Problem #$2$: $(30$ points$)$ The simple structure in Figure $2$a $($shown on the following page$)$ consists

of two members AB and AC$.$ Vertical bar AB is pinned at B and is pinned to bar AC at A$.$ Horizontal

bar AC is also pinned at C$,$ and it is subjected to a triangular load that varies in intensity from zero

at point C to w$\_($o$)($l$($b$)/($f$)$t$)$ at the left end of the bar. Bar ABE$=100$

GPa $,$ and yield stress $\backslash$sigma $\_($Y$)=70$MPa.AB that occurs in the plane of Figure $2$a$,$ the supports at A and B act like

pins. For buckling of bar AB that occurs in the plane that is perpendicular to Figure $2$a$,$ the support

at B acts like a fixed $($i$.$e$.$ clamped$)$ end, and the connection at A acts like a pin.

The cross section of member ABD$-$D AB as seen in Figure $2$a; the $160$ mm dimension is

perpendicular to the plane of Figure $2$a and corresponds to the depth of member AB not seen in

Figure $2$a$.$

aI$\_($in$-$plane $)$ needed to calculate the buckling load P$\_($in$-$plane $)$ of member

AB for buckling in the plane of Figure $2$a$,$ and use it to calculate the value of the buckling

load P$\_($in$-$plane $).$

bI$\_($perp $)$ needed to calculate the buckling load P$\_($perp $)$ of member AB for

buckling in the plane that is perpendicular to Figure $2$a$,$ and use it to calculate the value of

the buckling load P$\_($perp $).$

cAB. Express the result in terms of w$\_($o$).$

dw$\_($o$)$ before member AB buckles in the plane of Figure $2$a$,$ and find

the largest value of w$\_($o$)$ before member AB buckles in the plane that is perpendicular to Figure

$2$a$.$

ew$\_($o$)$ before the member AC yields. As w$\_($o$)$ increases gradually from

zero, how does member AB fail first, and at what value of w$\_($o$)?$ Explain.

fAB, then find the largest value of w$\_($o$)$ before member AB

buckles in the plane of Figure $2$a$.$ In this case, as w$\_($o$)$ increases gradually from zero, how does

member AB fail first, and at what value of w$\_($o$)?$ Explain.

Figure $2$a

Figure $2$b

Cross section of member AB as seen in view D$-$D

Please solve for all parts, in details