An engineered wood beam $($Figure $1)$ will replace a portion of a structural wall as part of a house renovation. The beam can be modeled as a simply supported beam with a span $\backslash ($ L$=9\backslash$mathrm$\{$~m$\}\backslash )$ and an uniform distributed load $\backslash ($ w$=4\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}\backslash ).$ The beam is to be constructed as an I$-$bearn with nails securing the flanges to the web. The flanges are $150$ mm wide and $25$ mm thick. The web has depth $450$ mm and thickness $75$ mm $.$ The maximum allowable shear stress in the web is $6$ MPa $.$

Part A $-$ Maximum shear load

Assuming the joints do not fail, what is the maximum shear load the beam can support?

Expresa your answer with appropriate units to three algnificant figures.

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Part B $-$ Shear flow at joint

What is the maximum shear flow at the joints connecting the web and flange under the applied load of $\backslash ($ w$=4\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}\backslash )?$

Exprese your answer with approprlate units to three algnificant figures.

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Part C $-$ Maximum nail spacing

Since the nails are joining the flanges to the web, they must resist the shear flow at the joint. What is the maximum spacing for the nails if each nail can support a shear force of $990$ N $?$

Expresa your anawer in millimeters to three algnificant figurea.

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s$=\backslash$mid $\backslash$quad $\backslash$mathrm$\{$mm$\}$

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