03-01 Chap Gere - 3 Torsion Torsional Deformations Problem...

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Torsional DeformationsProblem 3.2-1A copper rod of lengthL18.0 in. is to be twistedby torquesT(see figure) until the angle of rotation between the endsof the rod is 3.0°.If the allowable shear strain in the copper is 0.0006 rad, what isthe maximum permissible diameter of the rod?3Torsion
Problem 3.2-2A plastic bar of diameterd50 mm is to be twisted bytorquesT(see figure) until the angle of rotation between the ends of thebar is 5.0°.If the allowable shear strain in the plastic is 0.012 rad, what is theminimum permissible length of the bar?L
181
Problem 3.2-3A circular aluminum tube subjected to pure torsionby torquesT(see figure) has an outer radiusr2equal to twice the innerradiusr1(a)If the maximum shear strain in the tube is measured as400106rad, what is the shear strain1at the innersurface?(b)If the maximum allowable rate of twist is 0.15 degreesper foot and the maximum shear strain is to be kept at400106rad by adjusting the torqueT, what is theminimum required outer radius (r2)min?LTr1r2Tr22r1.182CHAPTER 3Torsion(a) SHEAR STRAIN AT INNER SURFACEProblems 3.2-3, 3.2-4, and 3.2-5
Problem 3.2-4A circular steel tube of lengthL0.90 m is loaded intorsion by torquesT(see figure).(a)If the inner radius of the tube isr140 mm and the measuredangle of twist between the ends is 0.5°, what is the shear strain1(in radians) at the inner surface?(b)If the maximum allowable shear strain is 0.0005 rad and the angleof twist is to be kept at 0.5° by adjusting the torqueT, what is themaximum permissible outer radius (r2)max?
SECTION 3.2Torsional Deformations183Solution 3.2-4Circular steel tubeL0.90 mr140 mm(a) SHEAR STRAIN AT INNER SURFACEFrom Eq. (3-5b):g1388106radgming1r1fL(40mm)(0.008727rad)900mmgmax0.0005rad0.008727radf0.5(0.5 )¢180raddegree(b) MAXIMUM OUTER RADIUSFrom Eq. (3-5a):(r2)max51.6mm(r2)max(0.0005rad)(900mm)0.008727radr2gmaxLfgmaxg2r2fL;r1r2Problem 3.2-5Solve the preceding problem if the lengthL50 in.,the inner radiusr11.5 in., the angle of twist is 0.6°, and the allowableshear strain is 0.0004 rad.

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Term
Spring
Professor
Korkolis

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