Engineering Structures 31 (2009) 2607–2616

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Engineering Structures

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Statistical and analytical models for roof components in existing light-framedwood structuresBagyalakshmi Shanmugam a, Bryant G. Nielson a,∗, David O. Prevatt b,1a Department of Civil Engineering, Clemson University, Clemson, SC 29634-0911, United Statesb Department of Civil and Coastal Engineering, University of Florida, Gainesville, FL, 32611-6580, United States

a r t i c l e i n f o

Article history:Received 29 September 2008Received in revised form10 June 2009Accepted 10 June 2009Available online 27 June 2009

Keywords:Light frame wood constructionRoof-to-wall toenail connectionPlank sheathingUplift capacityStatistical modelAnalytical model

a b s t r a c t

Residential wood-framed construction failures account for the majority of economic losses followinghurricanes. A common failure in these constructions during high wind events is loss of roof sheathing,especially in corner areas. Less common perhaps, but usually catastrophic, is the failure of the roof-to-wallconnections in these structures. Themain objective of the current researchproject is to evaluate the in-situcapacity of roof-to-wall connections and sheathing to rafter fasteners in light-framedwood constructions.The unique opportunity provided by Clemson University to access four residential structures locatedwithin a residential complex enabled the collection of perishable yet statistically significant data on thestrengths of existing residential structures. The uplift capacities of 100 roof-to-wall toenail connectionsand 34 plank sheathing units were evaluated from field and laboratory tests. Realizing the key role ofprobability distributions in developing fragility estimates and loss prediction models, distribution fitsand parameters for these structural components are postulated. One conclusion drawn is that the upliftcapacities of two and three nail connections are best described by a lognormal distribution. The initialstiffness and the vertical displacement at peak load of both two nail and three nail connections follow anormal and Weibull distribution respectively. The uplift capacity of plank sheathing follows a lognormaldistribution. An analytical model designed to approximate the uplift behavior of toenail connections isdeveloped to facilitate modeling of roof systems. These probabilistic and analytical models developedby this study allow for the performance of detailed reliability based studies on light-framed wood roofstructures.

© 2009 Elsevier Ltd. All rights reserved.

1. Introduction

The tremendous devastation caused by hurricanes mark themas one of the most significant natural hazards affecting the UnitedStates. The recent increase in the occurrence of hurricanes [1]and the continuing growth of construction activities along theshorelines has further increased the potential of hurricanedamage [2]. The losses suffered by the insurance companies andgovernments and also the hardships faced by the general publichave promoted research initiatives to focus on damage mitigationand loss prediction.One significant area of research is looking at performance and

damage mitigation of low-rise wood structures. Low–rise woodframed structures comprise the majority of residential structures(90%) andhave shownappreciable vulnerability to highwind loads.

∗ Corresponding address: Department of Civil Engineering, Clemson University,Lowry Hall, Clemson, SC 29634-0911, United States. Tel.: +1 864 656 3312.E-mail addresses: sshanmu@clemson.edu (B. Shanmugam),

bryant.nielson@ces.clemson.edu (B.G. Nielson), dprev@ce.ufl.edu (D.O. Prevatt).1 Tel.: +1 352 392 9357.

0141-0296/$ – see front matter© 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2009.06.009

For any structure to performwell, wind forces must be transferredfrom the roof and walls to the foundations through a completeand continuous vertical load path. Any discontinuity in this loadpath affects structural performance and subsequently reducesresistance to wind forces. Furthermore, load path discontinuitiesmay result in damage propagation to other structural componentsand increase the likelihood of complete failure of the structuralsystem.Two structural components within this vertical load path,

which demonstrate substantial vulnerabilities to extreme winds,are the roof sheathing to truss/rafter and roof-to-wall connections.According to the US Census Bureau [3], the vast majority ofresidential structures (over 80%) in U.S. hurricane-prone regionswere built before 1994 — the year building codes were upgradeddue to Hurricane Andrew. The failures of pre-1994 structureswere most often a result of an insufficient number of nails (nailschedule) in roof-to-wall and sheathing-to-rafter connections,resulting from inadequate or unenforced building codes at the timeof construction. While these types of connection are simple toinstall they were never designed to resist significant uplift loads.As a result, these connections fail at relatively low wind speedsresulting in brittle failure of the structure. Over 90% of the existing

2608 B. Shanmugam et al. / Engineering Structures 31 (2009) 2607–2616

Fig. 1. Douthit Hills duplex residential structure.

inventory of light wood frame houses utilized these connections.Therefore, much effort has been devoted to understanding theuplift performance of these components, to quantify infrastructurevulnerability [4–6] and to develop mitigation solutions.Numerous studies have been undertaken to understand the

uplift behavior of toe nailed connections [7–9] and to investigatevarious retrofit strategies using both commercial metal connectorsand adhesives [8–11]. Cost comparisons of various rafter tieinstallations indicated that the additional cost incurred by usingmetal connectors is negligible compared to the total cost of thestructure [9]. This resulted in a noteworthy conclusion stating thattoenail connections should not be permitted in hurricane proneregions [7].Recognizing that the apparent behavior of these connections

can be influenced by other elements in the framed structure,Reed et al. [8] also conducted laboratory experiments on systemsof connections. Even though the number of connections whichcould be tested was limited (less than 20), some basic statisticalestimators (i.e. mean and variance) of the uplift capacity wereobtained along with an estimate of an appropriate probabilitydistribution — Normal [12]. This type of information becomesessential for conducting vulnerability [4,13] and loss estimation [5]studies.The loss of roof sheathing during a high-wind event expo-

nentially increases building damage as it readily permits waterintrusion causing extensive damage to walls and interior con-tents [14]. Numerous experimental studies on uplift capacities forroof sheathing have been carried out. One such parametric study,estimated the uplift capacity of plywood sheathing for differenttypes and spacing of nail fasteners [15]. Additionally, a functionalrelationship between individual fastener capacities and sheathingcapacities has been proposed [16]. Past studies revealed that a sin-gle nail failure often resulted in progressive failure (i.e. completeloss) of entire pieces of roof sheathing and the uplift capacity canbe conveniently described using a normal distribution [16,17]. In-service conditions also had a significant influence on the capac-ity [18].The estimated probability models for roof component behav-

iors obtained by others [12,16] have been utilized to develop lossprediction models and fragility estimates for roof-to-wall con-nections and roof sheathings. However the laboratory conditionsunder which roof specimens are fabricated and tested can be ama-jor source of uncertainty. This is because lab conditions fail to ac-count for the variability due to actual construction practices whichmay significantly influence the resulting statistical parameters andprobability distributions.The current study seeks to add to the existing knowledge

base on the performance of existing low-rise light framed woodstructures exposed to high winds. Considering that there is alarge portion of the existing inventory that has details similar to

those contained in this study, the findings here will be relevantfor evaluating risk and the need to retrofit. Furthermore, thisperformance data can be used to design appropriate retrofitschemes if and when necessary. To this end, this study looks toaccount for and quantify the variability in the structural behaviorof two key components, namely the roof-to-wall connection androof sheathing, in their as-built condition. A significant numberof actual component specimens were made available for testingdue to the scheduled demolition of four residential structureslocated on the campus of Clemson University. One hundred as-built roof-to-wall toenail connections were tested to determinein-situ uplift capacities and find a general connection behavior(i.e. force–displacement). Additionally, 34 as-built roof panelsconstructed with solid wood plank sheathing were harvested andtested for uplift capacity. Relevant probabilitymodels are proposedusing these relatively large data sets. An analytical model for roof-to-wall toenail connections is also developed and presented tobetter facilitate the modeling and vulnerability assessment of roofsystems exposed to high winds.

2. Experimental study

The experimental tests were carried out on roof componentsfound in four identical houses located in the Douthit Hillsresidential community on the campus of Clemson University,Clemson, South Carolina, USA. The houses are typical residentialwooden structures constructed 50–60 years ago. These gableroofed duplex houses, scheduled for demolition, offered anexcellent opportunity to study the in-situ uplift capacity of anappreciable number of toe nail connections and also to collect roofpanel specimens for testing the uplift capacity of sheathing in thelaboratory. Fig. 1 shows a photo of one of the four houses havingplan dimensions of 8.23 m (27 ft) wide by 20.73 m (68 ft) long. Theroof frames were stick built using dimensional lumber and weremade up of 38 × 140 mm (nominal 2 × 6 in.) or 38 × 89 mm(nominal 2 × 4 in.) horizontal ceiling joists and 38 × 140 mm(nominal 2 × 6) rafters. A layout of the structure and the roofframing is given in Fig. 2. Framing members are spaced at 0.41m(16 in.) on the center and every fourth rafter was reinforced usinga collar tie. The rafters were placed at a 6:12 pitch and attached attheir lower ends to the side of the ceiling joist by means of three3.3 mm (0.131 in.) diameter, 63.5 mm (2.5 in.) long smooth shank8-d common nails. The ceiling joist was attached to the wall topplate using either two or three 4.1mm (0.161 in.) diameter, 89mm(3 12 in) long smooth shank 16-d common nails as illustrated inFig. 3. The roof sheathing was made up of solid wooden planksof 19 mm thick by 140 mm wide (nominal 1 × 6 in.). Each plankwas fastened using two 3.3 mm (0.131 in.) diameter, 63.5 mm (2.5in.) long smooth shank 8-d common nails to each rafter. Asphaltshingles covered the sheathing planks and the building exteriorwas covered with brick veneer and vinyl siding. Visual inspection

B. Shanmugam et al. / Engineering Structures 31 (2009) 2607–2616 2609

Fig. 2. Typical roof framing plan of structure.

Fig. 3. Roof-to-wall connection detail.

of the framing members revealed the wood type to be SouthernYellow Pine (SYP).

2.1. Roof-to-top plate toenail connections

2.1.1. Experimental set upPrevious studies carried out cyclic or monotonic uplift tests

on either full scale or reduced scale roof-to-top plate connectionsmodeled in the laboratory. Seldom were uplift tests carried outon in-situ roof to wall toenail connections. Even when conducted,in-situ tests did not control load rate or load sequence anddisplacements were not monitored. One must further recognizethat when tested in a group, the behavior of in-situ connections issignificantly influenced by the load redistribution and sharing bythe neighboring connections. Also the redundancy of the roofingsystem allows for stiffer connections to take higher loads thanweaker connections. Indeed three to four connections on eitherside of a given connection can participate in load sharingwhere thepercentage of load shared is inversely proportional to the distancefrom the connection considered and directly proportional to thestiffness of the connections themselves [19,20]. In the currentstudy, the load redistribution effect on the perceived capacityof an individual connection is acknowledged by carrying outuplift tests on systems of four roof-to-top plate (ceiling joist towall top plate) toenail connections. Furthermore, cyclic loadingwas applied in order to capture the hysteretic behavior of theconnection at relatively low levels of deformation and thereby

Fig. 4. Experimental setup for uplift tests.

enable quantification of energy dissipation by the connectionunder an extreme wind load event. This result can be used todevelop analytical models which mimic the behavior of toenailconnections.The weak link in the vertical load path of these structures is

considered to be the ceiling joist to top plate connection (not rafterto joist). This is because of the framing scheme used in the givenstructures. The detail, as presented in Fig. 3, shows that three 8-dnails fasten the rafter to ceiling joist and act in single shear whilethe toenail connections that attach the ceiling joist to top plate actin withdrawal. Hence the ceiling joist to top plate connection isconsidered to be the weak link and also represents typical toenailconnections in other structures.The test set up has two automated screw jacks mounted on

a reaction frame. The jacks carry a spreader beam which appliesequal deflection on a system of four connections as shown inFig. 4. Load cells attached to the top flange of the spreaderbeam both transfer and measure the load going to each joist.The number of connections to be tested in a given system waslimited by the capacities of the screw jacks and the size of thereaction frame. In order to exercise control over the influencefrom other structural, as well as non-structural components,the system of four connections was segmented from the otherstructural components and crossing members. The whole systemwas allowed to act as a unit by applying cyclic displacements viathe spreader beam.

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(a) 2-16d nails. (b) 3-16d nails.

Fig. 5. Typical response of connections failing due to (a) Nail withdrawal (b) Combination.

2.1.2. Data acquisitionComputer controlled data acquisition devices were used to

collect data from the four load cells and four LVDT’s. The load cellsare compression/tension capable and have a capacity of 22.2 kN (5kips) each. The LVDT’s have a stroke length of +50.8 mm (2 in.)and a spring return armature for easy installation. The screw jacks,driven by micro stepping motors, each have a capacity of 22.2 kN(5 kips) giving a total load capability of 45 kN (10 kips).

2.1.3. Experimental test procedureASTM-D1761 [21] protocol was used as the testing guideline for

this study. ASTMD1761 presents amethodology for evaluating thedirect withdrawal resistance of individual mechanical fastenersunder monotonic loads. However, only limited guidance isprovided to conduct tests on systems of connections for cyclicloading. In the absence of complete guidance, only the rate ofwithdrawal from monotonic loading test was adopted for thecurrent study.Cyclic deflections corresponding to 1.6, 3.2 and 4.8mm (0.0625,

0.125, 0.1875 in.) were applied to the test segment via thespreader beam, at a recommended fastener withdrawal rateof 2.54 mm/min (0.10 in./min) ± 25%, per ASTM-D1761. Thisdisplacement sequence was selected so as to adequately capturethe hysteretic behavior of the connection in the range of lowto moderate forces. One may expect that a roof connection mayreasonably see uplift loads that are above the expected serviceloads but below the extreme loads multiple times during itslifetime. Therefore, an understanding of the cyclic behavior in thisrange is desired.Once the 4.8 mm (0.1875 in.) deflection cycle was completed,

the load was increased at a constant rate until failure (i.e. loadpeaked out). The dead load on each set of connections wasestimated based on the recorded load after complete separationof the ceiling joist and top plate occurred. The dead load is theself-weight of the ceiling joist, crossing members and framingsystem. The uplift capacity of each connection is taken as themaximum measured load at each joint minus this dead load. Asthe applied load and measurement locations were not concentricto the connection considered, adjustments were made to accountfor the actual placements of LVDTs and load cells.

2.1.4. ResultsTwenty five specimens representing a total of 100 individual

roof-to-wall connections were tested for the current study. Outof the 100 connections, 81 were constructed using two 16d nailsand the remaining 19 used three 16d nails. Three different failuremechanisms were observed which are (1) failure due to nailwithdrawal from the wall top plate (2) failure due to splitting ofwood in the ceiling joist and (3) combination failure —withdrawalof one nail concurrent with the splitting of wood due to pull-through of the other nail. The latter two failure mechanisms areconsidered as brittlemodes of failure even though there is an initial

yielding of nails. This is because failure of the connection occursmainly due to the splitting of wood which is brittle in nature.However nail withdrawal involves yielding of a nail followed bypure withdrawal which exhibits a more ductile behavior.Fig. 5a shows the typical load–displacement curve of a two

nail connection that failed due to pure nail withdrawal. The initialresponse of the connection is characterized by hysteretic behaviorcapturing the yielding of nails and then followed by gradual offloading as the nails withdraw. Fig. 5b shows the typical responseof a three nail connection that experienced a combined modeof failure. The significant difference between the two behaviorsis that the combined failure is characterized by load stepping inthe load-displacement curve in the post ultimate load region. Thesudden drop in load is due to the brittle nature of splitting wood. Arepresentation of the withdrawal and combination failure modesis given in Fig. 6.The test data shows that 81% of the connections failed due to

nail withdrawal, 16% due to the combined failure mechanism andthe remaining 3% due to complete splitting of wood. The statisticsclearly indicate that pure nail withdrawal is the dominant modeof failure for aged in-situ construction. However, the capacities forconnections failing in one of the latter two failure modes indicatethat theymay bemore preferred because of their higher capacities.Because the dominant failuremodemay also be the least desirable,retrofitting the connections withmetal straps is often employed tocompensate.In addition to the nail embedment length, the withdrawal

capacity of the nail is a function of the angle of the nail, type andgrade of lumber and the moisture content. In order to account forthe effect of moisture on the capacity, the in-situ moisture contentof each connection was estimated using a two prong moisturemeter. After adjustments for type of lumber, the average moisturecontent was found to be 8.5% with a standard deviation of 0.63%.The estimate of the correlation between the moisture content andultimate uplift capacity was also examined and found to be 0.11.This indicated that over the range of moisture contents recorded(7.5%–9.5%), these two parameters were only slightly correlatedandhence can reasonably be ignored for reliability studies inwhichthese connections are involved.

2.1.4.1. Uplift capacity. Uplift capacity is the maximum loadsustained by the connection minus the dead load and is definedas the ultimate strength of the connection (Fult). The average upliftcapacity of the two nail connections in this study is 1.51 kN (341lbs) with a coefficient of variation (COV) of 0.36. The three nailconnections have, on average, a 30% larger uplift capacity thantheir two nail counterpart with a mean of 1.97 kN (442 lbs) and aCOV of 0.38. This is an interesting result in that one would havesuspected approximately a 50% increase in capacity since therewas a 50% increase in nail embedment length. One possibility forthis discrepancy is that with the two nail connection, the nails are

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Table 1Comparative table of uplift capacities of roof-to-wall connections.

Type of connection No. of specimen Average Ultimate capacity kN (lbs) COV Study

Toenail (SP)(a) 2-16d 81 1.51 (341) 0.36 Present study(b) 3-16d 19 1.97 (442) 0.38Toenail 2-16d box nail(a) Spruce Pine Fir (SPF) 16 1.56 (350) 0.164

[7](b) Douglas Fir (DF) 14 2.59 (584) 0.212(c) Southern Yellow Pine (SP) 14 2.69 (605) 0.155Toenail 3 -8d nail (SP/SPF)(a) Single 16 1.92 (430) 0.23 [8](b) Repetitive (System of 7 connections) 2 2.99 (670) naa

a Not available due to small sample size.

a b

Fig. 6. Failures by (a) nail withdrawal (b) wood split.

Fig. 7. Suspected failure mechanism of two and three nail connections.

driven at opposing angles, one on each side of the ceiling joist,and both must yield for the nails to withdraw. However, in thethree nail connection, two nails angle in from one side while thethird nail is driven at an opposing angle from the other side. Thisimbalance in the resistance causes the single nail to yield beforethe double nails. A small lateral shift occurs in the connection asone nail yields and the other two primarily avoid yielding whileonly experiencing direct withdrawal. Fig. 7 pictorially describesthis phenomenon.The wind pressure that could be safely withstood by the

connections is evaluated from the uplift capacities. This turned out

be 1.05 kPa (22 psf) for two nail connections and 1.34 kPa (28psf) for three nail connections. Generally a factor of safety (FOS)from 2 to 5 [7,8,22] is used to estimate the design capacity of theconnections. After applying a FOS of 2 the ultimate capacity ofconnection obtained in terms of pressurewas 0.53 kPa (11 psf) and0.67 kPa (14 psf) for two and three nail connections respectively.Although this does not account for the help given by the dead load,this is considerably lower than the wind pressures that would acton roofs at times of wind storms. Therefore it is clear that toenailconnections are not structurally safe against extreme wind loadsthat occur in hurricane prone regions.Table 1 presents the uplift capacity statistics for the two types

of toenail connection considered in this study and compares themwith the findings from previous research studies. These studiesapplied monotonic uplift loading on roof-to-wall connectionsas opposed to the cyclic loading applied in the current study.The comparison table presented herein assumes that there is nostrength degradation in the present case due to repetitive loading.The results from several other studies [10,23] are not presentedfor comparison as their complete statistics and sample sizes areunknown. The uplift capacity of in-situ connections was found tobe less than the uplift capacity of lab-tested toenail connections.The lower failure capacities observed in this study may be due tothe deterioration in the joint strength with age as the connectionsunder consideration were constructed 50–60 years before. Thedeterioration may be due to a decline in the wood quality, woodshrinkage or joint fatigue. Cyclic loading may also be a possiblecause for the reduced capacity. The most notable change observedfor the in-situ condition is the appreciable increase in the COVof the capacity. The larger mean values and smaller COVs forthe laboratory tests are likely due to the controlled manner in

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which the test specimenswere constructed. In-situ as-built testinghas the ability to capture the variability in connection behaviordue to actual construction practices. As seen in Table 1, the COVestimates resulting from laboratory tests can underestimate actualCOVs by as much as 50%. Failure to capture this uncertainty maysignificantly affect the reliability assessment of these connectionsunder wind loads. Sensitivity analyses may help to quantify theeffect of this increased COV on reliability assessments.The type of failure mechanism generally has a considerable

influence on the capacity of the connection. But due to insufficientnumber of samples in two of the failure mechanisms from thepresent study, statistically significant inferences cannot be madefrom the estimates. However, the mean estimate is providedherein for the sake of comparison. The results are for the twonail connections. Out of 81 two nail connections, 65 failed due tonail withdrawal, 3 due to wood split and 13 connections failedin a combined failure mode. The mean ultimate uplift capacity ofthe two nail connections is 1.43 kN (322 lbs), 2.26 kN (508 lbs)and 1.76 kN (395 lbs) for withdrawal, wood split and combinedfailure modes respectively. The above statistics represent anaverage increase in connection capacities of 25% to 55% over purewithdrawal, which reinforces the assertion that wood splitting,while more brittle, appears to be a preferred mode of failure.

2.1.4.2. Stiffness. Knowledge of the relative initial stiffness (ko)of the roof-to-wall connection is critical in understanding cyclicbehavior and in developing analytical models. Studies to estimatethe stiffness of toenail connections have seldom been carried outin the past. As such, one significant contribution of this study is theexplicit treatment of connection stiffness. Due to the nonlinearityof the connection behavior the secant stiffness is taken as arepresentative initial stiffness. Three displacement values wereconsidered as candidates for calculation of the secant stiffness —0.254 mm, 1.6 mm, 3.2 mm (0.01, 0.0625, 0.125 in.). The estimateof secant stiffness using the deflection at 0.254 mm was found tobe an unreasonable indicator because it is very sensitive to minorfluctuations in the recorded data. As such, this estimate is unstableand a poor indicator of generalized behavior. The secant stiffnessat 3.2 mm was also found to be misleading, as the response ofthe connection is mostly non-linear at this level. Hence, the secantstiffness taken at a 1.6mmdisplacement is assumed to be themostappropriate because of the numerical stability of the load at thisdisplacement and the overall response linearity.The average secant stiffness of the two nail connections is 0.37

kN/mm (2126 lbs/in.) with a COV of 0.36. The three nail connectionhas an average stiffness of 0.47 kN/mm (2696 lbs/in.) with a COV of0.42. The average stiffness of three nail connections is 27% greaterthan their two nail counterpart. The higher COV for 3-16d nails incomparison to 2-16d nails may be due to a smaller sample size.In order to check the influence of the failure mechanism on thestiffness of the connection, an estimate on the average stiffnessfor each failure mode is obtained. The average stiffness of the twonail connections that failed due to withdrawal was found to be0.360 kN/mm (2055 lbs/in.), for those which failed due to splittingit was 0.492 kN/mm (2807 lbs/in.) and for those connections thatfailed in a combined mode it was 0.407 kN/mm (2329 lbs/in.).Since only three connections failed due to splitting of the wood,themean stiffness reported herein is only for comparison purposesand no statistical inference ismade. One is able to observe the samerelationship between stiffness and failure mechanism as was seenbetween uplift capacity and failure mechanism.

2.1.4.3. Displacement at peak load. In an effort to help describethe non-linear behavior of roof-to-wall toenail connections, thevertical displacement coinciding with ultimate uplift capacity istracked (δPL). For the two nail connection the mean displacement

is found to be 11.2 mm (0.44 in.) with a COV of 0.54. The three nailconnection gives mean and COV values of 11.9 mm (0.47 in.) and0.51 respectively. One readily made observation is that the COVvalues for this parameter are much higher than for the stiffnessand capacity. The displacement value at which peak load occursshould be sensitive to the angle at which the nails are driveninto the connection. Considering that the tested connections areconstructed in the field under real circumstances (i.e. not havinglab type control), one would indeed expect that a great deal ofvariability exists.

2.2. Plank sheathing roof panels

Even though current construction practices include the useof plywood or OSB panels as the roof sheathing, there is still alarge inventory of existing buildings that have been constructedwith plank sheathing. Quantification of the uplift capacity ofplank sheathings in existing structures will facilitate developingappropriate retrofits, if necessary, that would protect them fromhigh wind loads. The present study aims to identify the upliftcapacity of plank sheathing and compares it with the upliftcapacity of plywood/OSB sheathing. The influence of failuremodesand nailing patterns is discussed.

2.2.1. Experimental setupCyclic testing of roof sheathing is the preferred testing

method as it considers the fatigue loss of uplift strength of roofsheathing. Cyclic pressures corresponding to the actual pressureon roof sheathings are applied while displacements are recorded.Unfortunately, BRERWULF (Building Research Establishment Real-time Uniform Load Follower), a testing apparatus generally usedto test the uplift capacity of roof sheathing under cyclic andmonotonic loadings is only capable of developing pressures up to8.5 kPa (178 psf). A preliminary test of the roof panels indicatedthat panel capacities would likely exceed this limit. Therefore, asuction chamber capable of developing the requisite pressureswasutilized but it was only capable of applying them in a monotonicfashion.The roof panel specimens had dimensions averaging 1295 mm

by 1650mm (51× 65 in.). The size of the specimens was driven bythe size of the suction chamber and also by feasibility of removalfrom the roof. Each panel specimen contained four rafters spacedat 410 mm (16 in.) o.c. Planks which were 19 mm × 140 mm(nominal 1× 6 in.) were attached to the rafters by two 8d smoothshank hand driven nails spaced at 76.2 mm (3 in.). From visualobservation it was noted that the framingmemberswere SouthernYellow Pine (SYP). The specimen was placed inside the suctionchamber, sheathing side downwith rafters spanning onto chamberwalls and sealed using plastic sheathing and duct tape (See Fig. 8a).It was ensured that no leakage of air occurred and then a negativepressure was applied uniformly over the entire roof unit. Suctionpressure was applied at a constant rate until failure — definedas the separation of at least one plank. Since failure of a woodenplank was followed by the failure of the entire roof sheathing unit,application of negative pressure was stopped when the failure ofthe first plank was observed. Fig. 8b shows a typical failure of onesuch plank sheathing specimen. Positive pressure acting on roofplank sheathing was not considered for the present study. Usingan electronic acquisition system the pressure inside the suctionchamber is recorded. The uplift capacity of the plank sheathing unitis taken as the maximum pressure withstood by the unit prior tofirst failure.

2.2.2. ResultsA total of 34 plank sheathing units were tested in the suction

chamber under increasing monotonic negative pressure and theaverage uplift capacity was 11.54 kPa (241 psf) with a COV of 0.15.

B. Shanmugam et al. / Engineering Structures 31 (2009) 2607–2616 2613

a b

Fig. 8. (a) Suction test apparatus for uplift test on roof sheathing planks. (b) Typical failure of a sheathing plank unit.

The average uplift pressures needed to pull off plank sheathingis significantly larger (about 11 times) than that required tofail the roof-to-wall connections examined in the present study.This indicates that under an extreme wind event, roof-to-wallconnections in buildings of similar construction are more likely tofail prior to loss of the sheathing. The above failure sequence iscatastrophic because when the roof system is lifted off; walls losetheir lateral support and will subsequently fail. The result from thepresent study is comparedwith the previous results from lab uplifttests on OSB/plywood sheathing.To justify this comparison, one must look at the failure modes

common to both types of sheathing (plank and OSB/plywood).In the present study, failure of plank sheathing was exclusivelydue to pull out of nails from the framing element. OSB/plywoodsheathings from previous studies have shown that failure canoccur from either nail pull out, nail pull through or a combinationthereof [15,16,24–26]. The type of failure was affected by the typeof load (uplift or uplift/lateral), sheathing thickness and nailingschedule. The studies on OSB/plywood showed that themajority ofthe sheathing subjected to uplift failed due to nail pull out. As such,a cursory comparison between the two types is appropriate as theyboth predominantly failed due to nail pull out. In one laboratorytest [17], 30 specimens of oriented strand board (OSB) sheathingpanels – 1.22 m × 2.44 m (4ft × 8 ft) – were constructed andtested using BRERWULF. The OSB sheets were 11.9 mm (15/32in.) thick and were attached to the southern pine framing systemspaced at 0.61 m (24 in.) using 8d nails at a spacing of 152 mm(6 in.). The mean uplift capacity was estimated to be 6.3 kPa (131psf) with a COV of 0.14. Though the results from the above studyare not directly comparable with the present result, it indicatesthat the capacity of OSB sheathing is significantly less than thatof plank sheathings. The mean capacity of plank sheathing fromthe current study is almost double (183%) the estimated capacityof OSB sheathings.Laboratory test of 10 specimens of 1.22 m × 2.44 m (4 ft × 8

ft), 11.9 mm (15/32 in.) thick plywood sheathing attached to aSpruce pine fir framing system spaced at 0.61 m (24 in.) using 8dnails at a spacing of 152 mm (6 in.)/304 mm (12 in.) estimatedthe capacity to be 2.87 kPa (60 psf) with a COV of 0.20 [4,15,16]. The capacity of 4 specimens using 6-d nails, for the samesheathing and framing system as above was estimated to be 1.2kPa (25 psf) with a COV of 0.15. Failure of sheathing in the abovetwo tests were primarily due to nail pull out. In all cases, thecapacity of plank sheathing from the present study was greaterthan the plywood sheathing but the COVs were very comparable.This higher capacity is understandable when one recognizes thattotal number of nails required for attaching plank sheathing isalmost double the number required for panel sheathing.

3. Statistical models

3.1. Roof-to-top plate toenail connections

To make statistical inferences and to carry out reliabilitystudies it is essential to identify appropriate statistical modelsfor describing the connection behavior parameters (i.e. upliftcapacity (Fult), initial stiffness (ko) and vertical displacement atpeak load (δPL)). Goodness-of-fit (GOF) tests are used to ascertainthe most plausible probability distributions that would describethe collected set of observations. The Anderson Darling GOF test,sensitive in the tails of the distribution, is used to check theplausibility of the distribution and the distribution parametersare calculated using the maximum likelihood method. Since a5% level of significance is traditionally used by experimenters,the same is used for the current study. Various distributiontypes including normal, lognormal, extreme value and Weibulldistributions are considered. The GOF tests are evaluated by the p-value where if the value of p is greater than the considered level ofsignificance i.e., 0.05, then the assumed distribution is consideredto be plausible. The larger the p-value, the stronger this statementbecomes.For the two nail connection, uplift capacity is most strongly a

lognormal distribution with a p-value of 0.627. The initial stiffnessis best described by a normal distribution (p-value = 0.454)while the displacement at peak load is only plausibly describedby a 3-parameter Weibull distribution (p-value = 0.085). Forthe three nail connection the distribution fits for uplift capacity,stiffness and peak displacement are taken as for the two nailconnections with respective p-values of 0.346, 0.097 and 0.101. Avisual comparison of theoretical and empirical CDFs (cumulativedistributive function) for the uplift capacity of both the three nailand two nail connections is given in Fig. 9. As expected, largerdeviations between the CDFs appear in the 3 nail connection datathan appear in the 2 nail connection data. This is because of theappreciably smaller sample size for the former. In short, one maysee that the CDFs reinforce the findings of the GOF test and thatthe larger deviations result in lower p-values. Similar trends areseen in Figs. 10 and 11 where the CDFs are given for stiffnessand displacement at peak load respectively. Estimated parametervalues for all selected distributions are presented in Table 2.Since three parameters of connection behavior are being

tracked, a measure of the statistical dependence between thethree is imperative. This measure is given through the correlationcoefficient — a term used for quantifying statistical dependencein many reliability based studies using a tool like the Nataftransformation [27]. The results of this study indicate thatuplift capacity and stiffness are significantly correlated havingcorrelation coefficients of 0.62 and 0.77 (ρFult,ko) for the two

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Fig. 9. Comparison of theoretical and empirical CDFs for uplift capacities.

Fig. 10. Comparison of theoretical and empirical CDFs for initial stiffnesses.

Fig. 11. Comparison of theoretical and empirical CDFs for peak load displacements.

and three nail connections respectively. Correlation coefficientsbetween δPL and the other two parameters tend to be appreciablylower with the following values – 2-nail ρko,δpL = 0.096 andρFult,δpL = 0.393 – 3-nail ρko,δpL = 0.194 and ρFult,δpL = 0.409.This low level of correlation associated with δPL, when consideredin conjunction with the high variability, further illustrates itssensitivity to nail placement.

Table 2Proposed probability distributions for connection behavior parameters.

Connection Type Uplift Capacity (Fult ) kN (lbs)Dist λ ζ

2–16d LN 0.356 0.35(5.771)

3–16d LN 0.613 0.36(6.028)

Initial Stiffness (ko) kN/mm (lbs/in.)Dist µ σ

2–16d N 0.372 0.134(2126) (768)

3–16d N 0.472 0.199(2696) (1138)

Displacement at Peak Load (δPL) mm (in.)Dist k u ε

2–16d aW 1.299 8.52 3.308(0.336) (0.130)

3–16d aW 1.333 8.54 3.988(0.336) (0.157)

a k= shape factor, u= scale factor, ε = threshold.

3.2. Plank sheathing

A-D GOF tests were carried out to estimate the best fit thatdescribes the uplift capacity of the plank sheathing. The twoparameter lognormal distribution having parameter values of λ =2.434 ln (kN/m2) [5.47 ln (lb/ft2)] and ζ = 0.15 is found to bethe most plausible. The associated p-value is 0.284.

4. Analytical model for roof-to-top plate connections

To better facilitate the evaluation of roof system responsesin both design and reliability based studies, an analytical modelapproximating the response of roof-to–wall toenail connectionsis developed. Though there are three failure mechanisms thatdescribe the failure of the toenail connection, the analytical modelpresented herein represents the dominant mode of failure –failure by nail withdrawal. In the past these connections weregenerally modeled as pinned connections having a specified upliftcapacity. This specific assumption fails to simulate the actual non-linear response, hysteretic behavior and subsequent failure of suchconnections when exposed to fluctuating extreme wind loads.Considering that this analytical model is likely to be used in

research based studies the open source finite element package,OpenSees [28], is selected for model development.The connection is modeled using a zero length element in

conjunction with a Pinching4 material. This material modelfacilitates multi-linear behavior with an ability to capture bothstrength and stiffness degradation. Furthermore, this materialprovides for a loss of strength beyond a user specified limit (u3).This feature is important in that it can model the failure of aconnection which is an essential part of roof system modeling.Complete documentation of this material may be found on theOpenSees website [28].The Pinching4 material requires the definition of 28 parame-

ters. These parameters are used to define the backbone and en-suing degradation rules of the material. However, many of thesequantities are set to zero for the proposed model. Fig. 12 presentsa schematic of the model backbone behavior and any nonzero pa-rameters required. This model requires the user to provide threeinputs — ultimate uplift capacity (Fult), initial secant stiffness (ko)and displacement at peak load (δPL). The ultimate displacement(u3) at which all strength is lost is taken to be 40 mm (1.57 in.)which is an approximate displacement value for complete with-drawal of 16d toenails. The only type of cyclic degradation used

B. Shanmugam et al. / Engineering Structures 31 (2009) 2607–2616 2615

Fig. 12. Proposed analytical model using a Pinching4 material for capturing theuplift behavior of a roof-to-wall connection.

in this model is unloading stiffness degradation (all gK — seeOpenSees documentation) taken to be −0.5. The reloading forceratio (rForceP) is taken to be 0.6. Though it is not possible nor war-ranted to simulate exactly the response of a connection, a gener-alized agreement of behavior including initial stiffness, ultimatecapacity and nonlinear action is sought. Fig. 13 gives a compari-son of the experimental and analytical models for a set of four con-nections. Fig. 13a (Connection A21) was previously presented inFig. 5a. The plots indeed demonstrate the ability of the proposedmodel to capture the desired behavior.To further validate the appropriateness of the proposed model,

the energy dissipated by the analytical model, when subjected tothe same displacement sequence as the experiment, is comparedwith experimental results. The errors or differences in theenergy dissipation are given in Fig. 13. Errors for the illustratedconnections range from 6.7% to 0.7% — well within acceptablelimits. One may note that connection A22 (Fig. 13b) exhibits thelargest discrepancy. The high initial stiffness and long plateauregion are some of the suspected reasons for this difference.

Fortunately few connections displayed these characteristics. Inthe case of connection A24 (Fig. 13d) a very strong agreement isachieved including hysteresis loops and off-loading stiffness.

5. Conclusions

The susceptibility of roof-to-wall connections and roof sheath-ing in light frame residential structures to damage fromhighwindshas always been a major concern. New building codes have man-dated using connections that do not rely on the limited strengthof toenail connections, such as, hurricane ties and metal straps forroof-to-wall connection to minimize the damage. However in ex-isting construction the use of toenail roof–to-wall connections andwood structural planks is prevalent in hurricane prone regions.Thus, an evaluation and subsequent modeling of their efficacy isnecessary. This study evaluated the component behavior of roofsunder uplift loads in a statistical fashion and it also developed ananalytical model of the structural behavior of roof-to-wall con-nections. This analytical model can be used to better quantify theredistribution of forces to connections which are part of a roof sys-tem. With the ability of the analytical model to capture the failureof individual connections – the sequence of roof failure during highwind events can be more closely examined.Three connection parameters (ultimate uplift capacity (Fult),

initial stiffness (ko) and vertical displacement at peak load(δPL)) are used to define the analytical model. As such relevantstatistics and probability distributions are proposed for thesethree parameters. This study proposes the use of the lognormaldistribution to model uplift capacities for both two and threenail connections. The normal distribution and three parameterWeibull distribution are proposed for ko and δPL respectively.These distributions and parameters can be used to evaluatethe component level reliability of toenail connections and roofsheathing.With awell defined limit state, the results can be used toassess the system reliability and thus can contribute significantly

a b

c d

Fig. 13. Comparison of experimental and analytical connection behavior.

2616 B. Shanmugam et al. / Engineering Structures 31 (2009) 2607–2616

to performance based evaluation of residential structures inhurricane prone areas. The probability models for connectionparameters can also be used to formulate damage prediction andloss calculation models.

Acknowledgements

This study has been supported by the National ScienceFoundation (NSF) under award number CMS-0642455. The authorswould also like to gratefully acknowledge the advice and directionprovided by Dr. Scott D. Schiff for this project. The views expressedin this paper are solely that of the authors and do not reflect theopinion of NSF.

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