concrete roof pavers: wind uplift aerodynamic mechanisms

Concrete Roof Pavers Wind UpliftAerodynamic Mechanisms and Design Guidelinesndash A Proposed Addition to ANSISPRI RP-4

Maryam Asghari Mooneghi PhDArup Advanced Technology and Research

560 Mission street ste 700 san francisco Ca 94105

Phone 415-659-4996 bull fax 415-957-9096 bull e-mail maryamasghariarupcom

Thomas L Smith RRC AIA FSEITLSmith Consulting Inc

16681 boswell Road Rockton Il 61072

Phone 815-629-2455 bull e-mail tlsmithhughesnet

Peter Irwin PhDArindam Gan Chowdhury PhDFlorida International University

10555 W flagler st engineering Center eC 3604 Miami fl 33174 Phone 305-348-0518 bull Fax 305-348-2802 bull E-mail peairwifiuedu amp chowdhurfiuedu

3 2 n d R C I I n t e R n a t I o n a l C o n v e n t I o n a n d t R a d e S h o w bull M a R C h 1 6 - 2 1 2 0 1 7 M o o n e g h I e t a l bull 5 1

Abstract

This paper presents large-scale experiments in the Wall of Wind a large-scale hurricane testing facility at Florida International University (FIU) Based on the experimental results simplified paver design guidelines were developed The guidelines include load reduction fac-tors associated with gaps and parapet height and are formatted for use with ASCE 7-10 The guidelines are proposed as an addition to the RP-4 Commentary in order to provide designers with specific credible design criteria for roof pavers

Speakers

Maryam Asghari Mooneghi PhD ndash Arup Advanced Technology and Research San Francisco CA

DR MARYAM ASGHARI MOONEGHI is a structural analyst in Advanced Technology and Research in Arup During her doctoral studies at FIU she performed extensive experiments in the Wall of Wind facility to investigate wind-loading mechanisms of roof pavers in order to develop guidelines for wind-resistant design of these systems She received a PhD in civil engineering from FIU and bachelorrsquos and masterrsquos degrees in aerospace engineering from Amirkabir University of Technology

Thomas L Smith RRC AIA FSEI ndash TLSmith Consulting Inc Rockton IL

TOM SMITH is president of TLSmith Consulting Inc He received the Carl G Cash Award from ASTM in 2013 for his body of work regarding wind damage investigations He was promot-ed to Fellow-grade membership of ASCErsquos Structural Engineering Institute (SEI) in 2013 The FSEI promotion was for his many years of service on the ASCE 7 Wind Loads Task Committee and for his body of work regarding wind damage investigations and wind design guides

Nonpresenting Coauthors

Peter Irwin PhD ndash Florida International University Miami FL

PETER IRWIN PHD is a Professor of Practice with the Department of Civil and Environmental EngineeringInternational Hurricane Research Center Florida International University Miami FL

Arindam Gan Chowdhury PhD ndash Florida International University Miami FL

ARINDAM GAN CHOWDHURY PHD is an Associate Professor in the Department of Civil and Environmental EngineeringInternational Hurricane Research Center Florida International University Miami FL

5 2 bull M o o n e g h I e t a l 3 2 n d R C I I n t e R n a t I o n a l C o n v e n t I o n a n d t R a d e S h o w bull M a R C h 1 6 - 2 1 2 0 1 7


1 INTRODUC TION ASCE 7 provides criteria for determining

wind uplift pressures for roof assemblies but there are no specific provisions on how to apply such pressures to ballasted roof systems However ANSISPRI RP-4 (2013) Wind Design Standard For Ballasted Single-ply Roofing Systems provides a method of designing wind uplift resistance of ballasted systems

This paper addresses square-edged con-crete paver ballast It presents a proposed addition to the RP-4 commentary The pro-posed addition (Appendix A) presents design guidelines that can be used to 1) reevaluate and update the design tables in RP-4 2) design paver ballast when conditions are outside of the RP-4 tables and 3) perform a wind vulnerability assessment of existing paver-ballasted roofs that are outside of the RP-4 Tables The recommended design guidelines are based on research con-ducted at Florida International University (Asghari Mooneghi 2016) and summarized in Sections 4 to 7 The Mooneghi paper includes discussion of previous research and has an extensive list of references

Section 2 presents an overview of RP-4 and Section 3 presents examples of paver wind uplift problems When pavers are lifted off wind-borne debris can puncture the roof membrane and cause a path for water leak-age Pavers blown from the roof can damage other building ele-ments and vehicles and can cause injury or death

2 ANSISPRI RP-4 A NSISPR I R P-4 (2013)

addresses four types of ballast aggregate (1frac12 and 2frac12 in nomi-nal) square-edged concrete pav-ers (18 and 22 pounds per sq ft [psf] minimum) interlocking light-weight concrete pavers (10 psf min-imum) and interlocking cementi-tious-coated extruded polystyrene panels (4 psf minimum)

The origin of the standard dates back to a 1985 paper (Gillenwater 1985) that presented a guideline that was being jointly developed by the Rubber Manufacturers Association (RMA) and the Single Ply Roofing Industry (SPRl) RMA issued the guideline in late 1985 and SPRI issued it in early 1986 In late 1988 the guideline became ANSISPRI RP-4 The guide was based on wind tunnel research conducted by Kind and Wardlaw1 and anecdotal stud-ies of actual field performance which led to development of a computer model to predict wind performance of ballasted systems Additional field studies were conducted to evaluate the computer model However there is no documentation of pavers being included in the field studies RP-4 was referenced in the 1994 and subsequent edi-tions of the Standard Building Code how-ever it was not referenced in the National Building Code nor the Uniform Building Code RP-4 was referenced in the 2000 and subsequent editions of the International Building Code (IBC)

RP-4 is relatively easy to use It provides lookup tables for various parapet heights The maximum allowable wind speed is a function of the parapet height building

Table 1 ndash Table IIC Maximum Allowable Stress Design Wind Speeds (mph)

height exposure and ballast type Pavers weighing 22 psf minimum are included in System 3 See Table 1 (Table IIC) which is for parapets from 12 in to less than 18 in

RP-4 (2013) references ASCE 7-10 for basic wind speeds which are strength design (ultimate) speeds However the max-imum allowable speeds in the tables are ldquoallowable stress designrdquo speeds RP-4 pro-vides the conversion from strength design to allowable stress design speed Strength design x radic06 = allowable stress design For example 115 mph (strength) x radic06 = 89 mph allowable stress design speed RP-4 mentions Exposure D but this exposure is not addressed in the tables

The tables do not address building heights greater than 150 ft For greater heights RP-4 says that the ldquohelliproof design shall be designed by a registered design professional using current wind engineer-ing practices consistent with ASCE 7 and the design shall be approved by the author-ity having jurisdictionrdquo Some additional guidance is given in the commentary but the guidance is insufficient The design guidelines in Appendix A address this shortcoming

RP-4 references research regarding the


Figure 1 ndash View of lifted pavers on the fifth floor roof The red arrow indicates a paver resting on the top of the parapet

influence of the space between and under-neath pavers (Bienkiewicz 1997) However the guidance is not easy for designers to use Although not explicitly stated the RP-4 tables are based on butted pavers resting on a fabric protection mat or the roof mem-brane Section 4 below discusses the influ-ence of gaps between pavers and the space underneath them These influences are accounted for in the recommended design guidelines in Appendix A

3 PAvER WIND UPLIFT PROBLEMS The real test of a design standard is

its comparison to field data However published informa-tion on the performance of concrete pavers in hurricanes or other high-wind events is very limited The follow-ing six case histories docu-ment some of the paver wind uplift problems that have occurred2 They provide an opportunity to establish a few data points for comparison to RP-4 (2013) and to the rec-ommended design guidelines in Appendix A There have been paver uplift problems in addition to the following case histories However often there is no effort to report the prob-lems or there is a deliberate effort to avoid reporting them Hence the frequency of prob-

lem occurrence is unclear The case histories include the follow-

ing information the estimated wind speed at the time of failure (the speeds are for a peak gust at 33 ft Exposure C) the basic wind speed given in ASCE 7-10 and a com-parison between RP-4 (2013) and installed conditions

Five of the case studies had roof heights exceeding 150 ft (the maximum roof height given in the RP-4 tables) Only one of these roofs incorporated wind uplift enhancement (ie metal strapping) At four of the case studies paver uplift generally occurred

Figure 2 ndash View of a paver that lifted shifted to the right and then sat down The lifted paver was near the parapet (red arrow)

in or near roof corners (see Section 4 for discussion of conical vortices near roof corners)

Hurricane Andrew (South Florida 1992)

Many pavers on the fifth floor roof of an office build-ing were lifted and broken (Smith 1994) (Figures 1 and 2) Some pavers on lower-level balconies also were lifted The building was located adjacent to the coast (Exposure D) The ASCE 7-10 basic wind speed is 169 mph (strength design speed) The equivalent allowable stress design wind speed for use with RP-4 is 131 mph The eventrsquos ma ximum wind

speed at this site was estimated to be in excess of 175 mph (Powell et al 1996)

The 30- x 30- x 2-in pavers weighed approximately 1495 pounds each (239 psf ) The pavers were on 1frac12-in-high plastic pedestals A parapet extended 3frac12 in above the top of the pavers The pavers were over a concrete plaza deck there was no bal-looning of the roof membrane This failure may have been due in part to the buildingrsquos stair shape

RP-4 Table IIA indicates that the installed paver system has a maximum allowable wind speed of 120 mph for


Figure 4 ndash Lifted pavers and paver fragments are indicated by the red arrows The dashed red line indicates where pavers where blown

away The dashed yellow arrow at the bottom of the figure indicates a paver leaning against

the parapet The blue X indicates a band of cast concrete that overturned The blue dashed

arrow indicates a band of concrete that lifted and shifted towards the parapet

Figure 3 ndash General view of the roof Scoured aggregate is shown by the dashed yellow arrows Lifted pavers occurred in the corner area (red arrow) The red arrow indicates the direction of view in Figure 4 and the primary wind direction

Exposure C3 The installation did not comply with the current edi-tion of RP-4 because the maximum allowable speed is less than the design speed The calculation procedure given in Appendix A shows paver uplift at a speed below the estimated speed

Hurricane Katrina (New Orleans 2005) This 27-story building had an aggregate ballasted membrane

with two rows of pavers (estimated to be 18 x 18 in) around the roof perimeter (FEMA P-549) A band of concrete about 3 ft wide was adjacent to the pavers The concrete was cast over insulation A parapet extended approximately 12 in above the top of the pav-ers Several pavers were lifted and broken (Figures 3 and 4) The office building was located in Exposure B The ASCE 7-10 basic wind speed is 144 mph The equivalent allowable stress design wind speed for use with RP-4 is 112 mph The eventrsquos estimated maximum wind speed at this site was 105 mph

The roof height exceeds the height given in the RP-4 tables Table IIB prescribes a maximum roof height of 75 ft with a 12-in parapet The calculation procedure given in Appendix A shows paver uplift at a speed below the estimated speed

Straight-Line wind (Midwest 2010)

Several pavers lifted and one blew off a 52nd-floor terrace roof of an office building (Irwin 2012) (Figure 5 ) The building was located in Exposure B The 2- x 2-ft pavers weighed 95 pounds each (2375 psf ) Figure 5 ndash View of lifted pavers (Irwin 2012 Figure 5)


A

Pavers on tabsB

Figure 6 ndash (A) Different types of paver systems B) wind flow through the paver gaps

The pavers were on 58-in-high pedestals The first two rows from the parapet had metal straps The ASCE 7-10 basic wind speed is 115 mph The equivalent allowable stress design wind speed for use with RP-4 is 89 mph The estimated maximum wind speed at this site was about 68 mph

The roof height exceeds the height given in the RP-4 tables With a parapet less than 24 in Table IID prescribes a maxi-mum roof height of 150 ft and a maximum allowable wind speed of 110 mph (which is 21 mph above the design wind speed) for unstrapped pavers The calculation proce-dure given in Appendix A shows paver uplift at a speed below the estimated speed

A wind tunnel investigation of this paver uplift problem contributed to the recom-mended design guidelines in the appendix

Straight-Line Wind (Midwest 2012) Five pavers adjacent to the parapet blew

off of a 600-ft-tall office building (Freeman 2016) These pavers were about 20 ft from a roof corner The building was located in Exposure B The 2-ft x 2-ft x 2-in pavers weighed approximately 22 to 24 psf A para-pet extended approximately 11 in above the top of the pavers The ASCE 7-10 basic wind speed is 115 mph The equivalent allowable stress design wind speed for use with RP-4 is 89 mph The eventrsquos estimated maximum wind speed at this site was 90 mph

The roof height exceeds the height given in the RP-4 tables Table IIB prescribes a maximum roof height of 75 ft with an 11-in

Pavers on pedestals

parapet The calcu-lation procedure given in Appendix A shows paver uplift at a speed below the estimated speed

Microburst (Midwest 2013)4

About 20 pavers lifted but did not

blow off a 30th-floor terrace roof of an office building (Freeman 2016) These pavers were in the field of the roof The building was located in Exposure B The 2-ft x 2-ft x 2-in pavers weighed approximately 22 - 24 psf A parapet extended approximately 42 in above the top of the pavers The ASCE 7-10 basic wind speed is 115 mph The equivalent allowable stress design wind speed for use with RP-4 is 89 mph The eventrsquos estimated wind speed was not determined

The roof height exceeds the height given in the RP-4 Tables With a 42-in parapet Table IIF prescribes a maximum roof height of 150 ft and a maximum allowable wind speed of 140 mph (which is substantially above the design wind speed) The calcula-tion procedure given in Appendix A shows paver uplift at a speed below the ASCE 7-10 basic wind speed

Straight-Line Wind (Midwest 2016) Five pavers in the second row from

Integrated leg pavers

the parapet lifted and one of them blew off the roof of a 260-ft-tall condominium building These pavers were in an area that experienced cornering wind The building was located in Exposure B The 2-ft x 2-ft x 2-in pavers weighed 92 pounds each (23 psf ) The pavers were tightly butted and rested on a fabric protection mat over the roof membrane All or a portion of the roof membrane was unadhered However because the concrete roof deck served as an air retarder membrane ballooning was judged not to have contributed to paver uplift A parapet extended nearly 12 in above the top of the pavers The ASCE 7-10 basic wind speed is 115 mph The equiva-lent allowable stress design wind speed for use with RP-4 is 89 mph The estimated maximum wind speed at this site was less than 60 mph

The roof height exceeds the height given in the RP-4 tables Table IIB prescribes a maximum roof height of 75 ft with a para-pet less than 12 in The calculation proce-dure given in Appendix A shows paver uplift at a speed below the estimated speed

4 PAv E R AE R O DYN AMIC ME C H ANI S M S

Pavers are often placed on the roof with gaps in between them and spacing under-neath the pavers above the roof membrane (using pedestals tabs integrated leg pav-ers etc [Figure 6A]) Since air can readily

Figure 7 ndash Paths of corner vortices and resulting suction variations on roof


A B

Figure 8 ndash General mechanism of uplift on roof pavers (A) Pressure distributions on upper and lower surfaces of a roof paver (B) Straps running transverse to the axis of the vortex

leak around the edges of pavers the pres-sure distribution produced by the wind flow over the outer surface of the roof pav-ers produces secondary flows through the spaces between and underneath the paver elements (Figure 6B )

The pressure distribution under the roof pavers is related to but different from that on the outer surface If there is sufficient permeability the response of underneath pressure to external pressure change is almost instantaneous Consequently the net wind load on a paver might be signifi-cantly lower than that on an impermeable roof surface due to the existence of a pressure field underneath the pavers that almost instantly responds to the external pressure change The pressure equalization effect greatly reduces the net uplift force on pavers in most areas of roofs However in areas where very high spatial gradients of pressure existmdashsuch as those that occur under conical vortices near roof cornersmdash significant net uplift pressures can still occur Figure 7 illustrates the typical path of the conical vortices over a low-slope roof for cornering winds

The pressure equalization effect is sub-ject to a number of influencing variables such as the paverrsquos location relative to a corner paver size and geometry parapet height building height gaps between pav-

ers and the stand-off distance of the pav-ers above the underlying roof surface The aerodynamic uplift force is the difference between the pressure on the lower surface of the paver PL and the pressure on the upper surface PU (Figure 8) The pressure on the upper surface due to the presence of a corner vortex (solid curve) is negative and has a concentrated peak The pressure on the lower surface tends to vary roughly linearly between the pressures at the paver edges and is depicted by the broken curve It is only due to the sharp peak of the negative pressure under a vortex (between points A and B) that a net uplift occurs signified by the large difference between the solid and broken curves If the upper surface pressure does not have the peak then pressure equalization caused by flow around the edges of the paver results in smaller net uplift as shown by the small differences between the solid and dashed curves on the pavers outside of the zone between points A and B

Interlocking

case the uplift force tends to be shared across several pavers Figure 8(b) shows a strapping system running transverse to the axis of the vortex that connects to the center of each paver The lift on the paver AB is now restrained not only by the weight of paver AB but also by at least part of the weight of the adjacent pavers on which there is little if any lift

At sufficient wind speed the aerody-namic uplift force andor the overturn-ing moment on the element may become higher than the weight andor the resisting moment due to gravity or other restraints such as strapping and liftoff will occur The aerodynamic mechanisms that cause uplift are quite complex but in this paper relatively simple guidance for the design of loose-laid roof pavers against wind uplift is presented The simplified guidance is a reasonably accurate method for calculating the net uplift force on paver systems from the existing external pressure coefficients in ASCE 7-10 and takes into account the effect of paversrsquo edge-gap to spacer height ratio relative parapet height and pressure equalization

5 EXPERIMENTAL SETUP AND RESEARCH TESTING PROTOCOL

A number of large-scale experiments were performed by three of the authors and have been described in earlier papers (Asghari Mooneghi et al 2014 Asghari Mooneghi 2016) Here a summary of the experimental setup and testing protocol is

A

B and strapping systems a re sometimes used to improve the wind perfor-mance of roof pavers In this

Figure 9 ndash Wall of Wind Florida International University (A) Inlet view (B) Outlet view spires and floor roughness elements


C

B

B

Figure 11 ndash Details of the experimental setup

(A) Pavers numbering (B) Critical pavers instrumented

with pressure taps

A A on the roof which can be considered as modeling typical 2-ft-square pavers at half scale (Figure 10(a)) The pavers were numbered from 1 to 100 (Figure 11(a)) In order to study the effects of the paversrsquo edge-gap to spacer height ratio adjust-able-height pedestals were used to change the space between the pavers and the roof deck (Hs Figure 10(c)) A constant G=0125-in space (at model scale) between adjacent pavers was maintained For the pressure measurements pavers with exactly the same dimensions as the concrete pavers were made from Plexiglas which made it more convenient to install pressure taps on both upper and lower surfaces (Figure 11(b))

A total of 13 experi-ments were carried out including three wind blow-off tests and 10 pressure measurement tests A sum-mary of the parameters for each test is given in Table 2Figure 10 ndash Test setup configuration

(A) Test building for wind blow-off sealed and rigid The rectangular The test procedure consisted of first tests sharp-edged parapets on the building conducting wind lift-off tests to find the

(B) Test building for pressure model were interchangeable which location where paver lift-off first occurred measurements allowed the parapet height to be Only one wind direction was tested which

(C) Geometric parameter definition adjusted There were no parapets on the leeward

presented and the reader is referred to the side of the building This earlier papers for a more comprehensive was done with the intent that description the model roof could then be

The experiments were performed in representative of the windward the 12-fan Wall of Wind (WOW) open jet corner of a larger roof structure facility at Florida International University on which the downwind par-(FIU) which is able to generate hurricane- apets would not significantly force winds up to Category 5 on the Saffir- influence flow over the upwind Simpson Scale The size of the WOW test portions of the roof (Asghari section is 20 ft wide by 14 ft high A set Mooneghi et al 2016) of triangular spires and floor-roughness Both wind blow-off testing elements was used to generate appropriate (ie blowing at sufficient speed turbulence and boundary layer characteris- to dislodge pavers) and pressure tics (Figure 9) measurements were performed

The size of the 12 test-building model For the wind blow-off tests was 11 by 11 ft in plan by 5 ft high rep- concrete pavers with dimen- Constant G=0125 in (at model scale) for all tests resenting (at half scale) a low-rise prototype sions of 1 ft by 1 ft by 1 in Parapet height was measured from top of the pavers building with a height of 10 ft The roof deck thickness with weight-per-unit

Test Number GHs (hpH)windward

Wind Uplift 1 025 005 Wind Uplift 2 0083 005 Wind Uplift 3 0028 005

Pressure 1-1 025 005 Pressure 1-2 025 0067 Pressure 1-3 025 01

Pressure 2-1 0083 0033 Pressure 2-2 0083 005 Pressure 2-3 0083 01 Pressure 2-4 0083 015


leeward building sides did not have any parapet was made from plywood and was completely area of 112 lbft2 were installed Table 2 ndash Test number and characteristics


Test Number Failure wind speed Failure wind speed when wobbling of when a couple of pavers pavers started (mph) lifted off from roof (mph)

Wind Uplift 1 1118 12012



Table 3 ndash Failure wind speed

was 45deg relative to the roof edge Based on past studies this wind direction was assessed to be the critical orientation for generating high paver uplift under coni-cal vortices on low-slope rectangular roofs (Holmes 2015) The failure wind speeds measured at the roof height of the test model (5-ft height) are reported in Table 3 These values are converted to full-scale values using Froude number scaling (ie full-scale velocity =radic2timesmodel velocity) The values reported in Table 3 are equivalent to three-second (3-s) gust speeds at full scale

The failure mechanism for the wind lift-off tests is explained in detail in the previ-ous paper by three of the authors (Asghari Mooneghi et al 2014) The failure in each case is shown in F ig ure 12

For pressure measurements the origi-nal concrete pavers were replaced by the Plexiglas pavers with installed pressure taps (total of 447 pressure taps were used) The pressure tap layout is given in Asghari Mooneghi et al 2014 Nine critical pavers were fitted with a total of 256 pressure taps to allow accurate measurements to be made of the pressure distribution on the top and bottom surfaces (F ig ure 11(a) )

Pressure measurements were carried out at a wind speed of 41 mph which was below the failure speed of concrete pavers A 512-channel Scanivalve Corporation pres-sure scanning system was used for pres-sure measurements Pressure data were acquired at a sampling frequency of 512 Hz for a period of three minutes Data

were low-pass filtered at

in the post-test analysis (Irwin et al 1979) To ensure the accuracy of the pressure measurements wind velocities for the pav-ersrsquo lift-off calculated from the pressure measurement results were compared to the results obtained from the wind lift-off tests (Asghari Mooneghi 2016)

6 E X P E R IME N TAL R E S U LT S AND D I S C U S SI O N 61 Aerodynamic Pressure Results

In this section the results from the pressure measurement experiments are discussed The mean pressure coefficient at any location was obtained from Equation 1

Where Pmean is the mean pressure P0 is the static reference pressure ρ is the air density at the time of the test (00765 lbft3) and U is the mean wind speed measured at the building height of the test model (5 ft) The peak pressure coefficient was obtained from Equation 2

Where Ppeak is the peak pressure and

A

B

C

30 Hz (equivalent to 21 is the peak 3-s gust at the reference U3s

Hz at full scale) A trans- height fer function was used to correct for tubing effects The tests were performed in a par-

tial turbulence simulation in which low-Figure 12 ndash Failure frequency turbulence cannot be simulated of roof pavers during correctlymdashmainly due to the size limitations wind blow-off tests of the wind testing facilities for large-scale (A) GHs=025 testing (Asghari Mooneghi et al 2014 and (B) GHs=0083 2016) In order to calculate the equivalent (C) GHs=0028 full-scale peak pressure Ppeak a method

called Partial Turbulence Simulation (PTS)


was used which ensures the accuracy of the results obtained from tests in flows with partial turbulence simulation The PTS method is discussed in detail in Asghari Mooneghi (2014) and Asghari Mooneghi et al (2016) For evaluation of these estimates the peak value with 85 probability of not being exceeded in one hour of full-spectrum wind was selected

The net total pressure coefficient defined as the instantaneous difference between the external and the corresponding underneath pressure coefficient at the same

Figure 13 ndash Pressure coefficient contours (GHs=0028 and hpH=0)location shown in Equation 3

Mean external and underneath pres-sure coefficient contours for the case of G Hs=0028 and hpH=0 (ie a no-parapet case) are given in Figure 13 The results of the tests show that pavers close to the edges and corners of the roof are subjected to the highest local negative pressures These areas are under the conical vortices As compared to external pressures the underneath pressures are lower in magni- Figure 14 ndash Definition of the point of action of the resultant lift force tude and show more uniformity In all tests (A) Plan view Paver 21 was shown to be the most critical (B) Side view (at Figure 2 the overturning moment [L]paver So in the rest of the paper results exceeded the resisting moment [W]) are calculated for this paver Where d is the moment arm defined as For hpH ratios beyond 01 the reduction

The overall wind lift load L(t) acting the distance from a selected axis to each factor reduces gradually ie improved per-on any single paver and the lift coefficient point on the paver (Figure 14) formance of the pavers can be expected CL(t) are obtained as shown in Equations 4 Figure 15 shows the highest local suc-and 5 tion coefficients for various GHs and hpH 52 Effect of Connecting Pavers

ratios The GHs ratio affects the underside Many types of interlocking and strap-pressures such that the higher the ratio the ping systems exist that can be used to less the net pressure on the pavers improve the wind performance of roof paver

The reduction in the net wind uplift can systems The effects of specific systems be expressed as shown in Equation 8 have not been dealt with during the experi-

ments in this study However guidance on Where A is the surface area of the paver the effectiveness of these systems can be

It should be noted that the highest suction obtained by evaluating the net uplift on on the paver does not necessarily occur at The reduction factor defined as the ratio groups of pavers rather than only one The the center of the paver This means that of the net lift coefficient to the external lift value is calculated for six different CLnet

even for cases where the total uplift force coefficient is plotted as a function of rela- cases shown in Figure 17 and compared is less than the weight of the paver the tive parapet height (hpH) for different GHs to the highest CLnet value observed during weight of the paver might not overcome the for Paver 21 (Figure 16 ) the experiments on Paver 21 (Figure 18) corresponding overturning moment from The results show that increasing the G In Figure 17 the highlighted pavers were the wind suction forces The overturn- Hs ratio decreases the reduction factor This assumed to act as a single unit for the case ing moment about a selected axis and the means that the correlation between upper of GHs=0083 and hpH=005 The most moment coefficient CM(t) can be obtained and lower surface pressures decreases by critical paver is shown with an X mark from Equations 6 and 7 decreasing the GHs ratio Thus increasing The results demonstrate the effect of

the ratio of the paversrsquo edge-gap to spacer connecting pavers together in reducing net height can reduce the net wind-induced uplift force Different degrees of improve-uplift loading on the pavers and improve ment can be expected for different strapping the performance of the pavers The reduc- or interlocking systems It should be noted tion factor is not very sensitive to parapet that the surface pressure variation along height for hpH values less than about 01 the axis of the vortex varies much more


Figure 15 ndash Highest local suction coefficients on the roof CLext on Paver 21 CLnet

Figure 16 ndash Reduction factor r= CLnet frasl CLext

Figure 17 ndash Interlocked pavers in different configurations

slowly than in the transverse direction So strapping in the direction roughly parallel to the axis of the vortex is not expected to be as effective in restraining pavers from liftoff as strapping in the transverse direction Real strapping systems rarely align directly with the vortex axis or transverse to it Therefore strapping in both orthogonal directions of a paving system is preferable

Asghari Mooneghi et al (2016) showed that the wobbling of the pavers starts at slightly lower speed than would be predicted purely on the basis of the mean CLnet

value However assuming that the full-gust speed is required to start wobbling of the pavers this would be on the conservative side (ie use the peak CLnet value)

7 DESIGN GUIDELINES FOR PAvERS Based on the results from the experiments Equation 9 is

proposed for the design of loose-laid roof pavers

Where R1 is a reduction factor for different gap ratios and is a reduction factor for different parapet heights These are R2

to be applied to the ASCE 7-10 exterior pressure coefficients for Figure 18 ndash Comparison between CLnet values for different

components and claddings in Zone 3 Here Zone 3 in ASCE configurations defined in Figure 17


Figure 19 ndash R1 reduction factor for different GHs ratios (based on ASCE 7-10 Fig 304-2A Zone 3)

7-10 is chosen as the worst-case scenario for design of roof pavers However R1 in Equation 9 can be modified to take into account the effects of location on the roof Failure is defined here as the start of wobbling R1 and R2 are to be calculated from the diagrams proposed in the following The equivalent uplift force can then be calculated by multiplying Equation 9 by the dynamic pressure at roof height

71 R_1 reduction factor Effect of GHs ratio The reduction factor is defined as CLnet

in which frasl CPext

is the ASCE 7-10 exterior pressure coefficient for com-CPext

ponents and cladding in Zone 3 and CLnet values were cal-

culated using the formula in Equation 10 in which failure is assumed to occur with the start of wobbling

Figure 20 ndash R2 reduction factor for different hpH ratios

Figure 21 ndash Critical wind speed vs GHs (hpH=005 for wind measurements)

The proposed reduction factor R1 based on GHs ratio is plotted in Figure 19 The value at GHs ~ 0 comes from assuming CLnet

=-2 in which CLext

is assumed to be -28 and CLint =-08 which

is approximately calculated from averaging the external peak pressure coefficients on pavers 11 12 21 22 31 and 32 The R1 fac-tor changes an exterior local peak pressure coefficient into a net lift coefficient taking into account the pressure distribution over the paver and the effect of GHs on pressure equalization

72 R2 Reduction Factor Effect of Parapet Height

reduction factor is proposed based R2

on results presented in Figure 16 For rela-tive parapet height ratios less than 01 no reduction in the C_L value is proposed (ie R2=1) In ASCE 7-10 Figure 304-2A it is stated that the external pressure coefficients for Zone 3 can be reduced to the values in Zone 2 for parapets higher that 3 ft This means about 36 reduction for hpH ratio of 03 and higher for the current experimental setup This value is considered as the upper limit of the reduction proposed in Figure 20 (ie hpH=03) Kind et al (1987) proposed hpH=01 hpH=002 and hpH=003 for low- mid- and high-rise buildings respec-tively above which a somewhat rapid reduc-tion in the worst suction values due to the parapet was observed This would imply that application of the reduction factor in Figure 20 to mid- and high-rise buildings would be conservative

Figure 21 shows the critical lift-off speeds from the measurements compared to values in the recommended guideline (black line) in Appendix A


8 RECOMMENDATIONS The following are recommended to the

SPRI RP-4 committee bull Reevaluate the tables using the cri-

teria in Appendix A bull Change the allowable wind speeds

in the tables to strength design speeds

bull Add Exposure D to the tables bull Ballot the design guidelines in

Appendix A for inclusion in the com-mentary

The following are recommended for future research

bull The recommended design guide-lines in Appendix A are based on 2-ft x 2-ft x 2-in paver research Research is needed to investigate the applicability of the guidelines for pavers with very different sizes and aspect ratios

bull The recommended design guidelines in Appendix A are expected to be conservative when applied to mid- and high-rise buildings However further research is needed to fully quantify the effects of these building heights

bull It is recommended that wind tunnel research at large scale or full scale be conducted to further evaluate mdash The characteristics and wind

performance of interlocking or strapping systems

mdash The effect of gap geometry (including gap depth) on air flow resistance

mdash The effects of ice or snow inover the gaps on wind performance

REFERENCES ANSISPRI RP-4 (2013) Wind Design

Standard for Ballasted Single-ply Roofing Systems Available at httpswwwspriorg

ASCE 7 (2010) Minimum Design Loads for Buildings and Other Structures American Society of Civil Engineers Virginia

M Asghari Mooneghi (2014) ldquoAnalytical and Experimental Methodologies for Predicting Peak Loads on Building Envelopes and Roofing Systemsrdquo FIU

Electronic Theses and Dissertations Paper 1846 httpdigitalcommons fiueduetd1846

M Asghari Mooneghi P Irwin and A Gan Chowdhury (2014) ldquoLarge-Scale Testing on Wind Uplift of Roof Paversrdquo Journal of Wind Engineering amp Industrial Aerodynamics Vol 128 22-36

M Asghari Mooneghi P Irwin and A Gan Chowdhury (2016) ldquoTowards Guidelines for Design of Loose-Laid Roof Pavers for Wind Upliftrdquo Wind and Structures Vol 22 No 2 133-160

M Asghari Mooneghi P Irwin and A Gan Chowdhury (2016) ldquoPartial Turbulence Simulation Method for Predicting Peak Wind Loads on Small Structures and Building Appurtenancesrdquo Journal of Wind Engineering amp Industrial Aerodynamics Vol 157 47-62

B Bienkiewicz and Y Sun (1997) ldquoWind Loading and Resistance of Loose-Laid Roof Paver Systemsrdquo Journal of Wind Engineering amp Industrial Aerodynamics Vol 72 401-410

FEMA P-549 2006 Mitigation Assessment Team Report Hurricane Katrina in the Gulf Coast Building Performance Observations Recommendations and Technical Guidance 5-59 and 5-63

TW Freeman TW Freeman Consultants LLC personal communication July 2016

RJ Gillenwater (1985) ldquoWind Design Guide for Ballasted Roofing Systemsrdquo Proceedings of the Second International Symposium on Roofing Technology NRCA 219-229

P Irwin K Cooper and R Girard (1979) ldquoCorrection of Distortion Effects Caused by Tubing Systems in Measurements of Fluctuating Pressuresrdquo Journal of Wind Engineering amp Industrial Aerodynamics Vol 5 (1-2) 93-107

P Irwin C Dragoiescu M Cicci and G Thompson (2012) ldquoWind Tunnel Model Studies of Aerodynamic Lifting of Roof Paversrdquo Proceedings of the Advances in Hurricane Engineering Conference ASCE and ATC Miami

Florida October RJ Kind MG Savage and RL

Wardlaw (1987) ldquoFurther Wind Tunnel Tests of Loose-Laid Roofing Systemsrdquo National Research Council of Canada Report LTR-LA-294

D Powell S Houston and T Reinhold (1996) ldquoHurricane Andrewrsquos Landfall in South Florida Part 1 Standardizing Measurements for Documentation of Surface Wind Fieldsrdquo Weather and Forecasting American Meteorological Society p 304

TJ Smith (1994) ldquoCauses of Roof Covering Damage and Failure Modes Insights Provided by Hurricane Andrewrdquo Hurricane of 1992 Lessons Learned and Implications for the Future ASCE p 309

FOOTNOTES 1 The references section of RP-4 pro-

vides a list of Kind and Wardlaw research reports and papers

2 All dimensions in Section 3 are approximate

3 RP-4 discusses Exposure D but does not provide guidance for use of the tables with this exposure

4 This wind damage was evaluated by TLSmith Consulting Inc

5 This procedure is based on Asghari Mooneghi 2017

6 For the RP-4 ballot insert Figure 19 If the ballot is based on the 2016 edition of ASCE 7 the R1 value will need to be adjusted to suit the revised pressure coefficient for low-rise buildings Also add R1 values for the low-rise perimeter and field zones and for heights greater than 60 ft

7 This is a conservative estimate Research is needed to refine this value

8 Prior to balloting R1 values for other pedestal dimensions could be added to Table X

9 For the RP-4 ballot insert Figure 20 10 For the RP-4 ballot insert Figure

14b 11 The 15 threshold is based on judg-

ment Research is needed to refine this value


APPENDIX AProposed Addition to RP-4 Commentary

Revise Section 32 to require designing squared-edged pavers in accordance with the following design procedure when the roof height exceeds 150 ft Also add narrative in the standard to allow use of this design procedure when the maximum allowable wind speed in the tables is less than the ASCE 7 basic wind speed

Delete the C32 text and replace with the following

C32 Square-edged 2- x 2-ft pavers are permitted on roofs with heights greater than 150 ft (46 m) or where the ASCE 7 basic wind speed exceeds the maximum allowable wind speed given in the RP-4 tables when designed by a registered design professional in accordance with the following procedure5

Step 1 Calculate the net uplift coefficient on the pavers using the following equation

= R1 times R2 times CCLnet p ASCE 7exteriorCampCZone 3

Where CLnet is the net uplift pressure coefficient R1 is a reduc-

tion factor based on the ratio of the gap between pavers (G) and the height of the space underneath pavers (Hs) R2 is a reduction factor based on the ratio of the height of the parapet above the top of the pavers (hp) and the height of the top of the parapet above grade (H) Cp is the ASCE 7 external pressure coefficient for the roof corner zone

Determine R1 from Figure 196 or Table X

GHs ratio R1

Butted pavers resting on a fabric protection mat or roof membrane

077

Pavers supported on pedestals that provide a 18-in-wide gap between and a 58-in space underneath pavers

0261

Table X ndash R1 reduction factor for different GHs ratios (based on Figure 19)8

Determine R2 from Figure 20 9

Step 2 Determine the uplift pressure on the pavers by cal-culating the velocity (dynamic) pressure per ASCE 7 and multiply that value by R1 and R2

The roof membrane shall be fully adhered or the roof assembly shall incorporate an air retarder that avoids ballooning of the roof membrane

Step 3 Determine the overturning moment induced by the uplift pressure For 2- x 2-ft pavers the overturning moment arm is conservatively estimated to occur 015 ft from the center of the paver (Figure 14b)10

Step 4 Determine the paverrsquos resisting moment The resist-ing moment shall be greater than the overturning moment If the

resisting moment is not greater than the overturning moment increase the needed resistance by specifying a heavier paver or by connecting the pavers See Step 5 for paver connection criteria

Step 5 Determine the uplift resistance of connected pavers Assume all pavers in the corner zone are connected If straps are used they shall run in both orthogonal directions and they shall be connected to the pavers with concrete screws Apply a reduction factor of 04 to the CLnet value obtained using Step 1 to calculate the CLnet value for the strapped case To obtain the uplift on a single paver multiply CLnet for the strapped case times the ASCE 7 veloc-ity (dynamic) pressure times the area of the paver Then repeat Steps 3 to 4 using this new value

To determine whether or not connecting is needed in the field andor perimeter zones repeat Steps 1 to 4 using the uncon-nected CLnet value and the ASCE 7 field and perimeter external pressure coefficients If connecting is not required in the field or perimeter zone the connected zone shall extend a minimum of two pavers into the unconnected zone

If the unstrapped overturning moment (Step 3) exceeds the unstrapped resisting moment (Step 4) by less than 15 a single strap in each orthogonal direction is permitted If it is 15 or greater there shall be two straps in each orthogonal direction11 The center of the straps shall be approximately 3 in from the edge of the pavers

Step 6 A perimeter restraint (such as an angle attached to the parapet) shall be designed to prevent the edge of the paver at the parapet from lifting

Example The following example illustrates the design pro-cedure using ASCE 7-10 30-ft-tall hospital (Risk Category III) 185-mph basic wind speed Exposure B 2- x 2-ft pavers weighing 22 psf on 18- x 58-in-high pedestals with a parapet that is 2 ft 11 in above the top of the pavers RP-4 (2013) Table IIE gives a maximum allowable stress design wind speed of 140 mph (which equals a strength design wind speed of 181 mph) which is less than the ASCE 7 basic wind speed To determine if the proposed system is acceptable

Step 1 calculate the net uplift coefficient on the pavers (CLnet) R1 x R2 x Cp

bull Determine R1 Gap divided by space underneath (GHs) = 18 in divided by 58 in = 02 On the horizontal axis of Figure 19 02 = 0261 on vertical axis which is R1 For the selected pedestal R1 can also be obtained from Table X

bull Determine R2 Height of the parapet above the top of the pavers (hp) divided by the height of the top of the parapet above grade (H) = 292 ft divided by 30 ft = 0095 On the horizontal axis of Figure 20 0095 = 1 on the vertical axis which is R2 Hence this parapet offers no load reduction

bull Determine Cp Pressure coefficient of the roof corner zone from Figure 304-2A in ASCE 7 = -28

Therefore CLnet = 0261 x 1 x -28 = -073


APPENDIX A (continued)Proposed Addition to RP-4 Commentary

Step 2 determine the uplift pressure on the pavers by calcu-lating the velocity (dynamic) pressure per ASCE 7 and then multi-plying that value by CLnet

bull Velocity pressure ASCE 7 equation 303-1 000256 x Kz

x Kzt x Kd x 1852 mph Kz for a 30-ft building = 070 Kzt

(topography) = 1 Kd (directionality factor) = 085 Therefore 000256 x 070 x 1 x 085 x 1852 = 5213

bull Velocity pressure multiplied by CLnet = 5213 x -073 = -3806 psf uplift

Step 3 determine the paverrsquos overturning moment induced by the uplift pressure

bull The uplift load on a single paver is -3806 psf x 4 sq ft = 152 lbs

bull The point of action of the net uplift force is 015 ft from the center of the paver (hence the moment arm is 115 ft) The overturning moment is therefore 115 ft x 152 lbs = 175 foot-pounds

Step 4 determine the paverrsquos resisting moment The dead load of a 22 psf 2- x 2-ft paver is 88 lbs The point of action of the net resisting force is 1 ft from the edge of the paver (hence the moment arm is 1 ft) The resisting moment is 1 ft x 88 lbs = 88 foot-pounds The 88 foot-pounds resisting moment is less than the 175 foot-pounds overturning moment

Therefore either pavers could be connected or heavier pavers could be specified or the height of the parapet could be increased First try connecting the pavers

Step 5 determine resistance of connected pavers 04 x CLnet x velocity pressure x area of one paver (04 x 3806 [from Step 2]) x 4 sq ft = 609 pounds of uplift force on a single paver The overturn-ing moment is 115 ft x 609 pounds = 70 foot-pounds The resist-ing moment is 88 foot-pounds (from Step 4) Hence the resistance provided by the strapped pavers is higher than the overturning moment and the paver array is stable

Alternatively try a taller parapet to reduce the uplift load on the pavers Table IIF is for parapets up to 6 ft however it gives the same maximum allowable speed as IIE Try a 7-ft parapet

Repeat Step 1 using R2 based on a 7-ft parapet bull Determine R2 Height of the parapet above the top of the

pavers (hp) divided by the height of the top of the parapet above grade (H) = 7 ft divided by 30 ft = 0233 On the horizontal axis of Figure 20 0233 = 076 on the vertical axis which is R2 Hence this parapet height offers load reduction

bull Therefore CLnet = 0261 x 076 x -28 = -056

Repeat Step 2 determine the uplift pressure on the pavers by calculating the velocity (dynamic) pressure per ASCE 7 and then multiply that value by CLnet

bull Velocity pressure = 5213 (from previous Step 2) bull Velocity pressure multiplied by CLnet = 5213 x -056 =

-2919 psf uplift

Repeat Step 3 determining the paverrsquos overturning moment induced by the uplift pressure

bull The uplift load on a single paver is -2919 psf x 4 sq ft = 11676 pounds

bull The overturning moment is therefore 115 ft x 11676 pounds = 1343 foot-pounds

It can be seen that the overturning moment is reduced by 1343175 = 077 when using a 7-ft parapet However for this case the overturning moment is still higher than the paverrsquos resisting moment (same as previous Step 4) = 88 foot-pounds Therefore stay with the 2-ft 11-in parapet and strap the pavers in the corner zone (plus extend two rows into the adjacent perimeter and field zones) Also calculate stability in the perimeter zone to deter-mine if that zone needs to be strapped (for brevity this calculation is not included in this example)


Abstract

This paper presents large-scale experiments in the Wall of Wind a large-scale hurricane testing facility at Florida International University (FIU) Based on the experimental results simplified paver design guidelines were developed The guidelines include load reduction fac-tors associated with gaps and parapet height and are formatted for use with ASCE 7-10 The guidelines are proposed as an addition to the RP-4 Commentary in order to provide designers with specific credible design criteria for roof pavers

Speakers

Maryam Asghari Mooneghi PhD ndash Arup Advanced Technology and Research San Francisco CA

DR MARYAM ASGHARI MOONEGHI is a structural analyst in Advanced Technology and Research in Arup During her doctoral studies at FIU she performed extensive experiments in the Wall of Wind facility to investigate wind-loading mechanisms of roof pavers in order to develop guidelines for wind-resistant design of these systems She received a PhD in civil engineering from FIU and bachelorrsquos and masterrsquos degrees in aerospace engineering from Amirkabir University of Technology

Thomas L Smith RRC AIA FSEI ndash TLSmith Consulting Inc Rockton IL

TOM SMITH is president of TLSmith Consulting Inc He received the Carl G Cash Award from ASTM in 2013 for his body of work regarding wind damage investigations He was promot-ed to Fellow-grade membership of ASCErsquos Structural Engineering Institute (SEI) in 2013 The FSEI promotion was for his many years of service on the ASCE 7 Wind Loads Task Committee and for his body of work regarding wind damage investigations and wind design guides

Nonpresenting Coauthors

Peter Irwin PhD ndash Florida International University Miami FL

PETER IRWIN PHD is a Professor of Practice with the Department of Civil and Environmental EngineeringInternational Hurricane Research Center Florida International University Miami FL

Arindam Gan Chowdhury PhD ndash Florida International University Miami FL

ARINDAM GAN CHOWDHURY PHD is an Associate Professor in the Department of Civil and Environmental EngineeringInternational Hurricane Research Center Florida International University Miami FL












































A

Pavers on tabsB








Pavers on pedestals














A B






Interlocking





A




C

B

B



with pressure taps































A

B

C








































=-2 in which CLext





























































GHs ratio R1


077


0261





































-2919 psf uplift
















































A

Pavers on tabsB








Pavers on pedestals














A B






Interlocking





A




C

B

B



with pressure taps































A

B

C








































=-2 in which CLext





























































GHs ratio R1


077


0261





































-2919 psf uplift






A B






Interlocking





A




C

B

B



with pressure taps































A

B

C








































=-2 in which CLext





























































GHs ratio R1


077


0261





































-2919 psf uplift






C

B

B



with pressure taps































A

B

C








































=-2 in which CLext





























































GHs ratio R1


077


0261





































-2919 psf uplift





















A

B

C








































=-2 in which CLext





























































GHs ratio R1


077


0261





































-2919 psf uplift








































=-2 in which CLext





























































GHs ratio R1


077


0261





































-2919 psf uplift



























































GHs ratio R1


077


0261





































-2919 psf uplift
























-2919 psf uplift






concrete roof pavers: wind uplift aerodynamic mechanisms

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