2. (25 points) A high altitude science balloon (called a NASA pumpkin balloon) is filled with...

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2. (25 points) A high altitude science balloon (called a NASA pumpkin balloon) is filled with gas on the ground then inflates to the shape shown as it ascends. It is made of a thin plastic membrane with stiff longitudinal cords glued onto the membrane periodically about its equator. Heating and cooling by the sun causes the internal pressure to fluctuate during its flight, so NASA uses sensors to monitor stress at several locations on the balloon's thin membrane. The membrane material has a uniaxial yield stress of 0 = 100 MPa. NASA determines the stress state at point A to be plane stress with ox= 30, Oy = 30, Txy = -30 MPa. X (a) Draw Mohr's circle for the stress state. (b) Determine the principal stresses and draw a rotated stress element depicting it. (c) How high can Txy reach before the material fails? Use Tresca failure criteria. 2. (25 points) A high altitude science balloon (called a NASA pumpkin balloon) is filled with gas on the ground then inflates to the shape shown as it ascends. It is made of a thin plastic membrane with stiff longitudinal cords glued onto the membrane periodically about its equator. Heating and cooling by the sun causes the internal pressure to fluctuate during its flight, so NASA uses sensors to monitor stress at several locations on the balloon's thin membrane. The membrane material has a uniaxial yield stress of 0 = 100 MPa. NASA determines the stress state at point A to be plane stress with ox= 30, Oy = 30, Txy = -30 MPa. X (a) Draw Mohr's circle for the stress state. (b) Determine the principal stresses and draw a rotated stress element depicting it. (c) How high can Txy reach before the material fails? Use Tresca failure criteria.