Find out change in length of circular bar, Mechanical Engineering

Assignment Help:

Find out change in length of circular bar of uniform taper

Sol.: The stress at any cross section can be found by dividing load by area of cross section and extension can be found by integrating extensions of small length over whole length of the bar. We shall consider following cases of variable cross section:

Consider circular bar which tapers uniformly from diameter d1 at bigger end to diameter d2 at smaller end, and subjected to axial tensile load P as shown in figure given below.

Let us consider small strip of length dx at distance x from the bigger end.

Diameter of elementary strip:

dx = d1  - [(d1  - d2)x]/L

= d1  - kx; where k = (d1  - d2)/L

 

551_Find out change in length of circular bar.png

The cross sectional area of strip,

1463_Find out change in length of circular bar1.png

Stress in the strip,

242_Find out change in length of circular bar2.png 
Strain in strip

862_Find out change in length of circular bar3.png 
Elongation of strip

887_Find out change in length of circular bar4.png 


The total elongation of tapering bar can be worked out by integrating above expression between limits  x = 0 to  x = L

1013_Find out change in length of circular bar5.png 
BY putting the value of  k = (d1 -  d2) /l in above expression, we obtain
208_Find out change in length of circular bar6.png 

  If the bar is of uniform diameter d throughout the length of it, then δL = 4.P.L/(Π.E.d2)

= P.L/[(Πd2/4).E] = P.l/A.E.


Related Discussions:- Find out change in length of circular bar

Die press assembly drawing, Die Press Assembly Drawing The objective of...

Die Press Assembly Drawing The objective of this assignment is to demonstrate the following concepts of design. • Extrude • Revolve • Fillet • Dimensioning • Tolerance • Bas

Difficulties with motion sickness, In designing rotating space stations to ...

In designing rotating space stations to give for artificial-gravity environments, one of the constraints that must be considered is motion sickness. Studies have shown that the neg

Opresion reserch, ppt of appling queuing model in railwy reservation

ppt of appling queuing model in railwy reservation

What are the instructions to charge a battery?, (a) How is specific gravity...

(a) How is specific gravity of electrolyte (battery water) measured and what should be the value of specific gravity? (b) How would you measure battery voltage and what is its reco

Determine the stress in composite bar, Determine the stress in composite ba...

Determine the stress in composite bar: How do you determine the stress in composite bar? What is Modular Ratio? Sol.: It becomes essential to have a compound tie or strut

Heat engine - thermodynamics, HEAT ENGINE - Thermodynamics: HE A T ...

HEAT ENGINE - Thermodynamics: HE A T ENGINE. A heat engine is a thermodynamics system that operates in a cycle in which heat can be transferred from heat source to heat si

Determine the thermal efficiency, A combined cycle plant is designed to dev...

A combined cycle plant is designed to develop 200MW power. The air is obtained by the compressor at 300K and 1 bar pressure. The maximum temperature of the gas turbine cycle is lim

Evaluate the natural frequency, (a) Evaluate the natural frequency of syste...

(a) Evaluate the natural frequency of system shown in figure and show that it will be equal to (b) calculate equivalent stiffness of two springs connected in parallel.

What is a turboprop engine, The grouping of the words turbine and propeller...

The grouping of the words turbine and propeller in techno jargon will give you the word "turboprop". A turboprop engine is a turbojet (gas turbine) engine, which powers the propell

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