Question 3 © "
al

15% an 0 denote he i in an element, the the van Mises sires i
2
s

(efecto)

.
3 .
B

Question

Question 3 © "
al

15% an 0 denote he i in an element, the the van Mises sires i
2
s

(efecto)

.
3 .
B

VIPSolutions · Accepted Answer

The question is asking for the formula for the von Mises stress in terms of the principal stresses $\sigma_1, \sigma_2, \sigma_3$.

The von Mises stress is given by:
$$
\sigma_v = \sqrt{\frac{(\sigma_1 - \sigma_2)^2 + (\sigma_2 - \sigma_3)^2 + (\sigma_3 - \sigma_1)^2}{2}}
$$

Looking at the options in the image, the correct answer is:

$$
\left[(\sigma_1^2 + \sigma_2^2 + \sigma_3^2 - \sigma_1\sigma_2 - \sigma_2\sigma_3 - \sigma_3\sigma_1)\right]^{1/2}
$$

This formula is mathematically equivalent to the one above after simplification.

So, the correct choice is the first one (option on line 4).

VIPSolutions · Answer

The correct option is the first one (the one on line 4), which expresses the von Mises stress as:

$$
\sigma_v = \sqrt{\sigma_1^2 + \sigma_2^2 + \sigma_3^2 - \sigma_1\sigma_2 - \sigma_2\sigma_3 - \sigma_3\sigma_1}
$$

This is the standard formula for von Mises stress in terms of the principal stresses.

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