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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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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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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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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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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