Internal Floating Roof Design

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Company Logo Internal Pontoon Floating Roof Design Per API 650, Appendix H Rev #

Rev Description

Rev By

Rev Date

1 2 3 4 Notes 1 2 3 4 5

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Page 1 of 38

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Internal Pontoon Floating Design A. Introduction This program designs pontoon floating roofs to the requirements of API 650, Appendix H (internal roofs) Design methodologies are as follows: 1. Pontoon ring is designed using section properties determined in accordance with the AISI Cold-Formed Steel Design Manual (accounts for local buckling of plates with large width to thickness ratios) 2. Floating roof legs are designed in accordance with AISC 360, Latest Edition for loads listed in API 650, Appendix H. 3. Deck stresses and deflections are determined in accordance with the paper: "Stresses in Ruptured Floating Roofs", H.I. Epstein and J.R. Buzek, 1978 ASME Journal of Pressure Vessel Technology. 4. Pontoon ring is modeled as a ring on elastic foundation. 5. Ponton ring strength is evaluated in accordance with AISI Cold-Formed Steel Design Manual.

B. Pontoon Geometry Diameter

Rim space

Pontoon width

D := 220 ⋅ ft

Srim := 8 ⋅ in

Wpon := 12 ⋅ ft

Width of inner rim extension

WiExt := 0 ⋅ in

Width of outer rim extension

WoExt := 0 ⋅ in

Height of inner rim

Height of outer rim

Hir := 30 ⋅ in

Hor := 30 ⋅ in

Height of outer rim extension

Backslope

Cover slope

HoExt := 3 ⋅ in

BS := 0 ⋅ in

in CSmin := −.1875 ⋅ ft

Deck thickness

Cover thickness

Bulkhead thickness

Inner rim thickness

Outer rim thickness

td := .1875 ⋅ in

tc := .1875 ⋅ in

tbh := .1875 ⋅ in

tir := .75 ⋅ in

tor := .75 ⋅ in

Suggested number of bulkheads

(D − 2 ⋅ Srim) ⋅ π = 38.70 17.75 ⋅ ft

Suggested number of posts per rafter

 Wpon   = 2.00  6 ⋅ ft 

floor 

Rafters per Pontoon

Number of bulkheads

Posts per Rafter

Spacing of weld to rafter

Length of weld per spacing

Weld size for cover to rafter connection

Nrp := 2

Nbh := 40

Npp := 2

Swr := 12 ⋅ in

Lwr := 2 ⋅ in

twr := .1875 ⋅ in

Angle Rafter

Channel Rafter

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Page 2 of 38

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Internal Pontoon Floating Roof Design C. Leg Geometry

Leg diameter

Leg thickness

Sleeve diameter

Sleeve thickness

dlegs := 2.875 ⋅ in

tlegs := .276 ⋅ in

dslv := 3.5 ⋅ in

tslv := .216 ⋅ in

Maximum leg spacing

Low leg setting

High leg setting

Sleeve extension below deck

SlegMax := 24 ⋅ ft

Hlow := 3 ⋅ ft

Hhi := 7 ⋅ ft

Hdslv := 3 ⋅ in

Radius to deck legs

Pin height for deck legs

 12     32  ⋅ ft Rlegs :=  52     72 

(

n := 1 .. rows Rlegs

 24     24  ⋅ in Hpin :=  24     24 

2

− Srim − Wpon = 97.33 ft

) Number of deck legs at each radius

 2 ⋅ π ⋅ Rlegs  n  NlegMin := ceil  n S legMax  

D



 4.00    9.00   NlegMin =  14.00     19.00 

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4     10  Nlegs :=  16     20 

Number of inner rim legs

Nirlegs := 36

Page 3 of 38

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Internal Pontoon Floating Roof Design D. Appurtenance Geometry

Weight of pontoon manway

Weight of center weight

Diameter of centerweight

wpmw := 75 ⋅ lbs

Wcw := 1 ⋅ lbs

Dcw := 20 ⋅ ft

Length of ladder track

Lltr := 45 ⋅ ft

Number of deck manways

Ndmw := 2

Number of bleeder vents

Weight of bleeder vents

Nbv := 2

wbv := 250 ⋅ lbs

Weight of deck manways

wdmw := 100 ⋅ lbs

E. Corrosion Allowances Outer rim corrosion allowance

Inner rim corrosion allowance

Deck corrosion allowance

Cover plate corrosion allowance

Corrosion allowance on legs

CAor := 0 ⋅ in

CAir := 0 ⋅ in

CAd := 0 ⋅ in

CAc := 0 ⋅ in

CAlegs := 0 ⋅ in

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Page 4 of 38

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Internal Pontoon Floating Roof Design SK

Pontoon Section

100

− 50

0

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50

Page 5 of 38

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Internal Pontoon Floating Roof Design

Plan View of Roof

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Page 6 of 38

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Internal Pontoon Floating Roof Design E. Material Properties Yield strength of rim plate

Yield strength of deck plate

Yield strength of plate

Yield strength of rafter

Fyrim := 36 ⋅ ksi

Fyd := 36 ⋅ ksi

Fyp := 36 ⋅ ksi

Fyr := 36 ⋅ ksi

Weld tensile strength

Leg yield strength

Fuw := 60 ⋅ ksi

Fylegs := 35 ⋅ ksi

F. Design Criteria Live load

LL := 12.5 ⋅ psf

Minimum specific gravity

SGmin := 0.7

Number of punctured pontoons

Fricition from seal

Unit weight of seal

lbs μseal := 15 ⋅ ft

wseal := 20 ⋅ plf

Np := 2

Radial force from seal

lbs kseal := 45 ⋅ ft

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Page 7 of 38

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Internal Pontoon Floating Roof Design G. Roof Weight

(

)

Wor := tor ⋅ Hor + WoExt ⋅ 2 ⋅ π ⋅ Ror ⋅ γs

Wor = 52595.50 ⋅ lbs

Weight of outer rim

Wir = 46822.82 ⋅ lbs

Weight of inner rim

Wpon   Rir + Ror   ⋅ tc ⋅ γs Wcover := ⋅ 2 ⋅ π ⋅  cos α c  2  

Wcover = 59663.93 ⋅ lbs

Weight of cover plate

Wpon   Rir + Ror   ⋅ td ⋅ γs WBS := ⋅ 2 ⋅ π ⋅  cos α BS  2  

WBS = 59650.99 ⋅ lbs

Weight of backslope

(

)

Wir := tir ⋅ Hir + WiExt ⋅ 2 ⋅ π ⋅ Rir ⋅ γs

( )

(

)

 Hir + ( Hor − HoExt)   ⋅ tbh ⋅ γs 2  

Wbh := Nbh ⋅ Wpon ⋅ 

Wbh = 8728.13 ⋅ lbs

Weight of bulkheads

wraft = 4.10 ⋅ plf Wpon Wraft := Nrp ⋅ Nbh ⋅ ⋅ wraft cos α c

( )

 Hor − HoExt + Hir   ⋅ wraft 2  

Wpost := Nrp ⋅ Npp ⋅ Nbh ⋅  Wseal := wseal ⋅ π ⋅ D Ffseal := μseal ⋅ π ⋅ D

Wraft = 3936.85 ⋅ lbs

Weight of rafters

Wpost = 1558.00 ⋅ lbs

Weight of posts

Wseal = 13823.01 ⋅ lbs Ffseal = 10367.26 ⋅ lbs

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Weight of seal

Total frictional force on seal

Page 8 of 38

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Internal Pontoon Floating Roof Design G. Roof Weight 2

Wdeck := π ⋅ Rir ⋅ td ⋅ γs ⋅ 1.05

Wslv :=

rows ( Hpin)   n=1  rows ( Hpin)   n = 1

Wdeck = 239264.61 ⋅ lbs

Weight of deck

∑

  Hpin + Hdslv + 2 ⋅ in ⋅ Nlegs  ⋅ wslv if SleeveType = 1 n n    

∑

  Hpin + Hlow + 2 ⋅ in ⋅ Nlegs  ⋅ wslv otherwise n n    Weight of deck sleeves

Wslv = 916.28 ⋅ lbs

(

)

rows H pin

∑

Wlegs :=

 Hpin + Hdslv + Hhi + 2 ⋅ in ⋅ Nlegs  ⋅ wlegs n n  

Weight of deck legs

n= 1

Wlegs = 3610.49 ⋅ lbs

(

)

Wpslv := Nbh ⋅ Hpslv + Nirlegs ⋅ Hirslv ⋅ wslv

Wpslv = 1728.92 ⋅ lbs

Weight of pontoon sleeves

Wplegs := Nbh ⋅ Hpslv + Hhi + Nirlegs ⋅ Hirslv + Hhi  ⋅ wlegs  

(

)

(

)

Weight of pontoon legs

Wplegs = 5827.90 ⋅ lbs

Weight of centerweight

Wcw = 1.00 ⋅ lbs Wpmw := wpmw ⋅ Nbh

Wpmw = 3000.00 ⋅ lbs

Weight of pontoon manways

Wdmw := Ndmw ⋅ wdmw

Wdmw = 200.00 ⋅ lbs

Weight of deck manways

Wbv := Nbv ⋅ wbv

Wbv = 500.00 ⋅ lbs

Weight of bleeder vents

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Page 9 of 38

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Internal Pontoon Floating Roof Design G. Roof Weight WPON := Wor + Wir + Wcover + WBS + Wbh + Wraft + Wseal + Wplegs + Wpslv + Wpmw + Wpost WPON = 257336.05 ⋅ lbs

Total pontoon weight

WdTOT := Wdeck + Wlegs + Wslv + Wbv + Wdmw

Total deck weight

WdTOT = 244491.38 ⋅ lbs Total roof weight

Wroof := WPON + WdTOT Wroof = 501827.43 ⋅ lbs γdeck :=

WdTOT π ⋅ Rir

2

γdeck = 8.21 ⋅ psf

Unit weight of deck considering appurtenances

H. Check Cover Slope CS :=

Hor − HoExt − BS − Hir

CSmin CS

Wpon

= −0.25 ⋅

in ft Check minimum cover slope

= 75.00 ⋅ %

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Page 10 of 38

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Internal Pontoon Floating Roof Design J. Check Rafters RafterName = "C3X4.1"

Rafter size used

wraft = 4.10 ⋅ plf

Weight of rafter per foot

Sro := Sro 7 ⋅ ft

2 ⋅ π ⋅ Ror

(

)

Nbh ⋅ Nrp + 1

Spacing at outer end of rafter

Check maximum spacing

= 81.78 ⋅ %

Sri :=

Sro = 5.72 ft

2 ⋅ π ⋅ Rir

(

)

Nbh ⋅ Nrp + 1

Spacing at inner end of rafter

Sri = 5.10 ft DL := γs ⋅ tc DL = 7.66 ⋅ psf LL = 12.50 ⋅ psf

Dead load on rafter

Live load on rafter

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Page 11 of 38

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Internal Pontoon Floating Roof Design J. Check Rafters

q1 :=

Sro Sri Sro ⋅ DL + wraft + Sro ⋅ LL if Wpon > + 2 2 Wpon ⋅ DL + wraft + Wpon ⋅ LL otherwise

q2 :=

Sro Sri Sri ⋅ DL + wraft + Sri ⋅ LL if Wpon > + 2 2

Uniform load toward outer end of rafter

Uniform load toward inner end of rafter

Wpon ⋅ DL + wraft + Wpon ⋅ LL otherwise

x1 :=

S ro 2

Sro S ri if Wpon > + 2 2

Wpon 2

x2 :=

S ri 2

2

Location of q1 loading form outer end

x2 = 2.55 ft

Location of q2 loading form inner end

otherwise

Sro S ri if Wpon > + 2 2

Wpon

x1 = 2.86 ft

otherwise

x3 := Wpon − x1 − x2 Width of transition loading

x3 = 6.59 ft qur ( x) :=

x x1

⋅ q1 if x < x1

Uniform load as a function of x

q1 −

(x − x1) ⋅ q − q ( 1 2) x

q2 −

x − ( x1 + x3) ⋅ q2 otherwise x

3

if

(x ≥ x1) ⋅ (x < x1 + x3)

2

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Page 12 of 38

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Internal Pontoon Floating Roof Design J. Check Rafters W ⌠ pon  qur ( x) ⋅ x dx  ⌡

R1 :=

Reaction at outer end of rafter

0 ⋅ ft

Wpon

R1 = 0.52 ⋅ kip xmax :=

xx ←

Wpon 3

⌠ while  ⌡

Location of maximum moment

xx

qur ( xx) dxx < R1

0 ⋅ ft

xx ← xx + .5 ⋅ in xx xmax = 5.92 ft ⌠ Mur ( x) := R1 ⋅ x −  ⌡

x

qur ( x1) ⋅ ( x − x1) dx1

Ultimate moment in rafter

0 ⋅ ft

(

)

Mur xmax = 1.86 ⋅ ft ⋅ kip Safety factor for bending

ΩB := 1.67

Nominal moment capacity of rafter per AISC 360-05

Mnr := S xr ⋅ Fyr

(

Mur xmax Mnr

vfr :=

) = 45.00⋅ %

R1 ⋅ Qr Ixr

Compare moment to nominal capacity

kip vfr = 0.15 ⋅ in

Ultimate shear flow at rafter cover connection

Ωw := 2 Lwr Fuw vfn := 0.6 ⋅ .7071 ⋅ twr ⋅ ⋅ Swr Ωw vfr vfn

Safety factor for weld kip vfn = 0.40 ⋅ in

Nominal shear strength of weld at rafter to cover connection Compare shear flow to nominal capacity

= 38.88 ⋅ %

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Page 13 of 38

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Internal Pontoon Floating Roof Design K. Check Legs

 12.00    32.00   Rlegs = ft  52.00     72.00 

 4.00    10.00   Nlegs =  16.00     20.00 

Nirlegs = 36.00

Nbh = 40.00

TLdeck := γdeck + LL TLdeck = 20.71 ⋅ psf

Deck load

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Page 14 of 38

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Internal Pontoon Floating Roof Design K. Check Legs Pulegs :=

(

for i ∈ 1 .. rows Rlegs

pi ←

)

2  Rlegs + Rir  i π ⋅  ⋅ TLdeck 2  

Nlegs i

(

(

if ( i = 1) ⋅ i = rows Rlegs

))

2 2  R  legsi+1 + Rlegsi   Rlegsi + Rlegsi−1   π ⋅   −   ⋅ TLdeck 2 2      pi ← if ( i > 1) ⋅ ( i < rows ( Rlegs) )

Nlegs i

2  R  legsi+1 + Rlegsi   π ⋅    ⋅ TLdeck 2    pi ← if ( i = 1) ⋅ ( i < rows ( Rlegs) ) ⋅  Rlegs > 0 ⋅ ft Nlegs i   i

pi ←

1 2

π ⋅  Rlegs ⋅



2   ⋅ TLdeck  if ( i = 1) ⋅ ( i < rows ( Rlegs) ) ⋅  Rlegs = 0 ⋅ ft i Nlegs   i+1 

i

2 2  R + R  Rlegs + Rlegs   legsi   ir i i−1 π ⋅   −   ⋅ TLdeck 2 2      if ( i > 1) ⋅ ( i = rows ( Rlegs) ) pi ←

Nlegs i

2 2  R  legsi+1 + Rlegsi   Rlegsi + Rlegsi−1   π ⋅   −   ⋅ TLdeck 2 2      pi ← otherwise

Nlegs i

p

 7.87    8.33   Pulegs = ⋅ kip  8.46     10.82 

Load at deck legs

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Page 15 of 38

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Internal Pontoon Floating Roof Design K. Check Legs

Puirlegs :=

2     Rir + Rlegs  rows ( Rlegs)  2  π ⋅ ( Rir) −    ⋅ TLdeck 2   

Nirlegs

  1 1.6 ⋅ π ⋅  Ror − Rir + ⋅ 4 Nbh 2

+

2

1 1.2 ⋅ WPON ⋅ ... 4 Nirlegs

if Nirlegs > 0

 ⋅ LL

0 ⋅ kip otherwise

Puirlegs = 7.29 ⋅ kip

Puplegs :=

Load at inner rim legs

2   Rir + Rlegs    rows ( Rlegs)  2  π ⋅ ( Rir) −    ⋅ TLdeck 1.2 ⋅ W 2 PON    + ... if Nirlegs = 0

1.6 ⋅ π ⋅  Ror − Rir   2

+

Nbh

Nbh

2 

 ⋅ LL

Nbh

  3 1.2 ⋅ WPON 3 1.6 ⋅ π ⋅  Ror − Rir ⋅ + ⋅ 4 Nbh 4 Nbh 2

Puplegs = 8.71 ⋅ kip

2

 ⋅ LL otherwise

Load at pontoon legs

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Page 16 of 38

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Internal Pontoon Floating Roof Design K. Check Legs 2   PRTOT := Nbh ⋅ Puplegs ⋅  Rir + ⋅ Wpon + Nirlegs ⋅ Puirlegs ⋅ Rir 3   PRTOT = 62234.58 ft ⋅ kip

(

)

rows Rlegs

∑

QRTOT :=

 Pulegs ⋅ Nlegs ⋅ Rlegs  n n n 

n= 1

QRTOT = 25659.11 ⋅ ft ⋅ kip

Kplegs := 2.0 ⋅

QRTOT + PRTOT PRTOT

Kplegs = 2.38 Klegs := 1.0

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Page 17 of 38

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Internal Pontoon Floating Roof Design K. Check Legs dlegs = 2.88 ⋅ in

Leg diameter

tlegs = 0.28 ⋅ in

Leg thickness

dclegs := dlegs − 2 ⋅ CAlegs

Leg diameter - corroded

tclegs := tlegs − CAlegs

Leg thickness - corroded

π 2 2 Aclegs := ⋅  dclegs − dclegs − 2 ⋅ tclegs    4

(

) (

Aclegs = 2.25 ⋅ in Iclegs :=

rclegs :=

Leg cross sectional area corroded

2

⋅ d 64  clegs π

)4 − (dclegs − 2 ⋅ tclegs)4

(

Iclegs = 1.92 ⋅ in Sclegs :=

)

Moment of inertia - corroded

4

2 ⋅ Iclegs dclegs Iclegs Aclegs

Sclegs = 1.34 ⋅ in

3

rclegs = 0.92 ⋅ in

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Section modulus

Radius of gyration

Page 18 of 38

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Internal Pontoon Floating Roof Design K. Check Legs λplegs :=

   2 Kplegs ⋅ Hhi −  ⋅ BS − Hdslv  3   rclegs

λplegs = 208.34

2

FEplegs :=

π ⋅ Es

(

λplegs

)

Euler buckling load for pontoon legs

2

Fylegs

Fcrplegs :=

.658

FEplegs

⋅ Fylegs if λplegs ≤ 4.71 ⋅

Es Fylegs

0.877 ⋅ FEplegs otherwise Fcrplegs = 5782.75 psi

Critical buckling load for pontoon legs

ΩC := 1.67

Safety factor for compression

Pnplegs := Puplegs Pnplegs

Fcrplegs ⋅ Aclegs ΩC

Allowable Strength fo pontoon legs

= 7803.384 ⋅ lbs

Check pontoon legs

= 111.64 ⋅ % 2

FEirlegs :=

π ⋅ Es

(λplegs)

Euler buckling load for inner rim legs

2

Fylegs

Fcrirlegs :=

.658

FEirlegs

⋅ Fylegs if λplegs ≤ 4.71 ⋅

Es Fylegs

0.877 ⋅ FEirlegs otherwise Critical buckling load for inner rim legs Fcrirlegs = 5782.75 psi Pnirlegs := Puirlegs Pnirlegs

Fcrirlegs ⋅ Aclegs ΩC

= 7803.384 ⋅ lbs

Allowable Strength fo inner rim legs

Check inner rim legs

= 93.37 ⋅ %

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Page 19 of 38

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Internal Pontoon Floating Roof Design K. Check Legs λlegs :=

Klegs ⋅ Hhi

λlegs = 90.90

rclegs 2

FElegs :=

π ⋅ Es

(

)

λlegs

Euler buckling load for deck legs

2

Fylegs

Fcrlegs :=

.658

FElegs

⋅ Fylegs if λlegs ≤ 4.71 ⋅

Es Fylegs

0.877 ⋅ FElegs otherwise Critical buckling load for deck rim legs

Fcrlegs = 22929.02 psi Pnlegs :=

Fcrlegs ⋅ Aclegs ΩC

= 30940.989 ⋅ lbs

 25.45    Pulegs 26.92   = ⋅% Pnlegs  27.34     34.96 

Allowable Strength for deck legs

Check deck legs

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Page 20 of 38

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Internal Pontoon Floating Roof Design L. Pontoon Ring Section Properties  BS    HBScone := Ror ⋅ tan  atan     Wpon   HBStrunc := HBScone − BS π  π ⋅R 2 ⋅H 2  − ⋅ Rir ⋅ HBStrunc or BScone 3 3 

2

VBS := π ⋅ Ror ⋅ BS − 

wdNET :=

WdTOT π Rir

2

 γs − SGmin ⋅ γw    γs

⋅

2

WPON + wdNET ⋅ π ⋅ Rir − VBS ⋅ SGmin ⋅ γw π ⋅  Ror − Rir  2

2



= 1.41 ⋅ ft

⋅ SGmin ⋅ γw

CRise := Hor − HoExt − Hir − BS

bc :=

2

CRise + Wpon

2

bc = 144.03 ⋅ in bBS :=

2

BS + Wpon

2

bBS = 12.00 ft

 BS    Wpon 

θ BS := atan 

(

)

(

)

Ap := bBS ⋅ td + bc ⋅ tc + Hir + WiExt ⋅ tir + Hor + WoExt ⋅ tor Ap = 99.01 ⋅ in

2

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Page 21 of 38

Client: Project Location: Project Desc:

Roof Desc: Job Number: Revision #:

Designed By: Checked By: Date:

Internal Pontoon Floating Roof Design L. Pontoon Ring Section Properties Hor Hir   1   ... cpy := ⋅ Hor ⋅ tor − CAor ⋅ + Hir ⋅ tir − CAir ⋅  BS + Ap  2 2    Hor − HoExt + BS + Hir    ... + bc ⋅ tc − CAc ⋅   2

    ( )     BS  bBS ⋅ ( td − CAd) ⋅   ...   2   WoExt ⋅ ( tor − CAor) ⋅ Hor + WiExt ⋅ ( tir − CAir) ⋅ ( BS + Hir) 

(

 +  +

)

(

)

cpy = 14.59 ⋅ in

(tor − CAor) ⋅ Hor3 + (tir − CAir) ⋅ Hir3 + H

2

 Hor   Izp := ⋅ t − CA ⋅ − cpy ... ( ) or or or 12 12  2  2 2 Hir    Hor − HoExt + BS + Hir  + Hir ⋅ ( tir − CAir) ⋅  BS + − cpy + bc ⋅ ( tc − CAc) ⋅  − cpy ... 2 2    

(

)2 ...

)(

+ WiExt ⋅ tir − CAir ⋅ BS + Hir − cpy

W ⌠ pon 2   x  td − CAd ⋅  ⋅ BS − cpy    Wpon  dx + W 2 + ⋅ tor − CAor ⋅ Hor − cpy oExt cos θ BS  ⌡

(

)

(

)

(

)(

)

0 ⋅ ft

Izp = 14355.32 ⋅ in

4

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Page 22 of 38

Client: Project Location: Project Desc:

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Internal Pontoon Floating Roof Design L. Pontoon Ring Section Properties

2 2  tor) WoExt ⋅ ( tor)  ( cpx := + Hir ⋅ ( tir) ⋅ Wpon + ⋅ Hor ⋅ ... Ap 2 2   WiExt   + W   ... ⋅ t ⋅W +  iExt ( ir)  pon  2    W  pon  + bc ⋅ ( tc) ⋅   ...   2     Wpon    + bBS ⋅ ( td) ⋅  2  

1

cpx = 6.01 ft 2 tor − CAor    + Hir ⋅ ( tir − CAir) ⋅ ( Wpon − cpx) 2 ... Iyp := Hor ⋅ ( tor − CAor) ⋅  cpx − 2   3 2 tc − CAc) ⋅ ( bc) bc   (  ... + + ( tc − CAc) ⋅ bc ⋅  cpx − 12 2   3 2 td − CAd) ⋅ ( bBS) bBS   (  ... + + ( td − CAd) ⋅ bBS ⋅  cpx − 12 2   3 2 tor − CAor) ⋅ WoExt WoExt   (  ... + + ( tor − CAor) ⋅ WoExt ⋅  cpx − 2  12  3 2 tir − CAir) ⋅ WiExt WiExt   ( + + ( tir − CAir) ⋅ WiExt ⋅  Wpon + − cpx 12 2  

Iyp = 325409.76 ⋅ in

4

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Page 23 of 38

Client: Project Location: Project Desc:

Roof Desc: Job Number: Revision #:

Designed By: Checked By: Date:

Internal Pontoon Floating Roof Design L. Pontoon Ring Section Properties 2

tw 

CwCH ( d , bf , tf , tw ) :=

ApJ :=

3

tw       bf −  ⋅ tf + 2 ⋅ ( d − tf ) ⋅ tw  2   2   ⋅   tw    ( d − tf ) ⋅ tw + 2 ⋅  bf − 2  ⋅ tw    

 

tf ⋅ ( d − tf ) ⋅  bf − 6

 Hor − HoExt + Hir    ( Wpon) 2  

JBHP :=

(

Wpon ⋅ td − CAd 3 +

)3 + Hor ⋅ (tor − CAor)3 + Hir ⋅ (tir − CAir)3 3

(

WoExt ⋅ tor − CAor 3

JBHP = 8.75 ⋅ in

3

...

)3 + WiExt ⋅ (tir − CAir)3 3

4 2

JRSF := Hor − HoExt tor − CAor

J :=

4 ⋅ ApJ +

Hir tir − CAir

+

bc tc − CAc

+

bBS td − CAd

JRSF if RoofType = 1 JBHP otherwise

J = 41789.27 ⋅ in

4

Torsional constant

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Page 24 of 38

Client: Project Location: Project Desc:

Roof Desc: Job Number: Revision #:

Designed By: Checked By: Date:

Internal Pontoon Floating Roof Design L. Pontoon Ring Section Properties tfCw :=

tir − CAir if Hor > Hir tor − CAor if Hir > Hor

(

min tir − CAir , tor − CAor tf2Cw :=

)

otherwise

tor − CAor if Hor > Hir tir − CAir if Hir > Hor

(

max tir − CAir , tor − CAor α w :=

)

otherwise

1 3

 min ( Hor , Hir)  tfCw ⋅ 1+   max ( Hor , Hir)  tf2Cw

α w = 0.50 D Reff := − Srim − cpx 2 Cw :=

0 ⋅ in

6

Effective radius of roof

Reff = 103.33 ft

if RoofType = 1

(

(

Warping constant

)

)

CwCH Wpon , min Hor , Hir , tfCw , td − CAd ⋅ α w otherwise

Cw = 0.00 ⋅ in

6

2

CT :=

π ⋅ Es ⋅ Cw

(1.7725 ⋅ Reff )2 11

CT = 4.66 × 10

+ G⋅J

⋅ lbs ⋅ in

Torsional rigidity

2

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Page 25 of 38

Client: Project Location: Project Desc:

Roof Desc: Job Number: Revision #:

Designed By: Checked By: Date:

Internal Pontoon Floating Roof Design L. Pontoon Ring Section Properties 2

2

 td − CAd  Fcrd := ⋅ = 177.75 psi 2  bBS  12 ⋅ 1 − ν   4 ⋅ π ⋅ Es

(

)

2

2

 tc − CAc  Fcrc := ⋅ = 177.67 psi 2   12 ⋅ 1 − ν  bc  4 ⋅ π ⋅ Es

(

)

2

 tor − CAor  Fcror := ⋅ 2  Hor − HoExt  12 ⋅ 1 − ν   4 ⋅ π ⋅ Es

(

2

)

Fcror = 80896.57 psi 2

 tir − CAir  Fcrir := ⋅ 2  12 ⋅ 1 − ν  Hir  4 ⋅ π ⋅ Es

(

2

)

Fcrir = 65526.22 psi λcrd ( f ) := λcrc ( f ) := λcror ( f ) := λcrir ( f ) :=

f Fcrd f Fcrc f Fcror f Fcrir

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Page 26 of 38

Client: Project Location: Project Desc:

Roof Desc: Job Number: Revision #:

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Internal Pontoon Floating Roof Design L. Pontoon Ring Section Properties .22

1− ρ crd ( f ) :=

λcrd ( f )

λcrd ( f ) .22

1− ρ crc ( f ) :=

λcrc ( f )

λcrc ( f ) 1−

ρ cror ( f ) :=

.22 λcror ( f )

λcror ( f )

1− ρ crir ( f ) :=

beffd ( f ) :=

.22 λcrir ( f )

λcrir ( f )

bBS if λcrd ( f ) ≤ .673 ρ crd ( f ) ⋅ bBS otherwise

beffc ( f ) :=

Wpon if λcrc ( f ) ≤ .673 ρ crc ( f ) ⋅ bc otherwise

beffor ( f ) :=

Hor if λcror ( f ) ≤ .673

(

)

ρ cror ( f ) ⋅ Hor − HoExt + HoExt otherwise beffir ( f ) :=

Hir if λcrir ( f ) ≤ .673

( )

ρ crir ( f ) ⋅ Hir

otherwise

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Page 27 of 38

Client: Project Location: Project Desc:

Roof Desc: Job Number: Revision #:

Designed By: Checked By: Date:

Internal Pontoon Floating Roof Design L. Pontoon Ring Section Properties

(tor − CAor) + beffir (f ) ⋅ (tir − CAir) + beffc ( f) ⋅ (tc − CAc) + beffd (f) ⋅ (td − CAd) ... (tor − CAor) + WiExt ⋅ (tir − CAir) + HoExt ⋅ (tor − CAor)  (Hor − HoExt) b (f) ⋅ t − CA  BS + Hir   1 ⋅ beffor ( f ) ⋅ ( tor − CAor) ⋅ + effir ... ( ir ir) ⋅  (f)  2   2

AeffC ( f ) := beffor ( f ) ⋅ + WoExt ⋅ ceffC ( f ) := AeffC

Rir ⋅ Reff Krad := Ap ⋅ Es

 +   + + 

 Hor − HoExt + BS + Hir   ... 2  HoExt    BS   ... beffd ( f ) ⋅ ( td − CAd) ⋅   + HoExt ⋅ ( tor − CAor) ⋅  Hor − 2   2   beffc ( f ) ⋅ tc − CAc ⋅ 

(

(

) )

(

)(

WoExt ⋅ tor − CAor ⋅ Hor + WiExt ⋅ tir − CAir ⋅ BS + Hir − 4 in

Krad = 5.04 × 10

⋅

2

)

      

Radial flexibility of pontoon ring

lbs

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Page 28 of 38

Client: Project Location: Project Desc:

Roof Desc: Job Number: Revision #:

Designed By: Checked By: Date:

Internal Pontoon Floating Roof Design L. Pontoon Ring Section Properties 3

3

 beffor ( f )   beffor ( f )  (tor − CAor) ⋅  2 + HoExt (tor − CAor) ⋅  2  IeffC ( f ) := + ... 12

+

+

+

+

+

12

2

(

+

3

 beffor ( f )  ⋅ ( tor − CAor) ⋅  − ceffC ( f )  + ... 2 4 12   2 beffor ( f )    + HoExt  beffor ( f )     2  + HoExt ⋅ ( tor − CAor) ⋅  Hor − − ceffC ( f ) ...  2 2      2 beffir ( f )  beffir ( f )  ⋅ ( tir − CAor) ⋅  + BS − ceffC ( f )  ... 2  4  2 beffir ( f ) beffir ( f )     − ceffC ( f ) ... ⋅ ( tir − CAor) ⋅  Hir + BS − 2 4    2 H − H + H  or  oExt ir beffc ( f ) ⋅ ( tc − CAc) ⋅  − ceffC ( f )  ... 2   beffor ( f )

)(

+ WiExt ⋅ tir − CAir ⋅ BS + Hir − ceffC ( f ) +

 beffir ( f )   2 ⋅ ( tir − CAir) ⋅   2 

beffd ( f ) 2 beffd ( f ) 2

)2 + WoExt ⋅ (tor − CAor) ⋅ (Hor − ceffC (f) )2 ...

2 beffd ( f ) BS    ... ⋅ ( td − CAd) ⋅ ceffC ( f ) − ⋅  4 Wpon  

beffd ( f ) BS     ⋅ ( td − CAd) ⋅ ceffC ( f ) −  BS − ⋅   4 Wpon    

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2

Page 29 of 38

Client: Project Location: Project Desc:

Roof Desc: Job Number: Revision #:

Designed By: Checked By: Date:

Internal Pontoon Floating Roof Design L. Pontoon Ring Section Properties 2

tor   FcrorB := ⋅ 2  Hor − HoExt  12 ⋅ 1 − ν   24 ⋅ π ⋅ Es

(

2

)

FcrorB = 485379.41 psi 2

 tir  FcrirB := ⋅ 2  Hir  12 ⋅ 1 − ν   24 ⋅ π ⋅ Es

(

2

)

FcrirB = 393157.32 psi f

λcrorB ( f ) :=

Fcror f

λcrirB( f ) :=

Fcrir 1−

ρ crorB ( f ) :=

.22 λcror ( f )

λcror ( f ) 1−

ρ crirB( f ) := befforB ( f ) :=

.22 λcrir ( f )

λcrir ( f ) Hor − HoExt if λcrorB ( f ) ≤ .673

(

)

ρ crorB ( f ) ⋅ Hor − HoExt beffirB ( f ) :=

otherwise

Hir if λcrirB( f ) ≤ .673

( )

ρ crirB ( f ) ⋅ Hir

otherwise

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Page 30 of 38

Client: Project Location: Project Desc:

Roof Desc: Job Number: Revision #:

Designed By: Checked By: Date:

Internal Pontoon Floating Roof Design L. Pontoon Ring Section Properties

(

)

(

)

(

)

(

)

AeffB ( f ) := befforB ( f ) ⋅ tor − CAor + beffirB ( f ) ⋅ tir − CAir + beffc ( f ) ⋅ tc − CAc + bBS ⋅ td − CAd ... + WoExt ⋅ tor − CAor + WiExt ⋅ tir − CAir + HoExt ⋅ tor − CAor

(

)

(

)

(

)

Hor − HoExt Hir     1  ... ceffB ( f ) := ⋅ befforB ( f ) ⋅ tor − CAor ⋅ + beffirB ( f ) ⋅ tir − CAir ⋅  BS + AeffB ( f )  2   2     Hor − HoExt + BS + Hir   ... + beffc ( f ) ⋅ tc − CAc ⋅   2

(

(

)

(

)

)

(

)

   HoExt     BS   ... + bBS ⋅ ( td − CAd) ⋅  + HoExt ⋅ ( tor − CAor) ⋅  Hor −   2   2   + W  oExt ⋅ ( tor − CAor) ⋅ Hor + WiExt ⋅ ( tir − CAir) ⋅ ( BS + Hir)

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    

Page 31 of 38

Client: Project Location: Project Desc:

Roof Desc: Job Number: Revision #:

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Internal Pontoon Floating Roof Design L. Pontoon Ring Section Properties 3

3

 befforB ( f )   befforB ( f )  (tor − CAor) ⋅  2 + HoExt (tor − CAor) ⋅  2  IeffB ( f ) := + ... 12

+

+

+

+

+

12

2

 beffirB ( f )   2 ⋅ ( tir − CAir) ⋅  2  

3

 befforB ( f )  ⋅ ( tor − CAor) ⋅  − ceffB ( f )  + ... 2 4 12   2 befforB ( f )    + HoExt  befforB ( f )     2  + HoExt ⋅ ( tor − CAor) ⋅  Hor − − ceffB ( f ) ...  2 2      2 beffirB ( f )  beffirB ( f )  ⋅ ( tir − CAor) ⋅  + BS − ceffB ( f )  ... 2 4   2 beffirB ( f ) beffirB ( f )     − ceffB ( f ) ... ⋅ ( tir − CAor) ⋅  Hir + BS − 2 4    2 H − H + H  or  oExt ir beffc ( f ) ⋅ ( tc − CAc) ⋅  − ceffB ( f )  ... 2   befforB ( f )

(

)(

+ WiExt ⋅ tir − CAir ⋅ BS + Hir − ceffB ( f )

)2 + WoExt ⋅ (tor − CAor) ⋅ (Hor − ceffB (f) )2 ...

W ⌠ pon 2   x ⋅ BS − c  td − CAd ⋅  ( f )  effB  Wpon    dx + cos θ BS  ⌡

(

)

(

)

0 ⋅ ft

SeffB ( f ) :=

IeffB ( f )

(

max ceffB ( f ) , Hor − ceffB ( f )

SeffB ( 10 ⋅ psi) = 6.47 ft

2.00

)

⋅ in

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Page 32 of 38

Client: Project Location: Project Desc:

Roof Desc: Job Number: Revision #:

Designed By: Checked By: Date:

Internal Pontoon Floating Roof Design M. Check Pontoon Ring Strength nrpE = 527.73 ⋅

lbs in

Ωc := 1.8 Ωb := 1.67 Pp := nrpE ⋅ Rir Pp = 616.39 ⋅ kip

(

F'cr ( n) :=

)

2

E ⋅ IeffC ( 36 ⋅ ksi) ⋅ n − 4



4 ⋅ Rir ⋅ Reff ⋅  1 + 2

 

4 ⋅ E ⋅ IeffC ( 36 ⋅ ksi)  2

n ⋅ CT

  

Kf := γw ⋅ SGmin ⋅ Wpon

F''cr ( n) := 4 ⋅

Kf ⋅ Reff Rir ⋅ n

2

2

lbs F''cr ( 4) = 14378.14 ⋅ ft

(

Fcrp := min F'cr ( 4) + F''cr ( 4) , F'cr ( 8) + F''cr ( 8) Fcrp = 15442.92 ⋅ Pcrp :=

1 Ωc

)

lbs ft

⋅ Fcrp ⋅ Rir

Pcrp = 835.06 ⋅ kip Pyp :=

1 Ωc

( )

⋅ AeffC Fyp ⋅ Fyp

Pyp = 996.63 ⋅ kip

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Page 33 of 38

Client: Project Location: Project Desc:

Roof Desc: Job Number: Revision #:

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Internal Pontoon Floating Roof Design M. Check Pontoon Ring Strength

(

Pn := min Pcrp , Pyp Pp Pn

)

= 73.81 ⋅ %

Mp = 401.74 ⋅ ft ⋅ kip Mn :=

1 Ωb

( )

⋅ SeffB Fyp ⋅ Fyp

Mn = 693.46 ⋅ ft ⋅ kip Mp Mn

= 57.93 ⋅ %

INTPM :=

Pp Pn

+

Mp Mn

if

Pp Pn

  P p Mp  +   P n Mn max   Mp   Pp +  P   yp Mn

≤ 0.15

     otherwise   

INTPM = 131.75 ⋅ % tor tir

= 100.00 ⋅ %

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Page 34 of 38

Client: Project Location: Project Desc:

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Internal Pontoon Floating Roof Design N. Check Pontoon Ring Floating Stability 2 ⋅ ∆TOT

(

Hir + Hor − HoExt − BS

)

= 83.93 ⋅ %

Check pontoon floating stability

∆TOT = −23.92 ⋅ in

0

Deflection Below Product Surface (in)

− 3.125 − 6.25 − 9.375 − 12.5 − 15.625 − 18.75 − 21.875 − 25

− 200

0

200

Circumferential Distance (ft) Pontoon Deflection Location of Critical Deflection

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Page 35 of 38

Client: Project Location: Project Desc:

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Internal Pontoon Floating Roof Design O. Plot of Results 3D Plot of Deflected Pontoon

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Page 36 of 38

Client: Project Location: Project Desc:

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Internal Pontoon Floating Roof Design O. Plot of Results

Deflection of deck relative to pontoon attachment

δ deck

(

rows δdeck

)

Deflection of deck relative to product surface

δ pon

= −24.85 ⋅ in δ deck

(

rows δdeck

)

+

(

rows δpon

)

+ δ pon 1 = −42.44 ⋅ in

2

Deflection of Deck Below Product Surface (in) 0 − 5.625 − 11.25 − 16.875 − 22.5 − 28.125 − 33.75 − 39.375 − 45 − 100

− 50

0

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50

100

Page 37 of 38

Client: Project Location: Project Desc:

Roof Desc: Job Number: Revision #:

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Internal Pontoon Floating Roof Design O. Plot of Results

(

)

i := 1 .. rows rdeck Safety factor for weld strength

Ωw := 2

Maximum unit for in weld per AISC 360 ndMax :=

(td − CAd) ⋅ .7071⋅ 0.6 ⋅ Fuw Ωw

i

ndMax = 2386.46 ⋅ 1

lbs in

Radial and Tangential Unit Forces (lbs/in) 4872.925 3654.694 2436.462

Unit Force

1218.231 0 − 1218.231 − 2436.462 − 3654.694 − 4872.925

0

20

40

60

80

100

Radius Radial Unit Force Tangential Unit Force Single Lap Weld Limit Single Lap Weld Limit Double Lap Weld Limit Double Lap Weld Limit

Unit force curves must be within single lap weld limit, otherwise double lap weld is required. If double lap weld is limit is exceeded, geometry must be changed. Deck shall have a 2" in 12" underside weld at all supports, bulkheads, and appurtenances as a minimum.

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Page 38 of 38