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This work is about the influence of rotational component of earthquake excitation to the response of high steel slender frames. In most of studies seismic input is being represented by translational only component of ground accelerations while the rotational one is ignored. This was due to the luck of records which measure the rotational component. Nowadays, technology provides such an instruments and relative records can be found. Elastic design response spectra for rotational components are introduced in regulations. Furthermore, the rotational component was not taken into account since its influence in low structures is not significant. In this paper the results in response and in internal forces of rotational component to the slender steel frame is examined. Time history analysis of a ten-story steel frame with and without rotational excitation component is performed. From the numerical results it is shown that the impact of rotational component in response and the internal forces of the frame is significant and should not be ignored to the design of structures.

Oil and gas offshore structures are essential infrastructures which are subjected to several categories of environmental loads such as wave and wind actions. These loads commonly designate the structural design of offshore platforms. Additionally, several offshore platforms are founded in earthquake-prone areas and the design of them is intensely affected by seismic ground motions. To be sure, various investigations have studied the earthquake response of offshore structures under the action of far-field seismic events. However, the inelastic behavior of platforms under the action of simple pulses has not been examined yet, where the latter loads can successfully simulate near-fault earthquakes. This work investigates, for the first time to our knowledge, the dynamic inelastic response of offshore platforms subjected to triangular, exponential, sinusoidal, and rectangular pulses. Thus, three-dimensional offshore structures are examined also considering the dynamic soil-pile-platform interaction effects, satisfying all the pertinent provisions of European Codes and taking into account geometric and material nonlinearities as well as the effects of the different angles of incidence of seismic waves on the overall/global response of offshore platforms.

Use of appropriate fragility curves for structures is an essential and basic tool for earthquake loss estimation. Fragility curves for frames made only of concrete or only of steel members are already available in the literature. In this paper, fragility curves for plane mixed concrete/steel moment resisting framed structures are developed. Parametric numerical results for these mixed structures are presented and discussed.

The seismic performance of steel structure-foundation systems subjected to near-fault earthquakes was assessed on the basis of response results from nonlinear time-history seismic analyses. The structural results included the maximum values for residual interstory drift ratios, base shears, and overturning moments of the steel structures, as well as the maximum values for residual settlement and tilting of the foundations. In order to reveal the influence of soil-building-interaction on the aforementioned response results, the steel building-foundation systems were designed according to Eurocode 8 provisions, assuming initially fixed and then compliant base conditions. It was concluded that for the case of near-fault seismic motions, good seismic performance of steel building-foundation hybrid systems designed according to European Codes was not guaranteed. A particular thing to note for these systems under near-fault seismic motions was that the seismic performance of the steel structure was most likely unacceptable, while one of the foundations was always acceptable.

In this work a seismic analysis of structure associated with the complete description of ground motion components is performed. All earthquake excitation components corresponding to the six degrees of freedom, translational and rotational ones need to be taken into account for a realistic simulation of structural performance. The impact of the rotational components of an earthquake to the overall response of a steel structure is examined. Typically, in response to the history analyses, the seismic input is descripted by its translational component only, while the rotational components are ignored. This is because the rotational component requires special devices to be recorded in adequate detail. This is one of the reasons why this component is often ignored. With the currently available technology, such an instrument can be constructed and provide detailed records that can be used for the response history analysis of structures. The applicable design codes using a simplified response spectrum analysis accounting for rotational components is proposed and elastic design response spectra are introduced. Another reason why the rotational component was not taken into account in structural analysis is that it does not have significant effect on low-rise buildings. In this work, the analysis results in terms of response and internal forces when accounting for the rotational component is demonstrated. A case study on the response history analysis of symmetrical and non-symmetrical steel structures subjected to earthquake excitation with and without the rotational component of the excitation was performed. Numerical results show that the influence of the rotational component on the structural behaviour is important and should be taken into account in the design process.

This paper summarizes the estimated results from three-dimensional non-linear time-history seismic analysis of tension-only concentrically braced steel structures. The braces of these type of steel structures are properly detailed in order to sustain only tension and no compression. In particular, a cheap and easy to fabricate brace detailing allows the brace to slide when in compression and to develop a resisting force when in tension. A comparison between steel structures designed with the proposed tension-only braces and with buckling-restrained braces is performed on the basis of commonly used seismic response and demand indices. It is shown that tension-only and buckling-restrained braced structures may exhibit similar behavior. Nevertheless, column overstress in compression is larger for the tension-only braced structures. Preliminary conclusions regarding the use of the proposed tension-only braces as a seismic force-resisting system for steel structures are drawn.

The equivalent damping concept originally proposed by Lydik Jacobsen in 1930 is revisited in order to be of use in the seismic analysis of building structures. After briefly recalling that the equivalent damping is obtained by a linearization of a frequency response transfer function and can be deformation-dependent, the paper is then focused on its potential application. In particular, the equivalent damping is employed a) to estimate the maximum seismic displacements of first-mode dominant structures, b) in linear modal analysis, c) in response spectrum analysis and d) in energy-based considerations. Examples are provided highlighting the aforementioned applications of the equivalent damping concept, aiming to retrieve the interest of the engineering community.

The dynamic response of rigid walls retaining a cross-anisotropic poroelastic soil layer over bedrock to seismic horizontal excitation is determined analytically under conditions of plane strain. The problem is treated as a special case of that of a pair of rigid walls with a large separation distance. Use is made of Biot’s anisotropic poroelastodynamic theory. Assuming time harmonic excitation, one is able to achieve an exact u-p formulation of the problem in the frequency domain. Expansion of the displacements and the pore-water pressure in terms of Fourier sine and cosine series along the horizontal direction, reduces the partial differential equations of motion in the frequency domain into a system of three ordinary differential equations, which can be easily solved analytically. Thus, closed form expressions for the seismic soil pressure, the distance from the base of the point of application of the resultant seismic pressure and the base shear force and bending moment are obtained. From the above cross-anisotropic poroelastic solution its special cases of isotropic poroelastic solution and cross-anisotropic elastic solution are obtained and compared with the corresponding existing analytical solutions for validation purposes. Finally, parametric studies are performed in order to assess the effect of cross-anisotropy on the seismic response of the wall-soil system.

A performance-based seismic design method for plane reinforced concrete (R/C) moment-resisting frames (MRF) is proposed. The method is a force-based seismic design one, utilizing not a single strength reduction factor as all modern codes do, but different such factors for each of the first significant modes of the frame. These modal strength reduction factors incorporate dynamic characteristics of the structure, different performance targets, and different soil types. Thus, the proposed method can automatically satisfy deformation demands at all performance levels without requiring deformation checks at the end of the design process, as it is the case with code-based design methods. Empirical expressions for those modal strength reduction factors as functions of the period, deformation/damage and soil types, which can be used directly in conjunction with the conventional elastic pseudo-acceleration design spectra with 5% damping for seismic design of R/C MRFs, are provided. These expressions have been obtained through extensive parametric studies involving non-linear dynamic analyses of 38 frames under 100 seismic motions. The method is illustrated by numerical examples which demonstrate its advantages over code-based seismic design methods.

A performance based seismic design method for eccentrically braced frames (EBFs) and buckling restrained braced frames (BRBFs) is developed herein. The method is a force-based seismic design one where the design base shear is obtained by using different modal strength reduction factors for each one of the first four modes of the frame, instead of using a constant behavior factor for all modes as in all current design codes. These modal strength reduction factors incorporate the dynamic characteristics of the structure, different soil types and different performance targets. Thus, the proposed method can automatically satisfy deformation demands at all performance levels without requiring deformation checks, as it is the case with code-based design methods. The basic concept of the method is associated with the determination of an equivalent elastic structure that retains the mass and initial stiffness of the original nonlinear one, and is characterized by high amounts of viscous damping in order to equilibrate the nonlinear energy of dissipation by the viscous one. The above mentioned factors are obtained through the use of extensive parametric studies on 98 steel plane frames subjected to 100 far-field ground motions. Empirical expressions for those modal strength reduction factors as functions of period, deformation/damage and soil types, which can be used directly in conjunction with the conventional elastic pseudo-acceleration design spectra with 5% damping for seismic design of steel EBFs and BRBFs, are provided. The proposed method is illustrated with representative numerical examples that demonstrate its advantage over code-based seismic design methods.

The dynamic response of rigid walls retaining a cross-anisotropic elastic soil layer over bedrock to seismic horizontal excitation is determined analytically under conditions of plane strain. The problem of a pair of rigid walls is solved first and the one with a single wall is obtained as a special case for a large separation distance between those walls. Assuming time harmonic motion, expansion of the unknown displacements in Fourier sine and cosine series along the horizontal direction, reduces the system of the two partial differential equations of motion in the frequency domain into a system of two ordinary differential equations, which is easily solved analytically. Thus, one can obtain closed form expressions for the seismic soil pressure, the distance from the base of the point of application of the resultant seismic pressure and the base shear force and bending moment. The above cross-anisotropic solution is first verified by comparing it for the special case of isotropy against existing isotropic solutions. Afterwards parametric studies are conducted in order to assess the effect of cross-anisotropy on the seismic response of the wall-soil system.

This paper summarizes estimated seismic response results from nonlinear inelastic seismic analyses of low-rise plane steel frames equipped with a seesaw system in which linear viscous dampers have been applied. More specifically, considering for each frame three different configurations of the seesaw system and two different orientations of columns, seismic response results involving height wise distributions for peak interstorey drift ratios (IDR), peak residual interstorey drift ratios (RIDR) and peak floor accelerations (PFA) have been obtained. Moreover, peak seismic demands in columns and in the steel plates of the seesaw are found. Results in terms of modal damping ratios are also provided for all frames and seesaw configurations examined. From the results presented, it can be concluded that the seesaw system provides a very attractive solution for typical low-rise steel frames offering significant damping capacity and reduction of their seismic response.

Traditional seismic design of framed structures uses a single constant value for the strength reduction factor. In this work, explicit expressions for different values of strength reduction factors for the first significant modes of steel moment resisting frames including strength deterioration and panel zone effects are developed. These factors are functions of modal periods and deformation/damage and are defined for four performance levels in a performance-based seismic design framework. The above factors are obtained through extensive parametric studies involving 20 steel frames and 100 far-field ground motions and following a two steps procedure: First an equivalent linear structure with the same mass and elastic stiffness of the original non-linear one is constructed based on equivalent modal damping ratios, which substitute the non-linearities; then use of these equivalent modal damping ratios in conjunction with modal damping reduction factors leads to modal strength reduction factors. Using these factors, one can obtain the seismic design base shear of a frame through response spectrum analysis. Thus, a more accurate and rational seismic design method is established. Numerical examples are presented to illustrate the method and demonstrate its advantages against conventional seismic design methods.

This paper summarizes estimated seismic response results from three-dimensional nonlinear inelastic time-history analyses of some steel buckling-restrained braced (BRB) structures taking into account soil-structure interaction (SSI). The response results involve mean values for peak interstorey drift ratios, peak interstorey residual drift ratios and peak floor accelerations. Moreover, mean seismic demands in terms of axial force and rotation in columns, of axial and shear forces and bending moment in BRB beams and of axial displacement in BRBs are also discussed. For comparison purposes, three separate configurations of the BRBs have been considered and the aforementioned seismic response and demands results have been obtained firstly by considering SSI effects and then by neglecting them. It is concluded that SSI, when considered, may lead to larger interstorey and residual interstorey drifts than when not. These drifts did not cause failure of columns and of the BRBs. However, the BRB beam may fail due to flexure.

An alternative design philosophy, for structures equipped with control devices, capable to resist an expected earthquake while remaining in the elastic range, is described. The idea is that a portion of the earthquake loading is under¬taken by the control system and the remaining by the structure which is designed to resist elastically. The earthquake forces assuming elastic behavior (elastic forces) and elastoplastic behavior (design forces) are first calculated ac¬cording to the codes. The required control forces are calculated as the difference from elastic to design forces. The maximum value of capacity of control devices is then compared to the required control force. If the capacity of the control devices is larger than the required control force then the control devices are accepted and installed in the structure and the structure is designed according to the design forces. If the capacity is smaller than the required control force then a scale factor, α, reducing the elastic forces to new design forces is calculated. The structure is redesigned and devices are installed. The proposed procedure ensures that the structure behaves elastically (without damage) for the expected earthquake at no additional cost, excluding that of buying and installing the control devices.

A performance-based seismic design method is proposed for three types of plane R/C structures, i.e., moment resisting frames, infilled moment resisting frames and wall-frame dual systems. It is a force-based design method using the concept of the equivalent viscous damping ratio ξ to account for inelastic energy dissipation instead of that of the behavior (or strength reduction) factor q (or R). More specifically, it uses equivalent modal damping ratios ξ k defined for the equivalent linear multi-degree-of-freedom system to the original non-linear multi-degree-of-freedom system. This equivalent system has the same mass and the elastic stiffness of the non-linear one. Furthermore, these equivalent modal damping ratios ξ k are constructed as functions of the periods of the structure, the target non-structural and structural deformation (both expressed in terms of inter-storey drift ratio and member plastic rotation) and soil type. Thus, the proposed method is more rational and leads to more accurate results in one step (only strength checking) than code-based design methods requiring two steps (strength and deformation checkings). In addition, it can be used as a performance-based seismic design method with two or more performance levels. Explicit expressions of these ξ k for the first few significant modes are proposed. These expressions have been obtained through extensive parametric studies involving non-linear dynamic analysis of 76 frames under 100 far-fault ground motions (corresponding to four soil types of EC8) for different deformation targets. These ξ k can be used for seismic design through linear analysis in conjunction with an elastic acceleration design spectrum modified for high amounts of damping. The proposed method is illustrated and validated by numerical examples which demonstrate its advantages over the Eurocode 8 seismic design method.

Oil and gas offshore platforms are important civil constructions, which are loaded by various types of environmental actions such as wave loads and wind forces. These actions usually govern the platforms’ structural design, while seismic action appears to have minor influence. Nonetheless, numerous offshore structures have been founded in earthquake-prone regions where the structural design can be strongly affected by earthquake action. Many studies have investigated the seismic behaviour of oil and gas offshore platforms examining traditional seismic records. This study investigates the application of simple pulses, i.e., exponential, triangular, rectangular and sinusoidal pulse waveforms, as an earthquake excitation for offshore platforms. To the best of the authors’ knowledge, this is the first time that the aforementioned set of simplified ground motions have been applied to assess the nonlinear seismic behaviour of offshore oil/gas platform. It should be mentioned that pulses could make important information concerning the dynamic response available considering that many intense seismic events enclose actually an acceleration pulse, which can lead to a nonlinear structural response. It is worth noticing that a small number of works have examined the nonlinear response of the platform and most of the previous works assumed fixed boundary conditions ignoring the soil-structure interaction. On the contrary, this study investigates the structural response of 3-D platforms under the action of simplified pulses, considering also the soil-pile-platform interaction. It should be mentioned that the structural design of these special structures fulfils the Eurocode 8 standards. Finally, this work investigates the effect of angle of earthquake waves incidence.

The dynamic response of a water-saturated linear poroelastic soil layer over bedrock retained by a pair of rigid cantilever walls to a horizontal seismic excitation is obtained analytically–numerically under plane strain conditions. Hysteretic damping in the soil skeleton may also be present. The problem is solved in the frequency domain and its exact solution is obtained analytically. This is accomplished with the aid of Fourier series along the horizontal direction and solution of the resulting system of ordinary differential equations to obtain the amplitudes of the soil skeleton displacements and the pore water pressure. Soil displacements and stresses, pore water pressure as well as wall pressures and resultant forces are explicitly presented. Their variation with frequency, hysteretic damping, porosity and permeability is numerically obtained and compared against an approximate solution, to assess the degree of validity of the assumptions.

A force-based seismic design method for eccentrically braced and buckling-restrained braced plane steel frames is proposed. The method makes use of equivalent modal damping ratios that play the role of the behavior (strength reduction) factor. A comparison of the proposed design method with the EC 8 design method is presented herein and conclusions are drawn.

A simple formula is proposed that provides interstorey velocities of steel framed structures at specific interstorey drift levels. The proposed equation is statistically derived from the variation of floor relative velocity results along the height of the structure. These results are obtained by non-linear inelastic time history analyses of a number of plane steel moment resisting frames. The proposed equation can then be used for seismic retrofit purposes, i.e., in dimensioning the linear or non-linear viscous dampers to be inserted in a steel frame. A detailed numerical example is provided and conclusions regarding the accuracy and the potential use of interstorey velocity are drawn.

A numerical comparison study of the interstorey and the residual interstorey seismic drifts of steel structures equipped with the seesaw system and buckling-restrained braces is carried out. This investigation involves inelastic time-history seismic analyses of 2-, 5- and 8-storey 3-D steel structures, with specific orientation of columns and configuration of braces, for the design basis earthquake. The effects of soil-structure interaction and seismic incident angle are also considered in these analyses. Comparison of the seismic drift responses experienced by the seesaw-braced and the buckling-restrained braced steel structures, reveals different peak interstorey drift values but in many cases similar drift concentration along the height of the structures. Furthermore, the seesaw-braced steel structures exhibit, in general, larger peak residual drifts than buckling-restrained braced steel structures.