Part $2$

Determine $Q_{\text{m}\text{a}\text{x}},$ the maximum value of the first moment of the area for the cross$-$section.

Answer: $Q_{\text{m}\text{a}\text{x}}=$

in$.{?}^3$

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Part $3$

Determine the maximum allowable shear force in the beam.

Answer: $V_{\text{m}\text{a}\text{x}}=$

lb

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Part $4$

Incorrect

It may be helpful to construct a shear$-$force diagram for the beam. See Example $7\mathrm{.}3.$ From that example, it is easy to

find an expression for this case for the maximum shear force $V_{\text{m}\text{a}\text{x}}$ as a function of distributed load $w.$ Substitute the

value of $V_{\text{m}\text{a}\text{x}}$ from Part $3$ of this solution and solve for the corresponding value of $w,$ which is $w_{\text{m}\text{a}\text{x}}.$

Determine the maximum allowable distributed load, $w.$

Answer: $w_{\text{m}\text{a}\text{x}}=$

$l\frac{b}{f}t$

eTextbook and Media Part $5$

Determine the shear force, $V,$ in the beam at $x=66$ in$.$ assuming the beam is subjected to the distributed load $w_{\text{m}\text{a}\text{x}}$ calculated in

Part $4.$

Answer: $V=$

$lb$

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Part $6$

Determine the first moment of the area at $H.$

Answer: $Q_H=$

in$.{?}^3$

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Part $7$

Incorrect

In Example $9\mathrm{.}2,$ the value of the shear stress at a point labeled $"d"$ is calculated. Review that example calculation.

Determine the shear stress at $H$ assuming the beam is subjected to the distributed load $w_{\text{m}\text{a}\text{x}}$ calculated in Part $4.$

Answer: ${}_H=$

psi

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Determine the maximum moment magnitude at any location in the beam when the beam is subjected to the distributed load $w_{\text{m}\text{a}\text{x}}$

calculated in Part $4.$

Answer: $M_{\text{m}\text{a}\text{x}}=$

$lb-ft$

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Part $9$

Determine the maximum tension bending stress at any location in the beam when the beam is subjected to the distributed load

$w_{\text{m}\text{a}\text{x}}$ calculated in Part $4.$

Answer: ${}_x=$

psi

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Incorrect

For a rectangular cross$-$section, the moment of inertia equals the factor $(1/12)$ times the width of the cross$-$section

times the cube of the depth of the cross$-$section. See Example $9\mathrm{.}2$ in which the calculation of the moment of inertia is

shown for a similar case.

A laminated wood beam consists of eight $2in.6\mathrm{.}75-$in$.$ planks glued together to form a section $b=6\mathrm{.}75$ in$.$ wide by $d=16$ in$.$

deep, as shown. If the allowable strength of the glue in shear is $130$ psi, determine

$($a$)$ the maximum uniformly distributed load $w$ that can be applied over the full length of the beam if the beam is simply supported

and has a span of $L=26ft.$

$($b$)$ the shear stress in the glue joint at $H,$ which is located $4$ in$.$ above the bottom of the beam and at a distance of $x=66in.$ from

the left support. Assume that the beam is subjected to the load w determined in part $($a$).$

$($c$)$ the maximum tension bending stress in the beam when the load of part $($a$)$ is applied.

Determine the moment of inertia for the cross$-$section about the $z$ centroidal axis.

Answer: $I_z=$

in$.{?}^4$

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Hint