What is the risk of this hydrologic design?

Civil UPSC ESE Exam Solution 2021

UPSC ESE Exam Solution 2021 for Civil Engineering UPSC ESE 2021 GS Paper 1 download exam paper from telegram https://telegram.me/civil_experiences

A bridge has an expected life of 25 years and is designed for a flood magnitude of return period 100 years. What is the risk of this hydrologic design?

[A] 1 – (100/99)²⁵
[B] (99/100)²⁵
[C] 1 – (99/100)²⁵
[D] (100/99)²⁵

ANSWER= [C] 1 – (99/100)²⁵

Detailed Solution for Civil Engineering Exam

Given data

Design life (n) = 25 years

Return Period (T) = 100 years

Risk = 1 – qⁿ

= 1 – (1 – p)ⁿ = 1 – ( 1 – (1/T) )ⁿ

Risk = 1 – (1-(1/100))²⁵

Risk = 1 – (99/100)²⁵