Lego man's cousin Duplo man is sitting around when someone puts a 50 kg weight on...

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Lego man's cousin Duplo man is sitting around when someone puts a 50 kg weight on his head. Unable to move (since he doesn't have legs) he just sits there and his body deforms. Assume that he is made of solid acrylonitrile butadiene styrene, which has a Young's modulus of 350 MPa and a Poisson's ratio of 0.4. Additionally assume that this head is a cylinder, his upper body is a pyramidal frustum (four sided pyramid with its top cut off), and this lower body is a rectangular prism, with all dimensions given in the figure below. Points A, B and C all lie on Duplo man's midline and are located halfway between the top and bottom of their respective body sections. Duplo Man X 2 cm 50 kg A B C midline 1 cm Front View 2 cm 2 cm 1 cm 1 cm A B C midline Side View 2 cm 11) Write the 3-D stress tensor at point A after the weight is placed on Duplo man's head 12) Determine the maximum shearing stress (xy) in a plane perpendicular to the z-axis and existing at point B, and the angle of x'-y' relative the current x-y coordinate system. 13) How wide is Duplo Man's lower body section in the x-direction after the weight is placed on his head? (Note: Assume the floor is frictionless) Lego man's cousin Duplo man is sitting around when someone puts a 50 kg weight on his head. Unable to move (since he doesn't have legs) he just sits there and his body deforms. Assume that he is made of solid acrylonitrile butadiene styrene, which has a Young's modulus of 350 MPa and a Poisson's ratio of 0.4. Additionally assume that this head is a cylinder, his upper body is a pyramidal frustum (four sided pyramid with its top cut off), and this lower body is a rectangular prism, with all dimensions given in the figure below. Points A, B and C all lie on Duplo man's midline and are located halfway between the top and bottom of their respective body sections. Duplo Man X 2 cm 50 kg A B C midline 1 cm Front View 2 cm 2 cm 1 cm 1 cm A B C midline Side View 2 cm 11) Write the 3-D stress tensor at point A after the weight is placed on Duplo man's head 12) Determine the maximum shearing stress (xy) in a plane perpendicular to the z-axis and existing at point B, and the angle of x'-y' relative the current x-y coordinate system. 13) How wide is Duplo Man's lower body section in the x-direction after the weight is placed on his head? (Note: Assume the floor is frictionless)

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