Approximate the tension, Mechanical Engineering

Approximate the tension:

A copper tube 38 mm external diameter and 35 mm internal diameter is nearly wound with a steel wire of 0.8 mm diameter. Approximate the tension at which the wire should have been wound if an internal pressure of 2 N/mm2 generates a tensile circumferential stress of 7 N/mm2 in the tube. Young's Modulus of steel is equal to 1.6 times that of copper. Take Poisson's ratio of copper is equal to  0.3.

Solution

Assume σp and σw be the stresses in the pipe and the wire, respectively, before applying the internal pressure.

Assume for 1 mm length of pipe, we know, Compressive force in pipe = Tensile force in wire.

σ p  × 2 × 1.5 = σ w  × (1/0.8)  × 2 × (π /4)× 0.82

σ p  = 0.419 σw

Because of internal pressure alone, let the stresses be σ′p and σ′w . Then, we know,

Tensile force in pipe + Tensile force in wire = Bursting force

σ′ p × 2 × 1.5 + σ′ w × (1/0.8)  × 2 × (π/4) × 0.82  = 2 × 35

 3σ′p  + 1.257 σ′w = 70

Longitudinal stress

pd /4t  = 2 × 35 / (4 × 1.5) = 11.67 N/mm2

Hoop strain in the pipe = Strain in wire at the junction

σ′p/ Ec - v (σl / Ec) = σ′w /Es

σ′p / Ec - 0.3 × (11.67 / Ec) = σ′w / (1.6 Es)

σ′p  - 3.5 = 0.625 σ′w

σ′p  - 0.625 σ′w = 3.5

Solving for σ′p and σ′w ,

σ′p  = 15.44 N/mm2

σ′w  = 19.11 N/mm2

∴  Final tensile stress in the pipe, 15.44 - σp = 7.

Using the relation between initial stresses, σp = 8.44 N/mm2.

∴  Tension in the wire = 20.15 N/mm2.

Posted Date: 1/21/2013 2:24:35 AM | Location : United States







Related Discussions:- Approximate the tension, Assignment Help, Ask Question on Approximate the tension, Get Answer, Expert's Help, Approximate the tension Discussions

Write discussion on Approximate the tension
Your posts are moderated
Related Questions
Determine the maximum uniformly distributed load: A timber beam 150 mm wide & 300 mm deep is supported simply over a span of 4 m. determine the maximum uniformly distribute

Determine least value of work: Q . Determine least value of W as shown in the figure given below to keep the system of connected bodies in equilibrium µ for surface of c

show that energy is property of system

A steel pipe with 50 mm OD is covered with a 6.4 mm asbestos insulation followed by a 25 mm layer of fiber-glass insulation [K = 0.0485 Wmk]. The pipe temperature is 393 K and the

Q. Safety considerations in multi-unit plants? Segregation of process units within large or multi-unit plants is necessary in order to reduce the risk of a fire spreading. This

Q. Module Assembly Site Preparation? To set a module on the piles installed on project site, the following preparations shall be made: The Designer shall provide design elev

Evaluate the maximum bending stresses: A beam of I-section illustrated in Figure is simply supported over a span of 10 m. It carries an uniform load of 4 kN/m over the whole s

Plastics are the common term for a wide range of synthetic or semi synthetic polymerization products. There are many dissimilar plastics; all have their own density!

Carbides Carbides of titanium, zirconium, boron and silicon are significant refractory materials. Though, the carbides have extremely high melting points so they lack oxidatio

why this great equation does not apply(involved) in nuclear reaction ?