$($please solve a$,$b$,$c$,$d$,$e$)$

Question No$.1$

Consider the shown limit load acting on the wing of a passenger aircraft. The dimensions of the

wing and wing$-$box are also given on the figure. Assume the wing$-$box carries all the wing loads,

the lift distribution is perpendicular to the beam axis, and the wing$-$box section does not change

along the wingspan $($prismatic beam$),$ and is clamped at the wing root. Ignore the dihedral angle of

the wing. The material of the wing$-$box is $2024-$T$6$ aluminum alloy $($ultimate strength $415$ MPA$)$

a$.$ Integrate the lift distribution over the half wing to calculate its resultant magnitude and

location.

b$.$ If the total weight of the aircraft, INCLUDING all four engines is $1,200kN,$ determine the

load factor at this moment.

c$.$ Calculate the maximum bending moment at the wing root section $(M_{\text{m}\text{a}\text{x}})$

d$.$ Calculate the second moment of area of the wing$-$box section, and hence calculate the

maximum bending stress.

e$.$ Determine the Ultimate Stress margin of safety. Comment on the result.