Analysing the base of precast column in socket foundations with smooth interfaces

This paper analyzes the behavior of the base of a precast column in the socket foundation with smooth interfaces. This research is motivated by the lack of information and guidelines on the behavior of column bases in the embedded region. An experimental program with two full-scale specimens was carried-out. These two specimens had smooth interfaces at the internal faces of the socket, different embedded lengths and were subjected to loads with large eccentricities. The experimental results showed that the failure of the specimens occurred by the yielding of the longitudinal reinforcement out of the embedded region, while the transverse reinforcement was not very stressed. Some recommendations on the anchorage of the longitudinal reinforcement and a strut-and-tie model for the behavior of column bases in the embedded region are proposed.CNPqFAPES

Buckling design of confined steel cylinders under external pressure

Thin-walled steel cylinders surrounded by an elastic medium, when subjected to uniform external pressure may buckle. In the present paper, using a two dimensional model with nonlinear finite elements, which accounts for both geometric and material nonlinearities, the structural response of those cylinders is investigated, towards developing relevant design guidelines. Special emphasis is given on the response of the confined cylinders in terms of initial imperfections; those are considered in the form of initial out-of-roundness of the cylinder and as an initial gap between the cylinder and the medium. Furthermore, the effects of the deformability of the surrounding medium are examined. The results indicate significant imperfection sensitivity and a strong dependency on the medium stiffness. The numerical results are employed to develop a simple and efficient design methodology, which is compatible with the recent general provisions of European design recommendations for shell buckling, and could be used for design purposes. Copyright © 2009 by ASME

Deformation of an Inertia-Loaded Thin Ring in a Rigid Cavity With Initial Clearance

BRIEF NOTES characteristics were observed for the limiting case of a rigid substrate considered by It may be observed that the load-deflection curves flatten and Q c decreases with decreasing values of the substrate stiffness K, and also that the unstable portion of each curve lies above those with higher K. This would seem to indicate that although buckling of the ring occurs at a lower load for a more compliant substrate, it appears to be accompanied by a less extensive "jump" in the deflection. This may be attributed to the smaller build up of strain energy preceding buckling for the more compliant system. We note here that, within the resolution of the figure, the curve corresponding to K/C= 10 3 in Let us first separate the systems considered into two categories, the first such that K> C the substrates of which shall be referred to as "stiff" substrates, and the second category such that K< C the substrates of which shall be said to be "compliant." One may first observe from For the compliant substrates (K<Q we observe a shifting to the right, of the corresponding load-deflection and loadinterface angle curves, as K decreases. This phenomenon offers the explanation that as the ring stiffness to substrate stiffness ratio increases, the system (initially) tends toward the behavior of a rigid ring confined by a compliant substrate, where for a rigid ring <j> = ir/2 for all finite K. We also observe, for K<C, that #-<j> mi n as <2 0 -*0 + and that the positive slopes of the corresponding Q 0 -<f> curves decrease with increasing K, indicating that the ring bends aways from the substrate with increasing Q 0 , immediately following the initial shrink dominated phase and that this behavior is more pronounced as if decreases. Chicurel, R., 1968, "Shrink Buckling of Circular Rings," ASME JOURNAL OF APPLIED MECHANICS, Vol. 35, El-Bayoumy, L., 1972, "Buckling of a Circular Elastic Ring Confined to a Uniformly Contracting Boundary," ASME JOURNAL OF APPLIED MECHANICS, Vol. 39, pp. 758-766. Hsu, P. T., Elkon, J., and Pian, T. H. H., 1964, "Note on the Instability of Circular Rings Confined to a Rigid Boundary," ASME JOURNAL OF APPLIED MECHANICS, Vol. Propagation of steady waves and shocks in viscoelastic materials has been reviewed by where we have now set x = 0. The variables e, v, and a are required to vanish as f --oo. The quantity a in (1) is now the stress divided by the constant mass density. Because of the small range of strains and times involved in laboratory measurements of steady waves in real viscoelastic materials The function/(e) is asymptotic to e when the strain is small. For the present discussion we suppose that /(e)/e is an increasing function of e, and for illustrative purposes we use the form f(e)=e[l + (e/e c ) p ](P>0). The asterisk in (2) denotes convolution over the interval (-oo, + oo), and the derivatives J' and a' are treated as generalized functions. J(t) is the compliance multiplied by the mass density. It is identically zero for /<0, with initial value J 0 = 7(0 +) = 0. For t> 0, J is an increasing function of t, with J' decreasing. Experimentally determined compliances for some real materials are given in Ferry's book BRIEF NOTES form Ct" J(t)=J 0 + J,(t/t r y (0<p<l). (4) Combining Note from (1) that v(t), which is more likely to be the observed quantity, is proportional to e(t). Warhola (1988) has devised a numerical algorithm for the solution of The quasi-elastic approximation furnishes a rigorous upper bound on the exact solution, and in cases of the type that are of main physical interest, the error in e q (t) is very small When P = 1 (a quadratic nonlinearity in/,) the wave form has the same shape as </(/). Schuler's (1970) observed wave forms are like those given by using (7) with a power-law compliance (4) with small p J'*e = J[T(t)]e(t), T(t) must be approximately equal to t when the strain history is nearly a simple step at time zero. A closer approximation e a (t) can be obtained by using a more refined estimate of T, Since /(T) is the average value of J(s) with respect to the weight function e' (t-s)/e(t), we estimate T as the average value of s itself with respect to the same weight function. With an integration by parts, this leads to the prescription with t (t)T(t)=\' e a (s)ds f(e a )/e a = lPJ(T). Integration of (10) with appropriate initial conditions then gives t as a function of e a . This procedure gives the exact solution if J has the form (4) with p = 0 or p = 1. For real materials with J concave, e a lies between e q and the exact solution e if U>U 0 . To test the accuracy of e q and e a , in some cases in which the exact solution is known, we use the forms (3) and (4) in For critical waves For P= 1, the factor K is unity at p = Q but 1/2 at p= 1, so e g (t) is accurate only at small/?. In contrast, the ratio e/e a is unity at both p = 0 and p= 1, and it is never less than about 0. with the upper sign for subcritical waves and the lower sign for supercritical waves. <2(rj) is defined as tf /p\. To test the approximation e a (t) in a subcritical case, let A{r)) be the correspondingly scaled version of e a {t), and let T be the scaled version of T. Then, in place of The integration can be carried out in finite form if p=l/N with N an integer. To lighten the notation, let us take P= 1. This is the exact solution when N=$p=$. For N=20(p = 0.05), the exact and approximate solutions are compared in Acknowledgment We are grateful for the support from NSF grant DMS-8702866 and from the U.S. Air Force