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Question: two pulleys are fixed to the solid circular shaft at...

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Two pulleys are fixed to the solid circular shaft, at the locations denoted as A and C, as shown in Figure 1. Assume that the shaft has a constant diameter d. The pulley at location A is keyed to the shaft between the roller bearings at O and B and the pulley at location C is keyed on the overhanging part of the shaft. During power transmission, the two pulleys are subjected to the static loads FA 400 lb and Fc-1600 lb (note that both loads are acting in the yz plane and are not tangential to the pitch circles of the pulleys). Assume that the bearings act as simple supports for the shaft and the weights of the shaft and the pulleys can be neglected 16 6 Pulley A 20 D 30° FA Pulley C 5 D 30°PART I. (i) Draw the free body diagrams, the shear force diagrams, and the bending moment diagrams for the shaft. Note that these diagrams must be drawn in both the xy plane and the xz plane. Also, draw the torque diagram for the shaft. (ii) From the diagrams in part (i) determine the location of the critical section of the shaft. (iii) Sketch the stress pattern on the critical section and label the stress magnitudes. (iv) Determine the location of the critical element at the critical section of the shaft. (v) Draw the critical element and label the state of stress on this element. (vi) Determine the principal stresses (normal and shear) acting on the critical element. PART II Determine the diameter of the solid circular shaft that will ensure that the critical element of the shaft has a static factor of safety n-3 for the following two scenarios: (i) Assume that the shaft material is UNS G10400 cold drawn steel having a tensile yield strength Svt -70 kpsi and an ultimate tensile strength Sut -85 kpsi. Since the material is ductile then use the von Mises (or distortion energy) theory of failure. Compare your answer with at least one other static theory of failure (ii) Assume that the shaft material is ASTM 60 cast iron having an ultimate tensile strength Sut-65 kpsi and an ultimate compressive strength Suc-200 kpsi. Since the material is brittle then use the Coulomb-Mohr theory for static failure.

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