The wing has a structural wing box $($shown in thick blue lines in Fig $1),$ which is expected to carry

all structural loads. The wing section has a chord of $2$ m $,$ with the dimensions of the structural

wing box as shown in Fig. $1.$ Let us consider the aircraft is in trim condition, i$.$e$.,$ steady and level

flight. We want to design the wing box section thickness such that its weight can be

minimised for all the loads acting on the aircraft during the flight conditions, while satisfying

the constraints on the material's yield stresses. The contribution of the other part of the wing

section for structural stress analysis can be neglected. Similarly, you do not need to calculate the

weight of those part of the wing. You can use thin$-$wall sections assumptions for all section

property calculations and structural analysis.

The wing can be easily represented by a cantilevered beam with one end fixed at the wing root, as

shown in Figs. $2$ and $3.$ The aircraft wing has a semi$-$span of $10$ m $.$ The elliptical lift distribution on

one half of the wing is as shown below in Fig. $3.$ Let us assume for simplifying the calculations

that the lift acts through the centre of pressure line of the wing, which is at a constant $27\mathrm{.}5\%$ of

the chord or $550$ mm from the leading edge of the wing section.

Please use the material properties as provided below:

Maximum allowable tensile $($or compressive$)$ yield stress: $250$ MPa

Maximum allowable shear yield stress: $150$ MPa

Material density: $2700$Kg$//$m$^(3)$

Shear modulus G: $25$ GPa

Figure $1$Wing section showing the structural wing box in thick blue lines. The structural wing box carries all structural

loads

Figure $2$ Semi span of the structural wing box showing fixed boundary conditions at the root and the line of action of

elliptical lift at the centre of pressure

Figure $3$ Structural wing box represented as a cantilevered beam showing elliptic lift distribution with lift$/$per unit

length of span of $3\mathrm{.}5$N$//$mm at the wing root

Need to work out the Bending moment, shear flow, shear centre and torsional force for t$1,$t$2,$t$3,$t$4=5$mm