Slender Walls Research Articles

Finite element modelling of reinforced masonry walls under axial compression

This paper presents the development of 3D finite element (FE) technique to model and analyse reinforced masonry (RM) walls under axial compression. The Arc-length algorithm integrated with initial geometric imperfection has been used to model the geometric nonlinear response of both the embedded steel and that of the RM wall to allow for the occurrence of buckling under concentric compression. A segmental modelling technique was developed to consider geometric and material nonlinearities of each component of a RM wall such as block, mortar, grout and reinforcement bars. The modelling parameters were calibrated using the RM wall experimental testing program previously conducted by the authors in which three series of RM walls with different slenderness ratios (4, 7 and 12) were tested under axial compression. The applicability of the models was verified using the experimental data in terms of axial load-deflection responses and strain in vertical steel bars. It was determined that the developed modelling technique was able to capture the experimental responses with reasonable accuracy. Further, the verified FE model was used to predict the responses of RM walls of higher slenderness ratios (21, 26, 32 and 42) to examine the probable buckling of taller RM walls. The failure modes and the ultimate capacity of slender RM walls have been reported and the potential of using the RM for taller walls are discussed against the existing code provisions.

Out-of-Plane Experimental Study of Strengthening Slender Non-Structural Masonry Walls

Non-structural masonry partition walls, which are mainly designed to functionally separate spaces in the buildings and provide physical barriers between rooms, were traditionally built from either solid or hollow clay units or autoclaved aerated concrete blocks. Recent earthquakes have revealed the high vulnerability of these elements, even in the case of low to moderate seismic events. Public buildings (e.g., hospitals and schools) are particularly vulnerable. Due to their greater floor-to-floor heights and the response spectra of floors, the dynamic response of primary structure may provoke significantly higher seismic loads on partition walls. The main goal of the presented experimental study was to investigate the behavior of slender partition walls loaded out-of-plane with a simple and cost-effective approach that may be applied through routine refurbishment works. Eleven full-scale slender non-structural masonry partition walls were built with brickwork and cement–lime mortar. Eight of them were additionally strengthened with different techniques, including glass fiber-reinforcing fabric and low-cost glass fiber-rendering mesh. To evaluate the efficiency of the applied strengthening solutions, out-of-plane quasi-static cyclic experiments were conducted. By applying meshes over the entire surfaces, the resistance was significantly improved with the low-cost approach reaching half of the resistance of the commercially available strengthening system preserving the same displacement capacity.

Fragility functions for local failure mechanisms in unreinforced masonry buildings: a typological study in Ferrara, Italy

Unreinforced masonry buildings undergoing seismic actions often exhibit local failure mechanisms which represent a serious life-safety hazard, as recent strong earthquakes have shown. Compared to new buildings, older unreinforced masonry buildings are more vulnerable, not only because they have been designed without or with limited seismic loading requirements, but also because horizontal structures and connections amid the walls are not always effective. Also, Out-Of-Plane (OOP) mechanisms can be caused by significant slenderness of the walls even if connections are effective. The purpose of this paper is to derive typological fragility functions for unreinforced masonry walls considering OOP local failure mechanisms. In the case of slender walls with good material properties, the OOP response can be modeled with reference to an assembly of rigid bodies undergoing rocking motion. In particular, depending on its configuration, a wall is assumed either as a single rigid body undergoing simple one-sided rocking or a system of two coupled rigid bodies rocking along their common edge. A set of 44 ground motions from earthquake events occurred from 1972 to 2017 in Italy is used in this study. The likelihood of collapse is calculated via Multiple Stripe Analysis (MSA) from a given wall undergoing a specific ground motion. Then, the single fragility functions are suitably combined to define a typological fragility function for a class of buildings. The procedure is applied to a historical aggregate in the city center of Ferrara (Italy) as a case study. The fragility functions developed in this research can be a helpful tool for assessing seismic damage and economic losses in unreinforced masonry buildings on a regional scale.

A drift-based design procedure for RC buildings considering the effect of shear wall-floor slabs junction

Reinforced Concrete (RC) structural wall is widely used in the lateral force resisting system for multistoried RC frame buildings located in earthquake-prone regions. In such buildings, the wall is connected to the RC slab at every floor level. The junction region of shear wall and floor slab constitutes an important link in the load path from slab to wall during earthquake shaking, thereby influencing the pattern of lateral load distribution in the shear wall. In case of multistoried building, the maximum elastic drift is estimated by carrying out linear static analysis for different load combinations as recommended by the Indian Earthquake Code IS 1893 (Part 1): 2016. However, during strong earthquake shaking, the inelastic lateral drift needs to be monitored to avoid undesirable levels of damage in structural members. The inelastic drift level of an isolated slender shear wall considering the behaviour of wall-slab junction has not been studied in the past. The present study aims to investigate the possible lateral drift limit of RC wall frame building considering the effect of floor slabs.

Designing GFRP-Reinforced Tilt-up Wall Panels

Tilt-up construction was effectively enabled on a wide scale in 1979, when the ACI committee 551 report on Tilt-up construction was published, the Recommended Tilt-Up Wall Design, aka, the Yellow Book and the subsequent ACI-SEASC Task, aka the Green Book, and another Tilt-up design and construction manual developed by the ACI in 1988. The Tilt-up Concrete Association was created in 1986 by a group of industry professionals who had the need of an organization dedicated to the industry. ACI 551 maintains a document outlining the standard practice for contemporary Tilt-up design and construction. The ACI 551 document does not consider walls reinforced with non-ferrous reinforcement. However, recent events have made glass fiber-reinforced polymer rebar a more economical option when compared to traditional steel reinforcement. This white paper is intended to provide the unfamiliar engineer a bridge between the ACI 318, ACI 551 and ACI 440 documents to engineer a tilt-up wall including differences between GFRP reinforcement and steel reinforcement with respect to design. Steel, is an isotropic ductile metal extensively used in construction, mechanical, and electronic devices. Steel is often designed as elastic-perfectly plastic where it has an elastic modulus of 29,000ksi and yield stress of 60ksi. GFRP reinforcement is considered brittle-elastic with an elastic modulus often between 6,000ksi – 8750ksi and guaranteed ultimate tensile strength between 90-150ksi. Figure 1 presents an example of the design-assumed uniaxial stress versus strain comparing traditional steel and GFRP. While GFRP reinforcement has different physical and mechanical properties the differences and behaviors are well understood by the engineering community. There are ASTM material standards for GFRP bars, namely ASTM D7957 and a complete suite of ASTM test method by which the basic properties are verified. The following sections will illustrate the differences between steel and GFRP reinforced concrete members with a focus on slender tilt-up wall panels.

Hot‐dip galvanizing of steel structural members: an alternative to passive fire insulation?

AbstractObservations from several experimental campaigns in the past years in Europe on unloaded steel members have highlighted the positive impact of hot‐dip galvanizing on the heating of steel profiles. Indeed, the temperature rises more slowly on a hot‐dip galvanized steel profile than on a bare one.This work led to a proposal for an amendment to Part 1‐2 of Eurocodes 3 and 4 regarding the fire design of steel (Eurocode 3) and composite steel and concrete (Eurocode 4) structural members. This amendment recommends a 50% reduction of the surface emissivity of a carbon steel profile as long as the applied zinc coating is present, followed by a “return to normal” of the fire behaviour of steel once the zinc layer has melted.Therefore, an experimental campaign was conducted in order to verify the recommendations of the proposed amendment on the one hand, and to calibrate an advanced calculation model on the other hand. This investigation, presented in this paper, has put into evidence the conservativeness of the proposed amendment. The latter can have a significant impact on the fire design of steel structures for low fire resistance requirements, especially in case of welded structural members which are often made of slender walls prone to heat up very quickly when exposed to a fire.

Numerical study of demountable shear wall system for multistory precast concrete buildings

The aim of this paper is to propose a demountable shear wall (DSW) system for multistory precast concrete buildings. For this purpose, instead of a large wall panel, several slender walls are used by connecting to adjacent beams. To evaluate the efficiency of the DSW system, nonlinear cyclic and time history analyses are performed on eighteen 4-, 8- and 12-story models, including three conventional shear wall models and fifteen DSW models with various wall numbers. The results indicate that for DSW system, when using more walls with a smaller width, the structural deformation tends from flexural-type to almost shear-type. This result prevents the plastic strain from concentrating on the columns and walls of the first story and causes the damage to be uniformly distributed on the walls of all stories. The DSW models exhibit hysteretic behavior without significant strength degradation at high drift levels. Also, DSW models with more walls, while increasing the ductility factor (up to 30%) and creating a more uniform distribution of drifts, reveal less value of maximum floor acceleration (up to 48%) and story shear (up to 53%), compared to conventional shear wall models.

Numerical Modelling of Reinforced Concrete Slender Walls Subjected to Coupled Axial Tension\u2013Flexure

Under strong earthquakes, reinforced concrete (RC) walls in high-rise buildings, particularly in wall piers that form part of a coupled or core wall system, may experience coupled axial tension–flexure loading. In this study, a detailed finite element model was developed in VecTor2 to provide an effective tool for the further investigation of the seismic behaviour of RC walls subjected to axial tension and cyclic lateral loading. The model was verified using experimental data from recent RC wall tests under axial tension and cyclic lateral loading, and results showed that the model can accurately capture the overall response of RC walls. Additional analyses were conducted using the developed model to investigate the effect of key design parameters on the peak strength, ultimate deformation capacity and plastic hinge length of RC walls under axial tension and cyclic lateral loading. On the basis of the analysis results, useful information were provided when designing or assessing the seismic behaviour of RC slender walls under coupled axial tension–flexure loading.

Behaviour of slender concrete shear walls with high-strength reinforcement under reverse cyclic loading

Research on seismic behaviour of shear walls with high-strength steel is limited. A combined experimental and analytical investigation was conducted to assess seismic behaviour of flexure-dominant shear walls. A large-scale concrete shear wall with Grade 690 MPa (ASTM A1035) reinforcement and 84 MPa concrete was tested under simulated seismic loading. The wall represented a 6-story building shear wall with 4.53 m height and 1.45 m length. It sustained a lateral drift of 1.8% prior to developing failure due to the rupturing of longitudinal reinforcement. This is 35% less than the drift capacity of a companion wall reinforced with 400 MPa reinforcement tested earlier. VecTor2 software was used to conduct an analytical parametric study to expand the experimental findings. The results indicate that the reinforcement grade has a significant impact on strength, ductility, and hysteretic behaviour of shear walls.

Formulation of an efficient shear-flexure interaction model for planar reinforced concrete walls

A research was conducted to develop a macroscopic modeling approach that integrates axial, flexure, and shear interaction under cyclic loading conditions to obtain reliable predictions of the nonlinear response of reinforced concrete (RC) structural walls. The model, named as Efficient-Shear-Flexure-Interaction (E-SFI), is intended to provide accurate results for squat, medium-rise, and slender planar walls, with a computationally efficient formulation that can be used under generalized conditions. The E-SFI model, which is based on the Shear-Flexure Interaction Multiple-Vertical-Line-Element-Model (SFI-MVLEM), incorporates a two-dimensional RC panel behavior described with a fixed-crack-angle approach. The novel formulation removes the internal degree of freedom per RC panel element of the SFI-MVLEM by incorporating a calibrated expression to compute the horizontal normal strain (εx), and therefore removing the assumption of zero resultant horizontal stress (σx=0) to increase the range of applicability of the model. Three RC wall specimen tests were selected to calibrate and validate the E-SFI model, as well as to prove the model efficiency, including a slender wall (shear span-to-depth ratio of 3.0), a medium-rise wall (shear span-to-depth ratio of 1.5), and a squat wall (shear span-to-depth ratio of 0.63). Analytical model results reveal the ability of the model to accurately reproduce the hysteretic response for all considered cases, with an important reduction in the runtime and an improved current tangent convergence rate compared with the SFI-MVLEM.

Yield displacement of slender cantilever RC walls as a function of the seismic demand features

Yield displacement of slender cantilever RC walls as a function of the seismic demand features

Seismic performance of confined masonry walls with joint reinforcement and aspect ratio: An experimental study

The effect of joint reinforcement, aspect ratio and their possible interaction, on the performance of confined masonry walls, was studied experimentally. Eight full scale confined masonry walls with four different height-to-length aspect ratios (hw/lw = 1.46, 1.0, 0.59, 0.4) and two different amounts of horizontal reinforcement per aspect ratio (phfyh=0.6,1.21N/mm2) were subjected to reversible cyclic shear loads and a fixed axial stress, representing the vertical load of five stories. The walls with hw/lw=1.0 were included from a previous study.The aspects ratios considered correspond to slender walls, square walls, long walls with one masonry panel and long walls with two masonry panels. Multiperforated concrete masonry units with 75% of net area were used. The performance of the walls is described in terms of strength, strength degradation, displacement capacity, ductility, dissipated energy, stiffness degradation, joint reinforcement (JR) deformation, cracking patterns, and crack opening.The results show that JR increased the shear strength of the walls and, in most cases, it had a negative impact on ductility; however, ductility increased as the aspect ratio decreased. Drift at peak strength increased with JR, and it had a clear tendency to grow as the walls were longer. Long walls tend to have a more brittle behavior.A detailed description of the experimental program and the results are given, after which, some conclusions are drawn.

Parametric study on module wall-core system of concrete modular high-rises considering the influence of vertical inter-module connections

High-rise modular buildings are attractive for metropolises, but few applications exist. One reason is the lack of relevant knowledge about their lateral force resistance. Existing high-rise modular buildings generally adopt cast-in-situ concrete cores, which can work with precast module walls in concrete modular buildings to resist lateral loads together. This study aims to parametrically examine the module wall-core system. A typical 40-story public residential building in Hong Kong was selected as the case building and re-designed to be a concrete modular building. A method called generalized modulus reduction method was adopted to consider the influence of vertical grouted connections on lateral behavior of slender precast concrete walls. A three-dimensional finite element model using this method was established to study the influence of three parameters on the structural responses of the case building under the Hong Kong code-specified wind loads, which were the module wall thickness, the reduced lateral stiffness of module walls, and the defect distribution scenarios of vertical inter-module connections. Results show that the developed method can well consider the influence of vertical grouted connections. The module wall-core system can provide sufficient stiffness and strength for the case building, and module walls play a leading or even a major role. It is beneficial to increase the thickness of module walls due to reduced site work for core walls without adverse effects on the structural responses of buildings. With the reduced lateral stiffness of module walls, the case building’s deflection increases speedily, with more serious wind-induced vibration and more vulnerable core walls. When more defective vertical inter-module connections are concentrated on the bottom stories, there are relatively small impacts on overall structural responses of the case building, while strong adverse impacts on core walls at the corresponding bottom stories. For ensuring safer structural design, the influence of vertical inter-module connections on the global lateral force resistance of concrete modular high-rises cannot be ignored.

Effect of material regularization in plastic hinge integration analysis of slender planar RC walls

Recently, mesh-objective (i.e., mesh insensitive) fiber-based numerical models have been developed to simulate RC walls with compression-controlled softening failure modes (i.e., concrete crushing and rebar buckling). These models regularize the post-peak stress-strain behavior of concrete and steel materials based on experimentally-calibrated failure energy equations. While the ultimate displacements of RC walls predicted by these models have been accurate, the local curvature and material strain demands are very sensitive to the selected mesh. Consequently, subsequent normalization of the section curvatures based on an assumed plastic hinge length has been proposed in the literature, resulting in a two-step analysis process. This normalization step uses approximate equations that are dependent on the structural configuration and that can be challenging to implement in cyclic analysis. In accordance with these limitations, this paper studies the effect of material regularization in force-based beam-column elements with a plastic hinge integration method to accurately simulate, in a one-step process, the softening behavior of slender planar RC walls under lateral loading. Numerical results are evaluated using available experimental measurements of eight slender flexural walls with compression-controlled failure modes from the literature. Previous research has shown that one of the biggest limitations of using conventional material models (i.e., without regularization of the stress-strain curves) is that the predicted ultimate displacements are significantly sensitive to the length of the critical integration point over which the nonlinear strains concentrate. This paper demonstrates that this sensitivity of the analysis results can be significantly reduced by using regularized material models and a plastic hinge integration method over a wide range of assumed plastic hinge lengths. The combination of material regularization and plastic hinge integration analysis can also predict the section curvatures and strains of RC walls, with no need for a separate normalization step, though these local responses are more sensitive to the assumed plastic hinge length.

Shear capacity of flexurally strengthened old low-performance concrete elements

This paper describes an experimental study to evaluate the shear capacity of small to medium height old buildings constructed in Israel more than 50 years ago with poor materials and construction practices resulting in low performance concrete (LPC), also known as plum concrete. Such LPC is characterized by its low compressive strength and in many cases – by the inclusion of large stones (up to ~300 mm) among its coarse aggregates. The tests conducted in this study were aimed at providing assessment of the shear capacity of existing slender LPC walls. The experimental program comprised beams sawed out of authentic samples, which were extracted from old buildings prior to their demolition, as well as larger specimens cast in the laboratory from concrete mixes designed to represent the main characteristics of authentic LPC. Control specimens, made of the lowest standard concrete class, were also tested. The 14 beam specimens failed in shear and their measured load capacities were compared with the shear capacity of beams without shear reinforcement, on the basis of their measured concrete compressive strength as prescribed by Eurocode 2 and ACI 318 provisions. This comparison indicates that the current Eurocode 2 formula, as well as that of ACI 318, provide reasonably conservative estimates for the shear capacity of LPC walls without shear reinforcement. Hence, engineers who lacked any information on how to assess the shear capacity of such low-performance concrete walls can now refer to this study. • Low Performance Concrete (LPC) in structural elements was studied. • Experiments were performed to evaluate the shear capacity of flexurally strengthened LPC elements. • Authentic sample beams, sawed out from old buildings, were tested. • Larger laboratory made specimens were tested as well. • Shear capacity of flexurally strengthened LPC walls can be evaluated based on the research findings.

Territorial seismic risk assessment of a sample of 13 masonry churches in Tuscany (Italy) through simplified indexes

Among heritage buildings, masonry churches are complex structures often characterized by an open plan layout with slender perimeter walls. Their vulnerability to earthquakes is frequently increased by the absence of adequate connections between the various parts of the structural complex, together with the presence of thrusting horizontal elements such as masonry vaults and timber roofs. In this paper, the vulnerability and the seismic risk of thirteen masonry churches located in Tuscany (Italy) have been analysed with simplified methods to establish a first screening of the risk of this heritage typology. The methods are that proposed by Lourenço and Roque in 2006 and the so-called first level of analysis (LA-1), introduced by the Italian code. For one of these churches, the Basilica of San Francesco in Arezzo, the analyses of second (LA-2) and third (LA-3) level have been also performed according to the same code. The results highlight the contribution of the simplified approaches to establish a first selection of the priorities for subsequent investigations and, if needed, proper interventions. Approximately one-half of the churches composing the sample have the normalized simplified indexes lower than one, indicating the need of further investigations. For the Basilica of San Francesco the results of LA-2 level of analysis confirm the conclusions obtained with the more simplified procedures, while a criticism is highlighted with the LA-3 approach when the N2 method is adopted in combination with a pushover methodology of analysis.

Multi-leaf masonry walls: Load transfer mechanisms sensitivity to mechanic and geometric parameters

The apparent monolithic behaviour of multi-leaf walls is compromised by the discontinuity planes that the load transfer mechanisms generate for the following reasons: i) difference between mechanical characteristics of layers; ii) lack or weakness of the structural interaction between core and external layers. The goal of this paper is to evaluate through parametric analysis the dimensional ratios by reference to core confinement effects of multi-leaf masonry walls with several interface and mechanical characteristics of layers. The study was carried out through the finite element analysis performed in non-linear field on two-dimensional plain strain models calibrated on experimental basis and numerical results are presented and discussed. The horizontal interfaces hand the load transfer and structural performances of multi-leaf walls. The behaviour of short specimens is controlled by confinement of external layers while for slender masonry walls the out of plane mechanisms affect the confinement effect.

Experimental study on the effects of bi‐directional loading pattern on rectangular reinforced concrete walls

AbstractIn this experimental study, three identical reinforced concrete (RC) walls were tested under three different lateral loading patterns. These loading patterns were cyclic in‐plane, skewed with 45° angle and clover leaf. The main objective was to investigate the effects of these bi‐directional loading patterns on the seismic behavior of slender rectangular RC walls. The results showed significant increase in tensile and compressive strains in concrete and longitudinal bars that led to earlier cover concrete spalling and bar buckling in the specimens subjected to bi‐directional loading. The neutral axis depth and compression zone were found to be substantially larger when subjected to bi‐directional loading and this led to the occurrence of concrete crushing and bar buckling in the web. Moreover, lateral instability failure triggered earlier in the specimens under bi‐directional loading, as a result of reduction of out‐of‐plane stiffness of the wall. However, bi‐directional loading did not significantly increase out‐of‐plane buckling of the wall in terms of out‐of‐plane displacement. In‐plane and out‐of‐plane shear cracks formed in one of the specimens subjected to bi‐directional loading, whereas the same wall under in‐plane loading developed only flexural cracks. It was also found that in‐plane shear deformation was larger when the wall was subjected to bi‐directional loading. The results of this experimental study emphasize the need for further investigation of the effects of bi‐directional loading on RC structural walls.

Experimental estimation of energy dissipation in rocking masonry walls restrained by an innovative seismic dissipator (LICORD)

This paper presents an innovative anti-seismic device for controlling the out-of-plane rocking motion of masonry walls with traditional tie-rods, called LInear COntrolled Rocking Device (LICORD). LICORD is a low-impact box connected to the extremity of the traditional tie-rod designed to mitigate rocking for medium–high intensity earthquakes. Additionally, the paper widens the knowledge about the dynamic behavior of rocking walls through the interpretation of the results of an extensive experimental campaign performed on masonry specimens composed by clay brick and cementitious mortar. Firstly, the LICORD’s single components are tested to identify their stiffness and damping properties. Secondly, free vibration tests provide actual values of coefficients of restitution on free-standing walls and walls restrained by LICORD, where the walls vary for the height to thickness ratio. For the stockier wall, the ratio of experimental/analytical coefficient of restitution varies from 88 to 98%, whereas for the slender wall, the results are less scattered, with a minimum value of 95% and a maximum value of 96%. The restrained walls are characterized by coefficients of restitution from 5 to 25% less than the values found for unrestrained walls, depending on the equivalent viscous coefficient of the shock absorbers. Moreover, LICORD demonstrated to properly absorb and damp the oscillations of the wall and control its rocking motion, strongly reducing the number of impacts and the rotation amplitudes up to 70%. Considerations about the effect of one-sided motion on the assessment of coefficient of restitution are also given. The equivalent viscous damping coefficients are observed to be on the range 4% (unrestrained wall) and 7–20% for walls restrained by LICORD.

Experimental testing of slender load-bearing masonry walls with realistic support conditions

Slender, load-bearing masonry walls with slenderness ratios (h/t) greater than 30 are required to be designed as pinned-pinned elements according to North American provisions for masonry, CSA S304-14 and TMS 402-16. This provision neglects the contribution of the reactive stiffness of the foundation to the strength of the wall and its effect on the redistribution of bending moments along its height. Eight full-scale masonry walls were built with different degrees of base stiffness and tested under an eccentric axial load. The results of the tests showed an increased load-bearing capacity and decreased deflections with increased rotational base stiffness. Experimental data were used to determine key design parameters, including the effective flexural rigidity and moment distribution along the height of the walls. Comparing the values of effective flexural rigidity determined from experimental results to code provisions, it was found that both codes tend to underestimate the effective flexural rigidity of the walls.