### Material constitutive relationship

#### Constitutive model of concrete

The high-strength lightweight concrete is obtained from the full stress-strain curve test (as shown in Fig. 11) on the 150×150×300mm prismoid specimen, and it is simulated with a damage model plastic from concrete.

#### Constitutive model of steel

The stress-strain relationship of steel adopts the ideal elasto-plastic model (Fig. 12) provided in ABAQUS and satisfies the von Mises elasticity criterion as shown in the equations. (1 and 2).

$${text{When}};varepsilon_{y} le varepsilon_{s} ,;sigma_{s} = f_{y} .$$

(1)

$${text{When}};varepsilon_{y} le varepsilon_{s} ,;sigma_{s} = f_{y} .$$

(2)

In the formula: (sigma_{s}), (varepsilon_{s}) and (E_{s}) represent respectively the stress, the deformation and the modulus of elasticity of the steel; (f_{y}) represents the yield strength of steel; (varepsilon_{y}) represents the elastic limit corresponding to the elastic limit.

### Finite element modeling process

The finite element analysis model of the SCAH column is established using the ABAQUS software. High-strength lightweight concrete, steel base plate and angle steel skeleton are simulated by the C3D8R reduced eight-node integral three-dimensional solid element. Angle steel and batten plate should be combined as angle steel skeleton. The angle steel skeleton is built in the concrete, and the concrete and steel base plate is bonded and connected. The top surface of the steel pad block is coupled as the center point. The axial displacement load control is used for finite element simulation, and the vertical displacement is applied to the coupling point of the upper surface of the steel cushion block. The concrete bottom is completely fixed as shown in Fig. 13.

Through the mesh sensitivity analysis at the beginning of the finite element simulation, it can be seen that when the concrete mesh is 12.5mm, if the mesh continues to be reduced, the calculation accuracy of the simulation by finite elements is less affected, while the calculation time increases more. At the same time, taking the concrete grid at 12.5 can avoid using the C3D8R element to simulate the hourglass mode of concrete, thus ensuring that the sample with the largest void ratio is divided into at least 4 elements in the direction of the thickness. The mesh of the angle steel and the steel base plate is 25mm. Before the generation of the grid, the irregular parts must be divided into structured grids. The division of the concrete mesh, the base plate and the steel angle can be seen in Figs. 14 and 15.

The stress distribution of the concrete and angle steel skeleton of the five SCAH columns above during the whole stressing process is analyzed. In order to facilitate the analysis, the longitudinal load-deformation curve of the specimen is divided into three stages (see Fig. 16): elastic section (OA), where the linear relationship exists between the load and the longitudinal deformation of the test tube; Elastic-plastic section (AB), where plastic deformation occurs in concrete and steel, the growth of the sample load at the stage is less than that of the longitudinal deformation, the curve is slightly convex, the slope gradually decreases and the ultimate bearing capacity of the specimen is reached at point B; Down section (BC), where the curve enters the down section after reaching the apex.

### Model verification

Finite element simulation is performed on five specimens according to the above method, and the accuracy of the finite element model is checked by the longitudinal load-deformation curve. It can be seen in Fig. 17 that the test results of the specimens are in good agreement with the results of the finite element simulation, and the error of the maximum load is about 10%.

### Results analysis

#### Longitudinal distribution of concrete stresses

The longitudinal stress (S33) represents the stress in the z axis. The positive value is the tensile stress and the negative value is the compressive stress. It can be seen in Fig. 18 that the concrete is in the elastic stage at point A, the compressive stress of the concrete at the lath is less than that between the laths, in which the compressive stress of the concrete at the lath is about – 6 at −13 MPa, the compressive stress of the concrete between the slats is about −13 to −20 MPa, and the compressive stress of the concrete is obviously lower than its axial compressive strength.

It can be seen in Fig. 19 that the concrete passes the plastic stage with the increase of the load between point A and point B, where the plasticity begins to develop and is at the elastic-plastic stage. The maximum compressive stress in the concrete core area is significantly increased for the low void ratio specimen at point B, where the axial compressive strength reaches −60 MPa with an increase of about 25%; For specimens with a large void ratio, the maximum compressive stress in the central zone of the concrete increases slightly compared to that of point A, and the compressive stress of the concrete increases from −26 to −36 MPa. The maximum compressive stress of the SCAH-1 column is distributed near the concrete core of the midsection of the specimen, the maximum compressive stress of the SCAH-2 column is distributed near the inner concrete wall at the height of the third point of the specimen (except the midsection), and the maximum compressive stress of the SCAH-4 column is distributed near the corner of the concrete square hole at the height of the fourth point of the specimen.

It can be seen in Fig. 20 that there is a descending section between point B and point C. The compressive stress on the outer surface of the concrete of the sample is low (about −6 to −13 MPa), and even low the stress (0 –8 MPa) occurs with increasing vertical strain. The maximum compressive stress of the SCAH-1 column is distributed near the concrete core at the midsection of the sample, and the compressive stress of the concrete core is highest (about -50 MPa). The compressive stress distribution of concrete near the circular hole in the middle section of the hollow column with circular hole is relatively uniform with a value of about −20 to −30 MPa. The compressive stress of the concrete at the corner of the square hole is greater than that near the middle of the side of the square hole. In particular, the concrete stress concentration at the corner of the section in the SCAH-4 sample is evident with a value of about −50 MPa.

#### Angle Steel Skeleton Stress Distribution

Von Mises stress is the fourth theory of resistance (such as equation (3)). According to the principle of conservation of energy, it is used to judge whether the material yields. Similarly, the stress of the angle steel skeleton is divided into three stages (as shown in Figs. 21, 22, 23): in the elastic stage (OA), the Mises stress of the steel of angle is significantly greater than that of the lath plate, and the Mises stress of the angle iron is less than 300 MPa, but it does not reach the elastic limit; At the same time, the stress of the angle between the two battens is significantly higher than that of the batten, and the Mises stress near the batten near the angle is significantly higher than that near the center of the batten.

$$(delta_{{_{1} }} – delta_{2} )^{2} + (delta_{2} – delta_{3} )^{2} + (delta_{3} – delta_{1} )^{2} = 2delta_{s}^{2} .$$

(3)

The sample enters the elastic-plastic (AB) phase with increasing load, and the yield strength (328 MPa) is reached along the entire length of the angle bar, while the lath stress is about 160 to 300 MPa with the impossibility of reaching the elastic limit. At this time, the Mises stress of the middle batten of the specimen is significantly higher than that of the end batten, and the Mises stress of the batten at the connection with the angle iron is significantly higher than that near the point center of the slat.

The specimen enters the descending section (BC) with the development of the load, the radial strain of the concrete increases rapidly, the tensile stress of the lath plate increases, and finally it reaches the yield point. Most specimens yield to the second and fifth slats.

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