Gaussian with mean of 50 kip-ft and coefficient of variation of 20%. Failure occurs if the moment capacity is exceeded anywhere in the beam.
The moment capacity M for the cantilever beam shown in the figure below is constant
throughout the entire span. Because of uncertainties in material strength, M is assumed to
be Gaussian with mean of 50 kip-ft and coefficient of variation of 20%. Failure occurs if the
moment capacity is exceeded anywhere in the beam.
(a) If only the concentrated load of 3
kips is applied at the free end, what is the probability that the beam will fail?
(b) If only the
uniform load of 0.5 kips/ft is applied on the entire beam, what is the probability that the beam
will fail?
(c) In rare cases, the beam may be subjected to the combination of the
concentrated load and the uniform load. What is the probability that the beam will fail in such
a case?
(d) Suppose that a probability of failure level of 0.005 is desired and that the beam
is subjected only to the uniform load w across the span. What would be the maximum
allowable value of w?
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