Learning Goal: Part C $-$ Maximum Distributed Load

Determine the maximum uniform distributed load $w$ that can be applied to the $W1214$ beam shown below if the maximum allowable bending stress is ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=30$ksi and the maximum allowable shear is ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=16\mathrm{.}7$ksi. The

distance between the supports is $20$ ft $.$

$($Figure $3)$

The geometric properties of the beam are listed in the table below.

Express your answer to three significant figures.

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To know how to use shear and bending$-$moment diagrams to determine the design requirements

of a steel beam used to support a loading.

When designing a steel beam to support a given loading. engineers often use bending

characteristics as the primary criterion; shear characteristics are then taken into account, and, if

multiple available designs are still viable, weight and cost are then considered to complete the

specification.

The bending design consideration requires the calculation of the beam's section modulus. This is

a property based solely on the geometry of the beam, specifically the moment of inertia and the

centroid:

$S=\frac{\text{I}}{c}.$

Once a loading is specified, we can use the flexure formula with the maximum bending moment,

$M_{\text{m}\text{a}\text{x}},$ to specify a lower bound on the section modulus:

$S_{\text{r}\text{e}\text{q}\text{u}\text{i}\text{r}\text{e}\text{d}}=\frac{M_{\text{m}\text{a}\text{x}}}{{}_{\text{a}\text{l}\text{l}\text{o}\text{w}}}$

Where the maximum bending stress, ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}},$ is a parameter generally given in the design

specifications

The shear specification,

${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}\frac{V_{\text{m}\text{a}\text{x}}Q}{It}$

is generally less specific than the bending$-$moment specification, so it is used as the secondary

design consideration

Part A $-$ Design a Circular Shaft

Determine the minimum allowable diameter of the circular shaft to the nearest millimeter if the design parameters require ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=4\mathrm{.}5$MPa and ${}_a$ allow $=500$kPa. The bearings at A and $D$ exert only vertical reactions on the

shaft. $($Figure $1)$

Express your answer to the nearest tenth of a millimeter.

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Previous Answers

Correct

Part B $-$ Determine Necessary Beam Width

Determine the minimum width, $w,$ of the beam that will safely support the loading $P=5$kip. The beam is $40$ ft long from the pin support to the point where $P$ is applied, $6$ in tall, has a rectangular cross$-$section, and made of a

material that has a maximum allowable bending stress of ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=26$ksi and a maximum allowable shear stress of ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=0\mathrm{.}5$ksi. $($Figure $2)$

Express your answer to three significant figures.

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$w=$

in