Problem$-1$: A steel beam having a cross$-$section as shown below is being bent about major principal axis $(x-x.$ The beam is heavily welded longitudinally. Steel is Grade$320$ with $f_y=300$MPa and $E_s=200$GPa.

$($a$)$ Calculate the moment cause yielding $M_{yx}$ and the corresponding curvature.

$($b$)$ Determine the plastic moment capacity $M_{px}$ and the corresponding curvature; the steel strain at fracture is $60$ times the strain at yield.

$($c$)$ Determine the design section moment capacity $Ms{x}_{sx}.$

Problem$-2$: Determine the plastic moment capacity $M_{py}$ of the beam in Problem $-1$ if it is bent about the minor principal axis $y-$y and the corresponding curvature; the steel strain at fracture is $60$ times the strain at yield.

Problem$-3$: Determine the design section moment capacity of a welded circular hollow section having an outer diameter $(d_0)$ of $1500$ mm and wall thickness $($ t $)$ of $10$ mm $.$ Assume the yield strength of steel to be $360$ MPa $.$