Finite Element Analysis of a Reinforced Concrete Dapped-End Beam under the Effects of Impact Velocity and Dapped-End Beam Cross-Section Geometry

Abstract

This study focuses on the behavior of a three-dimensional reinforced concrete dapped-end beam subjected to the effects of impact velocity and dapped-end beam cross-section geometry by numerical simulation using ABAQUS (V6.14) software under a constant impact load. The finite element software ABAQUS is utilized to simulate and analyze the drop impact to obtain accurate and detailed results. A sudden drop impact is a short-duration dynamic load that could involve very large deformations and damage to the reinforced concrete dapped-end beam. The finite element analysis has been completed by creating the geometry, material properties, boundary conditions, and loading conditions. In this study, a total of seven analyzes were conducted with different parameters, i.e., the effect of the velocity of the impact load and the geometry of the dapped-end beam cross-section. From the finite element analysis results, it can be concluded that as the impact velocity increases, the impact force and mid-span displacement of the reinforced concrete dapped-end beam also increases. The higher the impact velocity, the greater the amount of damage caused throughout the RC beam. When the recess length increases from 200 mm to 500 mm, the deflection increases by 13%. The depth of the nib has a great influence on the impact response and deflection of the reinforced concrete dapped end beam. The ABAQUS output shows that increasing the dapped end beam nib depth from 260 mm to 450 mm reduces the impact load by 50%, from 22733.6 N to 13640.16 N. On the other hand, the nib depth increased from 260 mm to 450 mm, and the maximum deflection was reduced from 1.10245 mm to 0.6892 mm, i.e., a 46.1% reduction.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Dapped-end beams are widely used in buildings and other constructions because they give improved lateral stability. Despite its complexity, the design of dapped-end connections is a crucial concern in a precast concrete structure. Analysis and design against abnormal loading conditions, such as impacts and blats, are of paramount importance in conventional structures in general and sensitive structures in particular. Loading conditions may be encountered in a wide variety of situations, for example, earthquakes, blasts and resulting fragments, wind- and tornado-generated missiles, accidental collisions involving vehicles, aircraft, trains, dropped objects, etc. There are two main approaches to designing the dapped ends (and corbels), which are the shear friction (PCI) method and the strut and tie (STM) modeling. Both approaches require the investigation of the potential failure modes. In addition, the designers frequently ignore some significant aspects, such as proper details and the need for checking the stresses in the concrete.

References [1, 2] Deep beams, pile tops, dapped terminating beams, and corbels are examples of nonlinear and nonprismatic members that are not covered by the conventional beam theory based on Bernoulli’s theorem. Because shear failure is more common than flexural failure, these structures cannot be analyzed or built using flexural analysis of beam theory. The strut and tie model (STM) is an analytical and design solution for nonlinear and disturbed zones in RC structures. Using the assumed strut and tie model, monotonic loads were applied to four pile tops, six corbels, three deep beams, and three dapped ending beams in this investigation. The failure loads were compared to the expected design loads. For the design of disturbed zones in RC structures, STM is a viable approach. In most cases, the actual failure loads were near the theoretical design loads. However, to generalize the STM as an alternative design strategy, more experimental work on nonlinear and disturbed regions is required [3, 4]. A drop-weight impact test was performed on eighteen RC beam specimens having a statically flexural failure mode. They had impact speeds ranging from 6 to 13 m/s and a drop weight of 33.6 kg. Throughout the test, the load, deflection, and strain were all monitored. Compressive strength (C27 and C40), bar diameter (dia6, dia8, and dia10), and drop height were all taken into account (at 5 m, 6 m, 7 m, and 8 m). The results showed that, as the reinforcement ratio and concrete strength increased, so did the stiffness and load-carrying capacity of beams. Nevertheless, as the reinforcement ratio and concrete strength increased, so did the static maximum deflection of the beams. The damage became more severe as the drop height increased, and crack-opening displacement increased; the drop height tended to affect the degree of local failure because the length of the local compressive concrete increased as the drop height increased; when the drop height exceeded 6 m, the beam developed plastic rotations around the mid-span.

According to [5, 6], shear damage to dapped-end beams (DEBs) is common when vertical loads are applied. These purlins can break suddenly under the accumulated snow loads, especially if the appropriate measures for thinned ends of reinforced concrete prefabricated purlins on roofs with conventional cross-sections are not considered during the design. The roof entirely collapses as a result of this predicament [7]. To address this flaw, it is planned to use of steel fiber reinforced concrete (SFRC) in order to improve the purlin’s shear capacity without affecting the cross-section shape or reinforcement. Experimental and numerical research has been carried out to achieve this goal. The important factors are the presence of steel fiber and the aspect ratio. The application of SFRC boosted energy dissipation by 2.58 times and shear capacity by 1.53 times, respectively. Furthermore, numerical simulations were conducted to establish the optimal length of SFRC to be utilized in concrete from beam ends and the fiber volume ratio to be employed, as well as to study the impacts of shear span to depth ratio (a/d). The results showed that a fiber volume ratio of 2% and SFRC length up to the point where dapped-end region ends are recommended. Furthermore, raising the a/d ratio reduces the weight-carrying capacity of the vehicle [8–10] stated that because of stress concentrations at the re-entrant corner, dapped-end connections are prone to inclined corner cracks during service loads. Furthermore, large shear forces are transferred across a much-reduced section of these connections. Because of these factors, failures along with a re-entrant corner crack and shear failures in the dapped-end region have been recognized as the two main failure types of dapped-end connections. The amount of dapped-end reinforcement and the ratio of dapped-end horizontal to vertical reinforcement area are the key test factors. The test specimens’ behavior is examined in detail in this paper, with detailed deformation measurements and an in-depth discussion. The influence of the test factors on dapped-end connection strength, fracture control, and rotation capacity is examined. It was discovered that connections with greater horizontal reinforcement are stronger for the same total area of horizontal and vertical reinforcement. While the orthogonal dapped-end reinforcement scheme did not provide adequate crack control under service loads, all connections, particularly the shear essential connections, showed significant rotation capability. A kinematics-based model and nonlinear finite element analysis are used to investigate the flow of internal forces within the test specimens [11]. Impact experiments were run on seven beams having a statically flexural failure mode at impact velocities ranging from 2.8 to 6.26 m/s. The flexural load capacity of RC beams is found to remain constant beyond a certain impact; increasing the stress rate does not increase their load-carrying capacity.

Reference [12] developed design guidelines for dapped ends to identify the most effective reinforcement schemes. They developed from experimental research findings presented in dapped ends of prestressed concrete thin stemmed members. Design and detailing recommendations are provided for the bend radius of the hanger reinforcement at the bottom corner of the full section to preclude compression failure of the strut extending into this corner design recommendation for the minimum length of the horizontal extension of hanger reinforcement into the full section has been developed based on bar development length and strand transfer length. Detailing recommendations intended to preclude premature splitting are also provided. Shallow nibs are vulnerable to diagonal tension failures across cracks extending from the re-entrant corner and over the top of the hanger reinforcement, especially where C-shaped hanger reinforcing bars are used. Equations to determine the design shear strength of the nib are provided.

Reference [13] modeled dapped-end beams using ABAQUS software that failed in flexure have been analyzed using the ABAQUS software. The nonlinearity is represented by the ABAQUS model, such as the concrete’s postcracking tensile stiffness and stress transfer across cracked blocks. The numerical model accurately describes the failure mode of dapped end beams, and the maximum load expected is very close to the failure load of test findings. Some parametric studies on the behavior of the beams include shear span to depth ratio (a/d), concrete compressive strength, and the main dapped-end reinforcement. The amount of main steel used has the greatest impact on the flexural strength of RC dapped-end beams. For several types of flexural failures in beams, maximum load and displacement have been represented. In general, this research shows that the flexural strength of dapped-end beams is impacted by the preceding parameters [11]. Twelve specimens of RC beams were subjected to a drop-weight impact test with impact velocities ranging from 0.15 m/s to 2.4 m/s. The impact responses of the RC beams were studied about drop height and longitudinal reinforcement. The maximum impact load, impulse, and maximum mid-span deflection all increased as the drop height increased, according to the findings.

The importance of this research is to see the performance of different parameters under impact loading, and the results of the study will be of great importance for the ever-growing building construction, bridge construction, and civil engineers. The main parameters used in this study were dapped-end beam cross-section geometry which was mainly measured by nib depth, recess length, and main depth. As each parameter’s dimensions vary, the resistance against distortion differs. At the same time when the impact velocity varies between 2500 mm/s and 10000 mm/s, we observe variation in distortion. So these parameters were very important to consider for our study. This study is concerned with the behavior of reinforced concrete dapped-end beams subject to accidental impact loading using finite element analysis software. The analysis of reinforced concrete dapped-end beam using ABAQUS [14], software is carried out for 3D frames subjected to different geometry of dapped beam and velocity. In this study the analysis was performed by using the same type of concrete compressive strength and the effect of damping is omitted since it has a small influence on the response of a collision impact, due to the relatively short duration of the load. Disturbed regions such as deep beams, dapped-end beams, pile caps, corbels, etc. normally fail in shear rather than flexure. In Reinforced, dapped-end beam stress concentration at a re-entrant corner is very high which leads to the cracking of beeped end beam finally failing due to corrosion of reinforcement and this study fills the gap which is not studied by the scholars related to the title and this was the main motive to conduct this research. The major goal of this study is to use a three-dimensional finite element analysis approach to investigate the behavior of a disturbed zone for a reinforced concrete dapped-end beam under the effects of impact velocity and dapped-end beam cross-section geometry.

2. Materials and Methods

2.1. General about ABAQUS Software

The finite element technique is becoming highly popular for modeling structures under different loading conditions such as static, dynamic, and cyclic. There is commercially available software such as ANSYS, DIANA, ADINA, and ABAQUS. However, the input parameters, particularly the choice of an appropriate concrete model, boundary conditions, and local and global imperfections, have a significant impact on the prediction accuracy of a finite element model. In this study, the general-purpose finite element program ABAQUS version 6.14-2 was used to create a finite element model of a dapped-end beam under the effects of impact velocity and dapped-end beam cross-section geometry ([15], (Abaqus, n.d.)). To check the accuracy and exactness of the finite element method, it is better to validate the analysis responses with the results of an experimental test. So, validation of finite element analysis has been done to check the precision of the finite element analysis results with experimental test results based on geometry, material properties, boundary conditions, and loading conditions. In the present study, the experimental work studied by [16] is used to validate finite element analysis. The model can be validated by matching load vs. displacements and failure patterns.

2.2. Properties of Dapped-End Beam

The model and simulation will be validated by previous experiments on dapped beams under vertical load conducted by [16] to investigate the response of reinforced concrete dapped-end beams subjected to drop hammer impact. The specimens have cross-sectional dimensions of 3,600 mm in length, 200 mm in width, 600 mm in depth, and 500 mm in recess length, as shown in Figure 1 below. A concrete cover of 40 mm was provided around the reinforcement cage, except at the ends, which had 25 mm of cover on both sides.

[figure(s) omitted; refer to PDF]

The flexure behavior of reinforced concrete dapped-end beams (D-E) by using the ABAQUS software on some parametric studies such as shear span to depth ratio (a/d), concrete compressive strength, and the main D-E reinforcement on the behavior of the beams under vertical load (at the static condition) was studied by [13] and concluded that the main steel amount has the most significant effect on the performance of flexural strength of RC D-E beams. The maximum load and displacement for various types of flexural failures in beams have been represented. But in our study, we focused on impact load and validated the result [16].

The ABAQUS software was selected due to its powerful set of engineering simulation programs based on the finite element method, which can solve problems ranging from relatively simple linear analyzes to the most challenging nonlinear simulations. The finite element analysis has been completed by creating the geometry, material properties, boundary conditions, and loading conditions. The finite element model of the beam impact test setup is presented, as shown in Figure 2 below. The flexural and shear steel reinforcements are modeled with 3D2-noded linear truss elements (T3D2), and the concrete have been discretized with eight-node hexahedron elements (C3D8R). A perfect bond is considered between the concrete and the reinforced bar.

[figure(s) omitted; refer to PDF]

2.3. Modeling of Materials

The concrete-damaged plasticity model was chosen for this investigation because it can simulate the entire inelastic concrete behavior in both tension and compression [17]. Damaged plasticity is thought to characterize concrete’s uniaxial tensile and compressive responses. The eight-node continuum elements (C3D8R), plasticity-based, damaged model for concrete are used to model the concrete beam in ABAQUS. The model concrete had a mass density of 2,400 ∗ 10⁻⁹ kg/mm³, a modulus of elasticity of 20 GPa, a Poisson’s ratio of 0.3, and a concrete compressive strength of 42 MPa at the time of testing, and a maximum aggregate size of 10 mm.

The steel reinforcement is modeled by two-node truss elements. Steel reinforcement bars have approximately linear elastic behavior when the steel stiffness introduced by the elastic modulus keeps constant at low strain magnitude and at high strain magnitude it converts to plasticity. The reinforced concrete has a length of 3600 mm and is supported at 150 mm from both ends throughout 3300 mm with specially designed devices that allow it to freely rotate while preventing it from moving out of displacement. Single point constraints are applied to constrain nodal displacement in X, Y, and Z directions on the nodes located at the bottom. A predefined velocity is applied for the impactor to induce the motion of the drop hammer corresponding to the drop height in a direction perpendicular to the top face of the reinforced concrete beam. The following equation is used to determine the impact velocity of the drop hammer from free fall given by equation.$$\begin{array}{}\text{(1)}& V=\sqrt{2g}h\text{,}\end{array}$$where $g$ is the acceleration due to gravity (9.8 m/s²), “$h$” is the drop height (m), and $V$ is the impact velocity (m/s) [11].

In the experimental study conducted by [16], the load vs displacement and failure mode in Figure 3 are compared, and the result shows that the finite element analysis and experimental results converge on each other, having an average difference of 9.55% for load vs displacement. Also, the failure mode has good agreement with the experimental and finite element software. Therefore, ABAQUA V6.14 is used to model and analyze the dapped-end beam to see its performance under different parameters.

[figure(s) omitted; refer to PDF]

The RC dapped-end beam selected for this study was taken from a previously studied specimen. To see the behavior of the dapped-end beam under static and dynamic loading, a specimen previously tested under static loads was used for modeling and the properties related to this beam were taken from [13, 16]. As shown in Figure 4(a), concrete ultimately crushes in a diagonal direction for dapped-ends of diagonal compression failure. The ultimate displacement and rotation are relatively high for dapped-end flexure failure, as seen in Figure 4(b) in red color. The concrete crushes and spalls in the area between the nib and the full-depth beam for tensile failure caused by the hanger bar yielding in dapped beams. The shear action in dapped-ends led to compression in a diagonal direction and tension in a perpendicular direction. Tables 1 and 2 present the analysis of the geometry and material properties of the RC dapped end beam as well as the reinforcement area and concrete cover used, based on Abdul-Jawad [13] and Wen-Yao Lu [16].

[figure(s) omitted; refer to PDF]

Table 1

Analysis of geometry and material properties of RC dapped-end beams.

Dapped-end beam designation	Dimension (mm)			Impact mass (kg)	Impact velocity (mm/sec)	Position of impact load
	Nib depth (mm)	Recess length (mm)	Main depth (mm)
Control beam	260	500	600	800	2,500	1/2L
DEB01V1					5,000
DEB01V2					10,000
DEB02 ND1	350	500	600	400	2,500	1/2L
DEB02 ND2	450
DEB03RL1	260	200	600	400	5,000	1/2L
DEB03RL2		350

Table 2

Reinforcement area and concrete cover used.

	Dapped main rebar	Hanger reinforcement	Vertical stirrup	Horizontal stirrup	Main bar	Shear reinforcement	Concrete cover (mm)
Diameter (mm)	2 Ø16	3 Ø14	4 Ø12	2 Ø12	4 Ø16	#3@150 c/c at end 250 c/c at middle	40
Area (mm2)	402.12	461.81	452.39	226.19	804.24	567.1

Table 3

Input material data for concrete.

Dilation angle (Ψ)	36°
Eccentricity (ϵ)	0.1
Biaxial/uniaxial (ƒbo⁄ƒco)	1.16
Κc ratio of the second stress invariant in tension to that in compression	0.667
Viscosity parameter	0.0001
Density	2400 kg/m3
Young’s modulus	20 GPa
Poisson’s ratio	0.2

The reinforced concrete dapped-end beam is modeled with solid elements. To simulate an impact loading condition, a free-falling hammer is used as an impact load on the exposed reinforced concrete dapped-end beam. In developing the structural elements, the impactor should be developed as a rigid element. The impactor is represented as a 4-node, 3-D bilinear rigid quadrilateral (R3D4) with steel material properties, including a 200 GPa elastic modulus and a 0.3 poison ratio. Figure 5 shows the steel reinforcement and concrete solid models.

[figure(s) omitted; refer to PDF]

The concrete damage plasticity model (CDPM) is used to define concrete’s nonlinear behavior. The CDPM in ABAQUS/Standard and ABAQUS/Explicit is developed for applications in which the concrete is subjected to arbitrary loading conditions, including cyclic loading, and is based on the assumption of scalar (isotropic) damage. In both tension and compression, the model considers the degradation of elastic stiffness caused by plastic straining. It also takes into account the impact of stiffness recovery after impact loading. In this research, the concrete-damaged plasticity approach is used. First, we define the CDPM parameters, such as the ratio of the second stress invariant in tension to that in compression (kc), (ψ) the dilation angle, (fb0/fcʹ) the ratio of the compressive strength under biaxial loading to uniaxial compressive strength, (e) flow potential eccentricity, and the viscosity parameter (μ).

2.4. Parameter Sensitivity Analysis of Concrete Damage Plasticity Model

There are five CDP parameters used to model concrete in ABAQUS: (Kc), (ψ), fb0/fcʹ, (e), and (μ). Among these parameters, dilation angle (ψ) and viscosity (μ) play very important roles in the simulation of reinforced concrete structures [18]. According to [18], increasing the viscosity value from 0.00005 to 0.001 gives a more converged result. Therefore, for this study, viscosity parameters of 0.00005, 0.0001, 0.0005, and 0.001 were used to check the accuracy of the results of the experiment. The dilation angle is the angle of internal friction of the material, and for normal-strength concrete, values ranging between 30° and 40° are recommended [19]. In this study, parametric was taken for dilation angles of 30, 36, and 40 degrees of internal friction and was used to check the finite element model with experimental data. From the finite element model, a dilation angle of 36 and viscosity of 0.0001 converge to experimental results, therefore they were taken for all analyzes as shown in Table 3. Stiffness recovery factors were assumed for compressive and tensile recovery of concrete. In this study, the compressive recover factor is one (wc = 1) by assuming compressive stiffness is fully recovered upon crack closure when the loading goes from tension to compression. And tensile stiffness recovery (wt) is zero by assuming tensile stiffness is not fully recovered as the load changes from compression to tension once the crushing of concrete is initiated.

2.5. Mesh Sensitivity Analysis

A mesh sensitivity analysis is carried out to arrive at an accurate size of mesh that yields mesh-independent results. For mesh analysis, an RC dapped-end beam with a full depth of 600 mm and a full length of 3600 mm with a nib depth of 260 mm, a length of 500 mm, and an impact mass of 400 kg is selected for mesh analysis. A mesh size of 20 mm, 25 mm, and 30 mm were chosen for the solid and truss elements. The sizes mentioned are not exact but are used to refer to the four different meshes. The details of these four meshes are shown in Table 4.

Table 4

Mesh data for different meshes considered for mesh sensitivity analysis.

RC dapped-end beam	Mesh size
	20 mm	25 mm	30 mm	30 mm
Solid concrete element	104546	47760	23168	14322
Rebar truss element	7245	5871	4734	4163

The mesh sensitivity in this study is checked using the impact force and time of a reinforced concrete dapped-end beam, as shown in Figure 6 below. From analysis, 35 mm and 30 mm mesh show a maximum impact force of 3758 KN and 6264 KN, respectively. The maximum impact forces for 25 mm mesh and 20 mm mesh are 10440.09 KN and 11600.01 KN, respectively. The difference in peak impact force for 35 mm and 30 mm was 40%, and for 25 mm mesh and 20 mm mesh, the peak impact difference was 10.5%. The overall shape of the impact force history for 25 mm mesh is much closer to that of 20 mm mesh. Therefore, a mesh size of 25 mm is used in this study for all the analyzes.

[figure(s) omitted; refer to PDF]

3. Results and Discussion

3.1. Effect of Impact Velocity

The impact analysis of a reinforced dapped-end beam for 2.5 m/s, 5 m/s, and 10 m/s velocities and a mass of 400 kg was examined to investigate the velocities’ effects. In Figure 7 below, the effects of velocity (2.5, 5, and 10 m/s) and mass (400 kg) were represented.

[figure(s) omitted; refer to PDF]

According to the results of the finite element comparison, the impact response is influenced by the hammer speed, which has a considerable impact on the deflection reaction and the impact force response. Tables 5 and 6 indicate that as the impact velocity increases, so does the impact force. For example, increasing the velocity from 2.5 to 10 m/s increases the impact force by 68.33 percent. On the one hand, there are considerable variances in the deflection response, with the deflection clearly increasing as the speed increases. When the hammer speed is increased from 2.5 m/s to 10 m/s, the peak value increases by more than 54.41 percent.

Table 5

Impact force analysis result at different velocity.

Peak impact force (KN)	Time (sec)	Average difference in peak impact force (%)	velocity@400 kg
3673.48	0.0125412	35.68	2.5 m/s
5711.55	0.0125		5 m/s
11597.73	0.00750982	68.33	10 m/s

Table 6

Load vs deflection analysis result at different velocity.

Max mid span deflection (mm)	Average difference (%)	Max load (KN)	Average difference (%)	velocity@400 kg
3.72	53.02	178.844	44.1	2.5 m/s
7.918		319.855		5 m/s
20.117	81.51	392.217	54.41	10 m/s

From Figure 8 of the finite element result, the RC dapped-end beam emerges with a tensile fracture due to the bending moment. Serious shear cracking occurs in the whole span, and the shear fracture extends from the top of the impact part to the bottom of the support section. As the velocity of drop impacts increases, the damage of the RC dapped-end beams increases. The comparison results show that the speed of the hammer is an important factor in the impact response, deflection response, and damage response.

[figure(s) omitted; refer to PDF]

3.2. Effect of Recess Length

To investigate the variation of the recess length of the reinforced concrete dapped-end beam, finite element analysis was carried out with recess lengths of 200 mm, 350 mm, and 500 mm.

From finite element analysis, the effect of recess length was highly influential on the deflection response and reaction force near the support. When the recess length increases from 200 mm to 500 mm, the deflection is increased by 13%. In the case of the reaction force at support, for recess lengths of 200 mm, 350 mm, and 500 mm, the reaction force was 212.774 KN, 183.494 KN, and 155.969 KN, respectively, as shown in Figures 9(a) and 9(b) above. This indicates that when the recess length increases, the reaction force at support greatly increases.

[figure(s) omitted; refer to PDF]

3.2.1. Damage due to Effect of Recess Length

From the damage output in Figure 10, it is recognized that the effect of recess length was highly affected by the crack initiation near the re-entrant corner. When the recess length increased from 200 mm to 500 mm, the crack increased near the re-entrant corner.

[figure(s) omitted; refer to PDF]

3.2.2. Effect of Nib Depth

In this study, nib depths of 260 mm, 350 mm, and 450 mm were used to examine the effect of nib depth on reinforced concrete dapped-end beams.

The effect of nib depth has a great influence on the impact response and deflection of reinforced concrete dapped-end beams. The ABAQUS output in Figure 11 shows that increasing the dapped-end nib depth from 260 mm to 450 mm reduces the impact load by 50%, from 22733.6 N to 13640.16 N. On the other hand, the nib depth increased from 260 mm to 450 mm, and the maximum deflection was reduced from 1.10245 mm to 0.6892 mm, i.e., a 46.1% reduction.

[figure(s) omitted; refer to PDF]

3.2.3. Damage due to Effect of Nib Depth

The finite element result indicates above in Figure 12, dapped-end Nib depth increases from 260 mm to 450 mm, and damage was reduced. In impact analysis, design and analysis are most of the time based on equivalent static loads where the dynamic load is directly converted to an equivalent static load by using the dynamic load factor. The dynamic load factor is the ratio of dynamic deflection to static deflection which mainly depends upon the span, stiffness, and impactors’ dynamic behavior. This study is conducted for 3300 mm span length reinforced concrete dapped-end beams it is known that loaded span length inversely affects the beam impact, this simply means that a short span member will experience greater dynamic impact than a long span member. In the AASHTO design manual, the provided impact factor is 33%, but here in this study, the calculated impact factor for 400 kg mass and 2.5 m/s velocity is 78.43% the result indicated the advantage of conducting the dynamic impact analysis.

[figure(s) omitted; refer to PDF]

4. Conclusions

This study investigated the performance of a reinforced concrete dapped-end beam subjected to the effects of impact velocity and dapped-end beam cross-section geometry with commercially available software ABAQUS. From the finite element analysis using ABAQUS, which was performed to investigate the effect of impact position, the following conclusions were drawn from the finite element analysis: As impact velocity increases, the peak impact forces and mid-span displacement increase, and the higher the impact velocity, the larger the amount of damage and deformation throughout the beam specimen, which is in great concurrence with the experimental results. The effect of recess length was highly influenced by the deflection response and reaction force near the support. When the recess length increases from 200 mm to 500 mm, the deflection is increased by 13%. In the case of the reaction force at the support, for recess lengths of 200 mm, 350 mm, and 500 mm, the reaction force was 212.774 KN, 183.494 KN, and 155.969 KN, respectively. This indicates that when the recess length increases, the reaction force at support greatly increases. The effect of nib depth has a great influence on the impact response and deflection of reinforced concrete dapped-end beams. The ABAQUS output shows that increasing the dapped-end nib depth from 260 mm to 450 mm reduces the impact load by 50%, from 22733.6 N to 13640.16 N. On the other hand, as the nib depth increased from 260 mm to 450 mm, the maximum deflection reduced from 1.10245 mm to 0.6892 mm, i.e. 46.1% reduction, which is very close to the experimental results. The finite element analysis results obtained from ABAQUS, 6.14 of this study show that the nib depth increases the impact load, damage, and deflection decrease. Decrease of recess length from 500 to 200 mm crack near the re-entrant corner is reduced. The depth of nib should be provided adequately enough to reduce deflection and damage and the recess length should be minimized to withstand crack propagation near the support. To reduce the damage near the re-entrant corner, different strengthening mechanisms should be used to it from damage.

Authors’ Contributions

All authors contributed to the study’s conception and design. Hibretu Kaske Kassa, Tekalign Behailu, and Getinet Melesse performed material preparation, performed data collection, and performed analysis of the study. The first draft of the manuscript was written by Hibretu Kaske Kassa and all authors commented on previous versions of the manuscript. All authors have read and approved the final manuscript. Tekalign Behailu was actively involved in reviewing and correcting the given comment by reviewers.

References

[1] A. E. Shah, E. Haq, S. Khan, "Analysis and design of disturbed regions in concrete structures," Procedia Engineering, vol. 14, pp. 3317-3324, DOI: 10.1016/j.proeng.2011.07.419, 2011.

[2] M. A. Yimer, T. W. Aure, "Numerical investigation of reinforced concrete and steel fiber-reinforced concrete exterior beam-column joints under cyclic loading," Iranian Journal of Science and Technology, Transactions of Civil Engineering, vol. 46 no. 3, pp. 2249-2273, DOI: 10.1007/s40996-021-00745-1, 2022.

[3] T. Z. Zhan, Z. Wang, J. Ning, "Failure behaviors of reinforced concrete beams subjected to high impact loading," Engineering Failure Analysis, vol. 56, pp. 233-243, DOI: 10.1016/j.engfailanal.2015.02.006, 2015.

[4] T. W. Woldeyes Tilaye Dife, Finite Element Analysis of Reinforced Concrete Frame Under Impact Loading, 2019.

[5] Y. Onuralp, C. a. Aksoylu, "Experimental and numerical investigations of steel fiber reinforced concrete dapped-end purlins," Journal of Building Engineering, vol. 36, pp. 102-119, 2021.

[6] C. a. Aksoylu, "Damages on prefabricated concrete dapped-end purlins due to snow loads and a novel reinforcement detail," Engineering Structures, vol. 225, 2020.

[7] H. K. Kassa, G. Melesse, G. Yabasa, "A study on using glass fiber-reinforced polymer composites for shear and flexural enhancement of reinforced concrete beams," Advances in Civil Engineering, vol. 2022,DOI: 10.1155/2022/5995103, 2022.

[8] C. a. Rajapakse, H. Degee, B. Mihaylov, "Investigation of shear and flexural failures of dapped-end connections with orthogonal reinforcement," Engineering Structures, vol. 260,DOI: 10.1016/j.engstruct.2022.114233, 2022.

[9] B. A. H. Mihaylov, C. Rajapakse, P. H. Berger, "Effect of steel fibers on the ultimate flexural behavior of dapped-end connections," Engineering Structures, vol. 259,DOI: 10.1016/j.engstruct.2022.114147, 2022.

[10] G. A. Melesse, S. Jima, T. Asale, Y. Moges, H. Kaske Kassa, "Study on mechanical behavior of fully encased composite slender columns with high-strength concrete using FEM simulation," Advances in Civil Engineering, vol. 2023,DOI: 10.1155/2023/3581727, 2023.

[11] K. A. Fujikake, B. Li, S. Soeun, "Impact response of reinforced concrete beam and its analytical evaluation," Journal of Structural Engineering, vol. 135 no. 8, pp. 938-950, DOI: 10.1061/(asce)st.1943-541x.0000039, 2009.

[12] G. Klein, A. Botros, B. Andrews, K. Holloway, "Dapped ends of prestressed concrete thin-stemmed members: Part 2, design," PCI Journal, vol. 62 no. 2,DOI: 10.15554/pcij62.2-02, 2017.

[13] H. M. Abdul-Jawad, "Modelling of dapped-end beams using ABAQUS software," International Journal of Civil Engineering & Technology, vol. 9 no. 1, 2018.

[14] Abaqus, "A material model for flexural crack simulation," 2010. http://bee-pg-031941:2080/v6.8/books/usb/default.html

[15] Abaqus, "Abaqus analysis user manual," 2008.

[16] T. C. C. J. Wen-Yao Lu, "Shear strength of reinforced concrete dapped-end beams with shear span-to-depth ratios larger than unity," Journal of Marine Science and Technology, vol. 23 no. 4, pp. 431-442, 2015.

[17] J. J. Lubliner, J. Oliver, S. Oller, E. Onate, "A plastic-damage model for concrete," International Journal of Solids and Structures, vol. 25 no. 3, pp. 299-326, DOI: 10.1016/0020-7683(89)90050-4, 1989.

[18] A. H. Demir, "Effect of viscosity parameter on the numerical simulation of reinforced concrete deep beam behavior," The Online Journal of Science and Technology, vol. 8 no. 3, pp. 50-56, 2018.

[19] P. a. Kmiecik, M. Kaminski, "Modelling of reinforced concrete structures and composite structures with concrete strength degradation taken into consideration," Archives of Civil and Mechanical Engineering, vol. 11 no. 3, pp. 623-636, DOI: 10.1016/s1644-9665(12)60105-8, 2011.