Online Weekly Assignment $-$ Week One

$An$ engineer $is$ currently tasked with designing a steel beam for a frame which $isto$

support a roofing system above $it.$ The weight $of$ the roofing system will act $asa$

distributed load over the length $of$ the beam, which $in$ turn will cause the beam $to$

bend. $Itis$ your task $to$ determine the most suitable cross$-$section for this beam

subject $to$ the design constraints given

From the manufacturer, there $is$ a selection $of$ cross$-$section types $to$ choose from,

$as$ shown below. All beams are made from the same steel material.

The design constraint $to$ satisfy here $is$ serviceability. Satisfying serviceability

constraints ensure that deformations $of$ a structural $or$ mechanical member $do$ not

exceed critical values that would prevent them from performing their desired

function. $In$ this case, $we$ wish $to$ minimise any deflections due $to$ bending $as$ much

$as$ possible.

Note: $We$ will learn later $in$ Week $7$ that the magnitude $of$ deflections due $to$ bending

are inverselyproportional $to$ the 'flexural rigidity' $of$ a mechanical member. The

flexural rigidity $is$ given $byEI,$ where $Eis$ the Young's modulus $of$ the material, and I $is$

the second moment $of$ area measured about the axis $of$ which bending $isto$ occur

Which $of$ the following cross$-$sections should the engineer select $to$ satisfy the design

constraint? Work through the following problem $to$ make your selection.

Cross$-$Section $A(Channel$ Cross$-$Section$)$

The first cross$-$section $is$ what $is$ often referred $toasan$ open 'channel' cross$-$

section. The dimensions are given $as$:

$-b=190mm$

$-d=270mm$

$-t=20mm$

b

With reference to the origin shown above, what are the coordinates of the centroid

for this cross$-$section:

$\stackrel{}{x}=$

$\frac{?}{\text{b}\text{a}\text{r}}(y)$

What is the maximum and minimum second moment of area about axes passing

through the centroid:

$I_{\text{m}\text{a}\text{x}}$

$I_{\text{m}\text{i}\text{n}}$

Cross$-$Section D $($L$-$Section$)$

The final cross$-$section to consider is the $"$L$-$section" shown below. The dimensions

are given as:

$b=190mm$

$d=270mm$

origin shown above, what are the coordinates of the centroid With reference to the orid

$*\stackrel{}{x}=,nm$

$\frac{*}{b}ar(y)=,nm$

What is the maximum and minimum second moment of area about axes passing

Selection of Cross$-$Section for Design:

Which of the cross$-$sections will be most suitable for the design constraint given

$($minimising any deflections of the beam due to bending

$($No answer given

$($No answer given$)$

Cross$-$Section A: Channel Section

Cross$-$Section B: T$-$Section

Cross$-$Section D: L$-$Section