Diffrence between external diameter and internal diameter, Mechanical Engineering

Assignment Help:

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


Related Discussions:- Diffrence between external diameter and internal diameter

Find out the horizontal and vertical components of the force, Find out the ...

Find out the horizontal and vertical components of the force: A force of 120 N is exerted on a hook in the ceiling as illustrated in Figure. Find out the horizontal and vertic

Show the types of changes in project, Q. Show the types of Changes in proje...

Q. Show the types of Changes in project? During the development and execution of a project, the following changes can occur:  Scope of work changes  Cost deviation

Refractory, extraction of refractories

extraction of refractories

Stone slab culverts with abutments, Stone Slab Culverts with Abutments and ...

Stone Slab Culverts with Abutments and Piers: Where good quality stone slabs are available like granite slabs, they can be used for superstructure of culverts, with suitable

Mechanical properties of materials, A tensile test on a specimen having an ...

A tensile test on a specimen having an initial diameter of 13.11 mm and an initial gauge length of 200.0 mm, gave the following data:

Find out load lifted by the machine, Find out load lifted by the machine: ...

Find out load lifted by the machine: An effort of 400 N is applied in a lifting machine. The distance moved through effort is 4 m and that by load is 40 cm. If the efficiency

How is rending stress designed in plain concrete footing, How is rending st...

How is rending stress designed in plain concrete footing? Rending Stresses Also design the plain concrete footing based on bending moment and shear considerations. In wall f

Chisel-tool and equipment , Chisel: Chisels are used in the combination of...

Chisel: Chisels are used in the combination of hammer to remove metals. A set of chisels is shown in Figure. Figure: Chisel

Iterature review, I have literature review and the title is "the effect of...

I have literature review and the title is "the effect of fluid cooling on the performance of building integrated photovoltaic thermal systems. Using some BIPVT prototypes measure

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd