For the following problems, a beam segment subjected to internal bending moments

at cross$-$sections A and B $($MA $=5\mathrm{.}8$ kN$-$m and MB $=3\mathrm{.}2$ kN$-$m$)$ is shown along with

a sketch of the cross$-$sectional dimensions.

$($a$)$ For the beam segment, prove that its centroid$$s y coordinate is $181\mathrm{.}154$ mm

$($reference at the bottom of the segment$)$ and the moment of inertia about z axis

is $140,739,231$ mm$4$

$.$

$($b$)$ Sketch a side view of the beam segment and plot the distribution of bending

stresses acting at cross$-$sections A and B$.$ Indicate the magnitude of key bending

stresses $($maximum tensile$/$compressive bending stresses of the segment and the

bending stresses $30$ mm below the top of the segment$)$ on the sketch.

$($c$)$ Determine the resultant forces acting in the x direction on component $(1)$ at

cross$-$sections A and B and show these resultant forces on the sketch.

$($d$)$ Is component $(1)$ in equilibrium with respect to forces acting in the x direction? If

not, determine the horizontal force required to satisfy equilibrium for

component $(1)$ and show the location and direction of this force on the sketch.

P$9\mathrm{.}3$ For the following problems, a beam segment subjected to internal bending moments at sections A

and B is shown along with a sketch of the cross$-$sectional dimensions. For each problem:

$($a$)$ Sketch a side view of the beam segment and plot the distribution of bending stresses acting at

sections A and B$.$ Indicate the magnitude of key bending stresses on the sketch.

$($b$)$ Determine the resultant forces acting in the x direction on the specified area at sections A and B and

show these resultant forces on the sketch.

$($c$)$ Is the specified area in equilibrium with respect to forces acting in the x direction? If not, determine

the horizontal force required to satisfy equilibrium for the specified area and show the location and

direction of this force on the sketch.

Consider area $(1)$ of the $500-$mm$-$long beam segment, which is subjected to internal bending momeFor the following problems, a beam segment subjected to internal bending moments

at cross$-$sections A and and $\{$:$M_B=-3\mathrm{.}2kN-m)$ is shown along with

a sketch of the cross$-$sectional dimensions.

$($a$)$ For the beam segment, prove that its centroid's y coordinate is $181\mathrm{.}154mm$

$($reference at the bottom of the segment$)$ and the moment of inertia about $z$ axis

is $140,739,231m{m}^4.$

$($b$)$ Sketch a side view of the beam segment and plot the distribution of bending

stresses acting at cross$-$sections A and B$.$ Indicate the magnitude of key bending

stresses $($maximum tensile$/$compressive bending stresses of the segment and the

bending stresses $30mm$ below the top of the segment$)$ on the sketch.

$($c$)$ Determine the resultant forces acting in the $x$ direction on component $(1)$ at

cross$-$sections A and $B$ and show these resultant forces on the sketch.

$($d$)$ Is component $(1)$ in equilibrium with respect to forces acting in the $x$ direction? If

not, determine the horizontal force required to satisfy equilibrium for

component $(1)$ and show the location and direction of this force on the sketch.