WO2006119132A2

WO2006119132A2 - Lightweight blast resistant container

Info

Publication number: WO2006119132A2
Application number: PCT/US2006/016504
Authority: WO
Original assignee: Friedman Research Corporation
Priority date: 2005-05-04
Filing date: 2006-04-28
Publication date: 2006-11-09
Also published as: US20060076350A1; WO2006119132A3

Abstract

This invention is a novel lightweight blast resistant container 1. It consists of containers made of a blast resistant fiber reinforced polymer resin matrix composite. The invention employs a novel construction configuration whereby the container is created by the appropriate nesting of composite parts to create a cube, box or multi-faceted geometry. As a result of the nesting, the box like geometry exhibits characteristics that cause the geometry to behave more like a sphere than a box when subjected to internal blast pressures 3. Such an approach provides an optimized minimum weight solution by fully utilizing the entire material volume, whereby ultimate tensile strength can be simultaneously developed everywhere in the container.

Description

TITLE Lightweight Blast Resistant Container

INVENTOR

Erich Weerth

RELATED APPLICATIONS

This application claims priority to US Application Serial Number

11/121,790, filed May 5, 2005, which in turn is a Continuation- in-Part of application Serial# 10/942,336

FEDERALLY SPONSORED RESEARCH

Not Applicable

SEQUENCE LISTING

Not Applicable

BACKGROUND OF THE INVENTION

[0001] The invention relates to a lightweight multi-sided container capable of resisting an explosive detonation due to bombs or other improvised explosive devices (IED' s) without rupture. The invention applies to any situation where an explosive device is detonated in a container. The invention is particularly applicable to cargo containers, such as Unit Load Devices used on aircraft, or shipping containers used on ships or trucks. [0002] One possible scenario for terrorist activity is to place explosive devices in cargo or luggage. Even a small explosive device is adequate to destroy an aircraft. Current practice on wide body aircraft is to put all cargo and luggage into containers called Unit Load Devices (ULD' s). Current ULD' s are constructed of lightweight aluminum, which provides no protection against an explosive blast. Although some ULD' s have been proposed which offer increased blast protection, all proposals to date are too heavy. The U.S. Federal Aviation Administration is actively encouraging the development of effective blast containment in aircraft luggage and cargo holds.

[0003] Similarly other containers such as those used on seagoing ships are vulnerable to explosive detonations. Mailboxes also fall into this category. Most containers for the transport of cargo, mail, and personal goods are constructed of thin metal, which becomes shrapnel during even a small explosion. Thus it is the object of this invention to provide containment of blast overpressure associated with explosive threats without venting or rupture of the containment structure.

BRIEF SUMMARY OF THE INVENTION [0004] One embodiment of the invention is a method of making a blast resistant container constructed at least in part of a composite fiber reinforced polymer resin matrix. The method includes utilizing a polymer resin with a viscosity suitable for Vacuum Infusion Processing and a shrinkage strain of at least 2% for the neat resin when fully cured.

[0005] In one aspect of the method the resin has a viscosity less than 350 centiposes. In another aspect, the resin has a styrene content of no more than 35%.

[0006] In another embodiment, the invention is a method of making a blast resistant container constructed at least in part of a composite fiber reinforced polymer resin matrix. The container is constructed as an assembly of three nested parts, such that circumferential hoop stresses are developed in the winding direction of the broadgoods associated with each part's geometry. The method includes applying a deformation to each of the three nested parts, characterized by an inward displacement applied to the middle of each of the four side walls so as to make each diagonal dimension of the part smaller than the measured diagonal in the original un-deformed container wall, such as to increase the induced compressive residual stresses during construction of the container. [0007] In one version of the method, the application of the deformation is accomplished by one-sided curing of the part, whereby, a high heating rate is applied to one side of the part thickness where the other side of the part thickness is in direct contact with a heat sink. In one aspect, the heating rate is a thermal heat-up ramp > about 60 °F/hr. In another aspect, the method includes constructing the parts such that one of the first or second of the three parts has at least one opening cut in at least one wall.

[0008] In a further embodiment, the invention is a blast resistant container constructed at least in part of a composite fiber reinforced polymer resin matrix, characterized by construction as an assembly of three nested parts, such that circumferential hoop stresses are developed in the winding direction of the broadgoods associated with each part's geometry; The container is further characterized by increased induced compressive residual stresses during construction of the container achieved by applying a deformation to each of the three nested parts. The deformation is an inward displacement applied to the middle of each of the four side walls so as to make each diagonal dimension of the part smaller than the measured diagonal in the original un-deformed part. [0009] In one version one of the firstmost inner or secondmost inner of the three parts has at least one opening cut in at least one wall.

[0010] In one aspect, the opening is closed by installing the outermost third part, and in the event of a blast the expansion of the inner parts to the outer parts seal the opening with a gasket.

[0011] In another aspect, the outermost third part has an opening hole which overlaps at least one opening in an at least one inner part, wherein the third part opening is sealed by a blast resistant accordion door of composite construction.

[0012] In another version of the container, the wall thickness, t, of each wall of the nested parts is determined by:

σ = pL/4t, where p is over pressure due to blast, L is the

length of the wall and σ is the membrane stress developed in the

wall as a result of the overpressure.

[0013] A further embodiment of the invention is a blast resistant accordion door of composite construction for sealing an opening in a blast resistant composite container wall. The door includes piano type hinges where the loops of the hinges constitute cured reinforcing fibers which are the result of folding sidewall fabric back over a Teflon shaft or rod prior to infusion and resin curing, such that the Teflon rod prevents resin from sticking to the shaft thereby allowing the shaft to be extracted after the container shell is fully cured. The Container further includes lightweight high density polyethylene (HDPE) track positioned along the top and bottom horizontal edges of the door opening, and hinge shafts made from continuous S-2 Glass filaments infused with epoxy resin to make a unidirectional reinforced S-2 Glass rod.

[0014 The door also includes a high strength, lightweight shaft to secure the door inserted into the mating hinges where the left and right sides of the accordion doors meet at the center of the door opening, wherein all tensile circumferential stresses developed by an explosive detonation in the container are transmitted through the door hinges and door panels when the door is closed and secured.

[0015] In one version of the door, the hinges are co-cured during the fabrication of door panels. [0016] Another embodiment of the invention is a blast resistant container constructed at least in part of a composite fiber reinforced polymer resin matrix, characterized by; construction as an assembly of three nested parts, such that circumferential hoop stresses are developed in the winding direction of the broadgoods associated with each part's geometry; and, the wall thickness, t, of each wall of the nested parts is determined by:

σ = pL/4t, where p is over pressure due to a blast, L is the

length of the wall and σ is the membrane stress developed in the

wall as a result of the overpressure.

BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The detailed description of how to make and use the invention will be facilitated by referring to the accompanying drawings .

Fig. 1 illustrates the problem solved by the invention where the container is a Unit Load Device

Fig. 2 shows one of the preferred construction configurations of the invention. Fig. 3 shows another construction configuration of the invention.

Fig. 4 shows the application of deformation during construction of the container.

Fig. 5 illustrates the derivation of the equations used to relate membrane stress and overpressure to the dimensions of the container

DETAILED DESCRIPTION OF THE INVENTION

[0018] The inventor has produced a completely new concept for blast protection containers, enabled in part by employing very different materials than currently used for container applications. Current container materials such as thin aluminum or steel provide little or no blast protection. Conventional materials exhibit relatively low specific strength and/or specific modulus. Consequently, blast resistant containers constructed using conventional materials do not offer a weight efficient solution. A new class of materials enables a different approach. Such materials are similar to fiberglass in that they utilize a reinforcing fiber architecture, which is infused with a polymer resin matrix. The most effective version of composite construction utilizes materials which exhibit high compressive and tensile specific strengths and high compressive and tensile specific moduli. Specific strength is defined as the ultimate compressive (or tensile) strength of the material divided by its density. Specific modulus is the elastic compression (or tensile) modulus of the material divided by its density. The polymer resin matrix is resistant to galvanic corrosion, solvents and chemical agents. The inventor has developed a particularly suitable version of the material, described in a co-pending application. In this version, the fiber reinforcement is treated with a special resin compatible sizing which develops a high specific laminate strength, high specific laminate modulus, high laminate strain to failure and high laminate fracture toughness. These materials have much higher resistance to blast per unit volume than metals. [0019] Such materials offer a very different type of blast protection system. Conventional metal ULD containers, which offer little to no resistance to a bomb blast, weigh 200 to 250 pounds. A ULD container made from the preferred composite, exhibiting adequate blast protection to withstand the specified explosive charge weight, would weigh less than 300 pounds, clearly within an acceptable weight range. [0020] Referring to Figure 1, a container, shown schematically as a ULD 1 contains items such as luggage 2. If an explosive device detonates in the container 3, the blast expands radially outward as a spherical overpressure front. A conventional container, such as an aluminum ULD, will be torn apart (i.e. rupture) by even a small bomb. Since the ULD' s are stored along the bottom of the aircraft fuselage, the blast pattern will likely blow through the fuselage, almost certainly causing airframe structural failure and/or failure of electrical/hydraulic subsystems.

[0021] A blast resistant composite for containers can be produced as follows. A lay-up tool or mandrel in the shape of the container is required. Broadgoods are unrolled from the payout drum and deposited onto the lay-up tool. The width of the reinforcement fiber broadgoods is sufficient to cover the required width dimension of the container. The reinforcement broadgoods are continuously wrapped around the tool (mandrel) in the direction represented by the black rectangles in 8, 11 and 16 of Figure 3, until the required laminate thickness is achieved. A Compressor draws a vacuum for ply stack debulking (i.e. consolidation of stacked plies) . The Compressor is also used for Resin Infusion if the Tool is stacked with dry Broadgoods rather than prepreg. A Convection Oven is used for Laminate Curing when Prepreg Broadgoods are used. The Oven consists of insulated walls and a heater with a recirculating forced air blower. If Vacuum Infusion Processing is used to fabricate parts then resin drums and infusion lines facilitate the delivery of resin into the vacuum bagged dry stack of Broadgoods.

[0022] The composite may be produced using vacuum assisted resin infusion capability. The vacuum being drawn on the bag sucks air out of the bag while drawing resin into the bag and simultaneously serves to consolidate the layers of reinforcement. The resin contains a catalyst which initiates the curing of the consolidated stack of plies at ambient temperature. Alternatively, the inventor believes a pre- impregnation manufacturing approach is also advantageous. The reinforcing fiber is pre-impregnated (commonly referred to as prepreg) with partially cured (i.e. B-staged) resin while still in broadgoods tape or woven fabric form. A release film is applied to the prepreg broadgoods which is peeled off prior to the stacking of prepreg layers onto the Tool or mold. The prepreg stack is intermittently consolidated (i.e. debulked) by vacuum bagging until the required number of plies are deposited onto the Tool. The ply stack is vacuum bagged and oven cured to net thickness. This approach eliminates the need for using wet resin during the fabrication of the container. The above processes can be repeated over the tool several times to form a multi-layer laminate of the composite [0023] Because an explosive blast creates a spherical overpressure wave front, blast protection requires three dimensional resistance. A fundamental design principle in the containment of explosive detonations states that the greater the interior container volume (relative to the volume of explosive) the lower the areal density required to prevent container rupture (where areal density is defined as the weight per unit surface area of the container) . However, container weight is the product of areal density and container surface area. Consequently, the optimum i.e. lightest container geometry for blast mitigation maximizes container internal volume while simultaneously minimizing container surface area. The geometry which best achieves this characteristic is a sphere. As a spherical shape is not practical for most container applications, the inventor uses a novel construction technique wherein a non-spherical geometry such as a cube, six-sided box or any other multi-faceted container, is made to act like a sphere in the way it reacts to internal pressure. As shown in Figure 2, the container is constructed as three nested parts. Part B at 7 fits inside of Part A at 5. When put together the two parts may or may not be bonded together with adhesives. The assembly may be mounted to a base 6 for some applications. The third part C at 4 fits over the A/B assembly. C may or may not be bonded. Also, C may or may not contain a doorway cutout. However the door is a weak point. Therefore, in one embodiment of the invention a doorway is cut out in part A and part C, which has no doorway cutout, is only installed after the container is loaded. If a blast occurs the overpressure will cause dilation of A/B into the walls of C. A gasket or other seal can be employed between C and A/B. Thus, in the event of a blast, the three nested parts provide three dimensional circumferential hoop constraint. Each of the three parts A, B and C attempt to deform into a cylindrical shape as each part resists the blast overpressure. Circumferential hoop stresses are developed in the winding direction of the broadgoods associated with each part's geometry. Such a tendency for each independent part, within the nested assembly, to dilate into a cylindrical shape, reduces the high stresses normally developed at the corners of a rigid box where three edges intersect. Such an approach offers an optimized minimum weight solution whereby the entire volume of material is simultaneously stressed to ultimate strength with no low stressed (i.e. thicker than required) portions of the container.

[0024] For the ULD application, the inventor envisions that C is held by a tool and installed after the cargo or luggage is loaded. Since part C is lightweight it may be raised or lowered mlanually, pneumatically (i.e. with positive or negative pressure) , hydraulically or mechanically.

[0025] ULD containers are shown in the figures by way of example. This is a particularly suitable application of the invention. However any container requiring blast resistance to internal detonations is contemplated by the invention. Other examples include mail boxes and containerized shipping. Also, police, firemen or demolition teams may use the invention as a lightweight portable container to safely detonate abandoned or concealed terrorist bombs. The invention may also be used to safely store explosives where accidental or unanticipated detonation will not damage surrounding personnel or property.

[0026] Figure 3 shows the construction of a blast resistant container utilizing fiber reinforced polymer composite laminate skins in combination with core materials to form a sandwich type construction. Part 8 is fabricated by winding dry fiber reinforcement broadgoods or pre-preg broadgoods around a tool or mandrel until the required laminate thickness is achieved. The pre-preg stack of broadgoods is then vacuum bagged and oven cured in such a fashion whereby residual process induced compressive membrane stresses are developed in each part after polymerization (i.e. curing) is completed or, in the case of dry broadgoods, resin infused and cured using a catalyst curing agent contained in the resin. Parts 11 and 16 are fabricated in similar fashion as Part 8 but on different sized mandrels.

[0027] The tool or mandrel for part 11 may be eliminated by using the bonded assembly of 8, 9 and 10 as the tool or mandrel for fabricating part 11. Similarly, the tool or mandrel for part 16 may be eliminated by using the bonded assembly of parts 8, 9, 10, 11, 12, 13, 14 and 15 as the tool or mandrel for fabricating part 16.

[0028] Low density core materials 9 and 10 may be bonded to the top and bottom of Part 8. Low density core materials may include but not be limited to, opened or closed cell foam, a honeycomb material, nomex, metal foam, balsa wood, etc. The assembly comprising 8, 9 and 10 is then inserted and possibly bonded into Part 11. Low density core materials 12, 13, 14 and 15 may then be placed on or bonded to the nested assembly comprised by parts 8, 9, 10 and 11. The entire assembly made up of 8, 9, 10, 11, 12, 13, 14, and 15 is inserted and possibly bonded into part 16. The entire nested assembly made up of parts 8 through and including 16 may be bonded to a base plate 6 shown in Figure 2. In one rendering of the invention the footprint of base plate 6 may be made equal to or greater than the footprint of 16. A non-circular doorway opening may be cut out from any side wall and an oversized doorway hatch may be inserted inside the container. As long as the doorway opening is not a circle, an internal hatch geometry may be designed to fit through the doorway opening. The surface area of the internal hatch is made to be greater than the surface area of the doorway opening. Such a configuration develops a self-sealing mechanism as the perimeter of the hatch presses against the inside surface of the container side wall when the container is pressurized by explosive detonation.

[0029] In another approach to creating a blast resistant door, one of the core material panels, namely, 12, 13, 14 or 15 may be eliminated. If 13 or 15 is eliminated then a gap exists between part H and part 16. A doorway opening may be cut out through parts 11 and 16 on the side of the container where the gap was created by the elimination of either 13 or 15. This gap may be used to insert a guillotine door from above which bottoms out on the base plate 6 by gravity. Similarly, if 12 or 14 is eliminated then a gap exists between part 8 and 16. A doorway opening may be cut out through parts 8 and 16 on the side of the container where the gap was created by the elimination of either 12 or 14. This gap may be used to insert a guillotine door from above which bottoms out on the base plate 6 by gravity. To prevent free sliding of the door while the container is in transit, door stops may be incorporated into the container.

[0030] The vertical guillotine door may become a left or right side sliding door by tipping the entire nested assembly on its side before bonding of the base plate 6, The base plate 6 is then bonded to the side wall of part 16 which rests on the ground. To prevent free sliding of the door while the container is in transit, door stops may be incorporated into the container.

[0030] Other advantageous embodiments of the invention will now be described. Details of the manufacturing process can lead to even more effective blast containment. In particular the type of resin used and how it is applied and cured are important details. A polymer resin should be used which exhibits a viscosity suitable for Vacuum Infusion Processing (VIP) . The viscosity of such a resin shall, in an embodiment of the invention, be less than 350 centipoises. In order to maintain high laminate mechanical properties, a styrene content of no more than 35% by weight should be used to achieve such a desired resin viscosity level. Also, the polymer resin should exhibit a shrinkage strain of at least 2% for the neat resin when fully cured (i.e. 100%ρolymerization) . Such a cure induced shrinkage strain will serve to cancel or reduce the magnitude of the tensile stress developed in the container wall as a result of blast overpressure during explosive detonation.

[0031] Another important aspect of the processing of the laminate for the container structure is the Temperature/Time thermal cycle diagram for laminate curing should preferentially be defined in such a fashion so as to develop process induced compressive residual stresses through the thickness of each of the nested container bands. Such a compressive residual stress will serve to cancel or reduce the magnitude of the tensile membrane stress developed in each container wall as a result of blast pressure during explosive detonation. This is accomplished by one-sided curing (i.e. heating) of the part, whereby, a high heating rate (i.e. high thermal heat-up ramp > 60 °F/hr approaching that of a thermal step change or thermal shock) is applied to one side of the part thickness where the other side of the part thickness is in direct contact with a heat sink.

[0032] As shown in Figure 4, during assembly of the nested containers each container can be deformed prior to nesting. The deformation shall consist of an inward displacement applied to the middle of each of the four side walls so as to make each diagonal dimension of the container smaller than the measured diagonal in the original un-deformed container. Such an induced shape during container assembly serves to develop assembly induced compressive residual stresses in addition to the compressive resin curing shrinkage induced residual stresses and the compressive thermal process induced residual stresses. Such assembly induced residual stresses will serve to cancel or reduce the magnitude of the tensile membrane stress developed in each container wall as a result of blast overpressure during explosive detonation. It is not desirable to combine the Core material contruction with process induced deformation, as both techniques reduce the volume of the container.

[0033] Detailed properties of the door may also be critical fox some applications. It may also be advantageous if the container shall have a door which minimizes the "sail area" of the door when the subject door is in the opened position. A minimum exposed "sail area" of the door is desirable when the container is in a windy environment where the door may constantly be subjected to wind loads. Additionally, the container door must be sufficiently robust so as to absorb the abuse of baggage handling personnel during both the loading and unloading of baggage from the container. The container door must be able to survive the overpressure of an explosive detonation inside stowed baggage placed inside the container. In the event of an explosive detonation inside the container, the container door must be capable of transmitting hoop tensile stresses across the width of the door when the door is in the closed position.

[0034] All of the above requirements are satisfied by the accordion door configuration shown at 17 in Figure 2. This accordion door exhibits piano type hinges where the loops of said hinges constitute cured reinforcing fibers which are the result of folding sidewall fabric back over a Teflon shaft (i.e. rod) prior to infusion and resin curing. The Teflon rod prevents resin from sticking to the shaft thereby allowing the shaft to be extracted after the container shell is fully cured. Similar hinges may be co-cured during the fabrication of door panels. The accordion doors are guided by a lightweight high density polyethylene (HDPE) track positioned along the top and bottom horizontal edges of the door opening in the External Shell 4. The actual hinge shafts are rods made from continuous S-2 Glass filaments infused with epoxy resin to make a unidirectional reinforced S-2 Glass rod. All tensile circumferential stresses developed by an explosive detonation are transmitted through the door hinges and door panels when the door is closed and secured. The door is secured by a high strength lightweight shaft inserted into the mating hinges where the left and right sides of the accordion doors meet at the center of the door opening. [0035] Figure 5 illustrates the derivation of the equations of equilibrium for each nested shell when the entire nested assembly is subjected to an internal overpressure, p. It should be noted that the nesting of all three (3) shells creates a condition where each container side consists of two (2) nested shell wall thicknesses. For simplicity the equations derived in Figure 6 assume an equal sided box where H = W = L (i.e. a cube) . Consequently, in this, simplified geometry it can be seen that the cube develops membrane stresses in each nested wall on

the order of σ = pL/4t, where t is the wall thickness. This is

similar in form to the membrane stress developed in a spherical

shell where σ = pD/4t. The characteristic dimension for the

sphere is the diameter, D, whereas, the characteristic dimension for each of the nested shells comprising the box is L. These equations are critical for determining the required wall thickness of each nested shell.

Claims

CLAIMS I claim:

1. A method of making a blast resistant container constructed at least in part of a composite fiber reinforced polymer resin matrix, comprising utilizing a polymer resin with a viscosity suitable for Vacuum Infusion Processing and a shrinkage strain of at least 2% for the neat resin when fully cured.

2. The method of claim 1 wherein the resin has a viscosity less than 350 centiposes.

3. The method of claim 1 wherein the resin has a styrene content of no more than 35%.

4. A method of making a blast resistant container constructed at least in part of a composite fiber reinforced polymer resin matrix, comprising; constructing the container as an assembly of three nested parts, such that circumferential hoop stresses are developed in the winding direction of the broadgoods associated with each part's geometry; and applying a deformation to each of the three nested parts, characterized by an inward displacement applied to the middle of each of the four side walls so as to make each diagonal dimension of the part smaller than the measured diagonal in the original un-deformed container wall such as to increase the induced compressive residual stresses during construction of the container.

5. The method of claim 4 wherein the application of the deformation is accomplished by one-sided curing of the part, whereby, a high heating rate is applied to one side of the part thickness where the other side of the part thickness is in direct contact with a heat sink.

6. The method of claim 5 wherein the heating rate is a thermal heat-up ramp > about 60 °F/hr.

7. The method of claim 4 further comprising constructing the parts such that one of the first or second of the three parts has at least one opening cut in at least one wall.

8. A blast resistant container constructed at least in part of a composite fiber reinforced polymer resin matrix, characterized by; construction as an assembly of three nested parts, such that circumferential hoop stresses are developed in the winding direction of the broadgoods associated with each part's geometry; and increased induced compressive residual stresses during construction of the container achieved by applying a deformation to each of the three nested parts, characterized by an inward displacement applied to the middle of each of the four side walls so as to make each diagonal dimension of the part smaller than the measured diagonal in the original un-deformed part.

9. The container of claim 8 wherein one of the firstmost inner or secondmost inner of the three parts has at least one opening cut in at least one wall.

10. The container of claim 9 wherein the opening is closed by installing the outermost third part, and in the event of a blast the expansion of the inner parts to the outer parts seal the opening with a gasket-

11. The container of claim 9 wherein the outermost third part has an opening hole which overlaps at least one opening in an at least one inner part, wherein the third part opening is sealed by a blast resistant accordion door of composite construction.

12. The container of claim 8 wherein the wall thickness, t, of each wall of the nested parts is determined by:

σ = pL/4t, where p is over pressure due to blast, L is the

length of the wall and σ is the membrane stress developed in the

wall as a result of the overpressure.

13. A blast resistant accordion door of composite construction for sealing an opening in a blast resistant composite container wall; comprising, piano type hinges where the loops of the hinges constitute cured reinforcing fibers which are the result of folding sidewall fabric back over a Teflon shaft or rod prior to infusion and resin curing, such that the Teflon rod prevents resin from sticking to the shaft thereby allowing the shaft to be extracted after the container shell is fully cured, lightweight high density polyethylene (HDPE) track positioned along the top and bottom horizontal edges of the door opening, hinge shafts made from continuous S-2 Glass filaments infused with epoxy resin to make a unidirectional reinforced S-2 Glass rod; and, a high strength lightweight shaft to secure the door inserted into the mating hinges where the left and right sides of the accordion doors meet at the center of the door opening, wherein all tensile circumferential stresses developed by an explosive detonation in the container are transmitted through the door hinges and door panels when the door is closed and secured.

14. The door of claim 10 wherein the hinges are co-cured during the fabrication of door panels.

15. A blast resistant container constructed at least in part of a composite fiber reinforced polymer resin matrix, characterized by; construction as an assembly of three nested parts, such that circumferential hoop stresses are developed in the winding direction of the broadgoods associated with each part's geometry; and, the wall thickness, t, of each wall of the nested parts is determined by:

σ = pL/4t, where p is over pressure due to a blast, L is the

length of the wall and σ is the membrane stress developed in the

wall as a result of the overpressure.