Showing papers in "Earthquake Engineering & Structural Dynamics in 1972"

Stability and accuracy analysis of direct integration methods

Abstract: A systematic procedure is presented for the stability and accuracy analysis of direct integration methods in structural dynamics. Amplitude decay and period elongation are used as the basic parameters in order to compare various integration methods. The specific methods studied are the Newmark generalized acceleration scheme, the Houbolt method and the Wilson θ-method. The advantages of each of these methods are discussed. In addition, it is shown how the direct integration of the equations of motion is related to the mode superposition analysis.

Scattering of plane sh waves by a semi‐cylindrical canyon

Abstract: The two-dimensional scattering and diffraction of plane SH waves by a semi-cylindrical canyon is analysed for a general angle of wave incidence The closed-form solution of the problem shows that the surface topography can have prominent effects on incident waves only when the wavelengths of incident motion are short compared to the radius of a canyon The surface amplification of displacement amplitudes around and in the canyon changes rapidly from one point to another, but the amplification is always less than 2 The over-all trends of amplification pattern are determined by two principal parameters: (1) γ, the angle of incidence of plane SH waves, and (2) η, the ratio of radius of the canyon to one-half wave length of incident waves The higher η leads to greater complexity of the pattern of surface displacement amplitudes characterized by more abrupt changes of amplification from one point to another, while γ mainly determines the over-all trends of displacement amplitudes For grazing and nearly grazing incidences, for example, a strong shadow zone is developed behind the canyon The qualitative analysis of the topographic effects on the Pacoima Dam accelerogram,1 based on the semi-cylindrical canyon, suggests that this strong-motion record was not seriously affected by surface topography of the recording site

Nonlinear dynamic analysis of complex structures

Abstract: A general step-by-step solution technique is presented for the evaluation of the dynamic response of structural systems with physical and geometrical nonlinearities. The algorithm is stable for all time increments and in the analysis of linear systems introduces a predictable amount of error for a specified time step. Guidelines are given for the selection of the time step size for different types of dynamic loadings. The method can be applied to the static and dynamic analysis of both discrete structural systems and continuous solids idealized as an assemblage of finite elements. Results of several nonlinear analyses are presented and compared with results obtained by other methods and from experiments.

Comparisons between ambient and forced vibration experiments

Abstract: The ambient and forced vibration techniques for testing full-scale structures are critically compared. Both methods, based on small level excitation, may be used to determine many mode shapes and frequencies of vibration and the corresponding damping values, with adequate accuracy for most purposes. The two techniques give mutually consistent results. The mode amplitudes determined by ambient and forced vibration tests show systematic departure for high modes and near the top levels of buildings tested. This phenomenon is attributed to the participation of all mode shapes and is a consequence of excitation by a concentrated force near the top of a building and at a frequency differing by only a few per cent from a natural frequency of vibrations. A new way of showing the effect of unwanted modes on the response near resonance of the mode being sought is developed. It is particularly useful for the analysis of steady, forced vibration tests of structures using eccentric mass vibration generators.

The earthquake experience at koyna dam and stresses in concrete gravity dams

Abstract: A number of questions concerning the response of concrete gravity dams to earthquakes, motivated by the structural damage caused to Koyna Dam, which has an unconventional cross section, by the December 1967 Koyna earthquake, are considered in this work. The study is not restricted to the earthquake experience at Koyna Dam, but includes consideration of a dam with a typical section and another earthquake motion having similar intensity but different peak acceleration and frequency characteristics compared to the Koyna ground motion. The earthquake response in a number of cases is analysed by the finite element method and results are presented. These results lead to a number of conclusions. Significant tensile stresses must have developed in Koyna Dam during the Koyna earthquake and similar stresses would have developed even in typical gravity dam sections. The Koyna ground motion is relatively more severe, compared to California earthquakes of similar intensity, on concrete gravity dams. The extra concrete mass near the crest of a gravity dam to support the roadway, etc. is responsible for causing a significant part of the critical tensile stresses; attention should therefore be given to developing lightweight supporting systems.

Earthquake resistance of buildings with a ‘soft’ first storey

Abstract: The dynamic, bi-linear response behaviour of a series of eight storey shear buildings subjected to simulated earthquake excitation is studied. The specific objective of the investigation is to determine under what conditions a yielding first storey can adequately protect the upper storeys from significant yielding. Two classes of buildings are considered: stiff (0.5 sec period) and flexible (2.0 sec period), and the basic parameters considered in the yielding first storey are the yield force level and the bi-linear stiffness. The results demonstrate that a very low yield force level and an essentially perfectly plastic yielding mechanism are required in the first storey to provide effective protection to the superstructure. Moreover, the required displacement capacity of such an effective first storey mechanism is found to be very large.

Effect of self-weight and vertical acceleration on the behaviour of tall structures during earthquake*

Abstract: The effect of self-weight and vertical ground acceleration during earthquakes on vertical cantilevers has been studied. The input is taken to be a bivariate normal random process, digitally simulated on a computer. The tip deflection, base moment and shear force have been obtained numerically for three structures of different natural frequencies. It is found that the presence of self-weight and vertical ground excitation could alter these three quantities considerably. This leads to the conclusion that with tall structures a refined analysis, similar to the one presented here, is advisable.

Behaviour of subaqueous tunnels during earthquakes

Abstract: Three-dimensional models of a subaqueous tunnel were built on a shaking table and vibrated for the purpose of investigating the dynamic behaviour of the tunnel. The material of the soft surface layer was gelatin gel and that tunnel was silicon rubber. In addition, earthquake observations at the site of the real subaqueous tunnel have been carried out using accelerometers and strain gauges set on the walls of the tunnel. At the site, micro-tremors were also measured. In these studies, it was noted that non-uniform displacements of the ground along the tunnel axis were caused variations of the dynamic behaviour of the ground, and that the tunnel deforms correspondingly to the varying deformations of the ground. From these experimental results, a mathematical model of the subaqueous tunnel was formulated for anti-seismic design studies.

Hydrodynamic pressures and response of gravity dams to vertical earthquake component

Abstract: Hydrodynamic pressures and structural response of concrete gravity dams, including dam-reservoir interaction, due to the vertical component of earthquake ground motions are investigated. The response of the dam is approximated by the deformations in the fundamental mode of vibration, and the effects of deformability of bed rock on hydrodynamic pressures are recognized in the analysis. Expressions for the complex frequency response functions for the dam displacement, dam acceleration and lateral hydrodynamic force are derived. These results along with the Fast Fourier Transform algorithm are utilized to compute the time-history of responses of dams of 100, 300 and 600 ft height, with full reservoir, for different values of elastic modulus of mass concrete: 3.0, 3.5, 4.0, 4.5 and 5.0 million psi, to the vertical component of El Centro, 1940, and Taft, 1952, ground motions. It is concluded that the hydrodynamic forces caused by vertical ground motion are affected substantially by damreservoir interaction and depend strongly on the modulus of elasticity of the dam. The dam response to the vertical component of ground motion is compared with that due to the horizontal component. It is concluded that because the vertical component of ground motion causes significant hydrodynamic forces in the horizontal direction on a vertical upstream face, responses to the vertical component of ground motion are of special importance in analysis of concrete gravity dams subjected to earthquakes.

Stochastic excitation of a simple system with impact damper

Abstract: An approximate analytical solution is obtained for the stationary response of a highly nonlinear auxiliary mass damper (impact damper) attached to a single-degree-of-freedom oscillator that is subjected to an excitation with white power spectral density and Gaussian probability distribution. Experimental measurements with an electronic analogue computer verify the analytical findings both qualitatively and quantitatively. Results are given for the mean-squared level and the power spectral density of the response. The effects of various damper parameters on the response of the primary system are determined. The impact damper under consideration is shown to be substantially more effective than the conventional dynamic vibration neutralizer in controlling the response of stochastically excited primary systems.

Forced vibration of a tall steel‐frame building

Abstract: The dynamic properties of the twenty-two-story, steel-frame San Diego Gas and Electric Company Building in San Diego, California, have been determined experimentally in a series of co-operative tests between the California Institute of Technology and the University of California at Los Angeles. The building was vibrated by two eccentric mass exciters capable of frequencies up to 10 c/sec and forces as much as 5000 Ib each. The natural frequencies, associated mode shapes and the amounts of damping were determined for the first six modes of vibration in each of the two translational directions, and also in torsion. The mode shapes and frequencies showed, in general, the regularity and uniformity that appears typical of many tall buildings, but the three fundamental modes (nominally NS, EW and torsion) of the structure showed a coupling of translational and rotational components to a degree that was unexpected in a building whose structural frame is essentially symmetric. It is believed that this may be a consequence of the exceptionally small differences among the three fundamental frequencies. The damping in the first eighteen modes of the structure varied from 1.6 to 4.4 per cent, with a slight tendency for the larger values to be associated with the higher modes. Of the simpler damping models that might be used for analysis of the building, constant modal damping appears most appropriate and stiffness or mass proportional damping would not be realistic.

Curved beam finite elements for coupled bending and torsional vibration

Abstract: Curved beam finite elements are presented for out of plane coupled bending and torsional vibration. The element formulation is based upon the exact differential equations of an infinitesimal element in static equilibrium. The effects of shear deformation and rotary inertia are allowed for in the analysis. The element stiffness and mass matrices can be easily restricted to those of a ‘thin’ beam without the secondary effects. Frequencies obtained using either formulation are shown to converge onto exact values using ‘thick’ or ‘thin’ beam theories.

Response of offshore towers to strong motion earthquakes

Abstract: Presented is a stochastic method of analysis of offshore towers subjected to strong motion earthquakes. A zero mean ergodic Gaussian process of finite duration is used to characterize horizontal ground acceleration and full fluid structure interaction effects are included. Numerical results for four representative deep water towers having heights of 475, 675, 875 and 1075 ft are compared with corresponding results obtained by the response spectrum method of analysis. Particular emphasis is placed on the maximum or extreme values of total transverse shear and total overturning moment. Comparisons are made with code values and the role of ductility is briefly discussed.

Free vibrations of coupled shear walls

Abstract: The continuous connection method of analysis is extended to deal with the free vibrations of a coupled shear wall structure. The natural modes and frequencies are determined from the Galerkin technique, and the dynamic response following an imposed lateral displacement is evaluated. A comparison is made between theoretical predictions of natural frequencies and the results from tests on model structures.

Long distance effects of the 28 march 1970 gediz turkey earthquake

Abstract: In this paper, soil-structure interaction studies are presented for buildings which collapsed at the Tofas automobile factory, Bursa, Turkey, during the 28 March 1970 Gediz earthquake. Acceleration response spectrum curves of the ground were determined using the vibrations of an after shock recorded by a Willmore velocity seismometer. These spectrum curves provide an essential source of information for establishing the reasons of collapse, as well as for explaining the relative response to the earthquake of various buildings in the factory area. The factory not only is 135 km away from the epicentre, but also is far outside the fifth degree damage intensity zone. The prime reason why a low value of ground acceleration caused such surprisingly heavy damage to modern reinforced concrete structures is concluded to be the resonance phenomenon arising from the natural period of the structures coinciding with the predominant period of the soil.

A stochastic model for predicting seismic failure in a soil deposit

Abstract: Liquefaction of saturated sand deposits under seismic excitation is studied on the basis of a fatigue failure approach. The model includes a stochastic treatment of the input, of the soil response and of the cumulative pore pressure effects produced by cycling stresses in the soil. A method of establishing safety factors against liquefaction is also considered. Results obtained from analysis of a case history confirm the applicability of the model for engineering purposes.

Finite strip analysis of the dynamic response of beam and slab highway bridges

Abstract: This paper presents a method of analysis for the dynamic response of a simply supported beam and slab bridge under the action of a moving vehicle. The bridge is idealized as an orthotropic plate and, in the analysis, is subdivided into a number of finite strips. The vehicle is idealized as a moving sprung mass. Viscous damping is taken into account for both bridge and vehicle. The results show that there is significant variation of response across transverse sections of the bridge. Furthermore the dynamic magnification is considerably greater than that predicted by a more approximate method in which the bridge is idealized as a simple prismatic beam.

Dynamic properties of planar, coupled shear walls

Abstract: The paper is a study of the natural frequencies and mode shapes of planar, coupled shear walls, a common lateral resistive element in building construction. The equations of motion are derived for the general case, and the eigenvalue problem associated with free vibrations of equal, constant shear walls is solved, both with and without the inclusion of the inertia of vertical motion. Explicit solutions are presented for the characteristic equation and the mode shapes and the results are illustrated with figures, including an example calculation based on the shear walls of the Mt. McKinley Building, damaged by the Alaskan earthquake of 1964. The results affirm the necessity of including vertical displacement of the shear walls in the analysis of such systems, and suggest that the inertia of vertical motion also must be considered in the analysis for certain ranges of the parameters.

An experimental assessment of the added mass of some plates vibrating in water

Abstract: A reservoir of water is contained by a concrete valley block, a ferrocement wall and a steel plate. Both wall and plate contain an array of pressure transducer sockets (Figures 1 and 2). Using the M.A.M.A.1 equipment pure modes of vibration are excited. Frequency and mode shape are measured with the reservoir empty. When the reservoir is full hydrodynamic pressure is also measured. These hydrodynamic pressures are compared with Chopra's2 two-dimensional, series solution, which includes compressibility of water, and with two- and three-dimensional finite element solutions of Laplace's equation, which do not include compressibility. Chopra's solution is unsatisfactory for modes which contain a vertical node line. The best agreement between experimental and theoretical hydrodynamic pressure is obtained when the latter is obtained from three-dimensional solutions of Laplace's equations, indicating that compressibility does not play a significant rǒle. This conclusion is supported by agreement between experimental frequencies (reservoir full) and those calculated using added mass obtained from the Laplace solution. Similar conclusions were reached from tests on a floating steel plate, suspended in the surface of the reservoir by a soft spring. Here, dynamic pressure measurements were not made, reliance being placed on agreement between calculated and measured frequencies and mode shapes.

On increasing the structural damping of a steel chimney

Abstract: Experimental results of a study which was commissioned to investigate the possible benefit of added structural damping in reducing the susceptibility of a steel chimney to wind-excited swaying vibrations are presented and discussed. The experimental and analytical techniques used are briefly described. The results indicated a significant increase in structural damping when pads of a special damping material were incorporated into the foundation structure of the chimney.

The generation of stochastic load functions to simulate wind loading on structures

Abstract: The simplest form of input required for step-by-step simulation of response of a structure to a gusty wind is a stochastic process having Gaussian distribution and a specified power spectrum. Methods for generating such a process are described in detail, and the extension outlined for generating a number of partially correlated input processes having specified power spectra and cross-spectra.

Multiphase cross bracing in earthquake resistant structures

Abstract: The concept of multiphase cross bracing is discussed and tests undertaken on a simple cross braced frame are described. From these experiments it is concluded that selected multiphase response may be achieved reliably in cross braced frames if sufficient attention is given to the determination of the material characteristics and to the structural detailing.

Vibration of cylindrical shells with clamped ends

Abstract: A general method is outlined for the determination of natural frequencies of cylindrical shells with any boundary conditions when the effects of rotatory inertia and transverse shear deformation are included in the analysis. This is applied to cylindrical shells with both ends clamped. It is shown that the inclusion of these effects tends to have a greater effect upon frequencies of cylindrical shells with clamped ends than it does for corresponding shells with simply supported ends, for which numerical results are available. The authors suggest an empirical relation, which together with the latter results enables rapid estimates to be made of the effects of rotatory inertia and shear deformation on the frequencies of a wide range of cylindrical shells with clamped ends. An assessment of the accuracy of the theory with these effects included is made by comparing frequencies with values from a three-dimensional elasticity theory, but this comparison has to be restricted to cylindrical shells with simply supported ends.

The vibration frequencies of an elastically supported cantilever column with variable cross‐section and distributed axial load

Abstract: The solution for transverse vibration frequencies of an elastically supported cantilevered column with continuously varying cross-section under distributed axial load is developed. Boundary conditions are formulated for fixed and elastic support. Values of the fundamental frequency are tabulated for various cross-sections and axial load distributions due to self-weight as functions of the ratios between the rigidities and also the axial loads at the fixed and free ends, the ratio between the actual and critical buckling axial load, the degree of polynomial approximation and the rotational stiffness of the elastic support.

Dynamic response of the KII building to the San Fernando earthquake

Abstract: The KII Building was subjected to the San Fernando earthquake on 9 February 1971 without suffering any damage. During the earthquake, strong motion accelerations were recorded at the base, middle and top of the building. The simulation analysis of the building was carried out taking into account the interaction between the building and the soil. The internal viscous damping theory considering the different damping coefficients for the building and the soil was adopted. Comparison of the calculated and observed acceleration time histories as well as the floor response spectra showed satisfactory agreement. On the basis of the response spectrum values, the fact that no damage was observed in this building is justified theoretically.

Measurements of sonic boom responses of structures due to concorde

Abstract: Measurements have been made of the responses of twelve different buildings and one cliff to the sonic booms produced during ten supersonic flights by Concorde 002 along the west coast route. Measurements were made of the levels of induced vibration and of any permanent movements of existing defects. The dynamic measurements show that, with the exception of roof structures, the vibration levels were generally similar to those produced by environmental loads. On roof structures, the sonic boom causes vibrations some two to three times those of the normal environment. The static measurements show that slow movements occur in the buildings due to temperature changes but none could be related to the sonic boom. No significant damage was observed at the monitored sites.