Sputo, Thomas

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Missouri University of Science and Technology (Missouri S&T): Scholars' Mine

Missouri University of Science and Technology Scholars' Mine International Specialty Conference on Cold-Formed Steel Structures (2010) - 20th International Specialty Conference on Cold-Formed Steel Structures Nov 3rd, 12:00 AM Steel Roof Deck Diaphragms on Cold-formed Steel Framing Thomas Sputo Follow this and additional works at: https://scholarsmine.mst.edu/isccss  Part of the Structural Engineering Commons Recommended Citation Sputo, Thomas, "Steel Roof Deck Diaphragms on Cold-formed Steel Framing" (2010). International Specialty Conference on Cold-Formed Steel Structures. 3. https://scholarsmine.mst.edu/isccss/20iccfss/20iccfss-session6/3 This Article - Conference proceedings is brought to you for free and open access by Scholars' Mine. It has been accepted for inclusion in International Specialty Conference on Cold-Formed Steel Structures by an authorized administrator of Scholars' Mine. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact scholarsmine@mst.edu.     Steel Roof Deck Diaphragms on Cold-Formed Steel Framing   Thomas Sputo1   Introduction  This paper addresses the design of steel roof deck diaphragms on cold-formed roof framing, either rafters or trusses, as shown in Figure 1.  Criteria for design strength and stiffness of plywood diaphragms on cold-formed framing are available from several sources, but no equivalent resource exists for steel deck on cold-formed framing.  Basic diaphragm theory is well established and is readily available in the Steel Deck Institute Diaphragm Design Manual (SDI, 2004) and the Metal Construction Association Primer on Diaphragm Design (MCA, 2004).  This paper will not repeat this theory, and the reader is directed to these two publications for this basic information.  This paper will address the modifications that are needed to the basic SDI diaphragm theory to develop diaphragm design tables that account for the properties of the supporting framing.  The tables contained in the Diaphragm Design Manual (SDI, 2004) assume support framing that is thick enough such that the behavior of the fastener in the support framing does not control.  This paper will provide tables for screw-connected diaphragms of standard 1-1/2” steel roof deck on 33 mil and 43 mil support framing.  Design tables assume lower bound material properties and industry standard thicknesses as shown in Table 1.  No. 10 screws (d = 0.190 in) are assumed for sidelap fasteners and No. 12 (d = 0.216 in) or 14 (d = 0.250 in) screws are assumed for support fasteners.   Screw fasteners shall conform to ASTM C1513.  Proper detailing of the diaphragm to carry in-plane forces into and out of the diaphragm is assumed.                                                              1 Technical Director, Steel Deck Institute, 10 SW 1st Avenue, Gainesville, FL 32601 (email:  sputoeng@mindspring.com)   Twentieth International Specialty Conference on Cold-Formed Steel Structures                           St. Louis, Missouri, U.S.A., November 3 & 4, 2010283Figure 1.  Steel Deck on Cold-Formed Framing  Table 1.  Material Properties    Design Thickness (in.) Fy (ksi) Fu (ksi) Deck 22 gage 0.0295 33 45 Deck 20 gage 0.0358 33 45 Deck 18 gage 0.0474 33 45 Framing 20 gage 0.0346 33 45 Framing 18 gage 0.0451 33 45   Screw Strength  SDI (2004) equations for screw strength in support steel assume a minimum thickness of the support of 0.0385 inches.  Because of this limitation, the screw strength equations contained in the AISI North American Specification for the Design of Cold-Formed Steel Structural Members (AISI, 2007) are used for this application.   Qf = Pns (per AISI (2007), E4.3.1)  The SDI (2004) criterion for stitch screw strength is used   Qs = 115 d t  284Screw Flexibility  The SDI (2004) equations for support screw flexibility do not consider the thickness of the support material.  MCA (2004) provides a rational modification to the SDI equation that includes the thickness of the support framing when the support framing is less than 0.0478 inches in thickness.  This equation applies for all load tables in this paper.   Sf = {1.3 + (3.0-1.3)[(0.0478 –ts)/(0.0478-t)]} / (1000 t0.5)  When the support thickness is greater than 0.0478 inches in thickness, the SDI (2004) equations may be used   Sf = 1.3 / (1000 t0.5)  The SDI (2004) criterion for stitch screw flexibility is used   Ss = 3.0 / (1000 t0.5)  Diaphragm Shear Stiffness  Using the SDI (2004) method, the diaphragm shear stiffness, assuming a deck span of 3 or more spans, is as follows   G’ = K2 / {K4 +(0.3Dxx/Lv) +(3K1Lv)}  The value of K1 is found in the load tables (Tables 6-11), while the values of Dxx, K2, and K4 are found in Tables 2 and 3.  Table 2.  K2 and K3  Deck Gage K2 K4 22 870 kip/in 3.78 20 1056 kip/in 3.78 18 1398 kip/in 3.78  285 Table 3.  Deck Warping Constant, Dxx (ft)  Deck Profile Fastener Pattern * 22 Gage 20 Gage 18 Gage WR 129 97 63 IR 226 169 111 NR 36/9 356 266 175 WR 129 97 63 IR 226 169 111 NR 36/7 356 266 175 WR 758 567 372 IR 886 663 435 NR 36/5 974 728 478 WR 1072 802 526 IR 1216 909 597 NR 36/4 1286 959 630 WR 2209 1652 1084 IR 2428 1816 1192 NR 36/3 2442 1827 1199 WR 129 97 63 IR 226 169 111 NR 30/6 356 266 175 WR 1377 1030 676 IR 1547 1157 760 NR 30/4 1608 1202 789 WR 1754 1312 861 IR 1943 1453 954 NR 30/3 1978 1480 971 *  See SDI (2004) for fastener pattern types  Load Tables  Load tables are presented in the SDI (2004) format that is familiar to engineers designing steel deck diaphragms on hot rolled framing.  Load tables were developed for 18, 20, and 22 gage, 1-1/2” steel roof deck on 18 gage and 20 gage support framing.  No. 12 or 14 screws used as support fasteners are installed per fastener layouts shown in Figure 1.  All calculations are conservatively based on No. 12 screws.  The number of No. 10 sidelap screws per deck span are indicated in the tables.  Load tables are as indicated in Table 4. 286 Table 4.  Diaphragm Load Tables  Table No. Deck Ga. Framing Ga. t2/t1 Qf (lbs) Sf (in/kip) Qs (lbs) Ss (in/kip) 6 18  18 0.95 841 0.0145 1018 0.0138 7 20  18 1.26 858 0.0118 769 0.0159 8 22  18 1.53 774 0.0076 633 0.0175 9 18  20 0.73 565 0.0180 1018 0.0138 10 20  20 0.97 565 0.0164 769 0.0159 11 22  20 1.17 589 0.0142 633 0.0175  The tables provide nominal capacities as limited by shear strength and panel buckling. Applicable resistance factors (Φ) and safety factors (Ω), in accordance with AISI (2007) are as shown in Table 5.    Table 5.  Resistance and Safety Factors    Φ (LRFD) Ω (ASD) Seismic 0.65 2.50 Wind 0.70 2.35 Panel Shear Strength Other 0.65 2.50 Panel Buckling All 0.80 2.00   The design capacity of the diaphragm is the lesser of the shear strength and panel buckling capacities.  Design Example 1 - Seismic Using allowable strength design (ASD), select a diaphragm for an in-plane seismic load of 330 plf, assuming 18 gage framing at 4 foot on center and 22 gage WR steel roof deck.  Steel deck panels are 36 inches wide.  Referring to Table 8, select a 36/7 fastener pattern.  Assuming 4 sidelap fasteners per span, check the panel shear strength:  S = 330 plf Sn = 860 plf Ω = 2.50 (seismic) Sn / Ω = 860 / 2.50 = 344 plf > 330 plf  OK  287Next, check panel buckling   Sn = 3205 plf Ω = 2.00 Sn / Ω = 3205 / 2.00 = 1602 plf > 400 plf  OK (Note: Panel buckling will rarely control design for most reasonable configurations)  The panel stiffness is calculated as follows   K1 = 0.239 ft-1 (Table 8)  K2 = 870 kip/in (Table 2)  K4 = 3.78  (Table 2)  Dxx = 129 ft  (Table 3)  Lv = 4 foot   G’ = 870 / {3.78 +(0.3 x 129/4) +(3 x 0.239 x 4)} =    53.3 kip/in  Diaphragm deflections are calculated using rational design methods.  Refer to SDI (2004) for additional information and design examples.  Other combinations of deck thickness and fastener spacing are possible.  Design Example 2 - Wind  Using allowable strength design (ASD), select a diaphragm for an in-plane wind load of 120 plf combined with 30 psf uplift, assuming 18 gage framing at 4 foot on center and 22 gage WR steel roof deck.  Steel deck panels are 36 inches wide.  Referring to Table 8, select a 36/7 fastener pattern.  Assuming 4 sidelap fasteners per span, check the panel shear strength:  S = 120 plf Sn = 860 plf Ω = 2.35 (wind) Sn / Ω = 860 / 2.35 = 366 plf > 120 plf  OK  Next, check panel buckling   Sn = 3205 plf 288Ω = 2.00 Sn / Ω = 3205 / 2.00 = 1602 plf > 180 plf  OK (Note: Panel buckling will rarely control design for most reasonable configurations)  Next, check fastener uplift capacity, using No. 12 support screws (d = 0.216 in; dh = 0.432 in)   Tn = 373 pounds (pullout) Controls  Tn = 860 pounds (pullover)   [Screw pullout and pullover calculated per AISI (2007)]  Tn / Ω = 373 / 3.0 = 124 pounds   k = 5(interior fasteners) + 2(edge fasteners)/2(shared) = 6.0  β = k / panel cover = 6.0 / 3 feet  = 2.0  T = wup (Lv/ β) = 30 (4/2.0)  = 60 pounds per screw   [Screw contributions k and β calculated per SDI (2004)]  Check interaction of uplift and shear per SDI (2004) criteria for combined shear and pullout on screw   (Ω T / Tn) + 0.85(Ω S / Sn)  <  1.0 (ASD)  (60/124) + 0.85 (120/366) = 0.76   OK   Note 1:  Interaction of screw pullout with shear for LRFD is: (Tu /ΦTn) + 0.85(Su /ΦSn) < 1.0 Note 2: For interaction of screw pullover with shear, refer to AISI (2007) Section E4.5 The panel stiffness is calculated as for Design Example 1. Other combinations of deck thickness and fastener spacing are possible.    Nomenclature  d = Screw major diameter, inches dh = Screw head diameter, inches Dxx = Panel warping constant, feet G’ = Diaphragm shear stiffness, kip/inch k = Effective number of support fasteners per panel width 289Lv  = Panel span, feet Pns = Nominal shear strength (resistance) per screw Qf = Support fastener strength, kips Qs = Sidelap fastener strength, kips S = Required allowable diaphragm shear strength, pounds (ASD) Sf = Support fastener flexibility factor Sn = Nominal shear strength of diaphragm, pounds Ss = Sidelap fastener flexibility factor Su = Required design shear strength of diaphragm, pounds (LRFD) T = Required allowable uplift capacity of screw, pounds (ASD) Tn = Nominal uplift capacity of screw, pounds Tu = Required design uplift capacity of screw, pounds (LRFD) t = Deck thickness, inches ts = Support framing thickness, inches t1 = Deck thickness in contact with screw head or washer, inches t2 = Support framing thickness not in contact with screw head or washer, inches wup = Uplift on deck, psf β = Fastener pattern factor Φ = Resistance factor (LRFD) Ω = Safety factor (ASD)  References  American Iron and Steel Institute (AISI) (2007). North American Specification for the Design of Cold-Formed Steel Structural Members and Commentary, Washington DC.  ASTM C1513 - 04(2009)e1 Standard Specification for Steel Tapping Screws for Cold-Formed Steel Framing Connections.  Metal Construction Association (MCA) (2004).  Primer on Diaphragm Design, 1st Edition, Glenview, IL.  Steel Deck Institute (SDI) (2004).  Diaphragm Design Manual, 3rd Edition, Fox River Grove, IL.  290  Table 6.  18 gage deck, 18 gage framing 291  Table 7.  20 gage deck, 18 gage framing 292  Table 8.  22 gage deck, 18 gage framing 293  Table 9.   18 gage deck, 20 gage framing 294  Table 10.   20 gage deck, 20 gage framing 295  Table 11.  22 gage deck, 18 gage framing 296

Steel Roof Deck Diaphragms on Cold-formed Steel Framing

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Steel Roof Deck Diaphragms on Cold-formed Steel Framing

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