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MENG $510$ : Stress Analysis Assignment No$.1$ Instructor: Ali Al Shaer

$*4-108.$ The bar having a diameter of $2$ in $.$ is fixed connected at its ends and supports the axial load $P.$ If the material is elastic perfectly plastic as shown by the stress$-$strain diagram, determine the smallest load $P$ needed to cause segment BC to yield. If this load is released, determine the permanent displacement of point $C.$

$4-109.$ Determine the elongation of the bar in Prob. $4-108$ when both the load $P$ and the supports are removed.

$5-130.$ The shaft is made of an elastic$-$perfectly plastic material as shown. Plot the shear$-$stress distribution acting along a radial line if it is subjected to a torque of $T=2kN*m.$ What is the residual stress distribution in the shaft when the torque is removed?

$8\mathrm{.}2$ Water is the working fluid in an ideal Rankine cycle. Superheated vapor enters the turbine at $10$MPa,$480C,$ and the condenser pressure is $6$ kPa $.$ Determine for the eycle

$($a$)$ the rate of heat transfer to the working fluid passing through the steam generator, in kJ per kg of steam flowing.

$($b$)$ the thermal efficiency.

$($c$)$ the rate of heat transfer from the working fluid passing through the condenser to the cooling water, in kJ per kg of steam fl

The curved beam is subjected to a bending moment of as shown. Determine the maximum compressive and tensile stresses in the section. Take M $=900$ N$.$m$,r_i=400mm,a=100mm,b=110mm,c=15mm,$ and $d=20mm.$