Seismic performance analysis of steel beam to CFST column connection with ductility and energy dissipation components

2.1.1. Numerical specimens

The steel beam to CFST column connection specimens with ductility and energy dissipation components are designed under the assumption that the side-span of beams and the mid-height of CFST column in a building are hinged. Detailed dimensions of square hollow section and H-shaped steel beam are listed in Table 1. The same geometric dimension of the square hollow steel tube with a cross-section of 250 mm×250 mm×6 mm and steel beam ($b_f$×$h_b$×$t_w$×$t_f$= 300 mm×150 mm×6.5 mm×9 mm) are applied for all specimens in the FEM. The height of CFST column is 1000mm.and the length of steel beam is 1360 mm. the material for steel members (i.e., steel tube, steel beam and end plate) adopts all use structural steel Q345 ($f_y=$345 MPa). The core concrete compressive strength is 50 MPa. The high strength bolts of grade 10.9 M20 are used as connection bolts. In the connecting joint CJ-1, steel beam and end plate are welded. The end plate is connected to the steel tube through eight penetrated high-strength bolts. In the CJ-2, the connection between the steel beam flange and the T-stub end plate extension using high-strength bolts. The connection of steel tube and T-stub bolted connections using eight penetrated high-strength bolts. Fig. 2 shows the configurations of specimens.

Fig. 2Dimensions of joints (unit: mm)

a) Specimens CJ-1

b) Specimens CJ-2

2.1.2. Element types and boundary conditions

An eight-node 3-D solid element with reduced integration (C3D8R) is employed to modeling the concrete, steel tube, steel beam and high-strength bolts. The structured meshing technique is used to generate a proper element shape. There are 3,4101 elements in the FEM of specimen CJ-1, and 3,4385 elements in the CJ-2. The pre-tightening force 100 kN is applied in bolts according to the Chinese Standard for design of steel structures (GB50017-2017) [18]. The bottom of the CFST column is set on a hinged bases in the FEM. The displacements in the $z$ direction and rotations around the $x$, $y$ axes on the middle line of the top base are all constrained. The initial constant axial load ($N_0$) is applied on the top of CFST column. The cyclic loads are then applied at the end of the steel beam using displacement control loading. The loading history of the vertical loads ($P$) at the end of the beam is determined based on ATC-24. [19] guidelines for cyclic loading. During the displacement control stage, the cycles loading is 0.25${\mathrm{\Delta }}_y$, 0.5${\mathrm{\Delta }}_y$, 0.7${\mathrm{\Delta }}_y$, 1.0${\mathrm{\Delta }}_y$, 1.5${\mathrm{\Delta }}_y$, 2.0${\mathrm{\Delta }}_y$, 3.0${\mathrm{\Delta }}_y$, 5.0${\mathrm{\Delta }}_y$, 7.0${\mathrm{\Delta }}_y$, 8.0${\mathrm{\Delta }}_y$…, respectively, where ${\mathrm{\Delta }}_y$ is the estimated yield displacement. The loads boundary and mesh of typical FEM are shown in Fig. 3(a). The displacement load history magnitude is shown in Fig. 3(b).

Fig. 3The boundary conditions and load magnitude of typical FEM

a) Boundary conditions

b) Schematic view of loading history

2.2.1. Material model of concrete

The analysis is conducted by using ABAQUS/Explicit module (ABAQUS.2010) [20]. The concrete damaged plasticity model in ABAQUS is adopted for concrete material. The yield surface is based on the function proposed by Lubliner et al. [21]. And elaborated by Lee and Fenves [22] to account for different evolution of strength under tension and compression. This model assumes a non-associated potential flow rule and isotropic damage. The confined concrete stress-strain relationship for the core concrete of CFST in compression is used presented by Han et al. [23]. The failure criterion is the criterion of Drucker-Prager. The strain-stress relationship is given as follows:

where, $x=\epsilon /{\epsilon }_0$, $y=\sigma /{\sigma }_0$, ${\sigma }_0=f_c^{\text{'}}$, $\epsilon$ and $\sigma$ are the compressive strain and stress, ${\sigma }_0$ and ${\epsilon }_0$ are the peak compressive stress and strain, respectively.

The evolution of compressive damage variable ($d_c$) is adopted to represent the damage of concrete. The compressive damage variable is calculated according to the Chinese Standard for design of concrete structures (GB50010-2010) [24]:

where, $k_c=f_c^{*}/{\epsilon }_c{E}_0$, $a_a$, $a_d$ is the uniaxial stress-strain relationship curve parameter value, respectively.

The tensile skeleton line adopts the double broken line model. The calculation formula of tensile crack stress is put forward by Han et al. [23]. The tensile crack stress is presented as follows:

where, ${\sigma }_{t0}$ is tensile crack stress, $f_c^{\text{'}}$ is the concrete compression strength.

2.2.2. Material model of steel

A nonlinear combined isotropic/kinematic model with a von Mises yield surface and an associated plastic flow rule is applied for steel members. This material model also accounts for the Bauschinger effect for steel under cyclic loading according to the Ref [25]. The stress-strain relationship curve is shown in Fig. 4.

Fig. 4The steel material constitutive model

Eq. (4) expresses the formula of the steel model. The modulus of elasticity ($E_s$) and Poisson’s ratio (${\mu }_s$) are 206,000 MPa and 0.3, respectively. The yield strength and ultimate strength of high-strength bolts are 900 MPa and 1000 MPa, respectively:

where, ${\sigma }_0$ and ${\epsilon }_0$ are the stresses and strains at the intersection of two asymptotes (B or D), respectively; ${\sigma }_r$ and ${\epsilon }_r$ are the stresses and strains at the strain reversal point (A or C), respectively; $R$ is a curve transition parameter; $R_0$ is an initial transition parameter between the elastic segment and the plastic segment; ${\epsilon }_y$ is the yield strain; ${\epsilon }_m$ is the largest or smallest unloading strain in history.

4.1.1. Load capacity analysis

Excessive friction contact relationship and excessive material deformation are likely to cause the calculation non-convergence problems in implicit solver. In the paper, the ABAQUS/Explicit display calculation method is used to overcome the above non-convergence problem. In addition, the efficiency of the operation is improved by setting the semi-automatic model quality scaling and controlling the total loading time. The calculation results of the $P$-$∆$ hysteresis curves are shown Fig. 9, and their skeleton curves are shown in Fig. 10. The hysteresis curve of CJ-2 is plumper than that of CJ-1, indicating that the CJ-2 has better energy dissipation behavior. With the increase of loading displacement, the stiffness degradation of joint CJ-1 is more obvious than that of CJ-2. From the $P$-$∆$ skeleton curve, the peak load capacity of CJ-2 is higher than that of CJ-1.

To further clarify the bearing capacity of the two types of CFST joints under cyclic load, Table 3 presents a comparison results of yield load, ultimate load and failure load. The definition of yield load and yield displacement is determined by the tangent method proposed by Han and Li [12]. The maximum load is selected as the ultimate load $P_{max}$, and the maximum displacement ${\mathrm{\Delta }}_{max}$ is defined as the displacement corresponding to the ultimate load $P_{max}$. The failure load $P_u$ is determined as $P_u=0.85P_{max}$, and the failure displacement ${\mathrm{\Delta }}_u$ is defined as the displacement according to the $P_u$. It can be seen that the yield load, ultimate load and failure load of CJ-2 are 28 %, 30 % and 30 % higher than those of CJ-1, respectively.

Fig. 9Hysteretic curves comparison of CJ-1 and CJ-2

a) CJ-1

b) CJ-2

Fig. 10Load-displacement skeleton curves

4.1.2. Stiffness degradation analysis

The stiffness degradation of joints can be reflected by the loop stiffness under the same level of deformation. The annular stiffness formula is shown as follows:

where, $K_j$ is the ring stiffness, $P_{ij}$ is the displacement load level $\mathrm{\Delta }/{\mathrm{\Delta }}_y=j$, the peak point load value of the $i$-th loading cycle, $u_{ij}$ is the displacement loading level $\mathrm{\Delta }/{\mathrm{\Delta }}_y=j$, the $i$ is the peak point deformation value of the secondary loading cycle, $n$ is the number of cycles. It can be seen from Fig. 11 that the stiffness of CJ-1 is decreases by 73 % from 5230 kN/m to 1400 KN/m. While the stiffness of CJ-2 degrade from 5666 KN/m to 2522 KN/m, with a reduction of 55 %.

Fig. 11Stiffness degradation curves

4.1.3. Calculation of displacement ductility and energy dissipation coefficient

The deformation capability of joints can be expressed by the joint ductility coefficient $\mu$. It is generally measured by the ratio of the structural damage ultimate displacement ${\mathrm{\Delta }}_u$ to the yield displacement ${\mathrm{\Delta }}_y$, i.e. $\mu ={\mathrm{\Delta }}_u/{\mathrm{\Delta }}_y$. It is found through calculation that the displacement ductility coefficient of CJ-1 is 1.6, while the displacement ductility coefficient of CJ-2 is 2.2. After the yield loads, the ability of CJ-2 is slightly better than that of CJ-1, and the yielding of the steel component prevents direct brittle fracture of the weld. The yield of the steel component prevents direct brittle fracture of the weld.

The equivalent viscosity coefficient $h_e$ and the energy dissipation coefficient $E$ are commonly used to measure the energy dissipation capacity of joints. According to JGJ101-96 [27], the energy dissipation coefficient $E$ of the component should be calculated according to Eq. (6). The greater the $E$ value, the stronger the energy dissipation capacity of the joints.

The expression for the equivalent viscosity coefficient $h_e$ is:

where, $S_{ABC}$ and $S_{CDA}$ denote the area of the upper half and the lower part of the hysteresis curve as shown in Fig. 12, respectively. $S_{OBG}$ and $S_{ODF}$ represent the triangle area respectively.

Fig. 12Hysteresis loop of load-displacement curve

The energy dissipation coefficient $E$ refers to the ratio of the total energy of the component to elastic energy of a hysteresis loop, namely:

The energy dissipation coefficient curve of the two type joints is obtained by using Eq. (7) as shown in Fig. 13. The energy dissipation coefficient of CJ-2 is higher than that of CJ-1, with an increase of 20 % indicating that the energy dissipation capacity of CJ-2 is better. Table 4 shows the comparison of displacement ductility coefficient and energy dissipation coefficient between two types of joints.

Fig. 13Comparison of energy dissipation coefficient of connections