Question:
A thin cylinder of 3m diameter is subjected to an internal pressure of 2.5MN/m^2. Using a factor of safety of 2.2 and a yield stress of 300MN/m^2, calculate the wall thickness based on the
a) Tresca
b) von-Mises yield criteria
Answer:
![](https://static.wixstatic.com/media/20c892_b2899d20c8b447b4b96421f1fabe4447~mv2.png/v1/fill/w_86,h_25,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_b2899d20c8b447b4b96421f1fabe4447~mv2.png)
We know:
![](https://static.wixstatic.com/media/20c892_c73bfa49d49f4462a730e0393c37c49d~mv2.png/v1/fill/w_79,h_8,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_c73bfa49d49f4462a730e0393c37c49d~mv2.png)
Hoop Stress:
![](https://static.wixstatic.com/media/20c892_72fa73ad601a49cd81afc91fd6afe00e~mv2.png/v1/fill/w_79,h_8,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_72fa73ad601a49cd81afc91fd6afe00e~mv2.png)
Longitudinal Stress:
![](https://static.wixstatic.com/media/20c892_fe132a49c3944ce6b8186d040bbd5e80~mv2.png/v1/fill/w_86,h_54,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_fe132a49c3944ce6b8186d040bbd5e80~mv2.png)
![](https://static.wixstatic.com/media/20c892_a504c50586194de1b319e43bd9d08805~mv2.png/v1/fill/w_77,h_48,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_a504c50586194de1b319e43bd9d08805~mv2.png)
Tresca stress model
As both stress values are positive, the second stress figure is set to zero to comply with Tresca Yield Criteria:
![](https://static.wixstatic.com/media/20c892_d41bfa2d1d66431d9d237925b3175211~mv2.png/v1/fill/w_77,h_22,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_d41bfa2d1d66431d9d237925b3175211~mv2.png)
Von-Mises:
![](https://static.wixstatic.com/media/20c892_1629b6d5d98d434999ade545fc5215bd~mv2.png/v1/fill/w_78,h_57,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_1629b6d5d98d434999ade545fc5215bd~mv2.png)