Diffrence between external diameter and internal diameter, Mechanical Engineering

Diffrence between external diameter and internal diameter:

A compound tube is built by shrinking one tube on another, the ultimate dimension being, 80 mm internal diameter, 160 mm external diameter and 120 mm being the diameter at the junction.

If the radial pressure at the junction because of shrinking is 15 N/mm2, discover the greatest tensile and compressive stresses induced in the material of the cylinder. What difference should there be in the external diameter of the inner cylinder & the internal diameter of the outer cylinder before shrinking?

Take Young's Modulus as 200 GPa.

Solution

For outer cylinder, at r = 60, σr = 15, and at r = 80, σr = 0.

We get, and

15 =       (b1 /602)    - a1

0 =    (b1 /802)    - a1

            135

On solving, we get b1 =864000/ 7 and a1 =   7  .

Circumferential stress at the inner surface,

σ h =( 864000/7 × 602 )+ (135/7) = 53.6 N/mm2  (tensile)

For inner cylinder, at r = 60, σr = 15, and r = 40, σr = 0.

We get, 15 = ( b 2/602 )- a2

and

0 =    b2/40     - a2

On solving out, we get b2 = - 43200 and a2 = - 27.

Circumferential stress at the inner surface,

σh = -( 43200/402) + (- 27) = - 54 N/mm2  (compressive)

Circumferential stress at the junction,

σ h  = - (43200 /602)+ (- 27) = - 39 N/mm2 (compressive)

Required difference in diameter,

= (Junction diameter / E) × (Algebraic difference between hoop stresses at the junction)

= (120/2 × 105)   (53.6 + 39) = 0.0556 mm

Posted Date: 1/21/2013 2:35:13 AM | Location : United States







Related Discussions:- Diffrence between external diameter and internal diameter, Assignment Help, Ask Question on Diffrence between external diameter and internal diameter, Get Answer, Expert's Help, Diffrence between external diameter and internal diameter Discussions

Write discussion on Diffrence between external diameter and internal diameter
Your posts are moderated
Related Questions
This type of holon is mainly concerned along with carrying out the work in a fine and correct way at correct time.

Determine magnitude of the couple: A square block having each side 1.5 m is acted upon by system of forces along its sides as shown in the adjoining figure. If system reduces

Carnot vapour Cycle: It is convenient to analyze the performance of steam power plants by means of idealized cycles that are theoretical approximations of real cycles. The Car

Shear Force and Bending Moment: Shea r Force (S.F.) Algebraic sum of all vertical forces at any section of beam to the right or left of the section is known as shear for

What are the Elements of Theory of Vibrations All bodies possessing mass and elasticity can vibrate or undergo vibratory motion. Let us understand a few basic definitions used

Transverse Wave Stretched String As a typical example of wave motion in one-dimension, let us consider the transverse harmonic waves on a long, taut string. We assume that in e

with the aid of notes and sketches describe how you would transfer the design from a sheet of paper onto the wooden panel prior to carving

Find out the angle of force: Q: A uniform wheel having 60 cm diameter weighing 1000 N rests against rectangular obstacle   15 cm high. Find least force required which when ac

Spark Plug: A spark jumps between the electrodes of the spark plug when the voltage developed by the ignition system reaches the required value. This electrical spark occurs at a

Neutra l Layer and Neutral Axis In the beam or cantilever, there is one layer which retains the original length of it even after bending. So in this layer tensile stress and c