$62$

a$)$ Draw and explain the stress$-$strain diagram for a mild steel material.

b $)$ Obtain a relation for change in length of a bar hanging freely under its own weight.

c$)$ A steel rod $20$ mm diameter and $4$ m long is connected to two grips and the rod is maintained at a temperature of $30\backslash$deg C$.$ Determine the stress and pull exerted when the temperature increases to $60\backslash$deg C If the ends do not yield.

d$)$ A bar of $35$ mm diameter is subjected to a pull of $65$kN$.$ The measured extension on gauge length of $190$ mm is $0\mathrm{.}075$ mm and the change in diameter is $0\mathrm{.}028$ mm$.$ Calculate the value of Poisson's ratio and the three moduli.

e$)$ Draw the SFD and BMD for a cantilever beam subjected to concentrated load at free end.

f$)$ Explain the theorem for conjugate beam method.

g$)$ Derive equation for pure bending with usual notations.

h$)$ Demonstrate Moment area method with an example.

i$)$ Show that maximum shear stress in a beam of rectangular section is $1\mathrm{.}5$ Qaverage

J$)$ Derive an expression for strain energy stored in a body due to torsion.

k$)$ Distinguish between flexural rigidity and torsional rigidity.

$1)$ Derive the Euler's buckling load for a column with one end fixed and other hinged.