Question 14.4: During construction of a pier, one of the vertical steel pil......
During construction of a pier, one of the vertical steel piles, diameter 0.508 m, thickness 12.5 mm, and length equal to the depth of water of 10 m, is subjected to a current of 0.5 {m}\,{s}^{-1} . The mass of the pile is 195 \mathrm{kg\,m}^{-1} . The modulus of elasticity is 200 10^9 \, N m ^{-2} . The second moment of area of the section is 6.0\times10^{-4}\,{\mathrm{m}}^{4} . The density of sea water is 1030 \mathrm{k}{{g}}{m}^{-3} .
Will this pile be subjected to flow-induced oscillations?
The inner diameter of the pile is 0.508 – 2 × 0.0125 = 0.483 m. The mass of entrained water per unit length is
1030 \times \frac{\pi}{4} \times 0.483^2=189 \, kg \,m ^{-1}The added mass per unit length is
1030 \times \frac{\pi}{4} \times 0.508^2=209 \, kg \,m ^{-1} .The effective mass per unit length, m_{\mathrm{e}}=195+189+209=593\,\mathrm{kg}\,\mathrm{m}^{-1} . The apparent fixity depth is 6 × 0.508 = 3.05 m. The effective length of the pile =10 + 3.05 = 13.05 m. The resonant frequency, f_{\mathrm{n}} , is
0.56\bigg(\frac{200\times10^{9}\times6.0\times10^{-4}}{593\times13.05^{4}}\bigg)^{1/2}=1.48\,\mathrm{Hz}.The reduced velocity, V^{\prime}=V/f_{\mathrm{n}}D=0.5/(1.48\times0.508)=0.66. Assuming that the damping factor for marine structure steel is 0.08,
K_{ s }=\frac{2 \times 593 \times 0.08}{1030 \times 0.508^2}=0.357 .
From Fig. 14.23, for K_{\mathrm{{s}}}= 0.357, the critical reduced velocity V_{\mathrm{c}}^{\prime} =1.33, which is larger than V'(= 0.66). Therefore in-line oscillations will not be initiated.
The kinematic viscosity is 10^{-6}{\mathrm{m}}^{2}{\mathrm{s}}^{-1} , and the Reynolds number is 0.5 \times 0.508 \times 10^6=2.4 \times 10^5 . From Fig. 14.24, the critical value of V / f_{ n } D=V_{ c }^{\prime}=\text { 4.7. As } V_{ c }^{\prime} is greater than V’, cross-flow oscillations will not occur.
