The displacement field in a rectangular beam bent by end couples is shown below. The

beam initially occupied the rectangular region $0xL($length$),-cyc($depth$)$

and $-bzb($width$),$ the centreline has been bent to radius of curvature $R.$

$u_x=\frac{1}{R}xy+my+nz+p$

$u_y=-\frac{1}{2R}[x^2+$var$(y^2-z^2)]-mx+az+c$

$u_z=-\frac{1}{R}$var$yz-ay-nx+b$