blast loading on structure
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DYNAMIC ANALYSIS OF INFILLED R C FRAME SUBJECTED
TO BLAST LOADING AS PER IS 4991-1968
A DISSERTATION
Submitted in partial fulfilment of the
Requirements for the award of the degree
of
MASTER OF TECHNOLOGY
In
Structural and Construction Engineering
By
Pravendra Yadav
(Roll No. 13217026)
Under the supervision of
Dr. Partap Singh
Professor
DEPARTMENT OF CIVIL ENGINEERING
Dr B R AMBEDKAR NATIONAL INSTITUTE OF
TECHNOLOGY
JALANDHAR – 144011 (INDIA)
JUNE, 2015
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DR. B. R. AMBEDKAR NATIONAL INSTITUTE OF TECHNOLOGY
DEPARTMENT OF CIVIL ENGINEERING
CANDIDATE’S DECLARATION I hereby certify that the work which is being presented in this dissertation report
entitled,“ Dynamic Analysis of Infilled R C Frame Subjected to Blast Loading as
per IS 4991-1968 ”, is presented in partial fulfilment of the requirement for the award
of the degree of “Master of Technology” in Structural and Construction Engineering
submitted to the Department of Civil Engineering at Dr. B. R. Ambedkar National
Institute of Technology, Jalandhar is an authentic record of my own work carried out
during a period from January to June 2015 under the supervision of Dr. Partap Singh.
The matter presented in this thesis has not been submitted by me in any other
University / Institute for the award of any degree.
Date: Pravendra Yadav
This is to certify that the above statement made by candidate is correct to the best of
my knowledge and belief.
Date: Dr. Partap Singh
Professor
The Viva Voice examination of Pravendra Yadav has been held on......................
Signature of Supervisor Signature of HOD Signature of External Examiner
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ACKNOWLEDGEMENT
I express my deep sense of gratitude to Dr. Partap Singh , Professor, Department of
Civil Engineering, Dr. B. R. Ambedkar National Institute of Technology, Jalandhar,
for his excellent guidance and whole hearted involvement during my research study
without whose invaluable suggestions, meticulous efforts, versatility and untiring
guidance, this report would not have been feasible. I am also indebted to him for his
encouragement and moral support and sparing their valuable time in giving me
concrete suggestions and increasing my knowledge through fruitful discussions
throughout the course of my study.
I owe thanks to entire staff of CAD lab for their immense cooperation. I also want tothanks the library staff of Dr. B. R. Ambedkar national institute of technology,
Jalandhar, for their full cooperation in providing the necessary literature.
I would like to thanks Mr. Singh Vikram Santosh for his assistance in completing my
dissertation.
Most importantly, I would like to give God the glory for all of the efforts I have put
into this project, and deeply obliged to my parents, my friends uplifting me when I am
down, for pushing me when I want to stop, and for teaching me how to tackle every
situation of life either its up or down, for showing me the right direction blue, for their
out of the continuous encouragement to keep me moving even at the oddest of times.
Pravendra Yadav
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ABSTRACT
The number and intensity of terrorist activities have increased our concern towards the
safety of our infrastructure. An explosion due to air blast or any other dynamic loading
in air generates a pressure bulb, which grow in size at very high rate. The resulting
blast wave releases energy over a small duration and in a small volume, thus generates
waves of finite amplitude travelling radially in all directions.
A six storey RC frame structure with 3.00 m storey height in seismic zone IV has been
considered in this present study, effect of charge weights 100 kg, 300 kg and 500 kg
has been studied in three phases. The phases are as follows:
Phase 1: Standoff distance = 30 m
Charge weight - 100 kg
Charge weight - 300 kg
Charge weight - 500 kg
Phase 2: Standoff distance = 35 m
Charge weight - 100 kg
Charge weight - 300 kg
Charge weight - 500 kg
Phase 3: Standoff distance = 40 m
Charge weight - 100 kg
Charge weight - 300 kg
Charge weight - 500 kg
The effect of different charge weights 100 kg, 300 kg and 500 kg has been studied for
nodal displacements, velocity, acceleration and stress resultants in three Phases – 1, 2
and 3 for standoff distance 30 m, 35 m and 40 m respectively.
The structure is modelled and analysed by using software Staad Pro V8i-2007. The
blast parameters are calculated for stand-off distances by adopting wave scaling law
given in IS 4991-1968.
Comparison of results is made for different parameters such as variation of blast loads,
variation of standoff distances. Bending moment, shear force and axial forces in beams
and columns are maximum on front face of the structure due to maximum explosive
weight and minimum standoff distance ‘Z’. As the weight of explosive (TNT)
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increases, bending moment, shear force and axial force in beams and columns, lateral
displacement and velocity at different floor levels, increases. If standoff distance
increases, bending moment, shear force and axial force in beams and columns, lateral
displacement and velocity at different floor levels decreases.
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TABLE OF CONTENTS
CANDIDATE’S DECLARATION i
ACKNOWLWDGEMENT ii
ABSTRACT iii
LIST OF CONTENTS v
LIST OF FIGURES viii
LIST OF TABLES ix
CHAPTER - 1 ................................................................................................................ 1
Introduction ................................................................................................................... 1
1.1 General .................................................................................................................. 1
1.2 Characteristics of explosions ................................................................................ 4
1.3 Basic parameters of explosion .............................................................................. 5
1.4 Blast waves ........................................................................................................... 5
1.5 Classification of blast ............................................................................................ 8
1.6 Lateral force resisting system ............................................................................... 9
1.6.1 Infill walls ...................................................................................................... 9
1.6.2 Types of infill walls ..................................................................................... 10
1.7 Objectives of the study ........................................................................................ 10
1.8 Organization of thesis work ................................................................................ 11
CHAPTER - 2 .............................................................................................................. 12
Review of Literature ................................................................................................... 12
2.1 General ................................................................................................................ 12
2.2 Review of literature ............................................................................................. 12
CHAPTER - 3 .............................................................................................................. 19
Blast Load on Structures ............................................................................................ 19
3.1 General ................................................................................................................ 19
3.2 Elastic sdof systems ............................................................................................ 213.3 Calculation of blast loading ................................................................................ 23
3.3.1 Steps for calculation of blast parameters ..................................................... 23
3.4 Infills modelling .................................................................................................. 24
3.4.1 Equivalent strut method ............................................................................... 24
3.5 Loads considered in the analysis ......................................................................... 25
3.5.1 Gravity loads ................................................................................................ 25
3.5.2 Blast loads .................................................................................................... 25
3.6 Analysis of framed building...............................................................................26
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CHAPTER - 4 .............................................................................................................. 27
Calculation of Blast Parameters ................................................................................ 27
4.1 General ................................................................................................................ 27
4.2 Description of building ....................................................................................... 27
4.3 Material properties..............................................................................................29
4.3.1 Properties of rcc...............................................................................................29
4.3.2 Properties of brick masonry.........................................................................30
4.4 Blast pressure parameters (as per IS:4991-1968) ............................................... 29
4.4.1 Phase - 1 ....................................................................................................... 29
4.4.2 Phase - 2 ....................................................................................................... 42
4.4.3 Phase - 3 ....................................................................................................... 45
CHAPTER - 5 .............................................................................................................. 48
Results and Discussion ................................................................................................ 48
5.1 Phase - 1 .............................................................................................................. 48
5.1.1 Nodal displacement ...................................................................................... 48
5.1.2 Velocity ........................................................................................................ 49
5.1.3 Acceleration ................................................................................................. 49
5.1.4 Stress resultants ............................................................................................ 50
5.1.4.1 Moment..................................................................................................50
5.1.4.2 Shear force.............................................................................................53
5.1.4.4 Axial force.............................................................................................56
5.2 Phase - 2 .............................................................................................................. 58
5.2.1 Nodal displacement ...................................................................................... 58
5.2.2 Velocity ........................................................................................................ 58
5.2.3 Acceleration ................................................................................................. 59
5.2.4 Stress resultants ............................................................................................ 59
5.2.4.1 Moment..................................................................................................59
5.2.4.2 Shear force.............................................................................................62
5.2.4.3 Axial force.............................................................................................65
5.3 Phase - 3 .............................................................................................................. 67
5.3.1 Nodal displacement ...................................................................................... 67
5.3.2 Velocity ........................................................................................................ 67
5.3.3 Acceleration ................................................................................................. 67
5.3.4 Stress resultants ............................................................................................ 68
5.3.4.1 Moment..................................................................................................68
5.3.4.2 Shear force.............................................................................................715.3.4.3 Axial force.............................................................................................74
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Fig. 5.1 to 5.66.......................................................................................................76-108
Table 5.1 to 5.36..................................................................................................109-120
CHAPTER – 6...........................................................................................................122
Conclusions................................................................................................................122
6.1 General.............................................................................................................122
6.2 Conclusions......................................................................................................122
6.2.1 Effect of different charge weights...............................................................122
6.3 Scope for future study.......................................................................................126
REFERENCES..........................................................................................................128
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LIST OF FIGURES
Fig. 1.1 Murrah federal building before explosion .................................................... 3
Fig. 1.2 Murrah federal building before explosion .................................................... 3
Fig. 1.3 Free field blast .............................................................................................. 6
Fig. 1.4 Blast loads on building ................................................................................. 6
Fig. 1.5 Blast pressure with time (IS 4991-1968) ...................................................... 7
Fig. 1.6 Blast pressure on building ............................................................................ 8
Fig. 3.1 Variation of pressure with distance ............................................................ 19
Fig. 3.2 Formation of shock front in a shock wave .................................................. 20
Fig. 3.3 Variation of overpressure with distance from centre of explosion at
various time................................................................................................. 20
Fig. 3.4 (a) SDOF system and (b) blast loading ....................................................... 22
Fig. 3.5 Simplified resistance function of an elasto-plastic SDOF system .............. 22
Fig. 3.6 Equivalent diagonal strut model ................................................................. 25
Fig. 3.7 Time history definition for force with time ................................................ 26
Fig. 4.1 Plan of building ........................................................................................... 30
Fig. 4.2 Elevation of Building .................................................................................. 31
Fig. 5.1 to 5.66....................................................................................................76-108
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LIST OF TABLES
Table 1.1 Conversion factors for explosives [Draganic. H] ...........................................5
Table 4.1 Blast parameters for W = 100 kg at Z = 30 m ..............................................39
Table 4.2 Blast parameters for W = 300 kg at Z = 30 m ..............................................41
Table 4.3 Blast parameters for W = 500 kg at Z = 30 m ..............................................42
Table 4.4 Blast parameters for W = 100 kg at Z = 35 m ..............................................43
Table 4.5 Blast parameters for W = 300 kg at Z = 35 m ..............................................44
Table 4.6 Blast parameters for W = 500 kg at Z = 35 m ..............................................45
Table 4.7 Blast parameters for W = 100 kg at Z = 40 m ..............................................46
Table 4.8 Blast parameters for W = 300 kg at Z = 40 m ..............................................47
Table 4.9 Blast parameters for W = 500 kg at Z = 40 m ..............................................48
Table 5.1 to 5.36 .................................................................................................109-120
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CHAPTER – 1
INTRODUCTION
1.1 GENERAL
In the past few decades, danger of explosion damage to a structure is increased as a
result of increase in number and intensity of terrorist activities all over the world.
Generally structures are not designed for blast load due to the reason that the
magnitude of load caused by blast is huge and the cost of design and construction is
much higher. As a result, the structure is susceptible to damage from blast load. Recent
past blast incidents in the country trigger the minds of developers, architects and
structural engineers to find solutions to protect the life of human-being and structures
from blast disasters i.e. from sudden impact.
Special importance has been given to blast loads on landmark structures, such as high
rise buildings in metropolitan cities; the explosion of explosives (Bombs,
trinitrotoluene TNT, etc.) inside and around buildings can cause catastrophic impacts
on the structural integrity of the building, such as damage to the external and internal
structural frames and collapse of walls. Moreover, loss of life can result from the
collapse of the structure.
The earthquake problem is rather old, but most of the knowledge on this subject has
been accumulated during the past decades. The blast problem is rather new,
information for the development in this field is mostly made available through the
publications of the Indian researchers, Army Corps of Engineers, Naval Facilities
Engineering Command, Air Force Civil Engineering Support Agency and the other
government/public offices and institutes. The guidelines for the blast loading are
published in Indian code IS 4991-1968.
Explosions occurring in urban areas or close to the facilities such as building and
protective structures may cause tremendous damage and loss of life. The immediate
effects of such explosions are blast over pressures propagating through the
atmosphere. The damages generated by the explosion and shock waves resulting from
the sudden release of energy by the explosives in the form of pressure bulbs (which are
exponentially growing in nature in all the directions), temperature and noise.
Conventional buildings are constructed quite differently than the military structures
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and as such generally quite vulnerable to blast and ballistic threats. In order to design
structures which are able to withstand, it is necessary to first quantify the effects of
such explosions. Typically it comes from specialists guide, experimental tests and
analytical tools to perfectly predict the effects. Keeping this in mind, developers,
architectures and engineers are seeking solutions for potential blasts, protecting
building occupants and the structures.
Following Disasters such as the terrorist bombings of the U.S. embassies in Nairobi in
1998, the Murrah Federal Building in Oklahoma City in 1995, and the World Trade
Centre in New York in 1993 have explained the need for a thorough examination of
the behaviour of structure subjected to blast loads. The blast occurred at the basement
of World Trade Centre in 1993 has the charge weight of 816.5 kg tri-nitro-toluene
(TNT). To provide the adequate protection against explosions, the design and
construction of public building are done with the new methods/techniques given by the
structural engineers. Problems arises due to the complexity in analysing, which
involves time dependent finite deformation, high strain rates and non-linear inelastic
behaviour of materials to overcome from these and simplify the model analysis
various assumptions and approximations have been made. Analysis of structures under
blast load requires a good understanding of the blast parameters and dynamic responseof the structural elements. The analysis consists of several steps:
(a) Estimation of the risk
(b) Computation of load according to the estimated risk
(c) Analysis of structural behaviour
(d) Selection of structural system
(e) Evaluation of structural behaviour
Blast resistant design is becoming a important part of the design for important
structures because of hazards due to widespread terrorist activities in various parts of
the world. Design must be such that it may adapt the protection to lives as well as
buildings itself. In the situations such as terrorist attacks where there is no warning
time shelters must be integrated in the buildings itself, design is no longer limited to
underground shelters and sensitive military sites. People must now be aware for
protection against explosions on day to day basis.
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Fig. 1.1 Murrah federal building before explosion
Fig. 1.2 Murrah federal building before explosion
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1.2 CHARACTERISTICS OF EXPLOSIONS
In general, an explosion is result of very rapid release of energy within a limited space
which occurs from chemical, mechanical and nuclear sources. Explosions can be
categorized on the basis of their nature as physical, nuclear and chemical event.
In physical explosion: Energy may be released from the catastrophic failure of a
cylinder of a compressed gas, volcanic eruption or even mixing of two liquid at
different temperature.
In nuclear explosion: Energy is released from the formation of different atomic
nuclei by the redistribution of the protons and neutrons within the inner acting nuclei.
In chemical explosion: The rapid oxidation of the fuel elements (carbon and
hydrogen atoms) is the main source of energy.
The principal mechanisms deriving an explosion are significantly different, depending
upon the source. However, from the point of view of the effects of explosions upon
structural systems, there exists a set of fundamental characteristics which must be
defined and considered, irrespective of the source.
Explosives can be classified according to their rates of burning i.e. low explosive
burns and high explosive burns, solid explosives are mainly high explosives. They can
also be classified on the basis of their sensitivity of ignition as primary or secondary
explosives. Materials such as mercury fulminate and lead azides are primary
explosives. Secondary explosives when explode create blast (shock) waves which can
result in widespread damage to surroundings. Examples include trinitrotoluene (TNT)
and ammonium nitrate/fuel oil (AN/FO) [Ngo et al.].
Low explosives: Items those are capable of exploding but whose primary function is
not act as explosives includes natural gas, liquid fuels such as gasoline etc. It is usually
mixture of combustible substances and oxidants those decomposes rapidly.
High explosives: these are normally employed to explode in mining and military
warheads. These compounds detonate at a rate ranging from 3 to 9 m/s. These are
usually nitrate products such as toluene, phenol, pentaerythritol, amines and glycerine.
Trinitrotoluene (TNT): it a solid chemical compound of yellowish in colour. This is
best known as useful explosive material with convenient handling properties. The
explosive yields of TNT are considered as the standard measure of the strength of
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bombs and other explosives. It is common misconception that dynamite and TNT are
same or dynamite contains TNT. In actual fact, TNT is a specific chemical compound
and dynamite is an absorbent mixture soaked in nitro-glycerine that is compressed in
to a cylindrical shape and warped in papers.
1.3 BASIC PARAMETERS OF EXPLOSION
Use of the TNT (Trinitrotoluene) as a reference for determining the scaled distance X,
is universal. The first step in quantifying the explosive wave from a source other than
the TNT, is to convert the charge mass into an equivalent mass of the TNT. It is
performed so that the charge mass of explosive is multiplied by the conversion factor
based on the specific energy of the charge and the TNT. Specific energy of different
explosive types and their conversion factors to that of the TNT are given in Table 1.1.
TABLE 1.1 CONVERSION FACTORS FOR EXPLOSIVES [DRAGANIC. H]
Explosive
Specific
Energy QxTNT equivalent
kJ/kg Qx/QTNT
Compound B (60 % RDX, 40 % TNT) 5190 1.148
HMX 5680 1.256
Nitro-glycerine (liquid) 6700 1.481
TNT 4520 1.000
Explosive gelatine (91 % nitro-glycerine, 7.9 %
nitrocellulose, 0.9 % antracid, 0.2 % water)4520 1.000
60 % Nitro-glycerine dynamite 2710 0.600
Semtex 5660 1.25
C4 6057 1.340
1.4 BLAST WAVES
Blast wave is an area of pressure expanding supersonically outward from an explosive
core. It has a leading shock front of compressed gases. The blast wave is followed by
a blast wind of negative pressure, which sucks items back in towards the center. If a
strong gas explosion occurs inside a process area or in a compartment, the surrounding
area will be subjected to blast wave. The magnitude of blast wave depends on:
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Source
Distance from explosion
The detonation of a condensed high explosive generates gasses under pressure up to
300 kilo bar and a temperature of about 3000-4000 oc . the hot gas expands forsing out
the volume it occupies.
Fig. 1.3 Free field blast
Fig. 1.4 Blast loads on building
The threat for a conventional bomb is defined by two equally important components,
the bomb size or charge weight W and the standoff distance Z between the blast source
and the target. The peak incident overpressure Pso is amplified by an reflection factor
as the shock wave encounters an object or structure in its path. There reflection factors
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are typically greatest for normal incidence. Reflection factor depends on the intensity
of shock wave and for large explosives at normal incident pressures by as much as an
order of magnitude.
The pressure-time profile, two main phases can be observed; part above ambient
pressure is called duration of positive phase to while below the ambient is called
negative phase duration. Negative phase is of longer duration and a lower intensity
then the positive duration. As the standoff distance increases, the duration of positive
phase blast increases resulting in a lower-amplitude and longer-duration shock pulse.
Fig. 1.5 Blast pressure with time (IS 4991-1968)
During negative phase weakened structure may be subjected to impact by debries that
may cause additional damage. If exterior building walls are capable of resisting the
blast load, the shock front wave penetrates through window and door openings,
subjecting the floors, ceiling, walls, contents and people to sudden pressures and
fragments from shattered windows, doors, etc. The components not capable of
resisting the waves will fracture and and be further fragmented and moved by the
dynamic pressure that immediately follows the shock front.
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Fig. 1.6 Blast pressure on building
1.5 CLASSIFICATION OF BLAST
There are different types of explosion such as nuclear, physical and chemical.
Chemical explosives are the most common artificial explosives that can occur
accidentally or may cause by the terrorist attacks. Chemical explosives are generally
liquids or in consolidated solid forms.
The type of burst mainly classified as:
(a) Air burst
(b) High altitude burst
(c) Under water burst
(d) Underground burst
(e) Surface burst
The discussion here is limited to air burst or surface burst. This information is then
used to determine the dynamic loads on surface structures that are subjected to such
blast pressures and to design them accordingly. It should be pointed out that surface
structure cannot be protected from a direct hit by a nuclear bomb; it can however, be
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designed to resist the blast pressures when it is located at some distance from the point
of burst.
The air burst environment is produced by detonation which occurred above the ground
surface and at distance from a protective structure so that the initial shock wave
propagating away from the explosion impinges on the ground surface prior to the
arrival at the structure. Impact of air burst is less than the surface burst. A charge
located on or very near to the ground surface is considered to be a surface burst.
1.6 LATERAL FORCE RESISTING SYSTEM
The Lateral force resisting system is used to resist forces resulting from sudden impact
due to blasts, wind or seismic activity. The Lateral force resisting frame systemsclassified as follows:
(a) Braced Frame System
(b) Moment Resisting Frame System
(c) Shear Wall System
(d) Tube System
(e) Infill Wall System
1.6.1 INFILL WALLS
In multi-story buildings, infill walls are one of the most important components to resist
lateral forces. Infill walls increases the stiffness of the structural members and these
are provided to give additional lateral rigidity to the structure against lateral forces.
Many times due to architectural or other requirements, some of the panels in a framed
structure are filled with reinforced concrete or brick-walls. When a large number of
panels are filled in continuation, their behaviour is somewhat similar to a shear-wall.
In some of the frames, practically all the panels may be filled. When panels are filled
with reinforced walls, the behaviour is very near to those of shear-walls. The shear -
walls for their exclusive behaviour are provided in high-rise buildings i.e. above 10
storeys. The panel filling is done even for lesser number of storeys. The strength of
such infilled panels contributes significantly to the overall strength and stiffness of the
structure. In the general frame-work analysis, such contributions towards structural
stiffness and strength are not considered.
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1.6.2 TYPES OF INFILL WALLS
1.6.2.1 PLANE INFILL WALLS
Infill walls take care of the horizontal sway especially due to wind usually termed as
the drift of the building. Infill walls are used when a beam-column frame has
insufficient stiffness to horizontal sway under lateral loads like sudden impact due to
blasts, wind and earthquake and they prove uneconomical and unsound for building
structures. Infill wall buildings are designed to satisfy certain basic structural and
functional requirements.
1.6.2.2 COUPLED INFILL WALLS
Many infill walls contain one or more vertical rows of openings. The common
example of such a structure is the “shear core” of a building structure which
accommodates elevator shafts, stair walls and service ducts. Access doors to these
shafts pierce the walls. Thus the walls on each side of openings may be inter -
connected by short and deep beams. Such walls are referred as being- coupled by
beams.
1.6.2.3 STAGGERED PANEL INFILL WALLS
The staggered wall beam system is a framing system that tends itself well to the
reinforced concrete construction and is particularly suited to high rise residential
buildings. It offers the residential building’s designer a wide range of interesting
possibilities in both interior layout and exterior treatment at the cost competitive with
other economical forms of construction. The staggered wall-system is best suited for
rectangular plans.
1.7 OBJECTIVES OF THE STUDY
A six storey R C frame structure has been chosen for investigating the effect of blast
loads. In this present study, effect of charge weights 100 kg, 300 kg and 500 kg has
been studied in three phases. The phases are as follows:
Phase 1: Standoff distance = 30 m
Charge weight – 100 kg
Charge weight – 300 kg
Charge weight – 500 kg
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Phase 2: Standoff distance = 35 m
Charge weight – 100 kg
Charge weight – 300 kg
Charge weight – 500 kg
Phase 3: Standoff distance = 40 m
Charge weight – 100 kg
Charge weight – 300 kg
Charge weight – 500 kg
The effect of different charge weights 100 kg, 300 kg and 500 kg has been studied for
nodal displacements, velocity, acceleration and stress resultants in phase - 1, 2 and 3
for stand-off distances 30 m, 35 m and 40 m respectively.
1.8 ORGANIZATION OF THESIS WORK
The work present in the dissertation has been divided into six chapters.
Chapter 1 deals with the introduction of the subject matter, objective and scope of the
study.
Chapter 2 gives a brief review of the earlier studies carried out by various authors.
Chapter 3 deals with blast loading on structures and explosion phenomenon.
Chapter 4 deals with types of loads and their intensities considered in the analysis.
The methods of analysis and calculation of blast parameters for charge weights
considered in the present study are also discussed in this chapter.
Chapter 5 gives the discussion of the result of the present study.
Chapter 6 deals with the conclusions drawn from the present study. The scope of
work for further study has also been identified and presented in this chapter.
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CHAPTER - 2
REVIEW OF LITERATURE
2.1 GENERALIn the designing of structures to resist the effects of blast loading due to explosions or
other severe loads, it is essential to have large energy absorbing capabilities because at
the time of blast the loss of life and injuries to occupants can result from many causes,
including direct blast-effects, structural collapse, debris impact, fire, and smoke. The
indirect effects can combine to inhibit or prevent timely evacuation, thereby
contributing to additional casualties. Structural elements with large plastic deformation
capacities are therefore desirable for such loadings. Many researchers have tried to
understand the properties of blast wave by estimating the blast wave parameters for
various charge weights placed at various distances to protect the structures from
damage due to sudden impact caused by the blasts.
2.2 REVIEW OF LITERATURE
Many researchers have given their contribution to this field which has been
discussed as follows:
Luccioni et al. (2003) studied the structural failure of a reinforced concrete building
caused by the blast load and the process of the explosive charge to the complete
demolition, including the propagation of the blast wave and its intraction with the
structure was reproduced. They carried out analysis with a hydocode.
They compared the analysed problem with the actual building that suffered to a
terrorist attack and the comparison of numerical results with photographs of the real
damage produced by the explosive charge shows that the numerical analysis accurately
reproduces the collapse of building under blast load confirming the location and
magnitude of the explosion.
Albanesi et al. (2004) studied the influence of infill walls in RC frame structure
seismic response by non-linear finite element model for the seismic analysis of an
infilled frame with two no-tension struts to simulate the interaction between the RC
frame and frame with infill wall, including windows and door openings, are calibrated
on numerical evaluations. The results of this study was that the effects of windows anddoor openings including their position can be accounted for by simply introducing two
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reduction factors which apply to stiffness and strength of the current equivalent strut
defined for a whole wall panel.
Shope L. (2006) studied the response of wide flange steel columns subjected to
constant axial load and lateral blast load. The finite element program ABAQUS was
used to model with different slenderness ratio and boundary conditions. Non-uniform
blast loads were considered. Changes in displacement time histories and plastic hinge
formations resulting from varying the axial load were examined.
Calvi et al. (2006) studied the Seismic Performance of Masonry-Infilled R.C.Frames,
benefits of slight reinforcements. In their study the experimental tests have been
performed on single bay, single storey specimens, single geometry and a single design
of the concrete frame has been considered and also a single type of masonry units was
used; the numerical analyses was performed by considering a single global geometry
and a single ductility level. A push-over approach was adopted for the analyses.
Experimental and numerical results were that frames with slightly reinforced masonry
infills generally perform better than bare frames, enhanced lateral capacity and energy
dissipation provide a significantly better behaviour in terms of operational limit states
and cost of repair.
Ngo et al. (2007) studied different methods for estimation of blast load and structural
response because a bomb explosion within or immediately nearby a building would
cause catastrophic damage on the building’s external and internal structural frames,
collapsing of walls, blowing out of large expanses of windows, and shutting down of
critical life-safety systems. Loss of life and injuries to occupants can result from many
causes, including direct blast-effects, structural collapse, debris impact, fire, and
smoke. The indirect effects can combine to inhibit or prevent timely evacuation,
thereby contributing to additional casualties. In addition, major catastrophes resulting
from gas-chemical explosions result in large dynamic loads, greater than the original
design loads.
Koccaz et al. (2008) focused on blast resistant building design theories, the
enhancement of building security against the effects of explosives in both
architectural, structural design process and the design techniques. Firstly, explosives
and explosion types were explained briefly. In addition, the general aspects ofexplosion process had been presented to clarify the effects of explosives on buildings.
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They focused on essential techniques for increasing the capacity of a building to
provide protection against explosive effects for both architectural and structural
approach. During the architectural design, the behaviour under extreme compression
loading of the structural form, structural elements e.g. walls, flooring and secondary
structural elements like cladding and glazing were considered so that the structural
design after an environmental and architectural blast resistant design, as well stands
for a great importance to prevent the overall collapse of a building, with correct
selection of the structural system.
Pujol et al. (2008) observed that masonry infill walls, an effective alternative for
seismic strengthening of low-rise reinforced concrete building structures. In order to
test this hypothesis, a full-scale three-story flat-plate structure was strengthened with
infill brick walls and tested under displacement reversals. The results of this test were
compared with results from a previous experiment in which the same building was
tested without infill walls. In the initial test, the structure experienced a punching shear
failure at a slab-column connection. The addition of infill walls helped to prevent slab
collapse and increased the stiffness and strength of the structure.
Jayasooriya et al. (2009) studied the blast response and the propagation of its effects
on a two dimensional reinforced concrete (RC) frame and designed to withstand
normal gravity loads, using LS DYNA for the analysis. Complete RC portal frame
seven storeys and six bays is modelled with reinforcement details and appropriate
materials to simulate strain rate effects. Explosion loads derived from standard
manuals and applied as idealized triangular pressures on the column faces of the
numerical models.
Izadifard and Maheri (2010) studied the importance of ductility in absorbing energy
and its improving the structural behaviour. In their study, nine short steel frames with
different spans and number of storeys, subjected to different blast loading had been
investigated. Non-linear pushover blast force displacement curves were evaluated for
each frame and the ductility parameters were extracted and found that the ductility
reduction factor under blast loading increases with increasing ductility ratio,
irrespective of the period of vibration of the system.
Mahmud et al. (2010) studied the behaviour of the reinforced concrete frame with brick masonry infill due to lateral loads. In this study, the behaviour of reinforced
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concrete (R.C.) frames with brick masonry infill for various parametric changes were
studied to observe their influences in deformation patterns of the frame. In both cases
of wind and earthquake loads, if number of bay increases, then the deflection
eventually decreases. As the story level of a building frame increases, deflection due to
lateral loads naturally increases due to additional lateral loads.
Raparla and Kumar (2011) studied the linear responses of different RC bare frames
for different ranges and charge weights according to different blast loads and in the
companion paper discussed the progressive collapse of the same. Initially, the blast
loads over the frames were calculated for different ranges and charge weights
according to TM 5-1300. Later these loads were applied on the bare frames taken from
the structures which were designed for the normal gravity and lateral loads. Four
fames (one story one bay, three story one bay, five story one bay and ten story-three
bays) were considered in their study and highly efficient numerical model AEM was
used. From their results it is clear that the even though the charge weight of the blast is
increasing the response is not increasing linearly. Also the response is low for heavy
structures compared to lighter structures.
Draganić and Sigmund (2012) the aim of their study was to became familiar with the
issue of blast load because of ever growing terrorist threat and the lack of guidelines
from national and European regulations on the verification of structures exposed to
explosions and described the process of determining the blast load on structures and
provides a numerical example of a fictive structure exposed to blast load. Calculated
blast load analytically as per TM-5 1300 and determined it as pressure-time history
and numerical model of the structure was created in SAP2000 and non-liner analysis
was performed. The aim of the analysis of the structure elements exposed to blast load
was to check their demanded ductility and compare it to the available ones. This
means that non-liner analysis is necessary and simple plastic hinge behaviour is
satisfactory.
Al-Ansari (2012) studied the response of buildings to blast and earthquake loadings
for the purpose of deriving a relationship in the form of formulae and charts between
blast and earthquake loads. He concluded from the analysis results that the responses
of the simulated models with different heights and standing off distances to blast
loading shows that the responses of building models to blast loads at the same
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standing-off distance are very close to each other. The building height was found to
have a small impact in structure responses to blast load. However it had a strong
impact on building responses due to earthquake load. The relationships derived by him
between blast and earthquake loads were used to compute equivalent earthquake
ground acceleration to a blast load on any building given the intensity of the blast, the
stand-off distance and the building height. Once the earthquake ground acceleration is
known the codes of design methodology could be easily used to determine the lateral
forces and design the building members accordingly.
Goel et al. (2012) studied empirical relations and calculation of blast load parameters.
Their study divided in two parts, in first part they includes various empirical relations
for calculation of blast load in the form of pressure time function resulting from the
explosion in the air. In second part these empirical techniques and charts were used for
calculation of various blast wave parameters.
Jayashree et al. (2013) studied the dynamic response of a space framed structure due
to blast load. In their study an attempt had been made to use slurry infiltrated fiber
reinforced concrete (SIFCON), a type of FRC with high fibre content as an alternative
material to reinforced cement concrete (RCC). Space framed models were developed
and time history analysis was carried out for blast load using the software package
SAP-2000 and derived the properties of SIFCON and RCC from the experiments.
Evaluated the dynamic characteristics such as fundamental frequency, mode shapes
and compared the displacement time history response of frames with SIFCON and
RCC due to blast load.
Samoila (2013) studied on seismic behaviour of masonry infill panels by analytical
modelling. The study present three one- bay, one- story frames, for which the diagonal
strut width and the strength to different failure types were determined. The effects of
the masonry infill panels upon the seismic behaviour of the frames structures were
rendered by the capacity curves obtained from the push-over analysis carried out on a
series of concrete frames with different number of stories.
Hirde and Bhoite (2013) analysed the effect of modelling of infill walls on the
performance of multi-storeyed RC building. Nonlinear static pushover analysis of
multi storey frame was carried out considering it as bare frame. The pushover analysisof same frame was carried out by modelling the infill walls for throughout the height
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and for modelling the infill walls excluding ground storey so as to make it as soft
storey. The results of bare frame analysis and frame with infill effects were compared
in the form of capacity spectrum curve, performance point and hinge formation at
performance point. It was seen that the masonry infill contribute significant lateral
stiffness, strength, overall ductility and energy dissipation capacity.
Kulkarni and Sambireddy (2014) studied the dynamic response of high rise regular
and irregular structures subjected to blast load. The fundamentals of blast hazards and
the interaction of blast waves with structures were examined in their study for the
lateral stability of a high rise building. The model building was subjected to two
different charge weights of 800 lbs and 1600 lbs TNT at a two different standoff
distances. The blast loads were calculated using the methods outlined in section 5 of
TM5-1300 and used nonlinear modal analysis for the dynamic load of the blast using
SAP-2000 and also studied the behaviour of R.C frame and concrete infill frame in
dynamic condition.
Kashif and Varma (2014) studied the effect of Blast loading on a five storey RCC
symmetric building. They analysed the building for blast load of TNT placed at a
distance of 30 m and calculated the blast load using code IS 4991-1968 as function of
pressure-time history. Numerical model of the structure was created in SAP-2000. The
influence of the lateral load response due to blast in terms of peak deflections,
velocity, accelerations, inter storey drift was calculated and compared.
Shallan et al (2014) numerically simulate the effects of blast loads on three buildings
with different aspect ratios. Used finite element models of these buildings were
developed using the finite element program AUTODYN. Blast loads located at two
different locations and spaced from the building with different standoff distances were
applied. The simulations of their study revealed that the effect of blast load decrease
with increasing the standoff distance from the building and with variation the aspect
ratios of the buildings there were no variation in the displacement of the column in the
face of the blast load but with increasing the aspect ratio the effect of blast load
decrease in other element in the building.
Abdallah and Osman (2014) studied the explosion phenomena and its load behaviour
on steel structure. Considered a steel structure which was subjected to blast loads withdifferent charge weights of 10 kg, 50 kg and 100 kg at 4.5 m standoff distance on same
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building situation, the main parameters considered in their study were displacement,
terrorist threat and demand capacity ratio (D/C). They calculated the reflected pressure
and the duration time using the code of U.S Army TM 5-1300. The blast load was
determined as pressure-time history and then the pressure-time history functions
defined for each member by using SAP-2000 software.
Singh et al (2014) studied various loading which can occur during a blast i.e, the
dynamic impact loading, varying rate concentrated loading and transverse blast
loading and the methods applied to analyze these loading. Compared the results with
Single Degree of Freedom (SDOF) model, those were obtained from Finite Element
Model (FEM) and non-linear dynamic analysis and discussed the suitability.
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CHAPTER - 3
BLAST LOAD ON STRUCTURES
3.1 GENERAL
An explosion is a phenomenon in which energy is released in a very fast and violent
manner and is accompanied by the release of gasses and generation of high
temperatures. There are different type of explosion; nuclear, physical and chemical.
Explosions due to volcanic eruption are classified as natural. Chemical explosion are
the most common type of artificial explosives that can occur accidentally or caused by
the terrorist attacks. Chemical explosives are generally in the form of solids or liquids.
In chemical explosion oxidation reactions takes place at very rate and generate
pressure waves, also called blast waves. The duration of blast waves only for few
milliseconds. The sudden release of energy initiates a pressure wave in the
surrounding medium, known as a shock wave as shown in Fig. 3.1. When an explosion
takes place, the expansion of the hot gases produces a pressure wave in the
surrounding air. As this wave moves away from the centre of explosion, the inner part
moves through the region that was previously compressed and is now heated by the
leading part of the wave.
Fig. 3.1 Variation of pressure with distance
After a short period of time the pressure wave front becomes abrupt, thus forming a
shock front somewhat similar to Fig. 3.2. The maximum overpressure occurs at the
shock front and is called the peak overpressure. Behind the shock front, the
overpressure drops very rapidly to about one-half the peak overpressure and remains
almost uniform in the central region of the explosion.
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Fig. 3.2 Formation of shock front in a shock wave
An expansion precedes, the overpressure in the shock front decreases steadily; the
pressure behind the front does not remain constant, fall off in a regular manner. After a
short time, at a certain distance from the centre of explosion, the pressure behind the
shock front becomes smaller than that of the surrounding atmosphere and so called
negative-phase or suction. The front of the blast waves weakens as it progresses
outward, and its velocity drops towards the velocity of the sound in the undisturbed
atmosphere. This sequence of events is shown in Fig. 3.3, the overpressure at time t 1,
t2…..t6 are indicated.
Fig. 3.3 Variation of overpressure with distance from centre of explosion at
various times
Complexity in the analysis of dynamic response of blast-loaded structures involves the
effect of high strain, the non-linear inelastic material behaviour, the uncertainties in
the blast load calculations and the time-dependent deformations. Therefore, to simplify
the analysis, a number of assumptions related to it and the loads has been proposed
and widely adopted. To establish general principles of this analysis, the structure is
idealized as a single degree of freedom (SDOF) system and the relationship between
the positive duration of the blast load and the natural period of vibration of the
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structure is established. This leads to blast load idealization and simplifies the
classification of the blast loading.
3.2 ELASTIC SDOF SYSTEMS
The simplest discretization of transient problems is by means of the SDOF approach.
The original structure can be replaced by an equivalent system of one lumped mass
and one weightless spring represents the resistance of the structure against
deformation. Such an idealized system is illustrated in Fig.3.4. The structural mass
‘M’ is under the effect of an external force F(t) and the structural resistance ‘R m’ is
expressed in terms of the vertical displacement ‘y’ and the spring constant ‘K’. The
blast load can also be idealized as a triangular pulse having a peak force Fm and
positive phase duration td (see Fig. 3.4). The forcing function is given as
F(t) = Fm(1 -
) ..................................................... (3.1)
The equation of motion of the un-damped elastic SDOF system for a time ranging
from 0 to the positive phase duration td is given by Biggs as follows
Mÿ + Ky = F(t) ........................................................ (3.2)
where
ÿ = Acceleration (Double derivative of displacement)
y = Displacement
the general solution can be expressed as
Displacement y(t) =
) ........................(3.3)
Velocity ẏ(t) = dy/dt =
...................... (3.4)
In above ‘ω’ is the natural frequency of vibration of the structure and ‘T’ is the natural
period of vibration of the structure which is given by
ω = ................................................. (3.5)
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Fig. 3.4 (a) SDOF system and (b) blast loading
The maximum response is defined by the maximum dynamic deflection ymax which
occurs at time tm
. The maximum dynamic deflection ymax
can be evaluated by setting
dy/dt in Equation 3.3 equal to zero, i.e. when the structural velocity is zero. The
dynamic amplification factor (DAF) is defined as the ratio of the maximum dynamic
deflection ymax to the static deflection ystatic which would have resulted from the static
application of the peak load Fm, which is shown as follow
The structural responses to blast loading is significantly influenced by the ratio t d/T or
ωtd (td / T = ωtd/ 2π ). Three loading regimes are categorized as follows:
- ωtd < 0.4 : impulse loading resime.
- ωtd < 0.4 : quasi-static resime.
- 0.4 < ωtd < 40 : dynamic loading resime
Fig. 3.5 Simplified resistance function of an elasto-plastic SDOF system
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3.3 CALCULATION OF BLAST LOADING
3.3.1 CALCULATION OF BLAST PARAMETERS
Calculation of blast parameters produced by the explosion sock front waves such as
Peak reflected overpressure, Dynamic pressure, Peak side-on pressure on structure as
per IS:4991-1968 are as follows.
Step 1: Determine the explosive weight as equivalent to TNT weight ‘W’ in tonnes
which is used as charge.
Step 2: Determine the Standoff distance / actual distance ‘Z’ of the point measured
from ground zero to the point under consideration.
Step 3: Determine the charge height at which it is placed above the ground surface.
Step 4: Determine the structural dimensions.
Step 5: Select different points on the structure (front face, roof, side and rear face) and
calculate the explosion parameters for each selected point.
i) Calculate the scaled distance ‘X’ as per scaling law.
Scaled distance ‘X’ = ........................................ (4.1)
ii) Determine the explosion’s parameters using Table 1 of IS:4991-1968 for above
calculated scaled distance ‘X’ and read the values.
a) Peak side-on overpressure Pso.
b) Peak reflected overpressure Pro.
c) Dynamic pressure qo.
d)
Mach number M.e) Positive phase duration to milliseconds (millisecond).
f) Duration of equivalent triangular pulse td milliseconds (millisecond).
The values scaled times to and td obtained from the Table 1 of code IS: 4991-1968 for
scaled distance ‘X’ are multiplied by to obtain the absolute values for actualexplosion of W tonnes charge weight.
Step 6: Net pressure acting on the front face of the structure at any time ‘t’ is
maximum of Pr or ( Pso + Cd.qo ).
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where
Cd = Value of drag coefficient given in Table 2 of IS:4991-1968.
Pr = Reflected overpressure which decrease from Pro to overpressure in
clearance time tc.
Step 7: Pressure on rear face is depends on time intervals are as follows.
i) Clearance time (tc) = 3S/U
ii) Travel time of shock wave from front face to rear face i.e transit time (tt) = L/U
iii) Pressure rise time on back face (tr ) = 4S/U
where
S = Height ‘H’ or half of the width ‘B/2’ whichever is less
U = Shock front velocity = M.a
a = velocity of sound in air may be taken as 344 m/sec at mean sea level
at 20 oc.
M = Mach number of the incident pulse.
= Decay of pressure with time is given by
Ps = Pso (1 -
) ............................................... (4.2)
q = qo (1 -
)2 ............................................... (4.3)
If pressure rise time is more than duration of equivalent triangular pulse, there will be
no pressure on rear face of the structure.
i.e {tr > td ; no pressure on rear face}
3.4 INFILLS MODELLING
3.4.1 EQUIVALENT STRUT METHOD
In this method, the analysis is carried out by simulating the action of infills similar to
that of diagonal struts bracing the frame. The infills are replaced by an equivalent strut
of length D and width Wef as shown in Fig. 3.6.
Pulay and Preistley (1992) suggested a conservative value useful for design proposal
given by.
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Wef = 0.25D.................................................... (3.7)
Fig. 3.6 Equivalent diagonal strut model
3.5 LOADS CONSIDERED IN THE ANALYSIS
The following loads are considered for the analysis of various phases of structure.
3.5.1 GRAVITY LOADS
The intensity of dead load and live load considered in the study are given below:
Dead loads
Dead load comprising of self-weight of members i.e. Beam, Column and Slab
and infill walls.
Live load
Live load of 4 KN/m2 on floor area.
3.5.2 BLAST LOADS
IS 4991-1968 is used for blast load calculations. The maximum values of the
positive side-on overpressure (Pso), reflected over pressure (Pro) and dynamic
pressure (qo), as caused by the explosion of one tonne explosive at various
distances from the point of explosion, are given in Table 1. And also the
duration of the positive phase of the blast to, and the equivalent time duration
of positive phase td are given in Table 1.
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3.6 ANALYSIS OF FRAMED BUILDING
In the present study a six storied building was modelled and analysed. The
three different cases have different values of Z and W has been considered for
present study. In the first case stand-off distance is taken as 30 m and the
different values of charge weights 100 kg, 300 kg and 500 kg while in case 2 nd
the stand-off distance is taken as 35 m and the different values of charge
weights 100 kg, 300 kg and 500 kg. In case 3nd the stand-off distance is taken
as 40 m and the different values of charge weights 100 kg, 300 kg and 500 kg.
The modelling and analysis of building subjected to blast loading was carried
out using software Staad-pro V8i. The blast forces which are acting on
contributing nodes are calculated in chapter-4.
Defining time history function
Fig. 3.7 Time history definition for force with time
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CHAPTER – 4
CALCULATION OF BLAST PARAMETERS
4.1 GENERAL
A six storey building has been chosen for investigating the effect of blast load in RC
frame structure with masonry in-filled walls at the periphery of the building.
The present work has been divided into three Phases, Phase 1, 2 and 3.
Phase 1: Standoff distance = 30 m
Charge weight - 100 kg
Charge weight - 300 kg
Charge weight - 500 kg
Phase 2: Standoff distance = 35 m
Charge weight - 100 kg
Charge weight - 300 kg
Charge weight - 500 kg
Phase 3: Standoff distance = 40 m
Charge weight - 100 kg
Charge weight - 300 kg
Charge weight - 500 kg
4.2 DESCRIPTION OF BUILDING
A six storey RC frame building with 18.0 m height situated in seismic zone IV has
been considered for the purpose of present study.
(i) Floor to floor height = 3.0 m
(ii)
Thickness of masonry infill walls = 230 mm(iii) Size of Columns = 500 mm × 500 mm
(iv) Size of Beam = 450 mm × 500 mm
(v) Thickness of slab = 150 mm
4.3 MATERIAL PROPERTIES
4.3.1 PROPERTIES OF RCC
(i) Characteristic compressive strength (f ck ) = 20 MPa
(ii) Poisson Ratio = 0.2
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(iii) Density = 25 kN/m3
(iv) Modulus of Elasticity (E) = 5000 = 22360.67 MPa(v) Damping = 0.05
4.3.2 PROPERTIES OF BRICK MASONRY (FOR INFILL WALL)
(i) Modulus of Elasticity (E) = 550 × f m
(Where f m is compressive strength of brick masonry; refer to FEMA - 273)
Crushing strength of bricks f m = 4 N/mm2
So, E = 2200 N/mm2
(ii) Poisson’s ratio (μ) = 0.15 to 0.2
(iii) Density (ρ) = 20 kN/m3
(iv) Damping = 0.05
Plan and elevation of the building in phase – 1, 2 and 3 are shown in figure 4.1 and
4.2.
Fig. 4.1 Plan of building
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Fig. 4.2 Elevation of building
4.4 BLAST PRESSURE PARAMETERS (AS PER IS:4991-1968)
4.4.1 PHASE - 1
4.4.1.1 CASE - 1 Charge weight (TNT) W= 100 Kg or 0.1 Tonne
Scaled distance ‘X’ =
=
= 64.65 m/tonne1/3
So values of to and td from Table 1 of IS:4991-1968
to = 37.71× = 17.5 millisecondstd = 28.32× = 13.15 millisecondsPressure on rear face:
S = H or B/2 (whichever is less) = 8 m.
U = M.a = 1.1369×344 = 391.09 where {M = 1.1369, a = 344 m/sec}
Clearance time tc = 3S/U
= 3×8/391.09 = 0.06136 sec = 61.36 milliseconds
Transit time tt = L/U
= 16/391.09 = 0.0409 sec = 40.9 milliseconds
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Pressure rise time tr = 4S/U
= 4×8/391.09 = 0.08181 sec = 81.81 milliseconds
Here tc > td, tt > td and tr > td
As tr > td no pressure on rear face.
Pressure on front face:
i) For 0.0 m height
a) For exterior nodes (1, 141)
Actual distance Z = 31.085 m
Scaled distance X = = 66.96 m/tonne
1/3
For X= 66.96, refer Table 1 of IS:4991-1968 and read values of to, td, Pso and Pro
to = {(38.05 +
)×(66.97 – 66)}× = 17.78 millisecondtd = {(28.76 +
)×(66.97 – 66)}× = 13.42 millisecond
Total positive phase = to + td = 17.78 + 13.42 = 31.20 millisecond
Pso = {(0.34 -
)×(66.97 – 66)}×100 = 33.35 kN/m2
Pro = {(0.77 - )×(66.97 – 66)}×100 = 75.38 kN/m2
Forces on exterior nodes = peak reflected overpressure × area
= 75.38 × (0.25 × 12) = 226.15 kN
b) For interior nodes (36, 106)
Actual distance Z = 30.303 m
Scaled distance X = = 65.29 m/tonne1/3
For X= 65.29, refer Table 1 of IS:4991-1968 and read values of to, td, Pso and Pro
to = {(37.30 +
)×(65.29 – 63)}× = 17.58 millisecondtd = {(27.8 +
)×(65.29 – 63)}× = 13.24 millisecond
Total positive phase = to + td = 17.58 + 13.24 = 30.82 millisecond
Pso = {(0.37 -
)×(65.29 – 63)}×100 = 34.71 kN/m
2
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Pro = {(0.85 -
)×(65.29 – 63)}×100 = 78.91 kN/m2
Forces on exterior nodes = peak reflected overpressure × area
= 78.91 × (0.5 × 12) = 473.44 kN
c) For interior node (71)
Actual distance Z = 30.037 m
Scaled distance X = = 64.71 m/tonne
1/3
For X=64.71, refer Table 1 of IS:4991-1968 and read values of to, td, Pso and Pro
to = {(37.30 +
)×( 64.71 – 63)}× = 17.51 millisecondtd = {(27.8 +
)×( 64.71 – 63)}× = 13.16 millisecond
Total positive phase = to + td = 17.51 + 13.16 = 30.67 millisecond
Pso = {(0.37 -
)×( 64.71 – 63)}×100 = 35.29 kN/m2
Pro = {(0.85 -
)×( 64.71 – 63)}×100 = 80.43 kN/m2
Forces on exterior nodes = peak reflected overpressure × area
= 80.43 × (0.5 × 12) = 473.44 kN
ii) For 3.0 m height
a) For exterior nodes (6, 146)
Actual distance Z = 31.085 m
Scaled distance X = = 66.97 m/tonne
1/3
For X= 66.97, refer Table 1 of IS:4991-1968 and read values of to, td, Pso and Pro
to = {(38.05 +
)×(66.97 – 66)}× = 17.78 millisecondtd = {(28.76 +
)×(66.97 – 66)}× = 13.42 millisecond
Total positive phase = to + td = 17.78 + 13.42 = 31.20 millisecond
Pso = {(0.34 -
)×(66.97 – 66)}×100 = 33.35 kN/m2
Pro = {(0.77 - )×(66.97 – 66)}×100 = 75.38 kN/m2
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Forces on exterior nodes = peak reflected overpressure × area
= 75.38 × (0.5 × 12) = 452.58 kN
b) For interior nodes (41, 111)
Actual distance Z = 30.303 m
Scaled distance X = = 65.29 m/tonne
1/3
For X= 65.29, refer Table 1 of IS:4991-1968 and read values of to, td, Pso and Pro
to = {(37.30 +
)×(65.29 – 63)}× = 17.58 millisecondtd = {(27.8 +
)×(65.29 – 63)}× = 13.24 millisecond
Total positive phase = to + td = 17.58 + 13.24 = 30.82 millisecond
Pso = {(0.37 -
)×(65.29 – 63)}×100 = 34.71 kN/m2
Pro = {(0.85 -
)×(65.29 – 63)}×100 = 78.91 kN/m2
Forces on exterior nodes = peak reflected overpressure × area
= 78.91 × (1.0 × 12) = 946.88 kN
c)
For interior node (76)
Actual distance Z = 30.037 m
Scaled distance X = = 64.71 m/tonne
1/3
For X=64.71, refer Table 1 of IS:4991-1968 and read values of to, td, Pso and Pro
to = {(37.30 +
)×( 64.71 – 63)}× = 17.51 millisecond
td = {(27.8 +
)×( 64.71 – 63)}× = 13.16 millisecond
Total positive phase = to + td = 17.51 + 13.16 = 30.67 millisecond
Pso = {(0.37 -
)×( 64.71 – 63)}×100 = 35.29 kN/m2
Pro = {(0.85 -
)×( 64.71 – 63)}×100 = 80.43 kN/m2
Forces on exterior nodes = peak reflected overpressure × area
= 80.43 × (1.0 × 12) = 965.16 kN
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iii) For 6.0 m height
a) For exterior nodes (11, 151)
Actual distance Z = 31.373 m
Scaled distance X = = 67.97 m/tonne1/3
For X= 67.97, refer Table 1 of IS:4991-1968 and read values of to, td, Pso and Pro
to = {(38.05 +
)×(67.97 – 66)}× = 17.85 millisecondtd = {(28.76 +
)×(67.97 – 66)}× = 13.47 millisecond
Total positive phase = to + td = 17.85 + 13.47 = 31.32 millisecond
Pso = {(0.34 - )×(67.97 – 66)}×100 = 32.94 kN/m2
Pro = {(0.77 -
)×(67.97 – 66)}×100 = 74.35 kN/m2
Forces on exterior nodes = peak reflected overpressure × area
= 74.35 × (0.5 × 12) = 446.09
b) For interior nodes (46,116)
Actual distance Z = 30.598 m
Scaled distance X = = 65.92 m/tonne
1/3
For X= 65.92, refer Table 1 of IS:4991-1968 and read values of to, td, Pso and Pro
to = {(37.30 +
)×(65.92 – 63)}× = 17.65 millisecondtd = {(27.8 +
)×(65.92 – 63)}× = 13.34 millisecond
Total positive phase = to + td = 17.58 + 13.24 = 30.99 millisecond
Pso = {(0.37 -
)×(65.92 – 63)}×100 = 34.08 kN/m2
Pro = {(0.85 -
)×(65.92 – 63)}×100 = 77.21 kN/m2
Forces on exterior nodes = peak reflected overpressure × area
= 77.21 × (1.0 × 12) = 926.50 kN
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c) For interior node (81)
Actual distance Z = 30.336 m
Scaled distance X = = 65.36 m/tonne
1/3
For X=65.36, refer Table 1 of IS:4991-1968 and read values of to, td, Pso and Pro
to = {(37.30 +
)×( 65.36 – 63)}× = 17.59 millisecondtd = {(27.8 +
)×( 65.36 – 63)}× = 13.25 millisecond
Total positive phase = to + td = 17.59 + 13.25 = 30.84 millisecond
Pso = {(0.37 -
)×( 65.36 – 63)}×100 = 34.64 kN/m2
Pro = {(0.85 - )×( 65.36 – 63)}×100 = 78.72 kN/m2
Forces on exterior nodes = peak reflected overpressure × area
= 78.72 × (1.0 × 12) = 944.60 kN
Similarly we calculate all the values interpolating directly from Table-1 for 9.0 m,
12.0 m, 15.0 m and 18.0 m heights are as follows
iv)
For 9.0 m height
a) For exterior nodes (16,156)
Actual distance Z = 31.941 m
Scaled distance X = 68.82 m/tonne1/3
For X=68.82, refer Table 1 of IS:4991-1968 and read values of to, td, Pso and Pro
Arrival time to = 17.99 millisecond
Equivalent triangular phase td = 13.56 millisecond
Total positive phase = to + td = 17.99 + 13.56 = 31.55 millisecond
Peak side-on overpressure Pso = 32.12 kN/m2
Peak reflected overpressure Pro = 72.31 kN/m2
Forces on exterior nodes = peak reflected overpressure × area
= 72.31 × (0.5 × 12) = 433.84 kN
b) For interior nodes (51,121)
Actual distance Z = 31.181 m
Scaled distance X = 67.10 m/tonne1/3
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For X=67.10, refer Table 1 of IS:4991-1968 and read values of to, td, Pso and Pro
Arrival time to = 17.80 millisecond
Equivalent triangular phase td = 13.44 millisecond
Total positive phase = to + td = 17.80 + 13.44 = 31.24 millisecond
Peak side-on overpressure Pso = 33.22 kN/m2
Peak reflected overpressure Pro = 75.04 kN/m2
Forces on exterior nodes = peak reflected overpressure × area
= 75.04 × (1.0 × 12) = 900.45 kN
c) For interior node (86)
Actual distance Z = 30.923 m
Scaled distance X = 66.62 m/tonne1/3
For X=66.62, refer Table 1 of IS:4991-1968 and read values of to, td, Pso and Pro
Arrival time to = 17.73 millisecond
Equivalent triangular phase td = 13.40 millisecond
Total positive phase = to + td = 17.73 + 13.40 = 31.13 millisecond
Peak side-on overpressure Pso = 33.59 kN/m2
Peak reflected overpressure Pro = 75.96 kN/m2
Forces on exterior nodes = peak reflected overpressure × area= 75.96 × (1.0 × 12) = 911.56 kN
v) For 12.0 m height
a) For exterior nodes (21,161)
Actual distance Z = 32.776 m
Scaled distance X = 70.61 m/tonne1/3
For X=70.61, refer Table 1 of IS:4991-1968 and read values of to, td, Pso and Pro
Arrival time to = 18.20 millisecond
Equivalent triangular phase td = 13.73 millisecond
Total positive phase = to + td = 18.20 + 13.73 = 31.93 millisecond
Peak side-on overpressure Pso = 30.92 kN/m2
Peak reflected overpressure Pro = 69.31 kN/m2
Forces on exterior nodes = peak reflected overpressure × area
= 69.31 × (0.5 × 12) = 415.87 kN
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b) For interior nodes (56,126)
Actual distance Z = 32.035 m
Scaled distance X = 69.02 m/tonne1/3
For X=69.02, refer Table 1 of IS:4991-1968 and read values of to, td, Pso and Pro
Arrival time to = 18.02 millisecond
Equivalent triangular phase td = 13.58 millisecond
Total positive phase = to + td = 18.02 + 13.58 = 31.59 millisecond
Peak side-on overpressure Pso = 31.99 kN/m2
Peak reflected overpressure Pro = 71.97 kN/m2
Forces on exterior nodes = peak reflected overpressure × area
= 71.97 × (1.0 × 12) = 863.65 kN
c) For interior node (91)
Actual distance Z = 31.784 m
Scaled distance X = 68.48 m/tonne1/3
For X=68.48, refer Table 1 of IS:4991-1968 and read values of to, td, Pso and Pro
Arrival time to = 17.95 millisecond
Equivalent triangular phase td = 13.54 millisecond
Total positive phase = to + td = 17.95 + 13.540 = 31.49 millisecondPeak side-on overpressure Pso = 33.59 kN/m
2
Peak reflected overpressure Pro = 75.96 kN/m2
Forces on exterior nodes = peak reflected overpressure × area
= 75.96 × (1.0 × 12) = 911.56 kN
vi) For 15.0 m height
a) For exterior nodes (26,166)
Actual distance Z = 33.856 m
Scaled distance X = 72.94 m/tonne1/3
For X=72.94, refer Table 1 of IS:4991-1968 and read values of to, td, Pso and Pro
Arrival time to = 18.47 millisecond
Equivalent triangular phase td = 13.99 millisecond
Total positive phase = to + td = 18.47 + 13.99 = 32.46 millisecond
Peak side-on overpressure Pso = 29.37 kN/m2
Peak reflected overpressure Pro = 65.43 kN/m2
Forces on exterior nodes = peak reflected overpressure × area
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= 65.43 × (0.5 × 12) = 392.59 kN
b) For interior nodes (61,131)
Actual distance Z = 33.140 m
Scaled distance X = 71.40 m/tonne1/3
For X=71.40, refer Table 1 of IS:4991-1968 and read values of to, td, Pso and Pro
Arrival time to = 18.29 millisecond
Equivalent triangular phase td = 13.81 millisecond
Total positive phase = to + td = 18.29 + 13.81 = 32.10 millisecond
Peak side-on overpressure Pso = 30.40 kN/m2
Peak reflected overpressure Pro = 68.00 kN/m2
Forces on exterior nodes = peak reflected overpressure × area
= 68.00 × (1.0 × 12) = 816.05 kN
c) For interior node (96)
Actual distance Z = 32.898 m
Scaled distance X = 70.88 m/tonne1/3
For X=70.88, refer Table 1 of IS:4991-1968 and read values of to, td, Pso and Pro
Arrival time to = 18.23 millisecond
Equivalent triangular phase td = 13.76 millisecond
Total positive phase = to + td = 18.23 + 13.76 = 31.99 millisecond
Peak side-on overpressure Pso = 30.75 kN/m2
Peak reflected overpressure Pro = 68.87 kN/m2
Forces on exterior nodes = peak reflected overpressure × area
= 68.87 × (1.0 × 12) = 826.49 kN
vii) For 18.0 m height
a) For exterior nodes (31,171)
Actual distance Z = 35.16 m
Scaled distance X = 75.75 m/tonne1/3
For X=75.75, refer Table 1 of IS:4991-1968 and read values of to, td, Pso and Pro
Arrival time to = 18.77 millisecond
Equivalent triangular phase td = 14.39 millisecond
Total positive phase = to + td = 18.77 + 14.39 = 33.16 millisecond
Peak side-on overpressure Pso = 27.50 kN/m2
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Peak reflected overpressure Pro = 61.00 kN/m2
Forces on exterior nodes = peak reflected overpressure × area
= 61.00 × (0.25 × 12) = 183.00 kN
b)
For interior nodes (66,136)
Actual distance Z = 34.47 m
Scaled distance X = 74.27 m/tonne1/3
For X=74.27, refer Table 1 of IS:4991-1968 and read values of to, td, Pso and Pro
Arrival time to = 18.63 millisecond
Equivalent triangular phase td = 14.16 millisecond
Total positive phase = to + td = 18.63 + 14.16 = 32.10 millisecond
Peak side-on overpressure Pso = 28.49 kN/m2
Peak reflected overpressure Pro = 63.22 kN/m2
Forces on exterior nodes = peak reflected overpressure × area
= 63.22 × (0.5 × 12) = 379.34 kN
c) For interior node (101)
Actual distance Z = 34.238 m
Scaled distance X = 73.76 m/tonne1/3
For X=73.76, refer Table 1 of IS:4991-1968 and read values of to, td, Pso and Pro
Arrival time to = 18.57 millisecond
Equivalent triangular phase td = 14.09 millisecond
Total positive phase = to + td = 18.57 + 14.09 = 32.66 millisecond
Peak side-on overpressure Pso = 28.82 kN/m2
Peak reflected overpressure Pro = 64.06 kN/m2
Forces on exterior nodes = peak reflected overpressure × area
= 64.06 × (0.5 × 12) = 384.36 kN
As the height of structure increases, Scaled distance increases and peak
reflected overpressure Pro, peak static overpressure Pso decreases corresponding to
scaled distance whereas the values of arrival time to (millisecond) and equivalent
triangular phase td (millisecond) increases by some amount. The blast parameters
along the height of the building are given in Table 4.1.
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TABLE 4.1 BLAST PARAMETERS FOR W = 100 Kg AT Z = 30 m
H Nodes Scaled
Distance
X
to
milli-
second
td
milli-
second
to+td
milli-
second
Pso
kN/m2
ProkN/m
2A
m2
Force
kN
0
1 66.97 17.78 13.42 31.20 33.35 75.38 3 226.15
36 65.29 17.58 13.24 30.82 34.71 78.91 6 473.44
71 64.71 17.51 13.16 30.67 35.29 80.43 6 482.58
106 65.29 17.58 13.24 30.82 34.71 78.91 6 473.44
141 66.97 17.78 13.42 31.20 33.35 75.38 3 226.15
3
6 66.97 17.78 13.42 31.20 33.35 75.38 6 452.30
41 65.29 17.58 13.24 30.82 34.71 78.91 12 946.88
76 64.71 17.51 13.16 30.67 35.29 80.43 12 965.16
111 65.29 17.58 13.24 30.82 34.71 78.91 12 946.88
146 66.97 17.78 13.42 31.20 33.35 75.38 6 452.30
6
11 67.59 17.85 13.47 31.32 32.94 74.35 6 446.09
46 65.92 17.65 13.34 30.99 34.08 77.21 12 926.50
81 65.36 17.59 13.25 30.84 34.64 78.72 12 944.60
116 65.92 17.65 13.34 30.99 34.08 77.21 12 926.50
151 67.59 17.85 13.47 31.32 32.94 74.35 6 446.09
9
16 68.82 17.99 13.56 31.55 32.12 72.31 6 433.84
51 67.18 17.80 13.44 31.24 33.22 75.04 12 900.45
86 66.62 17.73 13.40 31.13 33.59 75.96 12 911.56
121 67.18 17.80 13.44 31.24 33.22 75.04 12 900.45
156 68.82 17.99 13.56 31.55 32.12 72.31 6 433.84
12
21 70.61 18.20 13.73 31.93 30.92 69.31 6 415.87
56 69.02 18.02 13.58 31.59 31.99 71.97 12 863.65
91 68.48 17.95 13.54 31.49 32.35 72.87 12 874.45
126 69.02 18.02 13.58 31.59 31.99 71.97 12 863.65
161 70.61 18.20 13.73 31.93 30.92 69.31 6 415.87
15
26 72.94 18.47 13.99 32.46 29.37 65.43 6 392.5961 71.40 18.29 13.81 32.10 30.40 68.00 12 816.05
96 70.88 18.23 13.76 31.99 30.75 68.87 12 826.49
131 71.40 18.29 13.81 32.10 30.40 68.00 12 816.05
166 72.94 18.47 13.99 32.46 29.37 65.43 6 392.59
18
31 75.75 18.77 14.39 33.16 27.50 61.00 3 183.00
66 74.27 18.63 14.16 32.79 28.49 63.22 6 379.34
106 73.76 18.57 14.09 32.66 28.82 64.06 6 384.36
136 74.27 18.63 14.16 32.79 28.49 63.22 6 379.34
171 75.75 18.77 14.39 33.16 27.50 61.00 3 183.00
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TABLE 4.2 BLAST PARAMETERS FOR W = 300 Kg AT Z = 30 m
H Nodes Scaled
distance
X
to
milli-
second
td
milli-
second
to+td
milli-
second
Pso
kN/m2
Pro
kN/m2
A
m2
Force
kN
0
1 46.43 21.24 14.81 36.05 62.65 156.44 3 469.32
36 45.27 20.98 14.53 35.50 65.38 164.23 6 985.35
71 44.87 20.88 14.42 35.30 66.43 167.34 6 1004.06
106 45.27 20.98 14.53 35.50 65.38 164.23 6 985.35
141 46.43 21.24 14.81 36.05 62.65 156.44 3 469.32
3
6 46.43 21.24 14.81 36.05 62.65 156.44 6 938.63
41 45.27 20.98 14.53 35.50 65.38 164.23 12 1970.71
76 44.87 20.88 14.42 35.30 66.43 167.34 12 2008.12
111 45.27 20.98 14.53 35.50 65.38 164.23 12 1970.71
146 46.43 21.24 14.81 36.05 62.65 156.44 6 938.63
6
11 46.86 21.34 14.92 36.26 61.65 153.57 6 921.41
46 45.71 21.08 14.63 35.71 64.35 161.28 12 1935.39
81 45.32 20.99 14.54 35.53 65.26 163.90 12 1966.77
116 45.71 21.08 14.63 35.71 64.35 161.28 12 1935.39
151 46.86 21.34 14.92 36.26 61.65 153.57 6 921.41
9
16 47.71 21.53 15.13 36.66 59.67 147.91 6 887.44
51 46.58 21.28 14.85 36.12 62.32 155.48 12 1865.75
86 46.19 21.19 14.75 35.94 63.22 158.04 12 1896.54
121 46.58 21.28 14.85 36.12 62.32 155.48 12 1865.75
156 47.71 21.53 15.13 36.66 59.67 147.91 6 887.44
12
21 48.96 21.87 15.41 37.28 57.08 140.24 6 841.42
56 47.85 21.56 15.16 36.72 59.34 146.97 12 1763.67
91 47.48 21.48 15.07 36.55 60.21 149.47 12 1793.63
126 47.85 21.56 15.16 36.72 59.34 146.97 12 1763.67
161 48.96 21.87 15.41 37.28 57.08 140.24 6 841.42
15
26 50.57 22.32 15.77 38.09 53.85 130.55 6 783.31
61 49.50 22.02 15.53 37.55 55.99 136.97 12 1643