1.0 Zebranie obciążeń |
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qk |
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q |
Obciążenia stałe: |
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-dźwigar stalowy i stężenia blachownicowe |
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kN/m |
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kN/m |
(0,25*0,03+1,53*0,015+0,4*0,04)*1,25*(78,5+2,0) |
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4,67 |
1,2 |
5,61 |
jezdnia: |
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kN/m2 |
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kN/m2 |
-płyta żelbetowa (0,18+0,045)*24 |
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5,4 |
1,2 |
6,48 |
-izolacja-2 x papa 0,12 |
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0,12 |
1,5 |
0,18 |
-war. ścieralna + wiążąca ( 0,06+0,04)*23 |
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2,3 |
1,5 |
3,45 |
chodnik: |
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-płyta żelbetowa ( 0,18+0.025)*24 |
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4,92 |
1,2 |
5,90 |
-izolacja-2 x papa 0,12 |
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0,12 |
1,5 |
0,18 |
-warstwa wiążąca 0,04*23 |
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0,92 |
1,5 |
1,38 |
-płyta chodnikowa 0,2*24 |
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4,8 |
1,2 |
5,76 |
-gzyms (0,54*0,2/1,0)*24 |
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3,0 |
1,2 |
3,6 |
-asfalt lany 0,03*23 |
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0,69 |
1,5 |
1,04 |
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kN |
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kN |
-poręcz 0,2 |
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0,20 |
1,5 |
0,29 |
-bariera ochronna 0,4 |
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0,40 |
1,5 |
0,60 |
Obciążenia zmienne: |
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-obc. na jedno koło samochodu |
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k= 600 kN |
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kN |
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kN |
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(600/8)*1,24 |
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93 |
1,5 |
139,5 |
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kN/m2 |
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kN/m2 |
-obc.taborem samochodowym |
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q=3 kN/m2 |
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3,00 |
1,5 |
4,50 |
-obc. tłumem |
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q=2,5 kN/m2 |
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2,50 |
1,3 |
3,25 |
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2.0 Wyznaczenie linii rozdziału poprzecznego. |
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1,60 |
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4,80 |
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2,06m |
3,2 m |
3,2 m |
3,2 m |
2,06 m |
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n= |
4 |
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Sbi2=2*(1,62+4,82) |
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bk= |
4,8 |
m |
Sbi2= |
51,2 |
m2 |
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Linia rozdziału: |
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0,89 |
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0,7 |
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0,4 |
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0,1 |
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-0,2 |
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-0,39 |
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2.1 Obciążenie linii rozdziału poprzecznego |
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a) nacisk od obciążenia stałego |
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2,61m |
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9,0m |
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2,61m
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2,06m |
3,2 m |
3,2 m |
3,2 m |
2,06m |
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0,67 |
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0,74 |
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-0,17 |
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-0,24 |
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siła nacisku (na 1mb dźwigara): |
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N=0,29*(0,89-0,39)+0,6*(0,74-0,24)+17,88*0,5*(0,89+0,67)*2,36+ |
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-17,88*0,5(0,39+0,17)*2,36+10,11*0,5*(0,67*7,2-0,17*1,8)= |
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44,38 |
kN/m |
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b) nacisk od obciążenia ruchomego |
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P=139,5 kN |
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3,25 kN/m2 |
4,5 kN/m2 |
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3,2 m |
3,2 m |
3,2 m |
2,06m |
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0,75 |
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0,67 |
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0,61 |
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0,36 |
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Ns=139,5*(0,61+0,36)= |
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135,315 kN |
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Nt=3,25*0,5*(0,89+0,75)*1,5+4,5*0,5*0,67*7,2= |
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14,85 KN/m. |
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2.2 Wyznaczenie wartości momentów zginających |
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a) od obciążenia stałego |
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q= |
49,99 |
kN/m |
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Mmax = 0,125 * q * L2 |
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Mmax = 0,125 * 49,99 * 22 2= |
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3024,3 |
kNm |
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b) od obciążenia ruchomego |
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P=135,315 kN |
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4,9
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5,5 |
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Mmax = 135,315 * (4,9+5,5+4,9+4,3) + 14,85 * 0,5 * 22 * 5,5 = |
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3550,6 kNm |
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3.0 Wymiarowanie dźwigarów |
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przyjęto: |
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beton |
B30 |
= > |
Eb= |
32,4 |
GPa |
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stal |
18G2A |
= > |
Ea= |
205 |
GPa |
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szerokość współpracująca: |
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bz= bz1+bz2 |
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n=Ea/Eb |
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bz1=1,6*[1-(1,6/22)]= |
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1,48 |
m n=205/32,4= |
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6,33 |
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bz2=2,06*[1-(2,06/22)]= |
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1,87 |
m |
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bz= 1,48+1,87= |
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3,35 |
m |
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Przekrój sprowadzono do właściwości stali: |
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bz' = bz/n = |
0,53 |
m |
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3.1 Wyznaczenie środka ciężkości zastępczego przekroju stalowego: |
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A =20*53+5*4+3*25+1,5*153+4*40 = |
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1544,5 |
cm2 |
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Sx=20*53*174+5*4*162+3*25*158,5+1,5*153*78,5+4*40*2= |
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217903,25 |
cm3 |
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yc=217903,3/1544,5= |
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141,08 |
cm |
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3.2 Wyznaczenie momentu bezwładności |
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Jc =(53*203/12)+53*20*332+(5*43/12)+5*4*212+(25*33/12)+25*3*17,52+ |
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+(1,5*1533/12)+1,5*153*60,52+(40*43/12)+40*4*1392= |
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5451610,46 |
cm4 |
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3.3 Wyznaczenie wskaźników wytrzymałości |
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Wbg=(5451610/43)*6,33= |
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802527,772367442 |
cm3 |
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Wstd=5451610/141= |
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38663,9 |
cm3 |
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3.4 Wyznaczenie naprężeń |
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a) obciążenia stałe |
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M= |
3024,3 |
kNm = |
302432,466875 |
kNcm |
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-0,38 |
kN/cm2 = |
-3,80 |
MPa |
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7,82208899968705 |
kN/cm2 = |
78,2 |
MPa |
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b) obciążenia ruchome |
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M= |
3550,6 |
kNm = |
355060 |
kNcm |
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-0,44 |
kN/cm2 = |
-4,40 |
MPa |
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9,20 |
kN/cm2 = |
92,00 |
MPa |
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c) naprężenia całkowite |
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