Low-Velocity Impact Load Testing of RC Beams Strengthened in Flexure with Bonded FRP Sheets

Kishi, Norimitsu; Komuro, Masato; Kawarai, Tomoki; Mikami, Hiroshi

doi:10.1061/(ASCE)CC.1943-5614.0001048

Open access

Technical Papers

Jun 17, 2020

Low-Velocity Impact Load Testing of RC Beams Strengthened in Flexure with Bonded FRP Sheets

Authors: Norimitsu Kishi, Ph.D., M.ASCE https://orcid.org/0000-0002-9685-5761 [email protected], Masato Komuro, Ph.D. https://orcid.org/0000-0002-3487-9442, Tomoki Kawarai, and Hiroshi Mikami, Ph.D.Author Affiliations

Publication: Journal of Composites for Construction

Volume 24, Issue 5

https://doi.org/10.1061/(ASCE)CC.1943-5614.0001048

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Abstract

In this paper, which focuses on the fiber-reinforced polymer (FRP) sheet bonding method for improving the impact resistance of RC beams, low-velocity impact load tests are performed on RC beams strengthened with FRP sheets. Both aramid FRP (AFRP) and carbon FRP (CFRP) sheets are used to experimentally investigate the flexural strengthening effect of the sheet materials. The impact force is created by dropping a 300-kg steel weight from various heights. The experiments are conducted using a single loading method for each beam, and the drop height of the weight is increased until the sheet debonded. The results obtained from this study are as follows: the impact-resistance capacities of the beams are improved by flexural strengthening with FRP sheets; the strengthening effects of the sheets are similar, regardless of the sheet materials, when the axial stiffness values of the sheets are equal; and the maximum and residual deflections are approximately linearly distributed with increasing input impact energy until the FRP sheets debonded.

Introduction

Steel plate bonding and/or section enlargement methods are generally applied to strengthen existing RC members. However, these methods increase the dead load, require the use of corrosive materials, and increase construction difficulty. Fiber-reinforced polymer (FRP) composite materials, which are mainly developed for use in the aviation and space industries, are lightweight, noncorrosive, and have high strength-to-weight ratios, and they are relatively easy to install. Due to these characteristics, research and development on FRP applications in the field of civil engineering have been encouraged since the 1990s. In the early 1990s, Ritchie et al. (1991) experimentally investigated the external strengthening effects provided by bonding FRP plates to the tension-side surfaces of RC beams; they tested FRP plates consisting of glass, carbon, and aramid fibers. Saadatmanesh and Ehsami (1991) also experimentally investigated improvements in the static strengths of rectangular and T-section RC beams strengthened by bonding glass FRP plates to tension flanges. Triantafillou (1998) experimentally studied the applicability of carbon FRP (CFRP) laminates as shear strengthening materials for RC beams and analytically investigated the contributions of FRP materials to the shear load-carrying capacities of beams. These studies were followed by several investigations in the last two decades. The authors of the current investigation also experimentally and numerically studied the use of FRPs on RC beams (Kishi et al. 2001, 2002, 2005, 2016). Design guidelines for strengthening RC members with externally bonded FRP laminates have been established, such as in the case of ACI 440.2R-17 (ACI 2017), and have been widely applied in practice.

Currently, terrorism is a global problem, and civil infrastructures are at risk of severe damage from blast and impact loading; hence, some structures may require improved resistance capacities. Therefore, FRP materials may be applicable to strengthen RC members against not only static loading but also blast and impact loading. However, research on strengthening RC members under blast loading has suffered from a lack of sufficient experimental facilities. Herein, the strengthening effects of FRP sheets on the impact resistance of RC members were investigated only under low-velocity impact loading.

Regarding previous research on RC members strengthened with FRP sheets under low-velocity impacts, Erki and Meier (1999) investigated the impact-resistant behavior of RC beams strengthened with either CFRP laminates or steel plates; in their experiments, one end of the tested beam was lifted and then dropped from a certain height onto a support. Their results indicated that the RC beams performed well under impact loading due to the flexural strengthening provided by the CFRP laminates and that the CFRP laminates could not provide the same energy absorption capabilities as steel plates. However, their results are not easily applicable to simply supported RC beams impacted in the midspan area. Tang and Saadatmanesh (2003, 2005) performed drop-weight impact tests on non-shear-reinforced RC beams strengthened by bonding CFRP and/or Kevlar FRP laminates to the upper and lower surfaces of the beams to carry positive and negative moments. Their results showed that the impact resistance of the beams was significantly improved through strengthening with bonded FRP laminates and that the maximum deflections of the strengthened RC beams were 30%–40% less than those of unstrengthened beams. Kantar and Anil (2012) carried out impact loading tests for concrete beams strengthened in flexure with CFRP strips by varying the compressive strength of concrete, and they showed that CFRP strips could positively affect the impact resistance of the beams. The studies discussed previously involved flexural strengthening of RC members with FRPs.

Other studies have investigated shear strengthening of RC beams with FRPs. For instance, Yilmaz and Anil (2015) conducted impact load testing on shear deficient RC beams strengthened with CFRP U-wraps and confirmed the shear strengthening effects of the strips. Pham and Hao (2016a) investigated the impact behavior of FRP-strengthened RC beams and the FRP contribution to shear strength. In their study, RC beams without stirrups were strengthened with CFRP U-wraps and 45°-wraps. Their results showed that, using the same number of CFRP strips, 45°-wraps provided better performance than U-wraps in terms of the load-carrying capacities and deflections of the beams; moreover, the failure modes of the RC beams changed from ductile flexure failure under static loading to brittle shear failure under impact loading. Huo et al. (2018) also experimentally investigated the effects of a CFRP strengthening arrangement on the failure mechanisms of RC beams without stirrups under impact loading. From their experiments, it was noted that the strengthening effect of single 45°-CFRP wraps was much higher than that of CFRP U-wraps and crisscrossing CFRP wraps and that both the shear capacities and deflections of RC beams strengthened with CFRP U-wraps were slightly better than those of beams strengthened with crisscrossing CFRP wraps.

Yilmaz et al. (2018) performed drop-weight tests for two-way simply supported RC slabs strengthened with CFRP strips of varying arrangement and width. From these test results, it was revealed that by strengthening with 100-mm-wide, diagonally oriented CFRP strips placed in two directions, the impact resistance of the RC slabs can be significantly improved.

Thus, even though the strengthening effects of FRP laminates/sheets on the flexural and shear load-carrying capacities of RC beams and slabs under impact loading were investigated, studies on RC members strengthened with FRPs under impact loading are still extremely limited (Pham and Hao 2016b).

This study focuses on RC beams with stirrups that statically reach the ultimate state and exhibit flexural failures. In this study, low-velocity drop-weight impact tests are performed on RC beams strengthened by bonding FRP sheets to their tension-side surfaces. The strengthening effects of the FRP sheets on the impact resistance, impact-resistance characteristics, and failure behavior of the beams are investigated. Both aramid FRP (AFRP) and CFRP sheets are used in this experiment, and the material volumes are adjusted to produce sheets with approximately equal axial stiffnesses. The RC beam is always replaced with a new beam for each loading test, and the drop height of the weight is increased to reach the ultimate state with sheet debonding. A reference beam that is not strengthened with an FRP sheet is constructed for comparative analysis. Static load tests are also conducted to confirm the failure modes of the beams under static loading and to compare the load-carrying characteristics of the beams under static and impact loading.

Experimental Overview

Dimensions and Static Design Values of the RC Beams

Twelve specimens were used in this study. The material of the FRP sheet, the total axial stiffness of the bonded FRP sheet, and the calculated static flexural and shear load-carrying capacities of the beams are listed in Table 1. In this table, the specimen name is designated by the type of FRP material (N = none; A = AFRP; and C = CFRP) and the method of loading (S = static loading; and I = impact loading). In the case of impact loading, the specimen name is specified by adding the drop height of the weight (Hn) (n = drop height in metric units) with a hyphen. The estimated drop height (H′) was evaluated using the measured drop velocity of the behavior just before impacting the upper surface of the beam.

Table 1. List of specimens

Specimen	Sheet material	Set drop height of the weight H (m)	Measured drop height of the weight H′ (m)	Measured input impact energy E_i (kJ)	Total axial stiffness of the sheet E_fA_f (kN)	Total tensile capacity of the sheet (kN)	Compressive strength of the concrete $f_{c}^{'}$ (MPa)	Yield stress of the longitudinal rebar f_sy (MPa)	Calculated flexural capacity P_usc (kN)	Calculated shear capacity V_usc (kN)
NS	—	Static	—	—	—	—	32	382	55.0	329
NI-H2.5	—	2.5	2.3	6.7	—	—	32	382	55.0	329
AS	AFRP	Static	—	—	14 × 10³	236	35	382	102	332
AI-H1		1	1.1	3.3
AI-H2		2	2.2	6.4
AI-H2.5		2.5	2.4	7.1
AI-H3		3	3.2	9.5
CS	CFRP	Static	—	—	16 × 10³	264	33	403	106	329
CI-H1		1	1.1	3.3
CI-H2		2	1.8	5.2
CI-H2.5		2.5	2.3	6.7				407	108
CI-H3		3	3.1	9.0				403	106

The material volumes needed to produce AFRP and CFRP sheets with approximately equal values of total axial stiffness E_f A_f were determined, and the results are listed in Table 1. The calculated static load-carrying capacities of each beam were estimated according to the Japan Concrete Standard (JSCE 2007) using the material properties of concrete and the FRP sheets (see Table 2). Here, the ultimate compressive strain of concrete was assumed to be ɛ_cu = 0.35% in accordance with the standard (JSCE 2007). From this table, because the shear-flexural capacity ratios, α = V_usc/P_usc, for Beams AS/AI and CS/CI are larger than 3, it is confirmed that the strengthened RC beams would statically fail in flexure.

Table 2. Material properties of the FRP sheets

Sheet material	Mass per unit area (g/m²)	Thickness (mm)	Tensile strength f_f (GPa)	Elastic modulus E_f (GPa)	Failure strain ɛ_uf (%)
AFRP^a	830	0.57	2.1	118	1.75
CFRP^b	600	0.33	3.4	245	1.39

a

Catalog values of Fibex (2014).

b

Catalog values of Toray (2019).

All the test beams had rectangular cross sections with a 200-mm width, 250-mm depth, and 3-m clear-span length. The layout of the reinforcement (referred to hereinafter as rebar) for the beams is shown in Fig. 1. Two axial rebars with 19-mm diameters were cast in the upper and lower fibers, and the rebars were welded to 9-mm-thick steel plates at the ends of the beam to ensure full anchorage and to save the distance from the support point to the free edge to decrease the influence of the part on the impact response characteristics of the beam. Stirrups with 10-mm diameters were placed at 100-mm intervals. The FRP sheet was bonded to the tension-side surface, and 50 mm was left between the support point and the end of the sheet. The concrete surface used to bond with the FRP sheet was grit-blasted to a depth of approximately 1 mm to improve the bonding capacity. Beams AS/AI and CS/CI were strengthened by bonding one AFRP ply with an areal mass of 830 g/m² and one CFRP ply with an areal mass of 600 g/m².

The FRP sheet properties as provided by the manufacturers (Fibex 2014; Toray 2019) are reported in Table 2. These properties were determined by testing based on JIS K 7165 (JIS 2008). Table 2 shows that the elastic modulus E_f of the CFRP sheet is more than twice that of the AFRP sheet. However, the failure strain ɛ_uf of the AFRP sheet is 0.36% greater than that of the CFRP sheet.

Experimental Method for the Impact Loading Test

Drop-weight impact tests were conducted by dropping the weight from a prescribed height onto the midspan of the beam using the impact apparatus shown in Fig. 2. The 300-kg weight was a solid steel cylinder. The RC beams were placed on supports equipped with load cells to measure the reaction forces, and they were clamped at their ends using cross beams to prevent lifting. The supports were able to freely rotate while restraining the horizontal movement of the beam.

Fig. 2. Experimental setup for drop-weight impact testing.

In this experiment, the impact force P, the total reaction force (referred hereinafter as the reaction force) R, the midspan deflection (referred to hereinafter as the deflection) δ, and the axial strain distribution of the FRP sheet were measured. Additionally, the crack patterns of the side surface of the beam near the loading point were recorded with a high-speed camera at 2,000 fps. After each test, the residual deflection δ_rs was measured, and the crack patterns observed on the side surface of the beam were sketched for documentation. The deflection δ of the beam was measured at middepth using a laser-type linear variable displacement transducer (LVDT) with a maximum stroke of 200 mm. These analog data were converted into digital data at 0.1-ms time intervals.

Deflection Calculation Method

To estimate the deflection of the RC beams up to the ultimate state under static loading, the multilayered method (Kaklauskas et al. 1999), which is based on classical techniques of strength of materials extended to the application of the layered approach and full stress–strain material relationships, was applied.

The employed approaches and assumptions were as follows: (1) a plane section and perfect bonding between the concrete and reinforcement, including the FRP sheet, were assumed; (2) the smeared crack approach was used; (3) the layered approach was used; (4) the stress–strain relation was assumed for each material following the JSCE (2007), as shown in Fig. 3; and (5) constant stress–strain relationships were assumed for each layer.

Fig. 3. Stress–strain relationships: (a) concrete; (b) longitudinal rebar; and (c) FRP material.

To precisely determine the curvature and bending moment relationship for each strain level, the cross section of the beam was divided into horizontal thin layers of less than 5-mm thickness corresponding to either concrete or reinforcement. Following the aforementioned approaches and assumptions, the neutral axis and lower fiber strain corresponding to the arbitrary upper fiber strain of the cross section were determined by varying the lower strain gradually and taking the resultant force equilibrium of the whole layers. Using these upper and lower fiber strains, the corresponding curvature and sectional bending moment could be obtained.

For these relationships from zero to the ultimate state, ɛ_cu = 0.35% of the upper fiber strain of the concrete can be obtained by repeating the aforementioned procedures. Therefore, the curvature distribution along the span corresponding to the bending moment diagram for each loading step can be determined. Finally, midspan deflection was obtained by applying Mohr's integral technique, i.e., by calculating the moment at the midspan point of the simply supported beam subjected to the curvature distribution.

Experimental Results for Static Loading

The static load was applied to the beams by using a hydraulic jack with a 500-kN capacity and setting up a loading jig with a 100-mm width in the span direction. For Beam NS, which was not strengthened with an FRP sheet, the load gradually increased after the rebar yielded due to the plastic hardening effect of the rebar; therefore, the load was applied until the beam deflected to approximately 90 mm.

Load Deflection

Fig. 4 shows a comparison of the static load–deflection relations between RC beams strengthened with and without FRP sheets. In this figure, the numerical results are obtained by applying the aforementioned technique. For Beam NS, Fig. 4 shows that the deflection from the experimental results gradually increases after the rebar yielded. In contrast, the load–deflection curves of Beams AS and CS behaved similarly and finally reached the ultimate state due to FRP sheet debonding. The experimental results for the rebar yielding load and the maximum load for three beams are listed in Table 3. In Table 3, the maximum load for Beam NS is taken at the point when the deflection δ = 40 mm because the strengthened beams (i.e., Beams AS and CS) reach the ultimate state at this deflection level. Table 3 shows that, as a result of strengthening with the FRP sheets, the rebar yielding loads and maximum loads of Beams AS and CS are approximately 30% and 45% greater than those of Beam NS, respectively.

Table 3. Experimental results for static loading

Specimen	Rebar yield load (kN)	Max. load (kN)
Beam NS	57 (1.0)	67 (1.0)
Beam AS	74 (1.30)	98 (1.46)
Beam CS	74 (1.30)	98 (1.46)

Note: The values in parentheses indicate the ratios with respect to the corresponding values of Beam NS.

The following observations can be made by comparing the experimental and numerical results: (1) the numerical results showed that Beam NS reached the ultimate state immediately after the rebar yielded because of the upper fiber strain reaching the ultimate compressive state with ɛ_cu = 0.35%; (2) the experimental results for both Beams AS and CS were lower than the numerical results; (3) in particular, the difference in the experimental and numerical results after rebar yielding tended to increase as the deflection increased; and (4) the experimental results could not confirm the numerical maximum loads. Therefore, it was implied that both FRP sheets might have gradually debonded after the rebar yielded.

Crack Patterns After the Experiments

Fig. 5 shows comparisons of the crack patterns of three beams after the experiments. The following can be observed from this figure: (1) for Beam NS, the flexural cracks emanating from the lower concrete cover were concentrated near the midspan area; (2) the loading area was severely crushed; and (3) the beam was deformed permanently near the loading point. However, the flexural cracks in Beams AS and CS were more widely distributed than those in Beam NS, and the FRP sheets debonded in both beams. However, Beams AS and CS were less deformed than Beam NS due to the strengthening effect of the FRP sheet. Because the sheets debonded together with the lower concrete cover, the bonding strength of the sheet might be higher than the tensile strength of the concrete.

Fig. 5. Crack patterns after static loading: (a) beam NS; (b) beam AS; and (c) beam CS.

From these results, it was confirmed that the RC beams reached the ultimate state with flexural failure mode under static loading, regardless of whether they were strengthened with the FRP sheet.

Experimental Results for Impact Loading

Time Histories of Impact Force, Reaction Force, and Deflection

Fig. 6 shows the time histories of the impact force P, reaction force R, and deflection δ for all beams subjected to impact loading. In this figure, the origin of the time axis was taken as the actual time when the weight impacted the beam. The reaction force R in the upward direction was assumed to be positive as in the case of static loading.

Fig. 6. Time histories of dynamic responses: (a) impact force P; (b) reaction force R; and (c) deflection δ.

Fig. 6(a) shows the time histories of the impact force P during 25-ms intervals that started at the beginning of the impact. This figure shows that the responses had similar time histories regardless of the method of strengthening (or lack thereof) or the drop height of the weight (referred to hereinafter as the drop height). These similarities can be described as follows: (1) at the beginning of the impact, the time history exhibited a triangular shape with a high amplitude for a short time (approximately 1 ms), and (2) afterward, high-frequency components with low amplitudes were excited. The time histories of the three beams with the drop height of H = 2.5 m were similar until approximately 12 ms after the beginning of the impact regardless of strengthening with or without FRP sheets and the material properties of the FRP sheet.

The maximum impact forces of the three specimens are listed in Table 4. From this table, it can be observed that the maximum values are similar, even though the one for Beam CI is slightly smaller than those of the other beams. Generally, the magnitude of the maximum impact force at the beginning of the collision may be related to the drop weight, drop height of the weight, bending stiffness and dimensions of the beams, and contact stiffness of concrete. The contact stiffness may be the most influential factor among them. In this study, all conditions are similar among the three specimens except flexural strengthening with/without FRP sheets. This finding indicates that the impact force time history may depend on the contact stiffness of concrete (compressive strength, elastic modulus, and mass per unit volume).

Table 4. Experimental results for maximum responses to impact loading at H = 2.5 m

Specimen	Maximum impact force P_max (kN)	Maximum reaction force R_max (kN)	Maximum deflection δ_max (mm)
Beam NI	1,542 (1.00)	251 (1.00)	85.6 (1.00)
Beam AI	1,527 (1.01)	385 (1.53)	58.5 (0.68)
Beam CI	1,457 (0.94)	343 (1.37)	58.5 (0.68)

Note: The values in parentheses indicate the ratios with respect to the corresponding values of Beam NI.

Fig. 6(b) shows the time histories of the reaction force R during 100-ms intervals that started at the beginning of the impact. This figure shows the following phenomena: (1) at the beginning of the impact, a negative reaction force was excited [this phenomenon was also reported by Cotsovos (2010), Pham and Hao (2017) and Kishi and Mikami (2012)]; (2) the main response was composed of a triangular-shaped component with a duration of 30–50 ms and high-frequency components; and (3) the duration of the main response tended to be prolonged by increasing the drop height H. The negative reaction force excited at the beginning of the impact can be measured as follows: (1) the amplifier units of the load cells were initialized after the beam ends were tightened with the load cells using cross beams; (2) the beam ends tended to lift due to the rebound of the applied impact force; and (3) a negative reaction force was accurately measured up to a magnitude of approximately 50 kN for the tightening force. Pham and Hao (2017) accurately measured the negative reaction force by using the upper load cells installed at the supports, and this phenomenon can be explained based on the theory of stress waves. However, because the lower load cells were used only to measure the reaction forces in this study, further discussion is limited.

The time histories of the three beams for the drop height of H = 2.5 m showed that, even though the time histories of Beams AI and CI were approximately equal, the maximum reaction force and the duration of the main response of Beam NI were smaller and approximately 10 ms longer than those of Beams AI and CI, respectively. The maximum reaction forces of the three specimens are listed in Table 4. From this table, it is seen that the forces of the strengthened Beams AI and CI are almost 40%–50% greater than the reference Beam NI. The flexural stiffness of Beam NI is less than those of the strengthened beams and may significantly decrease due to its severe damage.

Fig. 6(c) shows the time histories of the deflection δ during 200-ms intervals that started at the beginning of the impact. This figure shows that the main response had the form of a half-sine wave; after the main response, the deflection was restrained, and the beams exhibited a damped-free vibration with a low frequency. The residual deflection δ_rs of the beam tended to increase with increasing drop height H.

The time histories of the three beams for the drop height of H = 2.5 m showed that (1) the two strengthened beams—Beams AI and CI—exhibited approximately equivalent time histories; and that (2) the unstrengthened beam—Beam NI—exhibited greater maximum and residual deflections and a longer damped-free vibration period than the strengthened beams. The maximum deflections of the three beams are listed in Table 4. The table indicates that the maximum deflection of the beams was decreased by more than 30% by strengthening with the FRP sheets. Therefore, it was confirmed that, by bonding FRP sheets to the tension-side surfaces of the beams: (1) the maximum and residual deflections could be improved; and (2) the strengthening effects of the two FRP sheets on the impact-resistant behavior of the beams were approximately equal.

For the drop height of H = 3 m, even though the FRP sheets debonded in both beams, both sheets debonded at similar times from the beginning of impact. Both beams reached the maximum deflection at the same time (t = 24 ms), and the time histories for both beams were approximately equal.

Temporal Transitions of FRP Strain Distributions and Crack Patterns of the Beams

Fig. 7 shows the temporal transitions of the FRP axial strain distributions and crack patterns on the side surfaces near the midspan areas of the beams at a drop height of H = 3 m. From this figure, at time t = 0.5 ms after the beginning of the impact (referred to hereinafter as time), double or triple diagonal cracks developed from both sides of the beams and were connected in a cap-shaped form in the midspan area without reaching the upper surface of the beam. In this time step, flexural cracks had not yet developed. The strain distributions showed that the tensile strain was distributed in the midspan areas of both beams, whereas the compressive strain was distributed in the outer areas for both beams. The compressive strain might have developed due to the fixed nature and small span length of the beam, wherein the compressive strain formed while the flexural wave propagated over the whole length of the beam.

Fig. 7. Temporal transitions of the FRP strain distributions and crack patterns of the beams at H = 3 m: (a) Beam AI; and (b) Beam CI.

At time t = 1 ms, the following details could be observed: (1) all diagonal cracks reached the edges of the lower concrete cover for both beams; (2) the tensile strain area expanded toward the support points; and (3) near the loading area, there tended to be an equibending state because the strain was flattened. The maximum tensile strain for both beams remained at approximately 0.5%.

At time t = 2 ms, a new diagonal crack developed across the existing cracks and reached the edge of the upper concrete cover for Beam CI. At time t = 5 ms, both beams changed to the simply supported state because the compressive strain disappeared, and the peaks of both sides of the tensile strain wave reached the support points. The strain was distributed in an approximately parabolic shape, as in the case of a uniformly distributed load acting on a simply supported beam.

At time t = 10 ms, some diagonal cracks formed, and flexural cracks originated from the lower concrete cover in the midspan areas of both beams. Additionally, compressive failure initiated at the upper concrete cover near the loading point. The strain distributions showed that the gradients of the strain distribution between the area near the support area and around the midspan were different and that the maximum strain reached approximately 1.25% near the midspan. These findings indicated that the axial rebars in the support area remained in an elastic state, whereas those in the midspan area remained in a plastic state.

At time t = 15–20 ms, the FRP sheets in both beams tended to debond from the tips of the diagonal cracks toward the support points due to a peeling action. Compressive failure was clearly indicated near the loading point. The strain distributions showed that the peak strain was flattened at approximately 1% because of the partial debonding of the sheets.

Times t = 26 and 22.5 ms for Beams AI and CI, respectively, were the times immediately before the FRP sheets fully debonded. For Beam AI, full debonding of the sheet was initiated after reaching the maximum deflection response at time t = 24 ms (see Fig. 6), while for Beam CI, full debonding of the sheet was initiated before reaching the maximum response. Therefore, even though maximum deflections for both beams occurred simultaneously, the times at which full debonding of the sheet initiated were slightly different.

At time t = 30–40 ms, the FRP sheets for both Beams AI and CI debonded from the tip of the diagonal crack toward the right-hand and left-hand edges, respectively, together with the concrete blocks of the lower concrete cover. From the strain distribution, it could be observed that the strain of the sheet was perfectly released because the sheet perfectly debonded on one side surface of the beam.

Pham and Hao (2017) measured the axial strain of the FRP strip when the strip debonded from the RC beams under impact loading. For strengthened RC beams with a longitudinal FRP strip and without a U-shaped transverse strip, the average axial strain was less than 0.5%, and the beam failed in a shear-flexure mode. This value was approximately 0.5% smaller than that obtained in the aforementioned study. This discrepancy might be due to the difference in the failure mode and/or strengthening ratio of the FRP material, referring to an unstrengthened beam.

Energy Dissipation

To compare the energy dissipation under impact loading among the three specimens in the case of H = 2.5 m, two evaluation methods were considered: (1) the method using the hysteretic loop between impact force P and deflection δ; and (2) the method using the region between the reaction force R and the deflection δ based on the quasistatic concept. Fig. 8 shows the hysteretic loops for the three specimens corresponding to the two methods until the weight was rebounded. The figure indicates that (1) the beams did not deflect at maximum impact force; (2) negative impact forces occurred during the beams deflection due to stress wave propagation; (3) negative reaction forces occurred until the beams deflected up to approximately 15–17 mm as mentioned previously; and (4) the loop with the reaction force exhibited an approximate parallelogram shape for Beam NI but a triangular shape for Beams AI and CI.

Fig. 8. Hysteretic loops between the force and deflection δ at H = 2.5 m: (a) relationship between the impact force P and the deflection δ; and (b) relationship between the reaction force R and the deflection δ.

Assuming that the negative force could not contribute to the dissipation energy, the energy for each beam is estimated as listed in Table 5. From this table, it is seen that the dissipation energies due to the impact force E_dp were less than a half the measured input impact energy (referred to hereinafter as input impact energy) E_i regardless of strengthening with/without FRP sheets; conversely, the energies due to the reaction force E_dr were greater than 0.75 of the input impact energy E_i. Although the impact force P was excited due to the weight impacting the beam, the reaction force R might be resistant to not only the impact force P but also the inertial force distributed along the whole span. Comparing the ratios of the dissipated energy refereeing to the input impact energy E_i among the three beams, even though the strengthened Beams AI and CI had less dissipate energy than the reference Beam NI, the difference was very small. Comparing the values between strengthened Beams AI and CI, these characteristics of the dissipation energy were not similar to each other and differed depending on the applied force (impact force P or reaction force R).

Table 5. Dissipation energy of beams for impact loading at H = 2.5 m

Specimen	Input impact energy E_i (kJ)	Dissipation energy due to impact force P E_dp (kJ)	Dissipation energy due to reaction force R E_dr (kJ)
Beam NI	6.7 (1.00)	3.2 (0.48)	6.5 (0.97)
Beam AI	7.1 (1.00)	3.1 (0.44)	5.5 (0.77)
Beam CI	6.7 (1.00)	2.3 (0.34)	6.4 (0.96)

Note: The values in parentheses indicate the ratios with respect to the input impact energy E_i for each beam.

Cracks Pattern of Test Specimens

Fig. 9 shows the crack patterns of the three beams after testing at the drop height H = 2.5 m. This figure shows that flexural cracks developed along the whole span and from both the lower and upper concrete covers; moreover, diagonal cracks also developed near the loading area, irrespective of whether the beam was strengthened with FRP sheets. These characteristics were significantly different from those of the static loading case (Fig. 5). The development of crack patterns from the upper concrete cover might be due to the flexural wave traveling toward the support points of the fixed beams at the beginning of impact, as mentioned previously. Therefore, Beam NI reached the ultimate state in the flexural-shear failure mode. In contrast, strengthened Beams AI and CI failed due to sheet debonding with a peeling action of the tip of the diagonal crack accompanying the flexural-shear failure mode.

Fig. 9. Crack patterns after impact loading at H = 2.5 m: (a) Beam NI; (b) Beam AI; and (c) Beam CI.

Pham and Hao (2017) also showed crack patterns of a reference beam without an FRP strip and strengthened beams. In these experiments, similar crack patterns to those shown in Fig. 9 are obtained, but flexural cracks develop from the upper toward the lower fiber.

A comparison of the deformation of the unstrengthened beam (Beam NI) with those of the strengthened beams (Beams AI and CI) showed that Beam NI was permanently deformed near the loading point; however, Beams AI and CI did not similarly deform because of the strengthening effect of the FRP sheet. Beams AI and CI exhibited similar crack distribution characteristics to each other.

Relationships between Maximum Responses and Input Impact Energy

Fig. 10 shows the distributions of the maximum impact force P_max, the maximum reaction force R_max, the maximum deflection δ_max, and the residual deflection δ_rs with respect to the input impact energy E_i as listed in Table 1. The residual deflection δ_rs was the permanent midspan deflection after the test was completed.

For the plot of the maximum impact force P_max in Fig. 10(a), even though the result for the drop height of H = 2 m (E_i = 6.4 kJ) was slightly lower for Beam AI than the other values, all the values were approximately linearly distributed with increasing input impact energy E_i, including the value for the case of the unstrengthened beam, Beam NI.

The results of the maximum reaction force R_max in Fig. 10(b) show that the values for Beams AI and CI tended to be linearly distributed with increasing input impact energy E_i, as was the case for the maximum impact force P_max, while the result for Beam NI was slightly lower. Comparing the distribution with that of the maximum impact force P_max [Fig. 10(a)], it can be observed that the maximum reaction forces R_max might be a quarter of the maximum impact forces P_max.

Fig. 10(c) shows the distribution of the maximum deflection δ_max. This figure shows that all the values, excluding the result for Beam NI, were approximately linearly distributed through the origin of the input impact energy E_i. Even though the FRP sheets debonded in both Beams AI and CI for the drop height of H = 3 m, the deflections had similar distribution characteristics. Because the value for the case of Beam NI was significantly different from those of Beams AI and CI, the strengthening effect of the FRP sheets was confirmed.

Fig. 10(d) shows the distribution of the residual deflection δ_rs. This figure shows the following: (1) the residual deflections of the strengthened beams (Beams AI and CI) increased approximately linearly from the origin until the FRP sheet debonded; (2) because Beams AI and CI reached the ultimate state due to the FRP sheet debonding at H = 3 m, these residual deflections were located above the linear distribution characteristics; and (3) these values were smaller than that for Beam NI with H = 2.5 m because the strengthening effect of the FRP sheet could be expected until the maximum deflection of the beams was reached.

Taking the ratio of the residual deflection δ_rs to the maximum deflection δ_max, those for the strengthened beams were distributed at approximately 1/2.5 until the FRP sheet debonded. Because these ratios of the unstrengthened beam (Beam NI) and strengthened beams (Beams AI and CI), in which the sheet debonded, were distributed in the region from 1/1.35 to 1/1.45, the restoring forces for those cases were very low.

Calculating the ratios of the maximum and residual deflections of the strengthened beams (Beams AI and CI) to those of the unstrengthened beam (Beam NI) at H = 2.5 m showed that these values were restrained by more than 30% and 60%, respectively. Therefore, even though the strengthening effect of the FRP sheet for the maximum deflection δ_max was similar to that at the rebar yield load under static loading, the effect for the residual deflection δ_rs was more than twice that for the maximum deflection δ_max.

Thus, from these experimental results, the maximum and residual deflections clearly were approximately linearly distributed with increasing input impact energy E_i through the origin until the beams reached the ultimate state and the FRP sheets debonded. These characteristics are similar to those in the case of unstrengthened beams (Kishi and Mikami 2012). Based on these characteristics, an impact-resistant design procedure for unstrengthened RC beams that includes the input impact energy E_i, the maximum deflection δ_max and/or residual deflection δ_rs, and the static load-carrying capacities P_usc of the beam was proposed. Therefore, by accumulating experimental and/or numerical results on the impact response characteristics of the strengthened RC beams with various FRP sheets, cross sections, span lengths, rebar ratios, input impact energies, and strengthening volumes of the FRP sheets, an impact-resistant design procedure for the strengthened RC beams could be established.

Conclusions

In this study, to investigate the strengthening effects of FRP sheets on the impact resistance of RC beams, low-velocity impact load tests are performed on beams strengthened by bonding FRP sheets to tension-side surfaces. AFRP and CFRP sheets are used in this study to investigate the influences of the material properties of the sheets on the behavior of RC beams under impact loading. The results obtained in this study are as follows:

1.

Although flexural cracks developed only from the lower concrete cover near the loading area under static loading, for impact loading, flexural cracks developed from the lower and upper concrete covers over the entire span area, and diagonal cracks developed directly below the loading point;

2.

The failure mode of the RC beams changed from flexural failure to flexural-shear failure when the loading changed from static to impact loads, regardless of whether they were strengthened with an FRP sheet, and the strengthened beams failed with sheet debonding due to the peeling action of the tip of the diagonal crack;

3.

The time histories of the impact force at the beginning of collision were similar, regardless of whether the specimen was strengthened with an FRP sheet, because the impacted concretes had the same material properties, such as compressive strength, elastic modulus, and mass per unit volume;

4.

Under impact loading, if the axial stiffnesses of both sheets were similar, the time histories of the impact force, reaction force, and loading point deflection were also similar;

5.

Both beams reached FRP sheet debonding at a similar input impact energy due to the peeling action at the tip of the diagonal crack;

6.

Even though the dissipated energy due to the beam tended to be decreased by flexural strengthening with FRP sheets, the effect might be small. In addition, depending on the sheet materials, the characteristics of the energy were different for each strengthened beam;

7.

Due to the flexural strengthening of the RC beams using FRP sheets, the maximum and residual deflections of the beams under impact loading were reduced by more than 30% and 60%, respectively; and

8.

The maximum and residual deflections tended to increase linearly with increasing input impact energy until the sheet debonded.

Data Availability Statement

All data generated or used during the study appear in the published article.

Notation

The following symbols are used in this paper:

A_f: cross-sectional area of the FRP sheet;
E_c: elastic modulus of concrete;
E_dp: dissipation energy due to impact force;
E_dr: dissipation energy due to reaction force;
E_f: elastic modulus of the FRP sheet;
E_i: measured input impact energy;
E_s: elastic modulus of rebar;
$f_{c}^{'}$: compressive strength of concrete;
f_f: ultimate strength of the FRP sheet;
f_sy: yield stress of longitudinal rebar;
f_t: tensile strength of concrete;
H: set drop height of weight;
H′: measured drop height of weight;
P: impact force;
P_max: maximum impact force;
P_usc: static calculated flexural load-carrying capacities of the RC beam;
R: total reaction force;
R_max: maximum total reaction force;
t: time after the beginning of impact;
V_usc: static calculated shear load-carrying capacities of the RC beam;
α: shear-flexural capacity ratio of the RC beam;
δ: midspan deflection of the RC beam;
δ_max: maximum midspan deflection of the RC beam;
δ_rs: residual midspan deflection of the RC beam;
ɛ: strain;
ɛ_cu: ultimate compressive strain of concrete;
ɛ_sy: yield strain of longitudinal rebar;
ɛ_uf: failure strain of the FRP sheet; and
σ: stress.

References

ACI (American Concrete Institute). 2017. Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures. ACI 440.2R-17. Farmington Hills, MI: ACI.

Abstract

Introduction

Experimental Overview

Dimensions and Static Design Values of the RC Beams

Experimental Method for the Impact Loading Test

Deflection Calculation Method

Experimental Results for Static Loading

Load Deflection

Crack Patterns After the Experiments

Experimental Results for Impact Loading

Time Histories of Impact Force, Reaction Force, and Deflection

Temporal Transitions of FRP Strain Distributions and Crack Patterns of the Beams

Energy Dissipation

Cracks Pattern of Test Specimens

Relationships between Maximum Responses and Input Impact Energy

Conclusions

Data Availability Statement

Notation

References

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