$1.$ Use the textbook Appendix $4,$ Allowable Buckling Stress Table, and select an economical

A$36$ steel wide flange section to serve as the columns to support a $15$ long beam carrying

a combined uniform rectangular load of $12,000$ plf and a $50-$kip concentrated load placed

at mid$-$span. The column is $12$ tall and is considered pinned at the top and bottom.

Hint: the column is pinned at the top, so there is no moment at the connection of the column and

the beam.

$2.$ Find the allowable load, Pall, for an A$36$ steel HP$13$x$60$ column that is $16$ tall, fixed top

and bottom, and braced at mid$-$height in the weak direction. Use the Allowable Buckling

Stress table found in Appendix $4$ of the textbook.

Hint: $1.)$ Since the column is braced mid$-$height in the weak direction, calculate the slenderness

ratio $($SR$)$ for both the strong and weak direction. The direction with the largest SR will govern. $2.)$

Also, remember that due to bracing in mid$-$height the length will be reduced to half i$.$e$.,$ L$/2$ in the

weak direction.