Theory of Arches

abscissas angle arc A D CAB Fig circle common catenary conjugate diameters corresponding cosec crown curve of equilibrium cylinder depth A Y determine direction directrix distance distributed draw ellipse Fig equation Example 1.-Let extrados force H geostatic arch H₁ half-arch hori horizontal and vertical horizontal component horizontal force horizontal lines horizontal load horizontal point horizontal pull horizontal thrust hydrostatic arch inclined intensity line of pressures linear arch little triangles load on A B middle third normal force normal load ordinate P₁ parabola parallel projections parallel to C B parallelogram of forces plane point of rupture Px dy quadrant radius of curvature Rankine's representing the forces soffit spandrel thrust tangents tension tical load tion transformed catenary triangle of forces V₁ cot vertical component vertical force vertical lines vertical load voussoirs weight zontal