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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−:=
cpe.45F cpe.1F cpe.1F cpe.10F−( ) logAF
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:=
cpe.30F cpe.1F cpe.1F cpe.10F−( ) logAF
m2
⋅− 0.7=:=
α45 45deg:= cpe.1F 0.7:= cpe.10F 0.7:=
cpe.45F cpe.1F cpe.1F cpe.10F−( ) logAF
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:=
cpe.45G cpe.1G cpe.1G cpe.10G−( ) logAG
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:=
cpe.30G cpe.1G cpe.1G cpe.10G−( ) logAG
m2
⋅− 0.7=:=
α45 45deg:= cpe.1G 0.7:= cpe.10G 0.7:=
cpe.45G cpe.1G cpe.1G cpe.10G−( ) logAG
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:=
cpe.45H cpe.1H cpe.1H cpe.10H−( ) logAH
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:=
cpe.30H cpe.1H cpe.1H cpe.10H−( ) logAH
m2
⋅− 0.4=:=
α45 45deg:= cpe.1H 0.6:= cpe.10H 0.6:=
cpe.45H cpe.1H cpe.1H cpe.10H−( ) logAH
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−:=
cpe.45I cpe.1I cpe.1I cpe.10I−( ) logAI
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:=
cpe.30I cpe.1I cpe.1I cpe.10I−( ) logAI
m2
⋅− 0=:=
α45 45deg:= cpe.1I 0:= cpe.10I 0:=
cpe.45I cpe.1I cpe.1I cpe.10I−( ) logAI
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−:=
cpe.45J cpe.1J cpe.1J cpe.10J−( ) logAJ
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:=
cpe.30J cpe.1J cpe.1J cpe.10J−( ) logAJ
m2
⋅− 0=:=
α45 45deg:= cpe.1I 0:= cpe.10I 0:=
cpe.45J cpe.1J cpe.1J cpe.10J−( ) logAJ
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⋅=:=
Pcy3 Pc3 cos α( )⋅ 0.655kN
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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Pcy4 Pc4 cos α( )⋅ 1.276kN
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⋅⋅=:=
2.1 Calculul la starea limita de rezistenta:
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⋅=:=
3.1 Calculul la starea limita de rezistenta:
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
λ.rel.m < 0.75 rezulta:
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⋅=:=
sageata data de incarcarile de durata scurta (vantul):•
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,
0.975=:= - coeficient de inaltime
tensiunea din incovoiere critica:• σm.crit.z 0.78b
pn 0.8⋅
( )
2
hpn lc⋅⋅ E0.05⋅ 130.198 N
mm2
⋅=:=
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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=:=
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 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
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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⋅=:=
sageata data de incarcarile de durata scurta (vantul):•
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
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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
⋅=:=
5.1 Calculul la starea limita ultima:
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,
0.975=:= - coeficient de inaltime
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=:=
Kcrit 1=- coeficient care ia in considerare fenomenul de instabilitate
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λ.rel.m < 0.75 rezulta:
Kls 1=- coeficient ce ia in considerare efectul sistemului asupra capacitatii portante
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
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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⋅=:=
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- 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
7.1 Calculul la starea limita ultima:
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⋅=:=
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- 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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