Startseite Effect of loading type in concrete deep beam with strut reinforcement
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Effect of loading type in concrete deep beam with strut reinforcement

  • Hussein Kamal Kadhim EMAIL logo und Mazin Diwan Abdullah
Veröffentlicht/Copyright: 8. März 2024
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Abstract

This study examined eight specimens of two groups of deep beam (DB) with the same dimensions and reinforcement quantity, where the first group had four specimens tested under two-point loads and the second group had four specimens tested under one-point load (Ammash HK, AL-Mousawi MM. Experimental investigation of deep beam reinforced with different types of reinforcement. Eng Technol Appl Sci Res. 2021;11(2):7585–90.) where both groups have the same reinforcement and the dimensions and difference between the groups was only the type of load. Digital image correlation technology software was used to verify the results. Upon examining the results, each group had one reference specimen with conventional reinforcement and the other three specimens were with strut reinforcement. It was observed that the strut reinforcement technique was more effective than the conventional reinforcement. This study also found that the load capacity was decreased at two-point loads from one-point load. The results from the present study were compared to those from a prior study (Ammash HK, AL-Mousawi MM. Experimental investigation of deep beam reinforced with different types of reinforcement. Eng Technol Appl Sci Res. 2021;11(2):7585–90.) that only employed a one-point load. The concrete type, its dimensions, and its method of reinforcing were the same as Ammash and AL-Mousawi’s (Experimental investigation of deep beam reinforced with different types of reinforcement. Eng Technol Appl Sci Res. 2021;11(2):7585–90.) study. The maximum load capacity for SC (Reference DB specimen) and S10 (the deep strut beam employed a specimen with 100% reinforcement from the reinforced web) specimens for one-point load were more tolerant to stress than the two-point loads, with 15% for SC and 27% for S10 as both specimens had comparable amounts of reinforcement. When a force is applied that is less than the sum of the two load points, cracks occur in the shear and flexural zones at one load point. We have found that the use of two-point loads leads to a decrease in the maximum load capacity of specimens when compared with a one-point load. It was also noted that cracks are formed in the shear and flexural zones at one-point load when a load less than the two-point load is applied. It was also observed that when two-point loads were applied to a specimen, the displacement was less than half of what it was when tested under a one-point load, and the strain in specimens examined under two-point load was lower than in specimens examined under one point load.

1 Introduction

Deep beams (DBs) are structural members characterized by their relatively large depth compared to their span. They are commonly used in various civil engineering applications, such as bridges, transfer girders, and foundation beams. Due to their unique geometry, DBs experience complex load distributions and stress patterns, requiring specialized design. One of the primary challenges in designing DBs is their ability to resist shear forces. Unlike regular beams, DBs are more prone to shear failures due to the increased amount of shear stress developed in their span. Researchers have extensively studied the behavior of DBs to develop effective design approaches and guidelines. Several failure modes can occur in DBs, including crushing of strut failure, diagonal-splitting failure, and shear-compression failure. Crushing of strut failure occurs when the concrete struts in the DB experience excessive compressive stresses, leading to concrete crushing. Diagonal-splitting failure occurs when inclined cracks propagate diagonally across the beam, usually from the loaded area toward the supports due to shear stresses exceeding the concrete’s shear strength (SS). Shear-compression failure involves the crushing or failure of concrete in the compression zone of the DB, resulting from high applied shear forces and resultant compressive stresses. Designing DBs involves considering factors such as concrete strength, reinforcement detailing, shear reinforcement, and load distribution. Various design codes and guidelines, such as the American Concrete Institute (ACI) and Eurocode, provide specifications and procedures for the design of DBs. These codes incorporate research findings and experimental data to ensure the reliability and efficient design of DBs in civil engineering structures. DBs play a crucial role in structural engineering, particularly in supporting heavy loads and spanning long distances. Understanding the behavior of DBs and incorporating appropriate design considerations are essential to ensure their structural integrity and safety. Ongoing research and advancements in design methodologies continue to contribute to the development of efficient and reliable DB designs. Cheng and Tan [1] used three experiments totaling 36 beams to demonstrate the superiority of strut-and-tie models (STMs). This diagonally fractured DB was utilized to construct this connected arch. Without web reinforcing, it has been shown that the SS of a beam declines with the member size. This is related to the phenomenon known as the size effect. In this investigation, the STM and the finite element model are used to examine the relationship between size and the SS of the DB. Research studies indicate that the principal cause of the size effect in concrete beams is the incorrect use of the shear transfer concept originally established for steel beams. The secondary features that may impact overall frame proportions include strut geometry and web reinforcement spacing. Oh and Sin [2] tested 15 concrete DBs with reinforcement subjected to a two-point load with compressive strengths ranging from 23 to 74 MPa to determine their ultimate shear and symmetric diagonal cracking strengths. Both the (a/d) and the (l/d) were shifted from 0.5 to 2.0 and 3.0 to 5.0, respectively. All the beams were reinforced with a single layer, with specific values for the transverse reinforcement (rt), vertical reinforcement (rv), and horizontal reinforcement (rh), which were 0.0129, 0.0034, and 0.0094, respectively. The ultimate shear failure mode of DB was defined by the a/d ratio regardless of the concrete strength. When the a/d was dropped, the DB produced with high-strength concrete (HSC) abruptly and unexpectedly collapsed, in contrast to the DB made from regular concrete, which gradually deteriorated. The findings show that the aspect ratio a/d is the most important element in determining the ultimate SS of DBs. When applied to DB with HSC, ACI Code Eqs. (11–29) and (11–30) considerably underestimates the significance of both concrete compressive strength (fc) and longitudinal steel reinforcement (rt). Adding horizontal shear reinforcement to DBs constructed of HSC does not improve the ultimate SS as a function of a/d. Lu et al. [3] reported the results of testing 16 distinct reinforced concrete DBs. The bearing plates took the brunt of the force in eight of the tests, while the columns did the heavy lifting. The presence of horizontal and vertical stirrups as well as the processes involved in force transmission were the primary foci of the investigation. An increase in compressive strength was shown to significantly enhance the SS, provided the shear span to depth ratios (a/d) of the DBs were maintained. However, the ratio of horizontal to vertical stirrups determined the extent to which SS was increased. The DBs’ crucial flexure sections were found to be the half load-bearing plate’s centroid and the load column’s sidewalls. By taking into account the processes responsible for force transmission, this research proposes an analytical technique for determining the SS of DBs. Both the ACI 318-08 [4] and the suggested technique were compared to existing test results and rated on their ability to forecast the SS. The SS predictions for reinforced concrete DBs were shown to be more accurate using the suggested approach than using the STM presented in ACI 318-08. Ismail [5] investigated 24 DBs of reinforced concrete, which is now underway as part of a comprehensive experimental program. Some of the variables examined were concrete strength, the a/h ratio, shear reinforcement, and member depth. The shear span’s stress magnitude and distribution were studied by finite element analysis (FEA) with the M4 microplane model in ABAQUS software. This model, realized as a VUMAT code, better represents concrete behavior and has been tested against practical testing on concrete DB with reinforcement. Using this model, a parametric study is conducted to assess the impacts of concrete strength, a/d, and shear reinforcement. Experiments and numerical simulations reveal that the concrete strength and a/h are the two most critical elements in determining the behavior of a concrete DB with reinforcement and that the SS varies depending on beam size. Furthermore, the findings demonstrate that the concrete strength parameter scales with size. The results showed that the shear capacity of reinforced concrete DBs might be increased by around 20% with the addition of a small amount of shear reinforcement, and much more than that would not appreciably enhance the capacity. Saleem et al. [6] studied the effect of a one- and two-point load on three DBs. Each sample measured 1 m in length and 150 mm × 400 mm in cross-sectional area. The ultimate capacities of beams often decrease when loads are moved out from the beam’s center onto its supports. Therefore, in the instance of a single focused force, the ultimate load capacity decreased by 30.2% as the a/d ratio decreased from 1.3 to 0.65. The DB’s ultimate load capacity was shown to decrease by 30.5% when subjected to two concentrated forces or uniform loading; however, this effect may be mitigated by increasing the a/d ratio from 1.02 to 0.37. Ammash et al. [7] conducted experiments on four different concrete DBs with standard reinforcement, strut reinforcement, and varied levels of web reinforcement to identify the most effective design for DBs. The geometry and principal material used to strengthen each sample were identical. The tested concrete DBs had their crack distribution measured, midpoint load–displacement studies conducted, and strain recorded using digital image correlation (DIC) technology at the center, axis, and edges. A greater capacity was found in the DB with strut reinforcement as compared to the control DB with conventional reinforcement, which showed less displacement. DB specimens with strut strengthening did not encounter the same level of stress as the control DB, which broke owing to diagonal tension strains in its struts. Along the strut’s axis, compression stresses were measured [8]. Zhang and Tan conducted an experimental program that included a set of 11 specimens divided into three groups. In most cases, the SS of DBs decreases as their height increases due to the size effect. It is known that after diagonal cracking occurs, DBs behave differently from shallow beams, with arch action predominating instead of flexure. However, the causes of size-related effects in DBs are still unknown. It is hypothesized that factors affecting the strength of the compression component, such as vertical reinforcement design and boundary conditions, also influence the size effect. The experimental program provides data to support the hypotheses developed from the strut-and-tie model. It has been shown that the size effect on the ultimate SS of plain concrete beams with large height-to-width ratios can be mitigated if the loading and support plates are carefully designed. The study also demonstrates that uniformly distributed vertical reinforcement can help reduce the size effect. The study also investigates the influence of nonlinear forces on the column strength. The modified STM is recommended as a more accurate tool for predicting SS, considering the sources of the size effect, compared to other tested techniques. Ismail [5], as part of an extensive experimental program, studied 24 concrete DB with reinforcement (in progress). The concrete strength, the ratio of a/h, shear reinforcement, and the member depth were among the factors studied. To gain a better understanding of the magnitude and distribution of stresses within the shear span, FEA using the M4 micro plane model in ABAQUS software was employed. This model, implemented as a VUMAT code, was validated against experimental tests on concrete DB with reinforcement, providing a more accurate representation of concrete behavior. An additional evaluation of the effects of the concrete strength, a/d, and shear reinforcement is performed using this model in parametric research. The results of the experiments and the numerical simulations show that the SS depends on the size of the beam and that the concrete strength and a/h are the two most important parameters in determining the behavior of concrete DB with reinforcement. In addition, the results show that the parameter of the concrete strength varies with size. Adding a small amount of shear reinforcement may boost the shear capacity of concrete DB with reinforcement by roughly 20%, but more than that does not significantly increase capacity, as shown by the findings of the study. Kondalraj and Appa Rao [9] experimentally evaluated 10 DBs having a/d of 1.0. Nine out of the ten DBs had web reinforcing applied, which increased their load-bearing capability by up to 15%. A 0.3 mm-wide diagonal fracture was reported at the beam’s service load. Both the vertical and horizontal web reinforcement ratios of the beam exceeded 0.46. By reinforcing webs in both directions, we can effectively limit the spread of diagonal cracks. Experimental tests conducted as part of the current study and extensive DB data points gathered from prior research were used to analyze the ACI 318-19 strut and tie modeling STM provisions for DB with web reinforcement. It has been found that ACI 318-19 provides more reliable predictions of DB shear capacities than AASHTO, and the average strength ratio is 0.67. The ACI 318-19 SS requirements have been proved to be conservative. Beams that failed for causes other than tie yielding have been used to estimate the ACI 318-19 strut coefficient. Studies have shown that the strut coefficient is very sensitive to the strength of concrete. Therefore, it is probable that a DB capacity prediction made with a single strut factor will be dangerous. Mohammad Al-Hamaydeh and Zakariac [10] used numerical simulations utilizing the Abaqus/standard program to examine the behavior of concrete DB with reinforcement web apertures. For many different factors, the verified specimens’ numerical findings agreed well with the experimental ones. These included the a/d, opening size and placement, main reinforcement ratio, and web reinforcement ratio. The results showed that the carrying capacity of concrete DB with reinforcement is reduced when they have apertures, especially those between 0.3 and 0.4 of the beam’s total height. Furthermore, hole cuts across the shear zone significantly reduce the maximum pressure, particularly along the loading path and near the bearing plate. This is because shear cracks tend to congregate in the corners of apertures along the loading path line. The size and location of web openings have a significant impact on the behavior of concrete DB with reinforcement. When the a/d is decreased, the ultimate load also increases. Increasing the compressive strength increases its ultimate bearing capacity. In a similar vein, increasing the main reinforcement ratio to reduce cracking results in a higher ultimate load. The same conclusion holds true for the bearing capacity of web-opened concrete DB with reinforcement when the web reinforcement ratio is considered. In order to improve the bearing capacity of the concrete DB with reinforcement by 11.36 and 3.26%, respectively, an increase in the main reinforcement ratio from 0.45 to 0.57% and an increase in the web reinforcement ratio from 0.29 to 0.33% are both possible. Kondalraj and Rao [11] selected a database containing 232 trials on concrete DB with reinforcement; however, none of the trials utilized web reinforcing. Based on experimental data, it appears that the flexural compression depth predicted by linear elastic analysis is a good approximation for DB. The ACI 318-14 strut efficiency factor (SEF) for struts without web reinforcement is 0.51 and is lower than the SEFs recommended by AASHTO and ACI 318-19. When using a mean strength ratio of 0.69 in the computation, the SS is estimated to be 4% higher than it actually is in accordance with the ACI 318-14 standard. This means that the actual SS is lower. SEF in ACI 318-19 can be reduced from 0.51 to 0.34 to eliminate the capacity over prediction. The average strength-to-weakness ratio consequently decreases by 0.51. The AASHTO strut efficiency is 0.45, which can be interpreted as an SEF of 5%. There is a correlation between an increase in the concrete strength and a drop in the SEF, according to the experimental results. It could be silly to count on the HSC while still employing the minimum strut efficiency mandated by ACI 318-19. This allows us to express the SEF as a linear function of the strength of the concrete. This permits an extremely accurate (to within 3%) estimate of the DB capacity. The factors that affect the amount of force needed to cause diagonal cracking are also explored. However, the AASHTO standard does not account for the fact that the beam depth affects the force required to cause diagonal cracking. The estimated diagonal cracking load is just as accurate as before and after the AASHTO method was updated, but the margin of error decreased from 13 to 5%. Smith and Johnson [12] investigated the behavior of simply supported reinforced concrete DBs under concentrated point loading. Experimental tests were conducted on DBs without any additional admixtures or reinforcements. The results showed that the load-carrying capacity of the DBs was influenced by factors such as beam depth, shear span-to-depth ratio, and flexural reinforcement ratio. The ultimate failure mode was observed to be shear failure along the diagonal compression strut. The research highlights the significance of beam depth, shear span-to-depth ratio, and flexural reinforcement ratio in determining the load-carrying capacity and failure mode of simply supported reinforced concrete DBs subjected to concentrated point loading. Chen and Wang [13] evaluated the performance of normal-strength reinforced concrete DBs under triangular distributed loading. Experimental tests were conducted on DBs without any supplementary additives. The findings revealed that the load-carrying capacity and deflection characteristics of the DBs were influenced by the loading pattern and the shear span-to-depth ratio. The presence of adequate flexural reinforcement contributed to enhanced beam stiffness and resistance to excessive deflection. The study emphasizes the influence of loading pattern and shear span-to-depth ratio on the load-carrying capacity and deflection characteristics of normal strength reinforced concrete DBs subjected to triangular distributed loading. Zhang and Liu [14] examined the behavior of reinforced concrete DBs under a combination of concentrated and uniformly distributed loading. Experimental tests were conducted on DBs made of ordinary concrete without any additional admixtures. The results demonstrated that the load-carrying capacity and crack propagation pattern of the DBs were affected by the ratio of concentrated to distributed loading, as well as the shear reinforcement ratio. The presence of appropriate shear reinforcement resulted in improved shear resistance and ductility. The investigation underscores the importance of the ratio of concentrated to distributed loading and the shear reinforcement ratio in determining the load-carrying capacity and crack propagation behavior of reinforced concrete DBs subjected to a combination of concentrated and uniformly distributed loading.

2 Research significance

This study aimed to investigate the effect of the loading type method on the ultimate strength of DB specimens with and without strut reinforcement loaded by one- and two-point loads

3 Experimental program

Eight samples were used in two groups: the first group had four samples under a two-point load, and the second group had four samples under a one-point load. All of the samples were made with normal strength concrete (30 MPa). The usual method of reinforcing reference beams is considered. The design standards of ACI code 318-14 (Ch23-strut and tie models) [15] and part (9-9) DB were used to make two DBs that were used as examples. In this study, four specimens were tested under a two-point load, and four specimens were tested under a one-point load. Using the STM method, the suggested model is the base for an optimization approach that is used on real examples. Tests were done on DBs to see how changing these factors affected how well they worked and how they acted. All of the examples of shapes are shown in Figure 1. The beam was 1,100 mm long, 150 mm wide, and 400 mm high, and the angle between the strut’s axis and the tie was 44°. The frame was strong and stable, with a span of 900 mm between supports and a constant a/d of 0.8. The beam was covered with a thin layer of clear concrete that was about 25 mm thick. Table 1 shows the names and descriptions of the tested DBs. The transparent concrete sheathing of the beam measured around 25 mm in thickness. The tested DBs were identified and are described in Table 1.

Figure 1 
               (a) Two-point load and (b) one-point load [7].
Figure 1

(a) Two-point load and (b) one-point load [7].

Table 1

Specimen names of tested DBs

No. Specimens Description
1 Sc Reference DB specimen
2 S0 The deep strut beam employed a specimen with 0% reinforcement from the reinforced web
3 S5 The deep strut beam employed a specimen with 50% reinforcement from the reinforced web
4 S10 The deep strut beam employed a specimen with 100% reinforcement from the reinforced web

3.1 The proposed strut and tie model

It is well known that as the beam depth increases, the shear capacity decreases. The shear behavior, represented by the diagonal compression strut, may thus be designed separately from the bending behavior of the DB. The suggested model is shown in Figure 2a and b. The concrete DB with reinforcement was represented as a truss, with the diagonal strut designed as an axially loaded compression column and the tension ties represented as flexural reinforcement, with the strut and ties linked at the nodes (ACI-code318-14). To prevent the strut from collapsing under its weight, the longitudinal compression reinforcement must run parallel to the strut’s axis. A closed tie running the length of the strut is also necessary to prevent the strut from buckling diagonally under the stress of beam bending.

Figure 2 
                  (a) Model DB strut and tie for uniform load application of two-point load. (b) Model DB strut and tie for uniform load application of one-point load [7].
Figure 2

(a) Model DB strut and tie for uniform load application of two-point load. (b) Model DB strut and tie for uniform load application of one-point load [7].

This technique was used to create 8 DBs (group 1 was constructed from two diagonal struts at an angle of 44° and one horizontal strut and group 2 was with two diagonal struts at an angle of 33°). With strut reinforcement (longitudinal steel bars (4Ø10) and closed ties (10 mm @100 mm) spaced evenly throughout the strut’s length. Reinforcement consisted of primarily three types of strut DBs based on the degree of web reinforcement. The weights of three reinforcement struts and four stirrups in the DB’s supports were abstracted from the overall weight of the web reinforcement in the reference specimen to derive the different quantities of the web, as shown in Figure 3.

Figure 3 
                  Detailed reinforcement of (a) SC, (b) S10, (c) S5, and (d) S0.
Figure 3

Detailed reinforcement of (a) SC, (b) S10, (c) S5, and (d) S0.

3.1.1 Group 1

SC: DB specimen with standard reinforcement (normal reinforcement) was under a two-point load.

S10: All the surplus weight from the web reinforcement was utilized for the three DBs in this set. The load-distributed reinforcement consists of (3Ø10 mm@250 mm) and (4Ø8 mm) vertical web reinforcement. Each diagonal strut has three rows of longitudinal reinforcement (4Ø10) and a closed tie (10Ø100mm) in addition to the main reinforcement (4Ø16).

S5: 50% surplus weight from the web reinforcement was utilized for the three DBs in this set. The load-distributed reinforcement consists of 1Ø10 mm@500 mm and 4Ø8 mm vertical web reinforcement. Each diagonal strut has three rows of longitudinal reinforcement (4Ø10) and a closed tie (10Ø100mm) in addition to the main reinforcement (4Ø16).

S0: 0% surplus weight from the web reinforcement was utilized for the three DBs in this set. The load-distributed reinforcement consists of 4Ø8 mm vertical web reinforcement. Each diagonal strut has three rows of longitudinal reinforcement (4Ø10) and a closed tie (10Ø100 mm) in addition to the main reinforcement (4Ø16) (Figure 3)

3.1.2 Group 2

SC: DB specimen with standard reinforcement (normal reinforcement) was under a one-point load.

S10: A one-point load with 100% excess weight of web reinforcement was utilized to create a DB model.

S5: A one-point load with 50% excess weight of web reinforcement was utilized to create a DB model,

S0: A one-point load with 0% excess weight of web reinforcement was utilized to create a DB model (Figure 4).

Figure 4 
                     Detailed reinforcement of (a) SC, (b) S10, (c) S5, and (d) S0 [7].
Figure 4

Detailed reinforcement of (a) SC, (b) S10, (c) S5, and (d) S0 [7].

4 Materials

Normal-strength concrete mixtures were used, formed in accordance with ACI211-05 [16]. Because of its 0.35 water-to-cement ratio, 1.06 cement-to-sand ratio, and 2.35 gravel-to-cement weight ratio, this particular mix was selected. At 28 days old, the combination was intended to have a resistance of 30 MPa. Table 2 mix design details, Table 3 for the normal compressive strength after 7 and 28 days. (Table 3).

Table 2

Mixing proportion for specimens (NSC)

Description Cement Fine aggregate Coarse aggregate Water Silica Additives
Mixing proportion 1 1.06 2.35 0.35 0 0
Quantities (kg/m³) 423 451 996 148 0 0
Table 3

Compressive strength at 7 and 28 days

Type of concrete Compressive strength fc (MPa) (cylinder) 7 days Compressive strength fc (MPa) (cylinder) 28 days
Normal strength concrete 30.46 36.53

4.1 Testing experiments

The hydraulic universal testing machine, shown in Figure 5, is used to test the beams. The apparatus is made up of a hydraulic actuator, a load cell, an extension support, a load-applying plate, a load-reading plate, and a collection of arms of varying lengths. While using a double-mounting system, the top portion remains stationary while the bottom portion is free to move. The machine capacity is around 2,000 kN at maximum (Figure 5).

Figure 5 
                  Steel reinforcement for Group 1 DBs.
Figure 5

Steel reinforcement for Group 1 DBs.

The strain was measured by using DIC with photogrammetry and digital image processing. This idea was crucial for the development of the DIC technique for comparing digital images. Using a mathematical correlation study, differences were found between the original (reference) and distorted (process) digital photographs. Inferred from differences between two images taken before and after the deformation, showing the movement of landmarks, GOM, a 2019 version of the Correlation Software Package program was used for measuring flat surfaces. There is a free 2D version and a premium 3D one, with the former relying on a single imaging source and the latter on two. This technique was used to measure displacement and strain, as well as monitor the movement and distance between locations in the specimens over time while they were under stress. To limit the DB’s lateral motion, a linear variable differential transducer (LVDT) was put underneath it at its midway (the point of highest bending force). In operation, the LVDT can handle a maximum capacitance of 75 mm. LVDT measured the amount by which the beam deflects to one side when subjected to a load. The effort made and the distance traversed were both recorded by the coder. The rate of loading applied at each reading was recorded by the device using a loading disc. Both gadgets are connected to the computer and activated using the UDAC16 program. The DB specimens were subjected to a static axial prepressed force applied from the top of the beam. A steel plate of dimensions (150, 100, and 10 mm) was used to focus the force of an experiment’s loading and stabilize a second steel plate of the same size. Figure 6 depicts a DB as the sole support for the structural framework (roller and pin), with each tested beam having an apparent span length of 900 mm (Figures 79).

Figure 6 
                  Steel reinforcement for Group 2 DBs [7].
Figure 6

Steel reinforcement for Group 2 DBs [7].

Figure 7 
                  Device for performing hydraulic tests on DB specimens: (a) two-point load and (b) one-point load [7].
Figure 7

Device for performing hydraulic tests on DB specimens: (a) two-point load and (b) one-point load [7].

Figure 8 
                  Information about the loading situation for two-point load: (a) beam under loading, (b) method of applying pressure, (c) pin support, and (d) roller support.
Figure 8

Information about the loading situation for two-point load: (a) beam under loading, (b) method of applying pressure, (c) pin support, and (d) roller support.

Figure 9 
                  Information about loading situation for one-point load. (a) Beam under loading, (b) pin support, and (c) roller support [7].
Figure 9

Information about loading situation for one-point load. (a) Beam under loading, (b) pin support, and (c) roller support [7].

5 Discussion on the outcomes of an experiment

Crack patterns, easily recognizable failure modes, loads parallel and perpendicular to the strut axis, and ultimate capacity will all be shown here as a consequence of the DB experimental testing system.

This study reports testing results of the transient response of T-shape concrete deep beams with large openings due to impact loading. Seven concrete deep beams with openings including two ordinary reinforced, four partially prestressed, and one solid ordinary reinforced as a reference beam were fabricated and tested. The effects of prestressing strand position and the intensity of the impact force were investigated [17].

Numerical models for impact load assessment are becoming increasingly reliable and accurate in recent years. The processing time duration for such analysis has been decreased to an acceptable level when combined with modern computer hardware. The aim of this study was to represent a simulation technique and to verify the validity of modern software in measuring the response of reinforced concrete beam strengthened by carbon fiber-reinforced polymer (CFRP) sheet subjected to impact loads at the ultimate load ranges. In this investigation, ABAQUS/Explicit Software s nonlinear finite element modeling had been used. The response of the impact force–time history and the displacement–time history graphs were compared to the existing experimental results. The adopted general-purpose finite element analysis is verified to be capable of simulating and accurately forecasting the impact behavior for structural systems. In addition, a parametric analysis was carried out to gain a better knowledge of the performance of reinforced concrete beams under impact loading [18].

5.1 General behavior of DB

5.1.1 Under two-point load

Two-point loads were applied to four DB specimens. The DBs studied exhibited elastic uncracked behavior both in the low load stage and under the applied stresses. As the load was increased, fractures emerged at the elastic cracked level of the DB, first in the flexural area and then in the shear span. The shear span area of the beams developed more fractures after this level. As the load was increased, the fracture appeared in the strut zone (shear span area), beginning at the middle depth of the beam shear span. The DB failed because the cracks began at the support plate and progressed toward the point of stress. The cracks widened and became larger in this area, which represents the shear area, which led to specimen failure.

5.1.2 Under one-point load

For all DBs, a perpendicular flexure crack manifested itself about midspan and progressed upwards in the direction of the bearing loading plate, representing a common failure mode. Then, a diagonal shear crack formed, beginning at the load sites and propagating toward the support points. When a strut fails due to crushing, many slanted fractures often form. A concrete compression strut collapses under pressure when the region of concrete between the slanted fissures is stressed. The shear compression mode, in which the concrete above the fracture collapsed by crushing and made a lot of noise due to the high compression that was revealed following the creation of the inclined crack. Less noise was produced by the less brittle diagonal splitting failure mode, which is characterized by a crucial diagonal fracture (strut of the DB) [7].

5.2 Crack pattern

According to Tan et al. [19], there are three main types of failure in DBs: crushing of strut failure, diagonal-splitting failure, and shear-compression failure. Video recordings and written notes were heavily relied upon to obtain precise data on the test outcomes. The DIC technique, which will be elaborated on further in this section, was utilized to determine the onset of cracking (see Table 4 and Figure 10).

Table 4

Maximum load capacity and crack’s pattern percent load for two- and one-point load specimens

ID Load (kN) Crack – flexural (%) Crack – diagonal (%)
One point Two point One point Two point One point Two point
SC 570 493.87 41.7 49 49 37
S0 492.32 517.92 32.7 61 42 64
S5 536.25 518.72 25.9 55 39 65
S10 670.9 530.1 24.3 58 37 62
Figure 10 
                  The first loads that cause cracks two and one are (a) flexural crack load and (b) shear crack load.
Figure 10

The first loads that cause cracks two and one are (a) flexural crack load and (b) shear crack load.

5.2.1 Under two-point load

The first crack in the specimens appeared at the mid-distance between the supports. In further studies, it was shown that fractures emerge at the strut (shear span zones) and spread radially outward toward the point load. Once the crack reaches a critical size and the concrete collapses under shear, the DB takes on as much weight as it can handle. Although this trend was seen in all test specimens, the specific kind of fracture that developed in each specimen varied according to the reinforcing details. In the strut failure crushing, there is more than one inclined crack. The inclined cracks of concrete were of compression parts. After the formation of the inclined crack, the concrete part above the upper end of this crack exposed high compression, and the concrete above the crack failed by crushing with high noise. Compression forces from the load caused the strut to fail. A large amount of noise was produced as a consequence of the strut’s failure mode, which was characterized by cracking and crushing, while traditional reinforcement showed diagonal-splitting failure. Initiation of cracking occurred at a load between 49.1 and 57.9% of the ultimate load in the midspan (flexure crack), and between 36.9 and 62% of the ultimate load in the struts (diagonal shear crack) (Table 5).

Table 5

Maximum load capacity and crack pattern load for two-point load specimens

Specimen ID Crack – flexural load (kN) at first flexural cracking Crack – diagonal load (kN) at first shear cracking Ultimate load Pu (kN)
Sc 242.67 182.18 493.87
S0 315.60 331.70 517.92
S5 285.30 337.17 518.72
S10 307.18 328.66 530.1

5.2.2 Under one-point load

Exposed to one-point load, crack patterns were certified throughout the length of the DBs at different load steps. It was observed, as shown in Table 6, that the first cracking load crack was between 24.3 and 41.7% from the maximum load capacity for positive flexural, and 37 and 49% from the maximum load capacity for shear crack (Table 6 [7]).

Table 6

Maximum load capacity and crack’s pattern load for one-point load specimens [7]

Specimen ID Crack – flexural load (kN) at first flexural cracking Crack – diagonal load (kN) at first shear cracking Ultimate load Pu (kN)
Sc 237.69 279.3 570
S0 160.98 206.77 492.32
S5 138.88 209.13 536.25
S10 163.02 248.23 670.9

5.3 Load midspan deflection curves

The load cell was used to monitor pressure, the LVDT was used to measure displacement, and the computational model was used for interpretation. There were three states: elasticity without cracks, elasticity with cracks, and plasticity. In the first stage after load release, the specimen reverts to its unaltered state. In other words, no fractures emerge in it, and when the load is removed, the sample does not deform but rather returns to its previous shape. The second stage sees the emergence of cracks, at which point the specimen is elastic enough to return to its original form. In the third stage at this point, the specimen has already failed and can no longer be restored to its former state.

5.3.1 Under two-point load

All specimens showed a similar progression through the three phases (elasticity from the start of loading till fracture development, elasticity with cracks from the start of crack formation, and (plastic) from peak load failure). The smallest displacement was found in the S10 specimen (2.14 mm), with the largest displacement (3.25 mm) found in the SC specimen; see the data in Figure 11.

Figure 11 
                     Load–displacement curve for all two-point load specimens.
Figure 11

Load–displacement curve for all two-point load specimens.

5.3.2 Under one-point load

Figure 12 displays the load-versus-displacement curves obtained from testing all DBs. In all cases, a linear relationship between load and displacement is seen during the first part of the loading process, followed by a transition to nonlinear behavior. This demonstrates the brittle nature of the specimens due to the control shear deformation. The DBs’ strength was reduced below the flexural strength as a result of their brittle failure mode. The smallest displacement was found in the S0 specimen (4 mm), while the largest displacement (12 mm) was found in the SC specimen [7].

Figure 12 
                     Load–displacement curve for all one-point load specimens [7].
Figure 12

Load–displacement curve for all one-point load specimens [7].

5.4 Causes of failures

Cleaning, staining, and stippling the specimens were the first steps in the inspection. The samples were then loaded into a crushing device, and recording started just before the equipment was about to begin processing. The load increased up to 10 kN until the specimens broke. The recording was cut off after that. After the video was converted to still photos, they were uploaded using the software (Soft Free Studio). Since the first picture was taken before any loads were applied, it was selected as the reference image. The software then matched each new picture with the original to calculate the amount of distortion, displacement, and cracking. All reinforced DB specimens under two-point loads are shown in Figure 13, and all specimens under one-point load are shown in Figure 14. The failure was caused by a shear fracture propagating from the supporting plates onto the point load along a diagonal. Therefore, a diagonal-splitting failure was the cause of the failure of the reference DB Sc. Previous strut-reinforced specimens (S0, S5, and S10) failed due to crushing of the struts. The shear in struts created by one inclined fracture at the strut’s margins in each shear span caused the failure of these DBs. As a result, the DBs collapsed due to the strut being crushed.

Figure 13 
                  DIC photo before loading, after loading, and after filer for specimens under two-point load: (a) SC, (b) S0, (c) S5, and (d) S10.
Figure 13

DIC photo before loading, after loading, and after filer for specimens under two-point load: (a) SC, (b) S0, (c) S5, and (d) S10.

Figure 14 
                  DIC photo before loading, after loading, and after filer for specimens under one-point load: (a) SC, (b) S0, (c) S5, and (d) S10 [7].
Figure 14

DIC photo before loading, after loading, and after filer for specimens under one-point load: (a) SC, (b) S0, (c) S5, and (d) S10 [7].

5.5 Load–strain behavior

Overall, recording the strain values provided insight regarding the highest stresses in the specimens, and measuring strain by DIC of DB recordings helped in better understanding the true stress flow from the site of loading to the plates at the supports. The key terms are explained in Table 7 for two-point load and Table 8 for one-point load.

Table 7

Names of strain points and locations of the two-point load specimens

Classification of recordings Location
CB Center beam
CBD Center beam bottom
S1 Left strut
S2 Right strut
Table 8

Names of strain points and locations of the one-point load specimens [7]

Recording designation Location
AS Axis of strut
ES1 Edge of strut 1
ES2 Edge of strut 2

After applying the load, we recorded the result for each 10 kN.

5.5.1 Under two-point load

Failure in the greatest tensile value areas was seen in all specimens. All specimens were separated into four regions and values were measured for each of these regions, which range from tensile (high values) to compressive (low values). The strain was greatest at the strut position, followed by the bottom of the beam center location, and finally the beam center location. The first image was captured at pre-loading, whereas the second was captured immediately after the failure. Each specimen’s results are shown graphically (Figures 1518).

Figure 15 
                     Load applied vs typical specimen concrete strain SC.
Figure 15

Load applied vs typical specimen concrete strain SC.

Figure 16 
                     Load applied vs typical specimen concrete strain S0.
Figure 16

Load applied vs typical specimen concrete strain S0.

Figure 17 
                     Load applied vs typical specimen concrete strain S5.
Figure 17

Load applied vs typical specimen concrete strain S5.

Figure 18 
                     Load applied vs typical specimen concrete strain S10.
Figure 18

Load applied vs typical specimen concrete strain S10.

5.5.2 Under one-point load

Load strain values of the axis strut were lower in all compression strut specimens compared to tension strain recorded specimens (SC). The DB (S10) experienced less compression and tension strain than the shallow beam (SC). This was mostly attributed to the improved reinforcing scheme that had been planned for the (S10) DB. Reducing the amount of web reinforcement in reinforcement strut DBs (S10, S5, and S0) had a direct effect on the ultimate SS of these beams, as shown in Figures 1922 [7].

Figure 19 
                     Load applied vs typical specimen concrete strain SC [7].
Figure 19

Load applied vs typical specimen concrete strain SC [7].

Figure 20 
                     Load applied vs typical specimen concrete strain S10 [7].
Figure 20

Load applied vs typical specimen concrete strain S10 [7].

Figure 21 
                     Load applied vs typical specimen concrete strain S5 [7].
Figure 21

Load applied vs typical specimen concrete strain S5 [7].

Figure 22 
                     Load applied vs typical specimen concrete strain S0 [7].
Figure 22

Load applied vs typical specimen concrete strain S0 [7].

6 Discussion of the test results

In this study, we have found that the use of a two-point load leads to a decrease in the maximum capacity of specimens when compared with a one-point load. For further clarification, note the points below.

6.1 Type of loading (one- and two-point load)

The results from the present study were compared to those from a prior study (Ammash and AL-Mousawi, [7]) that only employed a one-point load. The concrete type, its dimensions, and its method of reinforcing are all the same as Ammash and AL-Mousawi’s study [7]. We can accomplish this for comparison and because of the difference in the loading methodology. The maximum load capacity for Sc and S10 specimens for one-point load was more tolerant to stress than the two-point load, with 14% for Sc and 27% for S10, respectively. As the reinforcement levels in both samples were equivalent, just these two were compared (Table 9).

Table 9

Compared between specimens maximum load capacity and percent load

ID Load % Different
One point Two point One point Two point
Sc 570 493.87 100% 86% 14%
S10 670.9 530.1 100% 79% 21%

6.2 Pattern of crack

As the reinforcement levels in both specimens (S10 and Sc) were 100% equivalent, just these two were compared. Cracks are formed in the shear and flexural zones at a one-point load when a load less than the two-point load is applied as shown in Table 10.

Table 10

Cracks pattern load and percent for one- [7] and two-point load specimens

ID Crack-flexural (kN) Crack – diagonal (kN) Crack – flexural (%) Crack – diagonal (%)
One point Two point One point Two point One point Two point One point Two point
Sc 237.69 242.67 279.3 182.18 41.7 49 49 37
S0 160.98 315.60 206.77 331.70 32.7 61 42 64
S5 138.88 285.30 209.13 337.17 25.9 55 39 65
S10 163.02 307.18 248.23 328.66 24.3 58 37 62

7 Conclusions

In this study, we demonstrated that the use of a two-point load leads to a decrease in the maximum load capacity of specimens when compared with a one-point load. Cracks are formed in the shear and flexural zones at a one-point load and when a load less than the two-point load is applied. It was also observed that when a two-point load was applied to a specimen, the displacement was less than half of what was obtained when tested under a one-point load. It was also found that strain in specimens examined under a two-point load was lower than in specimens examined under a one-point load.

  1. Funding information: The authors state no funding involved.

  2. Conflict of interest: The authors state no conflict of interest.

  3. Data availability statement: Most datasets generated and analyzed in this study are given in this submitted manuscript. The other datasets are available on reasonable request from the corresponding author with the attached information.

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Received: 2023-06-04
Revised: 2023-07-05
Accepted: 2023-07-14
Published Online: 2024-03-08

© 2024 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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