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Based on existing experimental results, the finite element analyses were carried out on shear wall structures with steel truss coupling beams. This work studied the seismic behaviors and the working mechanism of the steel truss coupling beam at the ultimate state and put forward two parameters: the area ratio of web member to chord and the stiffness ratio of coupling beam to shear wall. The seismic optimum design method of the coupling beam was also proposed. Afterwards, a comparative analysis was implemented on the three-dimensional shear wall model with steel truss coupling beams designed by the proposed design method. The results show that the structures designed by the proposed method have excellent seismic behaviors, the steel truss coupling beams have enough stiffness to connect shear walls effectively, and its web members have appropriate cross sections to dissipate seismic energy.

Coupling beams (CBs) are important structural components to shear wall structures as they provide effective connections between shear wall limbs and increase global lateral stiffness. The seismic performance of shear wall structure is largely dependent on the behaviors of CBs. The steel CB has a lot of advantages such as light weight, good ductility, force clear, and easy to be replaced after the earthquake. Ever since the beginning of research on the steel CBs in the 1990s, the structural behaviors of steel CBs have been investigated by experiments and theoretical analysis [

In recent decades, composite structures [

Given the above reasons, this work presents a finite element study on the seismic behaviors of steel truss CBs; simulation results are compared with available test results. Seismic behaviors and mechanical performances under limit states are further discussed. Based on the working mechanism analysis, the area ratio of web member to chord and the stiffness ratio of coupling beam to shear wall are proposed for the evaluation of seismic performances of steel truss CBs.

This paper is structured as follows. In Section

Steel truss CBs are specific steel trusses with small span-depth ratio, which can effectively connect shear wall limbs under seismic actions, dissipate seismic energy, and reduce damage during earthquakes. The differences between the steel truss CB and conventional steel truss lie in the following: (1) diagonal web members can be utilized to dissipate seismic energy and (2) steel chords are presented as an effective connection between shear walls; chord members will remain in elastic stage during working without producing plastic hinges at the ends.

Taking into consideration the structural characteristics, the steel truss CB and steel truss will have similarities to some extent in the working mechanism. Thus, the area ratio of web member to chord

The shear wall limb deforms horizontally and inclines under horizontal seismic actions. Because of the global deformation of shear wall limb, the deformation of steel truss CB will include rigid body motion, the rotation at the end of CB chords, and relative displacements of top and bottom chord members. Thus, as shown in Figure

Deformation mode and internal force of steel truss CBs.

It is assumed that the shear force at level

By substituting (_{y}, it can be obtained that

Total shear force at the CB ends is composed of vertical force component of web member and the shear forces of chords. As the shear force of chords is generated from rotation at joints, which can be considered as the interstorey displacement angle

Before the web member reaches the plastic stage, the shear stiffness of CB can be derived based on interstorey shear deformation as

The lateral stiffness of shear wall can be obtained as

The finite element model of shear wall steel truss CBs, as shown in Figure

Shear wall specimens with steel truss CBs: (a) elevation; (b) reinforcement details of shear wall on the second floor; (c) reinforcement details of shear wall on the first floor; (d) dimensions of CBs.

The finite element model: (a) shear wall structure; (b) CBs.

Concrete stress-strain curve.

Constitutive relations of steel.

Mechanical behavior of samples.

Steel grade | Position | Diameter (mm) | Standard value of compression strength (N/mm^{2}) |
Ultimate strength (N/mm^{2}) |
Elastic modulus (N/mm^{2}) |
---|---|---|---|---|---|

HPB235 | Stirrup | 6 | 229.7 | 583.0 | 2.45 × 10^{5} |

HPB235 | Longitudinal bar | 8 | 318.1 | 457.3 | 1.86 × 10^{5} |

I10 | Chord member | Web | 342.6 | 400.5 | 1.87 × 10^{5} |

Flange | 307.69 | 387.5 | 1.92 × 10^{5} |
||

L30 × 3 | Web member | — | 463.8 | 521.7 | 1.82 × 10^{5} |

Concrete | Base | — | 48.98 | — | 3.45 × 10^{4} |

Since specimens were loaded under pseudodynamic tests, the positive and negative skeleton curves are found not strictly symmetrical because of the certain damage existed in specimens. As shown in Figure

Skeleton curves on top floor of the specimen.

Hysteretic curves on top floor of the specimen.

Comparison of the calculation results.

Yield load _{y} (kN) |
Ultimate load _{u} (kN) |
||||
---|---|---|---|---|---|

Test value | FEM | Error (%) | Test value | FEM | Error (%) |

69.44 | 63.36 | 8.75 | 116.18 | 115.58 | 0.52 |

Specimens details.

Span (m) | Depth (m) | Chord member size (mm) | Web angle steel properties (mm) | |
---|---|---|---|---|

Limb width | Thickness | |||

0.45 | 0.3 | Half-I10 | 30 | 3–7 |

0.45 | 0.3 | Half-I10 | 40 | 3–5 |

0.45 | 0.3 | Half-I10 | 45 | 4–6 |

0.45 | 0.3 | Half-I10 | 50 | 4–6 |

0.45 | 0.3 | Half-I10 | 56 | 4,5,8 |

0.45 | 0.3 | Half-I10 | 63 | 4–6, 8, 10 |

Several load-displacement curves of specimens are obtained and plotted in Figure

Base shear-displacement curves of the specimen.

Reversed displacement loadings have been applied on specimens with web members of L30 angle steel; hysteretic curve is shown in Figure

Load-displacement hysteresis curves of specimens: (a) L30 × 3; (b) L30 × 5; (c) L30 × 7.

Bearing capacities of the specimens.

Diagonal web member style | Case 1: diagonal web member yielding | Case 2: ultimate state | ||||
---|---|---|---|---|---|---|

Test value | Result from this work | FEM | Test value | Result from this work | FEM | |

L30 × 3 | 69.44 | 68.79 | 63.36 | 116.18 | 97.28 | 115.58 |

L30 × 4 | — | 87.33 | 95.78 | — | 115.67 | 101.43 |

L40 × 3 | — | 89.78 | 84.96 | — | 118.10 | 104.47 |

L40 × 4 | — | 115.31 | 115.11 | — | 143.43 | 142.87 |

L40 × 5 | — | 140.15 | 137.46 | — | 168.06 | 159.93 |

Equivalent viscous damping coefficient,

As shown in Figure

Equivalent viscous damping coefficients of specimens are calculated and plotted in Figure

In order to study the deformation styles of steel truss CBs under limit state, the deformation of specimens can be divided into three major types as shown in Figure

Type I: steel truss chords keep in elastic stage and the deformation is small; overall bending deformation occurs in diagonal web members, with

Type II: steel truss chords deform to some extent, diagonal web members buckle locally, it is likely that chord members will enter the plastic stage, but within a limited degree, with

Type III: wave style buckling and plastic deformation occur on chord members wavy deformation occurs, enter more plasticity, however, diagonal web members remain straight without bending deformation, with

Deformation modes of the coupling beams: (a) type I:

In the deformation type I, deformation of CB chord is small, chord members are in elastic stage; globally bending deformation occurs on diagonal web members. In the deformation type II, CB chord members deform to elastoplastic state; local buckling occurs on diagonal web members, which will have certain impact on the energy dissipation performances of steel truss CBs. In the deformation type III, the deformation of web members is small because of the big sizes of web members; however, large plastic deformation occurs on chords. In this case, seismic energy is majorly dissipated by the plastic deformation and plastic hinges occurred on chord members, which may result in a decrease of bearing capacity of steel truss CBs. The connection between shear wall limbs will also be reduced. Therefore, the deformation types I and II can satisfy the requirement of steel truss CBs; however, the deformation characteristics and energy dissipation performances of the type III are not satisfactory.

Taking into consideration the bearing capacity and energy dissipation performance analysis results, the reasonable area ratio and stiffness ratio of steel truss CBs can be obtained as the threshold value between the deformation types I and II, namely:

In order to ensure that the steel CBs will deform as the style I and II, it is suggested that the area ratio and stiffness ratio of steel truss CBs should not exceed 0.5.

The main function of steel truss CBs lies in an effective connection between shear wall limbs and energy dissipation under seismic actions through the plastic deformation of CB web members. Since the CB web member will definitely reach plastic deformation stage under heavy seismic actions, no specific provision could be found related to this situation. Therefore, it is not practical to design the steel truss CBs based on the ultimate limit state design method specified in current codes code of practice for building design. This research proposes steel truss CB design methods based on the foregoing characteristics. The proposed design method is to achieve certain seismic performances by appropriately designed stiffness ratio and area ratio of steel truss CBs. Specifically, reasonable designed area ratio will be used to ensure energy dissipation performances of web members, and the stiffness ratio will be utilized to provide an effective connection between shear wall limbs.

The effective length of chord member under compression is defined as

By substituting

The bearing capacity of the steel truss CB is evaluated by considering two cases:

Under small earthquakes, diagonal web members yield and the steel truss CBs reach the bearing capacity, then interstorey displacement can be calculated as

Under heavy earthquakes, in order to avoid shear failure of steel truss CBs, the bearing capacity can be calculated when the chord member yields. At this time, the interstorey displacement is

By substituting (

Table

In order to study the three-dimensional behaviors of the steel truss CBs and shear wall limbs, a six-storey three-dimensional shear wall model with steel truss CBs is established for numerical studies, as shown in Figures

Multilevel shear wall model with steel truss coupling beam.

Multilevel three-dimensional finite element shear wall model with steel truss CBs.

Specimen details of steel truss CB shear wall structure.

Specimen | Chord member type | Web member type | Area ratio | Stiffness ratio |
---|---|---|---|---|

WALL1 | Half-I10 | L30 × 3 | 0.2448 | 0.0765 |

WALL2 | Half-I10 | L40 × 4 | 0.4321 | 0.1435 |

WALL3 | Half-I10 | L56 × 5 | 0.758 | 0.26 |

Bottom shear force versus top displacement

Base shear force-top displacement curves of the specimens.

In order to evaluate the energy dissipation behaviors of the steel truss CB structure, bottom shear force versus top displacement hysteresis curves are plotted in Figure

Hysteretic curves of bottom shear force versus top displacement: (a) WALL1; (b) WALL2; (c) WALL3.

Equivalent viscous damping coefficients are calculated and presented in Figure

Equivalent viscous damping coefficient,

Judging from the deformation and stress states of the concrete shear wall limbs and steel truss CBs, the deformation and stress are large in the lower storey and relatively small in the upper storey. In order to investigate the failure deformation and characteristics, the shear wall deformation and Mises stress obtained under the largest deformation load are presented in Figure

Deformation and Mises stress (unit: N/m^{2}) of the shear walls: (a) specimen WALL1; (b) specimen WALL2; (c) specimen WALL3.

The deformation shape and Mises stress state of steel truss CBs under the largest displacement load are presented in Figure

Deformation and Mises stress (unit: N/m^{2}) of the steel truss CBs on the 1st floor: (a) specimen WALL1; (b) specimen WALL2; (c) specimen WALL2.

From the above analysis, it is understood that the stiffness ratio and area ratio of steel truss CBs have a significant impact on the shear wall rigidities, energy dissipation properties, stress distribution, and deformation model under seismic actions. Reasonable stiffness ratio and area ratio will result in better shear wall structures with excellent deformation properties and energy dissipation capacities under earthquakes.

This research investigates the mechanical properties and seismic performances of steel truss CBs. The stiffness ratio and area ratio are proposed for effective evaluation and design of the steel truss CB. Numerical simulations have been conducted to understand the structural and seismic performances by employing different types of steel truss CBs. Conclusions are made as follows:

Steel truss CB structures can achieve good seismic performances by the appropriate design of web and chord members. Steel members work cooperatively to satisfy strength and seismic capabilities required under seismic actions.

Three major deformation patterns of steel truss CBs, with specific threshold values of stiffness ratios and area ratios, are proposed for the classification of steel truss CB structures under heavy seismic action. It is suggested that the bearing capacities and seismic energy dissipation properties of the pattern II is the best, which can be further adopted in practical design.

The area ratio reflects the compatibility among steel truss members; reasonable area ratio will definitely result in good energy dissipation performances of steel truss CBs.

The stiffness ratio demonstrates relative rigidities between the steel truss CBs and shear walls, as major connections between shear wall limbs; reasonable stiffness ratio can ensure an effective combination between neighboring limbs.

The proposed seismic design methods based on the stiffness ratio and area ratio will provide efficient and effective seismic design of shear wall structures with steel truss CBs; it also helps to avoid compatibility problems among truss members in the structure design.

The steel truss CB shear wall structure with reasonable stiffness ratio and area ratio will have good deformation properties and energy dissipation capacities; meanwhile, reasonable stiffness ratio ensures effective connections between shear wall limbs. Therefore, it is understood that the proposed steel truss CB structure will perform satisfactorily during earthquakes.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Zhiheng Deng was the project leader. Changchun Xu is a PhD candidate who built the model and conducted the numerical simulation. Qiang Hu supervised the work. Jian Zeng helped to organize data and draw pictures. Ping Xiang analyzed the data and wrote the paper. All authors contributed to discussion of the results.

The work described in this paper was supported by grants from the National Natural Science Foundation of China (Grant no. 51268005), Guangxi Natural Science Foundation (Grant no. 2013GXNSFAA019311), and startup research funding from Central South University (Grant no. 502045006).