Determine the LRFD design strength and the ASD allowable strength for a W$12$x$65($ASTM A$992)$ column with L$=35$ ft with a fixed support at top and pinned support at bottom.

a$)$ Determine whether the section is slender or nonslender.

b$)$ Calculate the LRFD and ASD strengths using the equations of AISC Section E$3.$

c$)$ Using critical stress values in Table $4-22$ of the AISC Manual, determine the LRFD and ASD strengths and compare with part b$).$

d$)$ Repeat the problem using Table $4-1$ of the AISC Manual and compare with parts b$)$ and c$).$

e$)$ If supports are added to brace the column in the weak axis only at $10$ ft and $20$ ft from the bottom support, determine the new LRFD and ASD strengths using the critical stress values in Table $4-22.$ Repeat the problem using Table $4-1$ of the AISC Manual. Discuss how the added braces affected the column strength.