Live load and dynamic load are important load components for highway bridges. Rational load model... more Live load and dynamic load are important load components for highway bridges. Rational load models are needed for the development of LRFD design codes. The paper summarizes the available data base and calculation procedure. Live load model is based on the truck surveys. Maximum 75 year load effects are derived by extrapolation and simulations. Calculations are performed for single lane and two lane bridges. For two lanes, the maximum effect is obtained for two trucks side-by-side, with fully correlated weights. For the maximum 75 year moment or shear, each side-by-side truck is represented by the maximum 1.5 month truck. The approach to selection of the design live load is formulated. The acceptance criterium is uniformity of the mean-to-nominal ratio for various spans. Dynamic load is based on limited test data and special simulations. The major factors influencing dynamic load are the road roughness, bridge dynamics (frequency of vibrations) and vehicle dynamics (suspension system). Tests and analysis indicate that dynamic load (as a fraction of live load) is reduced for heavier trucks. It is also lower for two trucks compared to a single truck. It is recommended to use a uniform dynamic load for all the span lengths larger than 20 ft.
The aim of this paper is to quantify the dynamic behavior of a bridge which depends on its natura... more The aim of this paper is to quantify the dynamic behavior of a bridge which depends on its natural frequency, the road surface roughness and vehicle dynamics. The mathematical equations relating forces and deformations are formulated for the bridge and moving trucks; road surface roughness is measured in terms of the present serviceability index (PSI) as well as international roughness index (ISI); and the power spectral density function is determined using the IRI value in order to generate the random road profile. The results are plotted on normal probability; the maximum values for a bridge lifetime of 50 years are calculated by extrapolation; and the results of simulation for one truck and two truck cases are presented in tables and figures.
The paper discusses live load models for bridges, an important part of the bridge code developmen... more The paper discusses live load models for bridges, an important part of the bridge code development process. Considered are code provisions in the United States, Canada, Germany, Australia, and Japan. Current research is summarized; the information on bridge live loads, taken from weigh in motion (WIM) measurements, truck surveys and citation files is provided. This data serves as a basis for the prediction of extreme loads.
The major parameters which determine performance of wood structures are modulus of rupture (MOR),... more The major parameters which determine performance of wood structures are modulus of rupture (MOR), modulus of elasticity (MOE), and loads. These parameters are a subject to considerable variation and therefore, they are treated as random variables. The objective of this study is to develop an efficient procedure for evaluation of the structural reliability. The work will focus on wooden plank decks for highway bridges. In particular, the paper is focused on distribution of truck load to plank decks. The current AASHTO Specifications are unrealistic and too conservative in most cases. A plank element is modeled as a beam on elastic supports. Material properties, in particular MOE and MOR, are based on the actual test data. The major part of the load model is axle load, and in particular wheel load. The statistical analysis is based on the available weigh-in-motion measurements data. It was observed that truck parameters are strongly site-specific. For plank decks, live load considerat...
Journal of the Korea institute for structural maintenance and inspection, 2003
The objective of this work is to verify the Code specified girder distribution factors for short ... more 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.
The presented study deals with the development of design code for reinforced concrete and prestre... more The presented study deals with the development of design code for reinforced concrete and prestressed concrete beams, slabs and columns. The major steps in the code calibration procedure include the development of load and resistance models. It is assumed that the available load models are adequate. Therefore, the main focus of this study is the verification of resistance models. A considerable database is gathered on material strength: ordinary concrete, lightweight concrete, high-strength concrete, reinforcing steel, and prestressing steel. The test results were provided by industry and they are analyzed to determine the cumulative distribution functions and other statistical parameters. It is observed that there is a considerable improvement in quality of materials during the last 20-30 years, and this results in an increased reliability of structural components. The reliability analysis is performed to determine the reliability indices for components designed according to the current code (ACI 318-99). Based on the results, the target reliability indices are selected. New load and resistance factors are recommended based on closeness to the target reliability index.
Load and resistance parameters for bridges involve uncertainties due to natural randomness, imper... more Load and resistance parameters for bridges involve uncertainties due to natural randomness, imperfect models or human errors. Because of these uncertainties, absolute reliability is not an attainable goal. Selection of the optimum reliability level is an economical problem. Lower reliability results in frequent failures, while higher reliability requires more initial costs (materials and labor). Therefore, structural reliability is a convenient acceptability criterion in the development of a design code. The objective of this paper is to present a procedure for calculation of load and resistance factors.
The objective of this paper is to compare the reliability level of prestressed concrete bridge gi... more The objective of this paper is to compare the reliability level of prestressed concrete bridge girders designed using three codes:
Transportation Research Board 86th Annual MeetingTransportation Research Board, 2007
For a probabilistic risk assessment of an Arch bridge, an innovative prediction method for the co... more For a probabilistic risk assessment of an Arch bridge, an innovative prediction method for the combination of failure modes is proposed and compared with the conventional system reliability analysis method. The suggested method generates unexpected combinations of failure modes in significantly reduced time and efforts, compared with the previous permutation method or the conventional system reliability analysis method. In addition to that, the suggested method can be used for the verification of the system reliability with more specific predictions of failure modes. Component reliabilities of girders have been evaluated using the response surfaces of the design variables at the selected critical sections based on the maximum shear and negative moment locations. Response Surface Method (RSM) is successfully applied for reliability analyses for this relatively small probability of failure of the complex structure, which is laborious to be obtained by Monte-Carlo Simulations or by First Order Second Moment Method that can not easily calculate the derivative terms of implicit limit state functions. For the analysis of system reliability, the target bridge system is modeled as series connection system. The upper and lower probabilities of failure for the structural system have been evaluated and compared with the suggested prediction method for all the possible combination of failure modes.
Because load and resistance are subject to random vibration, reliability can be considered a rati... more Because load and resistance are subject to random vibration, reliability can be considered a rational measure of structural performance. The recently developed AASHTO 2004 bridge design code is based upon the assumption of a consistent safety level. Reliability is calculated using load and resistance models, and these models have an important effect on the results. Resistance can be considered as a function of material properties, geometry and dimensions, and the so-called professional (analysis) factor. The statistical parameters depend to a large extent on the quality of materials and workmanship. The code writers usually assume that the quality is at an average level; however, there is a considerable variation between different contractors. In particular, this applies to the properties of concrete. The aim of this paper is to establish the relationship between resistance parameters and reliability. An analysis is performed for girder bridges.
Bridge load and resistance parameters involve a considerable degree of uncertainty. Therefore, th... more Bridge load and resistance parameters involve a considerable degree of uncertainty. Therefore, the reliability analysis can be used to quantify the risk. There has been a considerable research activity in the area of structural reliability in the last two decades. There are methods available for calculation of the probability of failure for components of buildings, bridges and other structures. They are summarized in several books (e.g. Thoft-Christensen and Baker 1982; Ang and Tang 1986; Madsen, Krenk and Lind 1986; Melchers 1987). For given statistical models of loads and resistance the available methodology provides accurate results. Structural safety was evaluated for bridge components (e.g. Nowak and Grouni 1990).
The optimum safety level depends on the consequences of failure and cost of safety. Selection of ... more The optimum safety level depends on the consequences of failure and cost of safety. Selection of the target value can be based on consideration of these two parameters. Target reliability indices calculated for newly designed bridges and existing structures are different for many reasons. Reference time period is different for newly designed and existing bridges. Load model, used to calculate reliability index, depends on the reference time period. Single load path components require a different treatment than multiple load path components. The paper deals with the selection criteria for the target B for ultimate limit states (ULS) and serviceability limit states (SLS). For the covering abstract see ITRD E126028.
The development of rational design criteria requires efficient measures of structural performance... more The development of rational design criteria requires efficient measures of structural performance. Traditional methods of analysis do not reveal the actual safety reserve (degree of redundancy). Load and resistance parameters are random variables. Therefore, probabilistic methods are used to model behavior of bridges. The paper provides a review of the available methodology, including reliability measures, load models and resistance models for girder bridges.
The combination of dead load and live load is very important in design of bridge superstructure a... more The combination of dead load and live load is very important in design of bridge superstructure as, in practice, it controls the strength limit states. The basic set of load factors for the Strength I limit state is 1.25 for dead load and 1.75 for live load and dynamic load. For design cases when the dead load dominates, i.e. for Strength IV limit state, the dead load factor is 1.5. The acceptability criterion for load and resistance factors in the AASHTO LRFD Code is closeness to the target reliability index, which is assumed to be 3.5 for steel and concrete girder bridges. However, the reliability analysis performed for a full range of dead load to live load ratios indicates that when live load is about 10-20% of the total load, the reliability indices are about 3.0 which is lower than the target value of 3.5. This is an indication that the reliability level is insufficient and there is a need for increasing load factors. On the other hand, for dead load constituting about 100% of the total load (i.e. no live load), the reliability index is much higher than 3.5, which means that the load factor 1.5 can be reduced. Therefore, it is proposed to change the current Strength IV load factors to dead load of 1.4 and live load factor 1.4. The result is a more uniform reliability level for all combinations of dead load and live load. The results of reliability analysis are presented in graphs.
The major parameters which determine performance of wood structures are modulus of rupture (MOR),... more The major parameters which determine performance of wood structures are modulus of rupture (MOR), modulus of elasticity (MOE), and loads. These parameters are a subject to considerable variation and therefore, they are treated as random variables. The objective of this study is to develop an efficient procedure for evaluation of the structural reliability. The work will focus on wooden plank decks for highway bridges. In particular, the paper is focused on distribution of truck load to plank decks. The current AASHTO Specifications are unrealistic and too conservative in most cases. A plank element is modeled as a beam on elastic supports. Material properties, in particular MOE and MOR, are based on the actual test data. The major part of the load model is axle load, and in particular wheel load. The statistical analysis is based on the available weigh-inmotion measurements data. It was observed that truck parameters are strongly site-specific. For plank decks, live load consideration is focused on axle weights and wheel loads rather than whole vehicles. The reliability model will be used to develop rational design criteria for plank decks.
The objective of this paper is to present the development of the resistance factor for shear in r... more The objective of this paper is to present the development of the resistance factor for shear in reinforced concrete bridges made of lightweight concrete. The statistical model of resistance was based on the available limited experimental data. It was found that the current shear design procedures are about 15% less conservative for lightweight concrete when compared to normal weight concrete. The reliability analysis was performed and served as a basis for the selection of the resistance factor. The results indicate that a resistance factor equal to 0.8 can be applied for the shear design of lightweight concrete bridges.
Live load and dynamic load are important load components for highway bridges. Rational load model... more Live load and dynamic load are important load components for highway bridges. Rational load models are needed for the development of LRFD design codes. The paper summarizes the available data base and calculation procedure. Live load model is based on the truck surveys. Maximum 75 year load effects are derived by extrapolation and simulations. Calculations are performed for single lane and two lane bridges. For two lanes, the maximum effect is obtained for two trucks side-by-side, with fully correlated weights. For the maximum 75 year moment or shear, each side-by-side truck is represented by the maximum 1.5 month truck. The approach to selection of the design live load is formulated. The acceptance criterium is uniformity of the mean-to-nominal ratio for various spans. Dynamic load is based on limited test data and special simulations. The major factors influencing dynamic load are the road roughness, bridge dynamics (frequency of vibrations) and vehicle dynamics (suspension system). Tests and analysis indicate that dynamic load (as a fraction of live load) is reduced for heavier trucks. It is also lower for two trucks compared to a single truck. It is recommended to use a uniform dynamic load for all the span lengths larger than 20 ft.
The aim of this paper is to quantify the dynamic behavior of a bridge which depends on its natura... more The aim of this paper is to quantify the dynamic behavior of a bridge which depends on its natural frequency, the road surface roughness and vehicle dynamics. The mathematical equations relating forces and deformations are formulated for the bridge and moving trucks; road surface roughness is measured in terms of the present serviceability index (PSI) as well as international roughness index (ISI); and the power spectral density function is determined using the IRI value in order to generate the random road profile. The results are plotted on normal probability; the maximum values for a bridge lifetime of 50 years are calculated by extrapolation; and the results of simulation for one truck and two truck cases are presented in tables and figures.
The paper discusses live load models for bridges, an important part of the bridge code developmen... more The paper discusses live load models for bridges, an important part of the bridge code development process. Considered are code provisions in the United States, Canada, Germany, Australia, and Japan. Current research is summarized; the information on bridge live loads, taken from weigh in motion (WIM) measurements, truck surveys and citation files is provided. This data serves as a basis for the prediction of extreme loads.
The major parameters which determine performance of wood structures are modulus of rupture (MOR),... more The major parameters which determine performance of wood structures are modulus of rupture (MOR), modulus of elasticity (MOE), and loads. These parameters are a subject to considerable variation and therefore, they are treated as random variables. The objective of this study is to develop an efficient procedure for evaluation of the structural reliability. The work will focus on wooden plank decks for highway bridges. In particular, the paper is focused on distribution of truck load to plank decks. The current AASHTO Specifications are unrealistic and too conservative in most cases. A plank element is modeled as a beam on elastic supports. Material properties, in particular MOE and MOR, are based on the actual test data. The major part of the load model is axle load, and in particular wheel load. The statistical analysis is based on the available weigh-in-motion measurements data. It was observed that truck parameters are strongly site-specific. For plank decks, live load considerat...
Journal of the Korea institute for structural maintenance and inspection, 2003
The objective of this work is to verify the Code specified girder distribution factors for short ... more 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.
The presented study deals with the development of design code for reinforced concrete and prestre... more The presented study deals with the development of design code for reinforced concrete and prestressed concrete beams, slabs and columns. The major steps in the code calibration procedure include the development of load and resistance models. It is assumed that the available load models are adequate. Therefore, the main focus of this study is the verification of resistance models. A considerable database is gathered on material strength: ordinary concrete, lightweight concrete, high-strength concrete, reinforcing steel, and prestressing steel. The test results were provided by industry and they are analyzed to determine the cumulative distribution functions and other statistical parameters. It is observed that there is a considerable improvement in quality of materials during the last 20-30 years, and this results in an increased reliability of structural components. The reliability analysis is performed to determine the reliability indices for components designed according to the current code (ACI 318-99). Based on the results, the target reliability indices are selected. New load and resistance factors are recommended based on closeness to the target reliability index.
Load and resistance parameters for bridges involve uncertainties due to natural randomness, imper... more Load and resistance parameters for bridges involve uncertainties due to natural randomness, imperfect models or human errors. Because of these uncertainties, absolute reliability is not an attainable goal. Selection of the optimum reliability level is an economical problem. Lower reliability results in frequent failures, while higher reliability requires more initial costs (materials and labor). Therefore, structural reliability is a convenient acceptability criterion in the development of a design code. The objective of this paper is to present a procedure for calculation of load and resistance factors.
The objective of this paper is to compare the reliability level of prestressed concrete bridge gi... more The objective of this paper is to compare the reliability level of prestressed concrete bridge girders designed using three codes:
Transportation Research Board 86th Annual MeetingTransportation Research Board, 2007
For a probabilistic risk assessment of an Arch bridge, an innovative prediction method for the co... more For a probabilistic risk assessment of an Arch bridge, an innovative prediction method for the combination of failure modes is proposed and compared with the conventional system reliability analysis method. The suggested method generates unexpected combinations of failure modes in significantly reduced time and efforts, compared with the previous permutation method or the conventional system reliability analysis method. In addition to that, the suggested method can be used for the verification of the system reliability with more specific predictions of failure modes. Component reliabilities of girders have been evaluated using the response surfaces of the design variables at the selected critical sections based on the maximum shear and negative moment locations. Response Surface Method (RSM) is successfully applied for reliability analyses for this relatively small probability of failure of the complex structure, which is laborious to be obtained by Monte-Carlo Simulations or by First Order Second Moment Method that can not easily calculate the derivative terms of implicit limit state functions. For the analysis of system reliability, the target bridge system is modeled as series connection system. The upper and lower probabilities of failure for the structural system have been evaluated and compared with the suggested prediction method for all the possible combination of failure modes.
Because load and resistance are subject to random vibration, reliability can be considered a rati... more Because load and resistance are subject to random vibration, reliability can be considered a rational measure of structural performance. The recently developed AASHTO 2004 bridge design code is based upon the assumption of a consistent safety level. Reliability is calculated using load and resistance models, and these models have an important effect on the results. Resistance can be considered as a function of material properties, geometry and dimensions, and the so-called professional (analysis) factor. The statistical parameters depend to a large extent on the quality of materials and workmanship. The code writers usually assume that the quality is at an average level; however, there is a considerable variation between different contractors. In particular, this applies to the properties of concrete. The aim of this paper is to establish the relationship between resistance parameters and reliability. An analysis is performed for girder bridges.
Bridge load and resistance parameters involve a considerable degree of uncertainty. Therefore, th... more Bridge load and resistance parameters involve a considerable degree of uncertainty. Therefore, the reliability analysis can be used to quantify the risk. There has been a considerable research activity in the area of structural reliability in the last two decades. There are methods available for calculation of the probability of failure for components of buildings, bridges and other structures. They are summarized in several books (e.g. Thoft-Christensen and Baker 1982; Ang and Tang 1986; Madsen, Krenk and Lind 1986; Melchers 1987). For given statistical models of loads and resistance the available methodology provides accurate results. Structural safety was evaluated for bridge components (e.g. Nowak and Grouni 1990).
The optimum safety level depends on the consequences of failure and cost of safety. Selection of ... more The optimum safety level depends on the consequences of failure and cost of safety. Selection of the target value can be based on consideration of these two parameters. Target reliability indices calculated for newly designed bridges and existing structures are different for many reasons. Reference time period is different for newly designed and existing bridges. Load model, used to calculate reliability index, depends on the reference time period. Single load path components require a different treatment than multiple load path components. The paper deals with the selection criteria for the target B for ultimate limit states (ULS) and serviceability limit states (SLS). For the covering abstract see ITRD E126028.
The development of rational design criteria requires efficient measures of structural performance... more The development of rational design criteria requires efficient measures of structural performance. Traditional methods of analysis do not reveal the actual safety reserve (degree of redundancy). Load and resistance parameters are random variables. Therefore, probabilistic methods are used to model behavior of bridges. The paper provides a review of the available methodology, including reliability measures, load models and resistance models for girder bridges.
The combination of dead load and live load is very important in design of bridge superstructure a... more The combination of dead load and live load is very important in design of bridge superstructure as, in practice, it controls the strength limit states. The basic set of load factors for the Strength I limit state is 1.25 for dead load and 1.75 for live load and dynamic load. For design cases when the dead load dominates, i.e. for Strength IV limit state, the dead load factor is 1.5. The acceptability criterion for load and resistance factors in the AASHTO LRFD Code is closeness to the target reliability index, which is assumed to be 3.5 for steel and concrete girder bridges. However, the reliability analysis performed for a full range of dead load to live load ratios indicates that when live load is about 10-20% of the total load, the reliability indices are about 3.0 which is lower than the target value of 3.5. This is an indication that the reliability level is insufficient and there is a need for increasing load factors. On the other hand, for dead load constituting about 100% of the total load (i.e. no live load), the reliability index is much higher than 3.5, which means that the load factor 1.5 can be reduced. Therefore, it is proposed to change the current Strength IV load factors to dead load of 1.4 and live load factor 1.4. The result is a more uniform reliability level for all combinations of dead load and live load. The results of reliability analysis are presented in graphs.
The major parameters which determine performance of wood structures are modulus of rupture (MOR),... more The major parameters which determine performance of wood structures are modulus of rupture (MOR), modulus of elasticity (MOE), and loads. These parameters are a subject to considerable variation and therefore, they are treated as random variables. The objective of this study is to develop an efficient procedure for evaluation of the structural reliability. The work will focus on wooden plank decks for highway bridges. In particular, the paper is focused on distribution of truck load to plank decks. The current AASHTO Specifications are unrealistic and too conservative in most cases. A plank element is modeled as a beam on elastic supports. Material properties, in particular MOE and MOR, are based on the actual test data. The major part of the load model is axle load, and in particular wheel load. The statistical analysis is based on the available weigh-inmotion measurements data. It was observed that truck parameters are strongly site-specific. For plank decks, live load consideration is focused on axle weights and wheel loads rather than whole vehicles. The reliability model will be used to develop rational design criteria for plank decks.
The objective of this paper is to present the development of the resistance factor for shear in r... more The objective of this paper is to present the development of the resistance factor for shear in reinforced concrete bridges made of lightweight concrete. The statistical model of resistance was based on the available limited experimental data. It was found that the current shear design procedures are about 15% less conservative for lightweight concrete when compared to normal weight concrete. The reliability analysis was performed and served as a basis for the selection of the resistance factor. The results indicate that a resistance factor equal to 0.8 can be applied for the shear design of lightweight concrete bridges.
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Papers by Andrzej Nowak