mecanica zidariilor

DATE DE TEMA:

REGIM DE INALTIME: S+P+4E

INALTIME DE NIVEL: Hniv 2.80ACCELERATIA TERENULUI: ag 0.12PERIOADA DE COLT: Tc 0.7AMPLASAMENT : ORADEA

TIP DE CARAMIZI/BLOCURI: CPP (CARAMIDA PLINA PRESATA)TIP DE ZIDARIE: ZC (ZIDARIE COMFINATA)

CALCUL:1)CALCULUL DENSITATII PERETILOR STRUCTURAli:

p=densitatea peretilor structurali din tabelul 8.3 din P100 rezulta pn = densitate din normativ pn>5%Aznet = aria de zidariei structurala pe o directieApl = aria planseului

X

Y

Apl 16.575 11.375 Apl 188.541 m

a) pe directia x

Azx = aria pe directia x de zidarie brutaAxg =aria golurilor pe directia x

grosimea zidariei pe exterior este de 37.5 cm si la interior de 25 cmAxg = aria de pereti adaugati din marirea traveei

Azx 8.2875 2( ) 0.375 3.35 2.475( ) 0.25[ ] mpAzx 7.672 mpAxg 1 2.8 2.3 1.5 0.6( ) 0.375 1.2 1.2( ) 0.25[ ] mpAxg 3.675 mpAxad 0.3 0.3 0.3 0.3( ) mpAxad 1.2 mp pentru traveea marita de la 3.6 la 3.9 m

Aznetx Azx Axad Axg( ) 2 Aznetx 10.394 mp

px 100Aznetx

Apl px 5.513m

2

py 6.017

2)VERIFICAREA GROSIMILOR DE PERETI:

text = grosime perete exterior text 0.375 m

tint = grosime perete interior tint 0.25 mx = raportul intre inaltimea de nivel si grosimea peretelui si trebuie sa fie <15

xextHniv

text xext 7.467

xintHniv

tint xint 11.2

3)DETERMINAREA CARACTERISTICILOR GEOMETRICE ALE PERETILOR:

PERETE P1:

1

E

F 37.5

202.5

37.5

240

37.5

277.5

37.5

37.5 62.5100

277.5

ygp ygp

157.5

120

18.75

138.75

120

ygyg

127.7

149.8

b1 = grosimea inimii b1 0.375 mb2 = grosimea talpii b2 1 mh1 = inaltimea inimii h1 2.4 mh2 = grosimea talpii h2 0.375 mAb = aria de perete totala

Afb = aria de perete modificata

Ib = momentul de inertie a peretelui

yg = coordonata pe y a centrului de greutate

Ab b1 h1 b2 h2 Ab 1.275 mpn = coeficient de impartit Ab : n=1 pt perete fara bulbi n=1.1 pt perete cu 1 bulb n=1.2 pt perete cu 2 bulbi (la ambele capete)

AfbAb

1.1 Afb 1.159 mp

sumaAi1 b1 h1 sumaAi1 0.9 mpsumaAi2 b2 h2 sumaAi2 0.375 mp

ygph1

2 ygp 1.2m

yg

sumaAi2 ygph2

2

sumaAi1 sumaAi2 yg 0.298m

Iyp1h1 b1

312

b2 h23

12 b1 h1 yg

2 b2 h2 ygph2

2 yg

2

Iyp1 0.54m4

PERETE P2:

1

B

D

37.5

163.75

382.5

420

ygp ygp

yg yg

158.3

b1 = grosimea inimii b1 0.375 mb2 = grosimea talpii b2 1.6375 mh1 = inaltimea inimii h1 3.825 mh2 = grosimea talpii h2 0.375 mAb = aria de perete totala





AfbAb

1.1 Afb 1.862 mp


ygph1

2 ygp 1.913m

yg

sumaAi2 ygph2

2


Iyp2h1 b1

312

b2 h23

12 b1 h1 yg

2 b2 h2 ygph2

2 yg

2

Iyp2 1.946m4

PERETE P3:

37.5 82.5 37.5 86.25

243.7518.75 120 105

37.5

87.5

37.5

18.75

125

18.75

162.5

162.5

37.5 206.25

2 3

F

Gyg

ygp ygp

ygp 52.35

91.4

b1 = grosimea inimii b1 0.375 mb2 = grosimea talpii b2 2.4375 mh1 = inaltimea inimii h1 1.25 mh2 = grosimea talpii h2 0.375 mAb = aria de perete totala





AfbAb

1.1 Afb 1.257 mp


ygph1

2 ygp 0.625m

yg

sumaAi2 ygph2

2


Iyp3h1 b1

312

b2 h23

12 b1 h1 yg

2 b2 h2 ygph2

2 yg

2

Iyp3 0.306m4

PERETE P4:

25

118.75

F

G

3

ygp=yg ygp=yg

b1 = grosimea inimii b1 0.25 mb2 = grosimea talpii b2 0 mh1 = inaltimea inimii h1 1.1875 mh2 = grosimea talpii h2 0 mAb = aria de perete totala





AfbAb

1.1 Afb 0.27 mp

sumaAi1 b1 h1 sumaAi1 0.297 mpsumaAi2 b2 h2 sumaAi2 0 mp

ygph1

2 ygp 0.594m

yg

sumaAi2 ygph2

2

sumaAi1 sumaAi2 yg

Iyp4h1 b1

312

b2 h23

12 b1 h1 yg

2 b2 h2 ygph2

2 yg

2

Iyp4 1.546 103 m

4

PERETE P5:

3

140

25E

ygp=yg ygp=yg






AfbAb

1.1 Afb 0.318 mp


ygph1

2 ygp 0.7m

yg

sumaAi2 ygph2

2

sumaAi1 sumaAi2 yg 0

Iyp5h1 b1

312

b2 h23

12 b1 h1 yg

2 b2 h2 ygph2

2 yg

2

Iyp5 1.823 103 m

4

PERETE P6:

255

25

3

Dygp=yg ygp=yg






AfbAb

1.1 Afb 0.58 mp


ygph1

2 ygp 1.275m

yg

sumaAi2 ygph2

2


Iyp6h1 b1

312

b2 h23

12 b1 h1 yg

2 b2 h2 ygph2

2 yg

2

Iyp6 3.32 103 m

4

PERETE P7:

103.75

25

3

Cygp=yg ygp=yg






AfbAb

1.1 Afb 0.236 mp


ygph1

2 ygp 0.519m

yg

sumaAi2 ygph2

2


Iyp7h1 b1

312

b2 h23

12 b1 h1 yg

2 b2 h2 ygph2

2 yg

2

Iyp7 1.351 103 m

4

PERETE P8:

37.5

202.5

3

A

B

ygp=yg ygp=yg

82.5






AfbAb

1.1 Afb 0.69 mp


ygph1

2 ygp 1.012m

yg

sumaAi2 ygph2

2


Iyp8h1 b1

312

b2 h23

12 b1 h1 yg

2 b2 h2 ygph2

2 yg

2

Iyp8 8.899 103 m

4

PERETE P9:

37.5

333.75

25435

25243.75

1137.5

555

37.5

245 25 245

285 25 285

270

37.5

ygp

ygp

yg

yg

b2xh2

b3xh3

b4xh4

b5xh5

b1xh1

b1 = grosimea inimii b1 0.25 mb2 = grosimea talpii1 b2 2.7 mb3 = grosimea talpii3 b3 2.85 2 m b3 5.7mb4 = grosimea talpii4 b4 2.45 2 m b4 4.9mb5 = grosimea talpii5 b5 5.55 mh1 = inaltimea inimii h1 10.625 mh2 = grosimea talpi1i h2 0.375 mh3 = grosimea talpi1i h3 0.25 mh4 = grosimea talpi4i h4 0.25 mh5 = grosimea talpii5 h5 0.375 mAb = aria de perete totala




Ab b1 h1 b2 h2 b3 h3 b4 h4 b5 h5 Ab 8.4 mpn = coeficient de impartit Ab : n=1 pt perete fara bulbi n=1.1 pt perete cu 1 bulb n=1.2 pt perete cu 2 bulbi (la ambele capete)

AfbAb

1.2 Afb 7 mp

sumaAi1 b1 h1 sumaAi1 2.656 mpsumaAi2 b2 h2 sumaAi2 1.013 mpsumaAi3 b3 h3 sumaAi3 1.425 mpsumaAi4 b4 h4 sumaAi4 1.225 mpsumaAi5 b5 h5 sumaAi5 2.081 mp

4)DETERMINAREA MOMENTELOR DE INERTIE ALE STALPILOR :

PERETE P1:

1

E

F

ygyg

37.5

37.5

37.5

37.5

108.95

131.05

Pp1

Pp2

h1 0.375 m b1 0.375 m

h2 0.375 m b2 0.375 my2 1.3105 my1 1.0895 m

Iys11b1 h1

312

b1 h1 y12 Iys11 0.169m

4

Iys12b2 h2

312

b2 h2 y22 Iys12 0.243m

4

Iys1 Iys11 Iys12 Iys1 0.412m4

Iys11 = moment de inertie a stalpisorului Pp1Iys12 = moment de inertie a stalpisorului Pp2

PERETE P2:

1

B

D

yg yg

37.5

37.5

37.5

37.5

37.5

37.5

158.3

224.2

Pp1

Pp2 Pp3

h1 0.375 m b1 0.375 m y1 2.242 m

h2 0.375 m b2 0.375 m y2 1.583 m

h3 0.375 m b3 0.375 m y3 1.583 m

Iy21b1 h1

312

b1 h1 y12 Iy21 0.709m

4

Iy22b2 h2

312

b2 h2 y22 Iy22 0.354m

4

Iy23b3 h3

312

b3 h3 y32 Iy23 0.354m

4

Iys2 Iy21 Iy22 Iy23 Iys2 1.417m4

Iys21 = moment de inertie a stalpisorului Pp1Iys22 = moment de inertie a stalpisorului Pp2Iys23 = moment de inertie a stalpisorului Pp3

PERETE P3:

37.5

2 3

F

Gyg yg

37.5

37.5

37.5 37.5

37.5

52.35

72.65

Pp1

Pp2

Pp3

h1 0.375 m b1 0.375 m y1 0.5235 m

h2 0.375 m b2 0.375 m y2 0.7265 m

h3 0.375 m b3 0.375 m y3 0.5235 m

Iy31b1 h1

312

b1 h1 y12 Iy31 0.04m

4

Iy32b2 h2

312

b2 h2 y22 Iy32 0.076m

4

Iy33b3 h3

312

b3 h3 y32 Iy33 0.04m

4

Iys3 Iy31 Iy32 Iy33 Iys3 0.156m4

Iys31 = moment de inertie a stalpisorului Pp1Iys32 = moment de inertie a stalpisorului Pp2Iys33 = moment de inertie a stalpisorului Pp3

PERETE P4:

F

G

3

ygp=yg ygp=yg

25

2546.88

h1 0.25 m b1 0.25 m y1 0.4688 m

Iy41b1 h1

312

b1 h1 y12 Iy41 0.014m

4

Iys4 Iy41 Iys4 0.014m4

Iys41 = moment de inertie a stalpisorului Pp1

PERETE P5:

3

25E

ygp=yg ygp=yg

2525

25Pp1

Pp2

57.5

45

h1 0.25 m b1 0.25 m y1 0.45 m

h2 0.25 m b2 0.25 m y2 0.575 m

Iy51b1 h1

312

b1 h1 y12 Iy51 0.013m

4

Iy52b2 h2

312

b2 h2 y22 Iy52 0.021m

4

Iys5 Iy51 Iy52 Iys5 0.034m4


PERETE P6:

25

3

Dygp=yg ygp=yg

2525

25

115

115

Pp1

Pp2

h1 0.25 m b1 0.25 m y1 1.15 m

h2 0.25 m b2 0.25 m y2 1.15 m

Iy61b1 h1

312

b1 h1 y12 Iy61 0.083m

4

Iy62b2 h2

312

b2 h2 y22 Iy62 0.083m

4



h1 0.375 m b1 0.375 m y1 0.825 m

h2 0.375 m b2 0.375 m y2 0.825 m

Iy81b1 h1

312

b1 h1 y12 Iy81 0.097m

4

Iy82b2 h2

312

b2 h2 y22 Iy82 0.097m

4



PERETE P9:

yg yg

37.5

37.5

25

25

25

25

25

25

2525

25

25

25

25 25

25

25

25

37.5

37.5

Pp1

Pp2

Pp8 Pp9 Pp10

Pp7

Pp4 Pp5 Pp6

Pp3

197.6

77.4

349.9

537.4

777.4

902.4

37.5

37.5

37.5

37.5

Pp12Pp11

h1 0.375 m b1 0.375 m y1 9.024 mh2 0.375 m b2 0.375 m y2 1.976 mh3 0.25 m b3 0.25 m y3 7.774 mh4 0.25 m b4 0.25 m y4 5.374 mh5 0.25 m b5 0.25 m y5 5.374 mh6 0.25 m b6 0.25 m y6 5.374 mh7 0.25 m b7 0.25 m y7 3.499 mh8 0.25 m b8 0.25 m y8 0.774 mh9 0.25 m b9 0.25 m y9 0.774 mh10 0.25 m b10 0.25 m y10 0.774 mh11 0.375 m b11 0.375 m y11 1.976 mh12 0.375 m b12 0.375 m y12 1.976 m

Iys91 = moment de inertie a stalpisorului Pp1Iys92 = moment de inertie a stalpisorului Pp2Iys93 = moment de inertie a stalpisorului Pp3Iys94 = moment de inertie a stalpisorului Pp4Iys95 = moment de inertie a stalpisorului Pp5Iys96 = moment de inertie a stalpisorului Pp6Iys97 = moment de inertie a stalpisorului Pp7Iys98 = moment de inertie a stalpisorului Pp8Iys99 = moment de inertie a stalpisorului Pp9Iys910 = moment de inertie a stalpisorului Pp10Iys911 = moment de inertie a stalpisorului Pp11Iys912 = moment de inertie a stalpisorului Pp12

Iyb9 Iy91 Iy92 Iy93 Iy94 Iy95 Iy96 Iy97 Iy98 Iy99 Iy910 Iy911 Iy912

Iyb9 23.178m4

5)DETERMINAREA MOMENTELOR DE INERTIE ALE ZIDARIEI :

PERETE P1:

1

E

F

ygyg Pz1

11.05

37.5202.5

h1 2.025 m b1 0.375 m y1 0.1105 m

Iyz11b1 h1

312

b1 h1 y12 Iyz11 0.269m

4

Iyz1 Iyz11 Iyz1 0.269m4

Iyz11 = moment de inertie a zidariei Pz1

PERETE P2:

1

B

D

yg yg

158.3

Pz1

Pz2

88.7537.5

37.5

345

32.95

h1 3.45 m b1 0.375 m y1 0.3295 m

h2 0.375 m b2 0.8875 m y2 1.583 m

Iyz21b1 h1

312

b1 h1 y12 Iyz21 1.424m

4

Iyz22b2 h2

312

b2 h2 y22 Iyz22 0.838m

4

Iyz2 Iyz21 Iyz22 Iyz2 2.262m4

Iyz21 = moment de inertie a zidariei Pz1Iyz22 = moment de inertie a zidariei Pz2PERETE P3:

2 3

F

Gyg yg52

.3510.15

Pz1

Pz2

82.5

37.5

87.5

37.5

h1 0.375 m b1 0.825 m y1 0.5235 m

h2 0.875 m b2 0.375 m y2 0.1015 m

Iyz31b1 h1

312

b1 h1 y12 Iyz31 0.088m

4

Iyz32b2 h2

312

b2 h2 y22 Iyz32 0.024m

4

Iyz3 Iyz31 Iyz32 Iyz3 0.113m4

Iyz31 = moment de inertie a zidului Pz1Iyz32 = moment de inertie a zidului Pz2

PERETE P4:

25

93.75

F

G

3

ygp=yg ygp=yg

12.5

h1 0.9375 m b1 0.25 m y1 0.125 m

Iyz41b1 h1

312

b1 h1 y12 Iyz41 0.021m

4


Iyz41 = moment de inertie a zidului Pz1

PERETE P5:

3

E

ygp=yg ygp=yg45

25

90

h1 0.90 m b1 0.25 m y1 0 m

Iyz51b1 h1

312

b1 h1 y12 Iyz51 0.015m

4



PERETE P6:

3

Dygp=yg ygp=yg

25

205

102.5

h1 2.05 m b1 0.25 m y1 0 m

Iyz61b1 h1

312

b1 h1 y12 Iyz61 0.179m

4



PERETE P7:

3

Cygp=yg ygp=yg

12.5

25

78.75

h1 0.7875 m b1 0.25 m y1 0.125 m

Iyz71b1 h1

312

b1 h1 y12 Iyz71 0.013m

4



PERETE P8:

3

A

B

ygp=yg ygp=yg

37.5

127.5

h1 1.275 m b1 0.375 m y1 0 m

Iyz81b1 h1

312

b1 h1 y12 Iy81 0.097m

4



PERETE P9:

yg yg

25

25

243.75

220

247.5

220

162.5

260 260

215

93.75

116.25 116.25

37.5

Pz1 Pz2

Pz3

Pz4

Pz5 Pz6

Pz7

Pz8

Pz9 Pz10

Pz11

25

Pz12 Pz13

37.5

221.25

197.6

77.4

213.65

443.65

537.4

657.4

836.78902.4

56.98

37.5

221.25

h1 0.375 m b1 1.1625 m y1 9.024 mh2 0.375 m b2 1.1625 m y2 9.024 mh3 0.9375 m b3 0.25 m y3 8.3678 mh4 2.15 m b4 0.25 m y4 6.574 mh5 0.25 m b5 2.6 m y5 5.374 mh6 0.25 m b6 2.6 m y6 5.374 mh7 1.625 m b7 0.25 m y7 4.4365 mh8 2.475 m b8 0.25 m y8 2.1365 mh9 0.25 m b9 2.2 m y9 0.774 mh10 0.25 m b10 2.2 m y10 0.774 mh11 2.4375 m b11 0.25 m y11 0.5698 mh12 0.375 m b12 2.5875 m y12 1.976 mh13 0.375 m b13 2.5875 m y13 1.976 m

Iyz91b1 h1

312

b1 h1 y12 Iyz91 35.505m

4

Iyz92b2 h2

312

b2 h2 y22 Iyz92 35.505m

4

Iyz93b3 h3

312

b3 h3 y32 Iyz93 16.428m

4

Iyz94b4 h4

312

b4 h4 y42 Iyz94 23.436m

4

Iyz95b5 h5

312

b5 h5 y52 Iyz95 18.775m

4

Iyz96b6 h6

312

b6 h6 y62 Iyz96 18.775m

4

Iyz96b6 h6

312

b6 h6 y62 Iyz96 18.775m

4

Iyz97b7 h7

312

b7 h7 y72 Iyz97 8.085m

4

Iyz98b8 h8

312

b8 h8 y82 Iyz98 3.14m

4

Iyz99b9 h9

312

b9 h9 y92 Iyz99 0.332m

4

Iyz910b10 h10

312

b10 h10 y102 Iyz910 0.332m

4

Iyz911b11 h11

312

b11 h11 y112 Iyz911 0.5m

4

Iyz912b12 h12

312

b12 h12 y122 Iyz912 3.8m

4

Iyz913b13 h13

312

b13 h13 y132 Iyz913 3.8m

4

Iyzz91 Iyz91 Iyz92 Iyz93 Iyz94 Iyz95 Iyz96 Iyz97 Iyz98Iyzz92 Iyz99 Iyz910 Iyz911 Iyz912 Iyz913

Iyz9 Iyzz91 Iyzz92 Iyz9 168.414m4

Iyz91 = moment de inertie a zidului Pz1Iyz92 = moment de inertie a zidului Pz2Iyz93 = moment de inertie a zidului Pz3Iyz94 = moment de inertie a zidului Pz4Iyz95 = moment de inertie a zidului Pz5Iyz96 = moment de inertie a zidului Pz6Iyz97 = moment de inertie a zidului Pz7Iyz98 = moment de inertie a zidului Pz8Iyz99 = moment de inertie a zidului Pz9Iyz910 = moment de inertie a zidului Pz10Iyz911 = moment de inertie a zidului Pz11Iyz912 = moment de inertie a zidului Pz12Iyz913 = moment de inertie a zidului Pz13

6)DETERMINAREA MODULELOR DE ELASTICITATE (E) :

BETON:

Eb 27000N

mm2

PENTRU C16/18

ZIDARIE :

FORMULE :Ez=500*fk din tabel 4.9fk=K*fb0.70*fm0.30 din formula 4.1K=0.5 pt cpp la tabel 4.1pentru zidarie de 25 fk=2.3 N/mm2 tabel4.2a fb=6.1 cf tabel 31b pentru rezistenta de 7.5fm=5 pentru mortar M5

K 0.5 fb 6.1 fm 5

fk K fb0.7 fm

0.3 fk 2.873N

mm2

Ez 500 fk 103

N

mm2

Ez 1.437N

mm2

7)DETERMINAREA MODULELOR DE ELASTICITATE A ZIDARIEI COMFINATE(Ezc) :

FORMULE :Ezc = (Ez*Iz+Eb*Ib)/(Iz+Ib)Ezc = modulul de elasticitate a zidariei comfinateEz = modulul de elasticitate a zidariei dintr-un pereteEb = modulul de elasticitate a betonului stalpilorIz = momentul de inertie a zidariei Ib = momentul de inertie a betonului

PRTE P1:

Ezc1Ez Iyz1 Eb Iys1

Iyz1 Iys1 Ezc1 1.634 10

4N

mm2

PRTE P2:

Ezc2Ez Iyz2 Eb Iys2

Iyz2 Iys2 Ezc2 1.04 10

4N

mm2

PRTE P3:

Ezc3Ez Iyz3 Eb Iys3

Iyz3 Iys3 Ezc3 1.568 10

4N

mm2

PRTE P4:

Ezc4Ez Iyz4 Eb Iys4

Iyz4 Iys4 Ezc4 1.088 10

4N

mm2

Ezc5Ez Iyz5 Eb Iys5

Iyz5 Iys5 Ezc5 1.866 10

4N

mm2

PRTE P6:

Ezc6Ez Iyz6 Eb Iys6

Iyz6 Iys6 Ezc6 1.297 10

4N

mm2

Ezc7Ez Iyz7 Eb Iys7

Iyz7 Iys7 Ezc7 1.163 10

4N

mm2

PRTE P8:

Ezc8Ez Iyz8 Eb Iys8

Iyz8 Iys8 Ezc8 2.026 10

4N

mm2

PRTE P9:

Ezc9Ez Iyz9 Eb Iys9

Iyz9 Iys9 Ezc9 3.268 10

3N

mm2

mecanica zidariilor

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