. A treatise on the mathematical theory of elasticity . Fig. 74. The stress-resultants on the side a of the rectangle yield a force havingcomponents -T^BB/3, -S^BSI3, - N^BB^ parallel to the axes of x, y, z. The corresponding component forces for theside a -I- Sa are to be obtained by applying the usual formulae relating tomoving axes; for the quantities Ti, Si, iVj are the components of a vectorreferred to moving axes of x, y, z, which are defined by the tangent to thecurve /9 = const, which passes through any point and the normal to thestrained middle surface at the point. In resolving the f
. A treatise on the mathematical theory of elasticity . Fig. 74. The stress-resultants on the side a of the rectangle yield a force havingcomponents -T^BB/3, -S^BSI3, - N^BB^ parallel to the axes of x, y, z. The corresponding component forces for theside a -I- Sa are to be obtained by applying the usual formulae relating tomoving axes; for the quantities Ti, Si, iVj are the components of a vectorreferred to moving axes of x, y, z, which are defined by the tangent to thecurve /9 = const, which passes through any point and the normal to thestrained middle surface at the point. In resolving the forces acting across 538 EQUATIONS OF EQUILIBRIUM [CH. XXIV the side a + Ba parallel to the fixed axes, we have to allow for a changeof a into a + Ba, and for the small rotation (p/Sa, g/Sa, )\Sa). Hence thecomponents parallel to the axes of x, y, z of the force acting across the sidea + So. are respectively T,5S/3 + Sa I- {T,BB^) - S,BS^. + N,BS^. , da S,Bh^ + Bal {S,BBI3) - N,BS^ .p,Boi + T,BS/3. , 00. N,BS^ + Sa I- {N,BS^) - T,BB^. q/Ba
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Keywords: ., bookcentury1900, bookdecade1920, bookpublishercambr, bookyear1920
