15. The two member frame is pin connected at C, D and E. Two random forces F₁ and F₂ which follow normal distributions F₁ ~ N(150,2.5²) lb and F₂ ~ N(130,1.5²) lb act horizontally at A and vertically at B respectively. Determine the distributions of horizontal and vertical reactions at each pin. If the maximum horizontal and vertical load of connector C is 450 lb and 45 lb respectively, what is the probability of failure of this system?

Solution

Member DCB,

Member ACE,

Solving them, we have

Member DCB,

Member ACE,

Therefore, we can obtain

Finally, we obtain the distributions of all the components on C, D and E: C_x ~ N(416.7, 4.17²) lb, C_y ~ N(25, 6.25²) lb, D_x ~ N(416.7, 4.17²) lb, D_y ~ N(105, 6.43²) lb, E_x ~ N(266.7, 4.86 ²) lb and E_y ~ N(25, 6.25²) lb. Ans.

The maximum horizontal and vertical load of connector C is 450 lb and 45 lb respectively, therefore the probability of connector C to fail in the horizontal direction is

Ans.

And the probability of connector C to fail in the vertical direction is

Ans.