The heights of the H-shaped steel PEC columns studied are 1m, 2m and 3m. A series of the H-shaped steel columns have been studied in this research. The parameters of the specimens are shown in Table 1. The sketch sections of H-shaped steel PEC columns and H-shaped steel columns are shown in Fig. (1). According to the code for seismic design of buildings in China, the formula of axial compression ratio is µ=N/(A×f_c). N represents design values of axial force of PEC column, A represents cross-sectional area, and f_c represents design value of axial compressive strength of concrete. C30 and C25 are the concrete strength grade.

Fig. (1). Sections figure of H-shaped steel columns and H-shaped steel PEC columns.

1)The constitutive relation of adopted plain concrete Fig. (2a) in this paper is determined from Eq. (1).

Fig. (2). The figure of stress-strain relations.

(1)

1) The value of ε_o and ε_cu are 0.002 and 0.0033 respectively, recommended by Chinese Code for design of concrete structure. Design value of concrete tensile strength of C30 is 1.43 N/mm², and C25 is 1.27 N/mm².

2) The stress-strain relation of adopted steel Fig. (2b) is the ideal elastic-plastic model. Q235 is the grade of Chinese steel, and its yield value is 235MPa. Failure criteria of steel can be specified as the maximum mises stress.

The H-shaped steel PEC columns were modeled by using solid elements, SOLID45 is used for the 3-D modeling of solid structures. The element is defined by eight nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions. The element has plasticity, creep, swelling, stress stiffening, large deflection, and large strain capabilities. A reduced integration option with hourglass control is available. The geometry, node locations, and the coordinate system for this element are shown in Fig. (3a). The element is defined by eight nodes and the orthotropic material properties. SOLID65 (see Fig. 3b) is used for the 3-D modeling of solids with or without reinforcing bars (rebar). The solid is capable of cracking in tension and crushing in compression. The element is defined by eight nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions. The concrete element is similar to the SOLID45 (3-D Structural Solid) element with the addition of special cracking and crushing capabilities. The most important aspect of this element is the treatment of nonlinear material properties. The concrete is capable of cracking (in three orthogonal directions), crushing, plastic deformation, and creep. The rebar are capable of tension and compression, but not shear. They are also capable of plastic deformation and creep. The William—Warnke model (The value of open shear transfer coefficient and closed shear transfer coefficient are taken as 0.6 and 1.0 , respectively) was selected for the failure criterion of concrete . In the real test, shear connector was set between concrete and steel, in the circumstance of the existence of shear connector, the bond–slip relationship between steel and concrete wasn’t considered, Boolean operation was applied to glue steel and concrete together. Swept meshing method was applied for the specimen, employing elements size with 15mm in the x axis direction, 15mm in the y axis direction, and 16mm in the z axis direction. The precision of the specimen met the requirements. In order to avoid loading stress concentration, the steel plates with thickness of 20mm are added on loading end and fixed support. The model after meshing is shown in Fig. (4).

Fig. (3). Figures of geometries of solid45 and solid65.

Fig. (4). The figure of the model after meshing.

Firstly, apply the constant axial loading to the bottom of the columns, and then the lateral displacement with the direction of strong axis is applied until the failure of H-shaped steel PEC columns. The lateral displacement value applied on the H-shaped steel is the same with H-shaped steel PEC column. On the cycling loading condition, the constant axial loading is applied, then the cycle lateral displacement is applied by using displacement increment method, and before the column fractured, per level of displacement increment is 0.5 Δ_y, per level of displacement cycles once. Δ_y is the displacement value obtained by one-way loading, its value is the corresponding position of the turning point of the P-Δ curve.

The bearing capacity of PEC column is shown in Table 2.

Compared with H-shaped steel columns, the bearing capacity of H-shaped steel PEC columns with the same parameters is increased, with the increment of 17.50% on average. The bearing capacity of the columns is declined with the increment of calculating length. The reason lies in the bending moment which causes concrete crush with the increment of lateral force and p-δ effect. The bearing capacity of specimens is declined with the same geometric parameters and different axial compression ratio with the parameters from 1/2 to 1/3.

Define the ductility factor as µ=Δ_u/Δ_y, and define the relative deformation as ∂=Δ_u/L when considering slenderness. The initial stiffness, the ductility factor and the relative deformation of each column are shown in Table 3, all ductility factors of the PEC columns are more than 2.3, and these results show that the ductility is good. The PEC column is created by pouring concrete in the groove, and the groove is formed with the web and flange of H-shaped column. Due to the constraint of web and groove of H-shaped steel column, the concrete is in three-dimensional pressure state. Meanwhile, local buckling of steel will not occur due to the existence of concrete. As a result, the PEC columns have the advantages of both concrete and steel, which can improve the ductility and bearing capacity.

For PEC-11 and PEC-12 in Fig. (5), H-shaped steel columns haven’t been fractured when lateral displacements reach to the maximum values. However, due to the large scale of axial compression ratio, most pressed area of the concrete crushed earlier, making PEC columns fractured.Thus, the ductility factors don’t have effect on these kinds of H-steel columns.

Under the circumstance of same section size, compared PEC-1, PEC-3, PEC-5 with PEC-2, PEC-4, PEC-6, and also compared PEC-7, PEC-9, PEC-11with PEC-8, PEC-10, PEC-12, respectively. The comparison results exhibit that ultimate displacements are significantly decreased by 14.7%, 20.6%, 21.9% and 19.6%, 19.2%, 21% respectively, with the increment of compression ratio from 1/3 to 1/2. Meanwhile, ductility factors are reduced by 2.6%, 6%, 7.5% and 2.5%, 3.6%, 4.8%, respectively. The ductility factor is declined with the increment of the slenderness ratio.

Moreover, study the relationship between slenderness ratio and relative deformation ∂, it is found that the ductility factor is increased with the increment of the slenderness ratio among the PEC columns mentioned above.

The ultimate compressive strain distribution of the concrete and stress distribution of specimens are shown in Figs. (6) and (7).

Fig. (6). The distribution of ultimate compressive strain of concrete.

Fig. (7). The stress distribution of specimens.

In Fig. (6), the red zone is compressive strain exceeding ultimate compressive strain of concrete, which will crush in real test.

From Fig. (6), the failure of the PEC column lies in the crush of the part of the compressive zone of concrete. The shape of ultimate compressive strain distribution is V-shape, because of the concrete confined by the steel. Compared Fig. (6a) with Fig. (6b), the shapes of ultimate compressive strain distribution are quite different from each other under the circumstance of different confined effect. Moreover, the confined effect becomes obvious with the increment of the width of flanges.

The Fig. (7) shows the shapes of stress distribution of the PEC columns reaching to the ultimate displacement. It can be seen that the zone of compressive stress of concrete which exceeds ultimate compressive stress defined in material behaviors modeling is bigger than the zone of ultimate compressive strain of concrete in Fig. (6). The reason is that the confined effect by steel limits the deformation of concrete. Because of the weak confined effect, the shapes in (d), (e) and (f) are similar with those concrete columns.

In this paper, only the skeleton curves of PEC-5 and PEC-10 are listed in the Fig. (11). For the others have the same properties.

Fig. (11) shows that the shape of skeleton curve is similar with the shape of P-Δ curves in Fig. (5), while the bearing capacities are lower than the H-shaped steel PEC columns. Elastic stage, elastic-plastic stage and plastic stage are included in the curves. Meanwhile, the yield displacements in skeleton curves above are respectively 48mm and 18.2mm, close to the yield displacements of the PEC columns under the axial loading.

Fig. (11). Skeleton curves of PEC-5 and PEC-10.