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1.0. Dane projektowe i wstępne przyjęcie wymiarów |
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1.1. Dane projektowe |
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a[m] |
b[m] |
c[m] |
l[m] |
h[m] |
lr[m] |
n |
P[kN/m] |
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5 |
6 |
2,5 |
18 |
8 |
6 |
5 |
10 |
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Klasa betonu B-25 |
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1.2. Wstępne przyjęcie wymiarów |
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1.2.1. Pokrycie dachowe |
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- 3xpapa asfaltowa |
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- gładź cementowa |
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- warstwa ocieplenia |
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- płyty panwiowe |
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1.2.2. Wymiary łuku |
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- strzałka łuku |
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f= |
3,60 |
m |
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- wymiary przekroju poprzecznego łuku w zworniku |
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hp= |
0,45 |
m |
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hp |
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bp |
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bp= |
0,25 |
m |
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1.2.3. Wymiary słupa |
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hs |
- przyjęto przekrój |
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hs= |
0,45 |
m |
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bs |
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bs= |
0,25 |
m |
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1.2.4. Wymiary stopy fundamentowej |
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b2= |
2,00 |
m |
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b1= |
3,00 |
m |
h |
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h= |
0,80 |
m |
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b1 |
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1.2.5. Wymiary rygla |
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lr= |
6,00 |
m |
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br= |
0,25 |
m |
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hr= |
0,45 |
m |
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1.2.6 Ściana osłonowa |
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- jednowarstwowa wykonana z gazobetonu gr. 24cm |
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i ocieplona styropianem gr.6cm |
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2.0. Zebranie obciążeń |
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2.1. Obciążenia stałe |
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2.1.1. Ciężar pokrycia dachowego |
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obc.chr. |
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gf |
obc.obl. |
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- 3xpapa asfaltowa |
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0,2= |
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0,200 |
kN/m2 |
1,2 |
0,240 |
kN/m2 |
- gładź wyrównawcza |
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0,03*21= |
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0,630 |
kN/m2 |
1,3 |
0,819 |
kN/m2 |
- ocieplenie płytami z pianobetonu |
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0,10*8= |
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0,800 |
kN/m2 |
1,2 |
0,960 |
kN/m2 |
- płyty panwiowe |
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1,60= |
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1,600 |
kN/m2 |
1,1 |
1,760 |
kN/m2 |
- beton pachwinowy |
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0,11= |
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0,110 |
kN/m2 |
1,3 |
0,143 |
kN/m2 |
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g1ch |
3,340 |
kN/m2 |
g1o |
3,922 |
kN/m2 |
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2.1.2. Ciężar łuku |
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obc.chr. |
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gf |
obc.obl. |
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- ciężar własny łuku |
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0,25*0,45*24= |
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2,700 |
kN/m |
1,1 |
2,970 |
kN/m |
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g2ch |
2,700 |
kN/m |
g2o |
2,970 |
kN/m |
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2.1.3. Ciężar gzymsu |
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obc.chr. |
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gf |
obc.obl. |
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- ciężar własny gzymsu |
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(0,25*0,45+0,3*0,1)*24= |
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3,420 |
kN/m |
1,1 |
3,762 |
kN/m |
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g3ch |
3,420 |
kN/m |
g3o |
3,762 |
kN/m |
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2.1.4. Ciężar ściany osłonowej z ryglem |
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obc.chr. |
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gf |
obc.obl. |
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- ciężar tynku c-w |
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0,015*3,8*19*2= |
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2,166 |
kN/m |
1,3 |
2,816 |
kN/m |
- ciężar styropianu |
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0,06*3,8*0,45= |
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0,103 |
kN/m |
1,2 |
0,123 |
kN/m |
- ściana z gazobetonu |
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0,24*3,8*9= |
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7,776 |
kN/m |
1,1 |
8,554 |
kN/m |
- rygel |
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0,25*0,45*24= |
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3,000 |
kN/m |
1,1 |
3,300 |
kN/m |
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g4ch |
13,045 |
kN/m |
g4o |
14,793 |
kN/m |
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2.1.5. Ciężar słupa |
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- ciężar słupa |
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0,25*0,45*8,25*24= |
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22,275 |
kN |
1,1 |
24,503 |
kN |
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G1ch |
22,275 |
kN |
G1o |
24,503 |
kN |
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2.1.6. Ciężar stopy fundamentowej i gruntu nad stopą rśr=20kN/m3 |
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- ciężar stopy i gruntu |
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2*3*0,8*20= |
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96,000 |
kN |
1,1 |
105,600 |
kN |
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G2ch |
96,000 |
kN |
G2o |
105,600 |
kN |
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2.2. Obciążenia zmienne |
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2.2.1. Obciążenie śniegem ( Bydgoszcz strefa I PN-80/B-02010 Z1-3 ) |
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Qk= |
0,7 |
kN/m2 |
c1= |
0,8 |
c2= |
2,3 |
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Wariant I : |
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Sk1=Qk*c1=0,7*0,8= |
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0,560 |
kN/m2 |
1,4 |
0,784 |
kN/m2 |
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Wariant II : |
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2,254 |
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1,127 |
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Sk1=Qk*c2=0,7*2,3= |
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1,610 |
kN/m2 |
1,4 |
2,254 |
kN/m2 |
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2.2.2. Obciążenie wiatrem ( Bydgoszcz strefa I PN-77/B-02011 ) |
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Teren A: |
H= |
12 |
m |
qk= |
0,25 |
kN/m2 |
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B= |
18 |
m |
ce= |
1,064 |
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L= |
30 |
m |
b= |
1,8 |
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Ściany: Z1-1 |
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c3= |
0,7 |
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c4= |
-0,4 |
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obc.chr. |
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gf |
obc.obl. |
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pk1=qk*ce*b*c3=0,25*1,064*1,8*0,7= |
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0,335 |
kN/m2 |
1,3 |
0,436 |
kN/m2 |
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pk2=qk*ce*b*c4=0,25*1,064*1,8*(-0,4)= |
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-0,192 |
kN/m2 |
1,3 |
-0,249 |
kN/m2 |
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Dach: Z1-4 |
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cza= |
-0,5 |
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czb= |
-0,75 |
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czc= |
-0,4 |
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obc.chr. |
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gf |
obc.obl. |
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pka=qk*ce*b*cza=0,25*1,064*1,8*(-0,5)= |
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-0,239 |
kN/m2 |
1,3 |
-0,311 |
kN/m2 |
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pkb=qk*ce*b*czb=0,25*1,064*1,8*(-0,75)= |
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-0,359 |
kN/m2 |
1,3 |
-0,467 |
kN/m2 |
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pkc=qk*ce*b*czc=0,25*1,064*1,8*(-0,4)= |
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-0,192 |
kN/m2 |
1,3 |
-0,249 |
kN/m2 |
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-0,467 |
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-0,311 |
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-0,249 |
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3,6
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3.0. Wymiarowanie łuku i słupa |
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3.1. Zebranie obciążeń na łuk |
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3.1.1. Obciążenia stałe |
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- ciężar pokrycia dachowego poz. 2.1.1. |
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3,340 |
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obc.chr. |
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obc.obl. |
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3,922 |
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20,040 |
kN/m |
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23,532 |
kN/m |
- ciężar własny łuku poz. 2.1.2. |
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2,700 |
kN/m |
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2,970 |
kN/m |
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22,740 |
kN/m |
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26,502 |
kN/m |
3.1.1. Obciążenia zmienne |
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- obciążenie śniegem równomiernie rozłożone poz. 2.2.1 wariant I |
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0,560 |
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obc.chr. |
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obc.obl. |
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0,784 |
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3,360 |
kN/m |
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4,704 |
kN/m |
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- obciążenie śniegem równomiernie rozłożone poz. 2.2.1 wariant I |
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1,610 |
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obc.chr. |
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obc.obl. |
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2,254 |
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9,660 |
kN/m |
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13,524 |
kN/m |
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3.1.2. Obciążenie wiatrem nie uwzględniam ponieważ sanie jest bardzo małe |
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w porównaniu ciężarem dachu. |
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3.2. Schemat statyczny łuku |
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- Współrzedne łuku |
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f= |
3,60 |
m |
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l= |
18 |
m |
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x[m] |
y[m] |
x`[m] |
y`[m] |
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0,00 |
0,00 |
9,00 |
3,60 |
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1,50 |
1,10 |
7,50 |
3,50 |
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3,00 |
2,00 |
6,00 |
3,20 |
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4,50 |
2,70 |
4,50 |
2,70 |
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6,00 |
3,20 |
3,00 |
2,00 |
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7,50 |
3,50 |
1,50 |
1,10 |
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9,00 |
3,60 |
0,00 |
0,00 |
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3.3. Obciążenia działające na słup |
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3.3.1 Obciążenia stałe |
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3.3.1.1. Ciężar gzymsu poz.2.1.3 |
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3,420 |
kN/m |
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3,762 |
kN/m x |
6 |
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20,520 |
kN |
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22,572 |
kN |
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3.3.1.2. Ciężar ściany osłonowej poz.2.1.4 |
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13,045 |
kN/m |
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14,793 |
kN/m x |
6 |
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78,268 |
kN |
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88,755 |
kN |
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3.3.1.3. Ciężar słupa poz.2.1.5 |
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22,275 |
kN |
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24,503 |
kN |
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3.3.2 Obciążenia zmienne |
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3.3.2.1. Obciążenie śniegem poz.2.2.1 |
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Wariant I |
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0,560 |
kN/m2 |
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0,784 |
kN/m2 x |
6 |
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3,360 |
kN/m |
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4,704 |
kN/m |
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Wariant II,III; |
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1,610 |
kN/m2 |
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2,254 |
kN/m2 x |
6 |
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9,660 |
kN/m |
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13,524 |
kN/m |
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0,805 |
kN/m2 |
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1,127 |
kN/m2 x |
6 |
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4,830 |
kN/m |
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6,762 |
kN/m |
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3.3.2.2. Obciążenie wiatrem poz.2.2.2 |
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Nawietrzna: |
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0,335 |
kN/m2 |
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0,436 |
kN/m2 x |
6 |
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2,011 |
kN/m |
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2,614 |
kN/m |
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Zawietrzna: |
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-0,192 |
kN/m2 |
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-0,249 |
kN/m2 x |
6 |
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-1,149 |
kN/m |
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-1,494 |
kN/m |
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3.4. Obliczenia statyczne wykonano w programie RM-WIN |
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4.0. Wymiarowanie |
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4.1. Wymiarowanie ściągu |
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4.1.1. Sprawdzenie naprężeń w ściągu |
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- ściąg przenosi tylko siły ( obliczenia wykonano na programie RM-WIN ) |
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- program uwzględnia przemieszczenia |
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- przyjęto ściąg 2xf35mm ze stali 18G2 o R= |
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310 |
MPa |
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Nośność ściągu: |
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F= |
19,24 |
cm2 |
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Nist= |
347,39 |
kN |
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s= |
0,8*R |
248 |
MPa |
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Warunek spełniony: |
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4.1.2. Zakotwienie ściągu |
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- zakotwienie za pomocą płytki oporowej o wymiarach 300x300x30mm |
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- sprawdzenie strefy docisku |
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Rb= |
14300 |
kN/m2 |
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N= |
347,39 |
kN |
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Fd= |
0,09 |
m2 |
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s= |
0 |
MPa |
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ad= |
1 |
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- ponieważ Fd = Fr to Rd = Rb; |
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N= |
347,39 |
kN |
< |
1287 |
kN |
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- długość zakotwienia ściągu |
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a= |
0,3 |
m |
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b= |
0,3 |
m |
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Rbz= |
1030 |
kN/m2 |
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0,28 |
m |
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Warunek spełniony ponieważ hs=45cm: |
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4.2. Wymiarowanie łuku |
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4.2.1.Wymiary w przekroju na Nmax |
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A= |
0,1125 |
m2 |
M.= |
0 |
kNm |
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b= |
0,25 |
m. |
Ix= |
0,0018984375 |
m4 |
N= |
449,35 |
kN |
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h= |
0,45 |
m. |
i= |
0,129903810567666 |
m. |
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l= |
35,58 |
m. |
lł= |
18 |
m |
Ra= |
310000 |
kN/m2 |
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Y= |
0,6 |
Z1-1.2b |
f= |
3,6 |
m |
Rb= |
14300 |
kN/m2 |
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lo= |
21,3496234073905 |
m. |
V= |
0,2 |
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Rbz= |
1030 |
kN/m2 |
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s= |
35,583 |
m |
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- Smukłość |
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164,35 |
> |
35 |
l |
< |
104 |
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Należy uwzględnić wyboczenie. |
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- Mimośrody |
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0,06 |
m. |
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en=max(l/600;h/30;1cm)= |
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0,02 |
m. |
0,06 |
m. |
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0,01 |
m. |
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es= |
M/N= |
0,00 |
m. |
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eo= |
0,06 |
m. |
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Przyjęto wstępnie: |
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Dla h= |
1,9 |
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e= |
0,113 |
m. |
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Duży mimośród: |
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Założenie: |
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sb=sbgr= |
0,42 |
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x=xgr= |
0,6 |
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a= a`= |
0,04 |
m. |
xgr= |
xgr*ho= |
0,246 |
m. |
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ho= |
0,41 |
m. |
ea= |
e+h/2-a= |
0,298 |
m. |
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b= |
0,25 |
m. |
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Zbrojenie: |
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-0,00103435296841 |
m2 |
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Dla l= |
164,35 |
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0,15% |
<35 |
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0,20% |
35<<83 |
0,0025 |
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0,00025625 |
m2 |
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0,25% |
83< |
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Fac= |
-0,00103435296841 |
m2 |
< |
Facmin= |
0,00025625 |
m2 |
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Procedura II: |
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Procedura I: |
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Fac < Facmin |
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0,174 |
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Fac= |
0,00025625 |
m2 |
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Fac= |
0,00025625 |
m2 |
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0,192 |
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x= |
0,079 |
m |
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0,001643669354839 |
m2 |
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-jeżeli |
x= |
0,079 |
> |
2a`= |
0,08 |
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x= |
0,246 |
m |
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Uwzględniamy współprace betonu: |
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-jeżeli |
x= |
0,079 |
< |
2a`= |
0,08 |
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-0,00028483328651 |
m2 |
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Bez uwzględnienia betonu: |
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|
-0,000283327249142 |
m2 |
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|
Fa < 0 to Mały mimośród |
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0,072 |
m |
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Jeżeli |
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x= |
0,181 |
> |
h= |
0,45 |
m |
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|
0,181 |
m |
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to: |
x= h= |
0,45 |
m |
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-0,001428569184626 |
m2 |
> Facmin |
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Jeżeli |
|
x= |
0,181 |
< xgr= |
0,246 |
< h= |
0,45 |
m |
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-0,00063370728327 |
m2 |
< Facmin |
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-0,002311430815374 |
m2 |
> Famin |
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Fa= |
0,00025625 |
m2 |
> Famin |
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Procedura II: |
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Przyjęto : |
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Fac < Facmin |
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Fac= |
0,000256 |
m2 |
x= |
0,181 |
m |
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Fa= |
0,000256 |
m2 |
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|
0,573 |
|
Fac= |
0,00025625 |
m2 |
|
- Obliczenie siły krytycznej |
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Err:502 |
|
x= |
Err:502 |
m |
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0,132 |
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-0,117 |
> 0,05 |
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-jeżeli |
x= |
Err:502 |
> |
2a`= |
0,08 |
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Uwzględniamy współprace betonu: |
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Eb= |
30000000 |
kN/m2 |
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Ea= |
210000000 |
kN/m2 |
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Err:502 |
m2 |
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n= |
7,00 |
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Nd= |
357,79 |
kN |
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-jeżeli |
x= |
Err:502 |
< |
2a`= |
0,08 |
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Bez uwzględnienia betonu: |
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|
0,007005454172595 |
m4 |
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0,002106566435042 |
m2 |
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|
1,85486717414378E-05 |
m4 |
j= |
2 |
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|
1,796 |
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|
Fa < 0 to Mały mimośród |
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-0,676 |
m |
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|
998,617846455701 |
kN |
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Err:502 |
m |
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|
Jeżeli |
|
x= |
Err:502 |
< xgr= |
0,246 |
< h= |
0,45 |
m |
0,9hzał= |
1,71 |
1,82 |
< |
1,1hzał= |
2,09 |
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|
Err:502 |
m2 |
> Facmin |
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Warunek spełniony: |
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|
0,00025625 |
m2 |
> Famin |
|
4.2.2.Wymiary w przekroju na Mmax |
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A= |
0,1125 |
m2 |
M.= |
66,73 |
kNm |
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|
Jeżeli |
|
|
x= |
Err:502 |
> |
h= |
0,45 |
m |
b= |
0,25 |
m. |
Ix= |
0,0018984375 |
m4 |
N= |
357,54 |
kN |
|
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|
to: |
x= h= |
0,45 |
m |
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|
h= |
0,45 |
m. |
i= |
0,129903810567666 |
m. |
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|
l= |
35,58 |
m. |
lł= |
18 |
m |
Ra= |
310000 |
kN/m2 |
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|
0,000665163209236 |
m2 |
> Facmin |
|
Y= |
0,6 |
Z1-1.2b |
f= |
3,6 |
m |
Rb= |
14300 |
kN/m2 |
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|
lo= |
21,3496234073905 |
m. |
V= |
0,2 |
|
Rbz= |
1030 |
kN/m2 |
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s= |
35,583 |
m |
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|
- Smukłość |
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|
-0,004701324499559 |
m2 |
> Famin |
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|
164,35 |
> |
35 |
l |
< |
104 |
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|
Należy uwzględnić wyboczenie. |
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|
- Mimośrody |
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|
0,06 |
m. |
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|
en=max(l/600;h/30;1cm)= |
|
|
0,02 |
m. |
0,06 |
m. |
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|
0,01 |
m. |
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es= |
M/N= |
0,19 |
m. |
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|
eo= |
0,25 |
m. |
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|
Przyjęto wstępnie: |
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Dla h= |
3,5 |
|
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e= |
0,861 |
m. |
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|
Duży mimośród: |
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Założenie: |
|
sb=sbgr= |
0,42 |
|
|
x=xgr= |
0,6 |
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|
a= a`= |
0,04 |
m. |
xgr= |
xgr*ho= |
0,246 |
m. |
|
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ho= |
0,41 |
m. |
ea= |
e+h/2-a= |
1,046 |
m. |
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b= |
0,25 |
m. |
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Zbrojenie: |
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|
0,001059379425452 |
m2 |
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Dla l= |
164,35 |
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0,15% |
<35 |
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0,20% |
35<<83 |
0,0025 |
|
|
0,00025625 |
m2 |
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|
0,25% |
83< |
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|
Fac= |
0,001059379425452 |
m2 |
> |
Facmin= |
0,00025625 |
m2 |
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|
Procedura I: |
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Fac= |
0,001059379425452 |
m2 |
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|
0,001939830645161 |
m2 |
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x= |
0,246 |
m |
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Przyjęto : |
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Fac= |
0,001059 |
m2 |
x= |
0,246 |
m |
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Fa= |
0,001940 |
m2 |
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- Obliczenie siły krytycznej |
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0,547 |
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-0,117 |
> 0,05 |
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Eb= |
30000000 |
kN/m2 |
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Ea= |
210000000 |
kN/m2 |
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n= |
7,00 |
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Nd= |
357,79 |
kN |
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0,004070466 |
m4 |
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9,71295103307499E-05 |
m4 |
j= |
2 |
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2,001 |
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517,90718549269 |
kN |
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Procedura I: |
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0,9hzał= |
3,15 |
3,23 |
< |
1,1hzał= |
3,85 |
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Fac= |
0,00025625 |
m2 |
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Warunek spełniony: |
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4.2.3.Wymiary w przekroju na Mmin |
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0,001967411290323 |
m2 |
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A= |
0,1125 |
m2 |
M.= |
16,71 |
kNm |
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b= |
0,25 |
m. |
Ix= |
0,0018984375 |
m4 |
N= |
348,99 |
kN |
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x= |
0,246 |
m |
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h= |
0,45 |
m. |
i= |
0,129903810567666 |
m. |
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-jeżeli |
x= |
0,059 |
< |
2a`= |
0,08 |
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l= |
35,58 |
m. |
lł= |
18 |
m |
Ra= |
310000 |
kN/m2 |
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Bez uwzględnienia betonu: |
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Y= |
0,6 |
Z1-1.2b |
f= |
3,6 |
m |
Rb= |
14300 |
kN/m2 |
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lo= |
21,3496234073905 |
m. |
V= |
0,2 |
|
Rbz= |
1030 |
kN/m2 |
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-0,000171535597996 |
m2 |
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s= |
35,583 |
m |
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- Smukłość |
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Fa < 0 to Mały mimośród |
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164,35 |
> |
35 |
l |
< |
104 |
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Należy uwzględnić wyboczenie. |
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0,056 |
m |
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- Mimośrody |
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0,06 |
m. |
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en=max(l/600;h/30;1cm)= |
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0,02 |
m. |
0,06 |
m. |
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0,152 |
m |
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0,01 |
m. |
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Fa |
Fac |
|
es= |
M/N= |
0,05 |
m. |
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Jeżeli |
|
x= |
0,152 |
< xgr= |
0,246 |
< h= |
0,45 |
m |
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eo= |
0,11 |
m. |
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-0,00063037188215 |
m2 |
> Facmin |
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Przyjęto wstępnie: |
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|
0,00025625 |
m2 |
> Famin |
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Dla h= |
1,2 |
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e= |
0,129 |
m. |
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Jeżeli |
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x= |
0,152 |
> |
h= |
0,45 |
m |
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Duży mimośród: |
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to: |
x= h= |
0,45 |
m |
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Założenie: |
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sb=sbgr= |
0,42 |
|
|
x=xgr= |
0,6 |
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|
-0,001640519468964 |
m2 |
> Facmin |
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a= a`= |
0,04 |
m. |
xgr= |
xgr*ho= |
0,246 |
m. |
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ho= |
0,41 |
m. |
ea= |
e+h/2-a= |
0,314 |
m. |
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b= |
0,25 |
m. |
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-0,00242322246652 |
m2 |
> Famin |
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Zbrojenie: |
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-0,001246303252748 |
m2 |
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Dla l= |
164,35 |
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0,15% |
<35 |
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0,20% |
35<<83 |
0,0025 |
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|
0,00025625 |
m2 |
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|
0,25% |
83< |
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Fac= |
-0,001246303252748 |
m2 |
< |
Facmin= |
0,00025625 |
m2 |
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Procedura II: |
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Fac < Facmin |
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0,133 |
|
Fac= |
0,00025625 |
m2 |
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0,144 |
|
x= |
0,059 |
m |
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|
-jeżeli |
x= |
0,059 |
< |
2a`= |
0,08 |
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|
Nie uwzględniamy współprace betonu: |
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|
-0,000171535597996 |
m2 |
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Przyjęto : |
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Fac= |
0,000256 |
m2 |
x= |
0,059 |
m |
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Fa= |
0,000256 |
m2 |
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|
- Obliczenie siły krytycznej |
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0,238 |
|
|
|
-0,117 |
> 0,05 |
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|
Eb= |
30000000 |
kN/m2 |
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|
|
Ea= |
210000000 |
kN/m2 |
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n= |
7,00 |
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|
Nd= |
357,79 |
kN |
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|
0,019966555956293 |
m4 |
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|
3,16895726594847E-05 |
m4 |
j= |
2 |
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2,025 |
|
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1859,51128403894 |
kN |
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0,9hzał= |
1,08 |
1,23 |
< |
1,1hzał= |
1,32 |
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Warunek spełniony: |
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4.2.4. Ostateczne przyjęcie zbrojenia: |
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poz.4.2.1. |
|
0,000256 |
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0,000256 |
m2 |
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poz.4.2.2. |
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0,001059 |
0,001940 |
m2 |
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poz.4.2.3. |
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0,000256 |
0,000256 |
m2 |
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3f22 |
0,00114 |
m2 |
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6f22 |
0,00228 |
m2 |
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4.3. Wymiarowanie słupa |
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Procedura I: |
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4.3.1.Wymiary w przekroju na Nmax (Mmin) |
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A= |
0,1125 |
m2 |
M.= |
64,71 |
kNm |
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b= |
0,25 |
m. |
Ix= |
0,0018984375 |
m4 |
N= |
427,55 |
kN |
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Fac= |
0,00025625 |
m2 |
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h= |
0,45 |
m. |
i= |
0,129903810567666 |
m. |
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l= |
8,25 |
m. |
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Ra= |
310000 |
kN/m2 |
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0,001713991935484 |
m2 |
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Y= |
1,6 |
Z1-1.2b |
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Rb= |
14300 |
kN/m2 |
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lo= |
13,2 |
m. |
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Rbz= |
1030 |
kN/m2 |
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x= |
0,246 |
m |
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- Smukłość |
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101,61 |
> |
35 |
l |
< |
104 |
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Jeżeli |
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x= |
#REF! |
> |
h= |
0,45 |
m |
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Należy uwzględnić wyboczenie. |
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to: |
x= h= |
0,45 |
m |
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- Mimośrody |
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0,01 |
m. |
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-0,001130060483871 |
m2 |
> Facmin |
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en=max(l/600;h/30;1cm)= |
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0,02 |
m. |
0,02 |
m. |
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0,01 |
m. |
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es= |
M/N= |
0,15 |
m. |
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#REF! |
m2 |
> Famin |
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eo= |
0,17 |
m. |
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Przyjęto wstępnie: |
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Dla h= |
1,25 |
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e= |
0,208 |
m. |
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Duży mimośród: |
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Założenie: |
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sb=sbgr= |
0,42 |
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x=xgr= |
0,6 |
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a= a`= |
0,04 |
m. |
xgr= |
xgr*ho= |
0,246 |
m. |
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ho= |
0,41 |
m. |
ea= |
e+h/2-a= |
0,393 |
m. |
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b= |
0,25 |
m. |
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Zbrojenie: |
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-0,000735844267655 |
m2 |
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Dla l= |
101,61 |
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0,15% |
<35 |
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0,20% |
35<<83 |
0,0025 |
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0,00025625 |
m2 |
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0,25% |
83< |
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Fac= |
-0,000735844267655 |
m2 |
< |
Facmin= |
0,00025625 |
m2 |
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Procedura II: |
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Fac < Facmin |
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0,231 |
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Fac= |
0,00025625 |
m2 |
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0,266 |
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x= |
0,109 |
m |
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-jeżeli |
x= |
0,109 |
> |
2a`= |
0,08 |
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Uwzględniamy współprace betonu: |
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0,000134924415955 |
m2 |
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Przyjęto : |
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Fac= |
0,000256 |
m2 |
x= |
0,109 |
m |
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Fa= |
0,000256 |
m2 |
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Fa < 0 to Mały mimośród |
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- Obliczenie siły krytycznej |
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-0,099 |
m |
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0,370 |
0,064 |
> 0,05 |
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Err:502 |
m |
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Ea= |
210000000 |
kN/m2 |
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n= |
7,00 |
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Jeżeli |
|
x= |
Err:502 |
< xgr= |
0,246 |
< h= |
0,45 |
m |
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Nd= |
376,96 |
kN |
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Err:502 |
m2 |
> Facmin |
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|
0,013316825010763 |
m4 |
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0,00025625 |
m2 |
> Famin |
|
2,44277326954991E-05 |
m4 |
j= |
2 |
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Jeżeli |
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x= |
Err:502 |
> |
h= |
0,45 |
m |
|
1,882 |
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to: |
x= h= |
0,45 |
m |
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-0,000879711246731 |
m2 |
> Facmin |
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2794,73397026753 |
kN |
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-0,002957256495205 |
m2 |
> Famin |
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0,9hzał= |
1,125 |
1,18 |
< |
1,1hzał= |
1,375 |
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Warunek spełniony: |
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4.3.2.Wymiary w przekroju na Mmax |
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A= |
0,1125 |
m2 |
M.= |
93 |
kNm |
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b= |
0,25 |
m. |
Ix= |
0,0018984375 |
m4 |
N= |
419,29 |
kN |
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h= |
0,45 |
m. |
i= |
0,129903810567666 |
m. |
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l= |
8,25 |
m. |
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Ra= |
310000 |
kN/m2 |
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Y= |
1,6 |
Z1-1.2b |
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Rb= |
14300 |
kN/m2 |
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lo= |
13,2 |
m. |
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Rbz= |
1030 |
kN/m2 |
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- Smukłość |
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101,61 |
> |
35 |
l |
< |
104 |
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Należy uwzględnić wyboczenie. |
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- Mimośrody |
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en=max(l/600;h/30;1cm)= |
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0,01 |
m. |
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0,02 |
m. |
0,02 |
m. |
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0,01 |
m. |
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es= |
M/N= |
0,22 |
m. |
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eo= |
0,24 |
m. |
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Przyjęto wstępnie: |
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Dla h= |
1,2 |
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e= |
0,284 |
m. |
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Duży mimośród: |
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Założenie: |
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sb=sbgr= |
0,42 |
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x=xgr= |
0,6 |
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a= a`= |
0,04 |
m. |
xgr= |
xgr*ho= |
0,246 |
m. |
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ho= |
0,41 |
m. |
ea= |
e+h/2-a= |
0,469 |
m. |
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b= |
0,25 |
m. |
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Zbrojenie: |
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-0,000485495030514 |
m2 |
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Dla l= |
101,61 |
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0,15% |
<35 |
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0,20% |
35<<83 |
0,0025 |
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0,00025625 |
m2 |
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0,25% |
83< |
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Fac= |
-0,000485495030514 |
m2 |
< |
Facmin= |
0,00025625 |
m2 |
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Procedura II: |
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Fac < Facmin |
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0,278 |
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Fac= |
0,00025625 |
m2 |
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0,334 |
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x= |
0,137 |
m |
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-jeżeli |
x= |
0,137 |
> |
2a`= |
0,08 |
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Uwzględniamy współprace betonu: |
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0,000484398949958 |
m2 |
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Przyjęto : |
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Fac= |
0,000256 |
m2 |
x= |
0,137 |
m |
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Fa= |
0,000484 |
m2 |
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- Obliczenie siły krytycznej |
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0,526 |
0,064 |
> 0,05 |
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Ea= |
210000000 |
kN/m2 |
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n= |
7,00 |
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Nd= |
376,96 |
kN |
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0,010429420750596 |
m4 |
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3,84983403237957E-05 |
m4 |
j= |
2 |
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1,899 |
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1965,13870162542 |
kN |
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0,9hzał= |
1,08 |
1,27 |
< |
1,1hzał= |
1,32 |
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Warunek spełniony: |
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4.3.3. Ostateczne przyjęcie zbrojenia: |
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poz.4.3.1. |
|
0,000256 |
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0,000256 |
m2 |
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poz.4.3.2. |
|
0,000484 |
Fa |
Fac |
0,000256 |
m2 |
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3f16 |
0,000603 |
m2 |
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2f16 |
0,000402 |
m2 |
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5.0. Stopa fundamentowa |
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5.1. Zebranie obciążeń i przyjęcie mimośrodu przesunięcia |
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5.1.1. Siły działające na fundament |
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wariant I |
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wariant II |
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M1= |
93 |
kNm |
M2= |
-64,71 |
kNm |
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T1= |
16,07 |
kN |
T2= |
17,88 |
kN |
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N1= |
419,29 |
kN |
N2= |
427,55 |
kN |
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5.1.2. Średni mimośród |
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0,222 |
m |
-0,151 |
m |
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0,035 |
m |
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5.2. Wymiary stopy trapezowej |
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hz |
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h |
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
D
|
|
|
|
|
|
|
|
|
|
B = |
2,50 |
m |
|
|
|
|
a1= |
0,55 |
m |
|
|
|
C F
|
hs= |
0,45 |
m |
|
|
L |
a2 |
bs |
|
L = |
1,50 |
m |
|
|
|
|
B
|
|
a2= |
0,35 |
m |
|
|
|
|
a1
|
|
bs= |
0,25 |
m |
|
|
|
g = |
0,35 |
m |
|
|
h = |
0,60 |
m |
|
|
|
|
0,85 |
m |
|
|
|
|
|
|
|
|
|
|
5.3. Siły w poziomie posadowienia wariant I |
|
|
|
|
|
|
|
|
- ciężar fundamentu i gruntu na nim |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
76,98 |
kN |
|
|
|
|
|
|
|
|
|
|
|
|
|
gs= |
21,0 |
kN/m3 |
|
|
|
|
|
|
gf= |
1,15 |
|
|
|
|
|
- siła pionowa N |
|
|
|
|
|
|
|
|
|
|
N= |
419,29 |
kN |
|
|
|
|
- moment |
|
|
|
|
|
|
|
|
|
M=M1+T1*h-N1*es= |
|
87,872 |
kNm |
|
|
|
|
5.3.1. Mimośród e |
|
|
|
|
|
|
|
|
|
e=M/N= |
0,210 |
m |
|
|
|
|
|
5.3.2. Obliczenie oporu granicznego gruntu qf |
|
|
|
|
|
|
|
|
- przyjęto grunt Pr i Ps |
|
|
|
|
|
|
|
|
|
f = |
31 |
o |
|
|
|
|
|
|
g = |
19,5 |
kN/m3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
320,960 |
kN/m2 |
|
|
|
|
|
B`=B-2*e= |
2,08 |
m |
|
|
|
|
|
|
L`=L= |
1,5 |
m |
|
|
|
|
|
|
Dmin=hz-h= |
0,3 |
m |
|
|
|
|
|
|
ND = |
22 |
|
tgd =T/N = |
0,0383 |
|
|
|
|
NB = |
9,5 |
|
tgf = |
0,601 |
|
|
|
|
iD = |
0,5 |
|
tgd/tgf = |
0,0638 |
|
|
|
|
iB = |
0,3 |
|
|
|
|
|
|
|
gB=gD=g = |
19,5 |
kN/m3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5.3.3. Obliczenie naprężeń pod stopą i sprawdzenie warunków |
|
|
|
|
|
|
|
|
- naprężenia |
|
|
|
|
|
|
|
|
|
|
s1 = (N/B*L)*( 1+ 6*e/B ) = |
|
|
168,05 |
kN/m2 |
|
|
|
|
s2 = (N/B*L)*( 1- 6*e/B ) = |
|
|
55,57 |
kN/m2 |
|
|
|
|
ss = (s1+ s2) /2 = |
|
111,81 |
kN/m2 |
|
|
|
- warunki |
|
|
|
|
|
|
|
|
|
|
s1/s2= |
3,02 |
< 4 |
|
|
|
|
|
|
ss = |
111,81 |
<0,81*qf= |
259,98 |
kN/m2 |
|
|
|
|
s1= |
168,049 |
< 1,2*0,81*qf= |
|
311,97 |
kN/m2 |
|
|
|
|
|
|
|
|
|
|
5.3.4. Obliczenie odporu gruntu |
|
|
|
|
|
|
|
|
- naprężenia od ciężaru stopy i gruntu |
|
|
|
|
|
|
|
|
|
|
sg = G / B*L = |
|
20,53 |
kN/m2 |
|
|
|
|
|
|
|
|
|
|
|
|
- odpór gruntu |
|
|
|
|
|
|
|
|
|
s1`=s1+sg= |
|
147,52 |
kN/m2 |
|
|
|
|
|
|
|
|
|
s2`=s2+sg= |
|
35,05 |
kN/m2 |
|
|
|
|
|
|
|
|
|
ss`=(s1`+s2`)/2= |
|
91,28 |
kN/m2 |
s1` |
|
|
|
|
|
|
|
|
5.3.5. Obliczenie momentów i wyznaczenie zbrojenia |
|
|
|
|
|
|
|
|
- dla trapezu ABCD |
|
|
|
|
|
|
|
|
|
M=(B-hs+2*e)2*(2*L+bs)*s1`/24= |
|
|
|
121,79 |
kNm |
|
|
|
|
|
|
|
|
|
|
|
|
|
Fa=M/Ra*0,9*ho= |
|
0,00119334115924 |
m2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Ra= |
210000 |
kN/m2 |
A I St3S |
|
|
|
|
|
ho=h-0,06= |
0,54 |
m |
|
|
|
|
- dla trapezu CDEF |
|
|
|
|
|
|
|
|
|
|
M=(L-bs)2*(2*B+hs)*ss`/96= |
|
|
6,76 |
kNm |
|
|
|
|
|
|
|
|
|
|
|
|
|
Fa=M/Ra*0,9*ho= |
|
0,000066 |
m2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Ra= |
210000 |
kN/m2 |
|
|
|
|
|
|
ho=h-0,06= |
0,54 |
m |
|
|
|
|
5.3.6. Sprawdzenie przebicia |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
h |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
c1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
D
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
C F
|
|
|
|
|
L |
bs |
|
|
|
|
|
|
B
|
|
|
|
|
|
|
a1
|
|
|
|
|
|
|
|
|
|
|
A |
c2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
c1=(B-hs)/2-h= |
|
0,425 |
m |
|
|
|
|
|
c2=(B-a1)/2-(L-a2)/2= |
|
|
0,4 |
m |
|
|
|
- sprawdzenie warunku na przebicie |
|
|
|
|
|
|
|
|
|
|
Fo*s1` < 0,75*Rbz*ho*bsr |
|
|
|
|
|
|
|
|
Fo=0,5*(L+a2)*c1= |
|
0,393 |
m2 |
|
|
|
|
|
Rbz= |
1030 |
kN/m2 |
|
|
|
|
|
|
bsr=(L+a2)/2= |
|
0,925 |
m |
|
|
|
|
|
Fo*s1`= |
57,99 |
kN < |
385,86375 |
kN |
|
|
|
|
|
|
Warunek spełniony: |
|
|
|
|
|
|
|
|
|
|
|
|
|
5.4. Siły w poziomie posadowienia wariant II |
|
|
|
|
|
|
|
|
- ciężar fundamentu i gruntu na nim |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
76,98 |
kN |
|
|
|
|
|
|
|
|
|
|
|
|
|
gs= |
21,0 |
kN/m3 |
|
|
|
|
|
|
gf= |
1,15 |
|
|
|
|
|
- siła pionowa N |
|
|
|
|
|
|
|
|
|
|
N= |
427,55 |
kN |
|
|
|
|
- moment |
|
|
|
|
|
|
|
|
|
M=M2+T2*h+N2*es= |
|
90,499 |
kNm |
|
|
|
|
5.4.1. Mimośród e |
|
|
|
|
|
|
|
|
|
e=M/N= |
0,212 |
m |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5.4.2. Obliczenie oporu granicznego gruntu qf |
|
|
|
|
|
|
|
|
- przyjęto grunt Pr i Ps |
|
|
|
|
|
|
|
|
|
f = |
31 |
o |
|
|
|
|
|
|
g = |
19,5 |
kN/m3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
320,341 |
kN/m2 |
|
|
|
|
|
|
|
|
|
|
|
B`=B-2*e= |
2,08 |
m |
|
|
|
|
|
|
L`=L= |
1,5 |
m |
|
|
|
|
|
|
Dmin=hz-h= |
0,3 |
m |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ND = |
22 |
|
tgd =T/N = |
0,042 |
|
|
|
|
NB = |
9,5 |
|
tgf = |
0,601 |
|
|
|
|
|
|
|
|
|
|
|
|
|
iD = |
0,5 |
|
tgd/tgf = |
0,0696 |
|
|
|
|
iB = |
0,3 |
|
|
|
|
|
|
|
gB=gD=g = |
19,5 |
kN/m3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5.4.3. Obliczenie naprężeń pod stopą i sprawdzenie warunków |
|
|
|
|
|
|
|
|
- naprężenia |
|
|
|
|
|
|
|
|
|
|
s1 = (N/B*L)*( 1+ 6*e/B ) = |
|
|
171,93 |
kN/m2 |
|
|
|
|
s2 = (N/B*L)*( 1- 6*e/B ) = |
|
|
56,09 |
kN/m2 |
|
|
|
|
ss = (s1+ s2) /2 = |
|
114,01 |
kN/m2 |
|
|
|
- warunki |
|
|
|
|
|
|
|
|
|
|
s1/s2= |
3,07 |
< 4 |
|
|
|
|
|
|
ss = |
114,01 |
<0,81*qf= |
259,48 |
kN/m2 |
|
|
|
|
s1= |
171,933 |
< 1,2*0,81*qf= |
|
311,37 |
kN/m2 |
|
|
|
|
|
|
|
|
|
|
5.4.4. Obliczenie odporu gruntu |
|
|
|
|
|
|
|
|
- naprężenia od ciężaru stopy i gruntu |
|
|
|
|
|
|
|
|
|
|
sg = G / B*L = |
|
20,53 |
kN/m2 |
|
|
|
|
|
|
|
|
|
|
|
|
- odpór gruntu |
|
|
|
|
|
|
|
|
|
|
s1`=s1+sg= |
|
151,41 |
kN/m2 |
|
|
|
|
|
|
|
|
|
s2`=s2+sg= |
|
35,57 |
kN/m2 |
|
|
|
|
|
|
|
|
|
ss`=(s1`+s2`)/2= |
|
93,49 |
kN/m2 |
s1` |
|
|
|
|
|
|
|
|
5.4.5. Obliczenie momentów i wyznaczenie zbrojenia |
|
|
|
|
|
|
|
|
- dla trapezu ABCD |
|
|
|
|
|
|
|
|
|
M=(B-hs+2*e)2*(2*L+bs)*s1`/24= |
|
|
|
125,42 |
kNm |
|
|
|
|
|
|
|
|
|
|
|
|
|
Fa=M/Ra*0,9*ho= |
|
0,001228921955566 |
m2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Ra= |
210000 |
kN/m2 |
A I St3S |
|
|
|
|
|
ho=h-0,06= |
0,54 |
m |
|
|
|
|
- dla trapezu CDEF |
|
|
|
|
|
|
|
|
|
|
M=(L-bs)2*(2*B+hs)*ss`/96= |
|
|
6,92 |
kNm |
|
|
|
|
|
|
|
|
|
|
|
|
|
Fa=M/Ra*0,9*ho= |
|
0,000068 |
m2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Ra= |
210000 |
kN/m2 |
|
|
|
|
|
|
ho=h-0,06= |
0,54 |
m |
|
|
|
|
5.4.6. Sprawdzenie przebicia |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
h |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
c1 |
|
|
|
|
|
|
|
D
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
C F
|
|
|
|
|
L |
bs |
|
|
|
|
|
|
B
|
|
|
|
|
|
|
a1
|
|
|
|
|
|
|
|
|
|
|
A |
c2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
c1=(B-hs)/2-h= |
|
0,425 |
m |
|
|
|
|
|
c2=(B-a1)/2-(L-a2)/2= |
|
|
0,4 |
m |
|
|
|
- sprawdzenie warunku na przebicie |
|
|
|
|
|
|
|
|
|
|
Fo*s1` < 0,75*Rbz*ho*bsr |
|
|
|
|
|
|
|
|
Fo=0,5*(L+a2)*c1= |
|
0,393 |
m2 |
|
|
|
|
|
Rbz= |
1030 |
kN/m2 |
|
|
|
|
|
|
bsr=(L+a2)/2= |
|
0,925 |
m |
|
|
|
|
|
Fo*s1`= |
59,52 |
kN < |
385,86375 |
kN |
|
|
|
|
|
|
Warunek spełniony: |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5.5. Ostateczne przyjęcie zbrojenia |
|
|
|
|
|
|
|
|
- Wariant I: |
|
|
|
|
|
|
|
|
kierunek B: |
|
Fa= |
0,00119334115924 |
m2 |
|
|
|
|
kierunek L: |
|
Fa= |
0,000066 |
m2 |
|
|
|
|
- Wariant II: |
|
|
|
|
|
|
|
|
kierunek B: |
|
Fa= |
0,001228921955566 |
m2 |
|
|
|
|
kierunek L: |
|
Fa= |
0,000068 |
m2 |
|
|
|
|
|
kierunek B: |
|
f12 co 9cm o |
|
Fa= |
12,56 |
cm2 |
|
|
|
|
|
|
|
|
|
|
|
kierunek L: |
|
f12 co 16cm o |
|
Fa= |
7,07 |
cm2 |
|