Experimental Mechanics

, Volume 25, Issue 1, pp 12–23 | Cite as

Tests on microconcrete model of hyperbolic cooling tower

  • S. E. Swartz
  • C. C. Chien
  • K. K. Hu
  • H. Mozaffarian


In the past 18 years following the collapse of three cooling towers on November 1, 1965 in Ferrybridge, England, a considerable interest has developed in determining the buckling behavior of these thin-walled shells under the loadings normally encountered. An extensive number of theories exist attempting to predict buckling response and failure. Numerous tests on small, elastic models of metals or plastics have also been reported. However, little work has been reported on the physical testing to failure of concrete models.

This paper describes work on the construction, instrumentation and testing of a microconcrete model of a hyperboloid of revolution proportioned to exhibit buckling prior to collapse. This model is the first in a series of models which will be constructed and tested with a variety of load and support configurations.

The shell model was tested to failure under the action of uniform pressure (vacuum loading). The failure was of a local nature so the model was repaired and tested a second time to failure. The results of these tests showed good agreement with membrane theory (modified to account for geometric imperfections) for measured strains but the buckling mode of failure was of an unexpected type.


Mechanical Engineer Fluid Dynamics Shell Model Numerous Test Measured Strain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols


throat radius of shell

b, ζ

geometry parameters of shell


secant modulus of elasticity of concrete


modulus of elasticity of steel


tangent modulus of elasticity of concrete


ultimate, uniaxial compressive strength o concrete


yield strength of steel

Fθ,Fϕ,Qθ,Qϕ,kGθ,kGϕk, M, N,\(k,M,N,\bar S,\bar T,\bar q_{cr}\)

shell buckling parameters [see eqs (7)–(13) and Ref. 3]


shell thickness, horizontal radius and vertical coordinate respectively


meridional length for slope and imperfection measurements

K,\(\bar K\),nθ

imperfection parameters [see eqs (3)–(5) and Refs. 8 and 12]


shell-membrane forces in circumferential and meridional directions


shell-bending moments in circumferential and meridional directions


external lateral pressure and its value at the onset of local buckling


circumferential and meridional radii


horizontal radius at the top of the shell


deviation from ideal shell geometry in a meridional lengthH

Δ, Δi, Δj,k

radial deviation in shell middle surface as an average and at locations on the meridiani, j, k


cylinder strain at concrete strengthf′ c

νθ, νφ,\(\tilde \sigma _\theta ,\tilde \sigma _\phi\)

shell-membrane strains and stresses in the circumferential and meridional direction


meridional coordinate


Poisson's ratio


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Copyright information

© Society for Experimental Mechanics, Inc. 1985

Authors and Affiliations

  • S. E. Swartz
    • 1
  • C. C. Chien
    • 1
  • K. K. Hu
    • 1
  • H. Mozaffarian
    • 1
  1. 1.Department of Civil EngineeringKansas State UniversityManhattan

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