INTRODUCTION

Importance of Dynamic Analysis on structures

Structural analysis is mainly concerned with finding out the behaviour of a physical structure when subjected to force.

The distinction is made between the dynamic and the static analysis on the basis of whether the applied action has enough acceleration in comparison to the structure's natural enough acceleration in comparison to the structure's natural frequency.

Structural dynamics, therefore, is a type of Structural Analysis which covers the behaviour of structures subjected to dynamic (actions having high acceleration) loading.

Eg: wind, blasts, explosion, earthquake.

Advances in the modelling software and computing power, full inelastic dynamic time-history analysis of 3-D structural models that include diaphragm flexibility, statistical variations in element behaviour, etc. are currently not conducted for the majority of structures present today. Simple analysis methods and simple models are likely to be the major techniques.are likely to be the major techniques.

Engineers need conceptually simple methods for the following reasons:

(1) to design full structures

(2) to enable a rapid check of likely building performance

(3) to preliminary size members before some more

sophisticated studies are undertaken.

1. Seismic Design Category (SDC) concept to categorize structures according to the seismic risk they could pose. There are six SDCs ranging from A to F with structures posing minimal seismic risk assigned to

Earthquake resistant design concepts include:

structures posing minimal seismic risk assigned to SDC A and structures posing the highest seismic risk assigned to SDC F.

2. Site Class to categorize common soil conditions into broad classes to which typical ground motion attenuation and amplification effects are assigned.

3. Design ground motion: In order to determine the Seismic Design Category for a structure, it is first necessary to determine the design ground motion, which is one of the primary factors used to which is one of the primary factors used to determine the required seismic resistance (strength) of structures and supported non structural components.

4. Structural system selection : The next step in the design process consists of selecting an appropriate seismic force-resisting system (SFRS).

The seismic-force-resisting systems for building structures and non building structures with structural systems like buildings are categorized by

--construction material (e.g., concrete, masonry, steel, or wood),

--type of system (bearing wall, braced frame, moment frame, dual, or cantilever column), and

--level of seismic detailing (special, intermediate, ordinary, or not detailed for seismic resistance).

Many present design codes classify some of the structural irregularities into two categories:

(a) Vertical irregularities

Configuration and irregularity

(a) Vertical irregularities

(b) Plan irregularities.

(a) Vertical Irregularities (IS 1893 (part1):2002,Cl. 7.1):

1. Weight (mass) irregularity – Weight irregularity shall be considered to exist where the weight, Wi, of any storey is more than 150% of the weight of an adjacent storey. A roof that is lighter than the floor below need not be

considered. considered.

Difference in floor mass.

2. Vertical stiffness irregularity– Vertical stiffness irregularity shall be considered to exist when the lateral stiffness of the primary structure in a storey is less than 70% of the stiffness of any adjacent storey, or less than 80% of the average stiffness of the three storeys above or below.

3. Discontinuity in capacity (weak storey) – A weak storey is one in which the storey shear strength is less than 90% that in the storey above. The storey shear strength is the total strength of all vertical seismic-resisting elements of the primary structure sharing the storey shear for the direction under consideration.

4. Vertical geometric irregularity – Vertical geometric irregularity shall be considered to exist where the sum of the horizontal dimensions of the vertical elements of the primary structure in the direction under consideration in any storey is more than 130% of that in an adjacent storey. that in an adjacent storey.

(b) Plan Irregularities:

1. Torsional Irregularity: Torsional irregularity to be considered to exist when the maximum storey drift, computed with design eccentricity, at one end of the structures transverse to an axis is more than 1.2 times the structures transverse to an axis is more than 1.2 times the average of the storey drifts at the two ends of the structure

2. Re-entrant Corners :If a re entrant corner is unavoidable, it should be strengthened by using drag struts, or, preferably, a seismic separation should be provided.

3. Diaphragm Discontinuity: Diaphragms with abrupt discontinuities or variations in stiffness, including those having cut-out or open areas greater than 50 percent of the gross enclosed diaphragm area, or changes in effective gross enclosed diaphragm area, or changes in effective diaphragm stiffness of more than 50 percent from one storey to the next.

4. Out-of-Plane Offsets: Discontinuities in a lateral force resistance path, such as out-of-plane offsets of vertical elements. There should be a direct path for force transfer. Shear walls or other lateral load resisting elements should be continuous to the foundation. In-plane or out-of-plane offsets should be avoided.

5. Non parallel systems:

Examples of some common irregularities in structures

Motivation to study of irregularity no real structure is perfectly regular

as a result of accidental or intentional non-uniform mass, stiffness, strength, structural form, or a combination of these in the horizontal or vertical combination of these in the horizontal or vertical directions. Also structures with a high degree of irregularity have the possibility of behaving significantly differently from that of a nominally regular structure. This different behaviour may result in larger demands and less safe irregular structures, and in some cases; structures may even collapse.

In order to prevent the possible underestimation of actual demands, and to produce safer structures, world-wide codes (e.g., NZS 1170.5, IBC, Eurocode 8 ) provide limitations on the maximum degree of irregularity for structures designed according to simple analysis methodssimple analysis methods

But code regularity limits provide some insight on the likely undesired effects due to the presence of irregularities, these limits were developed by consensus, rather than being based on quantitative data

Eg: The SEAOC blue book, from which irregularity provisions in many worldwide codes are adopted, states that:

“Extensive engineering experience and judgment are required to quantify irregularities and provide guidance for special analysis. As yet, there is no complete prescription for all special analysis guidance for special analysis. As yet, there is no complete prescription for all special analysis considerations for irregularities”, (Cl. 104.5.1);

Literature survey :1. A simple methodology for evaluating vertical irregularity

effects for shear-type of structures was developed by Sadashiva et al. 2009.

steps include:

Define Engg demand para (EDP)- Define Engg demand para (EDP)-

eg: peak Inter Storey DR over building height.

Design a regular structure using ES method.

Introduce an irregularity into the structure, and redesignthis structure to the same target inter storey DR

Conduct inelastic THA to regular and irregular to obtain peak inter storey drift ratio.

define irregular configuration on the regular structure.

Redesign the structure for Design ISDR.

The sensitivity of the location and magnitude of irregularity was investigated by applying irregularities of varying degrees, separately at the first floor level, mid-height floor level and topmost floor level.mid-height floor level and topmost floor level.

For every IDTHA conducted, the peak inter storey drift ratio(ISDR) at every storey, and within the structure can obtain.

Evaluate the performance for all of the ground motion records as the difference between the median peak inter storey drifts of the two structures.

The increase in median peak ISDR due to irregularity, ISDR incr, is calculated by

ISDR incr =[(ISDR –I/ISDR-R)-1] *100%ISDR incr =[(ISDR –I/ISDR-R)-1] *100%

Repeat for all the combinations of structural form, structural ductility factor, design inter storey drift ratio, structure height, storey/floor level of irregularity, and degree of irregularity.

For each degree of irregularity, the maximum value of ISDR incr is found.

Findings:

IRR –Irregular response ratio % = 15 (Mass ratio-1)

For mass irregularity drift demands were sensitive to both the magnitude and floor level, generally produced higher drift demands at the mid-height level.

Coupled vertical stiffness-strength irregularity effects due to

(a) a change in member property at a storey of uniform (a) a change in member property at a storey of uniform storey height structures;

(b) a change to a storey height

were investigated.

(a)

The storey stiffness varied either in proportion to the storey strength (Group 1) or

with unequal modifications for storey stiffness and strength (Group 2)

Group 1 structures produced higher drift demands Group 1 structures produced higher drift demands than Group 2 structures. The topmost storey was more critical.

With equal storey placing stiffness-strength irregularity at the mid-height storey produced higher demands than the regular structures, for both building designs.

Stiffness-strength irregularity due to storey height modification :

Modified storey height that results in a change to storey stiffness alone produce more adverse irregularity effects.

For this group, the effects of a taller storey were more For this group, the effects of a taller storey were more than those due to a short storey in the structure.

2. N.Kara et.al studied effects of the structural irregularity which is produced by the discontinuity of a column in a plane frame subjected to seismic loads including the gravity loads is investigated.

.

Investigation is carried out by adopting the linear and the nonlinear static and dynamic analyses of the structural system such as, the pushover analysis and the time history analysis by considering various the time history analysis by considering various seismic records compatible with the spectrum provided in the Turkish seismic code.

relative maximum acceleration of the seismic records of 0.2, 0,4, 0.6 and 0.8 used

Knowledge gained:

The nonlinear story drift demand is significantly large, when the column discontinuity is in the lower stories of the frame.

High ductility demands in the neighbourhood of the story of the irregularity are observed.story of the irregularity are observed.

Column discontinuity produces the soft story in the frame, when the number of the column is small in a specific story.

SCOPE OF STUDY:

Most of the work conducted on irregularities evaluate one type of irregularity at a time.

It is possible that a structure can have a combination of different types of irregularities.of different types of irregularities.

Eg : mass + stiffness, torsional +diaphragm.

In such cases, structures with multiple irregularities may perform worse than those described earlier.

AIM OF STUDY:

Study about the effects of irregularity based on the change in response for a particular level of irregularity.

Study about the effect experienced on a structure Study about the effect experienced on a structure due to the combined presence of mass and stiffness irregularity.

Analysis to be carried out for the study:

1. Equivalent Static Analysis : in which dynamic effects are approximated by horizontal static forces applied to the structure. This method is quasi-dynamic in nature and is termed as the Seismic Coefficient Method in the IS code.

2. Response History Method or Time History Method : 2. Response History Method or Time History Method : in which direct input of the time history of a designed earthquake into a mathematical model of the structure using computer analyses.

3. Push over Analysis : The pushover analysis is a nonlinear static method which is used in a performance based analysis.

Studies conducted:

1. A comparitive study on seismic behaviour of irregular structures as priliminary study using staad pro:

analysis used for study:

1. Response spectra Analysis

2.Time history Analysis2.Time history Analysis

type of structures considered

1. With Mass irregularity, stiffness irregularity and Vertical irregularity

2. Compared with Regular structure.

Configuration of the structures

Size of beams : 500mm x 400mm –in x dir

450mm x 400mm –in z dir

Regular:

dimension: 22.7m x 14.4mdimension: 22.7m x 14.4m

no of floors: G + 20

Vertically irregular

Regular Stiffness irregular

Mass irregular

Mass irregularity: The structure is modelled as same as that of regular

structure except the loading due to swimming pool is provide in the 17th and 14th floor. Height of swimming pool considered- 1.8m. Loading due to swimming pool -18kN/m2.

Weight of the 17th and 14th floor > 2*weight of the adjacent floorfloor

Stiffness irregular: The structure is same as that of regular structure but the

ground storey has a height of 4.5 m and doesn‘t have brick infill.

Stiffness of each column= (12EI/L)^3 Stiffness of ground floor/stiffness of other floors = (3/4.5)^3 = 0.29< 0.7

Vertically geometric irregular:

- plan varies in different elevations:

1 to 5 floor plan

6 to 10 floor plan 11 to 15 floor plan

16 to 20 floor plan

Specification of structures:

1. live load = 1.5 KN/m2 on roof and 4 KN /m2 on other floors

2. Thickness of slab = 200mm.

3. Outside wall thickness = 200mm

4. Inner partition wall thickness = 150 mm

5. Height of each floor = 3 m5. Height of each floor = 3 m

6. Earth quake zone = IV

7. Damping ratio = 5%

8. Importance factor = 1

9. Type of soil = medium

10. Type of structure = special RC moment resisting frame

11. Response reduction factor = 5

Results and observations:

1. Response spectrum analysis was performed using STAAD PRO

Peak storey shear forces of all structures were calculated and graph was plotted for each structure.

10

15

20

25

vert irreg

regular

stiff irreg

0

5

10

0 500 1000 1500 2000 2500 3000

mass irreg KN

Comparison of Peak storey shear values of irregular with regular

structures in X dir.

Mass irregular having maximum base shear value.

But it almost converges with top storey shear of regular structure.

At storeys of mass irregularity slope of the graph suddenly changes.

Presence of soft storey in stiffness irregular structure Presence of soft storey in stiffness irregular structure makes less stiff than regular one resulted in increased base shear.

Base shear for vertically geometric irregular structure is found less compared to the regular.

Top storey shear for vertically geometric also found less.

Time history analysis was performed to find the accurate inter storey drift value.(In x dir)

13

14

15

16

17

18

19

20

21

0

1

2

3

4

5

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6 7

vert irreg

mass irregular

stiff irreg

reg

For stiffness irregular due to less stiff ground floor inter storey drift of is found to be more than regular.

Effect of extra mass on 14th and 17th floor, where higher inter storey drift observed.

Higher the position of extra mass, inertial force is more leading to larger displacement.

In case of vertically geometric irregular, In case of vertically geometric irregular,

Set back Irregularity provided on 5th ,10th and 15th floor resp.

From graph it is shown that slope of the graph suddenly decreases at these floors.

Vertically irregular structures experience less base shear and less storey drift may be due to the on the sides.distribution of irregularity equally

References [1]V.K Sadashiva. (2010) Quantifying structural irregularity effects

for simple seismic design. Ph.D. Thesis. University of Canterbury. New Zealand.

[2] Agarwal P., Shrikhande M.(2006) Earthquake resistant design of structures. PHI Learning Pvt. Ltd., New Delhi.

[3]Indian Standard Code 1893(Part 1):2002. [4]Kara N.,Celep Z.,(2012) Nonlinear seismic response of structural

systems having vertical irregularities due to discontinuities in [4]Kara N.,Celep Z.,(2012) Nonlinear seismic response of structural systems having vertical irregularities due to discontinuities in columns, 13th World Conference on Earthquake Engineering.

[5] Standards New Zealand. 2004. NZS 1170.5:2004 Structural Design Actions Part 5: Earthquake actions New Zealand.

[6] Chintanapakdee C.,Chopra A. K. (2004) Seismic response of vertically irregular frames: Response history and modal pushover analyses.

[7]Abdolahirad A., MacRae G.,Bull D., Yeow D. (2014) Seismic evaluation of buildings with out-of straightness ,New Zealand Society of Earthquake Engineering (NZSEE) Conference.

[8] SEAOC. Recommended lateral force requirements and commentary. Seventh Edition, Seismology Committee, Structural Engineers Association of California, 1999.