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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?
Most Upvoted Answer
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
Community Answer
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? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about 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? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
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? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about 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? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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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