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 . £Pmdm. The potential energy given up by the load= Gdmi while £he initial and final kinetic energies are bothnothing. .-. Gdm=y2mPdm . (5) That is, Pm=26r. Since at this instant the load is sub-jected to an upward force of 2G and to a downward forceof only G (gravity) it immediately begins an upward mo-tion, reaching the point whence the motion began, andthus the oscillation continues. We here suppose the elas
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 . £Pmdm. The potential energy given up by the load= Gdmi while £he initial and final kinetic energies are bothnothing. .-. Gdm=y2mPdm . (5) That is, Pm=26r. Since at this instant the load is sub-jected to an upward force of 2G and to a downward forceof only G (gravity) it immediately begins an upward mo-tion, reaching the point whence the motion began, andthus the oscillation continues. We here suppose the elas-ticity of the beam unimpaired. This is called the sud-den application of a load, and produces, as shown above,double the pressure on the beam which it does when grad-ually applied, and a double deflection. The work doneby the beam in raising the weight again is called its re-silience. Similarly, if the weight G is allowed to fall on the mid-dle of the beam from a height h, we shall have Gx(h+dm), or approx., Gh=)4Pmdm; and hence, since (4) gives dm in terms of Pm,. 256 MECHANICS OF ENGINEERING. This theory supposes the mass of the beam small com-pared with the falling weight. 234. Case II. Horizontal Prismatic Beam, Supported at BothEnds, Bearing a Single Eccentric Load. Weight of Beam Neg-lected.—Fig. 227. The reactionsof the points of support, PQ andPu are easily found by consider-ing the whole beam free, and put-ting first Ifmom.),, =0, whence Px~It I =Pl-t-lL, and then ^(mom.^^O, no 227. whence P0=P(ll—l)+l1. P0 and Pi will now be treated as known quantities. The elastic curves OG and CB, though having a commontangent line at G (and hence the same slope «c), and a com-mon ordinate at (7, have separate equations and are bothreferred to the same origin and axes, as shown in thefigure. The slope at 0, «o, and that at B,ait are unknownconstants, to be determined in the progress of the work. Equation of OC.—Considering as free a portion of thebeam extending from B to
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
