Punching Shear Strength of Reinforced Concrete Slabs Strengthened with Glass Fiber-Reinforced Polymer Laminates. Paper by Cheng-Chih Chen and Chung-Yan Li/AUTHORS’ CLOSURE
Discussion by Himat Solanki and Chandra Khoe
Professional Engineer, Building Dept., Sarasota County Government, Sarasota, Fla.; Engineer, MMXF Steel Corp., Tampa, Fla.
It is true that the strengthening with GFRP would increase the punching shear capacity of slabs. The discussers, however, would like to offer the following comments:
1. The test results appear to be inconclusive because when the concrete strength and GFRP maintain the same level in the slabs and the GFRP reinforcement ratio varies, the strength increase is significantly higher than the reinforcement ratio allows. This can be explained using the test specimens. For example, for test Specimen SR1-C2-F1, the average ultimate shear strength is 180.0 kN. When the shear strength is compared with Specimen SR2-C2-F1’s shear strength, the shear strength increases by approximately 46.6%. In test Specimen SR1-C2-F2, when comparing shear strength with test Specimen SR2-C2-F2, the shear strength increases by approximately 32.2%. When the reinforcement ratio (0.59% versus 1.31%) is considered in the test specimens, the shear strength increases approximately 23.0%;
2. The load displacement characteristic in Fig. 6 and 7 appears to be inconsistent when it compares with Fig. 8 and 9;
3. Based on Fig. 10, both flexural and punching shear strength would be equal at a reinforcement ratio of approximately 0.65. Why was the higher reinforcement ratio considered if specimens considered fail in punching shear?
4. From Fig. 12(a) and (b), it appears that the load-versusstrain relationship for a No. 3 bar and two layers of GFRP does not depart significantly, but the test shows higher shear strength.
5. The yield strength of GFRP fabric is lower than No. 3 reinforcing bar yield strength. This means the GFRP would fail prior to yielding of a No. 3 reinforcing bar. Therefore, it is very difficult to predict the correct value of T^sub s^;
6. The discussers believe Eq. (16) should be limited to d^sub eqv^ ≤ h, and Eq. (17) should be limited to ρ^sub eqv^ ≤ 2.0%; and
7. There are typographical errors in Eq. (4) and (5) and Table 3, V^sub u,predicted, JSCE^ and V^sub u,test^/V^sub u,predicted, JSCE^ for all specimens.
The authors would like to thank the discussers for their valuable comments and interest in the paper. In regards to the discussion by Esfahani and Moradi, the authors are especially grateful for their detailed comments regarding the proposed method to predict the ultimate punching shear strength of reinforced concrete slabs strengthened with GFRP laminates. Due to a typing error, the predicted punching shear strengths tabulated in Table 3 should be corrected as shown in Table C; however, the ratios of tested values to predictions in Table 3 were fairly correct. Equivalent depth d^sub eqv^ and equivalent reinforcement ratio ρ^sub eqv^ calculated by the authors are also included in Table C. Regarding the questions posed, Question 1 is related to the differences between the predictions calculated by the authors and the discussers. The inconsistency is now minor except for Specimen SR1-C1-F2, in which the discussers may have incorrect equivalent depth. Table C also presents the punching shear strengths predicted using the JSCE code. The JSCE(1) column indicates the punching shear strengths calculated by neglecting the limitation for β^sub d^ to investigate the effect of the depth on the punching shear strength. The JSCE(2) column considers the limitation for β^sub d^ hat is limited to 1.5. The β^sub d^ is related to the effective depth of the slab. As indicated in the ratios of tested-to-predicted strength, JSCE(2) gives a much more conservative prediction than JSCE(1) does. It should be noted that both the BS and JSCE codes use (1/d)^sup 1/4^ to calculate the punching shear strength, and there is no upper limit for that in the BS code. Questions 2 and 3 are related to the measured and calculated strains of reinforcing bars and GFRP laminates. The authors would like to point out that the proposed method is based on the hypothesis of Moe15 that the punching shear strength of a slab is calculated from its flexural strength. Equation (6) to (17) can be adopted to calculate the flexural strength. Therefore, the calculated strains shown in Table B provided by the discussers represent the ultimate strains of the reinforcing bars and GFRP laminates corresponding to the flexural strength. Punching shear failure occurs, however, rather than flexural failure for all specimens except Specimens SR1-C1-F0 and SR1-C2-F0. The strains measured at punching shear failure would be less than those corresponding to the flexural failure.
In regards to the discussion by H. Solanki and C. Khoe, the following presents a closure for each comment. With regards to Question 1, it is believed that GFRP laminates function as the tensile steel reinforcement. The punching shear strength of reinforced concrete slabs strengthened with GFRP laminates influenced by the laminates in addition to the steel reinforcement. Therefore, the authors proposed an equivalent reinforcement ratio to account for the contribution from both materials. The comparison presented by the discussers is not appropriate. Moreover, the relation between punching shear strength and reinforcement ratio is not linearly proportional, as seen from the BS and JSCE codes. Regarding Question 2, the load-displacement curves in Fig. 6 and 7 are different from those in Fig. 8 and 9, and that is contributed to the different amount of reinforcement. Specimens in Fig. 6 and 7 are lightly reinforced slabs and demonstrated a flexural punching or shear punching with higher post-peak strength than specimens in Fig. 8 and 9, which have more reinforcement. For Question 3, the tensile steel reinforcement is usually determined based on the requirement for flexural strength. The slabs subjected to a heavy load lead to a higher amount of the tensile steel reinforcement, which may fail in punching shear. Regarding Question 4, the authors fail to understand the discussers’ comment and would like to point out that Fig. 12(a) presents the strains of reinforcing bar for SR1-C2-F0, while Fig. 12(b) shows strains of reinforcing bar and GFRP laminates for SR1-C2-F1a, which has only a single-layer, not a double-layer, laminate. It is clear that, with the GFRP laminates, SR1-C2-F1a reached a higher shear strength than SR1-C2-F0. Regarding Question 5, the ultimate tensile strength is usually termed for the GFRP laminates instead of yield strength used by the discussers, because the GFRP laminates behave linearly elastic up to failure. Although the ultimate tensile strength of the GFRP laminates is lower than the yield strength of a No. 3 reinforcing bar, the ultimate tensile strains (0.018 and 0.021 for the single- and double-layer, respectively) of GFRP laminates are much higher than the yield strain (0.0024) of the reinforcing bar. Clearly, the GFRP laminates will not fracture before yielding of the reinforcing bar. Therefore, there is no problem in calculating any internal force, and the proposed method has been followed by the other discussers. For Question 6, the authors agree that the equivalent depth d^sub eqv^ will be definitely less than the slab thickness h and there is no need to specify. However, the authors disagree to limit the equivalent reinforcement ratio ρ^sub eqv^ to be less than 2.0%. It is important to recognize that the BS code limits the reinforcement ratio to 3%, while the JSCE code limits implicitly to 3.375%. For Question 7, Eq. (4) and (5) are both correct. For Eq. (4), a factor of ( f^sub cu^/25)^sup 1/3^ considering for concrete compressive strength greater than 25 MPa has been mentioned in the paragraph following Eq. (4). Comments related to Table 3 are addressed in the response to the other discussers.
Copyright American Concrete Institute May/Jun 2006
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