1
$\begingroup$

Consider the state of tension indicated in the Figure. Determine the range of τxz values for which the maximum tangential stress is less than or equal to 60 MPa.

enter image description here

I did σ(med)=(60+0)/2 = 30

To find the radius I did σ(max) = σ(I) = σ(med)+r <=> 100=30+r <=> r=70

But in the solution is enter image description here

My question is: why is my radius wrong?

$\endgroup$
4
  • 3
    $\begingroup$ Do not self-vandalize your questions, here or on other Stack Exchange sites like electronics.SE. This was a well-received question that was upvoted, with a good answer. The people answering have put in time and effort to write an answer -- These edits that remove the question contents are disrespectful to their work. $\endgroup$ – nanofarad Jan 14 at 21:53
  • 4
    $\begingroup$ The account needs to be blocked before the questions are restored. It all seems pretty childish. $\endgroup$ – Transistor Jan 14 at 22:03
  • $\begingroup$ While this behaviour is completely unacceptable, I Found it a bit humorous that OP immediately undid the edit after a user undid his original edit on making the post about 'deleted question' $\endgroup$ – Buraian Jan 14 at 22:38
  • 1
    $\begingroup$ @Buraian The answer saying the same thing is even stranger -- OP should seriously stop -- the question has been flagged for moderator intervention here and they have been notified on multiple sites about these edits (by mods and non-mod users alike) $\endgroup$ – nanofarad Jan 14 at 22:52
1
$\begingroup$

I'm not 100% sure, however one way to feel more confident on my reasoning, is to check whether my final value of $\tau_{xz}$ is the same with the solution. .

My understanding is the following :

$\sigma_{xx}$ and $\sigma_yy$ are principal stresses in the x-y plane. That means that $\sigma_1 \leftarrow \sigma_{yy}$, $\sigma_2 \leftarrow \sigma_{xx}$. The greatest tangential stress is going to be obtained by the $\sigma_{I}$ and $\sigma_{III}$.

In order to have $\tau_max=60[MPa]$, you'd need $\sigma_{I}-\sigma_{III}=120[MPa]$ Therefore, since, $\sigma_1=100[MPa]$, $\sigma_{III} \rightarrow -20[MPa]$.

Then on the x-z plane, you'd need to determine the $\tau_{xz}$, so that the lowest principal stress is -20[MPa]. Since, on that plane the $\sigma_{med} = 30[MPa]$, then the radius will be $\tau_{xz,max} = 50[MPa]$, which means that you need to have

$$50^2 \ge \tau_{xz}^2+ \left(\frac{\sigma_x - \sigma_z}{2}\right)^2$$ $$\tau_{xz}^2 \le 50^2 -\left(\frac{\sigma_x - \sigma_z}{2}\right)^2$$ $$\tau_{xz} \le \sqrt{50^2 -\left(\frac{60}{2}\right)^2}$$ $$\tau_{xz} \le \sqrt{50^2 - 30^2}$$

$$\tau_{xz} \le 40 [MPa]$$

Is this the right solution you are given?

$\endgroup$
0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy