Tutorial 1_Q2.pdf - Q2 Use Monte Carlo simulation(MCS to estimate the mean and standard deviation of the maximum deflection at the end of cantilever

Tutorial 1_Q2.pdf - Q2 Use Monte Carlo simulation(MCS to...

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Q2. Use Monte Carlo simulation (MCS) to estimate the mean and standard deviation of the maximum deflection at the end of cantilever beam shown below using Microsoft Excel. ult/files/p1as.jpg Beam cross-section is rectangular with B as width and D as depth of the beam, which means that moment of inertia (I) can be calculated as BD 3 /12. E is elastic modulus, which is constant and has magnitude 200 GPa. Parameters P, B, D, L are random variables. Assume the following: The load P, width B, depth D, length of the beam L has a nominal value of 5 N, 25 mm, 40 mm and 5 m respectively. The bias factor for (P, B, D, L) has a mean value of (1.1, 1.07, 1.15, 1.12) and a COV of (0.02, 0.03, 0.08, 0.05) respectively.
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Unformatted text preview: All random variables in this analysis can be modelled as normally distributed. Solution steps 1. Calculate standard deviation of random of the bias factors by using equation Standard deviation = mean value x COV 2. Simulate random numbers in between 0 and 1 in 4 columns for 4 random variables using command RAND(). In excel sheet, it is shown as U1, U2, U3 and U4. 3. Simulate Bias factor by using command NORMINV(probability,mean,standard_dev), In excel, it has been shown by Z1, Z2, Z3 and Z4. 4. Simulate P, B, D and L by multiplying Z1, Z2, Z3 and Z4 with corresponding nominal values respectively. 5. Calculate moment of inertia using I = BD 3 /12. 6. Now calculate maximum deflection using given equation. 7. Finally use AVERAGE() and STDEV() command to estimate mean and standard deviation of the maximum deflection....
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