PSI - Issue 72

Vera Vujović / Procedia Structural Integrity 72 (2025) 5 – 12

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2.1. External load External loads in arch supports cause bending moments. The vertical and horizontal support reactions oppose the compressive forces in the arch or vault. The shape of the arch supports allows the external load to be transmitted by the force of the pressure. For reconstruction calculations, all forces caused by the weight of the construction, the seismic and the hydraulic load are transferred to the foundation and then to the ground. Looking at the simplified model of a semicircular arc made of stone blocks, all the forces acting on the ring arc are the forces of pressure. The load on the crown is transferred to the ground under the influence of the pressure of each stone pressed downwards. As long as the stone is strong enough to resist crushing, the arc will stand in an equilibrium position. Decaying one of the stone blocks can cause damage or demolition of the arches. Practice has shown that the behavior of arched bridges is complex (in the arc wall, the stone must resist crushing due to the force of pressure, and must maintain its equilibrium position in the arc ring). The arch is trying to achieve the balance of a flat side with a tendency towards balance under the influence of external thrust, which must be opposed to the pillars at the ends of the onion ring. Stone and concrete have relatively low tensile strength, but are well tolerated by the force of pressure. Mortar bonding to stone has very low tensile strength. At the proportions of the old arcs, the stresses were negligible, and this was achieved by the ring of the semicircular arc. The arches can be described by the geometry and the drawing of the arc ring. The simplest and the most stable configuration of a semicircular arc or fully centered, from each point on the arc of an arc equidistant from the common center. If the arc described a circular arc smaller than 180o, the arc is considered segmental. This configuration, as well as arcs with an elliptical shape, allow for longer ranges and therefore a smaller rise to the ratio of the range. Straight configurations cause higher stresses in the arc ring and require heavier pillars that can resist their suppression. The walled arches that resemble the interior of the barrel, the width of which has a continuous ring, are called voussoir. The old builders have reached the boundaries imposed on them by building materials, as well as the technical possibilities of transport, design and installation. They mostly built well-proven bridge structures, fully applying the technologies of the time. 2.2. Fracture mechanism By forming a plastic joints in any section of a statically determinate structure, it will turn into a mechanism, while in statically indeterminate structures, the formation of a plastic joints will not endanger its load-bearing capacity. In the case of an n-fold statically indeterminate structure, the formation of n plastic joints will transform it into a stable statically determinate structure. It is necessary to form n+1 plastic joints for an n-fold statically indeterminate structure to become unstable. Then the structure will lose its load-bearing capacity and turn into a mechanism. To fully understand the arch, it is necessary to study its failure mechanisms. Plastic joints are formed due to:  direct loading,  deformation caused by settlement,  horizontal movement of the arch or temperature changes. If the supports of a simple stone arch of small diameter are moved, the arch will adapt to this range, and in order to achieve this, cracks will appear. Stone blocks will not slide due to friction, due to high stiffness, deformations will be negligible, but the blocks can rotate around the contact point between the two blocks. Cracks that can occur on the extrados and intrados are considered plastic joints. Due to changes in the shape of the arch, changes in the shape of the pressure line will occur. The result is that the pressure line touches the edge and plastic joints are created in these places. The formation of cracks in more complex structures is also created through the stone blocks, and not only between them. Cracks do not represent the beginning of the collapse of the objects, but indicate that unpredictable changes have occurred in the design environment.