Appendix I ESTIMATED DESIGN WIND PRESSURE AND STRENGTHS OF CONNECTIONS OF JOPLIN HOME DEPOT BUILDING

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1 ESTIMATED DESIGN WIND PRESSURE AND STRENGTHS OF CONNECTIONS OF JOPLIN HOME DEPOT BUILDING I.1 ESTIMATED DESIGN WIND PRESSURE BASED ON BOCA NBC/1996 Basic design wind speed: V = 90 mph (3 s gust) Exposure category: C Building parameters: Low rise, one story, 470 ft 250 ft in plan, with 28 ft mean roof height and 4 ft parapet Gust effect factor: G = 0.85 (rigid building) Partially enclosed. Internal pressure coefficient GC pi = ± 0.25 Importance factor: I = Design Wind Pressure for MWFRS: Basic velocity pressure: P V = V 2 = 20.7 lb/ft 2. Assume Condition I enclosure: GC Pi = ± 0.25 (see BOCA NBC/1996). The computed net internal pressure and internal suction based on BOCA NBC/1996 for the MWFRS of Home Depot building is shown below in Table I 1. The wind pressure distribution corresponding to the net internal pressure case, shown in Fig. I 1, represents the worst load case for wind uplift, with code level net uplift pressure of 26.2 lb/ft 2 (psf) on the roof. Note this calculated value is slightly less than the design uplift pressure of 28.2 psf indicated on the structural drawings of the Home Depot. This confirms that the wind uplift pressure used in designing the Home Depot was in conformance with (and slightly exceeding) the requirement of the building code in effect (BOCA NBC/1996). Design Wind Pressure for Component and Cladding: For BTS building, the roof system is an integral part of the MWFRS, not just cladding. Thus the estimated design wind pressure computed above for MWFRS that pertains to the roof could arguably be used for designing the roof. However, treating the roof as component and cladding could yield higher design wind pressure acting on the roof deck panels and the fasteners (puddle welds). The following 167 Assumed by NIST for this estimation based on Table Importance Factor (I) of BOCA NBC/1996. Design drawing obtained by NIST indicated a Wind Load Importance Factor I = 1.33 was used. However, this value was inconsistent with value specified by BOCA NBC/1996. NIST NCSTAR 3, Joplin Tornado Investigation 405

2 Draft for Public Comment Table I 1. Net internal pressure and internal suction for MWFRS of the Home Depot building. Surface Z (ft) G h K z C P P V IK h C P G h P V IK h GC Pi Net Pressure (psf) with Internal Pressure Internal Suction Windward ± ± ± ± ± ± Leeward All ± Side wall All ± Roof All ± psf 18.6 psf 17.8 psf MRH 20.4 psf 16.6 psf 15.2 psf psf 15 Figure I 1. Wind pressure distribution for MWFRS of the Home Depot building. calculation estimates the code level net uplift pressures, based on BOCA NBC/1996, on the roof deck panels and the fasterners if they are considered as component and cladding. Where, P = P V IK h [(GC p ) (GC pi )] P V IK h = psf (see above and Table I.1), NIST NCSTAR 3, Joplin Tornado Investigation

3 Draft for Public Comment Appendix I GC pi = ± 0.25, and GC p computed below based on effective wind areas of roof deck panel and tributary area of each fastener (puddle weld): Effective wind areas: Roof deck panel: A = 3 ft ft = ft 2 Fasterner (36/4 pattern): A = 5.8 ft 1.0 ft = 5.8 ft 2 Roof coefficient (GC p ): Component A (sq.ft) Zone 1 GC p 168 Zone 2 Roof deck panel Fastener Net roof component pressures, psf Component Roof deck panel Fastener Net Uplift Pressure Zone 1 Zone I.2 ROOF BRACING FORCES R T Force transferred to roof from lateral pressure on exterior of windward wall: 18.6 psf 17.8 psf 16.6 psf MRH R T Equating moments at base of wall (wall extends 2 ft below ground on top of footing): 15.2 psf 28 ଽ ( ய )( ) ( ) ( ய )( ) ( ) 13.5 psf 1 ( ய )( ) ( ) ( ய)( ) ( ) ( ய )( )( ଽ) ଽ ய ଗଓ ଡ଼ ୟଡ଼ଡ଼ 168 Zone 3 is treated as Zone 2 due to the 4 foot height parapet (greater than 3 ft) NIST NCSTAR 3, Joplin Tornado Investigation 407

4 Draft for Public Comment Force transferred to roof from uniform pressure on leeward wall: 14.6 psf MRH R T ଽ ( ய )( )( ) ய ଗଓ ଈଓଖକ ଙଖଖ 28 3 Force transferred to roof from uniform internal pressures on leeward wall: ± 5.77 psf R T ଽ ( ய )( )( ) L ய plf along roof 28 Net force R T per foot transferred to roof due to lateral wind load: With internal suction: Windward: R T = = plf Leeward: R T = = plf Net design roof bracing force due to lateral wind loads: W = = plf 408 NIST NCSTAR 3, Joplin Tornado Investigation

5 Draft for Public Comment Appendix I I.3 ROOF DIAPHRAGM SHEAR AND STIFFNESS Diaphragm Shear: Design diaphragm shear force: L=470 R = (L/2)(W) = 470 ½ = 137,968.5 lb Required nominal unit shear at side walls (design diaphragm shear): B=250 S = R/B = 137,968.5/250 = 552 plf Note: This calculated roof diaphragm shear value of 552 plf confirms the design diaphragm shear value of 560 plf shown on the Home Depot design drawings. W = plf Diaphragm Shear Stiffness G : Roof diaphragm shear stiffness G is a function of roof deck type and size, support joist spacing, and fastener types and pattern. For the Home Depot: Roof deck: B, 1.5 in. 22 gauge wide rib, 36 in. width, three span continuous Joist spacing L V : Varied from 5.4 ft to 5.8 ft (Note: This conforms to FM Global s recommended span of 6 ft for 22 gauge roof deck) Fasteners: At support: 5/8 in. puddle welds, 36/4 pattern Side laps: #10 Buildex screws, 7 per span G, based on SDI Deck Diaphragm Design Manual (2nd Edition) and CMC Joist and Deck Tables, for 5/8 in. puddle weld with 36/4 weld pattern and #10 Buildex screws side laps connection: ய ଽய ௱ ௫௫ ச ச Where: K 2 = 29,500t = 29,500(0.0295) = 870 (t : deck thickness = in. for 22 gauge deck) D xx = Deck warping factor, dependent on fastener pattern at supports = 1072 (for 36/4 pattern) K 1 = (factor relates to slip coefficient) NIST NCSTAR 3, Joplin Tornado Investigation 409

6 Draft for Public Comment ய ଽ ଽய ଟ ଽ ଟଽய ଟ ய ய ய ଐକ Note: 6.7 k/in. G = 13.9 k/in. 15 k/in. the Home Depot roof is a flexible roof diaphragm based on ACI 551 roof shear stiffness classifications. Roof diaphragm maximum shear deflection due to code level shear force: ( ய )( ଽ) ய ଐକଊଏ ஊ இஐ ௯ ( ய) ଽ ( ଽ) I.4 UPLIFT AND SHEAR CAPACITIES OF ROOF DECK TO JOIST CONNECTIONS Strength based on uplift alone: ASD governing load combination for net uplift force acting on deck to joist connection: 0.6D + W Where: D = 16 psf (service dead load shown on the Home Depot design drawings) W = 26.2 psf (service wind uplift load computed above based on BOCA NBC/1996) Required uplift resistance (or required tensile strength) of puddle welds, T, at service load: T = L V (0.6D + W)(1.1) = (5.8)[(0.6)(16) 26.2](1.1) = plf Nominal uplift resistance per foot along roof of puddle welds, T n, based on 36/4 weld pattern, 5/8 in. puddle weld, and 5.8 ft span length: Where: ଟ ௩ ଟ ௰ ௩ ௩ ௰ K = 2.7 (for 36/4 weld pattern, based on SDI Deck Diaphragm Design Manual, 2nd Edition) C = 3 ft (width of roof deck) P = 0.28t(d t)f u ) (Nominal uplift resistance per puddle weld, per AWS D1.3/D1.3M 2008 Structural Welding Code Sheet Steel) t = in. (thickness of 22 gauge metal roof deck) d = 5/8 in. (weld diameter) F u = 55 ksi 410 NIST NCSTAR 3, Joplin Tornado Investigation

7 Draft for Public Comment Appendix I L ଽய ଟଽயଽ ଟ ( ଽயଽ ) ଟ ଽய ଓଉଚ ଗଌଙ ଞଌଓଋ, ଇ L ௪ணப Thus, ன ய ଟ யଽ ய ଗଓ Safety factor for uplift strength of puddle weld: ௨ ய ଽ ய ய ய ଙଌଘଜଐଙଌଋ ଧ ଖଙ ଜଗଓଐଛ ଈଓଖକଌ Nominal uplift capacity of roof deck to joist connection: Note: L ௩ ய ଗଓ ய ଛ ய ଗଚ The 62.6 psf uplift capacity of the roof deck to joist connection exceeds the design uplift pressure of 26.2 psf by a safety factor of 2.4. This means a code level uplift pressure would not have caused the failure of the roof deck to joist connections (or the disconnection of the metal roof deck panels). Assuming the spatial relationship between lateral wind speed and uplift pressure in tornadoes is similar to that used in ASCE 7 standards, the 62.6 psf uplift capacity is equivalent to a lateral wind speed V = Strength based on combined uplift and shear: ASD shear and tension interaction equation for support fasteners (puddle welds): Where: த ௨௦டபண த ௨பத௧ ய ய ௨ ( ) ( ) யଽ u = 2.5 (safety factor for weld in tension) T = plf (above) T n = 1,800.7 plf (above) Q f no uplift = 2,010 lb (nominal shear strength per 5/8 in. puddle weld (tabulated in SDI manual and CDC Tables) Q f usable : Available nominal shear strength of puddle weld in the presence of an uplift force: ய Lயଅଆ L ௨ L ய ଟ ଽ ய த ௨௦டபண ( யଽ ( ) L ) ଟ த ௨பத௧ L ( யଽ ( ) ) ଟ ଽ ଽ ய ଓଉଚ ଽଽய L ய யଅଆ NIST NCSTAR 3, Joplin Tornado Investigation 411

8 Draft for Public Comment Required nominal unit shear at side walls: S n required = 552 plf (from roof bracing forces calculation above) Nominal shear strength S n of type B 1.5 in. 36 in. wide rib roof deck with 36/5 puddle weld pattern based on the SDI Deck Diaphragm Manual and CMC Joist and Deck Tables: For 5.5 ft deck span S n = 1,318 plf For 6.0 ft deck span S n = 1,230 plf Thus for L V = 5.8 ft deck span S n = 1318 ( )(0.3/0.5) = plf Available nominal deck shear strength adjusted for presence of uplift (accounting for effect of shear and tension interaction): ட௩டபடபண ( த ௨௦டபண த ௨பத௧ ) ய ( ய ଽ ଽ ) ଗଓ Factor of safety in combined shear and tension of deck to joist connection: ட௩டபடபண ய ய ண௨ண Roof deck to joist connection would not have failed under combined shear (lateral wind load) and tension (wind uplift) forces at code level wind load. However, the safety factor is slightly less than is typically required for this design. 412 NIST NCSTAR 3, Joplin Tornado Investigation