Non-Linear Static Analysis of RC Framed Buildings With Plan Irregularity

IJSRD - International Journal for Scientific Research & Development| Vol. 3, Issue 09, 2015 | ISSN (online): 2321-0613

All rights reserved by www.ijsrd.com 264

Non-Linear Static Analysis of RC Framed Buildings with Plan

Irregularity Mohammed Irfan

1 Sheik Abdulla

2

1M.Tech Student (Structural Engineering)

2Professor

1,2Department of Civil Engineering

1,2Khaja Banda Nawaz College of Engineering, Gulbarga - 585104

Abstract— Herein present study 3 new R.C structures of

unsymmetrical in plan (irregular) (designed as per IS

456:2000) is taken for analysis: 4, 8 & 20 storey cover the

large variety of low rise building, medium rise building &

high rise building constructions. For different modeling

were included through three models for every buildings

were bare frame with no infill wall, with infill wall as

membrane, replacing infill wall as equivalent diagonal strut

in earlier model. The equivalent strut method is convenient

for modeling the walls in a large buildings. The pushover

analysis carried out by using ETABS 9.5. Buildings situated

in Zone-IV have analyzed for comparative studies prepared

for above membranes. The analysis results are measures in

terms of Story Displacement, Drift ratio and Forced

Responses such as Base Tensional Moment & Base Shear.

Structures were designed to obtain the performance level,

allow immediate tenancy, is defined as performance based

design. CSM (capacity spectrum method) is used for seismic

performance of RC Structures.

Key words: R.C structures, CSM

I. INTRODUCTION

A. General

An earthquake is the sudden movement or tremors causing

the greatest damages as it originate naturally below the earth

surface. Earthquake forces are sudden in the nature &

unexpected. Since it exclude shock waves due to manmade

explosions and nuclear tests etc. The whole earth is made up

of plates. The intersection among these plates is called

faults. In Indian context fault is the main boundary

extending through the terrain province all the way from

Himachal Pradesh, Uttarakhand Assam, and Bihar to

Burma. Plates are comes down along Andaman Nicobar &

Bay of Bengal & into Indonesia. As the plate place of or

move the rocks are subject to stress, unexpectedly facture

develops & this is called as an earthquake.

The designing system should be enhancing for

breaking down the structures under demonstration of these

powers. Seismic tremor does not murder the people but

rather structures do. It's most imperative obligation of an

auxiliary planner to take out parameter from prior

encounters and take into all potential hazard that the

structure can be subjected to be in future utilized with the

end goal of protected and secure outline of the structure.

Execution based configuration is increasing new angle in the

seismic outline theory in which the close field ground

movement (quickening) is to be measured. Heaps of

Earthquake are chosen painstakingly displayed in order to

assess the real execution of structure with an unmistakable

seeing in order to harm is evaluated.

Pushover analysis is a procedure where structural

loading is gradually applied . by the result of which weak

links as well as the failure patterns of the structure are

easily distinguished.

B. Performance Based Seismic Design Necessity

Since the impacts of real quakes (as mid 1980s) it is chosen

that the seismic dangers into the urban territories are

expanding and are far from socio-monetarily attractive

levels. There is an imperative need to topple this

circumstance and it is comprehended that a standout

amongst the most proficient methods for doing this from:

1) The advancement of extra predictable seismic standard

and code necessities than those at present realistic and

2) Their brutal execution for the complete designing of

new building conveniences.

An execution based configuration (PBSE) is

expected at computing the basic harm base on precise

assessment of suitable reaction element. This is normal that

if more exact examinations are completed, tallying all

conceivable critical elements worried in the basic conduct.

C. Objectives the Present Study

1) Objectives

Making building models for flexible and inelastic

system of assesses.

Calculating horizontal forces of buildings by using

nonlinear pushover analysis method to evaluate the

results.

To study the effect of plan irregularity on the

fundamental natural period of the building and its effect

on performance of the structure during earthquake for

different building models selected.

Finding out the storey displacements and storey drifts at

each storey by using nonlinear pushover method.

To study the load carrying capability of different frames

using masonry wall as infill and equivalent diagonal

strut in terms of Base Shear at performance point.

Discovering the execution level of the building utilizing

nonlinear weakling investigation.

II. METHODOLOGY

A. General Terms

1) Capacity:

The normal extreme quality (in flexure, shear, or hub

stacking) of a basic segment barring the lessening (considers

regularly utilized configuration of solid individuals. The

limit more often than not alludes to the quality at the yield

purpose of the component or structure's ability bend. For

misshapening controlled segments, limit past as far as

possible for the most part incorporates the impacts of strain

solidifying.

Non-Linear Static Analysis of RC Framed Buildings with Plan Irregularity

(IJSRD/Vol. 3/Issue 09/2015/065)


2) Limit Curve:

it is the bend of aggregate parallel power, V, following up

on a structure versus horizontal redirection, d of the

structure which is known as the "mark" bend.

3) Limit Range Method:

A nonlinear static analysis procedure that provides a

graphical representation of the expected seismic

performance of the existing or retrofitted structure by the

intersection of the structure's capacity spectrum with a

response spectrum (demand spectrum) representation of the

earthquake's displacement demand on the structure. The

intersection is the performance point, and the displacement

coordinate, dp, of the performance point is the estimated

displacement demand on the structure for the specified level

of seismic hazard.

4) Components or Members:

The local concrete members that comprise the major

structural elements of the building such as columns, beams,

slabs, wall panels, boundary members, joints, etc. Concrete

frame building: A building with a monolithically cast

concrete structural framing system composed of horizontal

and vertical elements which support all vertical gravity

loads and also provide resistance to all lateral loads through

bending of the framing elements.

5) Ultimatum:

It is spoken to by an estimation of the-removals or

disfigurements that the structure is relied upon to

experience.

6) Ultimatum Range:

The reduced response spectrum used to represent the

earthquake ground motion in the capacity spectrum method

7) Elastic (Linear) Behavior:

Refers to the first segment of the bi-linear load-deformation

relationship plot of a component, element, or structure,

between the unloaded condition and the elastic limit or yield

point.

8) Performance Objective:

A desired level of seismic performance of the building

(performance level), generally described by specifying the

maximum allowable (or acceptable) structural and

nonstructural damage, for a specified level of seismic

hazard.

B. Pushover Analysis

In Target examination, a static level power profile, normally

corresponding to the outline power profiles indicated in the

codes, is connected to the structure. The power profile is

then increased in little steps and the structure is investigated

at every stride. As the heaps are expanded, the building

experiences yielding at a couple of areas. Each time such

yielding happens, the basic properties are changed roughly

to mirror the yielding. The investigation is proceeded till the

structure breakdown, or the building achieves certain level

of sidelong dislodging.

Fig. 3.1: Inverted Triangular Loading for Pushover Analysis

1) Need for Pushover Analysis

The models utilized as a part of this examination which is

subjected to seismic strengths acquired from configuration

spectra and decreased by power lessening elements.

Force reduction factors recommended in codes of

practice are approximate and do not necessarily represent

the specific structure under consideration.

When critical zones of a structure enter into the

inelastic range, the force and deformation distribution

change significantly. This change is not represented by a

global reduction of forces

The mechanism that will most likely perpetuate

collapse is unlikely to be that represented by the elastic

action and deformation distribution.

The global and particularly the local distribution of

deformations in the inelastic range may bear no resemblance

to those in the elastic range. The same applies to the values

of deformations, not just the distribution

C. Equivalent Diagonal Strut Method

Diagonal strut modeling is most popular. Specialists have

attempted to demonstrate the block stone work in numerous

corner to corner struts, i.e. single strut, two inclining struts,

and three askew struts. Perceiving results on this trial they

conclude that the single diagonal strut is the most effective

method of modeling for the masonry infill panel that work

best. Infill walls is modeled using diagonal strut method.

The infill walls assumed as diagonal strut and modeling of

frame is done as per beam element. Frame analysis

techniques are used for the elastic analysis. The idealization

is based on the assumption that there is a no bond between

frame and infill. Although there are various guess about the

width of diagonal strut which depends on length of contact

between the wall & the columns (αh) and between wall &

beams (αL).

1) Determination of Equivalent Strut Width

Fig. 3.7: Equivalent diagonal strut

The following are the formulae to calculate the width and

length of strut given Stafford Smith (1966) based on the

assumption that beams are on elastic foundation. Developed

the formulations for αh and αL on the basis of beam on an

elastic foundation.

4

2sin

4

2

tE

hIE

m

cf

h

4

2sin

4

tE

LIE

m

bf

L

where, Em = Elastic modulus of masonry wall




Ef = Elastic modulus of frame material

t,h,L = Thickness, height and length of the infill wall

Ic = Moment of inertia of the column

Ib = Moment of inertia of the beam

θ = tan-1

(h/L)

Hendry (1998) proposed the following equation to

determine the equivalent or effective strut width w, where

the strut is assumed to be subjected to uniform compressive

stress

22

2

1Lhw

2) Irregular Structure Effects

Impacts like backstay impacts can happen anyplace in a

building where there is a critical change in horizontal quality

or solidness in one story in respect to nearby stories. In tall

structures, this can happen at Asymmetric, which are areas

where the seismic power opposing framework altogether

changes in measurement over the base, Because of distortion

similarity and relative solidness impacts, the shorter

component in such an arrangement will draw in bigger

seismic strengths through the floor stomachs and gatherers

at the top.

Lopsided can likewise make a quality brokenness

that can bring about moved nonlinear conduct in the

framework at the area of the Asymmetric. On account of

solid dividers, the most alluring nonlinear conduct is a

flexural plastic pivot system at the base of the divider. A

configuration objective in such structures would be to

minimize torsional erraticism’s at the base of the structure

III. ANALYTICAL MODELLING

A. General

The main aim of doing a pushover analysis is to prevent a

building from damages and to prevent the damages on

structural components in oreder to estimate the performance

limit of the building .

Table 4.1: Dimensions of Building Frames

B. Explanation of Different Building Models

1) MODEL4A: The building model has no infill and

formed with 4 stories, as bare frame.

2) MODEL4B: The building has infill wall as {shell

element} in all stories, and formed with 4 stories. As

full infill

3) MODEL4C: The building has equivalent diagonal strut

as infill in all the stories. And formed as 4 stories. As

partial infill.





full infill

6) MODEL8C: The building has equivalent diagonal strut

as infill in all the stories. And formed as 8 stories. As

partial infill





full infill

9) MODEL20C: The building has equivalent diagonal

strut as infill in all the stories. And formed as 20 stories

as partial infill

Fig 3.1: {a}: Plan of 4, 8 & 20 stories Asymmetric Building

models

Fig. 3.1(b): 3D View of 4- story Bare Frame

Fig. 3.1(c): 3D View of 4- story Infilled frame as wall

Fig. 3.1(d): 3D View of 4- story Infilled frame as equivalent

diagonal strut




Fig. 3.1(e): 3D View of 8- story Bare Frame

Fig. 3.1(f): 3D View of 8- story Infilled frame as wall

Fig. 3.1(g): 3D View of 8- story Infilled frame as equivalent

diagonal strut

Fig. 3.1(h): 3D View of 20- story Bare Frame

.

Fig. 3.1(i): 3D View of 20- story Infilled frame as wall

Fig. 3.1(j): 3D View of 20- story Infilled frame as

equivalent diagonal strut

C. Assumptions

1) The material is linearly elastic, homogeneous &

isotropic.

2) All columns supports are considered as fixed at the

foundation.

3) Tensile strength of concrete is ignored in sections

subjected to bending.

4) The super structure is analyzed independently from

foundation and soil medium, on the assumptions that

foundations are fixed.

5) Due to its rigidity the floor acts as diaphragms.

6) Pushover hinges are assigned to all the member ends. In

case of Columns PMM hinges are provided at ends,

while in case of beams M3 hinges (i.e. Bending

Moment hinge) are provided at both the ends.

7) The maximum target displacement for each building is

kept at 4% of the height of the building = (4/100) X

height of building

IV. OUTCOMES AND DISCUSSIONS

The Outcomes found are of different parameters such as

Natural Periods, Storey drifts, displacement, Base force,

Twisting moment etc. principal outcomes found by carrying

out pushover Analysis using diagonal strut for Irregular

Structures for Four, eight and twenty storey structures are

discussed. Then, the consequences obtained by Carrying out

pushover analysis using masonry infill as four noded shell

element Method for Irregular Structures Four, Eight and

Twenty story Structure are Demonstrated.

A. Natural Period

Table 5.1: Fundamental Natural Time Period for Different

Building Models




Fig. 5.1: Fundamental Natural Time Period for Different

Building Models

From above, the percentage decrease of natural

period of model 4B is 88.87% related to as model 4A, and

model 4C is 76.88% as associated to model 4A.and model

8B is 66.94% associated to as model 8A, and model 8C is

80.42% as related to model 8A.and model 20B is 69.65%

associated to as model 20A, and model 20C is 60.93% as

likened to model 20A.

B. Base Force

Table 5.2: Base Shear for Different Models

Fig. 5.2: Base Shear of all Building Models in Y Direction

Fig. 5.3: Base Shear of all Building Models in X Direction

From above, it is seen that percentage increase of

base shear are 99.85%, 98.28% and 97.24% for model 4B,

8B and 20B compared to model 4A, 8A and 20A. The

percentage increase of base shear are 98.99%, 97.51% and

89.49% for model 4C, 8C and 20C compared to model 4A,

8A and 20A.

From fig 5.3: it is seen that percentage increase of

base shear are 98.71%, 97.10% and 98.58% for model 4B,

8B and 20B related to model 4A, 8A and 20A. percentage

increase of base shear are 97.05%, 96.86% and 93.72% for

model 4C, 8C and 20C associated to model 4A, 8A and

20A.

Table 5.4: Displacement and base Force along Y Dir. For all

Building Models

Table 5.5: Displacement and base Force along X Dir. For all

Building Models




C. Story Drifts

Table 5.6: Story Drifts for 4 Story Building Models

Fig. 5.6: Comparison of Story Drifts for 4 Story Building

Models in Y- Direction


Models in X- Direction

The extreme percentage decreases of Storey drifts

are 26.01% and 68.15 in Y Dir. And in X Dir. 60.07% and

68.15% for model 4B and 4C as related to model 4A.





Models in X- Direction

The extreme percentage reductions of Storey drifts

are 15.87% and 64.28% in Y Dir. And in X Dir. 34.28% and

56.87% for model 8B and 8C associate to model 8A.









It may be seen that extreme percentage reductions

of Storey drifts are 30.61% and 68.51% in Y Dir. And in X

Dir..35.87% and68.94% for model 20B and 20C as related

to model 20A.

D. Displacements

Table 5.9: Story Displacement for 4 Story Building Models

Fig. 5.12: Comparison of Story Displacement for 4 Story

Building Models in Y-Direction


Building Models in X-Direction

The supreme percentage drops of Storey

displacement are 69.33% and 52.71% for model 4B and 4C

as related to model 4A.

Table 5.10: Story Displacement for 8 Story Building Models








The concentrated percentage drop of Storey displacement

are 8.35% and 45% for model 8B and 8C as compared to

model 8A.

Table 5.11: Story Displacement for 20 Story Building

Models





The extreme percentage reductions of Storey

displacement are 46.06% and 67.88% for model 20B and

20C as compared to model 20A.

E. Ductility Ratio () and Response Reduction Factor (R)

Table 5.12: Ductility Ratio and Response Reduction Factor

along Y Direction

Fig. 5.18: Ductility Ratio along Y direction




Fig. 5.19: Response Reduction Factor along Y Direction

Table 5.12: Ductility Ratio and Response Reduction Factor

along X Direction

Fig. 5.20: Ductility Ratio along X direction

Fig. 5.21: Response Reduction Factor along X Direction

The ductility ratio for model 20C is larger than the

model 20A but less than 20B.

The retort reduction influence for model 20C is

superior than the model 20A but less than 20B.

V. CONCLUSIONS

1) Fundamental natural time period decreases in both use

of masonry full infill wall and equivalent diagonal

strut.

2) Storey drifts found inside the boundary as per codal

provision

3) At first hinge Base shear and displacement is more for

buildings 4C, 8C (strut) and vice versa for full infill

buildings 4B, 8B and 20B.base shear is more and

displacement is less in model 20C.(I,e.diagonal strut

model) .

4) Due to presence of the infill as equivalent strut,

displacement at top storey decreases for four, eight,

twenty stores (respectively) with respect to bare frame.

5) In fill walls should be considered for seismic analysis

of RC frames. Equivalent diagonal strut method are

effectively used for modeling the infill wall.

6) The seismic analysis of Bare frame (RC frame)

structure direct to under evaluation of Base shear.

Hence further response quantities for example storey

drift not considerable. Understatement of base force

may direct to fail of building during tremor pulsating.

So infill walls are very important to consider for

seismic analysis of structure.

7) Models 4C, 8C and 20C shows an extreme reduction

in terms of twisting moment as associate to full infill

buildings.

8) Equivalent diagonal strut building models displays

good effects in terms of hinge position. i.e; safety level

rises in diagonal strut simulations hinge status remains

in A-B.

9) For general behavior of infilled frames single diagonal

strut model is better to be used in analysis and it can be

usually correct due to its simplicity.

A. Scope for Future Work

As the performance based pushover analysis is very useful

method to design the structure at required performance

level, it can be applied in different structures

In the current concentrate full infill is taken in the

casings, halfway infill or 40% in fill can be taken in this

way, as to consider the opening in the casing incase of

(entryway and windows)

Single diagonal strut is considered in place of masonry

wall, double diagonal strut can be used.

In this current study, only irregular in plan is taken, so

additional study can be carried out for upright

indiscretions.

Maximum considered earthquake (MCE) level can be

taken for life safety performance level.

REFERENCES

[1] Kappos, A. J., Stylianidis, K. C. and Michailidis, C. N.,

(1998), “Analytical models for brick masonry infilled

R/C frames under lateral loading”, Journal of

Earthquake Engineering, Vol. 2, No.1, 59-87




[2] Fajfar P. 1999. Capacity spectrum method based on

inelastic demand spectra. Earthquake Engineering and

Structural Dynamics; pages 979–993

[3] Priestley MJN & Kowalsky MJ. 2000 Direct

displacement-based seismic design of concrete

buildings. Bulletin of the New Zealand Society for

Earthquake Engineering.

[4] Mander J.B., 2001, Future directions in seismic design

and performance-based engineering, Department of

Civil Engineering, University of Canterbury,

Christchurch, New Zealand, NZSEE 2001 Conference

[5] Klingner R.E., Bertero V.V. (2003) “Earthquake

resistance of infilled frames”, Journal of Structural

Engineering, ASCE, 104(ST6): 973-989

[6] ATC, 2006, Next-Generation Performance-Based

Seismic Design Guidelines: Program Plan for New and

Existing Buildings, FEMA 445, Federal Emergency

Management Agency, Washington, D.C.

[7] Dakshes J. Pambhar (2012), “Performance Based

Pushover Analysis of R.C.C. Frames”, International

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IJAERS/Vol. I/ Issue III/April-June, 2012/329-333.

[8] ETABS User’s Manual, “Integrated Building Design

Software”, Computer and Structure Inc. Berkeley, USA

[9] IS-1893:2002, Criteria for Earthquake resistant Design

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[10] M A M Akberuddin (2013) “Pushover Analysis of

Medium Rise Multi-Story RCC Frame With and

Without

Non-Linear Static Analysis of RC Framed Buildings With Plan Irregularity

Documents

pushover analysis

infill wall

c structures of unsymmetrical

large buildings

analysis results

performance based design

performance based seismi

performance level