model proiect metal

GRAUR ANDICFDP III gr.3

PROIECT

CONSTRUCTII METALICE

NOTE DE CALCUL N=12

Graur Andi-AugustinCFDP III gr 3-Poduri

PROIECT

Sa se stabileasca conceptia si dimensiunile componentelor structural pentru un pod de cale ferata normala cub grinzi principale cu inima plina calea jos,in aliniament si palier.

Date de proiectare:

1

-deschidereaL= 12+0,3*12= 15,6 m-grinzile principale sunt cu inaltime constanta-convoiul de calcul LM71 [SR EN 1991-2 : 2005]

1) Tema lucrarii si alcatuirea structurii metalice

-distanta dintre lonjeroni b= 1,6m=1600mm-numarul de panouri pentru contravantuirea principal

n = 4 , pentru 12m≤ L=15,6m≤ 20mλ = 3,9m= distanta dintre antretoaze

-numarul de subpanouri pentru contavantuirea lonjeronilorn' = 3 L=15,6m>15m

-inaltimea grinzilor principale cu inima plina Hi

hi = L/10=15,6/10 =1,56 =˃ 1,6m=1600mm pentru 12m≤ L=15,6m≤ 18m hi = L/10-inaltimea inimii antretoazelor ha=1/6 B

ha= 750mm-latimea maxima a talpilor

-250mm pentru lonjeroni-260mm pentru antretoaze-400mm pentru grinzile principale

- inaltimea inimii lonjeronilor hil = λ/10=˃hil = 3.9/10=390mm =˃ 400mm

Proiectarea lonjeronilor

I.1. Actiuni pentru lonjeroniI.1.1 Greutatea lonjeronilor

g= gsm + g caiigsm = 4KN/mgcaii= 8KN/m

=˃ g2L = 4+8 = 12KN/mI.1.2 Convoiul de calcul LM71 (SR EN 1991-2:2005)

2

r = 1500 mm distanta intre sinee≤ r/18=1500/18 =83,33mm= 0,0833m

Sectiune Transversala

3

R1=Qvk (b2 −e)b

=250(1600

2−50)

1600=124 ,99 KN

R2=Qvk−R1=250−124 ,99=125 . 01 KNR2=(1−k1 )∗Q vk=0,5∗Q vk

k 2=1−k1

cr=

b2

−e

b=

16002

−83 ,33

1600=0 ,55

Φ3= coeficient dinamic

4

Φ3=2,16

√LΦ−0,2+0 ,73=

2 ,16

√6 ,90−0,2+0 ,73=1 ,62

LΦ=λ+3 ,00m=3,9+3=6 ,90mI.1.3 Actiunea vantului ( cf SR EN 1991-1-4:2006)

ρ= densitatea aerului = 1,25 kg/m3

vb= viteza de referinta a vantului =25m/svb= cdir*cseason* vbo cdir= 1; cseason=1.vbo= vbo

**= 27m/sc= coeficient de forta a vantului

c=f (b'd total)=f (6500

5090 )c=2,3b '=4,5+2.00=6,5m=6500mmd total=4000+750+200+50+90=5090mm

Aref , x=d total∗L '=5090∗16200=82 ,46m2

L '=L+2∗0 ,30=15 ,6+2∗0 ,30=16 ,2m

q pz =

12∗ρ∗vb

2∗c=12∗1 ,25∗272∗2,3=105daN /m2

Fw=q pz∗c fx∗Aref , x=105∗2∗82 ,46=173 ,16KNm

pw=Fw

A ref , x

=173 ,1682, 46

=2,1

I.1.4 Serpuirea

QSK= 100KN

I.2 Diagrame de moment incovoietoare si forta taietoare

5

I.2.1 Greutatea permanenta g=12KN/m

M2L = 22,8KNm

V2L = ±23,4KN

6

I.2.2 Convoiul de calcul LM 71LI corespunzatoare V in Mmax= ±147,4KNLI VA

2L = -465,7 KN

7

LI Mmax = 331,3KNm

8

Predimensionarea lonjeronilora) Lonjeroni de capatb) Lonjeroni curenti

9

hw=λ/10=3900/10=390mmhw=400mmtw=12mm

Aria necesara pentru o talpa din conditia de oboseala:

A1 bf≥Mmax, LM 71

1L −Mw

hw∗Δσ c

γFf∗λ∗Φ2∗γ Mf

a)Lonjeroni de capat cr=0,55

Mmax, Lm711L =cr∗Mmax, LM 71=0 ,55∗331,3=182,22 KNm

b)Lonjeroni curenti cr=0,55

Mmax, Lm711L =cr∗0,8∗Mmax, LM 71=0 ,55∗0,8∗331 ,3=145 ,77 KNm

10

Mw = momentul preluat de inima =75,2KNm

Mw=W w , y∗fyd=320000∗235=75 ,2KNm

fyd=235N /mm2

W w , y=I yzmax

=b∗hw

2

6=12∗4002

6=320000mm3

Δσc= 80N/mm2

γFf= 1,00

λ= coeficient de echivalenta pentru degradari din obosealaλ=λ1+ λ2+ λ3+ λ4≤ λmax=1,4λ1=f(λ=3,9m)=1,08(tabelul9.3 SR EN 1993-2:2006)λ2=1,00λ3=1,00λ4=1,00

γMf= 1,35 - factor partial de siguranta pentru rezistenta la oboseala

Φ2 = 1,41

Φ2=1 ,44

√LΦ−0,2+0 ,82=

1 ,44

√6 ,90−0,2+0 ,82=1, 41

LΦ=λ+3 ,00m=3,9+3=6 ,90m

a)

Lonjeroni de capat

11

A1 bf≥Mmax, LM 71

1L −Mw

hw∗Δσ c

γFf∗λ∗Φ2∗γ Mf

=182 ,22−75 ,2

400∗801 ,08∗1 ,41∗1 ,35

=

A1 bf≥6810 ,37

b)Lonjeroni curenti

A1 bf≥Mmax, LM 71

1L −Mw

hw∗Δσ c

γFf∗λ∗Φ2∗γ Mf

=145 ,77−75 ,2

400∗801 ,08∗1 ,41∗1 ,35

=

A1 bf≥4491 ,66

a)

Lonjeroni de capat

Pt. bf = 250mm => tf = 27,24mm => tf = 30mm

b)Lonjeroni curenti

Pt. bf = 250mm => tf = 17,96mm => tf = 20mm

VERIFICARIClasa sectiunii inimii

12

a)Lonjeroni de capat

inima c =400 c/tw=400/12 => 33,33 ≤ 72ε => CLASA 1

talpa c=119

c/tf=119/30 => 3.96 ≤ 9ε => CLASA 1

b) Lonjeroni curenti

inima c =400 c/tw=400/12 => 33,33 ≤ 72ε => CLASA 1

talpa c=119

c/tf=119/20 => 5.95 ≤ 9ε => CLASA 1

I.

Starea limita ultima (SLU)

A) Verificarea la moment incovoietor Lonjeroni de capat

M Ed

MC ,Rd

≤1 ,00

M Edy

MC ,Rdy

≤1 ,00

M Edz

MC ,Rdz

≤1 ,00

MC ,Rd=M pl ,Rd

M pl ,Rd=W pl∗fyγ Mo

13

M Edy =γG∗MG

1L+γQ1∗MQ2L∗φ3∗cr+γQi∗Mwi

1L∗ψγG=1 ,35 ;γQ1=1 ,45 ; γQi=1,5 ;ψ=0,8

MG1L=11 , 4 KNm;MQ

2L=331 ,33 KNm;Mwi1 L=24 ,53 KNm.

φ3=1 ,62 :cr=0 ,55 ;w=2,1KN /m2 .

M Edy =1 ,35∗11 ,4+1 ,45∗331 ,33∗1 ,62∗0 ,55+1,5∗24 ,53∗0 .8

M Edy =472 ,47 KNm

Mw , ind=Rw∗hw ; Rw=w∗h ';qwind=Mw , ind

b.

Rw=2,1∗( 4000−650)=7 ,14hw=1650+650+200+240+30+120=2890mmMw , ind=7 ,14∗2 ,89=20 ,63

qwind=20 ,631,6

=12 ,90 KN /m

Mw , ind=qwind∗λ2

8=12,90∗3,92

8=24 ,53 KNm

MCRd

y =W y , pl ¿ fyγM 0

;W y , pl=2∗S y .

W y, pl=2∗[250∗30∗(4002

+302 )+400

2∗12∗400

4 ]=W y, pl=3705000mm3

14

MCRd

y =3705000∗2351

=870 ,68 KNm

M Edy

MC ,Rdy

≤1 ,00 ;472 ,47 KNm870 ,68 KNm

≤1⇒0 ,54≤1

⇒0 ,54≤12 )M Ed

z

MC ,Rdz

≤1 ,00 ;MEdz =valmax {M zEd

w ,direct∗γQM z ,Ed

serpuire∗γQ}Mwh=M z ,Ed

w ,direct=120

∗w∗a2

w=12∗qw ,direct=

12∗7 ,14=3 ,52

a2= λ '2=(3 . 93 )

2

Mwh=M z ,Edw ,direct=1

20∗3 ,52∗(3. 9

3 )2

=0 ,30 KNm

M z, Edw ,direct∗1 ,45=0 ,30∗1 ,45=0 ,44

15

M z ,Edserpuire=M s

l∗γQ=8 ,13∗1 ,45=11 ,79

M sl=0 ,25∗MOS=0 ,25∗32 ,5=8 ,13

MOS=100∗1,34

=32 ,5

⇒M z ,Ed=11 ,79 KNm

M z, Rd=W z, pl∗fy

γMo

W z , pl=2∗Sz=2∗2502

∗30∗2504

=468750mm3

M z, Rd=468750∗2351

=110 ,16 KNm

⇒11 ,79110 ,16

≤1 ,00⇒0 ,11≤1 ,00

3 )M Ed

y

M pl ,Rdy

+MEd

z

M pl ,Rdz

≤1 ,00⇒0 ,54+0 ,11=0 ,65≤1 ,00

16

Verificarea la moment incovoietorLonjeroni curenti

M Ed

MC ,Rd

≤1 ,00

M Edy

MC ,Rdy

≤1 ,00

M Edz

MC ,Rdz

≤1 ,00

MC ,Rd=M pl ,Rd

M pl ,Rd=W pl∗fyγ Mo

M Edy =γG∗MG

1L+γQ1∗MQ2L∗φ3∗cr+γQi∗Mwi

1L∗ψγG=1 ,35 ;γQ1=1 ,45 ; γQi=1,5 ;ψ=0,8

MG1L=11 , 4 KNm;MQ

2L=331 ,33 KNm;Mwi1 L=24 ,53 KNm .

φ3=1 ,62 :cr=0 ,55 ;w=2,1KN /m2 .

M Edy =1 ,35∗11 ,4+1 ,45∗331 ,33∗1 ,62∗0 ,55+1,5∗24 ,53∗0 .8

M Edy =472 ,47 KNm

Mw , ind=Rw∗hw ; Rw=w∗h ';qwind=Mw , ind

b.

Rw=2,1∗( 4000−650)=7 ,14hw=1650+650+200+240+30+120=2890mm

17

Mw , ind=7 ,14∗2 ,89=20 ,63

qwind=20 ,631,6

=12 ,90 KN /m

Mw , ind=qwind∗λ2

8=12,90∗3,92

8=24 ,93KNm

MCRd

y =W y , pl ¿ fyγM 0

;W y , pl=2∗S y .

W y, pl=2∗[250∗20∗(4002

+202 )+400

2∗12∗400

4 ]=W y, pl=3060000mm3

MCRd

y =3060000∗2351

=719 ,10 KNm

M Edy

MC ,Rdy

≤1 ,00 ;472 ,47 KNm719 ,10KNm

≤1⇒0 ,66≤1

⇒0 ,66≤1

18

2 )M Ed

z

MC ,Rdz

≤1 ,00 ;MEdz =valmax{M zEd

w ,direct∗γQM z ,Ed

serpuire∗γQ }Mwh=M z, Ed

w ,direct=120

∗w∗a2

w=12∗qw ,direct=

12∗7 ,14=3 ,52

a2= λ'2=(3 . 93 )

2

Mwh=M z, Edw ,direct=1

20∗3 ,52∗(3 . 9

3 )2

=0 ,30KNm

M z, Edw ,direct∗1 ,45=0 ,30∗1 ,45=0 , 44

M z ,Edserpuire=M s

l∗γQ=8 ,13∗1 ,45=11 ,79

M sl=0 ,25∗MOS=0 ,25∗32 ,5=8 ,13

MOS=100∗1,34

=32 ,5

⇒M z ,Ed=11 ,79 KNm

M z, Rd=W z, pl∗fy

γMo

19

W z , pl=2∗Sz=2∗2502

∗20∗2504

=312500mm3

M z, Rd=312500∗2351

=73 ,44 KNm

⇒11 ,7973 ,44

≤1 ,00⇒0 ,16≤1 ,00

3 )M Ed

y

M pl ,Rdy

+MEd

z

M pl ,Rdz

≤1 ,00⇒0 ,66+0 ,16=0 ,82≤1 ,00

20

B) Verificarea la forta taietoare Lonjeroni de capat+ Lonjeroni curenti

V Ed

V c ,Rd

≤1 ,00

V Ed=γG∗VG1L+γQ1∗VQ

2L∗φ3∗cr+γQi∗V wi1L∗ψ

γG=1 ,35 ;γQ1=1 ,45 ; γQi=1,5 ;ψ=0,8

VG1L=11 ,7 KN ;VQ

2L=147 ,4 KN ;V wi1 L=25 ,16 KN .

φ3=1 ,62 :cr=0 ,55 ;w=2,1KN /m2 .V Ed=1,35∗11 ,7+1 ,45∗147 ,4∗1 ,62∗0 ,55+1,5∗25 ,16∗0 . 8V Ed=236 ,42KN

V indw =

qw ,ind∗λ

2=

12 ,90∗3,92

=25 ,16KN

V c ,Rd=Av∗( fy /√3 )γ M 0

=400∗12∗235 /√3=915 ,82

V Ed

V c ,Rd

≤1 ,00⇒236 ,42915 ,82

=0 ,25≤1

21

C) Verificarea la Moment incovoietor + Forta taietoare

V pl , Rd=915 ,82KNV Ed=236 ,42 KN⇒

⇒V Ed<12V pl ,Rd ,236 ,42<

12

915 ,82=457 ,91⇒Sectiunea nu necesita verificare la incovoiere si forfecare.

II. Starea limita ultima de oboseala (SLUO)

Relatii de verificare

a )γFf∗ΔσE 2≤ΔσcγMf

b )γFf∗ΔτE2≤Δτ cγ Mf

c )(γFf∗Δσ E2

Δσ c/γ Mf)3

+(γFf∗Δτ E2

Δτ c/γ Mf)5

≤1

γ Ff=1 ,00 ; ΔσE2=λ∗Φ2∗ΔσP

λ=λ1∗λ2∗λ3∗λ4 ; λ1=1 ,08 ; λ2=λ3=λ4=1 ,00

Φ2=1 ,41 :Δσ c

γ Mf

=801 ,35

=59 N /mm2

Δσ P=|σ p,max−σ p ,min|; σ p ,min=0⇒Δσ P=σ p ,max

22

Lonjeroni de capat

σ p,max=Mmax, LM 71

1L

I y∗zmax=

16 ,57∗105

164837 ,5∗21 ,5=21 ,6 N /mm2

I y=1,2∗403

12+2∗25∗3∗(40

2+25

2 )2

=164837 ,5cm4

Δσ E2=1 ,08∗1 ,41∗21 ,6=33 N /mm2

Δσc = 80 N/mm2 (cf SREN 1993-1-9:2006,tabelul 8.4)

γ Mf=1 ,35

33≤801,35

⇒33N /mm2≤59N /mm2

Lonjeroni curenti

σ p,max=Mmax, LM 71

1L

I y∗zmax=

16 ,57∗105

112025∗21 ,5=31 ,8 N /mm2

I y=1,2∗403

12+2∗25∗2∗(40

2+25

2 )2

=112025cm4

Δσ E2=1 ,08∗1 ,41∗31 ,8=48 ,42N /mm2

23

γ Mf=1 ,35

48 ,42≤801 ,35

⇒48 ,42 N /mm2≤59 ,26 N /mm2

Lonjeronii se verifica la SLUO.

III. Starea limita de serviciu(SLS)

A) Limitarea eforturilor unitare

1)σ Ed , serv≤fyγM ,serv

2 )τ Ed , serv≤fy

√3∗γM ,serv

3 )√σ Ed , serv2 +3 τEd , serv

2 ≤fyγM ,serv

a) Lonjeroni de capat

1)σ Ed , serv=Mmax,serv

I y∗zmax=

19 ,83∗105

164837 ,5∗(40

2+3,0)=

σ Ed , serv=276 ,69daN /cm2=27 ,7 N /mm2

Mmax, serv=M max,g1L +Mmax, LM 71

1L ∗c∗Φ3+Mmax,wind1L =

¿11 ,4+182 ,22∗0 ,55∗1 ,62+24 ,53=198 ,29 KNmI y=164837 ,5cm4

σ Ed , serv=27 ,7 N /mm2≤fyγm,serv

=235 N /mm2

24

2 )τ Ed , serv=Vmax, serv

hw∗tw=244∗103

400∗12=50 ,83N /mm2

Vmax, serv=Vmax, g1L +V max,LM 71

1L ∗c∗Φ3+Vmax, wind1L =

¿11 ,7+232 ,85∗0 ,55∗1 ,62+25 ,16=244 ,33 KN

τ Ed , serv=50 ,83N /mm2≤fy√3∗γm,serv

=135 ,68 N /mm2

3 )√σ Ed , serv2 +3 τEd , serv

2 ≤fyγm,serv

=235 N /mm2

√27 ,72+3∗50 ,832=92 ,30N /mm2≤fyγm,serv

=235 N /mm2

b) Lonjeroni curenti

1)σ Ed , serv=Mmax,serv

I y∗zmax=

16 ,58∗105

112025∗(40

2+2,0)=

σ Ed , serv=325 ,61daN /cm2=32 ,6N /mm2

Mmax, serv=M max,g1L +Mmax, LM 71

1L ∗c∗Φ3+Mmax, wind1L =

¿11 ,4+145 ,77∗0 ,55∗1 ,62+24 ,53=165 ,81KNmI y=112025cm4

σ Ed , serv=32 ,6N /mm2≤fyγm ,serv

=235N /mm2

2 )τ Ed , serv=Vmax, serv

hw∗tw=244∗103

400∗12=50 ,83N /mm2

Vmax, serv=Vmax, g1L +V max,LM 71

1L ∗c∗Φ3+Vmax, wind1L =

¿11 ,7+232 ,85∗0 ,55∗1 ,62+25 ,16=244 ,33 KN

τ Ed , serv=50 ,83N /mm2≤fy√3∗γm,serv

=135 ,68 N /mm2

25

3 )√σ Ed , serv2 +3 τEd , serv

2 ≤fyγm,serv

=235 N /mm2

√32 ,62+3∗50 ,832=93 ,88N /mm2≤fyγm,serv

=235 N /mm2

B) Limitarea zveltetii lonjeronilor

hw

tw≤55+3,3 L≤250

hw=400 ; tw=12; L=15 ,6⇒ L=2040012

=33 ,33≤55+3,3∗20=121

C)Limitarea sagetii verticale

a)Lonjeroni de capat

δ=5∗Mmax, LM 71

1L ∗λ2

48∗E∗I y≤λ600

E=2,1∗106daN /cm2 ;Mmax, LM 71

1L =182 ,22 KNm=18 ,22∗105daNcm

λ=3,9m=390cm ;I y=164837 ,5cm4

δ=5∗18 ,22∗105∗3902

48∗2,1∗106∗164837 ,5=0 ,08≤390

600=0 ,65

b) Lonjeroni curenti

26

δ=5∗Mmax, LM 71

1L ∗λ2

48∗E∗I y≤λ600

E=2,1∗106daN /cm2 ;Mmax, LM 71

1L =145 ,77KNm=14 ,58∗105daNcm

λ=3,9m=390cm ;I y=112025 cm4

δ=5∗14 ,58∗105∗3902

48∗2,1∗106∗112025=0 ,10≤390

600=0 ,65

27