Maximum shear stress - state of stress, Civil Engineering

Maximum shear stress - state of stress:

Consider the state of stress.

(a) According to principal stress theory the equivalent stress for this case is simply σ1, i.e. 300 MPa.

(b) Let us consider principal strain theory.

The principal strain introduced in this case is as follows:

ε1 = 300/E -(0.3 × 200/E) = 240/E

This much of strain can be produced in uniaxial tension by a stress of 240 MPa and therefore, the equivalent stress according to principal strain theory is 240 MPa.

(c)        Maximum shear stress τmax  =300 - 200/2 = 50 MPa .

This could be produced through a uniaxial stress of 100 MPa and thus equivalent stress according to shear stress theory is just 100 MPa.

(d)        Strain energy density, u = 1/2E [3002 +2002 -2×0.3×300×200]

=47000/E                                                                                 . . .(i)

If the equivalent uniaxial stress is σe, then u = σ2e/2E          . . .       (ii)

i.e. σ2e/2E  =47000/E

238_Maximum shear stress - state of stress.png

Distortion energy density

ud  = 1/12G[(300-200)2 +3002+2002] = 70000/6G

If equivalent uniaxial stress is σ, then

ud  = 1/12G(σ2e2e) = σ2e/6G  

i.e. σ2e/6G    =70000/6G

342_Maximum shear stress - state of stress1.png

Even by we have previously analysed whether the solid is safe or not according to various theories, only through evaluating the equivalent stress, we are able to get an idea of the margin of safety according to every of the theories.

Posted Date: 1/30/2013 6:45:54 AM | Location : United States







Related Discussions:- Maximum shear stress - state of stress, Assignment Help, Ask Question on Maximum shear stress - state of stress, Get Answer, Expert's Help, Maximum shear stress - state of stress Discussions

Write discussion on Maximum shear stress - state of stress
Your posts are moderated
Related Questions
Major bridge - Major bridge is one of which has a total linear waterway of 18 m or more for multiple span and total linear water way of 12 m or more for single span. Important b

Determine the thickness of flexible pavement layer 2 given the following:  FACTS: Total Structural Number required = 7.0 Total number of layers = 2 Layer 1 consists of

Necessity of reinforcement in precast concrete manhole units Precast concrete manholes are generally constructed by placing the bases of manholes firstly. Walls of precast man

i want to know about the detailing at beam -column joint & beam- wall joint


different types of ashlar masonry

What is W.M.M. roads? Where its used ?

Q. Best efficiency point and operating point for pumps? In a pumping system, a system curve can be derived based on static head needed to lift up the fluid and variable head be

Calculate Roller Production An excavating contractor determined through a test strip, that a smooth steel-wheel vibrating roller compactor operating at 3-mph can compact a 6-in

Q. Diffrence between Rowe cell and Oedometer apparatus? The benefits of using Rowe cell over oedometer apparatus are:  (i)  It possesses control facilities for drainage and