Figure 1 shows an offshore wind turbine which is designed against structural failure in extreme wind...

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Figure 1 shows an offshore wind turbine which is designed against structural failure in extreme wind conditions. For the current design of the tower-bottom cross section, the strength (R) is governed by the plastic moment resistance, which is 319 kN m. The tower-bottom bending moment (S) due to a typhoon can be idealized by a uniform distribution as follows: 0, s < 290.0 1 fs(s) = 290.0 s 320.0 30' 0, x > 320.0 The probability density function is shown in Figure 2. 0.04+ 0.03 Probability density function 0.02 0.01 290 295 300 310 305 315 320 s, load [kNm] Figure 2 PDF of the typhoon-induced bending moment, S a) Generate a sample of the tower-bottom bending moment based on the principle of Monte Carlo Simulation. Consider a sample size of 10. Determine the failure probability based on your sample. You can pick some of the following random uniform distributed numbers: {0.12, 0.71, 0.21, 0.40, 0.99, 0.03, 0.78, 0.52, 0.45, 0.66, 0.47, 0.09, 0.27, 0.55). Blade Tower x Waves Mudline Monopile Pile S Soil Cross section of tower bottom Figure 1 Illustration of a wind turbine, bending moment (S), and a cross section Figure 1 shows an offshore wind turbine which is designed against structural failure in extreme wind conditions. For the current design of the tower-bottom cross section, the strength (R) is governed by the plastic moment resistance, which is 319 kN m. The tower-bottom bending moment (S) due to a typhoon can be idealized by a uniform distribution as follows: 0, s < 290.0 1 fs(s) = 290.0 s 320.0 30' 0, x > 320.0 The probability density function is shown in Figure 2. 0.04+ 0.03 Probability density function 0.02 0.01 290 295 300 310 305 315 320 s, load [kNm] Figure 2 PDF of the typhoon-induced bending moment, S a) Generate a sample of the tower-bottom bending moment based on the principle of Monte Carlo Simulation. Consider a sample size of 10. Determine the failure probability based on your sample. You can pick some of the following random uniform distributed numbers: {0.12, 0.71, 0.21, 0.40, 0.99, 0.03, 0.78, 0.52, 0.45, 0.66, 0.47, 0.09, 0.27, 0.55). Blade Tower x Waves Mudline Monopile Pile S Soil Cross section of tower bottom Figure 1 Illustration of a wind turbine, bending moment (S), and a cross section