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
Q. What is Corrosion inhibitors? Corrosion inhibitors are chemical substances that when added in small concentrations, stop or decrease the corrosion or reaction of metalwith t

Arrangement of piles in a pile cap to reduce bending moment induced in piles Let's consider that piles are designed to intersect at a single common point in a pile cap. The re

Q. What is Oil interceptors ? Oils and Grease are usually found in stormwater runoff from catchments. They come from spillage and leakage of fuels, lubricants, Vehicle coolants

Why hybridisation never take in isolated atom

Q. Show the Stresses during pile driving? Stresses during pile driving In pile driving operation, proper selection of piling hammers is necessary to prevent the damage of

long span bridge or continuous bridge which is more preferable and why ??? what is the major problem in continuous bridge and what would be its effect if there is any differential


how can find forebearing

A trapezoidal masonry retaining wall 1 m wide at top and 3 m wide at its bottom is 4 m high. The vertical face is retaining soil (φ = 30°) at a surcharge angle of 20° with the hori