analysis of reinforced concrete structure under blast

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ISSN 2348–2370

Vol.11,Issue.02,

February-2019,

Pages:81-99

Copyright @ 2019 IJATIR. All rights reserved.

Analysis of Reinforced Concrete Structure Under Blast Loading Condition

By Using SAP2000 SUDDULA SEKHAR

1, L. RAMA PRASAD REDDY

2

1PG Scholar, Dept of Civil Engineering, Brindavan Institute of Technology & Science, Peddatekur, Kurnool, AP, India,

E-mail: [email protected]. 2HOD, Dept of Civil Engineering, Brindavan Institute of Technology & Science, Peddatekur, Kurnool, AP, India.

Abstract: In the recent years the iconic and public buildings

have been the target of terrorist. Due to increase in

technology the terrorist are coming up with high intensities

of blasts. Arising problematic situation all over the world are

bomb blast and threats. The safety of the human life against

these attacks includes forecast, avoidance and variation of

such events. In recent years, design and analysis of such

impulsive loads subjected to structures are studied in detail

to find out the performance of the structural elements

subjected to sudden type of loading. It is given more

importance due to the effect which is caused by blast due to

high magnitude, sometimes blast may be even accidental.

Thus it is necessary to understand the effect of blast on the

structure and behaviour of structural elements due the load.

In present study, a seven storey reinforced concrete structure

with and without bracing is considered, which is subjected to

blast load of 100Kg RDX with standoff distance varying of

10m each, from 10m to 60m. The structure is analysed using

SAP 2000. The blast loads is calculated using the code UFC

3-340-02. The lateral stability of the structure gives the clear

effects of load on the structure. Based on the results, the

effect of blast load is higher when the detonation point is

closer to structure. The resistance of structure is seen when

bracings are added to the structure. The structure is efficient

when bracings are added to it.

Key Words: Displacement, Storey drift, SAP 2000, UFC 3-

340-02, Bracing.

I. INTRODUCTION

The rule of building design is to attain the dispensed goals

under the prescribed demand. Most recent decades have

observed great damages due to high levels of volatile loading

arising due to environmental loading, namely blast loading is

one of them. The vulnerability assessment of earthquake

resistant building structures is rather old, but most of the

knowledge on this subject has been accumulated during the

past fifty years. Similarity and dissimilarity of design

objectives under these two loadings are to protect/resist the

structural and non-structural performance in the predicted

manner. An earthquake resistant building structures is

allowed to take advantages of ductility during severe

earthquake loading, however, the same structures do not take

too much ductility under large blast loading. The blast

problem is rather new; information about the development in

this field is made available mostly through publication of the

Army Corps of Engineers, Department of Defence, U.S. Air

Force and other governmental office and public institutes.

Much of the work is done by the Massachusetts Institute of

Technology (MIT), the University of Illinois, and other

leading educational institutions. Accordingly the

performance of structural components subjected to blast

loading have been the theme of substantial investigate

attempt in current years. Conventional structures,

particularly that above grade, normally are not designed to

resist blast loads; and because the magnitudes of design

loads are significantly lower than those produced by most

explosions. With this in mind, developers, architects and

engineers increasingly are seeking solutions for potential

blast situations, to guard structure inhabitants and the

buildings.

Progressive collapse refers to failure of one or a group

of key structural load carrying elements that gives rise to

global failure of the structure. But in the explosions like the

World Trade Centre in New York in 1993, it remained very

difficult to arrest the progressive collapse of the structure.

The ultimate goal is that, the structure should be protected

from the blast effect, which is likely to be the Target of

terrorist attacks mostly. The dynamic response of the

structure to blast loading is complex to analyze, because of

the non-linear behaviour of the materials as well as the

geometry. Hence, analyses and design of blast loading

requires detailed knowledge of blast and its phenomena. An

explosion is defined as, rapid and sudden release of energy.

Explosive materials can be classified according to their

physical state as solids, liquids or gases. Solid explosives are

mainly high explosives for which blast effect are best

known. Materials such as mercury fulminates and lead azide

are primary explosives. Secondary explosives are those

create blast wave which can result in widespread damage to

the surroundings. Examples include trinitrotoluene (TNT)

and ANFO (Ammonium Nitrate Fuel Oil). In this project

work, the performance or behaviour of a thirty metres

structure under the blast loading is determined. Two

explosion weights were considered to determine the

behaviour of 30m structure.

SUDDULA SEKHAR, L. RAMA PRASAD REDDY

International Journal of Advanced Technology and Innovative Research

Volume. 10, IssueNo.02, February-2019, Pages: 81-99

The weights are of 10KN and 20KN. These explosion

weights were exploded in different three standoff distances,

said to be as 15, 30, and 45metres. At each standoff distance

the behaviour of structure is determined under two explosive

weights. The blast parameters were determined as per the

Army Corps of Engineers, Department of Defence, U.S. Air

Force[1]. The loading on the structure is dynamic in nature

so the resulted blast parameters which are determined is

given as the input for the structure in Time-History analysis

of SAP 2000. So as a result we can determine the

displacements, acceleration and velocities with respect to

corresponding Times, which are said to be as the

performance of the structure. In this project work, a deep

understanding of blast behaviour and response of structural

elements are focused in order to guide the structural

Engineer and architects to focus on these aspects while

planning and designing of any structural members.

II. BLASTING LOADS

A. Scaling Law Of Blast Wave

Blast parameters depend upon, the distance of source of

explosion and the energy released by that explosion. A

universal normalized description of the blast effect can be

given by scaling distance relative to (E/Po)1/3

and scaling

pressure relative to Po(atmospheric pressure). For

convenience, however, it is general practice the basic

explosive charge weight “W” as an equivalent mass of TNT.

The dimensionless distance parameter is given by

Scaled distance (Z) = R/W1/3

R = effective distance from explosion.

W = quantity or mass of bomb.

Scaling law provide the peak pressure and time

durations. They may be found from the peak values given in

IS: 4991-1968 (Re-affirmed 2003) table-1 and by some other

empirical expressions.

B. What Is An Explosion?

An explosion is defined as, rapid and sudden release of

energy. Explosive materials can be classified according to

their physical state as solids, liquids or gases. Solid

explosives are mainly high explosives for which blast effect

are best known. Materials such as mercury fulminates and

lead azide are primary explosives. Secondary explosives are

those create blast wave which can result in widespread

damage to the surroundings. Examples include

trinitrotoluene and ammonium nitrate fuel oil.

What Exactly Happens During Blasting?: The bursting of

condensed explosive generates hot gases under pressure and

a temperature of about 3000-4000oC. The hot gas expands

forcing out the volume, it occupies. As a consequence, a

layer of compressed air(blast wave) forms in front of this gas

volume most of the energy released by the explosion. Blast

wave instantaneously increases to a value of pressure more

than the ambient pressure. This is referred to as the side- on

overpressure that decays as the shock wave expands

outwards from the explosion source. After a short time the

pressure falls below the ambient pressure as shown in Fig-

3.2. This phase is nothing but the negative phase. The zone

which is having a peak overpressure more than the ambient

pressure and linearly decreased to the ambient pressure is

known as the positive phase. During negative phase a partial

vacuum is created and air is sucked in. This is accompanied

by high suction winds that carry the debris for long distance

away from the explosion source. Positive duration is much

lesser than the negative duration. The overpressure (pso) in

the positive duration is much greater than the pressure in the

negative pressure (pso-).

Fig.1. Blast wave propagation.

Fig.2. Blast wave pressure-time history.

C. Classification Of Explosions Explosion or blasting is mainly classified into two types.

They are:

Unconfined Explosion: The open air explosion causes a

wave that spreads from the source of detonation to the

structure without any wave amplification. These explosions

are situated at a given distance and height away from the

structure and there is a wave increase due to the reflection of

the ground before it contacts the structure. The height

limitations of these explosions are two to three times of the

height of a one-story or two-storey structure. The explosion

near the ground is an explosion occurring near or on the

ground and the initial pressure is immediately increased as a

result of refraction on the ground. Further unconfined

explosion is divided into two types. They are

Explosion near the Ground surface

Explosion in Air

Analysis of Reinforced Concrete Structure Under Blast Loading Condition By Using SAP2000



If the charge is located very close to the ground or on the

ground the explosion is termed near the ground. Refracted

wave arises as the initial blast wave is refracted and

increased by reflection of the ground. Unlike an explosion in

the air, the refracted wave is merged with the initial wave in

the detonation point, and they form a single wave as shown

in figure.

Fig.3. Explosion near the ground surface

Fig.4. Explosion in Air.

The explosion in the air is a phenomenon that occurs by

detonation of explosives above ground level at some

distance from the structure so that the blast wave that travels

toward the structure is refracted of the ground. The refracted

wave is the result of the initial wave amplification by

refraction of the ground. Through the front height are

occurring variations in pressure, but for the analysis they are

ignored, and are regarded as a plane wave across the front

height.

Confined Explosion: If the explosion occurs inside the

structure, the peak pressures associated with the initial wave

fronts are extremely high. They are enhanced by the

refraction within the structure. In addition to this, depending

on the degree of confinement, high temperatures and the

accumulation of gaseous products of chemical reactions in

the blast would produce more pressure and increase the load

duration within the structure. The combined effects of these

pressures can lead to the collapse of the structure, if the

structure is not designed to withstand internal pressure.

Appropriate ventilation reduces strength and duration of

pressure so the effect of pressure is different in structures

with openings and structures without openings.

IV. DETERMINATION OF BLAST LOADING

PARAMETERS

Blast loading can be determined by some empirical

expressions and by some other codes or by some provisions.

So in general the blast load is calculated by

Empirical expressions determined by some number

of experiments.

As per Indian code IS4991-1968(Re-affirmed 2003)

Provisions as per unified facilities criteria (UFC 3-

340-02, 5 December 2008.).

Indian code had mentioned only the effect of the

positive duration and positive over pressures. The effect of

the negative duration and the negative over pressure is not

considered. To determine the exact and near to exact

analysis of the building, the effect of negative over pressure

should also consider.

A. By Empirical Expressions Use of the TNT (Trinitrotoluene) as a reference for

determining the scaled distance Z, 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 their TNT. Specific energy

of different explosive types and their conversion factors of

that of the TNT are given in the next table.

TABLE I: Conversion Factors For Different Type Of

Explosives

Explosion wave front speed:

(1) Where ao= speed of sound in m/sec

Alternative expression U = 345(1+0.0083Pso2) in m/sec

Dynamic (blast wave) pressure:

(2) It can be written also as qo = 0.0032Pso

2 in kpa

Where Pso = peak over pressure

Po = ambient pressure

There are various proposals for calculation of the main

explosion parameters.




New marks and Hansen’s [9] proposed the use of

following values

(3)

Mills[10] proposed the following

(4)

Brode[11] gives the following expressions for to determine

the peak over pressures,

(5)

(6)

Where scaled distance Z =

R = distance from the centre of the spherical charge

W = charge mass expressed in kilogram of TNT

Other important parameters include:

to= duration of the positive phase during which the a

pressure is greater than the Pressure of the surrounding air.

is = the specific wave impulse that is equal to the area under

the pressure-time. Curve from the moment of arrival, tA, to

the end of the positive phase

And is given by expression

(7)

Where is the maximum value of negative pressure

Fig.5. Pressure-Time profile of Explosion Wave.

Brode [11] proposed the following expression for negative

pressure

(8)

And the corresponding negative impulse specific force

is given by

(9)

B. Provisions As Per Unified Facilities Criteria (UFC 3-

340-02, 5 December 2008.)

The Explosion In AIR: The explosion in the air is a

phenomenon that occurs by detonation of explosives above

ground level at some distance from the structure so that the

blast wave that travels toward the structure is refracted of the

ground. The refracted wave is the result of the initial wave

amplification by refraction of the ground. Through the front

height are occurring variations in pressure, but for the

analysis they are ignored, and are regarded as a plane wave

across the front height. The parameters are calculated as for

an explosion on the ground. Peak refracted pressure pr is

determined by above stated formula. Then the negative

phase peak refracted pressure is determined by Fig- 2-11 of

[1]. Using the scaled distance and the wave angle ‘α’

we can determine the impulse . As shown in Fig 3.5 of

[1]

Fig.6. Negative pressure shock wave parameters in Free

air explosion.

Fig.7. Air Burst blast environment.




The Explosion Near The Ground: If the charge is located

very close to the ground or on the ground the explosion is

termed near the ground. Refracted wave arises as the initial

blast wave is refracted and increased by reflection of the

ground. Unlike an explosion in the air, the refracted wave is

merged with the initial wave in the detonation point, and

they form a single wave see Fig-2-14 of [1].

Fig.8. Air blast environments in ground explosion.

Fig.9. Blast near the ground level.

Fig.10. Parameters of the positive phase blast wave near

the ground surface.

By knowing the scaled distance we can determine the

parameters of negative phase blast wave by reading the

values corresponding to the scaled distance from above

graph. By taking the corresponding values of the scaled

distance from below graph we can determine the positive

phase parameters.

C. Pressure Variation On The Structure After the time of arrival tA the pressure will attain a peak

over pressure value Pso. Then it will decrease in

exponentially to ambient pressure Po after a short duration of

time to. But for idealised positive curve so that it will attains

ambient pressure Po in time “tof”. The reduction speed of the

initial and dynamic pressure, after the passing of the wave

front, is a function of the peak pressure and the magnitude of

detonation. For the analysis purposes, the actual reduction of

the initial pressure can be assumed as a triangular pressure

impulse. The actual duration of the positive phase is replaced

by a fictitious duration and is expressed as a function of the

total positive impulse and the peak pressure

tof =

Fig.11. Idealized pressure-Time variations.

This expression can be used for the initial and for the

refracted pressure by taking the values of refracted impulse

pressure and peak refracted pressure, respectively. A similar

procedure applies for the values of the negative phase.

(10)

As the fictitious duration of the positive phase is shorter

than the actual duration, a difference between the fictitious

phase and the beginning of the negative phase is created.

This difference, shown in Fig. 2-190 of [1] should be

retained in the analysis because of the retention order of the

different stages of loading.

D. The Average Pressure On The Front Facade

The variation of the pressure on the front structural

facade, for a rectangular structure with sides parallel to the

wave front above the ground, in the area of low pressure is

subject of interest. The peak pressure on the front structural




facade in time of the explosion's arrival tA, will be the peak

refracted overpressure Pr, which is a function of the initial

pressure. This pressure then decreases in time interval [t', tA]

due to the passage of waves above and around the structure,

which is less than Pr(peak overpressure over and around the

structure will be Pos). The overpressure on the front surface

of the structure continues to decrease until the pressure is

equalized with the pressure of the surrounding air. Clearing

time (passing time), tc needed that the refracted pressure

drops to the level of the initial pressure can be expressed as,

Fig.12. The load on the front surface of the structure.

The clearence time or passing time tc =

Where S = length of the "clearing", is equal to the height of

the structure, H or a half-width of the structure, W/2,

whichever is less

R= ratio S/G, where G is the height of the structure, H or

half-width of the structure,

W/2, whichever is less.

Cr= coefficient of reflection or speed of sound in refracted

area.

Pressure that acts on the front surface after the time tc is

the algebraic sum of the initial pressure Ps and drag

dependent pressure (CDq).

(11)

Drag coefficient CD connects the dynamic pressure and

total translational pressure in the direction of the wind-

induced dynamic pressure and varies with Mach number,

Reynolds number in the area of low pressure), and depends

on the geometry of the structure. It can be taken as ≥ 1,0 for

the front facade, while for the side, rear and roof surfaces it

can be taken less than 1.The fictitious length of the refracted

wave front trf, is calculated according to the formula:

(12)

Where Pr is the refracted peak pressure.

E. The Average Pressure On The Roof And Sides

As the wave encloses the structure the pressure on the

top and sides of the structure is equal to the initial pressure

and then decreases to a negative pressure due to the drag

(Fig. B). The structural part that is loaded depends on the

magnitude of the initial pressure wave front, the location of

the wave front and the wavelength of the positive and

negative phases. The initial peak pressure on the roof surface

is reduced and the wavelength increases when the wave

encloses the structure. The equivalent uniform pressure

increases linearly from the wave-arrival time tf (point F on

the element) to the time td when the wave reaches the peak

value and gets to the point D. At the point B the equivalent

uniform pressure is reduced to zero.

Fig.13. The load on the roof and side surface of the

structure

The load coefficient CE, increase time and duration of an

equivalent uniform pressure is determined as explained in

Figs. 2 - 196 and 2 - 197 from [1]. It is a ratio of the

wavelength and range, LwT/L. The peak pressure that acts on

the roof, PR ,is the sum of the equivalent uniform pressure

and the drag pressure:

(13)

Psof = initial pressure at point F

qo= a dynamic pressure corresponding to the value CE Psof.

The value of the negative pressure that acts on the roof

surface, , is equal to CE¯.Psof where CE¯ is the negative

value and the equivalent negative pressure tsof is determined

from Figs 2- 198, [1]. Time increase of the negative phase is

equal to 0,25tsof.

F. The Average Pressure On Rear Surface As the wave passes over the ends of the roof and side

surfaces, pressures are spreading thus creating a secondary

wave that continues to spread across the rear surfaces of the

structure. The secondary waves that enclose the rear surface,

in the case of long structures, are the result of a wave

"overflow" from the roof and side surfaces. They are

amplified due to the refraction of the structural surfaces. The




increase of the waves from the roof is caused by the

refraction of the ground at the bottom of the rear surface, and

the increase of the waves "overflowed" from the side surface

is caused by their mutual collisions in half the length of the

surface, or collision with a wave "overflowed" from the roof.

Fig.14. The load on the rear surface.

For the loading analysis the procedure equivalent to the

procedure for the loading determination on the roof and side

surfaces (Fig. C) can be used. The peak pressure for

pressure-time history is determined using the peak pressure

on the extreme edge of the roof surface, Psof. Dynamic drag

pressure corresponds to the pressure CE. Psof, while the

preferred drag coefficients are equal to those for the roof and

the side surfaces.

G. Structural Response To Blast Loading

Complexity in analyzing the dynamic response of blast-

loaded structures involves the effect of high strain rates, the

non-linear inelastic material behaviour, the uncertainties of

blast load calculations and the time-dependent deformations.

Therefore, to simplify the analysis, a number of assumptions

related to the response of structures and the loads has been

proposed and widely accepted. To establish the principles of

this analysis, the structure is idealized as a single degree of

freedom (SDOF) system and the link between the positive

duration of the blast load and the natural period of vibration

of the structure is established. This leads to blast load

idealization and simplifies the classification of the blast

loading regimes.

Elastic SDOF Systems: The simplest discretization of

transient problems is by means of the SDOF approach. The

actual structure can be replaced by an equivalent system of

one concentrated mass and one weightless spring

representing the resistance of the structure against

deformation. Such an idealized system is illustrated in

Fig.5.1. The structural mass, M, is under the effect of an

external force, F(t), and the structural resistance, Rm, 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 Figure 3.5). The forcing function is given as

(14) The blast impulse is approximated as the area under the

force-time curve, and is given by

(15)

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 (1964) as

(16) The general solution can be expressed as:

(17)

(18)

Which ω is the natural circular frequency of vibration of the

structure and T is the natural period of vibration of the

structure which is given by equation,

(19)

The maximum response is defined by the maximum

dynamic deflection Ym which occurs at time tm. The

maximum dynamic deflection Ym can be evaluated by setting

dy/dtin above Equation equal to zero, i.e. when the structural

velocity is zero. The dynamic load factor, DLF, is defined as

the ratio of the maximum dynamic deflection Ym to the static

deflection yst which would have resulted from the static

application of the peak load Fm, which is shown as follows:

(20)

Fig.15. (a) SDOF system and (b) blast loading

The structural response to blast loading is significantly

influenced by the ratio td/T or ωtd(td/T= ωtd/ 2π). Three

loading regimes are categorized as follows:

ωtd<0.4: impulse loading regime.

ωtd<0.4: quasi-static regime.

0.4 <ωtd<40 : dynamic loading regime.




Elasto-Plastic SDOF Systems: Structural elements are

expected to undergo large inelastic deformation under blast

load or high velocity impact. Exact analysis of dynamic

response is then only possible by step-by-step numerical

solution requiring nonlinear dynamic finite- element

software. However, the degree of uncertainty in both the

determination of the loading and the interpretation of

acceptability of the resulting deformation is such that

solution of a postulated equivalent ideal elasto-plastic SDOF

system (Biggs, 1964) is commonly used. Interpretation is

based on the required ductility factor μ=ym/ye. For example,

uniform simply supported beam has first mode shape φ(x) =

sinπx/L and the equivalent mass M = (1/2)mL, where L is

the span of the beam and m is mass per unit length.

Fig.16. Simplified resistance function of an elasto-plastic

SDOF system.

The equivalent force corresponding to a uniformly

distributed load of intensity p is F =(2/π)pL. The response of

the ideal bilinear elasto-plastic system can be evaluated in

closed form for the triangular load pulse comprising rapid

rise and linear decay, with maximum value Fm and duration

td. The result for the maximum displacement is generally

presented in chart form TM 5-1300 [1], as a family of curves

for selected values of Ru/Fm showing the required ductility

μ as a function of td/T, in which Ru is the structural

resistance of the beam and T is the natural period.

Fig.17. Maximum response of elasto-plastic SDF system

to a triangular load.

V. COMPUTATION OF BLAST PARAMETERS

A. Analytical Solution We assumed that, the blast wave is considered as plane.

The blast parameters are determined as follows

Description Of Data For Trial-I:

Size of building 18m X 18m.

Distance of building from the origin of explosion,

R= 45 m

Height of the building H= 30m

Explosive weight W= 10 KN

Scaled distance Z= = 4.5 m/kg1/3

= 11.05 ft/

Determination Of Blast Parameters: Determination of

following free-field blast wave parameters at Point A:

peak positive incident pressure Pso

time of arrival of blast wave tA

wave length of positive pressure phase LW

duration of positive phase of blast pressure to.

From fig-2-15[1] for Z= 11.05 ft/ ;

Pso = 7.93 psi

= 5.154 ms/lb1/3

= 2.53

= 2.75 ms/lb1/3

Specific impulsive force is = 7.41x25001/3

= 100.57

psi ms

Front Wall Peak Positive Reflected Pressure: From fig-2-193[1] ;

Pso = 7.93 psi and α = 0o, Cra= 2.38.

Therefore reflected peak pressure is given by, Pra = Cra*Pso =

2.38*7.93 = 18.87.

Unit positive reflected impulse from fig-2-194[1] ;

= 12.81, ira= 174.05 psi.

Front Wall Loading Positive Phase:

Calculation of sound velocity in reflected over pressure

region,

Cr from 2-192[1]; Pso =7.93 psi Cr = 1.25 ft/ms

Clearing time for reflected pressure tc;

tc= = = 71.00 ms.

Where S= 30ft (60/2 =30);

G= 100/2 =50> 30, so G= 50




R = S/G = 30/50 =0.6

Calculation of fictitious positive phase duration,

tof = 2is/Pso = (2x100.57)/7.93 = 25.36 ms.

From fig- 2-3[1]; peak dynamic pressure is given by,

Pso = 7.93 psi then qo =1.43 psi.

Drag coefficient based on from suction,

CD =1.0 then Pso+CDqo = 7.93+ 1*1.43 = 9.36 psi.

Calculation of factitious duration of the reflected pressure

acc to equation

tr = = = 18.44 ms

Pressure time curve is plotted in fig.

Front Wall Loading Negative Phase:

Peak positive reflected pressure Pra =18.87 psi, then from fig

2-15[1]

Z(Pra) =11.20;

Peak Negative pressure is Pa- = 1.60 psi for Z = 11.20

Fictitious negative phase duration, trf- = 0.0139 *W

1/3 =

144.56 ms

Negative specific impulsive force is given by, = 18.80,

ira- = 246.34 psi ms

Therefore negative phase rise = 0.27 trf- = 0.27*144.56 =

39.03 ms

The negative phase time parameter to+0.27 trf- = 37.32+39.03

= 76.35 ms

Total negative phase duration, to+ trf- = 37.32+144.56 =

181.88 ms.

Side Wall Loading Positive Phase:

Calculation of loading on the rear half of the side wall L =30

ft

Wavelength to span ratio = Lw/L = 38/30 =1.27

Based on fig- 2-196, 2-197 and 2-198 [1] for point on B

Lw/L = 1.27,

Psof = 5.74 psi, CE =0.53, CE-=0.26, = 1.78, =

4.2, and = 11.52.

Where CE = equivalent load factor,

td = rise time

tr = fictitious reflected pressure duration

tof = fictitious positive pressure phase duration

Therefore peak positive pressure Pso = CE*Psof =0.53*5.74 =

3.04 psi

tr =1.78*25001/3

= 24.15 ms

tof= 5.2 * 25001/3

= 27.00 ms.

Peak dynamic pressure from fig-2-3[1]

CEPsof= 3.04 then qo= 0.23 psi.

Drag coefficient is given as CD = -0.4,

Calculation of peak positive pressure from equation

CEPsof + CDqo =3.04-0.4*0.23= 2.95 psi

Side Wall Negative Pressure Phase:

Peak negative reflected pressure (Pr-) = CE

-Psof

-= 0.26*5.74

=1.50 psi

Negative phase duration tof- = 11.52*2500

1/3 =156.35 ms

Negative phase rise time 0.27*t-of = 42.21 ms

The negative phase time parameter to =40.22 ms

Peak rise time to +0.27 * tof- = 40.25+42.21 = 82.46 ms

Total negative duration to + tof- = 40.25+156.35 =196.60 ms

Roof Loading – Positive Phase:

Calculation of roof loading, L= 60fts

Psof =4.44 psi

Based on fig 2-196, 2-197, 2-198[1];

CE = 0.35, CE- =0.22

= 2.49,

= 6.93; = 12.43

Hence peak positive pressure is CEPsof = 0.35*4.44 =1.56 psi

Rise time tr =2.49*25001/3

= 33.79 ms and tof = 84.05 ms

Peak dynamic pressure from fig-2-3[1];

For CEPsof =1.56 psi then qo =0.13 psi

Calculation of peak positive reflected pressure CEPsof+CDqo=

1.56-0.4*0.12= 1.51 psi

Roof Loading –Negative Pressure:




Peak negative reflected pressure Pr- = CE

-Psof

- =0.22*4.44=

0.98 psi.

Total Time of peak negative pressure tof-= 12.43*2500

1/3 =

168.70 ms

Negative pressure rise time 0.27*t-of = 0.27*168.70= 45.55

ms.

The negative pressure time parameter, to=42.48ms

Therefore peak rise is to+ 0.27*tof-= 42.48+45.55 = 88.03 ms.

Total duration is to + tof- = 42.48+168.70= 211.18 ms.

The negative pressure-time curve is plotted in figure.

TABLE II: Positive And Negative Peak Over And Under

Pressure For Various Faces Without Considering

Atmosphere Pressure

TABLE III: Positie And Negative Peak Pressures For

Various Faces After Considering The Ambient Pressure

(101325 Pascal Or 14.7 Psi)

The Pressure Vs Time Plots Are As Follows:

Fig.18. Pressure-time variation on front wall with and

without considering ambient pressure.

TABLE IV: Positive And Negative Peak Over And

Under Pressure For Various Faces Without Considering

Atmosphere Pressure

Fig.19. Pressure-time plot on side wall with and without

considering ambient pressure.




Fig.20. pressure-time plot on roof with and without

ambient pressure.

Description Of Data For Trial-2:


Distance of building from the origin of explosion

R= 45m.


Explosion weight W= 20KN

Scaled distance Z= = 8.77 ft/

Then the above procedure as in 10KN weight explosion is

repeated to determine the pressures for 20KN explosion. The

results were as follows.., For 20KN explosion weight, the

positive and negative pressures are calculated as.

TABLE V: Positive And Negative Peak Pressures For


(101325 Pascal Or 14.7 Psi)

The pressure and time plots are as follows:

Fig.21. Pressure-time variation on front wall without and

with considering ambient pressure.

Fig.22. Pressure-time plot on side wall with and without

considering ambient pressure.




Fig.23. Pressure-time plot on roof with and without

ambient pressure.




R= 30 m


Explosion weight W= 10 KN


TABLE VI: Positive And Negative Peak Over And


Atmosphere Pressure

TABLE VII: Positive And Negative Peak Pressures For


(101.325 Kilo Pascal Or 14.7 Psi)

Pressure And Time Plots:

Fig.24. Variation of blast pressure on front face without

atmospheric pressure.

Fig.25. Variation of blast pressure on side face without

ATM pressure.

Fig.26. Variation of blast pressure on Roof without

considering ATM pressure.




Description Of Data For Trail-4:



R= 30 m


Explosion weight W= 20 KN


TABLE VIII: Positive And Negative Peak Over And


Atmosphere Pressure

Fig.27. Pressure-Time plot on Front Face without

considering ATM pressure

Fig.28. Pressure-Time plot on side faces without


Fig:.29. Pressure-Time plot on Roof without considering

ATM pressure.




R= 15 m




TABLE IX: Positive And Negative Peak Pressures For



TABLE X: Positive And Negative Peak Over And Under

Pressure For Various Faces Without Considering

Atmosphere Pressure

TABLE XI: Positive And Negative Peak Pressures For






Fig.30. Pressure variation on front wall with and without

ATM pressure.

Fig.31. Pressure variation on side face with and without

ATM pressure.

Fig.32. Variation of pressure on roof with and without

ATM pressure.

DESCRIPTION OF DATA FOR TRAIL-6:



R= 15 m




TABLE XII: Positive And Negative Peak Over And


Atmosphere Pressure

TABLE XIII: Positive And Negative Peak Pressures For






Fig.33. Pressure-Time plot on Front face without


Fig.34. Pressure-Time plot on Side face without


Fig.35. Pressure-Time plot on Roof without considering

ATM pressure.

For two explosive weights 10KN and 20KN at a

standoff distances of 15m, 30m & 45m, the pressure

variation (positive and negative pressures) are determined on

different faces of the structure or building. In pressure-Time

plots the peak positive pressure is much greater than the

peak negative pressure. So we can conclude some points

from the pressure-Time plots. The main points that I have

observed is listed below.

As above said the peak positive pressure is much

greater than the peak negative pressure on all the faces

of the building.

The intensity of the peak reflected pressure are much

more than the peak positive pressure. So, the effect of

the reflected pressure is more on the front face (side

where explosion occurred) of the building or structure.

In case of side face and Roof of the building, the

reflected pressure is less than the peak positive

pressure. So the effect of the reflected pressure on

these face is low when compare with the front face.

Among the peak positive pressure and reflected

pressure, the greater value is considered on the face in

Pressure-Time plots.

The negative pressure on the front face started after the

end of the positive pressure that to not an immediate

occurrence, but started after some milliseconds as

shown in pressure-Time plots.

But in case of side faces of the structures, the Negative

pressure started before the end of the positive pressure

this is clearly observed in the pressure-Time plots.

In case of the Roof, the Negative pressure is started

much before departure of the positive pressure the

variation as shown in plots.

VI. MODELLING IN SAP 2000

A. About SAP2000 The SAP name has been synonymous with state-of-the-

art analytical methods since its introduction over 30 years

ago. SAP2000 follows in the same tradition featuring a very

sophisticated, intuitive and versatile user interface powered

by an unmatched analysis engine and design tools for

engineers working on transportation, industrial, public

works, sports, and other facilities. From its 3D object based

graphical modelling environment to the wide variety of

analysis and design options completely integrated across one

powerful user interface, SAP2000 has proven to be the most

integrated, productive and practical general purpose

structural program on the market today. This intuitive

interface allows us to create structural models rapidly and

intuitively without long learning curve delays. Now we can

harness the power of SAP2000 for all of your analysis and

design tasks, including small day-to-day problems. Complex

Models can be generated and meshed with powerful built in

templates. Integrated design code features can automatically

generate wind, wave, bridge, and seismic loads with

comprehensive automatic steel and concrete design code

checks per US, Canadian and international design standards.

Advanced analytical techniques allow for step-by-step large

deformation analysis, Eigen and Ritz analyses based on

stiffness of nonlinear cases, catenary cable analysis, material

nonlinear analysis with fibre hinges, multi-layered nonlinear

shell element, buckling analysis, progressive collapse




analysis, energy methods for drift control, velocity-

dependent dampers, base isolators, support plasticity and

nonlinear segmental construction analysis. Nonlinear

analyses can be static and/or time history, with options for

FNA nonlinear time history dynamic analysis and direct

integration. From a simple small 2D static frame analysis to

a large complex 3D nonlinear dynamic analysis, SAP2000 is

the easiest, most productive solution for structural analysis

and design needs.

B. General Introduction

For performing the linear and Non-linear analysis to the

framed structure by manually, is very difficult task and also

a time consuming process. So huge manual errors will occur

when we done by manually. To eliminate this type of errors

and recent few decades implemented some software’s to

eliminate the difficulties. If we want to know the

performance of any structure, firstly we should have to

model the structure. So for modelling I opted for SAP2000.

My intention is to determine the behaviour of the structure

under blast loading. So to determine that first we should

know the behaviour of explosion and shockwave then to

model that building and to provide appropriate structural

components. The performance capability of structural system

depends on the analysis method taken for analysis process.

Identification and quantification of damage of global and

local level is the key element for an effective analysis

procedure for blast resisting design. In order to accomplish

the desire objectives, linear and nonlinear model time history

analysis has been conducted on the building frames model in

SAP2000 in this study. Concrete frame buildings have been

taken where the frames have been used for performance

evaluation and model using the background of software

SAP2000. Using unified facilities criteria [1], the blast

pressure time functions have been estimated and were

applied to the building frames. Linear and nonlinear dynamic

modal time history analysis is conducted for the modelled

building frames. Subsequently analysis results were recorded

for performance evaluation.

C. Evaluation Of Blast Response

Today in this present era, where the world got advanced

with the latest technologies software’s that may analyze 2D

as well as 3D models with a good accuracy and better

simulation with the actual effect of the disastrous loads on

the structures. Using the environment of software it is now

possible to automobile nonlinear analysis using SAP2000 in

this study. Frame works modelled for linear and non linear

response were run using the estimated base shear and

response spectrum for linear analysis using blast pressure

time curves for nonlinear analysis and in this direction the

appropriate analysis is carried out. It seems some odd that

the frameworks are modelled previously in linear analysis

using response spectrum analysis for considered earthquake

ground motion. It is so, because it is very difficult to predict

the section which will be safe against blast. As the direction,

intensity, blast off distance and type of blast source is erratic.

So, in this study a model is taken, which is previously

checked for maximum effect of earthquake ground motion as

for linear analysis and performance of the structure is the

analyzed using nonlinear dynamic model time-history

analysis. Details of building frame work are as follows:

Size of the building 18m X 18m.

Height of the building 30 metres (10 storey building).

Explosion weights 10KN and 20KN.

Standoff distances are 15m, 30m and 45m.

D. Response Spectrum Analysis (RSA)

Response-spectrum analysis (RSA) is a linear-dynamic

statistical analysis method which measures the contribution

from each natural mode of vibration to indicate the likely

maximum seismic response of an essentially elastic

structure. Response-spectrum analysis provides insight into

dynamic behaviour by measuring pseudo-spectral

acceleration, velocity, or displacement as a function of

structural period for a given time history and level

of https://wiki .csiamerica.com/ display/kb /Damping

damping. It is practical to envelope response spectra such

that a smooth curve represents the peak response for each

realization of structural period. Response-spectrum analysis

is useful for design decision-making because it relates

structural type-selection to dynamic performance. Structures

of shorter period experience greater acceleration, whereas

those of longer period experience greater displacement.

Structural performance objectives should be taken into

account during preliminary design and response-spectrum

analysis.

TABLE XIV: The Dimensions Of All The Beams And

Column

Fig.36. Plan of RC building (G+10) in SAP 2000




Fig37.3-D model view of RC(G+10) building in SAP2000.

VIII. RESULTS

When the explosion weights of 10KN and 20KN are

exploded at a standoff distance of 15, 30 and 45 metres the

Impulsive force-Time plot as shown in figure-5.5 and 5.6 is

given as input to the nonlinear dynamic Time history

analysis, then the resulted plots are as follows, and the

maximum displacements of joint and maximum

accelerations are tabulated below:

TABLE XV: Maximum Displacements And Acceleration

Fig.38. Displacement – Time Plots for 10KN and 20KN

@ 15m Feet Standoff Distance Respectively.

Fig.39. Acceleration-Time Plots for 10KN and 20KN @

15m Standoff Distance Respectively.

Fig.40. Displacement – Time Plots for 10KN and 20KN

@ 30m Standoff Distance Respectively.




Fig.41. Acceleration-Time Plots For10KN and 20KN @


Fig.42. Displacement – Time Plots For 10KN and 20KN

@ 45m Standoff Distance Respectively.

Fig.43. Acceleration-Time Plots For10KN and 20KN @


Fig.44.

VIII. CONCLUSION

I didn’t considered the negative pressure in the Pressure-

Time plot, because under the impact of positive phase

duration, the displacement of the structure is more than the

displacement when considered the Negative pressure. This

will act as an safety factor, so the structure will be very safe.

The variation that I’m observed is given in below plots.

Fig.45. Displacement of 10KN @ 15m with Considering

Negative Pressure.

Fig.46. Displacement of 10KN@15m without Considering

Negative Pressure




In above plots the displacement of 10KN @ 15m is

74mm when the negative phase duration is considered. If the

negative phase duration is neglected, the displacement is

observed as 90mm. So by that we can know that there is

more deflection under the loading without considering the

Negative phase duration. So this matter behind that why our

Indian code didn’t considered the negative phase duration.

But Indian code didn’t provide the sufficient data for

determining the blast parameters when the explosion weight

is more than 1 tonne. Because the parameters were given

only for one tonne explosive weight, we need its revision.

A. Scope Of Future Study

Present study has limited scope with emphasis on

structure explosion interaction. To develop clear

understanding, it reveals that, more research should be done

on this topic. To determine the exact behaviour or the

performance of the building require some model analysis.

But it is very difficult to say that, which building is safe and

which one is not. Because the explosion like in World trade

centre (2001) will not able to withstand by any type of

building in the world. Some of the Recommendations for

future work are proposed as follows,

To know the better performance of any building,

development of prototype model is required.

Not only for that reason, IS code provides the data only

for one tonne explosive weight, so it is very difficult to

find the blast parameters for above one tonne explosive

weight by IS code.

Comparative study in terms of analytical approach

should be increased for finding the performance under

varying demand arising due to blast loading..

Study of structural elements (beam, columns, slabs etc)

needs to be given due weight age under blast loading.

Non structural elements behaviour also to be studied in

details for minimizing damage cost under loading

arising due to blast.

Interaction of structural and non structural elements in

terms of normalized damage index is developed.

Vulnerability Steel building may also be evaluated

under the prescribed conditions of blast loading.

IX. REFERENCES [1]TM 5-1300(UFC 3-340-02) U.S. Army Corps of

Engineers (1990), “Structures to Resist the Effects of

Accidental Explosions”, U.S. Army Corps of Engineers,

Washington, D.C., (also Navy NAVFAC P200-397 or Air

Force AFR 88-22).

[2]Edwards, A. T., and Northwood, T. D. “Experimental

Studies of the effects of Blasting on structures”, The

engineers, 1960, V.210, 538-546.

[3]Moon, Nitesh N. Prediction of Blast Loading and its

Impact on Buildings, Department of Civil Engineering,

National Institute of Technology, Rourkela, 2009.

[4]Duranovic,N.Eksperimentalnomodeliranjeimpulsomopter

eceniharmiranobetonskihploca.// Gradevinar, 54,8(2002), pp.

455-463.

[5]T. Ngo, P. Mendis, A. Gupta & J. Ramsay, “ Blast

Loading and Blast Effects on structure”, The University of

Melbourne, Australia, 2007.

[6]ZeynepKoccaz, FatihSutcu, and NecdetTorunbalci study

on “architectural and structural design for blast resistant

buildings”. 14 WCEE-05-01-0536.

[7]“Response Of Model Structure Under Simulated Blast-

Induced Ground Excitations”, by Yong LU, Hong HAO,

Guowei MA and Yingxin ZHOU.12 WCEE-2000-0972.

[8]Alexander M. Remennikov, (2003) “A review of methods

for predicting bomb blast effects on buildings”, Journal of

battlefield technology, vol 6, no 3. pp 155-161.

[9]“Prediction and Assessment of Loads from Various

Accidental Explosions for Simulating the Response of

Underground Structures using Finite Element Method” by

Akinola Johnson Olarewaju. Ppr.2013.032-alr.

[10]A.K. Pandey et al. (2006) “Non-linear response of

reinforced concrete containment structure under blast

loading” Nuclear Engineering and design 236. pp.993-1002.

[11]Impacts and Analysis for Buildings under Terrorist

Attacksby Edward Eskew, Shinae Jang Department of Civil

and Environmental Engineering University of Connecticut.

Ppr 2012.11.16.

[12]Newmark, N. M.; Hansen, R. J.Design of blast resistant

structures. // Shock and vibration Handbook, Vol. 3, Eds.

Harris and Crede. McGraw-Hill, New York, USA.1961.

[13]Mills, C. A. The design of concrete structure to resist

explosions and weapon effects. //Proceedings of the 1st Int.

Conference on concrete for hazard protections, Edinburgh,

UK, pp. 61-73, 1987.

[14]Brode, H. L. Numerical solution of spherical blast

waves. // Journal of Applied Physics, American Institute of

Physics,New York, 1955.

[15]IS 4991-1968 (RE-AFFIRMED 2003); criteria for blast

resistant design of structures for explosions above ground

(third Reprint AUGUEST 1993). Bureau of Indian

Standards, ManakBhavan 9, Bahadur shah Zafar Marag,

New Delhi, India.

[16]Remennikov, A. M. A Review of Methods for Predicting

Blast Effects on Buildings. // Journal of Battlefield

Technology, Aragon Press Pty Ltd., 6, 3(2003), pp. 5- 10.

analysis of reinforced concrete structure under blast

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