Brandschutz mit Mauerwerk — Stand der deutschen und europäischen Normung

Die Musterbauordnung (MBO) von 2002 wird zunehmend in allen Bundesländern umgesetzt. Das Ziel der MBO, für alle Bauprodukte Nachweise zu fordern und die Verantwortung für das Bauen auf die am Bau Beteiligten zu delegieren, wird erfüllt. Das bedeutet für den Brandschutz, dass Bauen nur noch mit und nach Verwendbarkeitsnachweisen möglich ist. Als Verwendbarkeitsnachweise stehen allgemeine bauaufsichtliche Prüfzeugnisse (abP), allgemeine bauaufsichtliche Zulassungen (abZ) sowie Nachweise nach DIN 4102‐4 und DIN 4102‐22 zur Verfügung. Für wesentliche Abweichungen sind Zustimmungen im Einzelfall (Z. i. E.) der obersten Bauaufsichten der Länder erforderlich. Dies gilt für Neubauten, Umbau oder die Modernisierung von Bestandsbauten. Gemäß dem politischen Willen werden die Feuerwehren in ihrem Personal begrenzt und die Bauaufsichten/Bauordnungsämter sollen in vielen Bereichen nur noch verteilen und verwalten. Damit wird das Bauen schwieriger. Die deutsche Normung wird immer mehr zurück gedrängt und durch europäische Normen ersetzt. Im Brandschutz ist das bisher führende deutsche Know‐how in vielen Bereichen aus Geldmangel nicht mehr vertreten. In europäischen Ländern werden Brandschutzexperten vom Staat dafür bezahlt, dass die nationalen Kenntnisse, Vorteile, über Jahrzehnte gewachsen, durchgesetzt werden. Es entstehen zunehmend Normen, die nichts oder wenig mit der deutschen Baukultur zu tun haben, oder die auch einfach nicht brauchbar sind. Hinzu kommt, dass durch die europäische Normung eine Flut von Normen/Papieren entsteht, die am Bau nicht mehr handhabbar ist. Aus der Prüfnorm DIN 4102 mit den Teilen 1‐3, 5‐9, 11‐20, sind in Europa mittlerweile ca. 40 Prüfnormen mit noch mehr Extrapolationsnormen für die Anwendung entstanden. Die Anwendungsnormen sind relativ weit eingeschränkt, ausgenommen, die Industrie hat rechtzeitig mitgearbeitet. Fire protection with masonry — state of the German and European standardization. The model building code (MBO) 2002 is moved increasingly in all federal states. The purpose of the MBO is to demand assessments for all building products and to delegate the responsibility for the construction on the people involved in building. I.e. for fire protection building is possible with and according to verification of applicability of construction products only. Verifications of applicability are “national test certificate” (abP), “national technical approvals” (abZ), as well as assessments are available to DIN 4102‐4 and DIN 4102‐22. For essential divergences approvals for the isolated case (Z. i. E.) of the ministry responsible for building of the federal states are necessary. This counts to new buildings, to rebuilding or modernization of existing constructions. According to the political will the fire brigades are limited in her staff and the construction supervisions / building government offices in many areas only distribute and administer. Therefore building becomes more difficult. The German standardization is forced back more and more and substituted with European norms. In the fire protection the leading German Know How is not represented in many areas because of shortage of money. In European countries fire experts are paid by the state for the fact that the national knowledge, advantages which have grown for decades is put through. Increasingly standards are set up which deal nothing or little with the German construction culture, or which are simply not useable. A flood of standards / papers from the European standardization are coming up which are not scuffle‐cash in the construction any more. Instead of the test standard DIN 4102 with the parts 1‐3, 5‐9, 11‐20, approx. 40 European test standards are set up with even more extrapolation standards for the application. The application standards are limited relatively far, unless the industry has co‐operated on time.     

Verification of the fire resistance of clay brick masonry – hints for efficient design

In Germany, structural fire design of masonry is carried out in a simplified way using tabulated minimum wall thicknesses depending on the loading level in fire. Against this background the procedure of structural fire design is shown briefly before two approaches for a more efficient verification of the fire resistance are explained. The first possibility is to determine the reduction factor for the design value of the actions in fire more precisely and thereby reduce the loading level. Secondly, a design methodology is presented which can be applied in case of masonry walls with low vertical load but a large load eccentricity at mid‐height of the wall. Finally, the verification of the fire resistance of masonry according to national technical approval is discussed with an explanation how to obtain the same loading level in fire if the design is based on DIN EN 1996‐3/NA as when it is based on DIN EN 1996‐1‐1/NA.     

Zukünftige Brandschutzbemessung von schlanken Kalksandstein‐Wänden mit deutlich höheren Auflasten

Die Feuerwiderstandsdauer von tragenden, raumabschließenden Mauerwerkswänden muss derzeit in Abhängigkeit des Ausnutzungsfaktors entsprechend den Regelungen in der Anlage zur Liste der technischen Baubestimmungen bestimmt werden. Die Beschränkung des Ausnutzungsfaktors auf 1,0 bedeutet, dass keine höheren Lasten auf die Wände einwirken dürfen als nach dem vereinfachten Verfahren in DIN 1053‐1 statisch nachweisbar sind. Anderenfalls muss die Wanddicke erhöht werden, um den Ausnutzungsfaktor entsprechend zu reduzieren. Um bei schlanken Kalksandsteinwänden die deutlich höheren zulässigen Las ten nach dem genaueren Berechnungsverfahren und insbesondere nach dem Teilsicherheitskonzept auch bei Anforderungen an den Brandschutz ausnutzen zu können, wurde von der euro päischen Kalksandsteinindustrie ein umfangreiches Forschungsprogramm durchgeführt, worüber bereits ausführlich berichtet wurde. In diesem Beitrag werden nunmehr die Auswirkungen auf die zukünftige Normung, insbesondere auf die derzeit in Bearbeitung befindlichen änderungen zu den Normen DIN 4102‐4 und ‐22, erläutert. Abschließend wird ein Vorschlag für die zukünftige Regelung zur Ermittlung der Feuerwiderstandsdauer von tragenden, raumabschlie ßenden Kalksandsteinwänden unterbreitet. Future calculation of the fire resistance of slender calcium silicate walls with explicitly higher loads. At present the fire resistance endurance of load bearing walls with a fire‐separating function has to be determined depending on the utilisation factor as given in the rules of the annex to the list of technical rules. The restriction of the utilisation factor to 1,0 means that no higher loads are allowed as calculated in the structural analysis according to the simplified calculation method in DIN 1053‐1. Otherwise the thickness of the wall has to be increased to reduce the utilisation factor. To take advantage for slender calcium silicate masonry walls in applying the permitted clearly higher loads according to the more exact calculation method in DIN 1053‐1 and especially according to the semi‐probabilistic safety concept also in case of requirements on fire protection, the European calcium silicate industry realized a substantial research project as already described in details earlier. Now in this article the effect on future standardisation projects, especially on the currently revised standards DIN 4102‐4 and ‐22, will be illustrated. Finally a proposal is given for future rules to determine the fire resistance period of load bear ing calcium silicate walls with a fire‐separating function.     

The simplified calculation method of DIN EN 1996‐3 in practice / Das vereinfachte Bemessungsverfahren von DIN EN 1996‐3 in der Praxis

The design and detailing of masonry buildings was usually undertaken in the past using the simplified procedure in Section 6 of DIN 1053‐1 (1996‐11). With the changeover to the new European code, a new procedure has been made available with the simplified calculation method of DIN EN 1996‐3, which promises similarly simple and safe handling for the user. The practical implementation of this new code has been underway for some time. The article investigates the standard design cases and explains the innovations and alterations compared to DIN 1053‐1.     

Reinforced masonry beams under shear load – Proposals for future designs / Bewehrte schubbeanspruchte Mauerwerksbalken – Vorschläge für zukünftige Bemessungen

This article is written against the backdrop of the work of the European standardisation committees on the amendment of EN 1996‐1‐1 [N 4] which will also exert an influence on the design of reinforced masonry in Germany. This paper focusses on the design approaches of DIN EN 1996‐1‐1 for untensioned reinforced masonry beams under shear load in the ultimate limit state (ULS). Proposals are made to discuss their revision. The contents of E DIN 1053‐3 [N 3] and of the final draft of the guideline ”Flat Lintels” [7] are taken into account.     

Wann kommt der EC 6 in Deutschland und was bedeutet das für die nationalen Bemessungsnormen?

Entsprechend der zwischen dem DIN und der europäischen Normungsorganisation CEN getroffenen Vereinbarungen sollen im Jahr 2010 alle europäischen Bemessungsnormen mit ihren nationalen Anhängen zur Verfügung stehen und diesen widersprechende nationale Normen zurückgezogen werden. Der Beitrag erläutert, wie der derzeitige Stand im Mauerwerksbau ist, ob und wie lange noch die deutschen Bemessungsnormen im Mauerwerksbau weiter angewendet werden können und was das für die überarbeitete DIN 1053‐1 bedeutet. Abschließend wird dem Wunsch der Praxis entsprechend zum Ausdruck gebracht, dass nur eine bauaufsichtliche Einführung als komplettes Dokument in der Liste der Technischen Baubestimmungen sinnvoll ist. When will be the EC 6 established for use in Germany and what means it for the national design codes? The European Design Codes with their National Annexes should be available in the year 2010 and contradictory national design standards withdrawn according to the agreement between DIN and the European Standardisation Organisation CEN. The contribution explains how the current state in masonry construction is, and how long the German design codes for masonry can be applied. Also the effect on the revised DIN 1053‐1 is described. Closing it will be expressed corresponding to the wish of practise that only a complete document should be introduced in the list of technically regulations for construction by the building authority.     

Flexural tensile tests with vertically perforated clay unit masonry with thin layer mortar / Biegezugversuche an Planziegelmauerwerk

As part of the EU project, INSYSME – INnovative SYStems for earthquake resistant Masonry Enclosures in reinforced concrete buildings – to optimise infill masonry the German project partners carried out an initial part of the project on flexural strength testing of high‐tech clay block masonry in accordance with DIN EN 1052‐2. In this a wide range of modern products was considered which at present is regulated in Germany by means of general building authority approvals. The test results show that the specifications for flexural tensile strength of high‐tech clay block masonry in DIN EN 1996 are very conservative in most cases.     

Shear resistance verification of late 19th century masonry according to EC 6 – State of the art

A large part of buildings in Central European cities like Vienna was built in the Gründerzeit period between about 1840 and 1918 [1]. These buildings were constructed according to traditional rules. Current urban development requires historic buildings to be structurally adapted, which requires retroactive analysis of the masonry walls; in Austria according to ÖNORM EN 1998‐3 [2] and ÖNORM EN 1996‐3 (EC 6) [3]. Here, special focus is on the load transfer of horizontal earthquake loads, i. e. the shear strength of masonry walls. This paper describes the verification of historic masonry in detail and discusses individual components. Initial shear strength, load‐influenced friction and the length of the compressed part of the wall are first determined using results from experimental testing and relevant literature and then compared to the approaches in EC 6. Based on this analysis, recommendations are provided to make theoretical approaches more realistic.     

Extension of the conditions for application of the simplified calculation methods according to DIN EN 1996‐3/NA for the design of unreinforced masonry walls

Dedicated to University Prof. Dr.‐Ing. Carl‐Alexander Graubner for his 60th birthday The simplified calculation methods for unreinforced masonry structures given in DIN EN 1996‐3/NA are an easily applicable design standard for an efficient and fast verification of the resistance of mainly vertically loaded masonry walls. However, the design rules are not based on mechanical models. Instead, they are empirical approaches for a simplified estimation of the load bearing capacity. For this reason, the range of application of DIN EN 1996‐3/NA is limited by several conditions to ensure a sufficient safety of this design procedure. With regard to extending the conditions for application, extensive comparative calculations were carried out. Thereby, considering clearly defined boundary conditions, the load bearing capacity according to DIN EN 1996‐3/NA was compared to that according to DIN EN 1996‐1‐1/NA. It was the aim of this comparison to identify load bearing reserves of the simplified calculation methods to point out potential for an extension regarding the maximum permissible clear wall height and the slab span. As a result, it can be stated, that an increase of the maximum wall height up to 6.0 m and the maximum slab span of 7.0 m is possible in certain cases.     

Tragfähigkeitstafeln für unbewehrtes Mauerwerk nach DIN EN 1996‐3/NA:2019‐12

Load‐bearing capacity tables for unreinforced masonry according to DIN EN 1996‐3/NA:2019‐12 Practical design aids are important tools in the day‐to‐day business of structural design. The design of primarily vertically loaded masonry walls in usual building construction can be carried out with the help of so‐called load‐bearing capacity tables. A table value is read off exclusively as a function of the geometric conditions, which – multiplied by the masonry compressive strength – results in the load‐bearing capacity of the wall for cold design and in case of fire. By comparing the acting and resisting force, the verification of structural design can be provided in a simple and yet economical form. The bearing capacity tables based on the simplified calculation methods according to DIN EN 1996‐3/NA:2019‐12 [1], [2] and DIN EN 1996‐1‐2/NA:2013‐06 [3], [4] are presented in this paper. Compared to the previous edition of Part 3 of Eurocode 6, the extended scope of application is taken into account, as well as the normative changes to the construction method with partially supported slabs.     

Veneer walls of masonry as specified in EC 6 (DIN EN 1996‐2/NA) / Zweischaliges Mauerwerk nach EC 6 (DIN EN 1996‐2/NA)

This article deals with the production of veneer walls as specified in DIN EN 1996‐2/NA [3]. Against this background of the extensive revision of the section for veneer walls an exposition in accordance with the previous requirements as specified in DIN 1053‐1 can hardly be recommended. The necessity for a basic revision of the section for veneer wall construction has already been discussed in detail and justified in several technical articles published in previous years, see [4] to [7]. With many changes and corrections in the section for veneer walls in the National Annex of DIN EN 1996‐2 [8] it is certainly not a question of new rules for this method of building, but an adjustment of the requirements in the previous standard on the basis of the practical experience gained over several years. The new requirements for the execution of cavity facing masonry enable a simple and economic implementation of this external wall construction.     

Field report on application of the dimensioning procedure according to E DIN 4109‐2 / Erfahrungsbericht zur Anwendung des Bemessungsverfahrens nach E DIN 4109‐2

For several years, the sound insulation ratings for multi‐storey buildings have been in transition and are being brought into line with the European calculation method according to EN 12354:2000. The drafts of DIN 4109 have been available since November 2013. The forecasting procedure for the expected airborne sound insulation in solid buildings will change considerably by comparison to the regulations in Supplement 1 to DIN 4109:1989. In recent years, the building acoustics testing unit of Xella Technologie‐ und Forschungsgesellschaft mbH has carried out numerous quality tests to determine the acoustic insulation of apartment partitioning walls and apartment partitioning floors in apartment buildings. The exterior walls of the buildings reviewed consist exclusively of plastered, autoclaved aerated concrete block walls. The interior walls were made primarily of autoclaved aerated concrete or limestone blocks. In a few cases, dry constructed or reinforced concrete inner walls were present. A comparison is presented between the test results of these quality tests and the design values of the assessed sound reduction index R’w according to E DIN 4109‐2:2013. During these tests, a discussion took place on the uncertainty that must be incorporated in the calculation so as to achieve an adequately high level of planning assurance.     

Example calculation of the sound insulation of a floor slab between residential units according to DIN 4109‐2:2016 / Beispielhafte Berechnung der Luftschalldämmung einer Wohnungstrenndecke im Mauerwerkbau nach DIN 4109‐2:2016

The DIN 4109 series of standards has been revised in recent years and harmonised with European design codes. After the drafts of DIN 4109 were issued in November 2013, the documents shall now be finally published in summer 2016. The calculation procedure according to DIN 4109‐2 is based on the simplified procedure from EN 12354:2000, in which the noise transmission routes are calculated individually, similarly to the calculation for framed buildings according to supplement 1 to DIN 4109. The procedure according to DIN 4109‐2 is based on formulae, which are filled with figures from the building element catalogue of parts 3‐2 to 3‐6. This article shows examples of calculation steps for the determination of the weighted airborne sound reduction R'_w,Raccording to DIN 4109‐2:2016 for a floor slab between residential units.     

Bauakustische Bemessung von Mehrgeschossbauten mit monolithischen Ziegelaußenwänden

Acoustic design of multi‐storey buildings with external walls of monolithic clay masonry For masonry buildings with monolithic, highly insulated walls of clay units, no acoustic design according to standard was practically possible under Supplement 1 to DIN 4109:1989. Therefore a design procedure regulated by approvals was introduced in 2010, with which acoustic calculations for a building could be performed with a high security of forecasting. This procedure has been taken up in the completely revised series of standards DIN 4109:2016/2018 “Sound insulation in buildings”. The basis for the application of this method is knowledge of the individual sound insulation quantities and joint sound insulation quantities for the relevant clay masonry products or product combinations. In order to simplify performance of the verification for clay masonry buildings, the clay masonry industry provides the program “Modul Schall 4.0” (Acoustic module 4.0), in which the decisive acoustic parameters of external wall products from numerous clay masonry unit producers are stored in a database. In this report, experience of application of the design procedure for clay masonry buildings is presented. There is good agreement between forecasts and tests on completed buildings.     

Spannungs‐Dehnungs‐Linien von Porenbeton bei hohen Temperaturen: ein erster Schritt zur versuchsbasierten Bemessung gemäß EN 1996‐1‐2

Stress‐strain curves of AAC at high temperatures: a first step toward the performance‐based design according to EN 1996‐1‐2 In this paper, the performance‐based approach for the design of autoclaved aerated concrete (AAC) masonry walls subjected to fire is presented. The problems associated with the calculation methods in the current version of EN 1996‐1‐2 for the assessment of AAC loadbearing walls are explained. The current version of EN 1996‐1‐2 offers only tabulated data as a reliable method for structural fire assessment. The content of current Annex C and D is generally considered as not being reliable for design because of the absence of an adequate validation by experimental tests. For this reason, a proposal is made for the improvement of the input parameters for mechanical models based on experimental tests on AAC masonry. On this basis, new stress‐strain curves as a function of temperature are proposed here and then compared with the stress‐strain curves currently included in the Annex D of EN 1996‐1‐2. The comparison results point out that the current curves do not correspond to the effective behaviour of AAC masonry under fire conditions. The proposed curves can be used as base to be implemented in the new version of EN 1996‐1‐2.     

Buckling of masonry walls – A new proposal for the Eurocode 6

The buckling of masonry wall depends on the deformation behaviour and can be described with the modulus of elasticity depending on masonry strength. The reduction factor solution considering buckling is described by the Gaussian bell‐shaped curve in Eurocode 6, Part 1‐1 Annex G and was calibrated for masonry with a modulus of elasticity between 700 and 1000 f_k, which describes the masonry currently used in most European countries. In case of historic masonry or where deformability is needed in new construction, the modulus of elasticity can actually be lower. In those cases the approximation procedure according to Annex G of the Eurocode 6 delivers results which do not represent the real behaviour and leads to uneconomical results. The present paper proposes a new empirical method, which can be applied over the whole practical range of the elastic modulus of masonry. The new proposed method has been verified with experimental data and shows a very good fit.     

Reinforced bending load‐stressed masonry – Suggestions for future designs / Bewehrtes biegedruckbeanspruchtes Mauerwerk – Vorschläge für zukünftige Bemessungen

European standardization bodies are currently working on the amendment to EN 1996‐1‐1, which will also affect the evaluation of reinforced masonry in Germany. For that reason, discussion suggestions are being made here for revisions to lay the groundwork for building materials evaluations and especially, evaluations of bending load‐stressed masonry walls or beams at their serviceability limit state (SLS) for load‐bearing capacities. Information already presented in E DIN 1053‐3:2008‐03 [N3] is being incorporated as well. Characteristic values for the compressive strength of the masonry parallel to the bed joints f_k,∥ are essential for the design of reinforced masonry, although they are currently not included in national application documents for Germany. For the time being, they can be mathematically calculated using conversion factors for the characteristic compressive strength values vertical to the bed joints f_k or by using the declared axial compressive strengths of the masonry units. The ultimate strains for masonry in general should be set consistently at ?_mu = ∣–0.002∣ as several masonry types do not exhibit higher compressive strain values. The use of steel strains higher than ?_su = 0.005 does not change any measurement results. Varying stress‐strain curves of the constitutive equations on masonry under compressive strain (parabolic, parabolic‐rectangular, tension block) lead to differing values of recordable bending moments despite having the same mechanical reinforcement percentage at higher normal forces. Therefore, clear guidelines should be made for the type of applicable constitutive equation for masonry walls under compressive strain. With the introduction of a tension block, the number values of the reduction factors λ for the compression zone height x, which is dependent on limit strains, and where applicable, reduced compressive strength, need to be determined, as with reinforced concrete construction. A modification of the bending moment based on the second order theory according to [N4] is presented for the calculation of reinforced masonry walls in danger of buckling. The use of reduction factors for the load capacity of the masonry cross section, such as for unreinforced masonry, does not appear to be appropriate as buckling safety evidence because here, the design task is the determination of a required reinforcement cross section.     

Design aids for unreinforced masonry under bending compression – Part 2: Application of design aids for structural design according to DIN EN 1996‐1‐1/NA

The semi‐probabilistic safety concept of divided safety factors for action and resistance of DIN EN 1990 [1] in combination with the structural design codes DIN EN 1996‐1‐1 [2] and DIN EN 1996‐1‐1/NA [3] include the requirement that acting normal forces N_Ed may not exceed the normal force resistances N_Rd for the structural design of masonry under bending compression. According to [3], fully plastic material behaviour can be assumed and the stress block used as the material law for masonry. Building on this, design aids and their theoretical basis were presented in Part 1 of this scientific paper [4], which are comparable with the ω tables (called the ? table here) and the general design diagram for massive construction. The application of the design aids is described in this second part of this scientific paper through calculation examples and the connection with the calculation approaches of [3] is made clear. The relation to the reduction factor ?_m, which covers effects of 2^nd order theory, is also obtained. With known values of the load eccentricities according to 1^st and 2^nd order theory, the design task becomes the analysis of the loadbearing capacity of the masonry section at half wall height. Knowing ?_m, the load eccentricity e₂ and the additional moment according to 2^nd order theory can subsequently be determined, which does not ensue from the calculation equations of [3]. With the general design diagram, the values of compression zone height and the assumed load eccentricities of the acting normal forces, which result from the reset rule for masonry sections with high load eccentricities, can be directly read off, greatly improving the clarity of this procedure.     

Schubtragfähigkeit von Mauerwerk aus Wärmedämmziegeln

Der Beitrag berichtet über zentrische und exzentrische Schubversuche an Mauerwerk aus Wärmedämmziegeln. Die Ergebnisse werden mit den aktuell gültigen Bemessungsansätzen in DIN 1053‐1 verglichen. Es wird gezeigt, dass die Versuchsergebnisse immer eine ausreichende Sicherheit gegenüber den Bemessungswerten nach DIN 1053‐1 aufweisen. Auch für Mauerwerk aus Wärmedämmziegeln mit allgemeiner bauaufsichtlicher Zulassung können somit die vereinfachten Bemessungsregeln der DIN 4149 ohne Abminderungen angewendet werden. In plane shear resistance of thermal insulating vertically perforated clay brick masonry. In plane shear tests on thermal insulating vertically perforated clay brick masonry are presented. The results are compared with the design rules from DIN 1053‐1. The test results exceeded the design predictions of DIN 1053‐1 by a significant safety margin. The simplified design rules from the German earthquake standard DIN 4149 can be applied to thermal insulating clay unit masonry with technical approvals without any reduction.     

Minimum reinforcement of beam‐type reinforced masonry constructions – proposals for future regulations

The minimum reinforcement of reinforced masonry under bending should according to DIN EN 1996‐1‐1:2013‐02 [N 1], Section 8.2.3(1), be not less than ρ_min = 0.05 % of the effective masonry cross‐section for building elements, in which the reinforcement makes a contribution to the loadbearing capacity of the section, with the effective masonry cross‐section being the product of the effective width (b_ef) and the usable height d of the building element. In order to limit cracking and increase the ductility of the element, the reinforcement area should according to [N 1], Section 8.2.3(3), be not less than 0.03 % of the gross cross‐sectional area (of a wall). Other regulations ([1], [N 2], [N 3], [N 4], [N 5], [N 6], [N 7]) also prescribe minimum reinforcements in order to avoid brittle behaviour of the building element when the first crack forms or to limit cracking. In this specialist article, the figures given in [N 1] for the minimum reinforcement of reinforced masonry beams, like flat lintels or prefabricated lintels, are checked. The work concentrates on avoiding brittle failure when the first crack forms. In addition to geometrical requirements, the amount of minimum reinforcement depends on the tensile strength of the masonry f_t,m. Values of ρ_min vary considerably depending on the magnitude of the tensile strength of the masonry that can be assumed. For lintels over openings in facing brickwork facades, the height of any capping or soldier courses under the reinforcement layer also has an enlarging influence on the value of ρ_min. With regard to future regulations in standards or Allgemeine bauaufsichtliche Zulassungen (national technical approvals), it is recommended not to give lump sum values for ρ_min but to undertake a calculation like for reinforced concrete, using the algorithms given in this article.