HW7 Solutions

# HW7 Solutions - Mechanics of Aircraft structures C.T Sun...

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Unformatted text preview: Mechanics of Aircraft structures C.T. Sun 3.5 The two-cell section in Fig.3.35 is obtained from the single-cell section of Fig.3.36 by adding a vertical web of the same thickness as the skin. Compare the torsional rigidity of the structures of Figs. 3.35 and 3.36 with and , , respectively. cm L L 10 2 1 = = cm L 5 1 = cm L 15 2 = cm t 3 . = Figure 3.35 Two-cell thin-walled section Figure 3.36 Single-cell section Solution: We denote as torsional rigidity. For the same material in comparison, only the torsion constant needs to be considered. GJ J (a) Single-cell thin-walled section The torsion constant is J ∫ = t ds A J / 4 2 (3.5.1) where A is the area enclosed by the centerline of the wall section. We have 2 3 2 1 200 10 20 ) ( cm L L L A = × = + = . The torsion constant can be simply derived as J 3.5.1 Mechanics of Aircraft structures C.T. Sun 4 2 3 2 1 2 3 2 1 2 1 800 3 . ) 10 20 ( 2 ) 200 ( 4 / ) ( 2 ] ) [( 4 / 4 cm t L L L L L L t ds A J cell = + = + + + = = ∫ (b) Two-cell thin-walled section (1) General Form We denote the shear flow on the left cell by , and the shear flow on the right cell by . The shear flow in the vertical web is 1 q 2 q 2 1 12 q q q − = Also, we have the torque for two-cell section 2 1 2 1 2 2 q A q A T + = (3.5.2) where 3 1 1 L L A = , 3 2 2 L L A = The twist angle of the section is obtained from eirher cell. For left cell we have ) ) ( ) 2 ( ( 2 1 2 1 3 2 1 3 1 1 3 1 1 1 1 L q q L L q t L GL t qds A G cell − + + = = ∫ θ (3.5.3) and for the right cell ) ) ( ) 2 ( ( 2 1 2 1 3 2 1 3 2 2 3 2 2 2 2 L q q L L q t L GL t qds A G cell − − + = = ∫...
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HW7 Solutions - Mechanics of Aircraft structures C.T Sun...

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