The finite element analysis shows the formation of damage at the base of the shear wall first, and then the damage occurs at the wall-plate connection area. The influence of two parameters on the behavior of wall-slab connection, namely (a) aspect ratio of wall panel and (b) vertical reinforcement ratio of shear wall, is studied using the finite element model of the joint.
L IST OF T ABLES
L IST OF F IGURES
L IST OF S YMBOLS
Vc = Nominal shear strength provided by concrete Vd = Shear force carried by the squat wall. Vf = Factored shear force Vn = Nominal shear strength Vs = Steel shear resistance Vu = Factored shear force.
I NTRODUCTION
O VERVIEW
However, seismic design of wall-slab connection, in view of damage in slab and wall, has not been considered in any of the previous studies. Stresses and damage patterns are monitored in the wall, slab and at the shear wall-slab junction to see the possible failure modes in both wall and slab.
O RGANISATION OF THE R ESEARCH S TUDY
To perform nonlinear static analysis, an external sliding wall-slab structure of a multi-storey building is considered. Furthermore, lateral drift criteria are proposed based on the observed damage at the wall-plate junction region of the samples.
R EVIEW OF L ITERATURE
O VERVIEW
F AILURE M ODES OF S TRUCTURAL W ALL
- Slender Walls
- Squat Walls
Web shear cracks and flexural shear cracks occur in the web and at the bottom of the wall, respectively. Providing diagonal reinforcement in the web of the wall tends to resist the sliding shear failure mode.
- Equivalent Frame Models
- Multisprings Models
- Finite Element Models
- Strut and Tie models
The proposed analysis method consists of the application of the strut-and-tie model and accounts for contributions to shear strength from concrete struts and web reinforcement. The force Dc can be further compared to the support capacity of the wall panel.
C OUPLED S TRUCTURAL W ALLS
- Beam Coupled Shear Walls
- Modeling and Analysis
- Reinforcement in Coupling Beam
- Slab Coupling of Shear Walls
For slab-coupled shear walls, the coupling action is mobilized through the response of the connecting floor slab (Figure 2.14a). Under lateral loading, a pair of coupled shear walls underwent relative displacements in the longitudinal direction of the walls (Figure 2.18).
S TRUCTURAL W ALL -S LAB J UNCTION
The aim of the research was to quantify the shear capacity and response from the wall plate system. A modern finite element analysis was performed to study the behavior of shear critical walls.
D ESIGN OF S TRUCTURAL W ALL
- Flexure Design
- Provisions of IS: 13920-2016
- Provision of Other Codes
- Shear Design
- Provisions of IS: 13920-2016
- Provision of ACI 318-14
- Provision of Canadian Code A23.3-14
The cracked flexural strength of the wall section must be greater than its uncracked flexural strength. Vertical reinforcement concentrated near the ends of the wall is more efficient in resisting the bending moment.
P LASTIC H INGE L ENGTH
- Beams and Columns
- RC Walls
It was proposed that the length of the plastic hinge in the column be between 0.5h and h, where h is the depth or height of the part. The equation was used to calculate the plastic hinge length of columns with different aspect ratios that were tested by other researchers and the obtained values of Lp were compared. In that study, the bending ductility requirement was not underestimated, and the plastic hinge length provided a good approximation of the portion of the wall height over which out-of-plane buckling can occur.
The axial compressive force P can either be determined by analysis or estimated from the gravity load at the top of the plastic hinge region of the wall. The proposed plastic hinge length was found to be 40%-50% of the length of the plastic zone, i.e. of the yielding region.
D RIFT C RITERIA FOR S HEAR W ALL B UILDINGS
All previous studies on the length of the plastic hinges in RC walls were conducted on insulated walls without any connected floor slab. Results of the tests indicate that the walls detailed using a displacement-based design had a lateral drift capacity of greater than 2% of the specimen height, which was greater than required by design guidelines (which were prescribed if performed not -linear static analysis of different wall samples by varying parameters such as wall length, ratio of shear force to wall length, axial load level, amount of longitudinal reinforcement of boundary elements and horizontal web reinforcement. The model was developed based on the observed response of 39 quasi- static and shaking table experiments on RC walls.
All past studies on deformation limits in RC walls or lateral slip limits have been performed on thin isolated walls. None of the studies focused on evaluating such limits for RC walls connected to floor slabs in a multi-story building.
F INITE E LEMENT M ODELLING A ND
V ALIDATION
O VERVIEW
M ATERIAL M ODELLING
E LASTO -P LASTIC M ODEL
C ONCRETE D AMAGE P LASTICITY M ODEL
- Uniaxial tension and compression behaviors
- Strain rate decomposition
- Stress-strain relations
- Yield function
- Uniaxial Cyclic Behaviour
- Behavior of Concrete and Steel Reinforcement
In uniaxial tension (Figure 3.1b), the stress-strain response follows a linear elastic relationship until the failure stress value t0 is reached. The stress-strain curves are also converted to stress-versus-plastic strain curves of the form Eo. The effective tensile and compressive cohesive stresses determine the size of the plastic surface and are given as,.
These variables control the evolution of the yield surface and the degradation of the elastic stiffness. The degradation of elastic stiffness is characterized by two damage variables, dt and dc, as given in Eqs.
A NALYSIS P ROCEDURE
V ALIDATION
Although the shear wall and plate are planar parts of the diaphragm, they exhibit distinctly different behaviors. Pantazopoulos and Imran (1992) have reported that flexural shear cracks developed in the slab at the intersection with the shear wall with a lateral displacement of 3.5 mm. The tensile damage patterns obtained analytically at the intersection of the shear wall and the plate at the lateral displacement level of 3.5 mm and 21 mm are shown in Figures 3.11c and 3.12c, respectively.
It was observed that the crack initiation started at the junction between the shear wall and the plate and propagated in the plate. Damage in the slab was mostly concentrated within the area next to the shear wall.
F INITE E LEMENT M ODELLING
- Detailing of Shear Wall-Slab Junction
- Methodology
- Mesh Convergence Study
In the area of contact, the longitudinal plate reinforcement is extended to the wall. Restraints were introduced at the lower edges of the specimens in the direction of the applied load. Therefore, out-of-plane wall motion is limited in this study.
In monotonic static analysis, a displacement in the plane of the shear wall is applied at the top node of the wall. In the present study, the accuracy of the FE solution is evaluated by comparing the tensile damage model.
S UMMARY
The choice to use 150 mm mesh size is based not only on the load-deflection response, but also on the comparison with the damage patterns. It is observed that the prevalence of tensile damage does not depend on the mesh size. By using the 150 mm mesh size, the number of elements is reduced and the analysis takes less time to complete than by considering smaller mesh sizes.
Since the 150 mm mesh size is not affecting the damage propagation and is not yielding the maximum capacity, for all subsequent analyses, the 150 mm mesh size is adopted.
A SSESSMENT OF T ENSILE D AMAGE
- O VERVIEW
- D ETAILS OF S PECIMENS
- R ESPONSE OF F INITE E LEMENT M ODELS
- Behaviour of FSWB4 Model
- Behaviour of EWSC Model
- Comparison of FSWB and EWSC Models
- Comparison of EWSC and SSW Models
- S UMMARY A ND C ONCLUSIONS
In all cases, concrete cracking started at the base of the shear wall at a lateral displacement of 0.04%. The development of cracks at the base of the shear wall starts at a drift of 0.04%. Yielding of slab and wall reinforcement adjacent to the wall-slab connection area occurs simultaneously.
Most vertical reinforcing bars are provided in the connection area between sliding wall and slab. The behavior of the shear wall slab structure (EWSC), with respect to maximum tensile stresses and tensile damage, is in good agreement with the five-storey building model (FSWB).
A NALYSIS OF W ALL -S LAB A SSEMBLAGE : A
P ARAMETRIC S TUDY
- O VERVIEW
- D ESCRIPTION OF THE A SSEMBLAGE S TUDIED
- R ESPONSE OF S HEAR W ALL - S LAB A SSEMBLAGE
- Shear Force - Drift Relationship
- Minimum Principal Stress
- Propagation of Crack and Damage
- Tensile and Compressive Damages
- D ISCUSSION OF R ESULTS
Concrete cracking starts at the base of the shear wall and propagates to the wall-slab junction. Maximum cracking is observed in the floor slab at both ends of the wall-slab joint area. In the region of the shear wall-slab joint, most of the vertical reinforcing bars are released.
In addition, large cracks develop in the slab on the tension face of the wall-slab junction. Distance from wall face (mm) Distance from wall face (mm).
C ONNECTED W ITH F LOOR S LABS
- O VERVIEW
- P LASTIC H INGE L ENGTH
- Previous Work on Plastic Hinge Length
- M ODELLING AND A NALYSIS D ETAILS
- R ESULTS OF N ONLINEAR A NALYSIS
- Plastic Hinge Length
- C ONCLUSIONS
The height of the wall between the floors (floor height, hs) is kept constant at 5 meters. Therefore, the possible plastic hinge length in the wall-slab junction region is not sensitive to the level of axial compression applied to the top surface of the wall. Extensive cracking is expected towards the edge of the wall in the wall-slab junction area at the mentioned drift level.
However, the proposed expressions only apply to the plastic hinge region adjacent to the wall plate junction region. The amount of vertical steel in the wall is not observed to affect the plastic hinge length at the wall-plate junction region.
D RIFT C RITERIA FOR RC S HEAR W ALL
B UILDINGS
- O VERVIEW
- M ODELLING D ETAILS AND P ARAMETERS
- A NALYSIS D ETAILS
- E VALUATION OF R ESULTS AND P ROPOSED D RIFT L IMITS
- Variation of wall thickness
- Variation of slab thickness
- Variation of aspect ratio of wall panel
- P ROPOSED D RIFT L IMITS
- C ONCLUSIONS
Then cracks begin to develop at the bottom of the shear wall and in the slab at the wall-slab junction. The greatest variation in the level of lateral drift is observed in the shear wall at the junction. As the slab thickness increases, the value of the observed displacement for the maximum damage at the bottom of the shear wall decreases.
With an increase in the thickness of the slab, the driving level decreases for maximum damage to the base of the shear wall. For the slab at the junction region, the maximum tensile damage depends on the length of the shear wall panel.
S UMMARY AND C ONCLUSIONS
- O VERVIEW
- S UMMARY
- C ONCLUSIONS
- R ECOMMENDATIONS S COPE FOR F UTURE W ORK
In the present study, displacement-based nonlinear static analysis of the wall-plate assembly is performed considering both monotonic and cyclic modes. The axial compression on wall and the wall panel aspect ratio are varied to represent close shape equations for plastic hinge length of the shear wall when connected to the floor slab. Lateral drift limit for shear wall connected to floor slab: To investigate the lateral drift limit of the shear wall, parametric study of the wall-slab assembly is performed.
The main variables are the aspect ratio of the wall panel, the thickness of the shear wall and the thickness of the floor slab. The portion of the floor slab connected to the walls suffers significant damage at higher levels of lateral displacement.
R EFERENCES
Nonlinear analysis methods for reinforced concrete buildings with shear walls. Proceedings of the 14th European Conference on Earthquake Engineering. Performance-Based Evaluation and Design of Squat Reinforced Concrete Shear Walls.” MCEER Technical Report-09-0010, MCEER, Buffalo. Plastic damage model for cyclic loading of reinforced concrete structures.” Journal of Engineering Mechanics, ASCE.
Plastic hinge length of reinforced concrete, slender shear walls.” Journal of Concrete Research, ICE Virtual Library. Seismic Design of Reinforced Concrete and Masonry Buildings." John Wiley and Sons Inc., New York.
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