A steel tube of $80-mm$ outer diameter is to carry a $165-kN$ load $P$ with an eccentricity of $15mm.$ The tubes available for use are made

with wall thicknesses in increments of $3mm$ from $6mm$ to $15mm.$ Using the interaction method and an allowable stress in bending of

$150$MPa, determine the lightest tube that can be used. Assume $E=200$GPa and ${}_Y=250$MPa.

The lightest tube that can be used should have a thickness of

mm$.$