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Considering the effect of confined end-zone and unbonded reinforcement, the yield curvature and ultimate curvature of rabbet-unbond horizontal connection (RHC) shear wall were calculated. Based on the curvature calculation result, the yield displacement and ultimate displacement were calculated using displacement superposition, which were compared with test values. The result showed that theoretical values were slightly smaller than test values; however, on the whole, both were in good agreement. The author studied the effect of unbonded reinforcement on yield displacement and ultimate displacement, and the result showed that the effect on ultimate displacement is more pronounced than yield displacement. The present work could be useful for the design of new prefabricated shear wall.

In recent years, due to high industrialized level, good quality, convenient installation, energy conservation, and environment protection, the precast concrete structure is widely used. In particular, the prefabricated shear wall structure with large rigidity and great bearing capacity is the first choice for high-rise housings. In this regard, China has made policies to promote the development of the prefabricated shear wall structure [

To date, addressing the ductility calculation of different shear wall structures, many engineers or scholars have made contributions. For the conventional cast-in-situ shear wall, Si et al. [

Therefore, here, firstly, for the newly horizontal connection, considering the effect of confined end-zone and unbonded reinforcement, yield curvature and ultimate curvature are calculated, which prepares for displacement calculation. And then, yield displacement and ultimate displacement are calculated using displacement superposition, which is verified by the test values. Finally, the effects of unbonded reinforcement on yield displacement and ultimate displacement are studied.

The arrangement of the rabbet-unbond horizontal connection (RHC) is shown in Figures

(a) Prefabricated shear wall, (b) the RHC details, and (c) conventional connection details. Note: For the sake of clarity, the lateral web reinforcements in the upper and lower walls are not shown in (b) and (c).

This section calculates yield curvature and ultimate curvature considering effect of confined end-zone and unbonded reinforcement, meanwhile, which prepares for calculation of yield displacement and ultimate displacement in Section

According to test phenomenon of literature [

Force in (a) bonded cross section and (b) unbonded cross section. Note: _{1} and _{2} represent the resultant force of compressive concrete, respectively.

Regarding the “strain lag,” the unbonded cross section’s average strain distribution is no longer linear but bilinear (Figure

Average strain distributions in (a) bonded cross section and (b) unbonded cross section.

For the bonded shear wall, the ductility’ calculation is based on the plane section assumption and the deformation coordination assumption between reinforcement and concrete. Because the maximum moment locates at the bottom of the shear wall, the plane section assumption regards a rectangular region at the bottom as the basic deformation coordination region (Figure

Deformation coordination region of (a) bonded shear wall and (b) unbonded shear wall.

For the unbonded shear wall, we assume that in the compressed zone of the wall, the deformation of the unbonded reinforcement is consistent with the concrete deformation, but in the tensile zone of the wall, the deformation of the unbonded reinforcement is not consistent with the concrete deformation. In this regard, the traditional plane section assumption is no longer applicable, and the shape of the deformation coordination region is changed from the rectangular to the trapezoidal (Figure

For the sake of convenience, regard the concrete edge compressive strain of the maximum bending moment cross section as the calculated value, correspondingly, the equivalent compressive height of

Partial unbonded reinforced concrete beam.

The formula of

Since the shear wall can be regarded as the cantilever beam, the author employs

The assumptions to calculate the ductility of RHC shear wall are stated as follows:

The concrete is based on the plane section assumption and its tensile strength is not considered.

The compressed stress-strain curve of concrete and stress calculation of the vertical reinforcement refer to China code “Code for the design of concrete structures (GB 50010-2010, 2010).” The ultimate tensile strain of the vertical reinforcement is 0.01.

In compressed zone, the unbonded reinforcement deformation is coordinated with the concrete deformation.

The deformation coordination region in the unbonded segment is from rectangular to trapezoidal. The tensile reinforcement strain in the trapezoidal region is uniformly distributed. Deformation in the trapezoidal region obeys linear distribution.

In the yield state, the lateral deformation of compressive concrete is small, so stirrup stress is small, and stirrup restraint in the confined end-zone is not considered. The stress-strain relationship of concrete adopts unconfined stress-strain relationship. Assume that when bonded reinforcement segments in confined end-zone yield, the shear wall yields. Stress of the compressive concrete is assumed to be the linear triangle distribution. Deformation of reinforcement and concrete in compressive zone is assumed to be consistent. Stress and strain distribution in the yield state is shown in Figure

Stress and strain distribution profile in the yield state.

According to the force equilibrium, the following equation can be obtained as follows:

According to assumption (1), the deformation coordination equation is

Solve above equations and

In the ultimate state, the lateral deformation of compressive concrete is great, so stirrup restraint in confined end-zone should be considered. The stress-strain relationship of concrete adopts the confined stress-strain relationship. Assume that when the compressive concrete strain in confined, end-zone reaches ultimate compressive strain and shear wall reaches the ultimate state. Deformation of reinforcement and concrete in compressive zone is assumed to be consistent. What is more, compressive reinforcements are assumed to yield. The compression effect of unconfined concrete is not considered. Stress and strain distribution in ultimate state is shown in Figure

Stress and strain distribution profile in the ultimate state.

According to the force equilibrium, the following equation can be obtained:

The constitutive law of confined concrete referring to literature [

According to assumption (1), the deformation coordination equation is

From (

When

When

When

When

When

When

Solve the above equations, and finally we can obtain the ultimate curvature

The displacement ductility

Assume that wall’s displacement consists of two parts approximately: one part is the displacement that the wall generates resisting external force when all reinforcements are bonded, and assume the wall is not a rigid body and another part is the displacement that elongation of unbonded reinforcements leads the wall to generate when the wall is RHC wall, and assume the wall is a rigid body.

The shear wall can be regarded as a cantilever member. In a cantilever member, the curvature distribution of plastic hinge region is very irregular (Figure

(a) Bending moment, (b) curvature, and (c) lateral displacement of cantilever shear wall.

Based on the displacement equivalent principle in maximum bending moment region, the curvature distribution of plastic hinge region can be simplified, which consists of two parts: the plastic deformation region and the elastic deformation region.

Curvature is defined as the corner angle unit height, so the corner angle relative to the base section at any height

Therefore, the lateral displacement relative to the base section at any height

Define that when the base section of cantilever shear wall yields, shear wall yields. The yield curvature is linear distribution along the wall height _{y} (Figure

Curvature of cantilever shear wall.

Applying above equations, the yield displacement can be derived as follows:

Assume that when shear wall reaches the ultimate state, there is a equivalent plastic hinge region height

Applying above equations, the ultimate displacement can be derived as follows:

When calculating

(a) Rigid body rotation and (b) unbonded reinforcement deformation of RHC shear wall.

When unbonded reinforcements in tensile confined end-zone yield, elongation of unbonded reinforcements can be expressed as

Applying above equations, the yield displacement can be derived as follows:

When calculating _{u} is the compressive zone depth in the ultimate state obtained by Section

For

Applying above equations, the ultimate displacement can be expressed as

Two full-scale specimens (RHC-1, RHC-2) are designed and tested. The RHC specimen is composed of a base and a wall. The wall has a height, length, and thickness of 3.4 m, 1.7 m, and 0.2 m, as shown in Figure

Dimension and reinforcement details of the RHC shear wall specimen (unit: mm).

All of the materials (concrete, steel, and mortar) employed in the tests are selected based on China code “Code for design of concrete structures (GB 50010-2010, 2010).” The grade of concrete is C35, which denotes that the ultimate compressive strength of the cubic concrete specimens (15 cm × 15 cm × 15 cm) cured in standard conditions is 35 MPa, and its Poisson’s ratio is 0.2. Here, six cubic concrete specimens are tested.

The grade of steel in the tests is HRB400, where HRB denotes hot-rolled ribbed-steel bar and the number 400 denotes the yield strength. Its elastic modulus is 200 GPa and Poisson’s ratio is 0.3, and three sets of steels with different diameters (

The high-performance mortar is tested (160 mm × 40 mm × 40 mm) with a type of H-80, which is a characteristic of early strength, high strength, no shrinkage, and high fluidity.

The mechanical parameters of all materials are presented in Tables

Mechanical property of concrete.

Specimen number | Failure load (kN) | Compressive strength (MPa) | Average compressive strength (MPa) |
---|---|---|---|

1 | 880 | 39.11 | 39.86 |

2 | 910 | 40.44 | |

3 | 822 | 36.53 | |

4 | 960 | 42.67 | |

5 | 950 | 42.22 | |

6 | 860 | 38.22 |

Mechanical property of steel.

Specimen number | Steel diameter | Yield strength (MPa) | Ultimate strength (MPa) | Ratio of tensile strength to yield strength | Elongation (%) |
---|---|---|---|---|---|

1-1 | 10 | 445 | 625 | 1.4 | 24 |

1-2 | 455 | 615 | 1.35 | 24 | |

Average value | 450 | 620 | 1.375 | 24 | |

2-1 | 12 | 445 | 575 | 1.29 | 25 |

2-2 | 460 | 585 | 1.27 | 25 | |

Average value | 452.5 | 580 | 1.28 | 25 | |

3–1 | 16 | 465 | 600 | 1.29 | 25 |

3-2 | 460 | 600 | 1.30 | 25 | |

Average value | 462.5 | 600 | 1.295 | 25 |

Mechanical property of high-performance mortar.

Test item | Time | Measured value |
---|---|---|

Compressive strength (MPa) | 1 d | 24.96 |

28 d | 93.52 | |

Rupture strength (MPa) | 1 d | 5.29 |

28 d | 10.44 |

The quasistatic cyclic tests of the RHC shear wall are performed. Axial load is applied by tensioning prestressed reinforcement strands, and the lateral load is applied by the 150 t hydraulic actuator. The loading protocol employed consists of a load control procedure first and a displacement control procedure then. Moreover, four steel supports are employed on both sides of the wall symmetrically to keep the lateral stability of the specimen during the testing process. The lateral displacements of the wall are monitored by seven displacement transducers. The testing system is shown in Figure

Test setup: (a) schematic and (b) photograph.

For the RHC-1 specimen, the first crack observed at 210 kN was horizontal flexural cracks when the specimen was pulled, which occurred near the bottom of the wall. The crack on the top interface of rabbet was generated at 240 kN when the specimen was pushed. However, for the RHC-2 specimen, the first crack was observed at 270 kN when the specimen was pushed, which occurred near the bottom of the wall. The crack on the top interface of rabbet was generated at 300 kN when the specimen was pushed.

The yield state was defined as when bonded reinforcement segments in the confined end-zone yielded, the specimen yielded. The increase of the applied load resulted in the propagation of cracks and initiation of new flexural cracks along the specimen. Further load increase extended the existing flexural cracks into flexure shear cracks and caused initiation of vertical cracks. In addition, the cracks in the center of the test specimen propagated to the compressed zone, and the crack width and the displacement increased. Finally, when the lateral resistance degenerated to 85% of the peak load, defined as the failure of the specimen, the failure mode was a typical flexural failure for each specimen, which was controlled by crushing concrete at the plastic region near the bottom of the wall. The final crack pattern and failure mode are shown in Figure

Final crack pattern and failure mode of (a) RHC-1 specimen and (b) RHC-2 specimen.

From Figure

The lateral load versus top displacement curves of the two specimens is shown in Figure

Hysteresis curves and skeleton curves of RHC-1 and RHC-2. (a) Hysteresis curve of RHC-1. (b) Skeleton curve of RHC-1. (c) Hysteresis curve of RHC-2. (d) Skeleton curve of RHC-2.

It is observed in Figure

From the tests, we obtain the crack load

Test results of two specimens.

Specimen |
_{cr} (kN) |
Δ_{cr} (mm) |
_{
y} (kN) |
Δ_{y} (mm) |
_{
m} (kN) |
Δ_{m} (mm) |
_{
u} (kN) |
Δ_{u} (mm) |
---|---|---|---|---|---|---|---|---|

RHC-1 | 210 | 12.28 | 330 | 18.30 | 610 | 85.44 | 518.50 | 137.70 |

RHC-2 | 270 | 11.74 | 420 | 13.60 | 718 | 46.49 | 610.30 | 75.50 |

Table

Applying (

Applying (

From (

Comparison of theoretical and test values of displacement ductility.

Specimens | Yield displacement (mm) | Ultimate displacement (mm) | Displacement ductility | ||||
---|---|---|---|---|---|---|---|

Theoretical | Test | Theoretical | Test | Theoretical | Test | Theoretical/test | |

RHC-1 | 15.23 | 18.30 | 133.57 | 137.70 | 8.77 | 7.52 | 1.16 |

RHC-2 | 11.74 | 13.60 | 68.52 | 75.50 | 5.83 | 5.60 | 1.04 |

Table

In order to study the effect of unbonded reinforcement on yield displacement and ultimate displacement, set RHC-2 as example, Table

Effect of unbonded reinforcement on yield displacement and ultimate displacement.

Yield displacement (mm) | Ultimate displacement (mm) | ||||||
---|---|---|---|---|---|---|---|

Δ_{y1} |
Δ_{y1}/Δ_{y} |
Δ_{y2} |
Δ_{y2}/Δ_{y} |
Δ_{u1} |
Δ_{u1}/Δ_{u} |
Δ_{u2} |
Δ_{u2}/Δ_{u} |

9.22 | 78.53% | 2.52 | 21.47% | 21.06 | 30.74% | 47.46 | 69.26% |

Table

In this paper, the curvature and displacement of RHC shear wall are analyzed, and the following conclusions can be drawn:

Considering the effect of confined end-zone and unbonded reinforcement on curvature, yield curvature and ultimate curvature are calculated.

In calculating displacement, assume that the displacement consists of two parts approximately: one part is that the wall generates resisting external force when all reinforcements are bonded, and assume the wall is not a rigid body and another part is that elongation of unbonded reinforcements leads the wall to generate when the wall is RHC shear wall, and assume the wall is a rigid body. Overlay the two parts linearly, and obtain the calculation equation of yield displacement and ultimate displacement. The theoretical and test values are compared. Also, the result shows that theoretical values are slightly smaller than test values, but both are in good agreement on the whole.

According to the theoretical equation, effects of unbonded reinforcement on yield displacement and ultimate displacement are studied. The result shows that the effect of unbonded reinforcement on ultimate displacement is more pronounced than that of yield displacement.

Only two specimens were applied to verify the displacement ductility in the paper, which was inadequate to convince. Numerous tests considering different parameters should be performed to verify the displacement ductility.

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

This work was financially supported by the Green Subway Construction Innovation Team of Jinan, National Natural Science Foundation for Young Scientists of China (Grant No. 51708260), the University Natural Science Foundation funded by the Jiangsu Province Government (Grant No. 2016TM045J).