HW $11$ Euler Buckling Load

Problem $1.$ Column Buckling

Given:

$-$ The AISC database.

$-$ A $24-$foot$-$long column is simply supported at the top and bottom, and subjected to an axial load of $350$ kips $.$ There is no moment applied to the column. $\backslash (\backslash$mathrm$\{$E$\}\_\{\backslash$text $\{$steel $\}\}=29,000\backslash$mathrm$\{$ksi$\}\backslash ).$

Find:

a$)$ Calculate the minimum area for the condition described.

b$)$ Choose the most efficient $\backslash ($ W $\backslash )$ section with a maximum depth of $14\mathrm{.}5$ inches, such that the allowable compressive stress of $36$ ksi is not exceeded.

c$)$ Report for your chosen member:

a$.$ Area

b$.$ strong and weak values of the moment of inertia, I

c$.$ strong and weak values of the radius of gyration, $\backslash ($ r $\backslash ).$

d$)$ Determine the slenderness ratio for this member. Based on this, would this member buckle?

e$)$ Calculate what the Euler buckling load is for this column. Based on this, would this member buckle?

f$)$ If the column is braced in the center, what is the buckling load? Based on this, would this member buckle?

$9)$ For a W$14$X$34$ W section, with the applied axial load of $250$ kips, what is the axial shortening?

Recall:

$\backslash [$

$\backslash$Delta$=\backslash$frac$\{$P L$\}\{$A E$\}$

$\backslash ]$