Extensometers attached to the external surface of a pressure vessel indicate that a = 0.002 and & = 0.005 along the longitudinal and transverse directions, respectively. Determine the corresponding stresses for E= 210 GPa and v = 0.4. What would be the error in these stresses if Poisson's ratio were not considered?

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= 14 MPa, S, = 29 MPa, and Sy = 39 MPa. (a) Determine the principal stresses (o,1 > op2) and the maximum in-plane shear stress Tmax acting at the point. (b) Find the smallest rotation angle 0, (counterclockwise is positive, clockwise is negative) that will rotate to principal directions. Then show these stresses in an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16) Sy Answers: Opl = i MPa. Op2 = i MPa. Tmax = i MPa. Op i

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The strain rosette shown was used to obtain normal strain data at a point on the free surface of a machine component. Given the values = -165 µμe, e = -155 μe, e = 50 μe, E = 10,600 ksi, and v=0.33, determine (a) the stress components o,,o,, and ry at the point. (b) the principal stresses and the maximum in-plane shear stress at the point; on paper, show these stresses on an appropriate sketch that indicates the orientation of the principal planes and the planes of maximum in-plane shear stress. (c) the magnitude of the absolute maximum shear stress at the point. 45° 45°