a b s t r a c tMany shear correction factors have appeared since the inception of Timoshenko beam theory in 1921. While rational bases for them have been offered, there continues to be some reluctance to their full acceptance because the explanations are not totally convincing and their efficacies have not been comprehensively evaluated over a range of application. Herein, three-dimensional static and dynamic information and results for a beam of general (both symmetric and non-symmetric) cross-section are brought to bear on these issues. Only homogeneous, isotropic beams are considered. Semi-analytical finite element (SAFE) computer codes provide static and dynamic response data for our purposes. Greater clarification of issues relating to the bases for shear correction factors can be seen. Also, comparisons of numerical results with Timoshenko beam data will show the effectiveness of these factors beyond the range of application of elementary (Bernoulli-Euler) theory.An issue concerning principal shear axes arose in the definition of shear correction factors for non-symmetric cross-sections. In this method, expressions for the shear energies of two transverse forces applied on the cross-section by beam and three-dimensional elasticity theories are equated to determine the shear correction factors. This led to the necessity for principal shear axes. We will argue against this concept and show that when two forces are applied simultaneously to a cross-section, it leads to an inconsistency. Only one force should be used at a time, and two sets of calculations are needed to establish the shear correction factors for a non-symmetrical cross-section.

Herein, we propose a method based on the existing second-order blind identification of underdetermined mixtures technique for identifying the modal characteristics-namely, natural frequencies, damping ratio, and real-valued partial mode shapes of all contributing modes-of structures with a limited number of sensors from recorded free/ ambient vibration data. In the second-order blind identification approach, second-order statistics of recorded signals are used to recover modal coordinates and mode shapes. Conventional versions of this approach require the number of sensors to be equal to or greater than the number of active modes. In the present study, we first employ a parallel factor technique to decompose the covariance tensor into rank-one tensors so that the partial mode shapes at the recording locations (sensors) can be estimated. The mode shape matrix identified in this manner is not square, which precludes the use of a simple inversion to extract the modal coordinates. As such, the natural frequencies are identified from the recovered modal coordinates' Autocovariances. The damping ratios are extracted using a least-squares technique from modal free vibrations, as they are not directly recoverable because of the inherent smearing produced by windowing processes. Finally, a Bayesian model updating approach is employed to complete the partial mode shapes-that is, to extract the mode shapes at the DOFs without sensors. We use simulated and physical data for verifying and validating this new identification method, and explore optimal sensor distribution in multistory structures for a given (limited) number of sensors. particular extraction method works without having the sources or the mixing processes-hence, the term blind-and employs second-order statistics of recorded response signals to recover the modal coordinate signals and the mode shape matrix. However, SOBI method does not work well in the presence of highly damped, low-energy or closely spaced modes, severe nonstationary excitations, and relatively large measurement noise. The issues of weakly nonstationary signals and noisy measurement were addressed in [20], whereas separability of low-energy modes was improved by employing stationary wavelet transform in [21]. Nevertheless, conventional versions of SOBI methods are limited to determined or overdetermined problems, in which the number of active modes is equal to or less than the number of recorded signals. For civil structures (e.g., tall buildings, long-span bridges, etc.), this constraint is often prohibitive.Various algorithms are presented in the signal processing literature for underdetermined problems, and in most such studies, the source signals (here, the modal coordinates) are assumed to be sparse [22,23]. Given this condition, time-frequency representations along with clustering techniques [24,25] or modal decompositions [26] are used to identify the source signals. Nevertheless, aforementioned methods are not suitable for modal identification of civil structures because their free or a...

SUMMARY Dynamic characteristics of structures — viz. natural frequencies, damping ratios, and mode shapes — are central to earthquake‐resistant design. These values identified from field measurements are useful for model validation and health‐monitoring. Most system identification methods require input excitations motions to be measured and the structural response; however, the true input motions are seldom recordable. For example, when soil–structure interaction effects are non‐negligible, neither the free‐field motions nor the recorded responses of the foundations may be assumed as ‘input’. Even in the absence of soil–structure interaction, in many instances, the foundation responses are not recorded (or are recorded with a low signal‐to‐noise ratio). Unfortunately, existing output‐only methods are limited to free vibration data, or weak stationary ambient excitations. However, it is well‐known that the dynamic characteristics of most civil structures are amplitude‐dependent; thus, parameters identified from low‐amplitude responses do not match well with those from strong excitations, which arguably are more pertinent to seismic design. In this study, we present a new identification method through which a structure's dynamic characteristics can be extracted using only seismic response (output) signals. In this method, first, the response signals’ spatial time‐frequency distributions are used for blindly identifying the classical mode shapes and the modal coordinate signals. Second, cross‐relations among the modal coordinates are employed to determine the system's natural frequencies and damping ratios on the premise of linear behavior for the system. We use simulated (but realistic) data to verify the method, and also apply it to a real‐life data set to demonstrate its utility. Copyright © 2012 John Wiley & Sons, Ltd.

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Effective post‐earthquake response requires a prompt and accurate assessment of earthquake‐induced damage. However, existing damage assessment methods cannot simultaneously meet these requirements. This study proposes a framework for real‐time regional seismic damage assessment that is based on a Long Short‐Term Memory (LSTM) neural network architecture. The proposed framework is not specially designed for individual structural types, but offers rapid estimates at regional scale. The framework is built around a workflow that establishes high‐performance mapping rules between ground motions and structural damage via region‐specific models. This workflow comprises three main parts—namely, region‐specific database generation, LSTM model training and verification, and model utilization for damage prediction. The influence of various LSTM architectures, hyperparameter selection, and dataset resampling procedures are systematically analyzed. As a testbed for the established framework, a case study is performed on the Tsinghua University campus buildings. The results demonstrate that the developed LSTM framework can perform damage assessment in real time at regional scale with high prediction accuracy and acceptable variance.