(From Marston) ──────────────────┬───────────────┬───────────────┬─────────── Symmetrical │Moment at Crown│ Moment at End │Compressive Vertical Loadings │ of Sewer │ of Horizontal │ Thrust at │ │ Diameter │ Crown │ │ │ │ │ │ ────────────┬─────┼───────────────┼───────────────┼─────────── Character │Width│ │ │ ────────────┼─────┼───────────────┼───────────────┼─────────── Concentrated│ 0°│+ .318_R__W_/12│- .182_R__W_/12│ 0.000 Uniform │ 60°│+ .207_R__W_/12│- .168_R__W_/12│ 0.000 Uniform │ 90°│+ .169_R__W_/12│- .154_R__W_/12│ 0.000 Uniform │ 180°│+ .125_R__W_/12│- .125_R__W_/12│ 0.000 ────────────┴─────┴───────────────┴───────────────┴─────────── ──────────────────┬────────────┬───────────┬────────── Symmetrical │Compressive │ Shear at │ Shear at Vertical Loadings │ Thrust at │ Crown │ End of │ End of │ │Horizontal │ Horizontal │ │ Diameter │ Diameter │ │ ────────────┬─────┼────────────┼───────────┼────────── Character │Width│ │ │ ────────────┼─────┼────────────┼───────────┼────────── Concentrated│ 0°│+ .500_W_/12│0.500_W_/12│ 0.000 Uniform │ 60°│+ .500_W_/12│0.000_W_/12│ 0.000 Uniform │ 90°│+ .500_W_/12│0.000_W_/12│ 0.000 Uniform │ 180°│+ .500_W_/12│0.000_W_/12│ 0.000 ────────────┴─────┴────────────┴───────────┴────────── _R_ = the radius of the pipe, _W_ = total weight of ditch filling and superimposed load plus ⅝ of the weight of the pipe itself (usually neglected), expressed in pounds per foot length of pipe. Moments are inch-pounds per inch length of pipe. Shears and thrusts are in pounds per inch length of pipe. =104. Analysis of Sewer Arches.=—The preceding method for the determination of the stresses in a sewer ring has referred only to a circular pipe uniformly loaded. Other methods must be used if the pipe is not circular or the load is not uniformly distributed. The simplest method, is the static or so-called vouissoir method. In this method the arch is assumed to be fixed at both ends, presumably at the springing line or line of intersection between the inside face of the arch and the abutment, and it is so designed that the resultant of all the forces acting on any section shall lie within the middle third of that section. [Illustration: FIG. 82.—Voussoir Arch Analysis. ] [Illustration: FIG. 83.—Force Polygon for Voussoir Arch Analysis. ]