mbulesa keson_ trau

7/29/2019 Mbulesa Keson_ Trau

1/44

NIVERSITETI I PRISHTINSFAKULTETI I NDRTIMTARIS DHE ARKITEKTURSDEGA E NDRTIMTARIS

KANDIDATI: ___________________________________

Nr. IND . ________________

DETYRA NR. 5 MBULESA KESON

Pr objektin e paraqitur n skemn m posht t bhet: Pozicionimi i elementeve t konstruksionit Dimensionimi i murit beton arme Dimensionimi i mbuless me lartsi konstante/ t ndryshuar Dimensionimi i traut .me lartsi konstante/ t ndryshuar Dimensionimi i shtylls Dimensionimi i themelit nn shtylln e shnuar Planet e armaturs pr pozicionet e prmendura m lart, n prpjes 1:20 (1:25) Specifikimi i armaturs pr pozicionet e llogaruara

T dhnat :

Klasa e betonit C- ......MPa

Lloji i elikt pr armim S- .......MPa

Hapsira x-x lx = ..... m

Hapsira y-y ly = ..... m

Lartsia dysh-dysh. H = ..... m

Gjersia e trarve bw = .....m

Nderjet e trollit [t]=.....Mpa

Ngarkesa e prk. Q=...........kN/m2

Numri i etazheve .................

AFATI I DORZIMIT T DETYRS : .... MAJ 2008

N PRISHTIN ASISTENTI I LNDS:

M: __________________

KATEDRA: MATERJALET DHEKONSTRUKSIONET

LNDA: KONSTRUKSIONET E BETONIT

VITI SHKOLLOR: 2007/2008


2/44

Prill, 2007Konstruksionet e Betonit

V. Shatri, B. Shefkiu 1

1. Pozicionimi i elementeve t konstruksionit:


3/44



2. Krakteristikat gjeometrike:

1.114.5

5

l

l

x

y , trajtimi si pllak e armuar n dy drejtime

0.211.15.0

Sipas ( EC 2 ), nga kushti i mostejkalimit t uljeve:

14.06cm32

450

32

ld minmin

Lartesia preliminare e pllakes:20mm15515

2

10

2

cd o1

m)(16.5mepervetesoj16.062.014.06ddn 1

3. Analiza e ngarkesave:

3.1 NGARKESAT E PRHERSHME:

mermer 0.0327 =0.810 kN/m2 lla imentoje 0.0224 =0.480 kN/m2 konstruksioni betonarme 0.16525 =4.125 kN/m2 suvatimi 0.0219 =0.380 kN/m2

Gk =5.795 kN/m2

3.2 NGARKESAT E PERKOSHME:

Pr objektin e dhn Qk =6.000 kN/m2

MERMER .....................................3.0 cm

LLAQ QIMENTO ..........................2.0 cm

KONSTRUK. BETONARME ........16.5 cmSUVATIMI ...................................2.0 cm


4/44



3.3 SHPRNDARJA E NGARKESAVE

y

Mx

MyA

x x

y

Mx'

My'A'

x

y

Mx"

My"A"

lx=4.50

ly=5.0

lx=4.50

ly=5.0

lx=4.50

ly=5.0

Gd=1.35 GK= 1.35 5.975 = 7.82325 kN/m2Qd=1.5 QK= 1.5 6 = 9 kN/m2

2ddd /m16.82325kN97.82325QGP

2dd

' /m12.32325kN2

97.82325

2

QGP

2d'' 4.5kN/m2

9

2

QP

3.4 SHPRNDARJA E NGARKESAVE N DREJTIM T X-it

2

44

4

2

44

4

44

4

""

2

44

4

44

4

''

kN/m0.15831

kN/m7172.255.4

550.4

kN/m7.441155.4

512.32325

yx

y

x

yx

y

x

yx

y

x

ll

lPP

ll

lPP

ll

lPP

3.5 SHPRNDARJA E NGARKESAVE N DREJTIM T Y-it

2

44

4

2

44

4""

2

44

4''

kN/m6.6648

kN/m7827.1

kN/m8821.4

xy

xy

xy

xy

xy

xy

ll

lPP

ll

lPP

ll

lPP


5/44



Kontrolla algjebrike e shprndarjes s ngarkesave:

mkNPPP

mkNPPP

mkNPPP

mkNPPP

mkNPPP

mkNPPP

yx

yyy

xxx

yx

yx

/8231.164999.43232.12

/8231.166648.61583.10

/6648.67827.18821.4

/1583.107172.24411.7

/4999.47827.17172.2"

/3232.128821.44411.7

'''

"'

"'

""

'''

4. LLOGARITJA E NDIKIMEVE STATIKE SIPAS METODS S MARCUS-it

1.114.5

5

l

l

x

y

0.59245*4.5*

8

14.5*2.7172*8

1

*651

l*P*8

1l*P*8

1

*651

70.7705*12.3232*

8

1

4.5*7.4411*128

9

*6

51

l*P*8

1

l*P*128

9

*6

51

2

2

2y

''

2

x

''

x''y

''x

2

2

2y

'

2x

'x

'y

'x

4.1 MOMENTET MAKSIMALE N FUSH

x

y

lx

ly Mx

Myp

x

y

lx

ly Mx'

My'p'

x

y

lx

ly Mx"

My"p"

m=9/128 m=1/8

m

=9/128

m

=1/8


6/44



kNm3.3138M

kNm9.9142M

3.30026.61400.592451.78278

1

0.770754.8821128

9lP

8

1lP

128

9M

kNm4.091M

kNm12.2398M

4.07748.16540.59244.52.717281

0.77074.57.4411128

9lP

8

1lP

128

9M

ymin

ymax

2

2"y

2y

"y

'y

2y

'yy

minmax

xmin

xmax

2

2"x

2x

"x

'x

2x

'xx

MINMAX

4.2 MOMENTET MINIMALE N MBSHTETS

kNm20.82758

56648.6

8minM

kNm25.71318

5.41583.10

8min

22by

22

y

y

xx

ax

lP

lPM

4.3 MOMENTET MAXIMALE N MBSHTETS

kNm9.68568

5)7827.18821.4(

8maxM

kNm11.95738

5.4)7172.24411.7(

8max

2"'

2by

2"'

2

yy

y

xxxa

x

PPl

PPl

M

4.4 MOMENTET E REDUKTUARA MBI MBSHTETS

kNm5778.1953.0*6648.68

18275.20

8

1

kNm9988.235.43.01583.10817131.25

81

ywyby

by

xwxax

ax

lbPMredM

lbPMredM


7/44



4.5 PASQYRA TABELARE E MOMENTEVE:

drejtimi Mf(kNm)maxmin )(kNmM

a

m

maxredmin (kNm)M

b

m

maxredmin

x-x 12.23984.091

-11.9573-23.9988-25.7135

y-y 9.91423.3138

-9.6856-19.5778-20.8275

5. LLOGARITJA E NDIKIMEVE SIPAS LSER-it 5.1 LLOGARITJA E MOMENTEVE NE FUSH

x

lx

Mx

Myp

x

lx

lyMx'

My'p'

x

lx

lyMx"

My"p"

(ax=2) mx=128/9

(ay=2)my=128/9

(ax=5) mx=8

(ay=5)my=8

111.15.4

5

lx

ly

Nga tabela i prgjigjet rasti nr. 4:

xm4 ym4 x4

1.10 31.090.408

45.321.063

0.5912 0.00801.20 27.01 56.01 0.6747

489.46100063.1)10.1111.1(32.45

64.30100408.0)111.12.1(01.27

64.30100408.0)10.1111.1(09.31

4

4

ym

xm

Nga tabela i prgjigjet rasti nr. 1:

xm4 ym4 x4

1.10 22.790.334

33.370.697

0.5942 0.0080

1.20 19.45 40.34 0.6747


8/44



1367.34100697.0)10.1111.1(37.33

42.22100334.0)111.12.1(45.19

42.22100334.0)10.1111.1(79.22

1

1

ym

xm

SHPRNDARJA E NGARKESAVE

kNm0799.4

kNm2088.12

5.442.22

5.4

64.30

32325.12"'

min

max

22

14

maxmin

M

M

lm

P

m

PMabs x

xx

x

kNm3.3313

kNm9225.9

51367.34

5.4

489.46

3232.12"'

min

max

22

14

maxmin

y

y

yy

y

M

M

lym

P

m

PMabs

5.2 LLOGARITJA E MOMENTETEVE MBI MBSHTETSA

SHPRNDARJA E NGARKESAVE SIPAS LOSER-it

3973.01

603.0100008.0)10.1111.1(5492.0

6027.01000080.0)11.120.1(6747.0

111.1

)1(

44

4

'4

''4

'

xy

x

xyxx

Pr

PPPP

3973.0

6027.0111.1

)1(

4

4

''4

''''4

''

y

x

xyxx

Pr

PPPP

2

2''1

''

2'4

'

/14.10

/7121.25.46027.0

/4272.732325.126027.0

mkNP

mkNPP

mkNPP

x

xx

xx


9/44



2

2''1

''

2'4

'

/68.6

/78785.15.43973.0

/892602.432325.123973.0

mkNP

mkNPP

mkNPP

y

yy

yy

kNm685.9

kNm11.957

826.2056648.68

1

8

1

713.255.41583.108

1

8

1

max

max

22min

22min

by

ax

yyby

xxax

M

M

kNmlPM

kNmlPM

Pasqyra tabelare e momenteve:

drejtimi (kNm)M fmaxmin )(kNmM

amb.

maxredmin

(kNm)Mbmb.maxredmin

x-x 12.20884.0799

-11.957-23.999-25.713

y-y 9.92253.3313

-9.685-19.578-20.826

6. DIMENSIONIMI:

POS-1, MBULESA BETON ARME

DIMENSIONIMI I PLLAKS ME LARTSI T NDRYSHUESHME:

a. drejtimi x-x, C-25/30, S-400/500

kNmM sd 398.12

c0

d1x

dx

h

d1y

dy

Asly

Aslx

3cm30mm2

101015

2cd

20mm2

1015

2

cd

y

x01y

x01x

Diametri i supozuar i shufrave n t dy drejtimet: 10 mm


10/44



892.0d

z;259.0;159.0

:lexojm%5.3dhe%10...

sds

c

d

x

pr s

mmfb

Md

cdsds

sdx 958.67

667.16159.01000

10239.12 6

mmdhd xx 145201651

035.066.161451000

10239.122

6

2

cdx

sdsd

fdb

M

Nga Tab. pr 035.0sds

965.0d

z099.0%1.1%10 s

d

xs

SIPRFAQJA E NEVOJSHME E ARMATURS:

2

2

26

5.21714510000015.00015.0

5.217400

14510006.06.0

47.251826.347145965.0

10239.12

mmbh

mmfbd

mmfd

M

Ayk

ydx

sd

reqsl

HAPI I ARMATURS

Pr 10 As= 79 mm.

350mmmax

217.5mm1451.5d1.51.5h

314.15mm1000251.47

791000AA

x

reqsl

1

s

ls

10/21cmetprvetsoh

2reqsl

provsl

2`

l

1sprov

sl

251.47mmA376.190A

376.190mm1000210

791000

s

AA

165mmh87.9582067.958ddh filestare1xx


11/44


V. Shatri, B. Shefkiu10

Dimensionimi dhe llogaritja e siprfaqes s armaturs n mbshtetsin a

kNmM redxa 998.23,

259.0d

x892.0

d

z15.0


sds

c

spr

Duke ruajtur hapin 210 mm pr10 me As=79 mm

26

,

,

,

608.205826.34719.376892.0

10998.23...

19.3761000210

791000

mmfA

Md

fd

MAnese

mms

AA

ydlprov

redxa

x

ydl

sl

l

slprov

sl

sl

mmchd

cmetpervetesohmmcdh

x 210)2

1015(230)

2(

)230(,226)2

1015(206)

2(

0

0

Aslyc0

d1x

dxh

d1y

dy

Aslx

~1:3

032.0667.162101000

10998.232

6

2

cdx

sdsds

fdb

M

0.0326pertabelaNga sds

22

c

19.376608.205

968.0d

z092.0

%01.1%10

mmmmAreq

s

sl


12/44



b. drejtimi y-y

MPaf

MPapr

MPafMPaf

MPapr

kNmM

s

yk

cd

c

ck

f

y

826.347f,15.1,400f400-S

1667.14,667.16f,5.1,25f25-C

914.9max

ydssk

cdcck

Aslyc0

d1x

d

x

h

d1y

d

y

slx

mmdhd

cmmmcd

yy

y

xy

13530165

3302

101015

2

1

01

892.0dz;259.0;159.0


sds

c

dx

pr s

0326.0667.161351000

10914.92

6

2

cdx

sdsd

fdb

M

9675.0d

z093.0

%02.1dhe%10:lexojm0326.0... csds

d

x

pr s

21

2

2

26

7910

5.20213510000015.00015.0

5.202400

13510006.06.0

223.218826.3471359675.0

10914.9

mmAmeper

mmbd

mmf

bd

mmfd

M

A

s

yk

yd

sd

reqsl


13/44



Hapi i armaturs:

22

`21

provsl

1

223.218395

3951000210

791000A

10/20

350max

5.2021355.15.15.1

015.3621000223.218

791000

mmAmmA

mms

A

etprvetsoh

mm

mmdh

mmAA

s

req

sl

prov

sl

l

s

x

reqsl

s

l

Llogaritja e siprfaqes s armaturs dhe lartsis s prerjes n mbshtetsin b

kNmM redyb 5778.19,

259.0892.0d

z159.0


sds

c

d

x

pr s

Duke ruajtur hapin sl = 200 per10 me As= 79 mm

2sl

sl

395mm1000200

791000

sl

AA

Duke pasur parasysh lartsin mbi mbshtets h= 230 mmsly

c0

d1x

dxh

d1y

dy

Aslx

~1:3

0.0870.9700.0870.95%

tab.ngalexojme0.029%pr

0.029316.6672001000

1019.5778

fdb

395mm290.088347.8262000.9675

1019.5778

fd

MA

20030230)2

1010(15230dhd

sc

sd

2

6

yd2

y

sdsds

6

ydy

req

1yy

sl

LLOGARITJA E GJATSIS S INKASTRIMIT


14/44



mmlmepervetesoj

ll

sMpafmmhNf

mm

l

lA

A

ll

xx

bxx

ackbd

b

bprov

req

aabneto

bneto

bneto

sl

sl

150

921.149)190.376

17.250(06.3227.0

7.0400,25)2/(7.2

10010

3.0

)(

)(

min)(

min

mmlmepervetesoj

ll

yy

bxx

bneto

bneto

150

548.124)395

223.218(06.3237.0

)(

min)(

7.Plani i armaturs


15/44



Pasqyra tabelare

drejtimi Mf(kNm)maxmin )(kNmMam

maxredmin

(kNm)Mbmmaxredmin

x-x 12.23984.091

-11.9573-23.9988-25.7135

y-y 9.91423.3138

-9.6856-19.5778-20.8275

Pr drejtimin x x n fush:

kNNfAF

kNNF

kNNF

kNfAF

kNNF

kNNF

kNNd

MF

mbeshtetesnexxdrejtiper

kNNfAF

kNNd

MF

kNNd

MF

ydprovsl

fso

fsl

fs

ydprovmb

so

mbsl

mbredsl

mmbsl

ydprovf

sd

sdf

sdfs

sl

sl

sl

3912.13727.137391826.347395

3712.2523.25371135975.0

103138.3

905.7544.759051359675.0

109142.9

fushny,-ydrejtiminpr

8486.130826.347190.376

196.183183196145968.0

107135.25

0578.11801.126493210968.0

109988.23

19.8522.85190145968.0

109573.11

...,min

8486.13066.130848826.347190.376

0863.29384.29086145965.0

10091.4

4681.87286.87468145965.0 102398.12

6

min,

6

max,

6

max,

6

,

6min

min,

6min

6

max,max,1

min,

Drejtimi y-y, n mbshtets:


16/44



kN

kNN

kNN

kNN

mb

mb

mb

mb

3912.137826.347395F

05.159159050145970.0

108275.20F

9164.10049.100916200970.0

105778.19F

124.7676124

145970.0

109685.9F

so

macs,

reds,

mins,

6

6

6

DIMNENSIONIMI I PLLAKS ME LARTSI KONSTANTE


17/44



c. drejtimi x-x, C-25/30, S-400/500

kNmM ax 998.23

mmfb

Md

cdsds

sdx 161.95

667.16159.01000

10998.23 6

h=dx+d1x=95.161+15+10/2=115.16mm (120mm), e prvetsuar h=160mm

dx=h-d1x=165-15-5=145mm

dy=dx-x/2- y/2=145-10/2-10/2=135mm

a) Llogaritja e siprfaqes s armaturs n drejtimin x-x n fush:

035.066.161451000

10239.122

6

2

cdx

sdsd

fdb

M

mmdhd xx 145201651

Nga tab. prsds=0.037

s=10, c=1.10, =0.099, =0.965

c0

d1x

dx

h

d1y

dy

Asly

Aslx

SIPRFAQJA E NEVOJSHME E ARMATURS:N fush:

2

2

26

5.21714510000015.00015.0

5.217400

14510006.06.0

47.251826.347145965.0

10239.12

mmbh

mmf

bd

mmfd

M

Ayk

ydx

sd

reqsl

HAPI I ARMATURS


18/44



Pr 10 As= 79 mm

2reqsl

provsl

2`

l

1sprov

sl

x

reqsl

1s

l

250.17mmA376.190A

376.190mm1000210

791000

s

AA

10/21cmetprvetsoh

350mmmax

217.5mm1451.5d1.51.5h

314.15mm1000251.47

791000

A

A

s

b) Llogaritja e siprfaqes s armaturs n mbshtetsin a:

kNmM ax 998.23

dx=h-d1x=165-15-5=145mm

068.066.161451000

10998.232

6

2

cdx

sdsd

fdb

M

Nga tab. prsds=0.0687s=10, c=1.65, =0.142, =0.948

Aslyc0

d1x

dx

h

d1y

dy

Aslx

2

2

26

5.21714510000015.00015.0

5.217400

14510006.06.0

931.501826.347145948.0

10998.23

mmbh

mmf

bd

mmfd

M

Ayk

ydx

sd

reqsl

Hapi i armaturs


19/44



Nga fusha e par kthehen:

2`prov

sl mm095.1882

376.19

A2

1

nga fusha e par dhe

2`provsl mm095.188

2

376.19A

2

1 nga fusha e dyt, e gjithsjt:

2`provsl mm19.376095.188095.188A

2`kthsl

reqsl 125.741mm376.19-501.931A-A

reqslA

Hapi nga fusha sht sy=210mm

1000A

1req

sl y

sl

s

A

,

21

sl 40.261000

210741.125

1000 mm

sA

A

yreqsl

prvetsohet: 6/210 me Aprovsl= (28.26/210)*1000=134.57 mm

Siprfaqja e trsishme e armatures mbi mbshtetsin a do tjet:

2,(a)provsl 76.51057.13419.376A mmAA

provsl

kthprovsl

Prv. 10/2*210+ 10/2*210+ 6/210

Dimensionimi n fush, drejtimi y-y

d. drejtimi y-y

kNmM fy

914.9max

Aslyc0

d1x

dx

h

d1y

dy

slx

dy=dx-x/2- y/2=145-10/2-10/2=135mm

0326.0667.161351000

10914.92

6

2

cdx

sdsds

fdb

M

9675.0d

z093.0

%02.1dhe%10:lexojm0326.0... csds

d

x

pr s


20/44



2

2

26

5.20213510000015.00015.0

5.202400

13510006.06.0

223.218826.3471359675.0

10914.9

mmbd

mmf

bd

mmfd

M

Ayk

yd

sd

reqsl

21 7910 mmAmeper s

Hapi i armatures :

22

`21

provsl

1

223.218395

3951000200

791000A

10/20

350max

5.2021355.15.15.1

015.3621000

223.218

791000

mmAmmA

mms

A

etprvetsoh

mm

mmdh

mm

A

A

s

reqsl

provsl

l

s

x

req

sl

s

l

Dimensionimi n mbshtetsin b

kNmM redyb 5778.19,

Aslyc0

d1x

dx

h

d1y

dy

Aslx

dy=dx-x/2- y/2=145-10/2-10/2=135mm

064.0667.161351000

10578.192

6

2

cdy

sdsds

fdb

M

Nga tab. prsds=0.065

s=10, c=1.6, =0. 95, =0.138

26

ydy

sdreqsl mm89.384

347.8263510.95

1019.5778

fd

MA


21/44



Nga fusha e par kthehen:

2`kth

sl mm3953952

1

9532

1

A 2`kth

slreqsl mm89.34395-89.384A-A

reqslA

Siprfaqja e nj shufre pr armatur shtes

21sl 77.8

1000

20089.43

1000mm

sAA x

reqsl

21sl 556.17

1000

200289.43

1000

2mm

sAA x

reqsl

prvetsohet: 6/2*200 me Aprov

sl= (28.26/2*200)*1000=70 mmSiprfaqja e trsishme e armaturs mbi mbshtetsin a do tjet:

2,(b)provsl 46570395A mmAA

provsl

kthprovsl

Prv. 10/400+ 10/400+ 6/400

LLOGARITJA E GJATSIS S INKASTRIMIT

mmlmepervetesoj

ll

sMpafmmhNf

mm

l

lA

A

ll

xx

bxx

ackbd

b

bprov

req

aabneto

bneto

bneto

sl

sl

150

921.149)190.376

17.250(06.3227.0

7.0400,25)2/(7.2

10010

3.0

)(

)(

min)(

min

mmlmepervetesoj

ll

yy

bxx

bneto

bneto

150

548.124)395

223.218(06.3237.0

)(

min)(


22/44



7.Plani i armatursPasqyra tabelare e ndikimeve:

drejtimi Mf(kNm)maxmin )(kNmMam

maxredmin

(kNm)Mbmmaxredmin

x-x 12.23984.091

-11.9573-23.9988-25.7135

y-y 9.91423.3138

-9.6856-19.5778-20.8275

Pr drejtimin x x n fush:

kNNfAF

kNNF

kNNF

kNfAF

kNNF

kNNF

kNNd

MF

ambeshtetnexxdrejtiper

kNNfAF

kNNd

MF

kNNd

MF

ydprovsl

fso

fsl

fs

ydprovmb

so

mbsl

mbredsl

mmbsl

ydprovf

sd

sdf

sdfs

sl

sl

sl

3912.13727.137391826.347395

3712.2523.253711359675.0

103138.3

905.7544.759051359675.0

109142.9

fushny,-ydrejtiminpr

65.177826.34776.510

06.18718706145948.0

107135.25

58.1740.174580210948.0

109988.23

98.8622.86980145948.0109573.11

""sin...,min

488.1300.130488826.347190.376

233.290.29230145965.0

10091.4

4681.87286.87468145965.0

102398.12

6

min,

6

max,

6

max,

6

,

6min

min,

6min

6max,

max,1

min,


23/44



Drejtimi y-y- mbshtetsi b:

kN

kNN

kNN

kNN

mb

mb

mb

mb

74.161826.347465F

397.16216239713595.0

108275.20F

592.1520.15259213595.0

105778.19F

73.770.777313595.0

109685.9F

so

macs,

reds,

mins,

6

6

6


24/44



POS 5, Trau b b TRA KONTINUAL

0.4*lx0.4*lx

Fsl,min

Fsl,max

Fsl,max_

mb.

Fsl,min_

mb.

lx lx

t t t

V2a(G,Q),x

Gek

Gv

Qek

lx lx

1

2

a b

V2b(G,Q),x

a

1V

1b(G

,Q),y

Gek

Gv

Qek

V2b(G,Q

),y

Q Q

G G

Qtrap

Qtrap

Gtrap

Gtrap

V2a(G,Q),x

V1b(G,Q

),y


25/44



7.1.1 Karakteristikat gjeometrike

45.052

5.4

240

30

4025.31.

66.4116

1.

12

1

max

min

..

l

l

h

b

cmmpervetsojlh

t

w

y

1. Analiza e ngarkesave:

Pesha vetjake

'/7625.125165.04.03.0 mkNhbG cwv

Ngarkesat nga pllaka

'/655.1989.177625.1

'/89.170775.2645.045.02121G

N/m'0775.264.5795.522

l

3232EK

min

mkNGGG

mkNG

kGG

EKv

PLL

Ngarkesat e prkohshme

'/53.182745.045.0212721)21(

275.4622

323232

min

mkNQQ

lQQ

EK

PLL

Ngarkesat e llogaritse

'/795.2753.1850.150.1

'/534.26655.1935.135.1

mkNQQ

mkNGG

d

d


26/44



7.2Llogaritja e ndikimeve statike

V1b(G,Q),y

Gek

Gv

Qek

V2b(G,Q),y

Qtrap Qtrap

Gtrap Gtrap

V1b(G,Q),y

0.4*lx0.4*lx

Fsl,min

Fsl,max

Fsl,max_

mb.

Fsl,min_

mb.

N fush:

2max yddf

sd lQbGaM

Nga tabelat e Vinklerit, pr tra t vazhduar me 3 mbshtetsa dhe 2 fusha:

Pr y=0.40ly

a=0.07; b=0.095; c=-0.0250

kNmM

lQbGaM

fsd

yddf

sd

45.112

5795.27095.0534.2607.0

max

22max

kNmM

lQcGaM

fsd

yddf

sd

063.29

5795.27025.0534.2607.0

min

22min

N mbshtets:

Nga tab. pr tra t vazhduar me 3 mbshtetsa dhe 2 fusha

Pr y=ly a=0.1250; b=0.000; c=-0.1250

kNmM

lQbGaM

mbsd

yddmbsd

92.82

5534.26125.0

max

22max

kNmM

lQcGaM

mbsd

yddmbsd

78.169

5795.27125.0534.26125.0

min

22min


27/44



Forcat Transferzale:

Pr y=0

kNlQbGaV yddsd 4.1135795.274375.0053.28375.0max

kNlQcGaV yddsd 91.435795.270625.0053.28375.0min

Pr y=ly

kNlQbGaV yddsd 67.875795.270.0053.28625.0max

kNlQcGaV yddsd 52.1745795.27625.0053.28625.0min

kNlQaGaR yddaps 4.1135795.274375.0053.28375.01max.

kNlQaGaR yddaps 05.3495795.2725.1053.2825.12max.

Diagramet e forcave transferzale:

t ln t

h

b

As1

113.4=Vsd0,min

43.91

(0) (1) (2)

lnt

87.67

Vsd1,min=174.52

113.4

43.91

a b

t/2+d t

174.52

87.67

As2


28/44



Dimensionimi i traut me lartsi konstante:

N fush

kNmM

d

z

d

x

macsd

sdcs

78.169

139.0;892.0;259.05.310/ 000

mmddmpervetesojhd

mmfb

Md

cdsds

sd

21.4612.4691.01.01.006.0

12.462667.16159.0300

1078.169

11

6

h=462.12+50=512.12mm

Prvetsojm h = 55 cm dhe prsrisim pikat paraprake

1. Karakteristikat gjeometrike

55.0

30.0

h

bw

2. Analiza e ngarkesave

Pesha vetjake

'/8875.225165.055.030.0 mkNhbG cwv

Ngarkesat nga pllaka

'/78.2089.178875.2

'/89.1721G

kN/m'0775.2622

l

32EK

min

mkNGGG

mkNG

GG

EKv

PLL


'/53.1821

'272

32

min

mkNQQ

kNml

QQ

EK

PLL

Ngarkesat llogaritse

'/795.2753.1850.150.1

'/053.2878.2035.135.1

mkNQQ

mkNGG

d

d


29/44



3. Llogaritja e ndikimeve statike

V1b(G,Q),y

Gek

Gv

Qek

V2b(G,Q),y

Qtrap Qtrap

Gtrap Gtrap

V1b(G,Q),y

0.4*lx0.4*lx

Fsl,m

in

Fsl,max

Fsl,max_

mb.

Fsl,m

in_

mb.

N fush:

Nga tab. pr tra t vazhduar me 3 mbshtetsa dhe 2 fusha

Pr y=0.40ly a=0.07; b=0.095; c=-0.0250

kNmM

lQbGaM

fsd

yddf

sd

105.115

5795.27095.0053.2807.0

max

22max

kNmM

lQcGaM

fsd

yddf

sd

72.31

5795.27025.0053.2807.0

min

22min

Mbi mbshtets:

Pr y=lya=0.1250; b=0.000; c=-0.1250

kNmM

lQbGaM

mbsd

yddmbsd

665.87

5053.281250.0

max

22

max

'515.174

5795.27125.0053.28125.0

min

22min

kNmM

lQcGaM

mbsd

yddmbsd


30/44



4. Dimensionimi i traut me lartsi konstante

Momenti n mbshtets:

mmdhdcmh

mpervetesojandajmmhmmh

mmddh

mmdmdd

mmd

kNmMsd

50050550550

...550618.518

618.5185061.468

)50(861.4661.4681.01.0

61.468667.16159.0300

10515.174

'515.174

1

sup

1

11

6

max

N fush, kNmM fsd 105.115max

cdeff

sdsds

fdb

M

2 , l0=0.85l=0.85*5.0= 4.25m

cml

cmhb

cmlb

by

fw

w

eff

5003605.16203020

1154255

130

5

10

cmbeff 115

024.0667.165001150

10105.1152

6

2

cdeff

sdsds

fdb

M

mmhmmdx

dz

dx

lexojmprtabnga

f

sc

sds

1650.39500078.0

973.0,078.01085.0

,024.0....

000

000

2

26

225400

5003006.06.0

21.680826.347500973.0

10105.115

mmf

db

mmfd

M

A

yk

w

yd

sd

req

sl


31/44



mmAmmmepervetesoj

A

A

n

mmAmempervetesojmmA

req

sl

reqsl

slreq

sl

sl

21.6808042014164

384.3201

21.680

2011621.680

2

22

Stafat: 8/25 prs 1/4max =16/4= 4mm

216 k.

416

210

30

55

hf

mmmmc

mmepervetsojmmm

mmc

2016max

2516max

200

ccnscb

cnnscb

w

w

0

0

2122

055.7

2016

2082523002 0

c

cscbn w

T gjitha shufrat mund t vendosen n nj rend.

mmscd

mmn

nscbc w

0.412

16825

2

667.5614 1648250300122

01

0

d=h-d1=550-41=509mm

Dimensionimi mbi mbshets

kNmM mbsd 78.169min

1358.0667.16500300

1078.169

50050550

50

2

6

2

1

1

cdw

mb

sdsfdb

M

mmdhd

mmd

sd

908.0228.01095.2

153.0....

000

000

d

z

d

x

lexojmepertabnga

sc

sds


32/44



2

26

5.862400

50011506.06.0

15.1075826.347500908.0

1078.169

mmf

db

mmfd

M

A

yk

eff

yd

sd

req

sl

22

2

)1(

2)1(2

15.107512062016166:

349.5201

15.1075

2011615.1075

mmAmmpervetsoj

mmA

An

mmAmepervetesojmmA

reqsl

sl

req

reqsl

sl

sl

30

55

216 k.

hf

416

210

216 nga f. II

Nga fusha e par kthehen 216mm,

Nga fusha e dyt kthehen 216mm,

416mm

+ konstruktive 216mm

gjithsejt mbi mbshtets: 616mm

mmdmmd 50536

)2/162016825(2)2/16825(4 sup11

d=h-d1=550-53=497mm

Llogaritja e gjatsis s inkastrimit

mmlmepervetesoj

lmml

f

fl

mm

mm

l

lA

All

bneto

bneto

sl

sl

b

a

bd

yd

bneto

b

bprov

req

aabneto

300

885.3001206

003.100629.5157.0

7.029.5157.2

826.347

4

16

4

100

16010

587.1543.0

)(

min

min


33/44



5. Plani i armaturs pr traun

N fush

kNfAF

kNd

MF

kNNd

MF

ydprovsl

fs

sdfs

sdfs

652.279826.347804

179.64509971.0

1072.31

89.2321000/39.230893509971.0

10105.115

0

6min

min

6max

max

N mbshtets;

kNfAF

kNd

MF

kNd

MF

yd

prov

sl

f

s

sdfs

sdfs

478.419826.3471206

914.349409896.0

10515.174

872.175497896.0

10665.87

0

6min

min

6max

max

Paraqitja skematike e armatures s prvetsuar:

lx lx

t

12 216 3 216 2

2

4 6/25/12.5

2' 216

1

30

55

16.

5

k k

1 12 2

30

55

16.5

1 1

k k2 22'2'

Prerja 1-1 Prerja 2-2


34/44



Sigurimi nga forcat transferzale

Mbshtetsi 1:

t ln t

h

b

As1

113.4=Vsd0,min

43.91

(0) (1) (2)

lnt

87.67

Vsd1,min=174.52

113.4

43.91

a b

t/2+d t

174.52

87.67

As2

dm=497mm

ab

91.4352.174 , a+b=l=5m

174.52*a=43.91*b ba 52.174

91.43,

a=0.2516*b

a+b=5 b=5-a=5-0.2516*b

b+0.2516*b=5

1.2516*b=5 b=5/1.2516=3.995

a

V

b

V 0 minsd,1

minsd,

a=0.2516*b

a=0.2516*3.995=1.005


35/44



t ln

43.91

(0) (1)

t

Vsd1,min

=174.52kNa=1.005m

b=3.995m

t/2+d t

174.52

Vsd1*

t=30cm, (shtylla: a/b=30/30cm)t/2+d=300/2+497=647mm=0.647

m

)2

t(-b

V

b

V * minsd,1

minsd,

d

)2

(b

V1 minsd,* dt

bVsd

256.146)647.0995.3(3.995

174.52* sdV

dbkV wcpRdRd 15.0)402.1( 11pr C-25/30,Rd=0.30N/mm2k=1.6-d=1.6-0.497=1.1031

02.0008.049730

1206

db

A

w

sll ln t

t/2+d t

lb,net d

Asl

7.49300.015.0)008.0402.1(103.103.01 RdV kNVV sdRd 256.14699.74

*1 , duhet t bhet sigurimi nga forcat transferzale

0

db

N

w

sdcp

Aftsia mbajtse e shufrave t shtypura:

VRd2=0.5**fcd*bw*kz*d

= 0.7-fck/200=0.7-25/200=0..575 0.5

VRd2=(0.5*0.575*16.66*300*0.908*497)*10 -3=648.45 kNVRd2=648.45 kN>Vsd

*=146.256kN (plotsohet kushti)

Siprfaqja minimale e stafave do t jet:

1) Vsd* 1/5*Vrd2 , smax=0.8*d 300 mm2) 1/5*VRd2< Vsd* 2/3*Vrd2 , smax=0.6*d 300 mm3) Vsd* > 2/3*Vrd2 , smax=0.3*d = 200 mm

N kt rast plotsohet kushti i dyt.

129.69 < Vsd*=146.256kN


36/44



smax=0.6*497=298.2 cm ( 30 cm )

Vsd= VRd3= Vcd= Vwd

Vsd= Vcd+ VwdVcd= VRd1

Vsd= VRd1+ Vwd

Vwd= Vsd- VRd1= 146.265-74.99=71.266kN

Hapi i vrtet i stafave:

wd

zywdsw

Rdsd

zdywsw

wV

dkfA

VV

dkfAs

1

pr stafat S-240/360, fyw= 240/1.15=208.7 N/mm2

cmsw 21.1310

10)

266.71

497908.069.2080.1(

1

3

Prvetsohet: 8/13cm

Asw,min= w,min*sw*bw*sin

29837.0100

497908.07.208

13266.71cm

dkf

sVA

zywd

wvdsw

002522.01300130

109837.0

sin

2min,

ww

sw

wbs

A

w


37/44



ln

b=3 .9 95m

28/13-20

?=2.3m

h

a=1.005m

(0)

43.91

dt

?=2 .3m

8/13 2 8/13-20 2 8/20

Vsd 1,m in

=174.52kN

Vs d 1*(1)

t

174.52

dt

8/13


38/44



POS Shtylla 2-b dhe POS 2-b Themeli

0.4*lx0.4*lx

Fsl,m

in

Fsl,max

Fsl,max_

mb.

Fsl,min_

mb.

lx lx

t t t

V2a(G,Q),x

Gek

Gv

Qek

lx=4.5m

1

2

a b

V2b(G,Q),x

a

1V

1b(G,Q

),y

Gek

Gv

Qek

ly=5m

V2b(G,Q

),y

Q Q

Qtrap

G G

Qtrap

Gtrap

Gtrap

V2a(G,Q),x

V1b(G,Q

),y

Pos 103

Pos105

Sh 1

lx=4.5m

ly=5m


39/44



6. Karakteristikat gjeometrike

Prvetsohen dimensionet e shtylls: a/b=30/30 cm (trau, 55.0

30.0h

bw (cm))

Dimensioni minimal pr shtylla t betonuara n vend: a/b=20/20cm

7. Analiza e ngarkesave

Ndikimet nga Pos 105 -trau b-b

Gsd=27.795 kN/m

Qsd=28.053 kN/m

V1b(G,Q),y

Gek

Gv

Qek

V2b(G,Q),y

Qtrap Qtrap

Gtrap Gtrap

V1b(G,Q),y

kNlQaGaR yddPos 05.3495795.2725.1053.2825.11052

Ndikimet nga Pos 103 -trau 2-2 n drejtimin x-x

V2a(G,Q),x

Gek

Gv

Qek

lx=4.5m

V2b(G,Q),x

Q Q

G G

V2a(G,Q),x

lx=4.5m


40/44



Pesha vetjake

'/8875.225165.055.030.0 mkNhbG cwv

R2,(Pos 103)

R2,(Pos 105)

Gv,sh

Nga pllaka:

Ngarkesat e prhershme

kN/m'1855.91298.618875.2GGG

kN/m'298.6126.07758

5G

8

5G

kN/m'0775.6222

5.4795.52

2

lGG

EKv

EK

minPLL


'/875.160.278

5

8

5

'0.27225.462

2 min

mkNQQ

kNml

QQ

EK

PLL


41/44



Ngarkesat llogaritse

'/3125.25875.1650.1'/90.251875.1935.1

2,

2,

mkNQQmkNGG

Qd

Gsd

kNlQaGaR yddPos 07.2885.43125.2525.19.2525.11032

Ngarkesa n shtylln 2-b- Pos- Sh1

Nga Pos 103 kNRPos 07.2881032

Nga Pos 105 kNRPos 05.3491052

Nga pasha vetjake e shtylls

'/442.72555.0330.030.035.1 mkNGshv

'/562.644 mkNN shsd

Dimensionimi i shtylls

'/562.644 mkNN shsd

Kontrollimi i epjes:

4298.0666,13030

562.644

cdc

sdu

fA

N , le=0.707*(H-ht)=0.707*291.75=206.27cm

79.2330289.0

75.291707.0

289.0

707.0

min

a

l

i

lk

88.22

4298.0

1515

25

max79.23 lim

u

k

, epja nuk merret parasysh

fcd=16.66N/mm2 , fyd=347.826N/mm

2

23

yd

sd

2provc

2

yd

cdcsd

reqsl

2.70cm347.826

10644.5620.15

f

N0.15

2,70cm30300.003A0.003

18.11cm34.7826

1.6660.853030644.562

f

f0.85AN

A


42/44



Prvetsohen 414mm, me 2provsl 16.6 cmA

Armatura trthore (stafat):

mm

mm

gj

s5.314

4

1

4

1

6min

me hapin:

mm

mmba

mm

s

l

w

300max

300

168141212

min

Prvetsohen: s6/300/150mm

Detaji i Armimit pr shtylln Sh-1 _ Pl=1:20, C-20/25, S-400/500

Prerja 1-1

1 1

2 212

1 212

3

6/12.5

/25

1 & 2 412

3 6/12.5/25

1

212

2

212


43/44



Dimensionimi i themelit

Nga shtylla Sh1: '/562.644 mkNNsh

sd

kNN

NQG

shsd 32.452

2

5.135.1562.644

2

Pesha vetjake e themelit: 0.12*645.325=77.44kN

NGth0.1Nsh =0.1*452.32=45.23kN, Nth=452.32+45.23=497.55kN

nga:th

thlejt

A

N,

lejt

thth

NA

, , t,lej=0.20MPa=0.20N/mm

2

2

1,

6.276411020.0

55.497cm

NA

lejt

thth

, cmath 72.15720.0

1055.497 3

ptok.

Nsd

A1 A1A2

prvetsohet a=160cm

)2( 2211 eAeApMMysd

xsd

2

1

2

2

1

ab

A ,

23

21

abe

aab

A

22 ,

22

12

abe

ababb

NMM

th

ysd

xsd

sd

224

2

2

3.06.123.06.16.124

6225,705 22

sdM

kNmM sd 93.67

26

, 55.394826.3475509.0

1093.67mm

fd

MA

yd

xsdreq

sl

suph=60cm, d=60-5=55cmpr =8mm, As

1=50mm2

mmbA

As

req

sll

sl

76.202160055.394

501

prv. 8/200mm, me

24001600200

50mmAprov

sl


44/44


Detaji i Armimit pr themelin e veuar _ Pl=1:20, C-20/25, S-400/500

1 8/15/30

2 8/15/30

2 10/15/30

18

/15/30

1 8/15/30

2

8/15/3

0

Nsd

mbulesa keson_ trau

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