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STEEL STRUCTURAL CALCULATION REPORT
00 REV. DATE N° DATE
XX
XX XX DESCRIZIONE DESCRIPTION
EMESSO CONTROLLATO ISSUED BY
CONTROLLED BY
APPROVATO APPROVED BY
1
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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
1.3
xx
CALCULATION CODES - Uniform Building Code Volume 2 - Minimum Design Loads for Buildings and other Structures - Manual of steel construction - Allowable Stress Design - Specification for Structural Steel Buildings AISC
1.4
UBC-97 UBC-97 AISC – ASD/01 360-05
MATERIAL AND CODE ALLOWABLE VALUES Material used for the structures : Yield stress fy: 235 Minimum Tensile stress fu: 400
JIS SS4002or equivalent N/mm (thickness ≤ 16 mm) N/mm2
2 2.1
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LOAD CALCULATION PRIMARY LOADS The decomposition of the loads into following primary loads : - Structure Self-Weight
(SLF):
- Extra Steelwork Weight
(EXTSTEEL):
- Platform
(EXTPLTF):
- Refractory Loads
(REFRACT):
- Pipe empty loads
(PPEMPT):
- Pipe Operating Loads
(PPOPER)
- Hydrostatic test loads
(PPTEST)
- Burners - Air Duct
(BURN): (ADUCT):
- Live Load 1
(LL1):
- Wind Load +X - Wind Load +Y - Earthquake Load +X - Earthquake Load +Y
WLX WLY EQX EQY
- Thermal Load
TMP
Weighs of the structural components automatically calculated by the program, and based on the model feature. Extra Steelwork weights not directly included in the model and not automatically calculated. Platform Extra Steelwork weights not directly included in the model and not automatically calculated. Weights of the refractory lining surfaces applied to the structural elements. Weights of all the operating pipes installed on the structure considered empty. 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. Weights of the pipes considered full of water as they are during the hydrostatic test conditions Weights of the burners applied to the radiant floor Weights of air duct installed on heater For the calculation of the foundation loads and structural analysis has been considered an overload of 500 Kg/m2 on each platforms. According to UBC-97 According to UBC-97 According to UBC-97 According to UBC-97 A thermal load has been considered on steel structures during normal operation according to spec n° 00-ZA-E205001-rev.02 Tmax on frame = 47°C Tmin on frame = 2°C Tmax on furnace skin = 83°C Tmin on furnace skin = 38°C
2.2 2.2.1
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LOADING DETAILS Radiant cell
2.2.1.1 Radiant Floor A.1
FLOOR
External Radius Internal Radius support internal Radius External Diameter Internal surface diameter support internal diameter Floor thickness Overall Surface Floor surface weight burners supporting surface External surface Refractory (wet) Wet D.ty M.W.C. 1:2:4 Thickness 75 Wet D.ty VLWC 1:0:5 Thickness 125 A 1.2 Burners Weight of each burner considered number of burners Overall
burners weight
A 1.3 Steelwork Extra steelwork not modelled Extra steelwork weight
2474 mm 1697 mm 515 mm 4948 mm 3394 mm 1060 mm 6 mm 2 19,2 m 905,7 Kg 8,16 11,1
9,06 KN
2
m 2 m
57,04KN 3 1930 Kg/m mm 3 1215 Kg/m mm
450 6
Kg
2700 Kg 27,00KN
40,00 Kg/m 769,15 Kg
2
7,69 KN
Input Sap Data
Overall refractory weight distribuited on surface Overall steelwork weight distribuited on surface Overall burners weight distributed on surface
Overall floor weight
100,79
KN
Internal surface
External surface
load case
2,97 0,4
REFRACT EXTSTEEL BURN
KN/m2 KN/m2 2,97 0,4 3,31
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2.2.1.2 Radiant Lateral walls LATERAL WALL External Diameter Height 9198,0 Thickness 5,0 Lateral Surface Lateral surface weight Refractory (wet) L.W.C. 124 Thickness 75 V.L.W.C 105 Thickness 100 Steelwork Extra steelwork not modelled Extra steelwork weight
4948
142,9 5609,1
1400 1215
mm mm mm 2 m Kg
56,1
KN
323,7
KN
Kg/m3 mm Kg/m3 mm
20,00 Kg 2858,1
Kg/m2 28,6 tot. weight
Overall refractory weight distribuited on surface Overall steelwork weight distribuited on surface
KN 408,4
KN
load case KN/m2 2,26 REFRACT EXTSTEEL 0,20
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2.2.1.3 Heater Arch ARCH Diameter 4948 Thickness 6 Surface 19,2 Arch surface weight Rectangular hole Lenght 4900 Width 1453 hole surface Arch surface without hole
905,7
mm mm m2 Kg
7,1
mm mm m2
12,11
m2
Refractory (wet) L.W.C. 124 Thickness 75 V.L.W.C 105 Thickness 125 Steelwork Extra steelwork not modelled Extra steelwork weight
1400 1215
20,00 242,2
KN
31,105
KN
Kg/m3 mm Kg/m3 mm
Kg Kg/m2 2,4 tot. weight
Overall refractory weight added to arch surface Overall steelwork weight added to arch surface
9,1
2,57 0,20
KN 42,6 KN/m2 KN/m2
KN REFRACT EXTSTEEL
2.2.2
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Radiant Internal coil
Type of fuel
Fuel Oil
Bare tubes O.D: Bare tubes thickness Bare tubes I.D. Maximum Operating fluid density Water density for hydrostatic test Pipe weight per meter Operating fluid weight per meter on each pipe Water weight per meter inside each pipe Number of tubes on each anchor Medium pipe lenght Return bends medium diameter Number of return bends on each anchor Bends unit weight Operating fluid on each return bend Water weight on each return bend
141,3 mm 6,55 mm 128,2 mm 556 Kg/m3 1000 Kg/m3 21,77 Kg/m 7,18 Kg/m 12,91 Kg/m 2,0 7,800 m 254,0 mm 2,0 8,7 Kg/each 2,9 Kg/each 5,1 Kg/each
Pipe empty weight on each anchor (2 tube + 2 bend) Pipe weight with operating fluid on each anchor (2 tube + 2 bend) Pipe full weight on each anchor (2 tube + 2 bend)
356,9 Kg 474,6 Kg 568,6 Kg
Crossing Tubes Number of crossing tubes Medium pipe lenght Empty crossing tubes weight Operating crossing tube weight (pipes + Op. fluid) Test crossing tube weight (pipes + water)
4,0 2,248 m 195,7 Kg 260,3 Kg 311,8 Kg
Anchor number Total number of tubes on each anchor Total number of bends on each anchor
24,0 48,0 48,0
Overall empty weight Overall operating weight (Pipe + Operating fluid) Overall test weight (Pipe + water)
8761,6 Kg 11650,5 Kg 116,5 13957,4 Kg 139,6
Point empty weight applied on each anchor (ELEV. 19050) Point operating weight applied on each anchor (ELEV. 19050) Point test weight applied on each anchor (ELEV. 19050)
87,6
KN KN KN
3,65 4,85 5,82
KN KN KN
PPEMPT PPOPER PPTEST
2.2.3
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Convection cell
2.2.3.1 Convection Lateral vertical walls Width 4900,0 Height 3555,0 Thickness 5,0 Surface 17,4 Weight of each convection wall Refractory (wet) D.ty LWC 1:2:4 Thickness 150 Steelwork not modelled Extra steelwork not modelled Extra steelwork weight
683,7
mm mm mm m2 Kg
1400
Kg/m3 mm
20,00 348,4
Kg/m2 Kg 3,5
Overall convection wall weight (2X) Overall refractory weight distributed each surface Overall steelwork weight added to each surface
6,8
KN
36,6
KN
KN 93,8
KN
2,10 0,20
KN/m2 KN/m2
REFRACT EXTSTEEL
2.2.3.2 Convection End tube sheets (E.T.S.) width 1453,0 Height 3555,0 Thickness 13,0 Surface 5,2 Weight of each convection wall Refractory (wet) Wet D.ty LWC Thickness 100
Steelwork not modelled Unit Weight
527,1
1400
mm mm mm m2 Kg
5,3
KN
7,2
KN
1,0
KN
13,5 27,1
KN KN
Kg/m3 mm
20 Kg/m2 tot. weight of each End Tube Sheet Overall End Tube Sheet weight
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 Width 2353,0 Height 4455,0 Surface 10,5 Steelwork not modelled sheet thickness Plate steelwork weight Refractory (wet) D.ty LWC 1:2:4 Thickness 50 Extra Steelwork not modelled Unit Weight
450
mm mm mm m2
5,0 411,4
mm Kg
1400
Kg/m3 mm
50 Kg/m2 tot. weight of each Header Box Overall Header Boxes weight
Overall refractory weight distributed on each E.T.S. surf. Overall steelwork weight distributed on each E.T.S. surf.
4,1
KN
7,3
KN
5,24
KN
16,7 33,4
KN KN
1,42 1,81
KN/m2 REFRACT KN/m2 EXTSTEEL
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2.2.3.4 Convection Piping (coil, inlet &outlet piping) CONVECTIVE PROCESS COIL type of fuel Operating fluid density Water density for Hydrostatic test
fuel oil 556 1000
Bare tube external diameter Bare tube thickness Bare tube internal diameter Bare tube length Nr of flow passes Number of tubes N° tubes/row Number of rows
141,3 6,55 128,2 5,226 4 44 4 11
Number of 180° return bends Medum diameter of 180° return bends
40 254
single empty tube weight per meter Operating fluid weight per meter inside each tube Water weight per meter inside each pipe
21,76 Kg/m 7,17 Kg/m 12,90 Kg/m
Weight of each empty bend Operating fluid weight per meter inside each bend Water weight per meter inside each bend curve
8,68 Kg/each 2,86 Kg/each 5,14 Kg/each
Overall empty coil weight (pipes + bends) Overall Operating coil weight (pipes + bends + operating fluid) Overall Test coil weight (pipes + bends + water)
5350
Kg/m3 Kg/m3 mm mm mm m
mm
Kg
53,50
KN
85,22
KN
98,26 115,90 129,98
KN KN KN
7113 Kg 71,13 KN 8522
Kg
STUDDED SURFACE AROUND CONVECTIVE COIL 25,40 mm Stud height Studs diameter 12,70 mm studs per meter 1260 stud /m Number of bare tubes not finned Number of studded tubes 28 5,026 m studded surface length (on each tube) 0,001013 m2 exposed surface of each stud studded exposed surface of each tube 6,414 m2 total exposed surface calculated (studs+ tubes) 242,04 m2 4476,4 Kg 44,76 Weight of studded surface Overall empty coil weight Overall Operating coil weight (tube + Op. fluid) Overall test coil weight (tube + water)
9826 11590 12998
Kg Kg Kg
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Height of End Tube Sheet portion Width of End Tube Sheet portion Heading surface with coil weight distributed
3555,0 1453,0 5,17
Overall empty tube weight distributed on each convection header surfaces Overall Operating weight distributed on each convection header surfaces (tube + Op. Fluid) Overall test weight distributed on each convection header surfaces (tube + water)
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mm mm m2
9,51 KN/m2
PPEMPT
11,22 KN/m2
PPOPER
12,58 KN/m2
PPTEST
2.2.3.5 Inlet & Outlet terminal points load TAG F xF yF N N N Nm Nm Nm N1 9342 17346 17346 7566 5694 5694 N2 9342 17346 17346 7566 5694 5694
2.2.4
z
M
x
M
y
M
z
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 Thickness 75 Overall breeching refractory weight
1400 1071
Kg/m3 mm 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 Overall breeching steelwork weight distributed on modelled surface0,30
KN/m2 REFRACT KN/m2 EXTSTEEL
2.2.5
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Platforms, Vertical ladders & Stairs Live load (for base foundation loads )
500
Kg/m
2
2
Grating 37 Structure 75 Handrail 16 Toe board
7
Total 135
Kg/m 2 Kg/m 2 Kg/m 2 Kg/m Kg/m
2
2.2.5.1 Platforms EL+ 3000 on plinth L
Dimension
LengthWidth mm mm 1250 1835
Plant platform at 0°
Surface m2 2,29 nr.supporting beam
load on middle beam KN/m
Total platform Dead load
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 Internal Radius
Dimension
mm 2474
Plant
Middle radius modelled mm 3104
External Radius
Angle (°)
mm 3854
360 nr.supp. beam
Total platform Dead load
3701,77
Total platform Live load
13710,24
Kg Kg
37,02
KN 2
137,10
KN 2
Surface m2 27,42 load on load on middle external beam beam KN/m KN/m 0,95 0,76 3,52 2,83
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2.2.5.3 Platforms EL+9000
Dimension
Plant
Internal Radius mm 2474
Middle radius modelled mm 2875
External Radius mm 3854
Angle (°)
Surface
345
m2 27,42
nr.supporting beam Total platform Dead load
3701,77 Kg
load on load on middle external beam beam KN/m KN/m
37,02
KN 2
1,07 0,80
137,10
KN 2
3,96 2,96
Kg Total platform Live load
13710,24
Dimension
Plant platform at 270° and 90°
Surface m2 5,79
Total length of beam modelled m 15,07 load on beams KN/m
Total platform Dead load
781,38 Kg
7,81
KN
0,52
Total platform Live load
2894,00
28,94
KN
1,92
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2.2.5.4 Platforms EL+12498 Dimension
Length mm 4000 6151 4000 6151
Plant platform at 0° Plant platform at 90° Plant platform at 180° Plant platform at 270°
Width mm 1124 1145 1124 1145
Surface m2 4,50 7,04 4,50 7,04
Dead Load on Plant platform at 0° Dead Load on Plant platform at 90° Dead Load on Plant platform at 180° Dead Load on Plant platform at 270°
606,96 950,79 606,96 950,79
Kg Kg Kg Kg
6,07 9,51 6,07 9,51
KN 1 KN 1 KN 1 KN 1
Load on each supp. beam column KN 0,76 0,77 0,76 0,77
Live load on Plant platform at 0° Live load on Plant platform at 90° Live load on Plant platform at 180° Live load on Plant platform at 270°
2248,00 3521,45 2248,00 3521,45
Kg Kg Kg Kg
22,48 35,21 22,48 35,21
KN 1 KN 1 KN 1 KN 1
2,81 2,86 2,81 2,86
Nr of portion consid.
2.2.5.5 Platforms EL+17203 Dimension Length mm Plant platform at 0° Plant platform at 90° Plant platform at 180° Plant platform at 270°
5133 1453 5133 1453
Width mm 1375 1349 1375 1349
Surface m2 7,06 1,96 7,06 1,96
Nr of portion consid. Dead Load on Plant platform at 0° Dead Load on Plant platform at 90° Dead Load on Plant platform at 180° Dead Load on Plant platform at 270°
952,81 264,61 952,81 264,61
Kg Kg Kg Kg
9,53 2,65 9,53 2,65
KN 1 KN 1 KN 1 KN 1
Load on each supporting beam column KN 0,93 0,91 0,93 0,91
Live load on Plant platform at 0° Live load on Plant platform at 90° Live load on Plant platform at 180° Live load on Plant platform at 270°
3528,94 980,05 3528,94 980,05
Kg Kg Kg Kg
35,29 9,80 35,29 9,80
KN 1 KN 1 KN 1 KN 1
3,44 3,37 3,44 3,37
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2.2.5.6 Vertical ladder and stairs E.1.8
Vertical ladder load (steelwork + live load)
Kg/m
Applicable to elev.
lenght (m)
weight (Kg)
3000 3000 11500 20000 25010
6,00 6,00 3,50 3,50 4,71
480 480 279,84 279,84 376,4
Applicable to elev.
lenght (m)
weight (Kg)
3000
5,25
1573,5
weight (KN)
80 LD.2 LD.2A LD.3 LD.4 LD.5 E.1.8
Stairs load (steelwork + live load)
Kg/m
4,80 KN 4,80 KN 2,80 KN 2,80 KN 3,76 KN
weight (KN)
300 SG.1
7,87 KN
2.2.6
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Wind Loads (WL)
WIND LOAD according toUBC-97 P = Ce*Cq*qs*Iw EXPOSURE Pressure coefficient on cilindrical surfaces Cq = Site elevation
D 0,8 19-25 m
Basic wind speed V =
44,4
wind stagnation pressure suggested for site elevation qs = Importance factor Iw =
m/s
According to spec. Nr. 00-ZA-E205001 rev.2 According to spec. Nr. 00-ZA-E205001 rev.2
1,30E-03 Mpa 1,15
1,30 KN/m2
(hazardous facilities)
2.2.6.1 Wind Load in X direction From To Elev. Elev. mm Radiant 3000 Radiant 7000 convection 12198 Stack I 17203 Stack II 27203 Stack III 37203
mm 7000 12198 17203 27203 37203 47203
Frontal dimension
Surface considered
mm 4948 19,8 4948 25,7 4900 24,5 1574 15,7 1570 15,7 1566 15,7
Ce
Specific Pressure on portion p(z)
2
1,48 1,62 1,71 1,83 1,93 2 2,39 37,5
Wind Load
kN/m2 KN 1,77 35,0 1,94 49,8 2,05 50,2 2,19 34,4 2,31 36,2
Total Wind X 243,18 KN INPUT SAP DATA Intermediate Portion columns Radiant 1 Radiant 1 Convection 2 Stack I 0 Stack II 0 Stack III 0
UNIT KN/m KN/m KN/m KN/m KN/m KN/m
wind load distributed 4,38 2,19 4,79 2,40 3,34 1,67 3,44 3,62 3,75
wind load distributed ext. Columns
load case WX WX WX WX WX WX
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2.2.6.2 Wind Load in Y direction WIND IN Y DIRECTION From Elev. To Elev. mm mm 3000 7000 7000 12198 12198 17203 17203 27203 27203 37203 37203 47203
Frontal dimension
Surface considered
m m2 4948 19,8 4948 25,7 1453 7,3 1574 15,7 1570 15,7 1566 15,7
Ce
Specific Pressure on stack p(z)
1,48 1,62 1,71 1,83 1,93 2 2,39 37,5 Total Wind Y Weight
Wind Load
kN/m2 KN 1,77 35,0 1,94 49,8 2,05 14,9 2,19 34,4 2,31 36,2
207,89 KN
INPUT SAP DATA Portion Radiant Radiant Convection Stack I Stack II Stack III
Intermediate columns
UNIT
2 2 1 0 0 0
KN/m KN/m KN/m KN/m KN/m KN/m
wind load distributed 2,92 1,46 3,20 1,60 1,49 3,44 3,62 3,75
wind load distributed ext. Columns
load case WY WY WY WY WY WY
2.2.7
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Earthquake Loads calculation (EQX/Y)
Earthquake load according to UBC-97 Sismic Zone Seismic zone factor Z Solid Profile Ca 0,40 Cv 0,56 I 1,25 R 4,5
4 0,4 SC
(*)
Notes According to spec. nr. 00-ZA-E-205001 rev.02 According to table 16-I of UBC-97 According to customer data According to table 16-Q of UBC-97 and for customer request According to table 16-R of UBC-97 and for customer request According to table 16-K “Hazardous facilities for toxic and explosives material” According 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: 3/4 T = C t * (hn ) = 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: C *I* V = v W R* T 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: 2.5 * Ca * I The value of base shear shall not exceed the value VMAX = *W R The value of base shear shall not be less than VMIN = 0.11* Ca * I * W 0,8* ZNv * I For seismic zone 4 the value of base shear shall also not be less than VMIN−Z4 = *W R Following are listed the values calculated for the heater in the different condition of work:
Work condition
Erection Operating Test Operating + 33% Live
Total Total base weight shear Vtot considered KN KN KN KN KN 1680 326 467 92.4 149.3 1748 341 485.6 96.16 155.4 1772 344 492.2 97.5 157.5 1937 379 538 106.5 172.2
VMAX
VMIN V
MIN-Z4
2.2.8
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Stack
2.2.8.1 Loading details Stack – sections JIS SS400 Stack Material 30000 mm Stack total Length Internal Stack Diameter 1550 mm Internal lining diameter 1450 mm
Stack portion I Casing and Refractory Height 10000 External diameter Shell thickness Lateral External surface Casing Weight
mm 1574 mm 12 mm 49,42 m2 4620,2 Kg
46,20 KN
Refractory LWC Refractory D.ty Thickness 50 Overall refractory weight
1400 Kg/m3 mm 3406,9 Kg
34,1 KN
20 Kg/m2 988,5 Kg
9,9 KN
Extra steel-work not modelled Safety margin Unit Weight Overall Extra Steelwork Weight Base skirt / flange weight Total base skirt weight
885,25 Kg
Intermediate stiffening rings weight Number 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
Overall Stack portion weight Overall Steelwork weight distributed along stack span Overall refractory weight distributed along portion span Point skirt weight at stack base
8,85 KN
1,97 KN
100,98 1,19 3,41 8,85
KN KN/m KN/m KN
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Stack portion II Casing and Refractory Height 10000 External diameter Shell thickness Lateral External surface Casing Weight
mm 1570 mm 10 mm 49,30 m2 3845,2 Kg
38,45 KN
Refractory LWC Refractory D.ty Thickness 50 Overall refractory weight
1400 Kg/m3 mm 3406,9 Kg
34,1 KN
20 Kg/m2 986,0 Kg
9,9 KN
Extra steel-work not modelled Safety margin Unit Weight Overall Extra Steelwork Weight Base skirt / flange weight Total base skirt weight
447,05 Kg
Intermediate stiffening rings weight Number 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
Overall Stack portion weight Overall Steelwork weight distributed along stack span Overall refractory weight distributed along portion span Point skirt weight at stack base
4,47 KN
1,96 KN
88,82 1,18 3,41 4,47
KN KN/m KN/m KN
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Stack portion III Casing and Refractory Height 10000 External diameter Shell thickness Lateral External surface Casing Weight
mm 1566 mm 8 mm 49,17 m2 3072,3 Kg
30,72 KN
Refractory LWC Refractory D.ty Thickness 50 Overall refractory weight
1400 Kg/m3 mm 3406,9 Kg
34,1 KN
20 Kg/m2 983,4 Kg
9,8 KN
Extra steel-work not modelled Safety margin Unit Weight Overall Extra Steelwork Weight Base skirt / flange weight Total base skirt weight Fan duct weight Overall Fan duct supporting stiffness weight Overall fan duct steelwork weight Overall refractory weight
443,59 Kg
4,44 KN
0,00 Kg Kg Kg
0,00 KN KN KN
Intermediate stiffening rings weight Number 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
Overall Stack portion weight Overall Steelwork weight distributed along stack span Overall refractory weight distributed along portion span Point skirt weight at stack base
1,96 KN
81,02 1,18 3,41 4,44
KN KN/m KN/m KN
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2.2.8.2 STACK VERIFICATION Stack stress verification are performed in according to API STANDARD 560.
Portion
From Elev.
To Elev.
I 17200 II 27200 III 37200
Stack general dimensions Refractory Shell Shell Outer internal thickness diameter diameter mm mm mm
Internal stack diameter mm
27200 1550 1450 12 1574 10000 A-75x75x9 4 37200 1550 1450 10 1570 10000 A-75x75x9 4 47200 1550 1450 8
1566
Portion height
Stiffness ring profile type
Nr. Of stiffness on span
A-75x75x10
4
mm
10000
Base & connecting flanges dimensions Rectangular stiffness Portion
I II III
Internal Plate diameter
External plate diameter
mm
mm
Lower plate thickness
Upper plate thickness
mm mm 2074 30 25 28 12 270 28 12 270 1890 30 30 1886 30 30
1574 1570 1566
Nr. Of stiffness on plate
Stiffness Height of thickness stiffness mm
Triangular stiffness Nr. Of stiffness on plate
mm
mm
0 0
Stiffness Height of thickness stiffness
30 28
8 8
mm 250 250
Bolts Dimensions Flanges at base of Portion Bolts nominal diameter Bolts number Bolt circle diameter M I 30 II 27 III 24
mm 36 30 28
2060 1662 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 Wind Load Shear Load Moment at uniformly at portion portion Portion Thk. distributed barycentre barycentre along height 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 30,7 3,76 37,64 188,20 37,64 188,20 III 8 1566 10000 Diameter Portion Portion at portion casing height Base weight
Resulting Resulting Shear at moment at portion portion base base
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According to what written in the previous paragraphs, the stack here described has the following characteristics:
Portion Thickness
Corroded Thickness
mm mm I 12 10 II 10 8 III 8 6
Conical / cilindrical Top External Diameter
Portion Length
mm 1574 1570 1566
Lateral Surface
mm m² Kg 10000 49,4 4620,2 10000 49,3 3845,2 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 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
mm
Kg
Casing Weight
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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: Overall Stack Height considered = Young modulus E = Yield stress for the material fy = Lining Thickness = Lining density =
JIS SS400 30 m 200000 N/mm² 235 N/mm² 50 mm 1400 Kg/m³
Overall casing lateral surface Overall Casing weight Overall lining weight Overall extra weight for Equipments appended: Overall extra steelwork, stiffening and flanges weight
147,9 m² 115,38 KN 102,21 KN 0 KN 53,23 KN
Total platform surface considered Overall structural platform weight Live load considered on each platform surface Overall non permanent live load
0 m² 0 KN 2 KN/m² 0 KN
Overall ladder length Overall ladder weight
0m 0 KN
Overall stack permanent weight Overall weight with 33% of live load
270,82 KN 270,82 KN
Maximum resulting shear at stack base Maximum resulting moment at stack base
108,8 KN 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 = Compression plate thickness assumed t5 = Gusset plate thickness assumed t6 = Base plate outer diameter De = Base plate bolt circle diameter Db = Base plate inner diameter Di = Minimum vertical load on base plate Nmin = Maximum vertical load on base plate Nmin = Maximum shear load at stack base Vmax = Maximum resulting moment at stack base Mmax = Number of bolts on base plate nb = Nominal diameter of anchor bolts db = Resistance section of anchor bolts Ares = Safety coefficient on yield stress n= Admissible stress for parts resistance check σadm = Max load on anchor bolts is given by: Nb =(-Nmin/nb)+(4Mmax/Nb*Db) =
30 mm 25 mm 12 mm 2074 mm 2060 mm 1574 mm 270,82 KN 270,82 KN 108,8 KN 1660,08 KNm 36 30 mm 561 mm² 1,5 156,67 N/mm²
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 = distance between stiffening bmax = external width of base plate l = ratio (l/ b)max =
150 mm 300 mm 250 mm 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
Mmax = c2*σb*b2 =
22,82 KNcm
with c1 = 0,0765 by interpolation 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 Where σb 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
Where: lt : overall bearing plate width = 250 mm bhd :bolt hole diameter in bearing plate = 33 mm
THICKNESS t4 ASSUMED VERIFIED
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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)] = Where: Mmax: P: lc : e: g1:
15,95 KNcm
Maximum bending moment acting on compression plate Maximum bolt load calculated above Radial distance from outside of skirt to outer edge of compression plate One-half distance across flats of bolting nuts = 23 mm 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: h: t g: P:
is the width of the gussets (inches) is the height of the gussets (inches) is the thickness of the gussets (inches) 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: P = P pmax −V = 2 2 ⋅ π D pe − D pi Af 4 The uniform load on middle flange diameter due to P mas-V is given by:
()
⎟D pe − D pi ⎟ ⎟ q p max −V = pmax −V ⋅⎟ ⎟ 2 ⎟ ⎟ ⎟ 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: M M Max pmax −W = Max = 2 2 π D pe − D pi ⋅Dcb A f Dcb 2 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: ⎟D pe − D pi ⎟ ⎟ q p max −W = 2 ⋅pmax −W ⋅⎟ ⎟ 2 ⎟ ⎟ ⎟ Where: P: is the maximum vertical load calculated at the base of the section considered Mmax is the maximum moment calculated at the base of the section considered Dpe & Dpi are the Outside and the Inside flange diameters Dcb is the Bolt Circle diameter
()
the worst load combination is given in the position where the two loads add one to the other: qmax = q p max −V + q p max −W With the geometry assumed it follows that the distance between the stiffness on bolt circle diameter is given by: πD bmax = cb − t s Ns
where: ts Ns
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is the thickness of the stiffness 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: 2 qmax ⋅bmax = Mf 8 The stress check of the flange is verified if
σMf = where: tf
Mf ≤ σadm− f 2 bmax ⋅t f 6 is the thickness of the flange (assumed)
In order to check the maximum stress of the stiffness placed on each flange they are calculated 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: 1 1 2 Rmax − s = qmax bmax M max − s = qmax bmax 2 12 From these values it is easy to calculate the maximum shear and bending stresses: 6 τmax − s = Rmax σmax − s = M max 2 hs t s t s hs 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 2 2 σid − s = σmax − s + 3τ max − s ≤ σ adm− f
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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 Stack External portion DIA
Stack Shell Thk
Flange Outside Dia
Flange inside Dia
Flange circular surface
Flange thk
ts
Dpe
Dpi
Af
tf
II 1570
10
1890
1570
869152
30
III 1566
8
1886
1566
867142,4
30
Dext mm mm mm mm mm2 mm
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 Uniform load Max moment at Max on middle section base due pressure on Section diameter due to wind or flange due to to vertical earthquake vertical load load PMax Mmax Pmax-V qpmax-V KN KNm N/mm2 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 Max Vertical load on flange
Max uniform load pressure on on middle flange due diameter due to wind to wind Pmax-W N/mm2
Max uniform load on flange
qpmax-W N/mm
qmax N/mm
Section distance between the stiffness Max Bending moment on flange Max stress on flange Check bmax mm II 189,46 0,51 17,99 III 203,06 0,18 6,07 Max reaction Max moment under stiffness under stiffness Rmax-s Mmax-s KN KNm II 26,98 0,29 3,45 13,49 23,62 OK III 9,10 0,10 1,25 4,55 7,98 OK
Section
Mf KNm
sMf N/mm2 OK OK
Max bending Max shear stress Max ideal stress Check stress on Stiffness on Stiffness on Stiffness smax-s tmax-s sid-s N/mm2 N/mm2 N/mm2
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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 2 τ adm-b = 264 N/mm 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: 4 M max N min − FN − b = nb Dcb nb From this follows that the highest axial stress on bolts is given by: σmax −b = FN − b Ares The maximum shear stress on each bolt is given by: τmax −b = Vmax Ares nb 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 is the maximum bending moment calculated at the base of the section Mmax considered Dcb is the bolt circle diameter nb is the total number of bolts considered on the flange Ares is the resistance section of the bolts considered The bolt are verified if 2 2 σid −b = σmax − b + 3τ max − b ≤ σ adm − b
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The data and the results of the procedure applied to each intermediate flange are following listed:
Section
Stack Ext. Dia.
Stack Shell thk.
Dext ts mm mm 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
Nr. of bolts on interm. flange
Bolt Bolt hole dia. Bolt Bolt resistance circle dia. on flange nominal Dia. section
Nb mm
Max moment at section base due to wind or earthquake
PMin VMax Mmax KN KN KNm II 169,8 74,0 746,2 54,2 118,1 5,4 118,5 III 81,0 37,6 188,2 13,3 37,6 3,8 38,2 OK
Db mm
db mm
M 0
Ares mm2
Max axial load on worst stressed bolt
Max axial stress on bolts
Max shear stress on bolts
Max ideal Check stress on bolts
FN-b KN
smax-b N/mm2
tmax-b N/mm2
sid-b N/mm2 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) External Wall thickness Portion A W corroded corroded diameter 3 mm mm cm² cm cm I 10 1570 493 19.359 II 8 1566 394 15.409 III 6 1562 294 11.497
I 4
1.519.703 1.206.494 897.954
Corroded casing weight KN 38,70 30,88 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 calculation of each section considered with thickness corroded
Portion
From Elevation
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To Elevation
Max Vertical Load at portion base (N)
mm mm KN KNm I 17200 27200 271 1.660 9,124 16,20 II 27200 37200 170 746 5,275 12,99 III 37200 47200 81
Max Moment at portion base (Mmax)
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Stress Calculated at base portion
σadm-2
cm4
KN/cm2
188 1,912 9,77
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 Vc2 = 6*Vc1 = 49,71 m/s
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ACCEPTABLE WITH STRAKES ACCEPTABLE
XX
Check
VERIFIED VERIFIED VERIFIED
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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)
Portion
From Elevation
To Elevation
Internal Diameter
Shell Thickness corroded
Stiffening Spacing
fr fv
fr/2fv Check
mm mm mm mm m I 17200 27200 1.550 10 2,00
10,3372,60
RINGS NOT
1,99 REQUIRED
RINGS NOT
II 27200 37200 1.550 8 2,00 8,269
2,60 1,59 REQUIRED
III 37200 47200 1.550 6 2,00 6,202
2,60 1,19 REQUIRED
RINGS NOT
2.3
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LOADING COMBINATIONS
2.3.1 Main Loads The 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*EQY CB10E = 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*EQX CB20E = 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*EQX CB7O = 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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Frame Profiles - Radiant body
C-150x75
A-75x6
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2A-90x10
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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 5.1
BASE PLATE AND ANCHOR BOLTS CHECK 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 the value 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). M e= N 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: a : eccentricity internal to the kernel of inertia 6 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: σc = N + M Ac Wc 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 : σc ≤ 0,44 * Rck where Rck is the cubic admissible resistance of the concrete considered. e≤
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 stiffeners:
σc x
=
σs xs
⇒ σs =
σc x a s 2
where assuming the neutral axis passing from the middle of the section: σs xs
is the value of sigma at stiffeners level is the distance between stiffeners and neutral axis
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Condition 2 for calculation of maximum stress on plinth: e>
a : eccentricity 6
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: b 3 + bd 2 + x x nAf (d + h) x − nAf h(d + h) = 0 6 2 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: N *x
σc =
2
b
x − nAf (h − x) 2
The stress of the maximum compression on plinth is verified if : σc ≤ 0,44 * Rck 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:
σc x
=
σs xs
⇒ σs =
σc x
xs
where (ref. to picture 1): σs is the value of sigma at stiffness level is the distance between stiffness and neutral axis xs = x- m1
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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: σ + σs q = m1* c 2 The maximum momentum given by this kind of restraint is: 2 2 q * l 2 − q * m2 = M Max 8 2 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:
σp = M Max = W
M Max ⎟m1 * thk 2 ⎟ ⎟ ⎟ ⎟ 6 ⎟ ⎟ ⎟
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.
5.1.2
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Stress check on Base Plates A – B – C – D – E – F
Plinth
Comb.
Fn
F1
F2
M1
M2
F
CB7O
KN 950,4
KN 60,7
KN -15,1
KNm 5,8
KNm 25,4
Yield Stress of the material JIS SS400 = Admissible stress of the base plate material = Cement Plinth cubic resistance Rck = Admissible stress on cement plinth = Base Plate thickness assumed = Considered 8 bolts M30
235 N/mm² 235 / 1,5 = 156,67 N/mm² 21 N/mm² 21 * 0,44 = 9,24 N/mm² 35 mm
Action dominant
M1 M2
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Plate dimension parallel to Moment (b) mm 500 500
Plate dimension perpendicular to Moment (a)
Plinth section (Ac)
mm 500 500
mm² 250000 250000
Distance Distance Total of between Nr. of bolts resistance normal bolts Action strengthen section of force strengthen dominant on last row bolts from and plate (nb) strengthen edge edge (Af) (d) (h)
M1 M2
Action dominant
M1 M2
Action dominant
M1 M2
mm 0 0
mm 3 3
Compression Stress on Plinth (σc) N/mm² 0,28 1,22
mm² 1683 1683
Plinth stress check
Sigma-c CLS OK Sigma-c CLS OK
mm 425 425 Sigma on stiffeness for proportion (σf) N/mm² 2,37 2,12
Plinth Elastic modulus (Wc) mm³ 20833333 20833333
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Eccentricity (e)
eccentricity case
mm 6,12 26,71
Case 1: e
Distance between Neutral axis and plate edge (x)
Distance between stiffness perp. to moment (l2)
mm 0 0
mm 200 176
uniform load on plate portion (q) N/mm 529,47 556,44
Distance Distance between between stiffness stiffness and plate and plate edge edge parallel perp. to to moment moment (m2) (l1) mm mm 138 150 150 138
Maximum moment on plate portion (Μmax) Nmm 3906450,71 2516204,32
Sigma on base plate for Moment Sigma resultant from both moment effect (σp) action (σmax)
N/mm² 138,65 82,16
XX
Resistance module with respect to the moment (Wp) mm³ 28175,00 30625,00
Plate stress check
N/mm² 138,65
Plate check OK
5.2 5.2.1
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ANCHOR BOLTS CHECK 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 the following equations have been considered: Axial load on bolt due to Fn (in strength condition) f t − Fn = Axial load due to moment in X direction
f t − Mx =
Axial load due to moment in Y direction
ft −M y =
Overall axial load on bolt Overall Shear Load Shear Load Acting on each bolt: Required Shear stress on each bolt: Where: nb : Ab : ymax / xmax: yi / xi: nbx / nby:
Fn
()nb ⋅Ab M x * ymax 2 nbx * Ab * ∑yi M y * xmax
2 nby * Ab * ∑xi f nt = f t − Fn + f t − Mx + f t − My
2 2 Vtot = Vx + V y
V Vb = tot nb V f nv = b Ab
overall number of bolts Resistance section of each bolt Distance between the plate edge and the farest bolt line parallel to x / y axis Distance between the plate edge and each bolt line parallel to x / y axis 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-350-05 Specified minimum tensile strength of the type of steel being used F u = 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 For tensile stress check the values are: Ra = fnt * Ab ' ' is the nominal tensile stress modified to include the effects of shearing stress Fn = Fnt calculated with the equation: F = Fnt ' nt
Ωf nv 1− Fnv
2
'
For combined tension and shear actions it has to be: Ra ≤ Rn = Fn Ab Ω Ω Where: Ra : is the required strength (ASD) is nominal strength Rn Ω=2 is the safety factor (ASD)
Total bolt number Nominal bolt diameter Section resistance Specified minimum tensile strength of the type of steel being used Fu = Nominal tensile Stress acc. AISC 350 cap.J Fnt =0,75*Fu Nominal shear Stress acc. AISC 350 cap.J Fnv =0,4*Fu
8 30 561 mm² 400 N/mm² 300 N/mm² 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 Combination with Max vertical load at base Combination with Min vertical load at base Combination with Max moment Mx at base Combination with Min moment Mx at base Combination with Max moment My at base Combination with Min moment My at base Combination with Max resulting shear at base
Required tensile stress on each bolt ft
Max Fz Min Fz Max Mx Min Mx Max My Min My Max shear
F CB7O C CB11O A CB15OT D CB21OT
FN KN
FX FY MX MY Max base shear KN KN KN-m KN-m KN 60,7 -15,1 5,8 25,4 62,5 51,3 4,8 -1,8 24,8 51,6
950,4 -438,9 545,9 -8,5 -44,2 660,4 24,0 43,1
25,5
-6,7 45,0 9,8 49,3
-24,7 F CB15OT 840,3 68,3 -14,4 840,3 32,7 C CB14OT 724,7 -47,7 3,6 -1,4 -27,5 F CB19OT860,39 71,70 -15,21 5,87 32,25
Overall shear load on plinth Vtot
Required shear sterss on each bolt fnv
N/mm² KN N/mm² N/mm² N/mm² Plinth Combo 31,7 62,5 13,9 295,4 17771,4 F CB7O 124,8 51,6 11,5 296,9 70001,7 C CB11O 32,8 45,0 10,0 297,6 18373,5 A CB15OT 35,0 49,3 11,0 297,2 19636,2 D CB21OT 38,8 69,8 15,6 294,3 21787,6 F CB15OT 29,4 47,8 10,6 297,3 16487,3 C CB14OT 38,7 73,3 16,3 293,7 21709,6 F CB19OT
nominal tensile stress modified to include the effects of shearing stress F'nt
required strength Ra
69,8 47,8 73,30
nominal strength check Rn/Ω
N/mm² 82865,5 83278,0 83485,9 83353,0 82544,4 83401,1 82377,9
OK OK OK OK OK OK OK
6 6.1
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6.2 DISPLACEMENTS CHECKING 6.2.1 Max Horizontal Joint displacement Maximum horizontal displacement: Column height: 5005 Load Combination: CB6E Joint : 803
7.56 mm
Allowable displacement checking for column height: h0/500 = 5050/500 = 10.01 mm > 7.56 OK
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Max deflection of beam Maximum deflection : Beam Span (L): Load Combination: Beam number :
-6.63 mm 1800 CB10 572
Allowable deflection checking: L/250 = 1500/250 = 7.2 mm > 6.63 OK
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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.
6.3.2
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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 1456 A-75X6 Beam CB1OT 0,965219 0,161650 112 H-200X200 Column CB3O 0,953768 0,756447 0,196224 0,001097 600 A-75X6 Beam CB14OT 0,953275 0,165027 604 A-75X6 Beam CB5O 0,943607 0,084699 624 A-75X6 Beam CB15OT 0,942381 0,132440 1401 A-75X6 Beam CB15OT 0,937742 0,202521 1493 A-75X6 Beam CB16OT 0,937390 0,204937 421 C-150+A-90 Beam CB16OT 0,935003 0,035953 0,505647 0,393404 1478 A-75X6 Beam CB1OT 0,929110 0,147188 571 2A-90X10 Column CB5O 0,926956 0,358888 418 2A-75X9 Brace CB15OT 0,925765 0,034595 1480 A-75X6 Beam CB1OT 0,924432 0,147620 580 A-75X6 Beam CB14OT 0,923496 0,147784 649 A-75X6 Beam CB1OT 0,919039 0,033808 53 H-200X200 Column CB17OT 0,917472 0,472758 374 A-75X6 Beam CB1E 0,912147 0,042444 648 A-75X6 Beam CB1OT 0,909268 0,030118 182 H-200X200 Beam CB2T 0,908771 0,047580 0,860007 0,001183 1483 A-75X6 Beam CB14OT 0,908534 0,211617 256 H-200X200 Beam CB2T 0,903900 0,046547 0,856190 0,001163 1499 A-75X6 Beam CB14OT 0,901629 0,195460 426 C-150+A-90 Beam CB1OT 0,897453 0,047167 0,332158 0,518128 55 H-200X200 Column CB2T 0,896269 0,674066 1454 A-75X6 Beam CB14OT 0,894490 0,121424 1462 A-75X6 Beam CB1OT 0,892025 0,127468 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 281 H-200X200 Beam CB3O 0,887922 0,043468 0,843420 0,001034 1430 A-75X6 Beam CB16OT 0,887220 0,102739 1489 A-75X6 Beam CB14OT 0,877898 0,107826 877 2A-75X9 Brace CB1OT 0,875967 0,288793 59 H-200X200 Column CB16OT 0,875616 0,461270 428 C-150+A-90 Beam CB1OT 0,872844 0,030797 0,347071 0,494976 57 H-200X200 Column CB14OT 0,872463 0,392222 1292 C-150X75 Beam CB2T 0,869653 0,047048 0,000246 0,822358 1473 A-75X6 Beam CB1OT 0,863535 0,115522 583 A-75X6 Beam CB14OT 0,861647 0,116420 1477 A-75X6 Beam CB14OT 0,861397 0,207367 1465 A-75X6 Beam CB17OT 0,860271 0,193673 378 A-75X6 Beam CB1OT 0,859413 0,024454 1437 A-75X6 Beam CB15OT 0,858939 0,181300 1466 A-75X6 Beam CB16OT 0,857086 0,087812 552 2A-90X10 Column CB16O 0,855683 0,325467 605 A-75X6 Beam CB2O 0,854839 0,050546 1270 C-150X75 Beam CB2T 0,854775 0,046878 0,000204 0,807693 623 A-75X6 Beam CB14OT 0,851941 0,132159
0,080941 0,855752 0,254303 0,549266 0,358192 0,288275 0,242276 0,308597 0,291222
0,430056 0,570633 0,567665 0,426625 0,441231
0,250400 0,531521 0,361460 0,206608 0,442762 0,448408 0,255147 0,521665 0,275288 0,500425 0,064643 0,820587 0,222467 0,222247 0,066102 0,803601 0,018807 0,860343 0,303369
0,393549
0,294025
0,412145
0,220158 0,002045 0,216681 0,556385 0,236725 0,527831
0,261598
0,129791
0,223223 0,561258 0,246853 0,523218 0,184038 0,403136 0,245492 0,168855 0,218124 0,262117 0,262514 0,485499 0,225185 0,520041 0,287349 0,366681 0,160535 0,506063 0,026175 0,808784 0,169390 0,508248 0,268493 0,500780 0,529317 0,000900 0,194234 0,610059 0,203057
0,516725
XX
