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0O cos 0O abscissa applied arch bridges ARCH WITHOUT HINGES arch-rib arch-ring assumed Axial Stress included Axial Stress neglected axis centre common method compute constant crown curve dead load described circle determined dimensions directrix Effect of Axial elastic arch employed Engineering equal and symmetrical equations equilibrium polygon factor of safety falseworks feet flanges formulas given in Table graphically hence horizontal thrust inches joints KxAs left support linear arch live load magnitude masonry arches maximum middle third moments of inertia morocco moving load obtained pounds per square radius radius of gyration relative error single horizontal load single load single vertical load skew-backs soffit span spandrel-braced spandrels square foot Substituting the value summation formulas symmetrical arch temperature terms containing three-point circle two-nosed catenary uniform load unity values of Hx
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