Impact response characterization of shear CFRP strengthened RC beams by Fourier and wavelet methods: tests and analyses

3.1 Fast Fourier transform

FFT has use in the measurement of the natural oscillation frequencies of structures and is a frequency-based transform widely used in the analysis of linear systems. It decomposes a signal into the sine waves of different frequencies, which sum to the original waveform, distinguishing different frequency sine waves and their respective amplitudes. FFT is of great importance to signal processing and has common use in the frequency content analysis of structures and detection damage in beams. The equation for continuous FFT is as follows:

Functions f(t) and F(ω) denote the given signal in the time domain and the Fourier transform in the frequency domain. The length of input time history is n time samples in total. In structural health monitoring theories, such as EMI and PZT techniques, which are present in literature and references [9–13] in depth, response due to excitation used for damage detection is linear, although damage and material non-linearity affect the properties of the system. However, system features during transient and steady-state responses are decomposed here to estimate the damage evolution, which is currently active. Thus, FFT theoretically applies for postdamage status assessment, dynamic damage evaluation, and CFRP strengthening effectivity, which are revealed well in this method. However, the Fourier transform cannot determine the information variations along the time domain. For instance, if there is a local oscillation representing a particular phenomenon occurring within the response time domain, its location is not recognized. The latter case is a non-stationary signal case where frequencies alter over time.

3.2 Continuous wavelet transformation

The wavelet transform breaks a signal into shifted and scaled versions of the mother wavelet, called as basis function, which are compact in both time and frequency domains [16]. Basis functions should integrate to zero and be square integrable with finite energy level. Unlike the FFT method, the data on both time and frequency domains are maintained depending on the scale-time range used in wavelet transformation. Here the time variable is to differentiate simultaneous damages at different locations in the algorithm for impulsive load cases. The equation for CWT is as follows:

In Equation (2), a and b parameters denote the scale and the position of the base function, respectively, along the time domain. High-frequency and high-period oscillations are obtained for a≺1 and a≻1 scale ranges, respectively. Coefficients W(a, b) represent the similarity correlation of the scaled wavelet to a specific section of response signal. In this study, the Morlet wavelet is the mother wavelet, as shown in Equation (3) [17], which efficiently measures the damage in concrete and crack propagation [18]. The selected base function with regular and square integrals is plotted in Figure 1, where the major part of excitation energy (square integral of wavelet function) is delimited to |t|≤2 s time domain.

Figure 1:

Morlet wavelet time function supplied with regular and square integrals.

The output of CWT analysis is a plot on which the x-axis represents the position along the time domain (b), the y-axis represents the scale (a), and the color at each x-y point represents the magnitude of the wavelet coefficients (c). The CWT coefficient plots are accurately the timescale view of the response signal. It is a different view of extracted data and depends on the time-frequency FFT content. When cracks propagate in concrete continuum, natural vibration frequencies of impact response decrease and damage occurs in RC member [19]. In other words, impact-induced damage results in oscillations with reduced stiffness and strength compared with applied resist energy, which finally lowers vibration frequencies and amplitudes of transient response. The decrease in frequency causes an increase in the wavelet scale and corresponding coefficient in the CWT. Therefore, CWT analysis detects the damage-induced structural property alterations more specifically.

4.1 Specimen preparation and CFRP retrofit

Normal weight concrete mixture with a maximum aggregate size of 10 mm is according to the ACI 211.1 [20] guidelines with a 0.6:1:2.4:1.9 weight proportion and a 90-mm slump for casting of six rectangular simply supported RC beams. Fresh concrete is molded in reinforcement-embedded 1200×200×100-mm formworks and consolidated in several layers that have two standard cylindrical molds for each specimen to determine consistent crushing strength. All samples are water cured for 21 days at a temperature of 17°C. Capped concrete cylinders are compressed quasistatically with a strain rate of 2×10^-5 (s^-1) in day 28. The average modulus, strength, and related strain acquired are 20.2 GPa, 25.5 MPa, and 0.25%, respectively.

Two D12 rebars with a 603-MPa yield stress in each bending sides at a 25-mm concrete cover are flexural reinforcements with ρ_s=1.3% flexural steel ratio for all beams. Moreover, D3 wire closed rectangular ties with a 390-MPa yield stress and a 50-mm spacing are shear reinforcements for all specimens with ρ_v=0.4% shear steel ratio for all beams. Longitudinal rebars have mechanical anchors at the ends using 8-mm-thick plates. Beam specimens have identical material and reinforcement layouts but different CFRP retrofit outlines. Specimens have three categories allocated with IN, UW, and CP letters, indicating nonstrengthened, unidirectional, and cross-ply sheet wrapping, respectively, followed by the sample number. Details and layout of all specimens are shown in Figure 2, and the construction properties of all specimens are presented in Table 1.

Figure 2:

Reinforcement and CFRP wrapping scheme configuration of specimens.

Two specimens are control prototypes (IN) without any retrofitting, but carbon fiber sheets with 0.17-mm thickness (t_f) wrap four specimens with unidirectional and cross-ply stacking. Specimens with UW letters have wraps in length using three 700×500-mm sheets with 150-mm overlaps and vertically oriented fiber direction (90°) according to ACI 440.2 regulations [21] that supply 0.3% shear CFRP ratio. Series with CP identification have wraps in length with a single 1200×500-mm horizontal fiber sheet initially and then bound with vertical fiber sheets analogous to UW scheme forming cross-ply stacking (0°/90°) that supply 0.5 and 0.3% CFRP ratios for flexure and shear, respectively. Epoxy resin is 1.0 mm in thickness for each CFRP sheet wrap, which provides the required bonding strength as recommended by researchers. Specifications of sample materials are presented in Table 2.

4.2 Impact load identification

Weight and height of drop are determined by generally considering the equilibrium of applied kinetic energy and the external work required to generate the total collapse of structure (either shear or flexural), which results in an impact force much higher than static capacity. Nominal flexure and shear capacities of nonstrengthened beam section are presented in Equations (4) and (5) separately according to ACI 318-08 regulations [22]. All specimens have a 1-m span (L) with a 100-mm overhang for each support. The width (b) and the effective depth of the section (d) are 100 and 175 mm, correspondingly:

According to the above-mentioned relations, the nominal strengths are 18.3 kN·m and 34.1 kN for flexure and shear, respectively, which is equal to 83.2 and 69.8 kN ultimate static loads for nonstrengthened beams loaded in the midspan location. The resultant collapse deflections for flexure (δ_flexure) and shear (δ_shear) of a simply supported beam if an ideal response condition (perfect yielding of steel rebars or stirrups) is governing the relevant response are presented in Equations (6) and (7) as follows:

Calculated collapse deflections are 27.3 and 11.2 mm for flexural and shear failure modes, respectively. On the basis of the extracted results, the dominant failure mode is shear for the reason that the strength of this mode is lower. However, the impact load intensifies the brittleness of the response regardless of the failure type (flexure or shear). The elastic-fracture characteristic of static response enables the triangular approximation of collapse-equivalent external work. On the basis of the current approach, the required kinetic energy of drop weight is 392.3 N·m to cause the collapse of nonstrengthened specimens. Therefore, the striking mass will be 40 kg in the current study if the drop height is 1.0 m for the low-velocity impact condition.

4.3 Test setup and instrumentation

The test setup and the instrumentation used for impact test are shown in Figure 3. The rigid base frame supplied by vertical guides, the steel weight drop, and the support pedestals are the main components of impact test setup for built RC beams. Test setup and ground are connected by 10-mm-thick isolators to avoid stress wave reflections in boundaries. Rail guides leading steel drop are fixed in all directions to secure frictionless carriage and uniform contact. Two 5-mm-thick plates fastened to supports by 20-mm anchors restrain uplift and rebound of members. Layout and impact loading pattern is a single drop weight colliding midspan location repeatedly with a 1.2-m spherical curvature radius to cause collapse according to the ASTM E695 standard. One MEMS accelerometer with a ±2000 g recording range is mounted to test members in the midspan location for the measurement of impact-induced acceleration. Optical laser LVDT with 50-mm stroke and 0.01-mm accuracy points is placed at the bottom surface of the midspan location.

Figure 3:

Setup and instrumentation used for drop weight impact test.

Output cables of sensors are linked to external bridges of a 10-channel wide-band digital dynamic data logger with a 20-kHz sampling rate. According to Nyquist’s sampling theorem, digitizing rate should at least be twice the highest frequency covered in record signal to avoid aliasing [23]. Thus, response signals with frequencies lower than 10 kHz are captured accurately in the current study. Experimental response is to have contents lower than 5.7 kHz, which covers 93% of modal mass participation according to elastic vibration eigenvalue analysis. Elastic frequencies are upper bonds of inelastic transient response due to material non-linearity and fracture mechanisms. Thus, experimental recording rate is quite enough to capture the continuous response of structure satisfying required accuracy.

5.1 Primary time history records

The midspan location deflection and acceleration histories of tested specimens are shown in Figure 4. There are no notable data for nonstrengthened samples (IN) after the fourth impact because of excessive shear damage. Weak vibrations after the first impact depict sudden stiffness loss of nonstrengthened samples. Ultimate reached peak deflection and residual limit at the fourth impact are 25.1 and 23.2 mm, respectively, where the relative difference is one small portion of overall value without any meaningful recovery. Midspan acceleration is 155.4 g at the first impact and sequentially drops to 41.9 g at the fourth impact.

Figure 4:

Midspan deflection and acceleration time history records.

Unidirectionally wrapped samples (UW) resisted six impacts, generating flexural plastic hinge at the midspan location without loosing stability. Restrained deflections have peak and residual values at 14.5 and 8.2 mm in the final impacts with sensible recovery. Considering the fourth impact, maximum and residual deflections decrease by 50 and 76%, respectively. Resisted acceleration at midspan point is 177.1 g for the first impact, increases up to 269.1 g at the third repeat, and remains almost the same for the rest of the load repeats.

Cross-ply fiber stacking (CP) improves dynamic response by transferring shear distortion into flexural extension over member span and contributes to impact-resisting internal forces. Peak and residual deflections here reach 9.8 and 3.5 mm, respectively, in the sixth impact with 32 and 43% additional mitigation rate considering unidirectional wrap scheme. Persistent deflection remains almost the same for the five impacts but slightly increases for the sixth repeat because of the rupture of longitudinal CFRP fibers. Midspan acceleration reaches 193.4 g for the first impact, rapidly increases up to 422.8 g at the third repeat, and starts dropping to 318.3 g at the end of the test.

5.2 Observed failure modes

The failure pattern of nonstrengthened and retrofitted RC beams is essential for the determination of the governing response. Figure 5 shows the failure modes of test beams and the numbered cracking sequence. Early diagonal cracks of IN beams initiate in the middle of the shear span and then propagate toward load points. The adjacent inclined cracks merge and form major wide shear cracks that rupture the steel stirrups and cause the rebar-concrete bond loss. The IN beams collapse as soon as major shear cracks reach load points, as also observed by Karayannis and Chalioris [24]. The flexural resin cracks form in UW beams at the midspan location as rebar yields. The dilation of CFRP-confined concrete accelerates the flexural crack propagation along beam height. The collapse of UW beams consists of concrete crushing, the rupture of CFRP fibers at the bottom surface, and stirrup yielding at the midspan. CP beams have less flexural cracks than others because of higher flexural stiffness. Then the flexural-shear cracks initiate in beam height and rupture the longitudinal fibers along crack path. In CP beams, the height of cracks and the dilation of confined concrete is less than UW beams, but the distribution length of cracks is higher. The collapse process of CP beams contains a progressive rupture of longitudinal fibers, splitting cross-ply fibers in the beam web and yielding stirrups.

Figure 5:

Failure modes of nonstrengthened and strengthened RC beams.

5.3 FFT spectrum content

The response signal is analyzed using the FFT method for a 0.2-s time domain when the system kinetic energy is ignorable, and the results are shown as spectra in Figure 6. Nonstrengthened samples have peak deflection amplitudes in 47.7, 26.5, 15.9, and 10.6 Hz with decreasing regime due to high-intensity shear damage. Here the stiffness degradation depends on the quadratic ratio of inelastic and first elastic (102.1 Hz) oscillation frequency. The effective residual stiffness is 23%, 7%, 3%, and 1% of the initial status assuming consistency of mass. Accelerations have also peaks at 78-, 58-, 39-, and 19-Hz frequencies, whereas the second mode heap is active in the spectrum. Shear fracture causes continuum discontinuities and leads to overall rigidity loss depicted as both vibration divergences. The stiffness of shear-deficient samples lacks in recovery and gives rise to higher deflection time and lower-resistance acceleration potential.

Figure 6:

FFT amplitude vs. frequency distribution of midspan deflection and acceleration.

Members with unidirectional CFRP wraps (UW) have peaks in 74.3 Hz for the first three impacts and 68.9, 63.6, and 58.4 Hz for the rest of the successive repeats regarding the 55%, 48%, 41%, and 38% conservation of elastic stiffness consequently. Spectra cover a 40-Hz frequency band and show dynamic strength upgrade compared with the nonstrengthened case. Damage rate is stabile for the first impacts then starts to increase within concrete failure, rebar yielding, and vertical CFRP fiber split as impact repeats. Almost all acceleration spectra have close peaks at 97.6 Hz for the first two loadings and 78.1 Hz for next four repeats. The capability of flexural response in the deflection and stiffness recovery of specimens reveals stable frequency content, stabilized damage level, and uniformity of active vibration amplitudes inside response.

Cross-ply CFRP orientations (CP) have a constant 79.6-Hz frequency for peak amplitudes of the first up to the fourth spectra, and then peak amplitudes occur at 74.3 and 68.9 Hz for the fifth and sixth impact repeats, respectively. Dynamic stiffness is 65 and 55% of undamaged case for the fifth and sixth impact repeats, respectively, supplied with a 60-Hz broad curve spread domain. Acceleration spectra own a sharp heap passing through the first elastic eigenvalue and have an adjacent smooth heap beyond the second elastic eigenvalue, 677.4 Hz. Shear deformation effect is stronger in higher vibration modes because of curvature variation and cross-ply CFRP skin stiffness. Peaks are for 605.5, 585.9, 566.4, 546.8, 527.3, and 507.8 Hz for the following impacts, which show incremental degradation in high-mode stiffness due to the fracture of horizontal CFRP fibers.

5.4 CWT correlation coefficient distribution

Coefficients calculated for each wavelet scale and position primarily for deflection signal are shown in Figure 7 as dark ridges. Nonstrengthened samples (IN) own local low-magnitude coefficients at the first impact, which shows the sudden generation of damage at a 0.005-s moment and then starts to progress over the time domain in the form of high-magnitude moving coefficients for large scales. Correlation ridges are getting wide and dark in the fourth impact, which denotes rapid stiffness degradation without any expansion over the time domain. The steadiness of ridges for various positions reveals prominent dynamic stiffness deficiency of nonstrengthened specimens. The sharp predisposition of ridges at low wavelet scales and the increase in correlation coefficient for high scales prove instant loss of shear strength and stiffness along subsequent impacts.

Figure 7:

CWT coefficient distribution for deflection response.

Unidirectional CFRP-wrapped beams (UW) exhibit unique response characteristics along impact test. The biased form of coefficient ridges turns into a swept-forward shape that confirms dynamic stiffness restoration. The position of high-amplitude ridge shifts to 0.01 s for the first and fourth impacts and denotes the improved and stabilized internal resisting strength of members. The distance between two adjacent ridges decreases, and additional ridges emerge consequently. The current pattern approves the stable plastic deformation of strengthened members, as multiple coefficient ridges within the fourth impact response. Also, disperse ridges stand for the enhanced damping potential of UW specimens. Ridges are active for a 0.06-s period in UW case, dissimilar to nonstrengthened cases with a 0.02-s period. Ridges observed in the fourth impact are changing their biased shape alternatively, denoting successive concrete cracking and rebar yielding throughout collision and rebound of drop weight.

Cross-ply wrapping (CP) reveals strengthening effectivity in another way unlike the UW scheme. Multiple ridges arise in the first impact within 0.04 s, and only the first ridge is in swept-forward mode, denoting the sudden activation of flexural stiffness before shear constraint. The predisposition of the first correlation ridge is getting sharper in the fourth impact response and demonstrates the increasing participation of flexural stiffness in advance. In addition, the distance between two adjacent ridges is increased, probably because of failures inside longitudinal CFRP fibers.

CWT coefficients calculated for acceleration signals are shown in Figure 8 and have different distributions compared with deflection signals. Nonstrengthened samples (IN) have high-coefficient ridge density for small wavelet scales at the beginning of the first impact response, but the related values decrease within a 0.03-s period because of the generation of major shear cracks. There is a local ridge escalation for the 0.04-s wavelet position caused by the restraining effect of steel stirrups followed by shear damage formation. The severity of shear fracture along beam span and the rupture of steel stirrups waive any meaningful amplitude for correlation ridges in the fourth impact. Small ridges that are limited to low scales with time positions <0.01 s stand for initial inertial-type resistance, which does not follow the stiffness-type potential. Primarily, scatter ridges followed by sudden diminishing at the final impact indicate the degradation of the specimen.

Figure 8:

CWT coefficient distribution for acceleration response.

Unidirectional fiber wrapping scheme (UW) affects the previously extracted pattern in a major manner. High-amplitude ridges are active, parallel with the first impact, and control the acceleration resistance up to the 0.07-s time span. Low-scale wavelet coefficients arise for the 0.005-, 0.015-, 0.03-, and 0.05-s time positions, where the vertically oriented fibers provide stiffness and restrain opening of shear cracks. Here the coefficient ridges are frequently changing their biased shape in a periodic mode, which stands for CFRP stiffness and specimen curvature dependence. In addition, ridges are getting straighter as response damps noticeably. As low-scale high-amplitude ridges are governing the acceleration of the fourth impact in advance, ridges become closer to each other, covering the 0.06-s time span, expressing further plastic deformations inside load-resisting elements. In addition, the sharpness of biased ridges decreases in the fourth impact as steel rebars are yielding, and the damping competence of UW specimens increases as well.

The most noteworthy phenomenon observed within tests is recorded for the cross-ply-wrapped (CP) samples, where the total pattern of wavelet coefficients is changed in a major manner regarding the UW scheme. Low-scale (stiff) and high-scale (soft) ridges expose in a separated outline in the first impact. The low-scale ridges expand in the 0.05-s time span and cover major part of dominant response, but the high-scale ridges only fill 0.02 s of the domain. The bending stiffness by longitudinal CFRP fibers thoroughly transfers high-amplitude ridges toward the low-scale region and maintains the biased form of coefficient ridges up to 0.07 s while the response damps entirely. Low-scale high-amplitude ridges are expanding toward the 0.06-s time as the fourth impact is applied, which demonstrates that longitudinal CFRP participation increases along the stiffness restoration of CP specimens. The remarkable incident in the fourth impact analysis is the amplitude shifting of midscale toward high-scale ridges, and the reason links to the partial softening of flexural response.