Using simple stress analysis techniques $($Euler$-$Bernoulli theory$),$ predict the magnitudes of the deflection $($Macaulay$\text{'}$s method$),$ neutral axis location, second moment of area, axial bending stresses at the strain gauge locations on the T$-$beam and bending moment along the beam.

Figure $3$ Schematic sketch of $($a$)$ T$-$beam loading and reaction positions and $($b$)$ T$-$beam cross$-$section and strain gauge positions

Density: $2770$ kg$/$m$3$ Young$$s Modulus: $69$ GPa Poisson$$s Ratio: Yield Strength: $0\mathrm{.}33270$ MPa Tangent Modulus: $500$ MPa

Deflection Recording table for T$-$beam in mm $\backslash$begin$\{$tabular$\}\{|$c$|$c$|\}$

$\backslash$hline $\backslash$begin$\{$tabular$\}\{$c$\}$

Total Load $\backslash \backslash$

$\backslash (\backslash$mathbf$\{$N$\}\backslash )$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Distance $\backslash (\backslash$mathbf$\{300\}\backslash )\backslash \backslash$

$\backslash (\backslash$mathbf$\{$m m$\}\backslash )$

$\backslash$end$\{$tabular$\}\backslash \backslash$

$\backslash$hline $\backslash (\backslash$mathbf$\{0\}\backslash )$ & $0\backslash \backslash$

$\backslash$hline $\backslash (\backslash$mathbf$\{200\}\backslash )$ & $0\mathrm{.}56\backslash \backslash$

$\backslash$hline $\backslash (\backslash$mathbf$\{400\}\backslash )$ & $1\mathrm{.}11\backslash \backslash$

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$\backslash$end$\{$tabular$\}$