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HW1 - 2 The dimensions of a steel(300M I-beam are b = 50mm...

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EAS4200C Aerospace Structures Homework #1 (Due: Sep. 4th) 1. 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 . 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 allowable = 2 allowable . Note that for closed thin-walled sections such as the one in the figure, the shear stress due to torsion is = T /(2 abt ) . Hint: The most efficient section maximizes the section modulus. Write the section modulus as a function of a or b . First assume that bending stress reaches allowable and check if shear stress is less than its allowable. If not, assume shear stress reaches allowable and check if bending stress is less than its allowable.
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Unformatted text preview: 2. The dimensions of a steel (300M) I-beam are b = 50mm , t = 5mm , and h = 200mm . Assume that t and h are to be fixed for an aluminum (7075-T6) I-beam. Find the width b for the aluminum beam so that its bending stiffness EI is equal to that of the steel beam. Compare the weights-per-unit length of these two beams. Which is more efficient weight-wise? The densities of steel and aluminum are 7.8 and 2.78g/cm 3 , respectively. 3. Compare the load-carrying capabilities of two beams having the respective cross-sections shown in the figure. Use bending stiffness as the criterion for comparison. It is given that a = 4cm , t = 0.2 cm , and the two cross-sections have the same area....
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