Mechanics of engineeringComprising statics and dynamics of solids: and the mechanics of the materials of constructions, or strength and elasticity of beams, columns, arches, shafts, etc . or tendency toslide) on oblique planes are opposite in direction to thosein the rod. Since the resultant stress on a given internal plane of abody is fully represented by its normal and tangentialcomponents, we are therefore justified in considering buttwo kinds of internal stress, normal or direct, and tangen-tial or shearing. 182. Stress on Oblique Section of Rod in Tension.—Considerb free a small cubic ele
Mechanics of engineeringComprising statics and dynamics of solids: and the mechanics of the materials of constructions, or strength and elasticity of beams, columns, arches, shafts, etc . or tendency toslide) on oblique planes are opposite in direction to thosein the rod. Since the resultant stress on a given internal plane of abody is fully represented by its normal and tangentialcomponents, we are therefore justified in considering buttwo kinds of internal stress, normal or direct, and tangen-tial or shearing. 182. Stress on Oblique Section of Rod in Tension.—Considerb free a small cubic element whose edge =a in length; it has twofaces parallel to the paper, beingtaken near the middle of the rodin Fig. 192. Let the angle whichthe face AB, Fig. 196, makes withthe axis of the rod be = a. Thisangle, for our present purpose, isconsidered to remain the samewhile the two forces P are acting,as before their action. The re-sultant stress on the face AB hav-ing an intensity p=P~F, (see ) per unit of transverse sectionof rod, is = p (a sin a) a. HenceFlG- m- its component normal to AB is pa2 sin2 a ; and the tangential or shearing component along —/^ w \ r A^ y c^ ^^. ELEMENTARY STRESSES, ETC. 201 AB=pa2 sin a cos a. Dividing by the area, a2, we havethe following: For a rod in simple tension we have, on a plane makingan angle, a, with the axis : a Normal Stress =p sin2 a per unit of area . (1)and a Shearing Stress =p sin a cos a per unit of area . (2) Unit of area here refers to the oblique plane in ques-tion, while p denotes the normal stress per unit of area ofa transverse section, , when a=90°, Fig. 194. The stresses on CD are the same in value as on AB,while for BG and A I) we substitute 90°—a for a. shows these normal and shearing stresses, and also,much exaggerated, the strains or change of form of theelement (see Fig. 192). 182a. Relation between Stress and Strain.—Experimentshows that so long as the stresses are of such moderatevalue that t
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888