Experimental and Numerical Study on the Capability Behavior of a Thick-Walled Spatial Cast-Steel Joint under Complex Load Conditions

A cast-steel joint is always used as an important component for the safety of the whole structure at key points, and the capability of the joint is important for the cast-steel joint. )is paper conducts an experimental and numerical study on a 1/2 scale model of a joint in a real project.)e experiment is used to validate the numerical model and thenmake further studies on the behavior of the joint by using a numerical method. Combining the result of the scale model test and numerical analysis shows that the joint can bear the prescribed load and it is still in the elastic stage.)is paper also discusses the influence of the absence of the secondary moment, torque, and shear force. For the core area of the joint, the secondary moment and torque have little effect on the stress distribution, and the axial force of the secondary branches can increase the capability of the joint. But the secondary shear forces do have some effect on the stress of core area, and an enhancement coefficient is used to enlarge the axial force and moment to cover the absence of shear in the test.


Introduction
Cast-steel members are widely used in many major projects.It can be used as stiffeners, connectors, or joints in the steel structure.Cast-steel members have obvious advantages.
ey are more flexible, cheap, and more convenient for connection purposes.At the same time, cast-steel members can also be used to produce items with a more compact size [1].Cast-steel members have a better seismic behavior [2][3][4].Cast-steel joint is one of the most useful forms of the caststeel members.It is often used in the key areas of structure for the following reasons: first, using cast-steel joints can avoid welding at the intersection of the members or move the welding area away from the joint area to prevent welding defects, residual stresses, and thermal deformation caused by welding [5].Second, cast-steel joint can also reduce the difficulty in construction and improve safety [6].ird, caststeel nodes exhibit better fatigue performance than other alternatives [7].Under cycle loads, some cast-steel members have properties of stress strengthening [8].Cast-steel also has a better fire resistance, and its mechanical properties obviously changes when exposed to temperature exceeding 700 °C [9].Although the cast-steel has excellent mechanical performance, the ductility of the cast-steel is less than that of the normal steel [10].
Cast-steel joints are widely used, and the researches on cast-steel joints have made a lot of progress.Du et al. [6] performed research on tree-like column cast-steel joints and summed up a formula for predicting the capacity of caststeel joints with branches under eccentric forces through an experiment and numerical analysis.Similarly, Du et al. [11] also carried out a numerical study on a tree-like cast-steel joint with three branches about the failure mode of the joint.Song et al. [12] presented an experiment on a huge cast-steel joint and verified the capability of the joint.
is paper conducts an experimental and numerical study on a 1/2 scale model based on a joint in a real project.
e project is performed at a culture center, and it has a large-span floor system.e floor structure is supported by four concrete core tubes with concealed steel trusses.e span of the floor and trusses is up to 101.3 m, the height is only 6.3 m, and the height-span ratio is about 1/16.In this project, the cast-steel joints are used to connect the main truss and the core tube as shown in Figure 1. is study takes one of the cast-steel joints as the prototype.
e joint connects multiple members, under a complex load condition, and the force transferring path is not clear.It is a key component of the structure, directly related to the safety of the building.
Figures 2 and 3 show the details of the joint.Figures 2(a) and 3 are in the same direction.N8 and N7 are embedded in the core tube, so they can be regarded as fixed.N1-N4 are the main members, and N5 and N6 are considered as the secondary members.To ensure that the joint can satisfy the requirement of the construction project, an experiment based on a 1/2 scale model of the cast-steel joint was carried out according to Technical Specification for Application of Connections of Structural Steel Casting [13].e specification demands that for the important joint which influences the safety of the entire structure or for complex connection, a test must be carried out to validate the capability and safety of the joint.And a finite element simulation must be used for assisting the real test as a contrast.
Although it is a 1/2 scale model test, the thickness of the test specimen in this experiment is still up to 150 mm.It is rare in cast-steel joints.In existing researches, most of the cast-steel joints do not have a thick cross section.Only few researches are about the thick cast-steel joints, and the thickness is no more than 80 mm.Existing research also advises that the thickness of the joint should be less than 150 mm [4].
is research can show the behavior of the thick-walled cast-steel joint.
Scale model experiment is a common method for huge joints.To make it possible for the loading equipment to exert the load, the joint can be scaled and the minimum scale of the prototype is 1/2 based on the request of the code [13].It is obvious that the employment of similitude theory can save considerable expense and time.Ramu et al. [14] carried out an analytical investigation for the scale model test and provided a useful tool for solving the relevant problems.Chang et al. [15] conducted a study on piers failing in shear by using the reduced scale specimens.However, the scale model of the huge joint can still be very huge for the experiment, and it will be difficult to load until failure.
e combination of the real test and the finite element (FE) model is a good method to understand the behavior of complex joints.is method can also help carry out further study on the elastic stage of the joint and the distribution of the stress when it is difficult to measure the stress.Wang et al. [16] presented a method to compare the calculated surface stresses with those obtained from the experiment, to validate the FE model, and then to judge the stress distribution inside the joint by using the FE model at the same time.In this method, the experiment is mainly used for the verification of the FE model, and we can use the verified model to solve the problem that is difficult in the real experiment.Similarly, Su et al. [17] presented a method combining nondestructive field tests and the FE simulation to judge the capability of the joint through the stress increments in large-span spatial structures.Liu et al. [18] carried out numerical simulations for the scaled test on a T-joint and received a good agreement between the tests and simulation.Jahangiri et al. [19] used a numerical simulation method to study the cyclic responses of an innovative connection for beam and column.
In this paper, we conduct an experiment to validate the numerical model, and then make further studies on the behavior of the joint by using a numerical method.e influence of the secondary load to the capability of the joint is also discussed by using the numerical method.is part mainly discusses how the secondary moment, torque, shear, and axial force from the secondary branches of the joint influence the stress distribution of the core area of the joint.

Test Specimen and Reaction Frame.
e test specimen is 1/2 scale model of the real joint in the construction project.Only one specimen is tested in the experiment.e material of the test specimens is G20Mn5QT cast-steel.e material properties are obtained from a tensile experiment listed in Table 1.
e sizes and details of the prototype can be seen in Figure 4. To suit the need of the stress equivalence principle, the load applied to the specimen should be 1/4 of the designed value.e value of the load combinations can be seen in Table 2.It is the most unfavorable load combination provided by the designer of the structure, including the dead load, live load, and seismic load.Considering it is very difficult to apply all the loads, some of the design loads are considered as the secondary load.A preliminary FE analysis is also used to distinguish the secondary load.A reaction frame is designed for the test based on the geometric characteristics and load of the joint.It is a spatial self-balance reaction frame.Figure 5(c) shows the model of the reaction frame.Figures 5(a) and 5(b) are the real pictures of the reaction frame and cast-steel joint.

Loading
Procedure.N7 and N8 are embedded in the core tube.In the experiment, they can be regarded as fixed boundary and do not need to be loaded.To reduce the difficulty of the test, the load should be simplified.First, N5 is a secondary member of the joint and its load is much smaller than the main members.So it can be ignored, and only N1-N4 are needed to be loaded.
Compared with the moment and axial force, the torque and the shear are secondary loads too.ey can also be ignored in the test, and in Section 4, we will make further discussion about the absence of the secondary loads.e moment can be replaced by an eccentricity in the test.
e loading procedure is a monotonic loading.Before the formal loading, a preloading was conducted to make sure the test specimen can have a good contact and work normally.During the preloading, the equipment and instruments can also be tested.e load value of preloading is only 50% of the designed value, and the loading procedure is divided into 5 levels; for each time, 10% of the designed value, is loaded.Each level of the loading continues for 5 minutes.e unloading of the preloading is divided into 2 2 Advances in Civil Engineering steps, and fir each time, 25% is unloaded.e formal loading is controlled by 0.1 times of the designed value.And when the loading of all N1-N4 is 1.3 times of the designed value, continue loading N4 until it is 1.5 times of the designed value.Increasing the load on N4 can ensure the safety of the joint.e determination of this coefficient will be further discussed in Section 4.4 later.e load level is listed in Table 3, and the axial load of N4 is loading eccentricity to replace the moment load.
During the loading procedure, the data of the strain gauge and displacement meter will be collected by the computer constantly.
e failure refers to the following criteria: (1) the specimen has obvious cracking; (2) the axial forces stop increasing when the loading procedure continues.If there is local buckling, the joint will also be regarded as damaged and the loading process will be stopped, but because of the thickness of the joint, it is almost impossible for the joint to buckle.e loading and unloading levels are listed in Table 3.

Measurement of Strain and Displacement.
Strain gauge and displacement meter are used to measure the strain and displacement.
ere are totally 41 three-direction rosette strain gauges for the measurement of the von Mises stress in the test.And 22 single-direction strain gauges are also used to obtain stress.3 displacement meters are set to measure the displacement of the main branch of the joint.e location of the strain gauges is shown in Figure 6.

Analysis and Discussion of the Results
During the loading procedure, the measured axial forces of N1-N4 are shown in Table 4, and the value of the load is listed in Table 4 (1.3 times of the designed value).
It can be seen in Figure 7 that, for most of the time, the measured value and the designed value of the load match well, but at level 1.0, the loading is not stable for N1 and N2.From load level 1.3 to 1.5, the load of N4 increases and the loads of N1-N3 are also influenced by N4.But it does not influence the result much because N4 is always stable and N4     Advances in Civil Engineering  Advances in Civil Engineering     Advances in Civil Engineering is the most important load.We think the unstable state is mainly caused by the bolted connections in the reaction frame.When it bears heavy load, a small slip may happen and nally lead to the unstable state during loading.

Position of the joint
Due to the thickness of the joint, it is almost impossible for the joint to buckle.e axial forces are mainly tensile, and the moment makes the stress of the upper area much larger than the lower area.So the danger area is the upper area of the joint where all the members intersect.T4, T6, T20, T22, T26, T27, T36, and T37 are the test points in this area, and they are the most representative test points for the core area of the joint.e position of the important points in core area is marked in Figure 8(b), and the stress of the points during the loading procedure is shown in Figure 8(a).
e result shows that the von Mises stress is increasing linearly during the loading procedure.And all the branches and the core of the joint do not yield, they are still in the elastic area, and even the loading of N4 is increased to 1.5 times because the displacement and the deformation are relatively small and the von Mises stress of the core area is always less than the yield strength.
In the test, the stress of all the test points should never exceed the yield stress.
e result is similar to the phenomenon of the test.e stress of some test points is not stable during the test.It is mainly caused by the instability of the load at level 1.0.Some test points near the stress concentration area are more easily a ected by the instability of load.In Figure 8(a), we can nd out that the decrease in the loading of N1 and N2 has di erent in uence on di erent measuring point.T20, T22, and T37 have an obvious increase, while T27 decreases.e in uence of the loading of N1 and N2 is discussed in Section 4.3.

Model of the Test Specimen.
e numerical analysis of the joint under complex loads is carried out by using the nite element method.e software used for the simulation is Abaqus.Abaqus has a good nonlinear mechanics analysis ability, and Wang et al. [20] carried out an analysis and optimized a cast-steel joint of a large reticulated shell structure by using Abaqus.
e 3D model of the joint is built and then imported with Abaqus.According to the experiment of the material property, the ideal elastic-plastic model is used to simulate the constitutive behavior of the material.e model is dened as a solid unit, and the material is G20Mn5QT, whose yield strength is 385 MPa, the tensile strength is about 555 MPa, and elastic modulus is 206000 N/mm 2 .Poisson's ratio is 0.3.e plastic behavior of the material is de ned by the kinematic hardening model.
Referred to the physical experiments, the boundary conditions of the numerical model are set as below: for N7 and N8, U1-U3, and UR1-UR3, totally 6 DOFs are xed.N1-N6 are coupled to the control points, and the loads are loaded on the points.e load (N1-N5) and the reaction (N7 and N8) are listed in Table 5, and Figure 9 shows the model and meshing of the joint in Abaqus.

Comparison of the Simulation and Experiment.
To validate the rationality of the FE model and the real physical model, the rst step of the simulation is comparing the von Mises stress of the key points in the core area of the joint.In this step, the load of the FE model is similar that of the test, and the result of the key points can be seen in Figure 10.
Comparing the result of FE and the test, when the load level is lower than 1.0, the FE model matches the test result well.However, after 1.0 level, the test value of the stress is always smaller than the FE value.It is mainly because the loading of N1 and N2 is unstable around load level 1.0, and the real load of N3 is smaller than the theoretical value during load level 1.0-1.3.When the load increases stably,     Advances in Civil Engineering the result matches well.Considering the possible slip in the reaction frame at level 1.0, some equipment problem in the real test can also cause the di erence between FE result and real test.It validates the e ectiveness of the numerical analysis.For some connection areas of the member and joint (also the stress concentration area), the result behaves di erent.e FE value is larger than the test value.It is mainly caused by the sharp element in the meshing and nally leads to the concentration of stress in the FE model.
To validate the FE simulation, the boundary conditions should also be validated.Take the xed branches N7 and N8 as examples, the reaction forces on the boundary is listed in Table 6.
e result validates the e ectiveness of the numerical analysis.e error of the stress and reaction force between the real test and the FE simulation is acceptable.It allows the further use of the FE model.We can use the FE model to deal with the problem which is di cult to solve in the real test.Figure 11 is the stress nephogram of the joint under test load.Obviously, the joint is still in the elastic stage.Figures 12(a) and 12(b) are the z direction and magnitude displacement nephogram of the joint under the test load.In the real test, the displacement of the joint is very small.Considering the equipment problem, the measured result can only serve as a reference.
e FE result of displacement shows that the maximum magnitude displacement is about 1.31 mm, close to the real test (1.35 mm).

Discussion of the Absence of the Secondary Load.
In the test, due to the limitation of the equipment, some secondary loads are ignored.We can exert all the secondary load and discuss the in uence of the absence of secondary load by using numerical analysis.Before we carry out the experiment, a preliminary FE analysis is used to con rm the secondary load.e main loads include the axial force of N1, N2, N3, N4, and the y direction moment of N4. e other moment and all the shear forces and torque are all considered as the secondary loads.In fact, the shear forces do have some in uence on the result, but they are di cult to load.So they are also considered as secondary loads, and an enhancement coe cient is used to insure the safety of the joint.e load on N5 is also too small, and the cross section of N5 is also much smaller than the main branch.e result of preliminary FE analysis also proves that N5 can be ignored in the real test.
In the numerical analysis, we can exert all the loads we want without the limitation of the loading equipment.First, the absence of small moment only leads to about 5% of the change in stress, and similarly, the torque is meaningless for the distribution of the stress.But the absence of shear force will lead to a much bigger di erence.As it is shown in Table 7, the di erence can be up to more than 30%, so the shear of the joint should be taken into consideration through other methods to ensure the safety of the joint.e stress state under all secondary loads is similar to that under secondary shear.It also shows that shear is the most inuential secondary load.
Although the secondary torque and moment do not make a di erence for the stress distribution in core area of the joint, it will actually a ect the stress concentration.e secondary torque only leads to about 1% di erence for the stress in core area, but the maximum stress increases from 265.2 MPa to 364.2 MPa.It is even more than the in uence of the shear.It shows that although the secondary load is very small, it can still have a great in uence on the concentration of the stress.For the design of the joint, to avoid the stress concentration, all the secondary load should be taken into consideration.e in uence for the stress concentration is shown in Table 8.Advances in Civil Engineering

Advances in Civil Engineering
It is obvious that the secondary shear forces will lead to the decrease in the capability of the joint.However, the secondary moment and torque still need more discussion.Although the secondary moment and torque sometimes have a positive influence on the stress of the joint (for example, the secondary moment for T20), but the secondary load will aggravate the stress concentration and finally lead to the plastic failure in the concentration area.e secondary moment and torque will also lead to the decrease in the capability.
e following is the discussion on the influence of secondary branches.It is obvious that the main branches of the joint are N4, N7, and N8.Both the size of the cross   Advances in Civil Engineering section and the value of the load of N4 are the biggest, and N7 is the continuation of N4.So N1, N2, N3, and N5 can all be considered as the secondary branches.e loads of all the secondary branches are axial compressive forces.To discuss the influence of the secondary branches, the result of the FE simulation without the secondary branches load is shown in Table 9. T26 and T27 are on the branch N2 and a little bit away from the core area.So the absence of the loading of N3 leads to a great decrease in stress.But for the core area, for example, T6, T22, and T36, the absence of the secondary branches causes the increase in the converted stress.We can come to a conclusion that, for the core area of this joint, the axial force from the secondary branches is a positive factor for the capability of the core of the joint.e absence of the secondary branch will lead to the decrease in the capability of the joint.In fact, the real test also validates this opinion.In Figure 8(a), when the loading of N1 and N2 decreases (at load level 1.0), the stress in core area increases while T27 decreases.

Discussion of the Enhancement Coefficient for Real Test.
Section 4.3 shows that the shear load will influence the converted stress of the joint greatly.To ensure the safety of the joint and the reliability of the test, in Section 2, we use an enhancement coefficient on the designed value of the load in the real test and enlarge the axial load and moment to replace the influence of the shear and other secondary load.
e enhancement coefficient is confirmed by FE simulation.Different enhancement coefficients are used in the model.e result of the FE simulation is listed in Table 10 and Figure 13 for the stress of core area under different enhancement coefficients.e stress under enhancement coefficients should always be larger than the stress under shear load and other secondary loads.Finally, we select 1.3 for N1-N3 and 1.5 for N4 as the values of enhancement coefficients based on the FE simulation and the advices of the designer.It is obvious that the enhancement coefficient can cover the absence of the shear and ensure the safety of the joint when it is difficult to load the secondary load.

Discussion of the Code Regulation.
e code requests that the strength check should be as follows: where β f is a coefficient for the converted stress, determined by the tension and compression situation in the area and c RE is the seismic adjustment coefficient.For this joint, β f � 1.0 and c RE � 0.9.If the joint can bear at least 2 times of the designed load in the real test or 3 times of the load in FE simulation, it is possible to ignore the stress check for the joint [13].Under 3 times of the designed load, the FE model shows that member N4 starts to yield but the core area is still in the elastic stage.e stress concentration is much more obviously under 3 times of the load.We can also find that the stress of the core area can still pass the strength check provided by the code.e stress nephogram of the joint can be seen in Figure 14. e z direction and magnitude displacement of the joint can be seen in Figure 15.e magnitude displacement is about 5.92 mm, still very small relative to its size.Under 4 times of the designed load, the core area of the joint still does not yield, and the upper area of member N4 yields.e core area does not completely yield even if the       16 Advances in Civil Engineering

Conclusions
e following conclusions can be made based on the test and the FE numerical analysis presented in this paper: (1) In the test, the joint can bear the designed load and it lasts still in the elastic area, and under 3 times of the designed load, the joint does not undergo failure.e core area of the joint does not yield when the branch yields.e joint is safe enough for the project and compliance with the requirements of the code.e test also proves that the thick cast-steel joint (up to 150 mm) also behaves well under complex loads.(2) e result of the FE and experiment shows that the FE simulation matches well.e stress distribution and the reaction forces are as expected.e method of testing the FE model through the experiment is acceptable, and we can obtain the result that is difficult to be obtained from the physical experiment due to the equipment and other limitations.(3) e absence of secondary moment and torque does not really affect the stress distribution in core area much, but the secondary load can lead to a more serious stress concentration.e axial forces from the secondary branches increase the capability of the joint.(4) e absence of shear leads to an obvious decrease in the stress.An enhancement coefficient can be used to enlarge the axial force and moment to cover the absence of the shear and ensure the safety and reliability of the model test.
(5) e joint has an obvious stress concentration at the connection area after 3 times of the designed load.18 Advances in Civil Engineering

Figure 1 :
Figure 1: e position of the joint.

Figure 4 :
Figure 4: Detailed measurement of the test specimen.

Figure 7 :Figure 8 :
Figure 7: e theoretical and measured force of loading.

Figure 9 :Figure 10 :
Figure 9: e model and meshing of the joint with Abaqus.

Figure 10 :
Figure 10: Comparing the test and FE simulation.

Figure 13 :
Figure 13: Core area stress for di erent enhancement coe cients.

Figure 14
Figure 14: e stress nephogram under 3 times of the load.

Figure 16 :Figure 17
Figure 16: e stress nephogram under 4 times of the load.

Table 1 :
e material properties.

Table 3 :
e load procedure.

Table 4 :
e theoretical and measured forces of loading.

Table 5 :
e load and the reaction of the joint.

Table 7 :
e influence of the secondary load.

Table 8 :
e influence of secondary load in stress concentration.

Table 9 :
e influence of secondary load.

Table 10 :
Core area stress for different enhancement coefficients (MPa).Test point Under design load With secondary shear With all secondary loads a