Task $2,$ Internal Loads for Wing Center Section and Outboard Wing Structure.

For the Anti$-$armor Mission, the A$-10$ aircraft carries three CBU$-105$ sensor fuzed weapons, each weighing $910$ pounds, at each of the weapons pylons $4,5,7,$ and $8.$ Based on the aircraft configuration and the external loading condition given in Figure $4,$ determine the shear and bending moment along the specified wing section$($s$).$ NOTE: The overall weight of the aircraft maintains the aircraft in equilibrium, but it is not included in the structural analysis.

FIGURE $4.$ A$-10$ Wing Loading for Anti$-$Armor Mission Configuration

NOTE: The distributed lift along the outer wing section is measured from the wing centerline, and the external loads on the lower portion of the wing center section include the pylon weights with the armament weights along with the main landing gear and landing gear pod weight.

Sketch a free body diagram for one$-$half of the wing center section and one outboard wing structure showing the values of the resultant and reaction forces applied to the structure. Neglect the actual weight of the structure in the analysis, and assume that the wing center section has a fixed support at the wing centerline.

Determine the shear force, $V(x),$ and bending moment, $M(x),$ equations for each span of the wing center section and outboard wing structure where the internal loads are continuous. Express each equation in polynomial form as a function of the wing span as measured from the wing centerline.

Wing Center Section $(x=0$ to $23$ in$)$

$V(x)=$

$M(x)=$

Wing Center Section $(x=66$ to $100$ in$)$

$V(x)=$

$M(x)=$

Wing Center Section $(x=23$ to $66$ in$)$

$V(x)=$

$$

$M(x)=$

$$

$V(x)=$

$$

$M(x)=$

$$

Outboard Wing Structure $(x=110$ to $345$ in$)$

$V(x)=$

$M(x)=$

Develop one equation using continuous functions for the shear load and another equation using continuous functions for the bending moment on the wing center section and outboard wing structure. Express each equation for the shear load and bending moment in polynomial form using continuous functions with the wing span measured from the wing centerline.

Shear Load and Bending Moment for A$-10$ Wing Structure $(x=0$ to $345$ in$)$

$V(x)=$

$q,$