Problem_08_01 - Problem 8.1 Given: Locate the shear center...

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Problem 8.1 Given: Locate the shear center for the hat section beam shown in Figure A of Table 8.1 by deriving the expression for e . Solution: An exact expression for the moment of inertia is: I x t2 b 1 h + () 3 12 2b t 3 12 + 2b t h 2 2 + = Ignoring the second term gives I x t2 b 1 h + () 3 12 2b t h 2 2 + = simplify I x t8 b 1 3 12 b 1 2 h + 6b 1 h 2 + h 3 + 6b h 2 + 12 = F 1 F 2 F 3 F 4 F 5 V` e Point A h b b 1 I x tb h 2 2 3 b 1 3 h 2 b b 1 2 hb + b 1 2b + h 12 b + 1 2 + = Σ F x = 0 gives: F 2 F 4 = Σ F y = 0 gives: V' F 1 F 3 + F 5 + = by symmetry: F 1 F 5 = Sum Moments about point A: V' e F 2 F 4 + () h 2 F 1 F 5 + () b = V' e F 2 h 2F 1 b = e 1 V' F 2 h 2F 1 b () = s h/2 b 1 b F 1 0 b 1 s τ t d = 0 b 1 s q
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This note was uploaded on 01/11/2011 for the course MAE 3040 taught by Professor Mechanicsofsolids during the Spring '10 term at Utah State University.

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Problem_08_01 - Problem 8.1 Given: Locate the shear center...

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