Abstract
A theoretical solution has been obtained for the stress distribution throughout a cylindrical specimen loaded in compression, which takes into account different degrees of friction at the end surfaces. To check the solution experimentally, a cylindrical model was constructed from epoxy sheets, with electrical-resistance strain gages embedded between the sheets and also bonded to the cylindrical surface. With the specimen under axial compression, strain measurements were recorded within the elastic range of the epoxy. Reasonable agreement with the theoretical solution was observed for the two types of end conditions. In one case the cylinder was in direct contact with the platens of the testing machine, in the other case a Teflon sheet was placed between the two surfaces.
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Abbreviations
- A, B, C, D :
-
arbitrary constants
- E :
-
modulus of elasticity
- F, G :
-
arbitrary constants
- H :
-
half length of cylinder
- i :
-
square root of (−1)
- J 0,J 1 :
-
Bessel functions of zero and first order, respectively
- k, M, N :
-
arbitrary constants
- P :
-
applied load
- Q :
-
arbitrary constant
- R :
-
radius of cylinder
- r :
-
distance along radius
- S :
-
arbitrary constant
- u, w :
-
radial and axial displacements, respectively
- Z :
-
axial distance
- γrθ, γθz, γrz :
-
shearing strains in therθ, θZ, andrZ planes, respectively
- ∈r,\( \in _z \), ∈θ :
-
radial, axial, and tangential strains, respectively
- ν:
-
Poisson's ratio
- σ 1,σ 3 :
-
average applied stress and confining pressure, respectively
- σ r,\(\sigma _z \),σ θ :
-
radial, axial, and tangential stresses, respectively
- τ r θ, τ θz , τ rz :
-
shearing stresses in therθ, θZ, andrZ planes, respectively
- ϕ:
-
stress function
- ψ:
-
tangential-strain factor
- Ω:
-
axial-strain factor
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Al-Chalabi, M., McCormick, F.J. & Huang, C.L. Strain distribution within compressed circular cylinders. Experimental Mechanics 14, 497–501 (1974). https://doi.org/10.1007/BF02323151
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DOI: https://doi.org/10.1007/BF02323151