Mohr's circle is shown for a point in a physical object that is subjected to plane stress. Each grid square is 480 psi in size. (a) Determine the stresses o, Oy, and the magnitude of Tyand show them on a stress element. (b) Determine the principal stresses and the magnitude of the maximum in-plane shear stress acting at the point and show these stresses on an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16). y

Mohr's circle is shown for a point in a physical object that is subjected to plane stress. Each grid square is 14 MPa in size. (a) Determine the stresses Ox, Oy, and the magnitude of Txy and show them on a stress element. (b) Determine the stresses On, ot, and the magnitude of Tnt and show them on a stress element that is properly rotated with respect to the x-y element. The sketch must include the magnitude of the angle between the x and n axes and an indication of the rotation direction (i.e., either clockwise or counterclockwise). σ n Answer: (a) ox= Oy= Txy= (b) on= Ot= Int= MPa MPa MPa MPa MPa MPa X

Mohr's circle is shown for a point in a physical object that is subjected to plane stress. Each grid square is 240 psi in size. (a) Determine the stresses Ox, Oy, and the magnitude of Txy and show them on a stress element. (b) Determine the principal stresses and the magnitude of the maximum in-plane shear stress acting at the point and show these stresses on an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16). D Answer: (a) σx= i Øy= Txy = (b) Op1= Op2 = Tmax in-plane Mi psi psi psi psi psi psi b

Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 24 MPa, Sy = 81 MPa, and Sxy = 16 MPa. (a) Determine the principal stresses and the maximum in-plane shear stress acting at the point. (b) Show these stresses on an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16) (c) Compute the absolute shear stress at the point.

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Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are 5x = 68 MPa, Sy=97 MPa, and Sxy = 27 MPa. (a) Determine the principal stresses and the maximum in-plane shear stress acting at the point. (b) Show these stresses on an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16) (c) Compute the absolute shear stress at the point. Sxy Answer: (a) Op1 = MPa MPa Op2 = MPa Tmax in-plane= (b) Show these stresses on an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16) MPa (c) Tmax abs

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Mohr’s circle is shown for a point in a physical object that is subjected to plane stress. Each grid square is 640 psi in size. (a) Determine the stresses σx, σy, and the magnitude of τxy and show them on a stress element. (b) Determine the principal stresses and the magnitude of the maximum in-plane shear stress acting at the point and show these stresses on an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16).

At a point in a machine component that is subjected to plane stress, the normal and shear stresses are σx= 100 MPa, σy= 35 MPa, and τxy= 70 MPa, acting in the directions shown in the figure. At this point, determine the strain components εx, εy, εz, and γxy. Assume that E = 72 GPa and v = 0.30 for the machine component.

Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 34 MPa, Sy = 73 MPa, and Sxy = 30 MPa. (a) Determine the principal stresses and the maximum in-plane shear stress acting at the point. (b) Show these stresses on an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16) (c) Compute the absolute shear stress at the point.