The bar assembly is missing, so i have attached it.
Answer:
Minimum required dimensions are; h1 = 2 inches and h2 = 4 inches
Explanation:
We are given;
Yield stress; σY = 45 ksi
Factor of safety; F.S = 1.5
Applying conditions of Equilibrium Σx = 0 and Σy = 0,
At segment AB in the diagram with Σx = 0 , we have;
-30 + N_ab = 0
N_ab = 30 kip
The cross sectional area of AB will be;
A_ab = (h1 × 0.5) in²
Now, since we have a factor of safety as 1.5,our allowable normal yield stress will be calculated from;
σ_allow = σY/F.S
So, σ_allow = 45/1.5
σ_allow = 30 ksi
Now, normal allowable yield stress is also calculated as;
σ_allow = N_ab/A_ab
So plugging in the relevant values, we can find h1.
So,
30 = 30/0.5h1
h1 = 30/(30 × 0.5)
h1 = 2 inches
Similarly, we can do the same for BC.
The cross sectional area of BC will be;
A_bc = (h2 × 0.5) in²
At segment BC in the diagram with Σx = 0 , we have;
-30 - 15 - 15 + N_bc = 0
N_bc = 60 kip
σ_allow = N_bc/A_bc
So,
30 = 60/0.5h2
h2 = 60/(0.5 × 30)
h2 = 4 inches
Minimum required dimensions are; h1 = 2 inches and h2 = 4 inches
