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STEEL STRUCTURAL
CALCULATION REPORT
00 XX XX XX
REV. DATE DESCRIZIONE EMESSO CONTROLLATO APPROVATO
N° DATE DESCRIPTION ISSUED BYCONTROLLED
BYAPPROVED BY
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1 CALCULATION ASSUMPTION
1.1 SCOPE
This report describes the calculation procedure and data considered in order to design the steel
structure of the HEATER.
1.2 REFERENCE DOCUMENTS & DRAWINGS
- Heater Assembly xx
- Foundation Assembly / Details with loads xx
1.3 CALCULATION CODES
- Uniform Building Code Volume 2 UBC-97
- Minimum Design Loads for Buildings and other Structures UBC-97
- Manual of steel construction - Allowable Stress Design AISC – ASD/01
- Specification for Structural Steel Buildings AISC 360-05
1.4 MATERIAL AND CODE ALLOWABLE VALUES
Material used for the structures : JIS SS400 or equivalent
Yield stress f y: 235 N/mm2(thickness ≤ 16 mm)
Minimum Tensile stress f u: 400 N/mm2
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2 LOAD CALCULATION
2.1 PRIMARY LOADS
The decomposition of the loads into following primary loads :
- Structure Self-Weight (SLF):Weighs of the structural components automatically
calculated by the program, and based on the model feature.
- Extra Steelwork Weight (EXTSTEEL): Extra Steelwork weights not directly included in the modeland not automatically calculated.
- Platform (EXTPLTF):Platform Extra Steelwork weights not directly included in
the model and not automatically calculated.
- Refractory Loads (REFRACT):Weights of the refractory lining surfaces applied to the
structural elements.
- Pipe empty loads (PPEMPT):Weights of all the operating pipes installed on the structure
considered empty.
- Pipe Operating Loads (PPOPER)
Weights of the pipes filled with gas or liquid fluid as they
are during the normal operation of the plant and load at
terminal points.
- Hydrostatic test loads (PPTEST)Weights of the pipes considered full of water as they are
during the hydrostatic test conditions
- Burners (BURN): Weights of the burners applied to the radiant floor
- Air Duct (ADUCT): Weights of air duct installed on heater
- Live Load 1 (LL1):
For the calculation of the foundation loads and structural
analysis has been considered an overload of 500 Kg/m2on
each platforms.
- Wind Load +X WLX According to UBC-97
- Wind Load +Y WLY According to UBC-97
- Earthquake Load +X EQX According to UBC-97
- Earthquake Load +Y EQY According to UBC-97
- Thermal Load TMP
A thermal load has been considered on steel structures
during normal operation according to spec n° 00-ZA-E-205001-rev.02
Tmax on frame = 47°C
Tmin on frame = 2°CTmax on furnace skin = 83°C
Tmin on furnace skin = 38°C
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2.2 LOADING DETAILS
2.2.1 Radiant cell
2.2.1.1 Radiant Floor
A.1 FLOOR
External Radius 2474 mm
Internal Radius 1697 mm
support internal Radius 515 mm
External Diameter 4948 mm
Internal surface diameter 3394 mm
support internal diameter 1060 mm
Floor thickness 6 mm
Overall Surface 19,2 m 2
Floor surface weight 905,7 Kg 9,06 KN
burners supporting surface 8,16 m 2
External surface 11,1 m 2
Refractory (wet) 57,04KN Wet D.ty M.W.C. 1:2:4 1930 Kg/m
3
Thickness 75 mm
Wet D.ty VLWC 1:0:5 1215 Kg/m 3
Thickness 125 mm
A 1.2 Burners
Weight of each burner considered 450 Kg
number of burners 6
Overall burners weight 2700 Kg 27,00KN
A 1.3 Steelwork
Extra steelwork not modelled 40,00 Kg/m 2
Extra steelwork weight 769,15 Kg 7,69 KN
Input Sap Data
Overall floor weight 100,79 KN
Internal surface External surface load case
KN/m2 KN/m2
Overall refractory weight distribuited on surface 2,97 2,97 REFRACTOverall steelwork weight distribuited on surface 0,4 0,4 EXTSTEEL
Overall burners weight distributed on surface 3,31 BURN
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2.2.1.2 Radiant Lateral walls
LATERAL WALL
External Diameter 4948 mm
Height 9198,0 mm
Thickness 5,0 mm
Lateral Surface 142,9 m 2
Lateral surface weight 5609,1 Kg 56,1 KN
Refractory (wet) 323,7 KN
L.W.C. 124 1400 Kg/m3
Thickness 75 mm
V.L.W.C 105 1215 Kg/m3
Thickness 100 mm
Steelwork
Extra steelwork notmodelled
20,00 Kg
Extra steelwork weight 2858,1 Kg/m2 28,6 KN
tot. weight 408,4 KN
loadcase
KN/m2
Overall refractory weight distribuited on surface 2,26 REFRACT
Overall steelwork weight distribuited on surface 0,20 EXTSTEEL
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2.2.1.3 Heater Arch
ARCH
Diameter 4948 mm
Thickness 6 mm
Surface 19,2 m2
Arch surface weight 905,7 Kg 9,1 KN
Rectangular hole
Lenght 4900 mm
Width 1453 mmhole surface 7,1 m2
Arch surface without hole 12,11 m2
Refractory (wet) 31,105 KN
L.W.C. 124 1400 Kg/m3
Thickness 75 mm
V.L.W.C 105 1215 Kg/m3
Thickness 125 mm
Steelwork
Extra steelwork not modelled 20,00 Kg
Extra steelwork weight 242,2 Kg/m2 2,4 KN
tot. weight 42,6 KN
Overall refractory weight added to arch surface 2,57 KN/m2 REFRACT
Overall steelwork weight added to arch surface 0,20 KN/m2 EXTSTEEL
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2.2.2 Radiant Internal coil
Type of fuel Fuel Oil
Bare tubes O.D: 141,3 mmBare tubes thickness 6,55 mmBare tubes I.D. 128,2 mmMaximum Operating fluid density 556 Kg/m3Water density for hydrostatic test 1000 Kg/m3Pipe weight per meter 21,77 Kg/mOperating fluid weight per meter on each pipe 7,18 Kg/m
Water weight per meter inside each pipe 12,91 Kg/mNumber of tubes on each anchor 2,0Medium pipe lenght 7,800 mReturn bends medium diameter 254,0 mmNumber of return bends on each anchor 2,0Bends unit weight 8,7 Kg/eachOperating fluid on each return bend 2,9 Kg/eachWater weight on each return bend 5,1 Kg/each
Pipe empty weight on each anchor(2 tube + 2 bend) 356,9 KgPipe weight with operating fluid on each anchor(2 tube + 2 bend) 474,6 Kg
Pipe full weight on each anchor(2 tube + 2 bend) 568,6 Kg
Crossing TubesNumber of crossing tubes 4,0Medium pipe lenght 2,248 mEmpty crossing tubes weight 195,7 KgOperating crossing tube weight (pipes + Op. fluid) 260,3 KgTest crossing tube weight (pipes + water) 311,8 Kg
Anchor number 24,0Total number of tubes on each anchor 48,0Total number of bends on each anchor 48,0
Overall empty weight 8761,6 Kg 87,6 KNOverall operating weight (Pipe + Operating fluid) 11650,5 Kg 116,5 KNOverall test weight (Pipe + water) 13957,4 Kg 139,6 KN
Point empty weight applied on each anchor (ELEV. 19050) 3,65 KN PPEMPTPoint operating weight applied on each anchor (ELEV. 19050) 4,85 KN PPOPERPoint test weight applied on each anchor (ELEV. 19050) 5,82 KN PPTEST
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2.2.3 Convection cell
2.2.3.1 Convection Lateral vertical walls
Width 4900,0 mm
Height 3555,0 mm
Thickness 5,0 mm
Surface 17,4 m2
Weight of each convection wall 683,7 Kg 6,8 KN
Refractory (wet) 36,6 KND.ty LWC 1:2:4 1400 Kg/m3
Thickness 150 mm
Steelwork not modelled
Extra steelwork not modelled 20,00 Kg/m2
Extra steelwork weight 348,4 Kg 3,5 KN
Overall convection wall weight (2X) 93,8 KN
Overall refractory weight distributed each surface 2,10 KN/m2 REFRACT
Overall steelwork weight added to each surface 0,20 KN/m2 EXTSTEEL
2.2.3.2 Convection End tube sheets (E.T.S.)
width 1453,0 mm
Height 3555,0 mm
Thickness 13,0 mm
Surface 5,2 m2
Weight of each convection wall 527,1 Kg 5,3 KN
Refractory (wet) 7,2 KN
Wet D.ty LWC 1400 Kg/m3
Thickness 100 mm
Steelwork not modelled 1,0 KN
Unit Weight 20 Kg/m2
tot. weight of each End Tube Sheet 13,5 KN
Overall End Tube Sheet weight 27,1 KN
Overall refractory weight added to each E.T.S. surface 1,40 KN/m2 REFRACT
Overall steelwork weight added each E.T.S. surface 0,20 KN/m2 EXTSTEEL
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2.2.3.3 Convection Header Boxes
Deep considered for the Header boxes 450 mm
Width 2353,0 mm
Height 4455,0 mm
Surface 10,5 m2
Steelwork not modelled
sheet thickness 5,0 mm
Plate steelwork weight 411,4 Kg 4,1 KN
Refractory (wet) 7,3 KN
D.ty LWC 1:2:4 1400 Kg/m3
Thickness 50 mm
Extra Steelwork not modelled 5,24 KN
Unit Weight 50 Kg/m2
tot. weight of each Header Box 16,7 KN
Overall Header Boxes weight 33,4 KN
Overall refractory weight distributed on each E.T.S. surf. 1,42 KN/m2 REFRACT
Overall steelwork weight distributed on each E.T.S. surf. 1,81 KN/m2 EXTSTEEL
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2.2.3.4 Convection Piping (coil, inlet &outlet piping)
CONVECTIVE PROCESS COIL
type of fuel fuel oil
Operating fluid density 556 Kg/m3
Water density for Hydrostatic test 1000 Kg/m3
Bare tube external diameter 141,3 mm
Bare tube thickness 6,55 mm
Bare tube internal diameter 128,2 mmBare tube length 5,226 m
Nr of flow passes 4
Number of tubes 44
N°tubes/row 4
Number of rows 11
Number of 180°return bends 40
Medum diameter of 180°return bends 254 mm
single empty tube weight per meter 21,76 Kg/m
Operating fluid weight per meter inside each tube 7,17 Kg/m
Water weight per meter inside each pipe 12,90 Kg/m
Weight of each empty bend 8,68 Kg/each
Operating fluid weight per meter inside each bend 2,86 Kg/each
Water weight per meter inside each bend curve 5,14 Kg/each
Overall empty coil weight (pipes + bends) 5350 Kg 53,50 KN
Overall Operating coil weight(pipes + bends + operating fluid)
7113 Kg 71,13 KN
Overall Test coil weight (pipes + bends + water) 8522 Kg 85,22 KN
STUDDED SURFACE AROUND CONVECTIVE COILStud height 25,40 mm
Studs diameter 12,70 mm
studs per meter 1260 stud /m
Number of bare tubes not finned
Number of studded tubes 28
studded surface length (on each tube) 5,026 m
exposed surface of each stud 0,001013 m2
studded exposed surface of each tube 6,414 m2
total exposed surface calculated (studs+ tubes) 242,04 m2
Weight of studded surface 4476,4 Kg 44,76
Overall empty coil weight 9826 Kg 98,26 KN
Overall Operating coil weight (tube + Op. fluid) 11590 Kg 115,90 KN
Overall test coil weight (tube + water) 12998 Kg 129,98 KN
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Height of End Tube Sheet portion 3555,0 mm
Width of End Tube Sheet portion 1453,0 mm
Heading surface with coil weight distributed 5,17 m2
Overall empty tube weight distributed on eachconvection header surfaces
9,51 KN/m2 PPEMPT
Overall Operating weight distributed on eachconvection header surfaces (tube + Op. Fluid)
11,22 KN/m2 PPOPER
Overall test weight distributed on eachconvection header surfaces (tube + water)
12,58 KN/m2 PPTEST
2.2.3.5 Inlet & Outlet terminal points load
TAG F x F y F z M x M y M z
N N N Nm Nm Nm
N1 9342 17346 17346 7566 5694 5694
N2 9342 17346 17346 7566 5694 5694
2.2.4 Breeching
C.1 BREECHING
Base lenght 4900 mm
Base width 1453 mm
plate thickness 5 mm
Overall SAP surface 10,2 m2
C.1.1 Refractory (wet)
Wet D.ty LWC 1:2:4 1400 Kg/m3
Thickness 75 mm
Overall breeching refractory weight 1071 Kg 10,71 KN
C.1.4 Steelwork not modelled
Steelwork not modelled 30Kg/m2
Overall steelwork not modelled weight 306Kg 3,06 KN
tot. Breeching Weight 13,77 KN
Overall breeching refractory weight distributed on modelled surface1,05 KN/m2 REFRACT
Overall breeching steelwork weight distributed on modelled surface0,30 KN/m2 EXTSTEEL
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2.2.5 Platforms, Vertical ladders & Stairs
Live load (for base foundation loads ) 500 Kg/m2
Grating 37 Kg/m2
Structure 75 Kg/m2
Handrail 16 Kg/m2
Toe board 7 Kg/m2
Total 135 Kg/m2
2.2.5.1 Platforms EL+ 3000 on plinth L
Dimension LengthWidth Surface
mm mm m2
Plant platform at 0° 1250 1835 2,29
nr.supportingbeam
load on middlebeam
KN/mTotal platform Deadload
309,66 Kg 3,10 KN 2 0,84
Total platform Live load 1146,88 11,47 KN 2 3,13
2.2.5.2 Platforms EL+ 3000
DimensionInternalRadius
Middleradius
modelled
ExternalRadius
Angle(°)
Surface
mm mm mm m2
Plant 2474 3104 3854 360 27,42
nr.supp.beam
load onmiddlebeam
load onexternal
beam
KN/m KN/m
Total platform Dead load 3701,77 Kg 37,02 KN 2 0,95 0,76
Kg
Total platform Live load 13710,24 137,10 KN 2 3,52 2,83
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2.2.5.3 Platforms EL+9000
DimensionInternalRadius
Middleradius
modelled
ExternalRadius
Angle (°) Surface
mm mm mm m2
Plant 2474 2875 3854 345 27,42
nr.supportingbeam
load on
middlebeam
load on
externalbeam
KN/m KN/mTotalplatformDeadload
3701,77 Kg 37,02 KN 2 1,07 0,80
KgTotalplatformLive load
13710,24 137,10 KN 2 3,96 2,96
Dimension SurfaceTotallength ofbeam
modelled
m2 m
Plant platform at 270°and 90° 5,79 15,07
load onbeams
KN/mTotalplatform
Deadload
781,38 Kg 7,81 KN 0,52
TotalplatformLive load
2894,00 28,94 KN 1,92
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2.2.5.4 Platforms EL+12498
Dimension Length Width Surface
mm mm m2
Plant platform at 0° 4000 1124 4,50
Plant platform at 90° 6151 1145 7,04
Plant platform at 180° 4000 1124 4,50
Plant platform at 270° 6151 1145 7,04
Nr ofportionconsid.
Load oneach supp.
beamcolumn
KN
Dead Load on Plant platform at 0° 606,96 Kg 6,07 KN 1 0,76
Dead Load on Plant platform at 90° 950,79 Kg 9,51 KN 1 0,77
Dead Load on Plant platform at 180° 606,96 Kg 6,07 KN 1 0,76
Dead Load on Plant platform at 270° 950,79 Kg 9,51 KN 1 0,77
Live load on Plant platform at 0° 2248,00 Kg 22,48 KN 1 2,81
Live load on Plant platform at 90° 3521,45 Kg 35,21 KN 1 2,86
Live load on Plant platform at 180° 2248,00 Kg 22,48 KN 1 2,81
Live load on Plant platform at 270° 3521,45 Kg 35,21 KN 1 2,86
2.2.5.5 Platforms EL+17203
Dimension Length Width Surface
mm mm m2
Plant platform at 0° 5133 1375 7,06
Plant platform at 90° 1453 1349 1,96
Plant platform at 180° 5133 1375 7,06
Plant platform at 270° 1453 1349 1,96
Nr of portionconsid.
Load on each supportingbeam column
KN
Dead Load on Plant platform at 0° 952,81 Kg 9,53 KN 1 0,93
Dead Load on Plant platform at 90° 264,61 Kg 2,65 KN 1 0,91
Dead Load on Plant platform at 180° 952,81 Kg 9,53 KN 1 0,93
Dead Load on Plant platform at 270° 264,61 Kg 2,65 KN 1 0,91
Live load on Plant platform at 0° 3528,94 Kg 35,29 KN 1 3,44
Live load on Plant platform at 90° 980,05 Kg 9,80 KN 1 3,37
Live load on Plant platform at 180° 3528,94 Kg 35,29 KN 1 3,44
Live load on Plant platform at 270° 980,05 Kg 9,80 KN 1 3,37
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2.2.5.6 Vertical ladder and stairs
E.1.8 Vertical ladder
load (steelwork + liveload)
Kg/mApplicable to
elev.lenght
(m)weight(Kg)
weight(KN)
80
LD.2 3000 6,00 480 4,80 KN
LD.2A 3000 6,00 480 4,80 KN
LD.3 11500 3,50 279,84 2,80 KN
LD.4 20000 3,50 279,84 2,80 KN LD.5 25010 4,71 376,4 3,76 KN
E.1.8 Stairs
load (steelwork + liveload)
Kg/mApplicable to
elev.lenght
(m)weight(Kg)
weight(KN)
300
SG.1 3000 5,25 1573,5 7,87 KN
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2.2.6 Wind Loads (WL)
WIND LOAD according toUBC-97
P = Ce*Cq*qs*Iw
EXPOSURE D
Pressure coefficient on cilindrical surfaces Cq = 0,8
Site elevation 19-25 mAccording to spec. Nr. 00-ZA-E-205001 rev.2
Basic wind speed V = 44,4 m/s
According to spec. Nr. 00-ZA-E-
205001 rev.2wind stagnation pressure suggested for siteelevation qs =
1,30E-03 Mpa 1,30 KN/m2
Importance factor Iw = 1,15 (hazardous facilities)
2.2.6.1 Wind Load in X direction
FromElev.
To Elev.Frontal
dimensionSurface
consideredCe
Specific Pressure onportion p(z)
WindLoad
mm mm m m2 kN/m2 KN
Radiant 3000 7000 4948 19,8 1,48 1,77 35,0
Radiant 7000 12198 4948 25,7 1,62 1,94 49,8
convection 12198 17203 4900 24,5 1,71 2,05 50,2
Stack I 17203 27203 1574 15,7 1,83 2,19 34,4
Stack II 27203 37203 1570 15,7 1,93 2,31 36,2
Stack III 37203 47203 1566 15,7 2 2,39 37,5
Total Wind X 243,18 KN
INPUT SAP DATAPortion
Intermediatecolumns
UNITwind loaddistributed
wind load distributed ext.Columns
loadcase
Radiant 1 KN/m 4,38 2,19 WX
Radiant 1 KN/m 4,79 2,40 WX
Convection 2 KN/m 3,34 1,67 WX
Stack I 0 KN/m 3,44 WX
Stack II 0 KN/m 3,62 WX
Stack III 0 KN/m 3,75 WX
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2.2.6.2 Wind Load in Y direction
WIND IN Y DIRECTION
From Elev. To Elev.Frontal
dimensionSurface
consideredCe
Specific Pressure onstack p(z)
WindLoad
mm mm m m2 kN/m2 KN
3000 7000 4948 19,8 1,48 1,77 35,0
7000 12198 4948 25,7 1,62 1,94 49,8
12198 17203 1453 7,3 1,71 2,05 14,917203 27203 1574 15,7 1,83 2,19 34,4
27203 37203 1570 15,7 1,93 2,31 36,2
37203 47203 1566 15,7 2 2,39 37,5
Total Wind Y Weight 207,89 KN
INPUT SAP DATA
PortionIntermediate
columnsUNIT
wind loaddistributed
wind load distributed ext.Columns
loadcase
Radiant 2 KN/m 2,92 1,46 WY
Radiant 2 KN/m 3,20 1,60 WY
Convection 1 KN/m 1,49 WY
Stack I 0 KN/m 3,44 WY
Stack II 0 KN/m 3,62 WY
Stack III 0 KN/m 3,75 WY
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2.2.7 Earthquake Loads calculation (EQX/Y)
Earthquake load according to UBC-97(*)
Notes
Sismic Zone 4 According to spec. nr. 00-ZA-E-205001 rev.02
Seismic zone factor Z 0,4 According to table 16-I of UBC-97
Solid Profile SC According to customer data
Ca 0,40 According to table 16-Q of UBC-97 and for customer request
Cv 0,56 According to table 16-R of UBC-97 and for customer requestI 1,25
According to table 16-K“Hazardous facilities for toxic and explosives material”
R 4,5According to table 16-N of UBC-97
“Moment Resisting Frame systems – OMRF – Steel”
(*) Note:
In order to calculate the earthquake effect on the structure, the previous data have been assigned as
input data to the model in SAP 2000 program and the effect of the earthquake as base reaction,
structure elements deformation and vertical distribution of the lateral forces have been calculated
automatically.
According to UBC- 97 the automatic calculation of the elastic fundamental period of vibration
(performed by SAP 2000) is based on following formulation based on method A:
4 / 3)(*nt hC T = = 0,802 s
where:
Ct = 0,0853 is the coefficient for the calculation of steel moment-resisting frames
hn = is the height of the structure above the base (m)
from this value of T it is automatically calculated the total design base shear according to:
W T R
I C V
v **
*=
where W is the total weight of the structure.
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According to UBC 97, the base shear so calculated has to respect the following limits:
The value of base shear shall not exceed the value W R
I C V
a MAX
***5.2
=
The value of base shear shall not be less than W I C V a MIN ***11.0=
For seismic zone 4 the value of base shear shall also not be less than W R
I ZN V
v Z MIN
***8,0
4 =−
Following are listed the values calculated for the heater in the different condition of work:
Work conditionTotal
weightconsidered
Total baseshear Vtot
VMAX VMIN V MIN-Z4
KN KN KN KN KNErection 1680 326 467 92.4 149.3
Operating 1748 341 485.6 96.16 155.4Test 1772 344 492.2 97.5 157.5
Operating + 33% Live 1937 379 538 106.5 172.2
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2.2.8 Stack
2.2.8.1 Loading details
Stack – sections
Stack Material JIS SS400
Stack total Length 30000 mm
Internal Stack Diameter 1550 mm
Internal lining diameter 1450 mm
Stack portion I
Casing and RefractoryHeight 10000 mm
External diameter 1574 mm
Shell thickness 12 mm
Lateral External surface 49,42 m2
Casing Weight 4620,2 Kg 46,20 KN
Refractory LWC
Refractory D.ty 1400 Kg/m3
Thickness 50 mm
Overall refractory weight 3406,9 Kg 34,1 KN
Extra steel-work not modelled
Safety margin Unit Weight 20 Kg/m2
Overall Extra Steelwork Weight 988,5 Kg 9,9 KN
Base skirt / flange weightTotal base skirt weight 885,25 Kg 8,85 KN
Intermediate stiffening rings weightNumber of A-75x75x9 stiffening rings on portion 4
A-75x75x9 weight per meter 9,96 Kg/m
Total A-75x75x9 stiffening rings weight 196,90 Kg 1,97 KN
Overall Stack portion weight 100,98 KN
Overall Steelwork weight distributed along stack span 1,19 KN/m
Overall refractory weight distributed along portion span 3,41 KN/m
Point skirt weight at stack base 8,85 KN
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Stack portion II
Casing and RefractoryHeight 10000 mm
External diameter 1570 mm
Shell thickness 10 mm
Lateral External surface 49,30 m2
Casing Weight 3845,2 Kg 38,45 KN
Refractory LWC
Refractory D.ty 1400 Kg/m3
Thickness 50 mm
Overall refractory weight 3406,9 Kg 34,1 KN
Extra steel-work not modelled
Safety margin Unit Weight 20 Kg/m2
Overall Extra Steelwork Weight 986,0 Kg 9,9 KN
Base skirt / flange weightTotal base skirt weight 447,05 Kg 4,47 KN
Intermediate stiffening rings weightNumber of A-75x75x9 stiffening rings on portion 4
A-75x75x9 weight per meter 9,96 Kg/m
Total A-75x75x9 stiffening rings weight 196,40 Kg 1,96 KN
Overall Stack portion weight 88,82 KN
Overall Steelwork weight distributed along stack span 1,18 KN/m
Overall refractory weight distributed along portion span 3,41 KN/m
Point skirt weight at stack base 4,47 KN
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Stack portion III
Casing and RefractoryHeight 10000 mm
External diameter 1566 mm
Shell thickness 8 mm
Lateral External surface 49,17 m2
Casing Weight 3072,3 Kg 30,72 KN
Refractory LWC
Refractory D.ty 1400 Kg/m3
Thickness 50 mm
Overall refractory weight 3406,9 Kg 34,1 KN
Extra steel-work not modelled
Safety margin Unit Weight 20 Kg/m2
Overall Extra Steelwork Weight 983,4 Kg 9,8 KN
Base skirt / flange weightTotal base skirt weight 443,59 Kg 4,44 KN
Fan duct weightOverall Fan duct supporting stiffness weight 0,00 Kg 0,00 KN
Overall fan duct steelwork weight Kg KN
Overall refractory weight Kg KN
Intermediate stiffening rings weightNumber of A-75x75x10 stiffening rings on portion 4
A-75x75x10 weight per meter 9,96 Kg/m
Total A-75x75x10 stiffening rings weight 195,90 Kg 1,96 KN
Overall Stack portion weight 81,02 KN
Overall Steelwork weight distributed along stack span 1,18 KN/m
Overall refractory weight distributed along portion span 3,41 KN/m
Point skirt weight at stack base 4,44 KN
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2.2.8.2 STACK VERIFICATION
Stack stress verification are performed in according to API STANDARD 560.
Stack general dimensions
PortionFromElev.
ToElev.
Internalstack
diameter
Refractoryinternal
diameter
Shellthickness
Shell Outerdiameter
Portionheight
Stiffness ringprofile type
Nr. Ofstiffness on
span
mm mm mm mm mm
I 17200 27200 1550 1450 12 1574 10000 A-75x75x9 4II 27200 37200 1550 1450 10 1570 10000 A-75x75x9 4
III 37200 47200 1550 1450 8 1566 10000 A-75x75x10 4
Base & connecting flanges dimensions
Rectangular stiffness Triangular stiffness
PortionInternalPlate
diameter
Externalplate
diameter
Lowerplate
thickness
Upperplate
thickness
Nr. Ofstiffnesson plate
Stiffnessthickness
Height ofstiffness
Nr. Ofstiffnesson plate
Stiffnessthickness
Height ofstiffness
mm mm mm mm mm mm mm mm
I 1574 2074 30 25 28 12 270 28 12 270
II 1570 1890 30 30 0 30 8 250
III 1566 1886 30 30 0 28 8 250
Bolts Dimensions
Flanges at base of Portion Bolts nominal diameter Bolts number Bolt circle diameter
M mm
I 30 36 2060
II 27 30 1662
III 24 28 1662
LOADS ANALYSIS AND STANDARD REFERENCE
Wind action
Checks are performed according to API 560 – Specification for steel chimneys
According to the values of wind load calculated on paragraph 0 following are calculated the value of
loads and moments at the base of each section of the stack
Portion Thk.
Diameter
at portion
Base
Portion
height
Portion
casing
weight
Wind Load
uniformly
distributed
along height
Shear Load
at portion
barycentre
Moment at
portion
barycentre
Resulting
Shear at
portion
base
Resulting
moment at
portion
base
mm mm mm mm KN/m KN KNm KNm KNm
I 12 1574 10000 46,2 3,48 34,83 174,16 108,80 1660,07
II 10 1570 10000 38,5 3,63 36,33 181,63 73,97 746,24
III 8 1566 10000 30,7 3,76 37,64 188,20 37,64 188,20
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According to what written in the previous paragraphs, the stack here described has the
following characteristics:
Portion ThicknessCorroded
Thickness
Conical / cilindrical Top External
Diameter
Portion
Length
Lateral
Surface
Casing
Weight
mm mm mm mm m² Kg
I 12 10 1574 10000 49,4 4620,2
II 10 8 1570 10000 49,3 3845,2
III 8 6 1566 10000 49,2 3072,3
Total 30000 147,9 11537,7
Lining thickness = 50 mm Specific weight = 1400 daN/m3
Refractory weight calculation
Portion Refractory Density Portion lenght with refractory Refractory Thickness Refractory Weight
Kg/m³ mm mm Kg
I 1400,0 10000,0 50,0 3406,9
II 1400,0 10000,0 50,0 3406,9
III 1400,0 10000,0 50,0 3406,9
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Max. Height of stack: 30 m
The values above listed do not consider the effect of the corrosion on the stack walls.
The corrosion on the walls it will be considered later.
Material considered for Stack: JIS SS400
Overall Stack Height considered = 30 m
Young modulus E = 200000 N/mm²
Yield stress for the material fy = 235 N/mm²
Lining Thickness = 50 mmLining density = 1400 Kg/m³
Overall casing lateral surface 147,9 m²
Overall Casing weight 115,38 KN
Overall lining weight 102,21 KN
Overall extra weight for Equipments appended: 0 KN
Overall extra steelwork, stiffening and flanges weight 53,23 KN
Total platform surface considered 0 m²Overall structural platform weight 0 KN
Live load considered on each platform surface 2 KN/m²
Overall non permanent live load 0 KN
Overall ladder length 0 m
Overall ladder weight 0 KN
Overall stack permanent weight 270,82 KN
Overall weight with 33% of live load 270,82 KN
Maximum resulting shear at stack base 108,8 KN
Maximum resulting moment at stack base 1660,08 KMn
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ANCHOR BOLTS AND GROUND RING
The design procedure described in this paragraph is written according to chapter 10 of the book :
“Process Equipment Design”
Written by: L.E. Brownell and E.H. Young
Publisher: Wiley Publishing
Bearing plate thickness assumed t4 = 30 mm
Compression plate thickness assumed t5 = 25 mmGusset plate thickness assumed t6 = 12 mm
Base plate outer diameter De = 2074 mm
Base plate bolt circle diameter Db = 2060 mm
Base plate inner diameter Di = 1574 mm
Minimum vertical load on base plate Nmin = 270,82 KN
Maximum vertical load on base plate Nmin = 270,82 KN
Maximum shear load at stack base Vmax = 108,8 KN
Maximum resulting moment at stack base Mmax = 1660,08 KNm
Number of bolts on base plate nb = 36
Nominal diameter of anchor bolts db = 30 mm
Resistance section of anchor bolts Ares = 561 mm²
Safety coefficient on yield stress n= 1,5
Admissible stress for parts resistance checkσadm = 156,67 N/mm²
Max load on anchor bolts is given by:
Nb =(-Nmin/nb)+(4Mmax/Nb*Db) = 82,02 KN
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Bearing plate design procedure:
Stress on net section of anchor bolt:
σb = Nb/Ab = 14,62 KN/cm2 VERIFIED
Maximum compression stress
σc = Nmax/(3,14*Db*c) + 4*Mmax/(3,14*Db2*c) = 0,22 KN/cm2
where:
c: Ring outer radius - medium shell radius = 1037 - 781 = 256 mm
Base plate is defined as follows:
distance between stiffening bmin = 150 mm
distance between stiffening bmax = 300 mm
external width of base plate l = 250 mm
ratio (l/ b)max = 0,834 mm
thickness of bearing plate tb = (6*Mmax/ σadm)0,5
= 29,6 mm
Where Mmax is calculated with the formulas:
Mmax = c1*σb*b2 = 14,53 KNcm with c1 = 0,0765 by interpolation
Mmax = c2*σb*b2 = 22,82 KNcm with c2 = -0,173 by interpolation
the value of “tb” has to be checked where the bolts are located
In order to do this the maximum bolt load P is given by the formula:
P = sb*Ab = 87,9 KN
Whereσb is the maximum stress admissible on bolts
The Maximum bending moment supported by bolts is given by:
Mmax = P*b/8 = 329,59 KN/cm
The bearing plate thickness calculated with the considerations above is:
tb=(6*Mmax/(lt-bhd)*σadm)0,5
= 24,2 mm THICKNESS t4 ASSUMED VERIFIED
Where:
lt : overall bearing plate width = 250 mm
bhd :bolt hole diameter in bearing plate = 33 mm
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Compression plate design procedure:
The thickness of the compression plate is calculated as follow:
Mymax = (P/4*π)*[(1,3*ln(2*l/ π*e)+(1-g1)] = 15,95 KNcm
Where:
Mmax: Maximum bending moment acting on compression plate
P: Maximum bolt load calculated above
lc : Radial distance from outside of skirt to outer edge of compression plate
e: One-half distance across flats of bolting nuts = 23 mm
g1: Constant = 0,472 (by interpolation)
The thickness of the compression plate is:
tc =(6*Mymax/sigma_amm)0,5
= 24,7 mm THICKNESS t5 ASSUMED VERIFIED
Vertical gussets plate design procedure:
The vertical gusset plated equally spaced may be considered to react as a vertical column.
From empirical calculations it comes that the minimum thickness required for the gusset plates
is given by the equation:
18000*l*tg³-P*tg²-h²*P/1500=0
Where:
l: is the width of the gussets (inches)
h: is the height of the gussets (inches)tg: is the thickness of the gussets (inches)
P: is the Maximum value of bolt load calculated (lbs)
According to the values above listed the minimum thickness required for the gussets is:
tg = 6,25 mm THICKNESS t6 ASSUMED VERIFIED
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INTERMEDIATE RING FLANGES STRESS CHECK
Flange Stress Check
The procedure considered for the stress check of the flanges is the following:
The maximum pressure on flange due to vertical load is given by:
()4
22max
pi pe f
V D D
P
A
P p
−⋅==
−
π
The uniform load on middle flange diameter due to Pmas-V is given by:
⎟⎟
⎟
⎟
⎟⎟
⎟
⎟ −⋅=
−−
2maxmax
pi pe
V V p
D D pq
Assuming that the neutral axis for maximum moment passes from the section axis and
assuming that the highest pressure value is located on bolt circle diameter, the maximum
pressure on flange due to wind is given by:
()2
22max
cb pi pe
Max
cb f
MaxW
D D D M
D A M p ⋅−==−
π
Assuming that this pressure is uniformly distributed on compressed side of the flange it
can be calculated the uniform load on middle flange diameter due to this pressure:
⎟⎟
⎟
⎟
⎟⎟
⎟
⎟ −⋅⋅=
−−
22 maxmax
pi pe
W W p
D D pq
Where:
P: is the maximum vertical load calculated at the base of the section consideredMmax is the maximum moment calculated at the base of the section considered
Dpe & Dpi are the Outside and the Inside flange diametersDcb is the Bolt Circle diameter
the worst load combination is given in the position where the two loads add one to the
other:
W pV p qqq −−+=
maxmaxmax
With the geometry assumed it follows that the distance between the stiffness on bolt
circle diameter is given by:
s
s
cbt
N
Db −=
πmax
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where:
ts is the thickness of the stiffness
Ns is the total number of stiffness (assumed)
Now each flange can be assumed as a beam simply supported in the position where it
joins to the stiffness, so the maximum moment calculated between the two supports is
given by:
8
2
maxmax bq
M f
⋅=
The stress check of the flange is verified if
f adm
f
f
Mf t b
M −
≤⋅
= σσ
6
2
max
where:
tf is the thickness of the flange (assumed)
In order to check the maximum stress of the stiffness placed on each flange they arecalculated the maximum shear load and the maximum moment acting at the base of each
stiffness.
In order to do this, the flange is considered as a beam uniformly loaded and supported by
each stiffness.
From this consideration the maximum reaction and the maximum moment calculated
under the stiffness are given by the equations:
maxmaxmax2
1bq R s
=−
2
maxmaxmax12
1bq M s
=−
From these values it is easy to calculate the maximum shear and bending stresses:
ss
st h
Rmaxmax =
−τ 2
maxmax
6
ss
sht
M =−σ
where:
ts is the thickness of the stiffness (assumed)
hs is the height of the stiffness (assumed)
The stress of the stiffness is verified if
f admsssid −−−− ≤+= στσσ
2
max
2
max 3
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Following are listed all the geometric data and the resulting value calculated according to the
procedure above described.
Flange at base of
portion
Stack External
DIA
Stack Shell
Thk
Flange
Outside Dia
Flange
inside Dia
Flange circular
surface
Flange
thk
Dext ts Dpe Dpi Af tf
mm mm mm mm mm2 mm
II 1570 10 1890 1570 869152 30
III 1566 8 1886 1566 867142,4 30
Section Bolt Circle diameter Nr. of stiffness on interm. flange Stiffness Height Stiffness Thk
Dcb Ns hs ts
mm mm mm
II 1662 30 250 8
III 1662 28 250 8
Section
Max
Verticalload on
flange
Max moment at
section base dueto wind or
earthquake
Max
pressure on
flange due to
vertical load
Uniform loadon middle
diameter due
to vertical
load
Max
pressure on
flange due
to wind
uniform load
on middle
diameter due
to wind
Max
uniform
load on
flange
PMax Mmax Pmax-V qpmax-V Pmax-W qpmax-W qmax
KN KNm N/mm2 N/mm N/mm2 N/mm N/mm
II 169,84 746,24 0,20 31,26 0,52 82,66 113,92
III 81,02 188,20 0,09 14,95 0,13 20,89 35,84
Section distance between the stiffness Max Bending moment on flange Max stress on flange Check
bmax Mf sMf
mm KNm N/mm2
II 189,46 0,51 17,99 OK
III 203,06 0,18 6,07 OK
SectionMax reaction
under stiffness
Max moment
under stiffness
Max bending
stress on Stiffness
Max shear stress
on Stiffness
Max ideal stress
on StiffnessCheck
Rmax-s Mmax-s smax-s tmax-s sid-s
KN KNm N/mm2 N/mm2 N/mm2
II 26,98 0,29 3,45 13,49 23,62 OK
III 9,10 0,10 1,25 4,55 7,98 OK
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Flange bolts stress check
The flange bolts considered in the following procedures are in class 8.8 with the
following values for admissible stress:
σadm-b = 373 N/mm2
τadm-b = 264 N/mm2
The procedure considered for the stress check of the flange bolts is the following:
The maximum axial load on each bolt is given by the difference of the axial load due to
bending moment at the base of each section and the minimum vertical load calculated in
the same section.
The maximum axial load on worst stressed bolt is given by:
bcbb
b N n
N
Dn
M F
minmax4−=
−
From this follows that the highest axial stress on bolts is given by:
res
b N b
AF −− =maxσ
The maximum shear stress on each bolt is given by:
bres
bn A
V maxmax =
−τ
where:
Nmin is the minimum vertical load calculated at the base of the section considered
Vmax is the maximum shear load calculated at the base of the section considered
Mmax is the maximum bending moment calculated at the base of the section
considered
Dcb is the bolt circle diameternb is the total number of bolts considered on the flange
Ares is the resistance section of the bolts considered
The bolt are verified if
badmbbbid −−−− ≤+= στσσ
2
max
2
max 3
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The data and the results of the procedure applied to each intermediate flange are following listed:
SectionStack
Ext. Dia.
Stack
Shell thk.
Nr. of bolts on
interm. flange
Bolt
circle dia.
Bolt hole dia.
on flange
Bolt
nominal Dia.
Bolt resistance
section
Dext ts Nb Db db M Ares
mm mm mm mm mm 0 mm2
II 1570 10 30 1662 30 27 459
III 1566 8 28 1662 27 24 353
Section
Min
Vertical
load on
flange
Max shear
load due to
wind or
earthquake
Max moment at
section base due
to wind or
earthquake
Max axial
load on
worst
stressed
bolt
Max
axial
stress on
bolts
Max
shear
stress on
bolts
Max
ideal
stress on
bolts
Check
PMin VMax Mmax FN-b smax-b tmax-b sid-b
KN KN KNm KN N/mm2 N/mm2 N/mm2
II 169,8 74,0 746,2 54,2 118,1 5,4 118,5 OK
III 81,0 37,6 188,2 13,3 37,6 3,8 38,2 OK
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CHECK OF CASING
With reference to the stack structure section, considering that the ratio between diameter (D) and thickness (t) is
very high, in the following they will be used simplified formulas:
A = π*D*t
W = (π*D2*t)/4
I = (π*D3*t)/8
Specific data for resistance check (thickness of corrosion = 2 mm)
PortionWall thickness
corroded
External
corroded
diameter
A W I
Corroded
casing
weight
mm mm cm² cm 3 cm 4 KN
I 10 1570 493 19.359 1.519.703 38,70
II 8 1566 394 15.409 1.206.494 30,88
III 6 1562 294 11.497 897.954 23,10
The overall structure stability value does not consider possible allowances due to fabrication, while the
possible corrosion allowance value is deducted at checks of resistance.
VERIFICATION
Check on stability are performed in connection with admissible compression stresses, as per API 560 Par. 9.3.
Admissible compression stress is the minimum value between:
σadm-1 = 0,5*Fy = 11,75 N/mm²
or
σadm-2= 0,56*E*t/(D*(1+(0,004*E/Fy)))
With values defined as follows:
t = is the corroded shell plate thickness (mm)
D = is the outside stack diameter (mm)
E = 200000 N/mm² is the Elastic Young Modulus
Fy = 235 N/mm² :is the material minimum yield strength at design temperature
Following are listed the data considered in order to check the stress status of each shell section.
The value of stress on each section is calculated with the vertical load coming from the weight calculationof each section considered with thickness corroded
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PortionFrom
Elevation
To
Elevation
Max Vertical
Load at portion
base (N)
Max Moment at
portion base
(Mmax)
Stress
Calculated at
base portionσadm-2 Check
mm mm KN KNm cm4 KN/cm2
I 17200 27200 271 1.660 9,124 16,20 VERIFIED
II 27200 37200 170 746 5,275 12,99 VERIFIED
III 37200 47200 81 188 1,912 9,77 VERIFIED
DYNAMIC CHECK ON WIND EFFECT
DYNAMIC CHECK
Dynamic check is performed according to point 9.5 of API 560.
Vc1 = 5*Dt*f Vc2 = 6*Vc1
Where:Dt = 1,562 m Diameter of stack top
f = first mode frequency
f = 0,5587*(E*I*g/W*H4)
0,5
where:
W = 46,33 lbs/in is the Weight per unit height of stack
E = 29007548,8 psi is the Young Elastic Modulus
g = 386 in/s2
is acceleration due to gravity
I = 29023,3 inch4 is the medium moment of inertia
H = 1181,1 in is the total stack height
f = 1,061 Hz
Vc1 = 5*Dt*f = 8,29 m/s ACCEPTABLE WITH STRAKESVc2 = 6*Vc1 = 49,71 m/s ACCEPTABLE
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STIFFENING RING PRESENCE CHECK
Dynamic check is performed according to point 9.5.5 of API 560
Stiffening ring are required to prevent ovalling if:
fr/2*fv<1
calculated with the formulas:
fr = 0.126*(tr*(E)0,5
)/Dr2
fv = 13.2/Dr
Where
fr = natural frequency of the free ring (cycle per second)
fv = vortex shedding frequency (cycle per second)
tr = corroded plate thickness (inches)
E = Young Elastic Modulus (psi)
Dr = internal stack diameter (feet)
PortionFrom
Elevation
To
Elevation
Internal
Diameter
Shell
Thickness
corroded
Stiffening
Spacingfr fv fr/2fv Check
mm mm mm mm m
I 17200 27200 1.550 10 2,00 10,3372,60 1,99RINGS NOT
REQUIRED
II 27200 37200 1.550 8 2,00 8,269 2,60 1,59RINGS NOT
REQUIRED
III 37200 47200 1.550 6 2,00 6,202 2,60 1,19RINGS NOT
REQUIRED
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2.3 LOADING COMBINATIONS
2.3.1 Main LoadsThe following main loads have been considered
Deads = SLF + ADUCT + BURN + EXTPLTF + EXTSTEEL + REFRACT
ERECT = Deads + PPEMPT
OPER = Deads + PPOPER
TEST = Deads + PPTEST
LT = TMP + LIVE1
Live Load LIVE1
Wind Load +X WLX
Wind Load +Y WLY
Earthquake Load +X EQX
Earthquake Load +Y EQY
Thermal Load TMP
2.3.2 Load Combinations
Combination with Erection conditions
CB1E = ERECT + LIVE1
CB2E = ERECT + WX
CB3E = ERECT - WX
CB4E = ERECT + WY
CB5E = ERECT - WY
CB6E = ERECT + 0,714*EQX
CB7E = ERECT -0,714*EQX
CB8E = ERECT + 0,714*EQY
CB9E = ERECT -0,714*EQYCB10E = 0,9*ERECT + 0,714*EQX
CB11E = 0,9*ERECT -0,714*EQX
CB12E = 0,9*ERECT + 0,714*EQY
CB13E = 0,9*ERECT -0,714*EQY
CB14E = ERECT + 0,75*LIVE1 + 0,75*WX
CB15E = ERECT + 0,75*LIVE1 -0,75*WX
CB16E = ERECT + 0,75*LIVE1 + 0,75*WY
CB17E = ERECT + 0,75*LIVE1 -0,75*WY
CB18E = ERECT + 0,75*LIVE1 + 0,535*EQX
CB19E = ERECT + 0,75*LIVE1 -0,535*EQXCB20E = ERECT + 0,75*LIVE1 + 0,535*EQY
CB21E = ERECT + 0,75*LIVE1 -0,535*EQY
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Combination with Operating conditions
CB1O = OPER + LIVE1
CB2O = OPER + WX
CB3O = OPER - WX
CB4O = OPER + WY
CB5O = OPER - WY
CB6O = OPER + 0,714*EQXCB7O = OPER -0,714*EQX
CB8O = OPER + 0,714*EQY
CB9O = OPER -0,714*EQY
CB10O = 0,9*OPER + 0,714*EQX
CB11O = 0,9*OPER -0,714*EQX
CB12O = 0,9*OPER + 0,714*EQY
CB13O = 0,9*OPER -0,714*EQY
CB14O = OPER + 0,75*LIVE1 + 0,75*WX
CB15O = OPER + 0,75*LIVE1 -0,75*WX
CB16O = OPER + 0,75*LIVE1 + 0,75*WY
CB17O = OPER + 0,75*LIVE1 -0,75*WY
CB18O = OPER + 0,75*LIVE1 + 0,535*EQX
CB19O = OPER + 0,75*LIVE1 -0,535*EQX
CB20O = OPER + 0,75*LIVE1 + 0,535*EQY
CB21O = OPER + 0,75*LIVE1 -0,535*EQY
CB1OT = OPER + LT
CB14OT = OPER + 0,75*LT + 0,75*WX
CB15OT = OPER + 0,75*LT -0,75*WX
CB16OT = OPER + 0,75*LT + 0,75*WY
CB17OT = OPER + 0,75*LT -0,75*WY
CB18OT = OPER + 0,75*LT + 0,535*EQX
CB19OT = OPER + 0,75*LT -0,535*EQX
CB20OT = OPER + 0,75*LT + 0,535*EQY
CB21OT = OPER + 0,75*LT -0,535*EQY
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Combination with Test conditions
CB1T = TEST + LIVE1
CB2T = TEST + WX
CB3T = TEST - WX
CB4T = TEST + WY
CB5T = TEST - WY
CB6T = TEST + 0,714*EQX
CB7T = TEST -0,714*EQX
CB8T = TEST + 0,714*EQY
CB9T = TEST -0,714*EQY
CB10T = 0,9*TEST + 0,714*EQX
CB11T = 0,9*TEST -0,714*EQX
CB12T = 0,9*TEST + 0,714*EQY
CB13T = 0,9*TEST -0,714*EQY
CB14T = TEST + 0,75*LIVE1 + 0,75*WX
CB15T = TEST + 0,75*LIVE1 -0,75*WX
CB16T = TEST + 0,75*LIVE1 + 0,75*WY
CB17T = TEST + 0,75*LIVE1 -0,75*WY
CB18T = TEST + 0,75*LIVE1 + 0,535*EQX
CB19T = TEST + 0,75*LIVE1 -0,535*EQX
CB20T = TEST + 0,75*LIVE1 + 0,535*EQY
CB21T = TEST + 0,75*LIVE1 -0,535*EQY
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3 STRUCTURE SYSTEM
3.1 THE MODEL
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3.2 BAR ELEMENTS NUMBERING
3.2.1 Frame numbering - Arch
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3.2.2 Frame numbering - Convection
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3.2.3 Frame numbering - Floor
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3.2.4 Frame numbering - Platform el. 9000
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3.2.5 Frame numbering - Platform el. 17203
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3.2.6 Frame numbering - Radiant body
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3.2.7 Frame Profiles - Radiant body
H-200x200
C-200x80
A-75x6
C-150x75 LL-150x100
2A-90x10
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3.2.8 Frame Profiles –Stack
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3.3 PRIMARY LOADS APPLICATION
3.3.1 Burners weight distribution
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3.3.2 Coil weight distribution on convection surface
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3.3.3 Coil weight distribution on radiant anchor
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3.3.4 External piping loads
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3.3.5 Platform weight and live load distribution
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3.3.6 Refractory & Extrasteel weight distribution
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3.3.7 Wind load distribution in X direction
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3.3.8 Wind load distribution in Y direction
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4 STRUCTURAL ANALYSIS
The Steel Structure is checked in accordance with ASC-ASD-1989.
Automatic members check is carried out by means of SAP 2000 – Steel Stress Check according
ASC-ASD-1989.
Structural checks and frame analysis are based on 3-d structure model.
The bars and the shells elements ave been designed for the worst loading combination cases.
5 BASE PLATE AND ANCHOR BOLTS CHECK
5.1 BASE PLATE CHECK
5.1.1 Base Plates stress check calculation procedure
In order to check the worst stress status of the plates at the base of the structure columns the
following procedure has to be performed.
The calculation of the maximum stress on the concrete plinths is performed considering thevalue of the eccentricity calculated as ratio between the value of the moment acting at the
base of the columns (M) and the compression load perpendicular to the base plate (N).
N
M e =
The value of this ratio detects the position of the neutral axis with respect to the kernel of
inertia of the section calculated as sixth part of the plate dimension perpendicular to the axis
of the moment considered (a) as shown in the following picture (where the load N has not to
be considered as a shear load but only an image for the position of the perpendicular load):
Picture 1
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According to the value of “e” calculated, the two following conditions have to be considered:
Condition 1 for calculation of maximum stress on plinth:
6
ae ≤ : eccentricity internal to the kernel of inertia
in this case the plinth can be assumed to be forced by only a compression load, so the
maximum compression stress on plinth is calculated as follows:
ccc
W
M
A
N
+=σ
where:
Ac : is the section area of the cement plinth
Wc: is the elastic modulus of the plinth
For conservative reasons both the geometric characteristics above listed are calculated
considering the plinth with same dimensions and section of the base plate.
The stress of the maximum compression on plinth is verified if :
ck c R*44,0≤σ
where Rck is the cubic admissible resistance of the concrete considered.
From the value of σc, it is calculated for proportion the value of the stress acting on the baseplate in correspondence of the section column flanges or stiffeners:
sc
s
s
sc x
a x x 2
σσ
σσ=⇒=
where assuming the neutral axis passing from the middle of the section:
σs is the value of sigma at stiffeners level
xs is the distance between stiffeners and neutral axis
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Condition 2 for calculation of maximum stress on plinth:
6
ae > : eccentricity external to the kernel of inertia
this condition forces to the research of the position of the real neutral axis.
The value of the position of the neutral axis is found by attempts with the following empirical
equation:
0)()(26
23=+−+++ hd hnA xhd nA x
bd x
b f f
Where (ref. to picture 1):
b is the plate dimension parallel to the moment axis
x is the position of the neutral axis with respect to the base edge
d is the position of perpendicular load with respect the plate edge
n = 15 is the homogenization coefficient between elastic modulus
Af = Ab*nb is the total area of the bolts strengthen
h is the distance between the base edge and the axis of the anchor bolts
strengthen
Once that the value of “x” is calculated the value of the maximum sigma acting on the cement
plinth is calculated with the formula:
)(2
*2
xhnA x
b
x N
f
c
−−
=σ
The stress of the maximum compression on plinth is verified if :
ck c R*44,0≤σ
where Rck is the cubic admissible resistance of the concrete considered.
From the value of σc, it is calculated for proportion the value of the stress acting on the base
plate in correspondence of the section column flanges or stiffness:
sc
s
s
sc x
x x x
σσ
σσ=⇒=
where (ref. to picture 1):
σs is the value of sigma at stiffness level
xs = x- m1 is the distance between stiffness and neutral axis
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Base Plate stress calculation
Once that the values of σc and σs have been calculated from one of the procedures above
described the stress check of the base plate continues as follows for both the conditions:
The base plate is now considered as a beam rigidly joined at level of stiffness and uniformly
loaded by a load “q” calculated as follows:
2*1 sc
mqσσ +
=
The maximum momentum given by this kind of restraint is:
2
2*
8
2*22
mqlq M Max
−=
where
l2 is the intermediate distance between the base plate stiffeners
m2 is the distance between the flange of the column section and the plate edge
The Maximum sigma acting on the flange is:
⎟⎟
⎟
⎟
⎟⎟
⎟
⎟
==
6*1 2thk m
M
W
M Max Max
p
σ
Where:
W is the resistance modulus of the section considered.
thk is the thickness of the plate (assumed)
Note:
The procedures above described are referred to a moment with axis parallel to direction 2.
In the case in which the moment considered is directed as axis 1 the related values of
geometric dimensions as “a”, “b”, “l”, “m” etc have to be considered.
In order to take into account the effect of both the moments acting at the base of the column,
the procedures above described are performed considering one at time both the moments
acting on the two main direction of the section.
The value of stress so found it has to be lower than the admissible stress calculated as ratio
between the yield stress of the material considered for the base plate and a safety coefficient.
If the stress is verified the thickness assumed has not to be increased.
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5.1.2 Stress check on Base Plates A – B – C – D – E – F
Plinth Comb. Fn F1 F2 M1 M2
KN KN KN KNm KNmF CB7O 950,4 60,7 -15,1 5,8 25,4
Yield Stress of the material JIS SS400 = 235 N/mm²Admissible stress of the base plate material = 235 / 1,5 = 156,67 N/mm²
Cement Plinth cubic resistance Rck = 21 N/mm²
Admissible stress on cement plinth = 21 * 0,44 = 9,24 N/mm²
Base Plate thickness assumed = 35 mm
Considered 8 bolts M30
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Action
dominant
Plate
dimension
parallel to
Moment (b)
Plate dimension
perpendicular to
Moment (a)
Plinth
section
(Ac)
Plinth
Elastic
modulus
(Wc)
Eccentricity
(e)
eccentricity
case
mm mm mm² mm³ mm
M1 500 500 250000 20833333 6,12 Case 1: e<a/6
M2 500 500 250000 20833333 26,71 Case 1: e<a/6
Action
dominant
Distanceof
normal
force
from
edge
(d)
Nr. of bolts
strengthen
on last row
(nb)
Totalresistance
section of
bolts
strengthen
(Af)
Distancebetween
bolts
strengthen
and plate
edge
(h)
Distancebetween
Neutral
axis and
plate
edge
(x)
Distancebetween
stiffness
perp. to
moment
(l2)
Distance
betweenstiffness
and plate
edge
perp. to
moment
(m2)
Distance
betweenstiffness
and plate
edge
parallel
to
moment
(l1)mm mm mm² mm mm mm mm mm
M1 0 3 1683 425 0 200 138 150
M2 0 3 1683 425 0 176 150 138
Action
dominant
Compression
Stress on
Plinth (σσσσσσσσσc)
Plinth stress
check
Sigma on
stiffeness for
proportion
(σσσσσσσσσf )
uniform
load on
plate
portion
(q)
Maximum
moment on
plate portion
(ΜΜΜΜΜΜΜΜΜmax)
Resistance
module with
respect to the
moment
(Wp)N/mm² N/mm² N/mm Nmm mm³
M1 0,28 Sigma-c CLS OK 2,37 529,47 3906450,71 28175,00
M2 1,22 Sigma-c CLS OK 2,12 556,44 2516204,32 30625,00
Action
dominant
Sigma on base plate for Moment
effect (σσσσσσσσσp)
Sigma resultant from both moment
action (σσσσσσσσσmax)
Plate stress
check
N/mm² N/mm²
M1 138,65
M2 82,16138,65 Plate check OK
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5.2 ANCHOR BOLTS CHECK
5.2.1 Anchor bolts on plinth A B C D E F according to Chapter J of AISC-350-05
In order to perform the check resistance of the bolts following are listed the calculation made
for the load combinations that make the higher stress on bolts in condition of maximum and
minimum axial load, moment and resulting shear.
According to this in order to calculate the axial and shear stress on worst stressed bolt thefollowing equations have been considered:
Axial load on bolt due to Fn (in strength condition)()
bb
nFnt
An
F f
⋅=
−
Axial load due to moment in X direction∑
=− 2
max
**
*
ibbx
x Mxt
y An
y M f
Axial load due to moment in Y direction∑
=− 2
max
**
*
ibby
y
M t x An
x M f
y
Overall axial load on bolt Myt Mxt F t nt f f f f n −−− ++=
Overall Shear Load22
y xtot V V V +=
Shear Load Acting on each bolt:
b
tot b
n
V V =
Required Shear stress on each bolt:b
bnv
A
V f =
Where:
nb : overall number of boltsAb : Resistance section of each bolt
ymax / xmax: Distance between the plate edge and the farest bolt line parallel to x / y axis
yi / xi: Distance between the plate edge and each bolt line parallel to x / y axis
nbx / nby: number of bolts on the farest bolt line parallel to x / y axis
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Once that the axial and shear stresses on bolt are calculated as previous described the design
procedure (according to Chapter J of AISC-350-05) can be applied as follows:
Design procedure according to Chapter J of AISC-350-05Specified minimum tensile strength of the type of steel being used Fu = 400 N/mm
2
Nominal tensile Stress acc. AISC 350 cap.J Fnt = 0,75*Fu = 300 N/mm2
Nominal shear Stress acc. AISC 350 cap.J Fnv = 0,4*Fu= 160 N/mm2
For tensile stress check the values are:
Ra = f nt * Ab ''
nt n F F = is the nominal tensile stress modified to include the effects of shearing stress
calculated with the equation:
2
'1
Ω−=
nv
nvnt nt
F
f F F
For combined tension and shear actions it has to be:Ω
=Ω
≤ bnna
AF R R
'
Where:Ra : is the required strength (ASD)
Rn is nominal strength
Ω = 2 is the safety factor (ASD)
Total bolt number 8
Nominal bolt diameter 30
Section resistance 561 mm²
Specified minimum tensile strength of the type of steel being used Fu = 400 N/mm²
Nominal tensile Stress acc. AISC 350 cap.J Fnt =0,75*Fu 300 N/mm²
Nominal shear Stress acc. AISC 350 cap.J Fnv =0,4*Fu 160 N/mm²
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According to the procedure above described following are listed the values calculated with the
load combination that makes higher status of axial, moment and shear on anchor bolts:
Plinth Combo FN FX FY MX MY Max base shear
KN KN KN KN-m KN-m KN
Combination with Max vertical load at base F CB7O 950,4 60,7 -15,1 5,8 25,4 62,5
Combination with Min vertical load at base C CB11O -438,9 51,3 4,8 -1,8 24,8 51,6
Combination with Max moment Mx at baseA CB15OT 545,9 -8,5 -44,2
25,5-6,7 45,0
Combination with Min moment Mx at base D CB21OT 660,4 24,0 43,1 -24,7 9,8 49,3
Combination with Max moment My at base F CB15OT 840,3 68,3 -14,4 840,3 32,7 69,8
Combination with Min moment My at base C CB14OT 724,7 -47,7 3,6 -1,4 -27,5 47,8
Combination with Max resulting shear at base F CB19OT860,39 71,70 -15,21 5,87 32,25 73,30
Requiredtensile
stress oneach bolt ft
Overallshear
load onplinthVtot
Requiredshear
sterss oneach bolt
fnv
nominaltensile stressmodified toinclude theeffects ofshearing
stress F'nt
requiredstrength
Ra
nominalstrength
Rn/ Ωcheck
Plinth Combo N/mm² KN N/mm² N/mm² N/mm² N/mm²
Max Fz F CB7O 31,7 62,5 13,9 295,4 17771,4 82865,5 OK
Min Fz C CB11O 124,8 51,6 11,5 296,9 70001,7 83278,0 OK
Max Mx A CB15OT 32,8 45,0 10,0 297,6 18373,5 83485,9 OK
Min Mx D CB21OT 35,0 49,3 11,0 297,2 19636,2 83353,0 OK
Max My F CB15OT 38,8 69,8 15,6 294,3 21787,6 82544,4 OK
Min My C CB14OT 29,4 47,8 10,6 297,3 16487,3 83401,1 OK
Max shear F CB19OT 38,7 73,3 16,3 293,7 21709,6 82377,9 OK
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6 RESULTS ANALYSIS
6.1 LOAD FOUNDATIONS
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6.2 DISPLACEMENTS CHECKING6.2.1 Max Horizontal Joint displacement
Maximum horizontal displacement: 7.56 mm
Column height: 5005
Load Combination: CB6E
Joint : 803
Allowable displacement checking for column height:
h0 /500 = 5050/500 = 10.01 mm > 7.56 OK
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6.2.2 Max deflection of beam
Maximum deflection : -6.63 mm
Beam Span (L): 1800
Load Combination: CB10
Beam number : 572
Allowable deflection checking:
L/250 = 1500/250 = 7.2 mm > 6.63 OK
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6.3 STRESS CHECKING
In the following pictures are the Design Stress Ratios Topography per line provided SAP.
These ratios correspond to the design stress in the bars over the allowable stress.
6.3.1 Maximum stress in main elements
Here below the maximum stress ratios in the main structural elements
Frame DesignSect DesignType Combo TotalRatio
211 C-150X75 Beam CB17O 0,970
112 H-200X200 Column CB3O 0,954
418 2A-75X9 Brace CB15OT 0,926
Here below the computer output detailed structural calculations of the main elements with the
maximum stress above mentioned.
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6.3.2 Data for worst stressed beam
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6.3.3 Data for worst stressed column
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6.3.4 Data for worst stressed brace
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6.3.5 Stress Ratios - Arch
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6.3.6 Stress Ratios - Convection
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6.3.7 Stress Ratios - Floor
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6.3.8 Stress Ratios - Platform el. 9000
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6.3.9 Stress Ratios - Platform el. 17203
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6.3.10 Stress Ratios - Radiant Body
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Structural elements stress checking computer output table
TABLE: Steel Design 2 - PMM Details - AISC-ASD 01
Table: Steel Design 2 - PMM Details - AISC-ASD01
Frame DesignSect DesignType Combo TotalRatio PRatio MMajRatio MMinRatio
211 C-150X75 Beam CB17O 0,970486 0,033793 0,080941 0,855752
1456 A-75X6 Beam CB1OT 0,965219 0,161650 0,254303 0,549266
112 H-200X200 Column CB3O 0,953768 0,756447 0,196224 0,001097
600 A-75X6 Beam CB14OT 0,953275 0,165027 0,358192 0,430056
604 A-75X6 Beam CB5O 0,943607 0,084699 0,288275 0,570633624 A-75X6 Beam CB15OT 0,942381 0,132440 0,242276 0,567665
1401 A-75X6 Beam CB15OT 0,937742 0,202521 0,308597 0,426625
1493 A-75X6 Beam CB16OT 0,937390 0,204937 0,291222 0,441231
421 C-150+A-90 Beam CB16OT 0,935003 0,035953 0,505647 0,393404
1478 A-75X6 Beam CB1OT 0,929110 0,147188 0,250400 0,531521
571 2A-90X10 Column CB5O 0,926956 0,358888 0,361460 0,206608
418 2A-75X9 Brace CB15OT 0,925765 0,034595 0,442762 0,448408
1480 A-75X6 Beam CB1OT 0,924432 0,147620 0,255147 0,521665
580 A-75X6 Beam CB14OT 0,923496 0,147784 0,275288 0,500425
649 A-75X6 Beam CB1OT 0,919039 0,033808 0,064643 0,820587
53 H-200X200 Column CB17OT 0,917472 0,472758 0,222467 0,222247
374 A-75X6 Beam CB1E 0,912147 0,042444 0,066102 0,803601
648 A-75X6 Beam CB1OT 0,909268 0,030118 0,018807 0,860343182 H-200X200 Beam CB2T 0,908771 0,047580 0,860007 0,001183
1483 A-75X6 Beam CB14OT 0,908534 0,211617 0,303369 0,393549
256 H-200X200 Beam CB2T 0,903900 0,046547 0,856190 0,001163
1499 A-75X6 Beam CB14OT 0,901629 0,195460 0,294025 0,412145
426 C-150+A-90 Beam CB1OT 0,897453 0,047167 0,332158 0,518128
55 H-200X200 Column CB2T 0,896269 0,674066 0,220158 0,002045
1454 A-75X6 Beam CB14OT 0,894490 0,121424 0,216681 0,556385
1462 A-75X6 Beam CB1OT 0,892025 0,127468 0,236725 0,527831
222 H-200X200 Beam CB3O 0,891576 0,046060 0,844568 0,000948
413 C-150+A-90 Beam CB1OT 0,891378 0,045020 0,331550 0,514807
2 H-200X200 Column CB15OT 0,891066 0,499677 0,261598 0,129791
281 H-200X200 Beam CB3O 0,887922 0,043468 0,843420 0,001034
1430 A-75X6 Beam CB16OT 0,887220 0,102739 0,223223 0,561258
1489 A-75X6 Beam CB14OT 0,877898 0,107826 0,246853 0,523218
877 2A-75X9 Brace CB1OT 0,875967 0,288793 0,184038 0,403136
59 H-200X200 Column CB16OT 0,875616 0,461270 0,245492 0,168855
428 C-150+A-90 Beam CB1OT 0,872844 0,030797 0,347071 0,494976
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