Assignment1-solution

Assignment1-solution - Homework I 8/23/2006 Problem...

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Homework I 8/23/2006 Problem overview b M T The beam of a rectangular thin-walled section (i.e. t is very small) is designed to carry both bending moment M and torque T . The following series of questions is intended to illuminate the weight efficiency issues associated with wing- box structural design. 1. For small thickness t, the cross-sectional area A and moment of inertia I can be approximated as 2 2( ) , ( 3 ) 6 tb Aa b tI ba =+ = + . Check the percent error in A and I for a section (typical of some wing boxes), where b=0.1a, t=0.2b . Compare the error when a and b are measured to the middle of the thickness with the error when they are measured to the end, as in the figure above. Explain why the percent error does not depend on the value of a , so you can take for convenience a=50 , b=5, t=1 . Assume that these values are the ones measured to the mid- thickness, so that if the values are measured to the end, then a is measured as 51 and b is measured as 6 . Solution: First find the exact solution of the given geometry.
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This note was uploaded on 11/29/2010 for the course AE 350 taught by Professor Achuthan during the Fall '09 term at Clarkson University .

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Assignment1-solution - Homework I 8/23/2006 Problem...

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