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 . g resistance along the convexsurface of the cylinder punched out. Hence if d = diam-eter of hole, and t = the thickness of the plate, the neces-sary force for the punching, the surface sheared beingF= tnd, is P=St7rd .... (2) Another example of shearing action is the stripping *of the threads of a screw, when the nut is forced off lon-gitudinally without turning, and resembles punching inits nature. 212. E an
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 . g resistance along the convexsurface of the cylinder punched out. Hence if d = diam-eter of hole, and t = the thickness of the plate, the neces-sary force for the punching, the surface sheared beingF= tnd, is P=St7rd .... (2) Another example of shearing action is the stripping *of the threads of a screw, when the nut is forced off lon-gitudinally without turning, and resembles punching inits nature. 212. E and Eg • Theoretical Relation.—In case a rod is intension within the elastic limit, the relative (linear) lateralcontraction (let this =m) is so connected with Et and Esthat if two of the three are known the third can be de-duced theoretically. This relation is proved as follows,by Prof. Burr. Taking an elemental cube with four of itsfaces at 45° with the axis of the piece, Fig. 209, the axialhalf-diagonal AD becomes of a length AD=AD+ stress, while the transverse half diagonal contractsto a length B/D/=AD— The angular distortion 3 A?** . A< Fig. 200. § Fig. 210. 230 MECHANICS OF ENGINEERING. is supposed very small compared with 90° and is due tothe shear ps per unit of area on the face BG (or BA).From the figure we have tan(45°—_) = _.~—m—e, approx. [But, Fig. 210, tan(45°—x)=l—2x nearly, where x is asmall angle, for, taking CA=Aty= AE, tan AD=AF=AE—EF. Now approximately EF=WG,^/2^ndiEG^BD^/2 =x^/2 .*. AF= 1—2x nearly.] Hence l_<5=l__m_£; or d=m+£ . (2) Eq. (2) holds good whatever the stresses producing thedeformation, but in the present case of a rod in tension,if it is an isotrope, and if p = tension per unit of area onits transverse section, (see § 181, putting a=45°), we haveEt=p+£ and Es=(ps on BC)-±-o= %p^-o. Putting also(m :e)=r, whence m=rs, eq. (2) may finally be written kHr+1)h^^m ? ? (3) Prof. Bauschinger, e
Size: 1742px × 1434px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
