. Railway maintenance engineering, with notes on construction . ^m^^^^. Fig. 107.—Effect of Unequal Distrubition of Tie Pressure on Sub-grade.(Am. Ry. Eng. Assn.—Schubert.) show the thickness of ballast necessary to produce an equal dis-tribution of the axle loads on the surface of the roadbed under-neath the ballast.* Referring to Fig. 108, the following formulae are suggested byMr. Johnson: For gravel x = b^+^d\ For stone x = b^+d\ * See Proceedings Am. Ry. Eng. and M. of W. Assn., Vol. 7, 1906,p. 104. 184 RAILWAY MAINTENANCE In the figure the arcs will approximate to parabolas and maybe con

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. Railway maintenance engineering, with notes on construction . ^m^^^^. Fig. 107.—Effect of Unequal Distrubition of Tie Pressure on Sub-grade.(Am. Ry. Eng. Assn.—Schubert.) show the thickness of ballast necessary to produce an equal dis-tribution of the axle loads on the surface of the roadbed under-neath the ballast.* Referring to Fig. 108, the following formulae are suggested byMr. Johnson: For gravel x = b^+^d\ For stone x = b^+d\ * See Proceedings Am. Ry. Eng. and M. of W. Assn., Vol. 7, 1906,p. 104. 184 RAILWAY MAINTENANCE In the figure the arcs will approximate to parabolas and maybe considered as such. The intensity of pressures is proportionate to the ordinatesof the curve. Areas of parabolic segment = fx?/; hence mean ordinate = §2/?or mean pressure = f maximum pressure, or maximum pressureequal to f mean pressure. Pressure at b = 0; hence, to obtain an approximately uniformdistribution over the surface of roadbed, the tie spacing S must

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