Textbook Problem $4\mathrm{.}7-$A $($HW to practice$)$

An HSS $128\frac{1}{2}$ made with preferred steel is used as a column as shown in the pictures below. Both of the pictures show the same column at two perpendicular elevation views. Please note the orientation of the column member in the two pictures. The total length is $16$ feet. Each beam to column connection is pinned, and the column base is the typical gravity column base $($look for what support condition is this in the notes$).$

a$.$ Determine the design strength using LRFD AISC spec equations.

b$.$ Determine the allowable strength using ASD AISC spec equations.

c$.$ Repeat the same problem $(a$ & b$)$ using AISC Manual Table $4-14.$

d$.$ Repeat the same problem $(a$ & b$)$ using AISC Manual Table $4-3.$

e$.$ Check the local slenderness of the column. Call the flat element in short dimension as flange and the flat element in long dimension as web. Hint: see more practices in question #$3$ and class note Section $4\mathrm{.}4.$

Answer key: a$.$ Design strength $={}_c{P}_n=674$ kips; b$.$ Allowable strength $=\frac{P_n}{{}_c}=448$ kips