AE304_fall09_HW5 - Homework 5 AE304 – Aircraft Structures...

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Unformatted text preview: Homework 5 AE304 – Aircraft Structures I – Fall 2009 Due: Monday, October 26, 2009 Exercise 1: A uniform thin‐walled beam ABD of open cross‐section (see Figure 1) is simply supported at points B and D with its web vertical. It carries a downward vertical force W at the end A in the plane of the web. Determine the vertical and horizontal deflections of the beam midway between the support B and D. The wall thickness t and Young’s modulus E are constant throughout. y D 2L 1 a y 2 B L x 2a x A 3 z W t 4 Figure 1 Exercise 2: A cantilevered thin‐walled beam is subjected to distributed load w = 30 N/m and concentrated load P = 50 N as shown in Figure 2. The dimensions of the cross‐section are indicated in Figure 2 with constant thickness t = 5 mm. All dimensions are in millimeters and, where appropriate, are given from the centerlines of the walls. The beam is made of Aluminum 7075‐T6 with a modulus of elasticity E = 71.7 GPa and Poisson’s ratio ν = 0.33. Determine: (a) the bending stress distribution at the fixed end section and (b) deflection of the tip end. y w 30 100 C x P 1500 70 Figure 2 Exercise 3: A wing box section is subjected to a moment M = 50 that passes through its centroid as shown in Figure 3. All dimensions are in inches. The stringer areas have relationship as follow: A3=A4=A, A2=A5=1.2 A, and A1=A6=1.5 A. Assume that all normal stresses are resisted by the stringers while the skin only effective in shear. Determine the required minimum area of the stringers if the maximum allowable normal stresses at the stringers are 3000 psi in tension and 2000 psi in compression. 15 15 y 6 M 5 4 5 5 1 C 60o x 2 3 8 Figure 3 Exercise 4: An idealized cantilevered wing box beam is subjected to an upward‐directed, spanwise‐distributed load acting along one of the top stringer and an aft‐directed distributed load acting along the midway between stringer 1 and 5, as shown in Figure 4. The stringer areas are listed in the table below. All dimensions are in millimeters, the length of wall 1‐5 is 1400 mm. Determine the normal stress in the stringers at the fixed end. y 12 N/mm x 8 N/mm 5000 5 4 250 1 z 2 3 The stringer areas: Stringer 1 2 3 4 5 Area (mm2) 600 500 450 450 600 5 400 4 400 3 500 460 420 1 2 800 Figure 4 ...
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This note was uploaded on 04/12/2011 for the course AE 304 taught by Professor Lestari during the Fall '10 term at Prescott.

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