The elasticity and resistance of the materials of engineering . , AB; and BC = =r, AB . (i) If / is the intensity ofvertical pressure at any point, /fax = —rrr wax^ AB (2) But by Eq. (i) : AB =. E E + E ^AC Also, if R is the radius of the roller: w AC=d-y; and AB = R ^ . E Hence, E E dP pdx — w . -^— (d — y) dx = —• . (3) ?^ E -\- E Rw ^ -^ 2 ^^^ From the equation of the circle : y = R — ^/R^ - x Art. 78.] CYLINDRICAL ROLLERS. 661 Since P= 2 dP, there results P = ^ i^f^E) (^ -^R-\-V2{R- er e + y2R^ stn-^£) (4) Eq. (4) can be very much simplified for all ordinary what has preceded :

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The elasticity and resistance of the materials of engineering . , AB; and BC = =r, AB . (i) If / is the intensity ofvertical pressure at any point, /fax = —rrr wax^ AB (2) But by Eq. (i) : AB =. E E + E ^AC Also, if R is the radius of the roller: w AC=d-y; and AB = R ^ . E Hence, E E dP pdx — w . -^— (d — y) dx = —• . (3) ?^ E -\- E Rw ^ -^ 2 ^^^ From the equation of the circle : y = R — ^/R^ - x Art. 78.] CYLINDRICAL ROLLERS. 661 Since P= 2 dP, there results P = ^ i^f^E) (^ -^R-\-V2{R- er e + y2R^ stn-^£) (4) Eq. (4) can be very much simplified for all ordinary what has preceded : When e is small : sin-^ -— = —-; ^ = ^2Rd -\- d^ ; and (R - cy^ = R--^^ in Eq. (4): ^^ rWVe)^^^^-^^ .... (5) Hence, as ^is small, nearly : p^R^f2W^^+^ (6) Or, for length /: P = RI^/2W^^±^ (7) A simple expression for conical rollers may be obtained byusing Eq. (6). 662 CONICAL ROLLERS, [Art. -jZ. As shown in Fig. 2, let z be the distance parallel to theaxis of any section from the apex of the cone ; then consider a. portion of the conical roller whose length is dz. Let R-^ be theradius of the base. The radius of the section under consider-ation will then be : R^-^R.; and the weight it will sustain :

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Keywords: ., book, bookcentury1800, booksubjectbuildingmaterials, bookyear1883