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A plastic-lined steel pipe has the cross-sectional shape shown in the figure. The steel pipe has outer diameter d3  100 mm and inner diameter d2  94 mm. The plastic liner has inner diameter d1  82 mm. The modulus of elas- ticity of the steel is 75 times the modulus of the plastic. Determine the allowable bending moment Mallow if the allowable stress in the steel is 35 MPa and in the plastic is 600 kPa.?
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A plastic-lined steel pipe has the cross-sectional shape shown in the ...




Solution:


Given data:


  • Outer diameter of steel pipe (d3): 100 mm

  • Inner diameter of steel pipe (d2): 94 mm

  • Inner diameter of plastic liner (d1): 82 mm

  • Modulus of elasticity of steel: 75 times the modulus of plastic

  • Allowable stress in steel: 35 MPa

  • Allowable stress in plastic: 600 kPa



Calculating the properties of steel and plastic:


  1. Calculate the outer radius of the steel pipe: r3 = d3/2 = 100/2 = 50 mm

  2. Calculate the inner radius of the steel pipe: r2 = d2/2 = 94/2 = 47 mm

  3. Calculate the cross-sectional area of the steel pipe: A3 = π(r3^2 - r2^2)

  4. Calculate the outer radius of the plastic liner: r1 = d1/2 = 82/2 = 41 mm

  5. Calculate the cross-sectional area of the plastic liner: A1 = πr1^2



Calculating the bending moment:


  • Assuming the steel and plastic are in pure bending, the bending stress in the steel pipe can be calculated using the formula: σ = M*y/I

  • Where σ is the bending stress, M is the bending moment, y is the distance from the neutral axis to the outer fiber of the steel pipe, and I is the moment of inertia of the steel pipe.

  • The distance from the neutral axis to the outer fiber of the steel pipe can be calculated as: y = (r3 + r2)/2

  • The moment of inertia of the steel pipe can be calculated as: I = (π/4)(r3^4 - r2^4)

  • Substituting the values in the formula, we get: σ = M*(r3 + r2)/(π/4)(r3^4 - r2^4)

  • Since the allowable stress in the steel is given as 35 MPa, we can rearrange the formula to solve for the allowable bending moment: Mallow = σ*(π/4)(r3^4 - r2^4)/(r3 + r2)

  • Similarly, the allowable bending moment in the plastic can be calculated using the formula: Mallow = σ*(π/4)r1^2

  • Given the allowable stress in the plastic as 600 kPa, we can substitute the values and solve for Mallow.



Conclusion:

The allowable bending moment in the steel is calculated as Mallow = σ*(π/4)(r3^4 - r2^4)/(r3 + r2), where σ is
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A plastic-lined steel pipe has the cross-sectional shape shown in the figure. The steel pipe has outer diameter d3  100 mm and inner diameter d2  94 mm. The plastic liner has inner diameter d1  82 mm. The modulus of elas- ticity of the steel is 75 times the modulus of the plastic. Determine the allowable bending moment Mallow if the allowable stress in the steel is 35 MPa and in the plastic is 600 kPa.?
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A plastic-lined steel pipe has the cross-sectional shape shown in the figure. The steel pipe has outer diameter d3  100 mm and inner diameter d2  94 mm. The plastic liner has inner diameter d1  82 mm. The modulus of elas- ticity of the steel is 75 times the modulus of the plastic. Determine the allowable bending moment Mallow if the allowable stress in the steel is 35 MPa and in the plastic is 600 kPa.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A plastic-lined steel pipe has the cross-sectional shape shown in the figure. The steel pipe has outer diameter d3  100 mm and inner diameter d2  94 mm. The plastic liner has inner diameter d1  82 mm. The modulus of elas- ticity of the steel is 75 times the modulus of the plastic. Determine the allowable bending moment Mallow if the allowable stress in the steel is 35 MPa and in the plastic is 600 kPa.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A plastic-lined steel pipe has the cross-sectional shape shown in the figure. The steel pipe has outer diameter d3  100 mm and inner diameter d2  94 mm. The plastic liner has inner diameter d1  82 mm. The modulus of elas- ticity of the steel is 75 times the modulus of the plastic. Determine the allowable bending moment Mallow if the allowable stress in the steel is 35 MPa and in the plastic is 600 kPa.?.
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