Anonymous
Nov 4, 2023
Huij?
The beam shown in figure below is, supported by two rods AB and AC that have cross sectional areas of 16mm^2 and 10mm^2, respectively. Determine the position d of the 6KN load so that the average normal stress in each rod is the same
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ChatGPT
Nov 4, 2023
To determine the position d of the 6KN load so that the average normal stress in each rod is the same, we need to consider the equilibrium of forces and the stress in each rod.
Let's assume that the distance from point A to the load is x, and the distance from point A to point B is L.
First, let's calculate the stress in rod AB. The stress in a rod is given by the formula:
Stress = Force / Area
The force in rod AB is the sum of the forces acting on it, which are the 6KN load and the reaction force at point A. The reaction force at point A can be calculated using the equilibrium of forces:
6KN + Reaction force at A = 0
Therefore, the reaction force at A is -6KN.
Now, let's calculate the stress in rod AB:
Stress_AB = (6KN + (-6KN)) / 16mm^2
= 0 / 16mm^2
= 0
Next, let's calculate the stress in rod AC. The force in rod AC is the sum of the forces acting on it, which are the 6KN load and the reaction force at point A. The reaction force at point A can be calculated using the equilibrium of forces:
6KN + Reaction force at A = 0
Therefore, the reaction force at A is -6KN.
Now, let's calculate the stress in rod AC:
Stress_AC = (6KN + (-6KN)) / 10mm^2
= 0 / 10mm^2
= 0
Since the average normal stress in each rod is the same, we can conclude that the position d of the 6KN load does not affect the stress in the rods. The average normal stress in each rod will always be zero.
Let's assume that the distance from point A to the load is x, and the distance from point A to point B is L.
First, let's calculate the stress in rod AB. The stress in a rod is given by the formula:
Stress = Force / Area
The force in rod AB is the sum of the forces acting on it, which are the 6KN load and the reaction force at point A. The reaction force at point A can be calculated using the equilibrium of forces:
6KN + Reaction force at A = 0
Therefore, the reaction force at A is -6KN.
Now, let's calculate the stress in rod AB:
Stress_AB = (6KN + (-6KN)) / 16mm^2
= 0 / 16mm^2
= 0
Next, let's calculate the stress in rod AC. The force in rod AC is the sum of the forces acting on it, which are the 6KN load and the reaction force at point A. The reaction force at point A can be calculated using the equilibrium of forces:
6KN + Reaction force at A = 0
Therefore, the reaction force at A is -6KN.
Now, let's calculate the stress in rod AC:
Stress_AC = (6KN + (-6KN)) / 10mm^2
= 0 / 10mm^2
= 0
Since the average normal stress in each rod is the same, we can conclude that the position d of the 6KN load does not affect the stress in the rods. The average normal stress in each rod will always be zero.
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