Question $3$

$(20$ Marks$)$

A beam with a T section has a flange with $($base $=0\mathrm{.}05m$ and height $=0\mathrm{.}01m)$ and a web with $($base $=0\mathrm{.}01m$ and height $=0\mathrm{.}1m).$ Respond to the following questions:

Question $3$a:

Find the centroid $($measured from the bottom edge of the section$).$

$(5$ marks$)$

Question $3$b:

Calculate the second moment of area about the $x-x$ axis and $y-y.$

$(10$ marks$)$

Question $3$c: Find the maximum bending moment for this section. If the maximum bending stress is $15$ MPa $.$

$(5$ marks$)$

Question $3(15$ marks$)$

Question $3$a

The cross section of a column built up of a timber section $)$ is shown in Figure below.

The cross$-$section of the column is a rectangle with dimensions $120mm200mm.$

The column built into the ground has length, $L=2\mathrm{.}8m,$ and is under axial compressive load P $.$

Use $K_e=2\mathrm{.}0.$

Calculate:

i$.$ The critical $($Euler$)$ load to buckle the column.

$(5$ marks$)$

ii$.$ If the factor of safety is F$.$S$.=2\mathrm{.}0,$ what is the allowable buckling load?

$(2$ marks$)$

Question $3$b

The Universal Column $250$UC$72\mathrm{.}9$ is used to construct a column with height of $8$ m and fixed at base and pinned at top.

Determine the total critical $($Euler$)$ load. $Es=200$GPa

$(8$ marks$)$