Consolidarea Unei Sarpante

8/19/2019 Consolidarea Unei Sarpante

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Reabilitarea sarpantei din lemn

Sa se dimensioneze elementele unei sarpante din lemn, conform Eurocode 5, avand urmatoarele caracteristici:

clasa de calitate a lemnului: II•

clasa de exploatare: 1•

modul de tratare a lemnului : ignifugat•

date geometrice : - deschiderea:•

- Inaltimea:

L1 7.5m:=

Ha 3m:=

A. EVALUAREA INCARCARILOR

1. Evaluarea actiunii zapezii (conform CR1-1-3-2012):

amplasament: Lipova (Arad)•

unghiul acoperisului:• αHa

L1

2

0.8=:= atan α( ) 38.66 deg⋅=

coeficient de forma a acoperisului:• i 0.860deg atan α( )−( )

30deg⋅ 0.569=:=

coeficient de expunere:• Ce 1:= coeficient termic:• Ct 1:=

valoarea caracteristica a incarcarii din zapada pe sol:• S0k

1.5kN

m2⋅:=

factorul de importanta:• γIs 1.15:=

incarcarea din zapada:• sk γIs Ce⋅ Ct⋅ i⋅ S0k ⋅ 0.982kN

m2

⋅=:=

2. Evaluarea actiunii vantului pe sarpanta (conform CR1-1-4-2012):

presiunea dinamica a vantului :• qref 0.4kPa:=

lungimea de rugozitate corespunzator categoriei IV de teren:• z0

1m:=

inaltimea constructiei :• z 0.6m 2 2.8⋅ m+ Ha+ 9.2m=:=

presiunea vantului la inaltimea z:• w e( ) gIW qref ⋅ Ce z( )⋅ Cpe⋅:= gIW

gIW 1:=

w z( ) w e( ):= w

coeficient aerodinamic de presiune:• Cp

factorul topografic:• Ct 1=

pentru zone urbane dens construite (pg. 8):• k rz0 0.233:=


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factorul de varf:• gvarf 3.5:= (valoare recomandata de normativ pg.12)

β 2.122

:=

factor de rugozitatei (pg. 9):• Crz k rz02

lnz

z0

2

⋅ 0.267=:=

intensitatea turbulentei:• Izβ

2.5 lnz

z0

⋅

0.382=:=

factorul de rafala:• Cpq 1 gvarf 2 Iz⋅( )⋅+ 3.675=:=

factor de expunere la inaltimea z deasupra terenului (pg. 12 ):• Cez Crz Cpq⋅ Ct⋅ 0.983=:=

Calculul coeficientilor de presiune/suctiune pentru fiecare zona(acoperis cu doua pante)

T 4.25m:= b 2 T⋅ 8.5m=:= h 0.8m 2 2.8⋅ m+ Ha+ 9.4m=:= e min b 2 h⋅,( ) 8.5m=:=

zona F - negativ:•

bF

e

42.125m=:= hF

e

100.85 m=:= AF bF hF⋅ 1.806m

2=:=

α30 30deg:= cpe.1F 1.5−:= cpe.10F 0.5−:=

cpe.30F cpe.1F cpe.1F cpe.10F−( ) logAF

m2

⋅− 1.243−=:=

α45 45deg:= cpe.1F 0−:= cpe.10F 0−:=


m2

⋅− 0=:=

α38.66 atan α( ) 38.66 deg⋅=:=

cpe.38.66nFatan α( ) α30−( ) cpe.45F cpe.30F−( )⋅

α45 α30−

cpe.30F+ 0.525−=:=

zona F - pozitiv•

α30 30deg:= cpe.1F 0.7:= cpe.10F 0.7:=


m2

⋅− 0.7=:=

α45 45deg:= cpe.1F 0.7:= cpe.10F 0.7:=


m2

⋅− 0.7=:=


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cpe.38.66pF

atan α( ) α30−( ) cpe.45F cpe.30F−( )⋅

α45 α30−

cpe.30F+ 0.7=:=

zona G - negativ:•

bG

b 2e

4

⋅− 4.25m=:= h

G

e

100.85 m=:= A

G b

G h

G⋅ 3.612m

2=:=

α30 30deg:= cpe.1G 1.5−:= cpe.10G 0.5−:=

cpe.30G cpe.1G cpe.1G cpe.10G−( ) logAG

m2

⋅− 0.942−=:=

α45 45deg:= cpe.1G 0:= cpe.10G 0:=


m2

⋅− 0=:=

cpe.38.66nG

atan α( ) α30−( ) cpe.45G cpe.30G−( )⋅

α45 α30−

cpe.30G+ 0.398−=:=

zona G - pozitiv:•

α30 30deg:= cpe.1G 0.7:= cpe.10G 0.7:=


m2

⋅− 0.7=:=

α45 45deg:= cpe.1G 0.7:= cpe.10G 0.7:=


m2

⋅− 0.7=:=

cpe.38.66pG

atan α( ) α30−( ) cpe.45G cpe.30G−( )⋅

α45 α30−

cpe.30G+ 0.7=:=

zona H - negativ:•

bH b 8.5 m=:= hHL1

2

e

10− 2.9m=:= AH bH hH⋅ 24.65m

2=:=

α30 30deg:= cpe.1H 0.2−:= cpe.10H 0.2−:=

cpe.30H cpe.1H cpe.1H cpe.10H−( ) logAH

m2

⋅− 0.2−=:=

α45 45deg:= cpe.1H 0:= cpe.10H 0:=


m2

⋅− 0=:=


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cpe.38.66nH

atan α( ) α30−( ) cpe.45H cpe.30H−( )⋅

α45 α30−

cpe.30H+ 0.085−=:=

zona H - pozitiv•

α30 30deg:= cpe.1H 0.4:= cpe.10H 0.4:=


m2

⋅− 0.4=:=

α45 45deg:= cpe.1H 0.6:= cpe.10H 0.6:=


m2

⋅− 0.6=:=

cpe.38.66pH

atan α( ) α30−( ) cpe.45H cpe.30H−( )⋅

α45 α30−

cpe.30H+ 0.515=:=

zona I - negativ:•

bI b 8.5 m=:= hI

L1

2

e

10− 2.9m=:= AI bI hI⋅ 24.65m

2=:=

α30 30deg:= cpe.1I 0.4−:= cpe.10I 0.4−:=

cpe.30I cpe.1I cpe.1I cpe.10I−( ) logAI

m2

⋅− 0.4−=:=

α45

45deg:= cpe.1I

0.2−:= cpe.10I

0.2−:=


m2

⋅− 0.2−=:=

cpe.38.66nI

atan α( ) α30−( ) cpe.45I cpe.30I−( )⋅

α45 α30−

cpe.30I+ 0.285−=:=

zona I - pozitiv•

α30 30deg:= cpe.1I 0:= cpe.10I 0:=


m2

⋅− 0=:=

α45 45deg:= cpe.1I 0:= cpe.10I 0:=


m2

⋅− 0=:=


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cpe.38.66pI

atan α( ) α30−( ) cpe.45I cpe.30I−( )⋅

α45 α30−

cpe.30I+ 0=:=

zona J - negativ:•

bJ b 8.5 m=:= hJ

e

100.85 m=:= AJ bJ hJ⋅ 7.225m

2=:=

α30 30deg:= cpe.1J 0.5−:= cpe.10J 0.5−:=

cpe.30J cpe.1J cpe.1J cpe.10J−( ) logAJ

m2

⋅− 0.5−=:=

α45 45deg:= cpe.1I 0.3−:= cpe.10I 0.3−:=


m2

⋅− 0.5−=:=

cpe.38.66nJ

atan α( ) α30−( ) cpe.45J cpe.30J−( )⋅

α45 α30−

cpe.30J+ 0.5−=:=

zona J - pozitiv•

α30 30deg:= cpe.1J 0:= cpe.10J 0:=


m2

⋅− 0=:=

α45 45deg:= cpe.1I 0:= cpe.10I 0:=


m2

⋅− 0=:=

cpe.38.66pJ

atan α( ) α30−( ) cpe.45J cpe.30J−( )⋅

α45 α30−

cpe.30J+ 0=:=

wpe.nF qref cpe.38.66nF⋅

0.21−

kPa⋅=:=

wpe.pF qref cpe.38.66pF⋅

0.28 kPa⋅=:=

wpe.nG qref cpe.38.66nF⋅ 0.21− kPa⋅=:= wpe.pG qref cpe.38.66pF⋅ 0.28 kPa⋅=:=

wpe.nH qref cpe.38.66nH⋅ 0.034− kPa⋅=:= wpe.pH qref cpe.38.66pH⋅ 0.206 kPa⋅=:=

wpe.nI qref cpe.38.66nI⋅ 0.114− kPa⋅=:= wpe.pI qref cpe.38.66pI⋅ 0 kPa⋅=:=

wpe.nJ qref cpe.38.66nJ⋅ 0.2− kPa⋅=:= wpe.pJ qref cpe.38.66pJ⋅ 0 kPa⋅=:=

B. CALCULUL ELEMENTELOR SARPANTEI

1. Verificarea sipcilor

distanta interax sipci:• ssipci 0.3m:= nrsipci 3:=(nr. sipcilor / m)


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distanta interax capriori:• sc 0.85m:=

dimensiuni sipci:• bs 38 mm⋅:= hs 58 mm⋅:=

invelitoare din tigla:• qinv 0.5kN

m2

⋅:=

densitatea lemnului:• ρmed 4.1kN

m3

⋅:=

Evaluarea incarcarilor:

Permanente:• Gk - greutatea proprie: gs bs hs⋅ ρmed⋅ 0.00904kN

m⋅=:=

- invelitoare: ginv

qinv ssipci⋅

cos α( )0.215

kN

m⋅=:=

Variabile:• Qk - zapada: qzs sk ssipci⋅ cos α( )⋅ 0.205

kN

m⋅=:=

- vantul: qws wpe.pF ssipci⋅ 0.084kN

m⋅=:=

qk 0.75kN

m2

⋅:= - din exploatare: qs qk ssipci⋅ cos α( )⋅ 0.157kN

m⋅=:=

- din om: Qk 1 kN⋅:=

Combinatii de incarcari pentru sipci:

1. 1.35*ΣGk+1.5*zapada +1.5*ψ0.1*vant

2. 1.35*ΣGk+1.5*qs

3. 1.35*ΣGk+1.5*Qk

4. 1.35*ΣGk+1.5*Qk +1.5*0.7*0.7kN/m2

Cazul 1: P1 1.35 gs⋅ 1.35 ginv⋅+ 1.5 qzs⋅+ 0.611kN

m⋅=:=

P1w 1.05 qws⋅ 0.088 kNm

⋅=:= Vantul actioneaza paralel cu directia y!

P1y P1 cos α( )⋅ P1w+ 0.514kN

m⋅=:=

P1z P1 sin α( )⋅ 0.438kN

m⋅=:=

Determinarea momentelor incovoietoare efective My.ef si Mz.ef :

M1y P1z

sc2

8

⋅ 0.04 kN m⋅⋅=:= Myds M1y 0.04 kN m⋅⋅=:=

M1z P1y

sc2

8⋅ 0.046 kN m⋅⋅=:= Mzds M1z 0.046 kN m⋅⋅=:=


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Calculul la SLU:

1.1 Calculul la starea limita de rezistenta:

clasa de calitate: C22•

f mk 22N

mm2

⋅:=rezistenta caracteristica la incovoiere:•

f c0k 20N

mm2

⋅:=rezistenta caracteristica la compresiune paralela cu fibrele:•

modulul de elasticitate mediu:• E0med 7kN

mm2

⋅:=

modulul de elasticitate conventional:• E0.05 6.7kN

mm2

⋅:=

rezistenta de calcul:•

γM 1.3:= pentru lemn masiv cf. EC5-1-1 pag.25

Kmod.z

0.6 gs ginv+( )⋅ 0.8 qzs⋅+

gs ginv+ qzs+0.696=:= 0.6 - pentru incarcare permanenta

0.8 - pentru incarcare de durata medie: zapada

f mzd Kmod.z

f mk

γM

⋅ 11.771N

mm2

⋅=:=

Kmod.y

0.6 gs ginv+( )⋅ 0.9 qws⋅+

gs ginv+ qws+0.682=:= 0.6 - pentru incarcare permanenta

0.9 - pentru incarcare de scurta durata: vantul

f myd Kmod.y

f mk

γM

⋅ 11.537N

mm2

⋅=:=

k m 0.7:=- factor ce tine seama de redistribuirea tensiunilor si eventualele neomogenitati

calculul tensiunilor:•

Wy

bs hs2

⋅

621305.333 mm

3⋅=:= σm.y.d

Myds

Wy

1.857N

mm2

⋅=:=

Wz

bs2

hs⋅

613958.667 mm

3⋅=:= σm.z.d

Mzds

Wz

3.323N

mm2

⋅=:=

relatiile de verificare:•


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σm.y.d

f myd

k m

σm.z.d

f mzd

⋅+ 0.359=


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uQk1.inst.y5

384

qws sc4

⋅

E0.05 Iz⋅⋅ 0.321 mm⋅=:= uQk1.inst.z

5

384

qzs sc4

⋅

E0.05 Iy⋅⋅ 0.337 mm⋅=:=

ψ0 0.7:= ψ2.2 0:= uQvant.fin.y uQk1.inst.y ψ0 ψ2.2 Kdefv⋅+( )⋅ 0.225 mm⋅=:=

uQvant.fin.z uQk1.inst.z ψ0 ψ2.2 Kdefv⋅+( )⋅ 0.236 mm⋅=:=

ufin uG.fin.y uQzapada.fin.y+ uQvant.fin.y+( )2

uG.fin.z uQzapada.fin.z+ uQvant.fin.z+( )2

+ 2.196 mm⋅=:=

verificare_sageata_sipci "ok" ufin

sc

150


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Lungimea capriorilor:•

cel mai mare deschidere: d 2.87 m⋅:=

Combinatii de incarcari pentru capriori:

1. 1.35*ΣGk+1.5*zapada +1.5*0.7*vant

2. 1.35*ΣGk+1.5*qs

3. 1.35*ΣGk+1.5*Qk

4. Σ (1.35) * perm+(1.5) * Qk +(1.5) * 0.7kN/m2 - cea mai defavorabila ipoteza

- aceasta ipoteza este exceptie de la ipoteza nr. 1; aici incarcarea data de zapada si forta

concentrata Qk nu poate fii mai mare de 0.7kN/m2 (SR EN 1991-1-1, N.A. - T6.10 Nota 5)

Cazul 1: Pc1 1.35 Pc.perm⋅ 1.5 qzc⋅+ 1.812kN

m⋅=:=

Pcw1 1.5 0.7⋅ qwc⋅ 0.174kN

m⋅=:= Vantul actioneaza paralel cu directia y!

Pcy1 Pc1 cos α( )⋅ Pcw1+ 1.436kN

m⋅=:=

Mcz1 Pcy1d

2

8⋅ 1.479 kN m⋅⋅=:=

Cazul 2: Pc2 1.35 Pc.perm⋅ 1.5 qsc⋅+ 1.606kN

m⋅=:=

Pcy2 Pc2 cos α( )⋅ 1.119kN

m⋅=:=

Mcz2 Pcy2d

2

8⋅ 1.152 kN m⋅⋅=:=

Cazul 3: Pc3 1.35 Pc.perm⋅ 0.94kN

m⋅=:=

P

c3Q

1.5 Q

k

⋅ 1.5 kN⋅=:=

PcyQ3 Pc3Q cos α( )⋅ 1.045 kN⋅=:=


m⋅=:=

Mcz3 PcyQ3d

4⋅ Pcy3

d2

8⋅+ 1.424 kN m⋅⋅=:=

Cazul 4: Pc4 1.35 Pc.perm⋅ sc 1.5⋅ 0.7⋅kN

m2

⋅+ 1.832kN

m⋅=:=

Pc4Q 1.5 Qk ⋅ 1.5 kN⋅=:=

PcyQ4 Pc4Q cos α( )⋅ 1.045 kN⋅=:=


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m⋅=:=

Mcz4 PcyQ4d

4⋅ Pcy4

d2

8⋅+ 2.064 kN m⋅⋅=:=

Eforturile la care se va dimensiona sectiunea::

Mzdc max Mcz1 Mcz2, Mcz3, Mcz4,( ) 2.064 kN m⋅⋅=:=


Wc

bc 7.5cm( )2

⋅

675 cm

3⋅=:=

σmd.c

Mzdc

Wc

27.521N

mm2

⋅=:=

Kmod0.6 Pc.perm⋅ 0.8 qzc⋅+

Pc.perm qzc+0.691=:=

Kh min150 mm⋅

hc 0.75⋅

0.2

1.3,

1.149=:= - coeficient de inaltime

tensiunea din incovoiere critica:• σm.crit.c 0.75bc

2

hc 0.75⋅ d⋅ E0.05⋅ 149.408

N

mm2

⋅=:=

zveltetea relativa:• mtr 0.88:=

λ rel.m.c

f mk mtr⋅

σm.crit.c

0.36=:=

Kcrit 1:=- coeficient care ia in considerare fenomenul de instabilitate

λ.rel.m < 0.75 rezulta:

Kls 1:=- coeficient ce ia in considerare efectul sistemului asupra capacitatii portante

γM 1.3= f md Kmod Kh⋅ Kcrit⋅ Kls⋅

f mk

γM⋅ 13.433

N

mm2⋅=:=

verificare_capriori "ok" σmd.c f md


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ug.inst5

384

Pc.perm cos α( )⋅ d4

⋅

E0.05 Ic⋅⋅ 22.733 mm⋅=:=

ug.fin ug.inst 1 Kdefp+( )⋅ 34.1 mm⋅=:=

sageata data de incarcarile de durata medie(zapada):•

uq.inst5

384

qzc d4

⋅

E0.05 Ic⋅⋅ 27.254 mm⋅=:=

ψ2.1 0.4:=

u

qz.fin

u

q.inst

1 ψ2.1

K

defz

⋅+

( )⋅ 29.979 mm⋅=:=

sageata data de incarcarile de durata scurta (vantul):•

uq.inst5

384

qwc d4

⋅

E0.05 Ic⋅⋅ 7.774 mm⋅=:=

ψ0 0.7:= ψ2.2 0:=

uqv.fin uq.inst ψ0 ψ2.2 Kdefv⋅+( )⋅ 5.442 mm⋅=:=

ufin_c ug.fin uqz.fin+ uqv.fin+ 69.52 mm⋅=:= uadm_cd

20014.35 mm⋅=:=

verificare_sageata_capriori "ok" ufin_c uadm_c


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modulul de elasticitate conventional:• E0.05.2 8.7kN

mm2

⋅:=

ne

E0.05.2

E0.05

1.299=:=

dimensinea capriorilor consolidati:• bc2 bc 8 cm⋅=:= hc2 hc 5 cm⋅ ne⋅+ 16.493 cm⋅=:=

Ac2 bc2 hc2⋅ 131.94 cm2⋅=:=


Wc_2

bc2 hc22

⋅

6362.672 cm

3⋅=:=

σmd.c_2

Mzdc

Wc_2

5.691N

mm2

⋅=:=

Kmod_2 Kmod 0.691=:=

Kh 1.149= - coeficient de inaltime

tensiunea din incovoiere critica:• σm.crit.c 149.408N

mm2

⋅=

zveltetea relativa:• mtr 0.88:=- factor de transformare a momentului real in moment echivalent

λ rel.m.c

f mk 0.6154⋅ f mk.2 0.3846⋅+( ) mtr⋅

σm.crit.c

0.399=:=

Kcrit 1=- coeficient care ia in considerare fenomenul de instabilitate


Kls 1=- coeficient ce ia in considerare efectul sistemului asupra capacitatii portante

γM 1.3= f md_2 Kmod_2 Kh⋅ Kcrit⋅ Kls⋅f mk 0.6154⋅ f mk.2 0.3846⋅+( )

γM

⋅ 16.486N

mm2

⋅=:=

verificare_capriori_2 "ok" σmd.c_2 f md_2


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Sectiunea consolidata:

bc 8cm:= hc 7.5cm:= bc2 8cm:= hc2 5cm:=

Ic_2

bc hc3

⋅

12b

c h

c⋅ 2.5 cm⋅( )

2⋅+ n

e b

c2⋅ h

c2⋅ 3.75 cm⋅( )

2⋅+ n

e

bc2 hc23

⋅

12⋅+ 1.495 10

3× cm

4⋅=:=

ug.inst_25

384

Pc.perm cos α( )⋅ d4

⋅

E0.05 0.5⋅ E0.05.2 0.5⋅+( ) Ic_2⋅⋅ 3.722 mm⋅=:=

ug.fin_2 ug.inst_2 1 Kdefp+( )⋅ 5.582 mm⋅=:=

sageata data de incarcarile de durata medie(zapada):•

uq.inst_25

384

qzc d4

⋅

E0.05 0.5⋅ E0.05.2 0.5⋅+( ) Ic_2⋅⋅ 4.462 mm⋅=:=

ψ2.1 0.4:=

uqz.fin_2 uq.inst_2 1 ψ2.1 Kdefz⋅+( )⋅ 4.908 mm⋅=:=


uq.inst_25

384

qwc d4

⋅

E0.05 0.5⋅ E0.05.2 0.5⋅+( ) Ic_2⋅⋅ 1.273 mm⋅=:=

ψ0 0.7:= ψ2.2 0:=

uqv.fin_2 uq.inst_2 ψ0 ψ2.2 Kdefv⋅+( )⋅ 0.891 mm⋅=:=

ufin_c2 ug.fin_2 uqz.fin_2+ uqv.fin_2+ 11.381 mm⋅=:= uadm_cd

20014.35 mm⋅=:=

verificare_sageata_capriori_2 "ok" ufin_c2 uadm_c


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Permanente:• Gk - greutatea proprie: gpn bpn hpn⋅ ρmed⋅ 0.105kN

m⋅=:=

- invelitoare: ginv.pn

qinv d⋅ sc⋅

cos α( )1.751 kN⋅=:=

- din sipci: gpn.sipci 3d

cos α( )⋅ bs⋅ hs⋅ ρmed⋅ 0.112 kN⋅=:=

- din capriori: gcpnd

cos α( )bc hc⋅( )⋅ ρmed⋅ 0.101 kN⋅=:=

TOTAL: Pppn ginv.pn gpn.sipci+ gcpn+ 1.964 kN⋅=:=

Variabile :• Qk - zapada: qzpn sk sc⋅ d⋅ cos α( ) 1.668 kN⋅=:=

- vantul: qwpn wpe.pF sc⋅ d⋅ cos α( ) 0.476 kN⋅=:=

- din exploatare: qspn qk sc⋅ d⋅ cos α( ) 1.275 kN⋅=:=

- din om: Qk 1 kN⋅=

Combinatii de incarcari pentru pane:

1. 1.35*ΣGk+1.5*zapada +1.5*0.7*vant - cea mai defavorabila ipoteza•

2. 1.35*ΣGk+1.5*qk•

3. 1.35*ΣGk+1.5*Qk•

4. 1.35*ΣGk+1.5*Qk +1.5*0.7kN/m2•

Cazul 1: Pgr.proprie 1.35 gpn⋅ 0.141kN

m⋅=:=

P1perm_z 1.35 Pppn⋅ 1.5 qzpn⋅+ 5.154 kN⋅=:=

P1ywpn 1.5 0.7⋅ qwpn⋅ sin α( )⋅ 0.358 kN⋅=:=

Mpz1

Pgr.proprie

lc

2⋅

8

4 P1perm_z⋅

lc

lc2

⋅

8+ 8.965 kN m⋅⋅=:=

Mpy1

4 P1ywpn⋅

lc

lc2

⋅

80.609 kN m⋅⋅=:=

Cazul 2: Pgr.proprie 0.141kN

m⋅=

P2perm_s 1.35 Pppn⋅ 1.5 qspn⋅+ 4.563 kN⋅=:=


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Mpz2

Pgr.proprie lc2

⋅

8

4 P2perm_s⋅

lc

lc2

⋅

8+ 7.961 kN m⋅⋅=:=

Mpy2 0 kN⋅ m:=

Cazul 3: Pgr.proprie 0.141

kN

m⋅=

P3perm 1.35 Pppn⋅ 2.651 kN⋅=:=

Mpz3

Pgr.proprie lc2

⋅

8

4 P3perm⋅

lc

lc2

⋅

8+

1.5Qk lc⋅

4+ 5.986 kN m⋅⋅=:=

Mpy3 0 kN⋅ m:=

Cazul 4: Pgr.proprie 0.141kN

m⋅=

P4perm 1.35 Pppn⋅ 2.651 kN⋅=:=

P4_07 sc 3.84⋅ m⋅ cos α( )⋅ 1.5⋅ 0.7⋅kN

m2

⋅ 2.388 kN⋅=:=

Mpz4Pgr.proprie lc

2

⋅

8

4 P4perm⋅

lc

lc2

⋅

8+ 1.5Qk lc⋅

4+

4 P4_07⋅

lc

lc2

⋅

8+ 10.045 kN m⋅⋅=:=

Mpy4 0 kN⋅ m:=

4.1 Calculul la starea limita ultima:

Mzdp Mpz1 8.965 kN m⋅⋅=:= Wpz

12cm hpn2

⋅

6578 cm

3⋅=:=

Mydp Mpy1 0.609 kN m⋅⋅=:= Wpy

hpn 12cm( )2

⋅

6 408 cm

3

⋅=:=

σmzdp

Mzdp

Wpz

15.511N

mm2

⋅=:= σmydp

Mydp

Wpy

1.494N

mm2

⋅=:=

Kmod

0.6 Pppn⋅ 0.8 qzpn⋅+

Pppn qzpn+0.692=:=

Kh min150 mm⋅

hpn

0.2

1.3,


tensiunea din incovoiere critica:• σm.crit.z 0.78b

pn 0.8⋅

( )

2

hpn lc⋅⋅ E0.05⋅ 130.198 N

mm2

⋅=:=


17/23

zveltetea relativa:• mtr 0.88= - factor de transformare a momentului real in moment echivalent

λ rel.m.pn

f mk mtr⋅

σm.crit.z

0.386=:=




γM 1.3= f mzd Kmod Kh⋅ Kcrit⋅ Kls⋅f mk

γM

⋅ 11.419N

mm2

⋅=:=

σmzdp 15.511N

mm2

⋅= < f mzd 11.419N

mm2

⋅=

verificare_pana "ok" σmzdp f mzd


18/23

uQzinst_y5

384

4 qzpn⋅

lc

lc

4⋅

E0.05 Izp⋅⋅ 10.376 mm⋅=:=

ψ2.1 0.4:=

uQzfin_y uQzinst_y 1 ψ2.1 Kdefz⋅+( )⋅ 11.413 mm⋅=:=

uQzinst_z 0 mm⋅:=

uQzfin_z uQzinst_z 1 ψ2.1 Kdefz⋅+( )⋅ 0 mm⋅=:=


uQvinst_y5

384

4 qwpn⋅

lc

lc

4⋅

E0.05 Izp⋅⋅ 2.96 mm⋅=:=

ψ0 0.7:= ψ2.2 0:=

uQvfin_y uQvinst_y ψ0 ψ2.2 Kdefv⋅+( )⋅ 2.072 mm⋅=:=

uQvinst_z 0 mm⋅:=

uQvfin_z uQvinst_z 1 ψ2.1 Kdefv⋅+( )⋅ 0 mm⋅=:=

umax_p uGfin_y uQzfin_y+ uQvfin_y+( )2

uGfin_z uQzfin_z+ uQvfin_z+( )2

+ 32.633 mm⋅=:=

uadm_p

lc

20017 mm⋅=:=

verificare_sageata_pana "ok" umax_p uadm_p


19/23

modulul de elasticitate conventional:• E0.05.2 7.4kN

mm2

⋅:=

ne

E0.05.2

E0.05

1.104=:=

Consolidarea costa in adaugarea de dulapi din lemn de rasinoase montat pe cele doua fete ale sectiunii panei.

bpn' 50mm:= hpn' 170mm:=

bpn2 12cm 2 50⋅ mm⋅+ 220 mm⋅=:= hpn2 170mm:=

ne 1.104=

Ipny

12 cm⋅ hpn3

⋅

12

2ne

bpn' hpn'3

⋅

12

⋅+ 9434.915 cm

4⋅=:=

Ipnz

hpn 12 cm⋅( )3

⋅

12

2ne

hpn' bpn'3

⋅

12

bpn' hpn'⋅bpn'

2

bpn 0.8⋅

2

+

2

⋅+

⋅+ 16404.915 cm4

⋅=:=


Mzdp 8.965 kN m⋅⋅= Mydp 0.609 kN m⋅⋅=

Wpz_2

I

pnzhpn

2

1.93 103× cm3⋅=:= Wpy_2

I

pny0.8bpn 2bpn'+

2

857.72 cm3⋅=:=

σmzdp_2

Mzdp

Wpz_2

4.645N

mm2

⋅=:= σmydp_2

Mydp

Wpy_2

0.71N

mm2

⋅=:=

Kmod

0.6 Pppn⋅ 0.8 qzpn⋅+

Pppn qzpn+0.692=:=

Kh min150 mm⋅

hpn

0.2

1.3,


tensiunea din incovoiere critica:• σm.crit.z_2 0.78bpn2

2

hpn lc⋅⋅ 0.55E0.05 0.45 E0.05.2⋅+( )⋅ 458.184

N

mm2

⋅=:=

zveltetea relativa:• mtr 0.88= - factor de transformare a momentului real in moment echivalent

λ rel.m.pn_2

0.55f mk 0.45 f mk.2⋅+( ) mtr⋅

σm.crit.z_2

0.21=:=



20/23



γM 1.3= f mzd_2 Kmod Kh⋅ Kcrit⋅ Kls⋅0.55f mk 0.45 f mk.2⋅+

γM

⋅ 11.886N

mm2

⋅=:=

verificare_pana_2 "ok" σmzdp_2 f mzd_2


21/23

ψ0 0.7:= ψ2.2 0:=

uQvfin_y uQvinst_y ψ0 ψ2.2 Kdefv⋅+( )⋅ 0.593 mm⋅=:=

uQvinst_z 0 mm⋅:=

uQvfin_z uQvinst_z 1 ψ2.1 Kdefv⋅+( )⋅ 0 mm⋅=:=

umax_p2 uGfin_y uQzfin_y+ uQvfin_y+( )2

uGfin_z uQzfin_z+ uQvfin_z+( )2

+ 9.334 mm⋅=:=

uadm_p2

lc

20017 mm⋅=:=

verificare_sageata_pana_2 "ok" umax_p2 uadm_p2 0.3 intervine flambajul!

Se calculeaza efortul axial din pop:•

- invelitoare: Gpop.inv

qinv

cos α( )

d

cos α( )⋅ lc⋅ 10.051 kN⋅=:=

- sipci: Gprop_sipci

bs hs⋅ ρmed⋅( )cos α( )

nrsipci

m⋅ 0.039

1

m2

kN⋅=:=

lc 3.4m=Gpop.sipci Gprop_sipci dcos α( )

⋅ lc⋅ 0.545 kN⋅=:=

Gpop.sipci.c 1.35 Gpop.sipci⋅ 0.736 kN⋅=:=


22/23

- capriori: Gprop.capr

bc hc⋅ ρmed⋅( )cos α( )

1

sc

⋅ 0.0421

m2

kN⋅=:=

Gpop.capr Gprop.caprd

cos α( )

⋅ lc⋅ 0.582 kN⋅=:=

- pana: Gpop.pana hpn bpn⋅ ρmed⋅ lc⋅ 0.355 kN⋅=:=

FG Gpop.sipci Gpop.capr+ Gpop.inv+ Gpop.pana+( ) 1.35⋅ 15.571 kN⋅=:=

FQ 1.5sk cos α( )⋅ 2.45⋅ 5⋅ 0.8⋅ m2

⋅ 10.054 kN⋅=:=

σc0d

FG FQ+

Ap

2.373N

mm2

⋅=:= βc 0.2:=

K 0.5 1 βc λ rel 0.3−( )⋅+ λ rel2

+⋅ 0.829=:=

Kc1

K K2

λ rel2

−+

0.851=:= Kmod

0.6 FG⋅ 0.8 FQ⋅+

FG FQ+0.678=:=

f c0d

Kmod f c0k ⋅

γM

10.438N

mm2

⋅=:=

verificare_pop "flambeaza"σc0d

Kc f c0d⋅1>if

"nu flambeaza" otherwise

:=σc0d

Kc f c0d⋅0.267=

verificare_pop "nu flambeaza"=

7. Verificarea clestilor degradati


Dimensiunile sectiunii initiale:• bcl

2.4cm:=

hcl 12cm:=

lcl 0.4m:=

Caracteristici geometrice• Wcl 2bcl 0.8hcl( )

2⋅

6

⋅ 73.728 cm

3⋅=:=

Evaluarea incarcarilor:

Permanente:• Gk - invelitoare: ginvcl

qinv 5⋅ sc d⋅

cos α( )

8.754 kN⋅=:=


23/23

- sipci: gcls

bs hs⋅ ρmed⋅nrs

m⋅ d⋅ t⋅

cos α( )0.475 kN⋅=:=

- capriori gpr.c

bc hc⋅ bc2 hc2⋅+( ) ρmed⋅

cos α( ) sc⋅0.069

kN

m

2⋅=:=

gccld

cos α( )t⋅ gpr.c⋅ 1.212 kN⋅=:=

- pana gpcl bpn2 hpn2⋅ t⋅ ρmed⋅ 0.652 kN⋅=:=

Variabile :• Qk - zapada: qzcl sk t⋅ cos α( )⋅

d

cos α( )⋅ 11.974 kN⋅=:=

Qt.cl qzcl 1.5⋅ 17.96 kN⋅=:=

FG.cl ginvcl gcls+ gccl+ gpcl+ 11.092 kN⋅=:=

Mef

FG.cl lcl⋅

41.109 kN m⋅⋅=:=

σcl

Mef

Wcl

15.045N

mm2

⋅=:=

- rezistenta la incovoiere statica: f md

f mk

γM

16.923N

mm2

⋅=:=

verificare_clesti "ok" σcl

f mk

γM

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