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(Solved): Consider the shaft shown (Figure 1) that has a diameter d=4.6cm. The length of each segment is L=3m ...



Consider the shaft shown (Figure 1) that has a diameter d=4.6cm. The length of each segment is L=3m and the loads P=1.9kN are applied horizontally and vertically as shown. The Learning Goal: To use the principle of superposition to calculate the bending stress in a circular shaft subject to bending along two perpendicular axes. The flexure formula \sigma =(My)/(I) only applies when the bending occurs about axes that are principal axes of inertia for the cross section of the beam. When a moment acts about a different axis, it must be resolved into components that are parallel to the principal axes. Then the principle of superposition can be used to determine the bending stresses due to the moment. A similar situation occurs when multiple loads are applied to a beam or shaft that are not in the same plane. For a circular shaft, the moment of inertia does not depend on the orientation of the axes. In this case, any convenient axes can be chosen as the principal axes. The angle of the resulting moment can be established using M_(z)=Mcos\theta and M_(y)=Msin\theta , where \theta is the angle between the moment and the z-axis. Once the moments about the principal axes are known, the angle of the neutral axis can be established. The direction of the neutral axis is related to this angle by tan\alpha =(I_(z))/(I_(y))tan\theta . For a circular section, this leads to \alpha =\theta . Part C - Maximum bending stress Use the results of Part A and Part B to calculate the magnitude of the maximum bending stress at point C. Figure 1 of 1 Express your answer with appropriate units to three significant figures. View Available Hint(s)


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