This document provides an overview of different seismic analysis methods for reinforced concrete buildings according to Indian code IS 1893-2002, including linear static, nonlinear static, linear dynamic, and nonlinear dynamic analysis. It describes the basic procedures for each analysis type and provides examples of how to calculate design seismic base shear, distribute seismic forces vertically and horizontally, and determine drift and overturning effects. Case studies are presented comparing the results of static and dynamic analysis for regular and irregular multi-storey buildings modeled in SAP2000.
Pushover is a static-nonlinear analysis method where a structure is subjected to gravity loading and a monotonic displacement-controlled lateral load pattern which continuously increases through elastic and inelastic behavior until an ultimate condition is reached. Lateral load may represent the range of base shear induced by earthquake loading, and its configuration may be proportional to the distribution of mass along building height, mode shapes, or another practical means.
The static pushover analysis is becoming a popular tool for seismic performance evaluation of existing and new structures. The expectation is that the pushover analysis will provide adequate information on seismic demands imposed by the design ground motion on the structural system and its components. The purpose of the paper is to summarize the basic concepts on which the pushover analysis can be based, assess the accuracy of pushover predictions, identify conditions under which the pushover will provide adequate information and, perhaps more importantly, identify cases in which the pushover predictions will be inadequate or even misleading.
The Pushover Analysis from basics - Rahul LeslieRahul Leslie
Pushover analysis has been in the academic-research arena for quite long. The papers published in this field usually deals mostly with proposed improvements to the approach, expecting the reader to know the basics of the topic... while the common structural design practitioner, not knowing the basics, is left out from participating in those discussions. Here I’m making an effort to bridge that gap by explaining the Pushover analysis, from basics, in its simplicity.
A write up on this topic can be found at http://rahulleslie.blogspot.in/p/blog-page.html, though does not cover the full spectrum presented in this slide show.
Pushover is a static-nonlinear analysis method where a structure is subjected to gravity loading and a monotonic displacement-controlled lateral load pattern which continuously increases through elastic and inelastic behavior until an ultimate condition is reached. Lateral load may represent the range of base shear induced by earthquake loading, and its configuration may be proportional to the distribution of mass along building height, mode shapes, or another practical means.
The static pushover analysis is becoming a popular tool for seismic performance evaluation of existing and new structures. The expectation is that the pushover analysis will provide adequate information on seismic demands imposed by the design ground motion on the structural system and its components. The purpose of the paper is to summarize the basic concepts on which the pushover analysis can be based, assess the accuracy of pushover predictions, identify conditions under which the pushover will provide adequate information and, perhaps more importantly, identify cases in which the pushover predictions will be inadequate or even misleading.
The Pushover Analysis from basics - Rahul LeslieRahul Leslie
Pushover analysis has been in the academic-research arena for quite long. The papers published in this field usually deals mostly with proposed improvements to the approach, expecting the reader to know the basics of the topic... while the common structural design practitioner, not knowing the basics, is left out from participating in those discussions. Here I’m making an effort to bridge that gap by explaining the Pushover analysis, from basics, in its simplicity.
A write up on this topic can be found at http://rahulleslie.blogspot.in/p/blog-page.html, though does not cover the full spectrum presented in this slide show.
DESIGN AND ANALYSIS OF G+3 RESIDENTIAL BUILDING BY S.MAHAMMAD FROM RAJIV GAND...Mahammad2251
Structural design is the primary aspect of civil engineering. The foremost basic in
structural engineering is the design of simple basic components and members of a building viz., Slabs,
Beams, Columns and Footings. In order to design them, it is important to first obtain the plan of the
particular building. Thereby depending on the suitability; plan layout of beams and the position of
columns are fixed.
Dhruvin Goyani
M.Tech Structural
This PPT is For All the Civil Engineering Students and Specially for M.tech Students Who Trying To Learn Something New on Earthquake and its Resisting Methods and also For Seismic Analysis
The dynamic behavior of structures is an important topic in many fields. Aerospace engineers must understand dynamics to simulate space vehicles and airplanes, while mechanical engineers must understand dynamics to isolate or control the vibration of machinery. In civil engineering, an understanding of structural dynamics is important in the design and retrofit of structures to withstand severe dynamic loading from earthquakes, hurricanes, and strong winds, or to identify the occurrence and location of damage within an existing structure.
DESIGN AND ANALYSIS OF G+3 RESIDENTIAL BUILDING BY S.MAHAMMAD FROM RAJIV GAND...Mahammad2251
Structural design is the primary aspect of civil engineering. The foremost basic in
structural engineering is the design of simple basic components and members of a building viz., Slabs,
Beams, Columns and Footings. In order to design them, it is important to first obtain the plan of the
particular building. Thereby depending on the suitability; plan layout of beams and the position of
columns are fixed.
Dhruvin Goyani
M.Tech Structural
This PPT is For All the Civil Engineering Students and Specially for M.tech Students Who Trying To Learn Something New on Earthquake and its Resisting Methods and also For Seismic Analysis
The dynamic behavior of structures is an important topic in many fields. Aerospace engineers must understand dynamics to simulate space vehicles and airplanes, while mechanical engineers must understand dynamics to isolate or control the vibration of machinery. In civil engineering, an understanding of structural dynamics is important in the design and retrofit of structures to withstand severe dynamic loading from earthquakes, hurricanes, and strong winds, or to identify the occurrence and location of damage within an existing structure.
Dynamic Response of High Rise Structures Under The Influence of Shear WallsIJERA Editor
This study presents the procedure for seismic performance estimation of high-rise buildings based on a concept of the capacity spectrum method. In 3D analytical model of thirty storied buildings have been generated for symmetric buildings Models and analyzed using structural analysis tool ETABS. The analytical model of the building includes all important components that influence the mass, strength, stiffness and deformability of the structure. To study the effect of concrete core wall & shear wall at different positions during earthquake, seismic analysis using both linear static, linear dynamic and non-linear static procedure has been performed. The deflections at each storey level has been compared by performing Equivalent static, response spectrum method as well as pushover method has also been performed to determine capacity, demand and performance level of the considered building models. From the below studies it has been observed that non-linear pushover analysis provide good estimate of global as well as local inelastic deformation demands and also reveals design weakness that may remain hidden in an elastic analysis and also the performance level of the structure. Storey drifts are found within the limit as specified by code (IS: 1893-2002) in Equivalent static, linear dynamic & non-linear static analysis.
Seismic Vulnerability of RC Building With and Without Soft Storey Effect Usi...IJMER
A soft storey is one which has less resistance to earthquake forces than the other storeys;
Buildings containing soft stories are extremely vulnerable to earthquake collapses, since one floor is
flexible compared to others. Vulnerability of buildings is important in causing risk to life hence special
consideration is necessary for such soft storey RC buildings. In the present study, analytical
investigation of a RC building by considering the effect of soft storey situated in seismic Zone-V of
India, in accordance with IS 1893-2002 (part-1), is taken as an example and the various analytical
approaches (linear static and nonlinear static analysis) are performed on the building to identify the
seismic demand and also pushover analysis is performed to determine the performance levels, and
Capacity spectrum of the considered, also Storey Shear is compared for 3 models by using Finite
Element Software Package ETAB’s 9.7.4 version.
Seismic performance of r c buildings on sloping grounds with different types ...eSAT Journals
Abstract
Structure are highly susceptible to serve damages in earthquake scenario, so choosing an appropriate lateral force resisting
bracing systems will have a significant effect on performance of the structure. So this present study is aimed at evaluating and
comparing various types of eccentric steel bracings for 12 storey RC frame building resisting on sloping ground configurations.
For this 5 types of bracing systems like X-Bracing, Diagonal bracing, K- bracing, V-bracing and inverted V bracing are
considered on the outer periphery of the buildings with step back and set back – step back type configurations are modeled and
analyzed. The models are compared for different aspects within the structure, such as the maximum storey displacement, base
shear, storey drift and storey shear, the structure is analyzed for seismic zone V and medium soil condition as per IS 1893:2002
using ETABS software. Results conclude that on sloping ground due to irregularity on ground surface, the structures are more
vulnerable to earthquakes. Hence use of eccentric steel bracing is an effective and economical way to resist earthquake forces,
Inverted V type bracing performs well compared to other bracing types. By using inverted V type bracing in step back buildings
types maximum storey displacement of 70% and storey drift of 66% are obtained. Similarly for setback – step back configuration
maximum storey displacement of 74% and storey drift of 70% are obtained respectively.
Keywords: X-Bracing, Diagonal Bracing, K- Bracing, V-Bracing and Inverted V Bracing
Capacity Spectrum Method for RC Building with Cracked and Uncracked SectionIOSR Journals
one of the most widespread procedures for the assessment of building behavior, due to earthquake, is the Capacity Spectrum Method (CSM). In the scope of this procedure, capacity of the structure compares with the demands of earthquake ground motion on the structure. The capacity of the structure is represented by a nonlinear force-displacement curve, referred to as a pushover curve. The base shear forces and roof displacements are converted to equivalent spectral accelerations and spectral displacements, respectively, by means of coefficients that represent effective modal masses and modal participation factors. These spectral values define the capacity spectrum. The demands of the earthquake ground motion are represented by response spectra. A graphical construction that includes both capacity and demand spectra, results in an intersection of the two curves that estimates the performance of the structure to the earthquake. In this study, for determination of the performance levels, G+10 R.C.C. Building with cracked and uncracked section were taken. The structural Capacity of cracked and uncracked section compared with performance point value, which shows the structural capacity of building having cracked section is lesser than the uncracked section. Different modeling issues were analyzed to study the effect on Capacity of the structure with cracked and uncracked section for different position of Shear wall.
Static and Dynamic Behavior of Reinforced Concrete Framed Building: A Compara...IOSR Journals
Reinforced concrete frame buildings are most common type of construction in urban India, which is subjected to several types of forces during their life time such as static forces and dynamic forces due to wind and earthquakes. The static loads are constant with time, while dynamic loads are time varying, causing considerable inertia effects .It depends mainly on location of building, importance of its use and size of the building. Its consideration in analysis makes the solution more complicated and time consuming and its negligence may sometimes becomes the cause of disaster during earthquake.
So it is growing interest in the process of designing civil engineering structures capable to withstand dynamic loads . The behavior of building under dynamic forces depends upon its mass and stiffness properties, whereas the static behavior is solely dependent upon the stiffness characteristics.
Strengthening of RC Framed Structure Using Energy Dissipation DevicesIOSR Journals
A large numbers of existing buildings in India are severely deficient against earthquake forces and
the number of such buildings is growing very rapidly. This paper presents a way of using energy dissipation
devices for seismic strengthening of a RC framed structure. The objective was to improve the seismic
performance of the building to resist the earthquake. The viscous dampers are used as an energy dissipation
device in the form of single, double, inverted V, V type of dampers with different percentages of damping such
as 10%, 20% and 30% to prevent building from collapse in a major earthquake and also to control the damage
during earthquake. The performance of the buildings is assessed as per the procedure prescribed in ATC-40
and FEMA 356.
Influence of Combine Vertical Irregularities in the Response of Earthquake Re...IOSRJMCE
This study investigates the effect of frame set-back with vertical irregularity in height on accuracy of Pushover Analysis for predicting target displacement, story drifts, base shear and performance point. The behavior of high rise building during strong earthquake motion depends on the distribution of mass, stiffness and strength in both horizontal and vertical planes of the buildings. The Indian IS code 1893:2002(Part 1) has pointed out of different structures irregularities like plan irregularity and vertical irregularity. In this study the seismic performance of G+ 16 storey having combine effect of vertical irregularity with R.C building are examined using Non Linear Static Analysis (Pushover Analysis). The Base shear, lateral displacement, storey drift and performance points are the response parameters use to quantify the performance of the structure. These irregularities are responsible for structural collapse of buildings under the action of dynamic loads. Five different types of building geometry are taken one regular and four irregular frames. The all buildings are modeled and analyzed in software SAP 2000. It was found that irregularity in elevation of the building reduce the performance level of structure.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
2. INTRODUCTION
• Since earthquake forces are random in nature and
unpredictable, the static and dynamic analysis of the
structures have become the primary concern of civil
engineers.
• The main parameters of the seismic analysis of
structures are load carrying capacity, ductility,
stiffness, damping and mass.
• IS 1893-2002 is used to carryout the seismic analysis
of multi-storey building. 2
3. SEISMIC ANALYSIS OF STRUCTURES
• The seismic analysis type that should be used to
analyse the structure depends upon :-
external action
the behavior of structure or structural
materials
the type of structural model selected
3
4. • The different analysis procedure are
Linear Static Analysis
Nonlinear Static Analysis
Linear Dynamic Analysis
Nonlinear Dynamic Analysis
4
6. • Also known as Equivalent Static method.
• Based on formulas given in the code of practice.
STEPS
• First, the design base shear is computed for the whole building.
• It is then distributed along the height of the building.
• The lateral forces at each floor levels thus obtained are distributed
to individual lateral load resisting elements.
6
7. 7
Equivalent lateral shear force along two orthogonal axis
(Source: Nouredine Bourahla, "Equivalent Static Analysis of Structures Subjected to
Seismic Actions", Encyclopedia of Earthquake Engineering, Springer-Verlag Berlin
Heidelberg, 2013)
8. 8
Limitations
The use of this method is restricted with respect to
• High seismic zones and height of the structure
• Buildings having higher modes of vibration than the
fundamental mode
• Structures having significant discontinuities in mass and
stiffness along the height
9. PROCEDURE
• Calculation of the Design Seismic Base Shear, VB
• Vertical distribution of base shear along the height of
the structure
• Horizontal distribution of the level forces across the
width and breadth of the structure
• Determination of the drift, overturning moment, and
P-Delta effect
9
10. Design Seismic Base Shear, VB
From IS 1893- 2002, Clause 7.5.3, the design base shear
where,
W - seismic weight of the building
Ah - horizontal seismic coefficient
Horizontal Seismic Coefficient, Ah
As per IS 1893(Part 1)-2002, Clause 6.4.2
Provided that for any structure with T < 0.1 s, the value of Ah will not be taken less
than Z/2 whatever be the value of I/R.
10
Ah =
VB= Ah W
11. Where,
Z - Zone factor
I - Importance factor
R- Response Reduction factor
Sa/g - Average response acceleration coefficient
T -Undamped Natural period of the structure
11
12. Zone Factor ( Z)
• It is the indicator of the maximum seismic risk characterized by
Maximum Considered Earthquake (MCE ) in the zone in which the
structure is located.
• According to IS 1893(Part 1)-2002, Seismic Zones are classified into
II, III, IV & V respectively.
Average response acceleration coefficient (Sa/g)
• It depends on the type of rock or soil sites and also the natural period
and damping of the structure.
• It is obtained from, Clause 6.4.5, IS 1893-2002.
12
13. Importance Factor (I)
• It depends on the occupancy category of the building.
• It is obtained from table 6, Clause 6.4.2, IS 1893-2002.
Site Class
• Site Class is determined based on the average properties of the soil within a
certain depth (30 m) from the ground surface.
Response Reduction factor (R)
• It is determined by the type of lateral load resisting system used.
• It is a measure of the system’s ability to accommodate earthquake loads and
absorb energy without collapse.
• It is obtained from table 7, IS 1893-2002.
13
14. Ta =
Fundamental Period
• The approximate fundamental natural period of vibration ( Ta ),
of a MRF building from Clause 7.6,
without brick infil panels,
with infil panels,
14
where,
h - height of the building
d- Base dimension of the building at the plinth level
Ta = 0.075 h0.75 for RC frame building
= 0.085 h0.75 for steel frame building
15. Vertical Distribution of Base Shear to Different Floor levels
The lateral force induced at any level hi as per Clause 7.7.1, IS 1893-
2002, can be determined by,
where,
Qi - Design lateral force at floor i
Wi - Seismic weight of floor i
hi - Height of floor i measured from base, and
n - Number of storey's in the building is the number of levels at
which the masses are located.
15
16. Horizontal Distribution of Base Shear
The horizontal distribution of base shear as per FEMA P749, can be
determined by
where,
Fij : force acting on the lateral force-resisting line j at a floor level i
nk : number of lateral force-resisting elements (lines)
Kij ,Kik : story stiffness of the lateral force-resisting element (line) k
and j at level i
Fi : seismic force at floor (level) i
16
17. Drift Story
• It is a measure of how much one floor or roof level displaces under
the lateral force relative to the floor level immediately below.
• It is the ratio of the difference in deflection between two adjacent
floors divided by the height of the story that separates the floors.
Overturning Moment and P-Delta Effects
• There is a tendency for the moment created by equivalent static
force acting above the base to overturn the structure.
• The dead weight of the building is sufficient to resist the overturning
force, but it must be checked always.
17
18. • The “stability coefficient” for each story as per FEMA P749, can
be calculated as,
where,
Pi - weight of the structure above the story being evaluated
i - is the design story drift determined
Vi - is the sum of the lateral seismic design forces above the story
hi - story height
18
=
20. • Also known as Pushover Analysis
• Used to estimate the strength and drift capacity of existing
structure and the seismic demand for this structure subjected to
selected earthquake.
• It can be used for checking the adequacy of new structural
design as well.
• It is an analysis in which, a mathematical model incorporates
the nonlinear load-deformation characteristics of individual
components and elements of the building which shall be
subjected to increasing lateral loads representing inertia forces
in an earthquake until a ‘target displacement’ is exceeded.
20
21. • Response characteristics that can be obtained from the pushover
analysis are
– Estimates of force and displacement capacities of the structure.
– Sequences of the failure of elements and the consequent effect
on the overall structural stability.
– Identification of the critical regions, where the inelastic
deformations are expected to be high and identification of
strength irregularities of the building.
21
22. PROCEDURE
In Pushover analysis the magnitude of the lateral load is
increased monotonically maintaining a predefined distribution
pattern along the height of the building.
Building is displaced till the ‘control node’ reaches ‘target
displacement’ or building collapses.
The sequence of cracking, plastic hinging and failure of the
structural components throughout the procedure is observed.
The relation between base shear and control node
displacement is plotted for all the pushover analysis.
22
23. 23
Schematic representation of pushover analysis procedure
(Source: Jan, T.S.; Liu, M.W. and Kao, Y.C. (2004), “An
upper-bond pushover analysis procedure for estimating
the seismic demands of high-rise buildings”. Engineering
structures. 117-128)
24. • Pushover analysis may be carried out twice:
(a) first time till the collapse of the building to estimate target
displacement.
(b) next time till the target displacement to estimate the seismic
demand.
• The seismic demands for the selected earthquake are calculated at
the target displacement level.
• The seismic demand is then compared with the corresponding
structural capacity to know what performance the structure will
exhibit.
24
25. Lateral Load Patterns
FEMA 356 suggests the use of at least two different patterns for
all pushover analysis.
Group – I
i) Code-based vertical distribution of lateral forces used in
equivalent static analysis
ii) A vertical distribution proportional to the shape of the
fundamental mode in the direction under consideration
iii) A vertical distribution proportional to the story shear
distribution calculated by combining modal responses from a
response spectrum analysis of the building
25
26. Group – II
i) A uniform distribution consisting of lateral forces at each level proportional to the
total mass at each level
ii) An adaptive load distribution that changes as the structure is displaced
26
Lateral load pattern for pushover analysis as per FEMA 356
(Source: Jan, T.S.; Liu, M.W. and Kao, Y.C. (2004), “An upper-bond
pushover analysis procedure for estimating the seismic demands of high-
rise buildings”. Engineering structures. 117-128)
27. Target Displacement
Two approaches to calculate target displacement:
(a) Displacement Coefficient Method (DCM) of FEMA 356
(b) Capacity Spectrum Method (CSM) of ATC 40
• Both of these approaches use pushover curve to calculate global
displacement demand on the building.
• The only difference in these two methods is the technique used.
27
28. Displacement Coefficient Method (FEMA 356)
• This method estimates the elastic displacement of an
equivalent SDOF system assuming initial linear
properties and damping for the ground motion
excitation under consideration.
• Then it estimates the total maximum inelastic
displacement response for the building at roof by
multiplying with a set of displacement coefficients.
28
29. Capacity Spectrum Method (ATC 40)
• Uses the estimates of ductility to calculate effective period and
damping.
• This procedure uses the pushover curve in an acceleration
displacement response spectrum (ADRS) format.
• This can be obtained through simple conversion using the
dynamic properties of the system.
• The pushover curve in an ADRS format is termed a ‘capacity
spectrum’ for the structure.
• The seismic ground motion is represented by a response spectrum
in the same ADRS format and it is termed as demand spectrum.
29
31. • Response spectrum method is a linear dynamic analysis
method.
• In this approach multiple mode shapes of the building
are taken into account.
• For each mode, a response is read from the design
spectrum, based on the modal frequency and the modal
mass.
• They are then combined to provide an estimate of the
total response of the structure using modal combination
methods.
31
32. Combination methods include the following:
• Absolute Sum method
• Square Root Sum of Squares (SRSS)
• Complete Quadratic Combination (CQC)
• The design base shear calculated using the dynamic
analysis procedure is compared with a base shear Vb ,
calculated using static analysis.
• If Vb is less than , all the response quantities, eg.
member forces, displacements, storey forces, storey
shears, and base reactions, should be multiplied by Vb /
32
33. • Buildings with plan irregularities and with vertical
irregularities cannot be modelled for dynamic analysis by
this method.
• For irregular buildings, lesser than 40m in height in
zones II and III, dynamic analysis, though not mandatory,
is recommended.
33
34. Modal Analysis
Modal Mass (clause 7.8.4.5(a))
Where,
- mode shape coefficient at the floor i in the mode k
- seismic weight of floor i
34
35. Modal Participation Factor (Clause 7.8.4.5 (b))
Design lateral force at each floor level in each
mode(clause7.8.4.5(c))
Where,
Qik - peak lateral force
Ak - design horizontal acceleration spectrum
35
36. Storey shear forces in each mode (clause 7.8.4.5(d))
The peak storey shear, Vik
Lateral forces at each storey due to all modes
considered(clause 7.8.4.5(f))
36
The design lateral forces, Froof and Fi, at roof and at floor i are
given by
37. Modal Combination
• The peak response quantities should be combined as per the
Complete Quadratic combinations (CQC) method
Where,
r - number of modes being consider
ρij - the cross-modal coefficient
λi, - response quantity in mode i
λj - response quantity in mode j
ξ - model damping ratio
β - frequency ratio 37
38. Square Root Sum of Squares (SRSS)
Absolute Sum method
• If the building has a few closely spaced modes the peak response
quantity λ* due to these modes should be obtained as
38
Where λk is the absolute value of quantity in mode k, and r is the number
of modes being considered.
40. • Also known as Time History Analysis(THA)
• To perform such an analysis, a representative earthquake
time history is required for a structure being evaluated.
• In this method, the mathematical model of the building is
subjected to accelerations from earthquake records that
represent the expected earthquake at the base of the
structure.
• The method consists of a step- by- step direct integration
over a time interval.
40
41. • The time-history method is applicable to both elastic
and inelastic analysis.
• In elastic analysis the stiffness characteristics of the
structure are assumed to be constant for the whole
duration of the earthquake.
• In the inelastic analysis, however, the stiffness is
assumed to be constant through the incremental time
only.
41
42. PROCEDURE
• An earthquake record representing the design earthquake is selected.
• The record is digitized as a series of small time intervals of about 1/40
to 1/25 of a second.
• A mathematical model of the building is set up, usually consisting of a
lumped mass at each floor. Damping is considered proportional to the
velocity in the computer formulation.
• The digitized record is applied to the model as accelerations at the
base of the structure.
• The equations of motions are then investigated with the help of
software program that gives a complete record of the acceleration,
velocity, and displacement of each lumped mass at each interval.
42
43. SAP2000
• It is a finite-element-based structural program for the
analysis and design of civil structures.
• SAP2000 is object based, meaning that the models are
created using members that represent the physical reality.
• All the seismic analysis procedures can be analysed
effectively in SAP2000.
43
45. Comparative Study of Static and Dynamic Analysis of
Multi-Storey Regular & Irregular Building
• This study was carried out by Saurabh G. Lonkar, in the year 2015.
objectives of this paper were
To study the seismic behavior of RC building and to analyse the structure
using equivalent static method, time history Method and response spectrum
method followed by Pushover analysis.
Determination of storey displacements.
To check the accuracy and exactness of Time History analysis, Response
Spectrum Analysis and Equivalent Static Analysis with respect to different
conditions & aspects.
Also to check the seismic behavior and relative displacement of regular &
irregular building in different seismic zone. 45
46. Structural Analysis and Modeling
• A 22 storey residential building was modelled for zone III
in SAP2000.
• The storey plan was changing for irregular building &
symmetric for regular building.
• The building had been analyzed by using equivalent static,
response spectrum and time history analysis, based on IS
codes.
• The maximum storey displacements result had been
obtained by using all methods of analysis.
46
47. Results and Discussions
• Displacement values between static and dynamic analysis is
insignificant for lower stories but the difference is increased in
higher stories and static analysis given higher values than
dynamic analysis.
• According to damage assessment of building, it was concluded
that the damage percentage of building was different for each
method of analysis.
• Static analysis is not sufficient for high rise building its
necessary to provide dynamic analysis because of specific & non
linear distribution of forces.
• Time history analysis should be performed as it predicts the
structural response more accurately than other two methods
based on damage assessment of building.
47
48. Comparative Study of Seismic Analysis of 3-Storey
RC Frame on SAP2000
• This study was carried out by Akshay Mathane, Saurabh Hete, Tushar
Kharabe, in the year 2016
The main Objectives were -
• To analyze the building as per code IS 1893-2002 part I
• To study the response of the structure such as base shear and
lateral displacement
• To study methods of earthquake analysis (Equivalent static and
Response spectrum method)
• To study seismic analysis of frame by SAP2000 48
49. Modeling
• 3 storey building with storey height 3m having 4 bays of
5 m in X and 3 bays of 5m in Y directions for seismic
zone V was modeled in SAP2000.
Results and Discussion
49
Storey Level Displacement (Manual in mm) Displacement (SAP in mm) Displacement (%)
4 0.052469 0.050533 0.036897
3 0.044383 0.042554 0.041209
2 0.0131142 0.024788 -0.890164
1 0.015023 0.014306 0.0477268
Comparison of Storey Displacements
50. Storey Level Displacement by ESM in mm
as per SAP
Displacement by RSM in mm
as per SAP
4 0.050533 0.043112
3 0.042554 0.037057
2 0.029788 0.026739
1 0.014306 0.013248
50
Sl. No. Manual shear( kN) Base shear in SAP (kN)
1 1269.64 1282.039
Comparison of Base reaction
Comparison of Storey Displacements in ESM & RSM
Sl.No. Base shear by ESM in SAP
(kN)
Base shear by RSM in SAP
(kN)
1 1282.039 1275.628
Comparison of Base reaction in ESM & RSM
51. • Equivalent static method was simpler than Response Spectrum method, but
Static analysis was not sufficient for high-rise building.
• SAP results for Equivalent static and Response spectrum method were
nearly same.
• The results obtained from static analysis method shows higher storey
displacement values as compared to response spectrum analysis.
• Manual and SAP result of story displacement, base reaction of Equivalent
Static method were approximately same.
• Response spectrum of irregular and multistory building was very tedious
work but for the analysis of any type of building this method can be
preferred to get better results.
• Response spectrum results were more accurate than Equivalent static
method.
51
52. STRUCTRAL ANALYSIS AND MODELLING
• A 2D Frame of floor height 3m was modelled by SAP2000.
• Building has 2 bays of 3 m in X direction.
• The grade of concrete is M25.
• Pushover analysis procedure were carried out for 2D frame.
• Lateral load of 10kN and a Vertical load of 100kN was applied at
the roof level.
• Hinge support was provided.
• P- Delta effects were included in analysis. 52
54. 54
Pushover Curve
• Pushover analyses using uniform lateral load pattern yielded capacity curves
with lower initial stiffness and base shear capacity but higher roof displacement
55. CONCLUSION
• Dynamic analysis for simple structures can be carried out manually,
but for complex structures finite element analysis can be used to
calculate the mode shapes and frequencies.
• Depending upon the accuracy of results needed and the importance
of the building that should be analysed various seismic analysis
procedures can be adopted like Linear Static Analysis, Nonlinear
Static Analysis, Linear Dynamic Analysis and Nonlinear Dynamic
Analysis.
• For smaller structures, response spectrum analysis or equivalent
static analysis can be used with little effort.
• If accurate and precise result is wanted from the analysis, then we
should carryout non-linear dynamic analysis.
55
56. • Nonlinear relationship between force and displacement
in multi-storey building structures may be determined
easy enough with the application of nonlinear static
pushover analysis.
• SAP2000 provides almost accurate results when
compared with manual calculations.
56
57. REFERENCE
[1] Chopra AK (1995). “Dynamics of Structures Theory and Application to Earthquake Engineering”, University of California at Berkeley, USA.
[2] Duggal S K (2010). “Earthquake Resistance Design of Structure”, Fourth Edition, Oxford University Press, New Delhi.
[3] FEMA 356 (2000), “Pre-standard and Commentary for the Seismic Rehabilitation of Buildings”, American Society of Civil Engineers, USA.
[4] IS 1893 Part 1 (2002). “Indian Standard Criteria for Earthquake Resistant Design of Structures”, Bureau of Indian Standards, New Delhi.
[5] Jan. T.S, Liu. M.W. and Kao. Y.C. (2004), “An upper-bond pushover analysis procedure for estimating the seismic demands of high-rise buildings”,
Engineering structures. 117-128.
[6] Nouredine Bourahla (2013), "Equivalent Static Analysis of Structures Subjected to Seismic Actions", Encyclopedia of Earthquake Engineering, Springer-
Verlag Berlin Heidelberg.
[7] Pankaj Agarwal and Manish Shrikhande (2014)."Earthquake Resistant Design of Structures", PHI Learning Private Limited, Delhi.
[8] Prof. Sakshi Manchalwar, Akshay Mathane, Saurabh Hete and Tushar Kharabe "Comparative Study of Seismic Analysis of 3-Storey RC Frame",
International Journal of Science, Engineering and Technology Research (IJSETR), April 2016, ISSN: 2278- 7798 .
[9] Saurabh G Lonkar and Riyaz Sameer Shah, ''Comparative Study of Static and Dynamic Analysis of Multi-Storey Regular & Irregular Building-A Review",
International Journal of Research in Engineering, Science and Technologies (IJRESTs), ISSN 2395-6453.
57