2-2. Truss ABC
shown is subjected to two independent random forces and
, that follow a distribution of
. The span is
. Each member has the
cross-sectional area
and modulus of
elasticity
. Determine the probability that
the displacement of joint B is greater than 1.8 mm.
Solution
(a) Find the displacement of joint B in the x direction
,
,
,
,
,
,
Methods of joints:
,
,
Since . We have
.
The elongation of
AB is equal to (the displacement of
joint B) in the x direction; then
Since ,
,
, we have
Thus,
Ans.