Plain and Reinforced Concrete Arches

abutments applied approximately arch curve arch-axis arch-points assumed axes axial thrust axis of abscissæ bending bending moment calculated center of gravity coefficient compressive stress constructed coordinates cos² cross-section crown thickness d₁ dead load defined by Eqs deflections deformation denotes depth of rib determined distance elastic elastic modulus end-reactions ends equations force polygon forces acting formulæ ft.-lbs full-span load funicular polygon H₁ half-span load Hence hingeless arch hinges horizontal thrust inertia influence lines joint-pressures line of resistance live load load G lower fiber masonry maximum stresses Melan moment of inertia moments neutral axis obtain ordinates P₁ parabola piers pole-distance produced radius of curvature ratio reinforced concrete arches resistance-line resultant rotation span spandrel filling sq.ft sq.in statically indeterminate Substituting symmetrical temperature tensile stresses tension three-hinged arch upper fiber vertical weights width X-axis X₁ бр