Zum statischen System von Kellerwänden aus unbewehrtem Beton unter Erddruck

Static System of Earth Pressure loaded Basement Walls made of Non‐Reinforced Concrete Basement walls in housing are usually made of masonry or reinforced concrete. Both styles are more labor‐ and material‐intensive and therefore more expensive than basement walls without reinforcement. The required wall‐thickness of non‐reinforced walls is the most important reason for the general restraint. The design according to DIN 1045‐1 results in thicker walls compared to the design of masonry according to DIN 1053. The article illustrates the reason for the conservative design according to DIN 1045‐1 and its supposed static system in comparison to the developed design method deduced from finite‐element‐simulations. Hereby the wall thickness of non‐reinforced concrete walls can be reduced by using their ability of deformation.     

Kellerwände aus unbewehrtem Beton

Basement Walls made of non‐reinforced Concrete In this contribution design nomogramms are developed on the basis of DIN 1045‐1 respectively DIN 1045 taking into account the ductility of non‐reinforced concrete walls in housing. Considering the deformation ability, the calculated load bearing capacity of walls under earth pressure can be increased significantly compared to common design rules. On behalf of the „Forschungsgemeinschaft Transportbeton e.V.”︁ a typed design ([5], [6]) was done on the basis of the design concept introduced here.     

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.     

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.     

Zur Auswahl eines geeigneten Verfahrens für die Berücksichtigung der Mitwirkung des Betons auf Zug

Die Auswahl eines geeigneten Verfahrens zur Berücksichtigung der Mitwirkung des Betons auf Zug sollte nach DIN 1045‐1:2001‐07, 8.5.1 (9), in Abhängigkeit von der jeweiligen Bemessungsaufgabe getroffen werden. In den Erläuterungen zu DIN 1045‐1 wird im Heft 525 des DAfStb als einziges Verfahren nur die Verringerung der Betonstahldehnung mit einer modifizierten Spannungs‐Dehnungslinie für Betonstahl erläutert. Verfahren, die mittlere wirksame Betonzugspannungen in der Betonzugzone berücksichtigen, werden erwähnt aber nicht erläutert. Mit den Ergebnissen nachgerechneter Moment‐Verkrümmungs‐Werte von Stahlbetonröhren aus drei Versuchen mit unterschiedlichen Längskräften wird gezeigt, dass die Mitwirkung des Betons auf Zug mit dem Verfahren nach Heft 525 DAfStb nur bei reiner Biegung befriedigend erfasst wird. Bei Biegung mit Längskraft werden besser mittlere wirksame Betonzugspannungen berücksichtigt. Es werden vier unterschiedliche Ansätze für die Betonzugspannungen besprochen. On the selection of an adequate method for considering the contribution of concrete in tension. The selection of an adequate method for considering the contribution of concrete in tension should according to DIN 1045‐1:2001‐07, 8.5.1 (9), be chosen with respect to the particular design problem. The explanations to DIN 1045‐1 in book 525 from DAfStb describe only one method, the method which reduces the steel strain taking a modified stress‐strain relationship into account. Methods that consider mean effective concrete stresses in tension are mentioned but not explained. The results of recomputed moment‐curvature values from three tests with different longitudinal forces show that the method in book 525 DAfStb covers the contribution of concrete in tension only for reinforced concrete members without longitudinal forces. For members with longitudinal forces methods with mean effective concrete stresses give better agreements. Four different assumptions for the concrete stresses in tension are discussed.     

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.     

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.     

Zur Druck‐Zug‐Festigkeit von Stahlbeton und stahlfaserverstärktem Stahlbeton

Während die Druckfestigkeit des Betons durch gleichzeitig wirkenden Querdruck gegenüber der einaxialen Druckfestigkeit erheblich gesteigert werden kann, führen Querzugbeanspruchung und Rissbildung zu einer Abminderung der Tragfähigkeit. Dies gilt für unbewehrten Beton und Stahlbeton gleichermaßen. In den einschlägigen Regelwerken finden sich hierzu international sehr unterschiedliche Bemessungsansätze, wobei die vorgesehenen Abminderungsbeiwerte für denselben Anwendungsfall um das bis zu Zweifache differieren. Die Frage der Druck‐Zug‐Festigkeit von Stahlbeton wurde in den vergangenen 40 Jahren von zahlreichen Wissenschaftlern untersucht. Ihre Ergebnisse sind allerdings zum Teil ebenso widersprüchlich wie die aktuelle Normensituation. Basierend auf eigenen experimentellen Untersuchungen sowie einer kritischen Auswertung und Einordnung als richtungweisend angesehener, früherer Versuchsreihen wird ein Vorschlag zur Abminderung der Druckfestigkeit des gerissenen Stahlbetons entwickelt. Erstmals wird dabei auch der Einfluss einer Faserzugabe in Kombination mit Stabstahlbewehrung berücksichtigt. Ein Vergleich mit den in DIN 1045‐1, CEB‐FIP Model Code 1990, Eurocode 2 und ACI Standard 318‐05 angegebenen Bemessungsregeln zeigt, dass allein DIN 1045‐1 die in den Versuchen beobachtete maximale Abminderung der Druckfestigkeit durch Querzug und Rissbildung zum Teil erheblich unterschätzt, so dass eine konservative Auslegung der Tragwerke nicht immer sichergestellt ist. Biaxial Compression‐Tension‐Strength of Reinforced Concrete and Reinforced Steel Fibre Concrete The compressive strength of concrete can be substantially increased in relation to uni‐axial compressive strength by transverse compression acting at the same time. In contrast, transverse tension and cracking lead to a reduction of the load‐carrying capacity. This holds true for plain concrete as well as for reinforced concrete. In international standards very different calculation rules can be found on this subject, whereby the provided reductions differ up to a factor of two for the same application. The question of biaxial compression‐tension‐strength of reinforced concrete was examined in the past 40 years by numerous scientists. Their results are, however, partially contradictory in the same way as the current standard situation. Based on own experimental investigations as well as on a critical review and classification of former test series regarded as trend‐setting, a proposal for the reduction of the compressive strength of cracked reinforced concrete is developed. For the first time, also the influence of fibres in addition to bar reinforcement is considered thereby. A comparison with the calculation rules in DIN 1045‐1, CEB‐FIP Model Code 1990, Eurocode 2, and ACI Standard 318‐05 shows, that exclusively DIN 1045‐1 underestimates sometimes substantially the maximum reduction of the compressive strength by transverse tension and cracking observed in the tests, so that a conservative design of structures cannot always be ensured.     

Zur Traglastermittlung von Druckstäben im Holzbau

Determination of ultimate loads for compression members in timber constructions. The design of compression members in timber constructions has to consider the increasing stress due to the non‐linear behaviour of the members. The determination of the ultimate load of compression members requires the consideration of non‐linear geometric behaviour, if the bending moments increase more than 10% in relation to the linear theory. In the German timber design code, DIN 1052 [1], two methods of calculation are suggested. The second method uses geometric non – linear theory (theory second order) for calculation of the ultimate load. According to DIN 1052 the load carrying capacity can be determined without reducing stiffness parameters using the modification factor. The calculation methods for compression members according to DIN 1052 are compared and differences between them are discussed. A calculation with identical results for the ultimate loads using either the first or the second method is proposed.     

Einheitliches Fachwerkmodell für Stahlbeton‐ und Spannbetonbauteile unter Querkraft‐ und Torsionsbeanspruchung

Uniform framework model for reinforced and prestressed concrete structural members under shear and torsion loading. Following the design provisions for shear and torsion according to DIN 1045‐1 the following two principle questions are raised: For a lot of situations in standard design praxis the allowable inclination of the concrete strut is determined to an angle as small as about 18° – while such a gentle strut angle in tests could only be proved in case of a high level additional compression force. Additionally, with the given two different design approaches a smooth transition between structures with and without required shear reinforcement is lacking. For the purpose of a general review experimental as well as theoretical investigations for beams under shear loading and torsion loading have been conducted. As consequence of the obtained results a uniform strut‐and‐tie model with simply application has been derived.     

Teilfertigdecken nach DIN 1045‐1. Wichtige Punkte der Bemessung und Konstruktion

Partly pre‐fabricated reinforced concrete Floors/Ceilings according to DIN 1045‐1. Important Points of Design and Construction There are invasive changes in design and construction of partly pre‐fabricated reinforced concrete floors/ceilings connected with the application of DIN 1045‐1, July 2001 issue. This applies specifically to the verification of acceptance of thrust force in the joint between pre‐cast slab and the on‐site concrete. The basic elements will be gathered for this extensive verification and an example is given. Regulations for the arrangement of lattice girders as bond/shear force reinforcement as well as concrete covers will be shown in detail. Structures of support are easier to implement in the future.     

Probabilistische Modellierung hochfester Stahlbetonstützen in Hochhäusern

Probabilistic Modelling of HPC Slender Columns in High‐Rise Buildings In Germany high strength concrete is used successfully since 1990. The extremely high compressive strength of this material allows considerable reduction in cross‐sectional dimensions of reinforced concrete columns and accordingly accomplishes highest architectural and functional requirements. This leads in many cases to extremely slender structures and therefore increases the risk of failure due to loss of stability. Because of the positive experience with high strength concrete up to now, the current study questions the initial conservative design provisions. In this context code procedures of DIN 1055‐3 and DIN 1045‐1 are compared with the results of probabilistic analysis and potential optimization will be indicated.     

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.     

Flachdecken in Elementbauweise. Hinweise zum Durchstanznachweis nach DIN 1045‐1

Flat Slabs built with Semi‐Precast Elements. Advices to Punching Shear Verification according DIN 1045‐1 Flat slabs are increasingly built with precast slabs and insitu topping. The bearing behaviour of these semi‐precast slabs with lattice girders is similar to cast in one concrete slabs. In principle this is also applied for areas where punching failure is endangered. This was shown in full‐scale tests, which were taken as the basis for derivation of design rules. However during design of semi‐precast slabs some specific items have to be considered. The revision of technical approvals for punching shear reinforcements to the new German design standard for concrete and reinforced concrete DIN 1045‐1 took place during the introduction of new punching shear reinforcement for semi‐precast elements. The required verification of punching shear in element slabs are arranged and explained for different types of punching shear reinforcement.     

Durchstanzmodell für Flachdecken mit Faserverbundbewehrung und großen Aussparungen in Stützennähe

Punching Model for Flat Slabs with FRP Reinforcement and large Openings near the supporting Surface Flat slabs with tension bars using glass‐ or carbon fiber reinforced polymer have a substantial lower punching load capacity then conventional steel reinforced plates. This is caused by the dependence of the shear force transportation on the stiffness and therefore on the elastic modulus of the reinforcement, after concrete is cracked: For glass fiber reinforced polymer the elastic modulus has an amount of approximately 35000 N/mm², which isn't more then one sixth of the steel value. Until now designing rules for concrete don't take into account this influence. Following a new developed punching model will be presented, that compared with DIN 1045 [2] and DIN 1045‐1 [3] directly includes the elastic modulus of the bending reinforcement and that also applicates the reduction of the punching load capacity by openings near the supporting surface in a realistic way.     

Verformungsvorhersage von vorgespannten und nicht vorgespannten Betonbauteilen

Deformation Forecast of Prestressed and Non‐Prestressed Concrete Members Comparative investigations have shown that the limitation of deformation, based on a permitted slenderness ratio as possible according to DIN 1045‐1 for reinforced concrete elements, do not always achieve the desired success. An exact calculation of the structure deformation is absolutely necessary for prestressed components and in the case of a non‐accomplished slenderness proof for reinforced concrete members. In this paper significant material influences of the deformation forecast will be discussed, proceeding from universal views of the component deformation proof. It will be clear, that an exact deformation calculation is only restricted possible. An approximation procedure for practical use to the forecast of deformations of reinforced and prestressed concrete structures will be formulated, afterwards. The accuracy of this developed approximation procedure will be estimated with the aid of comparative studies. At this, the results of the simplified formulation correlate well with the values of complex, numeric investigations in a range of practical use.     

Biegebemessung im Grenzzustand der Gebrauchstauglichkeit (GZG). Ein Kommentar zu DIN 1045‐1

Bending Design in limit State of Usability (GZG). Comment on DIN 1045‐1 The article brings a method of design in the limit state of usability up for discussion, which presupposes cracked concrete and a nonlinear performance. This method eliminates the difference in design results between the state of usability at stress limits according to DIN 1045‐1 11.1.2 and the limit state of load apacity. Tables for design will be shown and there use will be declared.     

Vergleich des ETV Beton und DIN 1045‐1

Comparison of the ETV Beton and DIN 1045‐1 The paper compares the safety elements of the ETV Beton and the valid German reinforced concrete code DIN 1045‐1. The comparison is carried out in general for the characteristic values of the actions, for the partial safety factors of the actions and the resistance and for the action combination factors as well. Additionally the comparison has been done in terms of calculation of the required amount of reinforcement in an example. The comparison yields to the result that especially the partial safety factor for dead load is substantially lower in the ETV Beton compared to DIN 1045‐1. Newer developments in the Eurocode suggesting a lower partial safety factor for dead load are therefore backed by the presented investigation.     

Tragverhalten von dünnen Bauteilen aus ultrahochfestem Faserfeinkornbeton

The Structural Behaviour of Thin Structural Members made of Ultra‐High Performance Fibre Reinforced Concrete Ultra‐high performance fibre reinforced concrete (UHPFRC) is especially suitable for thin structures or members due to its fine aggregates and high strengths. Based on own test results and theoretical assumptions the load bearing behaviour of UHPFRC under tension, compression and bending is examined. Thereby, the influence of fibre orientation is considered. The validity of the material laws used is checked by recalculating tests. A diagram for the interaction of bending moments and normal forces is presented for UHPFRC. Supplementary, plates and shell structures under combined bending and axial forces are examined using the Finite Element Analysis. The crack patterns and the capacities are compared with results derived from the yield line theory and the possible load redistribution is discussed. In order to demonstrate the practical application, a hot‐water tank for the seasonal storage of heat is analysed. For that the design procedure for nonlinear analyses of concrete structures according to DIN 1045‐1 is taken as a basis and is adapted to structures made of UHPFRC.