Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 Porto, Portugal, 30 June - 2 July 2014 A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.) ISSN: 2311-9020; ISBN: 978-972-752-165-4

Nonlinear analysis of reinforced concrete shear wall using fiber elements Dae-Han, Jun1 Department of Architectural Eng., Faculty of Civil&Architectural Engineering, Donseo University, Jurye-ro 47, Sasang-gu, Busan, Korea email: [email protected]

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ABSTRACT: Reinforced concrete shear walls are effective for resisting lateral loads imposed by wind or earthquakes. Observed damages of the shear wall in recent earthquakes in Chile(2010) and New Zealand(2011) exceeded expectations. Various analytical models have been proposed in order to incorporate such response features in predicting the inelastic response of RC shear walls. However, the model has not been implemented into widely available computer programs, and has not been sufficiently calibrated with and validated against extensive experimental data at both local and global response levels. This study investigates the effectiveness of a wall fiber element in predicting the flexural nonlinear response of reinforced concrete shear walls. Model results are compared with experimental results for reinforced concrete shear walls with rectangular cross sections subjected to high axial load. The analytical model is calibrated and the test measurements are processed to allow for a direct comparison of the predicted and measured flexural responses. Response results are compared at top displacements on the walls. Results obtained in the analytical model for rectangular wall cross sections compared favorably with experimentally responses for flexural capacity, stiffness, and deformability. KEY WORDS: Reinforced concrete shear walls; Fiber element; Nonlinear response; Plastic hinge. 1

BACKGROUND OF THE STUDY

Reinforced concrete shear wall is widely used as a structural element as it has excellent resistance to lateral force due to seismic excitation or wind load and it reduces lateral displacement by increasing horizontal stiffness of high-rise buildings. However, it is recently reported that structural damages of shear wall occur more than expected in recent earthquakes even in the buildings that are engineered by relatively good seismic design1). Accordingly, interest in seismic safety of high-rise apartments with shear walls widely constructed in Korea and social demand toward an accurate evaluation of seismic performance are increasing 2). Reinforced concrete shear wall structure is a structural system usually applied to high-rise apartments and hotels of which space is partitioned in a certain area, and it is designed so that the wall can resist shear force following a horizontal load. In high-rise buildings, high axial load is applied to shear walls. Stiffness and capacity evaluation of shear wall under high axial load are important structural design factors. To evaluate the nonlinear behavior of reinforced concrete shear walls to the lateral load, a number of experimental and analytical studies have been performed worldwide, and recently, various nonlinear analysis models that can represent the nonlinear behavior of reinforced concrete shear walls have been suggested.2),3),4) The representative analysis model to predict the nonlinear behavior of reinforced concrete shear walls can be classified into microscopic modeling and macroscopic modeling. Finite element method is used in the microscopic modeling, and bending moment and shear force on the reinforced concrete shear wall can be accurately described in this method. In particular, when the behavior of a squat shear wall is predicted using a microscopic modeling, it is known that the local behavior appearing on the actual shear walls can be considered in a relatively accurate way compared to the

macroscopic modeling. Therefore, as this method can accurately present the nonlinear behavior of reinforced concrete shear walls, a precise nonlinear analysis is possible in isolated walls on which bending-compression and shear behavior occur in complex. However, when various structural elements such as coupling beam and slab are used in complex in a building structure, large number of finite elements are required to be used to perform a nonlinear analysis. In that case, running time becomes long and stability problems occur in the numerical analysis, thus the microscopic modeling is not appropriate as an analytical model. The macroscopic modeling can be easily applied compared to the finite element analysis when the structure is a high-rise building or the plan is complicated. Its drawback is that the analysis result is valid only in limited conditions.2) To overcome this limitation, many researchers have suggested various macroscopic models of reinforced concrete walls. However, accurate prediction is hard as the behavior of the wall differs greatly depending on the modeling approaches. Therefore, to accomplish a precise seismic performance evaluation of high-rise buildings or apartments with reinforced concrete shear walls, a nonlinear analysis model that can make accurate evaluation on reinforced concrete shear walls having various systems such as isolated wall and coupling wall, is needed. In this paper, we will use the fiber element model that can make more accurate analysis on nonlinear behavior of shear walls and study the applicability of the analytical model based on the existing experimental data. To achieve a nonlinear analysis of reinforced concrete shear walls, a large number of studies have been performed using microscopic models and macroscopic models. However, since each modeling method includes errors in analysis result, it is hard to decide which nonlinear analysis model can make an accurate evaluation. If the fiber element is used to compose a nonlinear analysis model of shear walls, it can effectively

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represent bending deformation of the element, by reflecting the material nonlinearity of concrete and steel reinforcement, while a precise prediction of the shear deformation is not possible. To evaluate the seismic performance of a shear wall structure with accuracy, a nonlinear spring element that can represent the shear deformation should be added to the fiber element model. In this study, reinforced concrete shear walls were modeled with fiber elements, which cross section and reinforcement details of shear walls can be arranged freely, and nonlinear analysis was performed by adding nonlinear shear spring elements that can represent the shear deformation. This analysis result will be compared with the existing experiment results. To investigate the nonlinear behavior of reinforced concrete shear walls, reinforced concrete rectangular section single shear walls subjected to high axial loading were selected. 2

FAILURE MODE OF SHEAR WALLS

Based on the experiments previously performed, ASCE41-06 defined the behavior of reinforced concrete shear walls by classifying with shear span ratio6). Slender shear wall with shear span ratio higher than 3.0 was defined to a show a flexural behavior. A wall with a shear span ratio lower than 1.5(squat wall or short wall) was defined to show a shear behavior. A reinforced concrete shear wall with shear span ratio between 1.5 and 3.0 was classified to be affected by both flexure and shear. In Figure 2-1(a), the longitudinal reinforcement located at the base of the walls on the tension side is gradually tended and at the ultimate state, successive failures occur from the steel reinforcement located on the boundary region, forming a flexure failure. Figure 2-1(b) shows the shear failure mode. An inclined failure occurs on shear walls due to the lack of transverse reinforcement. When sufficient transverse reinforcement is added on the wall, inclined failure can be prevented and it can resist high shear force. Here, when the compression stress increases on the compression strut and exceeds the compression strength of the concrete, the compression strut experiences a compression crushing, and ultimately an inclined compression failure can occur. As shown in Figure 2-1(c), in the case of shear walls on which inclined failures and inclined compression failures are prevented, a sliding shear failure can occur. Figure 2-1(d) shows a web crushing failure of shear walls caused by a cyclic load. 3 3.1

ANALYSIS MODEL OF SHEAR WALLS Fiber element model

Figure 3-1 shows the common 3-dimensional structural behavior of reinforced concrete shear walls. To represent the 3-dimensional behavior of reinforced concrete shear walls, the cross section is divided into fiber slices as shown in Figure 32. These fiber elements can model steel slice and concrete slice by assigning a stress-strain relation to each slice. Fiber slice can express the axial force and the bending moment behavior in the walls. W, C1, and C2 represent the shear behavior of walls and the columns attached to the walls. W is the spring that represents the in-plane shear stiffness of the shear wall, and C1 and C2 are springs that represent Y

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direction shear stiffness of the attached columns. It is assumed that the cross section of the shear walls maintains plane when an in-plane wall deformation occurs. Following the plane section remain plane assumption, strain of the fiber element in the cross section is proportional to the distance from the neutral axis. The stress of each slice is calculated using the stress-strain relation from the strain of each fiber slice, and the bending moment is calculated by summing the moments to the center of the cross section. 3.2

Shear spring element

If a fiber element is used in the nonlinear analysis model of reinforced concrete shear walls, material nonlinearity of concrete and reinforcement is reflected and only flexure behavior of the shear wall can be evaluated efficiently. However, the shear deformation cannot be assigned only by fiber element. To compensate this shortcoming, a nonlinear shear spring element that can represent the shear deformation should be added in the analytical model. Figure 3-3 shows the force-displacement relation of the nonlinear shear spring element. To achieve an accurate prediction of nonlinear behavior of reinforced concrete shear walls, accurate evaluation of initial stiffness, cracking strength, shear yielding strength, and yielding displacement of the nonlinear shear spring are important. Various parameters that define the nonlinear shear spring should be established depending on the failure mode of the shear wall. Figure 3-4(a) shows the force-displacement relation of reinforced concrete shear walls having a preemptive shear failure. In the figure, the shear yielding strength is reached before the steel reinforcement on the tension side reaches yielding and a shear failure occurs. Figure 3-4(b) shows the force-displacement relation of a shear wall having flexure-shear failure. First, yielding of flexure tension bar occurs and it reaches to a shear failure of reinforced concrete shear walls5). As shown in these figures, defining each parameter of nonlinear shear spring considering the failure mode of the shear wall can predict the nonlinear behavior of reinforced concrete shear walls with accuracy. 3.3

Stress-strain of the material

As seen above, the fiber element model can idealize the steel element and the concrete element by assigning a stress-strain relation. Figure 3-5 shows the stress-strain relation of the steel slice and the concrete slice, respectively. 4

ANALYTICAL SHEAR WALL MODEL

In this paper, a rectangular section single wall subjected to high axial load as shown in Figure 4-1 was selected, and the experiment result and the analysis result were compared. As shown in Figure 4-1, height, length, and thickness of the rectangular section single wall are 1750mm, 700mm, and 100mm, respectively. Shapes of the specimens are all same. Strength of reinforcing bar and concrete strength of each specimen are set differently by specimen. Horizontal load is applied at 1500mm height from the bottom of the wall. The nonlinear response analysis of reinforced concrete shear wall was carried out using CANNY-2010 software7). In a nonlinear static response analysis, the lateral force increased until the base section of shear wall reached ultimate states.

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014

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DISCUSSION OF ANALYSIS RESULT

In this study, a nonlinear analysis of reinforced concrete shear wall was accomplished using a fiber element model described in the section 3.1 to verify the validity of the analytical model. The validity was confirmed by comparing the result of the experimental research and the result obtained from the nonlinear response analysis. In the analytical model to examine the nonlinear behavior of a rectangular section single wall subjected to high axial load, the cross section of the shear wall is divided into concrete slice and steel slice as shown in Figure 3-2, and for the nonlinear shear spring, the shear strength-shear deformation relation was set as shown in Figure 3-3. Various equations have been suggested to estimate the shear strength and the shear stiffness. The nonlinear shear spring parameters were estimated by JBDPA code equations8). The calculated parameters of the nonlinear shear spring used in this analysis are shown in Table 5-1. The analysis was implemented up to the yielding point and the result before and after the yielding was compared based on the yielding point. Here, the yielding point was set based on the time when the longitudinal reinforcement yields on the tension side of the wall. The flexure cracking strength was defined as the time when the concrete cracks. In a shear wall structure, the plastic hinges are concentrated on the lowest floor when an ultimate load is applied. Therefore, high curvature ductility is required to well absorb the seismic energy. Depending on how to set the length of a plastic hinge, the value of the plastic deformation angle and wall displacement differs. Plastic deformation angle and plastic hinge length can be used to determine the curvature of the wall, and the curvature effects on the lateral displacement. Usually, the length of a plastic hinge is (1/2)lw of effective depth of the wall.9),10) Figure 5-1 shows the lateral load-lateral displacement relation of the shear wall SW7. Overall behavior of the shear wall based on the stiffness and the displacement was similar in the experiment result and the analysis result. It was confirmed that the initial stiffness and the yield strength of the shear wall were almost same in the experimental result and the analysis result. However, the yielding displacement of the shear wall was higher in the experiment than the analysis. It is considered that the stiffness degradation following the cyclic loading causes this higher yielding displacement in the experiment result. Figure 5-2 shows the lateral load-lateral displacement relation of SW8. Overall lateral load-lateral displacement relation until reaching the yield point was similar in the experiment result and the analysis result. However, the analysis result showed some difference of the initial stiffness and the ultimate strength of the wall. It is considered that strain hardening effect of reinforcement causes this higher ultimate strength in the experiment result. Figure 5-3 shows the lateral load-lateral displacement relation of the shear wall SW9. This shear wall was controlled primarily by shear behavior in experiment. The analysis result showed some difference behavior pattern to the behavior of the wall in the experiment. Overall behavior of the shear wall based on lateral load-lateral displacement relation was similar in the experiment result and the analysis result. In this analysis

of shear wall, after nonlinear shear spring element was the first to reach the yield state and the shear wall became ultimate state. Assuming that the shear spring is elastic, the yield strength of shear wall increased. Thus, the yield strength of the shear wall was almost same in the experimental result and the analysis result. However, the yielding displacement of the shear wall was still higher in the experiment than the analysis. This issue will be discussed in detail in the future studies.

(a) Bending failure

(b) Shear failure

(c) Sliding failure

(d)Web crushing failure

Figure 2-1. Failure mode in shear walls10)

Figure 3-1 Structural behavior of shear walls

Figure 3-2 Fiber model for shear walls

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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014

(a) Steel stress-strain relations

Figure 3-3 Shear force-deformation relation of shear spring

(b) Idealized concrete stress-strain relations Figure 3-5 Stress-strain relation of fiber slice

(a) Pre-emptive shear failure

(b) Flexure-shear failure Figure 3-4 Force-displacement relation according to failure mode of shear wall

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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014

Figure 5-2 Lateral load-displacement relation of SW8

Figure 4-1 Geometry and reinforcement details of rectangular wall specimens

Figure 5-3 Lateral load-displacement relation of SW9

Figure 5-1. Lateral load-displacement relation of SW7

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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014

Table 4-1 Experimental parameters of rectangular wall specimens SW7

SW8

SW9

Concrete compression strength fck(MPa)

29.7

32.0

35.4

Yield stress(MPa)

405

432

375

Reinforcement

4-ϕ14 (ϕ6@50)*

4-ϕ12 (ϕ6@50)*

4-ϕ20(ϕ6@75)*

Yield stress(MPa)

305

305

305

Size and space (mm)

ϕ8@150

ϕ8@150

ϕ8@150

Yield stress (MPa)

305

305

305(ϕ8), 366(ϕ6)

Size and space (mm)

ϕ8@100

ϕ8@100

ϕ8@75+ϕ6@150

499

784

595

Main flexural reinforcement Longitudinal reinforcement Horizontal reinforcement

Axial load (kN) Dimension of the specimen(mm): Lengh×Thickness×Height

700×100×1500

Table 5-1 Shear force-deformation parameters in nonlinear shear spring (These values correspond to parameters in shown figure 3-3) Specimens

Initial elastic stiffness K0(kN/cm)

Cracked stiffness ratio A(%)

SW7

692708

16

SW8

694580

SW9

726031

Post-yielding stiffness ratio B(%)

Cracking strength Fc(kN)

Yielding strength Fy(kN)

0.1

146.5

251.8

16

0.1

156.5

261.8

16

0.1

153.3

258.6

ACKNOWLEDGMENTS This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(No. 2012R1A1A4A01011211). REFERENCES [1] Wallace, J.W., “Behavior, Design, and Modeling of Structural Walls and Coupling Beams-Lessons from Recent Laboratory Tests and Earthquakes”, International Journal of Concrete Structures and Mechanics, Vol.6, No.1, pp3-18, March 2012. [2] Kim, D., Eom, T., Lim, Y., Lee, H., Park, H., “Macroscopic Model for Nonlinear Analysis of Reinforced Concrete Walls”, Journal of Korea Concrete Institute, Vol. 23, No. 5, pp. 569-579, 2011. 10. [3] Chadchart Sittipunt, Sharon L. Wood, Paniran Lukkunaprasit, Pichai Pattararattanakul, "Cyclic Behavior of Reinforced Concrete Structural Walls with Diagonal Web Reinforcement" ACI Structural Journal, Vol. 98. No. 4, pp. 554-562, 2001. 07-08. [4] Yunfeng Zhang, Zhihao Wang, "Seismic Behavior of Reinfored Concrete Shear Walls Subjected to High Axial Loading" ACI Structural Journal, Vol. 97. No. 5, pp. 739-750, 2000. 09-10. [5] Krolicki, J., Maffei, J., and Calvi, C.M., “Shear Strength of Reinforced Concrete Walls Subjected to Cyclic Loading”, Journal of Earthquake Engineering, Vo. 15(S1), pp30-71, 2011. [6] ASCE/SEI, Seismic Rehabilitation of Existing Buildings, ASCE/SEI 4106, American Society of Civil Engineers [7] Li, Kang-Ning, Three-Dimensional Nonlinear Dynamic Structural Analysis Computer Program Package-Users Manual, CANNY. 2010. [8] AIJ, Guidelines for Performance Evaluation of Earthquake Resistant Reinforced Concrete Buildings(Draft), Maruzen, Tokyo, 2004.I

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[9] Robert E. Englekirk, Seismic Design of Reinforced and Precast Concrete Buildings, John Wiley&Sons, 2003. [10] Paulay, T., and Priestley, M.J.N., Seismic Design of Reinforced Concrete and Masonry Buildings, John Wiley&Sons, 1991