12. Two random forces F₁ ~ N(12, 0.5²) kN and F₂ ~ N(8,0.2²) kN act on the structural system. F₁ and F₂ are independent. Determine the normal reaction distribution at the roller A and distributions of horizontal and vertical components at pin B for equilibrium of the member.

Solution

Since, F₁ and F₂ follow the normal distributions which are independent with each other, we have

Therefore, we have N_A ~ N(10.05, 0.36²) kN, B_x ~ N(5.66, 0.14²) kN and B_y ~ N(7.61, 0.63²) kN. Ans.