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RE: shell stability

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Hello Steve,


Sorry for the late response – your tank is probably already constructed. 


I had a similar situation several years ago.  If I recall correctly, one important issue was imperfection sensitivity.  I found that some types of structures, such as shells and shallow arches, might exhibit many closely spaced buckling modes that can interact, resulting in reduced buckling capacity in the presence of even very small imperfections.  For our structure, linear elastic FEA buckling analysis (eigenvectors) closely matched hand calculations of Timoshenko buckling, but was very unconservative; nonlinear FEA with imposed, realistic imperfections yielded much smaller buckling capacity.  Again if I recall correctly, the AWWA D100 tank design manual had a factor to apply to Timoshenko-like buckling to account for this reduction. A theoretical but very well written description of this effect (attributed to Koiter) is provided in Bazant’s “Stability of Structures” book, Section 4.6.


I guess this is one more thing for Structural Engineers to lose sleep over…


Brian McDonald



From: Steve Gordin [mailto:sgordin(--nospam--at)]
Sent: Wednesday, October 27, 2010 6:43 PM
To: seaint(--nospam--at)
Subject: Re: shell stability



My problem is a large steel tank being used as a form for its own outer concrete shell with welded ties keeping the shell from buckling during the pour.  

Timoshenko's "Theory of Elastic Stability" was my knee-jerk-reaction reference.  I also looked into Roark (which actually cites Timoshenko's formulas for arches, not shells), as well as Vol'mir's "Flexible Plates and Shells", "Guide to Stability Design" (Galambos), and several designer's handbooks. 

Unfortunately, none of these sources provided a clear-cut solution for a problem at hand.  For example, the Timoshenko's formulas (referenced in Roark) do not appear quite applicable to shallow arches (my case), while other formulas that are applicable to such arches lead to quite paradoxical and seemingly theoretical results.     

I ended up modeling the shell in 3D FEA, evaluating stresses, analyzing the deflected shapes, and still applying the Timoshenko's arch formulas.  The results appear reasonable and corresponding to the field observations.         


V. Steve Gordin SE
SGE Consulting Structural Engineers

Alexander Bausk wrote:


Roark's Fomulas for Stress and Strain has and appropriate entry under paragraph 13.5, "Thin Shells of Revolution under External Pressure", as well as Table 13.1.

It also has a calculated example thereto all right.

On 27 October 2010 23:50, Steve Gordin <sgordin(--nospam--at)> wrote:
> Good afternoon,
> I am looking for a source of Practical analysis of a
> Shallow - Thin - Cylindrical Shell/panel
> under
> Uniform Radial Compression.
> The books I have on the subject turn to be of mostly academic value.
> Can anyone point me in a right direction?
> TIA,
> --
> Steve Gordin SE

Alexander Bausk
Civil/Structural design & inspection engineer, CAD professional
MSc Structural engineering, Ph.C. Engineering
Dnipropetrovsk, Ukraine
Tel. +38 068 4079692
Fax. +38 0562 470263