Problem $3(25\%)$

The reinforced concrete column in the figure has a rectangular cross section. The column is subjected to $80$

kips of axial compressive force at its top in addition to a uniform lateral load along the top $6ft$ of the column

height. The unit weight of concrete is $150pcf$ and the specified concrete strength, $f_c$ is $3,000.$ Do the

following:

$($a$)$ Draw the axial force and bending moment diagram of the column, show the bending moment in terms

of the lateral load w$.$

$($b$)$ If the lateral load is increased sufficiently to cause cracking in the column, where along the column is

the cracking most likely to occur? Draw the expected crack pattern.

$($c$)$ The lateral load $w$ is increased until cracking occurs in the column. What is the value of the uniform

lateral load at which the column cracks? $($Hint: Remember that the axial compressive force and column

self$-$weight increases the compressive stress in the column$)$