A structural element for a new bridge is designed for a constant load of 1000 psi. Its mean resistance is 1200 psi and the probability of failure is 1.9 X 10–3 . Find the element's safety factor as well as standard deviation, variance and coefficient of variation of its resistance. Clearly show units as appropriate.

i) SF = 0.83

ii) 10 psi

iii) 3.16 psi

iv) 0.0083

Explanation:

Constant load = 1000 Psi

mean resistance = 1200 psi

Probability of failure = 1.9 * 10^-3

Determine

i) Safety factor

S.F =  1 / (mean load / load design ) = 1 / ( 1200 / 1000 ) = 0.83

ii) Standard deviation

1.9 X 10^-3 = e  ( -1/2 ( μ / б) ^3  /  (2.5 * 6  )

0.004756 = e^- 20000 / б^3

hence std = 10 psi

iii) Variance

= = 3.16 psi

iv) coefficient of variation

Cv = std / mean resistance

    = 10 / 1200 = 0.0083

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