model proiect metal
TRANSCRIPT
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