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.