Mohr’s Circle - Stress

Example: The element shown below has the following stresses acting on its faces.

σ_x = 9 ksi, σ_y = 1 ksi, τ_xy = 3 ksi. Construct Mohr’s Circle. Determine the

maximum and minimum normal stresses and the maximum shear stress. Find the

angle of the plane on which the maximum shear stress acts and show the element.

Strategy: Identify face A and face B on the element. Construct Mohr’s Circle. Rotate from

plane A to determine the angle of the plane on which the maximum shear stress occurs.

The center of the circle is at σ_C = (σ_x + σ_y)/2 = 9 + 1)/2 = 5 and τ_xy = 0.

Plot point A and the center of the circle. From the figure below determine the radius.

Use triangle ADC in Mohr’s Circle. AD = 3, CD = 9 – 5 = 4 Therefore CA = 5 ksi

Also tan (2θ) = ¾ so 2θ = 36.9^o and 2β = 53.1^o . Recall rotation of on Mohr’s Circle

is twice that on the element.

Click here to continue with this example.

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