A concrete column with dimensions shown below.$$ The column must support the load in lbs$.$ noted on the drawing below.$$ If you plan to support this column with a square concrete footing resting on soil that can resist $80$ lb$/$sq$.$ inch $($including an appropriate safety factor$),$ what is the dimension of the footing $($f$)($inches$).$ Calculate the dimension f to the nearest inch $($see the figure below$).$If your calculated answer is $22\mathrm{.}13$ inches enter $22.$If you are within $+/-2\mathrm{.}5\%$ of the correct answer you well receive full credit.$$Bonus Question Column Dimensions dx d $($inches$)$

Footing Dimensions fxf $($inches$)$

Column Loading $=200,000$ lbs$.$

the size of the foundation footing to the cross$-$sectional area of the column. In engineering design, an appropriate safety factor, typically $\backslash (300\backslash \%\backslash ),$ is included in our calculation to insure against the unforeseen. Soils, unlike manufactured and engineered materials, are hardly homogenous in nature. In foundation design, safety factors can be several multiples. In our example, we will require a cross$-$sectional area of $\backslash (4,000\backslash$mathrm$\{$sq$\}\backslash ).$ inches of surface to distribute the column loading of $\backslash (400,000\backslash$mathrm$\{$lbs$\}\backslash ).$ In this example, a column footing of $\backslash (63\mathrm{.}25\backslash$times $63\mathrm{.}25\backslash )$ inches should be adequate. The engineering solution is to provide a mechanism for distributing our load over a greater area. In the past, a pyramid form was used to distribute this load $($Figure $2\mathrm{.}8).$ During the $19$th century, rafts made from used railroad ties buried in concrete were used to distribute the column loading; today, we can use reinforced concrete to solve this problem. Formwork, with carefully placed steel reinforcing bars, creates an homogeneous and continuous structure that transmits the column loads to the bearing material just below the foundation $($Figure $2\mathrm{.}8).$

Continuous footings can also be used to support an entire bearing wall. Usually found at the perimeter of the basement wall, a continuous footing has a cross$-$section similar to the reinforced concrete footing $($Figure $2\mathrm{.}8).$ Spread footings are useful when the bearing wall supports a significant portion of the weight from the floors and roof structure. When Foundation design

The simplest of foundations are spread footings. Used for centuries, spread footings take the loading from the columns and distribute it over a larger surface area $($Figure $1\mathrm{.}8).$ In this way, the foundation does not overburden the substrate beyond its bearing capacity or safe limit$.$ For example, a building with column loads at the foundation of $400$ kips $($equivalent to $\backslash (400,000\backslash$mathrm$\{$lbs$\}\backslash ))$ may be easily handled by a concrete column measuring $\backslash (10\backslash$times $10\backslash )$ inches $($a cross$-$sectional area of $100$ sq$.$ inches$).$ With a working stress level of approximately $\backslash (4,000\backslash$mathrm$\{$psi$\}\backslash ),$ there is a significant safety factor designed into these columns. However, if the soil substructure is able to support a maximum of only $100$ psi $($including an appropriate safety factor$),$ a column placed directly on the soil will exceed its safe limit and we can expect the building to settle or possibly collapse over time. To solve this problem, we will need to spread this load over a greater area. In this case, we need at least a ratio of $\backslash (40$: $1\backslash )$ in