Problem $1($Using the Manual of Steel Construction $-$ Part $1)$

$($a$)$ For the L$8$x$6$x$1$ angle, calculate the following geometric properties, and compare with the

values tabulated in the Manual of Steel Construction $($see Tables for rolled structural

shapes$)$:

Location of centre of gravity

Moments of Inertia $(I_Y$ and $I_x)$

Section Modulus $(S_Y$ and $S_x)$

Radius of Gyration and $\{$:$r_Z)$

$($b$)$ Two L$8$x$6$x$1$ are placed with their long legs back$-$to$-$back, but separated by a $\frac{3}{8}$ in space

because they are connected to a $\frac{3}{8}$ in stitch plate $($i$.$e$.$ a small spacer plate$)$ at periodic

intervals to ensure the two angles behave as a single member. What is the smallest radius of

gyration of this built$-$up structural member?

$($c$)$ Is this section available in A$572$ Grade $50$ and A$1043$ Grade $50$ steel $($based on Tables $2-3$ to

$2-5)?$

$($d$)$ If so$,$ what are the specified yield stress $($ Fy $)$ and tensile stress $($ Fu $)$ for these steels.

$($e$)$ Draw to scale $($on engineering paper$)$ a L $861$ angle and a $22\mathrm{.}51\mathrm{.}5\frac{3}{16}$ angle. Note that

the $L2\mathrm{.}5x1\mathrm{.}5\frac{3}{16}$ is one of the smallest angle available; you can guess its dimensions from

its designation $($i$.$e$.$ its name$).$ Draw them inside each other, with their corner $($heel$)$ at the

same point. How many times heavier is the L $8$ x $6$ x $1$ compared to the $L2\mathrm{.}51\mathrm{.}5\frac{3}{16}?$

$($f$)$ Comparing a W$6$x$16$ with a W$6$x$12$: Which one is heavier?Problem $1(Using$ the Manual $of$ Steel Construction $-$ Part $1)$

$(a)$ For the $L8x6x1$ angle, calculate the following geometric properties, and compare with the values tabulated $in$ the Manual $of$ Steel Construction $(see$ Tables for rolled structural shapes$)$:

Location $of$ centre $of$ gravity Moments $of$ Inertia $(IY$ and $IX)$ Section Modulus $(SY$ and $SX)$ Radius $of$ Gyration $(rY,rX$ and $rZ)$

$(b)$ Two $L8x6x1$ are placed with their long legs back$-to-$back, but separated $bya\frac{3}{8}in$ space because they are connected $toa\frac{3}{8}in$ stitch plate $(i.e.$ a small spacer plate$)at$ periodic intervals $to$ ensure the two angles behave $as$ a single member. What $is$ the smallest radius $of$ gyration $of$ this built$-up$ structural member?

$(c)Is$ this section available $inA572$ Grade $50$ and $A1043$ Grade $50$ steel $(basedon$ Tables $2-3to2-5)?$

$(d)Ifso,$ what are the specified yield stress $(Fy)$ and tensile stress $(Fu)$ for these steels.

$(e)$ Draw $to$ scale $(on$ engineering paper$)aL8x6x1$ angle and $aL2\mathrm{.}5x1\mathrm{.}5x\frac{3}{16}$ angle. Note that the $L2\mathrm{.}5x1\mathrm{.}5x\frac{3}{16}is$ one $of$ the smallest angle available; you can guess its dimensions from

its designation $(i.e.$ its name$).$ Draw them inside each other, with their corner $(heel)at$ the

same point. How many times heavier $is$ the $L8x6x1$ compared $to$ the $L2\mathrm{.}5x1\mathrm{.}5x\frac{3}{16}?$

$(f)$ Comparing $aW6x16$ with $aW6x12$: Which one $is$ heavier?