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Need Help with Mohr's Circle!

  1. Oct 23, 2012 #1
    1. The problem statement, all variables and given/known data
    http://imageshack.us/a/img27/6347/screenshot20121023at125.png [Broken]

    Uploaded with ImageShack.us

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


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


    3. 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 [itex]\alpha[/itex] is 35 degrees, I know that when I translate that to the Mohr's circle diagram its going to be 2[itex]\alpha[/itex], or 70 degrees. Knowing this, I know have the radius which will act as my hypotenuse and 2[itex]\alpha[/itex] 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
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
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