45 Figure 3.3 Construction of CM wall samples: (a) Masonry wall construction,. b) Casting of tie columns, (c) Construction of tie beams and plates.

## Introduction

*Overview**Motivation of the Study**Objectives of the Study**Organization of the Thesis*

In the past, backbone models have been developed for estimating the lateral bearing capacity, stiffness and deformability of CM walls. The applicability of the developed model in nonlinear seismic analysis of CM walls is emphasized.

## Review of Literature

Overview

Past Performance

### General Behavior

The contribution of the tensile columns (Vtc) in the shear resistance mainly comes after severe cracks in masonry wall (Meli et al. 2011). However, the four remaining models (M&L, S&R, Ria and M&C) estimate a relatively higher contribution of the connecting columns in the lateral strength of CM walls.

Experimental Behavior

*Experimental Study for Evaluating the Influence of Important Parameters…**Influence of type of masonry**Influence of overburden load**Influence of aspect ratio**Influence of number and spacing of tie-columns**Influence of reinforcement in tie-columns**Influence of wall to tie-column connection**Influence of wall reinforcement**Influence of openings in walls**Influence of number of stories**Comparison with Other Structural Systems*

Numerical Modeling and Analysis Methods

*Finite Element Model (FEM)**Wide Column Model (WCM)**Strut-and-Tie Model (STM)**Equivalent Strut/Shell Model (ESM)**Backbone Curve Model*

Design Methods

### Gap Areas

Several experimental studies have been carried out in the past to study the influence of wall reinforcement on the lateral load response of CM walls (Yoshimura et al. Comparison of in-plane response of CM and URM walls tested by: (a) Tomaževič and Klemenc ( 1997a), and (b) Yoshimura et al.

## Experimental Evaluation of Lateral Load Behavior

Overview

Description of Test Specimens

Material Characterization

Test Procedure and Instrumentation

Response of Specimens

*Crack Pattern and Failure Mechanism**Deformation Response**Strain in Longitudinal Reinforcements of Tie-Columns*

Evaluation of Influencing Parameters

*Response Envelope Curves**Stiffness Degradation**Strength Degradation**Energy Dissipation*

Idealization of Lateral Load-Displacement Relationship

*Idealization with Bilinear Relationship**Idealization with Trilinear Relationship*

### Summary

The geometric properties and reinforcement details of the half-scale test specimens are shown in Figs. Concrete in the tie columns was poured once the desired wall height was reached using formwork only on three levels of the tie columns. The lateral deformations of the specimens at different heights were recorded using four LVDTs, which were attached to the tie columns.

The lateral load behavior of the samples during quasi-static cyclic testing in the form of hysteretic response (lateral load-lateral drift) for the applied three cycles of each lateral drift level is shown in Fig. Sudden reduction of the lateral strength of the first sample S1 is evident from the hysteresis curves at a drift level of about 4%. Although the lateral strength of the third copy S3 was the greatest, it failed quite early due to severe damage to the connecting columns.

With increasing drift, the bending cracks began to form along the entire length of the anchor columns, in addition to the well-distributed damage in the masonry wall (Fig. 3.8b). However, plastic hinges were formed at the bottom of the connecting columns, much after the lateral strength. From the comparison of the experimental results, a strong influence of aspect ratio on lateral load responses was observed.

## Development of V-D Strut Model

Overview

FE Model Development

*Details of Specimens**Material Modeling**Yield surface and flow potential parameters**Material stress-strain parameters**Model Characterization*

Validation of FE Models

*Sensitivity Study**Results of FE Analyses*

Preliminary Comparative Study using Simplified Models

Analysis for Gravity Loads

Analysis for Lateral Loads

Characteristics of Diagonal Strut

*Data Obtained from Parametric FE Study**Data for Effective Shear Strength of Masonry (f ss ) and Empirical Formulation 95*

### Summary

Residual strength of 20% of the peak stress was considered in the stress-strain definitions for. 4.13, the axial forces in the connecting columns of the diagonal brace model (model 2) were overestimated by about 50%. It was observed that the maximum deflection of the tie beam is significantly large for the diagonal brace model (model 2) as well as the bare frame model (model 3), which is inconsistent with the shell model (model 1) which exhibits negligible tie beam deflection.

These modifications in the numerical simulation accurate displacement of tie-beam in the V-D strut model and ensure realistic vertical load distribution in different elements of the CM wall. The base of the tie columns was assumed to be fixed to reflect the boundary conditions used in the experiments. The effective shear strength parameter of masonry was developed in the present study to limit the axial strength of the diagonal brace in the V-D brace model.

This shows that the effectiveness of the V-D spring model depends on the accurate prediction of fss. The influence of the three most sensitive parameters (AR, fm and t) on the lateral strength of the CM walls was studied in more detail in the parametric study. Such a dramatic increase or decrease in lateral force was more noticeable in the case of the lowest AR value.

## Assessment of Design Provisions

*Overview**Shear Strength Provisions**Contribution of Different Elements**Estimation of Design Shear Strength**Flexural Strength Provisions**Contribution of Different Elements**Estimation of Design Axial Compressive Strength**Estimation of Design Flexural Strength**Comparative Assessment of Codes**Assessment using Present Experimental Results**Assessment using Past Experimental Results**Summary*

Thus, there is a need to assess the effectiveness of the existing codes to reliably predict design lateral forces of CM walls with different configurations. Additionally, Colombian and Costa Rican codes consider masonry shear strength in terms of fm as an estimate of vmd. Codes use different safety factors for evaluating the design value of masonry shear strength as given in Table 5.2 when the experimentally obtained value is used in design equations.

The design rules of Mexico and Costa Rica consider the contribution of horizontal reinforcement (Vwr) to Vdes as shown in Eqs. The wall cross-section CM consists of the cross-sectional area of the masonry wall and the adjacent AB limit columns. As indicated in these equations, PD is a function of the vertical compressive resistances of the masonry wall (Pm) and the resistance of the tie columns, including the contribution of concrete and longitudinal steel (Ptc) in the tie columns.

In order to assess the safety margins in different codes, the design shear strength (Vdes) and design flexural strength (Mdes) of the three tested specimens were compared with the experimental results. Values of the input parameters for the design lateral strength estimation of CM wall, such as, vmd, fAR, and PD obtained for all the twelve samples are shown in Fig. The rest of the input parameters for the estimation of Vdes and Mdes can be obtained from Tables 5.4 and 5.8, respectively.

## Development of Lateral Load-Displacement Backbone Model

Overview

Lateral Load-Displacement Models

*Models Developed in Past Studies**Status of Existing Codes of Practice*

Experimental Data

*Variation of Different Parameters**Material and Loading Parameters**Geometry and Detailing Parameters*

### Summarized Influence of Important Parameters

Thus, the recommended value of the lateral load at the ultimate limit (in the region after the peak) is 80% of the lateral force. From the comparison of the existing models, it was observed that the lateral force equation. 7.2 (i.e., 5% to 55% contribution of tie columns to lateral strength) shows a large variation in the estimated percent contribution of tie columns to lateral wall strength using different formulations.

Obviously, the force resultants obtained in the tie columns and masonry walls were highly dependent on the aspect ratio of the CM wall. The numbers in () are the lateral displacement values that correspond to the obtained force resultants R = the ratio of the force resultants in the connecting columns to the masonry wall. Such a representation of the shear force distribution in the tie columns resulted in the formation of characteristic bands for the Vtc/V distribution.

It is also recommended that the masonry walls are designed to withstand the full lateral strength of the CM walls. Therefore, it is considered essential to gain an in-depth understanding of the influence of tensile columns on the lateral load behavior of CM walls. Huge variation in the range of 5% to 55% was observed in the average percentage contribution of the connecting columns to the predicted lateral strength using different formulations.

Estimation of Responses Using Empirical Models

*Lateral Load – at Initial Cracking, Maximum Capacity, and Failure**Initial Lateral Stiffness**Lateral Drift at Initial Cracking, Lateral Strength, & Ultimate Load at Failure 144*

### Summary

The lateral load response of the CM walls can be assumed to be linearly elastic until the formation of the first visible crack in the masonry wall (point A) corresponding to the cracking force Vcr and the deformation Δcr. 6.22, and the Peruvian code considers an aspect ratio factor in the coefficient of the first part. The dotted line represents the mean value (± standard deviation) of the predicted to experimental load ratio for the specimens.

The predicted mean lateral strength values appear to be quite accurate using the equations of Marques and Lourenç (2013), Marques and Lourenç (2019) (Eq. 9a), Riah et al. To give a better insight into the results obtained, Table 6.8 shows the number of studies in which the equations overestimate or underestimate the lateral strength of closed masonry walls, together with the average error obtained for underestimating or overestimating the strength. It should be noted here that the lateral strength or lateral cracking load predicted by any of the equations was quite high for some single-span CM specimens, such as walls with 0.5% longitudinal reinforcement in the tie columns of the tested CM walls. by Varela-Rivera et al.

The effectiveness of the four equations in predicting the initial lateral stiffness (Table 6.2) was evaluated by applying them to the seventy-eight CM walls tested in past experimental studies as given in Table 6.10. Further, the average value of the lateral movement in lateral force predicted using both methods is about 0.3%, and both equations largely underpredict the movement in lateral force. The lateral displacement corresponding to the cracking load can be estimated from the initial in-plane stiffness and the lateral cracking load of the wall.

## Design Force Estimation in Different Members

Overview

Influence of Tie-Members on Seismic Behavior of CM Walls

Distribution of Forces in CM Members

*Distribution of Forces based on Existing Formulations**Distribution of Forces based on FE Analysis**At initial cracking stage**At lateral strength stage**At all the drift levels*

Parametric FE Study

Recommendations

### Summary

It has been observed in the shake table testing of CM walls with different variations in the axial reinforcement of the connecting columns that four times increases in the connecting columns. This methodology helped to gain some insight into the considered influence of tie columns on existing CM wall lateral strength formulations. Here, the tie column contribution represents the combined resistance from all tie columns in a CM wall.

The different parameters related to the contribution of tensile columns to the prediction of the lateral strength of CM walls are: diameter of longitudinal reinforcing bars (dbl), concrete compressive strength (fc), yield strength of longitudinal reinforcing bars (fyl), number of longitudinal reinforcing bars in a draft column (nr), number of total or intermediate draft columns in a CM wall (n or ni), geometric length ratio Li/Lp, and cross-sectional area of draft column (Ac) (Table 7.1). This comparative assessment for the contribution of the predicted CM wall lateral strength from masonry walls and connecting columns is also shown in Fig. all three copies.

Table 7.3 gives an overview of the obtained force results in connection columns and masonry walls of the three test pieces. In masonry walls, the SF generated was more than that in the connecting columns in all samples. Therefore, in the present study, a method was proposed to limit the distributed lateral shear to the connecting columns.

## Summary and Conclusions

Overview

Summary

*Experimental Evaluation of Lateral Load Behavior**Development of a Simplified Numerical Model**Assessment of Design Provisions**Development of Lateral Load-Displacement Backbone Model**Design Force Estimation in Different Members*

Conclusions

Recommendations for Future Work