Distortion energy theory, Civil Engineering

Distortion energy theory:

Let us now consider the solid shown in Figure.

1091_States of stress - principal stresses.png

(a)        By inspection we may see that the solid is safe according to principal stress theory (σ1 < 260).

(b)        Maximum principal strain ε1 = 200/E -0.3 (-100/E) = 230/E < 260/E

∴          The solid is safe according to principal strain theory too.

 (c)       Maximum shear stress τmax  =200- (-100)/2 =150>130

∴          Shear stress theory predicts failure.

(d)        Total strain energy density is as follows :

u =  1/2E  [2002 + (- 100)2  - 2 × 0.3 ×200 (- 100)]

=31000/E >      2602/E

∴          The solid is safe according to strain energy theory.

(e)        Distortion energy density is as follows:

ud = 1/12G([200 - (- 100)]2 + 2002  + 1002 )

70000/6G >     2602/6G

∴  Distortion energy theory predicts failure.

If what is safe according to one theory is unsafe according to the other theory although what is safe according to the second theory is unsafe according to while another theory, you might wonder whether to consider the solid as safe or not. Or should the solid be safe according to all the theories? That will put a extremely severe condition for safety. Shall we select a theory which we like best? Certainly not, we have to search out which theory correctly represents the failure criteria and choose it. It has been found from experience in which the shear stress theory (known as Tresca's Theory) suits brittle materials, although, the distortion energy theory (known as Von Mises' Theory) is appropriate for ductile materials. So depending on the nature of the material, the designer could choose the appropriate theory.

You might also remember, that it is not sufficient to be merely safe (irrespective of the theory), but that there should be a enough margin of safety, defined through the Factor of Safety selected depending on the nature of the problem.

Posted Date: 1/30/2013 6:42:06 AM | Location : United States







Related Discussions:- Distortion energy theory, Assignment Help, Ask Question on Distortion energy theory, Get Answer, Expert's Help, Distortion energy theory Discussions

Write discussion on Distortion energy theory
Your posts are moderated
Related Questions
Q. Insulating washer between steel bolts and aluminium plates? Corrosion of aluminium can be activated by putting it in contact with another metal in the presence of water. Thi

Sight Distance: Sight distance is the distance along a road at which a driver has a visibility of objects and can safely stop his vehicle or overtake another vehicle. Sto

Q. Increase in velocity of water due to afflux? Specific energy E f in m per m 3 of flow is the energy measured with respect to bottom and hence comprising potential head D a

growth of tree

determine the cross section of a rectangular beam of uniformly strength for a simply supported beam of 6m span subjected to central concentrated load of 20kN a)by keeping depth of

charring of timber

A  retaining wall, 4.5 m high, retains a soil with  c = 2 N/cm 2 ,  φ = 30° and g = 20 kN/m 3 , with horizontal surface level with the top of the wall. The backfill carries a surch

Question In soil compaction test , if test result exceeds 100%, should engineers accept result? Answer Soil compaction is method of increasing soil density by re

This assessment will test Learning Outcomes 3 and 4 as well as the component of Learning Outcome 1 as it refers to waste disposal for the Plumbing Technology. The student is expect

Q. Which are the Colloidal Impurities in water? The finely divided particles of soil such that their small quantities are not Visible to the naked eye are