End Restraint Effects Research Articles

Shear Stress and Pore Pressure in Triaxial Testing

The effects of frictional end restraint in triaxial testing may be avoided by using lubricated loading platens or segmental specimens. Segmental specimens consist of a central segment sandwiched between end segments that are sealed in a latex film. Pore pressures are measured only in the rather uniformly stressed central zone. Using this technique, the effects of stress history on pore pressure behavior in undrained shear are investigated, and the results are found to be significantly different from similar results obtained by conventional triaxial tests. Preliminary results of a study of the effects of strain rate on undrained shear strength are also described.

The Influence of End Restraint on the Compression Strength of a Cohesionless Soil

Synopsis Tests have been carried out on a cohesionless soil to examine the influence of boundary restraint on the observed strength and on the relationships between stress, strain and volume change. To eliminate extraneous errors the axial load in the triaxial compression test has been measured by means of a sensitive proving ring situated within the cell. The proving ring has been calibrated from time to time during the series of tests by a hydraulic system operated by the same dead-weight pressure gauge tester as was used to calibrate the gauge measuring the fluid pressure in the cell. Cylindrical compression tests have been carried out with unlubricated plattens and with one or more layers of rubber membrane lubricated with silicone grease interposed between the ends of the sample and the loading plattens. Samples with three different ratios of height to diameter have been tested. The results indicate that, for the material tested, the effect of end restraint is to increase the apparent strength of the sample, but that this effect decreases with increasing height to diameter ratio and is of little significance with the usual ratio of about 2 to 1. For lower ratios the influence of end restraint on strength is more important and only with very efficient lubrication can the apparent strength of short samples be reduced to that given by samples with the standard height to diameter ratio. Des essais ont été effectués sur un sol non cohérent pour examiner l'influence de la restriction aux extrémités sur la résistance observée et sur les relations entre contrainte, déformation et changement de volume. Pour éliminer des erreurs supplémentaires, la charge axiale dans l'essai de compression triaxiale a été mesurée au moyen d'un anneau d'essai dynamo-métrique situé à l'intérieur de la chambre. Durant la série d'essais, l'anneau d'essai dynamométrique a été calibré de temps à autre avec un systéme hydraulique fonctionnant par le même calibreur à poids mort utilisé pour calibrer le manométre mesurant la pression du fluide dans la chambre. Des essais de compression triaxiale ont été effectués avec des disques non lubrifiés et avec une ou plusiers couches de membranes en caoutchouc lubrifiées avec de la graisse au silicium et interposées entre l'échantillon et les disques transmettant la charge. Des échantillons de trois rapports différents de hauteur à diamétre ont été examinés. Les résultats montrent que pour le matériau essayé l'effet de restriction aux extrémités est d'augmenter la résistance apparente, mais aussi que cet effet diminue en augmentant le rapport de hauteur à diamétre, et qu'il devient négligeable avec le rapport habituel d'environ 2 à 1. Pour des rapports inférieurs, l'influence de la restriction aux extrémités est plus importante, et c'est seulement avec une lubrifaction trés efficace que la résistance apparente d'échantillons courts peut être réduite à celle obtenue avec des échantillons à rapport usuel de hauteur à diamétre.

Effect of End Conditions on the Burst Strength of Finite Cylinders

Solutions are presented for the bursting strength of thin-walled cylinders of finite length with various end restraints, including (a) two rigid end plates, (b) two hemispherical caps, and (c) one rigid end plate and one hemispherical cap. The deformation theory of plasticity is used, together with the Mises yield criterion, for materials obeying a linear strain-hardening law. Comparisons of the results are made to determine the influence of end restraints on burst pressure with numerical results presented for cylinder lengths from 0 (sphere) to ∞, and for a range of hardening constants. The results show that the effect of shortness is small (less than 8 percent), and the influence of end conditions negligible, in the range l > 3. For shorter cylinders, the finite length of the shell serves to increase burst pressures, to values nearly double those for the infinite cylinder, as l → 0. Also, the effect of end restraints becomes very pronounced, the cylinder with the two rigid end plates being the strongest, and that with two hemispherical caps the weakest; all other types of end closures are assumed to have a strengthening effect intermediate to these two cases.

APPROXIMATE BURST STRENGTH OF THIN-WALLED CYLINDERS WITH HEMISPHERICAL CAPS

An approximate solution is presented for the bursting strength of thin- walled cylinders with hemispherically capped ends. Deformation theory of plasticity is used, together with the Mises yield criterion and its associated flow rule. Solutions are presented for materials that strain-harden according to a Ludwik power law relation ship. Results obtained are compared with those for cylinders with rigid ends to determine the influence of end restraint on burst pressure. Numerical results are presented for cylinder lengths varying from zero to infinity and for a range of hardening coefficients from 0 to 1.0. For cylinders with a length/diameter ratio 1 larger than 2, the effect of end restraint, as represented by spherical heads or rigid caps, upon the burst strength is small, amounting to less than 13%. However, for values of 1 < 2.0, this effect becomes significant, the rigidly capped cylinder being considerably stronger than the hemispherically headed one. Furthermore, both shells are considerably stronger than the infinitely long cylinder. (auth)

Compression Tests on Thin-Walled Cylinders

SummaryThe paper describes compression tests on eight thin-walled cylinders of 3 ft. diameter and 0·035 in. wall thickness made of aluminium alloy plate. The lengths of the cylinders were either 6 ft. or 9 ft. Three of the cylinders were tested under axial compression up to buckling failure, and the initial buckling load, failing load and mode of buckling were observed. A further three cylinders were similarly tested, but these cylinders were subjected to internal pressure before applying the compressive load. The internal pressure had a twofold strengthening effect on these cylinders. Firstly, it induced a tensile pre-stress along the axis of the cylinder and, secondly, it resulted in the value of the compressive stress at which buckling occurred being greater than the buckling stress value for the unpressurised cylinders. The six cylinders were tested in a manner which allowed the end face of each cylinder to rotate about a diametral axis. A parallel platen device was used in testing the last two cylinders (in an unpressurised condition) which restrained rotation of the end faces of the cylinders. These tests enabled the effect of end restraint to be studied, and also enabled measurements of load-carrying capacity at large axial deflections to be made. The initial buckling loads, failing loads and modes of buckling observed in the tests were compared with existing large deflection theory.