Problem 3.10-10A thin-walled rectangular tube has uniform thickness tand dimensions a3bto the median line of the cross section (see figure). How does the shear stress in the tube vary with the ratio b5a/bifthe total length Lmof the median line of the cross section and the torque Tremain constant? From your results, show that the shear stress is smallest when thetube is square (b51).Solution 3.10-10Rectangular tube250CHAPTER 3Torsiontabtabt5thickness (constant)a, b5dimensions of the tubeT5constantSHEAR STRESSt5T2tAm5T(4)(11b)22tbLm252T(11b)2tLm2bAm5bLm24(11b)2b5Lm2(11b)ÊAm5bBLm1b)R2Lm52b1b)5constantt5T2tAmÊAm5ab5bb2Lm52(a1b)5constantb5abT, t, and Lmare constants.From the graph, we see that
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Tech.