Zur Torsionsbemessung von Stahlbeton‐ und Spannbetonbalken nach DIN 1045‐1

Torsion Design of reinforced and prestressed concrete Beams according to DIN 1045‐1 The DIN 1045‐1 provisions specify two different methods for torsion design regarding the concrete strut angle. The analysis of a database containing about 300 tests on reinforced and prestressed concrete beams under pure torsion or combined loading shows that under certain loading conditions the methods should not be used alternatively. In addition, the database also shows that the strength of the concrete strut according to DIN 1045‐1 overestimates the torsional capacity in general. On the basis of these results a suggestion for the definition of the concrete strut angle for torsion design in relation to DIN 1045‐1 is derived. Furthermore a design concept for the definition of the thickness of the shear flow zone is presented. Finally the database is analysed according to Eurocode 2 in its edition of April 2002.     

Querkraft‐ und Torsionsbemessung nach DIN 1045‐1 (07.01)

Design for shear and torsion in accordance with DIN 1045‐1 (07.01). For reinforced members in normal strength normal concrete, under shear and under torsion and also under their simplified combination, design diagrams are presented. An example shows the practical application.     

Stabwerke und Teilflächenbelastung nach DIN 1045‐1 und Eurocode 2 – Modelle und Anwendungen

Strut‐and‐Tie Models and Concentrated Loading according to DIN 1045‐1 and Eurocode 2 – Modelling and Application Strut‐and‐tie models are efficient tools for the demonstration of load‐bearing characteristics and for the design of reinforced and prestressed concrete structures. The illustration and determination of so called D‐regions is one of the most common areas of application. Another related problem is concentrated loading. In comparison to bending or shear design, the standards DIN 1045‐1 and Eurocode 2 (DIN EN 1992‐1‐1) provide only limited requirements and information for application of strut‐and‐tie models and concentrated loading problems. In praxis, the Engineer has to find possible solutions on basis of the principles given in the standards. The following paper compares the basic information of DIN 1045‐1 and Eurocodes 2 (DIN EN 1992‐1‐1) concerning strut‐and‐tie‐models and concentrated loading problems and gives additional proposals for certain application issues.     

Druckstrebentragfähigkeit torsionsbeanspruchter Stahlbetonbalken mit üblicher Betondeckung

Concrete struts bearing capacity of reinforced concrete beams in torsion with practical concrete cover The analysis of an experiment database according to DIN 1045‐1 provisions shows an overestimation of the strength of the concrete strut in torsion with increasing concrete cover. In addition significant differences can be detected when comparing international design codes in relation to the concrete covers contribution to the torsional resistance of a reinforced concrete beam. In this paper experimental as well as related theoretical investigations of the concrete struts bearing capacity of reinforced concrete beams in torsion with nowadays practical concrete cover are presented. With respect to the observed influences on the failure load an approach for a safe definition of the shear flow zone thickness on the basis of DIN 1045‐1 provisions but independent of the concrete cover is derived.     

Bemessungshilfen und Konstruktion bei geneigten Querkräften

Design Methods and Detailing for RC Beams with Inclined Shear Forces The shear‐resistant design of reinforced concrete (RC) beams with rectangular cross sections and inclined shear forces (biaxial shear) is presented. Equations for the shear resistances provided by the tensile strut and by the compressive strut are derived according to the design concepts of DIN 1045‐1 and EC 2. They are verified to experimental data and elaborated to gain design charts. Examples show the practical applications. Existing detailing provisions for the anchorage of stirrups and the horizontal displacement in the tensile force of the bending reinforcement can directly be applied to cases of biaxial shear, if the rotations of the neutral axis and of the resultant strut‐and‐tie system are taken into account.     

Finite‐Elemente‐Berechnungen zum Trag‐ und Verformungsverhalten von Kopfbolzendübeln

Finite Element Calculation of load bearing and deformation behavior of headed studs. In the scope of numerical simulations the composite joint between concrete slab and steel girder is represented by springs or interface elements considering bi‐linear as well as tri‐linear shear‐slip behavior. This method is established to determine the global load bearing behavior for any degree of shear connection. In order to illustrate the concentrated load introduction a three‐dimensional modeling of the shear connector is required. This paper describes a three‐dimensional nonlinear finite element model, which offers the possibility to investigate the local load bearing and deformation behavior of headed studs under shear load. It has been calibrated on shear tests performed by the Institute for Structural Concrete, of University of Technology, Aachen. On the basis of parametrical studies the influence of the concrete strength, the length of the stud as well as the formation of the welded collar have been determined. Furthermore, the limits of the simulation of shear tests are detected.     

Bemessung von Dübeln am Bauteilrand unter Querlast: Ingenieurmäßiger Ansatz zur Berücksichtigung der Lastrichtung

Design of Anchors close to an Edge under Shear Loads Engineering Approach for Consideration of the Load Direction A universally valid proposal is made for the design of anchors close to an edge under shear loads for concrete edge failure. The angle of the shear load is taken into account during determination of the load distribution on each anchor of a group. Thus the model may be used for applications without and with hole clearance and for shear loads as well as for torsion moments.     

Zur plastischen Tragfähigkeit von 3‐Blech‐Querschnitten unter Normalkraft,doppelter Biegung und Wölbkrafttorsion

Ultimate load capacity of 3‐plate‐cross‐sections under normal force, biaxial bending and warping torsion. The considered 3‐plate‐section includes as special cases double‐symmetric, single‐symmetric I‐sections, U‐, Z‐ as well as T‐ and L‐sections. For the general case of biaxial bending, normal force and torsion ultimate stress resultants are determined. The section then is always fully plasticized and a failure mechanism with plane strain distribution occurs. Especially the influence of plastification on primary and secondary moment of torsion is investigated. A simple formula for maximum angle of torsion in the state of ultimate load is given.     

Torsions‐Querschnittswerte für rechteckige Hohlprofile nach EN 10210‐2:2006 und EN 10219‐2:2006

The new European Standards EN 10210‐2:2006 and EN 10219‐2:2006 contain the necessary cross‐section values for calculation of primary torsion (St. Venant‐torsion). In the following paper all cross‐section values for secondary torsion are additionally given, so that calculation of normal and shear stresses of the warping torsion is possible. These stresses cannot be neglected, but occur only at certain points of disturbance. For hollow sections it is always necess‐ary to take into consideration the shear deformations of warping torsion.     

Stahlbetonträger mit zweiachsiger Querkraftbeanspruchung

Reinforced Concrete Beams subject to biaxial Shear Forces: strut‐and‐tie models, experiment and design approach Spatial strut‐and‐tie models are developed for the design of reinforced concrete beams subject to biaxial shear forces. They are derived from a resolution of the vector of the resultant shear force and valid for beams with rectangular cross sections. The models consist of tensile struts of stirrups and longitudinal bars, compressive concrete struts directed to each separate area of the longitudinal reinforcement in the cracked part of the cross section as well as compressive struts stiffening the stirrups. They are qualitatively verified by experiments and further elaborated to derive design charts for the design of the stirrups. An example shows the practical application of the charts.     

Stahl‐Beton‐Haftverbindungen für Verbundbrücken – Versuche und Bemessung

Connections by adherence for steel‐concrete composite bridges – tests and design. This paper presents experimental and analytical research that was conducted on new connections “by adherence” for steel‐concrete composite bridges. Their resistance is due to the frictional shear resistance of different interfaces positioned in a judicious manner. These connections makes it possible to erect the structure quickly with full‐depth precast concrete slabs, while the concreting works on site are as much as possible limited. Experimental results show that these connections exhibit a high resistance to horizontal shear forces and are very stiff compared to traditional connectors (headed studs). However, their ductility is limited. Based on the experimental results, a calculation model, taking into account the deformation observed during the tests and behavior laws for interfaces, was then developed and used in a parametric study. Some results are presented and discussed. A simplified method for determining the resistance of these connections, based on these results, some design rules as well as some recommendations for construction are finally proposed. The behavior of steel‐concrete composite beams with connections by adherence is also shortly discussed.     

Bemessung der Bügel,Querkraftzulagen und Schrägstäbe nach DIN 1045‐1 und nach EC2

Design of stirrups, shear assemblies and bent‐up bars after DIN 1045‐1 and after EC2. For members in normal strength normal concrete C20/25 up to C50/60 with shear reinforcement BSt 500 design diagrams are presented. These enable the determination of required stirrups, shear assemblies (without enclosing the longitudinal reinforcement) and bent‐up bars under 45°, in any combination. The bearing capacity of the compression struts can be verified and the shifting of the tension line determined too.     

Elementdecken bei nicht vorwiegend ruhender Belastung. Hinweise zur Anwendung von Gitterträgern nach Zulassung

Semi‐Precast Slabs under Fatigue Load Advices to the application of lattice girders according technical approval Semi precast slabs with lattice girders and an insitu topping have been used for many years also in case of fatigue loads. The range and design rules of this application have been developed by tests. The design rules in technical approvals for lattice girders had been adapted to the design concept of the new DIN 1045‐1. In addition to design rules which apply to insitu concrete constructions an upper limit of shear forces and the fatigue of the lattice girder diagonals have to be proven. Therefore the truss model with variable inclination of the compressive strut has to be considered. The development of the design rules in the technical approval for lattice girder will be explained and a design table will be introduced.     

Neue Untersuchungen zum Ermüdungsverhalten von Verbundträgern aus hochfesten Werkstoffen mit Kopfbolzendübeln und Puzzleleiste

New investigations on the fatigue behavior of composite beams made of high strength materials with two different kinds of shear connection. Scope of the research project [1] was the investigation of the fatigue behaviour of different shear connectors (headed studs ∅︁ 22 mm and puzzle‐strip) together with high strength materials (steel S 460 and concrete C 80/95). For both types of shear connectors cyclic push‐out‐tests as well as large scale experiments with composite beams under cyclic loading have been carried out. The headed studs failed after a mean lifetime of 2,3 million cycles, the residual strength after 1 million cycles was reduced by about 25% compared to the static push‐out strength. In the puzzle‐strip cracks were visible, however, the residual strength was not reduced at all. Further, the push‐out tests with headed studs show a slight improvement of the fatigue behaviour using high strongth concrete (HSC). The cyclic beam tests show that the prediction of the fatigue according to EC 4 – as for specimens with normal strength materials – is not satisfactory. A good prediction of the crack propagation (and fatigue) can rather be achieved by using a crack‐slip‐relationship [6]. Also for shear joints with continuous puzzle‐strips a threshold value can be determined by fracture mechanics to which no further crack propagation (theoretically) occurs. However, this depends on the state of the cutting‐induced heat treatment of the surface material and on the surface roughness.     

Torsionsträgheitsmoment und Schubmittelpunkt von Winkelprofilen

Torsional cross‐section properties for angles. Using the finite element method (FEM) it is possible to determine accurate torsional cross‐section properties for hot rolled angle‐profiles. These values partly show relative big discrepancies to the approximations used in practice. For this reason the accurate position of the shear centre as well as the St. Venant's torsion constant for the profiles of DIN EN 10056‐1 are specified. In addition the knowledge of these values can be used to improve familiar approximations and to develop new formulae for the torsional constant.     

Eine Finite‐Elemente‐Lösung auf der Basis eines erweiterten eindimensionalen Querschnittselementes für die freie Torsion dünnwandiger prismatischer Stäbe

A finite element solution on the basis of an extended one‐dimensional cross‐section‐element for the Saint‐Venant torsion of thin‐walled prismatic beams. It is presented a finite element solution on basis of an extended one‐dimensional cross‐section‐element to the calculation of the warping function, the torsional properties and the shear stresses, dependent on it, for thin‐walled prismatic beams under Saint‐Venant torsion. The formulated finite two‐node‐element with six element degrees of freedom can capture through inclusion of the torsion around the element axis the linear term of the variance of warping function perpendicular to the element axis. Only the shear stresses of the ring shear flows in the closed section parts unchangeable over the wall thickness can be calculated with the simple two‐node‐element with two element degrees of freedom. The extended two‐node‐element supplies in addition also the shear stresses of the cut open cross‐section linearly changeable over the wall thickness.     

钢筋砼剪、扭构件桁架模型理论的发展

本文在对桁架模型及软化砼本构关系作了简要的回顾后,着重介绍了软化变角桁架模型的国内外应用现况。结合国内近年的研究,还对某些问题展开了讨论或评述。     

L形柱结构附加扭转试验及剪扭承载力分析

在试验的基础上,考察了在低周反复荷载作用下L形柱所产生的扭转效应,并借鉴规范对复合受力构件剪扭承载力的计算方法,定量地分析了附加扭矩对L形柱所产生的影响.研究结果表明:单个L形柱和结构中的L形框架柱受扭性能不同,前者对水平荷载的加载角度表现敏感,非对称加载时,附加扭矩的影响不可忽略,设计中应考虑弯剪扭的复合作用;而后者作为结构中协同工作的一部分,抗扭性能明显改善.     

Tragverhalten und Bemessung von eingemörtelten Bewehrungsstäben unter zyklischer Beanspruchung im ungerissenen und gerissenen Beton

Bond Behaviour and Design of Post‐Installed Rebars under Cyclic Loading in Uncracked and Cracked Concrete This paper addresses the behaviour of deformed cast‐in‐place and post‐installed reinforcing bars (rebars) in uncracked and cracked concrete under monotonic and cyclic loading. The tests were performed at the University Stuttgart. The bond behaviour of post‐installed rebars is compared with the bond behaviour of cast‐in‐place rebars. Furthermore the relationship between the bond behaviour under monotonic and cyclic loading is presented. Based on the results a simplified design model for post‐installed rebar connections will be presented, which fulfils the requirements for straight deformed reinforced bars according to the codes.