By D.M. Griffin, Jr.
This worksheet using PTC Mathcad provides you with a scenario of a bridge that is built over a river. The design life of the bridge, based on obsolescence, is 25 years and the criteria for the bridge is that the water surface elevation in the river should not rise above a particular high water mark on the bridge piers more than once in 25 years. The probability of exceeding these criteria should not be greater than .1. This worksheet using PTC Mathcad shows you how to calculate what return period should be used for the flood event in the river.
To begin this standard binomial distribution problem, the author establishes that one should consider each of the 25 years as a Bernoulli trial, where each trial has two possible outcomes- the river exceeds or doesn't exceed the high water mark. Because the problem states that the river shouldn't exceed the high water mark more than once in 25 years with the probability of occurrence at .1, 1 or fewer exceedances of the high water mark should not fall below .9.
The worksheet then shows you how to write out the cumulative binomial distribution and the probability of occurrence of 1 or fewer exceedances no less than .9. After this equation is written out, it is plotted to indicate whether the river will exceed more than a single year. Then the worksheet shows you how to predict the actual single year probability of occurrence.
This worksheet provides you with notation, discussion, formulas, data, solutions, and graphs, to aid you in solving your own calculations.
Download and explore this worksheet yourself! You can download a free lifetime copy of PTC Mathcad Express and get 30 days of full functionality.