Learning Goal:

To determine the maximum shear force that can be applied to two shafts of varying cross sections: a solid square shaft and a hollow square shatt.

The two square cross sections shown below $($Figure $1)$ are each subjected to a vertical shear force, $V.$ The side length of each cross section is $s=5\mathrm{.}00$ in and the side length of the hollowed$-$out portion of the second cross section is $r=3\mathrm{.}50$ in$.$ The maximum allowable shear stress in each member is ${}_{\text{m}\text{a}\text{x}}=19\mathrm{.}0$ksi.

Figure

$1$ of $3$

Part A $-$ Moment of the area $A^{\text{'}}$ about the neutral axis of the solid square shaft

One of the first steps in analyzing the geometry of the solid square shaft is to determine the moment of the area $A^{\text{'}}$ about the neutral axis of the entire cross section. This value is denoted by $Q.$ What is $Q?($Figure $2)$

Express your answer to three significant figures and include appropriate units.

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Part B $-$ Moment of the area $A^{\text{'}}$ about the neutral axis of the hollow square shaft

One of the first steps in analyzing the geometry of the hollow square shaft is to determine the moment of the area $A^{\text{'}}$ about the neutral axis of the entire cross section. This value is denoted by $Q.$ What is $Q?($Figure $3)$

Express your answer to three significant figures and include appropriate units.

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$$

$Q=$

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Part C $-$ Maximum applicable shear force on the solid square shaft

Part D $-$ Maximum applicable shear force on the hollow square shaft

Please Answer part A$,$ B$,$ C and D

Thanks!