Part A $-$ Critical load for column $AB$

Learning Goal:

To analyze an ideal column with pin supports, determine the critical load and critical stress on the column, and determine the maximum applicable distributed load on the system.

As shown, beam $BC$ is supported by columns $AB$ and $CD$ and has length $L_w=21\mathrm{.}0ft.$ Both columns have the cross section shown and have lengths of $L_h=19\mathrm{.}5ft.$ Let $a=7\mathrm{.}50in,b=0\mathrm{.}75in,c=12\mathrm{.}00in,$ and $d=3\mathrm{.}00$ in$.$ Assume $E=27000$ksi. Column $AB$ is pinned at both ends.$($Figure $1)$

Determine the critical load, $P_{cr},$ that column $AB$ can support. Note that the columns are pinned in such a way to only allow bending in the $y-$direction.

Express your answer to three significant figures and include the appropriate units.

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$P_{cr}=$

Part B $-$ Critical stress for column $AB$

Determine the critical stress, ${}_{cr},$ that column $AB$ can support. Note that the columns are pinned in such a way to only allow bending in the $y-$direction.

Express your answer in psi to three significant figures.

View Available Hint$($s$)$

$\sqrt[7]{0}$

$A$

It

vec

$?$

${}_{cr}=$

psi

Part C $-$ Maximum applicable distributed load $w_{\text{m}\text{a}\text{x}}$

Figure

$1$ of $1$

Given the critical load for the column $AB,$ determine the maximum applicable distributed load that can be applied to the beam $BC$ assuming that column $AB$ will fail before column $CD$

Express your answer in $ki\frac{p}{f}t$ to three significant figures.

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