03-03ChapGere.0015

03-03ChapGere.0015 - 250 A-PDF Torsion CHAPTER 3 Split DEMO...

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Problem 3.10-10 A thin-walled rectangular tube has uniform thickness t and dimensions a 3 b to the median line of the cross section (see figure). How does the shear stress in the tube vary with the ratio b 5 a / b if the total length L m of the median line of the cross section and the torque T remain constant? From your results, show that the shear stress is smallest when the tube is square ( b 5 1). Solution 3.10-10 Rectangular tube 250 CHAPTER 3 Torsion t a b t a b t 5 thickness (constant) a , b 5 dimensions of the tube T 5 constant S HEAR STRESS t 5 T 2 tA m 5 T (4)(1 1 b ) 2 2 t b L m 2 5 2 T (1 1 b ) 2 tL m 2 b A m 5 b L m 2 4(1 1 b ) 2 b 5 L m 2(1 1 b ) Ê A m 5 b B L m 1 b ) R 2 L m 5 2 b 1 b ) 5 constant t 5 T 2 tA m Ê A m 5 ab 5 b b 2 L m 5 2( a 1 b ) 5 constant b 5 a b T , t , and L m are constants. From the graph, we see that
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