11.
A round column is 1.5 m long and is subjected to an axial force . The ends are pinned as shown in
the figure, and the modulus of elasticity is
GPa.
If the diameter of the column is
, and
and
are independent, determine the
probability of bending failure using the First Order Second Moment Method.
Solution
Based on the theory of Euler column formula, the critical load for unstable bending is
where
is a constant, depending on the
end conditions shown in the figure,
is the moment
of inertia, and
is the length of the column.
The
limit-state function is the actual load of the column subtracted from the critical
load. Failure occurs when.
where .
Using FOSM, we have
The probability of failure is then given by