4. DELINEATE METHODS 1,2,3
M1
membrane analysis : shells and supports with no water
M2 || simplified: i. Plate thickness t ≥ 0.9
ii. Hoop stress ≥ 2 psi
iii. 0.001 < t/R ≤ 0.003 if t/R > 0.003
iv. Material Fy ≥36 ksi
v. Uniform boundary support
vi. Verbal declaration: verify lower boundary
determined.
by M1 : 4 √RT proxim to boundary
M3 complex nonlinear buckling analysis
• : water filled.
°
R
5. M3Complex design
• Water-filled cones
• Water-filled cylinders
• Double-curved
• Checks
• Plate thickness
≥ 0.8 tbase where t/R ≥ 0.00143
≥ 0.7 tbase where t/R < 0.00143
Must verify T.14 value.
If T.14 is exceeded :
Assume value of
compressive failure
stress in presence of
circumferential tension,
Fch
vii. Shape
verification
°
6. Nonlinear buckling shall comply
• Analysis based on numerical solutions using finite-element, finite-
differences, or numerical-integration techniques.
• Analysis shall include material and geometric nonlinearities
Consider imperfections and gross structural
discontinuity
• Shell discontinuity
• Change in plate
• Plate misalignment o Imperfection tolerance
o 10.6.6.1 Local deviation from
Theoretical Shape
o Max local deviation
– Ex = 0.01 Lx
– Lx = 4 √RT
Erection Tolerances for Stability
R
Radius of exterior structure
7. REFER TO MCAD EBOOK AT METHOD 3
RE QUIRE ME NT S OF NONLINE AR BUCKLING
ANALYS IS
A. utilize a FE, FD or NI technique, to include material and geometric nonlinearities.
B. Analysis shall consider (i.i.) and gsd, similar to shell discontinuity junctures, changes in plate
thickness, and plate misalignment. The magnitude shal not be less than ex.
C. Length of imperfection < Lx. This shall be appropriate for the type of construction. The
location and shape of initial imperfections shall produce lowest critical buckling stress Fcr.
D. Location of boundaries and BCs will produce displacements with rotations at BCs similar to
actual structure.
E. H pressure shall be less than or equal to H pressure of operating. Loads required to force
instability or nonconvergence shall be added as meridional load to the shell.
F. Material will be represented at curve including residual stresses at fab and weld
practice.
G. An curve not including effects may be accessed. Considering (i.i.) > 2ex.
Critical stress Fcr will be determined at each shell course of different thickness. Analysis for
corrosion analysis will govern thickness.
8. ANALYSIS CRITERIA
Analysis to consider initial imperfections and gross structural
discontinuities
• Such as shell discontinuity junctures.
• Changes in plate thickness and misalignment
• Boundaries and boundary conditions shall relate to octral structure
• Hydrostatic pressure shall not exceed hydrostatic pressure at
operating conditions
• Incremental loads to force instability of non-convergence shall be
added as meridional load to the shell
• Material of construction
• Residual stressed caused by Fabrication & welding
• S-e does not include effect of residual stresses
• Thickness – Corrosion Allowance : Analysis – Shell course
thickness
9. 3.4.4 FLAT-PLATE ELEMENTS IN
SINGLE PEDESTAL TANKS.
• W = flat width between stiffened edges exclusive of radii.
• F = Octral stress in compression element width, psi
• T = plate thickness < 1in
• W = flat width between stiffened edges exclusive of radii, inches.
• W ≥ workpoint width – 6t
• Compression elements for gravity plus wind or seismic
• Use 0.75 x [(EQ or W) + G]
• Width – thickness limits
• Elements other than § 3.4.4 shall be designed with § B5 AISC ASD.
Le = b/A
= [7300 / √f ][ 1.0 – 1590 / {w/t} √f ]
• Le : design width ratio
between stiffened edges of
bent –plate compression
– Subjected to gravity loads
determined by
• 0 < Le ≤ w/t
• b = effective design width
10. § 3.5 SHELL GIRDER,
INTERMEDIATE STIFFENERS,
AND COMPRESSION RINGS
3.5.1 Top Shell Girder
• S = min Req’d modulus of top angle or girder including portion of
tank shell distance of the lesser of 16t or 0.78 ( RT )½ in2