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hw21_Solutions

# hw21_Solutions - AAE 221 Aerospace Structures II Spring...

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AAE 221 – Aerospace Structures II – Spring 2004 Chapter 2.1 – Beam Bending and Extension Solutions

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Problem 0

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1. (a) The Young’s modulus of the three sections are 7 3 2 7 1 10 1 10 3 ¥ = = ¥ = E E E First, the Young’s modulus of aluminum is chosen to be the reference modulus. The areas of each sub-component are at A at A at A 2 8 4 3 2 1 = = = The modulus weighted area is = * i i A E E A o The distances from the origin of the coordinate axis to the m.w. centroid are found from = = * * * * i i i i i i A y E E y A A z E E z A ) ( ) ( o o o o o o where the quantity o z etc. are the distances from the origin to the centroid of each sub- component. The location of the centroid is found to be symmetry) to (due 20 2 22 248 22 38 21 t a y t t a z = = = + = * * o o The moments and product of inertia can be found by first calculating the modulus weighted moments of inertia about our coordinate system origin, and then applying the parallel axis theorem to shift to the centroidal axis. The m.w. moments of inertia can be found from

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