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The numerical values of the pulse parametersat any given point in space depend mainly on thequantity of explosive and the distance of the pointof measurement from the source. The type of highexplosive makes a lesser difference to the pulsevalues. Pulses from improvised (or home-made)explosives may depart significantly from thepressure-time distribution pattern for pulses from

high explosive. Typical pressures from highexplosive blast are orders-of-magnitude greaterthan from wind loading, but durations are veryshort and measured in milliseconds. Note that thepositive phase of the pulse, in which pressures areabove atmospheric is followed by a negativephase in which they fall below atmosphericpressure. This can be important in its effect onwindow response, when the elastic rebound of anunbroken pane may coincide with the negativephase. Breakage might then occur during therebound rather than during the inward motion. This

effect is commonly observed.A basic parameter of a pulse is the integral ofthe pressure-time function (for both the positive andnegative phases). This is called the Impulse. Inconjunction with the initial pressure, its value issignificant in determining what the dynamicresponse of a flexible target will be.

The numerical values of the blast pulse para-meters from high explosive have been evaluatedfrom many test measurements (ref. 2). It has beenfound that whatever the weight of explosive, the initialpeak pressure, when plotted against scaled range,is the same. Scaled range is the actual rangedivided by the cube root of charge weight. Also,impulse divided by the cube root of charge weightplots against scaled range as a single curve.Similarly, all the remaining parameters describing anyblast pulse produced from high explosive can benormalised to produce single relationships which canall be expressed as polynomial functions. Thesecurves facilitate the rapid evaluation of blastparameters for any charge weight and range. Fig 215 of Reference 4 presents these curves.

The response motion of any unbroken structuralmember (of which an uncracked window pane is

an example) under high intensity, short durationloading is oscillatory, following closely simple

harmonic motion after the forcing phase of thepulse has finished. While the pulse is still forcing,the simple harmonic response is modified.Damping will cause this motion to decay rapidly.

If the pulse is very long compared with thenatural period of vibration of the member, thepulse will approximate to a static load and themember will oscillate about a mean deflectionwhile the pulse is still acting (provided it doesnt

reach its failure stress first). If the pulse durationis of similar order to the natural period of vibration,more complex interaction, involving a mixture ofthese two responses will occur.

In general terms, the magnitude of the deflec-tion (and the associated material stresses) duringthe motion determines whether the member fails ornot. More correctly for glass, the criterion for failuredepends upon whether the stress at the root of anysurface fissure in the glass reaches a critical value,which then leads to propagation of that fissure. Thecritical fissure need not be at the point in the paneof greatest surface stress, when considered as ahomogeneous member. This is because pro-pagation of a crack from a flaw depends on themicroscopic geometry of the random flaw, as wellas on the stress in the homogeneous plate.Calculation based on this fracture phenomenon(see Ref. 6) is more difficult than calculation ofstresses in a homogeneous plate, and the lattermodel is therefore commonly used as the failurecriterion. Both failure criteria models represent thesame random phenomenon, and therefore it is tobe expected that the plate stress criterion shouldalso have an associated confidence level.

An analytical approach to the dynamic responseinvolving complex dynamic computer analysis of

sandwich plates in three dimensions has beenintentionally avoided, since the main areas of

pressure

pressure

time

time

time

pressure

Short Duration Pulse

time

deflection

pressure

time

Long Duration Pulse

time

time

pressure

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uncertainty lie in the material properties of glass andpvb under high speed loading, and in the evaluationof the pulse felt by the pane itself. For practicalpurposes, dynamic analysis can be carried out withsufficient accuracy by assuming that the member inquestion, whether it be beam or plate, can berepresented by an equivalent single degree offreedom model. This comprises a discrete mass

reacting against a varying resistance. The resistanceneed not represent a purely elastic spring; it mayrepresent an elastic-plastic reaction, or even astepped resistance function. The single-degree-offreedom analysis then follows a time-steppingprocedure based on Newtons laws of motion. In thisanalysis the actual mass of the pane is factored toallow for the distribution of the actual mass over thewhole extent of the actual member. (The procedureis laid out in Reference 1, chapter 1).

To perform a time-stepping analysis on a win-dow pane, the resistance function of the pane mustbe derived. The resistance function relates the

instantaneous resistance to the instantaneousdeflection during the course of an excursion. Fora solid, plane pane in an elastic material withnegligible creep properties, this takes the followingform, which can be evaluated by well-known plateanalysis procedures. The relationship is linearinitially, becoming non-linear for large deflections.Glass panes are capable of deflecting well into thelarge deflection condition.

For a laminated pane under high speed loading,the resistance initially follows that of a homogeneouspane and then drops after the glass fractures.Thereafter, if the pane is held securely in the framerebates, the resistance will increase again as theresistance of the pvb interlayers, acting as amembrane, comes into effect. The general form ofthe complete resistance function will then be;

Such a curve is used in carrying out the time-stepping analysis of response for laminated glass.

In evaluating these resistance functions,representative values of the failure stress of glass,of the stiffness of the pvb membrane under highspeed loading and of the deflection of the pvbmembrane at the point of rupture, all need to beassessed. This paper does not discuss the

background work involved. It is sufficient to say herethat the values adopted have been derived from astudy and back-calculation from test results and theliterature. The problem of breakage stresses of glassunder relatively long duration loading has been welldiscussed by Colvin (Ref. 5), and these principlesare embodied in the draft code prEN 13474. Howeverit is less certain whether the breakage stress loadduration relationship extends into the very shortduration (a few milliseconds) area. This is a subjectof further investigation.

The current values of glass breakage tensilestresses under high speed loading which are used

by PSDB are 80 N/mm2for annealed glass and 200N/ mm2 for toughened glass. Recent testing hassuggested that 200 N/mm2for UK toughened glassis much too low. Tests have also indicated thatUS tempered glass is considerably weaker than UKtoughened glass. In the case of laminated glass,the stress at which the glass layers first crack hasa secondary effect on the calculated ultimateprotective capacity of the pane, since theprotection depends on the continued bonding ofthe glass to the pvb after it has crazed, and onthe ductile nature of pvb. These enable the pane

to continue to absorb energy and keep the roomsealed. Eventual loss of window integrity occurswhen the pvb tears. The design problem forlaminated glass thus reverts to predicting whethera given applied pulse will bring a particularlaminated pane to the condition of pvb tearing.

The high creep rate of pvb under slow loadingmeans that resistance functions for crazedlaminated glass measured under slow loading donot represent behaviour under blast loading. Wehave derived the effective high speed relationshipby back calculation from observations of blast-loaded laminated panes and on the assumptionthat the resistance-deflection relationship in thepost-crack, membrane phase is linear. We havealso found that the bonding of the glass plies tonormal pvb is extremely effective, as only glassdust is sprayed off the inside face. Most of theglass of the inner ply remains bonded on. The dustcan be reduced, if desired, by the addition ofpolyester film to the inside face. The recentavailability of stiffer interlayer plastics in laminatedglass offers few advantages under blast loading,when energy absorption is the prime requirement,although they give greater resistance to vandal

attack. The tendency for glass to de-bond underblast loading is also greater.

deflection

resistance

deflection

resistanceresistanceresistanceresistanceresistance

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The superior strength of plain toughened glassover plain annealed glass is a valuable property.However, when panes of toughened glass breakunder blast loading, the room is subjected to flyingfragments which, whilst being of a less injuriousshape than shards from annealed glass, fly at highvelocities due to the bigger pulses needed tobreak them. Although there may be a design pulse

(or a charge weight and range) specified for aparticular project, there can be no certainty thatthis will be the size of an actual terrorist attack.The advantage of laminated glass over plain glassis that even after the pvb has begun to tear, thehazards are not immediately acute, and theresidual pulse which enters through the tear will besmall compared with the total pulse. There is thusa large degree of protection from laminated glass,even when the threat is under-estimated and thepvb tears.

Presentation of Guidance Data

Design procedures for most live and environ-mental loads have factors built into loads andmaterial stresses to provided margins againstfailure due to uncertainties. However, in reality,blast loading, if it occurs, may fall within a widerange of values. The design blast threat for aparticular building, in terms of bomb size andstand-off always has to be assessed on asomewhat intuitive basis, based on the current andfuture expectations of terrorist activities, and takinginto account the importance and vulnerability of the

building. There are no codified factors of safetyagainst breakage. If any margins are provided,they are allowed for in the threat parameters on abuilding-by-building basis, based on conside-rations of risk, threat level and the importance ofthe building, and on consideration of acceptablehazard levels inside. This differs from the normalbuilding design approach of providing strengthand a margin of safety so that failures do notoccur. The provision of blast-resistant windows canbe expensive and the funds available will alsoaffect the measures adopted. Further discussionof such assessment is beyond the scope of thispaper.

The two parameters of the pulse which signi-ficantly affect a panes response are the initial peakpressure and the positive impulse. In the theo-retical time-stepping analysis, the shape of thepositive phase of the pulse is usually simplifiedfrom an approximately exponential decay to alinear decay. The equivalent triangular pulse isgiven an initial peak value the same as the actualvalue, but its positive phase duration is adjustedfrom the actual value so that the positive impulseremains unchanged. In this way, the two most

influential blast parameters for determining res-ponse are preserved. By making this idealisation

it becomes possible to present the resultingresponses to all pulses in terms of the initialpressure, P, and the positive impulse, I, on a plotof P against I. One diagram refers to one glasstype, thickness and pane size. Contour lines on thediagram connect all values of P-I pairs which giverise to the same deflection (and therefore the samestress) and are called iso-damage lines. The iso-

damage lines which correspond to the thresholdsof Hazard Levels are of particular interest. Forlaminated glass, the line of greatest interest is thatrepresenting the limit of tearing of the pvb inter-layer. Another significant line is that representinginitial crack of the glass, although this conditionis not of great importance in designating hazard.For plain glasses, the iso-damage lines of interestare those representing breakage with variousresidual velocities of fragments, which correspondto projection of fragments to the rear wall of thetest cubicle at various heights.

An overlay grid can be added to a P-I diagram

which relates weights of explosive (usually TNT asa standard). A complete pattern of response to allthreats can therefore be contained on a singlediagram. There is a unique P-I diagram for eachpane size, pane thickness and glass type.

A typical P-I diagram is reproduced below. The

P-I DIGRAM FOR 6.8 mm LAMINATED GLASS

(Overlay grid refers to fully reflected pressures fromhemispherical burst on large faade without clearing)

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co-ordinates of the resistance function from whichthe iso-damage lines are derived are tabulated atthe top. In the example diagram shown (for 6.8 mmlaminated glass), the upper iso-damage linedenotes all the combinations of P and I valueswhich bring the pvb membrane to the point oftearing (at about 200 mm central deflection for thissize of window). The lower line represents the

combinations of P and I values at which the glassjust cracks. The grid overlying the whole diagramrelates the weight of explosive (TNT) to stand-offdistance.

Further iso-damage lines could be added torepresent cracking at different stresses and tearingfor different values of tearing deflections. Thesewould give an indication of the sensitivity of theline positions to the assumed cracking and tearingvalues. Sensitivity to the size of the threat can beseen at a glance from the overlay grid.

Comparison with Tests

In the UK, range tests have been carried outon a regular basis since 1982 in order to observehazard levels behind windows of various types.Windows were mounted in the face of a closedcubicle, since free-standing rigs allow rear faceblast loading to affect the test performance in away which does not occur in a real building. Anarbitrary scale of Hazard levels was set up, basedon how far across the floor, or how high up the rearwall of the standard sized test cubicle fragmentsof plain glass were projected. When most frag-

ments fell less than one metre beyond the window,the Hazard is now termed Very Low (previouslyBreak Safe). When fragments hit the rear wall nothigher than half a metre above the floor the Hazardis termed Low, and when they hit higher than halfa metre, it is termed High. For laminated glasses,free-flying fragments do not occur (provided theedges of the pane are held), and major hazardsonly commence after the pvb has torn. Beforetearing, the hazard is termed Minimal. After thelaminated glass has started to tear and beforepieces have begun to be torn off, it still offerspartial protection and the hazard is termed Low.The single iso-damage line for commencement oftearing (the Low Hazard Threshold) is therefore theline of primary interest.

Empirical test observations of hazards incubicles, co-ordinated with measured values ofpressure and impulse on the front face, enabledobservations to be compared with calculatedpredictions.

The many different pane types tested, thevariety in blast parameters and the difficulty ofanticipating, when setting up a test, what the exactthreshold range will be, has meant that even after

20 years of testing, information for many of theless-commonly used pane types is very deficient.

The test charge sizes which were employed variedfrom 4.5 kg to 100 kg, whereas in reality, threatsmay vary from a few hundred grammes to a fewthousand kilogrammes. The end positions of iso-damage lines (which are asymptotes of rectangularhyperbolae, and represent very short and very longduration pulses) can be easily calculated fromtheory by hand methods (Ref. 1, art. 5.5), but in

practice, tests are needed to verify their accuracyand to identify whether any unforeseen effects areoccurring.

Measures for Protection

Reference has been made to the merits oflaminated glass. Great flexibility is possible in itsmake-up in respect of the number and thicknessesof glass plies and the number and thicknesses ofpvb layers. This enables resistance to almost anypulse to be designed for. The mass of the paneprovides inertia against acceleration from rest

(which affects the eventual deflection as a solidplate), while the thickness of pvb determines theultimate resistance to tearing after the glass hascrazed. There is an important additional requir-ement that the pane edges must be securely held.Suitably-robust frames are needed, with rebatedepths of the order of 35mm. Silicon sealantbedding is needed to hold the edges of the panes.The common detail of neoprene gaskets in shallowrebates with snap-in beading is not adequate forutilising the full tearing resistance of laminatedglass, except for glass of 6.4 mm thickness or less.

The performance of glazed facades with un-framed panes supported on bolts through holes inthe edges of the panes, has not been quantified,since this has not been a common feature in UKGovernment buildings. Engineering instinctsuggests that, thickness for thickness, the blastresistance will be substantially less than with fullframing. This is explained by the fact that plateswith unsupported edges cannot develop in-planeradial and circumferential stresses, which wouldcontribute to lateral strength. These glazingsystems are being used more frequently and theirblast performance is a subject we intend toaddress in due course.

Treatment for Existing Windows

When a terrorist threat is recognised, thecomplete replacement of all windows over largefacades with laminated panes in robust frames isoften not economically viable. A second option,which is cheaper, easier and quicker to install isthe addition of polyester film to the inside facesof the existing windows. UK practice has been touse it in conjunction with Bomb Blast Net Curtains.

Tests have shown that this installation gives asignificant reduction against a certain range of

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threats. However, its protection capacity is limited,and above certain threat levels, becomesnegligible. Testing is necessary to establish theselimits. The net curtains, woven from a high strengthpolyester filament in a strong weave, have weight-ed bottom hems and a generous surplus width andlength. The film binds the fractured pane as onesheet which the curtain is then able to arrest in

flight, whereas an unfilmed pane produces looseshards which cut through the curtain. For higherthreat levels, the random motion of the flying panealso starts to tear the film, breaking it into piecesand tearing through the curtain. The scope forincreasing the protection from this treatment doesnot match that from using laminated glass with aspecially-selected make-up, but for buildings withlarge facades which are more distant from the seatof the explosion, film and curtains will improve theprotection for a large number of people. On astatistical basis, this is therefore still very worth-while.

A difficulty arises in attempting to quantify fromtheoretical calculation the hazards arising fromfilmed glass. At present, empirical full-scale rangetesting has been the only way forward. Testobservations for filmed and curtained windowswere plotted on P-I diagrams for the correspondingplain glasses. The iso-damage lines calculated forthe same thickness of plain glass were then re-positioned on the diagrams to match the test

observations. However, uncertainties exist over thedirections, relative to the two axes, in which thisadjustment should be made, as the test obser-vations only cover a small part of the diagram.

Summary

A bomb blast will always create shock anddismay to those caught up in it. The element ofsurprise, and the rarity and severity of the eventall create an impression of irresistible power andconfrontation with the unknown. However, it ispossible to design blast-resisting windows on arational basis. The single-degree-of-freedom modelallows a simple, quick and accurate calculationprocedure to be followed. This short paper hasendeavoured to set out the principles involved.

References

[1] An Introduction to Structural Dynamics. J.M.Biggs.

McGraw-Hill[2] Explosions in Air. W.E.Baker Wilfred BakerEngineering, San Antonio, Texas.

[3] Explosion Hazards and Evaluation. W.E.Baker et al.Elsevier

[4] Structures to Resist the Effects of AccidentalExplosions. U.S. Departments of the Army, Navy andAir Force, November 1990.

[5] Glass Processing Days 1999 Short Course on CEN/TC129/WG8 Glass Strength. J.Colvin

[6] Glass Failure Prediction Model. W.L.Beason andJ.R.Morgan. J. Struct. E. A.S.C.E. Vol. 110 No.2 Feb1984