Review the derivation for each of the following mechanics of materials formulas and summarize the major steps or elements in the derivation. Define each term in the expression, and list the major assumptions and limitations for each expression. (a.) normal stress in an axial bar:  = P/A (b.) normal stress in a beam in bending:  = Mc/I (c.) shear stress in a bar in torsion:  = Tr/J (d.) shear stress due to transverse shear load:  = VQ/Ib

Agas contained within a piston-cylinder assembly e end nation about same energy states, 1 and 2, where pi 10 bar, v undergoes two processes, a and b, between the sam 0.1 m3, ui-400 kj and p2 1 bar, v2 1.0 m2, u2 200 kj: process a: process from 1 to 2 during which the pressure- volume relation is pv constant process b: constant-volume process from state 1 to a pressure of 2 bar, followed by a linear pressure-volume process to +20 0 state 2 kinetic and potential energy effects can be ignored. for each of the processes a and b, (a) sketch the process on p-v coordinates, (b) evaluate the work, in kj, and (c) evaluate process the heat transfer, in kj