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- Question : 1P - Classify the uncertainty associated with the following items as either aleatory or epistemic and explain your reason for your classification: average wind speed over a 30-day period, location of a certain applied load, change in strength of a soil caused by sampling method, capacity determined by a certain analysis method, magnitude of live load caused by vehicles traveling on a bridge, soil shear strength as measured by a certain method.
- Question : 2P - Figure 2.1 shows the PDF for a normal distribution determined from the unconfined compression tests shown in the histogram. Does the mean and standard deviation of this PDF represent aleatory or epistemic uncertainty? Explain.
- Question : 3P - List three sources of epistemic uncertainty associated with determining the soil strength at a given site and describe how you might reduce these uncertainties.
- Question : 4P - Using a random number generator create a sample of four relative densities using the PDF presented in Figure 2.2. Repeat the exercise to create three different sample sets. Compute the mean and standard deviation of your sample. Compute the mean and standard deviation of each sample set. Compare the means and standard deviations of your samples with each other and with the mean and standard deviation of the original distribution. Discuss the differences among the sample sets and the original distribution, including the type of uncertainties you are dealing with. How many samples do you think are needed to reliably determine the mean and standard deviation of the relative density of this particular soil?
- Question : 5P - A certain column will carry a dead load estimated to be 400 k with a COV of 0.1 and a live load of 200 k with a COV of 0.25. What is the mean and standard deviation of the total column load? Assuming the load is normally distributed, what is the probability that this load will exceed 750 k?
- Question : 6P - A simply supported beam has a length of 3 m and carries a distributed load with a mean of 5 kN/m and a COV of 0.2. Assuming the load is normally distributed, what are the mean and standard deviation of the maximum moment in the beam? What is the probability the maximum moment will exceed 7 kN- m?
- Question : 7P - Using the data shown in Figure 2.5, determine the probability that the tangent of the friction angle for the mudstone at the Confederation Bridge site is less than 0.25.
- Question : 8P - The capacity for a certain foundation system is estimated to be 620 kN with a COV of 0.3. The demand on the foundation is estimated to be 150 kN with a COV of 0.15. Compute the mean factor of safety of this foundation and its probability of failure assuming both capacity and demand are normally distributed.
- Question : 9P - We wish to design a shallow foundation with a probability of failure of 10-3. The footing supports a column carrying a dead load with a mean of 30 k and COV of 0.05 and a live load with a mean of 10 k and COV of 0.15. Based on the uncertainty of soil properties and our analysis method, we estimate the COV of the foundation capacity to be 0.2. For what mean capacity does the foundation need to be designed? Assume both loads and capacity are normally distributed.
- Question : 10P - Assume the foundation in Problem 2.9 was to support a high- voltage transmission line near the Danish city of
- Question : 11P - For the footing in Example 2.2, compute the factor of safety required for a probability of failure of 5 * 10-4 assuming the COV of the demand is 0.15
- Question : 12P - If the ASD design method has worked satisfactorily for over 50 years, what

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