How Do You Apply Mohr's Circle to Geotechnical Engineering Problems?

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Homework Statement

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This is for a class on Geotechnical Engineering for those who are interested.

Homework Equations

Basic understanding of Mohr's Circle concepts and general knowledge on subject. Kind of hard to list equations for this.

The Attempt at a Solution

What I did was ignore the fact that the square was on an angle of 20 degrees. My reasoning was that if the square is rotated on an angle and the normal forces are still normal to the planes, and the question asks for the stresses at a point with the angle of 35 degrees, we can make the whole problem relative to the initial 20 degrees.

Next since there are no shearing forces and just axial forces, the circle would be centered on the x-axis. By looking at it, if I assumed inwards to be positive the circle would span from 12 kPa to 52 Kpa, making the radius of the circle 20 kPa and the center located at 32 kPa.

Now since I know $\alpha$ is 35 degrees, I know that when I translate that to the Mohr's circle diagram its going to be 2$\alpha$, or 70 degrees. Knowing this, I know have the radius which will act as my hypotenuse and 2$\alpha$ will act as my angle to do sine and cosine functions to find the points of the shear and normal stresses relative to the center or my circle.

Because of this, I will have two values for each right? One being center of the circle plus sine(70)*hypotenuse / cosin(70)*hypotenuse respectively for shear and normal forces, and then the other set of values will be center minus the values obtained from the sine functions.

Is this right? Is my assumption correct to ignore the 20 degrees that the square is offset by?

Sorry if this seems excessive, but its for homework in a class where the class is formatted in such a way that homework can only hurt you. Excessively...

Thanks in advance

 

[KataKoniK]

Thank you for your question. It seems like you have a good understanding of Mohr's circle concepts and how to apply them in this problem. Your reasoning to ignore the 20 degrees offset is correct, as long as the normal forces are still normal to the planes.

Your approach to using sine and cosine functions to find the shear and normal stresses relative to the center of the circle is also correct. However, keep in mind that the center of the circle represents the average stress state, so the values you obtain from the sine and cosine functions will be added and subtracted from this average value to give you the maximum and minimum values at the point of interest.

Overall, your solution seems correct. Just make sure to double check your calculations and make sure they are consistent with the given values and the concepts of Mohr's circle. Good luck with your homework!