An I$-$beam has a flange width $\backslash ($ b$=400\backslash$mathrm$\{$~mm$\}\backslash ),$ height $\backslash ($ h$=400\backslash$mathrm$\{$~mm$\}\backslash ),$ web thickness $\backslash ($ t$\_\{$w$\}=13\backslash$mathrm$\{$~mm$\}\backslash ),$ and flange thickness $\backslash ($ t$\_\{$f$\}=21\backslash$mathrm$\{$~mm$\}\backslash ).$ Use the following steps to calculate the shear stress at a point $100$ mm above the neutral axis.

Part A $-$ Moment of inertia

The shear formula includes the moment of inertia of the whole cross section, $\backslash ($ I $\backslash ),$ about the neutral axis. Calculate the moment of inertia. Express your answer with appropriate units to three significant figures.

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Part B $-$ Q for the given point

The shear stress $100$ mm above the neutral axis depends on the value of $\backslash ($ Q $\backslash )$ for the area above that point. Calculate the value of $\backslash ($ Q $\backslash ).$ Express your answer with appropriate units to three significant figures.

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You used the wrong thickness for the web part.

You may want to review Hint $3.$ Contribution from the web.

Part C $-$ Shear stress

Use the results from Parts A and B to calculate the shear stress at a point $100$ mm above the neutral axis if the shear force on the section is $\backslash ($ V$=7\mathrm{.}8\backslash$mathrm$\{$kN$\}\backslash ).$

Express your answer with appropriate units to three significant figures.

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