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What should be the minimum length two a high strength steel rod of 12.5 mm diameter so that one end can be twisted by 30o with respect of the other end, without exceeding a shear stress of 270 N/mm2 given
modulus of rigidity G = 8 × 104 N/mm2
modulus of rigidity G = 8 × 104 N/mm2
_________________________ m
Correct answer is between '0.94,0.98'. Can you explain this answer?
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What should be the minimum length two a high strength steel rod of 12....
To determine the minimum length of the high strength steel rod, we need to use the formula for shear stress:
Shear stress = (Twisting moment * radius) / (Polar moment of inertia)
Given:
Shear stress = 270 N/mm^2
Diameter = 12.5 mm (radius = 6.25 mm)
Twisting moment = ?
Polar moment of inertia = ?
We also know that the polar moment of inertia can be calculated using the formula:
Polar moment of inertia = (pi/2) * (radius^4)
Substituting the given values, we can find the polar moment of inertia:
Polar moment of inertia = (pi/2) * (6.25^4) = 3062.5 mm^4
Now, rearranging the formula for shear stress, we can find the twisting moment:
Twisting moment = (Shear stress * Polar moment of inertia) / radius
Twisting moment = (270 * 3062.5) / 6.25 = 13320 Nmm
Finally, we can calculate the minimum length of the high strength steel rod using the formula:
Twisting moment = (G * Length^3) / (3 * pi * (radius^4))
Rearranging the formula, we can solve for Length:
Length = (3 * pi * (radius^4) * Twisting moment) / G
Length = (3 * pi * (6.25^4) * 13320) / 8
Length ≈ 334.76 mm
Therefore, the minimum length of the high strength steel rod should be approximately 334.76 mm.
Shear stress = (Twisting moment * radius) / (Polar moment of inertia)
Given:
Shear stress = 270 N/mm^2
Diameter = 12.5 mm (radius = 6.25 mm)
Twisting moment = ?
Polar moment of inertia = ?
We also know that the polar moment of inertia can be calculated using the formula:
Polar moment of inertia = (pi/2) * (radius^4)
Substituting the given values, we can find the polar moment of inertia:
Polar moment of inertia = (pi/2) * (6.25^4) = 3062.5 mm^4
Now, rearranging the formula for shear stress, we can find the twisting moment:
Twisting moment = (Shear stress * Polar moment of inertia) / radius
Twisting moment = (270 * 3062.5) / 6.25 = 13320 Nmm
Finally, we can calculate the minimum length of the high strength steel rod using the formula:
Twisting moment = (G * Length^3) / (3 * pi * (radius^4))
Rearranging the formula, we can solve for Length:
Length = (3 * pi * (radius^4) * Twisting moment) / G
Length = (3 * pi * (6.25^4) * 13320) / 8
Length ≈ 334.76 mm
Therefore, the minimum length of the high strength steel rod should be approximately 334.76 mm.
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What should be the minimum length two a high strength steel rod of 12.5 mm diameter so that one end can be twisted by 30o with respect of the other end, without exceeding a shear stress of 270 N/mm2 givenmodulus of rigidity G = 8 × 104 N/mm2_________________________ mCorrect answer is between '0.94,0.98'. Can you explain this answer?
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What should be the minimum length two a high strength steel rod of 12.5 mm diameter so that one end can be twisted by 30o with respect of the other end, without exceeding a shear stress of 270 N/mm2 givenmodulus of rigidity G = 8 × 104 N/mm2_________________________ mCorrect answer is between '0.94,0.98'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about What should be the minimum length two a high strength steel rod of 12.5 mm diameter so that one end can be twisted by 30o with respect of the other end, without exceeding a shear stress of 270 N/mm2 givenmodulus of rigidity G = 8 × 104 N/mm2_________________________ mCorrect answer is between '0.94,0.98'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What should be the minimum length two a high strength steel rod of 12.5 mm diameter so that one end can be twisted by 30o with respect of the other end, without exceeding a shear stress of 270 N/mm2 givenmodulus of rigidity G = 8 × 104 N/mm2_________________________ mCorrect answer is between '0.94,0.98'. Can you explain this answer?.
What should be the minimum length two a high strength steel rod of 12.5 mm diameter so that one end can be twisted by 30o with respect of the other end, without exceeding a shear stress of 270 N/mm2 givenmodulus of rigidity G = 8 × 104 N/mm2_________________________ mCorrect answer is between '0.94,0.98'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about What should be the minimum length two a high strength steel rod of 12.5 mm diameter so that one end can be twisted by 30o with respect of the other end, without exceeding a shear stress of 270 N/mm2 givenmodulus of rigidity G = 8 × 104 N/mm2_________________________ mCorrect answer is between '0.94,0.98'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What should be the minimum length two a high strength steel rod of 12.5 mm diameter so that one end can be twisted by 30o with respect of the other end, without exceeding a shear stress of 270 N/mm2 givenmodulus of rigidity G = 8 × 104 N/mm2_________________________ mCorrect answer is between '0.94,0.98'. Can you explain this answer?.
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