The+effects+of+blast+loading+on+laminated+glass

The Effects of Blast Loading on Laminated Glass //Nicholas Leonard, BAE, Penn State, 2012 // toc

Introduction
Tragedy occurred on the morning of April 19, 1995, when a truck detonated at 9:00am in front of the Alfred P. Murrah Federal Building, killing a total of 167 persons. The truck was estimated to contain in the range of 4000 to 5000 lbs of ammonium nitrate and fuel mixture, with effects seen stretching nearly a mile from ground zero. All of the casualties were caused by the massive force of the blast wave; however, 200 out of the 508 recorded injuries were due to glass shrapnel, reaching speeds up to 70 mph, and fragments projecting over ten feet from the glass fenestration. Since 39% of the injuries resulted from glass lacerations, abrasions, and contusions, an analysis of the surrounding area from ground zero in Oklahoma City was performed with respect to shattered glass and respective injuries. In this article, a further, in-depth look at the injuries caused by the breakage of glass will be discussed, and ultimately, how engineers can design to prevent glass related injuries in the future. I will explore two possible methods for the design of blast resistant glass, and compare the advantages and disadvantages of each method. .

Bombing of the Alfred P. Murrah Federal Building
The Oklahoma City bombing is just one example of the effects of blast waves on glass, and why it is imperative to design for laminated glass fenestration resistance to mitigate the injuries caused by glass fragmentation. Since my discussion will be focused on glass fragmentation, additional information on background and other bombing effects can be found at http://failures.wikispaces.com/Murrah+Federal+Building. To understand the glass fragmentation phenomena, we need to first understand the physics of the explosion itself, as well as the blast waves that soon follow. An explosion can be characterized as the rapid release of an enormous amount of energy, typically through a chemical reaction. That energy expands in all directions, or in a spherical shape, and thus is called a blast wave. There are two phases of a blast wave: a positive and negative phase. A structure resisting a blast wave will be subjected to an almost instantaneous peak overpressure which will rapidly decline within milliseconds. This is know as the positive phase. This is immediately followed by a longer, negative phase pressure where the force is acting on the structure in the opposite direction in an extended amount of duration, although the pressures are typically smaller. A representation of the blast phenomena is illustrated below in Figure 1.



Most designers consider the positive phase, only because the greatest amount of damage 99% of the time occurs during the positive phase, which can be clearly seen by the initial overpressure in Figure 1. If the structure can withstand the positive phase, it should be more than capable to withstand the negative phase. However, when we consider glass window design, the negative phase needs to be addressed as well. Because it is common for designers today to use a two-ply glass window, the positive phase will cause the interior ply to fracture as the pressure pushes on the pane. In general theory of bending, the interior glass ply will be in tension, while the exterior ply will be in compression. When the negative phase occurs, the pressure on the glass pane reverses, and the ply in compression will then be subjected to tensile forces, while the interior ply is subjected to compression. As a result, both of the plys will be fractured, with the potential of fragmentation on the interior and exterior of the building.

After field surveys had been performed on the site, it was noted by H. Scott Norville that glass had fractured as a result of the explosion as far as 1600m from ground zero. Considering that the surrounding buildings behave as a shield for farther buildings, the magnitude of this explosion can clearly be seen because of its ability to penetrate so deep into the city. Studies are still ongoing to evaluate the behavior of a blast wave, but some research shows that blast waves behave like sound waves, and can bend or move around obstacles. Luckily, as the blast wave travels farther from the detonation site, the strength of the pressure wave decreases exponentially. The total area of influence from the explosion at the Alfred P. Murrah building can be broken down into three zones:
 * __Zone 1:__ Contains a radius of roughly 1.5 blocks emanating from ground zero, in which most of the deaths occurred. Major structural damaged was observed, and was primarily the controlling concern, so glass effects were neglected in analysis.
 * __Zone 2:__ Includes light structural damage with 70-80% of the glassed shattered. All of the injuries were caused within Zones 1 and 2, or less than 1000 ft.
 * __Zone 3: I__ndicates 99% of the total glass breakage on site, stretching out as for as 21 blocks from ground zero. Because of the minimal amount of shrapnel in this zone, no reported injuries sustained from glass were reported.

An image of the three zones can be viewed below in Figure 2.

The closer a surrounding building was to ground zero, the more damage, both to the structure and the glass, was witnessed. This makes sense because the blast wave is at its strongest from the point of detonation, and becomes weaker as the wave travels farther. However, note that it can be seen that the pressure wave caused by the blast does have a major impact on glass panes that are significantly distant from the explosion, though no structural damaged occurred. After an analysis of the top 15 buildings affected by the explosion was performed by field investigators, it was deduced that roughly 50 % of the injuries were from persons standing within 10 ft of the glass fenestration, while the other 50% were caused from farther distances. Figures 3 and 4 are some examples of glass shattered from the explosion.



The main objective of designing laminated glass to resist blast loads is to prevent fragmentation altogether, or to produce a minimal amount of shrapnel projected at most 1 ft from the fenestration. Most activity in a building occurs generally five ft or more from a window, so by limiting the penetration of glass shrapnel to one foot from the windowpane, this will mitigate any harm to the civilians inside (or outside, although pedestrians should be more concerned of the actual blast wave itself). Glass itself would not be sufficient enough to withstand the force, so a polyvinylbutyral (PVB) interlayer is placed as a 'glue' to hold the fractured glass together. PVB is a viscoelastic material that has high ductile properties, thus able to stretch and stay intact during the explosion. There are many ways to design the windows; however, I will only discuss two of those methods: the ASTM Design Procedure and Linear Small Deflection Plate Theory. Both are valid methods and are used in practice. After a discussion of both of these methods, I will describe the pros and cons of both methods.

ASTM Design Procedure
This method originally became published by ASTM International in 2003. A fairly simple method of design, ASTM F2248 (Specifying an Equivalent 3-Second Duration Design Loading for Blast Resistant Glazing Fabricated with Laminated Glass) uses charge weights and standoff distances to convert a blast overpressure load to an equivalent 3-second duration static uniform load. This can be found by directly reading the information off of a chart. Charge weights are a way to measure the size/amount of a bomb. There are hundreds of types of explosives, and the best way to analyze is to convert the explosive size to an equivalent TNT weight (usually measure in lbs). For reference, a standard size briefcase can contain a 50 lb charge weight, while a sedan can contain an average of 4000 lbs, such as the case in the Oklahoma City bombing. Standoff distance is simply the direct distance from the detonation point, typically measured in feet. After obtaining the charge weight, the stand-off distance ,and interpolating a value from the appropriate ASTM 2248 - 09 graph, using ASTM E1300 (Determining Load Resistance of Glass in Buildings), a specific type of glass-laminate system can be selected. ASTM E1300 also designates the load required to design the hardware and supporting frame elements for the fenestration.

To provide a basis for comparison, I will consider an example to be analyzed by both methods, and compare the results. Example:

Charge Weight: 100 lb TNT Equivalent Standoff Distance: 75 ft Fenestration Size: 1325 mm x 1325 mm

Interpolating a value from Fig. 1 of ASTM 2248 -09, a 3-second equivalent design load of 100 psf can be used in ASTM E1300 - 12a. Observe that this equivalent load is comparable to a typical design live load of 100 psf in some office buildings. That type of load is typically supported by a concrete slab several inches thick. However, this 100 psf equivalent blast load will be resisted by only millimeters of glass. ASTM E1300 has many charts that are organized by thickness of glass and by support conditions. In our example, we are going to assume two plies of 4.76mm annealed glass (roughly 10 total), with 1.52 mm layer of PVB in between. Reading Fig. A1.8 in ASTM E1300 - 12a, this 10.0 mm, four-sided simply-supported window can resist 4.85 kPa (101.3 psf). This barely passes, but is able to still resist the load. Also, reading the same chart, and using an aspect ratio of 1 (1325mm/1325mm), the deflection at mid-span is 15 mm. This value will then be used to compare the deflection using the linear small deflection plate theory.

Linear Small Deflection Plate Theory
A much more analytical approach, the small deflection plate theory uses the equation of motion and blast force as a function of time to calculate the stresses of the glass at mid point. This method allows for the flexibility of complex designs to be analyzed; however, this method requires the solution of a fourth order differential equation, thus a substantial amount of time to calculate. To read into more detail about the equations used for this method, please refer to Jun Wei and Dharani's article, "Response of Laminated Architectural Glazing Subjected to Blast Loading," and follow their step-by-step process. Using an Excel worksheet, and the equations provided in the aforementioned document, I calculated a deflection value of 15 mm. As you can see, this matches the value determined from the previous method using the same parameters.



Discussion
As noted before, both methods of design resulted with a passing 10mm thick glass window and an estimated deflection of 15mm. Because of the simplicity of a square window, it just so happens that the two deflections were exactly the same. While performing calculations for other examples, I found the two values to deviate, but only slightly. The ASTM method is a significantly faster approach to determining the thickness of the glass plies, as apposed to the linear plate method, which involved long, tedious calculations and had to be completed in Excel. The drawback to using the ASTM method is that only simple rectangular windows can be designed. The graphs used by ASTM were developed by a long series of tests, using only rectangular shapes in their experiments. Thus, only simple rectangular shapes can be designed. The advantage of using the small plate deflection theory is because of the ability to design for more complex shapes, such as triangles or octagons, though a large portion of time will be spent running the calculations, but as a benefit you will get a more accurate design. In my opinion, if the fenestration is rectangular in shape, the easiest method is the ASTM standards. For simple shapes, the graphs in ASTM are reliable, so why not take advantage of that?

In conclusion, events such as the bombing of the Alfred P. Murrah building in Oklahoma City have pressured the industry to design against explosions, especially windows. Over 200 had been injured as a result of the bombing, and damage can be seen as far as 1600m from ground zero. To reduce the amount of injuries in the future, designers need to design glass fenestration to mitigate the amount of shrapnel produced. The ASTM standards and the linear small deflection plate theory are just two of the methods that can be used. Each has its pros and cons. With the ASTM standards to be faster, and the plate theory to be more accurate, both are viable methods to develop a solution.

Additional Resources and References

 * A.T.Blast. 2012. Applied Research Associations, Inc.**


 * A computer program whose sole purpose is to supply blast loads. Currently an experimental program.