An airplane wing spar (Figure P3.15) is made of an aluminum alloy (E = 72 GPa and ν = 0.33...

An airplane wing spar (Figure P3.15) is made of an aluminum alloy (E = 72 GPa and ν = 0.33), and it has a square cross section perpendicular to the plane of the figure. Stress components σxx and σyy are uniformly distributed as shown.

FIGURE P3.15

a. If σxx = 200 MPa, determine the magnitude of σyy so that the dimension b = 20 mm does not change under the load.

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b. Determine the amount by which the dimension a changes.

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c. Determine the change in the cross-sectional area of the spar.