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The bracket welded to the vertical plate by means of two fillet welds. Calculate the bending stress in the welds if P=40kN, leg=4mm and e=400mm.
- a)None of the listed
- b)34N/mm²
- c)24 N/mm²
- d)44 N/mm²
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The bracket welded to the vertical plate by means of two fillet welds....
Explanation: σ=My/I where y=250mm,I=2xtx500ᵌ/12 where t=4/.707.
Most Upvoted Answer
The bracket welded to the vertical plate by means of two fillet welds....
To calculate the bending stress in the welds, we need to find the moment of the applied force about the center of the welds.
The moment (M) can be calculated using the formula: M = P * e, where P is the applied force and e is the distance from the line of action of the force to the center of the welds.
Given:
P = 40 kN = 40,000 N
e = 400 mm = 0.4 m
M = 40,000 N * 0.4 m
M = 16,000 Nm
Now, let's calculate the bending stress (σ) in the welds using the formula: σ = M / (Z * A), where Z is the section modulus and A is the throat area of the fillet welds.
Since the welds are fillet welds, the throat area can be approximated as the leg size of the weld (4 mm) multiplied by the effective length of the weld (which is half the leg size, assuming equal leg fillet welds).
A = 4 mm * 2 = 8 mm^2 = 8 * 10^-6 m^2
The section modulus (Z) can be calculated using the formula: Z = (w * h^2) / 6, where w is the leg size of the weld and h is the distance from the center of the weld to the outer edge (assuming a triangular shape of the weld).
In this case, h can be approximated as half the leg size (2 mm).
Z = (4 mm * (2 mm)^2) / 6 = 16 mm^3 = 16 * 10^-9 m^3
Now, let's calculate the bending stress:
σ = 16,000 Nm / ((16 * 10^-9 m^3) * (8 * 10^-6 m^2))
σ = 34 N/mm^2
Therefore, the bending stress in the welds is 34 N/mm^2. The correct answer is b) 34 N/mm^2.
The moment (M) can be calculated using the formula: M = P * e, where P is the applied force and e is the distance from the line of action of the force to the center of the welds.
Given:
P = 40 kN = 40,000 N
e = 400 mm = 0.4 m
M = 40,000 N * 0.4 m
M = 16,000 Nm
Now, let's calculate the bending stress (σ) in the welds using the formula: σ = M / (Z * A), where Z is the section modulus and A is the throat area of the fillet welds.
Since the welds are fillet welds, the throat area can be approximated as the leg size of the weld (4 mm) multiplied by the effective length of the weld (which is half the leg size, assuming equal leg fillet welds).
A = 4 mm * 2 = 8 mm^2 = 8 * 10^-6 m^2
The section modulus (Z) can be calculated using the formula: Z = (w * h^2) / 6, where w is the leg size of the weld and h is the distance from the center of the weld to the outer edge (assuming a triangular shape of the weld).
In this case, h can be approximated as half the leg size (2 mm).
Z = (4 mm * (2 mm)^2) / 6 = 16 mm^3 = 16 * 10^-9 m^3
Now, let's calculate the bending stress:
σ = 16,000 Nm / ((16 * 10^-9 m^3) * (8 * 10^-6 m^2))
σ = 34 N/mm^2
Therefore, the bending stress in the welds is 34 N/mm^2. The correct answer is b) 34 N/mm^2.
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