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Return period for bridge design at 5% risk

Short answer

Risk 0.05 over 25 years yields (1-1/T)^25=0.95, so 1-1/T=0.99795, giving T=488 years.

What return period will you adopt in the design of a bridge on a river if you are allowed to accept only 5% risk of flooding in the 25 years of expected life of the bridge?

The probability that a flood of return period T occurs at least once in n years of the structure's life is the risk

Rˉ=1−(1−1T)n\bar R=1-\left(1-\frac1T\right)^{n}

Given Rˉ=0.05\bar R=0.05 and n=25n=25 years:

0.05=1−(1−1T)25 ⇒ (1−1T)25=0.950.05=1-\left(1-\frac1T\right)^{25}\ \Rightarrow\ \left(1-\frac1T\right)^{25}=0.95 1−1T=(0.95)1/25=0.997950 ⇒ 1T=0.0020501-\frac1T=(0.95)^{1/25}=0.997950\ \Rightarrow\ \frac1T=0.002050 T=487.9 yearsT=487.9 \text{ years}

Answer: adopt a return period of about 488 years (design for the ≈ 500-year flood).

✓ Answer checked by Claude Sonnet 5.5

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