. The action of materials under stress; . an angle 0 -Cd- The work expended in the torsion is / TdO 64/ From 9I: 2qd_^~ Qd Work and therefore /. ^ = Volume4C If C = I E and q^ =4/. work = vol- /?2 nme . ~ —, while5 E for flexure, as just shown, work = volume 6E a smaller 1l 4C quantity, so that the torsional momentdoes more work than the bending mo-ment. If this bar is bent into a helix andthe force P is applied at the centre, inthe direction of the axis of the cylinder,Fig. 100, to a horizontal arm whoselength is a, the arm possessing sufficientstiffness to be not appreciably bent, themoment
. The action of materials under stress; . an angle 0 -Cd- The work expended in the torsion is / TdO 64/ From 9I: 2qd_^~ Qd Work and therefore /. ^ = Volume4C If C = I E and q^ =4/. work = vol- /?2 nme . ~ —, while5 E for flexure, as just shown, work = volume 6E a smaller 1l 4C quantity, so that the torsional momentdoes more work than the bending mo-ment. If this bar is bent into a helix andthe force P is applied at the centre, inthe direction of the axis of the cylinder,Fig. 100, to a horizontal arm whoselength is a, the arm possessing sufficientstiffness to be not appreciably bent, themoment Ya will twist the bar throughout its. length. Then ^1 = 16 P^ -d or P 16 a SPRINGS. 253 The deflection of the sprino^ vs^ v = a d, since, as the force Pdescends, the spring descends, and the action is the same as ifthe spring remained in place and the arm revolved through anangle 6. The force P is too small to cause any appreciablecompression (or extension) of the material in the direction ofits length. 32 Va^ I lal q^ \-nd^ q^ ^° ^ ^ ? cT^ ^ ~d 0,^ ~ir ? C if ;/ = number of turns of the helix, and 1=2 -an. P may be tension in place of compression. If the section of the spring is not circular, substitute the proper value of q^ or the resisting moment from § 92. If the r d\ rod is hollow, multiply the exterior volume by j i ?— -^ I . For a square section and a given deflection, P will be about65% of the load for an equal circular section. C for steel isfrom 10, 500,000 to 12,000,000. Example.—A helical spring, of round steel rod, i in. diame-ter, making 8 turns of 3 in. radius, carries 1,000 lbs. ,000.
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Keywords: ., bookcentury1800, bookdecade1890, booksubjectstrengt, bookyear1897
