The Influence of End Friction and Poisson's Ratio on Stresses in Compressed Specimens
1970 Volume 19 Issue 196 Pages 63-69
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1970 Volume 19 Issue 196 Pages 63-69
The present paper is concerned with the influences of end friction and Poisson's ratio on stress in compressed rectangular and cylindrical specimens. In numerical calculations, the finite element method was employed. The following conclusions have been made on stress in the compressed specimens.
(1) The more the friction between the end of the specimen and the platten is reduced and the smaller Poisson's ratio becomes, the more uniform stress is developed in the specimen.
(2) For sufficiently small coefficients of the end friction, some portions of the end of the specimen slide and the shear stress on the end becomes terrace-like, and the axial stress becomes more or less uniform.
(3) The stress is similar in both the rectangular and the cylindrical specimens. The difference is that the deviations of the axial stresses from the average for various coefficients of friction and Poisson's ratios are larger in the cylindrical specimens than those in the rectangular ones.
(4) For a fixed Poisson's ratio with the coefficient of the end friction larger than a certain value, no lubrication can be practically expected, in other terms the stress in specimens with such coefficients of end friction are practically the same as the stress in the specimens completely restrained at the ends. This limit value of the coefficient of the friction varies with Poisson's ratio. For Poisson's ratios 1/3, 1/4, 1/5 and 1/6 in cylindrical specimen, for instance, the limit values of the coefficient of end friction become 0.52, 0.38, 0.31 and 0.26, respectively.
(5) The load required for the unit axial displacement of the ends of specimen is widely influenced by the Poisson's ratio, the coefficient of end friction and slenderness of the specimen. For the specimen with height-diameter ratio 0.5, for example, the loads required for the completely restrained specimen are larger than those of fully lubricated one by 16.5% and 3.3% with Poisson's ratios 1/3 and 1/6, respectively.
