PROBLEM $\backslash$# $3[25$ points$]$

Given: The spread footing depicted in Figure $1.$

Find: Determine the maximum capacity of the footing found in an older building based on the limit states of soil bearing, shear $(1-$way and $2-$way$),$ and flexure if the axial load is assumed to remain within the kern $(\backslash (\backslash$mathrm$\{$e$\}\backslash$leq $\backslash$mathrm$\{$L$\}/6\backslash )).$ Clearly indicate all assumptions and which of the four limit states governs.

Notes to accompany Figure $1.$

$-$ All concrete has $\backslash (\backslash$mathrm$\{$f$\}\_\{\backslash$mathrm$\{$c$\}\}\{\}^\{\backslash$prime$\}=4000\backslash$mathrm$\{$psi$\}\backslash )$

$-$ Steel is Grade $50(\backslash ($ f$\_\{$y$\}=50\backslash$mathrm$\{$ksi$\}\backslash ))$

$-75$ psf factored floor load applied to slab$-$on$-$grade

$-$ Allowable soil bearing capacity is $5500$ psf

$-$ Soil unit weight is $125$ pcf