This document presents an analytical model for analyzing the nonlinear behavior of composite beams with deformable shear connections. It describes a numerical procedure that accounts for the nonlinear behavior of concrete, steel, and shear connectors. The procedure models the beam as discrete elements and uses empirical stress-strain relationships and a load-slip relationship for connectors. It was validated by comparing analytical results to experimental data for four composite beams, showing good agreement. The modeling approach provides a tool for parametric studies of composite beams with full or partial shear connection.
Study of behaviour of composite beams with truss type shear connectoreSAT Journals
Abstract
Composite action of two concrete members is achieved by the interface shear transfer between the two members; this mechanism is of great significance. The interface shear carrying capacity is dependent on the surface properties and shear connectors provided. In the current research ATENA is used, it is FEM based software in which the interface properties between materials can be modeled to a great level of detail. In the present study the influence of angle of inclination, size and the depth of embedment of truss connector on the load carrying behavior is studied with the help of a beam model. The angles of inclination varied are 30o, 45o, 60o and 75o with varying bar diameters of 8mm, 10mm and 12mm. Angles between 60o to 75o are found most efficient with no significant changes when diameters are varied. The ultimate load for a given connector is found to be independent of the depth of embedment. Composite beams are also modeled to study the influence of cohesion and friction coefficient, and are compared with behavior of solid and non-composite beams.
Keywords: Truss shear connector, Composite slab, ATENA, Slab flexure test, Interface shear capacity
NONLINEAR FINITE ELEMENT ANALYSIS FOR REINFORCED CONCRETE SLABS UNDER PUNCHIN...IAEME Publication
This paper presents an implementation of a three-dimensional nonlinear finite element model for evaluating the behavior of reinforced concrete slabs under centric load. The concrete was idealized by using eight-nodded solid elements. While flexural reinforcement and the shear were modeled as line elements, a perfected bond between solid elements and line elements was assumed. The nonlinear behavior of concrete in compression is simulated by an elasto-plastic work-hardening model, and in tension a suitable post-cracking model based on tension stiffening and shear retention models are employed. The steel was simulated using an elastic-full plastic model. The validity of the theoretical formulations and the program used was verified through comparison with available experimental data, and the agreement has proven to be good. A parametric study has been also carried out to investigate the influence of the slab thickness on column-slab connection response
Buckling behavior of straight slot tubesunder oblique loading – A comparative...IJAEMSJORNAL
Hollow tubes are the most important or crucial parts of the rapidly growing automobile and construction industry. The tube is subjected to pure buckling. In theanalysis, one end is fixed and the force is applied to theother end and by application of different angles of inclinations ranging from 0˚ to 20˚ with different thicknessof the range of 0.5 to 2.0. Linear buckling code was used forfinding the critical buckling load. This research paper is about the effects of buckling under oblique loading. It is the process in which the tube is subjected to compressive oblique loading and the tube fails by the first increase in crossectional area and then bulging on any of the sides but in the case, oblique loading in hollow tube shell bulges internally or inside the perimeter of the tube.
Study of Linear and Non Linear Behavior of In filled FrameIJERA Editor
Reinforced concrete frame buildings often incorporate masonry infill panels as partitions to separate spaces
within a building or as cladding to complete the building envelope. However, the properties and construction
details of infilled panels can have a significant influence on the overall behavior of a structure. An infilled frame
typically consists of a steel or reinforced concrete frame with plain or reinforced brick masonry, block-work
infilling which restraint against lateral loads is provided by the composite action of the infill and the frame. With
the advancement of computational technology and ever going increasing trend of research activities, the demand
for inelastic design is increasing day by day. Since the brick masonry wall possesses highly heterogeneous, nonlinear
studies are inevitable. In this work, a study of non-linear behavior of reinforced concrete infilled frame
with brick masonry are carried out under lateral and combined loads using ANSYS software.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Study of behaviour of composite beams with truss type shear connectoreSAT Journals
Abstract
Composite action of two concrete members is achieved by the interface shear transfer between the two members; this mechanism is of great significance. The interface shear carrying capacity is dependent on the surface properties and shear connectors provided. In the current research ATENA is used, it is FEM based software in which the interface properties between materials can be modeled to a great level of detail. In the present study the influence of angle of inclination, size and the depth of embedment of truss connector on the load carrying behavior is studied with the help of a beam model. The angles of inclination varied are 30o, 45o, 60o and 75o with varying bar diameters of 8mm, 10mm and 12mm. Angles between 60o to 75o are found most efficient with no significant changes when diameters are varied. The ultimate load for a given connector is found to be independent of the depth of embedment. Composite beams are also modeled to study the influence of cohesion and friction coefficient, and are compared with behavior of solid and non-composite beams.
Keywords: Truss shear connector, Composite slab, ATENA, Slab flexure test, Interface shear capacity
NONLINEAR FINITE ELEMENT ANALYSIS FOR REINFORCED CONCRETE SLABS UNDER PUNCHIN...IAEME Publication
This paper presents an implementation of a three-dimensional nonlinear finite element model for evaluating the behavior of reinforced concrete slabs under centric load. The concrete was idealized by using eight-nodded solid elements. While flexural reinforcement and the shear were modeled as line elements, a perfected bond between solid elements and line elements was assumed. The nonlinear behavior of concrete in compression is simulated by an elasto-plastic work-hardening model, and in tension a suitable post-cracking model based on tension stiffening and shear retention models are employed. The steel was simulated using an elastic-full plastic model. The validity of the theoretical formulations and the program used was verified through comparison with available experimental data, and the agreement has proven to be good. A parametric study has been also carried out to investigate the influence of the slab thickness on column-slab connection response
Buckling behavior of straight slot tubesunder oblique loading – A comparative...IJAEMSJORNAL
Hollow tubes are the most important or crucial parts of the rapidly growing automobile and construction industry. The tube is subjected to pure buckling. In theanalysis, one end is fixed and the force is applied to theother end and by application of different angles of inclinations ranging from 0˚ to 20˚ with different thicknessof the range of 0.5 to 2.0. Linear buckling code was used forfinding the critical buckling load. This research paper is about the effects of buckling under oblique loading. It is the process in which the tube is subjected to compressive oblique loading and the tube fails by the first increase in crossectional area and then bulging on any of the sides but in the case, oblique loading in hollow tube shell bulges internally or inside the perimeter of the tube.
Study of Linear and Non Linear Behavior of In filled FrameIJERA Editor
Reinforced concrete frame buildings often incorporate masonry infill panels as partitions to separate spaces
within a building or as cladding to complete the building envelope. However, the properties and construction
details of infilled panels can have a significant influence on the overall behavior of a structure. An infilled frame
typically consists of a steel or reinforced concrete frame with plain or reinforced brick masonry, block-work
infilling which restraint against lateral loads is provided by the composite action of the infill and the frame. With
the advancement of computational technology and ever going increasing trend of research activities, the demand
for inelastic design is increasing day by day. Since the brick masonry wall possesses highly heterogeneous, nonlinear
studies are inevitable. In this work, a study of non-linear behavior of reinforced concrete infilled frame
with brick masonry are carried out under lateral and combined loads using ANSYS software.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Analysis of box culvert cost optimization for different aspect ratios of celleSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Analytical Investigation on External Beam-Column Joint Using ANSYS By Varying...IJERA Editor
The beam-column joint has been a topic of study for over 30 years now and still there are many things that yet to
be completely understood. The joint was considered to be rigid, however researches have shown that failure may
occur at the joint instead of the beam or column. This study was carried out to determine the effect of the
diameter of longitudinal reinforcement of the beam on the strength, deformation and ductility in the beamcolumn
joint using ANSYS. It was seen that the load carrying capacity and the deformation increases as the
diameter of reinforcement in the beam increases.
Analysis of Behaviour of U-Girder Bridge DecksIDES Editor
The concept of U-shaped bridge girder is now being
increasingly adopted in urban metro rail projects and for
replacing old bridges where there is a constraint on vertical
clearance. These bridge decks are commonly designed in
practice using simplified methods that assume beam action of
the webs in the longitudinal direction and similar flexural
action of the deck slab in the transverse direction. However,
such assumptions can lead to errors. This paper attempts to
assess the extent of error in the simplified analysis, by
comparing the results with a more rigorous three-dimensional
finite element analysis (3DFEA). A typical prototype railway
bridge girder has been taken as a case study. The results of
the 3DFEA, in terms of load-deflection plots, have been
validated by field testing.
Determination of load transfer in reinforced concrete solid slabs by finite e...IOSR Journals
According to the ACI building code, the concrete slab can be divided into two types depending on
the ratio of the long side to the short side. Regarding the results of the ratio, the concrete slab can be divided as
one-way and two-way slabs. The main objective of this paper is to study the stress or moments distribution in
solid slab panel in its two directions and compare with ACI code assumption that the load is transferred mainly
in short direction and most of the load is transferred in one direction only if the ratio of the longer span to the
shorter span is greater than one. This will be discussed by analyzing one panel of solid slab using the computer
software SAP2000. Two types of panels will be used; the first one a panel that is supported simply on its four
sides and the second panel is supported only by four pin supports and beams. This paper shows that the gravity
load on the slab is transferred to long and short direction. This means that one-way concrete solid slab doesn't
exist and all concrete solid slabs work as a two-way concrete slab.
Simulation Study on a Mixed Beams Structureiosrjce
IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of mechanical and civil engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mechanical and civil engineering. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
Crash Analysis And Design of Multi-Cell Octagonal S-Shape Members Under Axial...IRJESJOURNAL
Abstract : Crashworthiness of the structures used in automotive is widely being addressed as it is defining the safety. The present article aims to investigate crushing performance under axial and oblique impact performed under 10°, 20° and 30° for different cross-section configurations of S-shaped longitudinal members. Modeling and numerical analysis are carried out using finite element code LS-DYNA. The model was validated using experimental data. The complex proportional assessment (COPRAS) method is used to provide optimized alternative design by considering two conflicting criteria, energy absorption (EA) and peak crushing force (PCF). The results indicate that the structures (at which four blades connect the outer and the inner walls) with inner reinforcing blades have a high crash performance than the others (without connecting blades). Besides, the blades in multi-cell members, which connect the middle of edges (T4), lead to superior response in comparison with the other ones (which connect corners). Finally, dimensions (the wall thickness and the distance of inner and outer tubes) of T4 are optimized by design of experiment and response surface methodology techniques
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Comparative Study of Girders for Bridge by Using SoftwareIJERA Editor
According to various research papers, it has been found that composite bridge gives the maximum strength in
comparison to other bridges and the design and analysis of various girders for steel and concrete by using
various software for composite bridge design for girder. In this project, efforts will make to carry outto check
the analysis of girder by using SAP2000 software. Hence, in this project determine three girders which can be
effective to the composite bridges.
Engineering Fracture Mechanics. Engineers try to have high-strength, high ductility, high crack resistance, and faultless structures. The most reliable approach is "No cracks - no problems,"
When all is not possible, there are different methods of prevention of catastrophic failure: increase crack resistance by ductile material, by local heating; decrease SIF by placing holes on the crack path, by patching, by stiffing elements or by using composite materials. "Leak-before-break" is an effective strategy to prevent catastrophic failure of pressure vessels. It is better to allow a semi-elliptical crack to grow through the wall and to detect it by leaking than to have the dynamic start and failure of the whole vessel. There are two characteristics of the material: crack resistance for semi-elliptical crack and crack resistance for through crack.
Comparative Study on Anchorage in Reinforced Concrete Using Codes of Practice...IJERA Editor
The evaluations of anchorage strength of bars in reinforced concrete are varied in codes of practice and
equations by researchers on the base of their approaches and philosophies.
This paper (Part I) aims to have a comparative study between the predictions by codes of practice of BS8110
and EC2 and those equations by Darwin et al, Morita and Fuji, Batayneh and Nielsen and results of 164 tests
from literature.
In this part the case of straight anchorage bars without transverse pressure is considered. Some major parameters
including compressive strength, and in terms of ratio of concrete cover to bar diameter and ratio of anchorage
length to bar diameter , are addressed in detail.
Although various parameters are involved in anchorage design equations, it is observed that every code has
merit over the other codes in some aspect. The presented discussion highlights the major areas of differences
which need attentions in the future for more investigations.
The main conclusion has been presented in part II to include the study of straight anchorages with transverse
pressure. The conclusions should cover the both cases to obtain the fair assessments for bond strength by those
expressions used in this study.
Review on the Effect of Shear Connectors on Composite Deck SlabsIJAEMSJORNAL
This paper presents a review on the effect of shear connectors on composite deck slabs. Composite deck slabs consist of profile deck sheet and concrete. Several researchers have been studying the behaviour of composite slab but due to its complex behaviour yet it is not completely understood. The behaviour of composite slab directly depends on the deformability and contact strength. Here, some important literature reviews regarding composite slab behavior incorporating different profiles were discussed.
Nonlinear fe modelling of anchorage bond in reinforced concreteeSAT Journals
Abstract The transfer of forces from the surrounding concrete to the reinforcing bars in reinforced concrete (RC) can be influenced by several parameters. In this paper an attempt has been made to study the influence of specimen geometry, bar diameter, strength of concrete, lateral confinement and embedment length on the bond properties of concrete. The embedment length of the bar was varied between 50mm and 400mm by varying the diameter of the bar, strength of concrete and lateral confinement. The different bar diameters of 16, 20 and 25mm were selected along with three different concrete strengths of 25, 40 and 65MPa. The specimens with the above parameters were modeled by using a nonlinear finite element analysis package. It has been found that for the same geometry, the specimens with small bond length exhibited high bond strength. With the range of bar diameters considered the bond strength of concrete decreases as the diameter of the bar increases. The splitting failure has been observed in unconfined concrete, while the pullout failure was predominant when the concrete laterally confined. In case of large embedment length, the post peak plateau is prolonged with small diameter bars when compared to the large diameter bars. The descending branch of the bond stress-slip response with large diameter bars has been found to be steep. Keywords: Bond Stress, FE Analysis, Embedment Length, Confinement, Bar Diameter, Pull-out Specimens.
Two different schemes called “ties and longitudinal stiffeners” were proposed for improving the performance of stainless steel square thin walled tubes. An analytical study using finite element models loaded axially has been conducted. Both geometric and material nonlinearities were considered. Those models were verified against the results obtained from previous researches. The analytical study compared between unstiffened, ties stiffened and longitudinally stiffened stainless steel square thin walled tubes. The studied parameters were square thin walled tube width-to-thickness ratio (W/t) and the axial spacing of stiffening along the length. It was observed that the axial load strength can be enhanced by proposed ties stiffening schemes.
Finite Element Analysis of Composite Deck Slab Using Perfobond Rib as Shear C...IJERA Editor
Nowadays, the composite decks are very common to use in composite or steel construction. In this case of study
the composite slabs have been investigated numerically by Finite Element Method (FEM). Five composite slabs
were analyzed using finite element software LUSAS. The deflection of each model were obtained and compared
with experimental test. Results showed a good agreement with the experimental data and indicate that the
perfobond rib is appropriate shear connector for the bridges decks
Finite Element Analysis of Composite Deck Slab Using Perfobond Rib as Shear C...IJERA Editor
Nowadays, the composite decks are very common to use in composite or steel construction. In this case of study
the composite slabs have been investigated numerically by Finite Element Method (FEM). Five composite slabs
were analyzed using finite element software LUSAS. The deflection of each model were obtained and compared
with experimental test. Results showed a good agreement with the experimental data and indicate that the
perfobond rib is appropriate shear connector for the bridges decks.
Analysis of box culvert cost optimization for different aspect ratios of celleSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Analytical Investigation on External Beam-Column Joint Using ANSYS By Varying...IJERA Editor
The beam-column joint has been a topic of study for over 30 years now and still there are many things that yet to
be completely understood. The joint was considered to be rigid, however researches have shown that failure may
occur at the joint instead of the beam or column. This study was carried out to determine the effect of the
diameter of longitudinal reinforcement of the beam on the strength, deformation and ductility in the beamcolumn
joint using ANSYS. It was seen that the load carrying capacity and the deformation increases as the
diameter of reinforcement in the beam increases.
Analysis of Behaviour of U-Girder Bridge DecksIDES Editor
The concept of U-shaped bridge girder is now being
increasingly adopted in urban metro rail projects and for
replacing old bridges where there is a constraint on vertical
clearance. These bridge decks are commonly designed in
practice using simplified methods that assume beam action of
the webs in the longitudinal direction and similar flexural
action of the deck slab in the transverse direction. However,
such assumptions can lead to errors. This paper attempts to
assess the extent of error in the simplified analysis, by
comparing the results with a more rigorous three-dimensional
finite element analysis (3DFEA). A typical prototype railway
bridge girder has been taken as a case study. The results of
the 3DFEA, in terms of load-deflection plots, have been
validated by field testing.
Determination of load transfer in reinforced concrete solid slabs by finite e...IOSR Journals
According to the ACI building code, the concrete slab can be divided into two types depending on
the ratio of the long side to the short side. Regarding the results of the ratio, the concrete slab can be divided as
one-way and two-way slabs. The main objective of this paper is to study the stress or moments distribution in
solid slab panel in its two directions and compare with ACI code assumption that the load is transferred mainly
in short direction and most of the load is transferred in one direction only if the ratio of the longer span to the
shorter span is greater than one. This will be discussed by analyzing one panel of solid slab using the computer
software SAP2000. Two types of panels will be used; the first one a panel that is supported simply on its four
sides and the second panel is supported only by four pin supports and beams. This paper shows that the gravity
load on the slab is transferred to long and short direction. This means that one-way concrete solid slab doesn't
exist and all concrete solid slabs work as a two-way concrete slab.
Simulation Study on a Mixed Beams Structureiosrjce
IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of mechanical and civil engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mechanical and civil engineering. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
Crash Analysis And Design of Multi-Cell Octagonal S-Shape Members Under Axial...IRJESJOURNAL
Abstract : Crashworthiness of the structures used in automotive is widely being addressed as it is defining the safety. The present article aims to investigate crushing performance under axial and oblique impact performed under 10°, 20° and 30° for different cross-section configurations of S-shaped longitudinal members. Modeling and numerical analysis are carried out using finite element code LS-DYNA. The model was validated using experimental data. The complex proportional assessment (COPRAS) method is used to provide optimized alternative design by considering two conflicting criteria, energy absorption (EA) and peak crushing force (PCF). The results indicate that the structures (at which four blades connect the outer and the inner walls) with inner reinforcing blades have a high crash performance than the others (without connecting blades). Besides, the blades in multi-cell members, which connect the middle of edges (T4), lead to superior response in comparison with the other ones (which connect corners). Finally, dimensions (the wall thickness and the distance of inner and outer tubes) of T4 are optimized by design of experiment and response surface methodology techniques
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Comparative Study of Girders for Bridge by Using SoftwareIJERA Editor
According to various research papers, it has been found that composite bridge gives the maximum strength in
comparison to other bridges and the design and analysis of various girders for steel and concrete by using
various software for composite bridge design for girder. In this project, efforts will make to carry outto check
the analysis of girder by using SAP2000 software. Hence, in this project determine three girders which can be
effective to the composite bridges.
Engineering Fracture Mechanics. Engineers try to have high-strength, high ductility, high crack resistance, and faultless structures. The most reliable approach is "No cracks - no problems,"
When all is not possible, there are different methods of prevention of catastrophic failure: increase crack resistance by ductile material, by local heating; decrease SIF by placing holes on the crack path, by patching, by stiffing elements or by using composite materials. "Leak-before-break" is an effective strategy to prevent catastrophic failure of pressure vessels. It is better to allow a semi-elliptical crack to grow through the wall and to detect it by leaking than to have the dynamic start and failure of the whole vessel. There are two characteristics of the material: crack resistance for semi-elliptical crack and crack resistance for through crack.
Comparative Study on Anchorage in Reinforced Concrete Using Codes of Practice...IJERA Editor
The evaluations of anchorage strength of bars in reinforced concrete are varied in codes of practice and
equations by researchers on the base of their approaches and philosophies.
This paper (Part I) aims to have a comparative study between the predictions by codes of practice of BS8110
and EC2 and those equations by Darwin et al, Morita and Fuji, Batayneh and Nielsen and results of 164 tests
from literature.
In this part the case of straight anchorage bars without transverse pressure is considered. Some major parameters
including compressive strength, and in terms of ratio of concrete cover to bar diameter and ratio of anchorage
length to bar diameter , are addressed in detail.
Although various parameters are involved in anchorage design equations, it is observed that every code has
merit over the other codes in some aspect. The presented discussion highlights the major areas of differences
which need attentions in the future for more investigations.
The main conclusion has been presented in part II to include the study of straight anchorages with transverse
pressure. The conclusions should cover the both cases to obtain the fair assessments for bond strength by those
expressions used in this study.
Review on the Effect of Shear Connectors on Composite Deck SlabsIJAEMSJORNAL
This paper presents a review on the effect of shear connectors on composite deck slabs. Composite deck slabs consist of profile deck sheet and concrete. Several researchers have been studying the behaviour of composite slab but due to its complex behaviour yet it is not completely understood. The behaviour of composite slab directly depends on the deformability and contact strength. Here, some important literature reviews regarding composite slab behavior incorporating different profiles were discussed.
Nonlinear fe modelling of anchorage bond in reinforced concreteeSAT Journals
Abstract The transfer of forces from the surrounding concrete to the reinforcing bars in reinforced concrete (RC) can be influenced by several parameters. In this paper an attempt has been made to study the influence of specimen geometry, bar diameter, strength of concrete, lateral confinement and embedment length on the bond properties of concrete. The embedment length of the bar was varied between 50mm and 400mm by varying the diameter of the bar, strength of concrete and lateral confinement. The different bar diameters of 16, 20 and 25mm were selected along with three different concrete strengths of 25, 40 and 65MPa. The specimens with the above parameters were modeled by using a nonlinear finite element analysis package. It has been found that for the same geometry, the specimens with small bond length exhibited high bond strength. With the range of bar diameters considered the bond strength of concrete decreases as the diameter of the bar increases. The splitting failure has been observed in unconfined concrete, while the pullout failure was predominant when the concrete laterally confined. In case of large embedment length, the post peak plateau is prolonged with small diameter bars when compared to the large diameter bars. The descending branch of the bond stress-slip response with large diameter bars has been found to be steep. Keywords: Bond Stress, FE Analysis, Embedment Length, Confinement, Bar Diameter, Pull-out Specimens.
Two different schemes called “ties and longitudinal stiffeners” were proposed for improving the performance of stainless steel square thin walled tubes. An analytical study using finite element models loaded axially has been conducted. Both geometric and material nonlinearities were considered. Those models were verified against the results obtained from previous researches. The analytical study compared between unstiffened, ties stiffened and longitudinally stiffened stainless steel square thin walled tubes. The studied parameters were square thin walled tube width-to-thickness ratio (W/t) and the axial spacing of stiffening along the length. It was observed that the axial load strength can be enhanced by proposed ties stiffening schemes.
Finite Element Analysis of Composite Deck Slab Using Perfobond Rib as Shear C...IJERA Editor
Nowadays, the composite decks are very common to use in composite or steel construction. In this case of study
the composite slabs have been investigated numerically by Finite Element Method (FEM). Five composite slabs
were analyzed using finite element software LUSAS. The deflection of each model were obtained and compared
with experimental test. Results showed a good agreement with the experimental data and indicate that the
perfobond rib is appropriate shear connector for the bridges decks
Finite Element Analysis of Composite Deck Slab Using Perfobond Rib as Shear C...IJERA Editor
Nowadays, the composite decks are very common to use in composite or steel construction. In this case of study
the composite slabs have been investigated numerically by Finite Element Method (FEM). Five composite slabs
were analyzed using finite element software LUSAS. The deflection of each model were obtained and compared
with experimental test. Results showed a good agreement with the experimental data and indicate that the
perfobond rib is appropriate shear connector for the bridges decks.
Parametric Study of Square Concrete Filled Steel Tube Columns Subjected To Co...IJERA Editor
The Concrete Filled Steel Tube (CFST) member has many advantages compared with the conventional concrete structural member. This study presents on the behaviour of concrete-filled steel tube (CFST) columns under axial load by changing parameters. The parameters are thickness of steel tube, Grade of concrete and length of column. The study was conducted using ANSYS 13 finite element software. All the columns are 60 X 60 mm in size. The thickness of the tube is taken as 2, 3, 4, 5 and 6 mm for thickness variation. The grades of concrete infill are M25, M30, M40, M50, M60 and M70 used for grade variation. Lengths of columns are taken as 900, 1200, 1500, 1800, 2100, and 2400 mm for length variation. Buckling load is compared with Euro code 4 (1994).
SEISMIC BEHAVIOR OF STEEL RIGID FRAME WITH IMPERFECT BRACE MEMBERSIAEME Publication
Model of a steel rigid frame made of thin-walled box section with existence of I-section brace member with initial overall and local imperfection adopted to investigate buckling effects on steel structural behavior as it was subjected to earthquake excitation. In order to take into account of the influence of local deflections on structural response, shell elements were employed to model brace member as well as base columns. Cross sections components with relatively high amplitude of
buckling parameters were considered in different case studies to make it susceptible to develop local deflection. Beam elements were also utilized to develop models with the same specification. FEM method applied to conduct nonlinear time history analysis using earthquake record in in-plane and
out-of-plane direction
Experimental Testing Of Partially Encased Composite Beam ColumnsIJERA Editor
The past few decades have seen outstanding advances in the use of composite materials in structural
applications. There can be little doubt that, within engineering circles, composites have revolutionized
traditional design concepts and made possible an unparalleled range of new and exciting possibilities as viable
materials for construction.
In addition to the well-known advantages of composite columns, partially encased composite columns offered
simplified beam-to-column connection as well as reduced or omitted shuttering thus achieved more cost
effective construction. Some companies have patented these new types of partially encased composite column
made of light welded steel shapes; moreover, the Canadian Institute of Steel construction CISC has recognized
and codified this type of columns.
In This paper, Partially Encased Composite Beam Columns is introduced; experimental studies are made on five
partially encased beam columns to investigate the behavior of eccentrically loaded partially encased composite
columns using different parameters
Experimental Testing Of Partially Encased Composite Beam ColumnsIJERA Editor
The past few decades have seen outstanding advances in the use of composite materials in structural applications. There can be little doubt that, within engineering circles, composites have revolutionized traditional design concepts and made possible an unparalleled range of new and exciting possibilities as viable materials for construction. In addition to the well-known advantages of composite columns, partially encased composite columns offered simplified beam-to-column connection as well as reduced or omitted shuttering thus achieved more cost effective construction. Some companies have patented these new types of partially encased composite column made of light welded steel shapes; moreover, the Canadian Institute of Steel construction CISC has recognized and codified this type of columns. In This paper, Partially Encased Composite Beam Columns is introduced; experimental studies are made on five partially encased beam columns to investigate the behavior of eccentrically loaded partially encased composite columns using different parameters.
Finite Element Analysis of Cold-formed Steel ConnectionsCSCJournals
This paper presents a thorough investigation into the structural performance of cold-formed steel column base and beam column connections using single lipped C sections with bolted moment connections. Two specimens consisting of a column base and a beam column connection were carried out, and it was found that section failure under flexural buckling was always critical. Moreover, the proposed connections were demonstrated to be structurally efficient attaining moment resistances close to those of the connected sections. In order to examine the structural behavior of the column base and beam column connections, finite element models were established using shell and bar elements to model the sections and the bolted fastenings respectively. Material non-linearity was incorporated, and comparison between the test and the numerical results was presented in details. It was shown that the proposed analysis method was structurally adequate to predict the structural behavior for column base and beam column with similar connection configurations.
System shear connector jakarta digunakan sebagai aplikasi dalam konstruksi bangunan untuk menghasilkan kekuatan coran beton lebih kuat dan stabil sesuai dengan perhitungan engineering civil. Dalam hal ini ada 2 hal perhitungan kekuatan secara umum yaitu kekuatan kelengketan stud pada batang baja sesudah dilas. Dan yang kedua adalah kekuatan stud bolt yang digunakan.
This paper presents a study on flexural behaviour of concrete filled steel tube based on the former
work carried out by Manojkumar. An ANSYS model is developed that can predict the behaviour of concrete
filled steel tube to determine moment carrying capacity at ultimate point for beam Concrete filled steel tube
beams are studied and verified by the finite element program ANSYS against experimental data. The Main
parameters affecting the behaviour and strength of concrete filled beams are geometrical parameters, material
nonlinearities, loading, boundary conditions and degree of concrete confinement. To account for all these
properties ANSYS model is developed. The main parameters varied in analysis study are D/t ratio,
characteristic strength of infilled concrete. The proposed model predicts ultimate moment capacity for CFT
beams. In the numerical analysis, circular and rectangular CFT cross sections are considered using different
grades of concrete. The predicted values are compared with experimental results. Numerical analysis has
shown that for rectangular CFT’s a good confining effect can be provided. Moment capacity results obtained
from the ANSYS model are compared with the values predicted by Lin Han (2004) and different codes such as
AISC-LRFD (1999) and EC4 (1994).
Advanced Design of Composite Steel-Concrete Structural elementIJERA Editor
Composite framing system consisting of steel beams acting interactively with metal deck-concrete slab and concrete encased composite columns, has been as a viable alternative to the conventional steel or reinforced concrete system in the high-rise construction. However, in Indian context, it is comparatively new and no appropriate design codes are available for the same. Complications in the analysis and design of composite structures have led numerous researchers to develop simplified methods so as to eliminate a number of large scale tests needed for the design. In the present work, a simplified method of composite slabs, beams and columns design is used and software is developed with pre- and post- processing facilities in VB.NET. All principal design checks are incorporated in the software. The full and partial shear connection and the requirement for transverse reinforcement are also considered. To facilitate direct selection of steel section, a database is prepared and is available at the back end with the properties of all standard steel sections. Screen shots are included in the paper to illustrate the method employed for selecting the appropriate section and shear connectors and thus to verify the design adequacy.
Similar to Analytical modeling of nonlinear behavior of composite beams with deformable connection (20)
Quality defects in TMT Bars, Possible causes and Potential Solutions.PrashantGoswami42
Maintaining high-quality standards in the production of TMT bars is crucial for ensuring structural integrity in construction. Addressing common defects through careful monitoring, standardized processes, and advanced technology can significantly improve the quality of TMT bars. Continuous training and adherence to quality control measures will also play a pivotal role in minimizing these defects.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
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Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
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Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
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• Compatible with Backplane mount serial communication.
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• Remote control: Parallel or serial interface.
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• Indigenized local Support/presence in India.
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Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
Event Management System Vb Net Project Report.pdfKamal Acharya
In present era, the scopes of information technology growing with a very fast .We do not see any are untouched from this industry. The scope of information technology has become wider includes: Business and industry. Household Business, Communication, Education, Entertainment, Science, Medicine, Engineering, Distance Learning, Weather Forecasting. Carrier Searching and so on.
My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
In my system we have to make a system by which a user can record all events coordinated by a particular faculty. In our proposed system some more featured are added which differs it from the existing system such as security.
TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
AIRCRAFT GENERAL
The Single Aisle is the most advanced family aircraft in service today, with fly-by-wire flight controls.
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Courier management system project report.pdfKamal Acharya
It is now-a-days very important for the people to send or receive articles like imported furniture, electronic items, gifts, business goods and the like. People depend vastly on different transport systems which mostly use the manual way of receiving and delivering the articles. There is no way to track the articles till they are received and there is no way to let the customer know what happened in transit, once he booked some articles. In such a situation, we need a system which completely computerizes the cargo activities including time to time tracking of the articles sent. This need is fulfilled by Courier Management System software which is online software for the cargo management people that enables them to receive the goods from a source and send them to a required destination and track their status from time to time.
Analytical modeling of nonlinear behavior of composite beams with deformable connection
1. Journal of Constructional Steel Research 52 (1999) 195–218
www.elsevier.com/locate/jcsr
Analytical modeling of nonlinear behavior of
composite beams with deformable connection
N. Gattesco
Dipartimento di Ingegneria Civile, Universita’ di Udine, Via delle Scienze N. 208, 33100 Udine, Italy
Received 6 May 1998; received in revised form 25 January 1999; accepted 1 April 1999
Abstract
A numerical procedure for the analysis of steel and concrete composite beams is herein
presented. The program accounts for nonlinear behavior of concrete, steel and shear connec-
tors. In particular the most refined stress–strain constitutive relationships available in the litera-
ture can be used in the procedure. For shear connectors an empirical nonlinear load–slip
relationship is used. The accuracy and reliability of the program are demonstrated by the
analysis of four composite beams over the entire loading range up to failure. The analytical
results are compared with the corresponding experimental data with good agreement between
them. The reported results demonstrate that the numerical approach is a valid tool for extensive
parametric studies on composite beams with complete or partial shear connection. 1999
Elsevier Science Ltd. All rights reserved.
Keywords: Shear connection; Nonlinear analysis; Structural analysis; Composite structures; Stud
connectors
1. Introduction
The composite system considered here consists of a concrete slab connected by
means of shear connectors to a steel beam as normally used in bridge superstructures
and in floor systems for buildings. Very often the concrete slab is realized using
precast elements or a composite slab with profiled steel sheeting. These techniques
have the advantage of avoiding the use of formworks and, moreover, the structure
can be completed very quickly, but normally a wider connector spacing has to be
used. In fact, with solid precast slabs the connectors are welded to the steel beam
0143-974X/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved.
PII: S0143-974X(99)00026-7
2. 196 N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
in groups disposed at a certain distance from each other. When profiled steel sheeting
is used only one connector per trough may normally be adopted because the concrete
rib formed by a trough may not be strong enough to resist the force from two or
more connectors. These situations imply that for these kinds of composite beams,
complete shear connection can rarely be obtained.
For a given beam, loading, and design method, complete shear connection is
defined as the least number of connectors Nf such that the bending resistance of the
beam would not be increased if more connectors were provided. The number Nf can
be defined only in relation to particular methods of design and of testing connectors
(e.g. Eurocode No. 4 [1]). Partial shear connection is when the number of connectors
N used in a beam is lower than Nf.
In the design with complete shear connection, it is normally assumed that failure
of shear connectors does not occur and the influence of connector deformation on
the structural behavior can be neglected. With partial shear connection, the ultimate
resistance of the beam is governed by the connection, in fact it depends on the
ultimate resistance of the single connector and on its ductility. In these cases, the
correct evaluation of the slip at the interface between the concrete slab and the steel
flange, in order to check if the ductility of the connection used allows it, is of great
importance. Moreover, the slip can cause significant redistribution of stresses
between the connectors in both serviceability and ultimate limit states.
In Eurocode No. 4, Part 1 [1], two simplified design methods for partial shear
connections are proposed but only for members with compact steel sections (class
1 and class 2). Using ‘ductile’ connectors (normally headed studs with the shank
diameter ranging between 16 mm and 22 mm, with a shank length greater than four
times the diameter embedded in concrete with characteristic cylinder strength fck ⬍
30 MPa), the methods are the interpolation method and the equilibrium method [1,2]
(Fig. 1).
Fig. 1. Interpolation and equilibrium method of design.
3. 197
N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
The ultimate load capacities Wu and Ws relate to the composite member with full
interaction and to the steel member alone, respectively. They are obtained when
ultimate moments of resistance are reached in the critical sections, provided that
sufficient rotation capacity be allowed by internal support sections, otherwise the
maximum load has to be evaluated with respect to the maximum rotation capacity
allowed.
In the equilibrium design method (curve ABC in Fig. 1), ultimate moments in
critical sections are evaluated by simple equilibrium of stresses and using a com-
pressive force in the slab Nc ⫽ NQu (Fig. 2), where N ⬍ Nf is the number of connec-
tors used and Qu is the design resistance per connector.
Fig. 2. Beam subdivision in small elements of length ⌬l (a); 8 degree of freedom element (b).
4. 198 N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
The interpolation method is more conservative and is represented by the line AC
in Fig. 1. The maximum load is then immediately evaluated when the ultimate load
capacities of composite Wu and steel Ws members are known, in fact
W ⫽ Ws ⫹ n(Wu ⫺ Ws) (1)
where n ⫽ N/Nf is the degree of connection.
However, for both methods a minimum shear connection ratio nmin is specified.
Some results available in the literature [2,3] have shown that the curve ABC of Fig.
1 cannot be used for degrees of connection lower than nB (corresponding to point
B on the curve) due to a likely rupture of the connectors. In these cases a safe design
can be obtained using line BO; indications for point B can be found in the literature
[1–3].
These simplified methods are very useful for designing composite beams and are
proposed in some codes (e.g. Eurocode No. 4, Part 1 [1]) but they need further
numerical and experimental investigations in order to bring near the scattered results
for point B [2,3].
Therefore, reliable numerical approaches are necessary to increase the number and
quality of numerical results now available. For this purpose in the present paper, the
features of a powerful nonlinear numerical approach for studying the behavior of
steel and concrete composite beams with deformable connections are presented.
2. The proposed approach
The structure is subdivided into n elements of length ⌬li (Fig. 2a). Each single
element is schematically represented by two beam-type members (C concrete, S
steel) laid one upon the other and connected at their interface by two horizontal
springs (Fig. 2(b)) [4]. These elements have four nodal points with three degrees of
freedom per node: horizontal and vertical displacements and the rotation in the x–
y plane.
Some results available in the literature (i.e. [5,6]) show that the uplift of concrete
slab with respect to the steel member has a negligible effect on the distribution of
slip along the beam as well as on the ultimate load capacity of the beam. In the
proposed procedure uplift is not included. In fact, the following hypotheses are
assumed:
1. the distribution of strain is linear over the depth of both concrete and steel
elements;
2. the stress–strain relationship of steel is the same in tension and in compression;
3. the concrete slab and the steel member can slip along the connection without
separation (i.e. uplift neglected);
4. the concrete slab and the steel member sections have equal curvature.
Hypotheses (3) and (4) imply that the vertical displacement and the rotation of
the concrete slab are equal to those of the steel member. The number of degrees of
5. 199
N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
freedom of each element then reduces to eight (Fig. 2(b)). The procedure does not
consider buckling effects on the steel member.
2.1. Linear approach
Assuming a linear behavior for materials, the relationship between forces and
displacements for the general i-th element is
Fi ⫽ Ki Xi ⫺ F̄i (2)
where Fi is the vector of nodal forces, F̄i is the vector of fixed end forces, Xi is the
vector of nodal displacements and Ki is the stiffness matrix of the element. Vectors
Fi, F̄i and Xi have the dimensions [8 ⫻ 1]
Fi ⫽
冤
Nc,i
Ns,i
Vi
Mi
Nc,i ⫹ 1
Ns,i⫹1
Vi⫹1
Mi⫹1
冥F̄i ⫽
冤
N̄c,i
N̄s,i
V̄i
M̄i
N̄c,i⫹1
N̄s,i⫹1
V̄i⫹1
M̄i⫹1
冥Xi ⫽
冤
1,i
2,i
i
i
1,i⫹1
2,i⫹1
i⫹1
i⫹1
冥
and the stiffness matrix has the following form
Ki⫽
k1,i ⫹
EcAci
⌬1i
⫺ k1,i 0 ⫺ k1,i z ⫺
EcAci
⌬1i
0 0 0
k1,i ⫹
EsAsi
⌬1i
0 k1,iz 0 ⫺
EsAsi
⌬1i
0 0
12(EcIci ⫹ EsIsi)
⌬13
i
⫺
6(EcIci ⫹ EsIsi)
⌬12
i
0 0 ⫺
12(EcIci ⫹ EsIsi)
⌬13
i
⫺
6(EcIci ⫹ EsIsi)
⌬12
i
4(EcIci ⫹ EsIsi)
⌬1i
⫹ k1,iz2
0 0
6(EcIci ⫹ EsIsi)
⌬12
i
2(EcIci ⫹ EsIsi)
⌬1i
Symmetric k2,i ⫹
EcAci
⌬1i
⫺ k2,i 0 ⫺ k2iz
k2,i ⫹
EsAsi
⌬1i
0 k2iz
12(EcIci ⫹ EsIsi)
⌬13
i
6(EcIci ⫹ EsIsi)
⌬12
i
4(EcIci ⫹ EsIsi)
⌬1i
⫹ k2,iz2
where Aci, Asi, Ici, Isi are the area and moment of inertia of concrete slab and steel
beam, respectively, k1,i, k2,i are the stiffnesses of left and right springs of the i-th
element and z ⫽ hcb ⫹ hp ⫹ hst. The terms of the matrix express the forces and the
moments due to unitary displacements applied to any degree of freedom of the
element (Fig. 2(b)).
The equilibrium equations for the composite beam may be written in the form
AY ⫺ B ⫽ 0 (3)
6. 200 N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
where A is the global stiffness matrix, Y is the vector of nodal displacements, B is
the fixed external loading vector (assembling of fixed-end forces F̄i) related to a
reference load W̄ and the scalar is a load level parameter that multiplies B. The
latter assumption is valid only in case of proportional loading.
Solving Eq. (3), the nodal displacements corresponding to different values of the
load parameter l, are obtained. Then with Eq. (2) the axial forces (Nc, Ns), the shear
forces (Vc, Vs) and the bending moments (Mc, Ms), acting both on the concrete slab
and on the steel member may be evaluated in any section along the beam. The
moment of the composite section M can be calculated using the equation
Mi ⫽ Mc ⫹ Ms ⫹ Ns·z (4)
and the slip at the steel–concrete interface s may be obtained from the relationship
si ⫽ i,1 ⫺ i,2 ⫺ i·z. (5)
2.2. Nonlinear approach
The constitutive laws of materials (concrete and steel) and the load–slip relation-
ship of shear connectors are not linear so that the equilibrium equations assume the
general form
G(Y,) ⫽ R(Y) ⫺ B ⫽ 0 (6)
where G(Y,) is the gradient of the total potential energy and R(Y) is the internal
force vector (nonlinearly dependent on the displacements Y). In order to evaluate
the unknown displacements a linearized form of Eq. (6), via a truncated Taylor series,
is needed
G(Y(m)
l⫹1,(m)
l⫹1) ⫽ G(Y(m)
l ,(m)
l ) ⫹
∂G
∂Y
␦Yl ⫹
∂G
∂
␦l ⫽ G(Y(m)
l ,(m)
l )
⫹ AT␦Yl ⫺ B␦l ⫽ 0, (7)
where AT is the tangent stiffness matrix, the superscript m denotes the iterative loop
number and the subscript l denotes the iteration number. Eq. (7) has to be solved
iteratively until convergence to the real solution is reached. Specifically, Eq. (7)
introduces the Newton–Raphson technique, which is the most commonly used in
nonlinear problems.
Such a process needs the evaluation and factorization of the tangent stiffness at
each iteration, which is time consuming, so it is normally preferred to use the modi-
fied Newton–Raphson technique which uses the initial stiffness matrix at each iter-
ation. The stiffness matrix is then only formed and factorized at the beginning of
each load increment.
If the equilibrium curve has limit points, due for example to softening behavior,
the method fails ( ⫽ const.; Fig. 3) and it is difficult to evaluate correctly the
ultimate load as well as the corresponding displacements for structures with an
almost perfect plastic behavior. To overcome this problem, the curve bounding the
7. 201
N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
Fig. 3. Solution curve and constraint functions in a one-dimensional problem.
stiffness extrapolation of the solution curve has to be oblique or, alternatively, a
different function f(Y,) ⫽ 0 (Fig. 3) [7–9].
The numerical procedure COBENA presented herein uses the modified Newton–
Raphson technique with a linearized form of the arc-length method [10] (piecewise
linear constraint) as illustrated in Fig. 4.
In particular, the constraint function adopted has the form
f(Y(m)
l ,(m)
l ) ⫽ ⌬YT
l ␦Yl ⫹ ␦l⌬lBT
B ⫽ 0, (8)
where the vector ⌬Yl and the scalar ⌬l are incremental while the vector ␦Yl and
the scalar ␦l are the changes at each iteration (Fig. 5). Eq. (8) ensures the orthog-
onality between the iterative change (␦Yl, ␦lB) and the ‘secant change’ (⌬Yl,
⌬lB).
Provided that the constraint curve is oblique to ⫽ const., the value of the load
level varies at each iteration so there is one more unknown, the load magnitude
parameter , besides the n nodal displacements. Then Eq. (8) has to be added to Eq.
(7), leading to an enlarged system, the stiffness matrix of which is neither symmetric
nor banded
冋 A ⫺ B
⌬YT
l ⌬lBT
B
册 冋␦Yl
␦l
册⫽ ⫺ 冋G(Y(m)
l ,(m)
l )
0
册. (9)
Fig. 4. Arc-length method with piecewise linear constraint [10].
8. 202 N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
Fig. 5. Linearized arc-length method procedure and notation for one-dimensional problems.
Instead of solving Eq. (9) directly, the constraint represented in Eq. (8) may be
introduced by following the technique of Batoz and Dhatt [11] for displacement
control. In this case the iterative displacement ␦Yl is split in two parts, hence the
Newton change at the new unknown level, (m)
l⫹1 ⫽ (m)
l ⫹ ␦l, becomes
␦Yl ⫽ ⫺ A−1
T G(Y(m)
l ,(m)
l⫹1) ⫽ ⫺ A−1
T (R(Y(m)
l ) ⫺ (m)
l⫹1B) ⫽
⫺ A−1
T (G(Y(m)
l ,(m)
l ) ⫺ ␦lB). (10)
G(Y(m)
l ,(m)
l ) represents the out-of-balance force at the l-th iteration (m-th loading
step) and may be obtained from the equation
G(Y(m)
l ,(m)
l ) ⫽ R(Y(m)
l ) ⫺ (m)
l B, (11)
where the members on the right-hand side are internal and external forces, respect-
ively. Indicating with
␦Ȳl ⫽ ⫺ A−1
T G(Y(m)
l ,(m)
l ), (12)
the iterative change that would stem from the standard load-controlled ( ⫽ const.)
Newton–Raphson method (at a fixed load level, (m)
l ), and with
Y(m)
T ⫽ A−1
B (13)
the displacement vector corresponding to the fixed load vector B. Provided that the
modified Newton–Raphson method is used the vector Y(m)
T needs to be computed
only for the initial ‘predictor’ step because it does not change during iterations.
Substituting Eqs. (12) and (13) into Eq. (10) the iterative change expression becomes
␦Yl ⫽ ␦Ȳl ⫹ ␦lY(m)
T (14)
and so the new incremental displacements are
⌬Yl⫹1 ⫽ ⌬Yl ⫹ ␦Yl ⫽ ⌬Yl ⫹ ␦Ȳl ⫹ ␦lY(m)
T . (15)
On the right-hand side of Eq. (15) the term ␦l is still unknown and its value can
be obtained by combining Eq. (8) with Eq. (14)
9. 203
N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
␦l ⫽ ⫺
⌬YT
l ␦Ȳl
⌬YT
l Y(m)
T ⫹ ⌬lBT
B
. (16)
and consequently the new incremental load parameter
⌬l⫹1 ⫽ ⌬l ⫹ ␦l. (17)
The global displacement vector and the corresponding load parameter are then,
respectively,
Y(m)
l⫹1 ⫽ Y(m)
1 ⫹ ⌬Yl⫹1, (m)
l⫹1 ⫽ (m)
l ⫹ ⌬l⫹1. (18)
The iterations will stop when the following inequality is satisfied
|gk|
⌬l·|bk|
ⱕ ⑀1 (k ⫽ 1 to 4·n). (19)
where gk is the k-th element of the out-of-balance vector G(Y(m)
l ,(m)
l ) and bk is the
k-th element of the initial fixed-end force vector B. The tolerance error ⑀1 is normally
assumed equal to 10−6
.
The procedure continues in this way with other load increments up to the failure
of the beam due to one of the following three causes: crushing of concrete in com-
pression (excessive compression strain), ceasing of structural steel in tension
(excessive tensile strain) and rupture of shear connection (excessive slip).
The ‘predictor’ solution at the beginning of each iterative loop is given by the equ-
ation
⌬Y1 ⫽ ⌬1·Y(m)
T (20)
where the load increment factor ⌬1 has to be fixed. As a matter of fact only the
increment ⌬(1)
1 of the first iterative loop needs to be provided by the user (normally
1/5 of the total load) so as to obtain a starting arc-length increment using the equation
[7] (Fig. 5)
⌬a(1)
⫽ ⌬(1)
1 ·√Y(m)T
T Y(m)
T ⫹ BT
B. (21)
For subsequent iterative loops, the lengths may be adjusted so to achieve a nearly
constant number of iterations, hence the following criterion is considered [8,10]
⌬a(m⫹1)
⫽ ⌬a(m)
·冪
Id
Im
, (22)
where Im is the number of iterations required to achieve equilibrium at the m-th loop
and Id is the desired number of iterations for the m⫹1-th loop (normally Id ⫽ 5).
The initial increment loading parameter ⌬(m)
1 , for all loops other than the first,
are obtained from (Fig. 5),
⌬(m)
1 ⫽ ⫾
⌬a(m)
√Y(m)T
T Y(m)
T ⫹ BT
B
, (23)
10. 204 N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
the sign follows that of the previous increment unless the determinant of the tangent
stiffness matrix AT has changed sign, in which case, a sign reversal is applied [8].
This procedure is powerful when the aim is to obtain the complete load–deflection
curve up to beam collapse, which is, in contrast, very difficult to obtain with many
procedures available in the literature (e.g. [2,6]) when the structure has either a per-
fectly plastic or a softening behavior. A shortcoming of the proposed procedure
concerns its inadequacy for calculations at specific target loads because the load is
not known a priori. However, in these cases, if the target load is not too close to
the ultimate load, the modified Newton–Raphson technique with a horizontal con-
straint ( ⫽ const.) should be used.
2.3. Nonlinear behavior of sections
The internal forces vector R(Y(m)
l ) of Eq. (11) is evaluated by considering the
nonlinear behavior of sections. For simplicity, the superscript m (iterative loop
number) and subscript l (iteration number) are not reported in the following.
Once the displacement vector Y has been evaluated at each iteration, the axial
strains at the centroid fiber of concrete slab and of the steel beam as well as the
curvature at both ends of each element may be drawn by the equations
⑀ci ⫽
1,i⫹1 ⫺ 1,i
⌬li
⑀si ⫽
2,i⫹1 ⫺ 2,i
⌬li
1,i ⫽
6·(i⫹1 ⫺ i)
⌬l2
i
⫺
4i ⫹ 2i⫹1
⌬li
2,i ⫽ ⫺
6·(i⫹1 ⫺ i)
⌬l2
i
⫹
2i ⫹ 4i⫹1
⌬li
(24)
where the subscript i refers to the element number. Considering the sections of Fig.
6(a) (concrete slab) and Fig. 6(b) (steel member) the axial strains in any fiber of
them can be evaluated
⑀ci(y) ⫽ ⑀ci ⫹ i·y
⑀si(y) ⫽ ⑀si ⫹ i·y.
(25)
The constitutive relationships of materials (concrete and steel) allow us to deter-
mine the corresponding normal stresses in the concrete ci(y), in reinforcing steel
ri,j and in structural steel si(y). So the axial force in the sections can be calculated
by using the equations
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N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
Fig. 6. Discretization of concrete (a) and steel (b) sections for numerical integration of stresses.
Nci ⫽ 冕
hcb
⫺ hct
ci(y)·b(y)·dy ⫹ 冘
nl
j⫽1
ri,j·Asj
Nsi ⫽ 冕
hsb
⫺ hst
si(y)·b(y)·dy
(26)
where nl is the number of reinforcing steel layers and Asj is the steel area of each
layer. In the same way the moments in both sections can be evaluated
Mci ⫽ 冕
hcb
⫺ hct
ci(y)·y·b(y)·dy ⫹ 冘
nl
j⫽1
ri,j·ysj·Asj
Msi ⫽ 冕
hsb
⫺ hst
si(y)·y·b(y)·dy.
(27)
The vertical shear forces are obtained by equilibrium.
The integrals in Eqs. (26) and (27) are solved by numerical integration subdividing
12. 206 N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
the section into n strips, as indicated in Fig. 6, and then using a Gauss–Legendre
quadrature formula in each strip. The general integral of Eqs. (26) and (27) becomes
冕
hb
⫺ ht
S(y)·dy ⫽ 冘
n
p⫽1
冕
yp⫹1
yp
S(y)·dy ⬇ 冘
n
p⫽1
yp⫹1 ⫺ yp
2
·冘
5
q⫽1
wq·S(yq) (28)
where the variable yq is defined as follows
yq ⫽
yp⫹1 ⫹ yp
2
⫹
yp⫹1 ⫺ yp
2
·q, (29)
q and wq are the Gauss points in the interval [⫺1, ⫹1] and the weight factors,
respectively.
The slip at the steel–concrete interface is evaluated using the equation
sj ⫽ j,1 ⫺ j,2 ⫺ j·z (j⫽1,n⫹1) (30)
and the corresponding longitudinal shear force at the ends of each element
(Qi,1, Qi,2) are evaluated from the load–slip relationship of shear connectors. There-
fore, the actual nonlinear nodal forces can be evaluated. In particular, axial forces are
Nci,1 ⫽ ⫺ Nci ⫺ Qi,1
Nci,2 ⫽ ⫺ Nci ⫹ Qi,2
Nsi,1 ⫽ Nsi ⫺ Qi,1
Nsi,2 ⫽ Nsi ⫹ Qi,2
(31)
the bending moments and vertical shear forces at both ends of the i-th element are
Mi,1 ⫽ (Mci,1 ⫹ Msi,1) ⫹ Qi,1·z
Mi,2 ⫽ (Mci,2 ⫹ Msi,2) ⫺ Qi,2·z
Vi,1 ⫽ Vci,1 ⫹ Vsi,1
Vi,2 ⫽ Vci,2 ⫹ Vsi,2.
(32)
Assembling the forces of each element obtained with Eqs. (31) and (32) the actual
nonlinear nodal force vector of the structure R(Y) is obtained and so can be used in
Eq. (11).
2.4. Constitutive relationships
The numerical procedure allows us to consider various constitutive laws for the
materials of the composite beam. However, for simplicity, herein are presented the
most refined laws available for each material (Fig. 7). The relationship suggested by
the CEB Model Code 90 [12] is adopted for concrete both in compression and in
tension (Fig. 7(a)). In particular for concrete in compression
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N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
Fig. 7. Constitutive relationships for concrete (a), steel (b), shear connection (c) and interface slip (d).
c ⫽
k·⑀o ⫺ ⑀2
o
1 ⫹ (k ⫺ 2)·⑀o
·fck for 0 ⱕ ⑀o ⱕ ⑀u (33)
where k ⫽ Ec·⑀c1/fck, ⑀o ⫽ ⑀c/⑀c1, and ⑀u ⫽ ⑀cu/⑀c1 is the nondimensional strain corre-
sponding to half the compressive strength in the softening branch. Beyond this value
of the strain
c ⫽
fck
(·⑀u ⫺ 2)·冉⑀o
⑀u
冊2
⫹ (4 ⫺ ·⑀u)·冉⑀o
⑀u
冊
(34)
with
⫽ 4·
⑀2
u·(k ⫺ 2) ⫹ 2·⑀u ⫺ k
(⑀u·(k ⫺ 2) ⫹ 1)2
. (35)
For concrete in tension the following bilinear relationship is considered up to
cracking
ct ⫽ Ec·⑀c for 0 ⱕ ⑀c ⱕ 0.9·fctk/Ec (36)
14. 208 N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
and
ct ⫽ 0.9fctk ⫹ 0.1fctk·
⑀c ⫺ 0.9fctk/Ec
⑀ct1 ⫺ 0.9fctk/Ec
for 0.9fctk/Ec ⱕ ⑀c ⱕ ⑀ct1. (37)
The effect of tension stiffening is neglected.
Both for reinforcing steel and for structural steel a stress–strain relationship with
strain hardening is considered (Fig. 7(b)). Specifically, the relationship is linearly
elastic up to yielding, perfectly plastic between the elastic limit and the beginning
of strain hardening and follows the present equation in the strain hardening branch
s ⫽ fsy ⫹ Esh·(⑀s ⫺ ⑀sh)·冉1 ⫺ Esh·
⑀s ⫺ ⑀sh
4·(fsu ⫺ fsy)冊. (38)
The load–slip relationship of the connector is represented by the equation (Fig.
7(c))
Q ⫽ Qu·(1 ⫺ e−·s
)␣
(39)
where Qu is the ultimate load of the connector, and ␣ and  are coefficients to be
determined from the experimental results [2,4,5,13].
Moreover, in order to consider the bond at the steel–concrete interface, the follow-
ing relationship is assumed (Fig. 7(d)) [12]:
⫽ 1·√s/s1 0 ⱕ s ⱕ s1
⫽ 1 s1 ⱕ s ⱕ s2
⫽ 1·冪
s ⫺ s2
su ⫺ s2
s2 ⱕ s ⱕ su
(40)
where the coefficients 1, s1, s2 and su have to be determined from experimental
results. In the procedure, the bond effect is concentrated in the nodes so it is simu-
lated as fictitious additional connectors with an equivalent load–slip relationship,
Qbi ⫽ (s)·b·(⌬li⫺1 ⫹ ⌬li)/2, (41)
where (s) derives from Eq. (40), b is the top flange width and ⌬li is the length of
the ith element (Fig. 2).
3. Comparison with experimental data
Any analytical model for complex nonlinear problems has to be verified by means
of experimental data to ensure its validity and degree of accuracy. In this section
four different beams are analyzed using COBENA and the results are compared with
the corresponding experimental data. The first two examples concern simply sup-
ported composite beams while the other two refer to two span continuous beams.
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N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
3.1. Simply supported beams
The numerical simulation with COBENA of two simply supported beams, based
on those tested by Chapman and Balakrishnan at Imperial College of London [14]
was carried out. The beams have a span length of 5490 mm, an I-shaped steel mem-
ber 305 mm deep (12⬙ ⫻ 6⬙ ⫻ 44 lb/ft BSB) and a concrete slab 152 mm thick
(1220 mm wide). The first beam (beam E1) is subjected to a midspan point load
and the other (beam U4) is subjected to uniformly distributed loads. Shear connectors
are arranged according to the longitudinal shear: headed studs (12.7 mm diameter)
in pairs at 120 mm pitch for beam E1 and 32 headed studs (19 mm diameter) ‘tri-
angularly’ distributed for beam U4. The details of the beams are reported in Fig. 8
and in Table 1. In Table 2 the material properties as well as the value of the coef-
ficients characterizing the constitutive relationships used in the numerical simulation
are summarized.
The coefficients for the load–slip relationship of shear connectors were derived
from experimental push-out tests carried out by Chapman and Balakrishnan [14] on
the types of studs which were used in the beams. Moreover, provided that bonding
Fig. 8. Geometrical characteristics of simply supported beams: test E1 (a) and test U4 (b) [14].
16. 210 N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
Table 1
Geometrical characteristics of simply supported test beams
Beam identification E1 U4
Span length (mm) 5490 5490
Loading type Midspan point load Uniformly distrib.
Concrete slab Thickness (mm) 152.4 152.4
Width (mm) 1220 1220
Steel beam Section 12⬙ ⫻ 6⬙ ⫻ 44lb/ft BSB 12⬙ ⫻ 6⬙ ⫻ 44lb/ft BSB
Area (mm2
) 8400 8400
Shear connectors Kind of studs 12.7 ⫻ 50 19 ⫻ 102
Distribution of studs Uniform in pairs Triangular in pairs
Number of studs 100 32
Longitudinal Top (mm2
) 200 200
reinforcement Bottom (mm2
) 200 200
Table 2
Material properties and constitutive coefficient values
Beam identification E1 U4
Concrete Compressive strength fc (MPa) 32.7 33.8
Tensile strength fct (MPa) 3.07 3.14
Peak strain in compression ⑀c1 0.0022 0.0022
Peak strain in tension ⑀ct1 0.00015 0.00015
Steel Yield stress (MPa) Flange 250 269
Web 297 301
Reinforcement 320 320
Ultimate tensile Flange 465 470
stress (MPa) Web 460 479
Reinforcement 320 320
Strain–harden. Flange 0.00267 0.00196
strain ⑀sh Web 0.00144 0.00146
Elasticity modulus Es (MPa) 206 000 206 000
Strain–harden. modulus Esh (MPa) 3500 3500
Connection Qu (kN) 66 129
 (mm−1
) 0.8 1.3
␣ 0.45 0.65
Interface bond 1 (MPa) 1.5 1.5
s1 (mm) 0.05 0.05
s2 (mm) 0.15 0.15
su (mm) 0.60 0.60
was not prevented in test beams, account has been taken of its effect on the behavior
of the beam. In the experimental results [14] an average shear stress, calculated on
an elastic basis, at several loading phases was given. From these results it was poss-
ible to roughly estimate the coefficients for a bond relationship.
In the numerical simulation 26 elements per half span were used for both test
beams. Shear connectors were simulated in their actual position along the beam.
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N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
Figs. 9 and 10 show the comparison between numerical and experimental results
of beams E1 and U4, respectively. In particular the load versus midspan deflection
is plotted in Fig. 9(a) and Fig. 10(a), while the values of slip at the steel–concrete
interface along the beam axis are plotted in Fig. 9(b) and Fig. 10(b) for various
loading levels. The plots show the good agreement between the analytical results
and the experimental data. The small differences in the slip curves are likely due to
the bond relationship. In fact this relationship is extrapolated from the few average
experimental information [14] and is the same along the whole beam.
3.2. Continuous beams
In order to verify the numerical model in the presence of negative moments, two
continuous beams were studied. The beams, tested experimentally by Teraszkiewicz
[15] and by Ansourian [16], were simulated with the numerical model. Teraszkiew-
icz’s beam (beam CBI) has two equal spans of 3354 mm, an I-shaped steel member
Fig. 9. Comparison between numerical and experimental results of beam E1: deflection history (a), and
slip distribution along span at various load levels (b).
18. 212 N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
Fig. 10. Comparison between numerical and experimental results of beam U4: deflection history (a),
and slip distribution along span at various load levels (b).
152 mm deep (6⬙ ⫻ 3⬙ ⫻ 12 lb/ft BSB) and a concrete slab 60 mm thick (610 mm
wide). Stud shear connectors (9.5 mm diameter) are distributed in pairs at 146 mm
pitch along the beam. Ansourian’s beam (beam CTB4) has two equal spans of 4500
mm, an H-shaped steel member 190 mm deep (HEA 200) and a concrete slab 100
mm thick (800 mm wide). Stud connectors (19 mm diameter) are equally spaced in
trials at 350 mm along the beam except over the internal support (1050 mm both
sides) where the pitch reduces to 300 mm. Both beams are loaded symmetrically
with point loads at midspan. The details of the beams are reported in Fig. 11 and
in Table 3. The material properties as well as the value of the coefficients characteriz-
ing the constitutive relationships used in the numerical simulation are listed in
Table 4.
In these simulations bonding was not considered because the experimental beams
were greased at the steel–concrete interface to prevent bonding. A total number of
25 elements and 29 elements per span were used for beam CBI and beam CTB4,
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N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
Fig. 11. Geometrical characteristics of simply supported beams: test CBI (a) and test CTB4 (b).
Table 3
Geometrical characteristics of continuous test beams
Beam identification CBI CTB4
Span length (mm) 3354 4500
Loading type Midspan point load Midspan point load
Concrete slab Thickness (mm) 60 100
Width (mm) 610 800
Steel beam Section 6⬙ ⫻ 3⬙ ⫻ 12 lb/ft BSB HEA 200
Area (mm2
) 2276 5380
Shear connectors Kind of studs 9.5 ⫻ 50 19 ⫻ 75
Number of studs 96 84
Pitch of studs (mm) Sag 146 350
Hog 146 300
Longitudinal Hog top (mm2
) 445 804
reinforcement Hog bottom (mm2
) – 767
Sag top (mm2
) – 160
Sag bottom (mm2
) – 160
20. 214 N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
Table 4
Material properties and constitutive coefficient values for continuous test beams.
Beam identification CBI CTB4
Concrete Compressive strength fc (MPa) 46.7 34.0
Tensile strength fct (MPa) 3.89 3.15
Peak strain in compression ⑀c1 0.0022 0.0022
Peak strain in tension ⑀ct1 0.00015 0.00015
Steel Yield stress (MPa) Flange 301 236
Web 301 238
Reinforcement 321 430
Ultimate tensile Flange 470 393
stress (MPa) Web 470 401
Reinforcement 485 533
Strain–harden. Flange 0.012 0.018
strain ⑀sh Web 0.012 0.018
Reinforcement 0.010 0.010
Strain–harden. Steel beam 2500 3000
modulus Esh Reinforcement 2500 3500
Elasticity modulus Es (MPa) 206 000 206 000
Connection Qu (kN) 32.4 110
 (mm−1
) 4.72 1.2
␣ 1.0 0.85
respectively. As the beams were symmetric, only one half of the beams was modeled
to save computational time.
The comparison between some results of the simulation of beam CBI and the
corresponding experimental results is shown in Fig. 12. In particular the deflected
shape (Fig. 12(a)), the slip along the steel–concrete interface (Fig. 12(b)) and the
longitudinal strain profile along the lowermost fiber of the beam flange (Fig. 12(c))
are plotted. In compliance with experimental results these quantities were plotted at
W ⫽ 121.6 kN, which corresponds to 80.8% of the experimental ultimate load Wu
⫽ 150.5 kN. The predicted bearing capacity of the beam was 146.8 kN which is
within 2.5% of the corresponding experimental value.
In Fig. 12 the experimental results of the right span are plotted upon the results
of the left span to facilitate comparison with the numerical results. It can be noted
that the curve of the analytical results lies almost always among the experimental
results of the two halves of the beam.
The comparison between some results of the simulation of beam CTB4 and the
corresponding experimental results is shown in Fig. 13. In particular the load versus
sagging curvature (Fig. 13(a)) the load versus hogging curvature (Fig. 13(b)) and
the load versus midspace deflection relationships (Fig. 13(c)) are plotted. The sagging
curvature is evaluated at midspan and the hogging curvature is evaluated at 150 mm
from the support. It can be observed that the numerical curves and the experimental
results match rather closely, verifying the accuracy of the simulation.
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N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
Fig. 12. Comparison between numerical and experimental results of beam CBI: deflected shape (a), slip
distribution along span (b) and strain profile along the span in the bottom flange (c) at W ⫽ 121.6 kN.
4. Conclusions
The following conclusions can be drawn.
앫 The numerical procedure presented herein allows to consider the actual nonlinear
22. 216 N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
Fig. 13. Comparison between numerical and experimental results of beam CTB4: curvature at sagging
(a) and hogging (b) sections, and deflection history (c).
23. 217
N. Gattesco/Journal of Constructional Steel Research 52 (1999) 195–218
behavior of the component materials of steel and concrete composite beams as
well as the load–slip relationship of shear connectors.
앫 The shear transfer between concrete slab and steel beam occurs only where con-
nectors are located (in the absence of bonding) and it is then possible to study
beams with partial shear connections which normally means large connector pitch-
es.
앫 The arc-length method, implemented in the procedure, allows the collapse load
to be reached even for those structures whose load–deflection curve has either a
perfectly plastic or a softening behavior. This target is difficult to reach with many
procedures available in the literature (e.g. [2,6]).
앫 The program, in contrast to many other similar procedures, allows consideration
of bonding at the steel–concrete interface which may be useful, in some cases,
to predict its effect on the structural behavior.
앫 The favorable comparisons between the numerical results and the experimental
results available in the literature allows to state that this procedure is capable of
tracing the detailed response of composite beams over the whole loading range
up to failure, provided failure is not initiated by buckling (Figs. 9, 10, 12 and 13).
앫 Programs such the one described can be used to conduct extensive parametric
studies in order to better understand the inelastic response of continuous composite
beams with complete or partial shear connections.
Acknowledgements
The financial support of the Italian Ministry of University and Scientific Research
(M.U.R.S.T.) is gratefully acknowledged.
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