03-01 Chap Gere - 3 Torsion Torsional Deformations Problem 3.2-1 A copper rod of length L 18.0 in is to be twisted by torques T(see figure until the

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

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Torsional Deformations Problem 3.2-1A copper rod of length L18.0 in. is to be twisted by torques T(see figure) until the angle of rotation between the ends of the rod is 3.0°. If the allowable shear strain in the copper is 0.0006 rad, what is the maximum permissible diameter of the rod? 3 Torsion Problem 3.2-2A plastic bar of diameter d50 mm is to be twisted bytorques T(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
Problem 3.2-3A circular aluminum tube subjected to pure torsion by torques T(see figure) has an outer radius r2equal to twice the innerradius r1(a)If the maximum shear strain in the tube is measured as 400 106rad, what is the shear strain 1at the innersurface? (b)If the maximum allowable rate of twist is 0.15 degrees per foot and the maximum shear strain is to be kept at 400 106rad by adjusting the torque T, what is theminimum required outer radius (r2)min?Solution 3.2-3Circular aluminum tubeLTr1r2Tr22r1max400106rad(a) SHEAR STRAIN AT INNER SURFACEFrom Eq. (3-5b):g1200106radg112g212(400106rad)218.2106rad in.(0.15ft)¢180raddegree≤¢112ftin.uallow0.15ft(b) MINIMUM OUTER RADIUSFrom Eq. (3-5a):(r2)min1.83in.(r2)mingmaxuallow400106rad218.2106rad in.gmaxr2fLr2ur1r2Problem 3.2-4A circular steel tube of length L0.90 m is loaded intorsion by torques T(see figure). (a)If the inner radius of the tube is r140 mm and the measuredangle of twist between the ends is 0.5°, what is the shear strain 1(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 torque T, what is themaximum permissible outer radius (r2)max?Problems 3.2-3, 3.2-4, and 3.2-5 . 182 CHAPTER 3 Torsion
SECTION 3.2 Torsional Deformations 183 Solution 3.2-4 Circular steel tube L 0.90 m r 1 40 mm (a) S HEAR STRAIN AT INNER SURFACE From Eq. (3-5b): g 1 388 10 6 rad g min g 1 r 1 f L (40 mm)(0.008727 rad) 900 mm g max 0.0005 rad 0.008727 rad f 0.5 (0.5 ) ¢ 180 rad degree (b) M AXIMUM OUTER RADIUS From Eq. (3-5a): ( r 2 ) max 51.6 mm ( r 2 ) max (0.0005 rad)(900 mm) 0.008727 rad r 2 g max L f g max g 2 r 2 f L ; r 1 r 2 Problem 3.2-5 Solve the preceding problem if the length L 50 in., the inner radius r 1 1.5 in., the angle of twist is 0.6°, and the allowable shear strain is 0.0004 rad. Solution 3.2-5 Circular steel tube L 50 in. r 1 1.5 in. (a) S HEAR STRAIN AT INNER SURFACE From Eq. (3-5b): g 1 314 10 6 rad g min g 1 r 1 f L (1.5 in.)(0.010472 rad) 50 in.

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