SEISMIC ANALYSIS FOR THE RESTRAINT OF CEILING HUNG FIRE...

JMG CONSULTANTS, INC.

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

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Job Name: PS 177X

JMG Job No.: 13-011

1/30/2013Date:

Submittal No.: 1

Customer:

Drawing No.: JMG-011-01

Quick Response Sprinkler Corp.

SUPERIOR DESIGNS FOR THE SEISMIC PROTECTION OF NON-STRUCTURAL BUILDING COMPONENTS

JAY M. GUERINLICENSED PROFESSIONAL ENGINEERNEW YORK LICENSE NUMBER 086138

I. PURPOSE

This calculation is submitted to Quick Response Sprinkler Corp. for PS 177X 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 15 - 18 for details) and shall be covered under this P.E. sealed submission.

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Job Name: PS 177X

JMG Job No.: 13-011

1/30/2013Date:

Submittal No.: 1

Customer:



JMG CONSULTANTS, INC.SUPERIOR DESIGNS FOR THE SEISMIC PROTECTION OF NON-STRUCTURAL BUILDING COMPONENTS

PIPE PHYSICAL DATA:

PIPE DIMENSIONS: 8" diameterWEIGHT 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.

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Job Name: PS 177X

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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.

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Job Name: PS 177X

JMG Job No.: 13-011

1/30/2013Date:

Submittal No.: 1

Customer:




Figure 1. Schematic View of Ceiling Hung Pipe With Solid Arm Seismic Brace

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Job Name: PS 177X

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Tbrace

Fph

Wp

Y

X

Fpv

Fpv

C(rod)max = CFph + CFpv - Tw

Cbrace

T(rod)max = Tw + TFph + TFpv

Fph

N = # of rods at brace locations = 1Tw = Wp/N = 1431#

TFph = CFph = Fph tan45o = 716#

45o

TFpv = CFpv = Fpv/N = 239#


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Job Name: PS 177X

JMG Job No.: 13-011

1/30/2013Date:

Submittal No.: 1

Customer:



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.


Maximum Allowable Stress on Solid Arm Pipe Brace

Assumptions:

K = 1.0; both ends of member fixed from translation, but free to rotateL = 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 = 0.494 in2

Spipe = Fbrace/Asab = 2051 psi < 3730 psi (allowable maximum stress)

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Job Name: PS 177X

JMG Job No.: 13-011

1/30/2013Date:

Submittal No.: 1

Customer:




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).

Figure 2. Schematic View of Tolco Swivel Fitting

Fbrace sin(45o)

Fbrace cos(45o)

45o

Fbrace = 1349#

Ftb

Fvb

11/16"x

3"

1 1/2"

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Job Name: PS 177X

JMG Job No.: 13-011

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Y

X


Summing moments about point "x" yields the following:

Mx = 0; (11/16")Ftb + (1 ½")Fbrace(cos 45o) - (3")Fbrace(sin 45o) = 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;

Fhorizontal = 0; Fvb - Fbrace(cos 45o) = 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.

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Job Name: PS 177X

JMG Job No.: 13-011

1/30/2013Date:

Submittal No.: 1

Customer:




Combined Shear and Tension Check for A307 Bolt by AISC

Root area (abolt) for ½" bolt = .129 in2

Source: AISC ASD 9th ed. pg. 4-147

ftb = Ftb/abolt = 1563/.129 = 12.1 ksi

fvb = Fvb/abolt = 716/.129 = 5.6 ksi < 10 ksi allowable per AISC p. 5-73

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.

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Job Name: PS 177X

JMG Job No.: 13-011

1/30/2013Date:

Submittal No.: 1

Customer:




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 0.707 times the specified weld size.

For a 3/16" thick weld, the length of shear in the weld is 0.707 x (3/16") = 0.1325625". The allowable weld force (Fw)allow for a 3/16" weld is as follows:

(Fw)allow = 0.1325625 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

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Job Name: PS 177X

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1/30/2013Date:

Submittal No.: 1

Customer:




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Job Name: PS 177X

JMG Job No.: 13-011

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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


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 13.

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Job Name: PS 177X

JMG Job No.: 13-011

1/30/2013Date:

Submittal No.: 1

Customer:




APPENDIX A

The following is pertinent information on threaded rod, as per ASTM.

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Job Name: PS 177X

JMG Job No.: 13-011

1/30/2013Date:

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TABLE 1

Threaded Rod Diameter

Max AllowableUnbraced Length

3/8" 19"

1/2" 25"

5/8" 31"

3/4" 37"

Threaded Rod Without Stiffener

7/8" 43"

Threaded Rod Diameter Allowable Loads

3/8" 610 lbs.

1/2" 1130 lbs.

5/8" 1810 lbs.

3/4" 2710 lbs.

Threaded Rod Load Capacities (without stiffener)

7/8" 3770 lbs.

TABLE 2


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Job Name: PS 177X

JMG Job No.: 13-011

1/30/2013Date:

Submittal No.: 1

Customer:



LATERAL SEISMIC SWAY BRACEFOR CLEVIS HUNG FIRE PROTECTION PIPE

"Fast Clamp" Sway Brace Attachment(Tolco Fig. 1000 or AFCON Fig. 001/020)

Fire ProtectionPiping (Typ.)

Elevation View of Brace


1" Dia. Sch. 40Pipe Sway Brace(in locations where Pipe Brace exceeds 84" in length, increase brace pipe to 2" Dia.)

Plan View of Brace

Clevis Hanger

30'-0" Max o.c. (8" pipe)40'-0" Max o.c. (< 8" pipe)

± 5 °45

SCALE

N.T.S

If Support Rod Length is Equal to or Less Than 6",

Seismic Bracing is NOT Req'd

S1


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Job Name: PS 177X

JMG Job No.: 13-011

1/30/2013Date:

Submittal No.: 1

Customer:



LATERAL & LONGITUDINAL (4-WAY) SEISMIC SWAY BRACEFOR CLEVIS HUNG FIRE PROTECTION PIPE

"Fast Clamp"Sway Brace Attachment(Tolco Fig. 1000 or AFCON Fig. 001/020)


Elevation View of Brace


1" Dia. Sch. 40Pipe Sway Brace(in locations where Pipe Brace exceeds 84" in length, increase brace pipe to 2" Dia.)

Plan View of Brace

Clevis Hanger

± 5 °45

4-Way Longitudinal Sway Brace Attachment(Tolco Fig. 907 or AFCON Fig. 079)

30'-0" Max o.c. (8" pipe)40'-0" Max o.c. (< 8" pipe)

SCALE

N.T.S

If Support Rod Length is Equal to or Less Than 6",

Seismic Bracing is NOT Req'd

S2


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Job Name: PS 177X

JMG Job No.: 13-011

Date:

Submital No.: 1

Customer:


Quick Response Sprinkler Corp. 1/30/2013

SOLID ARM SEISMIC BRACE ATTACHMENTS TO STEEL

½" Dia. Bolt & Channel Nut- or -

3" of 3/16" Fillet Weld (1 ½" On Both Sides of Angle)

Structural Steel

SCALE

N.T.S.

Tolco Fig. 800 Adjustable Sway Brace Attachment to Steel (or equivalent)

Swivel Sway Brace Fitting (Tolco Fig. 910 or AFCON Fig. 077)

1" Dia. Sch. 40 Pipe Sway Brace


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Job Name: PS 177X

JMG Job No.: 13-011

Date:

Submital No.: 1

Customer:


Quick Response Sprinkler Corp. 1/30/13

SOLID ARM SEISMIC BRACE ATTACHMENT TO CONCRETE

½" Diameter Hilti Kwik Bolt TZ Expansion Anchor with 3 ¼" Embedment

Concrete Deck

SCALE

N.T.S.

Swivel Sway Brace Fitting (Tolco Fig. 910 or AFCON Fig. 077)

1" Dia. Sch. 40 Pipe Sway Brace

SEISMIC ANALYSIS FOR THE RESTRAINT OF CEILING HUNG FIRE...

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