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USHTRIMI 1.doc .1

USHTRIMI 1

Per planin e strukturave te treguar ne Figuren 1.1 jepen:

1. Materialet:

Betoni i klasit B-20 me R b =115 daN/cm2, R bt =9.18 daN/cm2 Celiku me Rs =2150 daN/cm

2

2. Shtresat si ne Figuren 1.2

3. Ngarkesa e perkohshme (shfrytezimit) pn =150 daN/m2; f =1.4

4 5 0

25

1

2

1

2

A B C

S-2d=10

S-1d=10

900 200

A B C

900 200

4 5 0

T-1

+3.06

+3.06

+3.06

2 5

25

25

2 5

Figura 1.1: Plani i Strukturave [cm]

Sh 1:50

Pllaka mermeri 2 cm (=2900daN/m3; f =1.2)

Llac 3 cm (=1800daN/m3; f =1.2)

Soleta 10 cm (=2500daN/m3; f =1.1)

Suva 1.5 cm (=1800daN/m3; f =1.2)

Figura 1.2: Shtresat

KERKOHET:

1. Llogaritja e elementeve b/a te planit te strukturave kundrejt momentit perkules2. Kontrolli kundrejt forces prerese

3. Konstruimi (vizatimi i elementeve)4. Sasite e materialeve te perdorura ([m

3] beton dhe [kg] armature)


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USHTRIMI 1.doc .2

1.1 LLOGARITJA E SOLETES S-1

Skema reale e soletes S-1 jepet ne Figuren 1.3:

+3.06

25 175 25

3 5

T-1

hs=10cm

1 0

Figura 1.3: Skema reale e soletes S-1 [cm]

Skema llogaritese e soletes S-1 jepet ne Figuren 1.4:

Gjatesia llogaritese (kalkuluese) e soletes cmd ld lk

192325175

325

330

192

q

q=g+p

Figura 1.4: Skema llogaritese e soletes S-1 [cm]

Seksioni llogarites i soletes S-1 jepet ne Figuren 1.5:

hs =1/35 * lk =1/35 * 192 =5.5 [cm] Pranojme hs =10 [cm] (hmin=7 cm)h0 = h-a = 10-1.5 = 8.5 cm

100

1 0

Figura 1.5: Seksioni llogarites i soletes S-1 [cm]

Llogaritja e ngarkesave:

E perhershme- prej pllakave 2 cm: 0.02 * 1 * 1 * 2900 = 58 daN/m

2* 1.2 = 69.6 daN/m

2

- prej llacit 3 cm: 0.03 * 1 * 1 * 1800 = 54 daN/m2 * 1.2 = 64.8 daN/m2

- prej soletes 10 cm: 0.10 * 1 * 1 * 2500 = 250 daN/m2 * 1.1 = 275 daN/m

2

- prej suvase 1.5 cm: 0.015 * 1 * 1 * 1800 = 27 daN/m2* 1.2 = 32.4 daN/m2

gn =389 daN/m

2 g = 442 daN/m

2

E perkohshme- pn = 150 daN/m2 p = 150 * 1.4 = 210 daN/m2

E plote

- q

n

= g

n

+ p

n

= 389 + 150 = 539 daN/m

2

- q = g + p = 442 +210 = 652 daN/m2


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USHTRIMI 1.doc .3

Llogaritja e forcave te brendshme maksimale Mmax dhe Qmax :

Mmax = 0.125 * q* lk 2 = 0.125 * 652 * 1.922 = 300 daNm

Qmax = 0.5 * q * lk = 0.5 * 652 * 1.92 = 626 daN

Q max=ql

2Q max

192

q

q=g+p

M

Q

Mmax=ql2

8

Figura 1.6: Forcat e brendshme M dhe Q ne element

Llogaritja e armatures:

036.01155.8100

10030022

0

0

b Rhb

M A

41.0)578.05.01(578.0)5.01(0 y y y A

578.0

1.1

758.02

758.0

1.12

y

758.05.1108.085.008.085.0 b

R [Kujdes !!!R b ne Mpa]

037.0036.0211211 0 A

Mqs 41.0036.0 00 y A A

ose 578.0037.0 y

elementi armohet me armature nje fishe (vetem ne zonen e terhequr).

Sasia e nevojshme e armatures llogaritet:

mlcm R

Rhb A

s

b

s/64.1

2150

1155.8100036.0 20

Per mlcm As

/64.1 2 ne tabelen e armatures zgjedhim ml/85 me 251.2 cm As

Duke ndjekur te njejten rruge, per soleten S-2 rezulton mlcm As

/16.10 2

Per mlcm As

/16.10 2 ne tabelen e armatures zgjedhim ml/129 me 218.10 cm As


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USHTRIMI 1.doc .4

A

B

C

S - 2 h = 1

0

S - 1

h = 1 0

9 0 0

2 0 0

A

B

C

9 0 0

2 0 0

450

T - 1

100

+ 3 . 0

6

+ 3 . 0

6

+ 3 . 0

6

1 0

25

2 5

2 5

25

1 0 0

10

1 2

1 2

Figura 1.7: Llogaritja e soletave S-1 dhe S-2


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USHTRIMI 1.doc .5

1 2

A

B

C

S - 2

h = 1 0

S - 1

h = 1 0

9 0 0

2 0 0

A

B

C

9 0 0

2 0 0

450

T - 1

+ 3 . 0

6

+ 3 . 0

6

+ 3 . 0

6

25

2 5

2 5

25

450

2 5

1 2

1 2 / m

8 / m

8 / m

1 2 / m

S h p . 4

1 0 / m

S h p . 4 8 / m

Figura 1.8: Plani strukturave ne kuoten +3.06m SH 1:50


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USHTRIMI 1.doc .6

1.2 LLOGARITJA E TRAUT T-1

Skema reale e traut T-1 jepet ne Figuren 1.9:

1 2

25425

25450

3 5

ht=35cmd=25

Figura 1.9: Skema reale e traut T-1

Skema llogaritese e traut T-1 jepet ne Figuren 1.10:

446

q = g + p

1 2

t t tq t

Figura 1.10: Skema llogaritese e traut T-1

lk = l0+d 1.05 * l0 (d-thellesia e mbeshtetjes)

l0+d = 425+25 = 450 cm1.05 * l0 = 1.05 * 425 = 446 cm

Pranojme lk = 446 cm

Seksioni llogarites i traut T-1 jepet ne Figuren 1.11:

ht = (1/10~1/12) * lk = (1/10~1/12) * 446ht = (44.6 ~ 37) cm

Pranojme ht = 35 cm, rrjedhimisht h0 = h – a = 35 – 3.5 = 31.5 cm

b = (1/2~1/3) * h = 1/2 * 35 = 17.5 cm

Pranojme bt = 25 cm

3 5

25

1 0

Figura 1.11: Seksioni llogarites i traut T-1


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USHTRIMI 1.doc .7

Ngarkesat ne tra:

Ngarkesa e murit = 210 daN/m2

H murit = 3 m

20

1 0

3 5

25

E perhershme

- prej soletes + shtresat ne te: 389*2/2 =389 daN/m; 442*2/2 =442 daN/m

- prej peshes se traut: 0.25*0.35*1*2500 =219 -//- 219*1.1 =241 -//-

- prej suvase ne tra: 0.015*(0.25+2*0.25)*1800 = 20 -//- 20*1.2 = 24 -//-

- prej murit mbi tra: 210*3 =630 -//- 630*1.1 =693 -//-

gntr = 1258 daN/m gtr =1400 daN/m

E perkohshme

-prej soletes: pntr =150*2/2=150daN/m; ptr =210*2/2=210daN/m

E plote

q ntr = gntr + p

ntr = 1258 + 150 = 1408 daN/m

q tr = gtr + ptr = 1400 + 210 = 1610 daN/m

Llogaritja e forcave te brendshme M dhe Q ne tra:

Qmax

Mmax=q 2

8t l

Qmax=

q 2

2t l

M

Q

q t

446

q = g + pt t t


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USHTRIMI 1.doc .8

M = 0.125 * q tr * lk 2 = 0.125 * 1610 * 4.46

2 = 4003 daNm

Q = 0.5 * q tr * lk = 0.5 * 1610 * 4.46 = 3590 daN

Llogaritja e siperfaqes se nevojshme te armatures se traut As:

14.01155.3125

100400322

0

0

b Rhb

M A

41.0)578.05.01(578.0)5.01(0 y y y A

578.0

1.1

758.02

758.0

1.12

y

758.05.1108.085.008.085.0 b

R

15.014.0211211 0 A

Mqs 41.014.0 00 y A A

ose 578.015.0 y

ath elementi armohet me armature punuese vetem ne zonen e terhequr (si element me

armature nje fishe).

Sasia e nevojshme e armatures do te llogaritet:

2

0 32.6

2150

1155.312515.0 cm

R

Rhb A

s

b

s

Per 232.6 cm As ne tabelen e armatures zgjedhim 164 me204.8 cm As

Gjithashtu do te mund te zgjidhnim 162142 me 201.7 cm As si rast me ekonomik.

Gjeresia e nevojshme e traut per vendosjen e ketyre shufrave ne 1 rradhe eshte b=19cm.

Si armature montuese do te pranojme konstruktivisht 142 .

Armimi i traut T-1 do te behet sipas variantit me shufra te kthyera dhe me shufra te

drejta duke perdorur si armature terthore stafe cm20/8 ne gjithe gjatesine e traut.


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USHTRIMI 1.doc .9

2. Kontrolli nga forca prerese

2.1 Kontrolli soletes S-1

Percaktojme forcen prerese qe mban betoni:

daN RhbQbt nbb

468218.95.8100016.01 04

Meqenese daN QdaN Q jb 6264682 , forca prerese perballohet nga vete betoni.

Soleta S-1 eshte e siguruar kundrejt forces prerese.

2.2 Kontrolli traut T-1

Percaktojme forcen prerese qe mban betoni:

daN RhbQbt nbb

433818.95.3125016.01 04

Meqenese daN QdaN Q jb 35904338 , forca prerese perballohet nga vete betoni.

Trau T-1 eshte i siguruar kundrejt forces prerese.

Gjithashtu mund te llogarisim forcen prerese totale qe perballon elementi:

mldaN

S

Ranq

w

swsw

sw/85

20

17005.02

daN q RhbQ swbt bbw 124448518.95.312524422

02

Pra forca prerese totale qe mund te perballoje trau T-1 i armuar me stafe cm20/8 eshte

kN Q 44.124 .


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USHTRIMI 1.doc .10

3. Vizatimi i elementeve

25 175 25

T-1

1 0

20 20

Figura 1.12: Armimi soletes S-1 sipas dy varianteve te ndryshme [cm]


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USHTRIMI 1.doc .11

1 2

5425

25450

3 5

20

25

3 5

25

3 5

Figura 1.13: Armimi traut T-1 sipas variantit me shufra te kthyera [cm]


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USHTRIMI 1.doc .12

1 2

25425

25450

3

5

d=2520

25

3 5

Figura 1.14: Armimi traut T-1 sipas variantit me shufra te drejta [cm]


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USHTRIMI 1.doc .13

4. Sasite e materialeve te perdorura

Figura 1.15: Tabela e specifikimit te armatures

Volumi betonit:

Soleta S-1: 301.11.075.4125.2 mV

Soleta S-2: 333.41.075.4125.9 mV

Trau T-1: 33.075.4)1.035.0(25.0 mV

Volumi total: 365.53.033.401.1 mV

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