Experimental and Numerical Investigation of Construction Defects in Reinforced Concrete Corbels

Abstract

Reinforced concrete corbels were examined in this study for the cracking behavior and strength evaluation, focusing on defects typically found in these structures. A total of 11 corbel specimens were tested, including healthy specimens (HS), specimens with lower concrete strength (LC), specimens with less reinforcement ratio (LR), and specimens with more concrete cover than specifications (MC). The HS specimens were designed using the ACI conventional method. The specimens were tested under static loading conditions, and the actual strengths along with the crack patterns were determined. In the experimental tests, the shear capacity of the HS specimens was 28.18% and 57.95% higher than the LR and LC specimens, respectively. Similarly, the moment capacity of the HS specimens was 25% and 57.52% greater than the LR and LC specimens, respectively. However, in the case of the built-up sections, the shear capacity of the HS specimens was 9.91% and 37.51% higher than the LR and LC specimens, respectively. Likewise, the moment capacity of the HS specimens was 39.91% and 14.30% higher than the LR and LC specimens, respectively. Moreover, a detailed nonlinear finite element model (FEM) was developed using ABAQUS, and a more user-friendly strut and tie model (STM) was investigated toward its suitability to assess the strengths of the corbels with construction defects. The results from FEM and STM were compared. It was found that the FEM results were in close agreement with their experimental counterparts.

1. Introduction

Cracks in reinforced concrete (RC) corbels are formed generally where tensile stress exists and exceeds the concrete’s designated tensile strength. Shear cracks are formed as a result of the inclined or principle tensile stresses acting on the corbels. Corbels generally fail according to the following sequence: (i) vertical shear–flexural cracks form at the shear span, (ii) crack propagation occurs in a crushed path toward the point of application of the point load approaching the compressive zone, and (iii) with further loads the cracks extend in two directions, the first is toward the compressive zone and the second is the horizontal path at the reinforcement level toward the support [1,2,3]. As the major type of failure in corbels is normally the shear failure, investigation of the crack patterns is fruitful in understanding the behavior of the cracked corbels.

Almost all bridges are basic supported beam constructions. These large beams, or major girders, are supported by corbels at each end that are attached to columns. In precast construction, the corbels are the basic connectors. The idea behind the precast construction entails casting individual components and then providing a way of connecting them. The connection between the beams and columns should be able to transfer the beams’ reactions to the columns. The footings finally experience these reactions after the columns. This also applies to walls as structural elements [4]. In many situations, it is necessary to strengthen corbels due to inadequate concrete strengths, steel, concrete cover, and others. It is of utmost importance to evaluate the failure behavior of the corbels with construction defects before strengthening them.

Many researchers who carried out experimental investigations employing corbels made of normal-strength concrete came to the following conclusions that the shear strength depends on: (i) the ratio of shear span to depth; (ii) the ratio of reinforcement; (iii) the concrete strength; and (iv) the proportion of the applied loads’ vertical and horizontal components. To prevent diagonal tension failure, a minimum quantity of horizontal stirrup reinforcements must be offered. Additionally, it was stated that the primary reinforcing steel typically yielded before failing. The test results indicated that for small corbels, little quantity of tension reinforcements was adequate, even though no stirrups were used, and the reinforcement ratio and shear span-to-depth ratio (a/d) as the main variables were investigated in light of these findings [5]. It was concluded from the study [6] that for corbels without stirrups, the failure was of the splitting type, some corbels had the flexural failure, and the failure of the other corbels was characterized by the expansion of one or more diagonal tension failures.

Construction defects affect the performance of RC elements. Studies such as [7] evaluated the dynamic characteristics of RC structures reinforced by fiber reinforced polymer (FRP) and their susceptibility to damage. Likewise, nano-modified epoxy resin was assessed for its potential to reinforce FRP-plated RC structures [8]. Furthermore, researchers discussed the fracture mechanics models that were applied to understand the crack behavior in RC elements [9].

By utilizing steel bars in experimental investigations, researchers looked at the flexural behavior of corbels built of plain or fibrous concrete. It was noted that the existence of higher steel reinforcement might prevent the main reinforcement from yielding completely, which caused a brittle failure because the compressed regions were crushed [10,11,12,13]. Using various parameters, including longitudinal reinforcement, shear reinforcement, the compressive strength of concrete, and a/d, an experimental study was conducted to determine the impact of crushed stone and its contribution to the shear strength of RC corbels. The ultimate shear strength was improved by about 99% and 22% by changing the longitudinal reinforcement ratio from 0.0026 to 0.005 and the shear reinforcement ratio from 0.00015 to 0.0024, respectively, and also the shear strength was enhanced by 58% when the compressive strength of concrete increased from 20 to 40 MPa [14,15,16].

Artificial intelligence (AI) and 3D printed concrete have been investigated. A generalized regression neural network model was used to design concrete components [17,18,19]. To boost the load-carrying capacity of corbels, an experimental study was also done on the corbels strengthened externally by carbon fiber reinforced plastic (CFRP). The crack patterns of the corbels were evaluated utilizing different strengthening arrangements. With the use of CFRP, the corbels’ ultimate load-carrying capacity was enhanced for all the specimens, with an increase in the range of 8% to 70% as compared to the control specimen. Many of the corbels had brittle failure modes, and as all the specimens’ stiffness rose, this led to an abrupt failure without a sufficient warning. Yet, all the upgraded specimens experienced cracking loads between 70% and 80% of their ultimate loads. Contrarily, the specimens with two CFRP attachment methods, diagonal and horizontal strips, exhibited an apparent delay in cracking until 85% of their ultimate loads [20]. In an experimental investigation, RC corbels with main bars only, main bars and steel or monofilament polypropylene fibers, and main bars and plastic mesh underwent vertical loading testing. The volumes of the main bars and a/d were modified, and the fibers or strips of plastic mesh were employed as secondary (shear) reinforcement. According to the tests, the main bar-reinforced corbels only failed explosively and abruptly, and the diagonal splitting was the failure mode. The degree of improvement depended on the type and shape of the secondary reinforcement, although adding secondary reinforcement typically resulted in improvements to the corbels’ strength and ductility. The findings also demonstrated that the corbels’ strength failure in flexure could be reasonably anticipated using the simple beam theory while taking secondary reinforcement into account [21]. In another experimental study, it was determined that applying CFRP wrapping techniques might boost the load-carrying capacity and energy absorption of corbel beams. The cracking behavior of the corbels varied before any particular strengthening technique could be applied [22].

Ordinary flexural theory analysis makes it difficult to predict the true behavior of members since it assumes that plane sections stay flat after bending, which is not true for non-flexural members such as corbels, deep beams, pile caps, etc. Such non-flexural members have been designed using a variety of empirical methods. In situations where the classic beam theory cannot be utilized for non-flexural components, the strut and tie model (STM) is one of the logical and fairly straightforward design options [21]. STM highlights two principles for the resistance of loads, i.e., compressive loads are resisted by concrete struts while the tensile stresses are resisted by primary reinforcement and stirrups. Steel and concrete are usually assumed to be plastic in the limit state by the lower bound theory of plasticity, which forms the foundation of STM. The uniaxial strength of concrete is then adjusted using efficiency parameters to account for concrete cracking and softening [21]. The strut and tie process consists of three crucial components listed below and is rather straightforward: (i) development of a STM, in which the struts and ties are used to concentrate the curvature of the real stress field on nodes and condense it into a smaller area, (ii) determination of the equilibrium strut and tie forces, and (iii) taking into account the crack width and orientation when dimensioning the struts and ties for internal forces. Many researchers have calculated the shear capacity of squat walls via STM [23], others deep beams, beam–column joints, dapped-end beams, and corbels [24,25].

The STM-based method has been used for determining the load-carrying capacity of RC corbels. In a study [23], it was found by STM that the strength of a corbel is controlled by shear rather than flexure. Theoretical strut and tie force values and strut and tie force values based on the load at the first shear fracture and failure loads were compared during the design of corbel beams [1,26]. The STM’s estimations of the load-carrying capacity correlated more closely with the corbels’ test findings from a large database of 455 test results. Further, the shear capacity of high-strength corbels was predicted using STM, and the results were compared to figures acquired from experimental observations [27,28]. A slight variation was observed between the experimental and theoretical values obtained utilizing STM. The suggested model took the strain compatibility and constitutive laws of cracked RC into account, in addition to the standard strut and tie force equilibrium criteria.

For the design of non-flexural components in RC buildings, such as deep beams and corbels, the STM technique is frequently employed. The aim of the present study is to resolve problems involved in predicting the capacity of high-strength double-faced RC corbels with defects in construction. Only regular-strength concrete and high-strength concrete are covered in the majority of the extant research on the behavior of corbels. This research focused on common defects of RC corbels, including corbels with less reinforcement ratio, corbels with lower concrete strength, and corbels with more concrete cover. Eleven corbels were made for this purpose. The investigation was carried out by means of a detailed nonlinear finite element model (FEM) and an adequately accurate strut and tie mechanism that makes it possible to do away with the current laborious and time-consuming computer processes. A formula-based Excel sheet was also prepared, which can be used by the field designers. In the sections to follow, the properties, dimensions, and loading arrangements of the corbels are discussed. The results obtained from STM are detailed along with the experimental results. The results of the nonlinear finite element analysis are presented along with the details of FEMs. Finally, the conclusions are drawn.

2. Experimental Program

2.1. Chosen Materials and Their Characteristics

2.1.1. Concrete

The healthy corbel specimen was designed based on the ACI conventional method (ACI 318-14) [29] for a vertical design load of 200 kN. The most common defects in the corbel construction were investigated by varying the concrete strength, reinforcement ratio, and clear concrete cover. Eleven corbel specimens were fabricated with the specifications given in the tables (

Table 1. List of specimens with corresponding symbols.

No.	Specimen	Symbol
1	Healthy specimen (with full concrete strength and steel reinforcement)	HS
2	Specimen with lower concrete strength	LC
3	Specimen with less steel reinforcement ratio	LR
4	Specimen with more concrete cover	MC

and

Table 2. Dimensions and reinforcements of specimens.

Name of Specimen	Number	h (mm)	l (mm)	d (mm)	Cover (mm)	f′c (MPa)	Primary Reinforcement	Secondary Reinforcement
HS	3	228.6	685.8	228.6	38	41.36	2 # 6 and 1 # 4	2 # 3 and 1 # 4
LC	3	228.6	685.8	228.6	38	20.64	2 # 6 and 1 # 4	2 # 3 and 1 # 4
LR	3	228.6	685.8	228.6	38	41.36	1 # 6 and 1 # 4	2 # 3 and 1 # 4
MC	2	228.6	685.8	228.6	76	41.36	2 # 6 and 1 # 4	2 # 3 and 1 # 4

). Top section of each specimen was 228.6 mm in height (h), 228.6 mm in depth (d), and 685.8 mm in length (l). A clear concrete cover of 38 mm was adopted. In the MC specimens, the clear cover was taken as 76 mm instead. The specimens were cured for 28 days until they achieved their full strength. From Table 2, it can be seen that the strength of concrete was 41.36 MPa in the HS, LR, and MC specimens, while it was 20.64 MPa in the LC specimens.

2.1.2. Reinforcements

Three HS specimens (control specimens) as per the original design, three LC specimens, three LR specimens, and two MC specimens were cast, as illustrated in Figure 1a–d. To depict the difference of lower-strength concrete, thin lines were used in Figure 1b.

Figure 2 shows dimensions of all the specimens. The area of primary reinforcement used in the HS, LC, and MC specimens was 696.77 mm², while the area of primary reinforcement utilized in the LR specimens was 412.90 mm². The area of secondary reinforcement employed in all the specimens was 270.96 mm².

2.2. Test Setup and Instrumentation

The response variables were the failure modes, crack patterns, and capacities. The cracking behaviors of all the specimens were studied, and their strengths were compared. The specimens were placed in the loading frame and the loads were applied at two points. Plaster of Paris was applied on the surface of the corbels, and steel plate was also placed under the specimens for smoothness and uniformity. Deflection control tests were performed. The arrangement of loading equipment is illustrated in Figure 3.

The specimens were shifted, placed, and levelled for uniform loading. In order to apply the loads, a hydraulic jack was used, and the proving ring was utilized for recording the loads, while deflection gauges were employed for recording the deflections on all four corners of the corbels.

2.3. Experimental Results

All the results of the tested corbel specimens were compared. The two MC specimens failed; therefore, the results were confined to the other three cases. The average moment and shear capacity values for nine specimens are presented in

Table 3. Comparison of results based on ACI method.

Specimen Name	Moment Capacity (kN.mm)			Shear Capacity (kN)
	Original Design	As per Built-Up Section	As per Experimental Result	Original Design	As per Built-Up Section	As per Experimental Result
HS	45,973.4	45,580.3	38,110.1	200.2	194.6	243.97
LC		39,059.1	16,187.6		121.6	102.57
LR		27,386.1	28,579.2		175.3	175.20

. The shear and moment capacities of the specimens were also compared according to the ACI-318 method. For this purpose, the moment and shear capacities were reported as per design, built-up section, and experiment (Table 3).

Compared to the HS specimens (control specimens), the moment and shear capacities of the LC specimens reduced 57.52% and 57.95%, respectively, while the moment and shear capacities of the built-up sections decreased 14.30% and 57.52%, respectively.

Similarly, compared to the HS specimens, the moment and shear capacities of the LR specimens reduced 25% and 28.18%, respectively, while the moment and shear capacities of the built-up sections decreased 39.91% and 9.91%, respectively.

Furthermore, compared to the LR specimens, the moment and shear capacities of the LC specimens reduced 43.35% and 41.45%, respectively, while the moment capacity of the built-up sections increased 42.62% and their shear capacity decreased 30.63%.

Thus, in the case of an RC corbel, the strength of concrete is more important than the reinforcement ratio.

The failure pattern in all the specimens was approximately similar. First, a bending crack started at the reentrant corner, and stress in tension reinforcement increased rapidly. The initial cracks in all the specimens were propagated along the column–corbel interface. Diagonal tension cracks then appeared in the corbels. The intersection of the slope face of the corbels and the columns faces, as well as the point of the inner edge of the bearing plates, were where these cracks were located.

However, it was noted that starting of the cracks was different in different corbels, although after propagating they ended with the same failure. Shear cracks were prominent in the case of the LC specimens, where they were initiated and followed by bending cracks, as displayed in Figure 4c, whereas in the case of the LR specimens, bending cracks appeared in the flexural zone at a smaller loading, and shear cracks became dominant as the load increased. By reducing the primary reinforcement in the LR specimens, the moment and shear capacities reduced by an equal amount. Thus, failure was due to the flexural action because the section resisted the moment less than its capacity. Steel started to yield first, which caused concrete to crush. This mode of failure is flexural tension failure, in which failure was initiated by flexural cracks, and failure was finally caused by steep bending-type cracks, as demonstrated in Figure 4b. In the case of the MC specimens, at the corners where the load was applied, the corbel crushed from the top and failed without taking further load, thus showing brittle behavior, as depicted in Figure 4d.

3. STM

For members such as deep beams and corbels, STM has typically been accepted as an appropriate logical design technique [27]. Additionally, the STM technique has been suggested as a design tool for RC corbels by the majority of contemporary design regulations [29].

Three corbel specimens were designed with the specifications given in Table 1 and Table 2, in which we had the HS specimen with full concrete strength (41.36 MPa) and full reinforcement (696.77 mm²), the LC specimen with lower concrete strength (20.64 MPa) and full reinforcement (696.77 mm²), and the LR specimen with less reinforcement (412.90 mm²) and full concrete strength (41.36 MPa). The yield strength of steel reinforcement (f′_y) was 413.68 MPa for all the three types of the corbels. The dimensions and technical parameters of the struts and ties are presented in

Table 4. Dimensions of STM members.

No.	Member	Unit	HS	LR	LC
1	AA’	mm	40.47	29.06	17.01
2	AB	mm	64.78	46.52	27.23
3	A’B’	mm	64.78	46.52	27.23
4	BB’	mm	32.37	23.25	13.61
5	BC	mm	40.47	29.06	17.01
6	B’C’	mm	40.47	29.06	17.01

and

Table 5. Technical parameters used for STM.

No.	Technical Parameter	Unit	HS	LR	LC
1	f′c	MPa	41.36	41.36	20.64
2	As	mm2	696.77	412.90	696.77
3	Shear capacity	kN	243.97	175.20	102.57
4	Clear concrete cover	mm	38.1	38.1	38.1
5	a/d	<1	0.6	0.6	0.6
6	Length	mm	685.8	685.8	685.8
7	Height	mm	228.6	228.6	228.6
8	Depth	mm	190.5	190.5	190.5
9	Angle	Rad	0.896	0.896	0.896
10	Shear span	mm	114.3	114.3	114.3

, respectively. Figure 5 depicts STM. The angle of the truss was 51°, while the effective depth was 190.5 mm.

Table 6. Capacities of STM members.

No.	Member	Maximum Shear Capacity = 243.97 kN	Maximum Shear Capacity = 175.20 kN	Maximum Shear Capacity = 102.57 kN
		HS Specimen	LR Specimen	LC Specimen
1	AA’	195.97	140.16	82.05
2	AB	312.43	224.37	131.35
3	A’B’	312.43	224.37	131.35
4	BB’	195.97	140.16	82.05
5	BC	243.97	175.20	102.57
6	B’C’	243.97	175.20	102.57

provides the capacity of each member of the RC corbel specimens, i.e., HS, LR, and LC. Member AA’ was a tie, while all the other members acted as struts in all the three types of the corbels.

4. Discussion

The comparisons of the theoretical STM values and measured values demonstrated a strong agreement with ACI-318. In the case of the HS specimen, the shear capacity of the struts and ties calculated by STM was found to be higher than the LR and LC specimens. In the case of the HS specimen, the shear capacity of the tie AA’ and strut BB’ was 195.97 kN, while it was 312.43 kN for the struts AB and A’B’. Similarly, the shear capacity was 243.97 kN for the struts B’C’ and BC. The members failed in shear.

In the case of the LR specimen, the failure was ductile due to bending. Flexural cracks were formed owing to yielding of the primary steel. The shear capacity of the struts and ties was lower compared to the HS specimen. However, the shear capacity of the LR specimen was higher than the LC specimen. The shear capacity of the tie AA’ and strut BB’ was 140.16 kN. The shear capacity of the struts A’B’ and AB was 224.37 kN, while it was 175.20 kN for B’C’ and BC. A reduction in the primary reinforcement ratio resulted in the reduced shear capacity compared to the HS specimen. The comparison of the obtained capacities revealed that the calculated results and experimental results were close to each other.

With the lower strength of concrete in the LC specimen, the shear failure predominated. The shear capacity of the tie AA’ was 82.05 kN, while it was 131.35 kN for the struts AB and A’B’. However, the shear capacity of the struts B’C’ and BC was 102.57 kN.

Furthermore, the shear capacity of the LC specimen with f′_c = 20.64 MPa was found lower than the HS and LR specimens with f′_c = 41.36 MPa, as the reduction in the concrete compressive strength reduced the shear resistance of the strut members. Therefore, the struts failed in shear before yielding of steel reinforcements.

The shear capacity of the HS specimens was 28.18% and 57.95% higher than the LR and LC specimens, respectively, while the shear capacity of the LR specimens was 70.81% greater than the LC specimens in the experimental tests. The MC specimen failed at very low strength, thus showing the brittle mode of failure.

5. Nonlinear Finite Element Analysis

5.1. Overview

In order to investigate the observed discrepancies between the RC design predictions and experimental results, we used ABAQUS, a well-established commercial finite element analysis package [24,25,26,27]. By using this advanced tool, nonlinear behaviors of steel and concrete can be captured efficiently through the three-dimensional (3D) nonlinear finite element analysis. This analysis is chosen based on the concrete’s nonlinear behavior under triaxial stress conditions, which usually leads to local failures. Additionally, non-homogeneity and redistribution of stress are considered after cracking occurs.

In this research, the RC corbels were analyzed using a powerful FEM. FEMs have been proven to be indispensable tools for simulating various structural conditions (i.e., various loadings and boundary conditions), and they are widely used in the evaluation of the structures’ performance, ranging from biomechanical to structural models [30]. By discretizing the corbels’ geometry into interconnected elements, FEMs approximated their continuous behavior. The concrete’s intricate nonlinear properties, including the stress–strain relationships and cracking behavior, were taken into account. When the geometry and boundary conditions of the corbels were precisely defined in FEMs, we were able to simulate real-world scenarios with great accuracy, applying static loads, and controlling displacements until failure.

The FEMs’ parameters were well-calibrated based on the experimental data, making them accurate and reliable models. In addition to validating the FEMs’ predictions against actual tests results, we could strengthen the credibility of our research work by utilizing these parameters. Moreover, we could better understand how the corbel specimens behaved under varying conditions, which contributed to improving the structural analysis and design.

5.2. Modeling

5.2.1. Modeling Concrete Plasticity

Currently, the behavior of the concrete material is described using the damage plasticity model, whose development is based on the Drucker–Prager strength hypothesis [31,32,33,34]. The stress–strain curves displayed in Figure 6a,b depict the concrete’s behavior in tension and compression, respectively. These curves are made up of an ascending and a descending (softening) branch, which represent the behavior of the material before and after reaching the peak stress. To enable the correct depiction and comprehension of the concrete’s behavior, the damage plasticity model’s characteristics were selected based on the research in [31]. This choice improves the model’s applicability and credibility in structural studies by making it possible to make trustworthy predictions about the actual performance.

5.2.2. Computation of Tensile and Compressive Stresses

The value of the single parameter d (scalar stiffness degradation variable), which ranges from 0 (undamaged state) to 1 (completely damaged state), was employed to model degradation as in Equation (1). Degradation was considered to be isotropic.

$${\sigma }_t=\frac{\left(1-d\right)\times D_0{}^{el}}{\epsilon -{\epsilon }^{pl}}=\frac{D^{el}}{\left(\epsilon -{\epsilon }^{pl}\right)\times \left(20\times a\right)}$$

(1)

$D_0{}^{el}$ is the concrete’s initial undamaged elastic stiffness, and $D^{el}$ = $\left(1-d\right)\times D_0{}^{el}$ is the concrete’s degraded elastic stiffness. The variable ${\epsilon }^{pl}$, which is connected to the microcracking and crushing process that concrete is considered to go through, indicates the corresponding plastic strains in tension or compression. These variables fundamentally regulate how the yield surface changes and how the elastic stiffness deteriorates.

5.3. Calibration of Control Model

The degradation seen becomes more pronounced as the plastic strain increases when unloading happens after entering the strain softening (descending) branch of the stress–strain curves depicting the concrete’s material behavior. The following crucial variables must be defined in the concrete damage plasticity model: (i) the angle of dilation ψ (i.e., the failure surface’s angle of inclination with reference to the hydrostatic axis), which governs the plastic flow, as well as (ii) the viscosity parameter [31].

A dense mesh of 3D brick (8-noded) components with an edge size of 45 mm was utilized to model the concrete medium [31]. Two-node single Gauss point truss elements inserted into the finite element mesh, simulating the concrete medium, were used to model reinforcement bars. Rigid elements were employed to apply displacement increments as the external load to FEM, which represented the RC part. These rigid components were utilized to evenly distribute the applied point loads or reaction forces and prevent the formation of high stress concentrations that could cause premature localized failure (at the supports or the location of the external load) and numerical instability. On the basis of the available experimental data, the crucial parameters used for completely defining the concrete damage plasticity model were calibrated [31]. The values of these parameters are listed in

Table 7. Parameters for concrete damage plasticity model in ABAQUS.

No.	Description	Value
1	Dilation angle, ψ	30
2	Eccentricity, ε	0.1
3	Stress ratio, σb0⁄σco	1.16
4	Shape factor, Kc	0.667
5	Viscosity parameter, v	0.001

. Once the static load reached a certain point, it was applied monotonically until displacement increments (displacement control) caused the failure. The damage plasticity model for concrete demonstrated promising potential based on the parameters presented in Table 7.

6. Comparison of Experimental and Numerical Results

The experimentally obtained load–deflection curves for the RC corbel specimens are shown in Figure 7a–c together with their numerically anticipated counterparts. The figure indicates that good correlations existed between the experimental and numerical results for the HS, LC, and LR specimens.

A local element coordinate system refers to a specific stress component (S33) and an inelastic strain component (IE33) in ABAQUS, version 2022. S33 is located along the z-axis, corresponding to the stress component in the axial direction. An example of this would be normal stress acting perpendicularly to a plane’s surface. IE33 is located along the z-axis (axial direction) in the local element coordinate system, corresponding to the inelastic strain component. The inelastic behavior of a plane causes irreversible deformation in the direction perpendicular to its surface.

Figure 8, Figure 9 and Figure 10 illustrate the comparisons of the predictions obtained from ABAQUS concerning the behavior of the specimens in the ultimate limit state. Figure 8a, Figure 9a and Figure 10a demonstrate the principal stress, i.e., S33, developing along the specimens, while Figure 8b, Figure 9b and Figure 10b indicate the associated principal inelastic strain, i.e., IE33, along the specimens. The positive values (+) for the primary stress and strain represent the tensile values, and the negative values (−) represent the compressive values. These figures revealed that the columns’ bases and the joints between the beams and columns had the highest levels of stress and strain. The degrees of the compression damage, i.e., DAMAGEC, experienced by concrete along the specimens are displayed in Figure 8c, Figure 9c and Figure 10c. Also, actively yields, i.e., AC YIELD, are presented in Figure 8d, Figure 9d and Figure 10d and the plastic strain magnitude, i.e., PEMAG, along the specimens are shown in Figure 8e, Figure 9e and Figure 10e.

7. Conclusions

This article experimentally and numerically studied RC corbels having construction defects. A total of 11 corbel specimens were tested, including HS, LC, LR, and MC specimens. The HS specimens were designed utilizing the ACI method. The specimens were tested under static loading conditions. A detailed FEM was developed employing ABAQUS. In addition, STM was investigated to assess the strengths of the specimens.

In the truss analogy, the failure concerns either yielding of steel reinforcement or crushing of the concrete struts. As per the experimental results, the shear capacity of the HS specimens was found to be higher than the LR and LC specimens, while the results of STM were also in close agreement with the experimental results.

In the experimental tests, the shear capacity of the HS specimens was 28.18% and 57.95% greater than the LR and LC specimens, respectively. Similarly, the moment capacity of the HS specimens was 25% and 57.52% higher than the LR and LC specimens, respectively. However, in the built-up sections, the shear capacity of the HS specimens was 9.91% and 37.51% greater than the LR and LC specimens, respectively. In addition, the moment capacity of the HS specimens was 39.91% and 14.30% higher than the LR and LC specimens, respectively. An increase in the reinforcement and compressive strength of concrete resulted in the increased capacity. The strength of concrete played a vital role in the struts, while the reinforcement ratio was a key parameter in the case of ties.

In the case of the LR specimens, the primary steel yielded before the failure of the concrete struts. The experimental values were consistent with the theoretical values using STM. Thus, the capacities calculated using STM were accurate and conservative. A reduction in the primary reinforcement led to the reduced shear capacity. For the MC specimens, the failure was governed by crushing of concrete from one side, thus demonstrating the brittle mode of failure.