An economic study is being made on the design of a small bridge. The traffic load has been studied with the following loads and occurrences noted during the last 5 years. Use a Poisson model for the occurrence of large loads.
In the first design under consideration, if a load T-1 occurs, a contribution to cumulative fatigue damage is expected that implies an eventual loss of useful life worth $500 to the state. Vehicle T-2 will involve an average damage of $100 each occurrence, while damage under T-3 "costs" $0.50 per occurrence. An alternate design costing more than the first design is being considered. This design is expected to have an average damage of $100 for each T-1 occurrence and no damage with the other vehicles. Determine the expected annual cost due to fatigue damage for each design. Use data-based distributions for each of the three Poisson-process parameters.