Fa, Allowable Compression Stress
K1l
r
Fa
(ksi) Main and Secondary Members
21 20.54 41 19.11 61 17.33 81 15.24 101 12.85 22 20.48 42 19.03 62 17.24 82 15.13 102 12.72 23 20.41 43 18.95 63 17.14 83 15.02 103 12.59 24 20.35 44 18.86 64 17.04 84 14.90 104 12.47 25 20.28 45 18.78 65 16.94 85 14.79 105 12.33 26 20.22 46 18.70 66 16.84 86 14.67 106 12.20 27 20.15 47 18.61 67 16.74 87 14.56 107 12.07 28 20.08 48 18.53 68 16.64 88 14.44 108 11.94 29 20.01 49 18.44 69 16.53 89 14.32 109 11.81 30 19.94 50 18.35 70 16.43 90 14.20 110 11.67 31 19.87 51 18.26 71 16.33 91 14.09 111 11.54 32 19.80 52 18.17 72 16.22 92 13.97 112 11.40 33 19.73 53 18.08 73 16.12 93 13.84 113 11.26 34 19.65 54 17.99 74 16.01 94 13.72 114 11.13 35 19.60 55 17.90 75 15.90 95 13.60 115 10.90 36 19.50 56 17.81 76 15.79 96 13.48 116 10.85 37 19.42 57 17.71 77 15.69 97 13.35 117 10.71 38 19.35 58 17.62 78 15.58 98 13.23 118 10.57 39 19.27 59 17.53 79 15.47 99 13.10 119 10.43 40 19.19 60 17.43 80 15.36 100 12.98 120 10.28
Co= Wo
N + 4Mbo
NDb , for the operating conditions CT = WT
N + 4MbT
NDb , for the test conditions
Where:
Db = Diameter of circle passing through centroids of
columns, mm (in.).
8. Calculate the maximum total axial uplift load (tensile) on the windward side of each column, kg (lb.).
To = −Wo
N + 4Mbo
NDb , for the operating conditions Te = −We
N + 4Mbo
NDb , for the empty vessel
9. Calculate the eccentric loads at the top of the column, kg (lb.).
P1= Wo
N + 4Mao
ND , for the operating conditions P1= WT
N + 4MaT
ND , for the test conditions
P2 = 4Mao
ND − Wo
N , for the operating conditions P2 = 4Mao
ND − We
N , for the empty vessel
10. Calculate the lateral force per column, F, for both the design and test cases, kg (lb.).
11. Calculate the individual and combined stresses in the column, and compare them to the allowable values.
a. Operating Conditions
Axial compression stress, fb:
SI Units English Units
fa = 9 810Co
A ,kPa fa = Co
A , psi
Bending stress, fb:
SI Units English Units
fb = 9 810 P1e Zx + 0.75FL Zx ,kPa fb =P1e Zx + 0. 75FL Zx , psi Where:
Zx = Section modulus of the column that resists
bending, mm3 (in.3).
e = Distance between vessel shell and centroid of the column, mm (in.).
b. Test conditions
Axial compression stress, fa:
SI Units English Units
fa = 9 810CT
A ,kPa fa = CT
A , psi
fb = 9 810 WTe NZx + 0.75FL Zx + P1e Zx ,kPa English Units fb = WTe NZx + 0.75FL Zx + P1e Zx ,psi
c. Combined compressive stress in the column, f, for the higher of either the operating or test conditions.
f = fa + fb, kPa (psi)
If the calculated value of "f" is no greater than the smaller of Fa or Fb that were determined in Steps 5
and 6, then the result is acceptable (but conservative). Proceed to Step 12 if this conservative limit is exceeded.
12. Compare the calculated stresses to the allowable values to determine the acceptability of the number and size of the columns selected. • If fa Fa ≤ 0.15, then fa Fa + fb Fb ≤ 1 • If fa Fa > 0.15, then fa Fa + Cmfb 1− fa Fe' Fb ≤ 1 Where: Cm = 0.85 Fe' = 12π2E 23 K1l 2
Note that Fa, Fb and Fe' may be increased by one-third where fa and fb are computed on the basis of wind or
seismic loads in combination with dead loads.
13. After the columns have been designed, the attachment details at the vessel shell must be developed. These attachment details must ensure that the vessel shell is not overstressed due to the locally applied loads, and will often include reinforcing pads or rings. This aspect of column support design is beyond the scope of MEX 202.03.
14. Confirm that the column support design that is specified in the Contractor Design Package is in accordance with the preceding procedure.
Work Aid 4B: Vertical Vessel on Skirt Support
This procedure may be used to determine the required thickness of the skirt for a vertical pressure vessel.
1. Determine the total weight of the pressure vessel, attachments, and contents to be included for the case under consideration. This information should be available from the vendor or contractor, or may be calculated using procedures that are contained in PEDP course CSE 110. Wo = kg (lb.), for operating conditions
WT = kg (lb.), for hydrotest conditions
We = kg (lb.), for empty conditions
2. Calculate or determine the bending moment at the base of the skirt, M, kg-mm (in.-lb.), due to wind (from procedures that are contained in CSE 110).
3. Calculate or determine the bending moment at the skirt to vessel shell intersection, Ms,as follows:
Where:
M = As determined in Step 2. V = qzDehs, kg (lb.)
hs =Skirt height, mm (in.)
De = Effective diameter of skirt, mm (in.)
qz = Wind pressure, kg/mm2 (psi)
De and qz may be determined using procedures that are
contained in CSE 110.
Note that for relatively short skirts and tall towers, the difference between Ms and M will not be large and Ms may
be taken as equal to M without being overly conservative. 4. Assume a value of skirt thickness, tsk, mm (in.). A good
initial assumption would be to choose tsk equal to the vessel shell thickness at the skirt attachment.
5. Calculate the longitudinal stress in the skirt at the base, σL.
SI Units English Units
σL = 9810 − W πDsktsk ± 4M πDsk2 t sk , kPa σL = − W πDsktsk ± 4M πDsk2 t sk , psi Where:
Dsk = Skirt diameter at the base in the middle of its thickness, mm (in.).
M = Bending moment at the base for the case under consideration, kg-mm (in.-lb.).
6. For the skirt material, determine the allowable stress in tension and compression per the ASME Code at ambient temperature, Sal1, kPa (psi).
• Allowable tensile stress determined per Work Aid 2A. • Allowable compressive stress determined per Work
Aid 3B.
7. Confirm that σL ≤ Sal1. If it is not, increase tsk and/or Dsk
and recalculate.
8. Determine the weld joint efficiency, E, for the skirt-to-shell weld. See Figure 33.
• E = 0.55 for Type 1 skirts • E = 0.80 for Type 2 skirts
9. Determine the allowable stresses of the skirt and vessel materials at the vessel design temperature. Use the lower of the two as Sal2, kPa (psi).
10. Recalculate tsk as follows: SI Units tsk = 9 810 W / πD
[
(
skv)
+ 4M(
s/πD2skv)
]
/ ESal2, mm English Units tsk = W / πD[
(
skv)
+ 4M(
s /πD2skv)
]
/ ESal2, in. Where:Dskv = Skirt diameter at its attachment to the vessel
in the middle of its thickness, mm (in.).
11. Set a uniform skirt thickness that is equal to the larger of that determined in Steps 7 or 10.
12. Confirm that the skirt support design that is specified in the Contractor Design Package is in accordance with the preceding procedure. ;;; ;;; (a) Straight ;;; ;;; (b) Flared 15°max. 15°max. Butt weld blends
smoothly into head contour
;;; ;;; (a) Straight ;;; ;;; (b) Flared Lap weld blends smoothly into shell contour
D D 2tsk 1.75tsk D