Engineering Structures 39 (2012) 79–88

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Engineering Structures

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Failure of wood-framed low-rise buildings under tornado wind loads

Nikhil Kumar, Vinay Dayal ⇑, Partha P. SarkarDepartment of Aerospace Engineering, Iowa State University, Ames, IA, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 14 April 2009Revised 5 February 2012Accepted 6 February 2012Available online 22 March 2012

Keywords:Wood-frameTornadoStress analysisFailure analysis

0141-0296/$ - see front matter � 2012 Elsevier Ltd. Adoi:10.1016/j.engstruct.2012.02.011

⇑ Corresponding author. Tel.: +1 515 294 0720; faxE-mail addresses: vdayal@iastate.edu (V. D

(P.P. Sarkar).

Buildings in the ‘‘tornado alley’’ of the United States, are built to withstand 3-s wind speeds of 90 mph(40.2 m/s), whereas 90% of the tornados are of F2 or lesser intensity that generate anywhere from 40to 157 mph (17.9–70.2 m/s). At the same time, these codes are based mostly on studying the effects ofstraight line winds and not on tornado type winds, especially on low-rise, wood framed buildings whichmake up majority of structures in the United States. Previous research at Iowa State University (ISU)includes extensive testing on a scaled down low-rise gable roof building model (1:100) to understand tor-nado induced loads as the tornado sweeps past the building. In the present work, Finite Element (FE)models were developed using ANSYS for full-scale numerical simulation of the gable roof buildings withthree different roof angles (13.4�, 25.5� and 35.1�). The nail is modeled as a non-linear element but thewood is assumed to be linear. The tornado-induced wind loads recorded in the laboratory were scaledup and applied to the models to determine the detailed stress distribution in the structure. This numer-ical study was performed using the same parameter as in the laboratory experiments such as those listedearlier. The deterministic FE model incorporated the damage criteria to assess the damage potential dueto tornadic forces. The stress distribution, pattern of failure, the order of failure and the type of failurehave been studied as the tornado sweeps past the building at different angles to the building centreline.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Tornados are violently rotating columns of air, extending from athunderstorm to the ground. Though they occur in many parts ofthe world, they are found to occur most frequently in the UnitedStates. There are around a thousand tornados reported annuallyin the US, causing around 60 fatalities, thousands of injuries,Grazulis [1], and resulting in damage of over a billion dollars.Though tornados have occurred in all fifty states, they are concen-trated in what is known as the ‘‘tornado alley’’, located in the cen-tral region of the country. According to the current design codes,low-rise buildings are built to withstand only up to 3-s gust of90 mph (40.2 m/s) of straight-line winds, while 90% of the tornadosare of F2 or lesser intensity that generate anywhere from 40 to157 mph (17.9–70.2 m/s) fastest 1=4-mile wind speed. At the sametime, these codes are based on studies involving the effects ofstraight line winds and not the tornado type winds. Also, the prop-erty damages that occur due to tornados are significant due towind-borne debris similar to the direct effect of high speed windon them. It is therefore necessary to assess the wind damagepotential of buildings as a function of distribution of local windspeed and map the generation of wind-borne debris from the

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: +1 515 294 4848.ayal), ppsarkar@iastate.edu

buildings. Extensive wind tunnel tests have been performed onthese types of structures under tornado type winds to obtain theforces acting on the structure. These tests were performed onlow-rise building models with a variety of commonly used roof an-gles and shapes.

It is needless to say that even though the buildings are designedfor 90 mph wind speeds, the probability of it being subjected totornado loads is small. Nevertheless, one fatality is too many andhence the building codes are developed to minimize such losses.

The main objective of this research work was to apply these tor-nado-induced wind loads, obtained in the laboratory using a scaledmodel of a low-rise building, to a numerical Finite Element model(FEM) of the building to assess its damage potential. Loads areapplied in the quasi-static manner, i.e. the experimental loadsare applied to the building at discrete intervals and analysis per-formed to calculate the internal stresses and failure criteria isapplied to determine the integrity of the elements. The model isassumed to be deterministic and the probabilistic nature of load-ing, material properties, nail pull-out have not been included.

1.1. Previous work

A lot of work has been done to deal with 3-D performances oftimber framed buildings. One of the first analytical models wasdeveloped by Tuomi and McCutcheon [2] which assumes linearelastic behavior of nails. The nail deformation here is defined by

Fig. 1. Building orientation with respect to the vortex translation direction (x-axis).

80 N. Kumar et al. / Engineering Structures 39 (2012) 79–88

the relative deformation of sheathing and frame at each point.Gupta and Kuo [3] presented a linear building model with shearwall elements using 9 degrees of freedom and seven superele-ments. This model used a strain energy formulation and analyzedthe building tested by Tuomi and McCutheon [2]. Foschi [4]developed a Finite Element model which included nonlinearload-deflection properties for fasteners. Frame elements weremodeled linearly and sheathing elements were modeled elasticand orthotropic. Kasal [5] used the Finite Element software ANSYSto develop a three-dimensional model. It consists of linear ortho-tropic 2-D shell elements and fasteners represented by three 1-Dspring elements at each node. The properties of nails, when pulledout and pulled through plywood and OSB boards were studied byHerzog and Yeh [6]. He et al. [7] developed a 3D model using theFE technique with plate, beam, and nonlinear nail connections.Kasal et al. [8] have developed a non-linear model of a completelight-frame wood structure and performed analysis under staticloads. They were able to get a good correlation between the theoryand experiments which were limited to static loads only. Collinset al. [9,10] published two papers where in the first one they havedescribed the details of the model of a three-dimensional lightframed wood building and in the second they have reported exper-imental investigation and analytical studies. They applied static-cyclic lateral loading and were able to get a reasonable correlationbetween energy dissipation, hysteretic response, the load sharingbetween the walls and the torsional response. They modeled thespring as non-linear springs under hysteretic loads and hence theirmodel and analysis is restricted to cyclic loads only. Foliente [11]also has modeled the wood joint and structural systems under hys-teretic behavior. The objective of the research has been to modelthe behavior of wood under seismic loads. Paevere et al. [12] hasstudied the load-sharing and redistribution in a one-story woodframed building which was subjected to lateral loading in staticand static-cyclic modes.

Thus, we observe that starting from very simple linear models,the development has taken place in the analysis and more andmore complex elements, such as orthotropic, and from linear tonon-linear nail models have been incorporated. Researchers havestudied the actual nail pull out and attempted to incorporate theseinto the Finite Element codes. This makes computation difficultand time consuming but with the development of faster and fastercomputers, these developments have been possible. One notice-able limitation of all these models has been the application ofloads. Only the plane fronted wind has been considered. Workhas also been done where the buildings were subjected to hyster-etic loads and lateral loads. The work presented here is concernedwith the tornadic loads on a wooden building.

The nail pullout of wood has been studied by Aune et al. [13] andChow et al. [14] and they have developed theoretical models too.But we decided that it would be more realistic to use experiment

Table 1Experimental simulator settings and the accompanying tornado vortex parameters.

Case name Vane angle (�) S at RMW RMW (m) V

Vane1 15 0.08 0.23 6Vane2 25 0.18 0.30 8Vane3 35 0.24 0.30 9Vane4 45 0.82 0.51 9Vane5 55 1.14 0.53 9

S: swirl ratio at RMW.RMW: radius of maximum wind.Vhmax: mean tangential wind velocity measured at the building height at RMW.VH: mean horizontal wind velocity measured at the building height at RMW.kT: time scale based on a velocity scale of Vhmax/50 and length scale of 1/100.Re: Reynolds number based on VH and building height.

based load–displacement relations and the details will be describedlater.

In this work, we have taken the pressure distribution measure-ments of Haan et al. [15]. The building was subjected to a movingtornado with a wind speed of 112 mph or 50 m/s (lower range ofan F2 tornado) and five different swirl ratios (S) as reported inTable 1. This table mentions a ‘vane angle’ which is the angle setin the tornado simulator to generate different swirl ratios (S) andhence the vane angle may be taken as a case number only. Wedefine the swirl ratio, S, as the ratio of the vortex circulation atthe radius of maximum tangential wind (RMW), rc, based on themaximum tangential wind speed (Vhmax), to the accompanying rateof inflow (Q) into the vortex ðS ¼ pVhmaxr2

c=QÞ. The pressure distri-butions for each model case were converted to full-scale values byadjusting the model pressure coefficients to full-scale equivalentsfirst and then multiplying them with the wind speed of 112 mph(50 m/s) of an F2 tornado (=8-s gust). This adjustment was accom-plished by adjusting the maximum tangential wind speeds (Vhmax)that were used to normalize the model pressure coefficients to ac-count for the difference in time averaging between model scale andfull scale. The averaging time for the velocity measurements of 26 swas converted to the full-scale equivalent ranging from 359 to510 s using the time scale (kT) mentioned in Table 1 correspondingto Vane1 to Vane 5 cases. The Vhmax corresponding to the full-scaleequivalent averaged speed was then adjusted to 8-s gust windspeed using the Durst gust factor curve. The reasoning for usingthe Durst curve that is strictly valid for straight-line wind is thatan equivalent gust factor curve is not available at this point fortornadoes.

Fig. 1 shows the building orientation with respect to the tor-nado translation axis. In each case tested, the tornado translationaxis passed through the center of the building model. For all dis-cussions in this paper the tornado approach angle h, will bereferred to as shown in Fig. 1. For all building orientations, four dif-ferent cases of tornado translation speeds 0.15, 0.30, 0.46 and0.61 m/s were used. Three one-story models with gable roof of

hmax (m/s) VH (m/s) Q (m3 s) kT Re � 104

.9 8.3 14.4 13.8 3.6

.3 9.5 13.1 16.6 4.2

.7 11.3 11.5 19.4 5.0

.8 12.0 9.7 19.6 5.3

.7 11.9 7.6 19.4 5.2

N. Kumar et al. / Engineering Structures 39 (2012) 79–88 81

13.4�, 25.5� and 35.1� roof angles have been studied and results arereported here.

2. Modeling the building

The numerical model was designed so as to reflect the behaviorof a typical American residential type, wood frame and low-rise ga-ble roofed building as close as possible. The FEA package ANSYS[16] was used to develop a mathematical model of the building.Different types of elements were used to represent the variousparts of the building such as the 2 � 4 s, nails and plywood clad-ding. There were five different types of elements that were usedin the model.

(1) 3-D beam element to simulate the 2 � 4 s.(2) 3-D layered shell for the walls and roof split into

layers for drywall, insulation and the outer ply-wood. The plywood can also be substituted forOriented Standard Boards (OSB) by just changingthe properties (Young’s modulus and Poisson’sratio) in the layered shell element.

(3), (4) and (5) Three spring-damping elements, for a nail to takeeffect in each of the UX, UY and UZ direction.

2.1. Element types used

2.1.1. FrameThe framework of 2 � 4 s is represented by a 3D element with

tension, compression, torsion, and bending capabilities. The ele-ment is capable of 6 degrees of freedom at each node: translationsin the nodal x, y, and z directions and rotations about the nodal x, y,and z axes. Each element is defined by three nodes (I, J and K), thecross-sectional area, two area moments of inertia (IZZ and IYY),two thicknesses (TKY and TKZ), an angle of orientation about theelement x-axis, the torsional moment of inertia (IXX), and thematerial properties. The element x-axis is oriented from node I to-ward node J. The node K defines a plane (with I and J) containingthe element x and z axes. If K is not defined and is equal to 0�the orientation of the element y-axis is automatically calculatedto be parallel to the global X–Y plane.

2.1.2. Plywood sheathingThe sheathing was represented by using the shell element type,

which is defined as an 8-node structural shell. This element iscapable of 6 degrees of freedom at each node: translations in thenodal x, y, and z directions and rotations about the nodal x, y,and z axes. The deformation shapes are quadratic in both in-planedirections. The element has plasticity, stress stiffening, largedeflection, and large strain capabilities.

2.1.3. NailsThe element type used to represent the nails was a unidirectional

element with nonlinear generalized force-deflection capability. The

Fig. 2. Nail pull test showing the

element has longitudinal or torsional capability in one, two, orthree-dimensional applications. The longitudinal option is a uniax-ial tension–compression element with up to 3 degrees of freedom ateach node: translations in the nodal x, y, and z directions. No bend-ing or torsion is considered. The torsional option is a purely rota-tional element with 3 degrees of freedom at each node: rotationsabout the nodal x, y, and z axes. This element has no mass capabili-ties. This element was defined by two node points and a generalizedforce-deflection curve. The points on this curve represent forceversus relative translation for structural analyses (see Fig. 3).

2.2. Nail pull-out test

In a typical wooden structure, all components such as the roofpanels, 2 � 4’s and plywood claddings are held together with nails.A realistic numerical model required the knowledge of the load–displacement response of the nails. The nail response was firststudied using the nail-pull tests that were conducted using theUniversal Testing Machine. Two pieces of 2 � 4’s were nailed toeach other and were pulled apart and the axial load vs. axial strokemeasured. This setup is shown in Fig. 2.

These tests were performed many times and average responsevalue has been determined for use in the model. It should be notedthat these tests were performed for one nail type and one woodtype. If any one of the two parameters is changed, the response willbe different. Results show that as the nail is pulled, initially it sus-tains the entire load. When the load increases such that it is largerthan the friction between the wood and nail, the nail starts to pullout of the wood. During this stage, as the nail comes out of thewood, the embedded length reduces and as a result the frictionarea reduces and it is progressively easier to pull the nail out ofthe wood. This shows up as a reduction in the pull load in Fig. 4.

It is observed that the nail pull-out displays non-linear load dis-placement behavior.

2.3. Model description

The entire model has been developed in the parametric formand hence it can be used for any dimension and any material prop-erty type.

The frame of 2 � 4 s was modeled using the Density, Elasticmodulus, Poisson’s ratio of Douglas-Fir lumber [17]. For the pres-ent analysis, the beam was assumed to be isotropic in nature.The gravity was turned on for the analysis to include the self-weight of the frame work. Typical cross-section dimensions of1.500 � 3.500 (38.1 � 88.9 mm) were used for the 2 � 4 beams. Thearea (A) and second moment of Inertias (IZZ and IYY) were calcu-lated to be 5.25 in.2, 5.3594 in.4 and 0.98435 in.4 (33.9 cm2,1195.55 cm4, and 40.32 cm4). The building has a square plan formof 75 ft. � 75 ft. (22.86 m � 22.86 m) with the 2 � 4 s placed verti-cally at every 16 in. (40.64 cm). The K nodes (as mentioned in thebeam element definition) of the 2 � 4 s are defined such that thenarrow faces of the 2 � 4 are oriented outward. The height of a

two 2 � 4 s and nail location.

Fig. 3. (a) Axial load (lbf) vs. axial stroke (in.) as the nail is pulled out of the wood. (b) Axial stroke (in.) as a function of time (s) for the test.

Fig. 4. 2 � 4 framework assembly, side view, (b) framework assembly, isometric view, and (c) exterior after meshing, isometric view.

82 N. Kumar et al. / Engineering Structures 39 (2012) 79–88

single story is 9 ft. (2.74 m) after which the roof starts. The vertical2 � 4 s are enclosed by a set of sole plates and top plates. The roofwas modeled using a ‘‘gable’’ truss and can also be modified if re-quired for other types of trusses commonly used such as ‘‘W’’, ‘‘M’’,and ‘‘Scissors’’. The distance between each truss structure of theroof was kept at 3200 (81.28 cm).

The Isometric view of the completed 2 � 4 framework is shownin Fig. 4a. The framework is covered by plywood sheathing beforemeshing, Fig. 4b.

Plywood was modeled as shell, as described earlier. The totalmass of the plywood sheathing was included as mass per unit areaand the thickness was kept at 0.5 in. (12.7 mm). The material prop-erties used were that of Douglas-Fir plywood [18] and wasassumed to be Isotropic for this analysis.

One of the main requirements of meshing is to have the appro-priate mesh type and mesh density. The mesh influences the accu-racy, convergence and speed of the solution. This was mainlydecided on the basis of the nail and 2 � 4 spacing. Another mainrequirement is that after meshing, the nodes of the 2 � 4 frameand plywood sheathing should coincide so that the nail elementcould be installed between them. The resulting building modelafter meshing is shown in Fig. 4c. This meshed model now hasthe nodes of the external plywood and 2 � 4 s coinciding at around1600 (40.64 cm) intervals. Three nail elements are installed at everycoincident node, one to act in each of the UX, UY and UZ directions.Since the nail element type does not have mass capabilities, themass of the nails were distributed among the mass of the plywoodsheathing. The stress–displacement curve was used as the materialcharacteristic and failure criteria for the nails. All the nodes at thebase are constrained in all directions. This means that the founda-tion was not simulated as flexible but fully constrained. This willresult in incorrect stresses in and around the foundation elementsbut the results of the upper part of the building will largely be

unaffected. Three gable building models were designed to betested with roof angles of 13.4�, 25.5�, and 35.1�.

The complexity and the computation time for this model is veryhigh because the loads are applied at various x/D, where x is thedistance of the tornado from the centre of the building and D isthe diameter of the tornado. As will be discussed in Section 5,the x/D is in steps of 15–35, depending on the case under study.The authors understand that the wood will behave in a non-linearfashion at very high loads, especially close to failure. In this analy-sis we have modeled the nail as non-linear since as the nail is beingpulled out the contact friction between the nail and wood changesand hence the non-linearity. To keep the computation time to areasonable limit, the wood is approximated to be linear till the fail-ure. This certainly is a limitation of this work.

3. Failure

Failure can mean different things to different readers. Hence theterm ‘‘failure’’ for different components is defines next.

Nail failure means that if the nail is pulled out completely fromthe wood then it is defined as failed.

The beam and shell are assumed to fail if the von Mises stresshas exceed the allowable stress. The reason this energy based fail-ure criteria was used since it predicts failure best in a mixed stressfield and stress interaction is considered. In a complex structurewith pressure loads from any arbitrary direction we felt that thiscriterion would be able to predict the failure.

In Section 5 we mention the failure of elements in the FiniteElement model. In ANSYS the element is deactivated but not com-pletely removed. It contributes a near-zero stiffness. The elementstiffness is multiplied by a factor of 1e�6 and hence is reducedto near zero. Also, the element loads, associated with deactivatedelements, are zeroed out of the load vector. Also, their mass and

Fig. 5. Maximum von Mises stresses vs. Building orientation for all cases (Tornado translational speeds are mentioned near markers).

N. Kumar et al. / Engineering Structures 39 (2012) 79–88 83

energy are set to zero. The element strain is also set to zero at theelements failure. These steps ensure that the elements do not con-tribute to the overall response of the structure.

4. Test procedure

Two major types of tests were conducted on the building mod-els. The first test was done without any failure condition imposedon the building and the second with a sub-routine having specificfailure criteria for every part of the building. Three different modelbuildings were tested namely the one-story gable roof with 13.4�,25.5�, and 35.1� roof angles. The experimental analysis was firstperformed on the 35.1� gable roof for all vane angles (refer to Table1). The results from this case clearly showed higher loads occurringfor Vane 1, which corresponds to the tornado with smaller coreradius. So the experiments for all the other different building mod-els were tested with smaller core radius (Vane 1). This scheme wasfollowed for the numerical analysis too. The 35.1� model wastested with three vane angles (vane angle 15�, 35�, and 55�) whilethe 13.4� gable and 25.5� gable roof buildings were tested with thesmallest vane angle available (vane 1, 15� vane angle).

Each of the three building models at each orientation and vaneangle were tested twice, one with slower moving tornado and witha faster moving tornado.

5. Results and discussion

Initially, the tests were run without including any failure crite-ria for any of the three element types – The 2 � 4 s, the nail ele-ments or the plywood shell surrounding the framework. This wasdone to study the changes in the stress distribution pattern onthe buildings. The peak stress encountered on all thirty cases isplotted in Fig. 5. The plot shows the maximum von Mises stressas the tornado approaches the building at different angles fromthe building centerline.

It is observed that all the buildings that experience tornadoforces with smaller vane angles, Vane 1 (S = 0.08) have higher peakstresses as compared to those that experience tornado forces withhigher vane angles, Vane 3 (S = 0.24) and Vane 5 (S = 1.14). Whilecomparing between the three buildings (13.4�, 25.5�, and 35.1�gable) tested under same vane angle, Vane 1 (S = 0.08), the peak

stresses encountered by the 25.5� gable roof in all cases is the max-imum. Also, the peak stresses for the 13.4� gable roof building ismore than what was experienced by the 35.1� gable roof in allcases except for the 90� orientation with a 15.0 m/s tornado trans-lational speed.

A graph of the location of the tornado with respect to the centerof the building when the maximum stress occurs is plotted inFig. 6. A negative x/D refers to the state when the tornado is in frontof the building and a positive value refers to the state when the tor-nado has crossed the center of the building.

This clearly shows that in almost all the cases, the peak stresson the building is felt only after the center of the tornado crossesthe center of the building, i.e. x/D is greater than zero. Althoughx/D is around 0.3 on an average for slower moving tornados, thisphenomenon is felt even more for faster moving ones. Here theaverage x/D value where the building undergoes maximum stressis around 1.4. A possible cause for the peak stress to occur afterthe center of the tornado has cleared the center of the building isgiven in Haan et al. [15] that a fast moving tornado has the lowerportion of the vortex lagging behind the upper portion. The fastermoving vortex exhibits a greater x-direction shift compared tothe slower moving vortex. A set of 30 composite movies were cre-ated (one for each case) showing the stress distribution pattern asthe tornado moves past the building. It is not possible to reproduceall the results due to space limitations. Fig. 7 shows one of suchcases for 13.1� gable roof with 15� vane angle, depicting level ofpeak stress distribution. From, a careful study of various cases itcan be inferred that the maximum stresses occur on the sides, atthe junctions where the roof meets the walls (eaves) and at thetop (ridge), where the two halves of the roofs meet. There is alsohigh stress concentration about half way between the roof edgeand the roof center which is at 1/4th the total length of the roof.When comparing between 13.4�, 25.5� and 35.1�, there is lesserstress on the ridge of the roof for higher roof angles. Anothernoticeable difference is that the stresses halfway between theeaves and the ridge decrease with the increase in roof angle. Also,as the roof angle increases, the gable area increases and the stres-ses there become more prominent.

We recorded the number of elements and the sequence inwhich they are deleted, as the tornado moves past the buildingfor each load step. It should be emphasized that an element is a

Fig. 6. Location of tornado with respect to building vs. test case.

Fig. 7. Snapshot of two cases 13.4� gable roof with 15� vane angle (S = 0.08) showing stage of peak stress (red arrow) distribution. (For interpretation of the references to colorin this figure legend, the reader is referred to the web version of this article.)

84 N. Kumar et al. / Engineering Structures 39 (2012) 79–88

mathematical entity and a structural component can have manyelements. Hence the failure of an element does not mean thatthe entire structure has failed. As an example, if an element ofthe roof panel fails, the panel may not have completely failed. Onthe other hand when the nail element fails we can safely concludethat the nail pullout was complete and denotes a complete failure.The total number of elements deleted vs. x/D for the five cases(13.4� gable roof with 15� Vane angle, 25.5� gable roof with 15�Vane angle, 35.1� gable roof with 15� Vane angle, 35.1� gable roofwith 35� Vane angle, and 13.4� gable roof with 55� Vane angle)were computed. Fig. 8 shows the results for total number of failedelements vs. x/D for 13.4� gable roof, 15� vane angle. Similar plotswere obtained for other cases and are shown in Figs. 9–12.

There are totally anywhere from 14,000 to 32,000 elements inthe whole building depending on the building type (13.4�, 25.5�or 35.1� gable). This includes all the three element types (2 � 4,nail and Shell). From the analysis of the type shown in Fig. 8, themaximum number of elements deleted is around 6000 and anaverage of 3000 for every run. This is a considerable amount ofdamage and makes up of about 10% of the total building areaand it will not be computationally accurate to continue using thesame pressure data for the damaged structure. Comparison of the

results shows that failure starts early on for cases which haveslower tornado translational speed (TS = 15.0 m/s) than for caseswith higher tornado translational speed (TS = 69.0 m/s). It is alsoobserved that for the slower moving tornados, the damage initiatesat an x/D value of �4.934 for the 13.4� gable roof, �5.086 for the25.5� gable roof and �5.543 for the 35.1� gable roof respectively.This shows that for a higher roof angle, the damage to the roofstarts much early on when the tornado is further away from thecenter of the building. We also observe that for faster moving tor-nados the damage initiates at an x/D value of �3.695 for the 13.4�gable roof, �3.847 for the 25.5� gable roof and �5.543 for the 35.1�gable roof respectively. Comparing the same three figures, thereseems to be a clear gap in-between the sets of slower and fastermoving tornados of around 1.0 x/D. But when comparing the samebuilding model (35.1� gable roof) with 3 different vane angles as inFigs. 10–12, the damage starts to rise at about the same x/D value.Also as mentioned earlier, the damage initiates closer to the centerof the building for higher vane angles.

The analysis of failed elements and their removal at each stepgives a visual presentation of the progress of failure. This inessence shows the sequential damage as the tornado goes pastthe building. An example of such a sequence is shown in Fig. 13

Fig. 8. Total number of failed elements vs. x/D for 13.1� gable roof, 15� vane angle.

Fig. 9. Total number of failed elements vs. x/D for 25� gable roof, 15� vane angle.

Fig. 10. Total number of failed elements vs. x/D for 35.1� gable roof, 15� vane angle.

N. Kumar et al. / Engineering Structures 39 (2012) 79–88 85

Fig. 11. Total number of failed elements vs. x/D for 35.1� gable roof, 35� vane angle.

90°90°

45°

45°

0°0°

Fig. 12. Total number of failed elements vs. x/D for 35.1� gable roof, 55� vane angle.

86 N. Kumar et al. / Engineering Structures 39 (2012) 79–88

where the test was run for a 35.1� gable roofed building andtornado approaching at 0� orientation with a translational speedof 15.0 m/s, and a swirl ratio 0.24.

Each frame in these four figures shows the elements that havefailed till that load step. A detailed analysis of various test casesshows that for most cases, the 2 � 4 joints at the four corners failvery early. Secondly, the plywood at the edges fails almost simul-taneously. Lastly, the front and rear of the wall starts to disinte-grate which happens as the rest of the roof fails. This last effect,which is the breaking up of the front and rear walls starting atthe apex of the gable is mainly noticeable for the 35.1� gable roofbuilding but not for the 13.4� or 25.5� gable roof building.

For each of the run cases with the failure criteria, details of thedeactivated elements, element types, their location and load-stepwhen it fails, were collected. From these one can determine thenumber of failed elements in each element type and the respectiveorder of failure. We have plotted the numbers of elements deacti-vated with respect to x/D for the three gable roofs, with the tor-nado approaching from the three angles of 0�, 45� and 90� andwith various speeds. Fig. 14 shows the Failure sequence of variouselements for a 35� gable roof for a tornado of swirl ratio 0.24

approaching at an angle of 90� at 0.8 m/s and 3.2 m/s. Observe thatin this case the 2 � 4’s fail first and then the nails start pulling outand very soon the roof elements start failing. Two major featureswhich are observed are: (1) the slowly approaching tornado causesmore damage and (2) the failure of roof elements dominate.

Fig. 15 presents the failure sequence of various elements for a35� gable roof for a tornado of swirl ratio 0.08 approaching at an an-gle of 0� at 1.0 m/s and 4.5 m/s. Again, we observe that the slowertornado causes more damage and even though initially more2 � 4’s had failed, the roof elements failure increases very soon. Atotal of 30 runs of similar tests were thus collected and the resultsplotted. Interested reader is referred to Kumar [19], for a completecompendium of results. The salient features of these tests are as fol-lows. Slower tornados always cause more damage than the fasterones. It is observed that the 2 � 4 s and the roof elements start fail-ing within a few time steps for the majority of the cases. They areclosely followed by the failure initiation of the nail elements. Insome cases the roof elements failed first but the beam elementsstart failing immediately in the next step. There is no specific trendobserved on the sequence of occurrence of the 2 � 4 or beam ele-ment at the start of the failure. Based on these results it can be said

Fig. 13. Snapshot of elements deleted (or failed) for example case no: 49 at (a) x/D = �4.76; 47 elements deleted, (b) at x/D = �4.608; 181 elements deleted, (c) x/D = -4.456;383, and (d) at x/D = �4.152. 861 elements deleted, isometric and top view.

Fig. 14. Number of elements failed vs. x/D, 35� Gable, 15� Vane angle (S = 0.08), 0� orientation and forward speed (a) 1.0 m/s and (b) 4.5 m/s.

Fig. 15. Number of elements failed vs. x/D, 35� Gable, 35� Vane angle(S = 0.24), 90� orientation and forward speed (a) 0.8 m/s and (b) 3.2 m/s.

N. Kumar et al. / Engineering Structures 39 (2012) 79–88 87

that irrespective of which element fails first, eventually the mostfailure occurs in the roof elements.

6. Conclusions

Full-scale numerical Finite Element models of gable roof build-ings with three different roof angles (13.4�, 25.5� and 35.1�) were

developed. The tornado induced wind loads recorded by the exper-imental procedure were applied on the model and the resultingstress distribution was studied. Also a routine in ANSYS wasdeveloped to incorporate a failure criterion for the building mod-els. The damage sequence and damage intensity have been studiedto estimate the debris formation. The following conclusions weremade from the results:

88 N. Kumar et al. / Engineering Structures 39 (2012) 79–88

� Buildings that experience tornado forces with smaller swirl ratio(0.08) have higher peak stresses than those that experiencetornado forces with higher swirl ratio (0.24, 1.14).� The peak stresses encountered by the 25.5� gable roof in all

cases is the maximum. This is more than the 13.4� gable roof,which is more than what is encountered by the 35.1� gable roof.� Maximum stresses occur on the sides, at the junctions where

the roof meets the walls (eaves) and at the top (ridge), wherethe two halves of the roofs meet.� There is also high stress concentration about half way between

the roof edge and the roof center (ridge) which is at 1/4th thetotal length of the roof. This high stress decreases with increasein roof angle.� As the roof angle increases, the gable area increases and the

pressure on the roof increase. This results in an increase instresses.� Failure starts early on for cases which have slower tornado

translational speed (TS = 15.0 m/s) than for cases with highertornado translational speed (TS = 69.0 m/s).� For a higher roof angle, the damage to the roof starts much early

on even when the tornado is further away from the center of thebuilding.� From the composite movies, it is generally noticed that for most

cases, the 2 � 4 joints at the four corners (vertical corners) failvery early.� Once the 2 � 4s fail, the plywood at the edges fails almost

simultaneously.� Lastly, the front and rear of the wall starts to disintegrate which

happens as the rest of the roof fails.

The breaking up of the front and rear walls starting at the apexof the gable is mainly noticeable for the 35.1� gable roof buildingbut not for the 13.4� or 25.5� gable roof building.

The conclusions listed above are applicable to a particularbuilding shape and hence should not be taken as general guidelinesfor any building type.

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