rotational restraint to purlins provided by standing seam

Research ArticleRotational Restraint to Purlins Provided by Standing SeamRoof Systems

Qin Yang1 Wei Luan 2 Shaole Yu 2 and Junjie Chen2

1East China Architectural Design amp Research Institute Co Ltd Shanghai 200011 China2China Construction Eighth Engineering Division Co Ltd Shanghai 200135 China

Correspondence should be addressed to Wei Luan lwei13163com

Received 19 July 2019 Accepted 3 December 2019 Published 23 December 2019

Academic Editor Tayfun Dede

Copyright copy 2019 Qin Yang et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

e finite element model used for analyzing the rotational restraint rigidity of standing seam roof systems was developed einfluences of different factors on the rotational restraint rigidity provided by two types of standing seam roof systems were studiede variables include local deformation of standing seam roof panels panel thickness clip tab thickness and the relative sliding ofclip tab and clip base e restraint mechanism of standing seam roof systems to the purlins was studied It is shown that therotational restraint rigidity provided by the two types of researching standing seam roof systems mainly depends on the slide tabthickness and the roof panel thickness Finally formulae for calculating rotational restraint rigidity of the LSIII and SS360 standingseam roof systems were also proposed based on parametric analysis results

1 Introduction

Cold-formed purlins are widely used in metal buildings dueto their economy ease of fabrication and high strength-to-weight ratios However these sections are weak in the lateraldirection and in torsion [1] Previous work shows thatconventional roof panels which are directly through-fas-tened to purlins by self-drilling screws can provide fulllateral bracing and some extent of rotational restraint to thepurlins by virtue of their shear rigidity and resistance to localbending at the connections [1ndash5] In order to accuratelycalculate the uplift capacity of purlins with top flangethrough-fastened to roof panels a series of tests wereconducted by several scholars [1ndash11] to determine the ro-tational restraint to purlins provided by the purlin-panelsystems and the test set-up and procedure were proposed byCelebi et al [1] improved by Pekoz et al [3] and adopted byEurocode 3-1-3 [12] Katnam et al [13 14] developed anonlinear finite element model to estimate the rotationalrestraint provided by the first and second generationtrapezoidal sheeting to the attached purlin e model wasapplicable to trough-fixed and crest-fixed single skin purlin-sheeting systems and the performance of which was

validated to be in good agreement with test results It openedthe way to the development of a design method for esti-mating the rotational restraint provided by the sheeting tocold-formed steel purlins To determine the rotational re-straint that sheathing provides to the flange of a cold-formedsteel floor joist or stud a series of cantilever tests on joiststud-sheathing assemblies were conducted by Schafer[15 16] e tests demonstrated that the rotational stiffnessmay be decomposed into two parts connector andsheathing e connector stiffness was due to the rotation ofthe fastener in the flange of the cold-formed steel memberand was most significantly influenced by the thickness of thecold-formed steel member itself e sheathing stiffness wasdue to bending of the sheathing itself and may be highlyvariable e results formed the basis for a new designmethod adopted in American standards (AISI-S210-10) [17]for incorporating restraint into design strength predictionsfor the distortional buckling mode Gao and Moen [18 19]proposed mechanics-based equations for predicting therotational restraint provided by through-fastened metalpanels to Z- and C-section girts or purlins e predictionequations were validated by conducting rotational restraintexperiments and the through-fastened connection stiffness

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 2709890 8 pageshttpsdoiorg10115520192709890

was also simulated in a finite strip elastic buckling analysiswith a rotational spring to demonstrate how system effectscan be included in design

In recent years standing seam roof systems are veryprevalent since they are well adapted to the thermal ex-pansion and contraction deformation caused by tempera-ture changes In these roof systems standing seam roofpanels are fastened to purlins through sliding clips so thatmovement of roof panels relative to the purlins is permittederefore the behavior of purlins in these roof systems isdirectly related to the rotational restraint provided by thestanding seam roof systems Liu et al [20] studied the ro-tational restraint to purlins provided by standing seam roofsystems through 28 groups of tests and it was confirmed thatthe total rotational rigidity of standing seam roof systems isformed by connecting the rotational rigidity of roof panelsclips and purlins in series However because there are manytypes of standing seam roof systems and the roof panelprofile standing seam configuration and sliding clip detailsare different and it is difficult to determine all of the ro-tational restraints provided by these roof systems throughtests So far the rotational restraint rigidity to purlinsprovided by the LSIII and SS360 standing seam roof systemshas not been specially studied us in this paper the ro-tational restraint to purlins provided by two types ofstanding seam roof systems widely used in China was an-alyzed using finite element models and the influence factorswere also investigated and formulae for calculating rota-tional restraint rigidity were also proposed and verified

2 Research Object

Two types of standing seam roof systems widely used inChina were taken as the research objects One type was theLSIII standing seam roof system consisted of LSIII standingseam roof panels fastened to the purlins with LS003 clipsAnother type was SS360 standing seam roof system con-sisted of SS360 standing seam roof panels fastened to thepurlins with S3PC-1 clips Both of these roof panels al-though from different manufacturers had very similarprofiles e panel sidelaps were mechanically seamed in thefield to form the 450deg and 360deg seams for LSIII and SS360roof systems respectively e yield stress of both roofpanels as reported by the manufacturers was 345MPa andthe mean measured thickness including coating was 06mme LS003 clip was composed of a clip base 20mm inthickness and a slide tab 10mm in thickness the slide tabwas 110mm in length and attached to the clip base with aninterlocking design that permits relative movement betweenthem e S3PC-1 clip consisted of an L-shaped clip base26mm in thickness and a thinner slide tab (08mm inthickness) the L-shaped clip base was 115mm in length witha rectangular slot on the vertical plane the slide tab wasattached to the clip base at the slotted interface which allowsthe movement of the slide tab within the confines of the slotlength (91mm) Both the clip bases were fastened to purlinswith two self-drilling screws and the dimensions andconnection details are shown in Figures 1ndash3 Z-purlins wereused in the experimental programe angle between the lip

and flange is 45deg for all the Z-sections e cross-sectiondimensions of the purlins (height flange width andthickness) varied between tests

3 Finite Element Analysis

Using the general purpose finite element analysis (FEA)program ANSYS finite element models used for calculatingthe rotational restraint rigidity provided by standing seamroof systems were developed according to [20] nonlinearanalysis was performed and the rotational restraints onpurlins provided by the two types of standing seam roofsystems were also analyzed

31 Finite Element Models As shown in Figure 4 the finiteelement model consisted of 3 pieces of roof panels supportedby two lines of purlins at ends with one row of clips con-nected at the midspan of the roof panels A pair of con-centrated forces with same value and opposite direction wasapplied at two screw connection points of each clip base tosimulate the torque transmitted from the purlin

e standing seam roof panels and clips were modeledusing the SHELL 181 element which is a 4-node shell elementwith six degrees of freedom at each node And based onreasonable consideration of the stress stiffening large rota-tion and large strain the SHELL 181 element is well suited foranalyzing thin to moderately thick shell structures e finiteelement mesh size of the models was investigated to provideboth accurate and time-efficient results e standing seamroof panels and clips were all modeled as nonlinear materialsusing the ideal elastic-plastic model the yield stress of whichwas obtained from product reports provided by the manu-facturerse full-scale tests on wind uplift capacity of purlinssupporting the standing seam roof systems presented by Luanand Li [21 22] showed that the mechanical seams of the panelsidelaps were fixed tightly and no failure or separation wereobserved erefore the translation freedoms of the corre-sponding nodes between the panels and the slide tabs werealso coupled as shown in Figure 5 Considering that themovement distance of the slide tab relative to the clip base wasgenerally not very large in the tests to simplify the finiteelement model it is assumed that no relative movement hadoccurred between the slide tab and clip base therefore alongthe longitudinal direction of the roof panel the translationfreedom of the corresponding nodes was also coupled einfluence of the relative movement was also specially studiede standing seam roof panels were supported by twoC-purlins at the ends and the roof panels were connectedwith purlins through sliding clips so the translation freedomsof the corresponding nodes between the clip base and sup-porting purlins were also coupled e purlins were assumedto be simply supported to simulate the boundary conditionand at both ends of each purlin the translation in the verticaldirection of the central point and the translations in the lateraldirection of the web line points were constrained etranslation in the longitudinal direction of the central point atone end of the purlin was also constrained to avoid rigid bodydisplacement

2 Advances in Civil Engineering

e element types material models and boundary con-ditions were exactly the same as that being used in the fullmodel presented by Luan and Li [21 22] in which the ac-curacy of the full model was verified by a comparison betweenthe experimental results and the finite element results and it is

shown that good agreement is achieved between the exper-imental results and finite element results for the flexuralstrength and the failure modes e difference of purlinflexural strength obtained from tests and finite elementanalysis was smaller than 5 e load-displacement curvesobtained from the finite element analysis were all in greatagreement with the test results erefore the finite elementmodels are reliable and can be used for further researches

32 Calculation of Rotational Restraint Rigidity Using thefinite element analysis results the rotational restraint rigidity(K) provided by the standing seam roof system can becalculated as follows

K T

θ

F times s

δ1 minus δ21113868111386811138681113868

1113868111386811138681113868s (1)

4794 64378

0

Female edge Male edge

527 76

2

6436080

(a)

603Female edgeMale edge

747

508

762

4890 6036096

(b)

Figure 1 Dimensions of standing seam roof panels (a) LSIII roof panel (b) SS360 roof panel

(a) (b)

Figure 2 Connection details of LSIII roof system (a) LS003 clip (b) 450deg mechanical seam of panel sidelaps

(a) (b)

Figure 3 Connection details of SS360 roof system (a) S3PC-1 clip (b) 360deg mechanical seam of panel sidelaps

Figure 4 Finite element model for analyzing rotational restraint ofstanding seam roof systems

Advances in Civil Engineering 3

where T is the torque applied on the clip base θ is thecorresponding rotation angle of the clip base F is theconcentrated force applied at the screw points s is the spacebetween the screws δ1 and δ2 are the corresponding dis-placements at two screw connection points

e rotational restraint rigidity on the unit length ofpurlin (Ktor) can be calculated by

Ktor K

wrf (2)

where wrf is the width of the standing seam roof panel

33 Finite ElementAnalysis Results Using the FE model therotational restraintsrsquo rigidity to purlins provided by the twotypes of standing seam roof systems studied in this paper wasanalyzed e thickness of the roof panel in both types ofroof systems was 06mm and the panel dimensions andconnection details were exactly the same as shown inFigures 1ndash3 Figure 6 shows the deformation and stressdistribution in the roof panel Figure 7 shows the defor-mation and stress distribution of two types of clips

As can be seen the bending stiffness of the two types ofstanding seam roof panels is large enough that the clipsalways fail before roof panels and the S3PC-1 clip is mucheasier to deform because the slide tab of which is thinner

34 Analysis of Influence Factors eoretically the rota-tional restraint rigidity provided by the standing seam roofsystems is mainly related to the bending stiffness of roof

panels and the sliding performance of clips e bendingstiffness of roof panels generally depends on the thicknessand the cross-section profile of the roof panel and thesliding performance of clips is mainly determined on thethickness of the slide tab Considering that significant out-of-plane bending deformation of the flat part of the roofpanel was observed in the tests the out-of-plane deflectionshould also be seen as a factor causing the change of thepanel cross-section profile erefore using the finite ele-ment model the influence of different factors on the rota-tional restraint rigidity provided by the two types of standingseam roof systems was studied e variables include therelative movement between the slide tab and clip base (Stb)the out-of-plane deflection at mid-point of the roof panelcross-section (Drf ) the roof panel thickness (trf ) and slidetab thickness (tst) Analysis results are shown in Figure 8 It isobserved that the rotational restraint rigidity mainly de-pends on the slide tab thickness and the roof panel thicknessbecause the slide tab is the weakest link in the rotationalrestraint transmission path of the standing seam roof systemand the performance of the mechanical seams connecting theslide tab and the roof panels is closely related to the thicknessof roof panel and slide tab e out-of-plane bending de-formation of roof panel and the relative movement betweenthe slide tab and clip base almost have no influence on therotational restraint rigidity except for LS003 clip when therelative movement distance is greater than 40mm and half ofthe slide tab separates from the clip base thus the rotationalrestraint rigidity sharply decreases however which is notexpected to occur in the actual engineering

4 Formulae for Rotational Restraint Rigidity

Considering the significant influence on rotational restraintrigidity from the thickness of roof panel and slide tabfurther parametric finite element analysis was conductedBased on the parametric analysis results formulae for cal-culating rotational restraint rigidity of the LSIII and SS360standing seam roof systems were generalized as follows

for LSIII roof system Ktor E

57t026rf t

037st (3)

for SS360 roof system Ktor E

50t032rf t

049st (4)

where trf is the thickness of the roof panel tst is the thicknessof the slide tab and E is Youngrsquos modulus

(a) (b)

Figure 5 Connection details of roof panels and clips in finite element models (a) LSIII roof system (b) SS360 roof system

000748538353

76699 15339 230081 306772115044 191735 268427 345118

Figure 6 Deformation and stress distribution of the roof panel


1475 96291 191106 285921 38073748883 143698 238514 333329 428144

(a)

036794742698

85027127357

169686212016

254345296675

339005381334

(b)

Figure 7 Deformation and stress distribution of sliding clips (a) LS003 clip and (b) S3PC-1 clip

0 10 20 30 40 502000

2500

3000

3500

K tor

(Nmiddotm

middotradndash1

middotmndash1

)

Stb (mm)

LSIIISS360

(a)

K tor

(Nmiddotm

middotradndash1

middotmndash1

)

LSIIISS360

0 20 40 60 80 100 120 1402800

2900

3000

3100

3200

Drf (mm)

(b)

K tor

(Nmiddotm

middotradndash1

middotmndash1

)

LSIIISS360

02 04 06 08 10 12 14 16 18 20 222000

2500

3000

3500

4000

trf (mm)

(c)

K tor

(Nmiddotm

middotradndash1

middotmndash1

)

LSIIISS360

05 10 15 20 25 30 352500

3000

3500

4000

4500

5000

tst (mm)

(d)

Figure 8 Correlation between the rotational restrain rigidity Ktor and factors (a) between Ktor and Stb (b) betweenKtor andDrf (c) betweenKtor and trf and (d) between Ktor and tst


To verify the accuracy of the formulae the rotationalrestraint rigidity calculated by the proposed formulae wascompared with the test results of similar standing seam roofsystems by Liu et al [20] However the rotational restraintrigidity obtained from the tests by Liu et al [20] is totalrigidity provided by roof panel clip and purlin (Kz) whichcan be calculated by

1Kz

1

Kz1+

1Kz2

(5)

where Kz1 is rotational restraint rigidity provided by the roofsystem which is the same as Ktor in this paper and Kz2 isrotational rigidity of purlin which is given by

Kz2 αEt3

4 1 minus ]2( ) 3b1 + b2 + αh( 1113857 (6)

where E is Youngrsquos modulus t is purlin thickness v isPoissonrsquos ratio b1 is the distance from the inside self-drilling screw to purlin web b2 is the space between twoself-drilling screws h is purlin height and α is the ri-gidity reduction factor of the top flange of purlin for

LSIII roof system it is 04 and for HX-478 roof system itis 05

e calculation results of Equations (3) and (4) cannot becompared with the test results directly erefore based onthe rotational restraint rigidity of roof system calculated byEquation (3) or Equation (4) using Equations (5) and (6)the total rotational restraint rigidity was calculated andcompared with the test results (Kzt) by Liu et al [20] Table 1shows the comparison results of LSIII roof system and it isobserved that the calculation results are in good agreementwith the test results e comparison results of SS360 roofsystem used in this paper and HX-478 roof system tested byLiu et al [20] are listed in Table 2 It can be seen that thelargest difference between the calculation results and the testresults reaches about 30 which is because although theconfiguration and working mechanism of SS360 roof systemand HX-478 roof system are exactly the same there are stillsome differences between them such as the width of roofpanel and the dimensions of clips And in general thecomparison shows that the rotational restraint rigidity ofstanding seam roof systems calculated by the formulaeproposed in this paper is reliable

Table 1 Comparison of rotational restraint rigidity calculated by Equation (3) with test result by Liu et al [20]

Test identification Purlin section trf (mm)Rotational restraint rigidity

(Nmiddotmmiddotradminus 1middotmminus 1) (Kzminus Kzt)Kzt ()Kz2 Ktor Kz Kzt

ML-8 Z250times 60times 20times15 06 424 3165 374 409 minus 850ML-7 Z250times 60times 20times 20 06 1006 3165 763 719 617ML-17 Z250times 60times 20times 20 06 1006 3165 763 712 722ML-20 Z250times 60times 20times 20 053 1006 3064 757 761 minus 047ML-13 Z250times 60times 20times 25 06 1965 3165 1212 1103 991ML-14 Z250times 60times 20times 25 053 1965 3064 1197 1120 690ML-9 Z200times 60times 20times15 06 478 3165 415 447 minus 718ML-10 Z200times 60times 20times15 053 478 3064 413 474 minus 1284ML-11 Z200times 60times 20times 20 06 1132 3165 834 738 1297ML-19 Z200times 60times 20times 20 06 1132 3165 834 825 105ML-12 Z200times 60times 20times 20 053 1132 3064 827 722 1448ML-18 Z200times 60times 20times 20 053 1132 3064 827 803 293ML-15 Z200times 60times 20times 25 06 2211 3165 1301 1214 721ML-16 Z200times 60times 20times 25 053 2211 3064 1284 1181 874Mean 347COV 819




HX-1 Z250times 70times 20times 25 05 1922 2959 1165 1297 minus 1016HX-7 Z250times 70times 20times 25 06 1922 3136 1192 1391 minus 1432HX-5 Z250times 70times 20times 25 06 1922 3136 1192 919 2969HX-3 Z200times 70times 20times 25 05 2157 2959 1247 1302 minus 419HX-2 Z200times 70times 20times 25 06 2157 3136 1278 1432 minus 1076HX-4 Z200times 70times 20times 20 06 1104 3136 817 841 minus 289HX-6 Z200times 70times 20times 20 06 1104 3136 817 690 1836HX-8 Z200times 70times 20times 20 08 1104 3439 836 680 2292Mean 358COV 1728


5 Conclusion

In order to study the rotational restraint rigidity provided bytwo types of standing seam roof systems widely used inChina the finite element model used for analyzing therotational restraint rigidity of standing seam roof systemswas developed based on a test verified full finite elementmodel e influences of different factors on the rotationalrestraint rigidity provided by two types of standing seamroof systems were also analyzed e variables include localdeformation of standing seam roof panels panel thicknessclip tab thickness and the relative sliding of clip tab and clipbase e analyses showed that the rotational restraint ri-gidity of standing seam roof systems mainly depended onthe roof panel thickness and slide tab thickness Formulaefor calculating rotational restraint rigidity of the LSIII andSS360 standing seam roof systems were also proposed andthe comparison between formulae calculating results andtest results showed that the rotational restraint rigidity ofstanding seam roof systems calculated by the formulaeproposed in this paper is reliable

Data Availability

e datasets generated during the current study are availablefrom the corresponding author on reasonable request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e research was from the topic of the National ScienceFoundation of China (no 51478331) and State Key Labo-ratory of Disaster Reduction in Civil Engineering (noSLDRCE14-B-06) e authors are grateful to USASBuilding System (Shanghai) Co Ltd and ABC BuildingSystems (China) for supplying the test specimens

References

[1] N Celebi G Winter and T Pekoz ldquoDiaphragm bracedchannel and Z-section beamsrdquo Report No 344 Departmentof Structural Engineering Cornell University Ithaca NYUSA 1972

[2] M A A Razak and T Pekoz ldquoProgress reportmdashultimatestrength of co1dFormed steel Z-purlinsrdquo Report No 80-3Department of Structural Engineering Cornell UniversityIthaca NY USA 1980

[3] T Pekoz and P Soroushian ldquoBehaviour of C- and Z-purlinsunder wind upliftrdquo in Proceedings of the 6th InternationalSpecialty Conference on Cold-Formed Steel Structurespp 409ndash429 University of Missouri-Rolla St Louis MOUSA November 1982

[4] G J Hancock M Celeban C Healy et al ldquoTests of purlinswith screw fastened sheeting under wind upliftrdquo in Pro-ceedings of the 10th International Specialty Conference onCold-formed Steel Structures pp 393ndash419 University ofMissouri-Rolla St Louis MO USA October 1990

[5] G J Hancock M Celeban and C Healy ldquoTests of continuouspurlins under downwards loadingrdquo in Proceedings of the 11thInternational Specialty Conference on Cold-formed SteelStructures pp 157ndash179 University of Missouri-Rolla StLouis MO USA October 1992

[6] R A LaBoube Laterally Unsupported Purlins Subjected toUplift Cornell University Ithaca NY USA 1983

[7] R W Haussler ldquoeory of cold-formed steel purlingirtflexurerdquo in Proceedings of the 9th International SpecialtyConference on Cold-formed Steel Structures pp 255ndash271University of Missouri-Rolla St Louis MO USA November1988

[8] H Wu and C D Moen Rotational and Translational Stiffnessprovided by Insulated Metal Panels to Girts and Purlins inMetal Building Wall and Roof Systems Virginia TechChennai India 2016

[9] R A LaBoube M Golovin D J Montague et al ldquoBehavior ofcontinuous span purlin systemsrdquo in Proceedings of the 9thInternational Specialty Conference on Cold-Formed SteelStructures pp 191ndash203 University of Missouri-Rolla StLouis MO USA November 1988

[10] C Zhao J Yang F Wang and A H C Chan ldquoRotationalstiffness of cold-formed steel roof purlin-sheeting con-nectionsrdquo Engineering Structures vol 59 pp 284ndash2972014

[11] C Zhao Investigations on Structural Interaction of Cold-Formed Steel Roof Purlin-Sheet System University of Bir-mingham Birmingham UK 2014

[12] European Commission for Standardization EN1993-1-3Eurocode 3 Design of Steel Structures Part 1-3 General RulesSupplementary Rules for Cold Formed in Gauge Membersand Sheeting European Commission for StandardizationBrussels Belgium 1996

[13] K B Katnam R Van Impe G Lagae et al ldquoA theoreticalnumerical study of the rotational restraint in cold-formedsteel single skin purlin-sheeting systemsrdquo Computers ampStructures vol 85 no 15-16 pp 1185ndash1193 2007

[14] K B Katnam R Van Impe G Lagae and M De StryckerldquoModelling of cold-formed steel sandwich purlin-sheetingsystems to estimate the rotational restraintrdquo in-walledStructures vol 45 no 6 pp 584ndash590 2007

[15] Y Guan Analytical Study on Rotational Restraint ofSheathing Report No RP08-2 American Iron and Steel In-stitute Washington DC USA 2008

[16] B W Schafer L C M Vieira Jr R H Sangree et al ldquoRo-tational restraint and distortional buckling in cold-formedsteel framing systemsrdquo Revista Sul-americana de EngenhariaEstrutural vol 7 no 1 2011

[17] AISI S210-10North American Standard for Cold-Formed SteelFraming - Floor and Roof System Design American Iron andSteel Institute Washington DC USA 2010

[18] T Gao and C D Moen ldquoExtending the direct strengthmethod for cold-formed steel design to through-fastenedsimple span girts and purlins with laterally unbraced com-pression flangesrdquo Journal of Structural Engineering vol 140no 6 pp 145ndash153 2013

[19] T Gao Direct Strength Method for the Flexural Design ofrough-Fastened Metal Building Roof and Wall Systemsunder Wind Uplift or Suction Virginia Tech Chennai India2012

[20] Y X Liu G S Tong and H L Du ldquoTest and finite elementanalysis on torsional restrain of corrugated steel sheet topurlin through clipsrdquo Journal of Building Structures vol 35pp 116ndash124 2014 in Chinese


[21] W Luan and Y Li ldquoExperimental study on uplift capacity ofpurlins considering restraints from standing seam roof sys-temsrdquo in Proceedings of the 11th International SpecialtyConference on Cold-Formed Steel Structures pp 157ndash179University of Missouri-Rolla St Louis MO USA October1992

[22] W Luan and Y-Q Li ldquoExperimental investigation on wind upliftcapacity of single span Z-purlins supporting standing seam roofsystemsrdquoin-Walled Structures vol144Article ID106324 2019


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was also simulated in a finite strip elastic buckling analysiswith a rotational spring to demonstrate how system effectscan be included in design

In recent years standing seam roof systems are veryprevalent since they are well adapted to the thermal ex-pansion and contraction deformation caused by tempera-ture changes In these roof systems standing seam roofpanels are fastened to purlins through sliding clips so thatmovement of roof panels relative to the purlins is permittederefore the behavior of purlins in these roof systems isdirectly related to the rotational restraint provided by thestanding seam roof systems Liu et al [20] studied the ro-tational restraint to purlins provided by standing seam roofsystems through 28 groups of tests and it was confirmed thatthe total rotational rigidity of standing seam roof systems isformed by connecting the rotational rigidity of roof panelsclips and purlins in series However because there are manytypes of standing seam roof systems and the roof panelprofile standing seam configuration and sliding clip detailsare different and it is difficult to determine all of the ro-tational restraints provided by these roof systems throughtests So far the rotational restraint rigidity to purlinsprovided by the LSIII and SS360 standing seam roof systemshas not been specially studied us in this paper the ro-tational restraint to purlins provided by two types ofstanding seam roof systems widely used in China was an-alyzed using finite element models and the influence factorswere also investigated and formulae for calculating rota-tional restraint rigidity were also proposed and verified

2 Research Object

Two types of standing seam roof systems widely used inChina were taken as the research objects One type was theLSIII standing seam roof system consisted of LSIII standingseam roof panels fastened to the purlins with LS003 clipsAnother type was SS360 standing seam roof system con-sisted of SS360 standing seam roof panels fastened to thepurlins with S3PC-1 clips Both of these roof panels al-though from different manufacturers had very similarprofiles e panel sidelaps were mechanically seamed in thefield to form the 450deg and 360deg seams for LSIII and SS360roof systems respectively e yield stress of both roofpanels as reported by the manufacturers was 345MPa andthe mean measured thickness including coating was 06mme LS003 clip was composed of a clip base 20mm inthickness and a slide tab 10mm in thickness the slide tabwas 110mm in length and attached to the clip base with aninterlocking design that permits relative movement betweenthem e S3PC-1 clip consisted of an L-shaped clip base26mm in thickness and a thinner slide tab (08mm inthickness) the L-shaped clip base was 115mm in length witha rectangular slot on the vertical plane the slide tab wasattached to the clip base at the slotted interface which allowsthe movement of the slide tab within the confines of the slotlength (91mm) Both the clip bases were fastened to purlinswith two self-drilling screws and the dimensions andconnection details are shown in Figures 1ndash3 Z-purlins wereused in the experimental programe angle between the lip

and flange is 45deg for all the Z-sections e cross-sectiondimensions of the purlins (height flange width andthickness) varied between tests

3 Finite Element Analysis

Using the general purpose finite element analysis (FEA)program ANSYS finite element models used for calculatingthe rotational restraint rigidity provided by standing seamroof systems were developed according to [20] nonlinearanalysis was performed and the rotational restraints onpurlins provided by the two types of standing seam roofsystems were also analyzed

31 Finite Element Models As shown in Figure 4 the finiteelement model consisted of 3 pieces of roof panels supportedby two lines of purlins at ends with one row of clips con-nected at the midspan of the roof panels A pair of con-centrated forces with same value and opposite direction wasapplied at two screw connection points of each clip base tosimulate the torque transmitted from the purlin

e standing seam roof panels and clips were modeledusing the SHELL 181 element which is a 4-node shell elementwith six degrees of freedom at each node And based onreasonable consideration of the stress stiffening large rota-tion and large strain the SHELL 181 element is well suited foranalyzing thin to moderately thick shell structures e finiteelement mesh size of the models was investigated to provideboth accurate and time-efficient results e standing seamroof panels and clips were all modeled as nonlinear materialsusing the ideal elastic-plastic model the yield stress of whichwas obtained from product reports provided by the manu-facturerse full-scale tests on wind uplift capacity of purlinssupporting the standing seam roof systems presented by Luanand Li [21 22] showed that the mechanical seams of the panelsidelaps were fixed tightly and no failure or separation wereobserved erefore the translation freedoms of the corre-sponding nodes between the panels and the slide tabs werealso coupled as shown in Figure 5 Considering that themovement distance of the slide tab relative to the clip base wasgenerally not very large in the tests to simplify the finiteelement model it is assumed that no relative movement hadoccurred between the slide tab and clip base therefore alongthe longitudinal direction of the roof panel the translationfreedom of the corresponding nodes was also coupled einfluence of the relative movement was also specially studiede standing seam roof panels were supported by twoC-purlins at the ends and the roof panels were connectedwith purlins through sliding clips so the translation freedomsof the corresponding nodes between the clip base and sup-porting purlins were also coupled e purlins were assumedto be simply supported to simulate the boundary conditionand at both ends of each purlin the translation in the verticaldirection of the central point and the translations in the lateraldirection of the web line points were constrained etranslation in the longitudinal direction of the central point atone end of the purlin was also constrained to avoid rigid bodydisplacement





K T

θ

F times s

δ1 minus δ21113868111386811138681113868

1113868111386811138681113868s (1)

4794 64378

0


527 76

2

6436080

(a)


747

508

762

4890 6036096

(b)


(a) (b)


(a) (b)






Ktor K

wrf (2)









57t026rf t

037st (3)


50t032rf t

049st (4)


(a) (b)


000748538353

76699 15339 230081 306772115044 191735 268427 345118



1475 96291 191106 285921 38073748883 143698 238514 333329 428144

(a)

036794742698

85027127357

169686212016

254345296675

339005381334

(b)


0 10 20 30 40 502000

2500

3000

3500

K tor

(Nmiddotm

middotradndash1

middotmndash1

)

Stb (mm)

LSIIISS360

(a)

K tor

(Nmiddotm

middotradndash1

middotmndash1

)

LSIIISS360

0 20 40 60 80 100 120 1402800

2900

3000

3100

3200

Drf (mm)

(b)

K tor

(Nmiddotm

middotradndash1

middotmndash1

)

LSIIISS360

02 04 06 08 10 12 14 16 18 20 222000

2500

3000

3500

4000

trf (mm)

(c)

K tor

(Nmiddotm

middotradndash1

middotmndash1

)

LSIIISS360

05 10 15 20 25 30 352500

3000

3500

4000

4500

5000

tst (mm)

(d)




1Kz

1

Kz1+

1Kz2

(5)


Kz2 αEt3

4 1 minus ]2( ) 3b1 + b2 + αh( 1113857 (6)













5 Conclusion


Data Availability




Acknowledgments


References



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





K T

θ

F times s

δ1 minus δ21113868111386811138681113868

1113868111386811138681113868s (1)

4794 64378

0


527 76

2

6436080

(a)


747

508

762

4890 6036096

(b)


(a) (b)


(a) (b)






Ktor K

wrf (2)









57t026rf t

037st (3)


50t032rf t

049st (4)


(a) (b)


000748538353

76699 15339 230081 306772115044 191735 268427 345118



1475 96291 191106 285921 38073748883 143698 238514 333329 428144

(a)

036794742698

85027127357

169686212016

254345296675

339005381334

(b)


0 10 20 30 40 502000

2500

3000

3500

K tor

(Nmiddotm

middotradndash1

middotmndash1

)

Stb (mm)

LSIIISS360

(a)

K tor

(Nmiddotm

middotradndash1

middotmndash1

)

LSIIISS360

0 20 40 60 80 100 120 1402800

2900

3000

3100

3200

Drf (mm)

(b)

K tor

(Nmiddotm

middotradndash1

middotmndash1

)

LSIIISS360

02 04 06 08 10 12 14 16 18 20 222000

2500

3000

3500

4000

trf (mm)

(c)

K tor

(Nmiddotm

middotradndash1

middotmndash1

)

LSIIISS360

05 10 15 20 25 30 352500

3000

3500

4000

4500

5000

tst (mm)

(d)




1Kz

1

Kz1+

1Kz2

(5)


Kz2 αEt3

4 1 minus ]2( ) 3b1 + b2 + αh( 1113857 (6)













5 Conclusion


Data Availability




Acknowledgments


References



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Ktor K

wrf (2)









57t026rf t

037st (3)


50t032rf t

049st (4)


(a) (b)


000748538353

76699 15339 230081 306772115044 191735 268427 345118



1475 96291 191106 285921 38073748883 143698 238514 333329 428144

(a)

036794742698

85027127357

169686212016

254345296675

339005381334

(b)


0 10 20 30 40 502000

2500

3000

3500

K tor

(Nmiddotm

middotradndash1

middotmndash1

)

Stb (mm)

LSIIISS360

(a)

K tor

(Nmiddotm

middotradndash1

middotmndash1

)

LSIIISS360

0 20 40 60 80 100 120 1402800

2900

3000

3100

3200

Drf (mm)

(b)

K tor

(Nmiddotm

middotradndash1

middotmndash1

)

LSIIISS360

02 04 06 08 10 12 14 16 18 20 222000

2500

3000

3500

4000

trf (mm)

(c)

K tor

(Nmiddotm

middotradndash1

middotmndash1

)

LSIIISS360

05 10 15 20 25 30 352500

3000

3500

4000

4500

5000

tst (mm)

(d)




1Kz

1

Kz1+

1Kz2

(5)


Kz2 αEt3

4 1 minus ]2( ) 3b1 + b2 + αh( 1113857 (6)













5 Conclusion


Data Availability




Acknowledgments


References



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


1475 96291 191106 285921 38073748883 143698 238514 333329 428144

(a)

036794742698

85027127357

169686212016

254345296675

339005381334

(b)


0 10 20 30 40 502000

2500

3000

3500

K tor

(Nmiddotm

middotradndash1

middotmndash1

)

Stb (mm)

LSIIISS360

(a)

K tor

(Nmiddotm

middotradndash1

middotmndash1

)

LSIIISS360

0 20 40 60 80 100 120 1402800

2900

3000

3100

3200

Drf (mm)

(b)

K tor

(Nmiddotm

middotradndash1

middotmndash1

)

LSIIISS360

02 04 06 08 10 12 14 16 18 20 222000

2500

3000

3500

4000

trf (mm)

(c)

K tor

(Nmiddotm

middotradndash1

middotmndash1

)

LSIIISS360

05 10 15 20 25 30 352500

3000

3500

4000

4500

5000

tst (mm)

(d)




1Kz

1

Kz1+

1Kz2

(5)


Kz2 αEt3

4 1 minus ]2( ) 3b1 + b2 + αh( 1113857 (6)













5 Conclusion


Data Availability




Acknowledgments


References



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



1Kz

1

Kz1+

1Kz2

(5)


Kz2 αEt3

4 1 minus ]2( ) 3b1 + b2 + αh( 1113857 (6)













5 Conclusion


Data Availability




Acknowledgments


References



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


5 Conclusion


Data Availability




Acknowledgments


References



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


rotational restraint to purlins provided by standing seam

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