QUESTION 2 Which of the following sets of vectors represent valid principal stress directions? [0,1,0] and [0.5,0,0] O [1,1,1] and [0,0,1) [0.5,0.5,0] and [1,2,3] [1,0,0] and [0,1,0] QUESTION 3 The stress vector and unit normal vector are the same vector with different magnitudes. Always True Always False Conditionally True QUESTION 4 If the principal stresses are known, then any corresponding shear stress can be found. True False Conditionally True QUESTION 5 If the stress components are known in one orientation, are you able to find the stress components acting in another orientation? O Yes No

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 = 72 MPa, Sy = 12 MPa, and Sxy = 39 MPa. (a) Draw Mohr's circle for this state of stress. (b) Determine the principal stresses and the maximum in-plane shear stress acting at the point. (c) Show these stresses on an appropriate sketch (e.g., see Fig. 12.15 or Fig. 12.16). (d) Determine the absolute maximum shear stress at the point. Sxy S Answer: (a) Draw Mohr's Circle for this state of stress. (b) Op1 = i MPa Op2 = i MPa Tmax in-plane i MPa (c) Show these stresses on an appropriate sketch (e.g., see Fig. 12.15 or Fig. 12.16) (d) Tabs max i MPa

For a rectangular curved beam in pure bending, polar coordinates are used. Neglecting body forces, the following Airy stress function has been suggested: Pre = A+ Blnr + Cr² + Dr²Inr, (r,0) where A, B, C, and D are constants. Can re) be an Airy stress function? If so, establish: re [0,]=| r

The stresses shown act at a point on the free surface of a machine component. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 22.6 ksi, Sy = 2.2 ksi, and Sxy = 3.8 ksi. Assume β=33∘β=33∘. Determine the normal stresses σxσx and σyσy and the shear stress τxyτx⁢y at the point.