Problem $1$

A cast iron pipe has an inside diameter of $d=208mm$ and an outside diameter of $D=236mm.$ The length of the pipe is $L=3\mathrm{.}0m.$ The coefficient of thermal expansion for cast iron is $=12\mathrm{.}1\frac{{10}^{-6}}{}C.$ Determine the dimension changes caused by an increase in temperature of $70C.$

Problem $2$

A standard ASTM tension specimen $($diameter $=d_0=0\mathrm{.}505$ in$.,$ gauge length $=L_0=2\mathrm{.}0$ in$.)$ was used to obtain the load$-$elongation data given in the table. Plot a curve of engineering stress, $,$ versus engineering strain, $,$ using the given data.

$\backslash$table$[[$Tensile Test Data$],[P($kips$),L($in$)],[1\mathrm{.}9,0\mathrm{.}0020],[3\mathrm{.}8,0\mathrm{.}0040],[5\mathrm{.}7,0\mathrm{.}0060],[7\mathrm{.}6,0\mathrm{.}0080],[9\mathrm{.}0,0\mathrm{.}0100],[9\mathrm{.}5,0\mathrm{.}0120],[10\mathrm{.}0,0\mathrm{.}0145],[10\mathrm{.}4,0\mathrm{.}0180],[10\mathrm{.}65,0\mathrm{.}0240],[11\mathrm{.}00,0\mathrm{.}0300],[11\mathrm{.}05,0\mathrm{.}0360]]$

Problem $3$

The rigid beam supports a load of $60kN.$ Determine the displacement at $B.$ Take $E=60$GPa, and $A_{BC}=2**{10}^{-3}{m}^2.$