WIM-Based Live Load for Bridges

Andrzej S. Nowak,Przemyslaw Rakoczy 대한토목학회 2013 KSCE JOURNAL OF CIVIL ENGINEERING Vol.17 No.3

Calibration of the AASHTO LRFD Code required the statistical parameters of load and resistance parameters. The basic load combination includes dead load, live load and dynamic load. In 1980’s, there was no reliable Weigh-in-Motion (WIM)data base and, therefore, the development of live load factors was based on a small scale truck survey. In the meantime, the WIM technology was improved and millions of vehicles were recorded in various geographical locations. The objective of this study is to review the available WIM data of about 35 million trucks and determine the statistical parameters of Gross Vehicle Weight (GVW) and live load moment. Moments were calculated for simple spans using influence lines. The span length range is from 30 to 200 ft (9 to 60 m). The Cumulative Distribution Functions (CDF) were plotted on the normal probability paper for an easier interpretation. CDF’s of GVW and moments show a considerable variation depending on WIM station location. Maximum expected values of live load depends on the considered time period and, in general, for strength limit states the time periods can be 75 or 100 years, and for service limit states they are much shorter, few days or weeks. Therefore, the statistical parameters are determined for time periods from 1 day through 100 years and for traffic volumes with ADTT from 100through 10,000. For longer time periods, the results were obtained by extrapolation of the available WIM data. The statistical analysis of moments provides a basis for the development of national live load parameters and live load factors in the bridge design code.

Reliability analysis of circular tunnel with consideration of the strength limit state

Ghasemi, Seyed Hooman,Nowak, Andrzej S. Techno-Press 2018 Geomechanics & engineering Vol.15 No.3

Probability-based design codes have been developed to sufficiently confirm the safety level of structures. One of the most acceptable probability-based approaches is Load Resistance Factor Design (LRFD), which measures the safety level of the structures in terms of the reliability index. The main contribution of this paper is to calibrate the load and resistance factors of the design code for tunnels. The load and resistance factors are calculated using the available statistical models and probability-based procedures. The major steps include selection of representative structures, consideration of the limit state functions, calculation of reliability for the selected structures, selection of the target reliability index and calculation of load factors and resistance factors. The load and resistance models are reviewed. Statistical models of resistance (load carrying capacity) are summarized for strength limit state in bending, shear and compression. The reliability indices are calculated for several segments of a selected circular tunnel designed according to the tunnel manual report (Tunnel Manual). The novelty of this paper is the selection of the target reliability. In doing so, the uniform spectrum of reliability indices is proposed based on the probability paper. The final recommendation is proposed based on the closeness to the target reliability index.

단.중경간 강형교 거더의 횡분배 모델

엄준식 ( Eom Jun-sik ),( Andrzej S. Nowak ),노병철 ( Lho Byeong-cheol ) 한국구조물진단유지관리공학회 2003 한국구조물진단유지관리공학회 논문집 Vol.7 No.2

The objective of this work is to verify the Code specified girder distribution factors for short and medium span bridges. To accomplish this objective, field tests were carried out on seventeen simply supported highway bridges. This paper presents the procedure and results of field tests that were performed to verify girder distribution factors. Finite Element analyses previously performed at the University of Michigan indicated that in most cases currently used girder distribution factors specified in AASHTO Codes are too conservative. However, these studies also showed that for short spans and short girder spacings, the girder distribution factors can be too permissive. Therefore, this paper focused on experimental evaluation of girder distribution factors for short and medium span steel girder bridges. The results were compared with the distribution factors specified by AASHTO Standard (2000) and AASHTO LRFD Code (1998). It has been found that the measured girder distribution factors are lower than AASHTO values in most cases, and sometimes the code specified values are overly conservative. The research work involved formulation of the testing procedure, selection of structure, installation of equipment, measurements, and interpretation of the results.

Truck Load Effects for Michigan Bridges

Jun-Sik Eom,Andrzej S. Nowak 상지대학교 환경과학기술연구소 2004 환경과학연구 Vol.10 No.1

  The paper provides a statistical background for bridge live load model, including static and dynamic components, and girder distribution factors. The static portion of live load includes truck weights (gross vehicle weight), axle loads, load effects (moments, shear forces, strain and stress). The data is based on field measurements carried out in Michigan. A considerable percentage of illegally overloaded trucks was observed, in particular on bridges located far from truck weigh stations. The cumulative distribution functions are shown for various locations in Michigan, and they are strongly site-specific. Dynamic load was measured on girder bridges. It turned out that there is almost no correlation between static and dynamic portions of live load. This means that dynamic load factor decreases for increasing static live load, or dynamic load factor decreases for heavier trucks. For a single heavy truck, the dynamic load factor is less than 0.20, and for two trucks side-by-side, dynamic load factor is less than 0.10. Girder distribution factors were also based on measurements, and compared to analytical values calculated using the code-specific procedures. It was observed that the code specified values are conservative in most cases. The statistical data can be used to update a basis for reliability analysis of girder bridges.

Reliability index for non-normal distributions of limit state functions

Seyed Hooman Ghasemi,Andrzej S. Nowak 국제구조공학회 2017 Structural Engineering and Mechanics, An Int'l Jou Vol.62 No.3

Reliability analysis is a probabilistic approach to determine a safety level of a system. Reliability is defined as a probability of a system (or a structure, in structural engineering) to functionally perform under given conditions. In the 1960s, Basler defined the reliability index as a measure to elucidate the safety level of the system, which until today is a commonly used parameter. However, the reliability index has been formulated based on the pivotal assumption which assumed that the considered limit state function is normally distributed. Nevertheless, it is not guaranteed that the limit state function of systems follow as normal distributions; therefore, there is a need to define a new reliability index for no-normal distributions. The main contribution of this paper is to define a sophisticated reliability index for limit state functions which their distributions are nonnormal. To do so, the new definition of reliability index is introduced for non-normal limit state functions according to the probability functions which are calculated based on the convolution theory. Eventually, as the state of the art, this paper introduces a simplified method to calculate the reliability index for non-normal distributions. The simplified method is developed to generate non-normal limit state in terms of normal distributions using series of Gaussian functions.