Shear Strength Evaluation of Precast Concrete Beam-Column Joints Considering Key Influencing Parameters

Abstract

This study evaluates the shear strength of precast concrete beam–column joints using a Combined Model based on the ACI code, with implications for sustainable structural design. A database of 87 specimens from the existing literature was compiled and classified by prestressing condition and failure mode to examine key variables affecting prediction accuracy. The model demonstrated high reliability, with average predicted-to-test shear strength ratios (V_test/V_cal) of 1.12 for non-prestressed joints and 0.99 for prestressed joints, supporting more efficient and reliable use of precast systems. By identifying cross-sectional geometry as the dominant factor governing shear strength and failure mode, the study highlights opportunities to optimize material use, enhance structural safety, and reduce overdesign, thereby contributing to resource-efficient and sustainable construction practices.

1. Introduction

Precast concrete (PC) structures, which are assembled on-site from factory-prefabricated members, have gained significant attention as off-site construction (OSC) due to the various advantages provided over cast-in-situ structures, such as rapid construction, minimization of on-site work, enhanced quality and manageability, superior durability, and all-weather constructability [1,2]. PC technology has evolved through continuous research and development. Starting in the 1950s, some European countries adopted PC methods to accelerate post-war economic and infrastructure recovery, and by the 1960s, other developed nations were also actively developing PC techniques [3]. In Korea, PC technology is widely applied to certain structures such as large buildings like logistics centers and knowledge industry centers, as well as underground parking lots in multi-unit housing. Recently, its application to mid-rise and tall buildings (e.g., multi-unit housing) has been increasing, and related research is actively being conducted [4,5].

For cast-in-place structures with continuous monolithic connections between members, stability is ensured through leakage prevention, thermal insulation, and integrated member behavior. However, in precast concrete (PC) structures, failure to ensure precise joint design and construction leads to various problems such as water leakage, thermal bridging, and insufficient strength. Consequently, residents react sensitively to structural cracks, leakage, and thermal insulation issues. This led to high dissatisfaction with PC housing in Korea during the early 1990s [6]. Subsequently, interest in the PC industry waned, and design and construction standards have not been developed for a certain period [7]. Moreover, unlike structures built using conventional cast-in-place methods, PC joints employ wet or mechanical connections, making joint design relatively complex. This complexity has limited the widespread application of PC structures until recently. Meanwhile, as the importance of seismic design gradually increased and related design standards were strengthened, there was a demand for member details, analysis techniques, and design methods capable of overcoming the inherent limitations of PC structures. However, the recent construction industry downturn, aging populations in developed countries (leading to a shortage of construction site labor [8]), and rising material prices have led to a re-evaluation of the PC structures as the OSC. Consequently, initiatives to revise the long-neglected design standards are now emerging. Seismic design is essential for constructing PC buildings such as apartment complexes. However, because design standards for PC structures have not been consistently updated, there remains room for improvement in the performance evaluation of joints for seismic design [9].

Joints play a crucial role in efficiently transferring forces between members, and they should be carefully considered during the seismic design process to ensure structural safety. In particular, beam-column joints are vulnerable to cyclic loads such as seismic forces, necessitating extensive research and development. The quality of these joints determines the overall performance and condition of the structure. Unlike conventional cast-in-place concrete joints, the PC joint connection utilizes prefabricated members on-site. By introducing high-quality field-produced PC members and prestressing techniques to control cracking and ensuring member integrity through detailed joint design, PC joints can achieve performance comparable to RC joints. Therefore, many researchers have proposed various connection methods—wet, dry, prestressed, hybrid—to investigate the behavior of diverse PC beam-column connections, ensure their ductility, and enhance seismic performance [10].

Ma et al. [11] proposed an internal beam-column wet connection method utilizing the excellent bonding and tensile properties of Ultra-High-Performance Concrete (UHPC). This study experimentally verified that even with significantly shorter lap lengths than conventional concrete (15d_b for straight bars, 11d_b for hook bars), the yield strength of the bars could be fully utilized. It also confirmed that UHPC significantly enhances the shear capacity of the joint, effectively reducing joint damage. Zhang et al. [12] proposed a dry joint method to minimize on-site casting, accelerate construction speed, and facilitate member replacement. Experiments on fully dry joints, where steel connectors are bolted between beams and columns, demonstrated that the steel connectors sufficiently transfer bending moments. Wada et al. [13] devised the ‘P/C MILD-PRESS-JOINT’ system, combining the compressive force from prestressing with the energy dissipation capacity of conventional steel bars, and conducted experimental studies on this system. This study proposed a joint method that induces origin-oriented behavior and minimizes residual deformation through post-tensioning with unbonded tendons, even when deformation occurs due to lateral loads. It demonstrated damage control performance where the damage in the specimen was observed solely at the beam-column joint interface. Yang et al. [14] introduced prestressing locally only in the beam-column joint area for construction efficiency and proposed a hybrid joint method combining metal fittings installation, high-strength PT bars, and grouting at the joint surface. The proposed joint method demonstrated seismic performance equivalent to that of cast-in-place concrete structures through experiments.

Kim et al. [15] investigated the shear strength of precast concrete beam–column joints by developing and validating a data-driven prediction approach based on an experimental database collected from the existing literature. A convolutional neural network (CNN)-based model is proposed to predict joint shear strength and is compared with conventional code-based methods, demonstrating improved prediction accuracy and reduced dispersion. The results highlight the dominant role of joint geometry and reinforcement characteristics in shear resistance and suggest that data-driven models can complement existing design codes by providing more reliable shear strength evaluations for precast beam–column joints in seismic design.

Past studies have established that precast concrete (PC) structures offer significant advantages over cast-in-place systems in construction speed, quality control, and labor efficiency, but have also identified beam–column joints as the critical factor governing structural and seismic performance. Early applications revealed problems such as leakage, cracking, and insufficient joint strength, leading to limited adoption and delayed development of design standards. Recent research has advanced PC joint technology through the use of UHPC wet joints, fully dry mechanical connections, and prestressed or hybrid systems, demonstrating that properly detailed PC joints can achieve strength, ductility, and seismic performance comparable to monolithic RC joints, with added benefits such as reduced damage and self-centering behavior. In parallel, data-driven approaches, such as machine-learning-based shear strength prediction models, have shown improved accuracy over conventional code equations. However, despite extensive experimental work on joint details, systematic evaluation of joint shear strength remains limited, particularly for prestressed and newly developed connection systems, and the applicability of ACI-based joint shear strength provisions—originally developed for cast-in-place RC joints—to modern PC joints remains uncertain, highlighting the need for further validation and refinement of seismic design criteria.

In addition, numerous studies have proposed various joint details and verified them through experiments [16,17]. However, research on evaluating the shear strength of the joints remains relatively scarce to date. While the shear strength of joints can be evaluated using the structural design criteria in the current standards, it is necessary to consider whether the joint strength equations specified in the standards are suitable for newly developed joint details. The American Concrete Institute (ACI) code [18,19] serves as the foundation for design codes in many countries, including KDS 14 20 of Korea. Therefore, this study aims to evaluate the shear strength of PC joints using the ACI code, based on an experimental database of precast concrete beam-column joints collected from the literature [18].

Despite extensive experimental studies on precast concrete beam–column joint details, the shear strength of PC joints—especially those with prestressing and newly developed connection systems—has not been sufficiently evaluated, and the applicability of ACI-based joint shear strength equations remains uncertain. This study aims to assess the accuracy and suitability of ACI code–based shear strength models for precast concrete beam–column joints using a comprehensive experimental database, and to identify key variables influencing joint shear strength and failure behavior for improved seismic design.

2. Theoretical Background of Joint Shear Strength

2.1. Nominal Shear Strength in the ACI Code

ACI 352R-02 [19], which provides design guidelines for reinforced concrete beam-column joints, defines the shear strength of the joint as follows:

$$V_j=0.083\gamma \sqrt{f_{ck}}{b}_j{h}_c$$

(1)

where f_ck is the compressive strength of cylinder concrete, h_c is the depth of the column in the direction of joint shear being considered. γ is the shear strength factor reflecting confinement of the joint by lateral members that takes into account non-seismic zones (Type 1) and seismic zones (Type 2) based on the classification of the joint connection. In addition, as shown in Figure 1, the effective joint width (b_j) can be calculated as follows:

$$b_j=\min ({\displaystyle \frac{b_b+b_c}{2}},b_b+{\displaystyle \sum \frac{m{h}_c}{2},b_c)}$$

(2)

where b_b and b_c are the widths of the beam and column sections, respectively. For joints where the eccentricity between the beam centerline and the column centroid exceeds b_c/8, m = 0.3 should be used; for all other cases, m = 0.5. The summation term should be applied on each side of the joint where the edge of the column extends beyond the edge of the beam. The value of mh_c/2 should not be taken larger than the extension of the column beyond the edge of the beam.

As shown in Figure 2, the horizontal shear force (V_jby) at the yield point of the main reinforcement of the beam can be calculated according to the internal and external beam-column joints, as follows:

$$V_{jby}=({\displaystyle \frac{l_c}{z_b}}-1)V_{by}{\displaystyle \frac{L_b}{l_c}}-{\displaystyle \frac{h_c}{z_b}}{V}_{by}$$

(3)

$$V_{jby}=({\displaystyle \frac{l_c}{z_b}}-1)V_{by}{\displaystyle \frac{2l_b+h_c}{2l_c}}$$

(4)

where l_c is the height of the column, l_b is the length from the adjacent face of the joint to support point of the beam, L_b is the total length of the beam at both ends at the internal joint, z_b is the spacing between the upper and lower reinforcement bars of the beam, and V_by is the vertical shear force in the beam when the main reinforcement yields, calculated as follows:

$$V_{by}={\displaystyle \frac{\min (M_{b1},M_{b2})}{a}}$$

(5)

Under cyclic loading, the positions of the compression and tension zones in the beam cross-section may differ depending on positive and negative moments, as shown in Figure 3. Therefore, V_by is determined as the smaller value of the bending moments (M_b1, M_b2) in the beam cross-section from Equation (5).

By comparing Equation (1) for $V_j$ and Equations (3) and (4) for $V_{jby}$, the smaller value is considered the shear strength of the beam-column joint. That is, in the case of $V_j<V_{jby}$, the shear force acting before plastic hinging occurs in the beam exceeds the joint strength, causing failure at the joint (J Failure). Conversely, when $V_j\ge V_{jby}$, as shown in Figure 4, the main reinforcement in the beam yields, and the plastic hinge formed in the beam determines the joint strength. However, the final failure mode in this case can again be divided into two types—BJ and B failures. BJ Failure occurs when the deformation of the beam propagates into the joint after a plastic hinge forms in the beam, ultimately causing failure at the joint. B Failure occurs when the deformation of the joint does not reach the failure point, and failure occurs solely in the beam. It is quite difficult to accurately distinguish the B and BJ failures. Therefore, this study aims to establish a database of beam-column joint specimens from the literature to identify valid variables affecting the failure mode.

2.2. Shear Friction Mechanism for Connections

The precast concrete beam-column joints feature a joint surface between members at the connection or concrete splice. Birkeland and Mattock [20] demonstrated that the degree of roughness on the joint surface causes sliding and separation along the vertical plane between the beam and column. This mechanism explains shear friction by the concept that tensile forces acting on the through-reinforcing bars compress the joint surface. Based on this concept, ACI 318 [18] defines the shear strength (V_nf) due to shear friction bars as follows:

$$V_{nf}=\mu A_{vf}{f}_y$$

(6)

where μ is the coefficient of friction, determined by the condition of the joint surface, A_vf is the cross-sectional area of the reinforcing bar assumed for shear resistance across the shear plane, and f_y is the yield strength of the reinforcing bar.

As presented in Figure 5, slippage at the joint interface between precast concrete beams and columns may cause the interface to separate owing to surface roughness between the members. Due to the nature of precast members, the surfaces undergo a process of smooth finishing during the factory manufacturing process. Therefore, if the concrete surface has no residual material and has not been intentionally roughened, a friction coefficient (μ) of 0.6 can be applied as specified in ACI 318.

2.3. Influence of Prestressing

When manufacturing precast concrete members in a factory, typically, the prestressing is applied to the members, which presents a favorable effect in crack control. Furthermore, when post-tensioning is introduced for connections between the members, a self-centering effect can be achieved. To design with the benefits of prestressing, it is required to accurately predict the performance of the PC joints considering the prestressing effect. When post-tensioning is applied with tendons penetrating the beam-column joint, a confinement effect on the joint can be expected, increasing the shear strength of the joint. However, Equation (1) presented in ACI 352R-02 does not account for this confinement effect. Therefore, the web-shear cracking mechanism can be applied to determine the joint strength incorporating the confinement [19].

From Mohr’s stress circle shown in Figure 6, the tensile strength (f_t) and shear strength (ν) with horizontal prestress can be derived as follows:

$$f_t=\sqrt{v^2+{\left({\displaystyle \frac{f_{pc}}{2}}\right)}^2}-\left({\displaystyle \frac{f_{pc}}{2}}\right)$$

(7)

$$v=f_t\sqrt{1+{\displaystyle \frac{f_{pc}}{f_t}}}$$

(8)

where f_pc is the compressive stress in concrete, after allowance for all prestress losses, at centroid of cross section resisting externally applied loads or at junction of web and flange where the centroid lies within the flange according to ACI 318-25 [18] and f_t is the tensile strength of concrete at the beam-column joint. The joint shear strength in Equation (1), as specified in the ACI code, was applied to determine f_t as $0.083\gamma \sqrt{f_{j,ck}}$ where f_j,ck is the compressive strength of concrete at the joint. Furthermore, although the prestressing strands do not penetrate the joint, precluding consideration of the web shear cracking effect at the joint, the prestressing effect of the tendons was reflected in the calculation of the nominal moment according to Equation (5) for the beams reinforced by the strands. Here, the tensile strength (f_ps) of the tendons at the nominal flexural strength of the section is determined as follows:

$$f_{ps}=\left\{\begin{array}{c}{f}_{pe}+f_y\\ 0.9f_{pu}\end{array}\right.\begin{array}{c}\mathrm{for} \mathrm{partially} \mathrm{prestressed} \mathrm{member}\\ \mathrm{for} \mathrm{fully} \mathrm{prestressed} \mathrm{member}\end{array}$$

(9)

where f_y is the yield strength of the reinforcing steel, f_pu is the tensile strength, and f_pe is the effective prestress of the tendons, for which 0.7f_pu was applied. Additionally, for simplified calculations, the tensile strength (f_ps,u) of the unbonded tendons at the nominal flexural strength of the section was assumed to be 0.5 f_ps.

2.4. Combined Model for the Shear Strength of PC Beam-Column Joints

The shear strength (V_j) of precast concrete beam-column joints considering the influence of prestressing is determined as follows:

$$V_j=f_t\sqrt{1+{\displaystyle \frac{f_{pc}}{f_t}}}{b}_j{h}_c$$

(10)

where

$$f_{pc}={\displaystyle \frac{f_{pe}{A}_{ps}}{A_c}}$$

(11)

In addition, the horizontal shear strength (V_jby) determined by the yield and shear friction is calculated as follows:

$$V_{jb}=\left\{\begin{array}{c}({\displaystyle \frac{l_c}{z_b}}-1)V_b{\displaystyle \frac{L_b}{l_c}}-{\displaystyle \frac{h_c}{z_b}}{V}_b\\ ({\displaystyle \frac{l_c}{z_b}}-1)V_b{\displaystyle \frac{2l_b+h_c}{2l_c}}\end{array}\right.\begin{array}{c}\begin{array}{l}\mathrm{for} \mathrm{internal} \mathrm{joints}\\ \end{array}\\ \mathrm{for} \mathrm{external} \mathrm{joints}\end{array}$$

(12)

$$V_b=\min (V_{by},V_f)=\min ({\displaystyle \frac{\min (M_{b1},M_{b2})}{a}},\mu A_{vf}{f}_y)$$

(13)

3. Experimental Database

3.1. Data Collection Criteria

In this study, a database was constructed by collecting extensive experimental data from the literature to evaluate the shear strength of PC beam-column joints based on the ACI codes. Here, Equations (9)–(13) were applied to evaluate the shear strength and distinguish the failure modes of PC joints, to analyze the influencing variables. To ensure the accuracy and reliability of the analysis, the following selection criteria were applied to the collected data:

First, the study selected only specimens where the presence or absence of prestressing, which significantly affects joint behavior, was clearly defined. In this context, specimens without prestressing and those with prestressing applied only to the beam without penetrating the joint were regarded as Non-Prestressed specimens. In Equation (10), when prestressing does not penetrate the joint, no restraining force acts on the joint. That is, with $f_{pc}=0$, the V_j calculation formula becomes identical to Equation (1) presented in the ACI code.

Second, the study selected specimens from the experimental research literature exhibiting identifiable failure modes to enable analysis of the shear failure behavior of the specimens. While J Failure can be predicted using shear strength calculation models, the criteria for B/BJ Failure remain unclear. Therefore, confirming the presence or absence of a failure mode is essential for identifying influential variables in distinguishing failure modes.

Third, the literature containing all detailed information on the test specimens was considered, and the data were collected for the calculation of the theoretical shear strength (V_cal). The literature includes the geometric dimensions of the members, detailed reinforcement arrangements, material strengths of concrete and reinforcement, detailed drawings of joints, test settings, and load protocols.

Fourth, only cases where the shear strength (V_test) obtained experimentally was clearly defined were included in the database for the validation of the Combined Model. In cases where the load on the actuator was documented in the literature, the load was converted to the shear strength (V_test) of the joint, considering the experimental setting.

Meanwhile, joint details out of the scope of this study were excluded. Specifically, specimens employing welding or bolted joints—where the stress mechanism was activated by wet bonding or differed from typical PC bonding—were excluded during database construction.

3.2. Classification of the Database

A total of 87 PC beam-column joint specimens were collected through the selection criteria. To thoroughly verify the applicability of the Combined Model, the specimens were classified according to two main criteria: (1) the presence or absence of prestressing, and (2) the failure mode, as shown in Table 1.

(1)

Classification by Prestressing Condition

To verify the accuracy of the joint shear strength evaluation in Equation (10), which is based on the joint calculation formula presented in the ACI code and incorporates the web-shear cracking mechanism considering prestressing effects, the collected specimens include 62 non-prestressed specimens and 25 prestressed specimens. The number of Prestressed specimens is somewhat smaller than that of Non-Prestressed specimens. For more accurate analysis, supplementary literature collection is required in the future.

(2)

Classification by Failure Mode

Test specimens were classified into three failure modes. For J Failure, as previously explained, the joint failure can be predicted using an equation, making this failure mode suitable for verifying the prediction accuracy of the shear strength (V_cal). B Failure occurs when the capacity of the beam is exhausted before the capacity of the joints, allowing the verification of whether the experimentally measured shear strength can be accurately evaluated using Equation (12). Finally, BJ Failure is difficult to determine using Equations (10) and (12), which define J Failure and B Failure. Therefore, BJ Failure is used to evaluate the rationality of the theoretical shear strength equation based on the failure modes reported in experimental research literature.

Table 1. Classification of the database by prestressed condition and failure modes.

	J Failure	BJ Failure	B Failure	Total
Non-Prestressed	15	23	24	62
Prestressed	12	3	10	25
Total	27	26	34	87

Table 1. Classification of the database by prestressed condition and failure modes.

	J Failure	BJ Failure	B Failure	Total
Non-Prestressed	15	23	24	62
Prestressed	12	3	10	25
Total	27	26	34	87

3.3. Range of Parameters

The constructed database is summarized in

Table 2. Detailed specification and results of the database.

Author(s)	Specimens	ST	Joint Type	PS	fj,ck (MPa)	fb,ck (MPa)	lc (mm)	lb (mm)	hc (mm)	bc (mm)	hb (mm)	bb (mm)	d/a	ρb	Vj/Vjby	Vtest/Vcal	Failure Mode of the Specimen
Parastesh et al. [21]	BCT2	PC	Ext	N-PS	24	25	2900	2150	400	400	450	400	0.173	0.0081	2.56	1.67	BJ Failure
	BCT3	PC	Ext	N-PS	25	27	2900	2150	400	400	450	400	0.173	0.0079	2.61	1.78	BJ Failure
	BCT4	PC	Ext	N-PS	23	22	2900	2150	400	400	450	400	0.173	0.0083	2.5	1.7	BJ Failure
	BC2	PC	Int	N-PS	27	25	2900	2150	400	400	450	400	0.173	0.0081	2.01	1.33	BJ Failure
	BC3	PC	Int	N-PS	25	27	2900	2150	400	400	450	400	0.173	0.0079	1.93	1.38	BJ Failure
	BC4	PC	Int	N-PS	28	22	2900	2150	400	400	450	400	0.173	0.0083	2.04	1.32	BJ Failure
Guan et al. (2016) [22]	SP1	PC	Int	N-PS	34.2	41.4	1950	1700	550	550	550	300	0.162	0.0091	3.21	0.99	B Failure
	SP2	PC	Int	N-PS	34.2	41.4	1950	1700	550	550	550	300	0.162	0.0091	3.21	0.94	B Failure
	SP3	PC	Int	N-PS	34.2	41.4	1950	1700	550	550	550	300	0.162	0.0091	3.21	0.95	B Failure
	SP4	PC	Int	N-PS	34.2	41.4	1950	1700	550	550	550	300	0.162	0.0091	3.21	0.86	B Failure
Hosoya et al. (2012) [23]	No2	PC	Int	N-PS	77.1	57.4	1320	1150	400	400	360	300	0.227	0.0236	1.54	1.04	BJ Failure
	No3	PC	Int	N-PS	77.1	57.4	1320	1150	400	400	360	300	0.227	0.0236	1.54	1.06	BJ Failure
	No4	PC	Int	N-PS	77.1	57.4	1320	1150	400	400	360	300	0.227	0.0236	1.54	1.06	BJ Failure
	No6	PC	Int	N-PS	118.8	78.4	1320	1150	400	400	360	300	0.227	0.0317	1.39	0.94	BJ Failure
	No8	PC	Int	N-PS	77.1	57.4	1320	1150	400	400	360	300	0.227	0.0236	1.54	1.11	B Failure
Ha et al. (2014) [24]	S3-1	PC	Int	N-PS	28.1	34.1	1680	1600	400	400	400	300	0.124	0.0231	1.35	1.2	BJ Failure
	S3-2	PC	Int	N-PS	28.1	34.1	1680	1600	400	400	400	300	0.124	0.0244	1.35	1.25	BJ Failure
	S3-3	PC	Int	N-PS	28.1	34.1	1680	1600	400	400	400	300	0.124	0.0244	1.35	1.22	BJ Failure
	S4-1	PC	Ext	N-PS	28.1	34.1	1680	2180	400	400	400	300	0.124	0.0244	1.32	0.5	B Failure
	S4-2	PC	Ext	N-PS	28.1	34.1	1680	2180	400	400	400	300	0.124	0.0244	1.32	0.71	B Failure
	B4-1	PC	Ext	N-PS	28.1	34.1	1680	2180	400	400	400	300	0.169	0.0251	0.97	0.32	B Failure
Yan et al. (2018) [25]	P1	PC	Int	N-PS	39.63	32.03	2150	1350	300	300	400	200	0.126	0.0062	2.82	1.16	J Failure
	P2	PC	Int	N-PS	39.63	32.03	2150	1350	300	300	350	200	0.126	0.0059	3.07	1.16	BJ Failure
	P3	PC	Int	N-PS	39.63	32.03	2150	1350	300	300	300	200	0.126	0.006	3.28	1.22	BJ Failure
	P4	PC	Int	N-PS	39.63	32.03	2150	1350	300	300	350	200	0.126	0.0059	3.07	1.23	B Failure
	P5	PC	Int	N-PS	39.63	32.03	2150	1350	300	300	350	200	0.126	0.0059	3.07	1.19	B Failure
Lee et al. (2014) [26]	PCBC1	PC	Int	N-PS	35.2	35.2	2600	1869	762	350	700	250	0.118	0.0158	2.28	1.04	J Failure
	PCBC2	PC	Int	N-PS	35.2	35.5	2600	1869	762	350	700	250	0.118	0.0157	2.3	1.06	BJ Failure
	PCBC3	PC	Int	N-PS	36.5	36.5	2600	1869	762	350	700	250	0.118	0.0157	2.33	0.86	BJ Failure
Im et al. (2010) [27]	SP1	PC	Int	N-PS	34.9	35.1	2700	2006	750	600	700	400	0.172	0.0262	1.15	0.84	BJ Failure
	SP2	PC	Int	N-PS	34.9	35.1	2700	2006	750	600	700	400	0.172	0.0262	1.15	0.82	BJ Failure
	SP3	PC	Int	N-PS	34.9	35.1	2700	2006	750	600	700	400	0.172	0.0262	1.15	0.85	BJ Failure
	SP4	PC	Int	N-PS	34.9	35.1	2700	2006	750	600	700	400	0.172	0.0262	1.15	0.76	BJ Failure
	SP5	PC	Int	N-PS	34.9	35.1	2700	2006	750	600	700	400	0.172	0.0262	1.15	1.05	BJ Failure
Masuda and Sugimoto (2008) [28]	LRV1-N	PC	Ext	N-PS	52.9	44.6	2100	1250	400	400	400	300	0.204	0.022	1.45	0.93	BJ Failure
	LRV2-N	PC	Ext	N-PS	54.3	45.4	2100	1250	400	400	400	300	0.204	0.0219	1.47	0.87	B Failure
Chen et al. (2023) [29]	EPC2	PC	Ext	N-PS	35.2	35.2	1980	1075	250	250	280	150	0.117	0.0144	2.09	1.66	B Failure
	EPC4	PC	Ext	N-PS	35.2	35.2	1980	1075	250	250	280	150	0.117	0.0144	2.09	2.47	B Failure
	EPCD2	PC	Ext	N-PS	35.2	35.2	1980	1075	250	250	280	150	0.117	0.0144	2.09	2.12	B Failure
	EPCD4	PC	Ext	N-PS	35.2	35.2	1980	1075	250	250	280	150	0.117	0.0144	2.09	2.88	B Failure
	IPC2	PC	Int	N-PS	35.2	35.2	1980	1075	250	250	280	150	0.117	0.0144	1.58	1.45	B Failure
	IPC4	PC	Int	N-PS	35.2	35.2	1980	1075	250	250	280	150	0.117	0.0144	1.58	1.7	B Failure
	IPCD2	PC	Int	N-PS	35.2	35.2	1980	1075	250	250	280	150	0.117	0.0144	1.58	1.39	J Failure
	IPCD4	PC	Int	N-PS	35.2	35.2	1980	1075	250	250	280	150	0.117	0.0144	1.58	1.78	J Failure
Zhang et al. (2021) [30]	PJ1	PC	Int	N-PS	45.9	40	2550	1700	400	400	450	250	0.15	0.0097	2.07	0.89	B Failure
	PJ2	PC	Int	N-PS	45.9	40	2550	1700	400	400	450	250	0.15	0.0209	1.09	0.66	J Failure
	PJ3	PC	Int	N-PS	45.9	40	2550	1700	400	400	450	250	0.15	0.0209	1.09	0.55	J Failure
Liu et al. (2024) [31]	PCCT	PC	Ext	N-PS	33.9	33.9	1800	1300	400	400	400	250	0.174	0.0078	3.89	1.08	B Failure
	PCTO	PC	Ext	N-PS	33.9	33.9	1800	1300	400	400	400	250	0.174	0.0089	3.8	0.95	B Failure
Chen et al. (2025) [32]	PC2	PC	Int	N-PS	55.6	55.6	2600	1550	400	400	500	300	0.204	0.0305	0.74	0.82	J Failure
	PC3	PC	Int	N-PS	66.4	66.4	2600	1550	400	400	500	300	0.204	0.0293	0.81	0.68	J Failure
	PC4	PC	Int	N-PS	55.6	55.6	2600	1550	400	400	500	300	0.204	0.0305	0.74	0.84	J Failure
	PC5	PC	Int	N-PS	55.6	55.6	2600	1550	400	400	500	300	0.204	0.0305	0.74	0.89	J Failure
	PC6	PC	Int	N-PS	55.6	55.6	2600	1550	400	400	500	300	0.204	0.0305	0.74	0.86	J Failure
Yang et al. (2024) [14]	SP-1	PC	Int	PS	44.7	44.7	3095	3000	600	600	600	400	0.139	0.0067	3.43	1.44	B Failure
	SP-2	PC	Int	PS	40	40	3095	3000	600	600	600	400	0.139	0.007	3.46	1.42	B Failure
	SP-3	PC	Int	PS	47.3	47.3	3095	3000	600	600	600	400	0.139	0.0065	3.37	1.35	B Failure
	SP-4	PC	Int	PS	41.7	41.7	3095	3000	600	600	600	400	0.139	0.0069	3.32	1.4	B Failure
	PC-1	PC	Int	PS	44.3	44.3	3095	3000	600	600	600	400	0.139	0.0067	3.41	1.38	B Failure
Ma et al. (2021) [11]	RUJ-2	PC	Int	N-PS	86.48	35.2	2280	1650	300	300	300	230	0.142	0.0103	2.55	0.83	B Failure
	RUJ-3	PC	Int	N-PS	86.48	35.2	2280	1650	300	300	300	230	0.142	0.0276	1.2	0.81	J Failure
	RUJ-4	PC	Int	N-PS	86.48	35.2	2280	1650	300	300	300	230	0.142	0.0276	1.23	0.78	J Failure
	RUJ-5	PC	Int	N-PS	86.48	35.2	2280	1650	300	300	300	230	0.142	0.0276	1.2	0.8	J Failure
	RUJ-6	PC	Int	N-PS	86.48	35.2	2280	1650	300	300	300	230	0.142	0.0276	1.2	0.83	B Failure
Yue et al. (2004) [33]	KPC1-1	PC	Ext	PS	30	30	1900	2100	250	250	300	200	0.142	0.0259	0.5	0.99	J Failure
	KPC1-2	PC	Ext	PS	30	30	1900	2100	250	250	300	200	0.142	0.0265	0.5	0.95	J Failure
	KPC2-1	PC	Ext	PS	30	30	1900	2100	250	250	300	200	0.142	0.0154	0.45	0.72	J Failure
	KPC2-2	PC	Ext	PS	30	30	1900	2100	250	250	300	200	0.142	0.016	0.46	0.71	J Failure
	KPC2-3	PC	Ext	PS	30	30	1900	2100	250	250	300	200	0.142	0.0154	0.45	0.71	J Failure
	KPC3	PC	Ext	PS	30	30	1900	2100	250	250	300	200	0.142	0.0142	0.43	1	J Failure
Kim et al. (2021) [34]	NMUP	PC	Int	PS	41.9	34.1	3545	3600	700	700	700	500	0.125	0.0091	2.57	1.17	B Failure
	NMOP	PC	Int	PS	41.9	34.1	3545	3600	700	700	700	500	0.125	0.0058	3.52	1.08	BJ Failure
Hamahara et al. (2007) [35]	A-PC1	PC	Ext	PS	23.5	23.5	2500	4000	500	500	600	400	0.116	0.0495	0.4	1.58	J Failure
	A-PC2	PC	Ext	PS	23.9	23.9	2500	4000	500	500	600	400	0.116	0.0497	0.4	1.78	BJ Failure
	B-PC1	PC	Ext	PS	26.3	26.3	2900	4000	550	500	600	400	0.117	0.0438	0.48	0.86	J Failure
	B-PC2	PC	Ext	PS	28.8	28.8	2900	4000	550	500	600	400	0.117	0.0446	0.49	0.95	J Failure
	B-PC3	PC	Ext	PS	30.4	30.4	2900	4000	550	500	600	400	0.117	0.0451	0.5	0.97	J Failure
	C-PC1	PC	Ext	PS	29.8	29.8	2900	4000	550	500	600	400	0.117	0.0331	0.6	0.61	J Failure
	C-PC2	PC	Ext	PS	31	31	2900	4000	550	500	600	400	0.117	0.0332	0.59	0.72	BJ Failure
	C-PC3	PC	Ext	PS	31.1	31.1	2900	4000	550	500	600	400	0.117	0.0332	0.6	0.66	J Failure
Wang et al. (2023) [36]	PTHC-1	PC	Ext	PS	41.22	41.22	2846	2475	400	400	400	250	0.123	0.015	1.71	0.5	B Failure
	PTHC-2	PC	Ext	PS	41.22	41.22	2846	2475	400	400	400	250	0.123	0.015	1.71	0.57	B Failure
	PTHC-3	PC	Ext	PS	45.75	45.75	2846	2475	400	400	400	250	0.123	0.0146	1.79	0.61	B Failure
	PTHC-4	PC	Ext	PS	46.55	46.55	2846	2475	400	400	400	250	0.123	0.0145	1.81	0.73	B Failure
Zhang et al. (2022) [12]	PJ	PC	Ext	N-PS	37.8	37.8	3000	2500	500	500	500	300	0.159	0.0123	2.11	1.02	B Failure
Restrepo et al. (1995) [37]	Unit6	PC	Int	N-PS	44	44	2800	1605	600	450	700	300	0.161	0.0073	3.29	0.98	B Failure
Kim (2020) [38]	PCB	PC	Int	N-PS	40	40	2490	1750	500	500	400	400	0.2	0.0085	2.18	1.31	J Failure

Note: ST: structure, Int: interior, Ext: exterior, N-PS: Non-Prestressed, PS: Prestressed, f_j,ck: compressive strength of the cylinder concrete of the joint, f_b,ck: compressive strength of the cylinder concrete of the beam, h_c: depth of the column in the direction of joint shear being considered, b_c: widths of the column, h_b: depth of the beam, b_b: widths of the beam, ρ_b: longitudinal reinforcement ratio, l_c: height of the column, l_b: length, d/a: shear span ratio.

, and the values of various design variables are presented as maximum, minimum, and average values in

Table 3. Range of parameters in the database.

	fj,ck	fb,ck	hc	bc	hb	bb	bj	ρb	lc	lb	d/a
	(Mpa)	(Mpa)	(mm)	(mm)	(mm)	(mm)	(mm)		(mm)	(mm)
Max	118.8	78.4	762	700	700	700	600	0.0497	3545	4000	0.409
Min	23	22	250	280	280	250	200	0.0058	1320	1075	0.170
Mean	42.4	37.7	439.5	411.5	457.5	411.5	355.5	0.018	2363.9	2174.7	0.245

Note: f_j,ck: compressive strength of the cylinder concrete of the joint, f_b,ck: compressive strength of the cylinder concrete of the beam, h_c: depth of the column in the direction of joint shear being considered, b_c: widths of the column, h_b: depth of the beam, b_b: widths of the beam, b_j: effective joint width, ρ_b: longitudinal reinforcement ratio, l_c: height of the column, l_b: length, d/a: shear span ratio.

. The concrete compressive strength at the PC beam-column joint may vary depending on the joint method, influencing both the beam and joint concrete compressive strength. First, the concrete compressive strength of the beam (f_b,ck) ranges from 22 MPa to 78.4 MPa, encompassing data from normal-strength concrete to high-strength concrete. The average value is 37.7 MPa, with most concrete compressive strengths being 40 MPa or below. The concrete compressive strength of the joint (f_j,ck) ranges from 118.8 MPa to 23 MPa, encompassing data from normal-strength to high-strength concrete. The average value is 42.4 MPa, higher than the concrete compressive strength of the beam (f_b,ck). It suggests an effort to increase joint strength and reduce joint damage. The range of beam and column cross-sectional sizes includes specimens from small sizes up to medium and large sizes close to actual structural dimensions. The shear strength of the beam (V_jb) is calculated as a function of the main reinforcement of the beam as presented in Equation (12). The range of the main reinforcement ratio (ρ_b) for beams is from 0.006 to 0.05, with an average value of 0.018, which falls between the minimum and maximum reinforcement ratios. The ranges for the total column height (l_c) and beam length (l_b) of the beam-column joint specimens are 1.3 m to 3.5 m and 1.0 m to 4.0 m, respectively. Furthermore, the shear span ratio (d/a) varies from 0.17 to 0.409. Therefore, the constructed database is deemed sufficient to evaluate the shear strength of the joint from multiple perspectives, as the key variables are distributed over a wide range.

4. Results and Discussion

A database was utilized for the evaluation of the shear strength of PC beam-column joints based on the ACI code and for determining the influence of various design variables on different failure modes. This section evaluates the predictive performance of the Combined Model for PC beam–column joint shear strength and examines the influence of key design variables on both shear capacity and failure mode. Particular emphasis is placed on identifying systematic trends, limitations of the current formulation, and implications for joint design.

The effect of each design variable on shear strength, depending on the presence or absence of prestressing, is shown in Figure 7. Calculating the Non-Prestressed and Prestressed specimens using the Combined Model presented average V_test/V_cal values of 1.12 and 0.99, respectively. The results indicate the model accurately predicts the shear strength of the specimens. While the trends were similar, the Prestressed specimens, which reflect the confinement effect of the joint, were evaluated with slightly higher accuracy. This suggests that the behavior of members with prestressing is more stable in achieving their performance, and the evaluation model predicts the behavior more accurately. The shear strength evaluation results for each key variable shown in Figure 7 can be summarized as follows:

①

As shown in Figure 7a, the shear strength was generally evaluated on the safe side (V_test/V_cal > 1) in the range where the concrete compressive strength (f_b,ck) was 40 MPa or less; however, the data dispersion is significantly large.

②

For the reinforcement ratio (ρ_b), in the low reinforcement ratio range (<1.5% or 0.0015), data points show a very conservative V_test/V_cal value of 2 or higher, and most fall on the safe side (V_test/V_cal > 1). Data with reinforcement ratios of 2% or higher tend to show V_test/V_cal values falling below 1, indicating a potential tendency to somewhat overestimate the shear strength of members with high reinforcement ratios.

③

All variables related to cross-sectional dimensions (b_c, h_c, b_b, h_b, b_j) show a similar trend. The variables predict a large shear strength compared to experimental values for small cross-sections, indicating a very conservative approach. As the cross-section increases, the safety margin tends to decrease. For columns, test specimens were generally close to square (i.e., $b_c\approx h_c$ and smaller column sizes tended to underestimate the shear strength at the joint. For beams, specimens with h_b larger than b_b were more common. Unlike columns, no distinct trend emerged for beams; underestimation of shear strength occurred for small beams and for relatively large beams around h_b = 600 mm and b_b = 400 mm.

Figure 7. Distribution of V_test/V_cal ratio by major design variables based on prestressed condition: (a) f_ck; (b) ρ_b; (c) h_b; (d) b_b; (e) h_c; (f) b_c; (g) b_j; (h) d/a; (i) l_c; (j) l_b.

Figure 7. Distribution of V_test/V_cal ratio by major design variables based on prestressed condition: (a) f_ck; (b) ρ_b; (c) h_b; (d) b_b; (e) h_c; (f) b_c; (g) b_j; (h) d/a; (i) l_c; (j) l_b.

Although the average prediction accuracy of the Combined Model is satisfactory, the dispersion of V_test/V_cal. indicates that joint shear behavior is influenced by multiple inter-acting mechanisms that are not fully represented by a single deterministic equation. In particular, the scatter observed in non-prestressed specimens reflects the sensitivity of joint performance to cracking patterns, reinforcement anchorage conditions, and local damage accumulation, which vary significantly among experimental setups. This disper-sion highlights the inherent uncertainty associated with joint shear resistance and suggests that mean accuracy alone is insufficient to fully evaluate model reliability.

The pronounced conservatism observed for specimens with relatively small beam and joint cross-sections can be attributed to the dominance of arching action and confinement effects that are not explicitly quantified in the ACI-based formulation. In small sections, stress trajectories tend to be shorter and more direct, allowing shear forces to be transferred efficiently through compression struts. As a result, the actual joint capacity exceeds the value predicted by the simplified shear strength model, which assumes a uniform stress distribution and does not account for beneficial confinement arising from member proportions.

The results consistently indicate that geometric parameters exert a greater influence on joint shear strength and failure mode than material strength parameters. This observation implies that joint behavior is governed primarily by force transfer paths and stress concentrations rather than by the nominal strength of concrete or reinforcement. Once cracking initiates, the ability of the joint to redistribute stresses depends largely on member dimensions and load paths, explaining why variations in concrete compressive strength alone do not produce proportional changes in shear capacity.

Figure 8 shows the results of analyzing the collected data according to failure mode. The key point here is that, as previously explained, distinguishing all failure modes solely by V_j/V_jby is challenging. Therefore, the study examines the distribution of J, BJ, and B failures for each variable to identify the primary variables influencing failure mode classification. Overall, as joint damage increases, the value of V_test/V_cal is close to 1. Conversely, for B Failure specimens with less joint damage, the value of V_test/V_cal tends to be significantly higher. Therefore, compared to J Failure specimens, which relatively accurately evaluated shear strength, the shear strength evaluation model for B Failure specimens, where shear strength was considerably underestimated, requires improvement. The analysis of failure modes for each variable is as follows.

①

Analysis of the effect of the beam concrete compressive strength (f_b,ck) on failure modes reveals that BJ and B Failure are more prevalent as the concrete compressive strength decreases. This is because lower concrete compressive strength reduces the load-carrying capacity of the beam, resulting in the joint strength primarily determined by V_jby.

②

The classification of failure modes based on the reinforcement ratio (ρ_b) was not clearly evident. Consequently, the influence of the reinforcement ratio (ρ_b) on determining the failure mode is judged to be negligible.

③

The classification of failure modes based on variables related to cross-sectional dimensions (b_c, h_c, b_b, h_b, b_j) was clearly evident. While no distinct trend in failure modes was observed for the cross-sectional elements of the column (b_c, h_c), the cross-sectional elements of the beam (h_b, b_b) showed a tendency for greater joint damage as the beam dimensions increased. This trend occurs because, as the beam cross-section decreases, the bending moment (M_b) in the beam cross-section also decreases. Consequently, the shear strength of the beam (V_jby) becomes smaller than the internal shear strength (V_j) at the joint, thereby reducing joint damage.

Figure 8. Distribution of V_test/V_cal ratio by major design variables based on failure modes: (a) f_ck; (b) ρ_b; (c) h_b; (d) b_b; (e) h_c; (f) b_c; (g) b_j; (h) d/a; (i) l_c; (j) l_b.

Figure 8. Distribution of V_test/V_cal ratio by major design variables based on failure modes: (a) f_ck; (b) ρ_b; (c) h_b; (d) b_b; (e) h_c; (f) b_c; (g) b_j; (h) d/a; (i) l_c; (j) l_b.

The transition from B Failure to BJ and J Failure can be interpreted as a competition between beam flexural demand and joint shear resistance. When beam flexural capacity is relatively low, damage localizes in the beam, limiting shear demand transferred to the joint. As beam capacity increases due to larger sections or higher reinforcement ratios, a greater portion of the applied load is transmitted through the joint core, increasing joint damage and shifting the failure mode toward BJ or J Failure. This transition mechanism explains why beam geometry plays a decisive role in failure mode classification.

Figure 7 and Figure 8 show that both the shear strength and failure mode of PC joints are significantly influenced by the geometry. Therefore, it appears reasonable to incorporate the geometric characteristics of the joint when distinguishing between B, J, and BJ failures. Furthermore, the Combined Model, which integrates web-shear cracking considering joint confinement effects with the joint shear strength Equation (1) from the ACI code, was verified to provide high accuracy in predicting the shear strength of prestressed beam-column joints. However, the joints with high reinforcement ratios (ρ_b) should be carefully designed since they were overestimated in terms of their shear strength. Furthermore, it is necessary to improve the shear strength evaluation equation to enhance the accuracy for specimens classified as B failure.

From a design perspective, the findings suggest that joint shear strength based solely on material properties may be insufficient for PC structures with large or heavily reinforced beams. In such cases, geometric compatibility between beam and joint dimensions should be explicitly verified to prevent unintended joint damage. Incorporating geometry-dependent modification factors or failure mode criteria could enhance the robustness of joint design provisions.

5. Conclusions

This study evaluated the shear strength of PC beam-column joints by constructing a database of 87 experimental specimens based on the literature. Based on the ACI code, a Combined Model was proposed that considers prestressing effects, shear friction mechanisms, and web-shear cracking. This model was used to analyze the accuracy and stability of the shear strength evaluation for the collected specimens, as well as the key influencing variables determining the failure mode. The main results and conclusions of this study are as follows.

• Analysis of all 87 specimens using the Combined Model showed average V_test/V_cal values of 1.12 for the Non-Prestressed group and 0.99 for the Prestressed group, demonstrating prediction performance close to actual test values for both groups. Notably, the shear strength evaluation accuracy was superior for specimens with prestressing, indicating that the Combined Model reasonably reflects the joint confinement effect.
• Analysis indicates that the cross-sectional element variable consistently exerts the greatest influence on both shear strength prediction and fracture mode classification. Therefore, incorporating the geometric characteristics of the joint when classifying the failure mode of the joint is deemed reasonable.
• For the reinforcement ratio (ρ_b), the V_test/V_cal value tends to fall below 1 when using a high reinforcement ratio. The results indicate a potential for slight overestimation of the shear strength of members with high reinforcement ratios, necessitating caution during design.
• The influence of the cross-sectional properties of the column (b_c, h_c) and reinforcement ratio (ρ_b) on the failure mode determination was negligible. However, the study confirmed that as the cross-sectional properties of the beam (h_b, b_b) increased, the damage at the joint tended to increase. Furthermore, as the damage at the joint increased, the safety factor decreased. The shear strength of members with significant beam damage was evaluated quite conservatively.
• Overall, high accuracy was achieved in predicting shear strength. However, to enable more precise analysis and a safer joint design, supplementary research through additional literature collection is required, along with improvements to the shear strength evaluation model for PC beam-column joints.
• The Combined Model can be used as a supplementary shear strength evaluation method for PC beam–column joints, particularly for prestressed members. Caution is recommended for joints with large beam sections or high reinforcement ratios, where shear strength may be slightly overestimated.
• Future work should expand the experimental database and include cyclic loading effects to improve prediction reliability. In addition, further refinement is needed to support code-oriented application of the model for PC beam–column joint design.