The 3×10^2kg concrete pipe has a center of mass at point G. if it is suspended from cables AB and AC. Determine the diameter of cable AB . so that the average normal stress in this cable is the same as in the 14mm diameter cable AC
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Oct 29, 2023
To determine the diameter of cable AB, we need to equate the average normal stress in cable AB to the average normal stress in cable AC.
The average normal stress in a cable can be calculated using the formula:
σ = F/A
Where σ is the average normal stress, F is the force acting on the cable, and A is the cross-sectional area of the cable.
Let's assume that the average normal stress in both cables is σ.
For cable AB, the force acting on it is the weight of the concrete pipe, which can be calculated using the formula:
F_AB = m * g
Where m is the mass of the concrete pipe and g is the acceleration due to gravity.
For cable AC, the force acting on it is also the weight of the concrete pipe.
Since the average normal stress is the same in both cables, we can equate the forces:
F_AB = F_AC
m * g = m * g
Now, let's calculate the cross-sectional areas of the cables.
For cable AB, the cross-sectional area can be calculated using the formula:
A_AB = π * (d_AB/2)^2
Where d_AB is the diameter of cable AB.
For cable AC, the cross-sectional area can be calculated using the formula:
A_AC = π * (d_AC/2)^2
Where d_AC is the diameter of cable AC.
Since the average normal stress is the same in both cables, we can equate the cross-sectional areas:
A_AB = A_AC
π * (d_AB/2)^2 = π * (d_AC/2)^2
Simplifying the equation:
(d_AB/2)^2 = (d_AC/2)^2
Taking the square root of both sides:
d_AB/2 = d_AC/2
d_AB = d_AC
Therefore, the diameter of cable AB should be the same as the diameter of cable AC, which is 14mm.