CÓDIGO PROCESAL CIVIL Y COMERCIAL DE ARGENTINA

In experimental research, the maximum curvature is typically studied at the constant moment span, while distribution of the curvature along the specimen, particularly at the shear span, is not noticed. This is significant as it shows the extent of cracking and contribution of the flexure in failure mechanism.

0 5 10 15 20 25 0 0.005 0.01 0.015 0.02 0.025 0.03 M om ent ( k N m ) Curvature (Øh) Experiment Numerical Analysis Bilinear Cracked 0 5 10 15 20 25 0 0.005 0.01 0.015 0.02 0.025 M om ent ( k N m ) Curvature (Øh) Experiment Bilinear Numerical Analysis

98

Table 15- Summary of experimental and analytical results (moment: kNm) Specimen Mcr Mu (Øh)cr (Øh)u Icr/Ig εfu* εcu* failure _mode

Non-prestressed (Experiment) 7 23.5 0.00025 0.024 — — — 1* Non-prestressed (Analysis) 7.5 23.15 0.00022 0.023 0.03 0.013 -0.003 < 1 Prestressed (Experiment) 13.15 21 0.0005 0.02 — — — 2* Prestressed (Analysis) 12.8 21.3 0.0004 0.023 0.015 0.02 > 0.0027 - 2

1= concrete crushing 2= tendon rupture εfu = maximum tensile strain at AFRP bar when specimen fails

εcu = maximum compressive stress at concrete when specimen fails

Given the deflection profile recorded by STPs, curvature distribution is computed using the finite difference method. Experimental deflection and curvature along the strip are then compared with the analytical results based on the bilinear moment-curvature response of the section which is a simple model that can be used for engineering calculations. The first step of such analysis is to determine the moment diagram along the specimen. For non-prestressed strip, experimental results showed a tiny negative curvature at the simple supports. Further investigation revealed that due to bending of the specimen a frictional force was developed between the steel support and concrete strip and resulted in a small negative moment at the support. Therefore, the moment diagram is modified to account for the effect of such a frictional force given the friction coefficient μ=0.5. This problem, however, was fixed before testing the prestressed strip by releasing the displacement of the support in x direction. The inclined shear diagonal cracks induce a tensile force in AFRP reinforcing bars in addition to the tension caused by flexure. This additional tension increases the moment at the shear span, and hence the moment diagram needs to be modified, accordingly (Park and Paulay 1995). The detail of such calculations to modify the moment diagram is presented as follows.

99

5.4.3.1 The effect of friction at support

As discussed about the non-prestressed strip, small amount of negative curvature was found close to the support indicating the presence of a negative moment. Further investigation revealed that the simple support is restrained against displacement in x direction; thereby a friction force was developed between the steel support and concrete strip as a result of bending. As shown in Fig. 44, assuming a friction coefficient factor of μ=0.5 gives the horizontal friction force equal to P/4 which induces a negative moment M'=Ph/8, where h is the height of the section. Although accounting for the effect of friction force does not cause a considerable negative moment, it results in a more accurate evaluation of the curvature distribution.

Fig. 44. Modification of moment diagram due to friction at support

5.4.3.2 The effect of shear diagonal cracks

Shear diagonal cracks increase the tension in the bottom reinforcement depending upon the magnitude of the shear and the angle of the diagonal crack. As a result of such an additional tension induced in the bottom reinforcement, the moment at the shear span increases, thereby the constant moment span becomes somewhat

0.338P Moment (kNm) P/2 P/2 P/2 P/4 P/2 P/4 M'=Ph/8 M'=Ph/8 0.313P -0.025P -0.025P CL

100

larger and the moment at support is no longer zero. As shown in Fig. 45, x indicates the extension of the constant moment span and ∆M represents the increase in moment. The additional tension induced by the shear diagonal crack in the bottom reinforcement, ∆T, can be found from (Park and Paulay 1990)

2V 4P T

tgθ tgθ

∆ = = ₍₇₎

where V is the shear force equal to P/2, and θ represents the slope of the crack. This additional tension induces an increase in moment equal to

( ) ₂V M T jd jd tgθ         ∆ = ∆ = ₍₈₎

the extension of the constant moment span now can be found using the following equation / 2 2 Vjd tg jd M tg V x x x tg θ α   _θ   ∆ = = = → = ₍₉₎

where α is the slope of the moment diagram.

Fig. 45. Modification of moment diagram due to shear diagonal cracks 0.338P

Moment (kNm)

P/2 P/2

P/2 P/2

CL

Modified for shear diagonal cracks θ

jd/tgθ jd

x

101

Having the moment diagram known, the theoretical curvature distribution based on the bilinear model is computed, and the deflection profile is subsequently found using the conjugate beam theory. Figs. 46 and 47 illustrate the curvature distribution for non- prestressed and prestressed strips close to failure. The results of analysis for non- prestressed strip shows that the bilinear model underestimates the maximum curvature and deflection at constant moment span, but gives nearly accurate values at the shear span. The curvature distribution shows that about 85% of the strip length is cracked before the specimen fails. Excessive cracking and low modulus of elasticity of AFRP bars results in a considerable deformability and desirable warning before failure which can offset the non-ductile behavior of AFRP reinforcing bars to some extent. For prestressed strip, the bilinear model seems to give conservative results particularly at the shear span. However, the maximum curvature at mid-span is in good agreement with the experimental result. The curvature distribution demonstrates that about 50% of the strip length is cracked before failure which indicates a more localized failure compared to the non-prestressed strip. The prestressing force increases the cracking strength and stiffness of the strip, but rather less capacity is left for flexure as there is an initial tensile and compressive strain in AFRP bars and concrete, respectively. As shown in Figs. 40 and 41, this was well inferred from the experiment as the prestressed specimen failed with a much localized cracking pattern at midspan.

5.5 Seam Strip Specimen