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











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


5.2.2 Velocity ........................................................................................................ 58

5.2.3 Acceleration ................................................................................................. 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


5.3.2 Velocity ........................................................................................................ 67

5.3.3 Acceleration ................................................................................................. 67


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 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:


Charge weight – 100 kg




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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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15

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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16

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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17

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.













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)


Scaled distance X = = 65.29 m/tonne1/3


to = {(37.30 +

)×(65.29 – 63)}× = 17.58 millisecondtd = {(27.8 +

)×(65.29 – 63)}× = 13.24 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


= 78.91 × (0.5 × 12) = 473.44 kN

c) For interior node (71)



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


Pso = {(0.37 -

)×( 64.71 – 63)}×100 = 35.29 kN/m2

Pro = {(0.85 -

)×( 64.71 – 63)}×100 = 80.43 kN/m2


= 80.43 × (0.5 × 12) = 473.44 kN

ii) For 3.0 m height




1/3


to = {(38.05 +

)×(66.97 – 66)}× = 17.78 millisecondtd = {(28.76 +

)×(66.97 – 66)}× = 13.42 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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= 75.38 × (0.5 × 12) = 452.58 kN

b) For interior nodes (41, 111)



1/3


to = {(37.30 +

)×(65.29 – 63)}× = 17.58 millisecondtd = {(27.8 +

)×(65.29 – 63)}× = 13.24 millisecond


Pso = {(0.37 -

)×(65.29 – 63)}×100 = 34.71 kN/m2

Pro = {(0.85 -

)×(65.29 – 63)}×100 = 78.91 kN/m2


= 78.91 × (1.0 × 12) = 946.88 kN

c)

For interior node (76)



1/3


to = {(37.30 +

)×( 64.71 – 63)}× = 17.51 millisecond

td = {(27.8 +

)×( 64.71 – 63)}× = 13.16 millisecond


Pso = {(0.37 -

)×( 64.71 – 63)}×100 = 35.29 kN/m2

Pro = {(0.85 -

)×( 64.71 – 63)}×100 = 80.43 kN/m2


= 80.43 × (1.0 × 12) = 965.16 kN


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iii) For 6.0 m height



Scaled distance X = = 67.97 m/tonne1/3


to = {(38.05 +

)×(67.97 – 66)}× = 17.85 millisecondtd = {(28.76 +

)×(67.97 – 66)}× = 13.47 millisecond


Pso = {(0.34 - )×(67.97 – 66)}×100 = 32.94 kN/m2

Pro = {(0.77 -

)×(67.97 – 66)}×100 = 74.35 kN/m2


= 74.35 × (0.5 × 12) = 446.09

b) For interior nodes (46,116)



1/3


to = {(37.30 +

)×(65.92 – 63)}× = 17.65 millisecondtd = {(27.8 +

)×(65.92 – 63)}× = 13.34 millisecond


Pso = {(0.37 -

)×(65.92 – 63)}×100 = 34.08 kN/m2

Pro = {(0.85 -

)×(65.92 – 63)}×100 = 77.21 kN/m2


= 77.21 × (1.0 × 12) = 926.50 kN


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1/3


to = {(37.30 +

)×( 65.36 – 63)}× = 17.59 millisecondtd = {(27.8 +

)×( 65.36 – 63)}× = 13.25 millisecond


Pso = {(0.37 -

)×( 65.36 – 63)}×100 = 34.64 kN/m2

Pro = {(0.85 - )×( 65.36 – 63)}×100 = 78.72 kN/m2


= 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)


Scaled distance X = 68.82 m/tonne1/3


Arrival time to = 17.99 millisecond

Equivalent triangular phase td = 13.56 millisecond


Peak side-on overpressure Pso = 32.12 kN/m2

Peak reflected overpressure Pro = 72.31 kN/m2


= 72.31 × (0.5 × 12) = 433.84 kN





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= 75.04 × (1.0 × 12) = 900.45 kN










Forces on exterior nodes = peak reflected overpressure × area= 75.96 × (1.0 × 12) = 911.56 kN

v) For 12.0 m height











= 69.31 × (0.5 × 12) = 415.87 kN


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= 71.97 × (1.0 × 12) = 863.65 kN







Total positive phase = to + td = 17.95 + 13.540 = 31.49 millisecondPeak side-on overpressure Pso = 33.59 kN/m

2



= 75.96 × (1.0 × 12) = 911.56 kN

vi) For 15.0 m height












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= 65.43 × (0.5 × 12) = 392.59 kN











= 68.00 × (1.0 × 12) = 816.05 kN











= 68.87 × (1.0 × 12) = 826.49 kN

vii) For 18.0 m height










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= 61.00 × (0.25 × 12) = 183.00 kN

b)

For interior nodes (66,136)










= 63.22 × (0.5 × 12) = 379.34 kN











= 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


50/140

40

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

blast loading on structure

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