dobor fundamentu

$= \frac{1}{m}$ p0 = 20 kPa

$C_{21} = \ C_{02}\left\lbrack 1 + 2\ \bullet \ \frac{a + b}{\ \bullet F} \right\rbrack\ \bullet \ \ \sqrt{\frac{p_{1}}{p_{0}}} = 27\ \left\lbrack \ 1 + 2\ \bullet \ \frac{5,25 + 3\ }{\ \bullet 15,75} \right\rbrack\ \bullet \sqrt{\frac{32,799}{20}} = \ 70,\ 799\ \frac{\text{MPa}}{m}$

$C_{22} = \ 25\ \left\lbrack \ 1 + 2\ \bullet \ \frac{5,25 + 3\ }{\ \bullet 15,75} \right\rbrack\ \bullet \sqrt{\frac{15,306}{20}} = \ 44,782\ \frac{\text{MPa}}{m}$

$C_{23} = \ 26\ \left\lbrack \ 1 + 2\ \bullet \ \frac{5,25 + 3\ }{\ \bullet 15,75} \right\rbrack\ \bullet \sqrt{\frac{4,373}{20}} = \ 24,895\ \frac{\text{MPa}}{m}$

${C'}_{21} = \ C_{02}\left\lbrack 1 + 2\ \bullet \ \frac{a + b}{\ \bullet F} \right\rbrack\ \bullet \ \ \sqrt{\frac{p_{1}'}{p}} = 27\ \left\lbrack \ 1 + 2\ \bullet \ \frac{5,25 + 3\ }{\ \bullet 15,75} \right\rbrack\ \bullet \sqrt{\frac{36,001}{20}} = \ 74,175\ \frac{\text{MPa}}{m}$

${C'}_{22} = \ C_{03}\left\lbrack 1 + 2\ \bullet \ \frac{a + b}{\ \bullet F} \right\rbrack\ \bullet \ \ \sqrt{\frac{p_{1}'}{p}} = 25\ \left\lbrack \ 1 + 2\ \bullet \ \frac{5,25 + 3\ }{\ \bullet 15,75} \right\rbrack\ \bullet \sqrt{\frac{23,632}{20}} = \ 55,645\ \frac{\text{MPa}}{m}$

${C'}_{23} = \ 26\ \left\lbrack \ 1 + 2\ \bullet \ \frac{5,25 + 3\ }{\ \bullet 15,75} \right\rbrack\ \bullet \sqrt{\frac{9,497}{20}} = \ 36,685\ \frac{\text{MPa}}{m}$

$C_{pxz1} = C_{02}\left\lbrack 1 + 2\ \bullet \ \frac{a + 3b}{\ \bullet F} \right\rbrack \bullet \ \sqrt{\frac{p_{1}'}{p_{0}}} = 27\left\lbrack \ 1 + 2\ \bullet \ \frac{5,25 + 3\ \bullet 3\ }{\ \bullet 15,75} \right\rbrack \bullet \sqrt{\frac{36,001}{20}} = 101,775\ \frac{\text{MPa}}{m}$

$C_{pxz2} = \ 25\ \left\lbrack \ 1 + 2\ \bullet \ \frac{5,25 + 3\ \bullet 3\ }{\ \bullet 15,75} \right\rbrack\ \bullet \sqrt{\frac{23,632}{20}} = \ 76,350\ \frac{\text{MPa}}{m}$

$C_{pxz3} = \ 26\ \left\lbrack \ 1 + 2\ \bullet \ \frac{5,25 + 3\ \bullet 3\ }{\ \bullet 15,75} \right\rbrack\ \bullet \sqrt{\frac{9,497}{20}} = \ 50,336\ \frac{\text{MPa}}{m}$

$C_{pyz1} = C_{02}\left\lbrack 1 + 2\ \bullet \ \frac{3a + b}{\ \bullet F} \right\rbrack \bullet \sqrt{\frac{p_{1}'}{p_{0}}} = 27\left\lbrack \ 1 + 2\ \bullet \ \frac{3 \bullet 5,25 + 3\ }{\ \bullet 15,75} \right\rbrack\ \bullet \sqrt{\frac{36,001}{20}} = 122,475\ \frac{\text{MPa}}{m}$

$C_{pyz2} = \ 25\ \left\lbrack \ 1 + 2\ \bullet \ \frac{3 \bullet \ 5,25 + 3\ }{\ \bullet 15,75} \right\rbrack\ \bullet \sqrt{\frac{23,632}{20}} = \ 91,878\ \frac{\text{MPa}}{m}$

$C_{pyz3} = \ 26\ \left\lbrack \ 1 + 2\ \bullet \ \frac{3 \bullet 5,25 + 3\ \ }{\ \bullet 15,75} \right\rbrack\ \bullet \sqrt{\frac{9,497}{20}} = \ 60,574\ \frac{\text{MPa}}{m}$


$$C_{x1} = 0,7 \bullet C_{z1} = 0,7 \bullet 70,799 = 49,559\frac{\text{MPa}}{m}$$


$$C_{x2} = 0,7 \bullet C_{z2} = 0,7 \bullet 44,782 = 31,348\frac{\text{MPa}}{m}$$


$$C_{x3} = 0,7 \bullet C_{z3} = 0,7 \bullet 24,895 = 17,426\frac{\text{MPa}}{m}$$


t1 = t1′=2 • d1m = 2 • 75 = 150 cm


t2 = t2′=2 • d2m = 2 • 45 = 90 cm


t3′=2 • d3m = 2 • 92, 132 = 184, 26 cm


t3 = 2 • d3m = 2 • 30 = 60 cm

$C_{z} = b \bullet \sqrt{2} \bullet \left( \frac{t_{1}'}{C_{21}'} + \frac{t_{2}'}{C_{22}'} + \frac{t_{3}'}{C_{23}'} \right)^{- 1} = 3\sqrt{2}\left( \frac{150}{74,175} + \frac{90}{55,645} + \frac{184,26}{36,685} \right)^{- 1} = 48,977\frac{\text{MPa}}{m}$

$C_{\text{φxz}} = b \bullet \sqrt{2} \bullet \left( \frac{t_{1}'}{C_{\varphi xz1}'} + \frac{t_{2}'}{C_{\varphi xz2}'} + \frac{t_{3}'}{C_{\varphi xz3}'} \right)^{- 1} = 3\sqrt{2}\left( \frac{150}{101,775} + \frac{90}{76,350} + \frac{184,26}{50,336} \right)^{- 1} = 48,977\frac{\text{MPa}}{m}$

5.2 Sztywność podłoża gruntowego


$$K_{z} = C_{z} \bullet F = 48,977 \bullet 15,75 = 771,388\frac{\text{MN}}{m}$$


$$K_{x} = C_{x} \bullet F = 32,117 \bullet 15,75 = 505,843\frac{\text{MN}}{m}$$


$$I_{\text{xs}} = \frac{a \bullet b^{3}}{12} = \frac{5,25 \bullet 3^{3}}{12} = 11,812m^{4}$$


$$I_{\text{ys}} = \frac{a^{3} \bullet b}{12} = \frac{{3 \bullet \left( 5,25 \right)}^{3}}{12}36,176m^{4}$$


Kφxz = Cφxz • Iys = 67, 202 • 36, 176 = 243, 100 MNm


Kφyz = Cφyz • Ixs = 80, 780 • 11, 812 = 955, 236 MNm

6. OBLICZENIA AMPLITUDY DRGAŃ WYMUSZONYCH FUNADAMENTU

6.1 Amplitudy drgań w płaszczyźnie XZ


oddalonego punktu  ∖ nod srodka ciezkosci                


$$A_{H} = \frac{P_{\text{zo}}}{K_{\text{φxz}}} \bullet x_{p} \bullet a_{f} \bullet v_{1}$$


$$m = \frac{Q_{f} + Q_{m}}{g} = \frac{599,38\ kN + 89,4\ kN}{9,81\frac{m}{s^{2}}} = 702122,03\ kg$$

$_{z} = \sqrt{\frac{K_{z}}{m}} = \sqrt{\frac{771,388\frac{\text{MN}}{m}}{70212,03\ kg} = 104,817\frac{\text{rad}}{s}}$


$$\eta_{z} = \frac{\omega}{_{z}} = \frac{40,8\frac{\text{rad}}{s}}{104,817\frac{\text{rad}}{s}} = 0,389$$


$$v_{z} = \frac{1}{\sqrt{\left( 1 - \eta_{z}^{2} \right)^{2} + \gamma^{2} + \eta_{z}^{2}}}$$


hs = hf + 0, 75 = 1, 6 + 0, 75 = 2, 35 m


$$z_{k} = \frac{S_{z}}{Q_{m} + Q_{f}}$$

$S_{z} = Q_{m} \bullet h_{s} + \rho_{z} \bullet a_{\text{tech}} \bullet b_{\text{tech}} \bullet h_{g} \bullet \left( h_{f} - \frac{h_{g}}{2} \right) + \rho_{z} \bullet a \bullet b \bullet h_{d} \bullet \frac{h_{d}}{2} = 89,4 \bullet 2,35 + 25 \bullet 5 \bullet 2,8 \bullet 0,7 \bullet \left( 1,6 - \frac{0,7}{2} \right) + 25 \bullet 5,25 \bullet 3 \bullet 0,9 \bullet \frac{0,9}{2} = 675,68\ kNm$


$$z_{k} = \frac{675,68}{89,4 + 599,38} = 0,981\ m$$

$_{1} = \sqrt{\frac{K_{x} \bullet K_{\text{φxz}}}{m\left( K_{x} \bullet {z_{k}}^{2} \bullet K_{\text{φxz}} \right)}} = \sqrt{\frac{505,843 \bullet 2431,1}{70212,03 \bullet \left( 505,843 \bullet \left( 0,981 \right)^{2} \bullet 2431,1 \right)}} = 77,476\frac{\text{rad}}{s}$


$$\eta_{1} = \frac{\omega}{_{1}} = \frac{40,8\frac{\text{rad}}{s}}{77,476\frac{\text{rad}}{s}} = 0,527\text{\ strefa\ pozarezonansowa},\ bo\ \eta_{1} < 0,750,80$$

γ = Φ • ω Φ = 0, 0045 s  bo glebokosc posadowienia  > 1, 5 m


Φ = 0, 0045 s


γ = 0, 0045 • 40, 8 = 0, 1836

dla γ = 0, 1826

z tłumieniami bez tłumień

$v_{x} = \frac{1}{\sqrt{\left( 1 - \left( 0,5277 \right)^{2} \right)^{2} + \left( 0,1836 \right)^{2} \bullet \left( 0,5277 \right)^{2}}} = 1,174$ $v_{z}' = \frac{1}{\left| 1 - {\eta_{z}}^{2} \right|} = 1,178$

$v_{1} = \frac{1}{\sqrt{\left( 1 - \left( 0,389 \right)^{2} \right)^{2}} + \left( 0,1836 \right)^{2} + \left( 0,389 \right)^{2}} = 1,372$ $v_{1}^{'} = \frac{1}{\left| 1 - {\eta_{1}}^{2} \right|} = 1,385$

dla γ = 0


$$v_{z} = \frac{1}{\sqrt{\left( {1 - \left( 0,389 \right)}^{2} \right)^{2}}} = 1,178\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v_{1} = \frac{1}{\sqrt{\left( {1 - \left( 0,527 \right)}^{2} \right)^{2}}} = 1,385$$

z uwzględnieniem tłumień

$A_{H} = \frac{P_{z0}}{K_{\text{φxz}}} \bullet x_{p} \bullet h_{f} \bullet v_{1} = \frac{30,166 \bullet 10^{3}}{2431,1 \bullet 10^{6}} \bullet 1,419 \bullet 1,6 \bullet 1,372 = 0,0386\ mm = 38,6\mu m < A_{\text{H.dop}} = 200\mu m$

$A_{v} = \frac{P_{z0}}{K_{z}} \bullet v_{2} + \frac{P_{z0}}{K_{\text{φxz}}} \bullet x_{p} \bullet a_{f} \bullet v_{1} = \frac{30,166 \bullet 10^{3}}{771,388 \bullet 10^{6}} \bullet 1,174 + \frac{30,166 \bullet 10^{3}}{2431,1 \bullet 10^{6}} \bullet 1,419 \bullet 2,625 \bullet 1,372 = 109,3\mu m < A_{\text{v.dop}} = 150\ \mu m$

bez uwzględnienia tłumień


$$A_{H}^{'} = \frac{P_{z0}}{K_{\text{φxz}}} \bullet x_{p} \bullet h_{f} \bullet v_{1}^{'} = \frac{30,166 \bullet 10^{3}}{2431,1 \bullet 10^{6}} \bullet 1,419 \bullet 1,6 \bullet 1,385 = 39,02\mu m$$

$A_{v}' = \frac{P_{z0}}{K_{z}} \bullet v_{2}' + \frac{P_{z0}}{K_{\text{φxz}}} \bullet x_{p} \bullet a_{f} \bullet v_{1}' = \frac{30,166 \bullet 10^{3}}{771,388 \bullet 10^{6}} \bullet 1,178 + \frac{30,166 \bullet 10^{3}}{2431,1 \bullet 10^{6}} \bullet 1,419 \bullet 2,625 \bullet 1,385 = 110,1\mu m$

6.2.1 Siły wzbudzające pionowe (płaszczyzna YZ)`123

zk = 0, 981m m = 70212, 03 kg

$K_{y} = K_{x} = 505,843\frac{\text{MN}}{m}$ $K_{z} = 771,388\frac{\text{MN}}{m}\backslash nK_{\text{φyz}} = 955,236\ MNm$ $b_{f} = \frac{b}{2} = \frac{3}{2} = 1,5m$

$_{z} = 104,817\frac{1}{s}$ ηz = 0, 062


$$_{1} = \sqrt{\frac{K_{y} \bullet K_{\text{φyz}}}{m\left( K_{y}{\bullet z_{k}}^{2} \bullet K_{\text{φyz}} \right)}} = \sqrt{\frac{505,843 \bullet 955,236}{70212,03\left( 505,843\left( 0,981 \right)^{2} \bullet 955,236 \right)} = 69.072\frac{\text{rad}}{s}}$$


$$\eta_{1} = \frac{\omega}{_{1}} = \frac{40,8\frac{\text{rad}}{s}}{69,072\frac{\text{rad}}{s}} = 0,59\ \text{\ sfera\ pozarezonansowa}$$

dla γ = 0, 1836

z tłumieniami bez tłumień

vz = 1, 178 (jak w punkcie 6.1) v2′=1, 178

$v_{1} = \frac{1}{\sqrt{\left( 1{- \left( 0,59 \right)}^{2} \right)^{2} + \left( 0,1836 \right)^{2} \bullet \left( 0,59 \right)^{2}}} = 1,513$ $v_{1}' = \frac{1}{\left| {1 - \eta_{1}}^{2} \right|} = 1,1534$

dla γ = 0


$$v_{2} = 1,178\ \left( jak\ w\ punkcie\ 6.1 \right)\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }v_{1} = \frac{1}{\sqrt{\left( 1 - \left( 0,59 \right)^{2} \right)^{2}}} = 1,534$$

z uwzględnieniem tłumienia

$A_{H} = \frac{P_{z0}}{K_{\text{φyz}}} \bullet \left| y_{p} \right| \bullet h_{f} \bullet v_{1} = \frac{30,166 \bullet 10^{3}}{955,236 \bullet 10^{6}} \bullet \left| - 0,442 \right| \bullet 1,6 \bullet 1,513 = 33,79\mu m < A_{\text{H.dop}}$

$A_{v} = \frac{P_{z0}}{K_{z}} \bullet v_{2} + \frac{P_{z0}}{K_{\text{φy}z}} \bullet \left| y_{p} \right| \bullet a_{f} \bullet v_{1} = \frac{30,166 \bullet 10^{3}}{771,388 \bullet 10^{6}} \bullet 1,174 + \frac{30,166 \bullet 10^{3}}{955,236 \bullet 10^{6}} \bullet \left| - 0,442 \right| \bullet 2,625 \bullet 1,513 = 77,59\mu m < A_{\text{v.dop}}$

bez uwzględnienia tłumień


$$A_{H}' = \frac{P_{z0}}{K_{\text{φyz}}} \bullet \left| y_{p} \right| \bullet h_{f} \bullet v_{1}^{'} = \frac{30,166 \bullet 10^{3}}{955,236 \bullet 10^{6}} \bullet \left| 0,442 \right| \bullet 1,6 \bullet 1,385 = 34,2\mu m$$

$A_{v}' = \frac{P_{z0}}{K_{z}} \bullet v_{2}' + \frac{P_{z0}}{K_{\text{φyz}}} \bullet \left| y_{p} \right| \bullet a_{f} \bullet v_{1}' = \frac{30,166 \bullet 10^{3}}{771,388 \bullet 10^{6}} \bullet 1,178 + \frac{30,166 \bullet 10^{3}}{955,236 \bullet 10^{6}} \bullet \left| 0,442 \right| \bullet 2,625 \bullet 1,385 = 78,18\mu m$

6.2.2 Siły wzbudzające poziome (płaszczyzna YZ)

z tłumieniami

$A_{H} = \frac{p_{y0}}{K_{y}} \bullet \left\lbrack 1 + \frac{K_{y} \bullet h_{s} \bullet h_{f}}{K_{\text{φyz}}} \right\rbrack \bullet v_{1} = \frac{32,434 \bullet 10^{3}}{505,843 \bullet 10^{6}} \bullet \left\lbrack 1 + \frac{505,843 \bullet 2,35 \bullet 1,6}{955,236} \right\rbrack \bullet 1,513 = 290,2\mu m > A_{\text{H.dop}}$

$A_{v} = \frac{P_{y0}}{K_{\text{φyz}}} \bullet h_{s} \bullet b_{f} \bullet v_{1} = \frac{32,434 \bullet 10^{3}}{955,236} \bullet 2,35 \bullet 1,5 \bullet 1,513 = 181,1\mu m > A_{\text{v.dop}}$

bez tłumienia

$A_{H}' = \frac{p_{y0}}{K_{y}} \bullet \left\lbrack 1 + \frac{K_{y} \bullet h_{s} \bullet h_{f}}{K_{\text{φyz}}} \right\rbrack \bullet v_{1}' = \frac{32,434 \bullet 10^{3}}{505,843 \bullet 10^{6}} \bullet \left\lbrack 1 + \frac{505,843 \bullet 2,35 \bullet 1,6}{955,236} \right\rbrack \bullet 1,534 = 294,2\mu m > A_{\text{H.dop}}$

$A_{v}' = \frac{P_{y0}}{K_{\text{φyz}}} \bullet h_{s} \bullet b_{f} \bullet v_{1}' = \frac{32,434 \bullet 10^{3}}{955,236} \bullet 2,35 \bullet 1,5 \bullet 1,543 = 183,6\mu m > A_{\text{v.dop}}$

7. OBLICZENIA NACISKU FUNDAMENTU NA PODŁOŻE GRUNTOWE


$$q_{r} + q_{d} = \frac{P}{F} + A_{0} \bullet C_{z} \leq q_{f}$$

$q_{d} = \frac{P_{d}}{F} = \frac{P_{d} \bullet v \bullet C_{z}}{F \bullet C_{z}} = \frac{P_{d}}{K_{z}} \bullet v \bullet C_{z} = A_{0} \bullet C_{z}$ - krawędziowy nacisk na podstawę

$q_{f} = \left( 1 + 0,3 \bullet \frac{B}{L} \right) \bullet N_{c} \bullet {c_{u}}^{\left( r \right)} + \left( 1 + 1,5\frac{B}{L} \right) \bullet N_{D} \bullet D_{\min}{\bullet \rho_{D}}^{\left( r \right)} \bullet g + \left( 1 + 0,25\frac{B}{L} \right) \bullet N_{B} \bullet {B \bullet \rho_{B}}^{\left( r \right)} \bullet g$

z PN-81-B/03020

B = 3,00 m

L = 5,25 m


Dmin = 1, 6m

Fundament posadowiony w II warstwie → iły półzwarte

Parametry fizyczne gruntów:

wart. charakterystyczne [0,9•γni]wart. oblicz.
ciężar objętościowy: piasków grubych
γnI = 19 kN/m3
iłów półzwartych
γnII = 21, 5 kN/m3
Gliny
γnIII = 22 kN/m3
żwiru
γnIV = 22, 5 kN/m3
kąt tarcia wewnętrznego dla iłów n = 13o
r = ⌀n • 0, 9 = 11, 7o
spójność dla iłów Cun = 60 kPa Cur = 0, 9 • Cur = 54kPa

Współczynniki nośności → aproksymacja dla kąta 11, 7o

ND = 2, 868


NC = 9, 019


NB = 0, 289


$$\gamma_{D_{I}r} = \frac{1,45m \bullet \gamma_{\text{rI}} + 0,15m{\bullet \gamma}_{\text{rII}}}{D_{\min}} = \frac{1,45m \bullet 17,1\frac{\text{kN}}{m^{3}} + 0,15m \bullet 19,45\frac{\text{kN}}{m^{3}}}{1,6m} = 17,311\frac{\text{kN}}{m^{3}}$$

Obliczona średnia gęstość objętościowa gruntów powyżej poziomu posadowienia.

$\gamma_{B_{I}r} = \frac{1,5m \bullet \gamma_{\text{rII}} + 0,9m \bullet \gamma_{\text{rIII}} + 0,6m \bullet \gamma_{r\text{IV}}}{B} = \frac{1,5 \bullet 19,35 + 0,9 \bullet 19,8 + 0,6 \bullet 20,25}{3} = 19,665\frac{\text{kN}}{m^{3}}$

Obliczona średnia gęstość objętościowa gruntów poniżej poziomu posadowienia do głębokości =3m

$q_{f} = \left( 1 + 0,3 \bullet \frac{3}{5,3} \right) \bullet 9,019 \bullet 54 + \left( 1 + 1,5 \bullet \frac{3}{5,3} \right) \bullet 2.868 \bullet 1,6 \bullet 17,311 + \left( 1 - 0,25 \bullet \frac{3}{5,3} \right) \bullet 0,289 \bullet 3 \bullet 19,665 = 731,248\ kPa$


vz = 1, 174


v1 = 1, 372

$A_{v} = \frac{P_{z0}}{K_{z}} \bullet v_{2} + \frac{P_{z0}}{K_{\text{φxz}}} \bullet x_{p} \bullet 0,5 \bullet a \bullet v_{1} = \frac{30,166 \bullet 10^{3}}{771,388 \bullet 10^{6}} \bullet 1,174 + \frac{30,166 \bullet 10^{3}}{2431,1 \bullet 10^{6}} \bullet 1,419 \bullet 0,5 \bullet 5,25 \bullet 1,372 = 109,3\mu m$


$$q_{d} = A_{v} \bullet C_{z} = 109,3\mu m \bullet 48,977\frac{\text{μPa}}{m} = 5,353\ kPa$$


$$q_{r} = \frac{P}{F} = \frac{688,78}{15,57} = 43,732\ kPa$$


qr + qd ≤ qf


43, 732 + 5, 535 ≤ 731, 248 kPa

49, 085 ≤ 731, 248 kPa → warunek spełniony


vz = 1, 174


v1 = 1, 513

$A_{v} = \frac{P_{z0}}{K_{z}} \bullet v_{2} + \frac{P_{z0}}{K_{\text{φyz}}} \bullet \left| y_{p} \right| \bullet 0,5 \bullet b \bullet v_{1} = \frac{30,166 \bullet 10^{3}}{771,388 \bullet 10^{6}} \bullet 1,174 + \frac{30,166 \bullet 10^{3}}{955,236 \bullet 10^{6}} \bullet \left| - 0,442 \right| \bullet 0,5 \bullet 3 \bullet 1,513 = 14,23\mu m$


$$q_{d} = A_{v} \bullet C_{z} = 14,23\mu m \bullet 48,977\frac{\text{MPa}}{m} = 0,695\ kPa$$

­­$q_{r} = \frac{P}{F} = \frac{688,78}{15,75} = 43,732\ kPa$


qr + qd ≤ qf


43, 732 kPa + 0, 695 kPa ≤ 731, 248 kPa

         44, 427 kPa ≤ 731, 248 kPa → warunek spełniony

z tłumieniem [μm] bez tłumienia [μm]
Płaszczyzna
AH

Av
XZ 38,2 109,3
YZ (siły pionowe) 33,79 77,59
YZ (siły poziome) 290,2 181,1

Wyszukiwarka