The capacity of an isolated spread footing foundation under a column is modeled

Question

The capacity of an isolated spread footing foundation under a column is modeled by a normal distribution with a mean of 300 kip and a COV of 20%. Suppose the column is subjected to a dead load of 100 kip and a live load of 150 kip. (a) Calculate the probability of failure of the foundation under dead load only. (b) Calculate the probability of failure of the foundation under the combined action of dead and live loads. (c) If the probability of failure of the foundation needs to be limited to 0.001, and the dead load of 100 kip cannot be changed, what is the maximum amount of live load that can be applied to the foundation?

Explanation / Answer

a) here std deviation =mean *COV =300*0.2=60

hence P(X<100) =P(Z<(100-300)/60) =P(Z<-3.333)=0.0004

b) with live liad P(X<250) =P(Z<-0.8333)=0.2023

c)for let weight iof live load =A

hence P(X<(100+A-300)/60)<0.001

(A-200)/60=-3.09023

A =14.586 Kg

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