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A solid circular beam with radius of 0.25 m and length of 2 m is subjected to a twisting moment of 20 kNm about the z-axis at the free end, which is the only load acting as shown in the figure. The stress component at Point M in the cross-section of the beam at a distance of 1m from the fixed end is?
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A solid circular beam with radius of 0.25 m and length of 2 m is subje...
Problem:
A solid circular beam with radius of 0.25 m and length of 2 m is subjected to a twisting moment of 20 kNm about the z-axis at the free end, which is the only load acting as shown in the figure. The stress component at Point M in the cross-section of the beam at a distance of 1m from the fixed end is? Explain in details.
Solution:
Step 1: Calculation of Polar Moment of Inertia
Polar Moment of Inertia (J) = πr⁴/2
where, r = radius of the beam = 0.25 m
Therefore, J = (3.14 x 0.25⁴)/2 = 0.00098275 m⁴
Step 2: Calculation of Shear Stress
The formula for shear stress (τ) due to torsion is given as:
τ = T*r/J
where, T = twisting moment = 20 kNm, r = distance of point M from the axis of rotation = 1m
Therefore, τ = (20 x 10³ x 1)/(0.00098275) = 20,352.94 kPa
Step 3: Calculation of Shear Strain
Shear strain (γ) is defined as the ratio of angular displacement (θ) to the length of the beam (L).
γ = θ/L
Since the beam is subjected to pure torsion, the angle of twist (θ) can be calculated using the formula:
θ = TL/GJ
where, G = Shear Modulus of Elasticity
For steel, the value of G is around 80 GPa
Therefore, θ = (20 x 10³ x 1)/(80 x 10⁹ x 0.00098275) = 0.002551 rad
Thus, γ = 0.002551/2 = 0.001275
Step 4: Calculation of Shear Strain
The shear stress (τ) and shear strain (γ) are related by the equation:
τ = Gγ
where, G = Shear Modulus of Elasticity
For steel, the value of G is around 80 GPa
Therefore, τ = 80 x 10⁹ x 0.001275 = 102,000 kPa
Step 5: Conclusion
The stress component at Point M in the cross-section of the beam at a distance of 1m from the fixed end is 102,000 kPa.
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A solid circular beam with radius of 0.25 m and length of 2 m is subjected to a twisting moment of 20 kNm about the z-axis at the free end, which is the only load acting as shown in the figure. The stress component at Point M in the cross-section of the beam at a distance of 1m from the fixed end is?
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A solid circular beam with radius of 0.25 m and length of 2 m is subjected to a twisting moment of 20 kNm about the z-axis at the free end, which is the only load acting as shown in the figure. The stress component at Point M in the cross-section of the beam at a distance of 1m from the fixed end is? 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 A solid circular beam with radius of 0.25 m and length of 2 m is subjected to a twisting moment of 20 kNm about the z-axis at the free end, which is the only load acting as shown in the figure. The stress component at Point M in the cross-section of the beam at a distance of 1m from the fixed end is? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid circular beam with radius of 0.25 m and length of 2 m is subjected to a twisting moment of 20 kNm about the z-axis at the free end, which is the only load acting as shown in the figure. The stress component at Point M in the cross-section of the beam at a distance of 1m from the fixed end is?.
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