Achintya Haldar

Bridge fatigue damage evaluation and updating using non-destructive inspections

Abstract A method is proposed to mitigate fatigue damage using information from non-destructive inspections. In spite of improvements in the design of fatigue-sensitive structures, periodic non-destructive inspections are still required by the profession. A linear elastic fracture mechanics-based reliability model is proposed which incorporates uncertainties from many different sources, including uncertainty in the results obtained from the non-destructive inspections. Regardless of whether or not it detects any cracks, each inspection provides additional information and the underlying fatigue reliability needs to be updated after each inspection. The updated information on the reliability can be used as a decision making tool as what to do next, in terms of whether to do nothing, reschedule the next inspection at an earlier date, or repair or replace the structure immediately. The application potential of the method is demonstrated with the help of examples. It is shown that the proposed method is much superior to the current S − N curve-based AASHTO method and can be used as an alternative to it.

Elasto-plastic large deformation analysis of PR steel frames for LRFD

Abstract An efficient second-order finite element-based method is presented here considering geometric and material nonlinear behavior of steel frames with nonlinear flexible connections and local plasticity effects. The assumed stress method is used to derive the governing equations which satisfy joint equilibrium and displacement compatibility conditions. An explicit form of the tangent stiffness matrix of the structure is obtained that makes the proposed method extremely efficient in nonlinear analysis. In deriving governing equations for large deformation, each element is characterized as a beam-column which undergoes arbitrary large rigid displacement but small relative displacement. The behavior of flexible connections is represented by an exponential function. In solving the nonlinear equations, the Newton-Raphson method with arc-length control is used in tracing the post-buckling behavior. Several numerical examples are given to demonstrate the robustness, accuracy and efficiency of the proposed method.

Nonlinear seismic response of steel structures with semi-rigid and composite connections

Abstract The nonlinear seismic responses of steel frames with fully restrained, partially restrained and composite connections are evaluated and compared in terms of the maximum interstory and maximum top lateral displacements. Steel frames are usually analyzed assuming all the connections are fully restrained. However, considering the practical design aspects of connections, this is rarely true. This practice introduces unintended flexibility in the frame. Using a nonlinear time domain seismic analysis algorithm developed by the authors, three steel frames are excited by 13 earthquake time histories. Twelve of them were recorded during the Northridge earthquake of 1994. Any one of these 12 earthquake time histories can be used to represent the Northridge earthquake in future designs. To define the rigidity of a connection, a parameter called the T ratio is introduced. It is the ratio of the moment the connection would have to carry according to the beam line theory and the fixed end moment of the girder. Initially, the T ratio of all the connections is assumed to be 0.9, making them fully restrained. The results indicate that this assumption is inappropriate and gives unconservative responses depending upon which time history of the same earthquake is being used. Several frames with a T ratio of 0.95 developed very large lateral displacements causing instability, although they behaved properly when the ratio was assumed to be 1.0. For composite connections, slab steel has a significant beneficial effect on the overall structural response. It increases the T ratio, making it closer to the FR connection. Even for composite connections with a T ratio of 0.95, the frames developed large lateral displacement. Further parametric study indicates that, at least for seismic analysis, PR or composite connections should be designed for a T ratio as close to 1 as possible to represent an FR connection. Otherwise, the lateral displacement failure criterion should also be checked for less than ideal FR connection conditions. Improvements in both the analysis and design of steel frames are necessary to make them more seismic load tolerant.

Practical random field discretization in stochastic finite element analysis

Abstract Stochastic finite element-based reliability analysis is applied to structures with distributed parameters that can be modeled as random fields. In this method, reliability is estimated through analytical computation of the sensitivity of stochastic response to the basic random variables. The random fields are discretized into sets of correlated random variables using two methods of discretization. The sensitivity measures are further used to selectively consider only a few of the distributed parameters as random fields, to ensure computational efficiency. The issue of choosing the appropriate mesh for the discretization of the random field is addressed through mesh refinement studies. With the help of three numerical examples, the paper examines the effects of the correlation characteristics of the random field on discretization and reliability analysis, and develops guidelines for efficient application of stochastic finite element analysis to structures with distributed parameters.

A random-fuzzy analysis of existing structures

Abstract Two approaches are proposed to estimate the reliability of existing structures by considering both the randomness in some of the design parameters and the fuzzy imprecision in some other parameters representing the in-place condition of the aged structures. In the first approach, the fuzzy imprecision is transformed into random uncertainty using the entropy concept, and the reliability of existing structures is estimated using well-established theories of probability. In the second approach, a hybrid approach in the random-fuzzy domain is used to evaluate the reliability using an α-level concept. The multiple fuzzy variables case is also considered. Both discrete and continuous fuzzy variables are considered. The results obtained from the proposed approaches are compared with other techniques available in the literature whenever possible. Both methods are applied to civil structural engineering problems in this paper. The results obtained are very encouraging and demonstrate the applicability and robustness of the algorithms.

Seismic reliability of non-linear frames with PR connections using systematic RSM

An effective, efficient, and robust reliability analysis algorithm is proposed for non-linear structures, where seismic loading can be applied in the time domain. The method is developed specifically for steel frame structures considering all major sources of non-linearity, including geometry, material, and partially restrained (PR) connections. The non-linearity due to PR connections is modeled by moment-relative rotation curves using the four-parameter Richard model. For seismic excitation, the loading, unloading, and reloading behavior at PR connections is modeled using moment-relative rotation curves and the Masing rule. The proposed algorithm intelligently integrates the response surface method, the finite element method, the first-order reliability method, and an iterative linear interpolation scheme. The uncertainties in all the random variables including the four parameters of Richard model are considered. Two unique features of the proposed algorithm are that (1) actual earthquake time histories can be used to excite structures in the presence of major sources of non-linearity and uncertainty and (2) it is possible to estimate the risk corresponding to both the serviceability and strength limit states. The algorithm is verified using the Monte Carlo simulation technique. The verified algorithm is first used to study the reliability of a frame structure in the presence of PR connections with different degrees of flexibility. Then the algorithm is used to estimate the reliability of a frame structure excited by 13 actual recorded earthquake time histories, 12 of them recorded during the Northridge earthquake of 1994. As expected, the reliabilities of the frame are found to be quite different, when excited by several time histories of the Northridge earthquake.

First-Order and Second-Order Reliability Methods

The need to incorporate uncertainties in an engineering design has long been recognized. The absolute safety of a structure cannot be guaranteed, because of the unpredictability of future loading conditions; the inability to obtain and express the in-place material properties accurately; the use of simplified assumptions in predicting the behavior of the structure due to the loading under consideration; the limitations in the numerical methods used; and human factors (e.g., errors and omissions). However, the probability of structural failure can be limited to a reasonable level. The estimation of structural failure probability is an important task for an engineer.

Elastoplastic nonlinear post-buckling analysis of partially restrained space structures

Abstract A method is proposed here to analyze a space structure with large deformation, partially restrained connections, and material nonlinearities using the plastic hinge concept. The assumed stress method is used to derive an explicit form of tangent stiffness satisfying joint equilibrium and displacement compatibility. The unique feature of the method is that it is extremely efficient since the tangent stiffness is expressed in an explicit form and can easily be modified to consider different factors. The method can be used to study both the pre- and post-buckling behavior of space structures. It is verified with experimental and numerical results available in the literature. The robustness of the algorithm is confirmed by applying it to analyze several problems of practical importance. The method is robust yet simple, accurate, and economical.

Some lessons learned from post‐earthquake damage survey of structures in Bam, Iran earthquake of 2003

Purpose – Some lessons learned from post‐earthquake damage survey of structures affected by the Bam earthquake of December 26, 2003 in Iran are encapsulated in this paper. The Bam earthquake caused catastrophic structural damage in the region.Design/methodology/approach – A method similar to that of rapid evaluation procedure (REP), recommended by the Applied Technology Council (ATC‐20) in the USA, was used for damage survey.Findings – Bam represents a typical ancient city in many countries around the world. Most of the structures in the region are made of adobe, unreinforced masonry, steel, and unreinforced/reinforced concrete. Some of the main types of structural damage, their causes, and potential remedial measures are characterized with an emphasis on the very basic fundamental principles of earthquake‐resistant design.Practical implications – The research reported has considerable implications for other seismic‐affected regions of the world.Originality/value – A first hand‐account of the catastrophic...

Structural responses considering the vertical component of earthquakes

Abstract The guidelines in the NEHRP Provisions and the Mexican Code regarding the effects of the vertical component of earthquakes on the response of frames are re-evaluated. Using a time domain nonlinear finite element program developed by the authors, the seismic responses of frames are evaluated realistically by simultaneously applying the horizontal and vertical components of earthquake motion. Three steel frames and 13 recorded earthquake motions are considered. The same response parameters are then estimated using the two codes, and their error is evaluated. It is found that, if the frames remain elastic, the NEHRP Provisions estimate the maximum horizontal deflection at the top of the frames and the bending moment in the columns very accurately; the Mexican Code overestimates them. If the frames develop plastic hinges, the Mexican Code conservatively overestimates them, but the NEHRP Provisions underestimate them in some cases. Both codes significantly underestimate the axial loads in columns. The underestimation increases as the frames develop plastic hinges. The underestimation is more for interior columns than for exterior columns. If the ratio R of the PGA of the vertical and horizontal components of an earthquake is higher than normal, the underestimation increases as R increases. The underestimation is not correlated with frame height. The vertical component may increase the axial load significantly. Since they are designed as beam–columns, the increase in the axial load will have a very detrimental effect on the performance of the columns. In light of the results obtained in this study, the design requirements for the vertical components need modification. At the very least, further study is required.