Modeling of Squat Structural Walls Controlled by Shear

ACI Structural Journal, Sep/Oct 2009 by Massone, Leonardo M, Orakcal, Kutay, Wallace, John W

Reinforced concrete squat walls are common in low-rise construction and as wall segments formed by window and door openings in perimeter walls. Existing approaches used to model the lateral force versus deformation responses of wall segments typically assume uncoupled axial/flexural and shear responses. A more comprehensive modeling approach, which incorporates flexure-shear interaction, is implemented, validated, and improved upon using test results. The experimental program consisted of reversed cyclic lateral load testing of heavily instrumented wall segments dominated by shear behavior. Model results indicate that variation in the assumed transverse normal stress or strain distribution produces important response variations. The use of the average experimentally recorded transverse normal strain data or a calibrated analytical expression resulted in better predictions of shear strength and lateral load-displacement behavior, as did incorporating a rotational spring at wall ends to model extension of longitudinal reinforcing bars within the pedestals.

Keywords: pier; reinforced concrete; shear strength; spandrel; squat wall.

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INTRODUCTION

Squat walls (with aspect ratios typically less than 1.5) are very common in low-rise construction and at lower levels of tall buildings (for example, parking level walls or basement walls). They can also be found in long walls with perforations due to window and door openings, resulting in wall segments between openings. The design of wall elements is usually oriented toward supplying sufficient shear strength to promote flexural yielding (for example, ACI 318-081 Section 21.9); therefore, a model that appropriately accounts for nonlinear flexural behavior is required. For low aspectratio walls or wall segments, behavior is often dominated by nonlinear shear responses, and the modeling parameters selected for shear stiffness and strength can have a significant impact on the predicted distribution of member forces and on building lateral drift. For example, FEMA 3562 recommends use of 0.4Ec to model the effective preyield shear stiffness despite the lack of test data to support the use of this value and the impact of shear cracking on effective stiffness. Additionally, the impact of flexural deformations on the overall load-deformation relation for wall segments with shear-dominant behavior (for example, with failure mode controlled by crushing along a diagonal compression strut and lateral displacements dominated by shear deformation associated with diagonal tension and cracking) may be important, although the FEMA 356 backbone relations appear to imply that nonlinear load-versus-deformation response is either due to flexure or shear, but not both.

According to experimental evidence, flexural and shear deformation interaction exists even for relatively slender walls with an aspect ratio of 3 to 4, with shear deformations contributing approximately 30% and 10% of the first-story and roof level lateral displacements, respectively.3 The degree of interaction for smaller aspect ratios, and particularly for squat walls with an aspect ratio of less than 1, is unclear. There is a need for relatively simple modeling approaches that consider interaction between flexure and shear responses, and capture important response features for a wide range of wall geometries and reinforcing details. Although a relatively large number of wall tests are reported in the literature, the primary focus for most of these tests is the assessment of wall shear strength and overall load versus lateral displacement response, as opposed to assessment of relative contributions of flexural, shear, and anchorage deformations to wall lateral displacements, which is necessary for validating existing and developing new modeling approaches. Therefore, experimental studies that incorporate very detailed instrumentation layouts are needed to allow development and verification of new approaches that focus on robust and mechanical and/or behavioral models to represent the load-deformation responses of squat walls controlled by shear.

Based on the preceding discussion, a modeling approach capable of incorporating flexure-shear interaction is implemented and evaluated using experimental results. Model improvements needed to capture the overall lateral load versus lateral displacement response, as well as the relative contribution of flexural and shear deformation responses, are implemented and validated using data from an experimental program conducted on lightly reinforced squat walls with shear-dominant behavior. Test results on heavily instrumented test specimens enabled a range of modeling parameters and assumptions to be investigated, ultimately yielding improved agreement between experimental and model results.

RESEARCH SIGNIFICANCE

Low-aspect-ratio reinforced concrete walls, with heightto- length ratios less than 1.5, are common in low-rise and perforated-wall-type construction. Accurate modeling of the load-versus-deformation response and the lateral-load stiffness of such walls is essential to estimate building lateral displacements as well as the distribution of forces among elements of the lateral-load-resisting system. A model that reasonably captures measured responses, including coupling of flexure-shear behavior, is proposed and model results are validated by comparison with test results from heavily instrumented wall segments. Based on the study, recommendations for modeling the load-deformation responses of squat walls are provided.