Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations...

46
Prepared For: PROVENT 3847 Wabash Dr. Mira Loma, CA 91725 951.685.1101 Prepared By: Lyons Warren Engineers + Architects 9560 Candida Street, San Diego, CA 92126 858.573.8999 Job No.: PRO1204 E1/E2 Effective Date: 20150423 Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, XP 036-060, ZF 036-072 Provent P/N 80-268-1314 and 1318 Form No: CBKD - 94 4/24/15 exp: 2/28/17

Transcript of Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations...

Page 1: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

Prepared For:

PROVENT

3847 Wabash Dr. Mira Loma, CA 91725

951.685.1101

Prepared By:

Lyons Warren Engineers + Architects

9560 Candida Street, San Diego, CA 92126

858.573.8999

Job No.: PRO1204 E1/E2

Effective Date: 20150423

Structural Calculations for

Roof Curbs for York Units SUNLINE 36-60 York Units

ZR 036-060, XP 036-060, ZF 036-072

Provent P/N 80-268-1314 and 1318

Form No: CBKD - 94

4/24/15exp: 2/28/17

Page 2: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

4/24/15exp: 2/28/17

Page 3: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

4/24/15exp: 2/28/17

Page 4: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

HVAC UNIT: Sunline 36-60 Heaviest

PROVENT STEEL CURB DESIGN

PROVENT PART NUMBER:80-268-1314 14" curb

Curb Information

Curb Number:

Hcurb 14 (Height from support structure to top of curb)

Lcurb 69 (Length of Curb - In to In)

Wcurb 33.25 (Width of Curb - In to In)

Lclip 45.75 (min Length in Long dir from end to clip)

# clips Long Side 2 (Shear + Uplift Clips)

# clips short side 1 (Shear Clips)

Unit Information:

Weight: 890 lbs (Weight of Unit - min weight governs design)

W c-max 479 lbs (Maximum corner weight)

W c-min 234 lbs (Minimum corner weight)

W mid 96 lbs (load B or E, 6 point load criteria for York curbs)

H unit 33 in (Height of unit above curb)

H cm 16 in (Height from top of curb to center of mass of unit)

L unit 82 in (Length of unit)

w unit 45 in (Width of unit)

Seismic Loading (2014 FBC)

Ss 0.2 (worst case for Florida State)

Fa 2.5 (worst case for site; Ss<0.25, Site Class E)

Sms 0.5 (=Fa*Ss)

Sds 0.33 (=2/3*Sms)

Ip 1.5 (=Worst case)

ap 2.5

Rp 6

Fp max 0.3 Wp (=0.4*ap*Sds*Wp*(1+2*z/h)/(Rp/Ip))

Fp ASD 159 lbs (=0.7*Fpmax)

Wind Loading (2014 FBC)

Wind Exposure: D

V 185 mph (Ultimate Wind Speed - Worst case:

Kzt 1.66

Kd 0.9

Kh 1.31 (Worst Case for 60 foot roof height)

GCf 3.1

qh 171 psf (ASD=0.6W)

F 532 psf (ultimate) F 319 psf (service)

A net/transv. 19 sf

Fwind transv 9906 lbs (ultimate) Fwind trnsv 5943 lbs (service)

A net/long 10 sf

Fwind long 5405 lbs (ultimate) Fwind long 3243 psf (service)

Controlling Lateral Load (Seismic vs. Wind)

Transverse 5943 lbs (ASD)

Long 3243 lbs (ASD)

page 1

Lyons Warren

Engineers Architects

9560 Candida Street

San Diego, CA 92123 (858) 573-8999

Page 5: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

HVAC UNIT: Sunline 36-60 Heaviest

PROVENT STEEL CURB DESIGN

PROVENT PART NUMBER:80-268-1314 14" curb

Wind Loading: Uplift (2014 FBC) 29.5-2 (GC=3.1 - FBC2014)

qh 171.5 psf

GCr 1.5

Fv (psf) 257.2 psf (ultimate)

Av 26 sf

Fv 6593 lbs (ultimate) Fv 3956 lbs (ASD: 0.6W)

Curb Loading:

Transverse direction:

OTM: 8079 lb-ft 0.6W: F max - transv * Hcm

M res. 878 lb-ft 0.6D: 2 * Wcrnmin *0.6* (width curb +4.25")

Net OTM: 7202 lb-ft 0.6D+0.6W: OTM-RM

Max Comp 3075 lbs /side 1.0D+0.6W: (2 x Wcrnmax + (Mot-Mres)/ (width curb +4.25"))

Max Tension 4282 lbs /side 0.6D+0.6W: (Mot-Mres)/(width curb +4.25")) + Fv/(2 sides)

Max Tension 2141 lbs /clip 0.6D+0.6W: Max tension/side /#clips

Max Corner: 947 lbs W c-max+ (Mot-Mres)/((w/curb+4.25")/Lcurb*(N-corner)/2/12

Max Interior: 1031 lbs W mid+ (Mot-Mres)/(width curb +4.25")/Lcurb*(N-mid)

Longitudinal direction:

OTM: 4408 lb-ft 0.6W: F max long * Hcm

RM 1720 lb-ft 0.6D: 2 X Wcrnmin x (Lcurb+4.25in)/12 x 0.6

Net OTM: 2688 lb-ft 0.6D+0.6W: OTM-RM

Max Comp = 1362 lbs /side 1.0D+0.6W: (2*Wcmax + (NetOTM)/Lclip)+ Fv/(U.C)

Max Tens = 2683 lbs /side 0.6D+0.6W: (Mot-Mres)/Lclip) + Fv/(2 sides)

Max Tension = 1694 lbs /clip 0.6D+0.6W: (Mot-Mres)/Lclip) + Fv/(2 sides)/#clips/side

Max Corner: 676 lbs W c-max+ (Mot-Mres)/Lcurb/Wcurb*(N-corner)/2

Connection of Unit to Curb

Screws in Uplift clips (Attach with 1/4 SMS into 14mil) Vall= 933 lbs/screw

Screws in Short Side Clips (Attach with #12 SMS into 14mil) Vall= 870 lbs/screw

UPLIFT CLIPS: UPLIFT CLIPS:

Shear: 811 lbs/clip 4 1/4" screws/clip

Uplift: 2141 lbs/clip Fdiag/screw 336 lbs/screw

F diag 1343 lbs/clip to curb F/screw outs. 268 lbs/screw

SCREWS OK

SHORTSIDE CLIPS SHORTSIDE CLIPS

Shear: 1621 lbs/clip 4 #12 screws/clip

F screw 405 lbs/screw

SCREWS OK

page 2

Lyons Warren

Engineers Architects

9560 Candida Street

San Diego, CA 92123 (858) 573-8999

Page 6: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

HVAC UNIT: Sunline 36-60 Heaviest

PROVENT STEEL CURB DESIGN

PROVENT PART NUMBER:80-268-1314 14" curb

Curb info

H curb 14 in, curb height

Fy 50 ksi

E 29000 ksi

Fu 65 ksi

gage: 14

R 0.1069

t 0.0713

R/t 1.50

h 13.71 in

Interior Curb

N 28 bearing length: 2*h

C 20

CR 0.1

CN 0.08

Ch 0.03

φw 0.85

Ωw 1.75

Pn 6.73 k

Pall 3.85 k

φPn 5.72 k

Pmax 1.03 k Pall>Pmax,curb OK,

Exterior Curb:

N total 28 2*curb height

N -BUS 1 bearing length with stiffener (built up section)

N - SWC 27 bearing length without stiffener (single web channel)

N 27 N 1

C 7.5 C 15.5

CR 0.08 CR 0.09CN 0.12 CN 0.08

Ch 0.05 Ch 0.04

φw 0.85 φw 0.75

Ωw 1.75 Ωw 2

Pn 1.76 k Pn 4.06 k

Pall 1.00 k Pall 2.03 k Pall 3.03 k

φPn 1.49 k φPn 3.04 k φPn 4.54 k

Pmax 0.95 k

Pall>Pmax,curb OK,

Exterior Curb SWC Exterior Curb BUS

Corner:

Lyons Warren

Engineers Architects

9560 Candida Street

San Diego, CA 92123 (858) 573-8999

Page 7: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

HVAC UNIT: Sunline 36-60 Heaviest

PROVENT STEEL CURB DESIGN

PROVENT PART NUMBER:80-268-1314 14" curb

Connection of Curb to Supporting Structure (ASD)

Transverse: 0.6D+0.6W

**Uplift (wind)= 6689 lbs

*Uplift (seismic) -154 lbs

Uplift max= 6689 lbs/long side

**Shear (wind) 8083 lbs

*Shear (seis) 159 lbs

Shear max= 8083 lbs/total curb

Longitudinal:

**Uplift (wind)= 3704 lbs

*Uplift (seismic) -346 lbs T max 6689 lbs/long

Uplift max= 3704 lbs/long side V max 8083 lbs/total

**Shear (wind) 4274 lbs

*Shear (seis) 159 lbs

Shear max= 4274 lbs/total curb

Wood Attachment: (Use 5/8" φ x 5" LAG SCREWS) W' 2284.8 lbs

(4" minimum embed into DF or SP wood) Z' 592 lbs

total screws required= 16

# screws: LONG SIDE 6

# screws: SHORT SIDE 2

W/screw (uplift) 1115 lbs

V/Screw 505 lbs

Angle 65.6 deg

Z (at angle) 1224 lbs

Atkinson Formula: Z' (at angle) 1536 lbs

WOOD SCREWS OK

Steel Deck Attach.: (Use 5/8" φ A307 Bolts attached to L5x5x1/4 below deck at each conn.point)

Tall= 6900 lbs

Vall= 3680 lbs

total bolts required= 8

# bolts: LONG SIDE 2

# bolts: SHORT SIDE 2

T/bolt (uplift) 3344 lbs

V/bolt 1010 lbs

fv 3.3 ksi OK

ft 10.8 ksi OK

Fnt' 46.3 ksi

Fnv 24.0 ksi

BOLTS OK

page 4

Lyons Warren

Engineers Architects

9560 Candida Street

San Diego, CA 92123 (858) 573-8999

Page 8: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

HVAC UNIT: Sunline 36-60 Heaviest

PROVENT STEEL CURB DESIGN

PROVENT PART NUMBER:80-268-1314 14" curb

Connection of Curb to Concrete Supporting Structure - STRENGTH DESIGN

Transverse: 0.9D +1.0(E or W)

**Uplift (wind)= 11195 lbs

*Uplift (seismic) 524 lbs *Rp*1.3/1.5/0.7asd

Uplift max= 11195 lbs/side (Per long side curb)

**Shear (wind) 13472 lbs (Maximum Lateral Force) (seismic: Rp=1.5 max)

*Shear (seis) 1178 lbs *Rp*1.3/1.5/0.7asd

Shear max= 13472 lbs (Total Curb)

Longitudinal:

**Uplift (wind)= 6249 lbs

*Uplift (seismic) 104 lbs Tu max 11195 lbs

Uplift max= 6249 lbs/side (Per long side curb) Vu max 13472 lbs

**Shear (wind) 7123 lbs

*Shear (seis) 1178 lbs

Shear max= 7123 lbs (Total Curb)

Concrete Attach.: (Use 5/8"φ Simpson Strong Bolt 2) phi-Tn 2900 lbs

phi-Vn 1200 lbs

(LRFD design)

Anchors Required for Uplift (long side only)= 3.9

Anchors Required for Shear (Total Curb)= 11.2

Anchors Required (long side only) = 4.0

anchors (long side) 6.0 OK

Simpson Strong Bolt 2 anchors (short side) 2.0

3 5/8" Embed anchors (total) 16 OK

(f'c=4000psi, 6" min total thickness - normal weight concrete) Tu 1866 OK

ESR Report - 3037 Vu 842 OK

Special Inspection Required

*Uplift and Shear seismic anchorage forces have been designed for an Rp of 1.5 max per ASCE 13.4.2

Anchorage design per ASCE 14.2.2.17/ACI D3.3 with strength reduction factors

not required in combination with Rp=1.5

** For wind force, shear at base for anchorage design, accounts for add'l area from curb width and height

page 5

Conc Anchors

Lyons Warren

Engineers Architects

9560 Candida Street

San Diego, CA 92123 (858) 573-8999

Page 9: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

HVAC UNIT: Sunline 36-60 Lightest

PROVENT STEEL CURB DESIGN

PROVENT PART NUMBER:80-268-1314 14" curb

Curb Information

Curb Number:

Hcurb 14 (Height from support structure to top of curb)

Lcurb 69 (Length of Curb - In to In)

Wcurb 33.25 (Width of Curb - In to In)

Lclip 45.75 (min Length in Long dir from end to clip)

# clips Long Side 2 (Shear + Uplift Clips)

# clips short side 1 (Shear Clips)

Unit Information:

Weight: 470 lbs (Weight of Unit - min weight governs design)

W c-max 167 lbs (Maximum corner weight)

W c-min 77 lbs (Minimum corner weight)

W mid 61 lbs (load B or E, 6 point load criteria for York curbs)

H unit 33 in (Height of unit above curb)

H cm 16 in (Height from top of curb to center of mass of unit)

L unit 82 in (Length of unit)

w unit 45 in (Width of unit)

Seismic Loading (2014 FBC)

Ss 0.2 (worst case for Florida State)

Fa 2.5 (worst case for site; Ss<0.25, Site Class E)

Sms 0.5 (=Fa*Ss)

Sds 0.33 (=2/3*Sms)

Ip 1.5 (=Worst case)

ap 2.5

Rp 6

Fp max 0.3 Wp (=0.4*ap*Sds*Wp*(1+2*z/h)/(Rp/Ip))

Fp ASD 84 lbs (=0.7*Fpmax)

Wind Loading (2014 FBC)

Wind Exposure: D

V 185 mph (Ultimate Wind Speed - Worst case:

Kzt 1.66

Kd 0.9

Kh 1.31 (Worst Case for 60 foot roof height)

GCf 3.1

qh 171 psf (ASD=0.6W)

F 532 psf (ultimate) F 319 psf (service)

A net/transv. 19 sf

Fwind transv 9906 lbs (ultimate) Fwind trnsv 5943 lbs (service)

A net/long 10 sf

Fwind long 5405 lbs (ultimate) Fwind long 3243 psf (service)

Controlling Lateral Load (Seismic vs. Wind)

Transverse 5943 lbs (ASD)

Long 3243 lbs (ASD)

page 1

Lyons Warren

Engineers Architects

9560 Candida Street

San Diego, CA 92123 (858) 573-8999

Page 10: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

HVAC UNIT: Sunline 36-60 Lightest

PROVENT STEEL CURB DESIGN

PROVENT PART NUMBER:80-268-1314 14" curb

Wind Loading: Uplift (2014 FBC) 29.5-2 (GC=3.1 - FBC2014)

qh 171.5 psf

GCr 1.5

Fv (psf) 257.2 psf (ultimate)

Av 26 sf

Fv 6593 lbs (ultimate) Fv 3956 lbs (ASD: 0.6W)

Curb Loading:

Transverse direction:

OTM: 8079 lb-ft 0.6W: F max - transv * Hcm

M res. 289 lb-ft 0.6D: 2 * Wcrnmin *0.6* (width curb +4.25")

Net OTM: 7791 lb-ft 0.6D+0.6W: OTM-RM

Max Comp 2765 lbs /side 1.0D+0.6W: (2 x Wcrnmax + (Mot-Mres)/ (width curb +4.25"))

Max Tension 4471 lbs /side 0.6D+0.6W: (Mot-Mres)/(width curb +4.25")) + Fv/(2 sides)

Max Tension 2235 lbs /clip 0.6D+0.6W: Max tension/side /#clips

Max Corner: 673 lbs W c-max+ (Mot-Mres)/((w/curb+4.25")/Lcurb*(N-corner)/2/12

Max Interior: 1073 lbs W mid+ (Mot-Mres)/(width curb +4.25")/Lcurb*(N-mid)

Longitudinal direction:

OTM: 4408 lb-ft 0.6W: F max long * Hcm

RM 566 lb-ft 0.6D: 2 X Wcrnmin x (Lcurb+4.25in)/12 x 0.6

Net OTM: 3842 lb-ft 0.6D+0.6W: OTM-RM

Max Comp = 1243 lbs /side 1.0D+0.6W: (2*Wcmax + (NetOTM)/Lclip)+ Fv/(U.C)

Max Tens = 2986 lbs /side 0.6D+0.6W: (Mot-Mres)/Lclip) + Fv/(2 sides)

Max Tension = 1997 lbs /clip 0.6D+0.6W: (Mot-Mres)/Lclip) + Fv/(2 sides)/#clips/side

Max Corner: 448 lbs W c-max+ (Mot-Mres)/Lcurb/Wcurb*(N-corner)/2

Connection of Unit to Curb

Screws in Uplift clips (Attach with 1/4 SMS into 14mil) Vall= 933 lbs/screw

Screws in Short Side Clips (Attach with #12 SMS into 14mil) Vall= 870 lbs/screw

UPLIFT CLIPS: UPLIFT CLIPS:

Shear: 811 lbs/clip 4 1/4" screws/clip

Uplift: 2235 lbs/clip Fdiag/screw 345 lbs/screw

F diag 1381 lbs/clip to curb F/screw outs. 279 lbs/screw

SCREWS OK

SHORTSIDE CLIPS SHORTSIDE CLIPS

Shear: 1621 lbs/clip 4 #12 screws/clip

F screw 405 lbs/screw

SCREWS OK

page 2

Lyons Warren

Engineers Architects

9560 Candida Street

San Diego, CA 92123 (858) 573-8999

Page 11: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

HVAC UNIT: Sunline 36-60 Lightest

PROVENT STEEL CURB DESIGN

PROVENT PART NUMBER:80-268-1314 14" curb

Curb info

H curb 14 in, curb height

Fy 50 ksi

E 29000 ksi

Fu 65 ksi

gage: 14

R 0.1069

t 0.0713

R/t 1.50

h 13.71 in

Interior Curb

N 28 bearing length: 2*h

C 20

CR 0.1

CN 0.08

Ch 0.03

φw 0.85

Ωw 1.75

Pn 6.73 k

Pall 3.85 k

φPn 5.72 k

Pmax 1.07 k Pall>Pmax,curb OK,

Exterior Curb:

N total 28 2*curb height

N -BUS 1 bearing length with stiffener (built up section)

N - SWC 27 bearing length without stiffener (single web channel)

N 27 N 1

C 7.5 C 15.5

CR 0.08 CR 0.09CN 0.12 CN 0.08

Ch 0.05 Ch 0.04

φw 0.85 φw 0.75

Ωw 1.75 Ωw 2

Pn 1.76 k Pn 4.06 k

Pall 1.00 k Pall 2.03 k Pall 3.03 k

φPn 1.49 k φPn 3.04 k φPn 4.54 k

Pmax 0.67 k

Pall>Pmax,curb OK,

Exterior Curb SWC Exterior Curb BUS

Corner:

Lyons Warren

Engineers Architects

9560 Candida Street

San Diego, CA 92123 (858) 573-8999

Page 12: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

HVAC UNIT: Sunline 36-60 Lightest

PROVENT STEEL CURB DESIGN

PROVENT PART NUMBER:80-268-1314 14" curb

Connection of Curb to Supporting Structure (ASD)

Transverse: 0.6D+0.6W

**Uplift (wind)= 6877 lbs

*Uplift (seismic) -25 lbs

Uplift max= 6877 lbs/long side

**Shear (wind) 8083 lbs

*Shear (seis) 84 lbs

Shear max= 8083 lbs/total curb

Longitudinal:

**Uplift (wind)= 4007 lbs

*Uplift (seismic) -93 lbs T max 6877 lbs/long

Uplift max= 4007 lbs/long side V max 8083 lbs/total

**Shear (wind) 4274 lbs

*Shear (seis) 84 lbs

Shear max= 4274 lbs/total curb

Wood Attachment: (Use 5/8" φ x 5" LAG SCREWS) W' 2284.8 lbs

(4" minimum embed into DF or SP wood) Z' 592 lbs

total screws required= 16

# screws: LONG SIDE 6

# screws: SHORT SIDE 2

W/screw (uplift) 1146 lbs

V/Screw 505 lbs

Angle 66.2 deg

Z (at angle) 1253 lbs

Atkinson Formula: Z' (at angle) 1559 lbs

WOOD SCREWS OK

Steel Deck Attach.: (Use 5/8" φ A307 Bolts attached to L5x5x1/4 below deck at each conn.point)

Tall= 6900 lbs

Vall= 3680 lbs

total bolts required= 8

# bolts: LONG SIDE 2

# bolts: SHORT SIDE 2

T/bolt (uplift) 3439 lbs

V/bolt 1010 lbs

fv 3.3 ksi OK

ft 11.1 ksi OK

Fnt' 46.3 ksi

Fnv 24.0 ksi

BOLTS OK

page 4

Lyons Warren

Engineers Architects

9560 Candida Street

San Diego, CA 92123 (858) 573-8999

Page 13: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

HVAC UNIT: Sunline 36-60 Lightest

PROVENT STEEL CURB DESIGN

PROVENT PART NUMBER:80-268-1314 14" curb

Connection of Curb to Concrete Supporting Structure - STRENGTH DESIGN

Transverse: 0.9D +1.0(E or W)

**Uplift (wind)= 11477 lbs

*Uplift (seismic) 361 lbs *Rp*1.3/1.5/0.7asd

Uplift max= 11477 lbs/side (Per long side curb)

**Shear (wind) 13472 lbs (Maximum Lateral Force) (seismic: Rp=1.5 max)

*Shear (seis) 622 lbs *Rp*1.3/1.5/0.7asd

Shear max= 13472 lbs (Total Curb)

Longitudinal:

**Uplift (wind)= 6703 lbs

*Uplift (seismic) 189 lbs Tu max 11477 lbs

Uplift max= 6703 lbs/side (Per long side curb) Vu max 13472 lbs

**Shear (wind) 7123 lbs

*Shear (seis) 622 lbs

Shear max= 7123 lbs (Total Curb)

Concrete Attach.: (Use 5/8"φ Simpson Strong Bolt 2) phi-Tn 2900 lbs

phi-Vn 1200 lbs

(LRFD design)

Anchors Required for Uplift (long side only)= 4.0

Anchors Required for Shear (Total Curb)= 11.2

Anchors Required (long side only) = 4.0

anchors (long side) 6.0 OK

Simpson Strong Bolt 2 anchors (short side) 2.0

3 5/8" Embed anchors (total) 16 OK

(f'c=4000psi, 6" min total thickness - normal weight concrete) Tu 1913 OK

ESR Report - 3037 Vu 842 OK

Special Inspection Required

*Uplift and Shear seismic anchorage forces have been designed for an Rp of 1.5 max per ASCE 13.4.2

Anchorage design per ASCE 14.2.2.17/ACI D3.3 with strength reduction factors

not required in combination with Rp=1.5

** For wind force, shear at base for anchorage design, accounts for add'l area from curb width and height

page 5

Conc Anchors

Lyons Warren

Engineers Architects

9560 Candida Street

San Diego, CA 92123 (858) 573-8999

Page 14: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

HVAC UNIT: Sunline 36-60 Heaviest

PROVENT STEEL CURB DESIGN

PROVENT PART NUMBER:80-268-1318 18" curb

Curb Information

Curb Number:

Hcurb 18 (Height from support structure to top of curb)

Lcurb 69 (Length of Curb - In to In)

Wcurb 33.25 (Width of Curb - In to In)

Lclip 45.75 (min Length in Long dir from end to clip)

# clips Long Side 2 (Shear + Uplift Clips)

# clips short side 1 (Shear Clips)

Unit Information:

Weight: 890 lbs (Weight of Unit - min weight governs design)

W c-max 479 lbs (Maximum corner weight)

W c-min 234 lbs (Minimum corner weight)

W mid 96 lbs (load B or E, 6 point load criteria for York curbs)

H unit 33 in (Height of unit above curb)

H cm 16 in (Height from top of curb to center of mass of unit)

L unit 82 in (Length of unit)

w unit 45 in (Width of unit)

Seismic Loading (2014 FBC)

Ss 0.2 (worst case for Florida State)

Fa 2.5 (worst case for site; Ss<0.25, Site Class E)

Sms 0.5 (=Fa*Ss)

Sds 0.33 (=2/3*Sms)

Ip 1.5 (=Worst case)

ap 2.5

Rp 6

Fp max 0.3 Wp (=0.4*ap*Sds*Wp*(1+2*z/h)/(Rp/Ip))

Fp ASD 159 lbs (=0.7*Fpmax)

Wind Loading (2014 FBC)

Wind Exposure: D

V 185 mph (Ultimate Wind Speed - Worst case:

Kzt 1.66

Kd 0.9

Kh 1.31 (Worst Case for 60 foot roof height)

GCf 3.1

qh 171 psf (ASD=0.6W)

F 532 psf (ultimate) F 319 psf (service)

A net/transv. 19 sf

Fwind transv 9906 lbs (ultimate) Fwind trnsv 5943 lbs (service)

A net/long 10 sf

Fwind long 5405 lbs (ultimate) Fwind long 3243 psf (service)

Controlling Lateral Load (Seismic vs. Wind)

Transverse 5943 lbs (ASD)

Long 3243 lbs (ASD)

page 1

Lyons Warren

Engineers Architects

9560 Candida Street

San Diego, CA 92123 (858) 573-8999

Page 15: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

HVAC UNIT: Sunline 36-60 Heaviest

PROVENT STEEL CURB DESIGN

PROVENT PART NUMBER:80-268-1318 18" curb

Wind Loading: Uplift (2014 FBC) 29.5-2 (GC=3.1 - FBC2014)

qh 171.5 psf

GCr 1.5

Fv (psf) 257.2 psf (ultimate)

Av 26 sf

Fv 6593 lbs (ultimate) Fv 3956 lbs (ASD: 0.6W)

Curb Loading:

Transverse direction:

OTM: 8079 lb-ft 0.6W: F max - transv * Hcm

M res. 878 lb-ft 0.6D: 2 * Wcrnmin *0.6* (width curb +4.25")

Net OTM: 7202 lb-ft 0.6D+0.6W: OTM-RM

Max Comp 3075 lbs /side 1.0D+0.6W: (2 x Wcrnmax + (Mot-Mres)/ (width curb +4.25"))

Max Tension 4282 lbs /side 0.6D+0.6W: (Mot-Mres)/(width curb +4.25")) + Fv/(2 sides)

Max Tension 2141 lbs /clip 0.6D+0.6W: Max tension/side /#clips

Max Corner: 1080 lbs W c-max+ (Mot-Mres)/((w/curb+4.25")/Lcurb*(N-corner)/2/12

Max Interior: 1298 lbs W mid+ (Mot-Mres)/(width curb +4.25")/Lcurb*(N-mid)

Longitudinal direction:

OTM: 4408 lb-ft 0.6W: F max long * Hcm

RM 1720 lb-ft 0.6D: 2 X Wcrnmin x (Lcurb+4.25in)/12 x 0.6

Net OTM: 2688 lb-ft 0.6D+0.6W: OTM-RM

Max Comp = 1362 lbs /side 1.0D+0.6W: (2*Wcmax + (NetOTM)/Lclip)+ Fv/(U.C)

Max Tens = 2683 lbs /side 0.6D+0.6W: (Mot-Mres)/Lclip) + Fv/(2 sides)

Max Tension = 1694 lbs /clip 0.6D+0.6W: (Mot-Mres)/Lclip) + Fv/(2 sides)/#clips/side

Max Corner: 732 lbs W c-max+ (Mot-Mres)/Lcurb/Wcurb*(N-corner)/2

Connection of Unit to Curb

Screws in Uplift clips (Attach with 1/4 SMS into 14mil) Vall= 933 lbs/screw

Screws in Short Side Clips (Attach with #12 SMS into 14mil) Vall= 870 lbs/screw

UPLIFT CLIPS: UPLIFT CLIPS:

Shear: 811 lbs/clip 4 1/4" screws/clip

Uplift: 2141 lbs/clip Fdiag/screw 336 lbs/screw

F diag 1343 lbs/clip to curb F/screw outs. 268 lbs/screw

SCREWS OK

SHORTSIDE CLIPS SHORTSIDE CLIPS

Shear: 1621 lbs/clip 4 #12 screws/clip

F screw 405 lbs/screw

SCREWS OK

page 2

Lyons Warren

Engineers Architects

9560 Candida Street

San Diego, CA 92123 (858) 573-8999

Page 16: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

HVAC UNIT: Sunline 36-60 Heaviest

PROVENT STEEL CURB DESIGN

PROVENT PART NUMBER:80-268-1318 18" curb

Curb info

H curb 18 in, curb height

Fy 50 ksi

E 29000 ksi

Fu 65 ksi

gage: 14

R 0.1069

t 0.0713

R/t 1.50

h 17.71 in

Interior Curb

N 36 bearing length: 2*h

C 20

CR 0.1

CN 0.08

Ch 0.03

φw 0.85

Ωw 1.75

Pn 6.58 k

Pall 3.76 k

φPn 5.59 k

Pmax 1.30 k Pall>Pmax,curb OK,

Exterior Curb:

N total 36 2*curb height

N -BUS 1 bearing length with stiffener (built up section)

N - SWC 35 bearing length without stiffener (single web channel)

N 35 N 1

C 7.5 C 15.5

CR 0.08 CR 0.09CN 0.12 CN 0.08

Ch 0.05 Ch 0.04

φw 0.85 φw 0.75

Ωw 1.75 Ωw 2

Pn 1.33 k Pn 3.37 k

Pall 0.76 k Pall 1.68 k Pall 2.45 k

φPn 1.13 k φPn 2.53 k φPn 3.66 k

Pmax 1.08 k

Pall>Pmax,curb OK,

Exterior Curb SWC Exterior Curb BUS

Corner:

Lyons Warren

Engineers Architects

9560 Candida Street

San Diego, CA 92123 (858) 573-8999

Page 17: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

HVAC UNIT: Sunline 36-60 Heaviest

PROVENT STEEL CURB DESIGN

PROVENT PART NUMBER:80-268-1318 18" curb

Connection of Curb to Supporting Structure (ASD)

Transverse: 0.6D+0.6W

**Uplift (wind)= 7527 lbs

*Uplift (seismic) -136 lbs

Uplift max= 7527 lbs/long side

**Shear (wind) 8694 lbs

*Shear (seis) 159 lbs

Shear max= 8694 lbs/total curb

Longitudinal:

**Uplift (wind)= 4054 lbs

*Uplift (seismic) -332 lbs T max 7527 lbs/long

Uplift max= 4054 lbs/long side V max 8694 lbs/total

**Shear (wind) 4568 lbs

*Shear (seis) 159 lbs

Shear max= 4568 lbs/total curb

Wood Attachment: (Use 5/8" φ x 5" LAG SCREWS) W' 2284.8 lbs

(4" minimum embed into DF or SP wood) Z' 592 lbs

total screws required= 16

# screws: LONG SIDE 6

# screws: SHORT SIDE 2

W/screw (uplift) 1254 lbs

V/Screw 543 lbs

Angle 66.6 deg

Z (at angle) 1367 lbs

Atkinson Formula: Z' (at angle) 1574 lbs

WOOD SCREWS OK

Steel Deck Attach.: (Use 5/8" φ A307 Bolts attached to L5x5x1/4 below deck at each conn.point)

Tall= 6900 lbs

Vall= 3680 lbs

total bolts required= 8

# bolts: LONG SIDE 2

# bolts: SHORT SIDE 2

T/bolt (uplift) 3763 lbs

V/bolt 1087 lbs

fv 3.5 ksi OK

ft 12.1 ksi OK

Fnt' 45.4 ksi

Fnv 24.0 ksi

BOLTS OK

page 4

Lyons Warren

Engineers Architects

9560 Candida Street

San Diego, CA 92123 (858) 573-8999

Page 18: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

HVAC UNIT: Sunline 36-60 Heaviest

PROVENT STEEL CURB DESIGN

PROVENT PART NUMBER:80-268-1318 18" curb

Connection of Curb to Concrete Supporting Structure - STRENGTH DESIGN

Transverse: 0.9D +1.0(E or W)

**Uplift (wind)= 12592 lbs

*Uplift (seismic) 653 lbs *Rp*1.3/1.5/0.7asd

Uplift max= 12592 lbs/side (Per long side curb)

**Shear (wind) 14491 lbs (Maximum Lateral Force) (seismic: Rp=1.5 max)

*Shear (seis) 1182 lbs *Rp*1.3/1.5/0.7asd

Shear max= 14491 lbs (Total Curb)

Longitudinal:

**Uplift (wind)= 6832 lbs

*Uplift (seismic) 210 lbs Tu max 12592 lbs

Uplift max= 6832 lbs/side (Per long side curb) Vu max 14491 lbs

**Shear (wind) 7614 lbs

*Shear (seis) 1182 lbs

Shear max= 7614 lbs (Total Curb)

Concrete Attach.: (Use 5/8"φ Simpson Strong Bolt 2) phi-Tn 2900 lbs

phi-Vn 1200 lbs

(LRFD design)

Anchors Required for Uplift (long side only)= 4.3

Anchors Required for Shear (Total Curb)= 12.1

Anchors Required (long side only) = 5.0

anchors (long side) 6.0 OK

Simpson Strong Bolt 2 anchors (short side) 2.0

3 5/8" Embed anchors (total) 16 OK

(f'c=4000psi, 6" min total thickness - normal weight concrete) Tu 2099 OK

ESR Report - 3037 Vu 906 OK

Special Inspection Required

*Uplift and Shear seismic anchorage forces have been designed for an Rp of 1.5 max per ASCE 13.4.2

Anchorage design per ASCE 14.2.2.17/ACI D3.3 with strength reduction factors

not required in combination with Rp=1.5

** For wind force, shear at base for anchorage design, accounts for add'l area from curb width and height

page 5

Conc Anchors

Lyons Warren

Engineers Architects

9560 Candida Street

San Diego, CA 92123 (858) 573-8999

Page 19: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

HVAC UNIT: Sunline 36-60 Lightest

PROVENT STEEL CURB DESIGN

PROVENT PART NUMBER:80-268-1318 18" curb

Curb Information

Curb Number:

Hcurb 18 (Height from support structure to top of curb)

Lcurb 69 (Length of Curb - In to In)

Wcurb 33.25 (Width of Curb - In to In)

Lclip 45.75 (min Length in Long dir from end to clip)

# clips Long Side 2 (Shear + Uplift Clips)

# clips short side 1 (Shear Clips)

Unit Information:

Weight: 470 lbs (Weight of Unit - min weight governs design)

W c-max 167 lbs (Maximum corner weight)

W c-min 77 lbs (Minimum corner weight)

W mid 61 lbs (load B or E, 6 point load criteria for York curbs)

H unit 33 in (Height of unit above curb)

H cm 16 in (Height from top of curb to center of mass of unit)

L unit 82 in (Length of unit)

w unit 45 in (Width of unit)

Seismic Loading (2014 FBC)

Ss 0.2 (worst case for Florida State)

Fa 2.5 (worst case for site; Ss<0.25, Site Class E)

Sms 0.5 (=Fa*Ss)

Sds 0.33 (=2/3*Sms)

Ip 1.5 (=Worst case)

ap 2.5

Rp 6

Fp max 0.3 Wp (=0.4*ap*Sds*Wp*(1+2*z/h)/(Rp/Ip))

Fp ASD 84 lbs (=0.7*Fpmax)

Wind Loading (2014 FBC)

Wind Exposure: D

V 185 mph (Ultimate Wind Speed - Worst case:

Kzt 1.66

Kd 0.9

Kh 1.31 (Worst Case for 60 foot roof height)

GCf 3.1

qh 171 psf (ASD=0.6W)

F 532 psf (ultimate) F 319 psf (service)

A net/transv. 19 sf

Fwind transv 9906 lbs (ultimate) Fwind trnsv 5943 lbs (service)

A net/long 10 sf

Fwind long 5405 lbs (ultimate) Fwind long 3243 psf (service)

Controlling Lateral Load (Seismic vs. Wind)

Transverse 5943 lbs (ASD)

Long 3243 lbs (ASD)

page 1

Lyons Warren

Engineers Architects

9560 Candida Street

San Diego, CA 92123 (858) 573-8999

Page 20: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

HVAC UNIT: Sunline 36-60 Lightest

PROVENT STEEL CURB DESIGN

PROVENT PART NUMBER:80-268-1318 18" curb

Wind Loading: Uplift (2014 FBC) 29.5-2 (GC=3.1 - FBC2014)

qh 171.5 psf

GCr 1.5

Fv (psf) 257.2 psf (ultimate)

Av 26 sf

Fv 6593 lbs (ultimate) Fv 3956 lbs (ASD: 0.6W)

Curb Loading:

Transverse direction:

OTM: 8079 lb-ft 0.6W: F max - transv * Hcm

M res. 289 lb-ft 0.6D: 2 * Wcrnmin *0.6* (width curb +4.25")

Net OTM: 7791 lb-ft 0.6D+0.6W: OTM-RM

Max Comp 2765 lbs /side 1.0D+0.6W: (2 x Wcrnmax + (Mot-Mres)/ (width curb +4.25"))

Max Tension 4471 lbs /side 0.6D+0.6W: (Mot-Mres)/(width curb +4.25")) + Fv/(2 sides)

Max Tension 2235 lbs /clip 0.6D+0.6W: Max tension/side /#clips

Max Corner: 817 lbs W c-max+ (Mot-Mres)/((w/curb+4.25")/Lcurb*(N-corner)/2/12

Max Interior: 1362 lbs W mid+ (Mot-Mres)/(width curb +4.25")/Lcurb*(N-mid)

Longitudinal direction:

OTM: 4408 lb-ft 0.6W: F max long * Hcm

RM 566 lb-ft 0.6D: 2 X Wcrnmin x (Lcurb+4.25in)/12 x 0.6

Net OTM: 3842 lb-ft 0.6D+0.6W: OTM-RM

Max Comp = 1243 lbs /side 1.0D+0.6W: (2*Wcmax + (NetOTM)/Lclip)+ Fv/(U.C)

Max Tens = 2986 lbs /side 0.6D+0.6W: (Mot-Mres)/Lclip) + Fv/(2 sides)

Max Tension = 1997 lbs /clip 0.6D+0.6W: (Mot-Mres)/Lclip) + Fv/(2 sides)/#clips/side

Max Corner: 529 lbs W c-max+ (Mot-Mres)/Lcurb/Wcurb*(N-corner)/2

Connection of Unit to Curb

Screws in Uplift clips (Attach with 1/4 SMS into 14mil) Vall= 933 lbs/screw

Screws in Short Side Clips (Attach with #12 SMS into 14mil) Vall= 870 lbs/screw

UPLIFT CLIPS: UPLIFT CLIPS:

Shear: 811 lbs/clip 4 1/4" screws/clip

Uplift: 2235 lbs/clip Fdiag/screw 345 lbs/screw

F diag 1381 lbs/clip to curb F/screw outs. 279 lbs/screw

SCREWS OK

SHORTSIDE CLIPS SHORTSIDE CLIPS

Shear: 1621 lbs/clip 4 #12 screws/clip

F screw 405 lbs/screw

SCREWS OK

page 2

Lyons Warren

Engineers Architects

9560 Candida Street

San Diego, CA 92123 (858) 573-8999

Page 21: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

HVAC UNIT: Sunline 36-60 Lightest

PROVENT STEEL CURB DESIGN

PROVENT PART NUMBER:80-268-1318 18" curb

Curb info

H curb 18 in, curb height

Fy 50 ksi

E 29000 ksi

Fu 65 ksi

gage: 14

R 0.1069

t 0.0713

R/t 1.50

h 17.71 in

Interior Curb

N 36 bearing length: 2*h

C 20

CR 0.1

CN 0.08

Ch 0.03

φw 0.85

Ωw 1.75

Pn 6.58 k

Pall 3.76 k

φPn 5.59 k

Pmax 1.36 k Pall>Pmax,curb OK,

Exterior Curb:

N total 36 2*curb height

N -BUS 1 bearing length with stiffener (built up section)

N - SWC 35 bearing length without stiffener (single web channel)

N 35 N 1

C 7.5 C 15.5

CR 0.08 CR 0.09CN 0.12 CN 0.08

Ch 0.05 Ch 0.04

φw 0.85 φw 0.75

Ωw 1.75 Ωw 2

Pn 1.33 k Pn 3.37 k

Pall 0.76 k Pall 1.68 k Pall 2.45 k

φPn 1.13 k φPn 2.53 k φPn 3.66 k

Pmax 0.82 k

Pall>Pmax,curb OK,

Exterior Curb SWC Exterior Curb BUS

Corner:

Lyons Warren

Engineers Architects

9560 Candida Street

San Diego, CA 92123 (858) 573-8999

Page 22: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

HVAC UNIT: Sunline 36-60 Lightest

PROVENT STEEL CURB DESIGN

PROVENT PART NUMBER:80-268-1318 18" curb

Connection of Curb to Supporting Structure (ASD)

Transverse: 0.6D+0.6W

**Uplift (wind)= 7715 lbs

*Uplift (seismic) -16 lbs

Uplift max= 7715 lbs/long side

**Shear (wind) 8694 lbs

*Shear (seis) 84 lbs

Shear max= 8694 lbs/total curb

Longitudinal:

**Uplift (wind)= 4357 lbs

*Uplift (seismic) -85 lbs T max 7715 lbs/long

Uplift max= 4357 lbs/long side V max 8694 lbs/total

**Shear (wind) 4568 lbs

*Shear (seis) 84 lbs

Shear max= 4568 lbs/total curb

Wood Attachment: (Use 5/8" φ x 5" LAG SCREWS) W' 2284.8 lbs

(4" minimum embed into DF or SP wood) Z' 592 lbs

total screws required= 16

# screws: LONG SIDE 6

# screws: SHORT SIDE 2

W/screw (uplift) 1286 lbs

V/Screw 543 lbs

Angle 67.1 deg

Z (at angle) 1396 lbs

Atkinson Formula: Z' (at angle) 1594 lbs

WOOD SCREWS OK

Steel Deck Attach.: (Use 5/8" φ A307 Bolts attached to L5x5x1/4 below deck at each conn.point)

Tall= 6900 lbs

Vall= 3680 lbs

total bolts required= 8

# bolts: LONG SIDE 2

# bolts: SHORT SIDE 2

T/bolt (uplift) 3858 lbs

V/bolt 1087 lbs

fv 3.5 ksi OK

ft 12.4 ksi OK

Fnt' 45.4 ksi

Fnv 24.0 ksi

BOLTS OK

page 4

Lyons Warren

Engineers Architects

9560 Candida Street

San Diego, CA 92123 (858) 573-8999

Page 23: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst

HVAC UNIT: Sunline 36-60 Lightest

PROVENT STEEL CURB DESIGN

PROVENT PART NUMBER:80-268-1318 18" curb

Connection of Curb to Concrete Supporting Structure - STRENGTH DESIGN

Transverse: 0.9D +1.0(E or W)

**Uplift (wind)= 12874 lbs

*Uplift (seismic) 429 lbs *Rp*1.3/1.5/0.7asd

Uplift max= 12874 lbs/side (Per long side curb)

**Shear (wind) 14491 lbs (Maximum Lateral Force) (seismic: Rp=1.5 max)

*Shear (seis) 624 lbs *Rp*1.3/1.5/0.7asd

Shear max= 14491 lbs (Total Curb)

Longitudinal:

**Uplift (wind)= 7286 lbs

*Uplift (seismic) 245 lbs Tu max 12874 lbs

Uplift max= 7286 lbs/side (Per long side curb) Vu max 14491 lbs

**Shear (wind) 7614 lbs

*Shear (seis) 624 lbs

Shear max= 7614 lbs (Total Curb)

Concrete Attach.: (Use 5/8"φ Simpson Strong Bolt 2) phi-Tn 2900 lbs

phi-Vn 1200 lbs

(LRFD design)

Anchors Required for Uplift (long side only)= 4.4

Anchors Required for Shear (Total Curb)= 12.1

Anchors Required (long side only) = 5.0

anchors (long side) 6.0 OK

Simpson Strong Bolt 2 anchors (short side) 2.0

3 5/8" Embed anchors (total) 16 OK

(f'c=4000psi, 6" min total thickness - normal weight concrete) Tu 2146 OK

ESR Report - 3037 Vu 906 OK

Special Inspection Required

*Uplift and Shear seismic anchorage forces have been designed for an Rp of 1.5 max per ASCE 13.4.2

Anchorage design per ASCE 14.2.2.17/ACI D3.3 with strength reduction factors

not required in combination with Rp=1.5

** For wind force, shear at base for anchorage design, accounts for add'l area from curb width and height

page 5

Conc Anchors

Lyons Warren

Engineers Architects

9560 Candida Street

San Diego, CA 92123 (858) 573-8999

Page 24: Structural Calculations for Roof Curbs for York Units … ·  · 2016-05-30Structural Calculations for Roof Curbs for York Units SUNLINE 36-60 York Units ZR 036-060, ... Ip 1.5(=Worst
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