States of stress - principal stresses, Civil Engineering

States of stress - principal stresses:

Now let us consider a few cases of solids of the similar material (mild steel) under various states of stress as display in Figure. The given states of stress have already been decreased within terms of principal stresses. Poisson's ratio v is given as 0.3.

Solution

Case a

First, let us consider the solid shown in Figure (a).

1091_States of stress - principal stresses.png

Figure

(a)        Since the major principal stress, σ1 (300 MPa) is more than

σy (260 MPa), the solid will fail according to principal stress theory.

(b)        The maximum principal strain, ε1 = 300/E -0.3 (+200)/E

=240/E < 260/E

∴          According to principal strain theory, the solid is safe.

(c)        Maximum shear stress, τmax  =300-200/2 = 50<<130

∴          The solid is safe according to shear stress theory too.

(d)        Total strain energy density in the solid, u is as follows:

 u = 1/2E [3002 +2002 -2 ×0.3×300×200] = 47000/E > 2602/2E

∴          The solid will fail according to total strain energy theory.

(e)        Distortion energy density in the solid, ud as follows:

ud = 1/12G [(300-200)2 + 2002 + 3002] = 70000/6G > 2602/6G

∴          Distortion energy theory also predicts that the solid will fail.

Posted Date: 1/30/2013 6:37:55 AM | Location : United States







Related Discussions:- States of stress - principal stresses, Assignment Help, Ask Question on States of stress - principal stresses, Get Answer, Expert's Help, States of stress - principal stresses Discussions

Write discussion on States of stress - principal stresses
Your posts are moderated
Related Questions
Describe the Geophysical Profileof Borings The variation in the thickness of the soil stratum for engineering application is known as the geophysical profile. Figure 1.2 shows

Q. Holes in steel plates connecting to H-piles There are two types of holes present in the steel plate associated to H-piles in the pile cap. The first type of holes is design


What is the easiest way to give proof the varignon''s theorem? Help please guys

What is the special feature of this system rather than other?? What do you mean by principal of looping system?

uses concrete slump test

Q. Show the Functions of sleepers in railway? Functions of sleepers in railway works are as below:  (i)  The primary function of a sleeper is to grip the rail to gauge and t

Change the model to take into account the variation in outdoor temperature for a "typical" day in the heating season based on the heat loss by the fabric and the heating of incomin

Explain Horizontal Circular Curves - Transportation Horizontal circular curve is a circular arc between two straight lines known as tangents.

how prepared for surveying?