Diseño, desarrollo y evaluación de la prueba de la división.

4.4.1 Introduction

(1)P Strengthening for torsion is deemed necessary when the applied factored torsional moment is greater than the corresponding torsional capacity. The latter shall be determined considering the contributions of both concrete and steel transverse reinforcing bars when available.

(2)P Torsional strengthening shall be verified at ULS only.

(3)P In the following of this document some specific configurations of FRP torsional strengthen- ing are considered. Other solutions are also possible, provided that their effectiveness is proven and their contribution to the shear capacity is quantified.

4.4.2 Strengthening configurations

(1) Strengthening for torsion is realized by applying one or more layers of FRP material exter- nally bonded to the surface of the member to be strengthened (Figure 4-7). External FRP reinforce- ment can be applied in a discontinuous fashion with gaps between following strips, or continuously with strips next to each other.

(2) Design of FRP reinforcement depends on FRP thickness, width, and spacing. Fibers shall be arranged with an angle β = 90° with respect to the longitudinal axis of the member.

(3) FRP shall be placed around the cross section as a completely wrapped system only (Figure 4-8).

(4) Strengthening for torsion may also be realized through the installation of FRP bars in dedi- cated slots made on the outer surface of the member to be strengthened as near-surface mounted re- inforcement. Such type of strengthening is not dealt with in this document. If used, its effectiveness shall be supported by experimental evidence.

4.4.3 Torsional capacity of FRP strengthened members

(1)P The following applies to prismatic members where an ideal ring-shaped resisting area can be identified.

4.4.3.1 Torsional capacity

(1) Torsional capacity of FRP strengthened members can be evaluated as follows:

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Rd min Rd,s Rd,f, Rd,max

T = T +T T (4.34)

where T_Rd,s is the existing steel contribution to the torsional capacity according to the current building code, and T_Rd,f is the FRP contribution to the torsional capacity, to be evaluated as indi- cated in the following. Torsional strength shall not be taken greater than T_Rd,max. This last value denotes the ultimate strength of the concretet strut, to be evaluated according to the current building code.

(2) The existing steel contribution to the torsional capacity, T_Rd,s, can be calculated as follows:

sw l

Rd,s e ywd e yd

e

min A 2 cot , A 2 tan

T B f B f

p θ u θ

⎧ ⎫

= _⎨ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ _⎬

⎩ ⎭ (4.35)

where A_sw is a one-leg steel stirrup area, p is the stirrups spacing, B_e is the area bounded by the polygon whose edges are the centers of gravity of the longitudinal steel bars, f_ywd is the design yield strength of transverse steel reinforcement, A₁ is the total area of existing steel longitudinal re- inforcement, u_e is the perimeter of the above mentioned polygon, f_yd is the design yield strength of the existing steel longitudinal reinforcement, and θ is the angle of the compressed struts with re- spect to the member longitudinal axis (the value θ = 45° can be assumed if a more accurate deter- mination is not available).

(3) T_Rd,max in Equation (4.34) shall be calculated as follows:

Rd,max 0.50 cd e s

T = ⋅f ⋅ ⋅ (4.36) B h

where f_cd is the design concrete compressive strength, and h_s is set equal to 1 6 of the diameter of the maximum circle enclosed in the polygon whose edges are the centers of gravity of the existing

steel longitudinal reinforcement.

(4) If Equation (4.35) shows that the minimum torsional capacity is due to the existing steel transverse reinforcement, the FRP contribution expressed in Equation (4.34) shall be calculated as follows: f Rd,f fed f Rd f 1 2 w cot T f t b h p θ γ = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ (4.37)

where the partial factor γ_Rd shall be set equal to 1.20 (Table 3-3, Section 3.4.2); f_fed is the FRP design effective strength to be evaluated as in Section 4.3.3.2; t_f is the thickness of the FRP strip or sheet; b and h are section width and depth, respectively; θ is the angle of the compressed struts with respect to the member longitudinal axis (the value θ = 45° can be assumed if a more accurate de- termination is not available); and w_f and p_f are width and center-to-center spacing of FRP strips measured orthogonally to the fiber direction, respectively. For FRP strips applied one next to each other the ratio w_f p_f shall be set equal to 1.0.

(5) If Equation (4.35) shows that the minimum torsional capacity is due to the existing steel lon- gitudinal reinforcement, FRP strengthening shall not be performed.

(6) In case of combined torsion, T_sd, and shear, V_sd, the following limitation shall be met:

Sd Sd

Rd,max Rd,max

1

T V

T +V ≤ (4.38)

where T_Rd,max and V_Rd,max are calculated according to Equations (4.36) and the requirements of the current building code, respectively. Because strengthening for shear and torsion are calculated separately, the overall strengthening area is given by the sum of the area deemed necessary for shear and torsional FRP strengthening.

4.4.3.2 Limitations and construction details

(1) For U-wrapped and completely wrapped configurations, a minimum 20 mm radius shall be provided when FRP sheets are installed around outside corners.

(2) For external FRP reinforcement in the form of discrete strips, strips width, w_f (mm), and cen- ter-to-center spacing between strips, p_f (mm), shall not exceed the following limitations, respec- tively: 50 mm≤ w_f ≤250mm, and w_f ≤ p_f ≤min

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