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 . axesII to wall. Uniform outlines semi-cubic parabolas. VSections similarrectangles. Fig. 291, (a). (y2v)=(y2h) W Fig. 291, (b). #«=(#% (5) (y2uy=(y2by (6) Fig. 291, (c). W=W? (6) 289.—Beams and cantilevers of circular cross-sectionsmay be dealt with similarly, and the proper longitudinaloutline given, to constitute them bodies of uniformstrength. As a consequence of the possession of thisproperty,
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 . axesII to wall. Uniform outlines semi-cubic parabolas. VSections similarrectangles. Fig. 291, (a). (y2v)=(y2h) W Fig. 291, (b). #«=(#% (5) (y2uy=(y2by (6) Fig. 291, (c). W=W? (6) 289.—Beams and cantilevers of circular cross-sectionsmay be dealt with similarly, and the proper longitudinaloutline given, to constitute them bodies of uniformstrength. As a consequence of the possession of thisproperty, with loading and mode of support of specifiedcharacter, the following maybe stated; that to find theequation of safe loading any cross-section whatever may beemployed. This refers to tension and compression. Asregards the shearing stresses in different parts of the beamthe condition of uniform strength is not necessarily ob-tained at the same time with that for normal stress in theouter fibres. DEFLECTION OF BEAMS OF UNIFORMSTRENGTH. 290. Case of § 283, the double wedge, but symmetrical,, li=l0=yi, Fig. 292. Here we shall find the use of the BEAMS OF UNIFORM STRENGTH. 343. Fig. 292. EI form — (of the three forms for the moment of the stress Pcouple, see eqs. (5), (6) and (7), §§ 229 and 231) of the most direct service in determining the form of the elastic curveOB, which is symmetrical, and has a common tangent atB, with the curve BC. First to find the radius of curva-ture, p, at any section n, we have for the free body nO,i(), whence EI /-r, r, i i f from eq. ) u ,_ ,,.,,,. ——-+}4Px=0 ; but | (3) § 283 J x= i#l and /= lvuh we have 1/1 E 9 uh3= %P -r and ?=Vi I E_P (1) from which all variables have disappeared in the righthand member; , p is constant, the same at all points ofthe elastic curve, hence the latter is the arc of a circle,having a horizontal tangent at B. To find the deflection, d, at B, consider Fig. 292, (b)where d=KB, and the full ci
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
