1.mathcad - incarcari climatice

8/19/2019 1.Mathcad - Incarcari Climatice

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UTCN - Facultatea de Constructii Proiect de diplom Evaluare încrcari

EVALUAREA ACTIUNII ZAPEZII

dupa SR EN 1991-1-3

Localitate Blaj

i 0.8:=coeficientul de forma al incarcarii date de zapada

Ce 1.00:=coeficientul de expunere

coeficientul termic =1.00Ct 1.00:=

sk 1.5kN

m2

:= valoarea caracteristica a incarcarii date de zapada pe sol

s

i

C

e

⋅ C

t

⋅ s

k

⋅ 1.2kN

m2

⋅=:=

EVALUAREA ACTIUNII DIN VANT

dupa SR EN 1991-1-4

Observatie !!!In cazul in care calculam actiunea vantului pe directia VE-EV este respectata relatia b


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Caz 1 :

Calculul actiunii vantului pe peretii verticali de la nivelul terenului pana la inaltimea "b"=10.95m

Localitate Blaj

Categoria terenului IV

cdir 1.00:=coeficient de directie =1.00

cseason 1.00:=factor de anotimp =1.00

vb.0 27m

s:= valoarea fundamentala a vitezei de

referinta a vantului (in Anexa Nationala)

viteza de referinta a vantului, definita in functie de

directia vantului si de anotimp la 10m deasupra

unui teren de categoria II

vb cdir cseason⋅ vb.0⋅ 27m

s⋅=:=

co Z( ) 1.00:=factor orografic =1.00

Zmin

10.00m:= inaltimea minima (tabel 4.1 sau Anexa Nationala)

Zmax 200m:=inaltimea maxima

Z 10.95m:= inaltimea de referinta pentru presiunea exterioara

lungimea de rugozitate pt un

teren de categoria II (tabel 4.1(Ro) - Anexa Nationala)Z0.II 0.05m:=

Z0 1.00m:=lungimea de rugozitate pt. categoria IV

factor de teren ce depinde de lungimea

de rugozitate Z.0k r 0.19Z0

Z

0.II

0.07

0.23=:=

cr Z( ) k r lnZ

Z0

⋅

Zmin Z≤ Zmax≤if

k r lnZmin

Z0

⋅

Z Zmin≤if

:=

factor de rugozitate

cr Z( ) 0.56=

vm Z( ) cr Z( ) co Z( )⋅ vb⋅:= viteza medie a vantului la o inaltime Z deasupra terenului

vm Z( ) 15.14m

s⋅=

k 1 1.00:=factor de turbulenta =1.00

σv k r vb⋅ k 1⋅ 6.33m

s⋅=:= abaterea standard a turbulentei

Iv Z( )σv

vm Z( ):= intensitatea turbulentei

Iv Z( ) 0.42=

ρ 1.25 s

2

m4

N:= densitatea aerului =1.25 kg/m^3

6


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qb1

2ρ⋅ vb

2⋅ 0.46

kN

m2

⋅=:= presiunea vitezei de referinta

qp Z( ) 1 7 Iv Z( )+( ) 1

2⋅ ρ⋅ vm Z( )

2⋅:= presiunea dinamica de varf

qp Z( ) 0.56kN

m2

⋅=

ce Z( )qp Z( )

qb

:= --> ce Z( ) 1.23= coeficient de expunere

Incarcarea din vant pe pereti

Directia vantului V-E sau E-V (zona inferioara)

Directiavantului

b 9.8m:=

d 38.4m:=

h b 9.8 m=:=

e min b 2 h⋅,( ) 9.80 m=:=

fig 1.

Lungimea zonelor

Ae

5e dif

d e 5 d⋅>if

:= B4e

5e dif

0 e 5 d⋅>if

:= C d e− e dif

0 e 5 d⋅>if

:=

Z0

k r

A 1.96 m= B 7.84 m= C 28.6 m=

Aria zonelor

AA A h⋅ 19.21 m2

⋅=:= AC C h⋅ 280.28 m2

⋅=:=AE b h⋅ 96.04 m

2⋅=:=

AB B h⋅ 76.83 m2

⋅=:= AD b h⋅ 96.04 m2

⋅=:=

7


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Zona A

cpe10 1.20−:= cpe1 1.40−:=

cpeA cpe1 AA 1m2

if

cpe1 cpe1 cpe10−( ) logAA

m2

⋅− otherwise

:= cpeA 1.2−=

wA qp Z( ) cpeA 0.67− kPa⋅=:=

Zona B

cpe10 0.80−:= cpe1 1.10−:=

cpeB cpe1 AB 1m2

if

cpe1 cpe1 cpe10−( ) logAB

m2

⋅− otherwise

:= cpeB 0.8−=

wB qp Z( ) cpeB 0.45− kPa⋅=:=

Zona C

cpeC 0.5−:=

wC qp Z( ) cpeC 0.28− kPa⋅=:=

Zona D

cpe10 0.80:= cpe1 1.00:=

cpeD cpe1 AD 1m2

if

cpe1 cpe1 cpe10−( ) logAD

m2

⋅− otherwise

:= cpeD 0.8=

wD qp Z( ) cpeD 0.45 kPa⋅=:=

8


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Zona E

cpeE 0.3−h

d0.25≤if

0.5− 0.25h

d< 1.00≤if

0.7− 1.00h

d< 5.00≤if

:= cpeE 0.5−=

wE qp Z( ) cpeE 0.28− kPa⋅=:=

Caz 2:

Calculul actiunii vantului pe zona superioara a peretilor verticali


lungimea de rugozitate pt un

teren de categoria II (tabel 4.1(Ro) - Anexa Nationala)Z0.II 0.05m:=




Z0.II

0.07

0.23=:=

cr Z( ) k r lnZ

Z0

⋅

Zmin Z≤ Zmax≤if

k r lnZmin

Z0

⋅

Z Zmin≤if

:=


cr Z( ) 0.62=


vm Z( ) 16.76m

s⋅=


σv k r vb⋅ k 1⋅ 6.33ms

⋅=:= abaterea standard a turbulentei

Iv Z( )σv


Iv Z( ) 0.38=

ρ 1.25s

2

m4


qb1

2

ρ⋅ vb2

⋅ 0.46kN

m2


qp Z( ) 1 7 Iv Z( )+( ) 1

2⋅ ρ⋅ vm Z( )


9


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qp Z( ) 0.64kN

m2

⋅=

ce Z( )qp Z( )

qb


Directia vantului V-E sau E-V (zona superioara)

Directiavantului

b 9.8m:=

d 38.4m:=

h Z 14.15 m=:=

e min b 2 h⋅,( ) 9.80 m=:=

fig. 1'

Lungimea zonelor

Ae

5e dif

d e 5 d⋅>if

:= B4e

5e dif

0 e 5 d⋅>if

:= C d e− e dif

0 e 5 d⋅>if

:=

Z0

k r

A 1.96 m= B 7.84 m= C 28.6 m=

Aria zonelor

AA A h b−( )⋅ 8.53 m2

⋅=:= AC C h b−( )⋅ 124.41 m2

⋅=:=AE b h b−( )⋅ 42.63 m

2⋅=:=

A

B

B h b−( )⋅ 34.1 m2

⋅=:= A

D

b h b−( )⋅ 42.63 m2

⋅=:=

Zona A

cpe10 1.20−:= cpe1 1.40−:=

cpeA cpe1 AA 1m2

if

cpe1 cpe1 cpe10−( ) log

AA

m2

⋅− otherwise

:= cpeA 1.21−=

wA qp Z( ) cpeA 0.78− kPa⋅=:=

10


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Zona B

cpe10 0.80−:= cpe1 1.10−:=

cpeB cpe1 AB 1m2

if


m2

⋅− otherwise

:= cpeB 0.8−=

wB qp Z( ) cpeB 0.51− kPa⋅=:=

Zona C

cpeC 0.5−:=

wC qp Z( ) cpeC 0.32− kPa⋅=:=

Zona D

cpe10 0.80:= cpe1 1.00:=

cpeD cpe1 AD 1m2

if


m2

⋅− otherwise

:= cpeD 0.8=


Zona E

cpeE 0.3−h

d

0.25≤if

0.5− 0.25h

d< 1.00≤if

0.7− 1.00h

d< 5.00≤if

:= cpeE 0.5−=


11


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Directia vantului N-S sau S-N

Directiavantului

b 38.4m:=

d 9.8m:=

h 14.15m:=

b h< 2 b⋅< 0=

h b< 1=

h 2 b⋅> 0=

e min b 2 h⋅,( ) 28.30 m=:=

fig. 2

Lungimea zonelor

Ae

5e dif

d e 5 d⋅>if

:= B4e

5e dif

0 e 5 d⋅>if

:= C d e− e dif

0 e 5 d⋅>if

:=

A 5.66 m= B 4.14 m= C 0 m=

Aria zonelor

AA A h⋅ 80.09 m2

⋅=:= AC C h⋅ 0 m2

⋅=:=AE b h⋅ 543.36 m

2⋅=:=

AB B h⋅ 58.58 m2

⋅=:= AD b h⋅ 543.36 m2

⋅=:=

Zona A

cpe10 1.20−:= cpe1 1.40−:=

cpeA cpe1 AA 1m2

if

cpe1 cpe1 cpe10−( ) logAA

m2

⋅− otherwise

:= cpeA 1.2−=

wA

qp

Z( ) cpeA

0.77− kPa⋅=:=

12


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Zona B

cpe10 0.80−:= cpe1 1.10−:=

cpeA cpe1 AB 1m2

if


m2

⋅− otherwise

:= cpeA 0.8−=

wB qp Z( ) cpeA 0.51− kPa⋅=:=

Zona D

cpe10 0.80:= cpe1 1.00:=

cpeD cpe1 AD 1m2

if


m2

⋅− otherwise

:= cpeD 0.8=


Zona E

cpeE 0.3−h

d0.25≤if

0.5− 0.25h

d< 1.00≤if

0.7− 1.00h

d< 5.00≤if

:= cpeE 0.7−=


13


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Incarcarea din vant pe acoperis


lungimea de rugozitate pt unteren de categoria II (tabel 4.1(Ro) - Anexa Nationala)

Z0.II 0.05m:=




Z0.II

0.07

0.23=:=

cr Z( ) k r lnZ

Z0

⋅

Zmin Z≤ Zmax≤if

k r lnZmin

Z0

⋅

Z Zmin≤if

:=


cr Z( ) 0.65=


vm Z( ) 17.44m

s⋅=


σv k r vb⋅ k 1⋅ 6.33

m

s⋅=:= abaterea standard a turbulentei

Iv Z( )σv


Iv Z( ) 0.36=

ρ 1.25s

2

m4


qb1

2ρ⋅ vb

2⋅ 0.46

kN

m2


qp Z( ) 1 7 Iv Z( )+( ) 1

2⋅ ρ⋅ vm Z( )


qp Z( ) 0.67kN

m2

⋅=

ce Z( )qp Z( )

qb


14


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8m 22.4m 8m

3 . 2 m

3 . 2 m

F FG

H

I

J

fig. 3α 25:=

d 9.8 m=

b 38.4 m=

h 16m:=

e min b 2 h⋅,( ) 32 m=:= rezultae

48 m=

e

103.2m=

Zona F

AFe

4

e

10

⋅ 25.6 m2

=:=

cpe.10 linterp15

30

0.2

0.7

, α,

0.53=:=

wF.max qp Z( ) cpe.10⋅ 0.36 kPa⋅=:=--> cazul in care in zona F apare presiune

cpe.10 linterp15

30

0.9−

0.5−

, α,

0.63−=:=

wF.min qp Z( ) cpe.10⋅ 0.43− kPa⋅=:=--> cazul in care in zona F apare suctiune

Zona G

AG b 2e

4⋅−

e

10⋅ 71.68m

2=:=

cpe.10 linterp15

30

0.2

0.7

, α,

0.53=:=

wG.max qp Z( ) cpe.10⋅ 0.36 kPa⋅=:=--> cazul in care in zona G apare presiune

cpe.10 linterp

15

30

0.8−

0.5−

,α,

0.6−=:=

wG.min qp Z( ) cpe.10⋅ 0.4− kPa⋅=:=--> cazul in care in zona G apare suctiune

15


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Zona H

AHd

2

e

10−

b⋅ 65.28m2

=:=

cpe.10 linterp15

30

0.2

0.4

, α,

0.33=:=

wH.max qp Z( ) cpe.10⋅ 0.22 kPa⋅=:=--> cazul in care in zona H apare presiune

cpe.10 linterp15

30

0.3−

0.2−

, α,

0.23−=:=

wH.min qp Z( ) cpe.10⋅ 0.16− kPa⋅=:=--> cazul in care in zona H apare suctiune

Zona I

AIe

10b⋅ 122.88 m2=:=

cpe.10 0.4−:=

wI qp Z( ) cpe.10⋅ 0.27− kPa⋅=:=Obs! - in zonele I si J apare doar suctiune

Zona J

AJd

2

e

10−

b⋅ 65.28m2

=:=

cpe.10 linterp15

30

1.0−

0.5−

, α,

0.67−=:=

wJ qp Z( ) cpe.10⋅ 0.45− kPa⋅=:=

α 20:=

d 9.8 m=

b 38.4 m=

h 16m:=

e min b 2 h⋅,( ) 32 m=:= rezultae

4

8 m=e

10

3.2m=

Zona F

AFe

4

e

10⋅ 25.6 m

2=:=

cpe.10 linterp15

30

0.2

0.7

, α,

0.37=:=

wF.max qp Z( ) cpe.10⋅ 0.25 kPa⋅=:=--> cazul in care in zona F apare presiune

cpe.10 linterp

15

30

0.9−

0.5−

,α,

0.77−=:=

wF.min qp Z( ) cpe.10⋅ 0.52− kPa⋅=:=--> cazul in care in zona F apare suctiune

16


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Zona G

AG b 2e

4⋅−

e

10⋅ 71.68m

2=:=

cpe.10 linterp

15

30

0.2

0.7

,α,

0.37=:=

wG.max qp Z( ) cpe.10⋅ 0.25 kPa⋅=:=--> cazul in care in zona G apare presiune

cpe.10 linterp15

30

0.8−

0.5−

, α,

0.7−=:=

wG.min qp Z( ) cpe.10⋅ 0.47− kPa⋅=:=--> cazul in care in zona G apare suctiune

Zona H

AHd

2

e

10−

b⋅ 65.28m2

=:=

cpe.10 linterp15

30

0.2

0.4

, α,

0.27=:=

wH.max qp Z( ) cpe.10⋅ 0.18 kPa⋅=:=--> cazul in care in zona H apare presiune

cpe.10 linterp15

30

0.3−

0.2−

, α,

0.27−=:=

wH.min qp Z( ) cpe.10⋅ 0.18− kPa⋅=:=--> cazul in care in zona H apare suctiune

Zona I

AIe

10b⋅ 122.88 m

2=:=

cpe.10 0.4−:=

wI qp Z( ) cpe.10⋅ 0.27− kPa⋅=:=Obs! - in zonele I si J apare doar suctiune

Zona J

AJd

2

e

10−

b⋅ 65.28m2

=:=

cpe.10 linterp15

30

1.0−

0.5−

, α,

0.83−=:=

wJ qp Z( ) cpe.10⋅ 0.56− kPa⋅=:=

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