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 . (weights uniform along the curve) the forces beingreversed in. direction. Fig. 329. Instead of compressionwe have tension, while the || vertical forces act toward in-stead of away from, the axis X Hence the curve of equi-librium of Fig. 328 is an inverted catenary (see § 48) whoseequation is 2/+c=^cp+e J (1) See Fig. 330. e = the Naperian Base. The par-ameter c may be determined by putting x = a, the
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 . (weights uniform along the curve) the forces beingreversed in. direction. Fig. 329. Instead of compressionwe have tension, while the || vertical forces act toward in-stead of away from, the axis X Hence the curve of equi-librium of Fig. 328 is an inverted catenary (see § 48) whoseequation is 2/+c=^cp+e J (1) See Fig. 330. e = the Naperian Base. The par-ameter c may be determined by putting x = a, the halfspan, and y= 0 Y, the rise, then solving for c by successive 388 MECHANICS OF EXGIXEEKIXG. approximations. The horizontal thrust or HQi is = qc,while if s = length of arch OA, along the curve, the thrustT at any point A is T=VHQ2+q2s2 (2.) From the foregoing it may be inferred that a series of vous- soirs of finite dimensions, arranged so as to contain the catenary curve, with joints ] to that curve and of equal weights for equal lengths of arc will be in equilibrium, and moreover in stable equilibrium on account of friction, and the finite width of the joints; see Fig, FIG. 331. 318. Linear Arches under Given Loading.—The linear archesto be considered further will be treated as without weightthemselves but as bearing vertically pressing loads (eachvoussoir its own). Problem.—Given the form of the linear arch, itself, it isrequired to find the law of vertical depth of loading underwhich the given linear arch will be in equilibrium. , given the curve ABC, , the linear arch itself, re-quired the form of the curve MON, or upper limit of load-ing, such that the linear arch ABC shall be in equilibriumunder the loads lying between the two curves. The load-ing is supposed homogeneous and of constant depth ~\ topaper; so that the ordinates z between the two curves areproportional to the load per horizontal linear unit Assumea height of load z0 at the crown, at
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectenginee, bookyear1888
