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# Question 4. The figure (not drawn to scale) shows a cylindrical column submitted to a combined load: bending and torsion. The column contains an hemispherical groove of radius $r$, located at a distance $L$ form the point of application of the force. You are given the column diameter $D=44 \mathrm{~mm}$, the groove radius $r=6 \mathrm{~mm}$, the distance $L=250 \mathrm{~mm}$, the bending load $P=110 \mathrm{kN}$, and the torque $T=1500 \mathrm{~N} . \mathrm{m}$. The material data are Young's modulus $E=208 \mathrm{GPa}$ Shear Modulus $G=92 \mathrm{GPa}$ Poisson's ratio $\nu=0.13$ and Yield strength $\sigma_{Y}=600 \mathrm{MPa}$. Important note: this is an open book design problem, and you might need to use data not provided in the text of the question but available on the module's blackboard site. Conversely, some of the data provided might not be needed. a) Write a numbered list of the calculation steps required to obtain the factor of safety in yielding based on the maximum energy (Von Mises) criterion. Enter your answer in the box below. (10 Marks) b) Calculate the factor of safety in yielding based on the maximum energy (Von Mises) criterion. The answer is acceptable within a tolerance of 0.01 . F.O.S. : (15 mark) correct answer please with solution  