Part A $-$ Maximum shear loadsecuring 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.

Learning Goal

To calculate the 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 l$-$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 beam is built up using plates,

the fasteners used must be able to resist the shear at the joints. The

loading resisted by the fasteners can be described in the force per unit

length of the beam and is called the shear flow.

The shear flow at some distance $y$ from the neutral axis can be

calculated using the shear formula $q=\frac{VQ}{\text{I}},$ where $V$ is the shear

force, $Q$ is the moment about the centroidal axis of the cross$-$sectional

area above $y,$ and I is the moment of inertia of the cross section.

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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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 $w=820l\frac{b}{f}t?$

Express your answer with appropriate units to three significant figures.

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 $210lb?$

Express your answer with appropriate units to three significant figures.

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.

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 $w=820l\frac{b}{f}t?$

Express your answer with appropriate units to three significant figures.

Part C $-$ Maximum nail spacing

Express your answer with appropriate units to three significant figures.