Stopa fundamentowa |
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Poz. 5 . Stopa fundamentowa. |
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1. Określenie wymiarów stopy |
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5.1 Określenie wymiarów stopy. |
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q= |
15 |
[kN/m3] |
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qfun= |
350 |
[kN/m2] |
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q = 22,5 kN/m3 |
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NSd= |
981,09 |
[kN] |
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qfu = 350 kN/m2 |
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Założono że: B = L = |
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N = 1062,44kN |
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1.1 Głębokość posadowieniastopy w stosunku do poziomu |
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założono : |
B = L = |
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h= |
1,6 |
[m] |
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G= B2 * h * q |
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h = 1,5 m -głębokość posadowienia stopy w stosunku do |
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1.2 Ciężar dla bryły fundament-grunt |
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poziomu posadzki parteru. |
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G= |
B2x24 |
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G= B2 *1,5*22,5 = 33,75 B2 kNm2 |
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m= |
0,81 |
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(350*0,81-33,75)*B2 1062,44 |
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249,75* B2 1062,44 |
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B2 4,25 |
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B 2,06 m |
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przyjęto : B = L = 2,1 m |
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5.2 Określenie zbrojenia na zginanie |
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d = 750 mm |
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Przyjęto B= |
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3,9 |
[m] |
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przyjęto 8 12 o As1 = 9,05 cm2 |
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2. Zbrojenie na zginanie |
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2.1 Odpór gruntu |
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w jednym kierunku w rozstawie co 286 mm |
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5.3 Sprawdzenie stopy na przebicie. |
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qr0= |
88,50 |
[kN/m] |
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d= |
550 |
[mm] |
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2.2 Moment zginający wspornik |
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aSB=aSL=h= |
300 |
[mm] |
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L=B= |
3,9 |
[m] |
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fyd= |
350 |
[N/mm2] |
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A = 19502 =3802500 mm2 = 3,8 m2 |
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NRd = 1,0*4600*750 =3450000 N = 3450 kN |
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Ma= |
387,113 |
[kNm] |
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Ostatecznie: |
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1062,44-3,8*274,67= 18,69 kN < NRd |
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2.3 Przyjęcie zbrojenia |
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WARUNEK SPEŁNIONY |
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As1= |
2234,41879886268 |
[mm2] |
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As1= |
22,3441879886268 |
[cm2] |
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Przyjęto 9o18 o As1= |
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22,9 |
[cm2] |
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Zestawienie obciążeń eksploatacyjnych |
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1.1 Obciążenia stałe eksploatacyjne |
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Rodzaj warstwy |
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qk [kN/m] |
gf |
g [kN/m] |
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parkiet |
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0,18x3,6 |
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0,65 |
1,30 |
0,84 |
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beton wylewny |
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1,15x3,6 |
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4,14 |
1,30 |
5,38 |
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styropian |
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0,02x3,6 |
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0,07 |
1,30 |
0,09 |
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strop FERT-45 |
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10,62 |
1,10 |
11,68 |
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tynk cem.-wap. |
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0,29*3,6 |
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1,04 |
1,30 |
1,36 |
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podciąg |
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(0,7-0,03)x25x0,35 |
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5,86 |
1,10 |
6,45 |
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Suma |
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22,39 |
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25,81 |
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1.2 Obciążenia zmienne |
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Rodzaj obciążenia |
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pk [kN/m] |
gf |
p [kN/m] |
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Obciążenie |
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użytkowe |
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2,00 |
1,40 |
2,80 |
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Obciążenie zastępcze |
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ścianek działowych |
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z cegły pełnej z |
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obustronnym tynkiem |
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1,66 |
1,20 |
1,99 |
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Suma |
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3,66 |
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4,79 |
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1.3 Obciążenie skupione od ścian działowych |
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Rodzaj warstwy |
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Gk [kN] |
gf |
G [kN] |
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ciężar ściany |
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6,34x3,6 |
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22,82 |
1,10 |
25,11 |
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1.4 Obciążenia całkowite |
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qk=qk+pk = 22,39 + 3,66 |
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qk= |
26,05 |
[kN/m] |
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q0=q0+p0 = 25,81 + 4,79 |
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q0= |
30,60 |
[kN/m] |
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2. Schemat statyczny |
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G |
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8,02 |
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7,65 |
7,65 |
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7,65 |
8,02 |
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3. Sprawdzenie statu granicznego nośności |
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3.1 Nośność na zginanie |
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3.1.1 Przyjęcie przekroju |
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l/20 = 8,02/20 < beff |
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800 |
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0,401 |
> 0,25 |
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Przyjęto |
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beff= |
250 |
[mm] |
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d= |
800 |
[mm] |
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250 |
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Przęsło skrajne I |
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Msd= |
162,18 |
[kNm] |
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Msd= |
162180000 |
[kNmm] |
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3.1.2 Obliczenie powierzchni zbrojenia |
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a= |
0,85 |
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3.1.2.1 Współczynnik |
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fcd= |
10,6 |
[N/mm2] |
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beff= |
250 |
[mm] |
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dla 34GS fyd= |
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350 |
[N/mm2] |
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sb= |
0,113 |
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3.1.2.2 Względny zasięg strefy ściskanej |
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Dla sb = 0,113 odczytano xeff,lim = |
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0,440 |
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sb,lim = |
0,343 |
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z= |
0,78 |
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Ponieważ sb,lim > sb jest to przekrój pojedynczo zbrojony |
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Ostatecznie powierzchnia zbrojenia wynosi |
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As1= |
742,58 |
[mm2] |
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As1= |
7,43 |
[cm2] |
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Przyjęto 5o14 o As1 |
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7,70 |
[cm2] |
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Przęsło środkowe II |
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Msd= |
68,06 |
[kNm] |
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Msd= |
68060000 |
[kNmm] |
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3.1.3 Obliczenie powierzchni zbrojenia |
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3.1.3.1 Współczynnik |
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sb= |
0,047 |
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3.1.3.2 Względny zasięg strefy ściskanej |
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Dla sb = 0,047 odczytano xeff,lim = |
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0,369 |
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sb,lim = |
0,3 |
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z= |
0,816 |
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Ponieważ sb,lim > sb jest to przekrój pojedynczo zbrojony |
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Ostatecznie powierzchnia zbrojenia wynosi |
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As1= |
953,22 |
[mm2] |
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As1= |
9,53 |
[cm2] |
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Przyjęto 5o16 o As1 |
|
10,05 |
[cm2] |
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Przęsło środkowe III |
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Msd= |
95,72 |
[kNm] |
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Msd= |
95720000 |
[kNmm] |
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3.1.4 Obliczenie powierzchni zbrojenia |
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3.1.4.1 Współczynnik |
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3.1.4.2 Względny zasięg strefy ściskanej |
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Dla sb = 0,066 odczytano xeff,lim = |
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0,389 |
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sb,lim = |
0,313 |
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z= |
0,806 |
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Ponieważ sb,lim > sb jest to przekrój pojedynczo zbrojony |
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Ostatecznie powierzchnia zbrojenia wynosi |
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As1= |
424,14 |
[mm2] |
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As1= |
4,24 |
[cm2] |
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Przyjęto 4o12 o As1 |
|
4,52 |
[cm2] |
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Podpora A |
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Msd= |
203,7 |
[kNm] |
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Msd= |
203700000 |
[kNmm] |
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3.1.5 Obliczenie powierzchni zbrojenia |
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3.1.5.1 Współczynnik |
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sb= |
0,141 |
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3.1.5.2 Względny zasięg strefy ściskanej |
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Dla sb = 0,141 odczytano xeff,lim = |
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0,473 |
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sb,lim = |
0,361 |
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z= |
0,763 |
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Ponieważ sb,lim > sb jest to przekrój pojedynczo zbrojony |
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Ostatecznie powierzchnia zbrojenia wynosi |
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As1= |
953,47 |
[mm2] |
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As1= |
9,53 |
[cm2] |
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Przyjęto 5o16 o As1 |
|
10,05 |
[cm2] |
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Podpora B |
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Msd= |
148,45 |
[kNm] |
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Msd= |
148450000 |
[kNmm] |
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3.1.6 Obliczenie powierzchni zbrojenia |
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3.1.6.1 Współczynnik |
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sb= |
0,103 |
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3.1.6.2 Względny zasięg strefy ściskanej |
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Dla sb = 0,103 odczytano xeff,lim = |
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0,429 |
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sb,lim = |
0,336 |
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z= |
0,786 |
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|
Ponieważ sb,lim > sb jest to przekrój pojedynczo zbrojony |
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Ostatecznie powierzchnia zbrojenia wynosi |
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As1= |
674,53 |
[mm2] |
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As1= |
6,75 |
[cm2] |
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Przyjęto 4o14 o As1 |
|
6,16 |
[cm2] |
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3.2 Sprawdzenie żebra na ścinanie |
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bw= |
250 |
[mm] |
|
Vsd= |
99,64 |
[kN] |
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d= |
800 |
[mm] |
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fck= |
16 |
[N/mm2] |
|
3.2.1 Stopień zbrojenia |
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AsL= |
3,08 |
[cm2] |
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Minimalny stopień zbrojenia |
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rL= |
0,0002 |
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r1 = 0,0015 (0,15%) |
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sCP = 0 |
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Dla fck=16 wartość tRd wynosi |
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|
0,22 |
[N/mm2] |
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Do podpory doprowadzone jest więcej niż 50% zbrojenia |
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k = 1,6 - d |
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k= |
0,8 |
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3.2.2 Nośność betonu na ścinanie |
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Vsd = |
99,64 |
> |
VRd1 = |
42,5 |
|
warunek nie spełniony |
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WYMAGANE ZBROJENIE NA ŚCINANIE |
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3.2.2.1 Przy zbrojeniu tylko strzemionami |
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z = 0,9 x d = 0,9 x 800 |
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z= |
720 |
[mm] |
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n= |
0,6 |
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VRd2= |
572400 |
[N] |
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PRZEKRÓJ WYSTARCZY ZBROIĆ STRZEMIONAMI PIONOWYMI |
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3.2.2.2 Rozstaw strzemion |
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Przyjęto strzemiona dwucięte o8 o Asw = 2 x 0,5 = 1,01cm2 |
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oraz czterocięte o8 o Asw = 4 x 0,5 = 2,01cm2 |
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Zbrojenie przy podporze A |
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3.2.2.3 Odcinek wymagający zbrojenia |
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q0= |
30,60 |
[kN/m] |
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Vsd= |
99,64 |
[kN] |
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= |
1,87 |
[m] |
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= |
153,26 |
[mm] |
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Przyjęto s= |
150 |
[mm] |
c=8x150 |
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c= |
1200 |
[mm] |
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Zbrojenie przy podporze B z lewej strony |
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3.2.2.4 Odcinek wymagający zbrojenia |
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q0= |
30,60 |
[kN/m] |
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VsdL = |
148,17 |
[kN] |
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= |
3,5 |
[m] |
> 3d = 3x0,8=2,4 |
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dlatego wstępnie c=c1+c2=1850+1650=3500mm |
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dla odcinka c2= |
|
1650 |
[mm] |
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= |
166,78 |
[mm] |
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Przyjęto s= |
150 |
[mm] |
c=11x150 |
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c= |
1650 |
[mm] |
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dla odcinka c1= |
|
1850 |
[mm] |
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= |
205,11 |
[mm] |
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|
Przyjęto s1= |
200 |
[mm] |
c1=9x200 |
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c1= |
1800 |
[mm] |
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|
Zbrojenie przy podporze B z prawej strony |
|
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|
3.2.2.5 Odcinek wymagający zbrojenia |
|
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|
q0= |
30,60 |
[kN/m] |
|
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|
VsdP = |
127,55 |
[kN] |
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|
= |
4,2 |
[m] |
> 3d = 3x0,8=2,4 |
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|
dlatego wstępnie c=c1+c2=2100+2100=4200mm |
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|
dla odcinka c2= |
|
2100 |
[mm] |
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|
Vsd2 = Vsd - qoxc1 |
|
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|
Vsd2 = |
63,29 |
[kN] |
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|
= |
241,29 |
[mm] |
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|
Przyjęto s= |
210 |
[mm] |
c=10x210 |
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|
c= |
2100 |
[mm] |
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|
dla odcinka c1= |
|
2100 |
[mm] |
|
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|
= |
238,27 |
[mm] |
|
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|
|
Przyjęto s1= |
210 |
[mm] |
c1=10x210 |
|
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|
|
c1= |
2100 |
[mm] |
|
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|
Zbrojenie przy podporze C z lewej strony |
|
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|
|
3.2.2.6 Odcinek wymagający zbrojenia |
|
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|
q0= |
30,60 |
[kN/m] |
|
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|
|
VsdL = |
113,15 |
[kN] |
|
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|
= |
3,7 |
[m] |
> 3d = 3x0,8=2,4 |
|
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|
dlatego wstępnie c=c1+c2=2000+1700=3700mm |
|
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|
|
dla odcinka c2= |
|
1700 |
[mm] |
|
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|
|
Vsd2 = Vsd - qoxc1 |
|
|
|
|
|
|
|
|
Vsd2 = |
51,95 |
[kN] |
|
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|
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|
= |
293,96 |
[mm] |
|
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|
|
|
Przyjęto s= |
215 |
[mm] |
c=8x215 |
|
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|
|
c= |
1720 |
[mm] |
|
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|
|
dla odcinka c1= |
|
2000 |
[mm] |
|
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|
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|
|
|
|
|
= |
268,59 |
[mm] |
|
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Przyjęto s1= |
200 |
[mm] |
c1=10x200 |
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c1= |
2000 |
[mm] |
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Zbrojenie przy podporze B z prawej strony |
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3.2.2.7 Odcinek wymagający zbrojenia |
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q0= |
30,60 |
[kN/m] |
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VsdP = |
120,38 |
[kN] |
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= |
3,9 |
[m] |
> 3d = 3x0,8=2,4 |
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dlatego wstępnie c=c1+c2=2000+1900=3900mm |
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dla odcinka c2= |
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1900 |
[mm] |
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Vsd2 = Vsd - qoxc1 |
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Vsd2 = |
59,18 |
[kN] |
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= |
258,05 |
[mm] |
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Przyjęto s= |
190 |
[mm] |
c=10x190 |
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c= |
1900 |
[mm] |
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dla odcinka c1= |
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2000 |
[mm] |
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= |
252,46 |
[mm] |
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Przyjęto s1= |
300 |
[mm] |
c1=8x234 |
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c1= |
1872 |
[mm] |
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4 Sprawdzenie stanu granicznego użytkowalności |
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4.1 Dla belki ciągłej ak wynosi |
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ak= |
0,091 |
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4.2 Współczynnik pełzania |
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f(oo,to)= |
2,4 |
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4.3 Moduł sprężystości |
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Ecm= |
27,50 |
[kN/mm2] |
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4.4 Efektywny moduł sprężystości |
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Ec,eff= |
8,09 |
[kN/mm2] |
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4.5 Współczynnik uwzględniający przyczepność zbrojenia |
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b1= |
1 |
stal żebrowana |
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4.6 Współczynnik uwzględniający czas trwania obciążenia |
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b2= |
0,5 |
obciążenie długotrwałe |
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4.7 Wartość stosunku |
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bw= |
250 |
[mm] |
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Wc= |
29400000 |
[mm3] |
h= |
840 |
[mm] |
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fctm= |
1,9 |
[N/mm2] |
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Es= |
200 |
[kN/mm2] |
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Mcr= |
55860000 |
[Nmm] |
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; |
0,34 |
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4.8 Moment bezwładności dla elementu niezarysowanego |
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24,73 |
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4.9 Moment bezwładności dla elementu zarysowanego |
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bw |
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4.9.1 Wysokość efektywna ściskanej strefy przekroju |
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h |
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xeff= |
119,64 |
[mm] |
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III= |
13436570260 |
[mm4] |
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Sztywność obliczeniowa przekroju |
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B(oo,to)= |
109504343008 |
[Nmm2] |
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Ugięcie |
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a(oo,to)= |
8,68 |
[mm] |
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alim= |
40,125 |
[mm] |
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a(oo,to) = |
8,68 |
< |
alim = |
40,125 |
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warunek spełniony |
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Zestawienie obciążeń eksploatacyjnych |
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1.1 Obciążenia stałe eksploatacyjne |
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Rodzaj warstwy |
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qk [kN/m2] |
gf |
g [kN/m2] |
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parkiet |
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7,0x0,025 |
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0,18 |
1,30 |
0,23 |
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beton wylewny |
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23,0x0,05 |
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1,15 |
1,30 |
1,50 |
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styropian |
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0,45x0,05 |
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0,02 |
1,30 |
0,03 |
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strop FERT-45 |
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2,95 |
1,10 |
3,25 |
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tynk cem.-wap. |
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19x0,015 |
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0,29 |
1,30 |
0,37 |
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Suma |
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4,58 |
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5,37 |
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1.2 Obciążenia zmienne |
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Rodzaj obciążenia |
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pk [kN/m2] |
gf |
p [kN/m2] |
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Obciążenie |
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użytkowe |
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2,00 |
1,40 |
2,80 |
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Obciążenie zastępcze |
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ścianek działowych |
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z cegły pełnej z |
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obustronnym tynkiem |
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1,66 |
1,40 |
2,32 |
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Suma |
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3,66 |
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5,12 |
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Przyjęto obciążenie zastępcze dla ścian działowych o ciężarze właściwym < 2,5 [kN/m2]. |
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Dla ściany o wysokości hs > 2,65 [m] obciążenie zastępcze ustalono proporcjonalnie. |
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Zaprojektowano ściane o hs = |
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3,52 |
[m] |
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hs/2,65 = x/1,25 |
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x= |
1,66 |
[kN/m2] |
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1.3 Obciążenia |
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qk(1)=qk+pk = 4,58 + 3,66 |
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qk(1)= |
8,24 |
[kN/m2] |
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q0(1)=q0+p0 = 5,37 + 5,12 |
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q0(1)= |
10,49 |
[kN/m2] |
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1.4 Obciążenia na 1m żebra |
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b= |
0,45 |
[m] |
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qk1=qk(1)xb = 8,24 x 0,45 |
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qk1= |
3,71 |
[kN/m] |
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q01=q0(1)xb = 10,49 x 0,45 |
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q01= |
4,72 |
[kN/m] |
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1.5 Zestawienie obciążenia montażowego |
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Rodzaj obciążenia |
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pk [kN/m2] |
gf |
p [kN/m2] |
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Ciężar stropu |
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2,95 |
1,1 |
3,25 |
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Obciążenie |
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montażowe |
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1,00 |
1,4 |
1,40 |
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Suma |
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3,95 |
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4,65 |
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2. Obliczenia statyczne |
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2.1 Określenie długości obliczeniowej |
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Przy oparciu stropu na ścianach o grubości 25cm rozpiętość w świetle ścian wynosi 335cm |
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357 |
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ls= |
335 |
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25 |
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360 |
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Określenie głebokości oparcia belki prefabrykowanej |
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c = (357 - 335) x 0,5 = 11,0 |
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[cm] |
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Przyjęto c= |
12 |
[cm] |
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Głębokość oparcia c= |
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0,12 |
[m] |
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Rozpiętość obliczeniowa stropu wynosi |
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lo = ls + c = 335 + 12 |
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[cm] |
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lo= |
347 |
[cm] |
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Rozpiętość obliczeniowa lo = |
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3,47 |
[m] |
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2.2 Schemat statyczny |
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= |
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Mmax= |
7,11 |
[kNm] |
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= |
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Q= |
8,19 |
[kN] |
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3. Wymiarowanie zbrojenia |
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3.1 Ustalenie szerokości płyty współpracującej z belką |
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lo2 = 0,85 x l1 |
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l02= |
3,06 |
[m] |
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beff |
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ht |
beff = |
0,696 |
[m] |
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beff |
> b=0,45 |
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h |
Przyjmuję beff= |
|
0,45 |
[m] |
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a
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3.2 Dane dla przekroju: |
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beff= |
0,45 |
[m] |
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bw= |
0,084 |
[m] |
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h= |
0,23 |
[m] |
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ht= |
0,03 |
[m] |
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d= |
0,21 |
[m] |
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a= |
0,02 |
[m] |
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3.3 Przyjęcie materiałów |
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Przyjęto beton klasy B-20 |
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fcd= |
10,6 |
[N/mm2] |
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Zbrojenie główne wykonano ze stali A-III (okrągłej, żebrowanej) |
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dla 34GS fyd= |
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350 |
[N/mm2] |
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Zbrojenie rozdzielcze wykonano ze stali A-I (okrągłej, gładkiej) |
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dla St3SX fyd= |
|
310 |
[N/mm2] |
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3.4 Sprawdzenie położenia osi obojętnej |
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a= |
0,85 |
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ht= |
30 |
[mm] |
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beff= |
450 |
[mm] |
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d= |
210 |
[mm] |
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Mnt= |
23718825 |
[Nmm] = |
23,72 |
[kNm] |
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Mnt > Msd = Mmax |
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23,72 |
> |
7,11 |
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warunek spełniony |
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Przekrój pracuje jako pozornie teowy, dlatego żebro wymiaruję |
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jako belkę o przekroju prostokątnym 0,45x0,21 |
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3.5 Obliczenie powierzchni zbrojenia |
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3.5.1 Współczynnik |
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Msd= |
7106088,00122936 |
[Nmm] |
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sb= |
0,040 |
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3.5.2 Względny zasięg strefy ściskanej |
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Dla sb = 0,040 odczytano xeff,lim = |
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0,361 |
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sb,lim = |
0,296 |
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z= |
0,819 |
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Ponieważ sb,lim > sb jest to przekrój pojedynczo zbrojony |
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Ostatecznie powierzchnia zbrojenia wynosi |
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As1= |
118,05 |
[mm2] |
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As1= |
1,18 |
[cm2] |
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Przyjęto 2o8 o As1 |
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1,01 |
[cm2] |
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3.6 Sprawdzenie żebra na ścinanie |
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Q= |
8,19 |
[kN] |
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c= |
0,12 |
[m] |
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3.6.1 Obliczenie siły tnącej krawędziowej |
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3.6.2 Stopień zbrojenia |
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Minimalny stopień zbrojenia |
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rL= |
0,0067 |
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r1 = 0,0015 (0,15%) |
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sCP = 0 |
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Dla fck=16 wartość tRd wynosi |
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0,22 |
[N/mm2] |
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Do podpory doprowadzone jest więcej niż 50% zbrojenia |
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k = 1,6 - d |
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k= |
1,39 |
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3.6.3 Nośność betonu na ścinanie |
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Vsd = |
7,62 |
< |
VRd1 = |
7,92 |
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warunek spełniony |
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4. Sprawdzenie ugięcia |
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4.1Msd - max wartość momentu wyznaczonego dla kombinacji obciążeń długotrwałych |
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qk1= |
3,71 |
[kN/m] |
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Msd= |
5,58 |
[kNm] |
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4.2 Dla belki wolnopodpartej ak wynosi |
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ak= |
0,1042 |
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4.3 Współczynnik pełzania |
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f(oo,to)= |
3,2 |
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4.4 Moduł sprężystości |
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Ecm= |
27,5 |
[kN/mm2] |
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4.5 Efektywny moduł sprężystości |
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Ec,eff= |
6,55 |
[kN/mm2] |
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4.6 Współczynnik uwzględniający przyczepność zbrojenia |
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b1= |
1 |
stal żebrowana |
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4.7 Współczynnik uwzględniający czas trwania obciążenia |
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b2= |
0,5 |
obciążenie długotrwałe |
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4.8 Wartość stosunku |
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Wc= |
740600 |
[mm3] |
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fctm= |
1,9 |
[N/mm2] |
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Es= |
200 |
[kN/mm2] |
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Mcr= |
1407140 |
[Nmm] |
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; |
0,25 |
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4.9 Moment bezwładności dla elementu niezarysowanego |
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30,55 |
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I1= |
112868357,6 |
[mm4] |
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4.10 Moment bezwładności dla elementu zarysowanego |
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bw |
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4.10.1 Wysokość efektywna ściskanej strefy przekroju |
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h |
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xeff= |
46,49 |
[mm] |
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III= |
61280180,06 |
[mm4] |
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Sztywność obliczeniowa przekroju |
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B(oo,to)= |
407150215,436768 |
[kNmm2] |
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Ugięcie |
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a(oo,to)= |
17,09 |
[mm] |
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alim= |
17,35 |
[mm] |
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a(oo,to) = |
17,09 |
< |
alim = |
17,35 |
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warunek spełniony |
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Żebro pod ścianką działową |
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120 |
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230 |
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Poz. IA |
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Zestawienie obciążeń eksploatacyjnych |
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1.1 Obciążenia stałe eksploatacyjne |
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Rodzaj warstwy |
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qk [kN/m2] |
gf |
g [kN/m2] |
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beton wylewny |
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23,0x0,05x0,45 |
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0,52 |
1,30 |
0,67 |
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strop FERT-45 |
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1,33 |
1,10 |
1,46 |
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dodatkowe żebro |
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25,0x0,13x0,23 |
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0,75 |
1,10 |
0,82 |
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ciężar ściany |
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0,12x3,52x15 |
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6,34 |
1,10 |
6,97 |
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Suma |
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8,93 |
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9,92 |
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1.2 Obciążenia zmienne |
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Rodzaj obciążenia |
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pk [kN/m2] |
gf |
p [kN/m2] |
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Obciążenie zmienne |
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technologiczne |
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2,00 |
1,40 |
2,80 |
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Suma |
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2,00 |
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2,80 |
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1.3 Obciążenia |
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qk(1)=qk+pk = 8,93 + 0,92 |
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qk(1)= |
10,93 |
[kN/m2] |
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q0(1)=q0+p0 = 9,92 + 2,80 |
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q0(1)= |
12,72 |
[kN/m2] |
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1.4 Obciążenia na 1m żebra |
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b - rozstaw żeber |
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b= |
0,45 |
[m] |
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qk1=qk(1)xb = 9,85 x 0,45 |
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qk1= |
4,92 |
[kN/m] |
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q01=q0(1)xb = 12,72 x 0,45 |
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q01= |
5,73 |
[kN/m] |
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2. Obliczenia statyczne |
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2.1 Określenie długości obliczeniowej |
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Przy oparciu stropu na ścianach o grubości 25cm rozpiętość w świetle ścian wynosi 335cm |
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357 |
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ls= |
335 |
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25 |
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360 |
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Określenie głebokości oparcia belki prefabrykowanej |
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c = (357 - 335) x 0,5 = 11,0 |
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[cm] |
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Przyjęto c= |
12 |
[cm] |
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Głębokość oparcia c= |
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0,12 |
[m] |
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Rozpiętość obliczeniowa stropu wynosi |
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lo = ls + c |
[cm] |
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lo= |
347 |
[cm] |
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Rozpiętość obliczeniowa lo = |
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3,47 |
[m] |
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Mmax= |
19,15 |
[kNm] |
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Q= |
22,08 |
[kN] |
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3. Wymiarowanie zbrojenia |
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3.1 Ustalenie szerokości płyty współpracującej z belką |
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beff |
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lo2 = 0,85 x l1 |
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l02= |
3,06 |
[m] |
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ht |
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h |
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beff = |
0,826 |
[m] |
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a
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beff |
> b=0,45 |
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Przyjmuję beff= |
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0,45 |
[m] |
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3.2 Dane dla przekroju: |
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beff= |
0,45 |
[m] |
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bw= |
0,214 |
[m] |
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h= |
0,23 |
[m] |
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ht= |
0,03 |
[m] |
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d= |
0,21 |
[m] |
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a= |
0,02 |
[m] |
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3.3 Przyjęcie materiałów |
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Przyjęto beton klasy B-20 |
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fcd= |
10,6 |
[N/mm2] |
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Zbrojenie główne wykonano ze stali A-III (okrągłej, żebrowanej) |
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dla 34GS fyd= |
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350 |
[N/mm2] |
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Zbrojenie rozdzielcze wykonano ze stali A-I (okrągłej, gładkiej) |
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dla St3SX fyd= |
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310 |
[N/mm2] |
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3.4 Sprawdzenie położenia osi obojętnej |
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a= |
0,85 |
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ht= |
30 |
[mm] |
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beff= |
450 |
[mm] |
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d= |
210 |
[mm] |
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Mnt= |
23718825 |
[Nmm] = |
23,72 |
[kNm] |
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Mnt > Msd = Mmax |
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23,72 |
> |
19,15 |
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warunek spełniony |
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Przekrój pracuje jako pozornie teowy, dlatego żebro wymiaruję |
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jako belkę o przekroju prostokątnym 0,45x0,21 |
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3.5 Obliczenie powierzchni zbrojenia |
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3.5.1 Współczynnik |
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Msd= |
19152330,795625 |
[Nmm] |
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sb= |
0,107 |
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3.5.2 Względny zasięg strefy ściskanej |
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Dla sb = 0,107 odczytano xeff,lim = |
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0,435 |
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sb,lim = |
0,339 |
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z= |
0,786 |
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Ponieważ sb,lim > sb jest to przekrój pojedynczo zbrojony |
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Ostatecznie powierzchnia zbrojenia wynosi |
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As1= |
331,52 |
[mm2] |
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As1= |
3,32 |
[cm2] |
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Przyjęto 2o16 o As1 |
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4,02 |
[cm2] |
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3.6 Sprawdzenie żebra na ścinanie |
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Q= |
22,08 |
[kN] |
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c= |
0,12 |
[m] |
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3.6.1 Obliczenie siły tnącej krawędziowej |
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3.6.2 Stopień zbrojenia |
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rL= |
0,0089 |
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r1 = 0,0015 (0,15%) |
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sCP = 0 |
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Dla fck=16 wartość tRd wynosi |
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0,22 |
[N/mm2] |
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Do podpory doprowadzone jest więcej niż 50% zbrojenia |
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k = 1,6 - d |
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k= |
1,39 |
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3.6.3 Nośność betonu na ścinanie |
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Vsd = |
21,39 |
< |
VRd1 = |
21,41 |
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warunek spełniony |
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4. Sprawdzenie ugięcia |
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4.1Msd - max wartość momentu wyznaczonego dla kombinacji obciążeń długotrwałych |
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qk1 = 8,93 x 0,45 |
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qk1 = |
4,02 |
[kN/m] |
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Msd= |
6,05 |
[kNm] |
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4.2 Dla belki wolnopodpartej ak wynosi |
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ak= |
0,1042 |
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4.3 Współczynnik pełzania |
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f(oo,to)= |
3,2 |
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4.4 Moduł sprężystości |
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Ecm= |
27,5 |
[kN/mm2] |
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4.5 Efektywny moduł sprężystości |
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4.6 Współczynnik uwzględniający przyczepność zbrojenia |
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b1= |
1 |
stal żebrowana |
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4.7 Współczynnik uwzględniający czas trwania obciążenia |
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b2= |
0,5 |
obciążenie długotrwałe |
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4.8 Wartość stosunku |
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Wc= |
1886766,66666667 |
[mm3] |
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fctm= |
1,9 |
[N/mm2] |
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Es= |
200 |
[kN/mm2] |
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Mcr= |
3584857 |
[Nmm] |
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; |
0,59 |
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4.9 Moment bezwładności dla elementu niezarysowanego |
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30,55 |
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I1= |
327742533,2 |
[mm4] |
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4.10 Moment bezwładności dla elementu zarysowanego |
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bw |
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4.10.1 Wysokość efektywna ściskanej strefy przekroju |
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h |
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xeff= |
72,97 |
[mm] |
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III= |
16684194,94 |
[mm4] |
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Sztywność obliczeniowa przekroju |
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B(oo,to)= |
131096625,170549 |
[kNmm2] |
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Ugięcie |
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a(oo,to)= |
5,91 |
[mm] |
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alim= |
17,35 |
[mm] |
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a(oo,to) = |
5,91 |
< |
alim = |
17,35 |
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warunek spełniony |
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