Simplified method for modeling reinforced concrete column–steel beam connections with tube plate

Abstract

In this article, the cyclic behavior of reinforced concrete column–steel beam connections is investigated. In this research, an experimental and numerical study is conducted on the performance assessment of the through-beam connections with two detailing. The model details consist of the tube plate and steel doubler plate for the joints. The results show that the steel doubler plate increases the yielding capacity and initial stiffness of the connection but has no effect on the maximum capacity of the connection. Results show that using tube plate alone could have a good performance and there is no need for doubler plates. Furthermore, in order to model this type of connection with tube plate, modified model based on the Cordova’s proposed model is presented, and the load-cycle repetition on the connection at both specimens is simulated utilizing the OpenSees software by taking into account the bearing distortions and joint shear, and the obtained results are verified with the experimental ones as well.

Keywords

composite structures reinforced concrete column–steel beam connection steel doubler plate through-beam tube plate

Introduction

Reinforced concrete column–steel beam (RCS) is known to perform a good structural behavior in terms of high ductility, energy dissipation capacity, and reducing the weight of the structure. These benefits lead to their growing utilization in tall buildings, especially in high seismic risk zones. Composite systems are able to have larger beam spans, and regarding constructability, there is no need for site welding at beam–column connections that speed up the construction. The use of RCS systems is becoming more popular, and the performance of their connections has attracted more and more attention of researchers. One of the most significant components of RCS structures is the connection between the columns and beams, which plays a key role in the frame integrity during an earthquake.

Kuramoto and Nishiyama (2004) demonstrated that there are two principal categories in RCS connections: through-column type and through-beam type connections. In the through-column type connection, the concrete column is confined by steel plates, and the flanges of steel beams are replaced with transverse stiffeners, and steel beams inter-cross a reinforced concrete column at the connection in the through-beam type.

Performance of the RCS connection has been investigated by researchers, which has led to a better understanding of the connection behavior.

Alizadeh et al. (2013, 2015) implemented several conducted experimental and numerical researches about the performance of through-beam-type RCS connections. The obtained results proved that the proposed connection had a good ductility, strength, energy dissipation capacity, and stiffness and it could be used as an alternative for traditional moment frames in seismic zones.

In an experimental study, Men et al. (2015) tested six composite reinforced concrete column-to-steel beam interior connections to study the failure mode and behavior of the panel zone. The results revealed that end plates, band plates, cover plates, and X shape reinforcement have much effect on the strength capacity of the connection.

One of the recent studies in this regard has been conducted by Xuan Huy Nguyen et al. (2017). They investigated the behavior of a new type of exterior connection. Results demonstrated that new detail had a good performance and RCS connection could be used as a dissipative element in the structures classified as medium ductility class.

Zhang et al. (2018) tested six specimens of concrete tube column–steel beam connection. They were tested under cyclic loading to investigate the seismic performance of the new composite frame structure. The results indicated that shear connectors could increase the transfer of the shear force, and the compound stirrups could efficiently modify joint ductility and bearing capacity.

Jafari et al. (2019) investigated the failure and behavior mechanism of circular reinforced concrete column steel beam (CRCS) connections with three different beam-to-column capacity ratios to address the impact of the steel doubler plate (SDP) and the tube plate (TP) on ultimate resistance of the moment-resisting frame. The results revealed that using the TP improves the performance of the panel zone by providing better confinement to the concrete, and the TP could be used instead of the SDP.

Some other study programs on composite structures were conducted by researchers such as Zibasokhan et al. (2016), Uy et al. (2017), and Shen (2010).

Utilizing the TP as one of the through-beam type connection has received limited attention. As it could be seen in previous researches, the use of SDP, band plate, and face bearing plate combination is more common in the through-beam-type category; however, recent researches show that the TP could replace them all.

In this study, the performances of through-beam connections using TP with and without SDP and their contribution on the energy absorption and performance of the connection are investigated based on the experimental and analytical results. The main concern of the article is to introduce a new simplified method for the numerical modeling of the through-beam connection with TP. The OpenSees software was used for modeling and verification of this simplified method. According to the best knowledge of the authors, this issue has not received any attention by the scientific communities.

Experimental and analytical program

Specimens and material properties

The test program included two 3/4-scale interior through-beam-type RCS connections, in which specimen 1 is a combination of TP and SDP, and specimen 2 has a TP only. The connections were designed based on ASCE (1993) guideline and its modifications by Cordova and Deierlein (2005). Both the specimens consisted of 3-m-long columns with 500-mm-diameter circular cross-section. The column spirals and longitudinal reinforcements were considered with φ10 steel bars and 16 φ20 steel bars. The beam of specimens was fabricated with IPE 300 steel sections with 3.9 m length. In both specimens, the thickness of the steel beams flanges was increased to 20 mm, for raising the connection demand and imposing larger loads to the panel zone. The details of the specimen joints are shown in Figure 1. For increasing shear strength at the panel zone, $46 \times 26 \times 0.8 c m^{3}$ SDP was added to the beam web of the first specimen. The first step of building specimens was to prepare the TP. The TP was cut with a Computer Numerical Control (CNC) machine to the size of the section of the beam, and then the beam was passed through it. After fitting the beam, the connecting between beam and tube were welded and the specimen was prepared for placing the reinforcement. The nominal compressive strength of the SCC concrete was 58.3 MPa at 28 days. Tensile tests were performed for the steel and longitudinal reinforcement and spirals, and the results are presented in Table 1.

Figure 1.

Details of the specimens.

Table 1.

Mechanical properties of steel materials.

Test specimens	Type	Yield strength (MPa)	Tensile strength (MPa)	Elongation (%)
1-2	Beam	397	482	31
1-2	Tube plate	328	466	34.5
1-2	Spirals	404	638	28
1-2	Longitudinal reinforcement	447	701	23.5
1	Steel doubler plate	338	464	17

Test results

The cyclic loading pattern is presented in Figure 2. The cyclic displacements are applied in 28 cycles, starting with a 0.2% and continued to 6% drift angle. The loading pattern is the combination of the loading patterns of ATC-24 (1992), ACI 3741-05 (2005), and AISC 341-10 (2010). The ultimate load is 0.8 of the maximum measured load capacity, and when the strength decreased below 80% of the test specimens, the test was stopped.

Figure 2.

Loading pattern.

The test set-up is depicted in Figure 3. Four post-tension rods were utilized to apply the 400 kN axial compressive load to the column, and for cycle loading, two 500 KN compression actuators were used at each side of the top of the column. Also, the forces are monitored by the load cells during the test. Strain gauges were utilized to measure the strains of the TP, web, and flange of the beam, and reinforcing rebars in the column. Also, several LVDTs (linear variable differential transformers) were installed to measure the rotations and distortions of the joint and shear deformation of the panel zone.

Figure 3.

Test set-up: (a) test specimen and (b) schematic configuration.

Results demonstrated that both specimens have a good performance in the cyclic load. The hysteresis curve is depicted in Figure 4.

Figure 4.

Lateral load response at deferent story drift: (a) specimen 1 and (b) specimen 2.

The failure patterns are shown in Figure 5 for two specimens, and according to this figure, failure has occurred in the beam. The beam web yielded first adjacent to the joint and then the beam yielded at two areas outside the connection at the same time at about 2%–3% of the story drift. At about 4% of the story drift, the local and overall buckling of the beam occurred in three zones, and then a number of column longitudinal reinforcements at the panel zone have yielded. Thus, both specimens show the same failure pattern.

Figure 5.

Failure pattern of specimens: (a) yield pattern and (b) failure pattern.

Connection rigidity

Connection rigidity has a significant impact on the design of steel structures, especially for the optimized design. AISC ANSI 360-05 (2005) specification classified connections between steel members not only as hinges and rigid connections but also as semi-rigid ones. The secant stiffness of the joint (K_s) at the loads is as follows

K_{s} = \frac{M_{s}}{θ_{s}} {\begin{matrix} K_{s} \frac{L}{E I} \geq 20 f u l l y r e s t r a i n e d c o n n e c t i o n \\ 2 \leq K_{s} \frac{L}{E I} \leq 20 p a r t i a l l y r e s t r a i n e d c o n n e c t i o n \\ K_{s} \frac{L}{E I} \leq 2 s i m p l e c o n n e c t i o n \end{matrix}

where M_s is the moment at the load level, and θ is the connection rotation at loads. EI and L are bending rigidity and the length of the beam, respectively.

The RCS connections should not only provide strength, but they also serve adequate stiffness. Two LVDTs recorded the rotation of the joint utilized in the middle of the TP. According to Figure 6, measurement of the connection rigidity presented that both connections can be placed as a fully restrained connection category. Comparison between the specimens proved that connection rigidity of the specimen 1 due to the existence of the doubler plate is more than that of specimen 2.

Figure 6.

Connection rigidity.

The contribution of deformation for each part

The contribution of beam, column, and connection deformations in different story drifts is divided into elastic and inelastic parts. Elastic part occurs when the displacements are small and the specimens have linear deformation. When the deformations become irreversible, we have to use inelastic equations. The equations are presented below

δ_{be} = \frac{2 V_{col} L_{nb}^{3} H_{c}^{2}}{3 E_{b} I_{b} L_{B}^{2}}

(1)

δ_{bph} = 2 (L_{nb} - \frac{L_{P}}{2}) θ_{Ph} \frac{H_{c}}{L_{B}}

(2)

δ_{ce} = \frac{V_{col} (H_{nct}^{3} + H_{ncb}^{3})}{3 E_{c} I_{col}}

(3)

δ_{cin} = (θ_{ct} H_{nct} + θ_{cb} H_{ncb}) - δ_{ce}

(4)

δ_{JSD} = γ (H_{c} - h_{j} - \frac{b_{j} H_{c}}{L_{B}})

(5)

δ_{RBR} = H_{c} θ_{RBR}

(6)

θ_{Ph} = \frac{Δ_{t} + Δ_{b}}{d_{v}}

(7)

θ_{cb} = \frac{Δ_{rb} + Δ_{lb}}{d_{h}}

(8)

θ_{ct} = \frac{Δ_{rt} + Δ_{lt}}{d_{h}}

(9)

θ_{RBR} = \frac{Δ_{r} + Δ_{l}}{d_{h}} - θ_{ct}

(10)

where the elastic deformations of the beam and column are $δ_{be}$ and $δ_{ce}$ , respectively. Also, $δ_{bph}$ and $δ_{cin}$ are the plastic hinges of the beam and inelastic deformation of the column, respectively. $δ_{JSD}$ and $δ_{RBR}$ are the influence of connection distortion, which are, respectively, joint shear distortion and joint rigid body rotation, and $d_{h}$ and $d_{v}$ are the distances between LVDTs attached to the column and beam.

For better understanding, schematic drawing is illustrated in Figure 7 for the above-mentioned parameters in equations (1) to (6). Also, Figure 8 exhibits the arrangement configuration of the LVDTs on specimens.

Figure 7.

Schematic deformations.

Figure 8.

Location of LVDTs.

The contribution of column, beam, and connection deformations in different story drifts is illustrated in Figure 9 for specimens.

Figure 9.

The contribution of the beam, column, joint shear distortion, and joint rigid body rotation deformations in different story drifts: (a) specimen 1 and (b) specimen 2.

As the results clearly show, the contribution of the beam is almost constant in different story drifts on both specimens, and the doubler plates have a small effect on the contribution of the beam’s displacements. But in specimen 2, due to lack of doubler plate, the connection deformations have increased and the contribution of the column deformations has decreased about 3%, at story drift equal to 4%; in the other words, the fracture percentage of concrete in the first specimen is more than the second one, and the failure has been transferred to the connection area. As it could be seen in Figure 9, the overall results indicate that although the total deformation of the specimen 2 is more than 1, the ratio of displacements is almost constant, which demonstrates the good performance of the TP for distributing the loads.

Load transfer mechanism

A moment-resisting connection must tolerate the forces moved to the panel zone by adjoining members. The forces acting on an interior connection subjected to lateral loads are displayed in Figure 10.

Figure 10.

Deformation shape of the connection.

Flange force transfer

To verify the force conditions in the flange of the beam, some strain gauges were put inside and outside the column at top of the flange in the panel zone. We only evaluated the positive section because of the similar cyclic loading in the tests. In Figure 11, the compressive and tension forces are demonstrated with CF and TF, respectively. The results displayed a drop in the compression strains measured in the flange of the beam inside the TP. The measure of the stress in the flange along the longitudinal axis of the beam as obtained from seven strain gauges for 1% and 4% story drifts is presented in Figure 12. This implies that a part of the stress in the flange is transferred to the concrete by friction and bearing of the TP and the web of the beam via shear forces. Also, the compression stress reduces about 25% of the stress value in the middle of the joint at 4% story drift.

Figure 11.

The portion of the top flange.

Figure 12.

Axial stress in the flange at the connection: (a) 1% drift and (b) 4% drift.

$V_{W}$ , $V_{t}$ , and $V_{cf}$ are the shear forces in the web, TP, and concrete core, respectively.

Joint shear

In the through-beam connection type, the concrete of column increases joint shear strength that the core column is impressive in decreasing joint shear forces by transferring the beam flange stress to the concrete directly.

The moment of the beam is obtained by the compressive and tensile loads in the beam flange, which could be evaluated as follows

T_{f} = C_{f} = \frac{M_{b}}{d_{b}}

To obtain the horizontal joint shear strength, we need to measure the following values: the shear force in the web $(V_{w})$ , shear force in the TP $(V_{t})$ , and the shear force in the concrete $(V_{cf})$ . According to the results obtained from the specimens, the web of the beam at the panel zone was always the first portion to reach its capacity.

The nominal joint shear strength, $V_{n}$ , is measured as the sum of the individual nominal shear strengths of the panel zone

V_{n} = V_{wn} + V_{tn} + V_{cfn}

where $V_{wn}$ , $V_{tn}$ , and $V_{cfn}$ are the nominal shear strengths of the web, the TP, and concrete, respectively.

On the other hand, the joint shear strength is equal to the shear capacity, which is obtained via the following equation

\frac{2 M_{b}}{d_{b}} - V_{c} = V_{wn} + V_{tn} + V_{cfn}

According to the above equation, the force applied on each part of the right equation is related to the moment capacity of the beam and the shear capacity of the column, which both depend on the geometric characteristics. To prevent joint failure, the nominal shear strength value must be more than the applied beam moment.

The main part of the resistance to joint shear is related to the beam web panel. The shear strength of the web is obtained as the sum of web shear yielding $(V_{wy})$ and the frame mechanism $(V_{f})$ which are obtained based on the following equations

M_{p f} = \frac{F_{y f} t_{f}^{2} b_{f}}{4} ➡ V_{f} = \frac{4 M_{p f}}{d_{b}}

(11)

V_{wy} = 0.5 F_{yf} d_{c} t_{w}

(12)

V_{wn} = V_{f} + V_{wy}

(13)

The web shear yielding is calculated as an average yield shear stress, which is obtained from the strain gauges installed in the web of the beam at the panel zone. The shear of the frame mechanism is obtained based on Sheikh (1987) and Deierlein (1988) studies, in which the beam flanges fail at four places, and plastic hinges are formed as in Figure 10.

For calculating the shear of the TP, the maximum shear force is measured according to the strain gauge installed in the center of the TP. The formula used for the shear of the TP is based on the work by Boresi et al. (1993), which is described as follows

V_{tn} = 0.6 F_{yt} \frac{π d_{c} t_{t}}{2}

Due to the lack of a strain gauge on the concrete core, we could not measure the shear strength of the concrete in the tests. To this end, we have used ACI-ASCE Committee 352 (2002) equations to acquire a share of concrete in the connection, which is calculated from the following equation

V_{cfn} = 1.99 \sqrt{{f'}_{c}} (\frac{π d_{c}^{2}}{4})

where the term $f'_{c}$ (MPa) is obtained from testing on cylindrical concrete samples. The above formula is for a reinforced concrete connection, in which the connection is the through-beam type. The layout of the strain gauges used is shown in Figure 13.

Figure 13.

Location of strain gauges.

The horizontal shear strengths for each portion are presented in Figure 14 for both the specimens.

Figure 14.

Shear load distribution of panel zone: (a) specimen 1 and (b) specimen 2.

As could be seen in Figure 14, the highest and lowest shear loads are for concrete core and frame, respectively, that they are approximately equal in specimens. About 40%–50% of the shear loads are the sum of the TP $V_{tn}$ and web $V_{wy}$ contribution, in the first specimen; major shear contribution is tolerated by web and SDP, that is, values $V_{wy}$ and $V_{tn}$ at ultimate load are 22% and 14%, respectively. But in specimen 2, after the yielding of the web, major shear contribution is transferred to TP, that is, values $V_{wy}$ and $V_{tn}$ at ultimate load are 14% and 33%, respectively. As could be seen from Figure 15, the proportion of web and TP in specimen 2 is greater than first specimen; at the ultimate load, it could be concluded that the use of a TP alone could have a good performance and does not require a doubler plate.

Figure 15.

The tube plate and web contribution in the shear capacity of connection.

Numerical results

The OpenSees software has been employed for modeling the inelastic behavior of the specimens. The lateral force–displacement results of the numerical models and those obtained via the experiments are compared.

For simulating the specimens in OpenSees software, “nonlinear beam–column element” was utilized for beam and column elements, “joint two-dimensional (2D) element” was used for modeling the joint distortions and two “zero length elements” were applied to simulate the bond slip in longitudinal reinforcements at the connection area. Thus, the “bond_SP” uniaxial (from OpenSees library) was assigned to the zero length; this behavior is based on the research of Zhao and Sritharan (2007). This material is appropriate for reinforcements that experience bond slip along a portion of the anchorage length due to strain penetration effects. As displayed in Figure 16, the geometry of models and all boundary conditions are considered based on the test setup shown in Figure 3. Also, the loading pattern was taken alike the tests.

Figure 16.

OpenSees model.

In modeling of this type of structures, the most important part of the model is the joint region. Here, joints are modeled based on the presented experimental results. Panel zone is considered as rotational spring which consists of two series of springs. Each of these springs represents panel shear distortions and vertical bearing deformations as well. For the simplified model, experiment results are estimated by lines drawn base on idealized force–displacement curve for NSP in ASCE41-17 (2017), to determine the vertical bearing spring. As could be seen in Figure 17, stiffness of SP1 is more than SP2, due to the use of the doubler plate, so the effect of the doubler plate considers the proposed model for connections. Finally, Table 2 summarizes the nonlinear behavior of the rotational spring representing the vertical bearing of RCS connections.

Figure 17.

Vertical bearing spring: (a) experimental result and (b) proposed models.

Table 2.

Proposed vertical bearing spring.

With tube plate and doubler plate		With tube plate
Moment	Rotation	Moment	Rotation
0.8M_vb	θ_vb	0.7M_vb	θ_vb
M_vb	4θ_vb	M_vb	4θ_vb
0.65M_vb	10θ_vb	0.65M_vb	10θ_vb

M_vb is determined according to ASCE (1993) guideline; θ_vb is proposed by Kanno (1993).

Here, M_vb and θ_vb are equivalent joint vertical bearing moment and the joint rotation corresponding to M_vb, respectively. They are evaluated using the following equation

M_{vb} = 0.7 h C_{cn} + h_{vr} (T_{vrn} + C_{vrn}) + 1.25 V_{on} d_{j}

(14)

θ_{vb} = 0.01 - 0.008 \sqrt{P}

(15)

where P is the applied axial force to the column and $C_{cn}$ is the vertical bearing force between beam and column. $T_{vrn}$ and $C_{vrn}$ are the nominal strengths in tension and compression of vertical joint reinforcement, respectively, and $V_{on}$ is the joint outer panel shear strength. Also, $h_{vr}$ and $d_{j}$ are the distance between bars and the beam flange centerlines, respectively.

For the material modeling, Concrete02 and the Steel02 material models have been exploited. Concrete02 material model was utilized to model the core and inner TP concrete, and Steel02 material model was employed for modeling of rebars and beams.

Also, the shear spring is based on Cordova and Deierlein (2005) research. The stiffness of spring is shown in the following equation

K_{es} = \frac{2 M_{PS}}{θ_{SD}}

(16)

θ_{SD} = 0.01 - 0.0067 \sqrt{P}

(17)

where $K_{es}$ is the initial stiffness of panel shear spring and $θ_{SD}$ is rotation at which the applied moment is $M_{PS}$ . Moreover, joint shear strength $(M_{PS})$ is determined from equation (18)

M_{PS} = V_{spn} d_{w} + V_{icn} d_{j} + 1.25 V_{on} d_{j}

(18)

where $V_{spn}$ is the steel web panel shear and $V_{icn}$ is the joint inner panel shear strength. Also, $d_{w}$ is the length of the beam web.

Figure 18 demonstrates the modeling results of specimens 1 and 2; as it could be observed, numerical models display good agreement regarding ultimate strength capacity, yield strength, stiffness degradation, elastic stiffness, and strength degradation of the connections. The proposed joint vertical bearing spring model captures the degrading point of the connection.

Figure 18.

OpenSees modeling based on proposed vertical bearing spring: (a) specimen 1 and (b) specimen 2.

The difference between the ultimate strength of the numerical model and the experimental results is shown in Table 3.

Table 3.

Difference between numerical and test results.

		Story drift
		0.6	0.8	1.2	1.5	2.5	3.7	5	Average
SP1	EXP	106	142	200	247	289	294	308
	NUM	101	136	201	255	292	302	311
	DIFF	4.7%	4.2%	0.5%	3.2%	4.4%	2.7%	0.9%	2.9%
SP2		0.55	0.75	1.25	1.75	2.8	3.8	4.85	Average
	EXP	92	119	181	225	283	298	293
	NUM	86	116	189	258	291	303	311
	DIFF	6.5%	2.5 %	4.4%	14.6%	2.8%	1.7%	6.1%	5.5%

Conclusion and discussion

This article presented two 3/4-scale interior connections with TPs of RCS structures. Quasi-static reversed cyclic loading tests of the specimens were conducted. Also, the load-cycle repetition on the connection at both specimens is simulated via the OpenSees software, and the obtained numerical results are verified with the experimental tests. It should be mentioned that there is a need for more tests and analysis for the completely verifying proposed model, but based on this study, the conclusions are summarized as follows:

The SDP increased the yielding capacity of the connection but had no effect on the maximum capacity of the connection, wherein the beam failure governs the maximum capacity of the connection.

Axial stress in the flange at the connection demonstrated that the 75% stress in the flange was transferred to the concrete, TP, and web of beam and only about 25% of the stress remained in the flange.

The shear load distribution in the panel zone indicated that the use of a TP alone could have a good performance on the cyclic loading and it could tolerate the excess shear load due to the lack of SDP.

The proposed finite element model could predict the behavior of the composite connection with proper precision. The average difference between the experimental and numerical values, for specimens 1 and 2, is 3% and 5%, respectively. The suggested connection model could be useful in the seismic calculation of RCS systems with high efficiency and reasonable precision on the overall behavior of the studied connections.

Footnotes

Appendix 1 Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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