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
Consider a car of mass m1 is towing a trailer of mass m2 through a tow bar of stiffness k. Drag forces proportional to the car velocity (b1 v1) and the trailer velocity (b2 v2) a

hiw can i fix the maximum temp of the aluminium

Explain with the aid of a sketch how a rotary vacuum (ROVAC) filter works. Derive describing equations to predict the ROVAC's filtration performance in terms of the effect of drum

Q. Illustrate Clay content test? Under this test, the clay content is measured by washing it off the sand sample. The standard dried sand sample (50 gm) is put in a mixing devi

COATED ELECTRODES AND THEIR CLASSIFICATIONS Welding technology has changed tremendously over the past decades. Its application is found in all sectors of industries, smaller or l

Q. Describe Cold extrusion? • Cold extrusion is done at room temperature or near room temperature. • The advantages of this over hot extrusion are the lack of

Rigid body and Momentum: Body : A body consists of a Number of particles, it has definite shape. Rigid body :   A rigid body can be defined as the combination of a large

A column of timber section 15cm x 20cm is 6 meter long both side being fixed. If the youngs modulus for timber is 17.5 KN/mm 2 , Evaluate: a) Crippling load and b) Safe load

what is relation between tool life and cutting speed?

Define Disadvantages of electro discharge machining? a) The wear rate on the electrode is significantly higher. b) The work piece must be electrically conductive to be machi