mathcad proiect metal gata

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


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


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


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


Iw

b3

t3 4 hc

3 t3

144

21.53

0.83 4 5

3 0.83

144 37.114 cm

4


io zo2

Iy Iz A

1.292 588 2.143 10

351.4

54.802



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


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


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


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


Iw

b3

t3 4 hc

3 t3

144

16.53

0.63 4 5

3 0.63

144 7.488 cm

4


io zo2

Iy Iz A

2.142 81 84.042

14.38 16.057



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


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


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


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


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


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


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


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


hc ey hc

N2 Mey

hc

tc 1.2 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


Nodul 4

M 13789.6 daN

N1 N2 M

N1 e N2 hc e

LPN 75x50x6 hc 5 cm fuw.Rd 3600 daN/cm2


hc ey hc

N2 Mey

hc

tc 0.6 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


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

mathcad proiect metal gata

Documents