Nonlinear Static Methods vs. Experimental Shaking Table Test Results

Three different Nonlinear Static Methods (NSM's), based on pushover analysis, are applied to a 3-story, 2-bay, RC frame. They are (i) the Capacity Spectrum Method (CSM), described in ATC-40, (ii) the Displacement Coefficient Method (DCM), presented in FEMA-273 and further developed in FEMA 356, and (iii) the N2 Method, implemented in the Eurocode 8. Pushover analyses are conducted with DRAIN-3DX by using four different lateral force distributions, according to the acceleration profile assumed along the height of the structure: uniform, triangular, modal-proportional, and multimodal fully adaptive. In the numerical model, RC members are modeled as fiber elements.

The numerical predictions of each method are compared to the experimental results of the shaking table tests carried out on two similar 1:3.3-scale structural models, with and without infilled masonry panels, respectively. The comparison is made in terms of maximum story displacements, interstory drifts, and shear forces. All the NSM's are found to predict with adequate accuracy the maximum seismic response of the structure, provided that the associated parameters are properly estimated. The lateral load pattern, instead, is found to little affect the accuracy of the results for the three-story model considered, even if collapse occurs with a soft story mechanism.     

SEISMIC DESIGN AND RESPONSE OF BARE AND MASONRY-INFILLED REINFORCED CONCRETE BUILDINGS. PART I: BARE STRUCTURES

Abstract

Eurocode 8 is applied for the complete design of 26 multi-storey reinforced concrete buildings to study its operationally and compare the implications of trading strength for ductility through designing the same structure for a different Ductility Class. The difference between the conventional full Capacity Design of columns in bending and the relaxed one allowed by Eurocode 8 is quantified, and the implications on the column capacities are examined. About half of the designed buildings, representative of the class of regular frames, are subjected to nonlinear dynamic response analyses to spectrum-compatible motions with intensities up to twice that of the design motion. Nonlinear modeling is very simple, but gives satisfactory agreement with available quasistatic or pseudodynamic test results on full scale structures. Results show that the three Ductility Classes of Eurocode 8 are essentially equivalent in terms of material quantities and seismic performance. Within the limitations of the nonlinear modelling, the response results suggest very satisfactory performance of structures designed to Eurocode 8, even under twice the design motion intensity. Softening of the structure due to concrete cracking and steel yielding significantly reduces the seismic force demands and contributes to the satisfactory performance, despite the increased P — 6 effects. Another important contributor to the good performance is the significant overstrength of the members considered in the analyses with their average as-built properties. Beam overstrength due to the contribution of the slab to flexural capacity is large enough to overcome the effects of the application of the relaxed Capacity Design rule to columns in bending. However, the resulting column plastic hinging does not lead to drift concentrations suggesting formation of storey-sway mechanisms.     

NON-LINEAR SEISMIC RESPONSE OF ECS DESIGNED RC BUILDING STRUCTURES

In this paper, results of an analytical study on the non-linear dynamic behaviour of reinforced concrete buildings designed according to modern European Codes (Eurocode 8) are presented. An investigation of the seismic performance of 8-storey regular and irregular buildings is carried out. The study is aimed at evaluating their seismic structural performance with a focus on the influence of several design parameters used in the code affecting non-linear response. Towards this aim, use is made of a suite of spectrum-compatible artificial accelerograms. It is concluded that EC8 provisions, although correct in principle, are conservative, at least for the structures and input motions considered, in view of the very low predicted damage levels observed in most cases.     

EXPERIMENTAL ASSESSMENT OF THE GLOBAL CYCLIC DAMAGE OF FRAMED R/C STRUCTURES

It is accepted that failure criteria for earthquake-resistant structures should be based on energy dissipation as well as on maximum ductility. Even though rational procedures to include low-cycle fatigue in the definition of the design spectra have been derived, major difficulties arise in the definition of the cyclic damageability of the structure. The work conducted so far was mainly based on cyclic tests conducted on simple structural elements, therefore, the extension to the complete structure is not an easy task. A final cyclic test was conducted at the ELSA reaction wall facility on a four-storey full-scale reinforced concrete frame designed according to Eurocode 8, at the end of a series of pseudodynamic tests. The results allow the performance during the pseudodynamic tests to be assessed and the cyclic damageability of a complete structure to be investigated. The effects of low-cycle fatigue on a high-ductility structure turned out to be more important than expected.     

Full-Scale Experimental Verification of Soft-Story-Only Retrofits of Wood-Frame Buildings using Hybrid Testing

The FEMA P-807 Guidelines were developed for retrofitting soft-story wood-frame buildings based on existing data, and the method had not been verified through full-scale experimental testing. This article presents two different retrofit designs based directly on the FEMA P-807 Guidelines that were examined at several different seismic intensity levels. The effects of the retrofits on damage to the upper stories were investigated. The results from the hybrid testing verify that designs following the FEMA P-807 Guidelines meet specified performance levels and appear to successfully prevent collapse at significantly higher seismic intensity levels well beyond for which they were designed. Based on the test results presented in this article, it is recommended that the soft-story-only retrofit procedure can be followed when financial or other constraints limit the retrofit from bringing the soft-story building up to current code or applying performance-based procedures.     

Seismic Vulnerability Assessment of Hybrid Steel-Timber Structure: Steel Moment-Resisting Frames with CLT Infill

In this article, seismic vulnerability assessment is carried-out on a novel hybrid structure (steel moment resisting frame (SMRF) and cross laminated timber (CLT) infill panels). For the seismicity of Vancouver, Canada, a three-bay, 3-, 6-, and 9-story height SMRFs are designed for two ductility levels (ductile and limited ductility). To study the seismic vulnerability CLT infilled building, parametric analysis was performed by varying infill configuration (bare frame, one-bay infilled, two-bay infilled, and fully infilled). The structure is modeled in OpenSees and nonlinear dynamic analysis is performed. Peak inter-story drift demand and corresponding FEMA performance limits (capacity) values are used to compute the corresponding fragility curves. From the analyses, it can be seen that as more bays are infilled, the fundamental period and seismic vulnerability is reduced significantly. The results highlight that, within the performance-based earthquake engineering, different objectives can be met with varying the CLT configuration.     

STRUCTURAL RESPONSE AND DAMAGE ASSESSMENT BY ENHANCED UNCOUPLED MODAL RESPONSE HISTORY ANALYSIS

The Uncoupled Modal Response History Analysis (UMRHA) method developed by Chopra et al. is modified in this paper to estimate damage to welded moment-resisting connections in a steel frame (MRSF) subjected to earthquake ground motions. The behaviour of these connections is modelled by a moment-rotation relationship that accounts for the cracking of the beam flange-to-column flange groove weld. The behaviour of the frame is approximated by a sequence of single-degree-of-freedom (SDOF) models for the first three modes to allow for the contribution of higher modes of vibration. The dynamic properties of these SDOF systems are determined by nonlinear static pushover analyses of the building frame. Because of the significant drop in connection strength caused by beam-to-column weld cracking, the pushover procedure uses a changing rather than invariant distribution of horizontal loads, while the structural responses are calculated from shapes that are based on the displaced shape of the frame after damage occurs. The accuracy of the method is demonstrated by a comparison with the results of a nonlinear time history analysis of the frame. This method can be used for rapid assessment of seismic damage or damage potential and to identify buildings requiring more detailed investigation.     

EVALUATION OF CONVENTIONAL AND ADAPTIVE PUSHOVER ANALYSIS II: COMPARATIVE RESULTS

In this paper, the methodology for evaluation of conventional and adaptive pushover analysis presented in a companion paper is applied to a set of eight different reinforced concrete buildings, covering various levels of irregularity in plan and elevation, structural ductility and directional effects. An extensive series of pushover analysis results, monitored on various levels is presented and compared to inelastic dynamic analysis under various strong motion records, using a new quantitative measure. It is concluded that advanced (adaptive) pushover analysis often gives results superior to those from conventional pushover. However, the consistency of the improvement is unreliable. It is also emphasised that global response parameter comparisons often give an incomplete and sometimes even misleading impression of the performance.     

EVALUATION OF CONVENTIONAL AND ADAPTIVE PUSHOVER ANALYSIS I: METHODOLOGY

In this paper, a methodology is suggested and tested for evaluating the relative performance of conventional and adaptive pushover methods for seismic response assessment. The basis of the evaluation procedure is a quantitative measure for the difference in response between these methods and inelastic dynamic analysis which is deemed to be the most accurate. Various structural levels of evaluation and different incremental representations for dynamic analysis are also suggested. This method is applied on a set of eight different reinforced concrete structural systems subjected to various strong motion records. Sample results are presented and discussed while the full results are presented alongside conclusions and recommendations, in a companion paper.     

Seismic Load Capacity of Historical Masonry Mosques by Rigid Body Kinetics

ABSTRACT

Kinetic analysis methods based on linear and nonlinear rigid body dynamics are used to evaluate earthquake safety of masonry structures. In this study, the formulas used to calculate the in-plane and out-of-plane load capacities of masonry load-bearing walls were evaluated and a procedure based on rigid body mechanism was proposed to calculate the out-of-plane load capacities of the walls of Ottoman period masonry mosques. New aspects of the method with respect to existing formulations is the inclusion of dynamic axial load and definition of the collapse limit spectral acceleration on the overturning wall. The calculated capacities of the mosque and individual walls were compared with the results of nonlinear pushover analysis and time history analyses performed under 1.0 and 0.5 scaled forms of nine different 3-component ground motion records. It was displayed that the seismic load capacity estimated by the proposed method is very close to the values calculated by pushover and time history analyses. The method was developed on Lala Pasha Mosque, and the reliability and applicability of the proposed methodology is verified on a different historical masonry mosque in comparison to finite element analyses results.     

Dome of the Basilica of Santa Maria Degli Angeli in Assisi: Static and Dynamic Assessment

This study presents the results of the static and dynamic assessment of the dome of the Basilica of Santa Maria degli Angeli in Assisi, designed by Galeazzo Alessi. The first section is devoted to an overview of the masonry domes designed by the Italian architect and focuses on the structural solutions adopted in the several cases described to better understand Alessi’s designing skills. In the second part, the drum-dome system is analyzed in order to attain a structural assessment. The static assessment is performed by means of limit analysis and finite element model approaches with non-linear mechanical behavior. The obtained results are consistent with the detected crack pattern and confirm the suitability of the reinforcement steel rings applied to the drum. The seismic assessment has been performed by response spectrum analysis. Due to the lack of specific information, a probabilistic approach for the material mechanical properties was used. The results obtained highlight an adequate seismic response of the structure that can be attributed to the dynamic properties of the slender drum-dome system. This finding justifies the good performance of the structure during the seismic events of 1832 and 1997.     

ADVANTAGES AND LIMITATIONS OF ADAPTIVE AND NON-ADAPTIVE FORCE-BASED PUSHOVER PROCEDURES

The recent drive for use of performance based methodologies in design and assessment of structures in seismic areas has significantly increased the demand for the development of reliable nonlinear inelastic static pushover analysis tools. As a result, the recent years have witnessed the introduction of the so-called adaptive pushover methods, which, unlike their conventional pushover counterparts, feature the ability to account for the effect that higher modes of vibration and progressive stiffness degradation might have on the distribution of seismic storey forces. In this paper, the accuracy of these force-based adaptive pushover methods in predicting the horizontal capacity of reinforced concrete buildings is explored, through comparison with results from a large number of nonlinear time-history dynamic analyses. It is concluded that, despite its apparent conceptual superiority, current force-based adaptive pushover features a relatively minor advantage over its traditional non-adaptive equivalent, particularly in what concerns the estimation of deformation patterns of buildings, which are poorly predicted by both types of analysis.     

Confidence Factor?

Eurocode 8 Part 3 (EC8-3) is devoted to assessment and retrofitting of existing buildings. In order to take into account the uncertainty in the knowledge of structural properties, EC8-3 defines, analogously to the ordinary material partial factors, an adjustment factor, called “confidence factor (CF),” whose value depends on the level of knowledge (KL) of properties such as geometry, reinforcement layout and detailing, and materials. This solution is plausible from a logical point of view but it cannot yet profit from the experience of its use in practice, hence it needs to be substantiated by a higher level probabilistic analysis accounting for and propagating epistemic uncertainty (i.e., incomplete knowledge of a structure) throughout the seismic assessment procedure. This article investigates the soundness of the format proposed in EC8-3. The approach taken rests on the simulation of the entire assessment procedure and the evaluation of the distribution of the assessment results (distance from the limit state of interest) conditional on the acquired knowledge. Based on this distribution, a criterion is employed to calibrate the CF values. The obtained values are then critically examined and compared with code-specified ones. The results pinpoint a number of deficiencies that appear to somewhat invalidate the approach. The methodological significance of the work extends beyond the assessment procedure in EC8-3, since similar factors appear in other international guidelines (e.g., the knowledge factor of FEMA356).     

A CAPACITY PREDICTION PROCEDURE FOR CONCRETE-FILLED STEEL COLUMNS

A seismic design procedure for partially concrete-filled box-shaped steel columns is presented in this paper. To determine the ultimate state of such columns, concrete and steel segments are modelled using beam-column elements and a pushover analysis procedure is adopted. This is done by means of a new failure criterion based on the average strain of concrete and steel at critical regions. The proposed procedure is applicable to columns having thin- and thick-walled sections, which are longitudinally stiffened or not. An uniaxial constitutive relation recently developed is employed for concrete filled in the thick-walled unstiffened section columns. Modifications are introduced to this model for other types of columns. Subsequently, the strength and ductility predictions obtained using the present and previous procedures are compared with the corresponding experimental results. Comparisons show that the present procedure yields better predictions. It is revealed that the inclusion of the confinement effects and softening behaviour of concrete is important in the present kind of prediction procedures. Furthermore, an extensive parametric study is carried out to examine the effects of procedures and geometrical and material properties on capacity predictions.     

Seismic Design of MRF-EBF Dual Systems with Vertical Links: EC8 vs Plastic Design

Despite the fact that Eccentrically Braced Frames with Vertical Links (VL-EBFs), also referred to as inverted Y-scheme, are codified in Eurocode 8, the issues related to their seismic response and design have not been widely investigated, so that design criteria commonly applied for Eccentrically Braced Frames with Horizontal Links (HL-EBFs) are commonly applied. However, the Theory of Plastic Mechanism Control (TPMC) has been recently extended to the case of VL-EBFs. The aims of this article, on one hand, are to provide a further validation of the recently proposed design procedure, based on TPMC, and, on the other hand, are to compare the seismic performance of dual systems composed by a moment-resisting part and VL-EBF part designed by means of TPMC with those occurring when Eurocode 8 design criteria are applied. The validation of the proposed design procedure is carried out by means of Incremental Dynamic Analyses (IDA). The main purpose of such analyses is the check of the fulfilment of the design goal of TPMC, i.e., the development of a pattern of yielding consistent with the collapse mechanism of global type. Such mechanism is universally recognized as the one leading to the highest energy dissipation capacity. In case of MRF-EBF dual systems, it is characterized by the yielding of all the links and all the beams at their ends. Conversely, all the columns and the diagonal braces remain in elastic range. Obviously, exception is made for the base sections of first story columns. In particular, two case studies are analyzed which are characterized by a different number of stories. Each building structure is designed according to both TPMC and Eurocode 8 provisions. The seismic response obtained is investigated by both push-over and IDA analyses. The attention is focused on the pattern of yielding obtained, the maximum interstory drift demand, the link plastic rotation demand and sharing of the seismic base shear between the moment-resisting part and the bracing part of the structural system. The results obtained point out improvement of the seismic response, compared to Eurocode 8 provisions, achieved by means of TPMC.     

AN EFFICIENT APPROACH FOR PUSHOVER ANALYSIS OF UNREINFORCED MASONRY (URM) STRUCTURES

This article presents a new method for the calculation of the moment-rotation (M-θ) curves of URM elements using an analytical phenomenogical closed form solution for flexure, combined with a hybrid analytical-statistical model for shear. These are used to define the constitutive law of nonlinear springs located at the areas of lumped inelasticity of an equivalent frame model. The method constitutes an analytical design/assessment tool, to be used by the practicing engineer, for the pushover analysis of URM buildings. The proposed procedure is implemented as a pre-processor to a commercial nonlinear software codes capable of static pushover analysis using the point hinge approach.     

A Single-Run Dynamic-Based Approach for Pushover Analysis of Structures Subjected to Near-Fault Pulse-Like Ground Motions

In this paper, a fairly effective procedure called dynamic load pattern (DLP), is proposed to account for the effects of near-fault ground motions in estimating the seismic demands of structures from pushover analyses. The seismic demands are obtained by enveloping the results of single-run conventional first-mode and single-run DLP pushover analyses. Improving the estimation of target displacement is another objective, implemented by performing response-spectrum analysis. Three special steel moment-resisting frames are considered and the seismic demands resulting from DLP are compared to those from the nonlinear time-history analysis as a benchmark solution, as well as to those predicted from modal pushover analysis.     

A Critical Review of European and American Provisions for the Seismic Assessment of Existing Steel Moment-Resisting Frame Buildings

The publication of Part 3 of Eurocode 8 (EC8-3), dedicated to the seismic assessment of existing buildings, took place a decade ago. However, its application in engineering practice has been limited. Moreover, no studies have been conducted regarding the application of EC8-3 to steel structures. In this paper, a critical review and practical application of EC8-3 and ASCE41-13 are carried out. Issues related to the definition of the performance requirements, compliance criteria, and the consistency of the analysis procedures proposed by both standards are identified. Conceptual differences between both documents are highlighted, and several inconsistencies in EC8-3 are discussed.     

Jet-Pacs Project: Dynamic Experimental Tests and Numerical Results Obtained for a Steel Frame Equipped with Hysteretic Damped Chevron Braces

The experimental and numerical results obtained by Research Units of the University of Basilicata and University of Calabria for a steel frame, bare or equipped with metallic yielding hysteretic dampers (HYDs), are compared. The shaking table tests were performed at the Structural Laboratory of the University of Basilicata within a wide research program, named JETPACS (“Joint Experimental Testing on Passive and semiActive Control Systems”), which involved many Research Units working for the Research Line 7 of the ReLUIS (Italian Network of University Laboratories of Earthquake Engineering) 2005–2008 project. The project was entirely founded by the Italian Department of Civil Protection. The test structure is a 1/1.5 scaled two-story, single-bay, three-dimensional steel frame. Four HYDs, two for each story, are inserted at the top of chevron braces installed within the bays of two parallel plane frames along the test direction. The HYDs, constituted of a low-carbon U-shaped steel plate, were designed with the performance objective of limiting the inter-story drifts so that the frame yielding is prevented. Two design solutions are considered, assuming the same stiffness of the chevron braces with HYDs, but different values of both ductility demand and yield strength of the HYDs. Seven recorded accelerograms matching on average the response spectrum of Eurocode 8 for a high-risk seismic region and a medium subsoil class are considered as seismic input. The experimental results are compared with the numerical ones obtained considering an elastic-linear law for the chevron braces (in tension and compression), providing that the buckling be prevented, and the Bouc-Wen model to simulate the response of HYDs.     

Probabilistic Calibration and Experimental Validation of the Seismic Design Criteria for One-Story Concrete Frames

This article investigates the seismic performance of one-story reinforced concrete structures for industrial buildings. To this aim, the seismic response of two structural prototypes, a cast-in-situ monolithic frame and a precast hinged frame, is compared for four different levels of translatory stiffness and seismic capacity. For these structures an incremental nonlinear dynamic analysis is performed within a Monte Carlo probabilistic simulation. The results obtained from the probabilistic analysis prove that precast structures have the same seismic capacity of the corresponding cast-in-situ structures and confirm the overall goodness of the design criteria proposed by Eurocode 8, even if a noteworthy dependency of the actual structural behavior from the prescribed response spectrum is pointed out.

The experimental verification of these theoretical results is searched for by means of pseudodynamic tests on full-scale structures. The results of these tests confirm the overall equivalence of the seismic behavior of precast and cast-in-situ structures. Moreover, two additional prototypes have been designed to investigate the seismic behavior of precast structures with roof elements placed side by side. The results of these further tests show that an effective horizontal diaphragm action can be activated even if the roof elements are not connected among them, and confirm the expected good seismic performance of these precast systems. Finally, the results of the experimental tests are compared with those obtained from nonlinear structural analyses. The good agreement between numerical and experimental results confirms the accuracy of the theoretical model and, with it, the results of the probabilistic investigation.