CÓDIGO DE PROCEDIMIENTO CIVIL DE VENEZUELA

Failure load analysis of steel reinforced concrete slabs can be done using the plastic methods of analysis such as yield line theory. This is applicable because of the ductility of the steel reinforced concrete section, which is the ability of sustaining inelastic deformations once the reinforcing steel yields. In contrast, FRP reinforced concrete

450 300 75 (seam) 75 75 75 Vu=1 305 100 18o 1.54 1.54 +1.54 +1.54 +1.54 1.54 1.54 Vu=1 +1.54 -3.23 _{-1.54 -1.54} -3.08 +2.17 +2.17 +2.17 Point A Point B 33

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sections do not exhibit ductility due to linear and brittle behavior of FRP bars, and hence plastic methods of analysis may not be viable for failure load analysis of the bridge deck slab. However, the experimental and analytical results of testing the strip elements of a full-scale AFRP concrete bridge deck slab showed a significant post-cracking deformation, so called deformability. This mainly originates from the low modulus of elasticity of AFRP bars resulting in low post-cracking flexural stiffness and larger deformations, consequently. For instance, the post-cracking curvature capacity was found 95 and 40 times the cracking curvature for non-prestressed and prestressed strips, respectively. When a two-way FRP slab cracks in the maximum moment direction, the moment is substantially redistributed to the other directions due to considerable drop in flexural stiffness of the slab section in the crack direction as a result of low modulus of elasticity of FRP reinforcement. This, in fact, has a similar impact on response of the slab as yielding of the reinforcing steel has. This considerable deformability offsets the lack of ductility to some extent and enhances the possibility for application of plastic analysis concept for failure load analysis of FRP reinforced concrete slabs. Although the interaction between strip elements in x and y directions should be considered when analyzing a two-way slab, the bilinear response of the strip elements with low post- cracking flexural stiffness brings the thought that the plastic methods of analysis may be applicable if the response is approximated with an equivalent elasto-plastic graph. 5.7 Conclusions

Four AFRP concrete strip specimens were selected from a full-scale AFRP concrete bridge deck slab and tested in an intent to characterize the behavior of the slab section in terms of strength, curvature capacity, and failure mode. The experimental program included the flexural test of non-prestressed and prestressed AFRP concrete strips representing the bridge deck section in parallel and perpendicular to the traffic direction, respectively. Also, two strip specimens representing the slab section at panel-to-panel seam were considered for shear and flexure test. The following conclusions are drawn from this study:

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1- Non-prestressed strip specimen failed due to concrete crushing in a shear-flexural manner with no evidence of tendon rupture. The ultimate strength Mu=23.5 kNm

and the curvature capacity (Øh)u=0.024 were found at failure. Significant

deformability was achieved as a result of excessive cracking and low modulus of elasticity of AFRP bars that can offset the non-ductile behavior induced by AFRP reinforcing bars.

2- Prestressed strip specimen failed due to rupture of the AFRP bars while crushing the concrete was already commenced. The ultimate strength Mu=21 kNm and the

curvature capacity (Øh)u=0.02 were found at failure. The deformability was

considerable; however, the strip failed with a localized cracking pattern as opposed to non-prestressed strip.

3- The result of moment-curvature analysis was in very good agreement with the experimental results in predicting the cracking and failure values. Modeling the tension stiffening via a rational equation is an influential factor affecting the accuracy of numerical analysis in post-cracking stages.

4- Studying the curvature distribution for the non-prestressed strip showed that the bilinear model underestimates the maximum curvature and deflection at midspan; however, it gives acceptable results in the shear span. For prestressed strip, the bilinear model seems to be a proper assumption, somewhat conservative though. The results confirmed the larger extent of cracking at failure in non-prestressed strip compared to the prestressed one due to the effect of prestressing force. 5- Flexure test of the seam strip specimen revealed a negligible flexural strength,

and the joint basically behaved like a hinge. This makes sense as the bars are bent at the joint and not continuous to transfer the tension to the concrete and connect the left and right parts of the seam.

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6- Shear test of the seam strip showed acceptable shear strength per ACI 318. The joint failed due to crushing of the diagonal concrete strut and the shear capacity was found equal to 41 kN (1 MPa). A compatibility strut and tie model was adopted to analyze the shear resistance of the joint which gave rise to shear capacity equal to 46 kN.

7- The observed bilinear response of the strip elements with low post-cracking flexural stiffness and considerable deformability that can be approximated with an equivalent elasto-plastic model raises the likelihood of applicability of the plastic analysis concept for failure load analysis of FRP concrete bridge deck slabs. Further investigation is still required to clarify this matter, though.

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6. MODIFIED YIELD LINE THEORY FOR FAILURE