Concrete-filled Steel Tube Beams Research Articles

Flexural performance of FRP-SWSSC-steel composite beams: Experimental and analytical investigation

The steel-concrete-fiber-reinforced polymer (FRP) composite structure was proposed in this paper, where FRP and steel were designed in the tensile region and compression region of concrete-filled steel tube (CFST) beams in the form of sheets, bars, and tubes, respectively, with the expectation of improving the performance of the structure. Epoxy mortar was used to modify the interfacial properties and part of the normal concrete (NC) was replaced by seawater sea sand concrete (SWSSC). A total of 10 FRP-SWSSC-steel composite beams were fabricated and subjected to four-point bending tests, and they exhibited the failure modes of local buckling. Reinforcing the tensile region significantly improved the flexural performance of the composite beams since the steel tube buckling and the concrete cracking were limited, and the flexural capacity of the composite beams was increased by 18.3%− 28.6% by designing FRP sheets or steel bars in the tensile region. Reinforcing the compression region had little effect since the existence of the in-built tube divided the monolithic concrete, and the confinement on the core concrete was not fully utilized. Based on research experience with CFST beams, a flexural strength model for FRP-SWSSC-steel composite beams was established.

CFRP-steel composite beams with seawater sea sand concrete cores subjected to bending

A redesign was attempted for the concrete-filled double-skin tube subjected to bending, and by adjusting the core tube position and applying carbon fiber-reinforced polymer (CFRP) sheets or steel bars in the tensile region, it was hoped to delay the cracking of the concrete in the tensile region. Epoxy mortar was used to modify the interface. Seawater and sea sand has been successfully applied from reinforced concrete beams to concrete-filled steel tube beams, benefiting from the corrosion-resistant properties of CFRP and epoxy mortar. The four-point bending test parameters included the type of core tube, the number of CFRP layers, and the diameter of the steel bars. The beams with FRP sheets exhibited better flexural capacity and residual stiffness, while the brittle fracture of FRP led to major crack in concrete. The beams with steel bars exhibited better initial stiffness and the cracks in concrete were more uniform in width. When the layers of CFRP or the diameter of the steel bars was increased, the flexural capacity of the composite beams increased by 11.0%-13.6% and 7.0%-9.1%, respectively. The enhancements provided by the core tubes were small, and the design of the composite beams should be considered from various perspectives. The moment-curvature relationships, ultimate states, and flexural stiffness were defined by considering concrete cracking, FRP fracturing, and steel buckling. Several formulas for calculating flexural stiffness in the code were evaluated in combination with the test data.

ELASTIC-PLASTIC DEFORMATION OF STEEL-CONCRETE BEAMS WITH LOCAL CRUMPLING DURING THREE-POINT BENDING

The study presents the results of experimental modeling of elastoplastic deformation of bent massive concrete filled steel tube beams under three-point bending. It has been shown that local deformations and local crushing in such structures have a significant impact on their behavior. The applicability of the theory of bending of a hollow steel beam according to the Bernoulli model is analyzed. A comparison has been made of the bearing capacity and stress-strain state of hollow steel tubes (according to the Bernoulli model and the results of experiments) and concrete filled steel tube beams, and the contribution of the concrete core to the bending resistance during elastoplastic deformation has been quantitatively assessed. The actual load-bearing capacity of a hollow pipe during three-point bending does not exceed 50% of the calculated theoretically determined one, which indicates the impossibility of using the classical bending model when designing systems of this kind. In this case, the concrete filled steel tube beam not only ensures the full functioning of the metal during the deformation process, preventing its disruption, but also provides some increase in load-bearing capacity due to the inclusion of a compressed zone in the concrete work. The increase in the load-bearing capacity of a beam due to the introduction of a concrete core can reach 70%. Despite their significant weight, bendable tube-concrete rods can be recommended in conditions of a complex stress-strain state, in which, in addition to transverse bending loads, significant longitudinal forces arise, as well as local force factors that contribute to the occurrence of local crushing deformations, since, unlike a thin-walled hollow tube, concrete the core significantly prevents these effects. Based on the results of the study, the potential effectiveness of flexible tube-concrete elements for a number of structures was proven.

Performance of circular concrete-filled steel tube beams under monotonic and cyclic loadings

This study explored the performance of concrete-filled steel tube (CFST) beams under monotonic and cyclic loadings. Experiments were performed on nine simply-supported 140-mm-diameter CFST beams, which were classified into three groups by the diameter-to-thickness (D/t) ratios of 56.0, 46.7, and 40.0, conforming to Eurocode 4. The experimental results indicated that CFST beams exhibited high ductility. The buckling of steel tubes governed the plastic behavior and the ultimate state of CFST beams. The deformation and curvature concentrated in the middle region of the beams, forming a plastic hinge. The yield load, ultimate load, and yield and plastic stiffness slightly increased when D/t decreased from 56.0 to 46.7. However, by further decreasing D/t to 40.0, the ultimate and yield loads were significantly increased by ∼100%, the elastic stiffness by up to 58.2%, and the plastic stiffness by at least 187.5%. With a decrease in D/t ratio, the yield deflections slightly increased, whereas the ultimate deflection significantly decreased by up to 56.3%. The strength degradation was more pronounced for CFST beams with a D/t ratio of 40.0. Decreasing D/t ratio increased the plastic-to-yield stiffness ratios. The absorbed energy increased linearly with the increase in deflection in the plastic range. The cyclic loading effect caused an average degradation of 1.7%/cycle for both loading and unloading stiffness, whereas it marginally impacted on strength degradation. A decoupling concept and simplifications were employed to propose a simple model for rapidly estimating the moment capacity of CFST beams, which can be useful in designing and evaluating CFST beams.

Performance assessment of post-tensioned concrete-filled steel tube beams using unbonded tendons with uncertainty quantification

The centerpiece of many research projects is evaluating the structural performance of the concrete-filled steel tubes (CFSTs). When these structural elements are employed as flexural members, some parts of the concrete infill are subjected to tension, and consequently the concrete is cracked so that the confinement effect is reduced. Therefore, the application of tendons and modification of the CFST configuration are deployed to improve the serviceability of the CFST beams. A non-linear finite element (FE) model considering the effects of the material and geometrical non-linearity and initial imperfection is developed. Concurrently, an analytical model based on the plastic stress distribution method (PSDM) is proposed to compare the results. In addition, a probabilistic assessment along with the uncertainty quantification is conducted to calculate the reliability indices and the sensitivity of the beams to the variation of the input variables. The results of the study demonstrate that the implemented measures considerably enhance the moment capacity and serviceability performance of the CFST beams. Moreover, the sensitivity analyses show the significance of the variables on the model output with different steel yield stress values and the importance is ordered as the steel tube width followed by the steel tube thickness and the concrete strength.

Flexural behavior and reliability analysis of rectangular concrete-filled cold-formed steel tabular beams

Concrete-filled steel tube (CFST) has been widely investigated for columns, whereas it has been less explored for beams. This study investigates the behavior and reliability of CFST beams under bending, both experimentally and theoretically. Experiments were performed on nine rectangular CFST beams and three steel tube (ST) beams under bending. The experimental results showed that local buckling was the failure of both ST and CFST beams. The load−deflection behavior of CFST beams was significantly better than that of ST beams. Load-carrying capacity and stiffness of CFST beams was found to be approximately 3.0 and 1.29 times those of ST beams, respectively. The mechanical properties of steel were much more efficiently exploited in CFST beams than in ST beams. The mean ductility of 8.19 classified CFST beams to be highly ductile. The average plastic hinge length approximately equals the height of CFST beams. An available model was used to predict the moment capacity of CFST beams, and the results confirmed the accuracy of the model. Results of reliability analyses showed that mean moment capacity was independent on any individual variable or a combination of variables. In contrast, the standard deviations heavily depended on the considered variables. Consequently, the reliability index due to variable of steel thickness is the highest at 32.2, followed that due to the steel strength at 24.5, whereas those due to other variables varied from 8.0 to 9.3.

Flexural behavior of circular concrete filled steel tubes with partially incorporated demolished concrete lumps

For the past decade, researchers have been experimenting with the use of Demolished Concrete Lumps (DCLs) in structural members, as it has been proven to be a promising method to recycle concrete in different field applications. Although there have been several studies on incorporating DCLs in Concrete Filled Steel Tube (CFST) members, there are no studies that evaluate its effect on the flexural performance of CFST beams. Therefore, this paper focuses on studying the flexural behavior of CFST beams with DCLs, where the DCLs are inserted at the center of the cross-section. In total, fourteen circular CFST and two circular Steel Tube (ST) specimens were tested under bending using a four-point loading setup. The specimens are categorized into two different steel tube sections, where two circular sections of D/t = 55 (C1) and D/t = 45 (C2) were considered. The CFST specimens within each steel tube category differ in DCLs particle sizes and DCLs inner occupation area. CFST beams filled completely with normal concrete were also tested as control specimens. In addition, two CFST specimens from the steel section C2 were left partially hollow at the center to study the contribution of DCLs to the overall flexural performance. The results were very promising as the flexural behavior of DCL CFST specimens was very similar to the control CFST specimens. The DCLs’ particle sizes and the inner occupation area had minimal effect on the ductility, stiffness, yielding capacity, and ultimate capacity of the CFST specimens. The maximum percentage reduction in the flexural capacity between DCL CFST and control specimens were less than 2% for both sections whereas the percentage gain was up to 7%. Furthermore, the obtained flexural capacities were compared with nominal predictions from different design codes and models. All codes underestimated the capacities of all CFST specimens, with Han's model being the most conservative, followed by EC4, BS-5400–5, and AISC-LRFD, respectively.

Study of impact factor of arch bridge made with continuous composite concrete filled steel tube beams

Impact factor is amplification factor of vertical dynamic effect produced by vehicles. It is a main parameter of bridge design and an important index of dynamic load effect evaluation. In order to study the influence of structure and excitation factors on the impact factor of highway bridges, and then obtain the real impact factor of the continuous beam arch composite bridge, taking a three-span arch bridge made with continuous composite concrete filled steel tube beams as an example, considering the vehicle-bridge coupling vibration effect, the spatial beam element model of the bridge and the half vehicle model with the three-axis are established by using ANSYS. The impact factor of different parts of the main beam and different responses affected by the deck surface roughness, the vehicle speed and the number of vehicles are analyzed. The binary regression formula of impact factor is obtained by taking the vehicle speed and the roughness of bridge deck as independent variables. Finally, the formula is verified by the measured data of two bridges with similar fundamental frequencies. The results show that the impact factor calculated by the current code is generally small for the bridge structure with complex structure and relatively low frequency, such as arch bridge made with continuous composite concrete filled steel tube beams. The impact factor is most affected by the roughness of bridge deck. When the roughness of bridge deck reaches grade B or above, the impact factor exceeds the specification value, and the maximum impact factor can reach 5.42 times of the specification value. For the main beam, the impact factors of different external excitation, different responses and different parts are not the same, and some impact factors exceed the specification value. The regression formula of impact factor given can be used to estimate the impact factor of main beams of similar structures.

Effects of support type and geometric shape of steel tube on concrete-encased concrete-filled steel tube beam under low velocity impact

Concrete-encased concrete-filled steel tube (CEFST) beams prepared by placing steel tube in RC beam is a beam type that has widespread use. The current study examines the effects of steel tube geometry and support conditions on the behavior of CEFST beams under low velocity impact loading. First, CEFST beam specimens with different lengths and different tube section geometries (circular and square) were produced in the laboratory. These four test specimens with two different support conditions were exposed to low velocity impact load tests. Finite element models of the test specimens were created using Abaqus\\Explicit software. In the next stage, 4 finite element models were verified by the experimentally obtained damage conditions, maximum displacements, and support reaction forces. In the final stage, as parametric study 12 finite element models were prepared in addition to 4 verified models and analyzed under low velocity impact loading. In addition to experimental values, Von Mises stresses, Equivalent plastic strain, Friction energy, and Damage energy values were also obtained by the numerical study and thus the effects of steel tube geometry and support conditions were comparatively examined. The obtained results showed that CEFST beams with a square tube section exhibited better performance under a sudden load such as impact compared to the beams with a circular tube section. Moreover, both numerical and experimental results pointed out that the beam length beyond support has a positive impact on the performance of beam under impact loading.

Experimental study on the flexural behavior of square high-strength concrete-filled steel tube beams with different CFRP wrapping schemes

Recently, carbon fiber reinforced polymer (CFRP) materials have been recommended for strengthening concrete-filled steel tube (CFST) members. In this paper, experimental study is presented to further investigate the flexural behavior of square high-strength concrete-filled steel tube beams with different CFRP wrapping schemes. Results reveal that all of the specimens display the failure of longitudinal fibers at the bottom of the tensile zone when reaching the ultimate state. Meanwhile, the performance of CFRP confined CFST (CFRP-CFST) beams is improved significantly due to the transverse confinement and longitudinal reinforcement of CFRP sheets. For example, the moment capacity of CFST beams of fcu = 62.8 MPa and 128.2 MPa increased by up to 22 % and 34 %, respectively, strengthened with the full scheme. Moreover, for CFST beams of fcu = 128.2 MPa, the half scheme achieved the similar enhancement effect (29 %) in comparison with the full scheme. Based on the experimental results, a simplified approach using the fiber element method is proposed to predict the moment–curvature relationship and ultimate moment capacity of the CFRP-CFST beams. The predictions are validated with the experimental results from this paper and other study. A stepwise analytic approach is developed for designing CFRP-CFST flexural members.

Numerical Investigation of the Flexural Performance of Slender CFST Beams with Varied Shapes of External Stiffeners

The concrete-filled steel tube (CFST) beams are recommended for adopting in the modern composite structure since it achieves a higher load capacity and ductility behaviour than the conventional structural members. Using CFST beams with slender steel cross-section led to reduce the overall cost of the structures compared to those with compact cross-sections; however, it is more likable to buckle under the compression stress. Therefore, providing external stiffeners along the four sides of CFST beams expected to reduce the overall self-weight also can provide more stiffening to the steel’s section that led to improve the loading capacity. In this study, a finite element (FE) method was adopted for numerically investigated the flexural performance of the square CFST beams stiffened with different shapes of external grooves that provided along the beam’s sides. The FE software named ABAQUS was adopted for this purpose where the original model of CFST beam analysed and verified with the corresponding tested specimen. After that, additional CFST model have been built and analysed to investigate further parameters including the effects of varied tube’s thickness, steel yielding strength, concrete compressive strength and different external grooves shape (V-shaped, U-shaped, C-shaped, double V-shaped). The results established from the numerical analyses showed that the ultimate bending capacity (Mu) of the stiffened CFST models was generally enhanced by increasing their concrete strength, steel yield strength and tube’s thickness but in varied percentages. For example, increasing the tube thickness from 1.5 mm to 3.0 mm achieved an improvement in Mu values of about 72.3\%. while fewer improvement percentages have been recorded of about 11.9\% when only the core concrete strength increased from 25 MPa to 55 MPa. Furthermore, the shape and number of grooves have positive impact on the bending capacity of stiffened CFST models, where using U-shape, C-shape and V-shape external grooves were led to improve the Mu value of about 2.8\%, 10.7\%, and 11.1\%, respectively. Thus, the energy absorption of these models was improved accordingly.

Effects of Support Type and Geometric Shape of Concrete-Encased Concrete-Filled Steel Tube Beam Under Impact Loading

Effects of Support Type and Geometric Shape of Concrete-Encased Concrete-Filled Steel Tube Beam Under Impact Loading

Flexural strengthening mechanism of concrete-filled steel tube beam by welding round steel at soffit of the beam

In the present study, the flexural behavior of concrete-filled steel tube (CFST) beams strengthened by welding round steel at the soffit of the beam has been investigated. First, a total of six specimens were tested under four-point bending load, which includes one reference beam and five retrofitted beams strengthened by welding round steel of different diameters at the soffit of the beams. Then, the corresponding nonlinear finite-element models have been developed and calibrated against the experimental results. By combining indoor experiments and numerical simulations, the bending moment versus mid-span curvature curves, the flexural capacities, flexural stiffness, ductility, vertical deflection curves, strain distribution across the cross-section, and neutral axis offset of the test beams have been systematically analyzed. The results show that the welded round steel at the soffit can improve the flexural bearing capacity and stiffness of the CFST beams significantly. This can be attributed to the CFST beams benefitting from the flexural bearing effect of the round steel and the downward offset of the neutral axis which causes more core concrete to be in compression. Further, the larger the diameter of the round steel, the greater the benefit. Finally, comparisons have been made with the flexural stiffness calculated using the existing design codes, such as AIJ standard, BS5400, Eurocode 4 and AISC specification. The comparisons show that the flexural stiffness of the unstrengthened CFST beam can be predicted by AIJ and BS5400 perfectly, whereas those of the strengthened CFST beams can only be accurately calculated by AISC.

The Experimental Behavior of the CFST Column and Beam Externally Bonded by CFRP Strips

This research article has been analyzed to examine the structural enhancement of concrete-filled steel tube (CFST) sections used externally with carbon fiber reinforced polymer. Due to their structural benefits, concrete-filled steel tubular sections are among the most common today. High strength, reduced cross-section, excellent seismic-resistant structural properties, increased fire resistance, and improved visible stiffness are just some of the advantages. Carbon fiber was used as a form of strips with a different number of layers and strip spacing on beam and column specimens. Twelve columns were tested, ten of which were externally reinforced with CFRP strips of various widths and spacing, and the remaining two columns were not reinforced with carbon fiber. However, ten beams were tested, eight of which were externally reinforced with CFRP strips of various widths and spacing, and the other two beams were not reinforced with carbon fiber. All specimens were tested at one point loading under a universal testing machine. Experimental results found that in comparison to the reference column and beam, the CFST column and beam specimens reinforced by carbon fiber have a higher load capacity.

Performance of the novel C-purlin tubular beams filled with recycled-lightweight concrete strengthened with CFRP sheet

This research investigates the performance of double C-purlin sections used in the concrete-filled steel tube (CFST) beams system. A recycled-lightweight concrete was used as infill material to reduce the newly suggested composite beam's self-weight and cost. Up to 70% of the raw coarse aggregate was replaced with the expanded polystyrene beads and recycled aggregate concrete. Also, the strengthening performance of the suggested CFST beam was investigated using carbon fiber reinforced polymer (CFRP) sheets. A total of seven specimens of concrete-filled C-purlin tubular sections were tested under four-point loads, and additional 12 models were numerically analyzed using finite element software. The conducted failure modes, flexural strength, flexural stiffness, and energy absorption index are presented and discussed. The results confirmed that the recycled-lightweight infill concrete material has a slightly lower influence on the investigated CFST beams' flexural performance than those with normal concrete (less than 10%). Like the conventional CFST beams, the double C-purlin tubular beams filled with recycled-lightweight concrete showed a normal response to the CFRP's strengthening quality. Moreover, the flexural strength capacity and stiffness values obtained from the current analyses are analogous with those theoretically predicted using the existing methods, which achieved mean values of about 0.759 and 1.126, respectively, as average prediction mean values of these methods.

Designing new hybrid artificial intelligence model for CFST beam flexural performance prediction

A substantial number of experimental studies have reported on the flexural performance of concrete-filled steel tube (CFST) beams. Due to the problem complexity, theoretically modeling of the flexural bending capacity (Mu) and the flexural stiffness at the initial and serviceability limits ( $$K_{{\text{i}}}$$ and $$K_{{\text{s}}}$$ ) of CFST beams remains challenging mission in the structural engineering field. Hence, this research proposes new numerical models for modeling the flexural capacities (Mu, $$K_{{\text{i}}}$$ , and $$K_{{\text{s}}}$$ ) of CFST beams under static bending load. For this purpose, numerous existing experimental and numerical results of CFST beams are collected for developing a new numerical model called as hybridized artificial neural network (ANN) model with particle swarm optimization (PSO) algorithm. The results of the proposed model validated against the existing results of CFST beams tested over the literature. In addition, PSO–ANN model verified with those obtained by the existing standards and approaches (EC4, BS5400, AISC, AIJ, and others) for the same corresponding beams. The proposed PSO–ANN model confirmed its capability to be used as an alternative theoretical approach to predict the flexural strength and stiffness capacities of CFST beams. The PSO–ANN model achieved mean values of about 0.933–0.989 with a coefficient of variation ranged from 4.98 to 9.53% compared to the existing results that obtained by others.

Flexural performance of square concrete-filled steel tube beams stiffened with V-shaped grooves

The outward steel tube buckling failure of concrete-filled steel tube (CFST) beams is still considered to be a serious concern due to the typical bending loads. This research conducts experimental and numerical investigations on the flexural performance of slender square steel tubes filled with normal concrete. A total of 6 cold-formed square CFST specimens were tested under static bending loads. The cross-sections of 4 specimens were stiffened by single and double V-shaped grooves along the tube cross-sections, and 2 specimens were tested as control specimens (unstiffened square specimens). The results showed that adopting this stiffening concept in the slender square CFST beams led to restriction of the buckling failure of the outward steel tube (at the top flange). Due to the increase in the steel confinement factor of the stiffened square CFST beams, the bending moment capacity, flexural stiffness, and energy absorption capability were improved by 25.4%, 7.2%, and 31.4%, respectively, compared to those of the corresponding unstiffened specimens. Finite element models were also developed to further investigate the performance of the proposed CFST specimens by varying certain chosen parameters. The bending moment capacity and the flexural stiffness results obtained from the experimental and numerical investigations were validated with predicted values from different existing standards.

Flexural performance of cold-formed square CFST beams strengthened with internal stiffeners

The tube outward local buckling of Concrete-Filled Steel Tube (CFST) beam under high compression stress is still considered a critical problem, especially for steel tubes with a slender section compared to semi-compact and compact sections. In this study, the flexural performance of stiffened slender cold-formed square tube beams filled with normal concrete was investigated. Fourteen (14) simply supported CFST specimens were tested under static bending loads, stiffened with different shapes and numbers of steel stiffeners that were provided at the inner sides of the tubes. Additional finite element (FE) CFST models were developed to further investigate the influence of using internal stiffeners with varied thickness. The results of tests and FE analyses indicated that the onset of local buckling, that occurs at the top half of the stiffened CFST beam cross-section at mid-span was substantially restricted to a smaller region. Generally, it was also observed that, due to increased steel area provided by the stiffeners, the bending capacity, flexural stiffness and energy absorption index of the stiffened beams were significantly improved. The average bending capacity and the initial flexural stiffness of the stiffened specimens for the various shapes, single stiffener situations have increased of about 25% and 39%, respectively. These improvements went up to 45% and 60%, for the double stiffeners situations. Moreover, the bending capacity and the flexural stiffness values obtained from the experimental tests and FE analyses validated well with the values computed from equations of the existing standards.

New empirical methods for predicting flexural capacity and stiffness of CFST beam

This paper presents new empirical methods to theoretically predict bending moment capacity (Mu) and flexural stiffness values at the initial and serviceability levels (Ki and Ks) of concrete-filled steel tube (CFST) composite beams. A wide range of results for Mu, Ki, and Ks covering various parameters of CFST beams are required to develop these empirical methods. Therefore, 144 numerical CFST models were developed in this study using finite element software. The adequacy of the newly developed empirical methods was validated with the results obtained from previously reported experimental and numerical studies conducted by other researchers. For example, using the new methods, mean values of 0.967 and 0.996 were achieved from the ratios of predicting Mu values to the previously reported values of the rectangular and circular CFST beams, respectively. The mean values were 1.074 and 1.050 from the predicted Ki, and Ks values, respectively. Furthermore, the results of these new methods were compared with the results obtained by the most commonly used standards and methods in this field, namely, EC4, AISC, AIJ, BS5400, and others.

Concrete constitutive models for low velocity impact simulations

Concrete structures are commonly exposed to low velocity impact loads originating from windborne/waterborne debris, vehicle/vessel collision, and rock fall. For the performance assessment of concrete structures under such loads, several constitutive models have been developed to date. To compare the accuracy of the available models for practical applications, the current study evaluates four constitutive models, i.e., continuous surface cap model (CSCM), elasto-plastic damage cap (EPDC) model, Karagozian and Case concrete (KCC) model, and Winfrith concrete model. For this purpose, the constitutive models are first examined at the material level through single element simulations under basic stress paths, such as uniaxial compression and tension, as well as triaxial compression. A range of measures, such as post-peak softening, shear dilation, and confinement effect, are extracted and compared. The investigation is then extended to understand how the concrete constitutive models perform at the structure level. This is achieved by replicating drop hammer tests on reinforced concrete (RC) and concrete filled steel tube (CFST) beams. Investigation of these two structural categories provides a unique opportunity to further evaluate the accuracy of the concrete constitutive models in interaction with the most common reinforcement details. To achieve this goal, the impact responses of RC and CFST beams are compared with full-scale experimental test data. Upon understanding the capabilities of each constitutive model in predicting the structural behavior and damage, the most important modeling parameters are examined. The outcome of this study facilitates the selection and use of concrete constitutive models for the design and assessment of concrete structures subjected to various low velocity impact loads.