A simply supported steel beam has a concentrated moment MA = 150 N·m applied at the left support and a concentrated force F = 500 N applied at the free end of the overhang on the right. Using singularity functions, determine the deflection midway between the supports and at C. Let L = 0.4 m, a = 0.4 m, and I = 2×10–8 m4.

Aturning operation is performed with following conditions: rake angle of 12°, a feed of 0.35 mm/rev, and a depth of cut of 1.1 mm. the work piece is aluminum alloy 6061 with t6 heat treatment (a16061-t6). the resultant chip thickness was measured to be 1.0 mm. estimate the cutting force, fc. use shear stress of 207 mpa and coefficient of friction on the tool face of 0.6.