Impact of Windborne Debris on Storm Shutters

Alexander Borges1, Ricardo R. López2, Luis A. Godoy3, Raúl E. Zapata López4

1 Graduate Student, University of Puerto Rico, Mayagüez, Puerto Rico, USA, alexander_brgs@yahoo.com2 Professor of Civil Engineering, University of Puerto Rico, Mayagüez, Puerto Rico, USA, ri.lopez@upr.edu

3 Professor of Civil Engineering, University of Puerto Rico, Mayagüez, Puerto Rico, USA, luis.godoy@upr.edu4Professor of Civil Engineering, University of Puerto Rico, Mayagüez, Puerto Rico, USA, raul.zapata@upr.edu

ABSTRACT

This paper investigates the non-linear dynamics of thin-walled folded plate structuresunder the localized impact of a rigid object. The research emerges in the context of thestructural design and assessment of storm shutters used to protect windows and doors duringhurricanes. The development of a testing facility for storm shutters panels and test results areintroduced as a fundamental source of information for the proposed analytical approach. Theanalyses were carried out using the general purpose finite element code ABAQUS. The modelsimulates the interaction of contact of windborne debris traveling at a specific velocity againstthe shutters. A field survey was carried out to establish the most typical or representative crosssections used in the fabrication of storm shutters panels. As a result, a non-linear dynamicsresponse was computed leading to plastic deformations of the shutters. Values of permanent andmaximum deformations and stresses to determine the most detrimental behavior of the stormshutter assembly were evaluated by means of parametric studies.

INTRODUCTION

Every year the Caribbean Islands, Central America, and the Southeastern part of the UnitedStates experience the threats of hurricanes. Hurricanes have been cause of concern in PuertoRico at least once every five years, leaving heavily damaged areas and several deaths behindthem. Recent events, such as Hurricanes Hugo (1989), Marilyn (1995), Hortense (1996),Georges (1998), and Jeanne (2004) are just remainders of our vulnerabilities and needs forproper preparedness and protection against hurricanes and storms.

The integrity of any structure depends on the strength and stiffness of individualcomponents (walls and roof). Damage usually starts with the breaking of weak elements, such asdoors and windows. These components need additional protection in order to prevent furtherdamage to the interior of the structure, which can otherwise lead to possible complete loss of theproperty and can endanger lives. Typical hurricane protection elements available in Puerto Ricoand Florida include storm shutters of different types and materials.

One of the most dangerous agents during the pass of a hurricane is the windborne debris;they could produce serious damage to storm shutters and to the elements protected by them. In1972, Minor [1] observed that windows are traditionally designed for wind pressures, but thebreakage from impact by windborne debris is the most common failure mechanism duringhurricanes. He identified roof gravel as the principal form of small debris that can be carried intoall elevations of buildings facades. In residential areas, Minor [2] concluded that the mostprevalent type of windborne debris was timber from wood frame houses. Such timber debris hasbeen observed to penetrate walls and roofs during tornadoes. These observations led to theselection of a 0.051 m x 0.102 m (2 in x 4 in) timber as the representative object for use indefining impact criteria for protection of residences.

This paper outlines an investigation using a computer simulation of the impact problem,in which the debris and the storm shutter are modeled using finite elements. To validate theproposed models devices such as a steel rigid frame and an air cannon were developed to permitthe measurement of maximum deflections and capacities of the shutter under impact loads. Thepurpose of this study is to investigate the structural behavior of a typical assembly of stormshutter panels under impact. As a result, a non-linear behavior due to a dynamic event isexpected.

1. TESTING DEVICES

Different types of testing have been presented in the literature to obtain the resistance capacity ofthe shutters in order to verify if they comply with the Puerto Rico Building Code. To performthese tests, devices such as a steel rigid frame and an air cannon were developed to perform thecomplete testing program [3, 4]. The devices helped to measure the maximum deflections andcapacities of the shutter. The measurements were obtained under the effects of different types ofloads and physical conditions of the shutters.

1.1. Assembly Test Support: Rigid Frame

The assembly test support consisted on a steel frame capable of sustaining the applied loads witha minimum displacement of the support. The restriction on displacement was established suchthat the measurements obtained on the specimens were not affected. A maximum displacementvalue of 0.00025 m (0.01 in) was established for this purpose. The frame was designed to testdifferent types and sizes of specimens. A system of panels or storm shutters covering a possiblemaximum area of 3.05 m x 4.57 m (10 ft x 15 ft) was established for testing. Therefore, thehorizontal frame elements could move vertically, such that different span length specimenswould be placed on the system according to the panel to be tested as shown in Figure 1. Basedon this pre-established covering area, the size of the frame was determined to be 4.57 m x 4.57 m(15 ft x 15 ft). The horizontal elements of the frame supported the material (concrete, wood)where the panel connections were attached. To provide more realistic behavior special concreteblocks were designed for this purpose.

Figure 1: Steel Rigid Frame

The beam deflection and the use of lightweight sections were the principal criteria forsizing the element of the frame. For this reason an intermediate support for the beams wasnecessary to obtain a more economical section and control the system displacement. Finally,steel W sections [5] were selected in the design of the main frame and the mentioned supports asshown in Figure 2.

Figure 2: Rigid Frame Final Assembly

1.2. Impact test device: Air Cannon

The impact setup consisted on an air cannon capable to shoot large and small missilesagainst the specimens. For the air cannon system a rigid support table was designed. Thesupport table was able to sustain the weight of the system, position the air cannon at differentheights from the ground and maintain it fixed during the tests. Considering the dimensions ofthe system, the support table was attached to four wheels to facilitate its movement to therequired position of the air cannon. Special PVC tubes were the principal components for the aircannon. These PVC tubes were used to store about 0.226 m3 of pressurized air which wasreleased instantaneously toward the cannon section of the system as shown in Figure 3. Asolenoid valve controlled the sudden air flow necessary to shoot the missile.

Figure 3: Rigid support table and special PVC tubes.

1.47 m(4.83 ft)

2.44 m (8 ft)

3.05 m(10 ft)

1.3. Impact Test and Results

Two tests were carried out to validate the functionality of the impact device. The tests were doneon a typical storm shutter panel system installed on the assembly test support or rigid frame.However, for each test the arrangement of each sheet in the system was different. For the firsttest, the panels followed the typical arrangement suggested by shutter manufacturers. One edgeof each sheet was placed over the previous sheet. For the second test, the panel subjected toimpact was installed without any edge supported from the other panels.

The air cannon was located at twenty feet in front of the system such the proposed impactwill be at the center of the panel system. The storm shutter systems used for each set aredescribed in Table 1.

Table 1. Storm Shutters tested

Material AluminumGauge 0.002 m (0.063 in)Height 0.051 m (2 in)Span 2.18 m (7.16 ft)

Number 3 - 5

Cover area* 1.67-2.79 m2

(18 - 30 ft2)End Support Condition Clips**No. of Panels / System 3

* Area to be protected ** Two or three clips per sheet

The proposed missile velocity for both tests was 22.35 m/s (50.0 mph) using an aircannon pressure of 124 kPa (18 psi). However, the velocity obtained during the tests rangedbetween 22.80 to 23.11 m/s (51.0 to 51.7 mph). Parameters like weight, length andimperfections were relevant in the velocity of the missile. For that reason a higher velocity wasobtained using the required air pressure. The impact location was at the middle span of thecenter sheet. The following results were obtained for each test.

a) For test #1, the impacted sheet lost the clips that were attached to it. The clipdeformation was too large so it could not be used again. A torsion deformationoccurred due to the one edge support. As one edge was able to have a freedisplacement, the restriction provided by the edge supported produced a torsion effecton the sheet. At middle span the permanent deformation was approximately 0.165 m (6½ in).

b) For test #2, the impacted sheet did not loose the encasing provided by the top endsupport. The permanent deformation of the panel showed no evidence of torsion as wasobtained in the previous case. The panel behavior in terms of deflection was similar toa simple beam under a concentrated load at mid span. At middle span the permanentdeformation ranged between 0.191 to 0.203 m (7 ½ to 8 in).

2. COMPUTER SIMULATION

The first step to perform the proposed study is to establish the most relevant parameters that willbe used to represent the real behavior of the system already tested. Therefore, informationrelated to the material and physical properties, boundary conditions, and geometric configuration

of panels, is used to develop an analytical model using ABAQUS. Missile conditions, likeposition and velocity, are discussed later.2.1 Panel Material

A field survey was carried out to establish the most typical material used in the fabrication ofstorm shutters panels. It was found that aluminum alloys and galvanized steel are the most usedmaterials for this purpose. Some characteristics, like light weight, strength, easy handling andstorage, and low fabrication cost, set these materials among the favorites of the localmanufacturers. The mechanical and physical properties of these two materials are used torepresent the material in the proposed model, as shown Table 2.

Table 2. Mechanical and physical properties for aluminum 3003-H14 alloy and galvanized steel panels.

Parameter Aluminum 3003 H14 Galvanized SteelDensity 2727 kg/m3 (0.0986 lb/in3) 7855 kg/m3 (0.2840 lb/in3)

Thickness 0.0016 m (0.0630 in) 0.0010 m (0396 in)Modulus of Elasticity 69.0 GPa (10,000 ksi) 200.0 GPa (29,000 ksi)Tensile Yield Strength 145.0 MPa (21,000 psi) 240.0 MPa (34,800 psi)

Ultimate Tensile Strength 152.0 MPa (22,000 psi) 358.0 MPa (51,900 psi)Poisson Ratio 0.33 0.28

Stress-strain curves based in the mechanical properties of each material are develop toconsider the non-linear behavior of the material during the simulation. One of the constraintsimposed by ABAQUS is the use of true values instead of engineering values. The engineeringstress-strain curve does not give a true indication of the deformation of the metal, because it isbased in the original cross section, Ao, during the deformation process of a tension test [6].However, if constancy of volume and a homogeneous distribution of strain are assumed, one canexpress the true stress, in terms of engineering values, by:

11 eseAoP (1)

where s is the calculated stress based in the original area Ao. In the case of true strain, can beexpress by:

oL

Le ln1ln (2)

where e is the typical calculated strain based in the ratio of L/Lo, Lo is the original length of thespecimen. Both equations should be used until the onset of necking. Beyond the maximumload, the true stress and strain should be determined from the actual cross section. The stress-strain curves necessary to define the material model under analysis are shown in Figure 4.

0

20

40

60

80

100

120

140

160

180

200

0 0.001 0.002 0.003

Strain (m/m)

Stre

ss (M

Pa)

NominalTRUE

0

50

100

150

200

250

300

350

400

0 0.001 0.002 0.003 0.004 0.005

Strain (m/m)

Stre

ss (M

Pa)

NominalTRUE

(a) (b)Figure 4: Stress-Strain Curve for (a) Aluminum 3003-H14 (b) Galvanized Steel

2.2 Boundary Conditions

Typical storm shutter assemblies consist in the attachment of two channel sections at the openingedges to be covered. Once the channel sections are fixed, the storm panels are added to thesystem fixing both edges as shown in Figure 5.

Figure 5: Typical Connections.

The upper edge of the panel is prevented of moving out of the plane due to the contactprovided by two sides of the channel. However the panel is free to move in the in-planedirection. A representation of this condition is adopted by using a roller support at the upperedge of the panel. For a more complex model two fixed surfaces are used to represent the sidesor wall of the top channel. In the case of the lower edge, the panel is attached to the systemusing bolt and washers. A pin support is used to restrain any lateral displacement and facilitate afree rotation at the bolt area.

2.3 Geometrical Configuration

Each manufacture suggests a different geometrical configuration of the panels. Theconfiguration or cross section has an effect in the physical behavior of the panel, especially in themoment of inertia. Two panels were measured to generate the cross sections shown in Figure 6and 7 (all dimensions in meters).

Figure 6: Cross Section #1

Figure 7: Cross Section #2

Cross section #1 was based in the sheets used in test #1 and #2. For cross section #2, theprofile was obtained from sheets produced by other local manufacturer. Both sections were usedin the simulation as different cases.

2.4 Contact interactions

The load application to the system under investigation consists in establishing contact zones thattransfer the forces produced by the windborne impact. ABAQUS has the capability of includingspecial algorithms to account for the effect of contact interactions between surfaces. Threecontact zones or contact pairs are specified in the simulation. Contact pairs are surfaces ofbodies that could potentially be in contact. For a hard contact, a node on one surface isconstrained not to penetrate the other surface. The node with constrain is on the slave surfaceand the surface with which it interacts is called the master surface. In principle, the nodes on themaster surface can penetrate the slave surface as will be the case of the missile.

As was mentioned above, three situations of contact pair are defined in the analysis. Thefirst situation is the contact between the missile and the selected panel area to be impacted.Based in the physical behavior of this interaction, the missile is defined as the master surface andthe panel as the slave surface. The second situation is the contact produced between the stormpanel edges in the assembly. As a standard procedure and previously mentioned, the panels areinstalled so that one of its edges is supported by the following panel, while the other one is free.In this case the definition of master-slave interaction is based in the level of mesh refinement.As a simple rule, the master surface is assigned to the finest mesh.

The third contact pair is the contact produced between the upper edge zone of the panelsand the header channel. As mentioned in Section 2.2, the upper edge of the sheets are embeddedinto the header channels such any out of plane movement is restrained. Therefore, surfacecontact is produced as the upper edge of the sheets move against the walls of the channel as aresult of the applied impact load. This contact pair was introduced in the more complex models.

2.5 Windborne definition

Many international authorities, like Dade County Building Code Compliance Office, havedeveloped a series of protocols oriented to testing storm shutters [7, 8, 9]. One of this is theimpact load test. The protocols include the definition of related materials, testing procedures,and testing facility requirements. As a testing material the protocols suggest the use of a 0.61 x1.22 m (2”x 4”) piece of wood as the most characteristic windborne material. A weight of 9 lb isestablished to perform the impact load test. The missile shall have a length of not less than 2.133m (7 ft) and not more than 2.74 m (9 ft). Seven feet length has been used for our study based ina specific mass density value. Table 3 summarizes the physical and mechanical properties of themissile used in the model.

Table 3. Windborne Debris or Missile properties.

2.6 Finite Element Model

Once the most relevant parameters have been defined the next step is to incorporate these intothe general purpose finite element code, ABAQUS. Storm panels are thin in comparison withtheir span. Thus, a discrete mesh composed of isoparametric general shell element is use tomodel the storm panels. Stresses due to membrane and bending action are calculated based inthe shell element formulation.

A simple model of two panels is used to represent the assembly. Therefore, the modelhas two finite element meshes, as shown Figure 8. The only difference between them is thenumber of elements used in each mesh generation. As only one panel is subject to the missileimpact, a high degree of refinement is required. Other parameters are the same. In the case ofthe missile, a mesh consisting of solid brick elements is used to obtain the necessary stiffness andmass transfer to the system by the impact action.

Figure 8. Finite Element Mesh used as Base Case Model.

Cross section 0.051 m x 0.102 m (2 in x 4 in)Length 2.13 m (7 ft)Weight 4.08 kg (9 lbs)Mass density 360 kg/m3 (0.013 lb/in3)

U2

U3

U1

2.7 Parametric Study

A base model is defined according to the typical assembly condition. Using the base model aparametric study is developed based in the following parameter combination shown in Table 4.

Base Case. Two aluminum panels supported with a roller - pin connection, upper andlower support respectively. The missile velocity is established as 22.35 m/s (50 mph) toimpact at the middle center of the panel just over the valley section. The cross section #1is used as the geometric configuration.

Case 1, Geometrical Configuration. Same as base case but using cross section #2. Case 2, Boundary Condition. Same as base case but panels supported with a pin – pin

connection at both ends. Case 3, Material. Same as base case but using galvanized steel as panel material. Case 4, Impact location. Same as base case but establish the impact location at the right

center of the panel just over the hill section. Case 5, Velocity Variation. Same as base case but the missile velocity is assumed as

11.18 m/s (25 mph). Case 6, Velocity Variation. Same as base case but the missile velocity is assumed as

33.53 m/s (75 mph). Case 7, Assembly configuration. Same as base case but a third panel is introduced to the

system (assembly condition used on test #1). Case 8, Top channel. Same as case #7 but the upper support is modeled or defined as two

fixed surfaces representing the channel walls or header. Case 9, Full Set up. A total shutter assembly consisting of five sheets is evaluated. A

missile velocity of 15.24 m/s (50 ft/s) to impact at the middle center of the panel. Missilevelocity based in testing protocols. The cross section #1 is used as the geometricconfiguration.

2.8 Frequency Analysis

For simplicity, during the evaluation of the base case no damping was included in the system.Therefore, it was found that when the load rebound from the structure it shows a freely vibratingundamped behavior. As a result long term oscillations of the panel do not permit theidentification of the maximum permanent deformation. This situation represents a high time costfor the analysis.

In performing nonlinear analysis, it is appropriate to define a proportional dampingmatrix for the initial elastic state of the system and to assume that this damping property remainsconstant during the response even though the stiffness may change and cause hysteretic energylosses in addition to the viscous damping losses. A simple way to formulate a proportionaldamping matrix is to make it proportional to either the mass or the stiffness matrix. Rayleigh[10] proposed the following relation, where two coefficients or matrix proportion are given by

221 n

n

on

aa

(3)

If the damping ratios associated with different frequencies are known, then the twodamping factors ao y a1 can be evaluated by the solution of simultaneous equations based in theRayleigh relation (equation 3). Assuming that the same damping ratio applies to bothfrequencies, the proportionality factors are given by a simplified relation

0.12

1

nm

nm

o

aa

(4)

where m typically is taken as the fundamental frequency of the system and n be set among ofthe higher frequencies of the modes that contribute significantly to the dynamic response.

Assuming a damping ratio in the first and third modes as 2 % of critical and performing afrequency analysis of the system, proportionality factors were obtain for each case as shown inTable 4.

Table 4. Proportionality factors for damped systems

Case ID Frequency FrequencyFirst Mode Third Modeωm (rad/sec) ωm (rad/sec) a o a 1

Base,4-9 169.23 408.08 4.78 6.93E-051 210.05 426.38 5.63 6.29E-052 172.78 411.54 4.86 6.85E-053 167.50 270.62 4.14 9.13E-05

ProportionalFactors

Those values are included in each model as part of the material properties under evaluation.ABAQUS allows the use of proportional factors to generate a mass matrix for the system.

2.9 Results and Discussion

In all cases the missile was located at an initial distance of 0.002 m (0.075 in) from the panelsurface to be impacted. As the analysis of the missile behavior is not part of the study, thespecified distance reduce the number of iterations required to perform the simulation. A timeincrement of 0.50 micro-seconds is established as the ∆t to obtain the solution for an event ofapproximately 0.30 seconds. Figure 9 shows a typical simulation sequence of deformation as thesolution for the complete event is obtained.

A comparison of the response of the two mentioned panel materials is shown in Figure10. The result shows a maximum deflection of 0.187 m (7.35 in) for the galvanized panel and0.173 m (6.82 in) for the aluminum panel. It is important to know that the evaluated galvanizedpanels have half of the thickness of the aluminum panels. The gage or thickness used forgalvanized panels corresponds to the manufacture requirement of providing a lightweightproduct at the moment of the assembly installation. Both materials present a maximumdeformation values that exceed the distance between panels and elements that shall be protect bythe system. Typically the distance between panels and windows or doors is approximately 3inches. In both materials the yielding stress was exceeded resulting in a permanent deformationof the panels.

Figure 9. Impact Simulation Sequence.

-0.2-0.18-0.16-0.14-0.12-0.1

-0.08-0.06-0.04-0.02

00 0.1 0.2 0.3 0.4

Time (sec)

U3 (m

eter

s)

Base CaseGalvanized Steel

Figure 10. Maximum and permanent deformation of aluminum (base case) and galvanized steel panels.Values obtained at the impact area according to the case.

Based in the stress strain relation of each material, the impact load produced a level ofstress larger than the ultimate stress without reaching failure, as shown in Figure 11. Thisphenomenon was evident at the impact area where the maximum values of stresses wereobtained.

020406080

100120140160180

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Time (sec)

Von

Mis

ses

Str

ess,

MPa

0

50

100

150

200

250

300

350

400

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Time (sec)

Von

Mis

ses

Stre

ss, M

Pa

Figure 11. Maximum Von Misses stresses acting at the impact zone for (a) aluminum and (b) galvanizedsteel panel.

Based in the previous results it is found that the elements to be protect by the stormshutter system will be affected by the excessive deformation of the panels. As an alternative,Figure 12 shows the effect of introducing a different cross section, additional panels, andmodifying the boundary condition at the upper edge of panels. As a result a reduction in Case 8of 0.052 m (2.05 in) was obtained in the maximum deformation of the panel. The extra supportprovided by a third panel and a restriction of full rotation at the end of the panels improve the

0.0 sec 0.005 sec 0.022 sec 0.300 sec

(a) (b)

capacity of the system against deformations. However, the level of improvement gained with theproposed alternatives is not enough when considering the damage that will suffer the protectingelements.

-0.2

-0.18

-0.16

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

00 0.1 0.2 0.3 0.4

Time (sec)

U3

(met

ers) Base Case

Case 1Case 7

-0.2-0.18-0.16-0.14-0.12-0.1

-0.08-0.06-0.04-0.02

00 0.1 0.2 0.3 0.4

Time (sec)

U3 (m

eter

s) Base CaseCase 2Case 8

(a) (b)

Figure 12. Alternatives for response improvement: (a) Use of different cross section and an additionalpanel. (b) Upper boundary modification.

During a hurricane, the impact of windborne debris will occur at any location of thepanels. Based in the protocols of testing storm shutter panels, a simulation where the missile hitthe panel at the middle right of its length is evaluated. This zone corresponds to the highestsection of the panel, called the hill. The impact over the hill generates a deformation processvery different to the other cases already mentioned. As the load is applied to the hill and thelateral sides connected to it, a buckling process begins due to the excessive compression stress inthe zone. The deformed section becomes flat and the panel tends to rotate or twist so that it willaccommodate to the new configuration. The missile tends to slip over the surface until it reachesthe edge of the panel. At the edge of the panel, the missile continues its displacement until thepanel does not restrain it. This panel behavior is shown as a sequence of deformations in Figure13.

Figure 13. Impact missile over the hill at different times.

0.001 sec 0.004 sec 0.008 sec

0.013 sec 0.022 sec

The permanent deformation of the panel obtained is 0.176 m (6.93 in). Once again theprotect elements will be damage due to the excessive deformation of the panels. In addition, adirect impact of the missile is expected in this case.

Another parameter that is unknown during a hurricane event is the velocity in which astorm shutter assembly will be impacted by windborne debris. A comparison of maximum andpermanent deformation of the base case at various velocities is shown in Figure 14. The resultsobtained show that velocities under 11.18 m/s (25 mph) will produce a permanent deformation of0.064 m (2.5 in), and the system will work in an efficiently manner during the event. However, apermanent deformation of 0.029 (1.15 in) is expected at the panel.

In the case of velocities larger than 75 mph the system will fail. The failure is based inthe excessive displacement of the panel at the upper boundary condition. As the base case is freeto move due to the roller support the panel will be able to deform as the distance between the twoedges is reduced. Notice that the channel section permits a maximum displacement according toits own dimensions. Typically the section length in contact with the panels is 0.064 m (2.5 in).Case 6 was found to exceed the channel length.

-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.1

00.1

0 0.1 0.2 0.3 0.4

Time (sec)

U3 (m

eter

s) Case 5: 25 mphBase case: 50 mphCase 6: 75 mph

-1-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.1

00.1

0 0.1 0.2 0.3 0.4

Time (sec)

U2

(met

ers)

Case 5: 25 mphCase Base: 50 mphCase 6: 75 mphCase 3: GalvanizedCase 7Case 8

(a) (b)Figure 14. Maximum obtained values for (a) Variation of missile velocity (b) Upper edge displacement.

As was mentioned before, several international authorities suggest the use of protocolsfor testing storm shutter systems, and some of the recommendations include the use of acomplete assembly to perform the proposed tests. A storm shutter system consisting in the totalnumber of panels necessary to cover the glass or window to be protected is required as a testingrule. In addition, a missile velocity of 15.24 m/s (50 ft/s) is defined to carry out the impact tests.A full setup is modeled consisting of five panels and an aluminum channel as top support. Amissile velocity of 34.1 mph (50 ft/s) is used. A total of 35,172 shell elements are used to modelthe five panels as shown in Figure 15.

Figure 15. Finite element model for a full set up

The impact load effect was evident in all the system. However, the response of panelslocated at the edge of the system was moderated. A maximum stress distribution acting over thesystem at the moment of maximum deformation is shown in Figure 16. The permanentdeformation of the panel obtained is 0.076 m (2.99 in). The protect elements will not be damagedue to the excessive deformation of the panels.

Case 9

-0.08-0.07-0.06-0.05-0.04-0.03-0.02-0.01

00.01

0 0.05 0.1 0.15 0.2

Time (sec)U3

(met

ers)

Case 9

(a) (b)

Figure 16. System Response. a) Stress distribution b) Maximum and permanent deformation

3. CONCLUSIONS

The main objective of this study was to simulate the interaction of contact of windborne debrisagainst the shutters using a general purpose finite element code. To attain this objective, aparametric study was performance based in the most influence parameters so that the mostdetrimental behavior of the panel in a typical assembly is obtained. The following conclusionscan be drawn from this study:

1. A non linear behavior occurs in all the cases considered. Based in the stress-strain relationsassumed, the yield stress values were exceeded resulting in a permanent deformation of thepanels.

2. Failure of the material was not achieved in any case. The flexibility of the typical assemblyto allow the free displacement of the upper edge of the panel avoids any possibility of failureby punching shear of the missile at the impact area. The energy induced in the system willbe dissipated via an excessive deformation of the panel.

3. The use of different boundary conditions and a change in the geometrical configurationproduces an improvement in the behavior of the panels specifically with respect to theexpected deformation. Additional panels provide support to free edges. As a result areduction of deformation is obtained at maximum values and during the vibration period ofthe system. In addition, the use of fixed surfaces to represent the top channel controls thefree rotation of the upper edge of the panels. Therefore, an improvement in maximum valuesis obtained. However, the reduction in deformation was not sufficient to prevent damage dueto the direct contact of the panels to the element to be protected.

4. Galvanized steel displays similar structural behavior than the aluminum alloy panel.However, if galvanized panels are used with a larger thickness than the evaluated, theresponse improves in comparison with the aluminum panels.

5. The most detrimental behavior is produced when the impact is located out of the center of thepanel. The geometric non-linearity results in a direct impact of the missile to the element tobe protected. As one side of the panel is not prevented from displacements, the change in thegeometry causes relocation in the missile trajectory such that the panel does not offer anyresistance, allowing a direct contact of the missile with the elements to be protected.

6. Case 8 is a good representation of the assembly used in test #1 in terms of defining itscomponents. However, the maximum deformation was less than the value obtained duringthe test. It is important to note that the tested system suffered a support lost as some clipswere damaged and released form the system. During the simulation support condition arenot affected. As a result, the stiffness of system remains during the event.

7. The full set up model showed that the contribution of panels that are located at edges of thesystem is reduced. However, based in the parameters used for this case a prevention ofdamage was achieved.

8. Run-time consuming and model development complexity are factors to be considered. Basedon the full set up model results a more simple technique to represent the storm shutter systemshall be defined for future analyses.

4. REFERENCES

[1] Minor, J.E., K.C. Metha and J.R. McDonald, “Failures of structure due to extreme winds.”ASCE Journal of Structural Engineering, 1972, vol. 98, 1972, pp. 2455-2471.

[2] Minor, J.E., “Windborne Debris and the Building Envelope,” Journal of Wind Engineering andIndustrial Aerodynamics, vol. 53, 1994, pp. 207-227.

[3] Borges A., López R., and Zapata R., “Guidelines for testing and Approval of Storm ProtectionShutter and Panels”, Report submitted to Federal Emergency Management Agency, FEMA,1997.

[4] Borges A., López R., and Zapata R.,”Testing of Storm Shutter Panels”, Fourth LACCEIInternational Latin American and Caribbean Conference for Engineering and Technology, 2006.

[5] AISC, “Manual of Steel Construction”, 2nd Edition, American Institute of Steel Construction, Inc.,Vol.1&2, 1994.

[6] Boyer H. E., Atlas of Stress-Strain Curves, ASM International, Ohio, 1987.

[7] Miami Dade County, Protocol PA 201-94, “Impact Test Procedures”, pp. 1-9.

[8] Miami Dade County, Protocol PA 202-94, “Criteria for Testing Impact and Non Impact ResistantBuilding Envelop Components using uniform static air pressure”, pp. 1-9.

[9] Miami Dade County, Protocol PA 203-94, “Criteria for Testing Products subject to cyclic windpressure loading”, pp. 1-8.

[10] Clough R. W. and Penzien J., Dynamics of Structures, McGraw-Hill, New York, 1975.