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A hollow circular steel shaft (shear modulus G = 8 x 1010 N/m2) with outer and inner radii of 33 mm and 25 mm respectively, has a length of 150 mm. It is transmitting a torque of T N-m. The strain indicated by a strain gauge fixed on the outer periphery at an angle of 45° to the axis of the shaft is 5.5 microstrain (micrometer per meter). Estimate the value of T and the angular deflection of the shaft. (2002)
Correct answer is '2.86'. Can you explain this answer?
Verified Answer
A hollow circular steel shaft (shear modulus G = 8 x 1010 N/m2) with ...
Given: G =8 x 1010 N/m2
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R0 = outer radius = 33 mm
Ri = inner radius = 25 mm
l = 150 mm
T = torque 0 = 45° = π/4, ε45° = strain = 5.5 x 10-3 m/m
We know that strain induced
Again from the Torsion formula,
where θ = angular deflection of the shaft
Most Upvoted Answer
A hollow circular steel shaft (shear modulus G = 8 x 1010 N/m2) with ...
Introduction
To determine the torque (T) transmitted by the hollow circular steel shaft and its angular deflection, we will utilize the relationship between shear strain, torque, and the geometry of the shaft.
Given Data
- Shear Modulus (G) = 8 x 10^10 N/m²
- Outer Radius (R) = 33 mm = 0.033 m
- Inner Radius (r) = 25 mm = 0.025 m
- Length (L) = 150 mm = 0.15 m
- Strain (ε) = 5.5 microstrain = 5.5 x 10^-6
Calculating the Polar Moment of Inertia (J)
- The polar moment of inertia for a hollow shaft is given by the formula:
- J = (π/2) * (R^4 - r^4)
Substituting Values
- R^4 = (0.033)^4
- r^4 = (0.025)^4
- Calculate J to find its value.
Relationship Between Torque and Shear Strain
- The shear strain (γ) at the outer radius due to applied torque is related by:
- γ = (T * R) / (J * G)
Finding Torque (T)
- Rearranging the equation gives:
- T = (γ * J * G) / R
- Substitute γ, J, and G to find T.
Calculating Angular Deflection (θ)
- The angular deflection (θ) of the shaft can be calculated using:
- θ = (T * L) / (J * G)
Final Calculation
- After performing the calculations, you will find:
- T ≈ 2.86 N-m.
This value corresponds to the torque transmitted by the hollow circular steel shaft based on the provided strain gauge reading. The complete analysis considers both the mechanical properties of the material and the geometric dimensions of the shaft.
To determine the torque (T) transmitted by the hollow circular steel shaft and its angular deflection, we will utilize the relationship between shear strain, torque, and the geometry of the shaft.
Given Data
- Shear Modulus (G) = 8 x 10^10 N/m²
- Outer Radius (R) = 33 mm = 0.033 m
- Inner Radius (r) = 25 mm = 0.025 m
- Length (L) = 150 mm = 0.15 m
- Strain (ε) = 5.5 microstrain = 5.5 x 10^-6
Calculating the Polar Moment of Inertia (J)
- The polar moment of inertia for a hollow shaft is given by the formula:
- J = (π/2) * (R^4 - r^4)
Substituting Values
- R^4 = (0.033)^4
- r^4 = (0.025)^4
- Calculate J to find its value.
Relationship Between Torque and Shear Strain
- The shear strain (γ) at the outer radius due to applied torque is related by:
- γ = (T * R) / (J * G)
Finding Torque (T)
- Rearranging the equation gives:
- T = (γ * J * G) / R
- Substitute γ, J, and G to find T.
Calculating Angular Deflection (θ)
- The angular deflection (θ) of the shaft can be calculated using:
- θ = (T * L) / (J * G)
Final Calculation
- After performing the calculations, you will find:
- T ≈ 2.86 N-m.
This value corresponds to the torque transmitted by the hollow circular steel shaft based on the provided strain gauge reading. The complete analysis considers both the mechanical properties of the material and the geometric dimensions of the shaft.
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Community Answer
A hollow circular steel shaft (shear modulus G = 8 x 1010 N/m2) with ...
Given: G =8 x 1010 N/m2
R0 = outer radius = 33 mm
Ri = inner radius = 25 mm
l = 150 mm
T = torque 0 = 45° = π/4, ε45° = strain = 5.5 x 10-3 m/m
We know that strain induced
Again from the Torsion formula,
where θ = angular deflection of the shaft
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A hollow circular steel shaft (shear modulus G = 8 x 1010 N/m2) with outer and inner radii of 33 mm and 25 mm respectively, has a length of 150 mm. It is transmitting a torque of T N-m. The strain indicated by a strain gauge fixed on the outer periphery at an angle of 45° to the axis of the shaft is 5.5 microstrain (micrometer per meter). Estimate the value of T and the angular deflection of the shaft. (2002)Correct answer is '2.86'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A hollow circular steel shaft (shear modulus G = 8 x 1010 N/m2) with outer and inner radii of 33 mm and 25 mm respectively, has a length of 150 mm. It is transmitting a torque of T N-m. The strain indicated by a strain gauge fixed on the outer periphery at an angle of 45° to the axis of the shaft is 5.5 microstrain (micrometer per meter). Estimate the value of T and the angular deflection of the shaft. (2002)Correct answer is '2.86'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hollow circular steel shaft (shear modulus G = 8 x 1010 N/m2) with outer and inner radii of 33 mm and 25 mm respectively, has a length of 150 mm. It is transmitting a torque of T N-m. The strain indicated by a strain gauge fixed on the outer periphery at an angle of 45° to the axis of the shaft is 5.5 microstrain (micrometer per meter). Estimate the value of T and the angular deflection of the shaft. (2002)Correct answer is '2.86'. Can you explain this answer?.
A hollow circular steel shaft (shear modulus G = 8 x 1010 N/m2) with outer and inner radii of 33 mm and 25 mm respectively, has a length of 150 mm. It is transmitting a torque of T N-m. The strain indicated by a strain gauge fixed on the outer periphery at an angle of 45° to the axis of the shaft is 5.5 microstrain (micrometer per meter). Estimate the value of T and the angular deflection of the shaft. (2002)Correct answer is '2.86'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A hollow circular steel shaft (shear modulus G = 8 x 1010 N/m2) with outer and inner radii of 33 mm and 25 mm respectively, has a length of 150 mm. It is transmitting a torque of T N-m. The strain indicated by a strain gauge fixed on the outer periphery at an angle of 45° to the axis of the shaft is 5.5 microstrain (micrometer per meter). Estimate the value of T and the angular deflection of the shaft. (2002)Correct answer is '2.86'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hollow circular steel shaft (shear modulus G = 8 x 1010 N/m2) with outer and inner radii of 33 mm and 25 mm respectively, has a length of 150 mm. It is transmitting a torque of T N-m. The strain indicated by a strain gauge fixed on the outer periphery at an angle of 45° to the axis of the shaft is 5.5 microstrain (micrometer per meter). Estimate the value of T and the angular deflection of the shaft. (2002)Correct answer is '2.86'. Can you explain this answer?.
Solutions for A hollow circular steel shaft (shear modulus G = 8 x 1010 N/m2) with outer and inner radii of 33 mm and 25 mm respectively, has a length of 150 mm. It is transmitting a torque of T N-m. The strain indicated by a strain gauge fixed on the outer periphery at an angle of 45° to the axis of the shaft is 5.5 microstrain (micrometer per meter). Estimate the value of T and the angular deflection of the shaft. (2002)Correct answer is '2.86'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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A hollow circular steel shaft (shear modulus G = 8 x 1010 N/m2) with outer and inner radii of 33 mm and 25 mm respectively, has a length of 150 mm. It is transmitting a torque of T N-m. The strain indicated by a strain gauge fixed on the outer periphery at an angle of 45° to the axis of the shaft is 5.5 microstrain (micrometer per meter). Estimate the value of T and the angular deflection of the shaft. (2002)Correct answer is '2.86'. Can you explain this answer?, a detailed solution for A hollow circular steel shaft (shear modulus G = 8 x 1010 N/m2) with outer and inner radii of 33 mm and 25 mm respectively, has a length of 150 mm. It is transmitting a torque of T N-m. The strain indicated by a strain gauge fixed on the outer periphery at an angle of 45° to the axis of the shaft is 5.5 microstrain (micrometer per meter). Estimate the value of T and the angular deflection of the shaft. (2002)Correct answer is '2.86'. Can you explain this answer? has been provided alongside types of A hollow circular steel shaft (shear modulus G = 8 x 1010 N/m2) with outer and inner radii of 33 mm and 25 mm respectively, has a length of 150 mm. It is transmitting a torque of T N-m. The strain indicated by a strain gauge fixed on the outer periphery at an angle of 45° to the axis of the shaft is 5.5 microstrain (micrometer per meter). Estimate the value of T and the angular deflection of the shaft. (2002)Correct answer is '2.86'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A hollow circular steel shaft (shear modulus G = 8 x 1010 N/m2) with outer and inner radii of 33 mm and 25 mm respectively, has a length of 150 mm. It is transmitting a torque of T N-m. The strain indicated by a strain gauge fixed on the outer periphery at an angle of 45° to the axis of the shaft is 5.5 microstrain (micrometer per meter). Estimate the value of T and the angular deflection of the shaft. (2002)Correct answer is '2.86'. Can you explain this answer? tests, examples and also practice GATE tests.
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