Base Fixity Research Articles

Discussion of “Effect of Base Fixity on Buckling of Heavy Column with End Load” by C. Y. Wang

Discussion of “Effect of Base Fixity on Buckling of Heavy Column with End Load” by C. Y. Wang

Closure to “Effect of Base Fixity on Buckling of Heavy Column with End Load” by C. Y. Wang

Closure to “Effect of Base Fixity on Buckling of Heavy Column with End Load” by C. Y. Wang

Discussion of “Effect of Base Fixity on Buckling of Heavy Column with End Load” by C. Y. Wang

This paper presents the classical flexural buckling solution to an ideal prismatic column with an intermediate lateral elastic restraint and subjected to a concentrated axial load at the top end only. The end conditions are ideal ~clamped, hinged, and free!. The discussor finds this paper useful, particularly for testing a matrix solution proposed by the writer that appears much more general and simpler to program. Consider the stepped column that connects points A and B ~Fig. 1!. This consists of two column segments, AC and CB, with semirigid connections at ends A and B and at the intermediate joint C. It is assumed that ~1! both column segments, AC and CB, are made of homogeneous linear elastic materials with mechanical and geometric properties Et It At ht and Eb Ib Ab hb ~where E5elastic modulus; I5moment of inertia; A5cross-sectional area; and h5span). The subindices t and b indicate the top and bottom column segments, respectively; ~2! the centroidal axis of each segment is a straight line with their centroidal axes lineup; ~3! the column is subject simultaneously to axial loading Pa and transverse load Va at point A, to concentrated loads Pc and Vc , and bending moment M c at the intermediate joint C; and ~4! the lateral sways of the column are partially inhibited by linear springs Sa and Sc located at A and C, respectively, and by an external rotational spring of magnitude SQ at joint C. The rotational fixity factors at ends A and B and the intermediate joint C ~of column segment AC! are assumed to be ra , rb , and rc , respectively. Further details of this model are given by Aristizabal-Ochoa ~1997b!. A general solution to the second-order analysis and buckling load of the column in Fig. 1 is as follows:

Effect of Base Fixity on Buckling of Heavy Column with End Load

This paper studies the effect of a rotationally restrained base on the buckling of a standing column subjected to both its own weight and a tip load. The characteristic equation is derived analytically in terms of Bessel functions. The results show stability is greatly compromised when the base is not securely fixed. Rotational spring constants for some simple base constraints are estimated.

System identification for evaluating soil-structure interaction effects in buildings from strong motion recordings

Parametric system identification is used to evaluate seismic soil–structure interaction effects in buildings. The input–output strong motion data pairs needed for evaluations of flexible- and fixed-base fundamental mode parameters are derived. Recordings of lateral free-field, foundation, and roof motions, as well as foundation rocking, are found to be necessary for direct evaluations of modal parameters for both cases of base fixity. For the common situation of missing free-field or base rocking motions, procedures are developed for estimating the modal parameters that cannot be directly evaluated. The accuracy of these estimation procedures for fundamental mode vibration period and damping is verified for eleven sites with complete instrumentation of the structure, foundation, and free-field. © 1998 John Wiley & Sons, Ltd.

Static buckling appraisal of an echinodome

The buckling behavior of an underwater shell of revolution structure of optimum form—an echinodome—is examined under axisymmetric and symmetric point loads both experimentally and theoretically. For the concentrated loadings, experimental predictions of critical buckling are based on the Southwell technique and a possible alternative method is suggested. Bifurcation and nonlinear collapse buckling analyses are described theoretically. Within the bifurcation investigation both linear and nonlinear approaches are included. The effects of base fixity on the instability of the structure are considered. Comparisons are made with earlier external-pressure loading effects and the relative significance of the two forms of loading are discussed.

Dynamics of Human Legs Subjected to Posterior Impact

This is a dynamic analysis of a three-mass, hinged beam model representing a standing human struck suddenly with a posterior, horizontal, step impact force. The results of parametric studies, presented in terms of nondimensional system variables, show the essential features of the dynamic moment responses in the lower leg. Included are the effects of the distribution of body mass, the location of the impact force, and the base fixity, with and without slip. Closed-form results show that the point of impact is not always the point of maximum bending moment on the lower leg. For step impact loads applied near the knee joint, peak moments are predicted near the midlength of the lower leg, the location coincident with about half of the observed fractures to the tibia and fibula of pedestrians struck by car bumpers near the knees.

Behavior of Unanchored Fluid-Filled Tanks Subjected to Ground Excitation

An analysis developed for the response of liquid storage tanks under horizontal base excitation is employed and numerical results are obtained for unanchored tanks. These results are compared and found to be in good agreement with experimental data. Base uplift is shown to cause a dramatic reduction in the effective beam-type stiffness of a tank, which in turn reduces the tank response frequency and changes the developed hydrodynamic loads significantly. Based on these results, an explanation is provided for some great qualitative and quantitative differences in the behavior of a tank, resulting from its base fixity condition alone.

Three-dimensional analysis of guyed logging spars

Trees are commonly guyed and used as spars to increase the capacity of cable logging systems in mountainous terrain. Spar response to loading is complex because of nonlinearities due to cable behavior, beam-column loading of the spar, and the geometric effects of large spar deflections. A numerical procedure has been developed to determine spar deformation and the resulting state of stress in the spar and the guylines due to the application of static loads. The Newton-Raphson algorithm is utilized to determine spar position which is denned by force equilibrium. A numerical damper is required to assure convergence. The problem is formulated using the finite element procedures where the spar is treated as an assemblage of three-dimensional beam elements, the guylines are modeled as nonlinear springs, and spar base fixity is provided by a linear rotational spring. The details of the solution method and an example problem are presented.

Experimental Studies on Earthquake Response Behavior of Cylindrical Tanks

A series of dynamic tests for the seismic behavior of ground-supported liquid storage tanks are evaluated and compared with previous theoretical studies. Two model tanks were subjected to shaking table tests with particular attention to the influence of base fixity and geometric imperfections in the tank walls. Test results support numerical calculations which show that base fixity conditions strongly influence the seismic response of tanks. Although high radial accelerations are induced by the imperfections, they are not found to be significant factors in tank failure.

Experimental Seismic Study of Cylindrical Tanks

Earthquake response behavior of ground-supported, thin-shell, cylindrical liquid storage tanks was studied experimentally by means of the University of California at Berkeley shaking table. 12-ft x 6-ft and 7-¾-ft x 15-ft models, fabricated from sheet aluminum to represent steel tanks three times larger, were subjected to simulated earthquake accelerations with intensities up to 0.5 g. Principal test parameters included base fixity (fixed or free to uplift) and top condition (open, fixed, or floating roof). The most significant observation was that out-of-round distortions were induced in both fixed and free-base tanks in addition to the expected lateral deflection. Stresses and deflections associated with the out-of-round response were not negligible. Also, the uplift behavior of unanchored tanks differed greatly from design prediction, with observed stresses several times larger than expected. The models performed satisfactorily despite the unexpected behavior characteristics.

Influence of Partial Base Fixity on Frame Stability

Buckling strength of pinned-base rigid frame is considerably lower than that of identical fixed-base frame; in United States, however, pinned column bases are preferred for economical reasons; paper shows that rotational restraint offered by commonly used pinned column bases is sufficient to increase buckling strength of these frames to almost that of identical fixed-base rigid frames.