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

Non-Linear Static Analysis of RC Framed Buildings with Plan Irregularity Mohammed Irfan1 Sheik Abdulla2 M.Tech Student (Structural Engineering) 2Professor 1,2 Department of Civil Engineering 1,2 Khaja Banda Nawaz College of Engineering, Gulbarga - 585104 1

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.

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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.

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.

 2

4

L  

4

h 

Fig. 3.1: Inverted Triangular Loading for Pushover Analysis

4E f Ich Emt sin 2 4E f Ib L Emt sin 2

where, Em = Elastic modulus of masonry wall

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Non-Linear Static Analysis of RC Framed Buildings with Plan Irregularity (IJSRD/Vol. 3/Issue 09/2015/065)

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

w

1 h2   L2 2

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

5)

6)

7) 8)

9)

MODEL8B: The building has infill wall as {shell element} in all stories, and formed with 8 stories. As full infill MODEL8C: The building has equivalent diagonal strut as infill in all the stories. And formed as 8 stories. As partial infill MODEL20A: The building model has no infill and formed with 20 stories, as bare frame.

MODEL20B: The building has infill wall as {shell element} in all stories, and formed with 20 stories. As full infill 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

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 .

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

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.

4) MODEL8A: The building model has no infill and formed with 8 stories, as 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

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Non-Linear Static Analysis of RC Framed Buildings with Plan Irregularity (IJSRD/Vol. 3/Issue 09/2015/065)

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(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

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

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

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

.

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

Table 5.1: Fundamental Natural Time Period for Different Building Models

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Non-Linear Static Analysis of RC Framed Buildings with Plan Irregularity (IJSRD/Vol. 3/Issue 09/2015/065)

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

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 5.2: Base Shear for Different Models

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

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

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Non-Linear Static Analysis of RC Framed Buildings with Plan Irregularity (IJSRD/Vol. 3/Issue 09/2015/065)

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

Fig. 5.8: Comparison of Story Drifts for 8 Story Building Models in Y- Direction

Fig. 5.9: Comparison of Story Drifts for 4 Story Building 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.

Fig. 5.7: Comparison of Story Drifts for 4 Story Building 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.

Table 5.8: Story Drifts for 20 Story Building Models Table 5.7: Story Drifts for 8 Story Building Models

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Non-Linear Static Analysis of RC Framed Buildings with Plan Irregularity (IJSRD/Vol. 3/Issue 09/2015/065)

Fig. 5.12: Comparison of Story Displacement for 4 Story Building Models in Y-Direction Fig. 5.10: Comparison of Story Drifts for 20 Story Building Models in Y- Direction

Fig. 5.13: Comparison of Story Displacement for 4 Story 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. Fig. 5.11: Comparison of Story Drifts for 20 Story Building Models in Y- Direction 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 5.10: Story Displacement for 8 Story Building Models

Table 5.9: Story Displacement for 4 Story Building Models

Fig. 5.14: Comparison of Story Displacement for 8 Story Building Models in Y-Direction

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Non-Linear Static Analysis of RC Framed Buildings with Plan Irregularity (IJSRD/Vol. 3/Issue 09/2015/065)

Fig. 5.15: Comparison of Story Displacement for 8 Story Building Models in X-Direction The concentrated percentage drop of Storey displacement are 8.35% and 45% for model 8B and 8C as compared to model 8A.

Fig. 5.17: Comparison of Story Displacement for 20 Story Building Models in X-Direction 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 (ď ­) and Response Reduction Factor (R)

Table 5.12: Ductility Ratio and Response Reduction Factor along Y Direction

Table 5.11: Story Displacement for 20 Story Building Models

Fig. 5.18: Ductility Ratio along Y direction

Fig. 5.16: Comparison of Story Displacement for 20 Story Building Models in Y-Direction

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Non-Linear Static Analysis of RC Framed Buildings with Plan Irregularity (IJSRD/Vol. 3/Issue 09/2015/065)

The retort reduction influence for model 20C is superior than the model 20A but less than 20B. V. CONCLUSIONS 1)

2) 3) Fig. 5.19: Response Reduction Factor along Y Direction 4)

5)

6)

Table 5.12: Ductility Ratio and Response Reduction Factor along X Direction

7)

8)

9)

Fig. 5.20: Ductility Ratio along X direction

Fundamental natural time period decreases in both use of masonry full infill wall and equivalent diagonal strut.

Storey drifts found inside the boundary as per codal provision 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) .

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.

In fill walls should be considered for seismic analysis of RC frames. Equivalent diagonal strut method are effectively used for modeling the infill wall.

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.

Models 4C, 8C and 20C shows an extreme reduction in terms of twisting moment as associate to full infill buildings.

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. 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

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.

[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

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[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 Journal of Advanced Engineering Research and Studies 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 of structures.

[10] M A M Akberuddin (2013) “Pushover Analysis of Medium Rise Multi-Story RCC Frame With and Without

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