Hello. I\'m taking a structures class and we have just recently been going over
ID: 1817431 • Letter: H
Question
Hello. I'm taking a structures class and we have just recently been going over maximum shears stresses by Mohr's circles. I understand some of the basics, but im still somewhat confused.
Can the maximum shear stress for plane stresses equal to zero (i.e max=0) ? How about plane strain maximum equal to zero (i.e max=0)? How will this affect Mohrs cicle will it only appear a single straight line? If so, is there an example problem you can show me where the max or max is given as zero and need to solve for something or whers when you solve for it equals to zero.
Please help. Thanks
Heres some background information:
http://www.engapplets.vt.edu/Mohr/java/nsfapplets/MohrCircles2-3D/Theory/theory.htm
http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/plane_stress_principal.cfm
http://en.wikibooks.org/wiki/Strength_of_Materials/General_State_of_Stress
Explanation / Answer
Hi,
I am taking an aerospace structures class right now on Mohr's circles as well. No, I don't think the max shear stress or max plain strain can equal zero, because that would mean without touching the object it falls apart (cannot handle zero stress or zero strain). The object would have to be able to handle some strain/ stress.
Here's the basics I have learned so far about Mohr's circles:
Stress:
We solve for two max normal stresses (sigma x and sigma y) and one max shear stress (Txy). We also solve for p.
If you are given the sigma x, sigma y, and Txy, solve as follows:
Graph has T in vertical direction and sigma in horizontal direction.
Point x is at (sigma x, -Txy)
Point y is at (sigma y, Txy)
Center, C, is at ((sigma x + sigma y)/2, 0). On the sigma axis.
Radius is square root of [(sigma x - c)^2 + (Txy)^2].
Point Tmax is at (Center, Radius).
Point Tmin is at (Center, -Radius).
Draw circle to go through Point x, y, Tmax, and Tmin, with C at the center of circle.
p is .5[tan^-1(2Txy/(sigma x - sigma y))]. Because 2p is angle from Line drawn between Point x and Point y, and the sigma axis.
May also find p as .5[sin^-1(Txy/r)]. This is angle at normal stress.
p max is 45 degrees plus Theta P. This is angle when max stresses.
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