5. (12 points total) Combined bending and tension. In figure 1, a 25-mm-diameter shaft with length...

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5. (12 points total) Combined bending and tension. In figure 1, a 25-mm-diameter shaft with length 100 mm is loaded with a force F = 10 kN and a force P = 20 kN applied axially, as depicted. The shaft is made of brittle ASTM class 25 gray cast iron. In this question, you will estimate and compare the factor of safety of the shaft at two different locations. Due to the combination of bending and tension, the stress state differs at different locations. (a) (4 points) For stress element A, estimate the factor of safety using an appropriate failure theory and state whether the material fails. Be sure to explain your choice of failure theory. Hint: This stress element experiences plane stress, with a normal stress due to axial tension, as well as a transverse shear stress due to bending (see Ch 3.11, Table 3.2). (b) (4 points) For stress element B, estimate the factor of safety using an appropriate failure theory and state whether the material fails. Be sure to explain your choice of failure theory. Hint: This stress element experiences plane stress, with a normal stress due to axial tension, and a normal stress due to bending (see Ch 3.10). (c) (4 points) Plot to scale the stress yield envelope for this material and the coordinates of the stress states of element A and B. By drawing the corresponding load line, estimate the factors of safety for each element by graphical measurement. B / = 100 mm d = 25 mm Figure 1: Circular Beam F P 5. (12 points total) Combined bending and tension. In figure 1, a 25-mm-diameter shaft with length 100 mm is loaded with a force F = 10 kN and a force P = 20 kN applied axially, as depicted. The shaft is made of brittle ASTM class 25 gray cast iron. In this question, you will estimate and compare the factor of safety of the shaft at two different locations. Due to the combination of bending and tension, the stress state differs at different locations. (a) (4 points) For stress element A, estimate the factor of safety using an appropriate failure theory and state whether the material fails. Be sure to explain your choice of failure theory. Hint: This stress element experiences plane stress, with a normal stress due to axial tension, as well as a transverse shear stress due to bending (see Ch 3.11, Table 3.2). (b) (4 points) For stress element B, estimate the factor of safety using an appropriate failure theory and state whether the material fails. Be sure to explain your choice of failure theory. Hint: This stress element experiences plane stress, with a normal stress due to axial tension, and a normal stress due to bending (see Ch 3.10). (c) (4 points) Plot to scale the stress yield envelope for this material and the coordinates of the stress states of element A and B. By drawing the corresponding load line, estimate the factors of safety for each element by graphical measurement. B / = 100 mm d = 25 mm Figure 1: Circular Beam F P