Find out change in length of circular bar, Mechanical Engineering

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.

Posted Date: 10/20/2012 8:42:57 AM | Location : United States







Related Discussions:- Find out change in length of circular bar, Assignment Help, Ask Question on Find out change in length of circular bar, Get Answer, Expert's Help, Find out change in length of circular bar Discussions

Write discussion on Find out change in length of circular bar
Your posts are moderated
Related Questions
Concurrent force system: It state that if force acting at a point on a rigid body, it can be considered to act at any other point on its line of action, given this point is ri

Explain frequency reuse In the cellular concept, service area is separated into regions called cells and the available frequency is divided among these cells. Every cellular b

Q. Determine the need for insulation? Equipment and piping shall be insulated as required for heat conservation, process heat control and personnel protection. The temperatu

ELECTRO SLAG WELDING   This process is similar to the electro gas welding process designed for making butt welding in the vertical position in one single pass and the plate

Estimate the Cutting Time A surface 115 mm wide and 250 mm long is to be rough milled with a depth of cut of 6 mm by a 16-tooth cemented carbide face mill 150 mm in diameter.

The Circular Orbits The bounded motion of a particle in a central force is in general an ellipse given by   where eccentricity e is related to semi-major and minor axes a

define environment and explain stockholm conference

Modal Dispersion in Step-Index Fibers Determine the core radius of a multi-mode step index fiber with a numerical aperture NA = 0.1 if the number of modes M = 5000 when the wave

Following sets of the three forces act on a body,. In which case resultant cannot be zero? 1) 10N, 10N, 10N 2)10N, 10N, 20N 3)10N, 20N, 20N 4010N, 20N, 40N Ans)      In 4th

I have been tasked to design a web based automatic feature recognition system for a press brake bending machine, how do I go about It?