Question

Q : A concrete footing, exerting an applied pressure of 200
kPa on the soil, may fail from bearing capacity (B) or excessive
settlement (S). Due to soil variation, the following are
given:

• Bearing capacity is normally distributed with mean, μ=500
kPa and standard deviation, σ = 200 kPa

• Settlement is log-normally distributed with μ=1.5 cm and σ
=0.3 cm.

• The probability that the footing fails in bearing capacity
knowing that it

had settled excessively is 0.2

• Maximum permissible settlement is 2.5 cm. (i.e. S> 2.5 cm
is considered

excessive settlement).

(a) Calculate the probability that the footing will
fail.

(b) If the foundation system of a multistory building consists
of 30 such footing,

calculate the probability that none of the footing will
fail.

Answer #1

K

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