READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE. https://nrc-publications.canada.ca/eng/copyright
Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n’arrivez pas à les repérer, communiquez avec nous à PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca.
Questions? Contact the NRC Publications Archive team at
PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. If you wish to email the authors directly, please see the first page of the publication for their contact information.
This publication could be one of several versions: author’s original, accepted manuscript or the publisher’s version. / La version de cette publication peut être l’une des suivantes : la version prépublication de l’auteur, la version acceptée du manuscrit ou la version de l’éditeur.
Access and use of this website and the material on it are subject to the Terms and Conditions set forth at
Dynamic evaluation of roofing systems using numerical models - an
introduction
Baskaran, B. A.; Kashef, A.
https://publications-cnrc.canada.ca/fra/droits
L’accès à ce site Web et l’utilisation de son contenu sont assujettis aux conditions présentées dans le site LISEZ CES CONDITIONS ATTENTIVEMENT AVANT D’UTILISER CE SITE WEB.
NRC Publications Record / Notice d'Archives des publications de CNRC:
https://nrc-publications.canada.ca/eng/view/object/?id=a067e8a2-ec55-4dcb-91bc-abb0ef9e2939 https://publications-cnrc.canada.ca/fra/voir/objet/?id=a067e8a2-ec55-4dcb-91bc-abb0ef9e2939DYNAMIC EVALUATION OF ROOFING SYSTEMS USING NUMERICAL MODELS - AN
INTRODUCTION A Baskaran and
A.
Kashef Building Performance laboratory Institute for Research in ConstructionNational Research Council
Canada
Ottawa, Ontario, Canada K1A CRGABSTRACT
Wind induced effects on roofing systems are dynamk: because of the wind's variationwith respect to time and space. In North America, existing performance evaluation procedures only address static conditions. In a project
-Dynamic
Evaluation of Roofing Systems,· at the Institutefor Researdl in Construction. National Research
Council Canada. test protocols and computer
models are being devek>ped to investigate roofing assemblies under dynamic conditions. Initial investigations have been started on single ply mechanically attached roofing assemblies. In such aroof,
a water proof membranethatis located to the outsideis directly exposed to dynamicwind
pressures. As a result the membrane deflects between the mechanical fasteners in a non-liner fashion typicallyknown as "Ballooning Eftea-. This paper introduces the varioustasks
of the project and refers to the progress made on developing numericaJ models to predict the performance of roofing systems.1. PROBLEM DEFINITION
Wind now over a typical roofing system is shown schemaUcalfy in Rgure 1. It can be observed from the figure that wind flow creates two types of pressure components. namely. negative pressure, p. and positive pressure. Pl' p. is created by flow separation on the exterior sida of the roof. P,is known as bUilding internal pressure. It is generated by air infiltration
through porous enve.lopes or through an opening in the windward wall as well as due to stack effect developed by temperature difference across the envelope. PI is especially important for large span industrial bUildings. supermarkets and structures of this nature. Since such bUilding envelopes are usually highly wind
permeable, the wind - induced internal pressure sometimes may equal the outside negative pressures. The design wind uplift is the vector addition of these pressure components. Wind induced pressure on a roofing membrane will have a stalic component (mean pressure) and a transient component. The latter varies as a random process and its dominant frequencies depend on the frequency of the upstreamwind and geometry of the building. Thus the wind
uplift pressure is time dependent.
FIgure
1
Wind flow schematic over roofing systemAs well. the wind pressurewill
vary
spatially over the roof. It has the largest values at the comer and perimeter due to flow vortex
and
will be moderate in the middle portion of the roof. Thisisdemonstrated in Rgure 2 which represents typical mean pressure coefficients measured in the wind tunnel. The datais for a square plan building model exposed to oblique wind direction. rtis evident from the figure that an imaginary flne of symmetry exists along the diagonal of the roof. The pressure coeffICients are maximum near the two leading edges. They decrease as one moves away towards the leeward edge. For this roof configuration a zero pressure coefficient represents occurrence of flow reattachment. After reattachment. the coefficients are positive. Thus itis clear that thewind induced pressures wilJ vaty with respect to
Figure
2
A typical spatial variation of wind pressureons building roof.The response of the roofing system is also dynamic (Baskaran and Dun, 1995). In other words. windinduced loads on the membrane can reach the structural supporting system throughtwo Joad paths, namely,
pneumatic load pathand structural load path. In thepneumatic loadpath the load is shared
among the layers (membrane, barrier, insulation) by differences in pressure across them. In the structural load path the load passes through the fasteners. If fluctuations of external wind pressures are slower than the membrane response time then theloads are transmitted through membrane tension to the fasteners, Le.• structural load path. For
fluctuations faster than the membrane response time, the load willbetransmined through
pneumatic adions. Measurements by Cook. (1992) showed that the higher the applied suction the greater the proportion borne direcUy by the merrorane (struelural path). Gerhardt
and
Gert>atsch (1.991) reported thaI for conunon spot fastener designs. the force applied on a fastener was approximately 2.5 times the wind uplln force.From the above discussion, it is clear that the problem of wind induced effects on roofs is both time
and
space dependent. This has been found true both for the driving force and for the system response. Therefore, a proper three-dimensional and time dependent (dynamic) analysis is essential for adequate estimation of wind effects on roofs.2. PRESENT FOCUS
Institute for Research in Construction of the National Research Council Canada (IRC/NRC) has started a project on the dynamic evaluation of roof attachment systems in collaboration with the Institute for Aerospace Researchot the National Research'
Council Canada (IARlNRC). Rgure 3 summarizes' the different aspects of the ongoing project In this project, test procedures and numerical models will be developed to evaluate the pertormance of
mechanically anached roofing systems under dynamic wind loading conditions. The analyses and the test results willbe combined to produce a design
ｾｮｵ｡ｬ for the roofing industry. Experimentalpart Includes laboratory tests to evaluate materials and systems pertormance and wind tunnel unsteady load measurements. Computer modeling involves the development of a Rnite Element Method (FEM) structural model and a CFO wind*loading modeL The paper is mainly focused on the numerical modeling of roof assemblies and thus the remaining part of the paper will present a progress report on this activity.
Figure 31RCINRC project flow-chart
2.1 Integrated Approach
Conventionally. experimental
procedures were used to evaluate the roofing system pertorrnance. Only limited studies such as Rossiter and Batts (1985). Gerhardt and Gert>atsch (1989). Easter ('990), Lewis (1990), larghamee (1 990) and Bienkiewic and Sun (1993) were made to evaluate the roofing system performance through numerical models.
Dynamic EvsJuation of Roofing Systems Using Numerical Models
Figure4 Cummt modeling approach for dynamic evaluation of roofing systems
""-...
_.
W.lJhun--.---.,
I
fEMVOOElIfG,---, I
r - - - - ,
ｬｬＭＭｾ
"""'" MlUIS,,,
...
,,""
the foliowing sections, the details of the numerical approaches willbe presented. Baskaran and Kashef (1995) identified severa]
research needsby systematically documenting the state-of·thErart in this area. Asa result. an integrated approach has been proposed as shown in Rgure 4. The IRClNRC modeling approachis unique and novel. Itisunique due 10 the fadthatall input conditions are measured as
part
of the project through labmeasurement at IRClNRC rather than assuming generic values or adapting material properties from the literature. This provides strong interaction between modelingandexperimental efforts. The present focus is novel because for thefirst
lime an integrated approach is aimed at a comprehensive dynamic analysis of the roofing systems. In other words. a core modulewillbe used for dynamic analysis of the roofingsystems subjected to various driving forces. IndividuaJ modules. at present two of them. namely,
wind
pressure fluduations andteflllerature variations,wiDbedeveloped for the driving forces. To feed the results from these modules to the core module, finks are
established. Asshown in the Rgure 4, this will allow to evaluate the roofing systems for various load combinations.
Present computer model needs three kindsof Inputs:
Driving forces: Such as the wind - induced unsteady loads on the roof can be obtained from CFD modeling andIor wind tunnel testing. Material properties: Such as, Young's modulus, poisson' ratio, coefficient of thennal expansion, etc. can be obtained fromlab measurement.
Assembly details: Dimensions and geometrical layout of the roofing system can be replicated similar to the system that has been tested at the wind tunnel or assemblies used at lab
measurements.
Most part of the numerical models is formulated basedon the scientifIC first
principles. Nevertheless, validating the model output with reliable measured data can earn the confidence of the end users on models. Bench mark data are hard to obtain. Since the present study hasaJsoincluded experimentwol1c, every effortwillbemade to gather dala for validation purposes. After validation, the numerical model will
be
used in an extensive parametric stUdy to produce an industry-oriented design manual. In2.2 Wind Flow Modelling Using CFD The present study employs Computational Fluid Dynamics (CFD)
techniques to numerically model the wind flow conditions. It engages the CFD solver
PHOENICS (Parabolic Hyperbolic Or Elliplic Numerical Integration Code Series) deveJoped by Spalding (1981) for the simulation.
PHOENICS' computer code can simulate fluid· flow, heat·transfer, chemica.l·reaction and
related phenomena. The present analyses were conducted using PHOENICS Version 2.0.
Besides the customizing procedures, two major sub-modules are needed to use PHOENICS for current wind flow modeling (Kashef and Baskaran, t 995). Rrst, the input module, known as the at file, is prepared. It consists of computational domain sizes, details for grid anangemenl, coordinates for building locations and other corrputational parameters such as values for initial How conditions. convergence criteria and relaxation factors. Second, the boundary module,known as GROUND, is carefully formulated. II includes the specification of boundary conditions, the
"
selectionofnecessary numerical schemes and
turbulence models. Detailsofthese
modifICations are reported in Baskaran (1994) andCHAM (1995).
•
conduding paramelric studies to investigate theeNeetof different parameters, e.g. membrane malerial fasteners spacing. roof geometry.･ｴｾＮ
on system responses.2.3 Dynamic Analysis Using FEM
where
K U+ C U'+ M U"
=
PThe dynamic analysis solution
procedure canbe summarized as:
• Calculating the stiffness. K, of the different roofing system components
• Evaluating the da"lling values. C, of the
different roofing system components. • caJculating the mass, M.ofrooflllg systems
based
on the densityandgeometry of eachoomponent.
• Assembling the governing equations under
the proposed loading system.
3. SIMULATED RESULTS AND DISCUSSION
A 3D numerical model has been developed having PHOENICS as the flow solver. Wind flow fields were computed for a square building (Figure 5) with the dimensions: length
=
3.0m. width=
3.0m and height=
1.4 m. Figure 5 also displays the selectedcomputational domain. Selection of the size of the computational domain to model such configuration depends mainly on the e>epected air flow panems and wakes around the buildings under investigation. Air flow. in tum. depends on building dimensions and local terrain . configuration. Researchers have commonly detennined the size of the domain as a multiple of bUilding dimensions. Itshould be also kept in mind that the increase in the domain increases the number of grid nodes and demands more CPU. time. Therefore. one must appropriatety seled the size of the domain so that a certain level of accuracy is maintained.
By
selecting several computational domains. sensitivity stUdies were carried out as described byBaskaran (1990). At the endofthe analysis. the dimensions of the selected computational
domain is shown in Figure 5.
3. 1 CFD Simulationｾ Wind Load Computation
It hasthe following dimensions for the nannal wind How condition: in the z direction' Up-Stream Distance (USD) = 13 m. and
ｄｯｾﾭ
Stream Distance (OSO) =71 m; in the x direction; Distances to Side. (D51) and {OS2} are equal to 23 m and in the y direction Distance to Top of the computational domain. (01)=23 m. Calculations have been made with 45 x 30 x 44 control volumes and the nodes are denser surrounding the building Vicinity. Approaching wind profile is expressed as a power law with an exponent equal 10 0.22. The turbulenceintensity varies from 18% to 2% over a relative height0.'7to0.83above the ground level. U =displacement
U' =veloctty U =acceleration
P
=
applieddynamic loadmodelling a three-dimensional roofing system to simulateitsresponse SUbjected to wind uplift forces.
perfonning dynamic analysis in which the Inertial effects are taken into
consideration. These inertial effects are
knownto cause the failure of fasteners in mechanically attached roofing systems with discrete fasteners.
Solving the governing equations using Rnrte Element numerical technique.
•
A FORTRAN computer code developed by Kashef (1992) for analyzing bridge decks with different assemblies subjected to dynamic or stallc loadingwill be used for the current
study.
The program
isa general purpose
computer program that has the abiltty to analyze very large three-dimensional systems subjected to tima vaJ)'ing force (Humar and Kashef, 1992). TIus program has been modified to evaluate roofing system response under dynamic loading conditions; this incJudes
•
Dynamic Evaluation of Roofing Systems Using Numerical Modsls
be obtained. Such outcome from CFD model
can be directly linked as input 10the FEM model to evaluale Ihe system response.
,
•
:
•
•
•
!
Figure 6 Mean pressure coefficients distribution on the building roof
3.2 FEM Analysis-System Response
Evaluation
Figure
5
Flat roof building model andcomputational domain
Computed mean pressures coefficients,
C•• are presented in Figures6. 11is evident from
the figurethatpressure coefficients decrease as
one moves from the windward 10 the leeward of
the building. Pressure coefficients range from
1.2to
1.3. Due to flow separation from the frontedge of the building roof. negative pressures
with higher values are developed. On the other hand. because of the reattachment of flow. at the back edge of the roof the uplift pressure and thus the pressure coefficients are reduced.
Following similar procedures, design wind
pressures for various building configurations can
•
•
•
11.
•
Analysis of rooting membrane * static
loading: In the following an example of the
application of FEM numerical technique to a one-component roofing assembly is presented. Computations are performed for a test specimen comprising only a membrane under a suction load of 500 Pa. Membrane dimensions are 3.8 m x 1.2 m x 0.002 m, fastener row separation of 0.9 m and faslener spacing of 0.25 m (Figure 7). The roofing membrane is constrained along the edges of the test specimen. The main purpose of the example is to present the capabilities of the numerical model and ability of reproducing the proper deformed shape of the membrane under constant pressure. Also the effect of varying membrane stiffness on the response is examined.
The analysis is carried out for a membrane with different modulus. In Figure 8. results from three of lhem namely, E1 =2760 Pa. E2= 11720 Pa and E3 =20680 Pa were grouped. It shows a lypical deformed shape for the membranes belween the attachments. The "Ballooning" phenomena of the membranes can be c1earfy observed from the figure. Figure 8
Figure
8Effect of ths Young's modulus on
msmbrane responsB under static loading---,
-,
..
ｾｲ
_ u.,
-.
ｾＮ..
117.'.,...
ｲＭｾｾｾｾＭｾＭｾＭＭＬThe 30 FEM model was used to analyze the response of the above roofing system. For this purpose, a preliminary FEM meshes comprising of 1140 nodesand 1026 finite elements representing the three strudUl layers; membrane, insulation and steel deck were constructed. The roofing structural components are constrained along the･､ｧｾ
the model. The aim is to use the pressureda collectedby the wind tunnel testing as input f the 3D dynamic analysis. One such input da for the FEM model is shown is10.
Figure 9 Cross section of the modeled roofing system
-1. . .0.0 10.0 20.0 1O.tI 0&0.0 14.0 IIJ
TIme(s)
second set building height is 1.5' and it incfud 10 cases. From these 30 cases, two cases w selected for modeling. Case 1: normal wind' free stream speed 27mls (- 60 mph), model
height 1.372 m (- 4.5')and open terrain. Cas 2: oblique wind with free stream speed 27ｭｉｾ
60 mph), model height 0.46 m (- 1.5') androl
terrain. The above two modeled cases represent a sample configuration from each s The cross section of the roofing system is shown in Figure 9.
Figure. 10 A typical time history of the
w
induced pressureonthe roofing membra• ..ue...
ｾ
-'"
"!.uE...
,
14OE-4 -'--g••-uoE-4WPa
4llE-4 IItMnUlll •ｾ WPa
---l • 0.002 m & p • 6lXI PII
E1.:mID ... & E2 -11'720 PII & ES • 2OS8O PIl Nc:clillllwdI)eAect5onAaoM Bectlan A-A
rr--"'!"
f'
c
'-
In
'0
Ｐｾ
ｾ
'j.-
,/""',..
ｾ
,
ｾｉ
....
u I . l U t . S l . A u U t . . 7 U U U""-Figure
7
Model configuration of the membrane under static loadingalso displays the relative displacement raUo on theY-axis for the three moduli at section A·A. The relative displacements are obtainedby nonnalizjng the maximum deflection withthatof E1 for comparison purposes. The profound effect of the membrane stiffness on its
deformation values are clear. The deflection of Ute membrane increases atmost Iinearfywiththe increase of the stiffness.
Analysis of roofing system -
Wind
loading:Asdiscussed in section 2. apilot
wind tunnel study has been carried out to measure the unsteadyloads on the membrane. Two sets of experiments were performed. The first set with model building height as 4.5' comprises of 20 experimental cases (different wind speed, exposure conditions and wind angles). Theu
u
u
i:
u
FIgure
12
Membrane deflection for oblique windｾ Case2
configuration.4 CONCLUDING REMARKS
This paper presented a novel integrated modeling approach for the performance
evaluation of roofing system under dynamic loading. The CFD technique is applied to simulate the wind induced flow and pressure distribution over building roofs and the FEM technique is used to calculate the roofing system response. A flat roof configuration was investigated for wind load computation.
Response of the membranes has been
predicted with static load conditions. Preliminary dynamic analyses were also made by modeling a complete roofing system similar to the one that has been tested in the wind tunnel. These demonstrations reveled that the present numerical model under development has potential for investigation of roofing systems under dynamic loading conditions.
aynsmic
Evaluation o(Roofing Systems USUlg Numerical ModslsFlfurs
11
Membrane deflection for nonnalWnd· Case
1
configuration.Among other paramertes, one of the output from the FEM analysis is the fasteners forces at different locations. Fastener forces are also measured at selected locations in the wind tunnel. In the future. comparisons willbemade between measured and computed fasteners forces as apartof model validation.
In Figure 11, the ballooning of the roofing membraneis shown for the case 1. contours representing the maximum deflection of the membrane are also shown. These deformations are independent of the time. In other
words.
to draw this figure the deformation at each nodal point is calculated for the duration of60seconds at intervals of 0.002 seconds and lhemaximum deflection is then selectedrepresenting one point on the surlace of the deformed shape. This is repeated for the whole roof nodes to draw the deformed surface
displayed in Figure 11. The maximum deflection of the membrane calculated in this case is 20 mm. Figure 12 is drawn for Case 2, in the same manner as that of Figure 11. In this case, the maximum deflection is 16 mm.
5 REFERENCES
ACKNOWLEDGMENT: Part of this research workhas been jointly sponsored by IRCINRC and the Department of National Defence (Mr. S.
Nagy).
Gerhardl, H.J. and Gerbalsch, R.W. (1991). ·Wind Resistance of Mechanically Attached. Single-Ply Systems - Fastener Load, Safety Considerations and Optimal Faslener Patterns·. Proceedings of the 1991 International Symposium on Roofing Technology, National Roofing Contractors Association, Rosemont. lllinois, USA. Humar, J.L. and Kashef, A.H. (1993). ·Oynamic Response of Bridges under Traveling Loads,· Canadian Journal of Civil Engineering 20, pp. 287-298.
Kashef, A and Baskaran, A. (1995). -Numerical Simulation of Airflow with Different Roof Configurations for the Prediction of Snow,· International Association for Wind Engineering, Ninth International Conference on Wind Engineering, New Delhi, India, 9-13 January, pp 1214 - 1224.
Kashef, A.M. (1992), -Dynamic Response
atHighway Bridges to Moving Vehicles,· A dissertation presented to caneton University in Partial Fulfillmentotthe Requirements for the Degree of Doctor of Philosophy. Ottawa, Canada.
Lewis, J.E. (1980). ·Preliminary Stress Evaluation of the Effects of Gaps Between Roof Insulation Panels-, Journal of Thennal Insulation. Vol. 4, pp.3-36.
ｒｯｳｳｾ･ｲＬ W.J .. Jr. and Baits, M.E. (1985).
·Rnite-Element Analysis of Temperature Induced Stresses in Single-Ply Roofing Membranes·, Durability of Building Materials. Vol. 2, pp. 195-208.
Spalding, -A General Purpose Computer Program for ｍｵｴｴｩｾｩｭ･ｮｳｩｯｮ｡ｬ One and Two-phase FlOW·, Math and Camp. Simulation, XXIII, 267, 1981.
Zarghamee, M. S. (1990). 'Wind Effects on Single-Ply Roofing Systems·, Journal of Structural Engineering, Vol. 116, No.1, January, pp. In-187, Paper No. 242n.
17. 16. 15. 14. 13. 11. 12. 10.
Baskaran, A. and Kashef. A. (1995), • Application of Numerical Models for the Dynamic Evaluation of Roofing System • Sfate of the Art Review", IRC Report • XXX. National Research Council Canada, Ottawa. Canada.
Baskaran, A.
and
Dun, O. (1995). -Evaluation of Roof Fasteners Under Dynamic Wind Loading-. ｐｲｯ｣･･ｾｩｮｧｳＮ of the International Wind Englneenng Conference, New -Delhi. India, January 8 -13, pp. 1207 -1218.Baskaran, A. (1990). "Computer Simulation of 30 Turbulent Wind Effects on Buildings·, Ph.D. Thesis. Concordia University, Montreal. Canada.
Baskaran, A. (1994). "A Numerical Model to Evaluate the Pertormance of Pressure
Equalized Rainscreen Walls-. Journal of Building and Environment, Vol. 29. No.2. 159-171.
Sienkiewicz. B. and Sun, Y. (1993).
-Numerical
and
Experimental Studies ofWind Loading on Loose-Laid Roofing
Systems-, Colorado State University, ｾｩｶｩｬ Engineering Department, Fort Collins. Colorado, USA.
Cook.
N.J. (1992). "Dynamic Response of Single-Ply Membrane R<.><>fing ｓｹｳｴ･ｾﾷＮJournalof Wind Engineenng and Industrial Aerodynamics, Vol. 41-44, pp. 1525-1536. CHAM Development Team. The
PHEONICS - 2.1 User Guide, CHAM, Bakery House, 40 High Street,
Wimbledon. London SW19 SAU, UK, 1995.
Easter, M.R. (1990). -Finite Element Analysis of Roofing Systems-. Roofing Research and Standards Development:
American Society for Testing am
Materials, Philadelphia, Vol, 2, STP 1088, pp.138-151.
Gerhardt, H.J. and Gerbatsch, RW. (1989). "Wind Loads on Single-Ply Membranes-, The Construction Specifier, November. pp. 60-71.
