$5\mathrm{.}8-13$ A square wood platform is $8ft8ft$ in area

and rests on masonry walls $($see figure$).$ The deck of

the platform is constructed of $2-$in$.$ nominal thick$-$

ness tongue$-$and$-$groove planks $($actual thickness

$1\mathrm{.}5$ in$.$; see Appendix G$)$ supported on two $8-$ft long

beams. The beams have $4in.6in.$ nominal dimen$-$

sions $($actual dimensions $3\mathrm{.}5in.5\mathrm{.}5in.).$

The planks are designed to support a uniformly

distributed load $w(l\frac{b}{f}{t}^2)$ acting over the entire top

surface of the platform. The allowable bending stress

for the planks is $2400$ and the allowable shear

stress is $100.$ When analyzing the planks, disre$-$

gard their weights and assume that their reactions

are uniformly distributed over the top surfaces of the

supporting beams.

$($a$)$ Determine the allowable platform load

$w_1(l\frac{b}{f}{t}^2)$ based upon the bending stress in the

planks.

$($b$)$ Determine the allowable platform load

$w_2(l\frac{b}{f}{t}^2)$ based upon the shear stress in the

planks.

$($c$)$ Which of the preceding values becomes the

allowable load $w_{\text{a}\text{l}\text{l}\text{o}\text{w}}$ on the platform?

Hints: Use care in constructing the loading dia$-$

gram for the planks, noting especially that the reac$-$

tions are distributed loads instead of concentrated

PROBLEM $5\mathrm{.}8-13$

loads. Also, note that the maximum shear forces

occur at the inside faces of the supporting beams.