STRUCTURAL VERIFICATION OF A 60.7 M DOME ROOF FOR TANK FB 2110

Transcription

1 CTS Netherlands B.V. Riga LW Barendrecht The Netherlands Tel.: +31 (0) (office) Fax: +31 (0) (office) Website: Chamber of commerce ING Bank BIC (Swift): INGBNL2A IBAN : NL70 INGB VAT: NL B01 STRUCTURAL VERIFICATION OF A 60.7 M DOME ROOF FOR TANK FB 2110 MG technical solutions Noordkade EZ Waddinxveen The Netherlands tel +31 (0) fax +31 (0) Report R16050_FB2110 Revision Date Description Author Checked: 0 4 Augustus 2016 First edition ir. M. Bakker CTS is ISO 9001 and SHE system (VCA**) certified by Lloyd s Register

2 Content Summary... 3 General data... 4 Design life and consequence class... 4 Materials... 4 Wind class... 4 Characteristic values of actions... 4 Dead Load... 4 Live Load... 4 Internal vacuum... 5 Internal pressure... 5 Water accumulation... 5 Snow loads... 5 Wind loads... 6 Load combinations... 7 Structural analysis... 7 Conversion factors... 7 Critical strut selection... 8 Forces and moments according to Eurocode... 8 Classification of cross-sections... 8 Local buckling resistance... 9 Resistance of cross-sections Flexural buckling resistance Lateral torsional buckling resistance Combined buckling criterion Conclusion Appendix A

3 Summary This report discusses the structural analysis of an aluminium dome roof for tank FB 2110 with diameter 60,7 m. The analysis is carried out according to the following applicable Eurocodes with Dutch national appendices: EN 1990: EN : EN : EN : EN : Basis of structural design Densities, self-weight, imposed loads for buildings General actions - Snow loads General actions - Wind actions Design of aluminium structures General structural rules The goal is to translate the current dome calculations prepared according to the American code API 650 to the European Eurocode standards listed above in order to ease interpretation for classification societies. The analyses in this report are solely based on data presented in CST project No , attached in Appendix A. It is concluded that all struts in the aluminium dome roof for tank FB 2110 with diameter 60,7 m, specified in Appendix A, comply with the conditions and criteria set out in the Eurocode EN 1990, 1991, and

4 General data Design life and consequence class The dome roof is classified to have an indicative design working life of 50 years according to design working life category 3 in Table 2.1 of EN Furthermore, the dome roof is categorised under consequence class CC1 according to Table B1 of EN The accompanying partial safety factors according to Table NB.5 of NEN EN 1990 NB are: =1.20 max (0.90 where unfavourable) combined with, =1.10 max (0.90 where unfavourable) combined with and, =1.35 max (0.00 where unfavourable) Materials The dome roof is made of aluminium 6061-T6 with properties according to Table 3.2b of EN , which are: 6061-T6 Density [kg/m 3 ] 2700 Young s modulus [MPa] Poisson s ratio [-] 0.33 Yield stress [MPa] 240 Buckling class [-] class A Partial safety factor [-] 1.10 Partial safety factor [-] 1.25 table 1: Material properties Wind class The dome roof will be installed in Amsterdam, The Netherlands. This site is located in wind area I according to Figure NB.1 of NEN EN Characteristic values of actions The following actions are taken into account for the dome roof analysis. Loads acting downward are taken positive, loads acting upwards are taken negative. Dead Load The total dead load is equal to (Appendix A, page 4): = kn/m 2 Live Load The dome roof is classified under category H: roofs according to Table 6.9 of NEN EN According to Table 6.10 and Appendix A, page 4 the associated total live load is equal to: The accompanying factors for category H buildings are: = kn/m 2 =0, =0, =0 4

5 Internal vacuum There is no internal vacuum applied to the tank. Internal pressure There is no internal pressure applied to the tank. Water accumulation Water accumulation is not a factor due to the slope of the dome roof. Snow loads The snow loads are computed according to EN , which states: = with = 1 is the exposure coefficient, = 1 is the thermal coefficient. Parameter is the characteristic value of snow load on the ground. According to NEN EN NB paragraph 4.1 all sites in The Netherlands should use a value of = 0.7 kn/m 2. As stated by EN the shape coefficient for cylindrical roofs are given in the following expressions: >60 =0 60 = h/ with =2.0 These expressions and associated parameters are visualised in Figure 5.5 and 5.6 from EN as shown below. The maximum roof inclination angle is given by the cut-off angle 1 2 = 3.6 in Appendix A, page 4. With a dome rise h = 3 = m and an anchor bolt diameter = = m, both taken from Appendix A, page 4, it is found that: = As shown in the figure above it is required to consider two cases: the undrafted load arrangement (case i) and the drifted load arrangement (case ii). These cases result in: Case i: =0.8 = Case ii: 0.5 = = = = A conservative estimate of the average load for the full roof surface area is given by the maximum of either or. /2, given by: = =max,. = kn m2 2 According to NEN EN 1990 NB the accompanying factors for snow loads concerning category H buildings are: =0, =0.20, =0 5

6 Wind loads The wind loads are computed according to EN The expression for the wind load is: = where is the peak velocity pressure as a function of the dome roof height. The current dome roof height is equal to =29,6 m. Interpolation in Table NB.5 of NEN EN NB for wind area I, without buildings provides a peak velocity pressure of: = 1.42 kn/m 2 The dome roof does not have a dominant size and is fully closed, i.e. there are no openings. Therefore, the internal pressure coefficient should be taken equal to: = 0.20 The external pressure coefficient will be determined by means of Figure 7.12 of EN , given below. With a dome rise = 3 = m, a diameter = 4 / = m, and a tank height of h = = 29.6 m the following ratios are obtained:, = 0.99, h/ = Linear interpolation of these ratios in the figure above results in the following external pressure coefficients for locations A, B, and C: Substituting these values into the expression for gives: = -0.96, = , = = cos 1 2 = cos 1 2 = kn/m 2 = = = kn/m 2 = cos 1 2 = cos 1 2 = kn/m 2 where cos transforms the normal pressures to vertical pressure components. For locations A and C the angle corresponds to the cut-off angle in Appendix A, page 4. For location B the normal pressure is already directed vertically, giving a zero angle, resulting in cos 0 =1. For the analysis, the following average wind load will be used: = = kn/m 2 6

7 According to NEN EN 1990 NB the accompanying factors for category H buildings are: =0, =0.20, =0 Load combinations In the previous section the following actions have been determined (downward positive, upward negative): Value [kn/m 2 ] Dead load total Live load total Internal vacuum 0 Internal pressure -0 Snow load Wind load table 2: Characteristic values of actions Given these actions, three load combinations will be considered: 1 = 1.2 = 0.17 kn/m 2 2 = = 1.19 kn/m 2 3 = = kn/m 2 Load combination ULS2 is the critical downward combination and ULS3 is the critical upward combination. Please note that the internal vacuum and internal pressure loads are multiplied by a ratio of 0.4, which is the ratio between normal operating pressure and design pressure of the American code API 650. Not applying this ratio factor would result in double built-in conservatism, both from the American as well as the European code. Structural analysis The structural analysis of the dome roof, as presented in Appendix A, is executed by the TEMCOR computational software. Both the input load combinations as well as the resulting stresses can be found in Appendix A. In this report no check will performed on the correctness of input or output data in Appendix A. It is assumed that the dome plate material attachment to the struts is strong enough, such that buckling about the minor axis is prevented and that the compressed upper flanges are not sensitive to lateral torsional buckling. Conversion factors The critical downward and upward load combinations in Appendix A are: Case 2: Dome dead load + dome live load = 0.86 kn/m 2 Case 4: Dead + ASCE wind case A = kn/m 2 According to the Eurocode the critical downward and upward load combinations (from the previous section) are: ULS2: 1.19 kn/m 2 ULS3: kn/m 2 This means that the output forces and moments for the critical downward and upward load cases from Appendix A need to be multiplied by the following conversion factors in order to correspond to the load combinations stated by the Eurocode:. 0,12 = , =

8 Critical strut selection With the conversion factors known, the next step is to make a selection of critical struts from the consolidated stress summary in Appendix A. The consolidated stress summary contains the most critical load case for each strut group. Further selection is based on: 1. the combined stress ratio 2. presence of compressive forces and consequently sensitive to buckling 3. the cross-sectional strut type dimensions 4. the strut group length Not every strut type is necessarily considered. For example, if it is clear that the most critical force and moment for strut type E-123 are equal or lower than that of strut type E-456, when at the same time cross-sectional thicknesses of strut type E-456 are larger, or the length is lower, than it is obvious that the latter strut is less critical. Based on the above selection criteria, the following struts are selected from Appendix A: Strut type and group Length [mm] Critical load case E-609 # Case 2: Dome dead load + dome live load E-614 # Case 2: Dome dead load + dome live load COMP01 # Case 4: Dead + ASCE wind case A table 3: Strut selection Forces and moments according to Eurocode Subsequently, the forces and moments for these strut groups will be multiplied by their corresponding factors determined above, resulting in the following forces (compression positive) and moments. Strut type and group [kn] [knm] E-609 # E-614 # COMP01 # table 4: Strut forces and moments according to Eurocode These forces and moments will then be tested according to EN Classification of cross-sections The role of cross-section classification is to identify the extent to which the resistance and rotation capacity of cross-sections is limited by its local buckling resistance. The classification of parts of cross-sections is linked to the values of the slenderness parameter as follows for beams: : class 1 < : class 2 < : class 3 : class 4 Parameters for internal (I) and external (SO) parts, as illustrated below, are: Internal parts: = , = 16 = 16.33, = 22 = External parts: = 3 = 3.062, = 4.5 = 4.593, = 6 = with = 250/ = 1.021, and = 240 MPa. The above values for are valid for class A material without welds. 8

9 Using the parameters in the figure above the values for can be derived as follows: Pure compression: Pure bending: Internal parts: = / External parts: = / Internal parts: =0.4 / External parts: = / Given the fact that the beam loads in the dome roof are dominated by compression, rather than bending, is conservatively taken as: Internal parts: = / External parts: = / Based on the cross-sectional dimensions given in Appendix A, the struts considered obtain the following classification: Strut type and group Class for Class for Class for E-609 # E-614 # COMP01 # table 5: Classification of parts of cross-sections Local buckling resistance Local buckling in class 4 members is generally allowed for by replacing the true section by an effective section. The effective section is obtained by employing a local buckling factor to factor down the thickness. is applied to any uniform thickness class 4 part that is wholly or partly in compression. The factor is given by the expressions below, separately for different parts of the section, in terms of the ratio /, where and are defined above and the constants and are: Internal parts: =32, =220 External parts: =10, =24 The above values for and are valid for class A material without welds. Based on the cross-sectional dimensions given in Appendix A, the struts considered obtain the following local buckling factors: Strut type and group for for for E-609 # E-614 # COMP01 # table 6: Local buckling factors Applying the local buckling factors to the cross-sectional properties in Appendix A results into the following reduced cross-sectional properties: 9

10 Strut type and group E-609 #7 E-614 #29 COMP01 #30 Effective area [mm] Effective x-axis MOI [mm 4 ] Effective section modulus 1, [mm 3 ] Effective section modulus 2, [mm 3 ] table 7: Reduced cross-sectional properties Resistance of cross-sections For compression and bending the following design resistances are defined for class 4 cross-sections: = / =, / where and are given in table 1. These equations result in the following design resistances for the struts considered: Strut type and group E-609 #7 E-614 #29 COMP01 #30 [kn] [knm] table 8: Design resistances Flexural buckling resistance Members in compression are prone to flexural buckling. The flexural buckling reduction factor can be computed by the following expression: where: 1 =, but <1.0 + = with =.0.2, = 0,1 for class A materials = with = /, is the strut length Based on the cross-sectional dimensions given in Appendix A, reduced cross-sectional properties given in table 7, strut lengths given in table 3, and material properties given in table 1, the struts considered obtain the following flexural buckling reduction factors: Strut type and group E-609 # E-614 # COMP01 # table 9: Flexural buckling reduction factors Lateral torsional buckling resistance Members is bending are prone to lateral torsional buckling. The lateral torsional buckling reduction factor can be computed by the following expression: 1 =, but <1.0 + where: = , + with =.0.2,, = 0.4 for class 3 and 4 cross-sections =, 10

11 with: = / and = , = and =,, = where h is the section depth, is the flange width, is the flange thickness, and is the web thickness, all to be found in Appendix A. Based on these and other cross-sectional dimensions given in Appendix A, reduced cross-sectional properties given in table 7, strut lengths given in table 3, and material properties given in table 1, the struts considered obtain the following lateral torsional buckling reduction factors: Strut type and group E-609 # E-614 # COMP01 # table 10: Lateral torsional buckling reduction factors Combined buckling criterion The buckling criterion for members in compression and bending is given by: where = 0.8 and 0 = = 1 for beam-columns without localized welds and with equal end moments. Based on the applied forces and moments and given in table 4, the design resistances and given in table 8, and the buckling reduction factors given in table 9 and table 10 the struts considered show the following buckling criterion results: Strut type and group Buckling criterion E-609 # E-614 # COMP01 # table 11: Buckling criterion results of struts All struts satisfy the buckling criterion as for all struts it is smaller than Conclusion It is concluded that all struts in the aluminium dome roof for tank FB 2110 with diameter 60.7 m, specified in Appendix A, comply with the conditions and criteria set out in the Eurocode EN 1990, 1991, and

12 Appendix A 12

13 Phone: (713) Fax: (936) N Loop 336 E Conroe, Texas USA STRUCTURAL ANALYSIS AND DESIGN SUMMARY CST COVERS ALUMINUM DOME FOR (1) 60.7m I.D. TANK FB 2110 AMSTERDAM, THE NETHERLANDS (CST COVERS JOB No ) ENGR: MWS CHCKD: FEA DATE: JUL. 27, 2016 PAGES: 1 THROUGH: 71

14 NOTATION f = Maximum member stress. F = Member allowable stress. F-X,F-Y,F-Z = Reaction forces acting in the indicated direction, in the global or local coordinate system. C-s = Roof slope factor. P-s = Sloped roof snow load. P-f = Flat roof snow load. K-z = Velocity pressure exposure coefficient. Q-z = Velocity pressure. G-h = Gust response factor. Y-BAR = Distance from the bottom flange to the neutral axis Rv = Maximum vertical (downward) reaction at the shoe. Rd = Maximum lateral reaction at the shoe. Rl = Maximum vertical (upward) reaction at the shoe. Sheet No. 2

15 ANALYSIS PROCEDURE This structure was analyzed on CST Covers proprietary dome analysis program using the stiffness method of analysis. The dome struts are modeled using three dimensional beam elements which consider torsion, bending about two axes, axial and shear deformation. Panel loads are transformed into triangular beam loads equal to the load times one third the adjacent panel area normal to the load. These beam loads are then transformed into components parallel and perpendicular to the plane of the beam web. Member dead load is applied as a uniform beam load along the length of the member using the strut area times the density of the specified material times a factor which accounts for the batten. Panel dead load is treated as another panel load. In addition to the beam loads, loads may be applied to the nodes if required. The program will handle multiple load combinations with each combination composed of multiple load types. The maximum member stresses have been calculated from individual member equilibrium equations using the member end forces obtained from the stiffness analysis procedure and the applied beam loads. Each beam is divided into 20 increments and forces and corresponding stress are calculated for each increment. Member allowable stresses are also calculated at each increment and compared to the computed stresses. Allowable stresses are computed in accordance with the formulas specified by the "Specifications for Aluminum Structures - Allowable Stress Design" (Sixth Edition, October 1994) as published by the Aluminum Association, Inc., Washington, D.C.. All the dome frame struts, tension ring and gussets are aluminum alloy 6061-T6 unless otherwise noted. All fasteners are either aluminum or stainless steel as specified. Sheet No. 3

16 DESIGN PARAMETER DESIGN LOADS REF. POINT DIAMETER : meters (D r ) ANCHOR BOLT DIAMETER : meters (D a ) DOME RISE : meters (H) CUTOFF ANGLE : degrees ( b ) SPHERICAL RADIUS : meters (R) NUMBER OF DOME SHOES : 36 DESIGN CODE : API TH ED. DEAD LOAD : kpa LIVE LOAD : kpa SNOW LOAD : kpa WIND LOAD : KPH WIND EXPOSURE : C In addition to the applied loads listed above, seismic effects have also been considered in the structural analysis. The degree to which seismic effects have an impact upon a structure's design depends most significantly on the structure's density. Due to the low mass to volume ratio of the aluminum dome, seismic effects do not control the dome design, nor the base shear reactions. Rather, applied wind loading on the large surface area on the dome results in the largest horizontal shear reactions. Therefore, wind load cases are presented in these Design Calculations. Other applied load cases and load combinations have been considered in the design; however, only the controlling load combinations are included in the following Design Calculations. Sheet No. 4

17 Sheet No. 5

18 EXTRUSION SECTION PROPERTIES E-609 : DOME STRUT #1 THROUGH DOME STRUT #26 DOME STRUT #28 1. GEOMETRIC PROPERTIES CROSS SECTIONAL AREA = mm 2 Y-BAR = mm DEPTH = mm TOP FLANGE DIMENSIONS = 4.3 X (mm) BOT FLANGE DIMENSIONS = 4.0 X (mm) WEB DIMENSIONS = X 2.8 (mm) 2. ELASTIC PROPERTIES TORSIONAL MOMENT OF INERTIA = mm 4 Y AXIS MOMENT OF INERTIA = mm 4 X AXIS MOMENT OF INERTIA = mm 4 Sheet No. 6

19 E-638 : DOME STRUT #27 1. GEOMETRIC PROPERTIES EXTRUSION SECTION PROPERTIES CROSS SECTIONAL AREA = mm 2 Y-BAR = mm DEPTH = mm TOP FLANGE DIMENSIONS = 6.0 X (mm) BOT FLANGE DIMENSIONS = 6.0 X (mm) WEB DIMENSIONS = X 3.8 (mm) 2. ELASTIC PROPERTIES TORSIONAL MOMENT OF INERTIA = mm 4 Y AXIS MOMENT OF INERTIA = mm 4 X AXIS MOMENT OF INERTIA = mm 4 Sheet No. 7

20 E-614 : PERIM DIAG #29 1. GEOMETRIC PROPERTIES EXTRUSION SECTION PROPERTIES CROSS SECTIONAL AREA = mm 2 Y-BAR = mm DEPTH = mm TOP FLANGE DIMENSIONS = 7.9 X (mm) BOT FLANGE DIMENSIONS = 7.9 X (mm) WEB DIMENSIONS = X 7.9 (mm) 2. ELASTIC PROPERTIES TORSIONAL MOMENT OF INERTIA = mm 4 Y AXIS MOMENT OF INERTIA = mm 4 X AXIS MOMENT OF INERTIA = mm 4 Sheet No. 8

21 COMP01 : TENS STRUT #30 EXTRUSION SECTION PROPERTIES 1. GEOMETRIC PROPERTIES I SECTION T SECTION CROSS SECTIONAL AREA = mm 2 Y-BAR = mm 74.2 mm DEPTH = mm 88.9 mm TOP FLANGE DIMENSIONS = 12.7 X (mm) 12.7 X (mm) BOT FLANGE DIMENSIONS = 12.7 X (mm) WEB DIMENSIONS = X 7.9 (mm) 76.2 X 7.9 (mm) 2. ELASTIC PROPERTIES TORSIONAL MOMENT OF INERTIA = mm 4 Y AXIS MOMENT OF INERTIA = mm 4 X AXIS MOMENT OF INERTIA = mm 4 AREA OF COMPOSITE SECTION = mm^2 Y-BAR OF COMPOSITE SECTION = mm^2 Sheet No. 9

22 E-705 : SHOE STRUT #31 1. GEOMETRIC PROPERTIES EXTRUSION SECTION PROPERTIES CROSS SECTIONAL AREA = mm 2 Y-BAR = mm DEPTH = mm TOP FLANGE DIMENSIONS = 12.7 X (mm) BOT FLANGE DIMENSIONS = 12.7 X (mm) WEB DIMENSIONS = X 7.9 (mm) 2. ELASTIC PROPERTIES TORSIONAL MOMENT OF INERTIA = mm 4 Y AXIS MOMENT OF INERTIA = mm 4 X AXIS MOMENT OF INERTIA = mm 4 Sheet No. 10

23 FASTENER INFORMATION NOMINAL BODY TENSION SHEAR FASTENER TYPE SIZE(mm) DIA (mm) (kn) (kn) STANDARD 300 series CW stainless steel OD PITCH (690 MPa minimum Ftu) BOLTS (Ft = MPa) (Fv = MPa) AND (586 MPa minimum Ftu) (Ft = MPa) NUTS (Fv = MPa) stainless steel (C6LBHS-U12/3LC-F12) LOCK 316 stainless steel (C6LB316-U12/3LC-F12) BOLTS 7075-T73 aluminum (C6LB-E12/3LC-F12) DRIVE RIVETS Aluminum body SPECIAL Pin FASTENER MAGNA-TITE Aluminum body Pin NOTES: 1. Shear strengths are based on the threads outside of the shear plane 2. Lockbolt values are based on the manufacturers guaranteed minimum values. 3. Safety factors are: = 2.34 for bolt tension = 2.34 for bolt shear Sheet No. 11

24 BASIC LOAD CASE NO. 1 DOME DEAD LOAD X Y Z DIRECTION DIRECTION DIRECTION FRACTION OF GRAVITY PANEL DEAD LOAD (kpa) FULL DOME LIVE LOAD (kpa) HALF DOME LIVE LOAD (kpa) GROUND SNOW LOAD - TOTAL DOME = (kpa) GROUND SNOW LOAD - DRIFT = (kpa) WIND LOAD - DYNAMIC PRESSURE = (kpa) INTERNAL PRESSURE LOAD = (kpa) TEMPERATURE CHANGE - TOP FLANGE = (Deg. C.) TEMPERATURE CHANGE - BTM FLANGE = (Deg. C.) ALLOWABLE STRESS FACTOR Sheet No. 12

25 BASIC LOAD CASE NO. 2 DOME DEAD LOAD + DOME LIVE LOAD KPA LIVE LOAD ON DOME X Y Z DIRECTION DIRECTION DIRECTION FRACTION OF GRAVITY PANEL DEAD LOAD (kpa) FULL DOME LIVE LOAD (kpa) HALF DOME LIVE LOAD (kpa) GROUND SNOW LOAD - TOTAL DOME = (kpa) GROUND SNOW LOAD - DRIFT = (kpa) WIND LOAD - DYNAMIC PRESSURE (kpa) INTERNAL PRESSURE LOAD = (kpa) TEMPERATURE CHANGE - TOP FLANGE = (Deg. C.) TEMPERATURE CHANGE - BTM FLANGE = (Deg. C.) ALLOWABLE STRESS FACTOR Sheet No. 13

26 BASIC LOAD CASE NO. 3 DOME DEAD LOAD + DOME UNBALANCED LIVE LOAD KPA LIVE LOAD ON DOME X Y Z DIRECTION DIRECTION DIRECTION FRACTION OF GRAVITY PANEL DEAD LOAD (kpa) FULL DOME LIVE LOAD (kpa) HALF DOME LIVE 90.0 DEG (kpa) GROUND SNOW LOAD - TOTAL DOME = (kpa) GROUND SNOW LOAD - DRIFT = (kpa) WIND LOAD - DYNAMIC PRESSURE = (kpa) INTERNAL PRESSURE LOAD = (kpa) TEMPERATURE CHANGE - TOP FLANGE = (Deg. C.) TEMPERATURE CHANGE - BTM FLANGE = (Deg. C.) ALLOWABLE STRESS FACTOR Sheet No. 14

27 BASIC LOAD CASE NO. 4 DEAD + ASCE WIND CASE A KPH PER API TH ED. X Y Z DIRECTION DIRECTION DIRECTION FRACTION OF GRAVITY PANEL DEAD LOAD (kpa) FULL DOME LIVE LOAD (kpa) HALF DOME LIVE LOAD (kpa) GROUND SNOW LOAD - TOTAL DOME = (kpa) GROUND SNOW LOAD - DRIFT = (kpa) WIND LOAD - DYNAMIC PRESSURE FROM DEG (kpa) INTERNAL PRESSURE LOAD = (kpa) TEMPERATURE CHANGE - TOP FLANGE = (Deg. C.) TEMPERATURE CHANGE - BTM FLANGE = (Deg. C.) ALLOWABLE STRESS FACTOR WIND LOAD FACTORS: (ASCE7-02, CASE A) (INPUT) VELOCITY (m/s) IMPORTANCE FACTOR : EXPOSURE CATEGORY C CURB HEIGHT (meters) TANK HEIGHT : (meters) TOPOGRAPHIC FACTOR Kzt : DIRECTIONALITY FACTOR Kd : (CALCULATED) DOME RISE-TO-SPAN RATIO : APEX ROOF HEIGHT (meters) TANK HEIGHT / DIAMETER RATIO : POWER LAW CONSTANT ALPHA : GRADIENT HEIGHT Z-g (meters) K-z : Q-z : (kpa) GUST RESPONSE FACTOR G-h (Eq. 6-4) TURBULENCE INTENSITY I-z : (Eq. 6-5) BACKGROUND RESPONSE Q : (Eq. 6-6) BUILDING LENGTH B (meters) LENGTH SCALE OF TURBULENCE L-z : (meters)(eq. 6-7) INTEGRAL LENGTH SCALE FACTOR l : (meters) INTEGRAL LENGTH SCALE POWER EXP.: 1/5.0 EQUIVALENT STRUCTURE HT. Z_bar : (meters) MINIMUM HEIGHT Z_min : (meters) CONSTANT A (Figure 6-7) CONSTANT B (Figure 6-7) : CONSTANT C (Figure 6-7) : THETA-25 : Degrees Sheet No. 15

28 BASIC LOAD CASE NO. 5 DEAD + ASCE WIND CASE B KPH PER API TH ED. X Y Z DIRECTION DIRECTION DIRECTION FRACTION OF GRAVITY PANEL DEAD LOAD (kpa) FULL DOME LIVE LOAD (kpa) HALF DOME LIVE LOAD (kpa) GROUND SNOW LOAD - TOTAL DOME = (kpa) GROUND SNOW LOAD - DRIFT = (kpa) WIND LOAD - DYNAMIC PRESSURE FROM DEG (kpa) INTERNAL PRESSURE LOAD = (kpa) TEMPERATURE CHANGE - TOP FLANGE = (Deg. C.) TEMPERATURE CHANGE - BTM FLANGE = (Deg. C.) ALLOWABLE STRESS FACTOR WIND LOAD FACTORS: (ASCE7-02, CASE B) (INPUT) VELOCITY (m/s) IMPORTANCE FACTOR : EXPOSURE CATEGORY C CURB HEIGHT (meters) TANK HEIGHT : (meters) TOPOGRAPHIC FACTOR Kzt : DIRECTIONALITY FACTOR Kd : (CALCULATED) DOME RISE-TO-SPAN RATIO : APEX ROOF HEIGHT (meters) TANK HEIGHT / DIAMETER RATIO : POWER LAW CONSTANT ALPHA : GRADIENT HEIGHT Z-g (meters) K-z : Q-z : (kpa) GUST RESPONSE FACTOR G-h (Eq. 6-4) TURBULENCE INTENSITY I-z : (Eq. 6-5) BACKGROUND RESPONSE Q : (Eq. 6-6) BUILDING LENGTH B (meters) LENGTH SCALE OF TURBULENCE L-z : (meters)(eq. 6-7) INTEGRAL LENGTH SCALE FACTOR l : (meters) INTEGRAL LENGTH SCALE POWER EXP.: 1/5.0 EQUIVALENT STRUCTURE HT. Z_bar : (meters) MINIMUM HEIGHT Z_min : (meters) CONSTANT A (Figure 6-7) CONSTANT B (Figure 6-7) : CONSTANT C (Figure 6-7) : THETA-25 : Degrees Sheet No. 16

29 R E A C T I O N S U M M A R Y BASIC LOAD CASE No 1 DOME DEAD LOAD MAXIMUM AND MINIMUM REACTIONS: RADIAL TANGENTIAL VERTICAL DIRECTION (kn) (kn) (kn) _ x-max x-min y-max y-min z-max z-min TOTAL MODEL REACTIONS: GLOBAL-X GLOBAL-Y GLOBAL-Z (kn) (kn) (kn) Sheet No. 17

30 R E A C T I O N S U M M A R Y BASIC LOAD CASE No 2 DOME DEAD LOAD + DOME LIVE LOAD KPA LIVE LOAD ON DOME MAXIMUM AND MINIMUM REACTIONS: RADIAL TANGENTIAL VERTICAL DIRECTION (kn) (kn) (kn) _ x-max x-min y-max y-min z-max z-min TOTAL MODEL REACTIONS: GLOBAL-X GLOBAL-Y GLOBAL-Z (kn) (kn) (kn) Sheet No. 18

31 R E A C T I O N S U M M A R Y BASIC LOAD CASE No 3 DOME DEAD LOAD + DOME UNBALANCED LIVE LOAD KPA LIVE LOAD ON DOME MAXIMUM AND MINIMUM REACTIONS: RADIAL TANGENTIAL VERTICAL DIRECTION (kn) (kn) (kn) _ x-max x-min y-max y-min z-max z-min TOTAL MODEL REACTIONS: GLOBAL-X GLOBAL-Y GLOBAL-Z (kn) (kn) (kn) Sheet No. 19

32 R E A C T I O N S U M M A R Y BASIC LOAD CASE No 4 DEAD + ASCE WIND CASE A KPH PER API TH ED. MAXIMUM AND MINIMUM REACTIONS: RADIAL TANGENTIAL VERTICAL DIRECTION (kn) (kn) (kn) _ x-max x-min y-max y-min z-max z-min TOTAL MODEL REACTIONS: GLOBAL-X GLOBAL-Y GLOBAL-Z (kn) (kn) (kn) Sheet No. 20

33 R E A C T I O N S U M M A R Y BASIC LOAD CASE No 5 DEAD + ASCE WIND CASE B KPH PER API TH ED. MAXIMUM AND MINIMUM REACTIONS: RADIAL TANGENTIAL VERTICAL DIRECTION (kn) (kn) (kn) _ x-max x-min y-max y-min z-max z-min TOTAL MODEL REACTIONS: GLOBAL-X GLOBAL-Y GLOBAL-Z (kn) (kn) (kn) Sheet No. 21

34 BASIC LOAD CASE No: 1 DOME DEAD LOAD S T R E S S S U M M A R Y CONTROLLING MEMBER STRESSES(MPa) AND FORCES(kN, kn-m) EXTRUSION TYPE AXIAL BENDING COMBINED (+)MOMENT (-)MOMENT STRESS COMP TENS COMP TENS RATIO E-609 (Struts 1 through 1) FORCE STRSS ALLOW f/f E-609 (Struts 2 through 2) FORCE STRSS ALLOW f/f E-609 (Struts 3 through 3) FORCE STRSS ALLOW f/f E-609 (Struts 4 through 4) FORCE STRSS ALLOW f/f E-609 (Struts 5 through 5) FORCE STRSS ALLOW f/f E-609 (Struts 6 through 6) FORCE STRSS ALLOW f/f E-609 (Struts 7 through 7) FORCE STRSS ALLOW f/f Sheet No. 22

35 BASIC LOAD CASE No: 1 DOME DEAD LOAD S T R E S S S U M M A R Y CONTROLLING MEMBER STRESSES(MPa) AND FORCES(kN, kn-m) EXTRUSION TYPE AXIAL BENDING COMBINED (+)MOMENT (-)MOMENT STRESS COMP TENS COMP TENS RATIO E-609 (Struts 8 through 8) FORCE STRSS ALLOW f/f E-609 (Struts 9 through 9) FORCE STRSS ALLOW f/f E-609 (Struts 10 through 10) FORCE STRSS ALLOW f/f E-609 (Struts 11 through 11) FORCE STRSS ALLOW f/f E-609 (Struts 12 through 12) FORCE STRSS ALLOW f/f E-609 (Struts 13 through 13) FORCE STRSS ALLOW f/f E-609 (Struts 14 through 14) FORCE STRSS ALLOW f/f Sheet No. 23

36 BASIC LOAD CASE No: 1 DOME DEAD LOAD S T R E S S S U M M A R Y CONTROLLING MEMBER STRESSES(MPa) AND FORCES(kN, kn-m) EXTRUSION TYPE AXIAL BENDING COMBINED (+)MOMENT (-)MOMENT STRESS COMP TENS COMP TENS RATIO E-609 (Struts 15 through 15) FORCE STRSS ALLOW f/f E-609 (Struts 16 through 16) FORCE STRSS ALLOW f/f E-609 (Struts 17 through 17) FORCE STRSS ALLOW f/f E-609 (Struts 18 through 18) FORCE STRSS ALLOW f/f E-609 (Struts 19 through 19) FORCE STRSS ALLOW f/f E-609 (Struts 20 through 20) FORCE STRSS ALLOW f/f E-609 (Struts 21 through 21) FORCE STRSS ALLOW f/f Sheet No. 24

37 BASIC LOAD CASE No: 1 DOME DEAD LOAD S T R E S S S U M M A R Y CONTROLLING MEMBER STRESSES(MPa) AND FORCES(kN, kn-m) EXTRUSION TYPE AXIAL BENDING COMBINED (+)MOMENT (-)MOMENT STRESS COMP TENS COMP TENS RATIO E-609 (Struts 22 through 22) FORCE STRSS ALLOW f/f E-609 (Struts 23 through 23) FORCE STRSS ALLOW f/f E-609 (Struts 24 through 24) FORCE STRSS ALLOW f/f E-609 (Struts 25 through 25) FORCE STRSS ALLOW f/f E-609 (Struts 26 through 26) FORCE STRSS ALLOW f/f E-638 (Struts 27 through 27) FORCE STRSS ALLOW f/f E-609 (Struts 28 through 28) FORCE STRSS ALLOW f/f Sheet No. 25

38 BASIC LOAD CASE No: 1 DOME DEAD LOAD S T R E S S S U M M A R Y CONTROLLING MEMBER STRESSES(MPa) AND FORCES(kN, kn-m) EXTRUSION TYPE AXIAL BENDING COMBINED (+)MOMENT (-)MOMENT STRESS COMP TENS COMP TENS RATIO E-614 (Struts 29 through 29) FORCE STRSS ALLOW f/f COMP01 (Struts 30 through 30) FORCE STRSS ALLOW f/f E-705 (Struts 31 through 31) FORCE STRSS ALLOW f/f Sheet No. 26

39 S T R E S S S U M M A R Y BASIC LOAD CASE No: 2 DOME DEAD LOAD + DOME LIVE LOAD KPA LIVE LOAD ON DOME CONTROLLING MEMBER STRESSES(MPa) AND FORCES(kN, kn-m) EXTRUSION TYPE AXIAL BENDING COMBINED (+)MOMENT (-)MOMENT STRESS COMP TENS COMP TENS RATIO E-609 (Struts 1 through 1) FORCE STRSS ALLOW f/f E-609 (Struts 2 through 2) FORCE STRSS ALLOW f/f E-609 (Struts 3 through 3) FORCE STRSS ALLOW f/f E-609 (Struts 4 through 4) FORCE STRSS ALLOW f/f E-609 (Struts 5 through 5) FORCE STRSS ALLOW f/f E-609 (Struts 6 through 6) FORCE STRSS ALLOW f/f E-609 (Struts 7 through 7) FORCE STRSS ALLOW f/f Sheet No. 27

40 S T R E S S S U M M A R Y BASIC LOAD CASE No: 2 DOME DEAD LOAD + DOME LIVE LOAD KPA LIVE LOAD ON DOME CONTROLLING MEMBER STRESSES(MPa) AND FORCES(kN, kn-m) EXTRUSION TYPE AXIAL BENDING COMBINED (+)MOMENT (-)MOMENT STRESS COMP TENS COMP TENS RATIO E-609 (Struts 8 through 8) FORCE STRSS ALLOW f/f E-609 (Struts 9 through 9) FORCE STRSS ALLOW f/f E-609 (Struts 10 through 10) FORCE STRSS ALLOW f/f E-609 (Struts 11 through 11) FORCE STRSS ALLOW f/f E-609 (Struts 12 through 12) FORCE STRSS ALLOW f/f E-609 (Struts 13 through 13) FORCE STRSS ALLOW f/f E-609 (Struts 14 through 14) FORCE STRSS ALLOW f/f Sheet No. 28

41 S T R E S S S U M M A R Y BASIC LOAD CASE No: 2 DOME DEAD LOAD + DOME LIVE LOAD KPA LIVE LOAD ON DOME CONTROLLING MEMBER STRESSES(MPa) AND FORCES(kN, kn-m) EXTRUSION TYPE AXIAL BENDING COMBINED (+)MOMENT (-)MOMENT STRESS COMP TENS COMP TENS RATIO E-609 (Struts 15 through 15) FORCE STRSS ALLOW f/f E-609 (Struts 16 through 16) FORCE STRSS ALLOW f/f E-609 (Struts 17 through 17) FORCE STRSS ALLOW f/f E-609 (Struts 18 through 18) FORCE STRSS ALLOW f/f E-609 (Struts 19 through 19) FORCE STRSS ALLOW f/f E-609 (Struts 20 through 20) FORCE STRSS ALLOW f/f E-609 (Struts 21 through 21) FORCE STRSS ALLOW f/f Sheet No. 29

42 S T R E S S S U M M A R Y BASIC LOAD CASE No: 2 DOME DEAD LOAD + DOME LIVE LOAD KPA LIVE LOAD ON DOME CONTROLLING MEMBER STRESSES(MPa) AND FORCES(kN, kn-m) EXTRUSION TYPE AXIAL BENDING COMBINED (+)MOMENT (-)MOMENT STRESS COMP TENS COMP TENS RATIO E-609 (Struts 22 through 22) FORCE STRSS ALLOW f/f E-609 (Struts 23 through 23) FORCE STRSS ALLOW f/f E-609 (Struts 24 through 24) FORCE STRSS ALLOW f/f E-609 (Struts 25 through 25) FORCE STRSS ALLOW f/f E-609 (Struts 26 through 26) FORCE STRSS ALLOW f/f E-638 (Struts 27 through 27) FORCE STRSS ALLOW f/f E-609 (Struts 28 through 28) FORCE STRSS ALLOW f/f Sheet No. 30

43 S T R E S S S U M M A R Y BASIC LOAD CASE No: 2 DOME DEAD LOAD + DOME LIVE LOAD KPA LIVE LOAD ON DOME CONTROLLING MEMBER STRESSES(MPa) AND FORCES(kN, kn-m) EXTRUSION TYPE AXIAL BENDING COMBINED (+)MOMENT (-)MOMENT STRESS COMP TENS COMP TENS RATIO E-614 (Struts 29 through 29) FORCE STRSS ALLOW f/f COMP01 (Struts 30 through 30) FORCE STRSS ALLOW f/f E-705 (Struts 31 through 31) FORCE STRSS ALLOW f/f Sheet No. 31

44 S T R E S S S U M M A R Y BASIC LOAD CASE No: 3 DOME DEAD LOAD + DOME UNBALANCED LIVE LOAD KPA LIVE LOAD ON DOME CONTROLLING MEMBER STRESSES(MPa) AND FORCES(kN, kn-m) EXTRUSION TYPE AXIAL BENDING COMBINED (+)MOMENT (-)MOMENT STRESS COMP TENS COMP TENS RATIO E-609 (Struts 1 through 1) FORCE STRSS ALLOW f/f E-609 (Struts 2 through 2) FORCE STRSS ALLOW f/f E-609 (Struts 3 through 3) FORCE STRSS ALLOW f/f E-609 (Struts 4 through 4) FORCE STRSS ALLOW f/f E-609 (Struts 5 through 5) FORCE STRSS ALLOW f/f E-609 (Struts 6 through 6) FORCE STRSS ALLOW f/f E-609 (Struts 7 through 7) FORCE STRSS ALLOW f/f Sheet No. 32

45 S T R E S S S U M M A R Y BASIC LOAD CASE No: 3 DOME DEAD LOAD + DOME UNBALANCED LIVE LOAD KPA LIVE LOAD ON DOME CONTROLLING MEMBER STRESSES(MPa) AND FORCES(kN, kn-m) EXTRUSION TYPE AXIAL BENDING COMBINED (+)MOMENT (-)MOMENT STRESS COMP TENS COMP TENS RATIO E-609 (Struts 8 through 8) FORCE STRSS ALLOW f/f E-609 (Struts 9 through 9) FORCE STRSS ALLOW f/f E-609 (Struts 10 through 10) FORCE STRSS ALLOW f/f E-609 (Struts 11 through 11) FORCE STRSS ALLOW f/f E-609 (Struts 12 through 12) FORCE STRSS ALLOW f/f E-609 (Struts 13 through 13) FORCE STRSS ALLOW f/f E-609 (Struts 14 through 14) FORCE STRSS ALLOW f/f Sheet No. 33

46 S T R E S S S U M M A R Y BASIC LOAD CASE No: 3 DOME DEAD LOAD + DOME UNBALANCED LIVE LOAD KPA LIVE LOAD ON DOME CONTROLLING MEMBER STRESSES(MPa) AND FORCES(kN, kn-m) EXTRUSION TYPE AXIAL BENDING COMBINED (+)MOMENT (-)MOMENT STRESS COMP TENS COMP TENS RATIO E-609 (Struts 15 through 15) FORCE STRSS ALLOW f/f E-609 (Struts 16 through 16) FORCE STRSS ALLOW f/f E-609 (Struts 17 through 17) FORCE STRSS ALLOW f/f E-609 (Struts 18 through 18) FORCE STRSS ALLOW f/f E-609 (Struts 19 through 19) FORCE STRSS ALLOW f/f E-609 (Struts 20 through 20) FORCE STRSS ALLOW f/f E-609 (Struts 21 through 21) FORCE STRSS ALLOW f/f Sheet No. 34

47 S T R E S S S U M M A R Y BASIC LOAD CASE No: 3 DOME DEAD LOAD + DOME UNBALANCED LIVE LOAD KPA LIVE LOAD ON DOME CONTROLLING MEMBER STRESSES(MPa) AND FORCES(kN, kn-m) EXTRUSION TYPE AXIAL BENDING COMBINED (+)MOMENT (-)MOMENT STRESS COMP TENS COMP TENS RATIO E-609 (Struts 22 through 22) FORCE STRSS ALLOW f/f E-609 (Struts 23 through 23) FORCE STRSS ALLOW f/f E-609 (Struts 24 through 24) FORCE STRSS ALLOW f/f E-609 (Struts 25 through 25) FORCE STRSS ALLOW f/f E-609 (Struts 26 through 26) FORCE STRSS ALLOW f/f E-638 (Struts 27 through 27) FORCE STRSS ALLOW f/f E-609 (Struts 28 through 28) FORCE STRSS ALLOW f/f Sheet No. 35

48 S T R E S S S U M M A R Y BASIC LOAD CASE No: 3 DOME DEAD LOAD + DOME UNBALANCED LIVE LOAD KPA LIVE LOAD ON DOME CONTROLLING MEMBER STRESSES(MPa) AND FORCES(kN, kn-m) EXTRUSION TYPE AXIAL BENDING COMBINED (+)MOMENT (-)MOMENT STRESS COMP TENS COMP TENS RATIO E-614 (Struts 29 through 29) FORCE STRSS ALLOW f/f COMP01 (Struts 30 through 30) FORCE STRSS ALLOW f/f E-705 (Struts 31 through 31) FORCE STRSS ALLOW f/f Sheet No. 36

49 S T R E S S S U M M A R Y BASIC LOAD CASE No: 4 DEAD + ASCE WIND CASE A KPH PER API TH ED. CONTROLLING MEMBER STRESSES(MPa) AND FORCES(kN, kn-m) EXTRUSION TYPE AXIAL BENDING COMBINED (+)MOMENT (-)MOMENT STRESS COMP TENS COMP TENS RATIO E-609 (Struts 1 through 1) FORCE STRSS ALLOW f/f E-609 (Struts 2 through 2) FORCE STRSS ALLOW f/f E-609 (Struts 3 through 3) FORCE STRSS ALLOW f/f E-609 (Struts 4 through 4) FORCE STRSS ALLOW f/f E-609 (Struts 5 through 5) FORCE STRSS ALLOW f/f E-609 (Struts 6 through 6) FORCE STRSS ALLOW f/f E-609 (Struts 7 through 7) FORCE STRSS ALLOW f/f Sheet No. 37