JMG CONSULTANTS, INC.

Transcription

1 SEISMIC ANALYSIS FOR THE RESTRAINT OF CEILING HUNG FIRE PROTECTION PIPING WITH SOLID ARM BRACING DWGS.: SP-01, SP-2, SP-3, SP-4, & SP-5 JAY M. GUERIN LICENSED PROFESSIONAL ENGINEER NEW YORK LICENSE NUMBER OF 18

2 I. PURPOSE This calculation is submitted to Quick Response Sprinkler Corp. for to certify that the seismic restraints as recommended by JMG Consultants, Inc. will safely accept loads resulting from seismic forces. II. SCOPE This calculation certifies that the components and specified hardware, when properly installed, are capable of safely resisting a seismic acceleration of 0.5 "g", as per NFPA 13. These calculations do not cover equipment supplied by vendors nor the superstructure or substructure to which the components or specified hardware are attached. III. STRATEGY AND ASSUMPTIONS The equipment must be restrained during an earthquake. Therefore, the sum of the forces and moments acting on the equipment must equal zero. The problem can be reduced to a static analysis. The following calculations are based on the restraint of a 30' section of 8" diameter Pipe. This section of Pipe represents the worst case condition for the drawings as listed on the cover page of this analysis and will be used as the model in this analysis. All remaining sections of ceiling hung Fire Protection Pipe, as found on Quick Response Sprinkler Corp. drawings SP-01, SP-2, SP-3, SP-4, and SP-5 will be restrained in a similar manner (see pages for details) and shall be covered under this P.E. sealed submission. 2 OF 18

3 PIPE PHYSICAL DATA: PIPE DIMENSIONS: 8" diameter WEIGHT PER FOOT: 47.7 lbs. LENGTH OF SECTION UNDER CONSIDERATION: 30 ft. TOTAL WEIGHT (Wp): 1431 lbs. IV. SEISMIC INPUT FORCES Total design horizontal seismic force, Fph = 0.5 x Wp, where: Fph = 0.5 x 1431 Fph = 716 lbs. The vertical and horizontal component of the seismic input shall be conservatively assumed to act simultaneously. The vertical component (Fpv) is taken to be 1/3 of the horizontal input. In equation form: Fpv = (1/3)Fph Fpv = 239 lbs. 3 OF 18

4 V. METHOD OF SEISMIC RESTRAINT At each brace location, the Pipe will be restrained with an AFCON "Fast Clamp" Sway Brace Attachment, or equivalent (using 1" diameter Sch. 40 pipe*). Attached to the other end of the pipe brace will be an AFCON Swivel Sway Brace Fitting, or equivalent. Swivel Fitting will be attached to the building structure by any of the following methods: 1. Bolted to structural steel with one (1) ½" diameter A307 bolt; 2. Welded directly to structural steel. Weld to be 3" of 3/16" fillet weld on three sides of the Swivel Fitting; 3. Anchored to concrete ceiling deck with one (1) ½" diameter Hilti Kwik Bolt TZ Expansion Anchor with a minimum embedment of 3 ¼" in 3000 psi stone aggregate concrete. See pages 15 through 18 for seismic brace and and attachments to structure details. 4 OF 18

5 C(rod)max = CFph + CFpv - Tw Y X T(rod)max = Tw + TFph + TFpv Tbrace 45o Cbrace Fpv Fph Fph N = # of rods at brace locations = 1 Tw = Wp/N = 1431# TFph = CFph = Fph tan45o = 716# TFpv = CFpv = Fpv/N = 239# Wp Fpv Figure 1. Schematic View of Ceiling Hung Pipe With Solid Arm Seismic Brace 5 OF 18

6 VI. CALCULATION OF SEISMIC FORCES ON SYSTEM Threaded Rod Assume the threaded rod will resist the forces in the vertical plane (T(rod)max & C(rod)max, respectively). The vertical forces which will act on the threaded rod due to the anticipated seismic forces are calculated as follows: T(rod)max = Tw + TFph + TFpv = 2386 lbs. C(rod)max = CFph + CFpv - Tw = -476 lbs. (negative sign indicates direction) See Tables 1 & 2 on page 14 for allowable loads and allowable unbraced lengths for standard threaded rod sizes. Solid Seismic Brace The solid seismic brace will resist the effects of the horizontal force, Fph. Since it was assumed, conservatively, that the vertical forces due to the seismic loading were being resisted by the threaded rod, neglect any resistance from the threaded rod for horizontal forces. Note that because the solid seismic brace can resist the effects of the horizontal force in both tension and compression (Tbrace & Cbrace, respectively), this force will be noted as Fbrace. Fbrace = Tbrace = Cbrace = Fph/cos45o Fbrace = 1013 lbs. This is the force on the Solid Arm Brace that is required to restrain the Pipe system from the imposed seismic forces. 6 OF 18

7 Maximum Allowable Stress on Solid Arm Pipe Brace Assumptions: K = 1.0; both ends of member fixed from translation, but free to rotate L = 84"; maximum length of bracing for 1" dia. Pipe, as per NFPA 13 r = 0.421"; radius of gyration for 1" dia. Schedule 40 pipe {K x L}/r = 200 The allowable maximum stress for a compression member with a KL/r ratio of 200, as found on page 3-16 of the ASD Manual of Steel Construction, 9th ed., is 3,730 psi. The actual stress (Spipe) on the brace is determined as follows: Fbrace = 1013 lbs. Asab = in2 Spipe = Fbrace/Asab = 2051 psi < 3730 psi (allowable maximum stress) 7 OF 18

8 VII. EVALUATE FORCES ON THE SWIVEL FITTING ATTACHMENTS When the swivel fitting is subjected to the brace load, the fitting tends to pry from the mounting surface. Figure 2 shows a free body diagram of the fitting with the force vectors. Summing moments and summing forces in the horizontal axis will determine the tensile and shear forces (Fvb and Ftb, respectively). Ftb Y 3" Fvb X 1 1/2" 11 x /16" Fbrace cos(45o) 45o Fbrace = 1349# Fbrace sin(45o) Figure 2. Schematic View of Tolco Swivel Fitting 8 OF 18

9 Summing moments about point "x" yields the following: (11/16")Ftb + (1 ½")Fbrace(cos 45o) - (3")Fbrace(sin 45o) = 0 Mx = 0; Ftb = {(3)Fbrace(sin 45o) - (1 ½)Fbrace(cos 45o)}/11/16 Ftb = 1563 lbs. Summing forces in the horizontal plane yields the following; Fvb - Fbrace(cos 45o) = 0 Fhorizontal = 0; Fvb = Fbrace(cos 45o) Fvb = 716 lbs. BOLT SUMMARY - Maximum forces imposed on the single bolt attachment: Shear: Fvb = 716 lbs. Tension: Ftb = 1563 lbs. 9 OF 18

10 Combined Shear and Tension Check for A307 Bolt by AISC Root area (abolt) for ½" bolt =.129 in2 Source: AISC ASD 9th ed. pg ftb = Ftb/abolt = 1563/.129 = 12.1 ksi fvb = Fvb/abolt = 716/.129 = 5.6 ksi < 10 ksi allowable per AISC p The maximum allowable tensile stress (ftall) is the lower of the following equations. Equation 1: Ftall = 26 - (1.8)fvb = 15.9 ksi Equation 2: Ftall = 20 ksi Therefore, the allowable tensile stress for a shear stress of 5.6 ksi is 15.9 ksi. Recall that the actual tensile stress, at 12.1 ksi, is below the allowable. 10 OF 18

11 Evaluate Weld Required to Attach the Swivel Fitting to Structural Steel The following information is from ASHRAE 1995 Ed. Chapter 50: The capacity of a weld is given per unit length of weld based on the shear strength of the weld material. For steel welds, the allowable shear capacity is 16,000 psi on the throat section of the weld. The section length is times the specified weld size. For a 3/16" thick weld, the length of shear in the weld is x (3/16") = ". The allowable weld force (Fw)allow for a 3/16" weld is as follows: (Fw)allow = x 16,000 = 2121 lbs. per inch of weld The effective weld force is the sum of the forces Ftb and Fvb as previously determined. Because they are perpendicular, they are added by the method of the square root of the sum of the squares: (Fw)eff = {(Ftb)2 + (Fvb)2}1/2 (Fw)eff = 1719 lbs. The length of the weld (WL) required is given by the following equation: WL = (Fw)eff / (Fw)allow WL = 787 / 2121 = 0.81" = 3/8" minimum required, per location USE: 3" of 3/16" fillet weld, at each Tolco Swivel Fitting attachment to steel 11 OF 18

12 Evaluate Anchorage to Concrete The allowable load ratings for the ½" diameter Hilti Kwik Bolt TZ Expansion Anchor with an embedment of 3 ¼" in 3000 psi (minimum) concrete, as per the 2011 Hiti North American Product Technical Guide (page 274) are as follows: Tension: Tallow = 2028 lbs. Shear: Vallow = 2390 lbs. To determine the adequacy of the concrete anchors, the combined effect of shear and tension are determined using the Interaction Formula. If "I" is less than or equal to one (1.0), the anchorage is considered adequate. I = {Vmax/Vallow}5/3 + {Tmax/Tallow}5/3 I = {716/2390}5/3 + {1563/2028}5/3 I = 0.78 < 1.0, therefore the anchorage is adequate 12 OF 18

13 VIII. CONCLUSION At each brace location, the Pipe will be restrained with an AFCON "Fast Clamp" Sway Brace Attachment, or equivalent (using 1" diameter Sch. 40 pipe*). Attached to the other end of the pipe brace will be an AFCON Swivel Sway Brace Fitting, or equivalent. Swivel Fitting will be attached to the building structure by any of the following methods: 1. Bolted to structural steel with one (1) ½" diameter A307 bolt; 2. Welded directly to structural steel. Weld to be 3" of 3/16" fillet weld on three sides of the Swivel Fitting; 3. Anchored to concrete ceiling deck with one (1) ½" diameter Hilti Kwik Bolt TZ Expansion Anchor with a minimum embedment of 3 ¼" in 3000 psi stone aggregate concrete. See pages 15 through 18 for seismic brace and and attachments to structure details. The seismic bracing of Ceiling Hung Fire Protection Pipe, as outlined herein, found on Quick Response Sprinkler Corp. drawings SP-01, SP-2, SP-3, SP-4, and SP-5, will resist the anticipated seismic loads generated by the seismic acceleration of 0.5 "g", as per NFPA OF 18

14 APPENDIX A The following is pertinent information on threaded rod, as per ASTM. TABLE 1 Threaded Rod Without Stiffener Threaded Rod Diameter Max Allowable Unbraced Length 3 /8 " 19" 1 /2 " 25" 5 /8 " 31" 3 /4 " 37" 7 /8 " 43" TABLE 2 Threaded Rod Load Capacities (without stiffener) Threaded Rod Diameter Allowable Loads 3 /8 " 610 lbs. 1 /2 " 1130 lbs. 5 /8 " 1810 lbs. 3 /4 " 2710 lbs. 7 /8 " 3770 lbs. 14 OF 18

15 S1 LATERAL SEISMIC SWAY BRACE FOR CLEVIS HUNG FIRE PROTECTION PIPE "Fast Clamp" Sway Brace Attachment (Tolco Fig or AFCON Fig. 001/020) Fire Protection Piping (Typ.) 1" Dia. Sch. 40 Pipe Sway Brace (in locations where Pipe Brace exceeds 84" in length, increase brace pipe to 2" Dia.) 45 ± 5 If Support Rod Length is Equal to or Less Than 6", Seismic Bracing is NOT Req'd Elevation View of Brace Clevis Hanger 30'-0" Max o.c. (8" pipe) 40'-0" Max o.c. (< 8" pipe) Fire Protection Piping (Typ.) Plan View of Brace SCALE N.T.S 15 OF 18

16 S2 LATERAL & LONGITUDINAL (4-WAY) SEISMIC SWAY BRACE FOR CLEVIS HUNG FIRE PROTECTION PIPE Fire Protection Piping (Typ.) If Support Rod Length is Equal to or Less Than 6", Seismic Bracing is NOT Req'd 1" Dia. Sch. 40 Pipe Sway Brace (in locations where Pipe Brace exceeds 84" in length, increase brace pipe to 2" Dia.) "Fast Clamp" 45 ± 5 Sway Brace Attachment (Tolco Fig or AFCON Fig. 001/020) 4-Way Longitudinal Sway Brace Attachment (Tolco Fig. 907 or AFCON Fig. 079) Elevation View of Brace Clevis Hanger 30'-0" Max o.c. (8" pipe) 40'-0" Max o.c. (< 8" pipe) Fire Protection Piping (Typ.) Plan View of Brace SCALE N.T.S 16 OF 18

17 SOLID ARM SEISMIC BRACE ATTACHMENTS TO STEEL Structural Steel Tolco Fig. 800 Adjustable Sway Brace Attachment to Steel (or equivalent) ½" Dia. Bolt & Channel Nut - or 3" of 3/16" Fillet Weld (1 ½" On Both Sides of Angle) Swivel Sway Brace Fitting (Tolco Fig. 910 or AFCON Fig. 077) 1" Dia. Sch. 40 Pipe Sway Brace SCALE N.T.S. 17 OF 18 Submital No.: 1

18 SOLID ARM SEISMIC BRACE ATTACHMENT TO CONCRETE ½" Diameter Hilti Kwik Bolt TZ Expansion Anchor with 3 ¼" Embedment Concrete Deck Swivel Sway Brace Fitting (Tolco Fig. 910 or AFCON Fig. 077) 1" Dia. Sch. 40 Pipe Sway Brace SCALE N.T.S. 18 OF 18 1/30/13 Submital No.: 1