States of stress - principal stresses, Civil Engineering

Assignment Help:

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.


Related Discussions:- States of stress - principal stresses

How double drainage occur, The loading period for a building extended from ...

The loading period for a building extended from Feb., 1957 to Feb., 1959. In Feb., 1962, the average measured settlement was found to be 117 mm. The ultimate settlement was expecte

Explain the selected bridges - underwater inspection, Explain the Selected ...

Explain the Selected Bridges - Underwater Inspection? Those bridges, which require underwater inspection must be noted for individual inspection and inventory records as well b

Enumerate about the bonded member, Enumerate about the Bonded Member It...

Enumerate about the Bonded Member It is a concrete member in which tendons are bonded to the concrete. They may be directly bonded to the concrete as in the case of pre-tension

Define the planning an underwater inspection, Define the Planning an Underw...

Define the Planning an Underwater Inspection? Planning for underwater inspection is important because of - Unknown factors which may be discovered during the diving - Th

Distortion energy theory, Distortion energy theory: Let us now conside...

Distortion energy theory: Let us now consider the solid shown in Figure. (a)        By inspection we may see that the solid is safe according to principal stress theor

Ild and rolling load, how to solve ild and rolling load problem for shear f...

how to solve ild and rolling load problem for shear force and bending moment with the diagram.

State the importance of structural element, State the importance of structu...

State the importance of structural element If this structural element is used as a beam element, subjected to self load and other imposed transverse loads, then the bottom fibr

Transportation issues, "We have one other pressing challenge that you could...

"We have one other pressing challenge that you could review for us," Alistair Wu says. "As you know, the Shanghai plant was our first facility in China, but we also have two other

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd