Maximum Normal Stress From Mohr's Circle

Question

Given This Diagram, I am to:

1. Determine Principal Stresses
   (My Ans: 92000 and -8500kPa confirmed with Answer Key)

2. Determine Max Shear

   (My Ans: 50500 kPa confirmed with Answer Key)

3. Find the Angle between the plane of the maximum (positive) shear stress and the original plane of stress.

   (My Ans 28deg Answer Key -61.8deg)

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My Mohr's Circle has C=42,000 and R=50,477 It is my understanding that my original point would be at (84,000 , 28,000) and the max shear stress is at the highest Y value of the circle (42,000,50,477)

As such I calculate:

• cos^-1(42/50.5) = 33 deg
• 90deg-33.7deg=56.2deg

• 56.2deg/2 = 28.1 deg

  Where am I going wrong?

Answer 1

This sould probably be written as comment, as I will give only partial answer. Your angle is wrong, you are in wrong quadrant, either you just forgotten to take in consideration sign (positive or negative stress) or you mixed stress axis orientation. It would help if you provide a sketch of Mohrs circle. One starting point should be ($\sigma_x$, $\tau_{xy}$), other ($\sigma_y$, -$\tau_{xy}$). From this pic you gave I suppose your $\sigma_y$ equals 0. This link provides procedure and examples of constructing Mohr's circle.