Learning Goal

make a built$-$up shear stress at the web$/$flange joint in a beam and use that stress to calculate the required nail spacing to make a built$-$up beam.

A built up beam can be constructed by fastening flat plates together. When an I$-$beam is subjected to a shear load, internal shear stress is developed at every cross section, with longitudinal shear stress balancing transverse shear stress. If the ples the fasteners used must be able to resist the shear at the joints. The loading resisted by the

The shear flow at some distance $\backslash ($ y $\backslash )$ from the neutral axis can be calculated using the shear formula $\backslash ($ q$=\backslash$frac$\{$V Q$\}\{$I$\}\backslash ),$ where $\backslash ($ V $\backslash )$ is the shear force, $\backslash ($ Q $\backslash )$ is the moment about the centroidal axis of the cross$-$sectional area above $\backslash ($ y $\backslash ),$ and $\backslash ($ I $\backslash )$ is the moment of inertia of the cross section.

Figure

$<mtext></mtext><mn>1</mn>$ of $1$

securing the flanges to the web. The flanges are $6$ in wide and $1$ in thick. The web has depth $18$ in and thickness $3$ in$.$ The maximum allowable shear stress in the web is $900$ psi $.$

Part A $-$ Maximum shear load

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

Express your answer with appropriate units to three significant figures.

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$\backslash [$

V$\_\{\backslash$max $\}=\backslash$text $\{$ Value $\}\backslash$quad $\backslash$mid $\backslash$text $\{$ Units $\}$

$\backslash ]$

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$=895\backslash$mathrm$\{$lb$\}/\backslash$mathrm$\{$ft$\}\backslash )?$

Express your answer with appropriate units to three significant 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 $250$ lb $?$

Express your answer with appropriate units to three significant figures.

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