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 . xdM= Mx = My; hence (1) becomes lz, = Iz+M(d*-2ax-2by), . ... (2) in which a and b are the x and y of the axis Z\ x and y referto the centre of gravity of the body. If Z is a gravity-axis(call it g), both x and y = 0, and (2) becomes Iz, =Ig + Md* or kz,* = V + d\ . (3) It is therefore evident that the mom. of inertia about a grav-ity-axis is smaller than about any other parallel axis. Eq. (3) incl
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 . xdM= Mx = My; hence (1) becomes lz, = Iz+M(d*-2ax-2by), . ... (2) in which a and b are the x and y of the axis Z\ x and y referto the centre of gravity of the body. If Z is a gravity-axis(call it g), both x and y = 0, and (2) becomes Iz, =Ig + Md* or kz,* = V + d\ . (3) It is therefore evident that the mom. of inertia about a grav-ity-axis is smaller than about any other parallel axis. Eq. (3) includes the particular case of a plane figure, by MOMENT OF INERTIA. 93 •writing area instead of mass, , when Z (now g) is a gravity-axis, (4) Iz,=Ig + FcT. 89. Other Reduction Formulae; for Plane Figures.—(The axeshere mentioned lie in the plane of the figure.) For two setsof rectangular axes, having the same origin, the following holdsgood. Fig. 100. Since Ix=ffdF, and IY=fx2dF, we have Ix + IY =f(x2 + f)dF Similarly, , Jn -f Iv =f{tf + u2)dF But since the x and y of any dFh&ve the same hypothenuse asthe u and v, we have v* + u* = x*-\- y*; .. Tx-\- 1Y = Iv-\-IV:>..
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
