Question:
. In a 2-D stress system compressive stresses of magnitudes 100 MPa and 150 MPa act
in two perpe...

Question

Question:
. In a 2-D stress system compressive stresses of magnitudes 100 MPa and 150 MPa act 
in two perpendicular directions. Shear stresses on these planes have magnitude of 80 
MPa. Use Mohr's circle to find, 
(i) Principal stresses and their planes 
(ii) Maximum shears stress and their planes and 
(iii) Normal and shear stresses on a plane inclined at 450 to 150 MPa stress.

CramX · Accepted Answer

Step 1: : Identify the given stresses and sketch the stress situation.. We are given a 2-D stress system with the following stress components: Step 2: : Construct Mohr's circle using the given stresses.. To construct Mohr's circle, we need to find two points on the circle, which are given by the stresses on the two perpendicular planes. Now, we can calculate the radius of Mohr's circle: The center of Mohr's circle is given by: Step 3: : Find the principal stresses and their planes.. The principal stresses are the maximum and minimum values of the normal stress on any plane in the 2-D stress system. They can be found by finding the points where Mohr's circle intersects the vertical axis. The maximum and minimum principal stresses act on the planes perpendicular to each other. Step 4: : Find the maximum shear stress and their planes.. The maximum shear stress occurs on planes that are oriented at 45 degrees to the principal stress planes. The magnitude of the maximum shear stress can be found by calculating the radius of Mohr's circle: Step 5: : Find the normal and shear stresses on a plane inclined at 45 degrees to the 150 MPa stress.. After rotating the stress diagram, we find that the normal and shear stresses on the plane inclined at 45 degrees to the 150 MPa stress are: Final Answer: (i) Principal stresses and their planes: - Maximum Principal Stress: $\sigma_{1} = -14.15$ MPa, acting on a plane perpendicular to a plane inclined at 45 degrees to the x-axis. - Minimum Principal Stress: $\sigma_{2} = -235.85$ MPa, acting on a plane perpendicular to a plane inclined at 45 degrees to the y-axis. (ii) Maximum shear stress and their planes: - Maximum Shear Stress: $	au_{max} = 110.85$ MPa, acting on planes inclined at 45 degrees to the principal stress planes. (iii) Normal and shear stresses on a plane inclined at 45 degrees to the 150 MPa stress: - Normal Stress: $\sigma = -125$ MPa - Shear Stress: $	au = -80$ MPa

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Full Solution Locked

Step 1:
: Identify the given stresses and sketch the stress situation.

Step 2:
: Construct Mohr's circle using the given stresses.

Step 3:
: Find the principal stresses and their planes.

Final Answer

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