Determine the column allowable compressive force capacity, Pa for the given $3$ x $8$ S$4$S Douglas Fir

sawn lumber column with an Fc $=1000$ psi and E $=1\mathrm{.}6$ x $106$ psi. Mid$-$height bracing is provided for

the weak axis of buckling. Assume CM $=1\mathrm{.}0,$ Ct $=1\mathrm{.}0,$ CF $=1\mathrm{.}0.$ Assume a $7-$day load duration. An

illustration of this column is found below. $(40$ points total$)$ Use Table A$1-$a on pg$.567$ for the column

dimensional properties.

$[$Hint: See Example problem $9\mathrm{.}8$ on slide $23$ in the lecture PowerPoint presentation titled $$Chapter $9$

REV wood only$$ found in Module $22.]$

$2\mathrm{.}1.$ Find the column cross$-$

cross$-$sectional

area, A $($in$2).(2$

points$)$ Make sure

you look up the

true dimensions

in Table A$1-$a in

the Appendix on

pg$.567$ of the

textbook.

$2\mathrm{.}2.$ Find the weak

axis effective

length, Le$,$y $($ft$).$

The weak axis is

the one that

makes the stud

depth wider than it

is deep. For this cross$-$section that would be the direction that is braced at mid$-$height and is

marked by $$a$)$ Weak axis$$ in the sketch. $(2$ points$)$

$2\mathrm{.}3.$ Using the smaller dimension of the stud cross$-$section calculate the weak axis slenderness

ratio, Le$,$y $/$dy $.$ Don$$t forget to convert Le$,$y to inches. $(2$ points$)$

$2\mathrm{.}4.$ Find the strong axis effective length, Le$,$x $($ft$).$ The strong axis is the one that makes the stud

depth deeper than it is wide. For this cross$-$section that would be the direction that is not

braced at mid$-$height and is marked by $$b$)$ Strong axis$$ in the sketch. $(2$ points$)$

$2\mathrm{.}5.$ Using the larger dimension of the stud cross$-$section calculate the strong axis slenderness

ratio, Le$,$x $/$dx $.$ Don$$t forget to convert Le$,$x to inches. $(2$ points$)$

$2\mathrm{.}6.$ Determine which slenderness ratio, L$/$d

governs. The largest one governs. $(2$

points$)$

$2\mathrm{.}7.$ Using Figure $9\mathrm{.}23$ to the right determine

the appropriate load duration factor, CD $.$

$(2$ points$)$

$2\mathrm{.}8.$ The equation for allowable stress in a

wood column is:

F$$C $=$ F$*$C Cp however

F$*$C $=$ FC CD CM Ct CF

Calculate F$*$C using the information you

were given above and the load duration

factor, CD from part $2\mathrm{.}7.$ We will calculate

F$$c later once we have Cp $.(4$ points$)$

$3$x$8$ S$4$S

Pa

$2\mathrm{.}9.$ Calculate the Euler critical buckling stress for columns, FcE $.$ The value of KcE $=0\mathrm{.}3$ for sawn

lumber.

FcE $=($KcE E$)/($L$/$d$)2$ for each direction.

$2\mathrm{.}9\mathrm{.}1.$ For the weak axis use Le$,$y $/$dy from part $2\mathrm{.}3$ above. $(4$ points$)$

$2\mathrm{.}9\mathrm{.}2.$ For the strong axis use Le$,$x $/$dx from part $2\mathrm{.}5$ above. $(4$ points$)$ You must show your work

to get credit however if you did part $2\mathrm{.}9\mathrm{.}2$ correctly the buckling stress limit for the

strong axis, FcE,x should be $891\mathrm{.}8$ psi.

This time the smaller one will govern the column$$s buckling capacity. This should be the same

direction that governed in the answer to part $2\mathrm{.}6$ above.

$2\mathrm{.}10.$ Now calculate the ratio FcE $/$F$*$C for only the direction that governed in both part $2\mathrm{.}6($and $2\mathrm{.}9).$

Use the smaller FcE from part $2\mathrm{.}9$ and the F $*$C from $2\mathrm{.}8.$ Round the number to two digits $($the

nearest $100$th $).(2$ points$)$

$2\mathrm{.}11.$ Using Table $9\mathrm{.}3$ on page $478$ of your textbook $($see partial Table below$)$ and the ratio from part

$2\mathrm{.}10$ determine the appropriate column stability factor, Cp $.(4$ points$)$ Note: If you cannot find

your ratio from part $2\mathrm{.}10$ above in the table below then you have made a miscalculation.

$2\mathrm{.}12.$ The column$$s allowable buckling compressive stress, F$$C $=$ Cp F$*$C $.$ Calculate the allowable

buckling compressive stress, F$$ C $.(4$ points$)$

$2\mathrm{.}13.$ Using the area, A calculated in part $2\mathrm{.}1$ above calculate the column allowable load Pa $=$ F$$C A$.(4$

points$)$