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Etapa 1:
1..Alegerea sistemului construuctiv de zabrele.Distanta dintre noduri. Constructie nezolata termic p%=5%
L 30 H 9 LT 8
h1
8
1
12
24 24
h 3
δadmL
250
30
250 0.12
hminL
2
5190 δadm 2 L30
2
5190 0.12 2 30 1.599
hmin Ceil hmin 0.05 1.6 m
rezulta:
h1 hmin 1.6 1.6 m
h2 h h1 3 1.6 1.4 m tgαh1L
2
explicit ALL1.630
2
0.107
distanta dintre noduri:
a = max 3 m α 6.18a 1 1.2( ) h 3 1 1.2( ) 1 1.2( ) h
cosα 0.9987a 3 sinα 0.0490numar de panouri:
L
a
30
3 10 panouri
conditia de transport tronsoane:
Daca L<12 m si h < 3,6 m => 1 tronson
Daca L>12 m si h > 1.25 m < 3.6 m => 2 tronsoane
2..Stabilirea inaltimii stalpului: Lc
Df 1 m
Lcs H Df δadm h2 explicit ALL 9 1 0.12 1.4 11.52
Lcs Ceil Lcs 0.5 12 m
Valori caracteristice pe metru patrat:Incarcari permanente (qk)
greutate invelitoare: ginv 10daN
m2
greutate proprie a panei:
gU30 46.2daN
m2
gU30
aexplicit ALL
46.2
3 15.4
daN
m2
gp
gU30
a15.4
daN
m2
greutate contravantuire:
gcv 5daN
m2
greutate instalatii electrice:daN
m2gel 10
greutate profil industrila:
gpi 10daN
m2
rezulta:
daN
m2qk
ginv
cosαgp gcv gel gpi
10
0.998715.4 5 10 10 50.413
Incarcari variabile:
din vant => efect de suctiune
din zapada:
μi 0.8 Ce 1 Ct 1 s0k 200 daN/m2
sk μi Ce Ct s0k 0.8 200 160 daN/m2
Incarcari de calcul:
SLU
qd 1.35 qk 1.5 sk a 1.35 50.413 1.5 160( ) 3 924.173 daN/m
qyd qd cosα 924.173 0.999 922.971 daN/m
qzd qd sinα 924.173 0.049 45.284 daN/m
SLS
qk qk sk a 50.413 160( ) 3 631.239 daN/m
qyk qk cosα 631.239 0.999 630.418 daN/m
qzk qk sinα 631.239 0.049 30.931 daN/m
Determinare solicitarilor de calcul:
daNm MyEd qyd
LT2
16 922.971
82
16 3.692 10
3
MzEd qzd
LT
3
2
1.32
8 45.284
8
3
2
1.32
8 68.027 daNm
VyEd 0.5 qyd LT 0.5 922.971 8 3.692 103 daN/m
VzEd 1.1 qzdLT
3 1.1 45.284
8
3 132.834 daN/m
Determinare sectiunii:
k7
1.54.667 pentru profile I
fyd 235 105 daN/m2
Wplnec 221 cm3
Wpl
MyEd k MzEd 106
fyd
3.692 103 4.667 68.027 10
6
235 105
170.61 cm3
Wplnec
MyEd k MzEd fyd
2213.692 10
3 4.667 68.027
235 105
1 cm3
Alegem un profil: IPE 200 Wply 221 cm3
h 200 mm Iy 1940 cm4
b 100 mm iy 8.26 cm
tw 5.6 mm Wply 221 cm3
tf 8.5 mm Iz 142 cm4
r2 12 mm iz 2.24 cm
A 28.5 mm2 Wplz 44.5 cm3
g 22.4 Kg/m fyd 2.35 107
Verificarea clasei sectiunii:
d h 2 r2 tf 200 2 12 8.5( ) 159 mm
cb
2
2 r2 tw 2
100
2
2 12 5.62
35.2 mm
ξfyd
235 105
1 N/mm2
λfc
tf
35.2
8.5 4.141
λf 9 ξ 4.141 9 1
λwd
tw
159
5.6
clasa 1
λw 72 ξ159
5.672 1
Verificarea sectiunii propuse:
Verificarea de rezistenta (SLU):
daNmMplyRd Wply 106 fyd 221 10
6 235 105 5.193 10
3
MplzRd Wplz 106 fyd 44.5 10
6 235 105 1.046 10
3 daNm
MyEd
MplyRd
MzEd
MplzRd 1
3.692 103
5.193 103
68.027
1.046 103
1 1
AVy A 2b
10 2
tf
10
tf
102 r2
tw
10
28.5 2100
10 2
8.5
10
8.5
102 12
5.6
10
15.376
cm2
VplyRd AVy
fyd 104
3 15.376
235 105 10
4
3 2.086 10
4
VyEd VplyRd 3.692 103 2.086 10
4 1
AVz Ad
10
tw
10 28.5
159
10
5.6
10 19.596 cm
2
daNVplzRd AVz 23510
3 19.596 235
10
3 2.659 10
4
VzEd VplzRd 132.834 2.659 104 1
Influenta fortei taietoare asupra momentului plastic:
VyEd 0.5 VplyRd 3.692 103 0.5 2.086 10
4 1
VzEd 0.5 VplzRd 132.834 0.5 2.659 104 1
Verificarea la stabilitate generala:
λzf zveltetea barei intre doua legaturi laterale,tiranti
Lc 0.2 LT explicit ALL 0.2 8 1.6 pentru 2 tiranti
k.c factor de corectie al zveltetii
kc1
1.60.625
λco 0.50
λ1 93.9 ξ 93.9ifz raza de giratie a sectiunii formate de talpa comprimata a inimii in raport cu axa minima
de zveltete a sectiunii
zG 0.326 cm
Ifz 76.28 cm4
Af 10.208 cm2
ifz
Ifz
Af2.734 cm
λzf Lc
kc
ifz 1.6
0.625
2.734 0.366
λzf.
λzf
λ1λco Wply
fyd
MyEd
0.366
93.90.5 221
235 105
3.692 103
1
Verificarea la starea limita de serviciu:
-sageata maxima:
δy 0.15 qyk10
2LT
4
Iy 0.15 630.418
102
84
1.94 103
1.997
δz 0.63 qzk
LT
31.3
4
102
Iz 0.63 30.931
8
31.3
4
102
142 0.198
δmax δy2
δz2
LT 100
200 1.997
20.198
28 100200
1 se verifica
Dimensionarea pana in camp marginal
Solicitarile de calcul:
MyEdII qyd
LT2
11 922.971
82
11 5.37 10
3 daNm
daNmMzEdII
qzd 1.3LT
3
2
8
45.284 1.38
3
2
8 68.027
Predimensionarea sectiunii campului marginal:
k16
111.455
Wplynec
MyEdII k MzEdII fyd
5.37 103 1.455 68.027
235 105
2.327 104 m
3
Wplynec 106 232.722 cm
4
cm4
Iynec Wplynec 106
h
2 10 2.327 10
4 106
200
2 10 2.327 10
3
Iy22U Iynec Iy 2.327 103 1.94 10
3 387.219 cm4
Iy2
Iy22U
2
387.219
2 193.609 cm
4
Se alege UPN 140:
hu 140 mm Iyu 605 mm4 Izu 62.7 mm4
bu 60 mmWelyu 86.4 mm3 Welzu 14.8 mm3
twu 7 mm
mm Wplyu 103 mm3tfu 10 Wplzu 28.3 mm3
mm iyu 5.45 mmr1u 10 izu 1.75 mmAVzu 10.41 mm
2ru2 5 mm
Au 20.40 mm2
du 98 mm
kg/m Gu 16
Caracteristicile elastice:
At A Au 2 28.5 20.40 2 69.3 cm2
Iyt Iy Iyu 2 1940 605 2 3.15 103 cm
3
Izt Iz Izu 2 142 62.7 2 267.4 cm3
Caracteristicile plastice:
Wplyt Wply Wplyu 2 explicit ALL 221 103 2 427 cm3
Wplzt Wplz 2 Wplzu Au izu
tw
2
44.5 2 28.3 20.40 1.755.6
2
286.74
cm3
Lungimea suplimentului este intersectia dintre parabola cu dreapta;
4 X0.875 LT X
0.875 LT qyd
LT2
11 qyd
LT2
16
X1 0.192 LT 0.192 8 1.536 m
X2 0.682 LT 0.682 8 5.456 m
Suplimentul se prelungeste departe si de alta de unde rezulta lungimea supliment:
Ls X2 X1 2 0.3 5.456 1.536 2 0.3 4.52 m
Verificarea sectiunii propuse:
MplyRd Wplyt 106 fyd 427 10
6 235 105 1.003 10
4 daNm
MplzRd Wplzt 106 fyd 286.74 10
6 235 105 6.738 10
3 daNm
MyEdII
MplyRd
MzEdII
MplzRd 1
5.37 103
1.003 104
68.027
6.738 103
1 1
Sageta maxima (SLS):
δyu 0.307 qyk 102
LT4
Iyt 0.307 630.418 10
28
4
3.15 103
2.517 mm
δzu 0.601 qzk
LT
31.3
4
102
Izt 0.601 30.931
8
31.3
4
102
267.4 0.1 mm
δmaxu δyu δzuLT 100
200 2.517 0.1
8 100200
1
Dimensionare tiranti
tbβLT3
a
83
3
8
β 83.65 cosβ 0.11062
N1 0.5 VzEd 0.5 132.834 66.417 daN
N2 N1 VzEd 66.417 132.834 199.252 daN
N3 N2 VzEd 199.252 132.834 332.086 daN
N4 N3 VzEd 332.086 132.834 464.92 daN
N5 N4 VzEd 464.92 132.834 597.755 daN
N55
N5
cosβ
597.755
0.111 5.404 10
3 daN
-efort maxim in tirant:
NmaxEd max N5 N55 max 597.755 5.404 103 5.404 10
3 daN
-dimensionare tirant:
γM2 1.25
fu 3700 daN/cm2 S235( )
NmaxEd NtRd
rezulta NtRd NmaxEd
ds 4 γM2NtRd
0.9 fu π 4 1.25
5.404 103
0.9 3.7 103 π
1.607
rezulta : d Ceilds
0.890.5
Ceil1.607
0.890.5
2 cm
Evaluarea actiunilor -- valori caracteristice pe cadrul transversal.
1 Actiuni permanente:
acoperis : ginv. 10 daN/m2
nrpane 10
gpana nrpaneg
LT 10
22.4
8 28 daN/m2
gcv 5 daN/m2
gel 10 daN/m2
gzi 10 daNm2
qka ginv gpana gcv gel gzi 10 28 5 10 10 63 daN/m2
qa qka LT 63 8 504 daN/m2
stalpi : gs 15 11 165 daN/m2
ginv ginv. LT 10 8 80 daN/m2
grigle 3 40LT
Lcs 3 40
8
12 80 daN/m
qs gs ginv grigle 165 80 80 325 daN/m
2. Actiuni variabile:
a) zapada uniforma:
zk sk LT 160 8 1.28 103 daN/m
a) zapada neuniforma:
sk1 0.5 μi Ce Ct s0k 0.5 0.8 200 80 daN/m2
zk1 sk1 LT 80 8 640 daN/m2
μ2 0.965
sk11 μ2 Ce Ct s0k 0.965 200 193
zk11 sk11 LT 193 8 1.544 103 daN/m2
b)vant:
cez --coeficinet de expunere functie de categoria de teren si inaltimea z
categoria de teren II
z Lcs h1 12 1.6 13.6 m
cez 2.5
υb0 35 m/s
csezon 1 factor de anotimpcdirectie 1 coeficient de directie
ρ 1.25 daN/m3 densitatea aerului
Vb cdirectie csezon υb0 1 35 35
qb1
2ρ Vb
2 101
1
21.25 35
2 101 76.563 daN/m2 presiunea vitezei de referinta
qpze cez qb 2.5 76.5625 191.406 valoarea de varf a presiunii vitezei
we qpze cpe cpe
vant transversal:
h Lcs 12
d L 30
h
d
12
30 0.4
b 8 9 72
e min b 2 h( ) min 72 2 12( ) 24
D: cpe10 0.75 cpe1 1
daN/m2weD qpze cpe10 10
1 191.406 0.75 101 14.355
qD weD LT 14.355 8 114.844 daN/m2
E: cpe10 0.4 cpe1 0.4
weE qpze cpe10 101 191.406 0.4 10
1 7.656 daN/m2
qE weE LT 7.65625 8 61.25 daN/m2
H: cpe10 0.566 cpe1 1.1
weH qpze cpe10 101 191.40625 0.566 10
1 10.834 daN/m2
qH weH LT 10.833593749999999 8 86.669 daN/m2
I: cpe10 0.578 cpe1 0.578
weI qpze cpe10 101 191.40625 0.578 10
1 11.063 daN/m2
qI weI LT 11.06328125 8 88.506 daN/m2
Vant longitudinal:
e min b 2 h( ) 24
e d 24 30
B: cpe10 0.8 cpe1 1.1
weB qpze cpe10 101 191.40625 0.8 10
1 15.313 daN/m2
qB weB LT 15.3125 8 122.5 daN/m2
H: cpe10 0.689 cpe1 1.2
weH qpze cpe1 101 191.40625 1.2 10
1 22.969 daN/m2
qH weH LT 22.96875 8 183.75 daN/m2
c)actiuni seismice:
Ct 0.085
Lcs 12
T1 Ct Lcs
3
4 0.085 12
3
4 0.548 s
Evaluarea masei seismice:
-acoperis macoperis qa L 504 30 1.512 104 daN
-stalp mstalp qs Lcs 325 12 3.9 103 daN
ferma qo 1.35 qa 1.3 1.5 zk 1.35 504 1.3 1.5 1280 2.805 103 daN
daNmMmax0 qoL
2
8 2804.52
302
8 3.155 10
5
Wynec
Mmax0
fyd
315508.5
235 105
0.013
h 3
Iynec Wynech
2 0.02
Acnec
Wynec
2 hexplicit ALL
0.013
2 3 2.238 10
3
rezulta LPN: 100 x 75x 10
gc 13
mferma 4 gc gc gc L 4 13 13 13( ) 30 2.34 103 daN
unde g.diagonala = g.montant = g.c :
mstructura macoperis mstalp mferma
mstructura 15120 3900 2340 2.136 104 daN
m mstructura 0.4 zk L 15120 3900 2340 0.4 1280 30 3.672 104 daN
Forta seismica:
S γI sdT1m
g λ γI
Suceava :
ag 0.2 g
T1 0.41 g 9.81Tc 0.7 s TB 0.1 Tc 0.07 s
TD 3 s γI 1
βT1 2.75 λ 1
β0 βT1 2.75
q 2.5
SdT1 ag 1
β0 1
q
TB
T1 1.839
S γI SdT1m
g λ 1.839
3.672 104
9.81 6.884 10
3 daN
etapa 6:
Pregatire date pentru modelarea numericaDeterminarea incarcarilor concentrate.
Incarcari permanente:
Qa qa a 504 3 1.512 103 daN
Incarcari variabile:
a) zapada uniforma:
z zk a 1280 3 3.84 103 daN
b) zapada neuniforma:
z1 zk1 a 640 3 1.92 103
z11 zk11 a 1544 3 4.632 103
c) vant transversal:
HD 3 qDLcs
8 3 114.844
12
8 516.797 daN
HE 3 qE Lcs
8 3 61.25
12
8 275.625 daN
VH qH a 183.75( ) 3 551.25 daN
VI qI a 88.50625( ) 3 265.519 daN
d) vant longitudinal:
HB 3 qbLcs
8 3 76.5625
12
8 344.531 daN
VH qH a 183.75( ) 3 551.25 daN
Grupari de incarcari:
G1= 1.35xG+1.5xZuniforma;
G2 =1.35xG+1.5xZaglomerata+1.05xVtransv
G3=1.35xG+1.5xVtransv.+1.05xZaglomerata
G4=1.5xG+1.5xVtransv+1.05xZuniforma
G5=G+0.4xZuniforma+S
G6(SLSD)=G+Z
etapa 7
Dimensionarea barelor grinzii cu zabrele
Determinarea lungimilor de flambaj
talpa superioara :T.S. Lcy=l (=lungimea barei)
Lcz=(distanta intre doua puncte fixe)=3l
diagonale (D) si montanti (M) Lcy=0.9l
Lcz=l
talpa inferioara Lcy=l
Lcz=(distanta intre doua antretoaze)
alegerea grosimii guseului:
tg 15
dimensiuniinime ale cornierelor:
aripi egale:
LPN 50x50x6aripi inegale:
LPN 60x50x6
Determinarea barelor comprimate talpa superioara
NTS 93589.1 l 2.405
Lcy l 2.405 2.405 m
Lcz 2 l 2 2.405 4.81 m
-barele comprimate cedeaza datorita pierderii stabilitatii flambaj prin incovoiere (Euler) flambaj prin incovoiere-rasucire-predimensionarea:flambaj datorita compresiunii:
fy 235NEd NbRd χo A
fy
γM0
γM0 1
fyd
fy 10
γM0
235 101
2.35 103 daN/mm2
impunem χo 0.8
Anec
NTS
fyd χo93589.1
2350 0.8 49.781
A1.
Anec
2
49.781
2 24.891 cm
2
Propunem LPN 100x75x8
A1 13.50 A 2 A1 27
Iy1 64.1 ez1 3.10 Iy Iy1 2 128.2
iy1 2.18 iy iy1 2.18
Iz1 133
iz1 3.14 Iz 2 Iz1 A1 ez1
tg 101
2
2
666.207
iz
Iz
A4.967
verificarea sectiunii propuse
λ1 93.9α 0.46
λy
Lcy 100
iy
2.405 1002.18
110.321ε 1
λz
Lcz 100
iz
4.81 1004.967
96.833 λmax max λy λz 110.321
λ.
λmax
λ1
110.321
93.9 1.175
ϕ 0.5 1 α λ. 0.2 λ.2
0.5 1 0.46 1.175 0.2( ) 1.175
2 1.414
χ1
ϕ ϕ2
λ.2
1
1.414 1.4142
1.1752
0.454
NbRd χ Afy 10
γM0 0.454 27
235 101
2.882 104
NTS NbRd 9.359 104 2.882 10
4 1
propunem
χmed
χo χ 2
0.8 0.4542
0.627
Anec
NTS
χmed fyd9.359 10
4
0.627 2.35 103
63.509 cm2
cm2
A1
Anec
231.755
Propunem LPN 150x15 corniere cu aripi egale
A1 43 ez1 4.25 A 2 A1 86
Iy1 898 ey 4.25 Iy Iy1 2 1.796 103
iy1 4.57 iy iy1 4.57
Iz1 898
iz1 4.57
Iz 2 Iz1 A1 ez1
tg 101
2
2
3.946 103
t 1.5b 31.5 iz
Iz
A6.774
hc 15zo ey
t
2 4.25
1.5
2 3.5 cm
It At2
3 86
1.52
3 64.5 cm
4
moment de inertie la rasucire libera
Iw
b3
t3 4 hc
3 t3
144
31.53
1.53 4 15
3 1.53
144 1.049 10
3 cm4
moment de inertie la rasucire impiedicata
io zo2
Iy Iz A
explicit ALL 3.52 1.796 10
3 3.946 103
86 79.017
raza polara fata de centrul de forfecare
Verificarea sectiunii propuse la flambaj prin incovoiere-rasucire
G 8.1 105 daN/cm2
E 2.1 106 daN/cm2
LcrT l 100 240.5 m
NcrT1
ioG It π
2E
Iw
LcrT2
6.659 105 daN
Lcrz 2 l 100 481
Ncrz π2
EIz
Lcrz2
π2
2.1 106
3.946 103
4812
3.535 105 daN
β 1zo
2
io 1
3.52
79.017 0.845
NcrFT
Ncrz NcrT 2 β
1 14 β NcrT Ncrz NcrT Ncrz 2
3.112 105 daN
NcrFT NcrT 1
λT. Afy 10
NcrFT 86
235 10
3.112 105
0.806
ϕT 0.5 1 α λT. 0.2 λT.2
0.964 0.964
ϕT1
ϕT ϕT λT.2
1
0.964 0.964 0.8062
0.656
NbRd χmed Afy 10
γM0 0.627 86
235 101
1.267 105
NTS NbRd 9.359 104 1.267 10
5 0
Solidarizarea barelor:
l1 mai mic decat 15imin1 bare comprimate
imin1 min iy1 iz1 15 68.55
rezulta imin1 60 cm
Diagonala
ND 51651.8 daN NEd ND 5.165 104
l 2.841 m
Lcy 0.9 l 2.557 cm
Lcz l 2.841 cm
predimensionarea :
NEd NbRd χ A fyd
χ 0.8
Anec
NEd
χ fyd51651.8
0.8 2350 27.474 A1
Anec
2
27.474
2 13.737
Propunem LPN 70x50x6
A1 6.89 ez 2.23 A 2 A1 13.78
Iy1 14.2 ey 1.25 Iy Iy1 2 28.4
iy1 1.43 iy iy1 1.43
Iz1 33.4
izi 2.20 Iz 2 Iz1 A1 ez
tg 101
2
2
189.172
t 0.6iz
Iz
A3.705 cmb 12 2 1.5 25.5
hc 8
verificarea sectiunii propuse
λ1 93.9α 0.46
λy
Lcy 100
iy
2.5569 1001.43
178.804ε 1
λz
Lcz 100
iz
2.841 1003.7051322817092123
76.677 λmax max λy λz 178.804
λ.
λmax
λ1
178.804
93.9 1.904
ϕ 0.5 1 α λ. 0.2 λ.2
0.5 1 0.46 1.904 0.2( ) 1.904
2 2.705
χ1
ϕ ϕ2
λ.2
1
2.705 2.7052
1.9042
0.216
NbRd χ Afy 10
γM0 0.216 13.78
235 101
7 103
NEd NbRd 5.165 104 7 10
3 1
propunem
χmed
χo χ 2
0.8 0.2162
0.508
Anec
NEd
χmed fyd5.165 10
4
0.508 2.35 103
43.26 cm2
A1
Anec
221.63 cm
2
Propunem LPN 150x75x12
A1 25.7 ez1 5.4 A 2 A1 51.4
Iy1 588 ey 1.69 Iy Iy1 588
iy1 4.78 iy iy1 4.78
Iz1 99.6
iz1 1.97 Iz 2 Iz1 A1 ez1
tg 101
2
2
2.143 103
t 0.8
b 21.5
hc 5iz
Iz
A6.457
cmzo eyt
2 1.69
0.8
2 1.29
It At2
3 51.4
0.82
3 10.965 cm
4
moment de inertie la rasucire libera
Iw
b3
t3 4 hc
3 t3
144
21.53
0.83 4 5
3 0.83
144 37.114 cm
4
moment de inertie la rasucire impiedicata
io zo2
Iy Iz A
1.292 588 2.143 10
351.4
54.802
raza polara fata de centrul de forfecare
Verificarea sectiunii propuse la flambaj prin incovoiere-rasucire
G 8.1 105 daN/cm2
E 2.1 106 daN/cm2
LcrT l 100 284.1 m
NcrT1
ioG It π
2E
Iw
LcrT2
1
54.8028.1 10
5 10.965 π2
2.1 106
37.114
284.12
1.622 105
Lcrz 3 l 100 852.3
Ncrz π2
EIz
Lcrz2
π2
2.1 106
2.143 103
852.32
6.115 104 daN
β 1zo
2
io 1
1.292
54.802 0.97
NcrFT
Ncrz NcrT 2 β
1 14 β NcrT Ncrz NcrT Ncrz 2
6.115 104 1.622 10
52 0.97
1 14 0.97 1.622 10
5 6.115 104
1.622 105 6.115 10
4 2
6.008 104
NcrFT NcrT 1
λT. Afy 10
NcrFT 1.418
ϕT 0.5 1 α λT. 0.2 λT.2
1.785 1.785
ϕT1
ϕT ϕT2
λT.2
1
1.785 1.7852
1.4182
0.348
NbRd χmed Afy 10
γM0 0.508 51.4
235 101
6.137 104
NEd NbRd 5.165 104 6.137 10
4 0
imind.comprimate min iy1 iz1 15 29.55
imind.comprimate 25 cm
imind.intinse min iy1 iz1 40 78.8
imind.intinse 70 cm
montan
NM 13789.6 daN NEd NM 1.379 104
l 2.675 m
Lcy 0.9 l 2.407 m
Lcz l 2.675 m
predimensionarea :
NEd NbRd χ A fyd
χ 0.8
Anec
NEd
χ fyd13789.6
0.8 2350 7.335 A1
Anec
2
7.335
2 3.667
Propunem LPN 75x50x6
A1 7.19 ez 1.21 A 2 A1 14.38
Iy1 40.5 ey 2.44 Iy Iy1 2 81
iy1 2.37 iy iy1 2.37
Iz1 14.4
iz1 1.42 Iz 2 Iz1 A1 ez
tg 101
2
2
84.042
t 0.6iz
Iz
A2.418b 16.5 16.5 cm
hc 5zo ey
t
2 2.44
0.6
2 2.14 cm
verificarea sectiunii propuse
λ1 93.9α 0.46
λy
Lcy 100
iy
2.407 1002.37
101.582ε 1
λmax max λy λz 101.582λz
Lcz 100
iz
2.675 1002.418
110.651
λ.
λmax
λ1
101.582
93.9 1.082
ϕ 0.5 1 α λ. 0.2 λ.2
0.5 1 0.46 1.082 0.2( ) 1.082
2 1.288
χ1
ϕ ϕ2
λ.2
1
1.288 1.2882
1.0822
0.503
NbRd χ Afy 10
γM0 0.503 14.38
235 101
1.701 104
NEd NbRd 1.379 104 1.701 10
4 0
It At2
3 14.38
0.62
3 1.726 cm
4
moment de inertie la rasucire libera
Iw
b3
t3 4 hc
3 t3
144
16.53
0.63 4 5
3 0.63
144 7.488 cm
4
moment de inertie la rasucire impiedicata
io zo2
Iy Iz A
2.142 81 84.042
14.38 16.057
raza polara fata de centrul de forfecare
Verificarea sectiunii propuse la flambaj prin incovoiere-rasucire
G 8.1 105 daN/cm2
E 2.1 106 daN/cm2
LcrT l 100 267.5 m
NcrT1
ioG It π
2E
Iw
LcrT2
1
16.0578.1 10
5 1.726 π2
2.1 106
7.488
267.52
8.718 104
Lcrz l 100 267.5
Ncrz π2
EIz
Lcrz2
π2
2.1 106
84.042
267.52
2.434 104 daN
β 1zo
2
io 1
2.142
16.057 0.715
NcrFT
Ncrz NcrT 2 β
1 14 β NcrT Ncrz NcrT Ncrz 2
2.434 104 8.718 10
42 0.715
1 14 0.715 8.718 10
4 2.434 104
8.718 104 2.434 10
4 2
2.218 104
NcrFT NcrT 1
λT. Afy 10
NcrFT 1.234
ϕT 0.5 1 α λT. 0.2 λT.2
1.5 1.5
χT1
ϕT ϕT2
λT.2
1
1.5 1.52
1.2342
0.425
NbRd χ Afy 10
γM0 0.503 14.38
235 101
1.701 104
NEd NbRd 1.379 104 1.701 10
4 0
imind.comprimate min iy1 iz1 15 21.3
imind.comprimate 20 cm
imind.intinse min iy1 iz1 40 56.8
imind.intinse 50 cm
Dimensionarea barelor intinse:Talpa inferioara:
NTI 84470 l 6
Lcy l 6 6 m
Lcz l 6 6 m
-barele comprimate cedeaza datorita pierderii stabilitatii flambaj prin incovoiere (Euler) flambaj prin incovoiere-rasucire-predimensionarea:flambaj datorita compresiunii:
fy 235
NTI NbRd χo Afy
γM0
γM0 1''
fyd
fy 10
γM0
235 101
2.35 103 daN/mm2
impunem χo 0.8
Anec
NTI
fyd χo84470
2350 0.8 44.931 A1.
Anec
2
44.931
2 22.465 cm
2
Propunem LPN 100x75x8
A1 25.7 A 2 A1 51.4ey1 5.4Iy1 588 ez1 3.10 Iy Iy1 2 1.176 10
3
iy1 4.78 iy iy1 4.78
Iz1 99.6
izi 1.97 Iz 2 Iz1 A1 ez1
tg 101
2
2
961.077
iz
Iz
A4.324
verificarea sectiunii propuse
λ1 93.9α 0.46
λy
Lcy 100
iy
6 1004.78
125.523ε 1
λz
Lcz 100
iz
6 1004.324116832524644
138.757 se verfica
Diagonale:
ND 68076.4 l 3.448
Lcy l 3.448 3.448 m
Lcz l 3.448 3.448 m
-barele comprimate cedeaza datorita pierderii stabilitatii flambaj prin incovoiere (Euler) flambaj prin incovoiere-rasucire-predimensionarea:flambaj datorita compresiunii:
fy 235ND NbRd χo A
fy
γM0
γM0 1
fyd
fy 10
γM0
235 101
2.35 103 daN/mm2
impunem χo 0.8
Anec
ND
fyd χo68076.4
2350 0.8 36.211 A1.
Anec
2
36.211
2 18.105 cm
2
A1 19.1LPN 150x75x9 ey1 4.88
ez1 1.42
Montanti:
NM 8663 l 3.448
Lcy l 3.448 3.448 m
Lcz l 3.448 3.448 m
-barele comprimate cedeaza datorita pierderii stabilitatii flambaj prin incovoiere (Euler) flambaj prin incovoiere-rasucire-predimensionarea:flambaj datorita compresiunii:
fy 235NM NbRd χo A
fy
γM0
γM0 1
fyd
fy 10
γM0
235 101
2.35 103 daN/mm2
impunem χo 0.8
Anec
NM
fyd χo8663
2350 0.8 4.608 A1.
Anec
2
4.608
2 2.304 cm
2
A 6.89 cm2
LPN 70x50x6
etapa 8:Alcatuirea nodurilor:
Calculul si prinderea diagonalelor de guseuNodul 1
D 51651.8 daN N1 D
N1 N2 D N2 D
N1 e N2 hc e
Nodul 1
LPN 150x75x9 hc 7.5 cm fuw.Rd 3600 daN/cm2
βw 0.8tg 1.5 cm ey 5.4 cm
tc 1.2 cm
a1 max 0.7 tg 0.8 tc 1.05 rezulta a 0.4 cm
l1.c Ceil N1
hc ey hc
2 afuw.Rd
3
1
Ceil 5.165 104
7.5 5.47.5
2 0.43.6 10
3
3
1
9 mm
l1 Ceil l1.c 2 a 1 Ceil 9 2 0.4 1( ) 10
l2.c Ceil N2
ey hc
2 afuw.Rd
3
1
Ceil 51651.8
5.4
7.5
2 0.43600
3
1
23
l2 Ceil l2.c 2 a 1 Ceil 23 2 0.4 1( ) 24
Nodul 2
M 13789.6 daN
N1 N2 M
N1 e N2 hc e
LPN 75x50x6hc 5 cm fuw.Rd 3600 daN/cm2
βw 0.8tg 1.5 cm ey 1.25 cmN1 M
hc ey hc
N2 Mey
hc
tc 0.6 cm
a1 max 0.7 tg 0.8 tc 1.05 rezulta a 0.4 cm
l1.c Ceil N1
hc ey hc
2 afuw.Rd
3
1
Ceil 13789.65 1.25
5
5 1.255
2 0.43600
3
1
5 mm
l1 Ceil l1.c 2 a 1 Ceil 5 2 0.4 1( ) 6
l2.c Ceil N2
ey hc
2 afuw.Rd
3
1
Ceil 13789.61.25
5
1.25
5
2 0.43600
3
1
1
l2 Ceil l2.c 10 2 a 1 Ceil 10 2 0.4 1( ) 11 mm
40 mm din conditii constructive
Nodul 3
M 32064.4 daN
N1 N2 M
N1 e N2 hc e
LPN 150x75x12 hc 15 cm fuw.Rd 3600 daN/cm2
βw 0.8tg 1.5 cm ey 5.4 cmN1 M
hc ey hc
N2 Mey
hc
tc 1.2 cm
a1 max 0.7 tg 0.8 tc 1.05 rezulta a 0.4 cm
l1.c Ceil N1
hc ey hc
2 afuw.Rd
3
1
Ceil 32064.415 5.4
15
15 5.415
2 0.43600
3
1
8 mm
l1 Ceil l1.c 10 2 a 1 Ceil 8 10 2 0.4 1( ) 81 mm
l2.c Ceil N2
ey hc
2 afuw.Rd
3
1
Ceil 32064.45.4
15
5.4
15
2 0.43600
3
1
3
l2 Ceil l2.c 10 2 a 1 Ceil 3 10 2 0.4 1( ) 31 mm
40 mm din conditii constructive
Nodul 4
M 13789.6 daN
N1 N2 M
N1 e N2 hc e
LPN 75x50x6 hc 5 cm fuw.Rd 3600 daN/cm2
βw 0.8tg 1.5 cm ey 1.25 cmN1 M
hc ey hc
N2 Mey
hc
tc 0.6 cm
a1 max 0.7 tg 0.8 tc 1.05 rezulta a 0.3 cm
l1.c Ceil N1
hc ey hc
2 afuw.Rd
3
1
Ceil 13789.65 1.25
5
5 1.255
2 0.33600
3
1
7 cm
l1 Ceil l1.c 10 2 a 1 Ceil 7 10 2 0.3 1( ) 71
l2.c Ceil N2
ey hc
2 afuw.Rd
3
10
Ceil 13789.61.25
5
1.25
5
2 0.33600
3
10
10
l2 Ceil l2.c 10 2 a 1 Ceil 10 10 2 0.3 1( ) 101 mm
4 mm din conditii constructive
nodul 5 il dimensionam la fel ca nodul 3,iar nodul 6 la fel ca nodul 2
Efortul rezistent al surubului:
Fb.Rd min Fs.Rd fv.Rd
Fs.Rd efort rezistent la lunecare
nF 1 numarul suprafetei de lunecare
μ 0.5ds 0.89 20 17.8
γM2 1.25fu.b 10000 daN/cm2 pentru clasa 10.9
As π17.8
2
4 248.846 mm
2
Fpc 0.7 100 As 1.742 104 daN
daNFs.Rd nF μ
Fpc
γM2 0.5
1.742 104
1.25 6.968 10
3
Fv.Rd efort rezistent la forfecare in tija
Fv.Rd 0.5 100As
γM2 0.5 100
248.84555409084754
1.25 9.954 10
3 daN
Fb.Rd max Fs.Rd Fv.Rd 9.954 103 daN
numarul de suruburi
nsurub
NTS
2
Fb.Rd
9.359 104
2
9.954 103
4.701
nsurub Ceil
NTS
2
Fb.Rd1
5
Verificarea ariei nete:
LPN 150x75x9NTI Npl.Rd A
fy
γMo A 25.7
NTI Nv.Rd Afu Anet β3
γM2
β3 0.6daN/cm2
fu 3600γM2 1.25
Anet 2 25.7 0.5 0.9 2.2( ) 21.74
Npl.Rd Afy
γM0 6.04 10
3
mai mic de NTI
Nv.Rd
fu Anet β3
γM2
3600 21.74 0.61.25
3.757 104
LPN 75x50x6
β3 0.6daN/cm2
fu 3600γM2 1.25
Anet 2 7.19 0.9 2.2( ) 10.42
Nv.Rd
fu Anet β3
γM2
3600 10.42 0.61.25
1.801 104mai mare de NTI
Verificaraea guseuluihg 200
α 36 sinα=0.588 cosα=0.809 ec 40Ved 51651.8 0.588 13789.6 4.416 10
4 do 2.2daN tg 1.5Ned 51651.8 0.809 8.663 4.179 10
4
Med Ned 6 2.508 105 daNcm
eo
hg
2ec 60
Anet 1.5 20 2.2( ) 26.7
Wnet
tg hg 0.1 do 2
6118.815
σNed
Anet
Med
Wnet 3.676 10
3
Dimensionare si verificarea stalpului
Eforturile sunt luate de pe infasuartoarea minmax din Axis:
Nxmax 54702 daN
Mmax 1319.2 daNcm
Vmax 119.9 daN
Lungimi de flambaj
Ls 8 m
Lcr.y 0.85 Ls 6.8 m
Lcr.z Ls 8
Predimensionare sectiunii
Wpl.y
Mmax
fy
Wpl.y
Mmax
fy 105
1319.2
235 105
5.614 105 m
3
metoda razelor de giratie: iy αy h αyIz αz b αz
impunem : αy 0.45αz 0.25λo 90
λy
Lcr.y
iy
6.8
αy 3 5.037 h Ceil
Lcr.y
αy λo0.001
0.168 m
b CeilLcr.z
αz λo0.001
0.356 mλz
Lcr.z
iz
8
4.324 1.85
propunem
HEA 600:
Wpl.y 5350 cm3
Ap 399 cm2
stabilitate generala
λo. 0.96 α 0.34 λo rezulta
ϕo 0.5 1 α λo. 0.2 λo.2
0.5 1 0.34 0.96 0.2( ) 0.962 1.09
χo1
ϕo ϕo2
λo.2
0.623
ky 1.8 valoare maxima
cmy 0.6
χLT 0.95 impunem
Nxmax
χo Ap 102
1.8 cmyMmax
χLT Wpl.y 102
2.205 104
Verificarae sectiunii propuse:
verificare de rezistenta
Npl.Rd Ap 102 fy 10
5 399 102 235 10
5 9.377 107 daN
Nxmax
Npl.Rd1
5.47 104
9.377 107
1 1
Vpl.Rd Ap 102 fy
105
3 399 10
2 23510
5
3 5.414 10
7
Vmax
Vpl.Rd1
119.9
5.414 107
1 1
Mpl.Rd Wpl.y 106 fy 10
5 5350 106 235 10
5 1.257 105
Mmax
Mpl.Rd1
1.319 103
1.257 105
1 1
verificarea influentei fortei taietoare si axiale asupra reducerii momentului plastic rezistent
Ned 0.25 Npl.Rd 4.179 104 0.25 9.377 10
7 1 daN
Aw 0.013 0.6
Ned 0.5 Aw fy 105 4.179 10
4 0.5 0.013 0.6 235 105 1
iy αy h 0.076Verificarea de stabilitate
iz αz b 0.089λy
Lcr.y
iy
6.8
0.0756 89.947
λy.
λy
λ10.958 nu apare flambaj
χy 1
χz 0.45λz
Lcr.z
iz
8
0.089 89.888
χLt 1
λz.
λz
λ10.957 nu apare flambaj
Nb.y.Rd χy fy 105 Ap 10
4 9.377 105 daN
Nb.z.Rd χz Ap 104 fy 10
5 4.219 105 daN
Mb.y.Rd χLT Wpl.y 106 fy 10
5 1.194 105 daNcm
Ved 0.5 Vpl.Rd 4.416 104 0.5 5.414 10
7 1
coeficienti de intereactiune
ny
Nxmax
Nb.y.Rd
54702
937650 0.058
nz
Nxmax
Nb.z.Rd
54702
421942.5 0.13
Ky 1 0.8 ny 1.047 Ky 1
Kzy 1 0.1 λz.nz
0.6 0.25 1 0.1 0.957
0.13
0.6 0.25 0.965
q 1 λy. 0.2 ny 1 0.958 0.2( ) 0.058 1.044
w 1 0.8 ny 1 0.8 0.058 1.047
Kzy q w 1 1
Ned
Nb.y.RdKy cmy
Mmax
Mb.y.Rd
4.179 104
9.377 105
0.61.319 10
3
1.194 105
0.051
Ned
Nb.z.RdKzy cmy
Mmax
Mb.y.Rd
4.179 104
4.219 105
0.965 0.61.319 10
3
1.194 105
0.105
verificarea de rezistenta
Ned
Npl.Rd0.25
4.179 104
9.377 107
0.25 1
Ved
Vpl.Rd0.5
4.416 104
5.414 107
0.5 1
Mmax
Mpl.Rd1
1.319 103
1.257 105
1 1
verificarea de stabilitate
Ned
Nb.y.RdKy cmy
Mmax
Mb.y.Rd 1
4.179 104
9.377 105
0.61.319 10
3
1.194 105
1 1
Ned
Nb.z.RdKzy cmy
Mmax
Mb.y.Rd 1
4.179 104
4.219 105
0.965 0.61.319 10
3
1.194 105
1 1
Nb.y.Rd χy fy 105 Ap 10
4 9.377 105 daN
Nb.z.Rd χz Ap 104 fy 10
5 4.219 105 daN
Mb.y.Rd χLT Wpl.y 106 fy 10
5 1.194 105 daNcm
ny
Nxmax
Nb.y.Rd
54702
937650 0.058
nz
Nxmax
Nb.z.Rd
54702
421942.5 0.13
Ned
Nb.y.RdKy cmy
Mmax
Mb.y.Rd
4.179 104
9.377 105
0.61.319 10
3
1.194 105
0.051
Ned
Nb.z.RdKzy cmy
Mmax
Mb.y.Rd
4.179 104
4.219 105
0.965 0.61.319 10
3
1.194 105
0.105
Baza stalpului:
eforturile de calcul in zona comprimata si zona intinsa a capitelului
h 60 tf 2.5
Fc.Ed
Ned
e
Med
h tf
4.179 104
24
2.508 105
60 2.5 6.103 10
3 daN
Ft.Ed
Ned
e
Med
h tf
2.62 103 daN
rezistenta surubuluifub 5000 daNcm2
se propun 2 suruburi in zona intinsa de clasa 5.6γM2 1.25 nb 8
Ftb.Rd 0.9 As 102
fub
γM2 0.9 248.846 10
25 10
31.25
8.958 103
Ft.Ed nb Ftb.Rd 2.62 103 8 8.958 10
3 1
rezulta dnec 0.89 cm
M24 d 28 mmVom adopta do 30 mm
cu aceste date stabilim dimensiunile placii
b 8 do 2 3.5 do 450 mm
l h 10 4 3.5 do 1.02 103 mm
tp 20 mm
Verificare baza stalp la eforturi axiale maxime
Nmax.Ed Nj.rd Aeff fjd fyd 2350fjd 112
c tp
fyd
3 fjd 35.2 20
2350
3 112 1
rezulta c tp
fyd
3 fjd
0.1 5.289 c 5 cm
leff 2 c tf 2 5 2.5 12.5 cm
Leff 2 c b 0.1 2 5 450 0.1 55 cm
Aeff 2 leff Leff 2 c tw h 2 c 2 tf 2.077 103 cm
2
Nj.Rd Aeff fjd 2077 112 2.326 105 daN
Nxmax Nj.Rd 54702 232624 1
Moment incovoietor
eMed
Ned
2.508 105
4.179 104
6
e 400 cmL 100
6500
Fc.l.Rd efort de rezistenta al placii la compresiune
Fc.r.Rd efrot de rezistenta al placii la intindere
Mc.Rd bl2
6 fyd 450
10202
6 2350 7.803 10
7 daNcm
Fc.fc.Rd
Mc.Rd
l tf78027650
1020 2.5 7.669 10
4 daNcm
Fc.pl.Rd fjd Leff leff 112 55 12.5 7.7 104 daNcm
Fc.l.Rd min Fc.pl.Rd Fc.fc.Rd 7.669 104
daNcm
Fc.r.Rd min Fc.pl.Rd Fc.fc.Rd 7.669 104
zona intinsa + zona comprimata
z h tf 60 2.5 57.5 cm
zc.l 0.5 z 28.75cmzc.r 0.5 z 28.75
Mj.Rd min Fc.l.Rdz
zc.r
e1
Fc.r.Rdz
zc.l
e1
1.163 106 daNcm
nx 10.5Fc.fc.Rd
Mc.Rd
h tf78027650
60 2.5 1.357 10
6
ex eFj.Rd leff Leff fjd 12.5 55 112 7.7 104 daN
Mpl.Rd 1tp
2
4 fyd
202
42350 2.35 10
5 daNcm
b1 4 nx 1.25 e 49.5
b2 e 2 nx 0.625 ex 84.75
b3 0.5 b 225
b4 0.5 w 2 nx 0.625 ex 14.74 cm
b5 4 π nx 131.947b6 2 π nx 4 e 89.973b7 2 π nx 2 w 68.067
beff min b1 b2 b3 b4 b5 b6 b7 14.74
F1.2.pl.Rd 2 fydbeff
nx 2 2.35 10
314.74
10.5 6.598 10
3 daN
Forta taietoarecf.d 0.2 coeficient de frecare pentru mortar de nisip si ciment
fyd 3000 daN/cm
Ft.Rd rezultanta la frecare dintre placa si mortar
αb 0.0003 fyd 0.9
Vmax.Ed Ff.Rd nb Fvb.Rd
Ff.Rd cf.d Ned 8.359 103 daN
Fvb.Rd αb
fub
γM2 0.9
5 103
1.25 3.6 10
3 daN
Vmax.Ed Ff.Rd nb Fvb.Rd 3.716 104 daN