mechanics of aircraft structure

mechanics of aircraft structure - 구조역하및 실험...

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Unformatted text preview: 구조역하및 실험 Problem Solution – Homework #1 항공우주정보시스템공학과 1.1 The beam of a rectangular thin-walled section (t is very small) is designed to carry both bending moment M and torque T. If the total wall contour length L = 2(a+b) is fixed, find the optimum b/a ratio to achieve the most efficient section if M=T and σ allowable = 2 τ allowable . Note that for closed thin-walled sections such as the one in Fig 1. 16, the shear stress due to torsion is τ = T 2abt Solution: First, we determine the moment of inertia of the section I = I outer − I inner = 1 12 ab 3 − 1 12 a − 2t ¡ b − 2t ¡ 3 = 1 12 ab 3 − 1 12 ab 3 − 6ab 2 t + 12abt 2 − 8at 3 − 2b 3 t + 12b 2 t 2 − 24bt 3 + 16t 4 ¡ Or we can also separate the section into two parts right-left and top-bottom sections which can be analyzed as follows I = I left − right + I top − bottom = 2 × ¢ 1 12 tb 3 £ + 2 × ¤ at 3 12 + at ¢ b 2 £ 2 ¥ = 1 6 tb 3 + 1 6 at 3 + 1 2 ab 2 t Since t is very small, then the power of t will make the value even smaller to be ignored. Then, I ≅ 1 6 b 2 t 3a + b) ¡ a) σ allowable = σ max We know that, σ max = Mc I Applying the moment of inertia to the equation, we will have normal stress at the farthest distance from neutral axis as M is applied to the system σ max = σ allow = M b 2 1 6 b 2 t 3a + b) ¡ L = 2 a + b ¢ a = L 2 − b σ max = 3M bt £ 3 £...
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mechanics of aircraft structure - 구조역하및 실험...

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