## Example 363

Two structures are designed to withstand a load with an expected value of 100 kN. The load can vary slightly; in fact, it is estimated to be a normally distributed variable with a standard deviation of 10 kN. Structure A is made of a highly tested material that produces consistent and repeatable results. Its strength is normally distributed with a mean strength of 150 kN and a standard deviation of only 5 kN. Structure B is composed of a stronger material but one that shows greater variability in its characteristics. Its strength is also normally distributed and has a mean of 200 kN but a standard deviation of 30 kN. The load and the strength in both structures are independent — and therefore uncorrelated. Quantify the safety using both a deterministic and a probabilistic approach and decide which structure is safer.

Answer

Using the deterministic approach, the factor of safety (FS) is defined as the ratio of the capacity of the structure to the demand placed on it.

Structure A

Structure B

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