(1)P Structural members with single or double curvature generally lose their functionality due to the formation of hinges that promote the mechanisms of collapse. Hinges form in such masonry structures due to the negligible tensile strength of the masonry.
(2)P Such hinges are located in regions of limited contact area, externally to the mid plane of the structure. As first approximation, they can be located either at the intrados or extrados of the ma- sonry panel. A masonry hinge can carry axial and shear forces. As a result, the hinged section can only carry an axial force having an eccentricity equal to half of the structure thickness.
(3)P FRP reinforcement delays both opening of cracks and formation of hinges within the ma- sonry panel located on the opposite side with respect to the one where the FRP system is installed. Therefore, a properly anchored FRP reinforcement applied to the extrados (intrados) prevent the formation of hinges on the opposite side of the intrados (extrados). FRP reinforcement is not rec- ommended when collapse is controlled by either crushing of the masonry or shear failure.
(4)P FRP reinforcement used as external strengthening of masonry structures is such to prevent the formation of certain hinges.
5.5.1 Arches
(1)P Two structural schemes can be taken into consideration:
• Arch scheme, for arches resting on fixed and/or hinged supports.
• Arch-pier scheme, also known as frame scheme, for arches resting on piers.
(2)P Both schemes generally tend to collapse due to the formation of at least four hinges. In par- ticular, a possible mechanism may be due to the formation of three (real) hinges and a double pen- dulum (pseudo-hinge) leading to a shear failure of a portion of the arch with respect to the other.
5.5.1.1 Arch scheme
(1)P To prevent the mechanism characterized by the formation of four hinges, FRP reinforcement may be bonded either to the extrados or the intrados of the masonry arch. Experimental evidence shows that application of FRP reinforcement on the side surface of the arch does not provide sig- nificant improvement of the structural behavior. In such a case, a premature debonding of the FRP reinforcement from the masonry face takes place. Such debonding is localized in the arch com- pressed region and it is due to local FRP instability, followed by a fast degradation of the bond be- tween masonry and FRP.
(2) FRP strengthening is preferably carried out by applying FRP reinforcement on the extrados of the masonry arch to prevent the formation of hinges on the intrados. Alternatively, FRP rein- forcement may be applied on the arch intrados to prevent the formation of hinges on the extrados. As a final remark, FRP reinforcement may also be applied to both extrados and intrados of the ma- sonry arch to prevent the formation of first and second type-hinge. However, this application is not common.
(3) Unless the formation of hinges is prevented in the region of the masonry arch close to sup- ports, when computing internal forces of the strengthened arch the formation of hinges at supports shall always be considered.
vent the possibility of formation of hinges responsible for the activation of a kinematic mechanism of the structure. However, when FRP strengthening is properly designed and realized, it may en- hance the structure’s ultimate capacity. It shall be preferable to do the following:
• Carry out complete FRP strengthening on the extrados or intrados of the arch.
• Choose FRP fabric over laminate, because they better fit the geometry of the masonry arch. • Apply FRP strengthening on the arch extrados; in this case the arch curvature is such to dis-
play compressive stress orthogonal to the FRP reinforcement. On the other hand, when FRP is installed on the intrados, the curvature is such to display tensile stress orthogonal to the FRP reinforcement that enhance debonding between FRP and masonry.
(5) When computing internal forces of the FRP strengthened masonry arch, the formation of hinges located on the opposite side with respect to the side of FRP installation shall be taken into account. A more realistic approach should consider that the hinge will form at a certain distance to the side located at the opposite face of FRP reinforcement. Such a distance depends on the masonry compressive strength; it increases as the masonry compressive strength decreases.
(6)P When masonry tensile stresses can be neglected, the following checks shall be performed for FRP strengthened arches:
• Overall stability of the structure.
• Combined bending and axial force, when failure occurs by either crushing of the masonry and/or FRP rupture.
• Shear.
• FRP debonding.
(7) Combined bending and axial force as well as shear check shall be in compliance with the procedure indicated for masonry panels. Check for FRP debonding shall be performed at a distance
b
l from the end of FRP reinforcement; the moment corresponding to such section shall be evalu-
ated using the FRP design strength according toSection 5.3.3 item (3).
5.5.1.2 Arch-pier scheme
(1) For arch-pier structures, application of FRP reinforcement to the arch intrados or extrados may not be sufficient to prevent relative displacements of the pier-arch connections. In such a case, it is preferable to either act on the piers or set a tie rod between the pier-arch connections.
(2)P Checks to be carried out are the same as those considered for the arch scheme.
5.5.2 Single curvature vaults: barrel vaults
(1)P In most situations, the study of barrel vaults is similar to that of a unit depth arch. Conse- quently, barrel vaults may be strengthened with FRP applied both on the extrados and intrados. To satisfy safety requirements, FRP strengthening shall be applied along the entire longitudinal length of the vault. For this reason, FRP reinforcement shall be placed at a center-to-center distance, pf, calculated as follows:
f 3 f
p ≤ ⋅ + (5.22) t b
where t is the vault thickness and bf is the FRP width. A greater distance is allowed only if prop- erly substantiated.
(2) Longitudinal FRP strengthening has only the secondary importance of bridging the ideal arches forming the barrel vault. Such mechanism is particularly important in cases of horizontal loading.
(3) Typically, it is suggested to install in the longitudinal direction at least 10 % of the FRP re- inforcement applied in the transversal direction. It shall be increased to 25 % for FRP strengthening in seismic area.
(4) If vaults are used in cellular buildings with small-size rooms, FRP strengthening should be performed on the building walls rather than the vault.
5.5.3 Double curvature vaults: domes
(1)P Domes exhibit membrane-type and flexural-type stresses.
5.5.3.1 Membrane-type stresses
(1) In a dome subjected to vertical loads, normal tensile stresses directed along the dome paral- lels are displayed. The typical cracking pattern with cracks located along the meridians is primarily due to the negligible tensile strength of the masonry. The mentioned crack pattern modifies the equilibrium condition of the dome enhancing the horizontal forces where the dome connects with the supporting structure. The use of FRP reinforcement applied in a circle around the lower portion of the dome’s perimeter may help in preventing the opening of cracks as well as reducing the mag- nitude of the horizontal force acting on the supporting structure.
(2)P The degree of safety of a masonry dome shall be performed by checking the following: • Tensile stress in FRP reinforcement.
• FRP debonding according to Section 5.3.3.
5.5.3.2 Flexural-type stresses
(1) Flexural-type stress is typically localized where the dome meets the supporting structure or at the edge of skylight, when available. In particular, flexural-type stress may cause collapse of por- tions of the dome delimitated by meridian cracks. If the load carrying capacity of such portions is controlled by failure of the region connecting the dome to the supporting structure, the dome may be strengthened by applying FRP reinforcement in a circle around the lower portion of the dome pe- rimeter. If the dome supporting structure does not show any displacement, the above mentioned FRP circular strengthening is inactive. In such a case, FRP reinforcement shall be applied along the dome meridians.
(2) P The degree of safety of a masonry dome shall be performed by checking the following: • Combined bending and axial force.
• Shear.
• FRP debonding.
For combined bending and axial loads as well as shear check, internal forces shall be evaluated on a unit dome element according to Sections 5.4.1.2.1 and 5.4.1.2.2. Possible strength reductions for the loading carrying capacity of the strengthened dome shall be considered due to the complexity of the internal forces associated to the analysis of dome structures. Precautions shall be taken in case of combined bending and axial load when the tensile zone in one direction corresponds to a compres- sion zone in the opposite direction. In such a case, unless a more rigorous analysis is performed, the ratio of the absolute value of the design applied moment to the nominal moment calculated under the applied axial load shall not be larger than 1. On the contrary, unless a more rigorous analysis is
performed, the specific flexural capacity in each plane can be assumed equal to the one resulting from a monoaxial loading condition.
Planar shear design can be performed according to the first of the two cases previously mentioned. It is to be noted that flexural and shear capacity shall be calculated with reference to the design compressive strength of the masonry by taking into account differences due to loading perpendicu- lar or parallel to the masonry texture (Section 5.2.3 item (6)P). Othogonal shear design can not take into account the presence of FRP reinforcement and shall be performed as in the case of unrein- forced masonry considering the complexity of the existing internal forces. Checks for FRP debond- ing shall consider tensile stresses acting perpendicular to the FRP reinforcement according to Sec- tion 5.3.3.
(3) To ensure proper behavior of the FRP system applied in a circle around the lower portion of the dome perimeter, FRP reinforcement shall be accurately anchored to the dome supporting struc- ture eventually by means of mechanical anchorage.
5.5.4 Double curvature vaults on a square plane
(1) FRP strengthening of double curvature vaults resting on a square plane shall primarily be performed on the masonry walls of the room that support the vault itself. For vertically loaded structures, integrity and stiffness of the supporting masonry walls ensure that the vault is primarily subjected to compression stresses. If this is not the case, FRP strengthening may be performed within the corner region of the vaults where tensile stress is expected to exist in a direction orthogo- nal to the room diagonals.