A square cast-iron bar is placed under 50 kN pressure. 6.3.1 Calculate the dimensions of the bar if the stress in the bar is not to exceed 300 kN.
Given data:
Pressure on the bar = 50 kN = 50000 N
Maximum allowable stress = 300 kN = 300000 N
Let the dimensions of the square cast-iron bar be:
Length = L
Width = W
Thickness = T
The formula for stress is:
Stress = Force / Area
Since the bar is square, its cross-sectional area can be calculated as:
Area = W * T
Given that Pressure on the bar = Force, we can write:
50000 / (W * T) <= 300000
Solving for W, we get:
W >= 50000 / (300000 / T)
W >= 1/6 T
Similarly, solving for T:
T >= 50000 / (300000 / W)
T >= 1/5 W
Since the bar is square, L = W. Therefore, substituting for W, we get:
L >= 1/6 T
This means that the dimensions of the square cast-iron bar should be as follows:
Length (L) >= 1/6 x Thickness (T)
Width (W) >= 1/6 x Thickness (T)
Thickness (T) >= 1/5 x Width (W)
Therefore, the dimensions of the bar can be designed such that the stress in the bar does not exceed 300 kN.