pls answer asap PLS An engineer is currently tasked with designing a steel beam which is to support a flooring system above it$.$

The weight af the flooring system will act as a distributed load aver the length of the beam, which in turn will

cause the beam to bend, and deflect. It is your task to check that the crass$-$section suitable subject to the design constraints givenc both "Strength" and "Serviceability".

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The length of the beam between supports is $L=4m.$ The Young's modulus of the material is $E=200$ GPa

The beam rests on supporting joists, which may be madelled as roller supports in our analys is as they only

constrain motion of points A and $B$ in the vertical direction. Since there are no lateral loads acting on the

Units of Design

Firatly, we calculats the limita for our disign wilch nead to be astigrse.

strensth

The following is an extract from Table C$.1$ in the Australian$/$New Zealand Standards for Structural Design

actians $($AS$1170\mathrm{.}0)$:

This extract from the table provides limits for deflections for various structural components to satisfy

serviceability. In this case, we are intere occurrence of 'sagging' of the beam.

Therefore we need to ersure the defiection of the mid$-$span of the beam is below "Span$/300",$ where span

$v_{\text{a}\text{l}\text{l}\text{o}\text{w}}=\frac{L}{300}=,nm$

The only unknown in your expression should be $x.$ Please enter exact known values of all other parameters $($use fractions rather than decinals$)$

$($use fractions rather than decimals$)$

Strength Analysis

:

$b=140mm$

$d=200m$

$b=140mm$ :$d=200mmt=35mm$

With reference to the origin shown above, what is the vertical coordinate of the centroid for this cross$-$

sectian: $\frac{?}{\text{b}\text{a}\text{r}}(y)$: What is the second moment of area about the horizontal axis passing through the centroid: For a linear elastic material, the depth of the centroid is also the depth of the neutral axis. $,Nm$

What is the largest magnitude of stress due to bending acting on the cross$-$section $($caleulate stress at

${}_{\text{m}\text{a}\text{x}}=,$MPa

Does this stress satisfy the design constrain for strength? $max<mi></mi>$ allow

$]$

Serviceability Analygis

Next, calculate the defiection of the beam at the mid$-$span due to the lads using the "integration' approach

taught in class. The cross$-$section is the l$-$beam shown earlier.

is re ststed to currature sccording to:

$\frac{d^{2}v}{d{x}^2}=\frac{1}{EI}*M(x)$

$\frac{dv}{dx}=\frac{1}{EI}$

The only unksowns in your expression should be

Integrate beam:

$v=\frac{1}{EI}$

The only unknowns in your expression should be $x$ and $C_1$ and $C_2.$ Please enter exact known values of