Full Thesis.pdf

CHAPTER 1 1.1 INTRODUCTION

Earthquake has been known as one of the critical natural disasters for thousands of years. It is an unpredictable hazardous natural phenomenon, which has proved disastrous at various instances in history. Mankind has always attempted to make structures safer against earthquakes to reduce loss of life and property. The increasing infrastructural growth incurs large investments and large section of society being served by them, it is necessary to make them safer against earthquakes and let people feel confident in their structures. It is also important to ensure the functionality of lifeline structures like hospitals, emergency command centres, transportation infrastructures, and power generating units in postearthquake scenario in order to mitigate the disaster. Current philosophy for earthquake resistant design of structures adopted in codal provisions is based on strength and ductility. Even with sufficient strength and ductility the structures may not acquire any damage but the functionality at the instance when it is most required is hampered. Shear walls are a type of structural system that provides lateral resistance to a building or structure. They oppose in plane loads that are connected along its tallness. The applied load is commonly transferred to the wall by a diaphragm. The productivity of a structural system is measured as far as their capacity to oppose parallel load, which increments with the tallness of the frame. Lateral deflection of framed buildings should be limited to avoid damage for the both structural and non-structural elements. Reinforced concrete (RC) structures frequently have vertical plate-like RC walls called Shear Walls in addition to slabs, beam and column. These walls for the most part begin at footing level and are constant all through the building stature. Their thickness can be as low as 150mm, or as high as

400mm in tall structures. Shear dividers are generally given along both length and width of structures. Shear walls resemble vertically-situated wide beam that carry seismic loads downwards to the footing. We cannot manage to pay for to manufacture concrete building meant to resist severe earthquake without shear wall. In high seismic region, shear wall require special detailing. Nowadays, building with shear wall are a popular choice in many earthquake susceptible countries like. Reinforced detailing of shear walls is relatively straight-forward and therefor it is easy to construct and implement at site. Shear dividers are productive; both as far as construction cost and properly designed and detailed building with Shear walls have performed good execution in past earthquakes. The strength and stiffness of building are depend upon the direction of orientation of shear wall. It means that shear wall provide large strength and stiffness to building in the direction of their orientation, which knowingly reduce the lateral sway of the building by which reduces damage to structure and its contents. In a building, shear wall should be provided along preferably both length and width. Shear wall in building must be symmetrically located in plan to reduce ill-effect of twist in buildings and they could be placed symmetrically along one or both direction in plan. The various cross section of shear wall like rectangular shape to more irregular cores such as channel, T, L, barbell shape, box etc. can be used. In fact, the number of multistory reinforced concrete moment-resisting frame structure with shear wall that enable their seismic energy to dissipate in a secure manner has rapidly been increased over past half century around the world including the united states.

1.2 OBJECTIVE OF THE STUDY

One of the main objectives of this study is to analyze the seismic performance of the building with or without shear wall as per code IS 1893-2002 part 1 criteria for earthquake resistant structure. For the accomplishment of the study different cases such as (i) a special RC moment-resistant frame building without shear wall(ii) shear wall placed parallel to the X (longitudinal direction) axis (iii)shear wall placed parallel to the Y (longitudinal direction) axis (iiii) shear wall is centrally located at exterior frame of both X and Z direction throughout height of the building (iiiii) shear wall located at exterior frame end corners of both X and Y direction throughout height of the building I. II. III. IV. V.

To design a G+9 RC SMRF building, for various location of shear wall using ETABS 2015 To model shear wall in different location of building Dynamic analysis of the building using time history analysis To get efficient and economical lateral stiffness system To compare storey displacement drift and various analysis result

1.3 SCOPE OF PRESENT STUDY: In the present study, a RC SMRF building is analysed using software ETABs by dynamic (time history method) analysis. Analysis has been carried out as per Indian code books. Based on the literature of previous studies most effective positioning of shear walls has been chosen. Analysis is done using five model with different position of shear wall. This study is done on RC SMRF framed multistory building with RC shear wall with fixed support conditions. 1.4 ORGANISAATION OF THE DISSERTATION The dissertation work is arranged in six chapters. Chapter (1) Introduction Chapter (2) literature review It explains the basis of this study and addresses the past findings on the subject. Various documents, standards, and reference works related to study have been elaborated.

Chapter (3) methodology It explains the basis of this study and addresses the past findings on the subject. Various documents, standards, and reference works related to study have been elaborated. Chapter (4) modelling and analysis This section of the report explains step by step process of model development and progression of analysis. It elaborates the assumptions and values adopted and calculated at various stages of the work. Chapter(5) consist of conclusion and scopes of future work regarding thesis are mentioned.

CHAPTER 2

LITERATURE REVIEW INTRODUCTION: One of the major concerns of developing countries like India is to effectively reduce the risk of a disaster. Having a good disaster mitigation strategy is not sufficient for disaster risk reduction, prevention and preparedness is more important. Regulations and codal provisions for ERD of structures currently in practice in India (IS 1893:2002) are not capable enough to reduce the impact and may at times add to the extent of a disaster. This necessitates adopting measures to make structures safer against hazards and thereby reducing the risk of occurrence of a disaster which can be achieved by reducing the vulnerability of the structure against the hazard. Lakshmi K.O., Prof. Jayasree Ramanujan, Mrs. Bindu Sunil, Dr. lajuKottallil, Prof Mercy Joseph Poweth (2014), have studied the effect of shear wall location based on linear and nonlinear analysis procedure and various parameter are to be compared. The various parameter like story drift, story shear, deflection, reinforcement requirement in column of a building under the lateral loads based on considered location of shear walls. They obtained lateral displacement values from static method of analysis which is indicate that shear wall provision along longitudinal and transverse directions are effective in reducing the displacement values in the same directions. The results were illustrated that the model with shear wall provided at core as well as on corners the story drift has significantly been reduced when compared to the bare frame model as well as those models in which shear walls are provided only in longitudinal or transverse directions. He also illustrate that the maximum reduction in displacement value is acquire for Frame with Core and corner shear wall.

Shaik Kamal Mohammed Azam, Vinod Hosur (2013), presented a study on seismic performance evaluation of multi-storeyed RC frame building with shear wall. A judgement on structural behaviour in terms of strength, stiffness and damping characteristic is done. The providing of shear wall has significant influence on lateral strength in taller building whereas it has less influence on lateral stiffness in taller buildings.The arrangement of shear wall has critical impact on lateral stiffness in building of shorter height while it has less impact on lateral strength. The impact of shear wall is significant in terms of the damping qualities and period at the performance point for tall building. Arrangement of shear wall symmetrically in the peripheral moment-resisting frame and ideally interconnected in commonly opposite heading framing the core will have better seismic performance in terms of strength and stiffness. Shahabodin, Zaregarizi (2013), presented a study on Comparative investigation on using shear wall and concrete infill to improve seismic performance of existing buildings.They were studied two systems including shear walls and concreteinfills was used for rehabilitation of a five story reinforced concrete building with unreinforced masonry infill walls and effectiveness of each method was studied through static nonlinear analysis. The result illustrated that concrete fills have significant strength than brick in fills while the displacement acceptance of brick infills is higher than concrete infills. Thus arrangement of concrete and brick infills can reduces the negative effects of brick and concrete infills. As lateral resisting elements masonry infills have significant strength which can prevent even collapse in reasonable earthquakes. HimaleeRahangdale, S.R.Satone (2013), presented a study on Design and analysis of Multistoreied building with effect of shear wall. Result show that in absence of shear wall axial load and moments are maximum on the column. Shear walls construction will provide larger stiffness to the building there by reducing the damage to structure and its contents. Mahdi Hosseini, N.V Ramana Rao (2015), have studied earthquake analysis of high rise building with shear wall at the center core and center of each side of the external perimeter with opening. Result show that location of shear wall in the outermost perimeter show better performance of displacement and drifts. Also the existence of opening in shear walls gave a result with a deviation of around 5% with that of shear wall without openings. JunwonSeo, Jong Wan Hu and Burte Davaajamts (2015), have studied seismic evaluation of twelve-story reinforced concrete moment-resisting frame structure with shear wall using 3D finite element models. The results show that the

maximum displacement for both response spectrum and nonlinear time history analysis increased along the height of structure and distribution of corresponding inter-story drift ratios for both analysis are slightly different maximum displacement because these ratios vary depending on relative story displacement and heights. As compared to response spectrum analysis, the time history analysis provided 28.1% and 54.0% greater values in maximum displacements and drift ratios. According to modal analysis the first and third mode shapes had the most dominant modal mass along the longitudinal and transverse direction.

CHAPTER 3

METHODOLOGY

3.1 INTRODUCTION: This chapter deals with the methods followed for design and analysis of model considered in this study. The analytical software ETABS 2015 has been used for this purpose. 3.2 DYNAMIC EQUATIONS OF MOTION: 3.2.1 Single Degree of Freedom System: The response of a linear single degree of freedom (SDOF) system to ground motions 𝑢̈ g is the solution to the diff erential equation [Chopra (2007)] m𝑢̈ + c𝑢̇ + ku=−m𝑢̈ g

(3.1)

Where m is the mass of the system, c is the damping constant and k is the stiff ness. Relative displacement of the system as a function of time is denoted as u(t). First derivative of the displacement is the velocity 𝑢̇ (t) and the second derivative is the acceleration of the system 𝑢̈ (t). By dividing the equation above with the mass m the normalized equation of motion is obtained. 𝑢̈ +2ζωn𝑢̇ + ωn2 u=−𝑢̈ g (3.2) whereωnis the natural angular frequency and ζ is the damping ratio of the system. ωn=√

𝑘 𝑚

(3.3)

ζ=

𝑐

(3.4)

2√𝑘𝑚

The relation between period T and natural angular frequency ωnis given by T =2π ωn= 2π√

𝑚 𝑘

(3.5)

3.2.2 Multiple Degrees of Freedom System: The dynamic behaviour of structures involves simultaneous motion of several masses in shapes that are unknown before the analysis. The theory of dynamics of a single degree of freedom can be extended to multiple discrete masses and distributed mass systems like beam and frame structures, as well as the whole building and structures such as bridges. The extension of the theory from one degree of freedom involving a single mass to multiple degrees of freedom, describes the coupled motion of several concentrated masses. This theory is called modal analysis and has ben explained in subsequent section. The dynamic response of a linear system with n degrees of freedom u(t)T = [u1(t),u2(t),...,un(t)] to ground motions is described by the set of second order diff erential equations m𝑢̈ + c𝑢̇ + ku =−mI𝑢̈ g

(3.6)

The physical parameters are: the mass matrix m, the viscous damping matrix c and the stiff ness matrix k. Eff ective earthquake forces are given by the vector −mI𝑢̈ g where I is the influence vector representing the displacements of the masses resulting from static application of a unit ground displacement. Mode shapes and periods are found by solving the generalized eigenvalue problem matrix

[k−ωn2m]φn = 0

(3.7)

The complete solution to the generalized eigenvalue problem consists of n sets of eigenvalues and eigenvectors, arranged as corresponding pairs of natural frequency ωj and mode shape vector φj. (ωj,φj)

j = 1,2,...,n (3.8)

3.3 DESIGN METHODOLOGY: The current design requirements illustrated in IS 1893:2002 (criteria for earthquake resistant design of structures) has been adopted here for design of concerned structure in this study. The theory of capacity design concept developed in 1970s has been adopted in IS 1893:2002. 3.3.1 Capacity based design: This method is an improvement over the force based method, under strength based design for ERD of structures. It considers the hierarchical allocation of strength to structural members. The hierarchy of structural member strength aims to ensure inelasticity being confined to predetermined and preferred structural members to delay failure modes in non-ductile structural behaviour. It considers providing sufficient stiffness and strength to structure both locally and globally as well as considers strong column weak beam philosophy. The design of members for shear is dependent on P-M interaction. The overall target of this philosophy is to design members with sufficiently larger shear capacity against maximum probable equilibrium compatible shear demand generated due to plastic hinge moment capacities mobilized at two ends. Within the member it is desired that the ductile flexural failure occurs before the non-ductile shear failure and axial compressive

failure in a beam. The collapse mechanism is governed by location of inelastic hinges and type of hinges. 3.3.2 Strong column weak beam concept: This hierarchy of strength between structural members is to ensure that columns do not form plastic hinges so to be capable of carrying vertical axial load and that beams do not carry axial load and develop ductile plastic hinges for inelastic energy dissipation. This is ensured by preventing non-ductile shear failure of individual beams and columns by capacity design as well as preventing non-ductile shear failure and anchorage failure of joints. This suggests that the ratio of flexural capacity of columns to over-strength flexural capacity of beams should be greater than 1. Further the foundation supporting columns is designed with higher strength than columns in the hierarchy. The beam-column joints are designed to have stiffness and strength as much as the adjoining beam and column so as to maintain the flow path between beam and column. 3.3.3 Ductility: The philosophy of deformation based design which is under development considers ductility to be an important parameter apart from stiffness and strength requirements. This philosophy which is by far most advanced for ERD of structures is necessary for important and life line structures. The importance of this concept has been identified in IS 1893: 2002 in terms of ductile detailing of members as per IS 4326:1993 (earthquake resistant design and construction of buildings-code of practice) or IS 13920:1993 (ductile detailing of RC structures subjected to seismic forces-code of practice) or SP 6 part6:1972 (handbook for structural engineers: application of plastic theory in design of steel structures).

3.3.4 Criteria for Earthquake Resistant Design of Structures (IS 1893 Part I2002): This section deals with guidelines provided in this documented as it is, which has been considered in design of the building under study. The document deals with various design aspects that has been referred to necessary documents. The most importantly it deals with procedures and methods for estimation of lateral load under seismic excitation and methods for analysis of structure under these conditions, necessary for ERD of structure. Following assumptions are made for ERD of structures i.

Earthquake causing impulsive ground motion is complex and irregular in nature, changing oscillation period and amplitude for small duration. As such occurrence of resonance is neglected.

ii.

Wind and maximum flood/sea waves are unlikely to occur simultaneously with earthquake.

iii.

Modulus of elasticity of materials is taken as per static analysis unless more definite value available for use in such condition (with reference to IS 456, IS 1343 and IS 800)

In limit state design of RC structures following load combinations is accounted for 1.5(DL + IL) 1.2(DL + IL ± EL)

(3.9)

1.5(DL ± EL) 0.9DL ± 1.5EL The orientation of horizontal orthogonal direction of lateral load resisting system and seismic load must be considered for design horizontal earthquake load. If this

effect is considered, the contribution of orthogonal loads on response is that of 30%.The motions and their responses are accordingly combined and maximum of the values is considered. Under seismic loading the permissible stresses are increased by one-third, in elastic method of design. Since the building designed has not incorporated the foundation and that the base is considered to be fixed and soil foundation system as rigid, the modification in allowable bearing pressure in soils has been neglected. 3.3.4.1 Plan and elevation criteria: It is suggested that building configuration be simple and regular both in plan and elevation. The building is considered to be irregular if it meets the conditions described in table 4 and table 5 of the document. It is also advised that the distribution of mass and stiffness be regular in both plan and elevation. The mass and stiffness irregularities have also been defined in the same table of the document. 3.3.4.2 Design spectrum: The design horizontal seismic coefficient Ah for a structure is given by following expression Ah=

𝑍𝐼𝑆𝑎 2𝑅𝑔

(3.10)

Where Z is the zone factor for maximum considered earthquake (MCE) and factor 2 in denominator is a modifier for ZMCE to Z Design Basis earthquake (DBE) Values of zone factor as per clause 6.4.2 of IS code 1893:2002 are given in following table

Table 3.3.4.2 (1) Zone factor, Z (After table 2, IS code 1893:2002) Seismic Zone II III IV V Seismic Low Moderate Severe Very Severe Intensity Z 0.10 0.16 0.24 0.36 I is the importance factor depending on building type as described in table 6in code IS 1893 (Part 1) :2002 .The value of I is 1.5 for important service and community buildings like hospitals and school buildings and I is 1.0 for all otherbuildings. R is the response reduction factor. The actual base shear generated for structural response to DBE being under elastic range, is reduced with this factor to obtain design lateral force.It should be noted that the ratio (I/R) must not be greater than 1.0. The value of R is as given in table 7 of the document depending on perceived seismic damage performance of the structure. Sa/g is the average response acceleration coefficient whose value depends on natural time period of the structure and the site condition of the building (Table 1.1). For 5% damping the values of spectral acceleration coefficient is given as follows for three site conditions 0.00≤T≤0.10

10≤T≤ a

a ≤T≤4.0

Rocky/hard soil sites

1+15T

2.50

1/T

Medium soil sites

1+15T

2.50

1.36/T

Soft soil sites

1+15T

2.50

1.67/T

Site condition

Time period

a = 0.40 for rocky/hard soil sites; 0.55 medium soil sites; 0.67 for soft soil sites

TABLE 3.3.2.4 (2) Sa/g values at 5% damping for various time periods of structure and various site conditions.

Where T is the approximate fundamental natural time period of vibration of building in seconds and is given as For moment resisting frame building without brick infill panells T=0.075h0.75, for RC frame building

(3.11)

T=0.085h0.75, for steel frame building

(3.12)

T=

0.09h √d

, for all other building types including MRF with brick infill panels (3.13)

Whereh is the height of the building in m and d is base dimension of the building at plinth level in considered direction of lateral force. 3.3.4.3 Design lateral forces: Total design lateral force or design seismic base shear (VB) along any principal direction is given as VB=AhW(3.14) Where W is the seismic weight of the building. Seismic weight of the building, it is the sum of the seismic weights of all the floors and has been calculated as per clause 7.4 of IS code 1893(Part I):2002. The seismicweight of each floor has been calculated by adding its full dead load and appropriateamount of imposed load as per table 8 of IS code 1893(Part I):2002 and Ahis horizontal seismic coefficient.

Table 3.3.4.3 Percentage of Imposed load to be considered in seismic weight calculation (As per table 8 of IS code 1893(Part I):2002) Imposed Uniformity distributed floor Percentage of Imposed load loads( KN/ m2) Upto and including 3.0

25

Above 3.0

50

3.3.4.4 Distribution of design forces The design base shear is distributed along the height of the building as per following expression 𝑊𝑖 ℎ𝑖2

Qi = VB∑𝑛

2 𝑖=1 𝑊𝑖 ℎ𝑖

(3.15)

Qi is design lateral force at ith floor, Wi is the seismic weight of ithfloor, hi is the height of ithfloor measured from the base and n is the no of storeys of the building. The distribution of the floor forces is in accordance with the diaphragm action. For rigid diaphragm action total shear in any horizontal plane is distributed to various vertical elements of lateral load resisting system, considering infinite rigidity in the horizontal plane. The effect of torsion if any should be evaluated by considering the design eccentricities as explained in section 7.9 of the document.

3.3.4.5 Procedure for dynamic analysis: The Indian standard IS 1893: 2002 suggests that dynamic analysis should be performed to evaluate design seismic forces and their distribution along the building height and to various lateral load resisting members. It mandates that dynamic analysis should be performed for irregular buildings greater than 12m in height in zones IV and V, and those greater than 40m height in zones II and III. The methods suggested for dynamic analysis are time history method and response spectrum method. The value of damping may be taken as 2% and 5% of the critical for steel and RC buildings respectively, for performing dynamic analysis. 3.4 METHODOLOGY FOR ANALYSIS: 3.4.1 Modal Analysis: Modal analysis evaluates the dynamic properties of structures under vibrational excitation. In structural engineering, modal analysis utilizes the overall mass and stiffness of structure to find various periods at which it would naturally resonate. Normal mode of an oscillating system is the pattern of motion in which all parts of system move in sinusoidal manner with same frequency and have a fixed phase relation. Eigenvector analysis determines un-damped free vibration mode shapes and frequencies of system. The natural modes provide excellent insight into behaviour of the structure. Ritz vector analysis seeks to find modes excited by a particular loading. Ritz vectors provide a better basis than eigenvectors when used for response-spectrum or time-history analyses that is based on modal superposition. Thus, modal analysis is done by following methods, i. Eigenvector analysis ii. Ritz vector analysis

3.4.1.1 Eigenvector analysis: Eigenvector analysis determines un-damped free-vibration mode shapes and frequencies of system. These natural modes provide insight into behaviour of structure. Free vibration of linear MDOF systems without damping with p (t) = 0 is given as, 𝑚𝑢̈ + 𝑘𝑢 = 0 (3.16) When floors of a frame are at their extreme displacement at the same time as well as pass through the equilibrium position, then each characteristic deflected shape obtained is known as natural mode of vibration of a MDOF system. During natural mode of vibration of a MDOF system the point of Zero displacement that does not move at all is called as node. The number of mode increases with the number of nodes.

On substitution, 𝑢(𝑡) = ∅𝑛 (𝐴𝑛 cos 𝜔𝑛 𝑡 + 𝐵𝑛 sin 𝜔𝑛 𝑡) (3.17) Where, 𝐴𝑛 and 𝐵𝑛 are constants. ∅𝑛 = The deflected shape. 𝜔𝑛 = natural frequency for nth number of mode. Substituting the value of u (t) in the above expression, we obtain

[−𝜔𝑛2 𝑚∅𝑛 + 𝑘∅𝑛 ]𝑞𝑛 (𝑡) = 0 (3.18) For solution either𝑞𝑛 (𝑡) = 0, which indicates u(t)=0 and there is no motion in the system (known as trivial solution). Or the other solution can be given as, 𝑘∅𝑛 = 𝜔𝑛2 𝑚∅𝑛 (3.19) [𝑘 − 𝜔𝑛2 𝑚]∅𝑛 = 0

(3.20)

This equation is the matrix eigenvalue problem and it has non-trivial solutions if Det [𝑘 − 𝜔𝑛2 𝑚 ] = 0 (3.21) On expanding the determinant a polynomial of order N in 𝜔𝑛2 is obtained. Hence the above expression is known as frequency equation. The N roots, 𝜔𝑛2 of the equation determine the N natural frequencies 𝜔𝑛 (n = 1, 2,.....N) of vibration. Corresponding to N natural vibration frequencies 𝜔𝑛 of N-DOF system, there is N independent vectors ∅𝑛 which are known as natural modes of vibration, or natural mode shapes of vibration. The natural mode ∅𝑛 natural frequency 𝜔𝑛

corresponding to the

has an element ∅𝑗𝑛 where j indicates the DOFs. The N

eigenvectors can be displayed in a single square matrix of size NxN, whose each column represents a natural mode:

∅ = ∅𝑗𝑛

∅11 ∅ = [ 21

∅12 ∅22 ⋮

∅𝑁1 ∅𝑁2 (3.22)

⋯

∅1𝑁

⋱ ⋮ ⋯ ∅𝑁𝑁

]

The N eigenvalues assembled into a diagonal matrix Ω2, is known as Spectral matrix of eigenvalue problem, 𝜔12 0 2 Ω2 = 0 𝜔1 0 0 [ 0 0

0 0 0 0 ⋱ 0 0 𝜔12 ]

(3.23) 3.4.1.2 Ritz vector analysis: Ritz vector analysis is performed for structures oscillating under external excitation. Ritz vectors 𝜑𝑗 are shape vectors which are linearly combined along with generalized coordinates 𝑧𝑗 (𝑡) to express displacement as per Rayleigh-Ritz method using following expression 𝐽

𝑢(𝑡) = ∑𝑗=1 𝑧𝑗 (𝑡)𝜑𝑗 (3.24) Ritz vectors approximate natural modes of vibration. The reliability of method depends on proper selection of Ritz vectors. It is suggested to select force dependent Ritz vectors obtained by using spatial force distribution vector. Using the force dependent Ritz vectors the coupled reduced system of equations are solved with time stepping methods using above expression. For numerical evaluation of dynamic response using time stepping method can either be explicit or implicit. For linear systems with non-classical damping Central Difference Method and New mark’s method have been developed whereas for nonlinear systems Average acceleration method, Modified Newton-Ramphson iteration and Wilson’s method are available.

3.4.2 Time History Analysis: Time history analysis of the structure is carried out to determine its response under a given dynamic loading. The response history is divided into time increments of Δt and the structure is subjected to a sequence of individual time-independent force pulses Δf (t). The nonlinear response is hence approximated by series of piecewise linear systems. Here 3 time history records of 1994 Northridge Earthquake is used for the time history analysis. Various time history analysis methods are available. The non-linear time history (FNA- fast numerical analysis) method has been used, as it gives better result over the direct integration method. ASCE 7-10 specifies the procedure to carry out non-linear time history analysis by selecting a minimum of 3 ground motion records and scaling them to a given response spectrum record. In order to perform the time history analysis the method of modal analysis is employed with the external excitation being an accelerogram of a previously occurred earthquake. The application of ground motion in this particular study uses multiple support excitation theory, where total displacement response is a combination of dynamic and quasi-static displacements. To evaluate forces on structural elements total structural displacement and prescribed support displacement are used by following method of nodal displacements using element stiffness properties. In order to perform time history analysis it is suggested to not use raw accelerogram data of recorded earthquakes, instead obtain a synthetic accelerogram for the selected time history record of the earthquake.

CHAPTER 4

MODELLING AND ANALYSIS

4.1 PREAMBLE: This chapter elaborates in detail the process of modelling and design of the particular structure under study and subsequently the process of analysis performed. The tool used for the purpose of this analytical study is a commercial software package ETABS 2015. 4.2 DESCRIPTION OF ETABS 2015: The software used is a software package developed and distributed by Computers and Structures Inc. it is a FEM based software. The software is a powerful tool for modelling, analysis and design of various types of buildings. It has the capability to perform non-linear analysis as well as model structure and various elements in non-linear manner. The software has provisions for modelling of various types of link elements to represent non-linear behaviour as well as model isolators and dampers. The software also has capability for generating synthetic accelerogram using time history data record available with software package. 4.3 MODELLING PROCEDURE: 4.3.1 Description of structure: The structure under consideration is a G+9 floors hospital building. The building is an open frame building. The frame has been

modelled as a RC special moment resisting frame. The building is assumed to exist in seismic Zone IV. 4.3.2 Geometry of building: the building is irregular in its configuration in plan and regular in its configuration inelevation. The building is 15x15 m2 in plan. In either direction, in plan, the building is divided into 5 bays each of width 3m along y-axis and 3 bays each of width 5m along x-axis. The total height of the building is 31.2 m. Plinth height above GL is 0.55 m and the foundation is at 0.65 m below the ground floor. All other storey heights above plinth level are 3 m. 4.3.3 Grid definition: The grid system defined for modelling the building has been defined specific to the geometry of the building. The grid system is in SI units. The choice of units has been made prior to defining grid. The unit choice can be altered at any instance of process as per user suitability. The grid has been defined in a manner to make structural elements coincide with the grid lines. The grid definition is in global coordinates. 4.3.4 Unit definition: as stated above the units used are SI where length is in meters (m), mass in kilograms (kg), time in seconds (s) and temperature in degree Celsius (0C).

BUILDING DETAIL ARE AS FOLLOW FOR ALL MODEL Building frame type

SMRF

No of story

10

Storey height

3m

Total storey height

31.2 m

Size ofcolumn

0.50 m x 0.50 m

Size of beams

0.30 m x 0.45 m

Thickness of slab

150 mm

Thickness of shear wall

200 mm

Outer wall thickness

0.23 m

Inner wall thickness

0.15 m

Plinth height above GL

0.55 m

Depth of foundation below GL

0.65 m

Parapet height

1.5 m Loading detail of building

Live load on floor

3 KN/m2

Live load on roof

1.5 KN/m2

Floor finishes

1 KN/m2

Roof treatment

1.5 KN/m2

Site located in zone

IV

Soil condition

II

Important factor

1

Density of concrete

25 KN/m3

Density of masonry

20 KN/m3

The Modal is adopted for the study is a symmetric nine storey (G+9) residential building having of story height 3m and plinth level 1.2m from the foundation For this study I have consider five modal with or without different location of shear wall MODEL I-(Mws): This model is unsymmetric in plan and modelled with only column elements and no shear wall MODEL II-(Mx): Model consist of shear wall provided along with shear walls placed parallel to the x (Longitudinal) axis with 10m length thought height MODEL III-(My): Model consist of shear wall provided along with shear walls placed parallel to the y (Longitudinal) axis with 10m length thought height MODEL IV-(Mxy): Model consist of shear wall provided along with shear wall in both direction parallel to x axis and y axis with 20m length thought height MODEL V-(Mc): Model consist of shear wall provided at corner with 32m length

Plan and elevation view of the building model Mws

Figure: plan and elevation of model Mx

Above fig: 4.3.4 (1)

Fig: 4.3.4 (2)

Fig: 4.3.4 (3) plan and elevation of model 3

Fig:4.3.4 (4) plan view of model Mxy and Mc

4.3.5 Material definition: Since the material definition follows selection of a particular standard, hence in detail property of material has not been presented until and unless not necessary, as it shall follow specifics mentioned in the relevant code (IS 456:2000). Grade of concrete used- M30 Grade of steel used- HYSD Fe 415 (conforming to IS: 1786) 4.3.6 Load definitions: Guidelines in IS 875 Part 1, 2 and 5 for dead load, imposed load and load combinations have been used to define gravity loads on the building. And IS 1893:2002 has been used to define seismic load on the building. The load patterns defined are as follows Dead load- elemental self-weight

Wall dead-superimposed dead load to incorporate the weight of wall Live and roof live- imposed loads for floors. Earthquake loads-Ex and Ey have been defined for following conditions Natural time period of building T=0.99 sec; seismic zone factor Z=0.24; Importance factor I=1; Response reduction factor R=5 The site II have been used for all model of 5 building. The mass source definition includes default definition of elemental self-mass and additional mass. The modal case used in preliminary modelling and design process of original building follows eigenvalue method with default definitions. Load combinations- auto generated load combination for design purpose have been defined. A total of 14 load combinations have been generated as per definitions in IS 1893:2002 section 6.3 4.3.7 Draw frame structure: The building as stated earlier is an open frame structure; hence the model of the open frame structure for given geometric configuration is drawn using inbuilt tools in the software. The step by step process includes draw column, draw beam and finally draw shells/floors. 4.3.8 Assign properties: Once the frame wire model is ready then different section of the frame are assigned requisite properties and loads. In current model following frame properties have been assigned

All beamAll columnSlab 150mm thickness All the floor are assigned a rigid diaphragm action. The base is fixed to restrain in all 6 DOFs. Various other assignments are picked by program itself to simulate the analysis process. 4.3.9 Load assignments: Various load patterns defined above are assigned to frame elements and shell elementsColumns are not assigned any imposed vertical load.By default it is assigned only dead load. The beams along with default dead load are assigned wall dead load as uniformly distributed load in following manner External wall load intensity at all external beam except roof level- 11.73 KN/m Internal wall load intensity at all internal beam except roof level -7.65 KN/m Parapet wall load intensity at all exterior beam roof level-6.9 KN/m Floor finish load intensity- 1 KN/m Roof treatment load intensity- 1.5 KN/m Live load intensity- 3 KN/m At the base level no load can be assigned in any manner. The seismic loads are not assigned separately they are by default included and assigned during analysis process. Load cases generated are not for assignment to frame but for purpose of analysis process so as to identify what load cases the frame has to be analysed. The load combinations generated are again neither for the purpose of assignment nor analysis. Instead they are used in design process.

4.3.10 Analysis: Set all the load cases including modal-eigen for run analysis. Once the analysis process completes perform design/check for analysed model to verify members passing or failing as well as check various stress levels and member forces in the frame. This includes the design of model to be studied. 5 different model have been created with different position of shear wall by varying the definition of seismic loads Ex and Ey as per Indian standard on ERD of structures. 4.3.11 Assign non-linear hinge properties: For beams- use auto hinge assignment property from definitions in ASCE 41-13. Use table 10-7 definition for concrete beams (flexure) and M3 degree of freedom. In each beam the hinges are assigned at relative distance of 0 and 1. For columns- use auto hinge assignment property from definitions in ASCE 41-13. Use table 10-8 definition for concrete columns and P-M2-M3 degree of freedom. In each column the hinges are assigned at relative distance of 0 and 1. The failure condition is for both flexure and shear. For braces-to assign hinge properties to braces (shall be used later) definition of auto hinge assignment property for buckling restrained brace is used and assigned at relative distance of 0 and 1.

4.4 MODELING OF SHEAR WALL Modeling of shear wall is done on ETAB software by using code IS 456:2000

4.5 ANALYSIS PROCEDURE: The analysis method adopted in this study is non-linear dynamic analysis. The time history analysis is a non-linear dynamic analysis method. This analysis procedure requires definition of a time history function suitable to user which can be either a known mathematical function like sine, cosine, ramp etc. or a suitable accelerogram record of earthquake occurred in past. Since it is suggested to generate a synthetic accelerogram, a response spectrum function has also to be defined. This defined time history function is used as external load to excite the structure and perform the required analysis.

4.5.1 Define functions: 4.5.1.1 Define Response spectrum function A response spectrum function has been defined using IS 1893: 2002. The spectrum specified in the standard is used as the response spectrum function. The response spectrum function defined here is for a damping of 5% and Z=0.24. One response spectrums have been defined for five categories of model for medium soil site condition. Hence in the definition of response spectrum function the soil type has to be specified same as that the building is designed for. 4.5.1.2 Define Time History function For a realistic problem accelerogram record of past earthquake has been used. The software provides a set of accelerogram records of various past earthquakes. The record used in this study is the SYLMARFF county hospital parking lot record of the 1994 Northridge Earthquake. 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

2

4

6

8

10

12

FIGURE 4.5.1.2 (1) Design response spectra for site conditions II as per IS 1893:2002 (part 1) 1000 800 600 400 200 0 -200 -400 -600 -800 0

10

20

30

40

50

60

70

600 500 400 300 200 100 0 -100 -200 -300 -400 0

5

10

15

20

25

30

35

time (sec)

FIGURE 4.5.1.2 (2) Accelerogram record from SYLMARFF county hospital parking

lot record of the 1994 Northridge Earthquake at (a) 0 0and (b)900 . The record is a set of acceleration data at equal time interval of 0.02 seconds.

The record is in form of text file of 2985 points of acceleration data at 0.02 sec intervals in units of cm/s2. The PGA values of the selected records are 826.76 cm/s2 and 524.985 cm/s2 . 4.5.1.3 Generate synthetic accelerogram

To generate synthetic accelerogram for time history records, the time history function data is matched to targeted response spectrum function, both of which are defined earlier. This is done using the definition of define time history function matched to response spectrum. The spectral matching is done in frequency domain. The matching parameter is set in a frequency range of 0.01 cycles/sec to 100 cycles/sec. A synthetic accelerogram is generated for the above defined time history function 4.5.2 Define load cases: 4.5.2.1 Non-linear gravity load case A non-linear static load case intended to act vertically is defined to begin analysis from initial unstressed state. The definition includes the effects of dead and live loads with respective scale factors. The definition is set to modal case and P-delta effect. 4.5.2.2 Modal case definition The modal case defined here is eigenvector modal case. The loads for this case are defined using acceleration load applied in all 2 directions of translation. A minimum of 1 and a maximum of 12 modes is requested. This case continues at the end of above case.

4.5.2.3 Time History load case definition The time history load case defined in this study is a non-linear modal time history which uses Fast numerical analysis (FNA). This load case has been defined using synthetic accelerogram in 2 directions (U1 and U2) simultaneously, to create multi-support excitation condition. The directions are set in global coordinate system. The definition uses scale factor of 0.01 since the record is in cm/s2 and a time factor of 1 and modal damping at 0.05. 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 0

5

10

15

20

25

30

0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 0

5

10

15

20

25

30

35

FIGURE 4.5.2.3 Synthetic accelerogram generated using accelerogram record of FIGURE 4.5 for site condition II at (a) 00and(b)900.

CALCULATION 4.6 SEISMIC BASE SHEAR Seismic base shear of (G+9) Storey building has been calculated according to guidelines mentioned in IS code 1893:2002 which has been explained earlier in Methodology section. 4.6.1 SEISMIC WEIGHT OF BUILDING (W) • Weight of slab, Wslab = 15 X 15 X 0.15 X 25 = 843.75 KN • Weight of beams on one floor, Wbeam =0.3X0.45X (15X4+15X6)X25 = 506.25 KN • Weight of columns of one storey, Wcoloumn =0.5X0.5X24X3X25= 450 KN • Weight of column at roof level, Wcolumn=0.5X450=225 KN

• Weight of roof treatment, WRT= 1.5X15X15=337.5 KN •

Weight of floor finishes,

Wff=1X15X15== 225 KN

• Live load on floor, Wfloor = 3X15X15= 675 KN

• Live load on roof, Wlive = 1.5X225=337.5 KN • External wall load intensity, Wwall= 0.23X(3-0.45)X20=11.73 KN/m One each floor = 11.73X52 = 609.96 KN • Internal wall load intensity, Wwall=0.15X(3-0.45)X20=7.65 KN/m Load on floor = 7.65X89=680.85 KN • Parapet wall intensity, =0.23X1X1.5X20=6.9 KN/m Load on roof level =6.9X52=358.85 KN Seismic Weight of a Floor (Wfloor) = Wslab+Wbeams+ 1/2Wcoloumn below floor+ 1/2Wcoloumnabove floor+ 1/2 (Wwallbelow floor + Wwallabove floor)+WLive+ WFF = 3259.5 KN Seismic weight of Roof(Wroof) = Wslab+Wbeams+ 1/2Wcoloumn below floor +1/2Wwall below roof+WRT + Wroof wall = 2355.725 KN Total seismic Weight (W) =10XWfloor+ Wroof =34950.725 KN

Fig:4.6.1 Schematic of lumped mass at different storey levels of building for model 1

4.6.2 FUNDAMENTAL NATURAL PERIOD (Ta)

The approximate fundamental natural period of vibration (Ta), in seconds, for moment- resisting frame buildings without brick infil panels is calculated as per clause 7.6.1 of IS code 1893(Part I):2002. It is estimated by following empirical expression: Ta=0.075h0.75 = 0.99 seconds 4.6.3 DESIGN HORIZONTAL ACCELERATION SPECTRA (Ah) As the building is assumed to be located in medium soil i.e., type II soil from figure (2) of IS code 1893 part I For Ta= 0.99 s, the value of Sa/g =1.36/Ta=1.3737

Ah=

𝑍𝐼𝑆𝑎 2𝑅𝑔

=0.03296

Design Base Shear =Ah X W =1151.97 KN 4.3.5 (VB/VB) CORRECTION As per clause 7.8.2 of IS code 1893:2002 part I, design base shear VB has been compared with a base shear (VB), calculated using a fundamental period Ta , where Ta is as per clause 7.6 of IS code 1893:2002 part I for dynamic analysis. Design base shear calculated using ETAB 2015 Base Shear = 961 KN in X Base Shear = 1154 KN in Y Therefore, VB/VB= 1151/961 in x and 1151/1154 =1.197 = 0.997 So new scale factor for EQ-X =0.281 So new scale factor for EQ-Y =0.234

CHAPTER 5 RESULTS AND DISCUSSIONS

5.1 INTRODUCTION: This chapter presents the results of the study carried out and discusses them to justify the problem statement. The results of time history analysis have been presented for the current study. The response results for the analysis have been discussed in terms of max storey displacements and storey drifts. The time history response effects on location of shear wall have also been illustrated. A special RC moment resisting frame (G+9) with or without shear wall with different location of plan considered for this study. For the purpose of analysis synthetic accelerogram matched to response spectrum defined in IS 1893:2002 for different site conditions was generated using the ground acceleration records of SYLMARF station of 1994 Northridge Earthquake. 5.2 Maximum story displacement: The maximum story displacement is shown below in figure 5.1 for all five model in X direction and Y direction with story no.

Story level

12 11 10 9 8 7 6 5 4 3 2 1 0

Mws Mx My Mxy Mc

0

2

4

6

8

10

12

14

16

18

20

22

24

Displacement along-x (mm)

story level

Figure 5.1 maximum story displacement in X-direction for all five model 12 11 10 9 8 7 6 5 4 3 2 1 0

Mws Mx My Mxy Mc

0

2

4

6

8

10

12

14

16

18

Displacement along-y (mm)

Figure 5.1 maximum story displacement in Y-direction for all five model Percentage reduction in maximum story displacement values in X and Y direction MODEL

X direction

Y direction

Mx

37.09

4.72

My

1.07

19.68

Mxy

46.23

25.43

Mc

70.43

35.43

TABLE 5.1 Percentage reduction in maximum story displacement values in X and Y direction The maximum displacement of top story of all model with shear wall is decrease as compare to the without shear wall model. The maximum reduction in displacement value in X direction is for model Mc (corner shear wall) with 70.43%. The maximum reduction in displacement value in Y direction is for model Mc 35.43%. For this case study 24m length of shear wall have been considered in model Mc. More length have been provided in X direction.

story level

5.3 Maximum story drift

12 11 10 9 8 7 6 5 4 3 2 1 0

Mws Mx My Mxy Mc

0

0.25 0.5 0.75

1

1.25 1.5 1.75

2

2.25 2.5 2.75

drift along-x (mm)

Figure 5.3 story drift along-x (mm) Story drift can be defined as the lateral displacement of one level relative to the level above or below it: as per clause no 7.11.1 of IS 1893 (Part 1): 2002, the story drift in any story due to specified design lateral force with partial load factor of 1.0,

story level

shall not exceed 0.004 times the story height. Maximum drift permitted 0.004 times story height. It means that 0.004x3000=12mm. 12 11 10 9 8 7 6 5 4 3 2 1 0

Mws Mx My Mxy Mc

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

drift long-y (mm)

Figure 5.4 story drift along-y (mm) By comparing the drift values obtained for all models, it could be seen in figure 5.3 and 5.4 shows that model with shear wall provided at corner the inter story drift has considerably been reduced 69.56% in X direction and 50% in Y direction when compare to the Mws model Percentage variation in maximum story drift values in X and Y directions in comparison with Mws model Model

X direction

Y direction

Mx

39.13

My

-4.34

39.89

Mxy

47.82

45

Mc

69.56

50

0.2

TABLE 5.1 Percentage reduction in maximum story drift values in X and Y direction

CHAPTER 6

CONCLUSION • A significant amount of decrease in story displacement has been observed in all model with shear wall. Maximum 70.43% of reduction lateral displacement is obtained in model Mc (corner shear wall) along x-direction and 35.43% along y-direction. Lateral stiffness is centrally located at corner along both direction through out height of the building. • A significant amount of decrease in maximum story drift has been observed in case of model Mx, Mxy and Mc with 39.13%,47.82% and 69.56% along x-direction and in case, along y-direction My, Mxy and Mc with 39.89%, 45% and 50%. • To resist the lateral loads in irregular structure shear wall is suitable. • By provided shear wall in building we can reduce the size of column in as compared to without shear wall. • It is observed that maximum story displacement and maximum story drift is controlled as much level by providing shear wall in building.

SCOPE • Since the study was performed for only one type of RC shear wall, the further study should be made for different types of shear wall • Damping ratio of 5% for the model was performed. Further studies should carried out for damping ratios 10%, 15% and so on.