Experimental Mechanics

, Volume 9, Issue 3, pp 129–136 | Cite as

Stresses in shallow axisymmetric shells using a casting procedure

Authors describe semiexperimental method of determining bending and membrane stresses in shallow thin shells of revolution experiencing large axisymmetrical deflections. Calculations proceed from radial slope measurements on epoxy castings of the deflected and undeflected shell surfaces
  • W. Soedel
  • R. Cohen


Normal and radial displacements of a shallow thin sheil of revolution are related by theoretical considerations. Radial displacements are calculated from slope measurements on the generatrices of the initial shell surface (before loading) and of the final shell surface (after loading). Membrane and bending stresses over the entire shell surface are then computed from the measured slope values and the calculated radial displacements.

A measuring technique is developed which is especially suitable for shallow shells enclosed in small spaces. It consists mainly of making a cast of the initial and final shell surface using an epoxy platic. The disklike cast is cut along its diameter. The slope values are measured optically along the line which is formed by the intersection of the cutting plane with the deflection surface.

The method is applied to a shallow thin shell of revolution in contact with a concentric piston and to a clamped circular plate, both experiencing large axisymmetric deflection.


Epoxy Fluid Dynamics Measuring Technique Theoretical Consideration Circular Plate 
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

σrm, σtm

radial and tangential membrane stress

σrb, σtb

radial and tangential bending stress

rm, ∈tm

radial and tangential membrane strain

rb, ∈tb

radial and tangential bending strain


modulus of elasticity


Poisson's ratio


element length

r, θ

polar coordinates

dr, dθ



normal deflection


radial slope


radial deflection


distance from neutral plane


integration constants

ui, uo

radial displacement at inner and outer boundary

Ri, Ro

radius of inner and outer boundary


uncorrected slope data


angle between axis of shell and normal to reference plane


tiltage angle


boundary radius, reference radius


boundary radius


uniform pressure


nondimensionalized pressure


shell thickness


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Copyright information

© Society for Experimental Mechanics, Inc. 1969

Authors and Affiliations

  • W. Soedel
    • 1
  • R. Cohen
    • 1
  1. 1.School of Mechanical Engineering, Ray W. Herrick LaboratoriesPurdue UniversityLafayette

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