How Can θp and θs Have the Same Sign in Mohr's Circle?

• fonseh
In summary, the question is about how the angles $$\theta_p$$ and $$\theta_s$$ can have the same sign when they are rotated in different directions. The author provides an example from the Internet where positive is defined as counterclockwise rotation and positive shear causes a clockwise rotation. This raises the question of whether the example in the video is incorrect.
fonseh

Homework Statement

In this question , how could the $$\theta_p$$ and $$\theta_s$$ has the same sign ?
For $$\theta_p$$ , it is to be rotated clockwise to horizontal axis , right ?
For $$\theta_s$$ , it is to be rotated anticlockwise to vertical axis , right ?
They are in different direction , how could they have the same negative sign ?

1. What is the significance of the sign of angle in Mohr's circle?

The sign of angle in Mohr's circle represents the orientation of the normal stress with respect to the x-axis. It also indicates the direction of shear stress with respect to the normal stress.

2. How is the sign of angle determined in Mohr's circle?

The sign of angle is determined by the direction of the shear stress with respect to the normal stress. If the shear stress is clockwise from the normal stress, the sign is negative. If it is counterclockwise, the sign is positive.

3. Can the sign of angle change in Mohr's circle?

Yes, the sign of angle can change if the direction of the shear stress changes. This can happen if the applied loads or boundary conditions change.

4. What is the significance of the sign of angle for stress analysis?

The sign of angle is important for understanding the principal stresses and their directions in a material. It also helps in determining the failure criteria and predicting the failure mode of a material under different loading conditions.

5. Are there any limitations to using the sign of angle in Mohr's circle?

While the sign of angle is a useful tool for stress analysis, it only applies to two-dimensional stress states. In three-dimensional stress states, a more complex approach is needed to determine the orientation of the principal stresses.

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