Question

PROBLEM 7.6 For the given state of stress, determine (a) the principal planes, (b) the principal stresses, (c) the orientation of the planes of maximum in-plane shearing stress, (d) the maximum in-plane shearing stress, and (e) the corresponding normal stress. 20 ksi 4 ksi 6 ksi $$\theta_p = 18.43^\circ, 108.43^\circ$$ $$\sigma_{\text{max}} = 22.0 \text{ ksi}$$ $$\sigma_{\text{min}} = 2.00 \text{ ksi}$$ $$\theta_s = -26.6^\circ, 63.4^\circ$$ $$\tau_{\text{max}} = 10.00 \text{ ksi}$$ $$\sigma' = 12.00 \text{ ksi}$$

Name: problem 76 for the given state of stress determine a the principal planes b the principal stresses c the orientation of the planes of maximum in plane shearing stress d the maximum in plane 46329
Uploaded: 2024-05-23T17:33:51-08:00
Duration: 6 min 16 s
Channel: Adi S
Description: problem 76 for the given state of stress determine a the principal planes b the principal stresses c the orientation of the planes of maximum in plane shearing stress d the maximum in plane 46329

          PROBLEM 7.6
For the given state of stress, determine (a) the principal planes, (b) the principal stresses, (c) the orientation of the planes of maximum in-plane shearing stress, (d) the maximum in-plane shearing stress, and (e) the corresponding normal stress.
20 ksi
4 ksi
6 ksi
$$\theta_p = 18.43^\circ, 108.43^\circ$$
$$\sigma_{\text{max}} = 22.0 \text{ ksi}$$
$$\sigma_{\text{min}} = 2.00 \text{ ksi}$$
$$\theta_s = -26.6^\circ, 63.4^\circ$$
$$\tau_{\text{max}} = 10.00 \text{ ksi}$$
$$\sigma' = 12.00 \text{ ksi}$$

problem 76 for the given state of stress determine a the principal planes b the principal stresses c the orientation of the planes of maximum in plane shearing stress d the maximum in plane 46329

Added by Lisa F.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

05/23/2024

Step 1

From the image, we have: $$\sigma_x = 20 \text{ ksi}$$ (tensile, so positive) $$\sigma_y = 6 \text{ ksi}$$ (tensile, so positive) $$\tau_{xy} = 4 \text{ ksi}$$ (positive, as it tends to rotate the element counter-clockwise) Show more…

Show all steps

Thanks for your feedback!

PROBLEM 7.6 For the given state of stress, determine (a) the principal planes, (b) the principal stresses, (c) the orientation of the planes of maximum in-plane shearing stress, (d) the maximum in-plane shearing stress, and (e) the corresponding normal stress. 20 ksi 4 ksi 6 ksi $$\theta_p = 18.43^\circ, 108.43^\circ$$ $$\sigma_{\text{max}} = 22.0 \text{ ksi}$$ $$\sigma_{\text{min}} = 2.00 \text{ ksi}$$ $$\theta_s = -26.6^\circ, 63.4^\circ$$ $$\tau_{\text{max}} = 10.00 \text{ ksi}$$ $$\sigma' = 12.00 \text{ ksi}$$