Problem #$4(20$ pts$)$

Dr$.$ Nelson likes to flyfish and many times

has crossed wobbly boards laid across

streams. A $1\mathrm{.}5$ inch by $5\mathrm{.}5$ inch rectangular

board is laid across a stream $($assume the en

are simply supported $-$ that is they resist for

but not moments$).$ Dr$.$ Nelson stands in the

middle of the board's $6$ ft span and

jumps off at an angle of $60$ degrees

from the horizontal in a plane parallel

to the yz plane. A rough estimate for

the peak take$-$off force is about $3\mathrm{.}5$

times the body weight of the person $-$

so let's assume that the take$-$off force is

$F=900lbs.$

$($a$)$ Draw the shear, and moment diagrams for the $xy$ and $xz$ planes $($note it may help to solve for

reaction forces and to draw a force diagram for the $xy$ and $xz$ planes first$)$

$0$

$($b$)$ Fill in the terms for finding the maximum tensile bending stress in the plank. You do NOT need

to compute the stress, just fill in the terms with the appropriate values. Careful of your signs.

$\{\begin{array}{c}\text{:}0\mathrm{.}7sin(\frac{1ft}{12(h)})=0\mathrm{.}0625ft\\ {}_x=-\frac{(M_z)(y)}{(I_z)}+\frac{(M_y)(z)}{(I_y)}\end{array}$