8 mm

3=:=

qa3.gp

VEd.a3.gpSy.b.gp.a3

Iy.m.gp.a3

314.203kN

m=:=

Qa3.gp qa3.gpa3 2812.113 kN=:=

na3.gp

Qa3.gp

PRd

30.995=:=

-Grupa 1a:

VEd.a3.sd 1.35 VTS.k VUDL.k+ VPietoni.k+( ):=VEd.a3.sd 1104.705 kN=

Iy.m.sd.a3 Iy.m.sd 3.413 1011

mm4

=:=

Sy.b.sd.a3

beff.a3

n0

ht z'g.m.sd

ht

2

1.288 10

8 mm

3=:=

qa3.sd

VEd.a3.sdSy.b.sd.a3

Iy.m.sd.a3

416.946kN

m=:=

Qa3.sd qa3.sda3 3731.666 kN=:=

na3.sd

Qa3.sd

PRd

41.13=:=


**Dispunerea definitiva a conectorilor

*Dispunerea conectorilor pe zona "a1" :

Propun o dispunere transversala pe 3 randuri ==> numarul de conector i pe aceasta zona este multiplu de 3

n'a1 110.578= ==> na1 111:=

ea1

buf 2.eD

2195.5 mm=:= ea1 emin> 1= ( se verifica )

s'a1

a1

na1

3

222 mm=:= ==> sa1 220mm:=

smin sa1< smax< 1= ( se verifica )


34/38



n'a2 100.052= ==> na2 102:=

ea2

buf 2.eD

2195.5 mm=:= ea2 emin> 1= ( se verifica )

s'a2

a2

na2

3

263 mm=:= ==> sa2 250mm:=




n'a3 72.124= ==> na3 72:=

ea3 buf 2.eD 391 mm=:= ea3 emin> 1= ( se verifica )

s'a3

a3

na3

2

249 mm=:= ==> sa3 250mm:=


**Calculul imbinarii de montaj (sectiunea x= 13.55m)

*Imbinarea talpii superioare:

Imbinarea talpii superioare se face prin sudura in "x"

*Imbinarea talpii inferioare:

Imbinarea talpii inferiaore se face cu SIRP M24 clasa 10.9 . Categoria imbinarii este C ( lunecare impiedicata la starea

limita ultima ). Clasa suprafetelor de frecare este B ( suprafete sablate si metalizate ).

fub 1000 N

mm2

:= d 24mm:= d0 26mm:= As 353mm2

:=

0.4:=

355 355

760

t

t 60

18-Dimensiunile ecliselor:

t'

bbf tbf

bbf 2 355 mm+ 31.02 mm=:=

==> t 32mm:=

-Dispunerea suruburilor:

e1min 1.2 d0 31.2 mm=:=

e1max 4 t 40mm+ 168 mm=:=

Adopt e1 35mm:=

e2min 1.2 d0 31.2 mm=:=

e2max 4 t 40mm+ 168 mm=:=

Adopt e2 35mm:=


35/38

p1min 2.2 d0 57.2 mm=:=

p1max min 14t 200mm,( ) 200 mm=:=

Adopt p1 65mm:=

p2min 2.4 d0 62.4 mm=:=

p2max min 14t 200mm,( ) 200 mm=:=

Propun dispunearea acate5 randuri de suruburi de o parte si de alta a inimii==> p2

355mm 2 e2

471.25 mm=:=

p2min p2< p2max< 1= ( se verifica )

-Forta de pretensionare de calcul:

Fp.C 0.7 As fub 247.1 kN=:=

-Rezistenta de calcul la lunecarea a unui surub:

n 2:=

ks 1:=

M3 1.25:=

Fs.Rd

ksn

M3

Fp.C 158.144 kN=:=

-Forta capabila la presiune pe gaura a unui surub:

fu 470N

mm2

:=

k1 min 2.8

e2

d0 1.7 1.4

p2

d0 1.7, 2.5,

2.069=:=

d mine1

3 d0

p1

3 d0

1

4,

0.449=:=

ab min d

fub

fu

, 1,

0.449=:=

M2 1.25:=

Fb.Rd

k1ab fu d tbf

M2

502.728 kN=:=

-Numarul minim de suruburi necesar pentru imbinarea talpii :

ME2.k.i 1079.5 kN m:= ME3.k.i 921.6 kN m:=

ME4.k.i 20957.3kN m:= ME5.k.i 9227kN m:=

MTS.k.i 7924.7kN m:= MUDL.k.i 8260.8kN m:= MPietoni.k.i 1180.9kN m:=

o1.i

1.35 ME2.k.i( )Iy.o

zgNcs

Am.c

1 ME3.k.i

Iy.m.c

zo1.c+

+

0.6 1.35 0.4 1+( ) ME4.k.i0.6Iy.m.gp 0.4 Iy.m.c+

0.6zo1.gp 0.4 zo1.c+( )1.35 ME5.k.i

Iy.m.gp

zo1.gp++

...

1.35 0.75 MTS.k.i 0.4 MUDL.k.i+ 0.4 MPietoni.k.i+( )Iy.m.sd

zo1.sd+

...

292.602N

mm2

=:=


36/38

n's.bf.05

o1.ibbf tbf

min Fs.Rd Fb.Rd,( ) 84.37=:= ==> ns.bf.05 90:=

==> ns.bf 2 ns.bf.05 180=:=

-Forta capabila a talpii inferioare in aria neta:

Abf.net tbf bbf 10 tbf d0 30000 mm2

=:=

Nnet.Rd

Abf.netfybf

M0

10050 kN=:=

NEd o1.ibbf tbf 13342.642 kN=:=

Nnet.Rd NEd> 0= ( nu se verifica )

*Imbinarea inimii:

Imbinarea inimii se face cu SIRP M24 clasa 10.9 . Categoria imbinarii este C ( lunecare impiedicata la starea limita ultima )

Clasa suprafetelor de frecare este B ( suprafete sablate si metalizate ).

-Dimensiunile ecliselor:

h'1 hw 2 50 mm 2400 mm=:= ==> h1 2150mm:=

t1

hwtw

2 h1 10.465 mm=:= ==> t1 12mm:=

-Dispunerea suruburilor:

e1min 1.2 d0 31.2 mm=:=

e1max 4 t1 40mm+ 88 mm=:=

Adopt e1 35mm:=

e2min 1.2 d0 31.2 mm=:=

e2max 4 t1 40mm+ 88 mm=:=

Adopt e2 35mm:=

p1min 2.2 d0 57.2 mm=:=

p1max

min 14t1

200mm,

( ) 168 mm=:=

p2min 2.4 d0 62.4 mm=:=

p2max min 14t1 200mm,( ) 168 mm=:=

p'min max p1min p2min,( ) 62.4 mm=:= ==> pmin 65mm:=

p'max max p1max p2max,( ) 168 mm=:= ==> pmax 170mm:=

-Rezistenta de calcul la lunecarea a unui surub:

n 2:=ks 1:=

Fs.Rd

ksn

M3

Fp.C 158.144 kN=:=


37/38

-Forta capabila la presiune pe gaura a unui surub:

fu 470N

mm2

:=

k1 min 2.8e2

d0

1.7 1.4pmin

d0

1.7, 2.5,

1.8=:=

d min

e1

3 d0

pmin

3 d0

1

4,

0.449=:=

ab min d

fub

fu

, 1,

0.449=:=

Fb.Rd

k1ab fu d tw

M2

131.195 kN=:=

-Distributia suruburilor pe inaltimea inimii:

Propun o distributie pe 3 randuri de o parte si de alta a rostului de imbinare, corelata cu diagrama de

eforturi unitare normale .

o1.i 292.602N

mm2

=

o2.i

1.35 ME2.k.i

Iy.o

z'gNcs

Am.c

1 ME3.k.i

Iy.m.c

zo2.c

+

0.6 1.35 0.4 1+( ) ME4.k.i

0.6Iy.m.gp 0.4 Iy.m.c+ 0.6zo2.gp 0.4 zo2.c+( )

1.35 ME5.k.i

Iy.m.gp

zo2.gp++

...

1.35 0.75 MTS.k.i 0.4 MUDL.k.i+ 0.4 MPietoni.k.i+( )Iy.m.sd

zo2.sd+

...

138.001 N

mm2

=:=

7x

80

7x

65

65

505

1225

1290

1355

1420

35 8x65 72 358x65

50

40 4x70 120 404x70

85 1

90 2

95 4

00

20

125

230

440

520

600

680

760

1485

1550

1160

11x

105

610 7

15

1615

335

840

920

1080

7x

80

7x

65

11x

105

-Calculul fortei rezultante in surubul cel mai solicitat:

Iyw

twhw3

122.344 10

10 mm

4=:=

Mw1.35ME2.k.i

Iy.o

Iyw1 ME3.k.i

Iy.m.c

Iyw+0.6 1.35 0.4 1+( ) ME4.k.i0.6Iy.m.gp 0.4 Iy.m.c+

Iyw+

1.35 ME5.k.i

Iy.m.gp

Iyw1.35 0.75 MTS.k.i 0.4 MUDL.k.i+ 0.4 MPietoni.k.i+( )

Iy.m.sd

Iyw++

... 3904.157 kN m=:=


38/38

Fh

Mw1615 mm

3 16152

15502

+ 14852

+ 14202

+ 13552

+ 12902

+ 12252

+ 11602

+ 10802

+ 9202

+

8402

7602

+ 6802

+ 6002

+ 5202

+ 4402

+ 3352

+ 2302

+ 1252

+ 202

+ 852

+ 1902

++

...

2952

4002

+ 5052

+ 6102

+ 7152

++

...

mm2

:=

Fh 96.539 kN=

VE2.k.i 365.2 kN:= VE3.k.i 329.5 kN:= VE4.k.i 1222kN:= VE5.k.i 274.8kN:=VTS.k.i 449.9kN:= VUDL.k.i 320.6kN:= VPietoni.k.i 47.8kN:=

VEd.i 1.35 VE2.k.i VE5.k.i+( ) 1VE3.k.i+ 0.6 1.35 0.4 1+( ) VE4.k.i+1.35 0.75 VTS.k.i 0.4 VUDL.k.i+ 0.4 VPietoni.k.i+( )+

... 1681.54 kN=:=

ns.w.05 81:=

Fv

VEd.i

ns.w.05

20.76 kN=:=

R Fh2

Fv2

+ 98.746 kN=:= < min Fs.Rd Fb.Rd,( ) 131.195 kN= ( se verifica )

Proiect Poduri Metalice - Badulecu Gabriel

Documents

Transcript of Proiect Poduri Metalice - Badulecu Gabriel