How Do Tresca and von Mises Theories Compare in Calculating Safety Factors?

[donniemateno]

I have been given these questions as homework and completed them , but you enter them on our online homework system to check if they are correct. It doesn't say which one is wrong though and its frustrating as I don't know where I have gone wrong! I know I have one right as it does say 1/2 is correct :)

the question is :

A component is made of mild steel with yield stress 240MPa. The state of stress is
pure shear τ =50MPa at a point on the component
 Calculate factor of safety by Tresca failure theory
 Calculate factor of safety by von Mises failure theory

I have attached relevant formulas as a attachment

My working out so far is part 1:

Tresca = 240MPa / 50 = 4.8

Part 2:

von Mises :
q1=50 q2= 0 q3=-50

√0.5((50-0)^2+(0--50)^2+(0-50)^2)) = 61.24

240 / 61.24 = 3.92

 

[Chestermiller]

I don't think you wrote down the three principal stresses for pure shear correctly, or, if you did write them down correctly, you did not apply them correctly in either of the two formulas. Please write down what you used for the three principal stresses. Then try again to substitute them into the two formulas. For Tresca, I get a safety factor of 2.4, and for von Misces, I get a safety factor of 2.77.

 

[donniemateno]

chestermiller

not sure how you got 2.4 as the only information you are given is 240 and 50. so my initial reaction is to divide by 240 / 50

 

[Chestermiller]

If it's "pure shear," the principal stresses are 50, 0, and -50. That is, one of the principal stresses is zero, and the other principal stresses are equal in magnitude and opposite in sign. So the maximum principal stress minus the minimum principal stress is 50 - (-50) =100. The differences in the principal stresses are 50 - 0, (0 - (-50), and 50 - (-50).

 

[afreiden]

not sure how you got 2.4 as the only information you are given is 240 and 50. so my initial reaction is to divide by 240 / 50

chestermiller is definitely right for von Mises (I can't recall the tresca criteria at the moment).
one reason why it's not simply 240/50 is because there's a √3 in the von Mises formula..