Question

4. The state of stress of a particle of a body made from an isotropic, linearly elastic-ideally plastic material with a tied stress $\sigma_{yield} = 200$ MPa is given as $\sigma = \begin{bmatrix} -60 & 40 & 0 \\ 40 & 80 & 0 \\ 0 & 0 & \sigma_{33} \end{bmatrix} MPa$ Compute the value of $\sigma_{33}$ required for yielding if the materials obeys: 1. Tresca Criteria 2. Von Mises Criteria

Name: 4 the state of stress of a particle of a body made from an isotropic linearly elastic ideally plastic material with a tied stress sigmayield 200 mpa is given as sigma beginbmatrix 60 40 0 4 33264
Uploaded: 2023-10-04T09:40:09-08:00
Duration: 1 min 29 s
Channel: Adi S
Description: 4 the state of stress of a particle of a body made from an isotropic linearly elastic ideally plastic material with a tied stress sigmayield 200 mpa is given as sigma beginbmatrix 60 40 0 4 33264

          4. The state of stress of a particle of a body made from an isotropic, linearly elastic-ideally plastic material with a tied stress $\sigma_{yield} = 200$ MPa is given as
$\sigma = \begin{bmatrix} -60 & 40 & 0 \\ 40 & 80 & 0 \\ 0 & 0 & \sigma_{33} \end{bmatrix} MPa$
Compute the value of $\sigma_{33}$ required for yielding if the materials obeys:
1. Tresca Criteria
2. Von Mises Criteria

4 the state of stress of a particle of a body made from an isotropic linearly elastic ideally plastic material with a tied stress sigmayield 200 mpa is given as sigma beginbmatrix 60 40 0 4 33264

Added by Carla K.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

10/04/2023

Step 1

We can find these by solving the characteristic equation: $det(\sigma - \lambda I) = 0$ where $\lambda$ represents the principal stresses and $I$ is the identity matrix. Show more…

Show all steps

Thanks for your feedback!

4. The state of stress of a particle of a body made from an isotropic, linearly elastic-ideally plastic material with a tied stress $\sigma_{yield} = 200$ MPa is given as $\sigma = \begin{bmatrix} -60 & 40 & 0 \\ 40 & 80 & 0 \\ 0 & 0 & \sigma_{33} \end{bmatrix} MPa$ Compute the value of $\sigma_{33}$ required for yielding if the materials obeys: 1. Tresca Criteria 2. Von Mises Criteria