(Solved): 2.31 The engineering strain matrix at a particular point in a structure is []eng= ...

2.31 The engineering strain matrix at a particular point in a structure is $[?{]}_{\text{eng }}=?\begin{array}{lll}{?}_x& {?}_{xy}& {?}_{xz}\\ {?}_{yx}& {?}_y& {?}_{yz}\\ {?}_{zx}& {?}_{zy}& {?}_z\end{array}?=?\begin{array}{rrr}?4& 0& 2\\ 0& 3& ?2\\ 2& ?2& ?1\end{array}?\times 10^{?4}$ Determine the engineering strain matrix relative to a coordinate system defined by first rotating the $xyz$ coordinate system $?30^{?}$ about the $x$ axis, then rotating $40^{?}$ about the new $y$ axis.