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.     

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.     

Zur Tragfähigkeit unbewehrter Betonwände

Load Bearing Capacity of Non‐Reinforced Concrete Walls The simplified approach for the design of compression members made of non‐reinforced concrete according to DIN 1045‐1 leads to large cross sections for slender walls with eccentric loading. Based on the principles of DIN 1045‐1 a design method is deduced in this article. The use of this method allows a simple, standardised and economic design of non‐reinforced compression members. A further increase in load bearing capacity can be achieved by taking into account the concrete tensile strength.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Zur Ermittlung der Beton‐ und Stahlspannungen

On the Determination of Concrete and Steel Stresses The limitation of concrete and steel stresses is required in DIN 1045‐1 [1] as well as in EC 2 [2]. A general procedure of their determination is reported for reinforced concrete sections subjected to bending and longitudinal force. Finally tables for usual practical cases are presented.     

Bemessungsvorschlag für Holz/Beton‐Verbundbalken unter Beachtung abgestufter Verbindungsmittelabstände

Design proposal for timber/concrete composite beams with graded connnector distances. The distance of connections of timber/concrete composite beams is often graded for economical reasons according the shear force distribution. The load‐carrying capacity of composite beams according to DIN 1052 respectively E DIN 1052 with internal forces, which are linearly determined, (γ‐procedure) are clearly reduced compared to beams without graded distances of connectors. The actual load‐bearing behaviour distinctly shows non‐linearities. The influence of the gradations of the connectors on the load‐bearing behaviour of composite beams is investigated, because the influence of the stiffness of connections on the load‐bearing capacity of composite beams is small. The paper presents a comparison between failure loads determined by FE‐analysis and the working loads according to the current design rule. It is shown that the decrease of load‐bearing capacity is smaller than assumed by current code of practice. Structures with several different distances of connections have the largest safety‐factor. These systems can more economically be designed. As the result of the investigations, a new design proposal is presented, which takes non‐linearities into account and guarantees a constant safety‐zone between failure load and working load. These proposal permits an economic design of timber/concrete composite beams.     

Zum Querkraftwiderstand bei Leichtbetonbalken ohne Querkraftbewehrung

In diesem Beitrag wird über Biegeschubversuche mit Leichtbetonbalken ohne Querkraftbewehrung berichtet, die ein ausgeprägtes Nachbruchverhalten aufwiesen. Die Versuchsergebnisse der Leichtbetonbalken werfen die Frage auf, ob die Querkraftbemessung in der neuen DIN 1045‐1 in der Lage ist, hoch spröde Betone wie ALWAC (All Lightweight Aggregate Concrete) hinreichend sicher zu erfassen. In diesem Zusammenhang wird näher auf den Maßstabseffekt eingegangen. Es wurde ein Modell für das Tragverhalten von Biegeschubbalken nach Auftreten des Biegeschubrisses entwickelt, das auf der Kinematik von miteinander verbundenen Festkörpern anstelle von Fachwerkstäben beruht. Ein Ansatz der Tragkapazität im Nachbruchbereich für die Praxis wird nicht empfohlen. Shear Strength of Lightweight Concrete without Shear Reinforcement This paper presents results of shear beam tests with lightweight concrete and without shear reinforcement exhibiting a distinct post peak behavior. The shear test results raise the question whether the shear design in DIN 1045‐1 can also cover very brittle concrete types as ALWAC (All Lightweight Aggregate Concrete) with a sufficient safety level. The size effect in shear beams is discussed. A model for the load bearing behavior after formation of the inclined crack based on the kinematics of a set of rigid bodies is developed. A consideration of the additional load capacity in the post peak range in design formulas is not recommended.     

Berücksichtigung der Längsbewehrung beim Durchstanznachweis nach Eurocode 2 (DIN EN 1992‐1‐1/NA)

Consideration of flexural reinforcement in punching shear provisions according to Eurocode 2 (DIN EN 1992‐1‐1/NA) With introduction of Eurocode 2 in Germany in 2012, the pun ching shear design provisions of flat slabs and column bases were revised compared to DIN 1045‐1. Particularly the consi deration of flexural reinforcement caused some irritations for practical engineers. In this context, this paper presents recent recommendations of DIN technical committee ”NABau“ (DIN: German institute for standardization) for the distribution of minimum flexural reinforcement for wall corners and wall edges as well as for the width and anchorage of flexural reinforcement for the calculation of the flexural reinforcement ratio in flat slabs and column bases.     

Untersuchungen zum Durchstanzverhalten von Stahlbetonfundamenten

Investigations on the Punching Behaviour of RC Footings. The punching shear capacity of footings varies significantly for different codes. The amount of the soil reaction to be deducted from the punching load differs from one code to another. The aim of the present investigation is to derive an advanced design model for footings taking into account the soil‐structure‐interaction. The results of five punching tests on reinforced concrete footings supported on soil are presented. The experimental results indicate that the angle of the shear failure plane is steeper than observed by punching tests on flat slabs, and the shear slenderness seems to affect the punching shear capacity significantly. In order to reach a better insight of the load carrying capacity, nonlinear finite element simulations are performed. Based upon the findings and a test data bank an advanced design model is derived, which is based upon the DIN 1045‐1 provisions.     

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.     

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.