Investigation Of Load Slip Behavior And Fatigue Life Of Headed Shear Stud Connector

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Investigation of Load-Slip Behavior and Fatigue Life of Headed Shear Stud Connector

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Author : Md Manik Mia
Publisher :
ISBN 13 :
Total Pages : 128 pages
Book Rating : 4.:/5 (113 download)

Book Synopsis Investigation of Load-Slip Behavior and Fatigue Life of Headed Shear Stud Connector by : Md Manik Mia

Download or read book Investigation of Load-Slip Behavior and Fatigue Life of Headed Shear Stud Connector written by Md Manik Mia and published by . This book was released on 2017 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of composite structures in highway bridges has become a widespread practice and for developing composite action between steel beam and concrete slab, shear connectors are widely used. These shear connectors transfer the longitudinal shear forces developed at the interface between concrete slab and steel beam. Among different types of shear connectors, headed shear stud is most commonly used in practice. The strength and ductility of these connectors greatly influence the capacity of composite structures. In bridges, these shear studs are subjected to rapidly fluctuating stresses which may result in fatigue failure during the lifetime of the structure. Thus, the fatigue resistance of shear studs in composite beams is significant for the safe of whole structure and needs to be well investigated. The aim of this research work is to investigate the load-slip behavior and fatigue life of headed shear studs and assess the strength and fatigue requirements of current Canadian Standard, CSA S6-14. A three-dimensional finite element (FE) model of push out test is developed using commercial software package ABAQUS for predicting both fatigue life and static strength of headed shear studs. The FE model included both geometric and material nonlinearities. For fatigue life prediction both fatigue crack initiation life and crack propagation life are estimated. Excellent correlation against the test results for both fatigue life and static strength of shear stud is found. After validation, an extensive parametric study has been performed to investigate the effects of different parameters on load-slip behavior and fatigue life of shear stud connectors. Results from the FE analysis were also compared with current code of practices, such as European code (EC4), American code (AASHTO LRFD), Canadian code (CSA S6-14). The parametric study showed that both AASHTO and CSA S6-14 usually overestimate the static strength of headed shear stud connectors. The design provisions of European code, EC4 is found to give conservative estimation of shear capacity of headed shear stud. For fatigue life of shear stud a significant underestimation was found in case of AASHTO LRFD, while notable amount of overestimation was observed in case of CSA S6-14 demanding more study in this area. Currently, there is no provision available for fatigue life of shear studs when they are subjected to tension. This research project also examines the applicability of the current Canadian fatigue curves for design of shear studs when they are subjected to tension.

The Static and Fatigue Behaviour of Through-bolt Shear Connectors in Steel-precast Composite Bridge Girders

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Author : Kyle Daniel Balkos
Publisher :
ISBN 13 :
Total Pages : 161 pages
Book Rating : 4.:/5 (15 download)

Book Synopsis The Static and Fatigue Behaviour of Through-bolt Shear Connectors in Steel-precast Composite Bridge Girders by : Kyle Daniel Balkos

Download or read book The Static and Fatigue Behaviour of Through-bolt Shear Connectors in Steel-precast Composite Bridge Girders written by Kyle Daniel Balkos and published by . This book was released on 2018 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Increasing demand for the rapid and economically efficient construction of bridges has encouraged engineers to employ the use of accelerated bridge construction through modular assembly. The replacement of vehicular bridges in highly populated areas using traditional construction methods typically results in significant social and economic impacts as a consequence of lengthy closures of these bridges during construction. Accelerated bridge construction through modular assembly offers an advantageous alternative, as it can drastically reduce the duration for which the bridge is out of service, therefore minimizing the corresponding impacts. Full-depth, precast concrete decks connected to steel girders using mechanical shear connectors is one form of accelerated bridge construction where the major components can be fabricated off-site. Employing modular bridge components takes advantage of improved quality and efficient construction through prefabrication, resulting in easier and more rapid installation on-site. Currently, welded, headed shear studs are the most common type of shear connector used in composite bridge construction. An attractive alternative to this connection type is the use of slip-critical through-bolt shear connectors as they are expected to offer advantages with regards to their reduced installation and disassembly times, as well as their fatigue performance. Currently, relatively little is known about the true static load-slip and the fatigue behaviour of slip-critical through-bolt shear connectors in composite beams. Therefore, the following research project investigates the static and fatigue performance of these connectors. In order to do this, three large-scale composite beam specimens were fabricated, instrumented, and tested in an experimental program involving both static and fatigue loading. In order to better understand the static load-slip behaviour of this connector type, a mechanistic model was also developed, along with a nonlinear finite element (FE) model of a through-bolt connection. Results of the beam tests were compared with results from a previous study employing a simpler push test configuration, in order to understand the behaviour differences resulting from the choice of test configuration. Comparisons were also made between the experimental results and load-slip predictions made using the developed mechanistic and FE models. The fatigue testing did not result in the failure of any through-bolt shear connectors for the configurations considered in this experimental program. The fatigue performance of the through-bolt shear connectors far exceeded the predicted fatigue life obtained using the current fatigue design provisions for welded, headed shear studs. The static beam test and the push test resulted in similar peak shear loads prior to the onset of failure of the through-bolts. However, the slopes of the two load-slip curves were quite different, with the through-bolt shear connectors behaving in a much less stiff manner when tested in a beam test relative to a push test. Moreover, the slip required to produce a through-bolt failure is seen to be much higher in a beam test. The static load-slip behaviour of a through-bolt push test specimen was predicted using a mechanistic model. Comparison of the load-slip curves generated by the mechanistic model with the available push test results revealed that the mechanistic model is capable of accurately predicting the load-slip behaviour of through-bolt shear connectors. A comparison of the load-slip curves generated by the FE analysis revealed that the FE models are also able to predict the load-slip behaviour of through-bolt shear connectors. The findings in this study suggest that the performance of composite bridges, in terms of fatigue life, could be significantly improved if through-bolts were used in place of traditional headed shear studs. However, further experimental testing is recommended to fully develop this connection concept.

Proceedings of the Canadian Society of Civil Engineering Annual Conference 2022

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Author : Rishi Gupta
Publisher : Springer Nature
ISBN 13 : 3031341597
Total Pages : 1180 pages
Book Rating : 4.0/5 (313 download)

Book Synopsis Proceedings of the Canadian Society of Civil Engineering Annual Conference 2022 by : Rishi Gupta

Download or read book Proceedings of the Canadian Society of Civil Engineering Annual Conference 2022 written by Rishi Gupta and published by Springer Nature. This book was released on 2023-08-05 with total page 1180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises the proceedings of the Annual Conference of the Canadian Society of Civil Engineering 2022. The contents of this volume focus on specialty conferences in construction, environmental, hydrotechnical, materials, structures, transportation engineering, etc. This volume will prove a valuable resource for those in academia and industry.

Final Report on Fatigue Strength of Shear Connectors to the Committees of Structural Steel and Steel Plate-Producers of American Iron and Steel Institute

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Author : Roger G. Slutter
Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.E/5 ( download)

Book Synopsis Final Report on Fatigue Strength of Shear Connectors to the Committees of Structural Steel and Steel Plate-Producers of American Iron and Steel Institute by : Roger G. Slutter

Download or read book Final Report on Fatigue Strength of Shear Connectors to the Committees of Structural Steel and Steel Plate-Producers of American Iron and Steel Institute written by Roger G. Slutter and published by . This book was released on 1967 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Recent Advances in Durability Improvement and Low-Carbon Strategy of Engineering Materials and Structures

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Author : Zhongya Zhang
Publisher : Frontiers Media SA
ISBN 13 : 2832553672
Total Pages : 222 pages
Book Rating : 4.8/5 (325 download)

Book Synopsis Recent Advances in Durability Improvement and Low-Carbon Strategy of Engineering Materials and Structures by : Zhongya Zhang

Download or read book Recent Advances in Durability Improvement and Low-Carbon Strategy of Engineering Materials and Structures written by Zhongya Zhang and published by Frontiers Media SA. This book was released on 2024-08-28 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Global warming, caused by a significant increase in the concentration of greenhouse gases (GHGs) such as CO2, has become a concern all over the world. The whole process carbon emissions of the civil engineering industry account for nearly 40% of global energy and process-related CO2 emissions, more than half of which come from the process of producing, using, constructing and dismantling in civil engineering materials and structures, resulting in the embodied carbon emissions. With the acceleration of global warming, warmer and uncertain climates will make engineering materials and structures subject to more severe environmental conditions. A series of durability issues will occur more frequently, such as the significant variations of humidity in air, the chloride-induced corrosion caused by the severe chloride ingress, concrete cracking caused by the expansion of rusts, and more severe carbonation of concrete structures due to the increase in CO2 concentration. The adoption of positive measures to address climate change has become a global consensus, as global warming has led to serious threats and challenges to the survival and development of humankind.

Life-Cycle Civil Engineering: Innovation, Theory and Practice

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Author : Airong Chen
Publisher : CRC Press
ISBN 13 : 1000342085
Total Pages : 2619 pages
Book Rating : 4.0/5 (3 download)

Book Synopsis Life-Cycle Civil Engineering: Innovation, Theory and Practice by : Airong Chen

Download or read book Life-Cycle Civil Engineering: Innovation, Theory and Practice written by Airong Chen and published by CRC Press. This book was released on 2021-02-26 with total page 2619 pages. Available in PDF, EPUB and Kindle. Book excerpt: Life-Cycle Civil Engineering: Innovation, Theory and Practice contains the lectures and papers presented at IALCCE2020, the Seventh International Symposium on Life-Cycle Civil Engineering, held in Shanghai, China, October 27-30, 2020. It consists of a book of extended abstracts and a USB card containing the full papers of 230 contributions, including the Fazlur R. Khan lecture, eight keynote lectures, and 221 technical papers from all over the world. All major aspects of life-cycle engineering are addressed, with special emphasis on life-cycle design, assessment, maintenance and management of structures and infrastructure systems under various deterioration mechanisms due to various environmental hazards. It is expected that the proceedings of IALCCE2020 will serve as a valuable reference to anyone interested in life-cycle of civil infrastructure systems, including students, researchers, engineers and practitioners from all areas of engineering and industry.

Finite Element Analysis and Design of Steel and Steel–Concrete Composite Bridges

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Author : Ehab Ellobody
Publisher : Butterworth-Heinemann
ISBN 13 : 0124173039
Total Pages : 683 pages
Book Rating : 4.1/5 (241 download)

Book Synopsis Finite Element Analysis and Design of Steel and Steel–Concrete Composite Bridges by : Ehab Ellobody

Download or read book Finite Element Analysis and Design of Steel and Steel–Concrete Composite Bridges written by Ehab Ellobody and published by Butterworth-Heinemann. This book was released on 2014-05-30 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, bridge engineers and researchers are increasingly turning to the finite element method for the design of Steel and Steel-Concrete Composite Bridges. However, the complexity of the method has made the transition slow. Based on twenty years of experience, Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges provides structural engineers and researchers with detailed modeling techniques for creating robust design models. The book’s seven chapters begin with an overview of the various forms of modern steel and steel–concrete composite bridges as well as current design codes. This is followed by self-contained chapters concerning: nonlinear material behavior of the bridge components, applied loads and stability of steel and steel–concrete composite bridges, and design of steel and steel–concrete composite bridge components. Constitutive models for construction materials including material non-linearity and geometric non-linearity The mechanical approach including problem setup, strain energy, external energy and potential energy), mathematics behind the method Commonly available finite elements codes for the design of steel bridges Explains how the design information from Finite Element Analysis is incorporated into Building information models to obtain quantity information, cost analysis

Bridge Maintenance, Safety, Management, Life-Cycle Sustainability and Innovations

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Author : Hiroshi Yokota
Publisher : CRC Press
ISBN 13 : 100017381X
Total Pages : 8732 pages
Book Rating : 4.0/5 (1 download)

Book Synopsis Bridge Maintenance, Safety, Management, Life-Cycle Sustainability and Innovations by : Hiroshi Yokota

Download or read book Bridge Maintenance, Safety, Management, Life-Cycle Sustainability and Innovations written by Hiroshi Yokota and published by CRC Press. This book was released on 2021-04-20 with total page 8732 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridge Maintenance, Safety, Management, Life-Cycle Sustainability and Innovations contains lectures and papers presented at the Tenth International Conference on Bridge Maintenance, Safety and Management (IABMAS 2020), held in Sapporo, Hokkaido, Japan, April 11–15, 2021. This volume consists of a book of extended abstracts and a USB card containing the full papers of 571 contributions presented at IABMAS 2020, including the T.Y. Lin Lecture, 9 Keynote Lectures, and 561 technical papers from 40 countries. The contributions presented at IABMAS 2020 deal with the state of the art as well as emerging concepts and innovative applications related to the main aspects of maintenance, safety, management, life-cycle sustainability and technological innovations of bridges. Major topics include: advanced bridge design, construction and maintenance approaches, safety, reliability and risk evaluation, life-cycle management, life-cycle sustainability, standardization, analytical models, bridge management systems, service life prediction, maintenance and management strategies, structural health monitoring, non-destructive testing and field testing, safety, resilience, robustness and redundancy, durability enhancement, repair and rehabilitation, fatigue and corrosion, extreme loads, and application of information and computer technology and artificial intelligence for bridges, among others. This volume provides both an up-to-date overview of the field of bridge engineering and significant contributions to the process of making more rational decisions on maintenance, safety, management, life-cycle sustainability and technological innovations of bridges for the purpose of enhancing the welfare of society. The Editors hope that these Proceedings will serve as a valuable reference to all concerned with bridge structure and infrastructure systems, including engineers, researchers, academics and students from all areas of bridge engineering.

Recommendations for Fatigue Design of Welded Joints and Components

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Author : A. F. Hobbacher
Publisher : Springer
ISBN 13 : 3319237578
Total Pages : 153 pages
Book Rating : 4.3/5 (192 download)

Book Synopsis Recommendations for Fatigue Design of Welded Joints and Components by : A. F. Hobbacher

Download or read book Recommendations for Fatigue Design of Welded Joints and Components written by A. F. Hobbacher and published by Springer. This book was released on 2015-12-23 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a basis for the design and analysis of welded components that are subjected to fluctuating forces, to avoid failure by fatigue. It is also a valuable resource for those on boards or commissions who are establishing fatigue design codes. For maximum benefit, readers should already have a working knowledge of the basics of fatigue and fracture mechanics. The purpose of designing a structure taking into consideration the limit state for fatigue damage is to ensure that the performance is satisfactory during the design life and that the survival probability is acceptable. The latter is achieved by the use of appropriate partial safety factors. This document has been prepared as the result of an initiative by Commissions XIII and XV of the International Institute of Welding (IIW).

Fracture, Fatigue, Failure and Damage Evolution, Volume 7

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Author : Jay Carroll
Publisher : Springer
ISBN 13 : 3319628313
Total Pages : 123 pages
Book Rating : 4.3/5 (196 download)

Book Synopsis Fracture, Fatigue, Failure and Damage Evolution, Volume 7 by : Jay Carroll

Download or read book Fracture, Fatigue, Failure and Damage Evolution, Volume 7 written by Jay Carroll and published by Springer. This book was released on 2017-08-24 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fracture, Fatigue, Failure and Damage Evolution, Volume 7 of the Proceedings of the 2017 SEM Annual Conference & Exposition on Experimental and Applied Mechanics, the seventh volume of nine from the Conference, brings together contributions to this important area of research and engineering. Session organizers include: Jay Carroll, Shuman Xia, Allison Beese, Ryan Berke, Garrett Pataky, Samantha Daly, Kavan Hazeli, Antonios Kontsos, Omer Ozgur Capraz, Scott Grutzik, Onome Scott-Emaukpor The collection presents early findings and case studies on a wide range of areas, including: Mechanics of Energy & Energetic Materials Vibration Effects in Fracture & Fatigue Fracture & Fatigue of Additively Manufactured Materials In Situ Techniques for Fatigue & Fracture Microscale & Microstructural Effects on Mechanical Behavior Fracture & Fatigue of Composites Integration & Validation of Models with Experiments Fracture & Fatigue in Extreme Environments Novel Experimental Methods for Fatigue and Fracture Fracture of Brittle & Ductile Materials Interfacial Fracture

Improvement of Buildings' Structural Quality by New Technologies

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Author : Christian Schauer
Publisher : CRC Press
ISBN 13 : 0203970845
Total Pages : 763 pages
Book Rating : 4.2/5 (39 download)

Book Synopsis Improvement of Buildings' Structural Quality by New Technologies by : Christian Schauer

Download or read book Improvement of Buildings' Structural Quality by New Technologies written by Christian Schauer and published by CRC Press. This book was released on 2005-01-20 with total page 763 pages. Available in PDF, EPUB and Kindle. Book excerpt: Launched in May 2000, the aims of the COST C12 cooperative action were:to develop, combine and disseminate new technical engineering technologiesto improve the quality of urban buildingsto propose new technical solutions to architects and plannersto reduce the disturbance caused by construction in urban areas and improve urban quality of life.This

PRO 21: International RILEM Symposium on Connections Between Steel and Concrete (Set)

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Author : Rolf Eligehausen
Publisher : RILEM Publications
ISBN 13 : 9782912143259
Total Pages : 736 pages
Book Rating : 4.1/5 (432 download)

Book Synopsis PRO 21: International RILEM Symposium on Connections Between Steel and Concrete (Set) by : Rolf Eligehausen

Download or read book PRO 21: International RILEM Symposium on Connections Between Steel and Concrete (Set) written by Rolf Eligehausen and published by RILEM Publications. This book was released on 2001 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Behaviour of Headed-stud Shear Connectors in Composite L-beams

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Author : Mohammed Salah Bessioud
Publisher :
ISBN 13 :
Total Pages : 167 pages
Book Rating : 4.:/5 (117 download)

Book Synopsis Behaviour of Headed-stud Shear Connectors in Composite L-beams by : Mohammed Salah Bessioud

Download or read book Behaviour of Headed-stud Shear Connectors in Composite L-beams written by Mohammed Salah Bessioud and published by . This book was released on 1988 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: The results of tests of twenty-nine push-out specimens are described. Twenty-five specimens were nominally reinforced; fifteen of these had F60 profiled sheeting, seven had F32S profiled sheeting, and three were solid slabs. The remaining four specimens were reinforced as follows: (i) three specimens had 6mm diameter mild steel stirrups along the expected failure zone and; (ii) one specimen had 2 x 8mm diameter mild steel bars looped around the studs. The influence of the concrete cover to the stud connector, bc, on the behaviour and the failure modes of the composite L-Beams in floors, through asymmetic push-out specimens, was the major variable investigated. Other parameters including the average thickness of the concrete slab, hc, the thickness, t, the rib height, h, and the average rib width, W, of the steel sheeting have also been investigated. Also investigated were the effects of looping the reinforcement around the studs and placing stirrups along the expected failure planes. The experimentally determined strengths, the behaviour during testing and the failure modes have been monitored during testing. The results are compared with results obtained and proposals made by other investigators. The ductility of the connection has also been measured, by means of the slip at 90% of the measured failure loads, in order to study the behaviour of the stud shear connectors in push-out specimens. For all three types of profiles, the ratio of Q, the asymmetric specimens strength to Qfw the strength of specimens having full width slabs have been plotted against the concrete cover to the studs, bc. Linear regressions have been carried out to give a set of three mathematical equations describing this behaviour. These equations could form the basis of a design method for predicting the strength of stud shear connectors in.

Lifetime-Oriented Structural Design Concepts

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Author : Friedhelm Stangenberg
Publisher : Springer Science & Business Media
ISBN 13 : 3642014623
Total Pages : 765 pages
Book Rating : 4.6/5 (42 download)

Book Synopsis Lifetime-Oriented Structural Design Concepts by : Friedhelm Stangenberg

Download or read book Lifetime-Oriented Structural Design Concepts written by Friedhelm Stangenberg and published by Springer Science & Business Media. This book was released on 2009-11-26 with total page 765 pages. Available in PDF, EPUB and Kindle. Book excerpt: Safety and reliability are important for the whole expected service duration of an engineering structure. Therefore, prognostical solutions for different building types are needed and uncertainties have to be handled. Life-cycle strategies to control future structural degradations by concepts of appropriate design have to be developed, in case including means of inspection, maintenance, and repair. Aspects of costs and sustainability also matter. The Cooperative Research Center for Lifetime-Oriented Design Concepts (SFB 398) at Ruhr University in Bochum combines the wide range of scientific topics between structural engineering, structural and soil mechanics and material sciences regarding structural lifetime management in this present extraordinary monolithic format. The characterization and modeling of lifetime-related external actions of multiple origin are presented in this book as well as the physical description, the modeling and the validation of material degradation. Adaptive numerical methods and simulation techniques are provided for the lifetime-oriented design concepts to forecast material and structural degradation. Stochastic aspects, mathematical optimization methods and interactions between various influences are included. Thus, a solid basis is provided for future practical use and also for standardization of structural design with respect to lifetime-prediction.

Maintenance, Safety, Risk, Management and Life-Cycle Performance of Bridges

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Author : Nigel Powers
Publisher : CRC Press
ISBN 13 : 1351745972
Total Pages : 550 pages
Book Rating : 4.3/5 (517 download)

Book Synopsis Maintenance, Safety, Risk, Management and Life-Cycle Performance of Bridges by : Nigel Powers

Download or read book Maintenance, Safety, Risk, Management and Life-Cycle Performance of Bridges written by Nigel Powers and published by CRC Press. This book was released on 2018-07-04 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maintenance, Safety, Risk, Management and Life-Cycle Performance of Bridges contains lectures and papers presented at the Ninth International Conference on Bridge Maintenance, Safety and Management (IABMAS 2018), held in Melbourne, Australia, 9-13 July 2018. This volume consists of a book of extended abstracts and a USB card containing the full papers of 393 contributions presented at IABMAS 2018, including the T.Y. Lin Lecture, 10 Keynote Lectures, and 382 technical papers from 40 countries. The contributions presented at IABMAS 2018 deal with the state of the art as well as emerging concepts and innovative applications related to the main aspects of bridge maintenance, safety, risk, management and life-cycle performance. Major topics include: new design methods, bridge codes, heavy vehicle and load models, bridge management systems, prediction of future traffic models, service life prediction, residual service life, sustainability and life-cycle assessments, maintenance strategies, bridge diagnostics, health monitoring, non-destructive testing, field testing, safety and serviceability, assessment and evaluation, damage identification, deterioration modelling, repair and retrofitting strategies, bridge reliability, fatigue and corrosion, extreme loads, advanced experimental simulations, and advanced computer simulations, among others. This volume provides both an up-to-date overview of the field of bridge engineering and significant contributions to the process of more rational decision-making on bridge maintenance, safety, risk, management and life-cycle performance of bridges for the purpose of enhancing the welfare of society. The Editors hope that these Proceedings will serve as a valuable reference to all concerned with bridge structure and infrastructure systems, including students, researchers and engineers from all areas of bridge engineering.

IABSE Symposium Budapest 2006

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Author :
Publisher :
ISBN 13 :
Total Pages : 508 pages
Book Rating : 4.0/5 ( download)

Book Synopsis IABSE Symposium Budapest 2006 by :

Download or read book IABSE Symposium Budapest 2006 written by and published by . This book was released on 2006 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advanced Concretes and Their Structural Applications-Volume II

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Author : Zhigang Zhang
Publisher : Frontiers Media SA
ISBN 13 : 2832529283
Total Pages : 235 pages
Book Rating : 4.8/5 (325 download)

Book Synopsis Advanced Concretes and Their Structural Applications-Volume II by : Zhigang Zhang

Download or read book Advanced Concretes and Their Structural Applications-Volume II written by Zhigang Zhang and published by Frontiers Media SA. This book was released on 2023-07-10 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: