SAFETY EVALUATION

5.2.1 Structural modelling

(1)P Design of FRP reinforcement shall be based on a structural scheme representing the behav- ior of the building for the expected future use.

(2)P Internal forces acting on the masonry shall be determined using the methods of structural analysis. In particular, the structure can be modeled as either linear elastic or through proven non linear models capable of simulating the inelastic behavior and the negligible tensile strength of the masonry.

(3) Simplified schemes can also be used to describe the behavior of the structure. For example, provided that tensile stresses are directly taken by the FRP system, the stress level may be deter- mined by adopting a simplified distribution of stresses that satisfies the equilibrium conditions but not necessarily the compatibility of strain. The use of simplified stress distributions should be very carefully chosen because a statically satisfactory stress level could have already caused the structure to collapse due to the brittle nature of the FRP-masonry system. In case of structures with regular or repetitive parts, partial structural schemes may be identified that allow for a rapid evaluation of the overall behavior of the strengthened structure. Likewise, simplified models may be adopted for verifications of local failure mechanisms, provided that their use is correctly motivated.

5.2.2 Verification criteria

(1)P Possible failure modes of masonry walls strengthened with FRP systems can be summarized as follows:

• Excessive cracking due to tensile stresses in the wall. • Crushing of masonry.

• Shear-slip of masonry. • FRP rupture.

• FRP debonding.

Failure mode of FRP strengthened masonry structures usually involves a combination of the above mentioned mechanisms.

5.2.3 Safety verifications

(1) Masonry can be considered an anisotropic material exhibiting a non-linear behavior. The stress-strain relationship may vary quite significantly depending whether the structure is built using artificial or natural blocks as well as the type of mortar employed.

(2) Masonry exhibits a brittle behavior when subjected to tensile loading; the corresponding tensile strength is negligible compared to its compressive strength. For design purposes, it is ac- cepted to neglect tensile strength of masonry.

(3)P Laboratory tests show that the stress-strain diagram of masonry blocks subjected to com- pressive loads can be described as follows:

• Basically linear for low strain values.

• Non-linear as the load increases up to the ultimate value.

• Non-linear softening after the load at ultimate has been reached.

(4) The masonry behavior for compressive load also depends on the availability of transverse confinement. By increasing the transverse confinement, strength and ductility of the material is im- proved.

(5)P Masonry shear strength depends on the applied axial load because it usually relies upon co- hesion and friction of the material.

(6)P The characteristic values for strength are as follows: • f_mk for vertical compression.

• f_mkh for horizontal compression. • f_vk for shear.

Such values shall be determined in compliance with the current building code. A reference value for h

mk

f is 50 % of f_mk.

(7) Design values for mechanical properties of masonry are computed by dividing the character- istics’ values by the partial factor of the material γ_m =γ_M as well as by the partial factor for resis- tance model, γ_Rd, according to the current building code and the present document.

(8)P For most engineering applications, the behavior of masonry under uniaxial loads may be simplified as follows:

• tensile stress: neglected.

• compression: linear behavior with slope equal to the secant modulus of elasticity up to both design strength of f_md and design strain of ε ; design strength equal to _m f_mk for strain be- tween ε_m ≤ε ≤ε_mu; and zero strength for strain larger than ε_mu.

(9)P Unless experimental data is available, the masonry ultimate design strain, ε_mu, may be as- sumed equal to 0.35 %.

(10) Alternatively, appropriate stress-strain diagrams embracing the behavior described in (3)P may be used, provided that their performance is validated on the basis of experimental investiga- tions.

(11)P FRP materials are characterized by an anisotropic behavior, as described in detail in Section 6.2. When stressed in the fiber direction, FRP exhibits a linear elastic behavior up to failure, whose characteristic value is f_fk.

The maximum design strain allowed to the FRP system shall be expressed as follows: fk fd a fdd f min ε , ε η ε γ ⎧ ⎫ = _⎨ ⋅ _⎬ ⎩ ⎭ (5.1)

where ε represents the FRP characteristic strain at failure, and _fk ε_fdd is the maximum FRP strain once FRP debonding takes place (see next section). Unless more accurate data is available, ε_fdd shall be taken from item (7) of Section 5.3.2. The values to be assigned to the conversion factor,

a

η , and the partial factor, γ_m =γ_f, are indicated in Table 3-4 and Table 3-2, respectively.

(12)P Design recommendations are based on limit-states-design principles. For ultimate limit states analysis, two possible approaches may be recognized depending upon the type of structural analysis performed. If non linear models are used, the member’s load carrying capacity shall be lar- ger than the factored applied load. The latter is computed according to the current building code. Care shall be taken to ensure that the proposed solution is not affected by the particular discretiza- tion adopted for the computation. If linear elastic models or simplified schemes adopting a balanced distribution of stresses that satisfy equilibrium conditions but not necessarily compatibility of strain are used, the resulting stress on each structural member shall be verified. In particular, for bi- dimensional members (slabs, shells), the unit stress shall be considered (e.g., those evaluated per unit length of the member). Assuming that a plane section before loading remains plane after load- ing, the design criteria is met when factored shear forces and bending moments due to the applied loads are smaller than the corresponding design factored shear and flexural capacities. The latter shall be evaluated as a function of the applied axial force, considering the non linear behavior of the material represented by the simplified stress-strain diagram introduced in item (8)P.

(13)P Other limit states shall be verified according to the current building code requirements.