0727735217 blast effects on buildingsb

Blast effects on buildingsDesign of buildings to optimizeresistance to blast loading

I

Blast effects on buildingsDesign of buildings to optimizeresistance to blast loading

Edited byG. C. Mays and P. D. Smith

mmn1 Thomas Telford

A Structural Design Guide prepared by a Working Party convened by theStructures and Buildings Board of the Institution of Civil Engineers.

Working Party Membership:

Brigadier C. L. ElliottP. JacksonMajor R. J. JenkinsonD. MairsProf. G. C. MaysP. D. Smith1. ThirlwallC. J. R. Veale

Ministry of DefenceR. T. James and Partners LtdMinistry of DefenceWhitby and BirdCranfield UniversityCranfield UniversityR. T. James and Partners LtdMinistry of Defence

Published by Thomas Telford Publications, Thomas Telford Services Ltd, 1 HeronQuay, London E14 4JD

First published 1995

Distributors for Thomas Telford books areUSA: American Society of Civil Engineers , Publications Sales Department , 345 East47th Street, New York, NY 10017-2398Japan: Maruzen Co. Ltd, Book Department, 3-10 Nihonbashi 2-chome, Chuo-ku,Tokyo 103Australia: DA Books and journals, 11 Station Street, Mitcham 3132, Victoria

A catalogue record for this book is available from the British Library

ISBN: 0 7277 2030 9

© The Authors , 1995, unless otherwise stated.

All rights, including translation, reserved. Except for fair copying, no part of thispublication may be reproduced , stored in a retrieval system or transmitted in any formor by any means, electronic, mechanical, photocopying or otherwise, without the priorwritten permission of the Publisher: Books, Publications Division, Thomas TelfordServices Ltd, Thomas Telford House, 1 Heron Quay, London E14 4JD.

The book is published on the understanding that the authors are solely responsiblefor the statements made and opinions expressed in it and that its publication doesnot necessarily imply that such statements and/or opinions are or reflect the viewsor opinions of the publishers.

Typeset by MHL Typesetting Ltd, Coventry

Printed in Great Britain by Redwood Books, Trowbridge, Wilts

Contents

Editors' note

1. IntroductionC. L. Elliott

ObjectivesScopeTerrorismRiskThe special effects of catastrophic failurePartial safety factors in blast designA design philosophy: planning for protectionReference

2. Basic guidelines for enhancing building resilience 8P. Jackson, I. Thirlwall and C. J. R. Veale

Introduction 8The requirements of the client 14Architectural aspects and design features 15Provision of shelter areas 16Location of key equipment and services 19Building form 19Design of individual structural elements 20Building layout 22References 23

3. Blast loadingP. D. Smith

NotationIntroductionExplosionsExplosion processes terminology

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24252526

BLAST EFFECTS ON BUILDINGS

Explosives classificationBlast waves in air from condensed high explosivesBlast wavefront parametersOther important blast wave parametersBlast wave scaling lawsHemispherical surface burstsBlast wave pressure profilesBlast wave interactionsRegular and Mach reflectionBlast wave external loading on structuresInternal blast loading of structuresConclusionsReferences

4. Structural response to blast loadingP. D. Smith

NotationIntroductionElastic SDOF structurePositive phase duration and natural periodEvaluation of the limits of responsePressure-impulse diagramsEnergy solutions for specific structural componentsLumped mass equivalent SDOF systemsResistance functions for specific structural formsConclusionsReferences

5. Design of elements in reinforced concrete andstructural steelG. C. Mays

NotationObjectivesDesign loadsDesign strengthsDeformation limitsIntroduction to the behaviour of reinforced concrete

46

66

6668697071

and structural steelwork subject to blast loading 72Introduction to the design of reinforced concrete

elements to resist blast loadingIntroduction to the design of structural steel elements

to resist blast loadingReferences

77

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6. Implications for building operationC. J. R. Veale

Health and safety regulationsThreat assessmentPre-event contingency planningFurther considerationsPost-event contingency planningReference

Appendix A. Simplified design procedure fordetermining the appropriate level ofglazing protection

Appendix B. Transformation factors for beams andone-way slabs

Appendix C. Maximum deflection and response timefor elasto-plastic single degree offreedom systems

Appendix D. Design flow chart

CONTENTS

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959596979898

99

102

110

119

Ed itors' note

Wherever possible the notation has been made consistent betweenchapters. However, there may be come instances where, for clarity, ithas been decided to retain the notation used in the source material. Forthis reason the notation has been separately defined for each chapter.There may also be some instances where the definitions used do notexactly match those used in conventional design standards.

vii

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I Introduction

ObjectivesThis book is aimed at all engineers and architects involved in the designof building structures, and should enable them to have a betterunderstanding of their own and their client's responsibilities in providingbuildings which, in the event of an explosion, minimize damage to peopleand property.

The intended purpose of this book is to explain the theory of the designof structures to resist blast loading and then to suggest relatively simpletechniques for maximizing the potential of a building to provide protectionagainst explosive effects. The book does not encourage designers toproduce hardened structures, nor should it be seen as a precursor to a'super code'; although guidance is given as to where to look for furtherdetails should they be required. In addition, some broad design objectivesconcerning the protection of people, the protection of equipment and theminimizing of damage to structures are given. The book is produced inparallel with a companion document sponsored by the Institution ofStructural Engineers concerning the structural engineer's response tobomb damage [1].

ScopeFollowing this introduction putting the subject in context, the book starts

with some basic guidelines for enhancing the resilience of buildings toblast loading (Chapter 2). 1Sn explanation of the nature of explosions andthe mechanism of blast waves in free air is then given.[Ois leads to adiscussion of the loading that explosions place on structures, both insideand out, and the concept of an idealized loading is introduced (Chapter3). the response of buildings, people and equipment to blast loading isillustrated. A method of analysis is suggested whereby the strain energyabsorbed is equated to the work done or kinetic energy imparted and thestructure reduced to a single degree of freedom (Chapter 4). Methods forthe design of structures and individual elements using different


construction materials are then given (Chapter 5). The book concludesby providing a summary of the implications of the foregoing for building

operation (Chapter 6).The scope of the book is limited to blast effects which derive from above

ground, non-nuclear, high-order explosions and the design only coversstructures that contain a degree of ductility. Only passing mention is madeof the effects of fire, secondary fragments and ground shock.

The discussion is not solely concerned with the protection of structuresagainst terrorist explosions, although this remains a strong themethroughout. The authors suggest that, although there is a wide knowledgeof the effects of terrorism, many public and corporate buildings andinstallations have been built and are still being built with little concernfor the destructive effects of terrorist attacks. As a result they offer theirinhabitants and contents too little protection. It is hoped that this bookwill provide clues as to how to give reasonable and affordable protectionagainst present, and future, threats. Within this introduction and as asetting to the future chapters, some of the special circumstances of terroristattacks will be illustrated, the idea of risk assessment introduced and ageneral philosophy for protection offered.

`TerrorismIf modern terrorism is described as the deliberate use of violence to

create a sense of shock, fear and outrage in the minds of a targetpopulation, several factors in the way we now live have made terrorismmuch more easy to conduct in modern society;

First, terrorists are able to make use of the media as never before tocarry a sense of terror to their target population. Television gives terroristsa political leverage out of all proportion to their other powers. Second,developed societies have become very dependent on complex andvulnerable systems (e.g. railways, airlines, gas pipelines, large shoppingareas and business centres) which allow.,, a terrorist many suitabletargets. Third, terrorists hide behind the cam'o flage of normal daily life.This means that almost all effective measures to combat terrorism alsocarry considerable constraints on individual freedoms, which governmentsare rightly reluctant to impose, and often will not.

The foregoing leads to several conclusions: terrorism today is mucheasier to contain than to eliminate; there are few completely acceptableantidotes to it; the prc"d€nt design will allow for its effects wherever itis possible and affordable.

RiskProtection is not an absolute concept and there is a level of protection

where the cost of protection provided with respect to the cost of the poten-tial loss is optimized. Protection can never offer a guarantee of safety;

INTRODUCTION

conversely, too much protection is a waste of resources with regard towhat is being saved. Furthermore, the consequences of loss vary; someloss is incremental, but certain losses,. ^p.^rch as human life, essential recordsor specialist equipment are cata^ffophic. For these reasons a riskassessment should be made to assess a combination of the type, thelikelihood and the consequences of an attack. Some risks will have to beaccepted, while others must be deflected at all costs. Advice on how toconduct a terrorist threat assessment can be found in Chapter 6.

The special effects of catastrophic failureThe special effects of catastrophic failure or large numbers of casualties

need special attention. In terrorist attacks, the number of casualties causedis often decided by whether or not a warning is given before a terroristdevice is detonated; a warning allows emergency action to be taken. Inthe UK we have become used to one form of terrorism, Irish terrorism,which has its roots in a Christian culture and where the hysterical suicideof a terrorist bomber is not admired. These terrorists have generallywanted to exert pressure through mass publicity rather than to cause masscasualties per se. By contrast, terrorists from the Middle East have alwayssought casualties with abandon, and a group in the future may take actionagainst our society.

Thus, if a structure is to have a useful life of several decades, the effectof an attack without prior warning must be anticipated. Consider whatwould have happened if the bombs in London at St Mary's Axe in 1992(see Plates 1 and 2) or Bishopsgate in 1993 had exploded during workinghours and without warning. The deaths from flying glass in theCommercial Union building could have been into the hundreds (quiteapart from the many other people who would have been badly injured)and few would have escaped unhurt from the collapsed front of theChamber of Shipping. A more important consequence in such situationscould be the public perception of the effects of no warning being givenand their possible reluctance to work in unprotected buildings while thepotential for another attack remains. These arguments are important whentrying to decide the cost/benefit of protective measures.

Partial safety factors in blast designWhen designing structural elements in accordance with limit state

principles, partial safety factors are applied to loads and the strengthsof materials. In designing against blast loading, the following specialconditions will usually apply:

(a) The incident will be an unusual event.(b) The threat will be specified in terms of an explosive charge weight

at a stand-off, which can only be an estimate and already subjectto a risk assessment.

2


Plate 1. Devastating effects of bombing in St Mary's Axe, April 1992

For economic design, some Mastic -deformation-is no_r_mallypermitted. The level of damage is specified in terms of the limitingmember deflection or support rotations.

(d) The strengths of materials will be enhanced because of the highrate of strain to which they will be subjected.

(e) The strengths of in situ materials often exceed the characteristicvalues.

For these reasons, the design initially should becarried_QUtat-the-ultimatelimmt`ate, wig-- tiapar I safety.-faeters-for-both-load-and-materials set at1.0. However, special enhancement factors may be applied to material

INTRODUCTION

strengths. These are considered in further detail in Chapter 5. A limitis usually placed on the deformation of members to permit somefunctionality after the event.

A design philosophy : planning for protectionA starting point for the design of a building that resists blast loading

is to consider the building layout and arrangements. The aim here is todecide what eds_pntection (the contents or the structure itself); toimagine how damage or injury will be caused; and to consider how thebuilding or structure can be arranged to give the best inherent protection.Specifically for protection against terrorist attacks, the building designshould achieve one or all of the following:

(a) Deflect a terrorist attack by showing, through layout, security anddefences, that the chance of success for the terrorist is small; targetsthat are otherwise attractive to terrorists should be madeanonymous.

(b) Disguise the valuable parts of a potential target, so that the energyof attack is wasted on the wrong area and the attack, although

Plate 2. Debris and destruction: Bishopsgate, April 1993

4 5


completed, fails to make the impact the terrorist seeks; it is reduced

to an acceptableannoyance.

(c) Disperse a potential target, so that an attack could never cover a largeenough area to cause significant destruction, and thereby impact;this is suitable for a rural industrial installation, but probablyunachievable for any inner-city building.

(d) Stop an attack reaching a potential target by erecting a physicalbarrier to the method of attack; this covers a range of measures fromvehicle bollards and barriers to pedestrian entry controls. Againsta very large car bomb, in particular, this is the only defence thatwill be successful.

(e) Blunt the attack once it reaches its target, by hardening the structureto absorb the energy of the attack and protect valuable assets.

The first three of these objectives can often be met at no cost, while thelast two require extra funds or special detailing. The final objective, toblunt the attack, is the subject of the remainder of this book and involvesthe following procedure.

From a threat analysis, one can find the size and location of theexplosion to protect against. By using the relationship that the intensityof a blast decays in relation to the cube of the distance from the explosionone can adopt an idealized blast wave at the target. Using published data(Chapter 3) the characteristics of that blast wave can be determined.

The positive phase duration of the blast wave is then compared withthe natural period of response of the structure or structural element. Theresponse is defined by the two possible extremes: impulsive (where theload pulse is short compared to the natural period of vibration of thestructure) and quasi-static or pressure (where the load duration is longcompared with the natural response time of the structure). In betweenis a regime where the load duration and structural response times aresimilar, and loading in this condition is referred to as dynamic orpressure-time.

For impulsive loading most of the deformation will occur after the blastload has finished. The impulse, which can be determined, imparts kineticenergy to the structure, which deforms and acquires strain energy. Thestrain energy is equivalent to the area beneath the resistance-deflectionfunction for the structure. This function is the graph of the variation ofthe resistance that the structure offers to the applied loading as thedisplacement of the structure increases. It should be based upon thedynamic behaviour of the structure, taking due account of compressiveand tensile membrane action.

For quasi-static loading, the blast will cause the structure to deformwhilst the loading is still being applied. The loading does work on thestructure, causing it to deform and acquire strain energy as before.

INTRODUCTION

For dynamic-loading, if the design cannot be covered by the twoprevious methods, the structural response may involve solving theequation of motion of the structural system.

Reference

1. Institution of Structural Engineers, The structural engineer's response to bombexplosion. (In press).

I

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BASIC GUIDELINES-FOR ENHANCING BUILDING RESILIENCE

2 Basic guidelines for enhancingbuilding resilience

IntroductionEffects of an external explosionAn explosion is a very fast chemical reaction producing transient airpressure waves called blast waves 1 The processes of blast wave formationand quantification are discussed in detail in Chapter 3^For a ground-levelexplosive device (such as a bomb in a vehicle), the pressure wave will travelaway from the source in the form of a hemispherical wavefront if thereare no obstructions in its path) The peak overpressure (the pressure abovenormal atmospheric pressure) and the duration of the overpressure varywith distance from the device. The magnitude of these parameters alsodepends on the explosive materials from which the bomb is made andthe packaging method for the bomb. Usually the size of the bomb is givenin terms of a weight of TN-T. Methods exist for the design of structuralelements subjected to blast loads from bombs of specified charge weights:these are discussed in Chapter 5.

City streets confine the blast wave and prevent it from radiatinghemispherically and this tends to increase the pressures to whichbuildings are subjected.rhe blast pressure waves will also be reflectedand refracted by buildings, travelling around the corners and curves ofa building. Blast waves are very intrusive: they will travel down sidestreets and over the tops of buildings, and thus all sides of a buildingwill be subject to overpressures. As the wave moves further from thesource of the explosion, the peak overpressure drops. However, theconfining effect of buildings, called 'funnelling', and rising ground meansthat the pressure drops more slowly than in open ground and buildingscan be at risk at what might normally be considered safe distances (seePlate 3).

When blast waves impinge directly onto the face of a building, theyare reflected from the building. The effective pressure applied to that faceof the building is magnified when this occurs. If a bomb is very close toa building, the building will also be impacted by shrapnel from the bomb

Plate 3. Confining effects of narrow city streets

packaging and by debris from the break-up of 'street furniture' such aslitter bins and so on (Plate 4). This shrapnel moves at high velocity andwill penetrate thin building facades and unprotected glazing. This effectwill be hazardous to personnel who should, if possible, have the chanceto avail themselves of the protection offered by solid internal walls. Designmethods are available which can mitigate this effect.

All of the above factors contribute to the variation in the effects of an

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explosion experienced by a particular building. For a city centre buildingin particular, the exact location of a bomb relative to the building is veryimportantlTherefore, it is impossible to predict with great accuracy theeffects of a bomb explosion on a particular building at the design stage.Instead, the designer should attempt to form an opinion about the possiblethreats and the likely effects of such threats.

Stand-off distance (the distance between the bomb and the building)is a fundamental parameter when determining the blast pressuresexperienced by a building€As stand-off distance increases, blast pressuredrops significantly Therefore, putting distance between the building andthe bomb is extremely helpful in reducing blast effects on the building.However, that isZnot always a controllable parameter. or example, ina city, space is at a premium and the provision of large stand-off distancesmay be impossible Indeed the question as to whether the building needsto occupy a high-risk site should be addressed. A further factor that shouldbe noted is that the client may be unable to prevent a device being placedimmediately outside the entrance to the building. However, it should bepossible to take measures to(maintain stand-off that would prevent, forexample, a vehicle mounting the pavement outside a building, parkingadjacent to the building or approaching the front entrance.\ The installationof bollards and other substantial items of street furniture could beconsidered. It may also be worth investing in 'hard' landscaping -incorporating steps or mounds adjacent to the building entrance tocontribute to stand-off. However, care should be taken if considering 'soft'landscaping to ensure that concealment places for the smaller carrieddevices are not created by dense planting.

For a device placed inside a building (the stand-off distance being noweffectively zero), greater damage and more injuries would be caused thanif the same sized device were deployed outside the building. Therefore,the installation of an access control system on both pedestrian andvehicular entrances will minimize the opportunity for placement of themajority of the types of device that could be introduced into a building.This will lead to a minimization of the hazard to both people and property.

The response of a building

Loads from blasts are transient, so th^ ductility and natural period ofvibration of the structure govern its response to a given explosioilt) Thenatural period can be calculated crudely using methods in the Uniform

il ing Code [1]AIn general, a tall building will have a low naturalfrequency and thus a long response time in relation to the duration ofthe loads Individual elements (e.g. columns and beams) will have naturalresponse times that may approach the loading duration.kDuctile elementsmade of steel and reinforced concrete can absorb a lot of strain energy(i.e. they can undergo substantial bending without breaking), while

BASIC GUIDELINES FOR ENHANCING BUILDING RESILIENCE

Plate 4. Street debris generated by a blast

elements made of brittle materials such as glas , brick, timber and cast-iron fail abruptly with little prior deformation

lexible components such as high-mass, long-span beams and floorscan absorb a great deal of the energy delivered by a blast loaddOn theother hand, rigid, short-span lightweight elements (e.g. conventionalglazing components ) are poor energy absorbers and can fail catastrophi-cally (Plate 5). This response is a function both of the material propertiesand the way such materials are used . For example, it is possible to useconcrete to create both a flexible frame or a much more rigid bunker-likestructure . Massive structures , in general, respond better than those oflightweight construction.

to € II


Plate 5. Widespread damage to conventional glazing

It is worth commenting on techniques for enhancing the resistance ofglazing elements to blast loading. Such techniques do not involve thestrengthening of the glazing lights alone: without proper dynamic designof the frames, the resulting assembly may perform even worse than withno treatment.

There are three main ways of providinglglazing protection) These are:

(a) The application of transparent polyester anti-shatter film (ASF) tothe inner surface of the glazing with the optional provision of bombblast net curtains (BBNC).

(b) The use of blast-resistant glass.


(c) The installation of blast-resistant secondary glazing inside the(existing) exterior glazing.

Blast-resistant glazing generally consists of laminated annealed glass orlaminated toughened glass or, in double-glazed units, combinations oftoughened and laminated glass.;In double-glazed units laminated glazingis generally the inner pane though, for preference, both should belaminated material. As noted above, a suitably designed robust frame andfixings will need to be used to install the glazing.

The primary purpose of glazing protection is to reduce the number ofsharp-edged fragments that are created when ordinary annealed ortoughened glass is subjected to blast loading. 9:'hese shards, which travelat high speed, can cause severe injuries to personnel, can damage delicateequipment inside buildings such as the hardware for computer systemsand cause major problems should they enter the air-conditioning system.Blast. si nt azing has the capability to decrease greatly (by up to 90%)the number of loose shards produced. In addition, the amount of glassfalling from the building after an explosive event is greatly reduced(Plate 6). This enables subsequent access to the building to be very muchquicker and, since the majority of the glazing is attached either to theASF or to thelaminated glass polymeric 'inter-layer', clearing up is easierand quicker than without such glazing protection. A simplified procedureis presented in Appendix A for use as a guide to the design of glazingto resist blast loading.

I

Plate 6. Europa Hotel, Belfast: laminated glazing panels are retained in robust framesdespite large deflections. Photograph courtesy of Kirk McClure Morton

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As well as windows, doors and service openings are vulnerable pointson a building which external blasts can penetrate. In the case of biggerexplosions, the structure as a whole becomes affected Although framedbuildings generally perform better than panel or load-bearingconstruction3kit is possible that all floors could be momentarily lifted bythe blast that has entered Blast pressures can also damage equipmentwithin the building and travel to its heart (e.g. to plant rooms) via airducts.

As well as incurring ear and lung injuries from the blast overpressure,occupants can suffer injury from missiles such as glass and shrapnel andfrom high-speed spalling of concrete cover as elements flex. Somequantification of injury levels is presented in Chapter 4. The suddenmovement of the building structure can also displace features such asheavy suspended ceilings and office furnishings such as filing cabinetsand desks.

The requirements of the clientThe type of building being considered in this chapter is a typical

commercial multi-storey office block, assumed to be a completely newstructure without a retained facade. The client or architect has a numberof choices to make regarding the fundamental aspects of the buildingdesign. The engineer can advise the client regarding these choices basedon the points made in this chapter. However, the building will notsuddenly become blast resilient by compliance with these basic rules, andthe client should understand this.

The client has to decide to what expense he or she is prepared to goin order to protect the building. There are features- that can be includedin the design which will enhance the resilience, but these are expensive.The level of protection provided has to be decided in terms of performanceunder various conditions. For example, consideration should be givento the theoretical stand-off distance for a particular device at which theglazing should remain intact. Also, providing protection against a higherblast pressure from a bigger or closer device will be more expensive. Therecould be savings in the future if an incident were to occur, but the riskof this occurring has to be balanced against the initial expense of theresilience provisions.

The fundamental requirement is safety of the building's occupants. TheBuilding Regulations [2] specify that a local collapse should not prejudicethe overall stability of a structure. This requirement was included as aresult of the collapse of the Ronan Point block in 1968 which occurredas the result of a gas explosion. This philosophy is pertinent for a terroristattack where a large device placed close to the structure could sever oneor more columns. The ability of the building to survive without collapse,except in the immediate locality of the explosion, will save the lives of

BASIC GUIDELINES, FOR ENHANCING BUILDING RESILIENCE

occupants and assist rescue of those who are trapped. As only framedbuildings can be considered to offer the ability to survive against a terroristattack, it is therefore advised that all framed structures should be designedin accordance with the robustness clauses of BS 5950 [3] or BS 8110 [4]as a minimum.

The provision of bomb shelter areas (BSAs) is a second requirementand is considered a better option than evacuation, in many circumstances.These are areas within the building in which the occupants can seek refugein the event of an alert and will be discussed in more detail later in thischapter.

The client will then have to decide the size of the device loading fromwhich he or she requires the building to survive and be subsequentlyrepairable (i.e. the building should suffer no major structural defects).This implies that a limit would need to be placed on the magnitude ofplastic deformations. If the client requires survival of the building's glazingthen the loading on the building would need to be kept much lower toelicit a truly resilient performance. It is worth noting, therefore, that certaindesign details can mean that outwardly similar buildings have dissimilarperformances. Some extra expense for design enhancements can save agreat deal of money in the amount of repair required.

As a consequence of this, the client must be presented with clear optionsregarding the required level of protection with due regard to the potentialblast loading from various devices placed at various stand-off distances.The client is then in a position to assess the cost implications of theseand choose the appropriate level of protection.

Architectural aspects and design featuresThe architect may well be wishing to design a building with notable

features such as a large glazed frontage, possibly in conjunction with aglazed atrium. These are examples of features that would lead to veryvulnerable structures with little inherent resistance to blast loads. Theyalso cause high hazards from secondary fragments generated by failureof parts of the structure. If such features are to be specified, then thepotential repair bill is likely to be large. Also, there could be implicationsfor building insurance: premiums have already increased for the provisionof cover against acts of terrorism and an obviously vulnerable buildingis likely to attract a higher premium.

Therefore, there are several aspects of the design of the facade of abuilding that should be considered when attempting to minimize thevulnerability of the people within the building and the damage to thebuilding itself as described below.

(a) As a general rule, it is a good idea to minimize the amount of glazingon the facade of the building. This limits the amount of internal

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(b)

damage from the glazing and the level of the blast loading that canenter the building to cause damage to fixtures and fittings.Ensure that the cladding is securely fixed to the structure with easilyaccessible fixings. This will allow rapid inspection and, if necessary,replacement, after an event.

(c) Ensure that the cladding system allows for the easy removal andinstallation of individual panels. This will avoid the need to removeall the panels after an event if only one is damaged.

(d) Avoid the use of deep reveals and deep, flat window sills whichare accessible from ground level as these provide ideal concealmentplaces for small devices.

(e) Minimize the use of deep surface profiling because such featurescan enhance blast effects by virtue of the complex reflectionsproduced and lead to a greater level of damage than would beproduced with a plane facade.

Likewise certain structural elements already present in a building can bearranged to advantage to provide protection, e.g. a diaphragm wallotherwise designed to produce shear resistance. The building would alsobenefit if design takes into account the need for post-event inspectionof details.

Provision of shelter areasIn order to safeguard people from the effects of a blast, the first action

that must be taken is to move them as far away from the device as possible:a natural reaction might well be to evacuate personnel swiftly out to thestreet. However, this may not always be easily and safely accomplished.Consideration then should be given to moving people to a BSA.

The shelter concept has been employed over many centuries in timesof conflict. During the Second World War shelters took many formsranging from the arch-shaped corrugated steel Anderson shelters thatwere built in many back gardens and the steel Morrison tables for usewithin the home, to the use of London Underground stations wherewhole communities sought refuge from the Blitz. Thus, the provision ofa BSA at the design stage of a new building or its creation within anexisting building will be beneficial even though-such a provision will notprovide complete protection.

It is worth commenting on the BSA philosophy in the context of thepresent terrorist threat. The philosophy is based on the examination ofthe effects of blast from large vehicle bombs (in both Britain and NorthernIreland) on various structural frames. The conclusions drawn from thisexamination are:

(a) Structural frames of modern reinforced concrete and structural steel


Plate 7. Grand Opera House, Belfast: some load-bearing masonry walls are unstable,while others remain relatively intact - the structure was subsequently repaired

buildings remain relatively intact and do not suffer major collapse,although lightweight cladding and internal partitions and ceilingsare totally destroyed.

(b) Heavy masonry fronted and internal steel-framed buildingsconstructed at the turn of the century also remain relatively intact(Plate 7).

(c) Internal rooms of the buildings described in (a) and (b) where wallsare constructed of reinforced concrete or masonry also remainrelatively intact.

On the other hand, severe personal injuries from falling glass and otherdebris are likely to occur at considerable distance from the seat of a largeexplosion. For a device comprising 1 tonne of home-made explosive(HME), injuries from falling glass may occur at up to 250 m from theexplosion and, from metal fragments, at up to 500 m (Plate 8).

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Plate 8. The disintegration of buildings in Bangor, N. Ireland due to blast loadingproduces fragments that could inflict serious injuries. Photograph courtesy of KirkMcClure Morton

The conclusion to be drawn from this evidence is that moving staff toareas within a building rather than evacuating onto the streets in the eventof a bomb alert is the best policy for very large vehicle bombs as well asother kinds of smaller externally deployed devices. For buildings of thetypes described above, BSAs should be located:

o remote from windows, external doors and wallso remote from the 'perimeter structural bay' (i.e. that part of the floor

structure, at all levels, between the building's perimeter and thefirst line of supporting columns)

e in areas surrounded by full-height masonry or concrete walls (e.g.internal corridors, toilet areas or conference rooms).

BSAs should not be located in stairwells or in areas with access to lift-shafts as these generally open out at ground floor level directly to thestreet. However, in certain buildings where the stair and lift cores aretotally enclosed, a very good BSA may be established.

It is important to have adequate communications established withindesignated BSAs to inform staff of any subsequent action which may needto be taken - e.g. to remain within the BSA, to move to another BSA(if the location of a device presents a particular threat), to evacuate thebuilding or to give the 'all clear'. The system of communication may be


a public address system (which may require stand-by power should anexplosion cut the main electricity supply), hand-held radio transmitter/receivers or other stand-alone audio-communication links. Furtherinformation on such contingency planning may be found in Chapter 6.

Location of key equipment and servicesThe most essential assets for the client (e.g. central computing facilities)

should be safeguarded and the option for back-up facilities should beconsidered. Operational resilience could involve having duplicate criticalsystems either located in another building situated at least 1 kilometreaway or, if it is large enough, located at the opposite end of the buildingunder threat.

If, however, a critical asset cannot be duplicated then blast effects shouldbe minimized by locating it in internal and relatively safe rooms thatshould, ideally, offer the same level of protection provided by a BSA inthe building.

Building form?The essential requirement is for a ductile structure to resist the worsteffects of blast loading.Whis requirement forces the designer to considerconstruction of reinforced concrete or steel-framed buildings'(Plate 9f /Aframed building, tied together adequately, will have many different load

Plate 9. Comparative blast damage to steel framed flats and a church with load-bearing walls. Photograph courtesy of Francis Walley

18 1 19


paths by which to transfer loads to the ground . If this aspect is coupledwith ductile behaviour, the structure will fulfil its primary safetyrequireme t.As noted Vove, internal partitions can be a serious hazardto safety . They are generally lightweight and can be easily demolishedunder relatively low levels of blast loading and would cause a secondaryflying debris hazard. Careful detailing to either remove or providesufficient strength for partitions will remove the hazard . Floors shouldbe tied to the frame, and have the potential to withstand stress reversals.

3Blast loads can often impart uplift pressures that are sufficient to overcomegravity loads on a floor. Unless the floor is tied down, it will dislodge. )Floors can act as diaphragms which transfer lateral loads between frames,and the loss of these floors could initiate a progressive collaps& Suitablemeasures to counter these effects are the provision of continuous spansand, particularly in lower floors , the introduction of reinforcement in bothfaces of the slab (e.g. mesh mats should be cast in the top of the slab).

Design of individual structural elementsJust as with structures designed for static loading, the engineer should

use limit state design techniques: ultimate limit state (ULS) (collapse) andserviceability limit state (SLS) (functionality after event) approaches.{ The collapse state requires sufficient ductility to dissipate the blastenergy without causing collapse eams should have symmetrical primaryreinforcement and sufficient shear links to provide restraint and preventpremature shear failures Deflections are usually allowed to exceed theelastic limit by up to a certain factor, known as the ductility ratio.However, it is not envisaged that a dynamic design calculation needalways be undertaken by structural engineers designing an office. building.In some cases, by designing in accordance with BS 5950 [3] or BS 8110[4, 5], a satisfactory design may be achieved as long as moment-resistingstructures with continuous spans are detailed. It should be noted,however, that these standards have not been prepared to deal specificallywith terrorist explosions. For example, the minimum horizontal load tobe applied to the exterior of a building is not applicable and the pressureof 34 kN/m2 specified for the design of key elements has been based oninternal domestic gas explosions.

In other cases it will be necessary to design elements specifically to resistthe blast loading. The design of structural elements to resist blast loadingat the ULS is covered in some depth in Chapter 5. Bearing in mind thatthe cost of the structural frame in a building may represent only 25-30%of total building costs, there is evidence [6] to show that the requiredincreases in element size may result in an increase in cost of no more than2-3% overall.

The performance of the connections is vital to the behaviour at ULS(Plate 10). In steel-framed construction, particularly, the joints must be


Plate 10. Failure of beam-column joint in reinforced concrete frame due to poordetailing

detailed to carry moments around the frame^, ;rhe joints should be capableof resisting stress reversals , as should the structure as a wholes A column-beam joint may not transfer moment into the column in static designbecause the moment at each beam end equalizes . However, in a blastsituation which could impose large sway deflections on the structure andgenerate substantial moments, these moments have to be transferred tothe columns from the beams.

At ULS, the frame will survive, but may be so badly deformed as tobe suitable only for demolition . Therefore , limitations are often placedupon the magnitude of material stresses and member deflections toprovide some level of post-event functionality . A further SLS requirementis the maintenance of windows , cladding and internal fixings. Theseshould have a measure of blast resilience ; flexible or ductile partitionstied to the structural frame are therefore required . Windows are to belaminated , or have ASF applied (as described above), if a reasonable levelof resistance is to be provided in a moderate risk area.

20 1 21


Plate 11. Concrete framed structure with concrete cladding panels, whose fixings

have failed either partially or completely

Serviceability design could entail the design of details that enablestraightforward repair of the damaged fenestration. Cladding may beallowed to yield, so long as fixings do not fail (Plate 11). The buildingshould remain weathertight, and repair could be effected without majorinterruption of the operation of the office.

Building layoutThe layout of the building can enhance the performance of the structure

when subjected to blast loading and enable the provision of BSAs. Suchperformance enhancements can be achieved by adherence to some or allof the following guidelines:

(a) A building should be three bays wide at least, to allow personnel


to move away from windows and into the relative safety of a centralcorridor or core area.

(b) Buildings should have structural core areas, preferably formed inreinforced concrete, for use as BSAs.

(c) Re-entrant corners should be avoided since they increase blastpressures locally because of the complex reflections created. (Seealso comments on building facades above.)

(d) Reductions in blast loads can be achieved by, for example, settingback upper floors to increase the stand off. This can only be effectivefor relatively low buildings with a large floor area.

References

1. ICBO. Uniform Building Code. International Conference for Building Officials,Whittier, USA, 1985.

2. HMSO. The Building Regulations. HMSO, London, 1985.3. British Standards Institution. Structural use of steelwork in building. Code of

practice for design in simple and continuous construction : hot rolled sections. BSI,London, 1985, BS 5950: Part 1.

4. British Standards Institution. Structural use of concrete. Code of practice fordesign and construction. BSI, London, 1985 (amended 1993), BS 8110: Part 1.

5. British Standards Institution. Structural use of concrete. Code of practice forspecial circumstances. BSI, London, 1985, BS 8110: Part 2.

6. Elliott C.L., Mays G.C. and Smith P.D. The protection of buildings againstterrorism and disorder. Proc. Instn Civ. Engrs, Structures and Buildings, 1992,94, 287-297. Discussion, 1994, 104, 343-350.

22 23

BLAST LOADING

3 Blast loading

Notation

ao speed of sound in air at ambient conditionsA area of target loaded by blastAs total inside surface area of structureb wavefront parameterB target dimensionsC, reflection coefficientCo drag coefficientd charge diameterFo drag forceH target dimensionsig gas pressure impulseis specific side-on impulsei, specific reflected impulsei- negative phase specific impulsep pressurepo atmospheric pressurepQs peak quasi- static gas pressurepr peak reflected overpressure

P. peak side-on overpressurepstag stagnation pressureOpm;n peak underpressureqs peak dynamic pressureQ mass specific energy of condensed high explosiveR range from charge centreS target dimensionst timet' pressure reduction timet, arrival time of blast wave fronttmax blowdown time for internal explosiontr reverberation timeTs positive phase durationTr positive phase duration of reflected waveus particle velocity behind blast wave front

U, blast wave front speedfi Mach number of wavefront particle velocityU Mach number of wavefrontV volume33 mass of spherical TNT chargeZ scaled distancea, ratio of vent area to wall areaa' angle of incidencey specific heat ratioX scale factor

IntroductionThis chapter deals with the formation and quantification of blast wavesproduced by condensed high explosives. In particular it presentsinformation allowing the reader to evaluate peak overpressures and theassociated impulses for a range of explosives expressed in terms of a scaleddistance based on range and the mass of TNT equivalent to the actualexplosive being considered for both spherical and hemispherical charges. SThe pressure produced by the processes of reflection are evaluated andthe forces that result on structures are described both for explosivesexternal to a building and for explosions inside a structures In the lattercase, the effect of the so-called gas pressure loading produced by theproducts of detonation is quantified.

Explosions,../ Explosions can be categorized as physical, nuclear or chemical events.

Examples of physical explosions include the catastrophic failure of acylinder of compressed gas, the eruption of a volcano or the violent mixingof two liquids at different temperatures. In a nuclear explosion the energyreleased arises from the formation of different atomic nuclei by theredistribution of the protons and neutrons within the interacting nuclei.

A chemical explosion involves the rapid oxidation of fuel elements(carbon and hydrogen atoms) forming part of the explosive compound.The oxygen needed for this reaction is also contained within thecompound so that air is not necessary for the reaction to occur. To beuseful, a chemical explosive must only explode when required to andshould be inert and stable. The rate of reaction (much greater than theburning of a fuel in atmospheric air) will determine the usefulness of theexplosive material for practical applications.(Most explosives in commonuse are 'condensed': they are either solids or liquids. When the explosiveis caused to react it will d compose violently with the evolution of heatand the production of gas The rapid expansion of this gas results in thegeneration of shock pressures in any solid material with which theexplosive is in contact orcblast waves if the expansion occurs in a mediumsuch as air. S

24 4 25

BLAST EFFECTS ON BUILDINGSII

BLAST LOADING

Although far less commonly deployed by terrorists, mention shouldbe made of 'fuel-air' or 'vapour cloud' explosions which can producedamage to structures commensurate with that produced by condensedhigh explosives. In such events the chemical reaction is generallydeflagrative (see below) producing pressures that may not be as high ata given range from the explosion centre as for an equivalent quantity ofcondensed explosive but which remain at a significant level for a longerperiod.

Explosion processes terminologyCombustion is the term used to describe any oxidation reactions,

including those requiring the presence of oxygen from outside as wellas those that use oxygen which is an integral part of the reactingcompound.

In the case of explosive materials which decompose at a rate much belowthe speed of sound in the material, the combustion process is known asdeflagration) Deflagration is propagated by the liberated heat of reaction:the flow direction of the reaction products is in opposition to the directionof decomposition.

Detonation is the explosive reaction which produces a high intensityshock wave. Most explosives can be detonated if given sufficient stimulus.The reaction is accompanied by large pressure and temperature gradientsat the shock wave front and the reaction is initiated instantaneously. Thereaction rate, described by the detonation velocity, lies between about1500 and 9000m/s which is appreciably faster than propagation by thethermal processes active in deflagration. It is worth noting that, if acondensed high explosive is detonated in contact with a structure, theimpact of the detonation wave producesS a shattering effect on the materialof the structure known as 'brisance'.1

Explosives classificationHigh explosives detonate to create shock waves, burst or shatter

materials in or on which they are located, penetrate materials, producelift and heave of materials and, when detonated in aiF or under water,produce air-blast or underwater pressure pulses. Low explosivesdeflagrate to produce pressure pulses generally of smaller amplitude andlonger duration than high explosives) Examples include propellants forlaunching projectiles and explosive mixtures such as gunpowder.

Classification of these materials is generally on the basis of theirsensitivity to initiation. A primary explosive is one that can be easilydetonated by simple ignition from a spark, flame or impact. Materials suchas mercury fulminate, and lead azide are primary explosives. They arethe type of materials that can be found in the percussion cap of firearmammunition. Secondary explosives can be detonated, although less easily

than primary explosives. Examples include TNT and RDX (also knownas cyclonite) among many others. In firearm ammunition, a secondaryexplosive would be used for the main explosive charge of the shell orcartridge.

In order to achieve the required properties of safety, reliability andperformance (also paying due regard to economic considerations), it iscommon practice in both military and commercial explosives manufactureto blend explosive compounds. For commercial use, explosives aregenerally made from cheaper ingredients: TNT or nitroglycerine mightbe mixed with low-cost nitrates, for instance. Such material has a generallyshort shelf-life. Military explosives are composed of more expensiveingredients (such as binary mixtures of stable compounds like TNT andRDX or HMX with TNT) and generally have a long shelf-life.

Terrorist organizations typically only have limited quantities of military-style high explosives such as Semtex and as a consequence oftenmanufacture their own explosive materials, from farm fertilizer, forinstance. In the quantities necessary to attack substantial structures, thismaterial behaves as a detonating high-eexplosive material.

Blast waves in air from condensed high explosivesWhen a condensed high explosive is initiated the following sequence

of events occurs. Firstly, the explosion reaction generates hot gas whichcan be at a pressure from 100 up to 300 kilobar and at a temperature ofabout 3000-4000°C. A violent expansion of this gas then occurs and thesurrounding air is forced out of the volume it occupies. As a consequencea layer of compressed air - the blast wave - forms in front of this gascontaining most of the energy released by the explosion. As the gasexpands its pressure falls to atmospheric pressure as the blast wave movesoutwards from the source. The pressure of the compressed air at the blastwavefront also falls with increasing distance. Eventually, as the gascontinues to expand it cools and its pressure falls a little below atmosphericpressure. This 'overexpansion' is associated with the momentum of thegas molecules. The result of overexpansion is a reversal of flow towardsthe source driven by the small pressure differential between atmosphericconditions and the pressure of the gas. The effect on the blast wave shapeis to induce a region of 'underpressure' (i.e. pressure is below atmosphericpressure) which is the 'negative phase' of the blast wave. Eventually thesituation returns to equilibrium as the motions of the air and gas pushedaway from the source cease.

Blast wavefront parametersOf particular importance are the blast wavefront parameters. Analytical

solutions for these quantities were first given by Rankine and Hugoniotin 1870 [1] to describe normal shocks in ideal gases and are available in

26 27


a number of references such as Liepmann and Roshko [2]. The equationsfor blast wavefront velocity, Us, and the maximum dynamic pressure,qs, are given below

6ps + 7Po

US 7Poao

5P29:= 2(Ps+7po)

(3.1)

(3.2)

where ps is peak static overpressure at the wavefront, po is ambient airpressure and ao is the speed of sound in air at ambient pressure.

The analysis due to Brode [3] leads to the following results for peakstatic overpressure in the near field (when p, is greater that 10 bar) andin the medium to far field (p5 between 0.1 and 10 bar)

p, = 23 + 1 bar (ps > 10 bar) (3.3)

Ps = 0.9751-425 + 5235 - 0019 bar (0.1 < ps < 10 bar).

Here Z is scaled distance given by

Z = R/Wvs (3.4)

where R is the distance from the centre of a spherical charge in metresand W is the charge mass expressed in kilograms of TNT.

The use of TNT as the 'reference' explosive in forming Z is universal.The first stage in quantifying blast waves from sources other than TNTis to convert the actual mass of the charge into a TNT equivalent mass.The simplest way of achieving this is to multiply the mass of explosiveby a conversion factor based on its specific energy and that of TNT.Conversion factors for a number of explosives are shown in Table 3.1adapted from Baker et al. [4]. From the table it can be seen that a 100 kgcharge of RDX converts to 118.5 kg of TNT since the ratio of the specificenergies is 5360/4520 (=1185).

An alternative approach described in [5] makes use of two conversionfactors. The choice of which to use depends on whether the peak over-pressure or the impulse delivered is to be matched for the actual explosiveand the TNT equivalent. Thus, for Compound B the equivalent pressurefactor is 1.11 while that for impulse is 0.98.

The TNT equivalence of terrorist-manufactured explosive material(known as home-made explosive or HME) is difficult to define preciselybecause of the variability of its formulation and the quality of the controlused in its manufacture. TNT-equivalent factors ranging from as low as0.4 (for poor quality HME) up to almost unity have been suggested.

BLAST LOADING

Table 3.1. Conversion factors for explosives

Explosive Mass specificenergy

Q.(kJ/kg)

TNTequivalent(Qx/QTNT)

Compound B (60% RDX 40% TNT)RDX (Cyclonite)HMXNitroglycerin (liquid)TNTBlasting Gelatin (91% nitroglycerin, 7.9%nitrocellulose , 0.9% antacid , 0.2% water)60% Nitroglycerin dynamiteSemtex

51905360568067004520

452027105660

11481.185125614811000

10000.6001250

Similarly for fuel-air or vapour cloud explosions, TNT equivalence is hardto specify accurately though a factor of between 0.4 and 0. 6 is sometimesused.

Other important blast wave parametersOther significant blast wave parameters include Ts, the duration of the

positive phase (the time when the pressure is in excess of ambientpressure) and is the specific impulse of the wave which is the areabeneath the pressure-time curve from arrival at time t, to the end of thepositive phase as given by

is= J^a +T ps(t) dt (3.5)

A typical pressure-time profile for a blast wave in free air is shown inFig. 3.1, where Apmin is the greatest value of underpressure (pressurebelow ambient) in the negative phase of the blast. This is the rarefactionor underpressure component of the blast wave. Brode's solution for

APmin (bar) is

05 (Z > 1.6) (3.6)Pmin =

and the associated specific impulse in this phase i- is given by

I - - is112Z1]

(3.7)

A convenient way of representing significant blast wave parameters isto plot them against scaled distance as shown on Fig. 3.2 which is adapted

2B € 29


1 Pa)

Area is

Po-4Pmm

Ts

!s

Fig. 3.1. Typical pressure-time profile for blast wave in free air (10)

from graphs presented in a number of references such as Baker et al. [4]and the design code TM5-1300 [6].

The directory of significant blast-wave parameters should also includedynamic pressure, q, blast-wave front speed Us expressed as U (= Us/ao),particle velocity just behind the wavefront, us, expressed as u (=us/ao)and the waveform parameter b in the equation describing the pressure-time history of the blast wave [(eqn (3.10)]. Figure 3.3 shows theseparameters plotted against scaled distance Z.

Blast wave scaling lawsThe most widely used approach to blast-wave scaling is that formulated

independently by Hopkinson [7] and Cranz [8]. Hopkinson-Cranz scalingis commonly described as cube-root scaling. Thus, if the two chargemasses are W1 and W2 of diameter d1 and d2, respectively then, for thesame explosive material, since W1 is proportional to Al and W2 isproportional to d2, it follows that

/3

d2 = WW(3.8)

Therefore, if the two charge diameters are in the ratio d1/d2 = X, thenif the same overpressure ps is to be produced from the two charges the

BLAST LOADING

10 10° 10' 10Z = RIW /: m/k9,

Fig. 3.2. Side-on blast wave parameters for spherical charges of TNT in free air (41

ratio of the ranges at which the particular overpressure is developed willalso be X, as will the positive phase duration ratio and the impulse ratio.Ranges at which a given overpressure is produced can thus be calculatedusing the results of eqn (3.8). For example

\ I1/3(3.9)R2 = (W1 2

where R1 is the range at which a given overpressure is produced bycharge W1 and R2 is the range at which the same overpressure isgenerated by charge W2.

The Hopkinson-Cranz approach leads readily to the specification of thescaled distance Z (=R/W113) introduced above: it is clear that Z is theconstant of proportionality in relationships such as those of eqn (3.8). Theuse of Z in Figs 3.2, 3.3 and 3.5 allows a compact and efficient presentationof blast wave data for a wide range of situations.

30 31


1o3

10°

10'

.1

1o5

10°

103L10.3 10-'

102

0

0°

10

0-

10

10-"10° 10' 10' 1o3

a mik9'

Fig. 3.3. Additional blast wave parameters for spherical charges of TNT in free air I41

Hemispherical surface burstsThe foregoing sections refer to free-air bursts remote from any reflecting

surface and are usually categorized as spherical airbursts. Whenattempting to quantify overpressures generated by the detonation of highexplosive sources in contact with the ground, modifications must be madeto charge weight before using the graphs presented earlier.

Good correlation for hemispherical surface bursts of condensed highexplosives with free air burst data results if an enhancement factor of 1 - 8is assumed. In other words, surface bursts produce blast waves thatappear to come from free air bursts of 1.8 times the actual source energy.It should be noted that, if the ground were a perfect reflector and noenergy was dissipated (in producing a crater and groundshock) thereflection factor would be 2 (Plate 12).

BLAST LOADING

Plate 12. Bishopsgate crater generated by vehicle bomo

Blast wave pressure profilesThe pressure-time history of a blast wave is often described by

exponential functions such as the Friedlander equation [in which b is calledthe waveform parameter (see above)].

P(t) = Ps[1 - Ts] expI Ts)(3.10)

For many purposes, however, approximations are quite satisfactory. Thus,linear decay is often used in design where a conservative approach wouldbe to represent the pressure-time history by line I in Fig. 3.4. Alternativelyit might be desirable to preserve the same impulse in the idealized waveshape compared with the real profile as illustrated by line II in Fig. 3.4where the areas beneath the actual decay and the approximation are equal.

Blast wave interactionsWhen blast waves encounter a solid surface or an object made of a

medium more dense than air, they will reflect from it and, dependingon its geometry and size, diffract around it. The simplest case is that of

32 33


Ps

Fig. 3.4. Idealization of pressure-time profile f101

an infinitely large rigid wall on which the blast wave impinges at zeroangle of incidence. In this case the incident blast wave front, travellingat velocity Us, undergoes reflection when the forward moving airmolecules in the blast wave are brought to rest and further compressedinducing a reflected overpressure on the wall which is of higher magnitudethan the incident overpressure.

Rankine and Hugoniot derived the equation for reflected overpressurepr (assuming that air behaves as a real gas with specific heat ratio Cp/C„= y) in terms of incident peak overpressure and dynamic pressure [givenby eqn (3.2)] as

t

Pr = 2ps + (y + 1)qs (3.11)

Substitution of qs into this equation gives

pr_ = 2Ps7po+4ps

7Po_+N(3.12)

when, for air, y is set equal to 1 - 4. If a reflection coefficient Cr is definedas the ratio of pr to ps then inspection of this equation indicates an upperand lower limit for Cr. When the incident overpressure ps is a lot lessthan ambient pressure (e.g. at long range from a small charge) the lowerlimit of Cr is 2. When ps is much greater than ambient pressure (e.g. atshort range from a large charge) we have an upper limit for Cr of 8.However, because of gas dissociation effects at very close range, measure-ments of Cr of up to 20 have been made. Figure 3.5 shows reflectedoverpressure and impulse it for normally reflected blast wave parametersplotted against scaled distance Z.

BLAST LOADING

10i°

1o°F

10° F

10- l-

104-

10.

-410°

-4105

10^ 10310-2 10-' 100 10 ' 10° 10'

Z = R/W'F3: mIkg'F3

Fig. 3.5. Normally reflected blast wave parameters for spherical charges of TNT 141

Regular and Mach reflectionIn the discussion above, the angle of incidence at of the blast wave on

the surface of the target structure was zero. When a1 is 90° there is noreflection and the target surface is loaded by the peak static overpressurewhich is sometimes referred to as 'side-on' pressure. Regular reflectionoccurs for angles of incidence from 0° up to approximately 40° in air afterwhich Mach reflection takes place. Figure 3.6 shows the concepts of side-on pressure, regular reflection at both 0° angle of incidence (often called'face-on' loading) and at at between 0° and 40° together with Machreflection (when at exceeds 40°). Figure 3.7 shows reflection coefficientCr plotted against at for a range of incident overpressures. Note that theRankine-Hugoniot prediction of a maximum reflection coefficient of 8is clearly exceeded at higher values of ps.

34 35


Reflected wave

(c)

Slipstream - - _

PM(t) --t-'--® U.

Mach stem

of

Fig. 3.6. Side-on and face-on pressure loading, regular and Mach reflection

As noted above, the Mach reflection process occurs when a) exceedsabout 40° in air. Mach reflection is a complex process and is sometimesdescribed as a 'spurt'-type effect where the incident wave 'skims' off thereflecting surface rather than 'bouncing' as is the case at lower valuesof a1. The result of this process is that the reflected wave catches up withand fuses with the incident wave at some point above the reflecting surfaceto produce a third wave front called the Mach stem. The point ofcoalescence of the three waves is called the triple point. In the regionbehind the Mach stem and reflected waves is a slipstream region where,although pressure is the same, different densities and particle velocitiesexist. The formation-of a Mach stem is important when a conventionaldevice detonates at some height above the ground and also occurs whena device is detonated inside a structure where the angles of incidence ofthe blast waves on the internal surfaces can vary over a wide range.

Incident wave

'Face-on' loading: al = 0

(b)

Reflected wave Incident wave

P5(t) ,Z \ ^/ °u

BLAST LOADING

Numbers next to curvesindicate the peak positiveincident pressure ps (bar)

10 20 30 40 50 60 70 80 90of

Fig. 3.7. Effect of angle of incidence on reflection coefficient [6]

Blast wave external loading on structuresThe foregoing discussion is centred on reflecting surfaces that are

essentially infinite and do not allow diffraction to occur. In the case offinite target structures three classes of blast wave-structure interactioncan be identified.

36 37


The first of these is associated with a large- scale blast wave: here thetarget structure is engulfed and crushed by the blast wave. There willalso be a translational force tending to move the whole structure laterally(a drag force) but because of the size and nature of the structure it isunlikely actually to be moved: this is diffraction loading.

The second category is where a large scale blast wave interacts witha small structure such as a vehicle. Here the target will again be engulfedand crushed. There will be a more or less equal 'squashing' overpressureacting on all parts of the target and any resultant translatory force willonly last for a short time. However, more significantly, a translationalforce due to dynamic or drag loading will act for sufficiently long to movethe target and it is likely that a substantial part of the resulting damagewill be as a consequence of this motion.

Finally, consider the case of a blast wave produced by the detonationof a relatively small charge loading a substantial structure. Here, theresponse of individual elements of the structure needs to be analysedseparately since the components are likely to be loaded sequentially.

For the first and second situations above, consider the load profile foreach structure with reference to Fig. 3.8. Each. experiences twosimultaneous components of load. The diffraction of the blast around thestructure will engulf the target and cause a normal squashing force onevery exposed surface. The structure experiences a push to the right asthe left-hand side of the structure is loaded followed closely by a slightlylower intensity push to the right as diffraction is completed. The dragloading component causes a push on the left side of the structure followedby a suction force on the right-hand side as the blast wave dynamicpressure (the blast wind) passes over and around the structure.

With reference to Fig. 3.8 which shows the 'squashing' and dynamicpressure variation at significant times on the structure, the followingpoints should be noted.

In Fig. 3.8(a) the peak pressure experienced by the front face of the targetat time t2 will be the peak reflected overpressure pr. This pressure willthen decay in the time interval (t' - t2) because the pressure of the blastwave passing over the top of the structure and round the sides is lessthan pr (the peak top and side overpressure will be ps). Thus, decay infront face overpressure continues until the pressure is equal to thestagnation pressure pstag(t) which is the sum of the time-varying staticand dynamic pressures. The time t' is given approximately by

t = 3 x SIU5 (3.13)

where S is the smaller of B/2 or H where B is structure breadth, H is heightand Us is the blast front velocity. In Fig. 3.8(b) the deviation from thelinear decay of pressure on top and sides after time t3 is due to thecomplex vortices formed at the intersection of the top and the sides with

Approachingblast wave

Left

Frontface Structure

Right

Rearface

P(t) =P:(r) + q(t)

(c)

(d)

(e)

Fig. 3.8. Blast wave external loading on structures [10]

BLAST LOADING

Elevation ofstructure

Diffraction loads(front face)

Diffraction loads(top and sidefaces)

Diffraction loads(rear face)

Drag loads(front face)

Time

38 39


14

Region I: Diffraction loaddue to overpressure

Region II: Drag loaddue to blast wind

Time

Fig. 3.9. External translational force-time profile for a structure (10]

the front. In Fig. 3.8(c) the load profile on the rear face is of finite risetime because of the time required by the blast wave to travel down therear of the target to complete the diffraction process. Figures 3.8(d) and(e) show the forces exerted on the front and rear faces of the target bythe 'blast wind' forces. The resulting drag force FD is given by

FD = CD x qs(t) x A (3.14)

where A is the area loaded by the pressure and CD is the drag coefficientof the target which depends on target geometry.

Combining the loading from both diffraction and drag components givesthe overall translatory force-time profile as shown in Fig. 3.9.

If the target is relatively small (having only short sides) the interval(t4-t2) is small and area I in Fig. 3.9 is small, while area II isproportionately bigger. This loading is characteristic of a drag target.

Internal blast loading of structuresWhen an explosion occurs within a structure it is possible to describe

the structure as either unvented or vented. An unvented structure wouldneed to be stronger to resist a particular explosion than a vented structurewhere some form of pressure relief would be activated (e.g. by breakingof windows, etc.).

The detonation of a condensed high explosive inside a structureproduces two loading phases. Firstly, reflected blast overpressure isgenerated and, because of the confinement provided by the structure,

BLAST LOADING

re-reflection will occur. This process will produce a train of blast wavesof decaying amplitude. While this is happening the second loading phasedevelops as the gaseous products of detonation independently cause abuild-up of pressure: this is called gas pressure loading. The load profilefor the structure is likely to be complex.

The provision of venting in buildings may be beneficial for the protectionof the structure against the build-up of potentially damaging gaspressures. However, for the protection of personnel, venting offers littleadvantage because injuries will be associated with the initial blast wave.

It is fairly straightforward to estimate the magnitude of the initialreflected blast wave parameters (pr, ir) by using the scaled distancecurves shown in Fig. 3.5. Quantification of the re-reflected waves isgenerally more difficult particularly in the situations where Mach stemwaves are produced. However, it is possible to undertake an approximateanalysis of internal pressure-time histories by making some simplifyingassumptions by approximating the pressure pulses of both incident andreflected waves as being triangular in shape with pressure-time historygiven by

P,W = Pr 1Tr

(3.15)

where Tr is the equivalent positive phase duration of the reflected wave.The area under the pressure-time curve for the actual pulse is the specificimpulse it and this is set equal to the area beneath the equivalenttriangular pulse. Thus, if the actual reflected specific impulse is it then

and= 2T,Pr (3.16)

(3.17)Tr = 2ir/Pr

To quantify subsequent reflections the approach suggested by Baker etat. [4] is to assume that the peak pressure is halved on each re-reflection.Hence the impulse is also halved if duration of each pulse is consideredto remain constant. After three reflections, the pressure of any reflectedwave is assumed to be zero. With reference to Fig. 3.10, the situation canbe described thus

Pre = 2Pry. Pr3 = zPg = yPry. Pro = 0

Srr = 21r1' tr3 = 2tr2 = glrl, ir4 = 0 (3.18)

where it is assumed that positive phase durations remain unchanged foreach reflection.

In Fig. 3.10 the reverberation time - the time delay between each blastwave arriving at the structure internal surface - is assumed constant attr (= 2ta where to is arrival time of the first blast wave at the reflecting

40 1 41


A

I. I. + T, 3ta 3ta + Tr Ste

t

Fig. 3.10. Simplified internal blast wave reflections [4]

Ste

surface). This assumption is not strictly true because successive shockswill be weaker and so will travel slower than the first.

A further simplification suggested in [4] can be made particularly if theresponse time of the structure is much longer than the total load duration(5ta + Tr) (see Chapter 4) when all three pulses may be combined intoa single pulse having 'total' peak pressure PrT delivering a total specificimpulse irT. Thus

PrT = Pry + Pre + Pr3 = 1'75 Prt

trT = iri + i,, + ir3 = 1.75 in (3.19)

These approximations can be justified in that, when assessing theresponse of a structure, the use of the approximate input will lead to anoverestimate of response leading to a conservative design.

While the reverberating blast waves are decaying the gas pressure loadis developing. Its magnitude at a particular time will depend on thevolume of the structure, the area of any vents in the structure and thecharacteristics of the particular explosive. A typical pressure-time historyfor a structure with some form of venting is shown in Fig. 3.11.

The figure shows a series of reverberating blast waves [approximatelythree in number, confirming the validity of the approach of eqn (3.18)]and a developing gas pressure load which peaks at point B and thendecays. Reference [4] presents an approach allowing quantification of theimportant features of the history by use of a simplified form of the gas

BLAST LOADING

pressure component of the record. An approximate equation describingthe pressure-time history of the gas pressure decay is

p(t) = (pQs + po) of-2 13ri (3.20)

where pQS is peak quasi-static pressure , po is ambient pressure and

aeAs tao

V(3.21)

where ae is the ratio of vent area to wall area, A. is the total insidesurface area of the structure, V is the structure volume and ao is thespeed of sound at ambient conditions. This equation is valid for the partof the history showing decaying pressure. The rise of gas pressure isassumed to be linear and peaks at a time corresponding to the end ofthe reverberation phase (5ta + Tr). The gas pressure history is shown bythe dashed line in the figure. The area under the curve (ignoring the initiallinear rise) is termed the gas impulse i6 which can be written

rm..ig = o (p(t) - Po) dt = [1 - e-cima.] - Potmax (3.22)

in which pi = pQS + po and

C = 2.13a0Aaa0IV (3.23)

From experimental data from several sources (for example [9]) the curvesof Fig. 3.12 adapted from [4] and [5] have been shown to give reasonablepredictions of peak quasi-static pressure, 'blowdown' time (tmeX) and gaspressure impulse.

Reflected shocks

9

a B

M

q

-

uasi-static pressureApproximate

tme.

Time

Fig. 3.11. Typical pressure- time profile for internal blast loading of a partially-vented structure [51

42 43

BLAST EFFECTS ON BUILDINGS BLAST LOADING

to obtain the pressure and impulse values necessary to allow the designprocess described in Chapter 5 to be used to produce a structure capableof resisting these loads. It should be noted that the level of damagesuffered by a structure cannot be determined solely from knowledge ofthe pressure and impulse values from a particular explosion. It is alsoimportant to know the characteristics of the blast-loaded building, inparticular the dynamic properties of the materials of construction and theform of the structure. Interdependence of loading and buildingcharacteristics is discussed in Chapter 4.

(b)

1o° m'

Fig. 3.12. Prediction of gas pressure impulse (i5), 'blowdown' time (t and peakquasi-static pressure (pQS) (41

ConclusionsThis chapter has provided a summary of the methods of blast load

quantification from both external and internal explosions (more detailsabout which can be obtained from reference [101) and allows the designer

References1. Rankine W.J.H. Phil. Trans. Roy. Soc., 1870, 160, 277-288.2. Liepmann H.W. and Roshko A. Elements of Gas Dynamics. John Wiley, New

York, 1957.3. Brode H.L. Numerical solution of spherical blast waves. J. App. Phys., 1955,

No. 6, June.4. Baker W.E., Cox P.A., Westine P.S., Kulesz J.J. and Strehlow R.A. Explosion

Hazards and Evaluation . Elsevier, 1983.5. U.S. Department of the Army Technical Manual, TM5-855-1. Fundamentals

of protective design for conventional weapons. Washington DC, 1987.6. U.S. Department of the Army Technical Manual, TM5-1300. Design of structures

to resist the effects of accidental explosions. Washington DC, 1990.7. Hopkinson B. British ordnance board minutes 13565, 1915.8. Cranz C. Lehrbuch der Ballistik. Springer, Berlin, 1926.9. Weibull H.R.W. Pressures recorded in partially closed chambers at explosion

of TNT charges. Annals of the New York Academy of Sciences, 1968, 152, Article 1,357-361.

10. Smith P.D. and Hetherington J.G. Blast and Ballistic Loading of Structures.Butterworth-Heinemann, 1994.

44 1 45

STRUCTURAL RESPONSE TO BLAST LOADING

4 Structural response to blastloading

Notationd depth of beamE Young's modulus of elasticityF peak blast load of idealized triangular pulseF(t) blast load from idealized triangular pulsei, specific reflected impulseis specific side-on impulsei, scaled impulseI impulseK stiffnessK' empirical constantK, equivalent stiffnessKL load factorKM mass factorKLM load-mass factorK, stiffness factorKE kinetic energyL length of beamin mass of human subjectM structure massMe equivalent mass

Pa atmospheric pressurep, peak reflected pressurep, peak side-on overpressurep, scaled pressureP blast loadP, equivalent blast loadR range, structure resistance, static load to cause same deflection as

blast loadRB radius for category B damaget timetd duration of idealized triangular blast loadtm time to reach maximum dynamic displacementT natural period of vibration of structure

T scaled blast wave durationU strain energyV dynamic reactionW charge massWD work done by blast loadWp maximum displacementx displacementxm,x maximum dynamic displacementx„ static displacementR centroid of deflected shapeZ scaled distancep densityay yield stressm natural circular frequency of vibration

IntroductionIn assessing the behaviour of a blast-loaded structure it is often the casethat the calculation of final states is the principal requirement for adesigner rather than a detailed knowledge of its displacement-timehistory. To establish the principles of this analysis, the response of a singledegree of freedom (SDOF) elastic structure is considered and the linkbetween the duration of the blast load and the natural period of vibrationof the structure established. This leads to the concept of 'impulsive' and'quasi-static' response regimes and the representation of such responseon pressure-impulse diagrams. Pressure-impulse diagrams both forbuilding structures and other targets such as personnel are described.The principles of analysis for an SDOF system are extended to specificstructural elements which can then be converted back to equivalentlumped mass structures by means of load and mass factors. Totalstructural resistance can thus be represented by the sum of an inertialterm (based on the mass of the structure) and the so-called 'resistancefunction' (based on the structure's geometrical and material properties)which act in opposition to the applied blast load.

Elastic SDOF structureConsider a structure which has been idealized as a SDOF elastic

structure and which is to be subjected to a blast load idealized as atriangular pulse delivering a peak force F. The positive phase durationof the blast load is td. The situation is illustrated in Fig. 4.1.

The load pulse is described by the equation

F(t)=FI1-tal

(4.1)

46 1 47

Fig. 4.1. Single degree of freedom (SDOF) elastic structure subject to idealized blastpulse [111

This blast load will deliver an impulse I to the target structure given bythe equation

I = 2Ftd (4.2)

here I is the area beneath the load function for 0 < t < td. The equationof motion for this structure is

Mz+Kx=F(I-ttd / I

(4.3)\\

If we confine the problem to response for times less than the positivephase duration, the solution can be written as

x(t) = F (1-cos wt) +F ( sin cot

t (4.4)K Ktd w

where co [ = .J(K/M)) is the natural frequency of vibration of the structure.By limiting analysis to the worst case of response the maximum dynamic

structure displacement, Xmax, is required which will occur when thevelocity of the structure is zero. Differentiating eqn (4.4) and setting dx/dtto zero gives

0 = w sin (wtm) + 1 cos(wtm)to

1

td(4.5)

In this equation tm is the time at which the displacement reaches xmax.Equation (4.5) may be solved to obtain a relationship of the general form

wtm = f(wta) (4.6)

From this it is clear that a similar form of equation can be obtained formaximum dynamic displacement

Xmax

F/K _'k (-td) = V (T) (4.7)


where ik and ,G' are functions of wtd and td/T, respectively and T is thenatural period of response of the structure. Solutions of this form indicatethat there is a strong relationship between T and td. To proceed further,consider the relative magnitudes of these quantities.

Positive phase duration and natural periodPositive phase long compared with natural period

First consider the situation where td is much longer than T. In the limitthe load may be considered as remaining constant whilst the structureattains its maximum deflection. For example, this could be the case fora structure loaded by a blast from a domestic gas explosion. In this casethe maximum displacement xmax is solely a function of the peak blastload F and the stiffness K. The situation can be represented graphically,and Fig. 4.2 shows the variation of both blast load and the developmentof structure resistance, R(t), with time. The structure is seen to havereached its maximum displacement before the blast load has undergoneany significant decay. Such loading is referred to as quasi-static or pressureloading.

Positive phase short compared with natural periodNow consider the situation in which td is much shorter than T. In this

case the load has finished acting before the structure has had time torespond significantly - most deformation occurs at times greater thantd. Thus, we can say that displacement is a function of impulse, stiffnessand mass which can be represented graphically (Fig. 4.3).

Inspection of these graphs indicates that the blast load pulse has fallento zero before any significant displacement occurs. In the limit, the blast

Fig. 4.2. Quasi-static loading (111

48 1 49


load will be over before the structure has moved: this situation is describedas impulsive loading.

Positive phase duration and natural period similarIn this case, with td and T approximately the same, the assessment of

response is more complex, possibly requiring complete solution of theequation of motion of the structure.

These three regimes can be summarized in terms of the product wtd(which is proportional to the ratio of T to td) as indicated below

« td (short)1 ImpulsiveT (long) J

L atd (long)

T (short)Quasi-static

tdT

= 1 Dynamic. (4.8)

Evaluation of the limits of responseIn the case of quasi-static loading the load pulse can be idealized as

shown in Fig. 4.4(a) while the elastic structure resistance can berepresented by the graph of Fig. 4.4(b).

The basic principle of the analysis is to equate the work done on thestructure and the strain energy acquired by the structure as it deforms.The work done by the load as it causes a displacement xmax is WD givenby

WD = Fxmax

la

Fig. 4.3. Impulsive loading (111

t

(4.9)

tm


xm Xmx x

(a) (b)

Fig. 4.4. Idealized load and resistance-deflection function for quasi-static loading (111

The strain energy acquired by the structure, U, is the area beneath theresistance displacement graph given by

U = 2KXma 2X

Equating WD and U (after some rearrangement ) results in

Xmax = Xmax - 2

(F/K) xst

(4.10)

(4.11)

where xst is the static displacement that would result if the force F wereapplied statically. Equation (4.11) represents the so-called dynamic loadfactor (DLF) which gives the upper bound of response and is called the'quasi-static asymptote'.

When an impulse is delivered to a structure it produces an instantaneousvelocity change: momentum is acquired and the structure gains kineticenergy which is converted to strain energy. The impulse causes an initiallystationary structure to acquire a velocity zo (= I/M). From this the kinetic

energy delivered, KE, is given by

KE = 1 Mza =P

(4.12)2 2M

The structure will acquire the same strain energy U as before becauseit displaces by xmax. Thus if KE and U are equated, after somerearrangement we obtain

Xmax = Xmax

F/K XStwtd

which is the equation of the 'impulsive asymptote' of response.

(4.13)

If these two asymptotes are drawn on a response curve of wtd against

so R 51

BLAST EFFECTS ON BUILDINGS STRUCTURAL RESPONSE TO BLAST LOADING

E

11

Damagex>xma,

W to

Fig. 4.5. Graphical representation of quasi-static (1), impulsive (11) and dynamic (III)

response [111

LL

G-s

II I

xmax/(F/K), the actual response of the structure can then be sketchedwithout recourse to further analysis as shown in Fig. 4.5.

The three regimes of quasi-static, impulsive and dynamic response areidentified on the resulting graph as regions' I, II'and III, respectively.

Pressure- impulse diagramsIt is now easily possible to convert Fig. 4.5 to a pressure-impulse (P-1)

diagram which allows the load-impulse combination that will cause aspecified level of damage to be assessed very readily. The bounds onbehaviour of a target structure are characterized by a pressure (or, as here,force) and a total impulse I (as here) or a specific impulse is or ir.

Equation (4.11) can be rewritten as

2F [_ maximum load 1 = 1 (4.14)Kxmax L maximum resistance J

which is the equation of a modified quasi-static asymptote plotted on agraph with ordinate 2F/Kxmax. If the abscissa of Fig. 4.5 is multiplied bythe inverse of the ordinate of Fig. 4.5, and recalling that co = (K/M) we

obtain

(Ftd1Kxmax) -JKIM = 211(xmax,IKM ) (4.15)

which is a non-dimensionalized impulse. Noting that the impulsive as mtote of Fig. 4 .5 is given by eqn (4.13), using an abscissa I/(xmax -̀ '1CM)

No damage

1 \/(KM))

Fig. 4.6. Non-dimensionalized pressure-impulse diagram for SDOF elastic system [21

means that the new impulsive asymptote is given by I/(xmax-TMM) = 1and the response curve can be re-plotted to obtain Fig. 4.6.

The form of this graph allows easy assessment of response to a specifiedload. Once a maximum displacement or damage level is defined this curvethen indicates the combinations of load and impulse that will cause failure.Combinations of pressure and impulse that fall to the left of and belowthe curve will not induce failure while those to the right and above thegraph will produce damage in excess of the allowable limit.

Whereas the foregoing relates to analytically derived pressure-impulsediagrams it is possible to derive P-I curves from experimental evidenceor real-life events. P-I curves have been derived from a study of housesdamaged by bombs dropped on the UK in the Second World War [1].The results of such investigations are used in the evaluation of safe stand-off distances for explosive testing in the UK. In this instance the axes ofthe curves are simply side-on peak overpressure pa and side-on specificimpulse is as shown in Fig. 4.7. These curves can also be used withreasonable confidence to predict the damage to other structures such assmall office buildings and light-framed factories.

The levels of damage are less precise than those obtained by analysis.As quoted in [1], A corresponds to almost complete demolition of thebuilding and B means damage severe enough to necessitate demolition.

52 1 53


GP2000 - General purpose 2000 lb bomb

Fig. 4.7. Isodamage curves with range-charge weight overlay for brick-built

houses (11)

P:: Pa


Table 4.1. Overpressure and sealed distance for various types of blast damage

Structuralelement

Failure mode 1 t TNTp, (kPa) Z (m/kgr13)

10 t TNTp, (kPa) Z (m/kg113)

Window panes 5% broken 1.1 72.2 0.7 96-0

10% broken 2.5 38.6 1.7 51.6

90% broken 6.3 19.6 4.2 26.9

Houses Tiles displaced 4.5 25-6 2.9 34.7Doors /windowframes blown in 9.1 14.6 6.0 20.4

Category D 5 23.7 3.1 33-6Category C. 13 11.4 8 16.1

Category Cb 28 6.5 17 9.2

Category B 80 3.6 36 5.6

Category A 185 2.4 80 3.6

giving the radius of B type damage (R5) is 5.6. Radii for types A and Cbare given approximately by 0 - 675 RB and 1.74 RB, respectively.

Further analysis allows the addition of 'range-charge weight' overlaysto P-I curves enabling the damaging potential of a particular threatdefined in terms of explosive yield and stand-off to be assessed. Suchoverlays are included in Fig. 4.7 for a number of threats and distances.

As a complement to the information presented in Fig. 4.7, Table 4.1(extracted from [3]) gives the overpressure and scaled distance for anumber of types of building blast damage from charges of TNT of 1 and10 tonnes.

Table 4.1 dearly demonstrates the importance of positive phase durationas wellas overpressure in determining damage: a larger charge can causethe same level of damage as a smaller charge even though the associatedoverpressure is less. This is because the larger device generates a pulseof longer duration. Thus impulse should be given equal considerationwith overpressure when assessing the damage potential of a given threat.

Pressure-impulse diagrams for human response to blast loadingGenerally, three categories of blast-induced injury are identified. These

are:

Category Cb implies damage rendering the house temporarily uninhabit-able with the roof and one or two external walls partially collapsed. Load-bearing partitions would be severely damaged and would requirereplacement. In contrast, category C. indicates relatively minor structuraldamage though still sufficient to make the house temporarily unin-habitable with partitions and joinery being wrenched from fixings.Finally, category D refers to damage calling for urgent repair but is notsevere enough to make the building uninhabitable: there would bedamage to ceilings and tiling and more than 10% of glazing would bebroken.

The use of pressure-impulse diagrams in conjunction with blastparameter versus scaled distance graphs allows the development ofequations to describe specific damage levels. An example for the curvesabove is of the general form

R -K' W 1/3 (4.16)

[1+(3175(W )2]116

where R is range in metres, W is mass of explosive in kilograms of TNTand K' is an empirical constant. The value of K' in the equation above

(a) Primary injury: due directly to blast wave overpressure and durationwhich can be combined to form specific impulse. Overpressuresare induced in the body following arrival of the blast and the level ofinjury sustained depends on a person's size, gender and (possibly)age. The location of most severe injuries is where density differencesbetween adjacent body tissues are greatest. Likely damage sites thusinclude the lungs which are prone to haemorrhage and oedema

54 1 55


(collection of fluid), the ears (particularly the middle ear) which canrupture, the larynx, trachea and the abdominal cavity.

(b) Secondary injury: due to impact by missiles (e.g. fragments from aweapon's casing). Such missiles produce lacerations, penetrationand blunt trauma (a severe form of bruising).

(c) Tertiary injury: due to displacement of the entire body which willinevitably be followed by high decelerative impact loading whenmost damage occurs. Even when the person is wearing a goodprotective system, skull fracture is possible.

In the particular case of primary injury associated with damage to thelungs, P-I diagrams have been developed as shown in Fig. 4.8(a)constructed by Baker et al. [2] from a number of sources.

The axes are scaled pressure ps = ps/po, where ps is peak incidentpressure and po is ambient (usually atmospheric) pressure and scaledimpulse is. This is obtained by defining a scaled positive phase duration

t(= tdp /2o /m 1/3), where m is the mass of the person and the blast waveis taken as a triangular pulse. Then

s = - -112 (4.17)

The addition of a range-charge weight overlay to Fig. 4.8(a) leads, witha little modification, to the survival prediction curves of Fig. 4.8(b) whichrelate to a 70 kg man [3].

Similar diagrams are available for assessment of primary injury to theear, although since less information is available about variability ofresponse as blast duration changes, damage levels are generally relatedto an overpressure value as summarized in Table 4.2 [3].

It should be noted that secondary and tertiary injuries can be just aslikely and possibly more severe than primary effects. For secondary injurycriteria reference should be made to Ahlers [4] summarized in [5, 11].In the case of tertiary injuries [6], summarized in [4, 5, and 11] isrecommended.

Table 4.2. Summary of overpressure values

Z (m/kg113)

5-634 - 883.933.132.542.14

ps (kPa)

35.645.467.710501630243.0

Eardrum damage: %

51025507590

102

10'

n

100

10-1110-1


1% Survivalroi

/ieo".90%'99%

Threshold

10° 101

!, /(P?%m'/'): Pa'/zs/kg'/a

(a)

102 10'

00 kg 1000 kg 10 000 kg 100 000 kgMass of TNT

(b)

Fig. 4.8. (a) Isodamage curves for lung damage to humans from blast [2]. (b)

Isodamage curves with modified range-charge weight overlay for lung damage to

70 kg man [3]

Energy solutions for specific structural componentsElastic analysis

The approach adopted here is essentially the Rayleigh-Ritz methodof analysis [7] and is suitable for specific structural members in anuncoupled analysis. This means that the response of structural elements

56 1 57


to a blast load may be considered in isolation assuming that the supportconditions are essentially rigid. In the implementation described here theapproach produces worst cases of response rather than displacement-timehistories.

Firstly, a mathematical representation of the deformed shape is selectedfor the structure which satisfies all the necessary boundary conditionsrelating to displacement. Then, by operating on the deformed shape, thecurvature and hence strain of deformation is obtained from which thetotal strain energy of the element can be calculated.

Consideration must now be given to the nature of the blast loadimpinging on the structure. If the loading is impulsive then a calculationof total kinetic energy delivered to the structure is made. If, however,the load is quasi-static, the work done by the load is found by consideringthe work done on a small element of the structure then integrating over

+ the loaded area. In the impulsive realm, response is evaluated by equatingthe kinetic energy_acquired to the strain_e_nergy produced in the structure.In the quasi-static realm response is assessed by equating the work doneby the load to stran_energy. Having done this, it is possible to quantifyparticular aspects of response such as maximum displacement, maximumstrains and maximum stresses.

If this technique is used, for example, to analyse the response of acantilever of depth d to impulsive loading then the maximumdisplacement W o of the structure of length L made of material of Young'smodulus E and density p loaded by a reflected specific impulse it is givenby

Lo= C1

[ d j [ 1 (EP) j(4.18)

where the exact value of the coefficient Cl (equal to approximately two)will depend on the choice of deflected shape of the structure.

If the same cantilever is now loaded quasi-statically and an analysis iscarried out assuming that the blast pressure on the structure remainssteady during structure deformation (i.e. the peak reflected overpressure,pr, remains constant), the resulting maximum displacement is nowobtained as

o 3-CZ[diL E(4.19)

where the exact value of C2 (equal to approximately three) depends onthe deflected shape chosen.

Plastic analysisThe approach to the analysis of structural elements that deform beyond

their elastic limits proceeds in a similar way. For example, consider a


simply supported beam loaded impulsively made of material with stress-strain characteristics idealized as 'rigid-plastic'.

The analytical approach described above leads to an expression formaximum (central) displacement Wo given by

W0/L = ft14aypd'

where ay is the yield strength of the material.

(4.20)

Just as in the case of the SDOF system detailed above, P-I diagramscan be constructed for these or any other structural elements.

Lumped mass equivalent SDOF systemsThe analysis presented above is valuable, though for more complex

structural elements and load configurations, implementation of thisapproach could be rather time-consuming. To aid assessment of response,the behaviour of complex structures can be approached by representingthe structure as a SDOF lumped-mass system - the so-called equivalentsystem. The equation of motion so derived will be similar to eqn (4.3) andcan be solved either analytically or numerically to obtain a deformation-time history for the structure. Often, as described above, maximumdisplacement may be all that is required. This approach, although failingto provide detailed aspects of response, allows a good insight into impor-tant features of behaviour and will, furthermore, give an over-assessmentof response. This conservative analysis, therefore, has attraction for thedesigner.

Equation of motion for an SDOF systemEquation (4.3) can be rewritten with the spring resistance term replaced

by a more general resistance function R(x) as

Mi + R(x) = P(t) (4.21)

In creating an equivalent SDOF structure it must be realized that realstructures are multi-degree of freedom systems where every mass particlehas its own equation of motion. Thus, to simplify the situation it isnecessary to make assumptions about response and in particularcharacterize deformation in terms of a single point displacement.Examples are shown in Fig. 4.9(a) and (b) where in the SDOF systemthe suffix e means equivalent.

The method relies, as in the examples above, on considering theenergies of the real structure and the equivalent system and equatingthem. This means that, by ensuring equal displacements and velocitiesin the two systems, kinematic similarity is maintained. The completeenergy relationship may be written as

WD = U + KE (4.22)

S8 1 59


1 d d A p(f)Iunit length

Mass M

xme

Beam stiffness K


Equating the work terms from the two analyses leads to the definitionof a load factor, KL as

KL = Pe(t)/P(t) = 16/25 = 0.64

with the value particular to the beam given.Equating strain energy for the two systems and recalling that the

stiffness of a flexing structure is given by load per unit displacement,

T7Portal stiffness K

(a) Suffix e: equivalent

Mass M

(b)

Fig. 4.9. Real and equivalent structural systems [11l

In the derivations of impulsive and quasi-static response described aboveit was this equation that was simplified in analysing the two extremesof behaviour.

Example of the approachConsider a simply supported beam responding elastically as shown in

Fig. 4.9(a). Firstly, a suitable deformed shape is assumed such as thedisplacement under a uniformly distributed static load. The evaluationof work done, strain energy and kinetic energy for the beam is then made.The equivalent system will be as shown in Fig. 4.9(a) which will havethe same maximum displacement Wo and maximum initial velocity Woas for the real structure. The evaluation of WD, U and KE is much simplerhere

WD = P5(t)W0

U = 'Ka Wo

KE = zMeWo (4.23)

definition of a stiffness factor, Ks is given by

Ks = Ke/K = 0.6401

with the value for this particular structural element as shown.

(4.24)

(4.25)

Finally, equating kinetic energy for the two systems leads to definitionof a mass factor, KM, as

KM = McIM = 0-504 (4.26)

with the particular value for this structure as shown.It is worth noting that the load and stiffness factors are very similar

and it is general practice to set them equal: thus we have Ka = KL. Alsoit is often convenient to define a load-mass factor KLM = KM/KL thevalue of which approach is easily seen. The equivalent system equationof motion can be expressed in terms of mass and load factors. Divisionby load factor (assuming that stiffness and load factors are equal) yields,for an elastic system

KLMMX + Kx = P(t) (4.27)

Thus, an equivalent system equation of motion can be derived merelyby factoring the actual structure mass by KLM.

One further important calculation that should be made is of the dynamicsupport reactions generated by the blast load. For the specific exampleof the simply supported beam, by considering half of the beam, momentsare taken about the centre of inertial resistance of the beam which is takento coincide with the centroid of the shape swept out by the beam as itdeforms. For the shape chosen here the centroid can be shown to be x =61L/192 from the end of the beam. Taking moments about this point leadsto an equation for dynamic reaction V(t) as

V(t) = 0.393R + 0•107P(t) (4.28)

where R is the static load needed to cause the same deflection as the blastload [P(t)]. The same analysis can be used to develop load and massfactors for plastically deforming structures.

Appendix B gives load and mass factors as well as dynamic reactionsfor a variety of one-way spanning structural elements for both elastic andplastic response. The reader is also referred to the text by Biggs [8] inwhich the concepts outlined above were originally developed.

60 161


Resistance functions for specific structural formsAs noted earlier in this chapter, the term R (x) is known as the resistance

function of the element. In developing the resistance function for astructural element, it is assumed that the element will offer essentiallythe same resistance to deflection when deformed dynamically as it willwhen deformed quasi-statically. The only adjustment incorporated is anenhancement in the ultimate resistance of the element, due to theimprovement in strength observed in dynamic loading. The general formof the resistance function for a common structural form will be presentedbelow.

Resistance functions - general descriptionThe resistance-deflection function for a structural element is strictly

a graph of the uniform pressure which would be necessary to causedeflection at the central point of the element during its transientdisplacement.

A typical resistance-deflection curve for a laterally restrained elementis shown in Fig. 4 .10. The initial portion of the curve is due primarilyto flexural action . If lateral restraint prevents small motions , in-planecompressive membrane forces are developed . However, the increasedcapacity due to these forces is normally neglected [9] and is not shownin the figure. Following the loss of flexural capacity , the provision ofadequate lateral restraint may permit the development of tensilemembrane action . The increase in resistance with increasing deflectionup to incipient failure is shown as the dashed line in the figure.

In practice , when designing for smaller deflections , a simplified function

Actual resistancedeflection function

Idealized resistancedeflection function

Concrete crushes,loss of flexuralresistance

x

Fig. 4.10. Typical resistance -deflection curve for large deflections

t


0 X. XPx

Fig. 4.11. Simplified resistance function for reinforced concrete element (11]

is used which is a prediction of the resistance which the element wouldoffer in a quasi-static test. Figure 4.11 shows the resistance function whichwould be adopted for a reinforced concrete wall with built-in supportsalong two edges but no support along the other two, i.e. a one-way-spanning slab. The initial part of the graph, OA, represents the elasticdeformation of the slab. At the point A, yield lines develop along the built-in supports, allowing rotation. During this phase, AB, deformations inthe central part of the slab are elastic whilst rotation occurs in the yieldlines. The increments of displacement during this elasto-plastic phase areestimated from the elastic stiffness of a simply supported one-wayspanning slab. More complicated structural forms, e.g. a two-way-spanning slab with built in supports, may have two or more elasto-plasticphases as the yield-line system develops progressively in the slab. Thephase BC represents the ultimate resistance of the element once a sufficientsystem of yield lines has been established to form a collapse mechanismin the slab. This fully plastic phase will last until failure at one of thesupports occurs. For the case of two-way spanning slabs it is possiblefor failure to occur along two opposite supports whilst the other pair ofsupports remains intact. In this case the slab will continue to offerresistance, but at a lower level. Experience shows that a negligible erroris introduced by replacing the resistance function OABC with the bilinearfunction ODC, provided the area under both graphs is the same. Thisapproach is adopted in the document TM5-1300 [9]. Tables for derivingthe components of the resistance function for a variety of one-wayspanning elements may be found in Appendix B.

62 1 1 63


ConclusionsMethods for analysing the response of blast-loaded structures have been

presented. It is worth noting that many of the concepts of providingprotection are by no means new. The work by Christopherson [10]presented the essence of the approach which has been the basis of anumber of subsequent publications. Of particular importance to thedesigner is the use of these principles in establishing the factors that allowformation of equivalent SDOF systems which, when combined with theloading information presented in Chapter 3, form the basis of thesubsequent design process. For structures which respond within theimpulsive regime, design is normally based upon an energy solution_ir,_which the kinetic energy delivered [eqn (4.12) ] is equated to the strainenergy produced in deforming to a limited deflection - that is the areaunder the resistance function. In the quasi-static regime it is the workdone on the structure by the load that must be equated to the strain energyproduced. For response within the intermediate, or dynamic regime, theresponse charts presented in Appendix C, which are based on numericalsolutions of the full equation of motion, may be used in the design process.Further details about analysis of structures subjected to blast loading canbe obtained from [11]. The application of these techniques to the designof elements in reinforced concrete and structural steel is more fullydescribed in Chapter 5.

References1. Jarrett D.E. Derivation of British explosives safety distances. Annals of the New

York Academy of Sciences, 1968, 152, Article 1, 18-35.2. Baker WE., Cox P.A., Westine P.S., Kulesz J.J. and Strehlow R.A. Explosion

Hazards and Evaluation. Elsevier, London, 1983.3. Merrifield R. Simplified calculations of blast induced injuries and damage. Health

and Safety Executive Specialist Inspector, April 1993, Report No. 37.4. Ahlers E.B. Fragment hazard study. Minutes of the 11th explosives safety seminar,

Vol. 1. Armed Services Explosives Safety Board, Washington DC, 1969.5. Baker WE., Westine P.S., Kulesz J.J., Wilbeck J.S. and Cox P.A. A manual

for the prediction of blast and fragment loading on structures. Departmentof Energy, Amarillo, Texas, 1980, DOE/TIC-11268 US.

6. Baker WE., Kulesz J.J., Ricker R.E., Bessey R.L., Westine P.S., Parr V.B.and Oldham G.A. Workbook for predicting pressure wave and fragment effects ofexploding propellant tanks and gas storage vessels. NASA Lewis Research Centre,1975 (reprinted 1977), NASA CR-134906.

7. Todd J.D. Structural theory and analysis. MacMillan, 1974.8. Biggs J.M. Introduction to structural dynamics. McGraw-Hill, New York, 1964.9. US Department of the Army Technical Manual, TM5-1300. Design of structures

to resist the effects of accidental explosions. Washington DC, 1990.


10. Christopherson D.G. Structural defence. Ministry of Home Security Researchand Experiments Department, January 1946, Report RC 450.

11. Smith P.D. and Hetherington J.G. Blast and ballistic loading of structures.Butterworth-Heinemann, 1994.

64 65

DESIGN OF ELEMENTS IN REINFORCED CONCRETE AND STRUCTURAL STEEL

5 Design of elements inreinforced concrete andstructural steel

Notation

Ad area of diagonal bars at the support within a width bA, area of tension reinforcement within a width bAs area of compression reinforcement within a width bA„ total area of stirrups in tension within a distance s and a width bA„, area of web of steel sectionb width of flexural memberd distance from extreme compression fibre to centroid of tension

reinforcementd' distance from extreme compression fibre to centroid of compression

do

DIFEEcE,

ff.fdcufdcfds

fdufd,,fayf.fyFH

reinforcementdistance between the centroids of the compression and tensionreinforcementdynamic increase factormodulus of elasticitymodulus of elasticity of concretemodulus of elasticity of reinforcement or steel sectionstressstatic ultimate compressive strength of concrete at 28 daysdynamic ultimate compressive strength of concrete at 28 daysdynamic design stress for concretedynamic design stress for reinforcement or steel sectiondynamic ultimate stress of reinforcement or steel sectiondynamic design shear stress for steel sectiondynamic yield stress of reinforcement or steel sectionstatic ultimate stress of reinforcementstatic yield stress of reinforcementcoefficient for moment of inertia of cracked sectionspan heightunit positive impulseunit positive normal reflected impulse

I moment of inertia!c moment of inertia of cracked concrete section of width bKe elastic unit stiffness

Kep elasto-plastic unit stiffnessKs equivalent elastic unit stiffnessKL load factorKIM load-mass factorKM mass factorL span lengthm unit massme effective unit mass

Mn ultimate negative moment capacityMP ultimate positive moment capacityn modular ratiop pressurePmax peak pressure

Pc peak positive normal reflected pressureP loadre elastic unit resistancereP elasto-plastic resistancer„ ultimate unit resistanceR total internal resistanceR„ total ultimate resistances spacing of stirrups in the direction parallel to the longitudinal

reinforcementS plastic section modulust timetd duration of positive phase of blast pressuret, time at which maximum deflection occursTc thickness of concrete sectionT effective natural period of vibrationvc ultimate shear stress permitted in an unreinforced concrete webv„ ultimate shear stressV support reactionVd ultimate direct shear capacity of the concrete of width bVP ultimate shear capacity of steel sectionV, shear at the support per unit widthx depth of neutral axis below extreme compression fibre in a flexural

memberX deflectionXm maximum transient deflectionXE equivalent elastic deflectionZ elastic section modulusa coefficient applied to total internal resistance R to determine

dynamic reaction Vit coefficient applied to total load P to determine dynamic reaction V

'Ym partial safety factor for materialS side-sway deflectione strainB support rotation angleµ ductility ratio

66 67


p densityPs tension reinforcement ratiopi compression reinforcement ratio

Objectives

The prime objective in the design of blast load-resisting structural elementsis to provide sufficient ductility to enable the element to deflect by anamount consistent with the degree of damage permitted; this will entailan initial design based upon extensive flexural plastic deformation. In sodeforming, the element should not fail prematurely due to other loadeffects, for example shear or local instability.

Unless the element is to be subjected to repeated blast loading, forexample in a test facility, the design should be based on the ultimate limitstate. Simple supports should be avoided wherever possible and jointsbetween elements should be carefully detailed to facilitate load transfer(see Plates 13, 14).

The overall design process is summarized in the logic flow chartpresented in Appendix D.

Plate 73. Failure of the connections in a precast concrete frame


Plate 14. Failure due to insufficient ties, poor concrete quality and detailing of joints

Design loadsThe blast loading for which resistance is to be provided is likely to be

an extreme event, and as such has a low probability of occurrence. Thus,it is appropriate to set the partial safety factor for blast loading to a valueof unity.

Dead loads, storage and other permanent loads should also be assigneda partial safety factor of unity.

The magnitude of imposed loads and wind loads acting simultaneouslywith the blast load are likely to be only a small proportion of theirrespective design values. A factor of 0.33 may be applied to the designvalues of the variable imposed and wind loads when acting in combinationwith the blast load, as recommended in BS 5950: Part 1 [1] and BS 8110:Part 1 [2].

When other loads are present at the time of the blast loading they maybe assumed to act constantly throughout the application of the blast load.The effect of these other loads generally will be to reduce the effectiveresistance of an element. However, where mass is associated with such

68 69


loads there may be a beneficial effect as a result of the inertial effects ofthese loads.

Design strengthsThe design should generally be based upon the characteristic strength

of materials - that is with a partial safety factor of unity, unless thereis evidence to show that the mean strengths of a particular material aregenerally higher than the specified minimum. For example, the charac-teristic yield stress for grade 50 or lower structural steel may be increasedby 10% in design calculations involving blast loading.

Under the action of rapidly applied loads the rate of strain applicationincreases and this may have a marked influence on the mechanicalproperties of structural materials. In comparison with the mechanicalproperties under static loading the effects may be summarized as follows:

(a) The yield stress of structural steel or steel reinforcement bars, fy,increases significantly to the dynamic yield stress, fdy.

(b) The ultimate tensile strength of structural steel or steel reinforce-ment bars, f,,, in which account is taken of strain hardeningeffects, increases slightly to the dynamic ultimate strength, fd,,.

(c) The compressive strength of concrete, fo, increases significantlyto the dynamic compressive strength, fdru.

(d) The modulus of elasticity of both steel and concrete remainsinsensitive to the rate of loading.

(e) The elongation at failure of structural steel is relatively insensitiveto the rate of loading.

The factor by which the static stress is enhanced in order to calculate thedynamic stress is known as the dynamic increase factor (DIF). Typicalvalues of DIF for structural steel and reinforced concrete are given in Table5.1. The dynamic stress to be used in the design of reinforced concrete

Table 5.1. Dynamic increase factors (DIF) for design of reinforced concrete andstructural steel elements

Type of stress Concrete Reinforcing bars Structural steel

Jt

dcu /flculJdylfy

lduI

t.

!/dy/

ty*

ldu If.

Bending 1-25 1-20 1.05 1.20 1-05Shear 1.00 1.10 1-00 1-20 1-05Compression 1-15 1.10 - 1.10 -

* Minimum specified fy for grade 50 steel or less may be enhanced by the averagestrength increase factor of 1.10.


and structural steel elements depends upon the deformation or damagelimits imposed - these are considered later on in the chapter.

Deformation limitsThe controlling criterion in the design of blast-resistant structural

elements is normally a limit on the deformation or deflection of theelement. In this way the degree of damage sustained by the element maybe controlled. The damage level that may be tolerated in any particularsituation will depend on what is to be protected, for example, the structureitself, the occupants of a building or equipment within the building.

There are two methods by which limiting element deformations maybe specified: by using the support rotation, 0 (see Fig. 5.1) and the ductilityratio

total deflection _ X,,,

deflection at elastic limit XE

In general, deformations in reinforced concrete elements are expressedin terms of support rotations whilst ductility ratios are used for structuralsteel elements.

For the protection of personnel and equipment through the attenuationof blast pressures and to shield them from the effects of primary andsecondary fragments and falling portions of the structure, recommendeddeformation limits are given under protection category 1 in Table 5.2.

For the protection of structural elements themselves from collapse underthe action of blast loading, the recommended deformation limits are givenunder protection category 2 in Table 5.2. It should be noted that theselimits imply extensive plastic deformation of the elements and the needfor subsequent repair or replacement before they may be re-used. Forsituations where re-use is required without repair, deformations shouldbe maintained within the elastic range, i.e. tt .5 1. This latter designcondition is likely to lead to massive and consequently costly construction.

In addition to these considerations for individual elements thereremains, of course, a requirement for the overall structure to remain stablein the event of being subject to blast loading. TM5-1300 [3] recommendsthat the maximum member end rotation, 0, as shown in Fig. 5.2, should

\0

Beam, slab or panel

Fig. 5.1. Member support rotations [3]

x

70 71


Table 5.2. Deformation limits

Reinforced concrete beams and slabs

Structural steel beams and platesf

0

20*

2°

Protection categ

Notapplicable

10

0

4°f

12°

ry

2

/A

Not

applicable20

* Shear reinforcement in the form of open or closed 'blast links' must be provided inslabs for 0 > 1°. Closed links (shape code 74 to B5 4466) [4) must be provided in allbeams.t Support rotations of up to 8° may be permitted when the element has sufficientlateral restraint to develop tensile membrane action. Further guidance regarding thetensile membrane capacity of reinforced concrete slabs may be found in TM5-1300 [3].t Adequate bracing must be provided to assure the corresponding level of ductilebehaviour.

Frame

Fig. 5.2. Member end rotations for beams and frames 131

be 2° and the maximum side-sway deflection, S, be limited to 1/25 of thestorey height, H, in framed steel structures.

Introduction to the behaviour of reinforced concreteand structural steelwork subject to blast loadingStructural response of reinforced concrete

When a reinforced concrete element is dynamically loaded, the elementdeflects until such time as the strain energy of the element is developed


/Failure of compression concrete

Beginning of strainhardening

x, (a = 2') x,(o = 4')Deflection

Fig. 5.3. Typical resistance-deflection curve for flexural response of concreteelements [3]

sufficiently to balance the energy delivered by the blast load and theelement comes to rest, or fragmentation of the concrete occurs. Theresistance-deflection curve shown in Fig. 5.3 demonstrates the flexuralaction of a reinforced concrete element.

When the element is first loaded , the resistance increases linearly withdeflection until yielding of the reinforcement occurs. Thereafter theresistance remains constant with increasing deflection until , at a deflectionxi corresponding to a support rotation , 0, of 2°, the concrete crushes incompression . Thus, for 0 in the range 0°-2° the concrete is effective inresisting moment and the concrete cover on both surfaces of the elementremains intact. This is referred to as a type 1 section (see Fig. 5.4a). Type1 elements may be singly or doubly reinforced , although to cater forrebound effects some compression reinforcement is usually desirable. Theultimate moment capacity , Mp, of type 1 sections may be determinedusing conventional plastic theory for reinforced concrete based upon thedynamic design stresses of the concrete (fdc) and the reinforcement steel(fds)•

For B > 2° the compression forces are transferred from the concreteto the compression reinforcement which results in a slight loss of capacityas shown in Fig. 5.3. In the absence of any compression reinforcementthe crushing of the concrete would result in failure of the element.Sufficient compression reinforcement must be available to fully developthe tension steel, i.e. symmetrical reinforcement must be provided. Therequirement for the provision of 'blast links ' for support rotations in excessof 10 is to properly tie this flexural reinforcement. Elements which sustaincrushing of the concrete without any disengagement of the cover on the

72 1 73


No crushingor spoiling

Type i

Cracking (a)

--- Crushing

Crushing

Type 2

(b)

Fig. 5.4. Typical reinforced concrete cross sections [31

4

d

d, T.


tensile face are known as type 2 sections (see Fig. 5.4b) and occur for 0in the range 2°-5°. The ultimate moment capacity, Mp, of type 2sections of width b is given by

M P = A fds dp b

where As is the area of reinforcement on each face and d, is the distancebetween the centroid of the reinforcement on the tension and compressionfaces.

As the element is further deflected, the reinforcement enters its strainhardening region and the resistance increases with increasing deflection(Plate 15). In the absence of any tensile membrane action the blast linkswill restrain the compression reinforcement from buckling for a short timeinto its strain hardening region. At a deflection x2 corresponding to a 0value of about 4° the element will lose its structural integrity and fail unlessother forms of restraint, for example, lacing reinforcement, are used. Lacedreinforced elements may be used in specialized explosive storage facilitiesbut are unlikely to be appropriate for buildings because of the complexityof the reinforcement detailing.

Although there is little, if any, evidence of shear failures under blastloading, premature shear failures must be avoided in order to fullydevelop the flexural capacity of an element. The shear capacity of theconcrete alone may be enhanced by providing additional shearreinforcement.

Structural response of steelworkStructural steel can generally be considered as exhibiting a linear stress-

strain relationship up to the yield point, beyond which it can strainsubstantially without appreciable increase in stress. This yield plateauextends to a ductility ratio, µ, of between 10 and 15. Beyond this rangestrain hardening occurs and after reaching a maximum stress - knownas the tensile strength - a drop in stress accompanies further elongationand precedes fracture at a strain of approximately 20-30%. Typical staticand dynamic stress-strain curves for steel are shown in Fig. 5.5.

Structural steels of strengths higher than grade 50 generally exhibitsmaller elongations at rupture and should be used with caution whenvery large ductilities are a prerequisite of design.

The design plastic moment, Mp, for steel elements with µ s 3 is givenby

Plate 15. Ductility and spalling of reinforced concrete. Photograph courtesy ofFrancis Walley

Mp = fds (Z+S)/2

where Z and S are the elastic and plastic section moduli , respectively.For µ > 3

MP = fdsS

74 l 75


t,.t„

v

in

Z

Normal strain rate

- - - - Rapid strain rate

0070 < e„ < 0.23 approx.

0.01-0 02 approx.

Strain:

Fig. 5.5. i;rpical stress-strain curves for steel [31

As with reinforced concrete sections, sufficient shear capacity must beprovided and local buckling failures, avoided in order to develop fully theflexural capacity of an element.

Comparison of responseReinforced concrete is relatively massive and, as such, is more

appropriate than steel to resist the close-in effects of large explosions inthe impulsive regime. Steelwork is better suited to resist relatively lowpressures of a quasi-static nature (Plate 16). The massive nature ofreinforced concrete implies 'stocky' sections whose ultimate capacity isreasonably predictable. The slender nature of structural steel sections cancause local instability and unpredictable ultimate capacities (Plate 17).

There are two other significant differences between the materials. First,the rebound in concrete structures is small because cracking causesinternal damping. In steel, the rebound can be quite large, particularlyfor short duration loads on relatively flexible elements. Therefore, steelstructures must be designed to support significant reversals of loading.Second, in reinforced concrete, separate reinforcing steel is provided toresist flexure, shear and torsion. In steel, complex stress combinationsoccur which are difficult to predict and which can potentially causedistress. Stress concentrations at welds and notches must also be carefullyconsidered if the full strength of the section is to be realized.


Introduction to the design of reinforced concreteelements to resist blast loading

The design methods recommended in this chapter are based on thosedescribed in [3]. As such, the design techniques set forth are based uponthe results of numerous full- and small-scale structural response andexplosive effects tests of various materials conducted in conjunction withthe developments described in [3] or related projects.

Design stressesTable 5.3 summarizes the relevant dynamic stresses fdC and fds to be

used in the design of reinforced concrete elements.

Idealization of structural responseThe structural response of a reinforced concrete element subjected to

flexure may be represented by the idealized resistance-deflection functionshown in Fig. 5.6, where ru is the unit ultimate dynamic resistance

Plate 16. Survivability of steel-framed buildings

76 1 77


Plate 17. Severe damage to both the structure's steel frame and its lightweight metalcladding: Boucher Street, Belfast

Table 5.3. Dynamic design stresses for reinforced concrete

Type of stress

Bending

Shear

Compression

Protection

category

1 and 2

Dynamic design stress

Concretefdc

Reinforcing barsfds

fdcu

fdcu

fdcu

fdcu

fdcu

^! fdy

fay + V du - fdy)l4

fdy

fdy

fdy

determined using plastic theory, modified to account for static loadspresent at the time of the blast loading, XE is the deflection at the limitof elastic behaviour, KE is the elastic stiffness and Xm is the maximumpermitted deflection corresponding to the limiting support rotation, 0,given in Table 5.2 for the appropriate protection category.


X.

Fig. 5.6. Idealized resistance -deflection curve (3)

Response to impulse. Idealization of blast load. The blast load may be idealized to a triangular

pressure-time function with zero rise time as shown in Fig. 5.7. In theimpulsive regime, the duration of the applied load, td, is short in relationto the response time, tm, of the element (the time for the element toattain a deflection Xm), such that tm/td a 3. The loading is assumed tobe uniformly distributed and is represented by the specific impulse, i.

Design for flexure.

(a) Design objective. To provide flexural strength and ductility so thatthe kinetic energy delivered by the impulsive load may be resistedby the strain energy developed by the member in deflecting to Xm.

(b) Basic impulse equation. For support rotations, 0 < 5°, the elastic partof the idealized resistance-deflection function must be consideredsuch that

Idealized resistancedeflection function

Deflection

d

d4

0td

Time

Fig. 5.7. Idealization of blast load [3]

78 1 79


i2 r„ X+ ru(Xm - XE)

2KLMm 2

where KLM is the appropriate load-mass factor obained fromTable B.1 (in Appendix B) and in is the unit mass of the element.

(c) Design steps.

Step 1. Define the resistance-deflection function in terms of:(i) r„ = f(MP, L) (see Table B.3), where

M = Asfds da b

for a type 2 section and

A,ps

bd

where p, is the steel ratio and hence Mp = psfdsd2.(ii) Xm

{= 1 (B).

(iii) KE = f(E, I, L) (see Table B.4), where I = Fbd3 (see Fig. 5.8)and E is the modulus of elasticity of concrete.

(iv) XE = r„/KE.

Step 2. Determine KLM (see Table B.1) and m = pd, where p is thedensity of concrete.

Step 3. Solve for do based on assumed value of pc.

Step 4. Calculate tan = i/ru, hence tmltd and check whether appro-priate design procedure has been used, i.e. quasi-static/dynamic orimpulse.

Design for shear. After the flexural design of the element has beencompleted, the required quantity of shear reinforcement must bedetermined. The ultimate shear is developed when the resistance reachesthe ultimate value, r,,, and hence the shear reinforcement is a functionof the resistance of the element and not of the applied load.

There are two critical locations where shear must be considered in thedesign of reinforced concrete elements. The ultimate shear stress, vu, iscalculated at a distance do from the supports to check the diagonaltension stress and to provide shear reinforcement in-the form of stirrups,as necessary. The direct shear force or the ultimate support shear, Vs,is calculated at the face of the support to determine the required quantityof diagonal bars.

(a) Ultimate shear stresses. Values of ultimate shear stresses, v,,, atdistance d, from the face of the support are given in Table 13.5.

(b) Shear capacity of concrete. The capacity of the concrete, v,, may betaken from BS 8110: Part 1 Table 3.9 with the partial safety factor,Yin = 1.25, removed.


007

0.06

0 05

003

002

001

0004 0.008 0.012Reinforcement ratio: p = A, /bd

0-016 0020

Fig, 5.8. Coefficient for moment of inertia of cracked sections with equalreinforcement on opposite faces [31

(c) Design of shear reinforcement . Whenever the ultimate shear stress, v,,,exceeds the shear capacity of the concrete, v,, shear reinforcementmust be provided to carry the excess. The required area of stirrups,A,,, is calculated from

A = (v„ - vc)bs

fas

80 1 61


where s is the spacing of stirrups in the direction parallel to thelongitudinal reinforcement. For type 2 sections, the minimum designstress, (v„ - va), to be used in the calculation of shear reinforcementis 0.85vc.

(d) Ultimate support shears. Values of ultimate support shears, Vs, at thesupports are given in Table B.6.

(e) Direct shear capacity of concrete. For type 2 sections where the designsupport rotation, 0, exceeds 2°, the ultimate direct shear capacity ofthe concrete, Vd, is zero and diagonal bars are required to take alldirect shear.

(f) Design of diagonal bars. The required area of diagonal bars at 45°, Ad,is determined from

Ad = Vsb/fd:

Response to quasi-static/dynamic loadingIdealization of blast load. The blast load may be idealized into a triangular

pressure-time function with zero rise time as shown in Fig. 5.7 or to otheridealizations for which response charts based on SDOF analyses areavailable. These may include square pulses with zero rise time, graduallyapplied loads, or triangular pulses with a finite rise time (see AppendixQ. In the quasi-static/dynamic response regimes, the duration of theapplied load, td, is long in relation to the response time of the element,tm, such that tm/td < 3. The loading is assumed to be uniformly distri-buted and is represented by the pressure, p, which varies with time, t.

Design for flexure.

(a) Design objective. To provide flexural strength and ductility such thatthe work done by the applied blast load may be resisted by the strainenergy developed by the member in deflecting to Xm.

(b) Design steps.

Step 1. Define resistance-deflection function in terms of:(i) r„ = f(MP, L) (see Table B.3),

where

MP = Asbfd, (d - 0.45x) for a type 1 section and

x Asfds

0.6bfd.

is the depth from the compression face to the neutral axis andd is the effective depth of the tension reinforcement and ps =(As/bd).

(ii) X. = f(6)•


007

0.06

0-05

003

002

00

0004

n = 5,15,

= Fbd'

I I0008 0,012 0.016

Reinforcement ratio: p = A, Pod

Fig. 5.9. Coefficient for moment of inertia of cracked sections with tensionreinforcement only [3]

0020

(iii) KE = f(E, I, L) (see Table B.4), where I = Fbd3 (see Fig. 5.9).(iv) XE = r„/KE.

Step 2. Calculate natural period of element

KypgmT=2i

KE

82 1 83


where KLM is the appropriate load-mass factor from Table B.1 andm is the unit mass of the element.

Step 3. Refer to appropriate SDOF response chart in Appendix C foran elasto-plastic system under idealized load to obtain:(i) /2 = Xm/XE, hence X. and 0(ii) tmltd and hence check whether the appropriate design procedure

has been used, i.e. quasi-static/dynamic or impulse.

Design for shear. The design for shear of type 1 reinforced concreteelements responding in the pressure-time regime is similar to that fortype 2 elements responding to impulse with the following exceptions:

(a) Ultimate shear stresses.(i) Unless specifically required as shear reinforcement, stirrups are

not required in slabs for which 0 <_ 10 .(ii) The values of ultimate shear stresses should be calculated at

distance, d, from the supports, rather than dc as given inTable B.S.

(b) Ultimate support shears.(i) For type 1 sections where 0 <- 2°, the ultimate direct shear force

that can be resisted by the concrete, Vd, is given by

Vd = 0.15fdCbd

(ii) The corresponding area of 45° diagonal bars, Ad, requiredbecomes

Ad =Vsb - Vd

fds

Dynamic reactionsWhen a reinforced concrete element is loaded dynamically, the loads

transferred to the supports are known as the dynamic reactions. Themagnitude of these reactions, which may be used as the basis of designof supporting elements, is a function of both the total resistance, R, andthe total load, P, applied to the element, both of which vary with time.They may be expressed generally in the form V = aR + OP. Table B.7provides values of a and 0 for differing support and loading arrangements.

It should be noted that the procedures described in this chapter arelargely concerned with the design of elements. This is likely to be thecritical design consideration when dealing with relatively large quantitiesof explosive at close proximity to a building structure. In situations wherethe overall stability of the building becomes critical, the designer will needto consider the provision of stabilizing elements such as shear walls. Theexternal loading on complete structures and the associated blast wave-structure interaction is fully described in Chapter 3.


Design example 1: reinforced concrete cantilever to resistimpulsive load

A cantilever blast wall is to be designed in reinforced concrete towithstand the impulse due to the detonation of 100 kg TNT at groundlevel at a stand-off of 4 m.

Take the wall height to be 3 m and assume a wall symmetricallyreinforced with grade 460 steel such that ps = 0.5%. The concrete maybe taken as grade 40 with a density of 2400 kg/m3.

Idealization of blast load. For a hemispherical surface burst, the relevantblast resultants at the wall are:

o positive phase duration, Ts = td = 4.83 ms (Fig. 3.2)o reflected impulse, i, = 5030 kPa-ms (kN-ms/m2)5

Design for flexure. For a unit width of cantilever retaining wall of height,H, effective depth, do and a type 2 section:

(a) Design steps.

Step 1.

(i) ru = H2n (see Table 13.3)

where

Mn = PsfdsdzC

hence

2 zru = H2 (Psfdsd C

2 )

Now fds = fay + vdu - fay)/4 (see Table 5.3)

where

fdy = 120 x 460 = 552 N/mmz and

fdu = 1.05 x 550 = 578 N/mmz (see Table 5.1). Hence

fds = 560 N/mm2 = 560 x 106 N/m2. Thus

ru = 2 (0005 x 560 x 106)d2N/m23.02

= 622 x 103d2 N/m2

(ii) For protection category 2

Xm = H tan 4° = 0.21 m (see Table 5.2)

(iii) KE = 8EI/H4 (see Table 13.4)

84 1 85


Take

Es = 200kN/mm2 = 200 x 109N/m2

Ec = 28kN/mm2 = 28 x 109N/m2

n = 200/28 = 7-14 and

ps = 0.005. Hence

I = 0.0245bd3 (see Fig . 5.8). Thus

(8 x 28 x 109 x 0.0245 x 1 )d3N/m2/m

KE 3 04 /

= 67-8 x 106d3N/m2/m

(iv) XE = ru /KE

622 x 103d2 9-2 x 10-3

67.810 d3c dom

Step 2. KLM = 0.66 (see Table B.1) m = pdc = 2400d,kg/m2.

Step 3. The basic impulse equation from page 80 is

i2 ru XE+ ru(Xm - XE)

2KLMm 2

Xm 2ru \ XE

For i = 5030 kPa-ms = 5030 N-s/m2 we obtain

50302 = 2 x 0-66 x 2400d, x 622 x 103d2(0.21 -

and simplifying gives

92x10-3

2d,

413.8 x 106d C - 9.06 x 106d c = 25.3 x 106

which gives do = 0.398 m, say 400 mm.

As = 0.005 x 400 x 1000 = 2000 mm2/m, therefore use T20 barsat 150 mm centres on each face. Hence, the overall section thickness,using 40 mm cover, is

Tc = 40 + 10 + 400 + 10 + 40 = 500 mm

Step 4. tm = i/r,,. Now r„ = 622 x 103 x 0.42 = 99 520 N/m2, hence

tm5030 = 0.0505 s = 50.5 ms which gives

99 520

tmltd = 50-5/4-83 = 10-5 ? 3

Therefore impulsive loading design is valid.


Design for shear

(a) The ultimate shear stress, distance do = 400 mm from support, isgiven as

ru(L - dc)

v° dc

= 99520(3-0 - 0.4)/0.4

= 646 900 N/m2 = 0.65 N/mm2(see Table B.5).

(b) 100A5 = 0.52, fcu = 40N/mm2bd,

Therefore

vc = 0.58 N/mm2 (BS 8110, Part I: Table 3.9),

(v„ - vc),= 0.07N/mm2 x (0-85v, = 0-49N/mm2).

(c) The required area of stirrups of width, b = 150 mm and spacing,s= 300 mm

A.,(vu - vc)bs

fd,

Using grade 250 steel , fds = fay = 11 x 250 = 275 N/mm2 (seeTables 5.1 and 5.3 ), hence

A _ 0.49 x 150 x 300 = 80.2 mm2° 275

Therefore use R10 stirrups at 300 mm centres.(d) The ultimate support shear is given by

Vs = r„L= 99520 x 3.0= 298 600 N/m = 299 N/mm (see Table B.6)

(e)

(f)Vd=0The required area of diagonal bars at 45° and spacing of b = 150 mm;

fd,)Ad = (VsUsing grade 460 steel, fds = fay = 1.1 x 460 = 506 N/mm2 (Tables5.1 and 5.3), hence

Ad = 299 x 150/506 = 88.2 mm2

Therefore use one row of T12 bars at 150 mm centres or two rowsof T8 bars at 150 mm centres.The designer should now proceed to check the overall stability of thewall and the detailed design of the foundations.

8786


Design example 2: reinforced concrete wall panel to resistquasi-static/dynamic load

The flexural capacity of a fixed ended reinforced concrete wall panel,600 mm thick and spanning vertically over an effective height of 7 m, isto be checked for protection category 1 against a specified blast loadingthreat. The wall is reinforced symmetrically with grade 460 bars such thatps = ps = 0.35%, d = 550 mm and d' = 50 mm. The concrete is grade 40.

Idealization of blast load. The specified blast loading threat may beidealized to a triangular pressure-time function with pr = 220 kPa andtd = 60 ms.

Design for flexure. For a unit width of wall of effective height, H,effective depth, d, and a type 1 section.

(a) Design steps.

Step 1.

(i)8(M„ + MP)

ru = H2 (see Table B.3), where

Mn= MP = Ands (d - 0.45x)

_ Asfasx0.6bfd,

for a symmetrically reinforced type 1 section in which thecontribution of the 'compression reinforcement ' is ignored. Now

f& = fay = 1.2 x 460 = 552N/mm2 (Tables 5.1 and 5.3)

and fdc = fdc„ = 1.25 x 40 = 50 N/mm2 (Tables 5.1 and 5.3)

Also A. = As = 0-35 x 1000 x 550 / 100mm2/m= 1925 mm2/m

Therefore , x = 1925 x 552/(0 . 6 x 1000 x 50 mm)= 35.5 mm

(this justifies ignoring the contribution of the 'compressionreinforcement') and

Mn = MP = 1925 x 552 (550 - 0 . 45 x 35-5) x 10-3Nm/m= 566 000 Nm/m

Hence r„ = 8 x 2 x 566 000 /7.02 = 184800N/m2

(ii) For protection category 1, B is limited to 2° (Table 5.2). In theabsence of stirrups, 0 is further limited to 1°.

Therefore , assume that X. = 3.5 tan 1 ° = 0.0611 m = 61.1 mm

and


(iii) KE = 307EI/H4 (see Table B.4)

As in Example 1, n = 7.14. Also, ps = 0.0035

Hence I = 0.018bd3 (Fig. 5.9).

Thus

307 x 28 x 109 x 0-018 x 1 x 0.553KE = 7.04

= 10-72 x 106 N/m2/m

(iv) XE = ru/KE

=184800/10.72 x 106=0.0172m= 17.2 mm

Step 2.

T = 2 KLMm

KE

Now

(10-72

0.72 x 1440 v2

0.77 + 0.66KLM = 2 = 0-72

and m = 2400 x 0.6 = 1440 kg/m2. Therefore

T=2r=0.0618sx106

= 61.8 ms

Step 3. Referring to the SDOF response chart C.1, r„/P =184800/220 000 = 0-84 and td/T = 60/61-8 = 0.97. Hence, Xm/XE =2.7 and X. = 2.7 x 17.2 = 46.4 mm < 61.1 mm which is satis-factory. Referring to the SDOF response chart C.2, tm/td = 0.67 < 3.Therefore quasi-static/dynamic loading design is valid and the flexuralcapacity is adequate. Further checks may be necessary for shearcapacity and the magnitude of dynamic reactions applied to the topand bottom supporting elements.

Introduction to the design of structural steel elementsto resist blast loadingDesign stresses

Table 5.4 summarizes the relevant dynamic stresses, fas and fdv forflexure and shear, respectively, to be used in the design of structural steelelements.

8889


Table 5.4. Dynamic design stresses for structural steel

Type of stress Protectioncategory

Dynamic design stress

Bending

Shear

1

2

1 and 2

fds =fdy

fds = fdy + (td. - fdy)/4

fdv = 0.55 fds

Idealization of structural responseThe structural response of a steel element subjected to flexure may be

represented by the idealized resistance-deflection function shown in Fig.5.6, where r„ is the unit ultimate dynamic resistance determined usingplastic theory modified to account for static loads present at the time ofthe blast loading; XE is the deflection at the limit of elastic behaviour;KE is the elastic stiffness and X. is the maximum permitted deflectioncorresponding to the more critical of the limiting support rotation, 0, orductility ratio, µ, given in Table 5.2 for the appropriate protection category.

Response to quasi-static/dynamic loading

Idealization of blast load. The blast load maybe idealized into a triangularpressure-time function with zero rise time as illustrated in Fig. 5.7 orto other idealizations for which response charts based upon SDOFanalyses are available (see Appendix C).

Design for flexure.

(a) Design objective. To provide flexural strength and ductility such thatthe work done by the applied blast load may be resisted by the strainenergy developed by the member in deflecting to Xm.

(b) Design steps.

Step 1. Carry out preliminary design assuming an equivalent staticultimate resistance as defined in Table 5.5.

(i) Determine the required resistance, r,,, using Table 5.5.(ii) Determine the required plastic moment of resistance, MP =

f(r, L) (use Table B.3).

Table 5.5. Equivalent static ultimate resistance for preliminary design of steel

elements in flexure

Protection category

12

Equivalent static ultimate resistance

r„ = 1'O Pm.,.


(iii) Select a steel member using appropriate relationship betweenMP, fds, S and Z.

Step 2. Calculate the natural period of the element using the followingequation

T = 27 I KLMm,NJ KE

where KLM is the appropriate load-mass factor from Table B.1 andm is the unit mass of the element.

Step 3. Refer to appropriate SDOF response chart in Appendix C foran elasto-plastic system under idealized load to obtain

(i) It = Xm/XE, hence X. and 6, and(ii) tmltd and hence check whether the appropriate design procedure

has been used, i.e. quasi-static/dynamic.

Check for shear and secondary effects.

(a) Ultimate support shear. Values of ultimate support shears, Vs, aregiven in Table B.6.

(b) Ultimate shear capacity. The ultimate shear capacity is given by Vt, _fdv A,,,, where A„, is the area of the web.

(c) Local buckling and web stiffeners. In order to ensure that a steel beamwill attain fully plastic behaviour and hence the required ductility atplastic hinge locations, it is necessary that the elements of a beamsection meet the normal minimum thickness requirements sufficientto prevent a local buckling failure. Similarly, web stiffeners shouldbe employed at locations of concentrated loads and reactions toprovide a gradual transfer of forces to the web.

(d) Lateral bracing. Members subjected to bending about their strong axesmay be susceptible to lateral-torsional buckling in the direction of theirweak axes if their compression flange is not laterally braced. In orderfor a plastically designed member to reach its collapse mechanism,lateral supports must be provided at and adjacent to the location ofplastic hinges. In designing such bracing due consideration shouldbe given to the possibility of rebound which induces stress reversal.

Design example 3: structural steel beam to resist quasi-static/dynamic load

A simply supported steel floor beam is to be designed for protectioncategory 1 against a specified blast-loading threat. The floor beam is oneof a series of beams spaced at 1-4m which are to support a 4mm thicksteel deck plate over an effective span of 5.2 m. Take fy = 275 N/mm2,Es = 210 kN/mm2 and p = 7850 kg/m3.

90 91


Idealization of blast load. The specified blast loading threat may beidealized to a triangular pressure-time function with p, = 50 kPa andtd = 40 ms.

Design for flexure.

Step 1. For protection category 1, 0 <_ 2° and µ s 10.

(i) For a preliminary design take r„ = 1.0 p, (see Table 5.5).Thus, the required resistance per unit length is given as

r„ = 1.0 x 50 x 1.4 = 70kN1m.

(ii) The required plastic moment of resistance is

MPr$z = 70 $5 2 2

(see Table B.3)

= 236-6kNm

(iii) Take Mp = fdsS where

fd s = fay = 1'1 x 1.20 x 275 = 363 N/mm2 and

S a 2366 x 106/363 = 0.652 x 106mm3

Select a 356 x 127 x 39 kg/m universal beam (S = 0.654 x106mm3, MP = 0-654 x 106 x 363 = 237 x 106Nmm =237 kN m).

Step 2.

KLM = 2 0.72 (see Table B.1)

Mass, m, per unit length = 39 + (7850 x 1-4 x 0.004) = 83.Okg/m

KE = 384EI (see Table B.4),5L4

where I = 100.87 x 106mm4.

Thus

384 x 210 x 103 x 100 .87 x 106KE

5 x (5-2 x 103)4

= 2-225 N/mm/mm= 2-225 x 106 N/m/m.

Hence

T = 2a VI<LMm

KE

0-78 + 0.66


1/0.72 x 83.0\1112.2\2.225 x 106)

= 0-0326s= 32.6 ms

Step 3.

(i) Referring to the SDOF response chart CA

r. =° Lz 5 22

= 70-1 x 103N/mP = 50 x 103 x 1.4 = 70 x 103 N / m

Thus, r„/P = 1-00 and td/T = 40/32-6 = 1-23. Hence, Xm/XE _µ = 2.1 < 10, which is satisfactory.

rXm=µXE=µK

E

= 2.1 x 70.1 x 103/2.225 X 106= 0.0662 m= 66.2 mm

tan 0 =Xm

=66.2x2/5.2x103L/2

Thus, 0 = 1.46° <- 2° which is satisfactory. The beam is slightlyover-designed and there may be some scope for furtherrefinement of the section.

(ii) Referring to SDOF response chart C.2, tm/td = 0.51 < 3.Therefore pressure-time loading design is valid and the flexuralcapacity is adequate.

Check for shear and secondary effects.

(a) The ultimate support shear is

Vs = r2L = 70.1 x 103 x 5-2/2

= 182-3 x 103 N

(b) The ultimate shear capacity is

fd„ = 0.55fds = 0.55 x 363= 200 N/mm2

V p= f d„A,,. = 200 x 352.8 x 6.5= 458-6 x 103N

VP > V, which is satisfactory.

92 93


(c) Check for local buckling and provide web stiffeners at support.(d) Top flange of beam is laterally restrained under normal downward

loading. Provide lateral bracing to lower flange in the event of loadreversals.

References1. British Standards Institution. Structural use of steelwork in building. Code of practice

for design in simple and continuous construction. BSI, London, 1985, BS 5950: Part 1.

2. British Standards Institution. Structural use of concrete. Code of practice for design

and construction. BSI, London, 1985, BS 8110: Part 1.

3. US Department of the Army Technical Manual, TM5-1300. Design of structuresto resist the effects of accidental explosions. 1990.

4. British Standards Institution. Bending dimensions and scheduling of reinforcementor concrete. BSI, London, 1981, BS 4466.

5. Hyde D.W. CONWEP: weapons effects calculation program based on US

Department of the Army Technical Manual, TM5-855-1. Fundamentals of protective

design for conventional weapons. 1992.

6 Implications for buildingoperation

Health and safety regulationsThe Management of Health and Safety at Work Regulations, 1992, whichcame into force on 1 January 1993, oblige an employer to establish and,where necessary, give effect to appropriate procedures to be followed inthe event of serious and imminent danger to persons at work in his orher undertaking. Current legal opinion implies that this legislation maybe interpreted to include the safety of employees when there is a threatof a terrorist act or other violent act perpetrated by, for example, adisgruntled employee. Further, The Construction Products Directive ofthe European Community contains, within Annex 1, essentialrequirements to ensure that products are fit for their intended use. Thisincludes safety in use and in particular it specifies that 'the constructionwork must be designed and built in such a way that it does not presentunacceptable risks of accidents in service or in operation such as slipping,falling, collision, burns, electrocution, injury from explosion [author'semphasis].' The attention of the reader is also drawn to the Construction(Design and Management) Regulations, 1994. These clarify the duties ofthose involved with the management of risks arising from buildings andstructures throughout their life cycle. Therefore, it is imperative to havewell-established and practised contingency procedures in place.

Threat assessmentThe following factors should be taken into consideration in the

preparation of a threat assessment for a particular building:

• Advice from the local police force which may be based upon theHome Office document Bombs - protecting people and property [1].

• The current national and international situation as determined fromnews coverage.

• Any special circumstances of the occupants.• The building location, for example whether there is a 'high risk'

94 95


building close by, an attack on which may result in collateral damageto the building in question.

Pre-event contingency planningWhen preparing the pre-event plan certain important aspects need to

be considered. They fall into two categories: initiating and managing theplan in response to a threat; and the response actions relating to thevarious threats.

Initiating and managing the planIt is important to appoint a single person (a security coordinator) to have

full responsibility for initiating and managing the plan. He or she mustreceive total support from senior management. Further, all staff, includingthe senior management, must accept and act on this person's instructionsduring the emergency. The security coordinator will need deputies.

The plan should be discussed with the police and fire brigade as earlyas possible. The Home Office booklet Bombs - Protecting People and Properly/contains a great deal of valuable advice and is an excellent aid to drawingup contingency plans.

To ensure that the plan works satisfactorily under a real threat, andthat staff appreciate what is expected of them, it must be regularlypractised and further, it must be kept up to date.

Response actions

(a) The telephoned bomb threat. On receipt of a bomb threat call, thesecurity coordinator should be informed of the contents of the callin order that they can make a considered assessment of the threat.Based on the result of this assessment the security coordinator willinform the police and initiate one of the following:

(i) Do nothing.(ii) Undertake a limited search.(iii) Undertake a full search then either evacuate staff or assemble

staff in the bomb shelter area (BSA).

(b) The delivered item (letter bomb or package bomb). If a letter or packageis suspected of containing an explosive device, then the followingactions should be undertaken:

(i) Leave it alone.(ii) Clear the room plus the rooms either side, above and below.(iii) Inform the police.

Ensure that the person who discovered the suspect package remainson hand to assist the police when they arrive.

IMPLICATIONS FOR BUILDING OPERATION

It is important that all personnel who-are involved in receivingmail and delivered items should be made aware of the aboveprocedures.

(c) The internal improvised explosive device (IED). If it is believed that anIED has been deposited inside the building then the followingprocedures for searching the building should be contained in theplan:

(i) Appointed teams to search the common public areas.(ii) Individual staff to search their own work place.

If the suspected IED is found the area should be cleared and itslocation reported to the security coordinator. The security coordi-nator will then have to consider continuing the search of other areassince more than one device may have been planted. Also, this willassist when-the decision to re-occupy the building has to be taken.

Depending upon the location of the device, consideration shouldbe given to using the BSA or evacuating the building.

(d) The external IED. Typically the external IED falls into two categories:the small carried device, e.g. briefcase, carrier bag, duffle bag, etc.,and the vehicle-borne device ranging from a car to a large lorry.

Generally the reaction to both the small and large device will besimilar. However, when the location of the small device is knownand it is assessed that there are no other devices in the area then,depending on the size and spread of the building, the reaction plancan be applied to a limited area of the building. If evacuation is theadopted policy, as the building is such that it does not offer a BSA,then the assembly points will have to be a minimum of 400 m fromthe building. Consideration will also have to be given to the poten-tial deployment, by the terrorist, of a secondary device designedto cause injuries to the authorities attending the aftermath of theoriginal device.

Further considerationsTo enable the plan to be initiated and managed efficiently and

effectively, communications between the security coordinator and all thestaff and between the security coordinator and the police will be necessarythroughout the whole of the incident. Therefore consideration should begiven to the provision of a voice alarm system (VAS) within the buildingand a number of portable telephones for external communication.

If the BSA philosophy is adopted it is important to ensure that thecontrol point from where the security coordinator is able to communicatewith staff and police offers the same level of protection as that providedby the BSA.

96 i 97


To aid the retrieval of data and thus minimize the disruption to thebusiness, consideration should be given to implementing the followingat the end of each working day and whenever assembly in the BSAs orevacuation is actioned.

• Cover IT equipment, particularly the data storage systems;• Impose a clear desk policy.

Post-event contingency planningA post-event contingency plan is essential for business survival. It is

not only necessary for dealing with terrorist outrages but also for manyother forms of disaster from flooding to fire and from a majorcommunications failure to a plane crash.

There are many commercially available pre-designed plans orconsultants capable of providing a business specific plan. To assist inensuring that the finally adopted plan is what is required, a list of criticalpoints which should be included are set out below.

(a) A pre-identified team to manage the disaster whose initial tasks willinclude assessing the extent of the damage, setting an objective,e.g. 'Business as usual on Monday' and communicating with staff.The recovery procedures should be put in hand by empowerment,i.e. giving full authority to a staff member to take all reasonablemeasures to fulfil his or her allotted task (e.g. no requirement forthree competitive quotations for the purchase of equipment, etc.),communicating with the media (proactive if possible), communi-cating with staff in non-affected offices, shareholders, clients, etc.

(b) A pre-identified team to continue the core business.(c) A communication cascade system for all staff.(d) Recovery procedures shall include the establishment of a communi-

cations centre, including a help desk and the establishment of acomputer facility for data retrieval and usage.

One vitally important point is to ensure that copies of the plan are easilyavailable in the event of a disaster. It is not sufficient to have one copysupposedly held safely in the building. Further, the plan and data mustbe kept up to date. Telephone numbers and names and location of stafffrequently change.

Reference

1. Home Office. Bombs - protecting people and property. A handbook for managersand security officers, March, 1994.

Append ix S implified designprocedure for determ iningthe appropriate level ofglazing protection

When using this design guidance it is important to note the followingpoints when considering the larger devices, i.e. van bombs and above.

o The structure is capable of withstanding the blast.o At small stand-off distances the cladding, local to the device, will

not survive.o The glazing and frame is not stronger than the cladding to which

it is fixed.

The simplified design procedure for determining the appropriate levelof glazing protection is as follows.

(a) Determine the threat. Select the size of device based on the threatassessment (see Chapter 6).

(b) Establish the stand-off distance. Measure the stand-off distance fromthe perimeter of the building to the location where the selecteddevice could be sited.

(c) Extract the stand-off distance for internal flying glass (4 mm annealed).From Table A.1, for the selected device size extract the stand-offthat will produce internal flying glass (4 mm annealed) and hencecause personal injury.

(d) Calculate the 'comparative value'. The 'comparative value' is calculatedby dividing the stand-off for internal glass ( item c ) by the measuredstand-off distance (item b),

comparative value =stand-off 4 mm annealed

stand-off measured

(e) Selecting the glazing. Select appropriate glazing by matching thecalculated 'comparative value' (item d) with the values given inTable A.2. Note that if laminated glass, single or double, is selectedthen the use of the frame and fixing design parameters in Table A.3is necessary.

98 99


Table A.1. Stand-off distances to produce internal flying glass

Device

Small packageSmall briefcaseLarge briefcaseSuitcaseCarSmall van*Large vanSmall lorrytLarge lorry

Stand-off for 4mm annealed glass: m

1014202660

120140160200

Note. Stand-off distance is the distance from the centre of the explosion to the objectunder consideration (in this case the glazing). These distances are approximate. Incertain circumstances , such as where the configuration of surrounding buildings causesa local concentration of the blast effect, the distances could be increased byup to 30%.* St Mary Axe, City of London device.t Bishopsgate , City of London device.

Table A.2. Internal flying glass. Comparison of levels of protection provided byvarious glass types and applied protective measures

ComparativeGlazing type value

Annealed glass (A)4mm 1.04mm + ASF* 1.74mm + ASF + BBNCt 2-0Toughened glass (T)6mm 2.06mm + ASF 2.5Smut 2-5Scorn, + ASF 2-910 mm 2.910mm + ASF 3.3

ComparativeGlazing type value

Laminated glass (L)$6.4 mm or 6.8 mm 2.57.5 mm 2.911.5 mm 3.3Double glazed unitst6mmT+6mmT 2.56 mm A + 7.5 mm L 3.36mmT+7.5 mmL 4.0

i.e. 6.4 mm laminated glass is 2.5 times better than 4mm annealed glass.

* ASF - anti-shatter film, 100 µm thick.t BBNC - bomb blast net curtains.* For laminated glass to be effective it must be securely fixed into its frames preferablywith structural silicon and the frames must have glazing rebates of a minimum of25 mm deep. However , in special frames with deeper rebates (35 mm) the percentageimprovement will increase . The frames in turn must be securely fixed to thesurrounding structure.

APPENDIX A

Table A.3. Frame and fixing design parameters for laminated glass

Laminated glass Approx. glass Equivalent ultimate Minimum glazingthickness: mm pane size: m2 static load: kN/m2 rebate: mm

6-4

6-8

7.5

11.5

0-6 6.0 251 - 8 3.0 253-0 3.0 300-6 8.0 251-8 4-0 253.0 4-0 300-6 12-0 251-8 7.0 303.0 6-0 300-6 18.0 251-8 11.0 303-0 9 - 0 30

The frames and fixings should be designed to accommodate two modes of actionoccurring simultaneously:

(i) A line load of F kN /m acting on the frame perpendicular to the plane of thewindow.

(ii) A line load of 0-5FkN /m acting on the frame in the plane of the window,towards the centre of the pane.

F is defined as the average edge reaction , i.e. F = (WAIF), where W = theequivalent ultimate static load, kN /m2, A = the area of the window , m2, and P = theperimeter of the window, m.

The above figures for equivalent static loads are a guide only.

(f ) Worked example.

(i) Threat assessment determines a small van-sized device.(ii) The closest a vehicle can get to the building is measured as 30 m.(iii) The stand-off for 4 mm annealed for a small van is 120 m.(iv) The calculated comparative value is 120/30 = 4.0.(v) The glazing type with a 4-0 or more comparative value is:

6mm toughened + 7.5 mm laminated.

Note that frames and fixings are to be designed using theappropriate loading parameters.

100101

APPENDIX B

Append ix B . Transformationfactors for beams andone-way slabs*

* Refer to Chapter 5 for notation.

Table B.1. Transformation factors for one-way elements (after US Department of the

Army Technical Manual, TM5 - 1300. Design of structures to resist the effects of

accidental explosions, 1990)

Edge conditions and loading diagrams Range of Load Mass Load-massbehaviour factor factor factor

KL KM KLM

Elastic 0.50 0.33 0.66

L Plastic 050 033 066

Elastic 1.0 0.49 0.49

U2 U2 Plastic 1.0 033 033

Elastic 0.58 0.45 0-78

plasto-

L plastic 064 050 078

Plastic 0.50 0.33 0-66

Elastic 1.0 0.43 0-43PElasto-

L/2 U2 plastic 1.0 0 . 49 0.49

Plastic 1.0 0.33 0-33

Elastic 0-53 0.41 0.77

Elasto-

plastic 064 0 -50 078

Plastic 0.50 0.33 0.66.

PElastic 1.0 037 037

U2 U" Plastic 1.0 0-33 033

Elastic 0-40 0.26 0.65

2 L Plastic 0-50 0-33 0.66

PElastic 1.0 0-24 0.24

L Plastic 1.0 0-33 033

P/2 P/2Elastic 0-87 0-52 0-60

L/3 U3 U3 Plastic 1.0 0-56 0-56

103

102


Table B.2. Elastic and elasto-plastic unit resistances for one-way elements (as perTable B.1)

Edge conditions and loading diagrams Elastic Elasto-plasticresistance , r, resistance, rep

q qL

P

U2 U2 R„

BM N8ML r.

P 16MNR

U2 U2 3L

12M N

Lz

P BM NR

U2 ^2L

L r.

P

L R

P/2 P/2

U3 U3 U3 R°

APPENDIX B

Table B.3. Ultimate unit resistances for one-way elements (as per Table B.1)

Edge conditions and loading diagrams

L

L

Ultimate resistance

$ML2

4MR„= L

4(MN + 2Mp)

Lz

P

L12 u2R =

2(MN + 2Mp)L

r^ -n - P,

Lz

P 4(MN + Me)R „=

U2 U2L

2MNLz

MNR„ = L

L

104 105


Table B.4. Elastic, elasto-plastic and equivalent elastic stiffnesses for one-wayelements (as per Table B. 1)

Edge conditions and loading diagrams Elastic Elasto-plastic Equivalentstiffness, stiffness, elasticK^ Kep stiffness

K E

p 35L£1 35Lg q _

5L4 45L4

P48EI 48E1

U2 U2 L3 L3

185EI 384EI 160E1*

L L4 5L4 L4

P107E1 48£] 106EI*

U2 U2 L3 L3 L3

384EI 384EI 307E]*L

L4 5L4 L4

P192£1 48EIt 192EI*

U2 L/2 I L3 L3 L3

8E1 8EI

•^`^' L4

P 3EI 3E]

E3 L3

P/2 P/2 56.4E1 56.481

U3 U3 U3 L3 L3

* Valid only if MN = Mp,t Valid only if M,N, < M.

106

APPENDIX B

Table B.S. Ultimate shear stress at distance d, from face of support for one-wayelements (as per Table B.1)

Edge conditions and loading diagrams Ultimate shear stress, v„

Lrul2 L - ac)

P R„

U2 U2 2d,

/ \Left support ru I $L -dr I /d,

/Right support r„` 38 -d,)ld,

`P11R„

Left support16d

5RURight support

16dr

ru(2 L - dc)L d

p

R„

U2 , 12 2d,

r„ (L - d^)

L d,

L dc


Table B.6. Support shears for one-way elements (as per Table B.1)

Edge conditions and loading diagrams Support reactions, V,

r, LL 2

P R

U2 L/2 2

Left reaction5r„L

8

LRight reaction,y

3ruL$

P Left reaction11R„16

U2 U2Right reaction

5R„

16

L

2

P Ru

U2 j, U2 2

L r„L

L R,

P/2 P/2 R

U3 U3 U3 2

APPENDIX B

Table B.7. Dynamic reactions for one-way elements (after Biggs J.M. Introductionto structural dynamics. McGraw-Hill, New York, 1964)

Dynamic reactions V

Edge conditions and loading diagrams Elastic Elasto - Plasticplastic

Pi` - P = pL 0.39R+0-11P - 0.38R +0.12P

P

L/2 U20-78R-0.28P - 0.75R-0-25P

P Left reaction

p . pL Right 19P 0-39R +011P 0 38R+0 12PRight reaction0-26R +0.12P ±MNIL ±MNIL

p Left reaction

0.54R+0.14P 0-78R-0.28P 0-75R-0.25PL/2 U2 Right reaction

0-25R +0.07P ±MNIL ±MNIL

PP = PL

^t

0^36R+0-141` 0-39R +0.11P 0.38R +0.12P

P0-71R -021P - 0-75R-0-25P

U2 U2

PP=pL

P

L

P/2 P/20.53R-0-03P - 0.528-0.02P

U3 U3 L/3

108 109

Appendix C. Maximumdeflection and response timefor elasto -plastic singledegree of freedom systems*

01100

50

20

10

0.5

0-2

0.1

02 05 1

td IT2 5 10 20

XE tmResistance Displacement

function function0.1 02 05 1 2 5

td IT10 20

40

40

Fig. C. 1. Maximum deflection of elasto-plastic, one degree of freedom system fortriangular load (after US Department of the Army Technical Manual, TM5-1300.Design of structures to resist the effects of accidental explosions, 1990)

* Refer to Chapter 5 for notation.

10

5

2

1

05

02

01

0.05

002

001

L PXm -_-

^ I

e XE

Triangular Resistance Displacementload t function function

APPENDIX C

r. /P = 0.1

0-2

03

2-0

I0.1 0-2 0.5 1 2 5 10 20

to IT

Fig. C.2. Maximum response time of elasto -plastic, one degree of freedom system fortriangular load (as per Fig. Cl.).

110III


20

10

8

5

1

08

05

02

0.1

Gradually applied Resistanceload function

I

0.1 02 0.5 0-8 1 2td IT

5 8 10 20

Fig. C.3. Maximum deflection of elasto-plastic, one degree of freedom system forgradually applied load (as per Fig. Cl.)

APPENDIX C

0 51-

02 -

Pru

load function function

Xm

i I/ II

Xa

Gradually applied Resistance Displacement

b-i 02 0.5 0.8 1 2 5 8 10 20

td IT

Fig C.4. Maximum response time of elasto-plastic, one degree of freedom system forgradually applied load (as per Fig. Cl.).

112 1 113

BLAST EFFECTS ON BUILDINGS APPENDIX C

10

5

03

0.5

02f-

0.10

P

ty

Rectangularload

r„Xm

Xe tmResistance Displacement

function function

02 0.5 1 2 5 10 20 40

to IT

Fig. C. 5. Maximum deflection of elasto-plastic, one degree of freedom system forrectangular load (as per Fig. C. 1.)

2

0-5

02

01

0.05

002

0010.1

P

tdRectangular

load

0-2

ru I

Xe tmResistance Displacement

ru /P = 02

0 - 5

1 . 00

10

04

06

08

101

1-02

05

1 - 15

1620

function function

05td IT2 5 20 40

Fig. C.6. Maximum response time of elasto-plastic, one degree of freedom system forrectangular load (as per Fig. C.1.)

114 1 115


01

OS td to

Triangular pulse Resistance Displacementload function function

0.1 02 0.5 0.8 1 2to IT

5 8 10

Fig. C. 7. Maximum deflection of elasto-plastic, one degree of freedom system fortriangular pulse load (as per Fig. C. I.)

APPENDIX C

in

a

5

2

1008

05

0-2

of 02 0.5 0.8 1 2to IT

5 8 10

Fig. C.B. Maximum response time of elasto-plastic, one degree of freedom system for

triangular pulse load (as per Fig. C. 1.)

116 1 117

}

Appendix D . Design flowchart

Notes

1. As an approximate rule, reinforced concrete elements designed forprotection category 1 (B <- 2°) will exhibit a type 1 section and are likelyto respond within the pressure - time (or dynamic) regime, whereasthose desi;ned for protection category 2 (0 > 2°) will exhibit a type2 section and are likely to respond within the impulsive regime.However, this is not a hard and fast rule and the response time of theelement-(tm) must always be calculated and compared with theduration of the load (td) to check that the correct response regime hasbeen assumed in design.

2. For the unusual case of protection category 2 and response within thepressure-time (or dynamic) regime, a type 2 section should beassumed at this stage.

3. For the unusual case of protection category 1 and response within theimpulsive regime, a type 1 section should be assumed at this stage.

4. Structural steel sections usually respond within the pressure-time (ordynamic) regime. However, if the calculated response time (tm) islarge in relation to the duration of the applied load (td) an impulsivedesign procedure may be more appropriate.

119

Establish design loadsApply partial safety factors

Select structural materialEstablish characteristic strengthsApply dynamic increase factor

Choose protection categoryEstablish limiting support rotations and ductility ratios

Calculate reflected impulseand duration (td) ofidealized blast load

Define resistance -deflection function fortype 2 section in terms ofd^

El

Fig. D.1. Flow chart of design procedures

1Calculate load - mass factorand unit mass of elementin terms ofd,

ASolve basic impulseequation for d,

ICalculate response time ofelement (tm)

Reinforced Iconcrete 1

Establish dynamic design stresses for concrete andreinforcing bars

as / __- .- . No

Protectioncategory 1(Note 1)

I

Calculate peak reflected pressure andduration (td) of idealized blast load

Define resistance- deflection functionfor assumed typek section (Note 2)

r

Calculate natural period of element

Refer to appropriate SDOF responsecharts and determine ductility ratio,support rotation and response time (tm)

Calculate dynamicreactions and designsupporting elements

Structuralsteelwork

Establish dynamic design stresses forstructural steel

Calculate peak reflected pressure andduration, (td). of idealized blast load

ICarry out preliminary design usingequivalent static resistance and selectsteel section,

Calculate natural period of element

Refer to appropriate SDOF responsecharts and determine ductility ratio,support rotation and response time(tm) (Note 3)

V

No

' Are 'ductility ratioSelect revised

section and support rotationwithin limits?

Yes

Design for shear, local buckling andlateral bracing

(Fig. D.I. cntd.)

0727735217 blast effects on buildingsb

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