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A circular beam is subjected to a shear force of 10 kN. Calculate the value of maximum shear stress in N/mm2. [Take area = 176 cm2]. (Answer up to two decimal places)
Correct answer is '0.76'. Can you explain this answer?
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A circular beam is subjected to a shear force of 10 kN. Calculate the...
Given Area (A) = 176 cm2 = 17600 mm2
Shear Force (F) = 10 kN = 10000 N
For circular cross section, the maximum shear stress is equal to 4/3 times of average shear stress.
Maximum shear force = (4/3) × (F/A) = (4/3) × (10000/17600) = 0.76 N/mm2
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A circular beam is subjected to a shear force of 10 kN. Calculate the...
Calculation of Maximum Shear Stress:
Given:
Shear force = 10 kN
Area = 176 cm²
We are required to calculate the maximum shear stress.
Step 1: Convert Units
We need to convert the units of shear force and area to be consistent. Since we are given the area in cm², it is convenient to convert the shear force to N (Newton) and the area to mm².
1 kN = 1000 N
1 cm² = 100 mm²
Converting the shear force:
10 kN = 10,000 N
Converting the area:
176 cm² = 17600 mm²
Step 2: Calculate Shear Stress
Shear stress is defined as the ratio of shear force to the cross-sectional area of the beam. Mathematically, it can be expressed as:
Shear stress = Shear force / Area
Substituting the given values:
Shear stress = 10,000 N / 17600 mm²
Step 3: Simplify the Expression
To simplify the expression, we can divide both the numerator and denominator by 1000. This will convert the units of shear stress from N/mm² to kN/mm².
Shear stress = (10,000 N / 1000) / (17600 mm² / 1000)
Simplifying further:
Shear stress = 10 kN / 17.6 mm²
Step 4: Calculate the Maximum Shear Stress
To find the maximum shear stress, we need to divide the shear force by the minimum cross-sectional area of the beam.
Since the cross-sectional area of a circular beam is constant throughout, the maximum shear stress will be equal to the shear stress calculated in Step 3.
Maximum shear stress = 10 kN / 17.6 mm²
Calculating the value:
Maximum shear stress = 0.568 kN/mm²
Rounding the value to two decimal places, the maximum shear stress is approximately 0.57 N/mm².
The correct answer given is '0.76', which seems to be an error. The correct value, as calculated above, is 0.57 N/mm².
Given:
Shear force = 10 kN
Area = 176 cm²
We are required to calculate the maximum shear stress.
Step 1: Convert Units
We need to convert the units of shear force and area to be consistent. Since we are given the area in cm², it is convenient to convert the shear force to N (Newton) and the area to mm².
1 kN = 1000 N
1 cm² = 100 mm²
Converting the shear force:
10 kN = 10,000 N
Converting the area:
176 cm² = 17600 mm²
Step 2: Calculate Shear Stress
Shear stress is defined as the ratio of shear force to the cross-sectional area of the beam. Mathematically, it can be expressed as:
Shear stress = Shear force / Area
Substituting the given values:
Shear stress = 10,000 N / 17600 mm²
Step 3: Simplify the Expression
To simplify the expression, we can divide both the numerator and denominator by 1000. This will convert the units of shear stress from N/mm² to kN/mm².
Shear stress = (10,000 N / 1000) / (17600 mm² / 1000)
Simplifying further:
Shear stress = 10 kN / 17.6 mm²
Step 4: Calculate the Maximum Shear Stress
To find the maximum shear stress, we need to divide the shear force by the minimum cross-sectional area of the beam.
Since the cross-sectional area of a circular beam is constant throughout, the maximum shear stress will be equal to the shear stress calculated in Step 3.
Maximum shear stress = 10 kN / 17.6 mm²
Calculating the value:
Maximum shear stress = 0.568 kN/mm²
Rounding the value to two decimal places, the maximum shear stress is approximately 0.57 N/mm².
The correct answer given is '0.76', which seems to be an error. The correct value, as calculated above, is 0.57 N/mm².
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A circular beam is subjected to a shear force of 10 kN. Calculate the value of maximum shear stress in N/mm2. [Take area = 176 cm2]. (Answer up to two decimal places)Correct answer is '0.76'. Can you explain this answer?
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