$1.$ A simple span beam, Douglas Fir$-$Larch $($North$),$ #$1$ grade timber, has a span of $18$ ft$.$ with three concentrated loads of PDL $=2$ kip and PLL $=1$ kips each at the quarter points

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a$.$ Size the beam based on bending stress $(10$ pts$)$

$$ M $=$ PL$/2$

$$ fb $=$ M$/$S

$$ F$$b $=$ FbCDCMCtCLCFCfuCiCr

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b$.$ Check the selected beam for shear stress $(8$ pts$)$

$$ V $=3$P$/2$

$$ fv $=1\mathrm{.}5$V$/$A

$$ F$$v $=$ FvCDCMCtCi

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c$.$ Investigate for deflection $(10$ pts$)$

$$ E$=$ ECMCtCi

$$ACT $=19$PL$3/384$E$$I

$$ALL $=$ L$/240$

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o$$ CD $=$ CM $=$ Ct $=$ CL $=$ Cfu $=$ Ci $=$ Cr $=1\mathrm{.}0$

o$$ Assume CF $=0\mathrm{.}9$

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