# Infill Walls And Their Hidden Power Engineering Essay

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Nowadays, the most widespread form of construction in seismic regions worldwide is based on non-ductile concrete frame structures. Infill panels, which are made of bricks or concrete blocks, are mostly used as external walls as well as interior. The latter are not used in numerical calculations due to complexity of analytical models and inadequate knowledge and competency. According to many researchers and designers, such assumption may lead to inaccurate estimation of strength, ductility and stiffness of concrete frame building's structural performance. These masonry infill walls, as secondary structures of a building, tend to affect the behaviour of the structure when they are exposed to loads, especially due to seismic activity. Do infill walls have a significant role against earthquakes? Does their design require any special considerations?

Many countries lie in areas susceptible to earthquakes. Therefore, structures in these areas need to be designed to withstand seismic loads. Earthquake tremors produce lateral forces that are a matter of great concern and need special consideration in the design of structures. At the same time, infilled walls are not considered in the design process but once they are connected to the frame, the total system acts as a single unit and the overall behaviour of the structure is ameliorated. According to designers, their interaction between the infill walls and the bounding frame is ignored in design but their strengths are not negligible, and the first will interact with the bounding frame when the structure is subjected to lateral forces. This interaction may or may not be beneficial to the performance of the structure, and it has been a topic of much debate in the last few decades. Until now, the structural analysis is based on the bare-frame structures and the only contribution of these non-structural components is their masses.

In the last five decades, their effects on the structural analysis and design of structures were particularly studied by experimental procedures and analytical theories. In present, there is need for an effective computation procedure in order to predict the behaviour of infill walls. This can eventually lead to a simplified seismic structure design (Abrams et al. 1994). The presence of infill walls increases the structural strength and stiffness, influencing at a significance level the seismic response of the structure (Moghaddam and Dowling, 1987). On the other hand, they introduce a brittle failure mechanism related to the wall failure and the wall-frame contact. Masonry infilled walls may have major influence to the structure performance as a result the linearity performance of building, which is progressive effect. To conclude, infill walls generally reduce the damage suffered by reinforced concrete frame members during earthquakes.

- Background

Researches have assessed and estimated that a fully infilled-framed structure has the lowest collapse risk under seismic load compared to partially-infilled and bare-framed structures. Masonry infill walls may have major influence on the structure performance as a result of the linearity performance of building, which is progressive effect. Many researchers have acknowledged the benefits of infill masonry structures. According to Nollet and Smith (1998), structures that lack infill masonry walls tend to be affected to a great extent by seismic behaviour.

- Aims

To analyse and demonstrate the importance of masonry infill walls against seismic loads.

To compare and contrast the available seismic design methods proposed by Eurocodes.

- Objectives

Study on structural seismic performance

Evaluation of structural seismic performance of the structure using non-linear structural analysis methods proposed by Structural Eurocodes

Estimation of Masonry Infill Stiffness

Comparison of bare and infill frames structure using analytical and computer techniques

- Project Deliverables

The successful completion of this project will assist in reducing the risk of collapse in building structures worst hit by earthquake disasters. The presence of masonry infill walls affects the seismic behaviour in the following ways:

Increasing the stiffness of buildings.

Decreasing the fundamental period.

Increasing the base shear.

Lateral stiffness in plan and elevation is modified.

The structural system is more reliable during seismic action as long as the load is carried by the infill.

Energy dissipation capacity of the building is significantly increased.

- Approach

This study will assess he seismic performance of reinforce concrete buildings, by analysing moment resisting reinforced concrete framed models in order to obtain structural predictions of the infill walls behaviour. Bearing in mind the above, the project will pointed out this subject, which requires further research and carried out in an efficient way to increase awareness on the subject. This will be achieved by carrying out a research on the existing literature and by analysing a case study with is investigating the importance of masonry infill walls in relation to seismic lateral loads. A comparison between structures with infill walls and bare-frame ones will be considered to help us determine the best structures to be established in for earthquake prone areas. The investigation will be was further extended in order to compare seismic design methods proposed by Eurocode 8.

- Summary

The project is organized into seven chapters covering a range of topics. From the theoretical effect of masonry infills, on the seismic performance of structures, to analytical and computer methods, demonstration of proposed infilled structure models.

Chapter 2 is intended to be a best practice guide. In this chapter the importance of seismic codes and the procedure of Eurocode 8 are presented. The abstracts of the codes are presented and special cases that were used in the case studied are further analysed.

Chapter 3 deals with the Behavior and Design Aspects of Moment Resisting structures.

Chapter 4 delves on literature regarding infill panel walls. It presents the analytical model used in this study that selected by the author.

Chapter 5 presents seismic analysis results used to asses and demonstrate the importance of masonry infill walls.

Chapter 6 Compares and discuss the selected case studies.

Chapter 7 concludes this study and offers a summary of observations and findings.

## 2.1-Introduction

The earthquake is considered as the independent natural phenomenon of vibration of the ground. It poses a threat to people when it causes landslides and it becomes a dangerous phenomenon only by affecting structures. This is due to the fact that the structures are meant to withstand gravity loads only and not lateral loads generated from the cyclic motion of earthquake.

## 2.2 - Seismic Action Performance

EC8 provides seismic design with main performance objectives the protection of life under a seismic action, by prevention of collapse of the structure and reduction of property loss. These objectives are achieved by combine structure's strength and ductility with dimensioning and detailing its elements. Furthermore the damage control is achieved by limiting the lateral displacements of the structure to an acceptable level for its parts including the integrity of masonry infills.

## 2.2.1 - Analysis procedures

EC8 provides the following seismic analysis options for design and for evaluation of the performance of buildings:

Linear static (lateral force method).

Linear modal response spectrum analysis.

Nonlinear static analysis ("pushover").

Nonlinear dynamic (response time-history).

A force-based design on the basis of the results of linear elastic analysis methods, for the elastic spectrum reduced by the behaviour factor q. EC8 allows also design on the basis of nonlinear analysis, static or dynamic.

Linear modal response spectrum method is the standard procedure and is applicable to all types of buildings. In the other hand, the lateral force procedure can be applied when:

The fundamental period is less than 2sec and 4 times the transition â€¨period Tc

There are no significant irregularities in elevation.

The lateral force method of analysis derives the base shear by transfer the total mass to the 1st translational and use values of the fundamental period estimated through empirical expressions e.g. T1=0.075H3/4 for Reinforced Concrete frames, T1=0.05H3/4 for RC wall buildings.Then the total lateral force is distributed to the storeys.

In the response spectrum analysis modal contributions are combined by using application like the SRSS (square root of the sum of the squares) or CQC (complete quadratic combination) rules for the final seismic action effects i.e. displacements.

## 2.2.2 - Design seismic motion

The seismic motion consists of two horizontal components and one vertical and their design are defined on the free surface of the ground. It is assumed, that this motion is constant from the ground surface to the foundation level. The design seismic motions are determined by design acceleration spectra that give the maximum value of the acceleration Rd(T) calculated on a simple oscillator with natural period T during the design earthquake.

## 2.2.3 - Design spectrum for elastic analysis

The capacity of structural systems to resist seismic actions in the non-linear range generally permits their design for resistance to seismic forces smaller than those corresponding to a linear elastic response.

To avoid explicit inelastic structural analysis in design, the capacity of the structure to dissipate energy, through mainly ductile behaviour of its elements and/or other mechanisms, is taken into account by performing an elastic analysis based on a response spectrum reduced with respect to the elastic one, henceforth called a ''design spectrum''. This reduction is accomplished by introducing the behaviour factor q.

The behaviour factor q is an approximation of the ratio of the seismic forces that the structure would experience if its response was completely elastic with 5% viscous damping, to the seismic forces that may be used in the design, with a conventional elastic analysis model, still ensuring a satisfactory response of the structure.

The values of the behaviour factor q, which also account for the influence of the viscous damping being different from 5%, are given for various materials and structural systems according to the relevant ductility classes in the various Parts of EN 1998. The value of the behaviour factor q may be different in different horizontal directions of the structure, although the ductility classification shall be the same in all directions.

For the horizontal components of the seismic action the design spectrum, Sd (T), shall be defined by the following expressions:

## 0 â‰¤ T â‰¤ T : (T) = a* S*{(2/3) + (T/T) *[(2.5/q)-(2/3)]}

## T â‰¤ T â‰¤ T : Sd (T) =a*S*2.5/q

## T â‰¤ T â‰¤ T : Sd(T)=a*S*(2.5/q)*(T/T)

## T â‰¤ T Sd(T)=a*S*(2.5/q)*(TT/T2)

Where:

a:Design ground acceleration

S: Soil factor

T: Value defining the beginning of the constant displacement response range of the spectrum

T, T: Limits of the constant spectral acceleration branch

Sd(T):design spectrum acceleration

T: Vibration period of a freedom system

q: Behavior factor

Î² :Lower bound factor for the horizontal design spectrum.

## 2.2.4 - Soil classification

With respect to seismic risk soils are divided in five classes A, B, C, D, and E. To construct on soil of category E first requires detailed research and improvement of the soil properties.

The elastic response spectrum that used to design seismic action is anchored to the "reference" ground acceleration on rock, Î±gR, to be mapped in national zoning maps. The spectrum includes information of constant spectral acceleration and displacement and depends on the regional seismotectonic environment and the soil type.

Soil types are:

Type A: rock, with a lower limit on the average shear wave velocity in the top 30m, vs, of 800m/s;

Type B: very dense sand or gravel, or very stiff clay, with vs from 360 to 800m/sec;

Type C: medium-dense sand or gravel, or stiff clay, with vs from 180m/sec to 360m/sec;

Type D: loose-to-medium sand or gravel, or soft-to-firm clay, with vs less than 180m/sec;

Type E: 5m to 20m thick soil with vs less than 360m/sec, underlain by rock.

Furthermore, for the two special ground types S1 or S2, special studies for the definition of the seismic action are required. For these types, and particularly for S2, the possibility of soil failure under the seismic action shall be taken into account.

## 2.2.5 - Representation of ground Spectra types

Type 1: Used for moderate to large magnitude earthquakes

Type 2: Used for earthquakes with low magnitude

Macintosh HD:Users:constantinosandreou:Desktop:Untitled.png

FIGURE: Elastic response spectra of Type 1 (left) and 2 (right) recommended in EC8 for the five standard ground types

Figure 1 shows recommended types of spectra for Î¶=5%, Î³I=1 and PGA on rock of 1.0g. They were developed on large database of available records from the South of Europe and the Mediterranean area and are trusted to be currently more representative of the seismic hazard of the region than the more refined description of elastic spectra in recent US codes.

Additionally EC8 gives detailed description of the vertical elastic response spectrum, the peak ground displacement and the displacement response spectrum. These items have been based on data from Europe and are recommended as function of soil type, type of spectrum (1 or 2) and acceleration of the horizontal component.

## 2.2.6 - Ground seismic acceleration

In order for this code to be applied, a region has been separated in four seismic Risk Zones I, II, III, and IV. To every seismic risk zone there is a corresponding value of ground seismic acceleration a.

## 2.2.7 - Important categories and importance factors 'Î³':

Structures are divided into four categories of importance, depending on the consequences of collapse for human life, on their importance for public safety and civil protection in the immediate post-earthquake period, and on the social and economic consequences of collapse. Every category of importance there is a corresponding value of the importance factor 'Î³'.

## 2.2.8 - Seismic behavior factor 'q'

For buildings that are regular in elevation, the basic values of qo are given from Table 5.1 EC8.

## STRUCTURAL TYPE

## DCM

## DCH

Frame system, dual system, coupled wall system

3.0 Î±u / Î±1

4.5 Î±u / Î±1

Uncoupled wall system

3.0

4.0 Î±u / Î±1

Torsional flexible system

2.0

3.0

Inverted pendulum system

1.5

2.0

Table 5.1: Basic value of the behaviour factor, qo, for systems regular in elevation

For buildings that are not regular in elevation, the value of qo should be reduced by 20%.

Î±1 and Î±u are defined as follows:

Î±1 is the value by which the horizontal seismic design action is multiplied in order to first reach the flexural resistance in any member in the structure, while all other design actions remain constant.

Î±u is the value by which the horizontal seismic design action is multiplied, in order to form plastic hinges in a number of sections sufficient for the development of overall structural instability, while all other design actions remain constant.

When the multiplication factor Î±u / Î±1 has not been evaluated through an explicit calculation, for buildings which are regular in plan the following approximate values of Î±u / Î±1 may be used:

Frame-equivalent dual systems:

One-storey buildings: Î±u / Î±1 = 1.1

Multi-storey, one-bay frames: Î±u / Î±1 = 1.2

Multi-storey, multi-bay frames or frame-equivalent dual structures: Î±u / Î±1 = 1.3

## 2.2.9 - Values of the parameters ( TB, TC, TD )

## GROUND TYPE

## S

## TB(S)

## TC(S)

## TD(S)

## A

1.0

0.15

0.4

2.0

## B

1.2

0.15

0.5

2.0

## C

1.15

0.20

0.6

2.0

## D

1.35

0.20

0.8

2.0

## E

1.4

0.15

0.5

2.0

Table 3.2: Values of the parameters describing the recommended Type 1 elastic response spectra

## GROUND TYPE

## S

## TB(S)

## TC(S)

## TD(S)

## A

1.0

0.05

0.25

1.2

## B

1.35

0.05

0.25

1.2

## C

1.5

0.10

0.25

1.2

## D

1.8

0.10

0.30

1.2

## E

1.6

0.05

0.25

1.2

Table 3.3: Values of the parameters describing the recommended Type 2 elastic response spectra

## 2.3 - Methods of Seismic Response Analysis

Several methods are available for the structural analysis. Depending on the structural characteristics of the building one of the following two types of linear-elastic analysis may be used:

Equivalent plastic method.

Response spectrum method.

As an alternative to a linear method, a non-linear method may also be used, such as:

Non-linear static (pushover) analysis;

Non-linear time history (dynamic) analysis

Within this project only the two linear elastic analyses are considered

## 2.3.1 - Equivalent Static Method - (Lateral Force Method)

Historically, seismic loads were taken as equivalent static accelerations which were modified by various factors, depending on the location's seismicity, its soil properties, the natural frequency of the structure, and its intended use.

The method was refined over the years to enable increasingly adequate designs. The underlying design philosophy was basically unchanged; some modifications were made to the coefficients as a result of strong earthquakes. Other modifications to account for new information were introduced by specifying acceptable structural details for different construction materials. (http://.hlaengineers.com.)

General

This type of analysis may be applied to buildings whose response is not significantly affected by contributions from modes of vibration higher than the fundamental mode in each principal direction.

Base Shear Force

The seismic base shear force Fb, for each horizontal direction in which the building is analysed, shall be determined using the following expression:

Where

Sd (T) is the ordinate of the design spectrum at period T

T is the fundamental period of vibration of the building for lateral motion in the direction considered

m is the total mass of the building, above the foundation or above the top of a rigid basement.

Distribution of the horizontal seismic forces

The fundamental mode shapes in the horizontal directions of analysis of the building may be calculated using methods of structural dynamics or may be approximated by horizontal displacements increasing linearly along the height of the building.

The seismic action effects shall be determined by applying, to the two planar models, horizontal forces Fi to all storeys.

Where

Fi is the horizontal force acting on storey i

Fb is the seismic base shear

zi, zj are the displacements of masses mi, mj in the fundamental mode shape

mi, mj are the storey masses

## 2.3.2 - Modal Response Spectrum Method - (Response Spectrum Method)

## This method is one of the most popular methods in modern earthquake engineering. This is because it offers logical results and because it is more economical. The method requires the determination of a response spectrum from measured seismic activity.

## This data is then reduced into a spectrum of seismic action versus natural frequency. The seismic action could be displacement, velocity, or acceleration, although the typical value used is acceleration. Detailed information from the structural model is coupled with the corresponding spectral values for each specific mode of vibration.

The independent results are then combined using an appropriate technique to determine the response of the overall structure. A typical response spectrum is shown in figure 4.1.

Figure 4.1: Spectral acceleration against Periods (www.hlaengineers.com).

To calculate the base shear using the response spectrum method, there are some steps that must be followed. The method is described and given reference.

Formation of mass matrix (M)

For the formation of the mass matrix, we create a 6 x 6 (depending on the stories of building) matrix that all the values are zero except the middle diagonal where the values are the masses of each floor in tones.

Formation of the matrix stiffness (K)

The building is analyzed as shear building by assuming that all floors are rigid so that no joint can rotate, all the columns are inextensible, and that the deformation of the structure does not depend on the axial forces present in the columns. The assumptions indicate that there is one degree of freedom per floor.

Where:

K = is the bending stiffness provided by each column and the total lateral stiffness of a particular story is found by summing the column stiffness for that story.

L = is the height of the story.

E is the concrete grade extracted from Eurocode 2 (29 KN / mm2).

I is the second moment of area about y-y axis.

The form of the matrix that we created is:

Calculate the modal natural period Ti

The formula [k - Ï‰ 2M] was used (where k stiffness matrix and M mass matrix) and solved and different values of Ï‰, one for each mode were calculated.

Calculation of the vibration mode shapes Î¦i

Using the formula:

[k - Ï‰ 2 *M]*[ Î¦i] = 0

Î¦i mode vectors were found where i is number of stories.

Calculation of the generalized mass M*

Mi* = Î¦iT M Î¦i

Calculation of the earthquake participation factor Li

Li = Î¦iT *M * I

Calculation of design spectral acceleration

Using the appropriate formulae for the appropriate value of natural period T the design spectral acceleration Sd(Ti) were found for each mode.

Calculation of spectral displacement (Sdi)

Calculation of story displacement (ui)

Ui = (Li/Mi*) Sdi Î¦i*

Calculation of the horizontal story forces

Fi = (Li/Mi*) Sd(Ti) M Î¦i

Calculation of base shear

Base shear was calculated using the Square Root of the Sum of the Squares (SRS):

Fb = ( Fb12 +Fb22 +â€¦ + Fbj2)1/2

Chapter 3

Behaviour and Design Aspects of Moment Resisting R.C Framed Buildings

3.1 - Background

Accordingly to researches, more concrete structures than steel ones have failed in earthquakes. Nevertheless, concrete is the first choice building material in many countries. The reason is that the technology is familiar and at least some of the materials are locally available while the finished structure can possess good sound and thermal insulation properties.

Concrete structures which are properly conceived and detailed possess excellent ductility in bending that can equals that of structural steel. The use of concrete classes lower than C 20/25 for DC "M" and DC "H" or C 16/20 for DC "L" is not permitted.

- Reinforcing steel

Ribbed bars are only allowed as reinforcing steel in critical regions, except for closed stirrups or cross-ties. These are economical, have a long working life and require little maintenance. Also they resists corrosion and decay, can be precisely moulded to shape, they can resist fire and withstands high winds. However ribbed bars have low tensile strength, Low strength-to-weight ratio and are susceptible to cracking.

## 3.3 - Seismic Behaviour of Beams

## A large portion of seismic energy dissipation takes place, through stable flexural yield mechanisms at beams as a result the need for a design at a sufficiently ductile behaviour (Booth 1994).

Beams Capacity design procedure

According to Eurocode 8, to obtain bending moments of beams for all ductility classes the analysis of the structure for the seismic loading combinations is required. However, beams need additional compression reinforcement at their supports equal to 50% of the corresponding tension reinforcement, in order to ensure an adequate ductility level. Established by capacity design concepts, these reinforcement bars are anchored in concrete and can operate as tension reinforcement in case of moment reversal. As a result, the moment resistance envelope of the beams is significantly improved so they can carry larger moment fluctuations generated by an earthquakes that the design action moments.

In the other hand, the structural element has to be secured against early shear failure in order to assurance this behavior. For that reason, the design shear value should not be the result from the analysis, but the corresponding amount to the equilibrium of the beam under gravity load and a rational adverse combination of the actual bending resistances of its the cross-sections (Penelis and Kappos, 1997).

## 3.4 - Seismic Behaviour of Columns

## An essential principle of capacity design is that in Reinforced Columns buildings the formation of plastic hinge should be avoided. To succeed this, column design moments are resulting from equilibrium conditions at beam-column, considering the actual resisting moments of beams framing into the joint (Architectural Institute of Japan, 1970). Still, there are a number of reasons why the capacity procedure included in EC8 cannot achieve this goal (Penelis and Kappos, 1997).

3.5 - Column Capacity design procedure

It has already been stressed that the formation of plastic hinges in the columns during an earthquake should be avoided, in order to make sure that seismic energy must be dissipated by the beams only and the formation of plastic hinges in columns, during earthquakes should be avoided. The reasons for this requirement are stated by Key, 1988 and are the following:

Columns have less available ductility than beams due to axial compression. On the other hand, for the same displacement of frame, are required much larger plastic column than beam rotations. Therefore, a larger column ductility expressed in rotations is required, for the creation of a column failure mechanism than the beam ductility needed for the creation of a beam failure mechanism.

Comparing failure mechanisms, beam failure displays cracking only in the tension zones due to the yielding of the reinforcement, column failure mode presents spilling of the concrete, breaking of ties, crushing of the concrete core and buckling of the longitudinal reinforcement bars. Column failure mechanism results, leads to the creation of a collapse mechanism due to their inability to carry the axial gravity. Hence, is much more crucial for the overall safety of the structure, to avoiding column failure than beam failure.

The formation of plastic hinges in the columns may lead to significant inter-storey drifts as a result the relevant second-order effects may cause the collapse of the structure.

In order to reduce the likelihood of plastic hinge formation in the columns frames EC8 states the following concept: 'The sum of the resisting moments of the columns, taking into account the action, should be greater than the sum of the resisting moments of all adjacent beams for each (positive or negative) direction of the seismic action' (Penelis and Kappos, 1997).

3.6 - Ductility

The property of being capable to sustain large plastic deformations without fracture is called ductility. The most wide spread methods for determining ductility is the calculation of the ultimate elongation of a testing sample

A ductile material is any material that fails under shear stress (Maguire, Wyatt, 1999).

Reinforced concrete ductility is the capability of a reinforced concrete entity to respond to greater post-elastic deformations without a significant reduction in the carrying capability. Adding to that, ductility is a characteristic of steel, while reinforced concrete ductility is a characteristic of a reinforced concrete entity (Okamoto, 1973).

3.7 - Damage in Reinforced Concrete Structural Members

It is common that a strong earthquakes leads to improvements of nowadays design codes, modifications to design methods and rejuvenation of the sense of responsibility for the design of construction works (Penelis and Kappos. 1997).

To continue with, it is not easy to classify the damage caused by an earthquake, and even more difficult to relate it in a quantitative manner to the cause of the damage. This is result of the dynamic character of the seismic action and the inelastic response of the structure (Penelis and Kappos, 1997).

3.7.1 - Damage to Columns

Damage to columns caused by an earthquake:

Damage due to cyclic flexure and low shear under strong axial compression.

Damage due to cyclic shear and low flexure under strong axial compression.

The first type of damage manifests itself with failure at the top and bottom of the column and it occurs in columns of high slenderness.

The high bending moment at these points combined with the axial force leads to the crushing of the compression zone of concrete successively on both faces of the column. The crushing of the compression zones is manifested first by spilling of the reinforcement concrete cover. Subsequently the concrete core expands and crushes. This phenomenon is usually accompanied by buckling of bars in compression and by hoop fracture.

This type of damage is the most serious because the column loses its stiffness and also its ability to carry vertical loads as a result the buildings damaged in their R/C structural systems. Adding to this, there is a redistribution of stress in the structure since the column has shortened due to the disintegration of the concrete in the above-mentioned areas (Penelis and Kappos, 1997). Finally, the low quality of concrete, the inadequate number of ties in the critical areas, the presence of strong beams which leads to the columns failure at first and finally the strong seismic excitation inducing many loading cycles in the inelastic range, are other considerable reasons that should be mentioned.

The second type of damage is of the shear type and is manifested in the form of X-shaped cracks in the weakest zone of the columns. It occurs in columns with moderate to small slenderness ratio. As an example of damage to columns shown in figure 3.1 (Maguire, Wyatt, 1999).

damage to columns after ,wyatt 99 43.JPG

Figure 3.1 characteristic of column damage.

The ultimate form of this type of the damage is the explosive cleavage failure of short columns which usually leads to a spectacular collapse of the building. Usually the flexural capacity of the columns with moderate to small slenderness ratio is higher than their shear capacity and as a result shear failure prevails. It usually occurs in the columns of the ground floor, where the slenderness ratio is low because of the large dimensions of the cross-section of the columns,

It also occurs in short columns which have either been designed as short, or have been shorten to adjacent masonry construction which was not accounted in the design (Barbat, 2006).

Figure 3.2: Level of seismic damage of reinforced concrete columns or walls (dh, dv denote residual horizontal and vertical displacements) (www.info4education.com)

To conclude, column damage is very dangerous for structures temporary support should be provided immediately (Penelis and Kappos, 1997).

untitled 2.bmp

Figure 3.3 Column damage due to strong axial compression and cyclic bending moment.

## 3.7.2 - Damage to R/C Walls

Damage to Infill walls due to earthquakes

X-shaped shear cracks.

Sliding at the construction joint.

Damage of flexural character.

the appearance of cracks at the construction joint is the most frequent type of damage and is mainly due to the fact that old concrete is not properly bonded with fresh concrete (Booth, 1994).

The appearance of X-shaped cracks in R/C walls is the next most frequent damage. This is a shear type of brittle failure.

Damage of flexural type occurs very rarely. It is the authors' belief that this is due to the fact that the bending moments developing at the base of the wall are much smaller than those calculated for the design, because the footing rotates as the soil deforms during the earthquake. untitled 4.bmp

Figure 3.4 Damage in column in contact with masonry on one side only (Millais, 1997).

3.7.3 - Damage to Beams

Reinforced concrete beams damage due to earthquakes:

Cracks orthogonal to the beam axis along the tension zone of the span

Shear failure near supports

Flexural cracks on the upper or lower face of the beam at the supports

Shear or flexural failure at the points were secondary beams or cut-off columns are supported by the bream under consideration

X-shaped shear cracks in short beams which connect shear walls.

Damage to beams although does not endanger the safety of the structure. Cracks in the tension zone of the span constitute the most common type of damage. This type of damage cannot be explained using analytical evidence given the fact that the action of the seismic force does not increase the bending moment in the span. However the vertical component of the seismic action due to its cyclic character simply makes visible the micro cracks which are due to the bending of the tension zone thus creating the impression of earthquake damage (American Society of Civil Engineers, 1996).

This is the reason why the large majority of the cases of beams with this type of damage do not put at risk that overall stability of the structure. It is also understood that the high frequency of this type of damage is rather misleading since in most cases is just a manifestation of already existing normal cracking than of earthquake damage.

The bending-shear failure near the supports is the second most frequent type of damage in beams. Undoubtedly it constitutes a more serious type of damage than the previous one given its brittle character. However in only very few cases do it expose the overall stability of the structure to risk. (Coburn,Spence, 2002).

The flexural cracks on the upper and lower face of the beam at the supports can be fully explained if the earthquake phenomenon is statically approximated with horizontal forces. From the frequency point of view this type of damage is rarer than the shear type. Most of the time cracking of the lower face is due to the bad anchorage of the bottom reinforcement into the supports in which case one or two wide cracks form close to the support (Scarlat, 1996).

The shear or flexural failure where secondary beams or cut-off columns are supported appears quite frequently. It is due to the vertical component of the earthquake which amplifies the concentrated load.

X-shaped shear cracks in short beams coupling shear walls also appear quite often. It is a shear failure to that which occurs in short columns but not so dangerous for the stability of the building. (Yong, Tassios, Vintzileou, 1999).

untitled 5.bmp

Figure 3.5 Shear wall damage at a construction joint.

3.7.4 - Damage to Slabs

Types of damage which occur in slabs (Cook, Hinks, 1992):

Cracks parallel or transverse to the reinforcement at random locations.

Cracks at critical sections of large spans or large cantilevers, transverse to the main reinforcement.

Cracks at locations of floor discontinuities, such as the corners of large openings accommodating internal stairways, light shafts and so on.

Cracks in areas of concentration of large seismic load effects, particularly in the connection zones of slabs to shear walls or to columns in flat plate systems.

With the exception of the last type, damage in slabs generally cannot be considered as dangerous for the stability of the structure. However, they create serious aesthetic and functional problems, so they must be repaired. Moreover, the creation of such damage leads to the reduction of the available strength, stiffness and energy dissipation capacity of the structure in case of a future earthquake, and this is an additional reason for their repair (Beckett and Alexandrou, 1997).

The first type of damage is the most frequent. Most of the time it is due to the widening of already existing micro-cracks which are formed either because of bending action or temperature changes or shrinkage and they become visible after the dynamic seismic excitation.

The second and third types of damage are typically due to the vertical component of the earthquake action.

The fourth type of damage is usually related to punching shear failure, aggravated by the cyclic bending caused by the earthquake (Englekirk, 2002).

Chapter 4

## 4.1 - Introduction

## 4.2 - Effects of Masonry Infilled Walls in Structural Analysis

This study assumes that infill walls behave as structural components offering further stiffness to the structure. According to Diptesh Das and C.V.R. Murty (2004), the infills of reinforced concrete structures, has contributed some extra strength and stiffness to the structure compared to bare frame. Design stages of the infill walls should further be conceder by designers to improve their functions and minimize their negative impacts. Infill walls may contribute to minimization of drifting in inter-story structures and increase the strength and stiffness of it.

The infill masonry walls resist lateral forces with an effective action on the structure. They also offer the walls the required strength to withstand seismic loads. This reveals that structures with infill walls are stronger and more effective in earthquake zones than those with lack infill walls. The dynamic behavior of the structure also changes. The seismic behavior of buildings is affected by the presence of masonry infill walls in the following ways (Penelis and Kappos, 1997):

Infill walls increase in stiffness of buildings, the fundamental period is decreased and the base shear is increased.

The lateral stiffness in plan and elevation is modified.

Part of the load is carried by the infill wall so the structural system is relieved of seismic action.

Energy dissipation capacity of the building is significantly increased.

Masonry infill walls in reinforced concrete frames cannot only increase the overall lateral load capacity but they can modify the structure of the frame. Masonry infill can change the future structural response of buildings attracting forces that have not been designed to resist against them (Paulay and Priestley, 1992).

Despite the advantages, infills can reduce the structure's ductility. Other factors that determine the strength of infill masonry are the quality of material used, the workmanship and the type of frame-infill interface. More negative impacts include torsional and short columns effects which are caused by irregular plans and soft-story effects.

Indicating results from researches, uncertainties on the analysis of buildings due to effects of infill includes:

Their mechanical properties are variable hence there is low trustworthiness in their strength and stiffness.

There is tightness when connected to the surrounding frame.

The potential modification of their integrity during the use of the building.

Safety of the structure cannot rely on the infills but only their negative influence is taken into account because of the non-uniform degree of their damage during the earthquake (Penelis and Kappos, 1997).

## 4.3 - Background Examinations

Polyacob (1960), acknowledges that the infill system behave as a braced frame with the wall forming 'compression' struts. Stafford-Smith (1962), and Mainstone (1971), suggested strategies for calculating the effective width of the diagonal strut using experimental models. Some other researches like Klinger and Bertero (1978) were tested representation of scaled structural buildings and concluded that infill wall panels reduce the risk of incremental collapse compared to bare framed structures. Supported from Polyacob (1960), Holmes (1961), proposed a linear equivalent strut for figuring stiffness and strength of panel walls and Stafford-Smith (1962) established analytical calculation methods for the effective width of the strut and cracking and crashing loads, functional to frame's lengths and wall's properties. A multistrut model, known as the 'compression-only three struts model', was also investigated by Chrysostomou et al. (1992).

Ali and Dhanasekar (Ali, 1987; Dhanasekar, 1985) also researched on further aspects of the static analysis of masonry and their work has been instrumental in the development of the current code provisions related to the design of masonry structures for bi-axial loading, concentrated loads, and in plane loading of masonry walls.

Early research mostly focused on developing improved seismically resistant design, analysis and construction techniques for new structures. Little research was done to investigate the seismic performance of existing structures with non-ductile detailing. Only a limited amount of research has been undertaken on infilled frames with openings.

Further researchers used finite element models for the evaluation of wall behavior aspects. Most popular form was the combination of smeared and discrete crack approaches by Stavridis and Shing (2009), who captured different failure modes of RC frames with masonry infills, from their nonlinear finite element models. In the other hand, Dolsek and Fajfar (2008), used plasticity column elements with equivalent strut wall elements, looking at 'damage limitation', significant damage' and 'near collapse' limit state.

Until now, there are impediments to reliable modeling of infill walls. More known are discontinuities of infill, large variation in their construction and changes of materials over time. The strut model system is simple and mathematically attractive although not stable in practice. Diagonal struts that are used to identify stiffness of the infill masonry are not effective particularly when openings like doors and windows exist in a structure. Any damage on masonry area cannot be predicted. It is simple and computational attractive but theoretically weak. Continuum model is accurate through computational representation from material and geometrical perspectives. This is only applicable when the origin of nonlinearity and properties of masonry are carefully looked at (Hao, Ma and Lu, 2002).

The response of the infilled frame can be modeled by replacing the panel by a system of diagonal struts. Stress and strain relationship for masonry in compression can be idealized by a polynomial function. Compression is used for the determination of the strength parameters in that strut (Mander et al. 1988). The masonry struts are considered to be ineffective in tension since the tensile strength of masonry is negligible. The key in this situation is that the diagonal strut provides lateral load resisting mechanism for the opposite lateral directions of loading.

The proposed method takes into account the elastoplastic behavior of infilled materials such as the infill aspect ratio, the shear stress at the infill-frame interface and the relative column and beam strengths.

## 4.4 - Common Design Codes

As stated above, over the last decades, to mimic the behaviour of infill panel walls were developed many types of analytical models. The most known is the single strut model that reported to give better results as it is the simplest than the multistrut model and can be used to for analysis of structures with more storeys (Das and Murthy, 2004).

Provisions on reinforced concrete frames with infill masonry walls were made by few designs codes until now. The specific frames were modelled as equivalent braced frames and infill walls were replaced with diagonal strut.

The design codes for infill are very few. The common codes are;

Eurocode 8

Nepal building code 201 and

Indian seismic code.

The Eurocode 8 (EC 8) refers to RC frames and infill of brick masonry as a dual system. This infill is classified thrice depending on ductility, mainly low, medium and low. The design for the infill depends on its asymmetrical arrangement that cause irregularities in the structural plan that increases the eccentricity factor (Diptesh Das and C.V.R. Murphy 2004 p.40). The modification factor affects the performance of the infill except from the displacement of RC frames.

The Nepal Building Code 201 provides a clear standard for up to three-story structures that lie in low seismic zones. These standards are raised for structures that lie in high seismic zones. The structures are designed to withstand seismic forces through composite reaction.

The Indian seismic code dwells on linear elastic analysis for the structure without including the brick infills. The specifications rely on response reduction factor (2R) acquired from the expected seismic damage of the building that is reflected on deformations from ductility (Diptesh Das and C.V.R. Murty 2004 p. 42).

4.6 - Modes of failure of masonry infilled RC frames

Moreover, Infills possess large lateral stiffness and hence draw a significant share of the lateral force. In cases that infill walls are strong, strength contributed by the infills may be comparable to the strength of the bare frame itself. The failure modes of an infilled frame or wall depends on the relative strengths of frame and infill and, its ductility depends on infill properties, the relative strengths of frame and infill and last to distribution of infills in plan and elevation of the building.

Weak Infill

Strong Infill

Weak Frame

## -

Diagonal cracks in infill

Plastic hinges in columns

Frame with Weak Joints

and Strong Members

Corner crushing of infills

Cracks in beam-column joints

Diagonal cracks in infill

Cracks in beam-column joints

Strong Frame

Horizontal sliding in infills

## -

Table 1: Modes of failure of masonry infilled RC frames

## -

## 4.7 - Equivalent Diagonal Strut

The analytical models adopted so far can be categorised into two main groups. 'Micro-modeling', where the masonry units, the mortar and the masonry unit interface, is modeled separately and 'macro-modeling' where the masonry is a homogeneous continuum with no distinction between the individual units and joints. Kappos and Ellul proved and conclude that EC8 is over conservative by disregarding the contribution to strength of the infills. Combescure and Pegon carried out numerical studies and a testing programme on infilled frame structures. Both micro (panel element) and macro (strut element) models were considered and both showed the validity of the diagonal strut model and emphasized the importance of identifying appropriate strut properties.

Researches are being carried out in the concerned regions of the world to clearly arrive at a consensus by disclosing the complex behavior of interaction between panels and frames. From time to time laboratory tests are being conducted and mathematical models are being developed that can best simulate the behavior of infilled frames.

Equivalent-strut methods, starting with Stafford-Smith (1966), used single strut to represent infill behavior. Several multiple strut methods of analysis have been proposed (Chrysostomon et al., 1988 ; Thiruvengadam, 1985; Mander et al., 1994) for more accurate modeling of frame/panel interaction.

As there is still drawback in modeling force transfer-slip at the frame panel interfaces (Gergely et al., 1994), non-linear finite element analysis can be used (Shing et al., 1994; Mosalan et al., 1994). Computational limitations, on analyzing more than one panel at a time are difficulties with the later method.

In the case that masonry infill walls are not isolated from the concrete frame members and the floor, masonry elements should be included in the model of the physical structure. The mathematical model of the physical structure should represent the distribution of mass and stiffness of the structure to an extent that is adequate for the calculation of the significant features of its dynamic response.

There are impediments to reliable modeling. The first being discontinuities of infill, resulting from soft stories or checkered patterns. The second is the large variation in construction practice over different geographic regions and changes of materials over time.

Ali and Dhanasekar (Ali, 1987; Dhanasekar, 1985) researched on further aspects of the static analysis of masonry. Their work has been instrumental in the development of the current code provisions related to the design of masonry structures for bi-axial loading, concentrated loads, and in plane loading of masonry.

## 4.8 - Stiffness of Masonry Infill

Stafford Smith has defined a dimensionless relative stiffness parameter to determinate the degree of frame-infill interaction, thereby the effective width of the strut. He used an elastic theory to show that this width was function of the infill stiffness to the boundary frame. Finally, Smith developed a set of empirical curves to relate the stiffness parameter to the effective width of an equivalent strut. By modelling the infill as an equivalent diagonal strut the contact length parameter ( and width (w) can be computed.

The single strut model is the most suitable for large structures (Das and Murphy, 2004) and according to this model, as the value for (Î») increases the width of the equivalent strut decreases. To continue with, frames with unreinforced masonry walls can be modeled as equivalent braced frames with infill walls replaced by equivalent diagonal strut. As suggested by Mainstone the strut area that is depended from the strut width is given by:

and

dm

Figure 2: Equivalent Diagonal 'compression' strut

Where:

h = column height between centrelines of beams, cm.

hm = height of masonry infill panel, cm.

Ef = modulus of elasticity of frame material, MPa

Em = modulus of elasticity of infill material, MPa

Icol = moment of inertia of column, cm4.

lm = length of infill panel, cm.

dm = diagonal length of infill panel, cm.

tm = thickness of infill panel, cm.

Î¸ = angle whose tangent is the infill height-to-length aspect ratio

Î»I = Coefficient used to determine equivalent width of infill strut.

This method accounts for inelastic and plastic behavior of the infill considering its material properties. Adding to this, it is estimate through a rational approach the lateral strength and stiffness of the frame.

Sliding Shear Failure of Wall

Maximum Shear strength from Mohr-Coulomb failure criteria:

Where:

Ï„o - Cohesive capacity of the mortar bed.

Î¼ - Sliding friction coefficient along the bed joint.

ÏƒN - Vertical compression stress in the infill walls.

Maximum horizontal shear force Vf :

tm - Infill wall thickness.

lm - Length of infill panel.

N - Vertical load in infill walls.

N estimated as the sum of applied vertical load on the panel and the vertical component of the diagonal compression force Rc. Usually the former is zero.

Figure 2: Lateral force and diagonal compression parameters

Therefore, the maximum shear force is:

â‡’ Horizontal component of strut

## â‡’

Ï„0 is within the range

For the purpose of analysis, Ï„0= 0.04 f m and Î¼ = 0.5 (Paulay and Priestley, 1992)

Compression Failure

Compression failure of infill walls is based on the compression failure of the equivalent diagonal strut.

Where:

Vc - shear at the compression failure of equivalent diagonal strut.

Z - Width of equivalent diagonal compression strut.

tm - thickness of infill panel and equivalent strut.

f m - Compressive strength of masonry

Î¸ - Angle whose tangent is the infill height-to-length aspect ratio, radians.

The relationship between lateral force and infill material assumed to be a smooth curve bounded by the strength envelope. After post-peak residual shear force Vp ensue, the yield force Vy with an initial elastic stiffness and the maximum force Vm with a post yield degraded stiffness, reached as a result the formation of the curve.

Figure :Strength Envelope for Masonry Infill Panel (Mostafaei et al, 2003)

Figure :Developed Shear force and Displacement

Where:

Vm, Um - Maximum shear force and displacement.

Vy, Uy - Shear force at yielding and displacement.

Vp, Up - Post-peak residual shear force and displacement.

K0 - Initial Stiffness of the infill panel.

Î± - The ratio of the post-yield stiffness to the pre-yield stiffness.

Maximum lateral strength, Vm , should be taken to be the minimum value between the two critical failure modes, sliding shear and compression failures. In the other hand, the maximum displacement at the maximum lateral force is:

## ;

Where:

Um - Maximum displacement at the maximum lateral force.

Îµ'm - Masonry compression strain at the maximum compression stress.

Hence the initial stiffness of the infill panel is given by:

(Madan et al, 1997)

Where:

K0 - Initial stiffness of the masonry infill panel.

Chapter 5

Case Studies

5.1 - Introduction

This extensive study has as basic subject the seismic behavior of reinforced multistory structures. Particular interest were given, on the effect of stiffness which provided by non-structural members (infill walls), to these structures. The contribution of infill walls was not considered in the final strength of those structures. In Chapter 5 a comparison has been made that measured the response under earthquake load of six-story, three framed structures, symmetrical in plan and elevation with different infill wall configurations. The masonry infill configurations for this case study were:

Bare Frame

Partially Infilled Frame

Fully Infilled Frame

5.1.1 - Structural Form and Layout

## Story

## Height (m)

## Column section (m)

## Beam section (m)

1

5

0.6 x 0.6

0.4 x 0.5

2

3

0.5 x 0.5

0.4 x 0.5

3

3

0.45 x 0.45

0.4 x 0.45

4

3

0.450.45

0.4 x 0.45

5

3

0.35 x 0.35

0.35 x 0.4

6

3

0.35 x 0.35

0.35 x 0.4

The above structures were designed for similar seismic requirements in accordance with Eurocode 8. Concerned for their seismic behavior, the above structures were designed to satisfy requirements for ductility class 'Medium' with design peak ground acceleration of 0.15g and corresponding 'q' factor was 3.9.

Table 1: Column and Beam dimensions and the height that correspond to each story.

Furthermore, other design assumptions were soil profile A, spectrum type B, concrete class C20 (characteristic compressive strength 20MPa), permanent load 2.2 KN/m2 and variable load 2.5 KN/m2 as the structure was assumed for office use. The total height of the building is 20m.Full design specifications are provided with in the calculations. The frame configuration and the typical plan and dimensions of beams and columns are shown in figures 1

Figure 1: Different infill configurations (Bare Frame - Partially Infilled - Fully Infilled)

5.1.2 - Masonry Infill Properties

The strength of masonry walls does not have direct consequences to the ductile reinforced concrete frames. Eurocode 8 (2004), states that the shear capacity of columns is required to be checked for shear forces that generated by the diagonal strut. This can be achieved by considering the vertical component of the width of strut as the contact area between reinforced concrete frame and infill wall. Recommended strut width is until now an unspecified fraction of diagonal panel length. Calculation procedures for the strut width have been proposed by many researches until now. In this study the strut width is designed following the procedure selected by the author in Chapter 4.

The code specifies minimum wall thickness of 240 mm and maximum slenderness ratio (height / thickness) of 15. As a result, first story infill wall thickness was taken to be 350 mm (slenderness ratio = 13.6) and 250 mm at the other stories.

Furthermore, modulus of elasticity of frame material, modulus of elasticity of infill material and the compressive strength of masonry were taken to be: Ef = 24000 MPa; Em = 3300 MPa; fm' = 4.37 respectively (Paulay and Priestlley, 1992).

5.1.3 - Procedure

Three cases were considered: (i) A frame having no infills, (ii) frame with infills and (iii) frame with no infills in ground floor and infills in all the other floors. The structures analyzed, were moment resisting reinforced concrete frame and to determinate the earthquake response of the structural systems the linear analysis method used. As stated in Chapter 2, this method varies in methodology as linear static (lateral force method) and linear modal response spectrum analysis. The masonry infill wall stiffness was calculated as the procedure stated in Chapter 4. The sum of stiffness from infills at each story was added to the same story column's summation of stiffness. Afterwards, both linear methods were repeated and the results were compared and discussed in Chapter 6. Calculations are stated as follow:

5.2 -Vertical loads

5.3 -Combination of seismic actions with other

5.4 -Stiffness Calculation

5.5 -Equivalent Static Method for Bare Frame

5.6 - Response spectrum method

5.7 - Calculation of the horizontal storey forces

5.8 - Determination of Infill Stiffness

5.9 - Repeat of 5.5, 5.6 and 5.7 for Fully Infilled Case

*Calculations for Partially infilled frame are not presented but used in Ch.6.

It is notable that only infills walls in A - A' direction were taken into account. By the time an earthquake happens, it is assumed that applies the same seismic load in both directions. In the other hand, impact to the structure's strength and stiffness is given only by infills walls found in direction that a load is applied. That means walls seen in elevation B - B' does not affect structure's behavior, if load applied in A - A' direction. The above methods calculate the base shear of model which is the same for both directions. For safety design purposes, this load should distributed through the story levels of A - A' direction as this is the weakest compared to B - B'. As a result the weakest direction, A - A', were selected for a comparison.

Chapter 6

Comparison and Distribution of Results

6.1 - Earthquakes

Earthquakes are one of the most frightening phenomena that can occur in nature. They have always been considered as one of the most serious natural threat in the human life and the property. An earthquake is a phenomenon which is usually expressed without explicit warning, cannot be avoided despite its small duration; it can cause big material damage in the human infrastructures, as a consequence serious wounds and losses of human lives. Scientific understanding, of earthquakes is of vital importance to any country. As the population increases, the urban development expands and construction works encroach upon areas, susceptible to earthquakes. With a greater understanding of the causes and effects of earthquakes, we may be able to reduce damage and loss of life from this destructive phenomenon.

6.2 - Comparison of Seismic Analysis Methods

With Equivalent Static method two empirical equations were used in order to estimate the fundamental period of vibration T and it was also carried out in less time by doing few and simple calculations. The approximated values resulted from empirical equation proposed by Eurocodes. The first one, T = Ct x H3/4, took into consideration only the height of model. On the other hand, the second method took into account only the maximum displacement at the top storey, using the equation T = 2. This lateral elastic displacement at the top of the building was the result of gravity loads applied in the horizontal direction and the stiffness, at each floor.

## BASE SHEAR (KN)

## Structure

T = Ct x H3/4

T = 2.(d)^0.5

Bare Frame

373.3

472.60

Partially Infilled Frame

373.3

601.50

Fully Infilled Frame

373.3

696.50

Table 1: Base Shear approximations using Equivalent Static Method

In this simplified equivalent static analysis, temporal variations are neglected and only the maximum possible responses are considered. Formula that take into account the stiffness, approximate better the base shear of the structures. Results are different as stiffness change between case studies. As it was expected, fully infilled frame model has greater base shear than the bare frame model. To summarise, equivalent static method can be used in preliminary design situations, but only for certain buildings up to 10 storey height as mentioned by EC8.To continue with, comparing the base shear using the equivalent static method and the response spectrum method, the following difference was noticed.

Figure 1: Base Shear comparison using Response Spectrum and Equivalent Static Method

Response Spectrum method approximates better the fundamental period of vibration (T) as a consequence to present more accurate and responsible results concerning base shear of structures. Response spectrum method yields much more accurate results than the equivalent static method. As can be seen from figure 1 there is a percentage difference that ranges from 15 - 18 between the results of two methods. Response spectrum method is used for constructing buildings. Equivalent can be used for the purpose to give an initial idea for magnitude that will be acted due to a possible earthquake. The response spectrum involves simplifying assumptions; however, it can yield important information such as the effects of varying. Additionally, this method errs on the side of safety since the maximum values of response are represented. Even more complex analyses of dynamic responses rely on calculation of the response spectrum (Hudson, 1956). Compared to th