MohrsCircle - North Carolina State University Department of...

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North Carolina State University Department of Mechanical & Aerospace Engineering MAE 314 Solid Mechanics 1 Supplemental Material: Mohr’s Circle for Plane Stress For the given state of stress determine the principal planes, principle stresses, and the orientation of the planes of maximum in plane shearing stress. Also determine the normal and shearing stresses after the element has been rotated 30 o clockwise and 12 o counterclockwise. First, recall the positive stress state is defined as below. So, from the given stress state, we have: σ x = 60 MPa, σ y = 90 MPa, and τ xy = 30 MPa. Construction of Mohr’s Circle Step 1. Draw the axis and plot O ( σ avg , 0), which is the center of the circle. Step 2. Plot points X ( σ x , ± τ xy ) and Y ( σ y , ± τ xy ). Step 3. Draw a line connecting points X, Y, and O. This is the diameter of the circle. Step 4. Draw the circle. 90 MPa 30 MPa 60 MPa + σ y + τ xy + σ x
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North Carolina State University Department of Mechanical & Aerospace Engineering MAE 314 Solid Mechanics 2 ߪ ௔௩௚ ߪ ൅ ߪ 2 െ60ܯܲܽ ൅ 90ܯܲܽ 2 ൌ 15ܯܲܽ Recall the sign convention for shearing stress is as follows. So point X is ( σ x , ‐τ xy )=( 60, 30) since, for the given stress state, the shear on the element face perpendicular to the x axis rotates the element counterclockwise.
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