Journal of Structural Engineering

As the use of buckling-restrained braced frames (BRBFs) has increased in the United States, the need has grown for knowledge about member and system behavior under seismic loads and for implementing this knowledge into design provisions. In particular, methods for designing BRBFs and predicting seismic response require validation. To address this need, along with the need for experiments demonstrating system-level BRBF performance, a research program composed of numerical and large-scale experimental simulations was initiated at the ATLSS Center, Lehigh University. This paper describes the nonlinear dynamic analyses that were conducted as part of this research program. Numerical simulations of BRBF response were conducted using ground motion records scaled to two seismic hazard levels. The performance of the prototype BRBF was acceptable and performance objectives were met in terms of structural damage. It is shown that the currently accepted deflection amplification factor underestimates mean inelastic lateral displacements under design-level earthquakes and the system overstrength factor may be unconservative. The current method for predicting BRB maximum ductility demands is also shown to be unconservative and a more rigorous method for predicting BRB maximum ductility demands is provided.

As buckling-restrained braced frames (BRBFs) have been used increasingly in the United States, the need for knowledge about BRBF behavior has grown. In particular, large-scale experimental evaluations of BRBFs are necessary to demonstrate the seismic performance of the system. Although tests of buckling-restrained braces (BRBs) have demonstrated their ability to withstand significant ductility demands, large-scale BRBF tests have exhibited poor performance at story drifts between 0.02 and $0.025\mathrm{rad}$ . These tests indicate that the large stiffness of the typical beam-column-brace connection detail leads to large flexural demands that cause undesirable failure modes. As part of a research program composed of numerical and experimental simulations, a large-scale BRBF with improved connection details was tested at the ATLSS Center, Lehigh University. During multiple earthquake simulations, which were conducted using a hybrid pseudodynamic testing method, the test frame sustained story drifts of close to $0.05\mathrm{rad}$ and BRB maximum ductility demands of over 25 with minimal damage and no stiffness or strength degradation. The testing program demonstrated that a properly detailed BRBF can withstand severe seismic input and maintain its full load-carrying capacity.

To investigate the effectiveness of several seismic strengthening techniques, a full-scale unreinforced masonry (URM) structure was subjected to slowly applied lateral load reversals after the application of fiber reinforced plastic overlays, near surface mounted rods, and vertical posttensioning. Results showed that all techniques were effective for improving the seismic resistance of the previously tested URM building structure. Each system either increased the lateral in-plane strength and/or provided continuity of pier and spandrel elements over increased lateral displacements. In addition, the response of the test structure (overall height to base ratio of approximately one) showed that global issues such as flange effects, the effects of overturning moment, and global rocking can be substantial and must be considered.

An experimental study investigating the influence of lateral displacement on the vertical stiffness of elastomeric and lead–rubber seismic isolation bearings is summarized. Two identically constructed low-damping rubber and lead–rubber seismic isolation bearings were subjected to a series of tests with varying levels of combined lateral displacement and axial (compressive) loading to study this relationship. The results of these tests showed the vertical stiffness decreases with increasing lateral displacement for each bearing tested. Additionally, the vertical stiffness data are used to evaluate four formulations for the estimation of the vertical stiffness as a function of the lateral displacement. From this comparison, two formulations, one based on the Koh–Kelly two-spring model and the other on a piecewise linear relationship, showed good agreement with the experimental data over the wide range of lateral displacements considered in this study.

Nonlinear static procedures (NSPs) presented in the FEMA-440 document are evaluated for nondegrading three- to nine-story reinforced concrete moment-resisting frame systems. Evaluations are based on peak single-degree-of-freedom displacement, peak roof, and interstory drifts estimations. A total of 78 soil site records and 24 buildings with fundamental periods varying between $0.3\mathrm{s}–1.3\mathrm{s}$ are used in 2,832 linear and nonlinear response-history analyses to derive the descriptive statistics. The moment magnitude of the ground motions varies between 5.7 and 7.6. All records are within $23\mathrm{km}$ of the causative fault representing near-fault ground motions with and without pulse signals. The statistics presented suggest that lateral loading patterns used in pushover analysis to idealize the building systems play a role in the accuracy of NSPs investigated. Both procedures yield fairly good deformation demand estimations on the median. Displacement coefficient method (DCM) tends to overestimate the global deformation demands with respect to the capacity spectrum method (CSM). The conservative deformation demand estimations of DCM are correlated with the normalized lateral strength ratio, $R$ . The CSM tends to overestimate the deformation demands for the increasing displacement ductility, $\mu$ .

This article suggests the process of structural health monitoring (SHM) in the context of a nonstatistical damage detection paradigm. We particularly focus on applying the theory of possibility to the damage detection problem. The basic idea behind the proposed approach is that the application of possibility theory does not require probabilistic knowledge or assumptions on the damage feature and thus encompasses aleatoric and epistemic types of uncertainties. The approach is not damage feature dependent and thus is generic for use in many SHM systems. Additionally, two new damage metrics are introduced. These metrics extract information concerning damage evidence from observations performed at unknown health states of structures. Damage detection with the aid of the proposed approach is demonstrated by means of a case study.

Vibration-based damage detection (VBDD) methods use damage-induced changes to the dynamic properties of a structure to detect, locate, and sometimes quantify the extent of damage. This paper describes a laboratory-based experimental and finite element analysis study conducted to evaluate the ability of five different VBDD methods to detect and localize low levels of damage on the deck slab of a two-girder, simply supported bridge, with a focus on using a small number of sensors and only the fundamental mode of vibration. It is demonstrated that damage can be detected and localized longitudinally within a distance equivalent to the spacing between measurement points using data for only the fundamental mode shape before and after damage, defined by as few as five evenly spaced measurement points. The localization resolution declines by approximately 50% near supports. Increasing the number of measurement points improves the localization resolution of the techniques, although not always in proportion to the resulting decrease in measurement point spacing. Incorporating data from two additional modes was not found to significantly improve the localization performance.

Composite slabs utilizing cold-formed profiled steel decks are commonly used for floor systems in steel framed buildings. The behavior and strength of composite slabs are normally controlled by the horizontal shear bond between the steel deck and the concrete. The strength of the horizontal shear bond depends on many factors and it is not possible to provide representative design values that can be applied to all slab conditions a priori. Thus, present design standards require that the design parameters be obtained from full-size bending tests, which are typically one or two deck panels wide and a single span. However, because these full-size tests can be expensive and time consuming, smaller size specimens, referred to as elemental tests, are desirable and have been the subject of a great deal of research. Details for a new elemental test method for composite slab specimens under bending are presented. Test results consisting of maximum applied load, end slips, and failure modes are presented and compared with the results of full-size specimens with similar end details, spans, etc. It is shown that the performance of the elemental test developed in this study is in good agreement with the performance of the full-size specimens. Application of test data to current design specifications is also presented.

This paper presents results from a systematic finite-element (FE) study on the static strength of moment loaded thick-walled circular hollow section (CHS) X-joints, and compares the results with CIDECT and ISO/CD 13819-2 recommendations. For thick-walled joints subjected to brace out-of-plane bending, the CIDECT formulation excludes the $\gamma$ dependency in the joint strength, which is different from the ISO equation and the present FE observations. The current study compares the different load paths mobilized in the X-joint under various brace loading conditions, through a detailed three-dimensional finite-element study. The numerical results reveal the significance of the joint geometric parameters and the tensile chord stress effect on the ultimate joint strength. Based on the present detailed study, a new chord stress function which incorporates the geometric dependency and the tensile chord stress effect is proposed.

A design-oriented confinement model for square and rectangular columns confined with bonded fiber-reinforced polymer (FRP) jackets, and shape-modified square and rectangular sections confined with posttensioned FRP shells is developed. The proposed design model for FRP-confined concrete columns is based on the bilinear four-parameter formulation by Richard and Abbott. The axial compressive strength of FRP-confined concrete is obtained using concrete plasticity theory based on the five parameter Willam and Warnke model. The ultimate axial strain of FRP-confined concrete is obtained from a strain-based approach depending on either passive or active confinement; the ultimate axial strain is based on the concepts of secant concrete modulus and strain dependent stiffness established by Pantazopoulou and Mills. Comparisons of the proposed stress-strain model with uniaxial compression experiments for columns with bonded FRP jackets or posttensioned FRP shells, performed by the writers and other researchers, show satisfactory agreement for the entire stress-strain curve.

This paper examines the effect of corrosion of reinforcing steel on flexural and shear strength, and subsequently on reliability, of reinforced concrete beams. Two types of corrosion—general and pitting—are considered, with particular emphasis on the influence of pitting corrosion of stirrups on the performance of beams in shear. Variability of pitting corrosion along a beam is considered and the possibility of failure at a number of the beam cross sections is taken into account. Probabilities of failure are evaluated using Monte Carlo simulation. Uncertainties in material properties, geometry, loads, and corrosion modeling are taken into account. Results show that corrosion of stirrups, especially pitting corrosion, has a significant influence on the reliability of reinforced concrete beams.

The paper investigates the long-term behavior of wood-concrete composite beams with notched connection detail. The experimental program comprised the characterization of the component materials (wood, concrete, and connection detail) and long-term tests on beam specimens. The beam specimens were monitored during the construction process, and for an overall period of 133 days after the application of the service load. The experimental results have then been extended to the entire service life of the structure using a one-dimensional finite-element model. It was found that the increase in moisture content due to the bleeding of the fresh concrete is not an issue for the durability of the wood deck, and the type of construction (shored or unshored) does not significantly affect the structural performance. The rheological phenomena experienced by the component materials lead to quite large deflections over the entire service life, whereas the variation in stress is not significant. If the limitation of the deflection is required for serviceability considerations, the use of concrete with reduced shrinkage and the precambering of the wood deck are to be recommended. A simplified approach based on closed form solutions for composite beams with smeared flexible connectors is finally proposed for the prediction of the long-term behavior.

This study contributes to the critical need for safety assessment tools for existing reinforced concrete structures. Of particular concern is the possibility of collapse due to shear failure followed by axial failure of columns supporting gravity loads. This is a potential threat to a number of existing buildings in seismically active regions. Due to unavoidable uncertainties, drift capacity predictions can only be made in a probabilistic manner. This is addressed by the development of probabilistic drift capacity models at two performance levels: lateral strength degradation and axial load failure. First, a classification method is proposed to approximately distinguish between shear-dominated columns and flexure-dominated columns. Second, for each type of column, a probabilistic shear capacity model is developed by applying an existing Bayesian methodology to an experimental database. The focus of the presentation is on the physical insight gained from the model development. Third, a probabilistic model is developed for the drift capacity at axial load failure. Finally, the probabilistic drift capacity models are employed to develop fragility curves—with confidence bounds—that are utilized to assess the probability of failure implied by current seismic rehabilitation guidelines.

A gradient-based optimization algorithm is used to simultaneously control all interstory displacements in nonlinearly degrading steel buildings using optimal viscous dampers. Optimal damping ratios are computed in each mode of vibration such that the sum of the errors between the interstory displacements and the “just-yielded” performance objectives is minimized. A representative damping formulation is used to determine the sizes and locations of the damper devices. The members of the buildings are assumed to degrade smoothly according to a constitutive rule that was developed to model the behavior of kinematically strain-hardened materials. Numerical examples are used to demonstrate the ability of the algorithm to control potential damages in a 10-story building and also in an 8-story building responding at significant higher modes of vibration. It is found that the interstory displacements in the 10-story building are very adequately controlled. Although demands in the 8-story building are significantly reduced, some modes remain overdamped and not all performance levels are exactly met as some stories remain marginally damaged. Finally, the algorithm is applied in a 20-story benchmark building, and it is shown that the interstory displacements, postyield curvatures, and plastic damages are very adequately controlled.

Analytical sensitivity equations for the plastic rotation of beam-column finite elements are derived for reliability and optimization algorithms in structural engineering and for the assessment of plastic rotation sensitivity to uncertain design parameters and modeling assumptions. The plastic rotation is defined by elastic unloading of element forces in a basic system, which makes the corresponding sensitivity computations applicable to most material nonlinear beam-column formulations available in the literature. The analytical response sensitivity is verified by finite differences then applied to a first-order reliability analysis of a steel subassemblage where the performance function places a limit on plastic rotation.