Conversion: $1$in$.=25\mathrm{.}4mm$;$1m=1000mm$;$1$MPa$=1$

$\frac{N}{m}{m}^2$;$1N=1kg**\frac{m}{s^2}$

Formulas: $f_c=$ Force$/$Area; Density$=$Mass$/$Volume;

Force$=$Mass$*$Acceleration

Density $=\frac{M_{\text{A}\text{I}\text{R}}}{M_{\text{A}\text{I}\text{R}}-M_{\text{W}\text{A}\text{T}\text{E}\text{R}}}**D_{\text{W}\text{A}\text{T}\text{E}\text{R}}$

Question $1$:

If concrete with a compressive strength of $25$ MPa is

used for a circular column to support a factored load of

$5\mathrm{.}75$ MN $,$ what diameter of column $($inches$)$ is required

to withstand the factored load?

Question $2$:

A rectangular column with dimensions of $16$ in$.$ x $18$

in$.$ will be constructed to support a balcony. The

calculated loads acting on the column equal $4400$ kN $.$

Using a factor of safety of $1\mathrm{.}25,$ determine the

compressive strength $($MPa$)$ required for the concrete

which will safely handle the factored loads.

Question $3$:

A $700$ mm diameter concrete column has a density of

concrete $2420k\frac{g}{m^3}$ and height of $3200$ mm $.$

Determine the dead load $($ kN $)$ exerted on the

foundation due to the mass of the column above.

Question $4$:

A$)$ In a lab, a core sample $($cylinder$)$ was weighed

first in air and then in water. Calculate the density

$(k\frac{g}{m^3}).$ Refer to Lab for density calculation.

Mass in air $(A)=13\mathrm{.}1kg$

Mass in

water $(B)=7\mathrm{.}8kg$

B$)$ Based on the density calculated, calculate the

diameter $($ mm $)$ of the cylinder knowing that the

length to width ratio is $2$:$1.$