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.     

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.     

Simplified verification method for unreinforced masonry shear walls

According to the German National Annex to DIN EN 1996‐3, a calculative verification of the bracing system may be omitted if, besides other requirements, an obviously sufficient number of sufficiently long shear walls is in place. If it is questionable whether a building complies with this requirement, a time‐consuming verification of the bracing system according to DIN EN 1996‐1‐1/NA is unavoidable. This article therefore presents a simplified verification method for the bracing system, which will prospectively be included in the next revision of DIN EN 1996‐3. The simplified bracing verification can already be used as a decision‐making aid to omit the calculative bracing verification according to DIN EN 1996‐1‐1/NA.     

Proposal for the simplified design of basement walls under lateral earth pressure

This paper deals with the design of basement walls subjected to lateral earth pressure. The current simplified calculation method according to DIN EN 1996‐3/NA only covers active earth pressure, which is the lower limiting value of the earth pressure. Designing according to DIN EN 1996‐1‐1/NA, higher coefficients of earth pressure (like earth pressure at rest) can be considered, with an additional verification of the shear resistance being necessary. This paper presents a theoretical model, which forms the basis for an analytical derivation of the loadbearing capacity, and explains the required minimum values of the acting normal force to ensure sufficient resistance to cover bending and shear. Based on these results, a simplified equation is proposed for the determination of the required minimum normal force, based on the design according to DIN EN 1996‐3/NA and providing identical values in case of an earth pressure coefficient of 1/3. The required minimum load resulting from this approach fulfils the described requirement to cover bending and shear. The presented solution is verified and the conditions for application are defined. Finally, the minimum required normal forces are evaluated and tabulated for common cases relevant to building practice.     

Minimum surcharge load of URM walls under flexure and axial force / Mindestauflast bei Biegung mit Normalkraft

This paper suggests a detailed parametric study, which has been drawn up in connection with the question of the necessity of verification of masonry wall by a minimum vertical load subject to bending and normal force by the author and his team [7]. It assumes the actual eccentricities from supporting due floors and takes into account the second order theory in middle of wall according to DIN EN 1996‐1‐1 or the German NA. In some cases, the model is derived for very high wind loads to its limits. Using the arch model which is introduced in DIN EN 1996‐1‐1 and may be applied by NA, is helpful and effective. This method may provide higher capacity rather than for example, with the bar or plate model. In this article the verification by means of the arch model will be presented and discussed. It is also shown that, forming an arch opposing to the horizontal wind load and low vertical loads may not come to a stability failure.     

Design tables for the utilisation factor α6,fi for the structural fire design of masonry according to DIN EN 1996‐1‐2/NA in the simplified calculation method

Easy‐to‐use verification equations are available for the verifications in the simplified calculation method. This applies also for the structural fire design of those masonry types for which a verification with the utilisation factor α_fi is given in the National Annex DIN EN 1996‐1‐2/NA. In specific applications, however, a classification can only be made applying the utilisation factor α_6,fi. In these cases, the verification for the structural fire design by calculation is considerably more complex than the mathematical verification of the structural design in the ”cold state“. The present paper shows how the design equation for α_6,fi can be made significantly easier with regard to its application by reference to the design value of the vertical load bearing resistance in the simplified method. Moreover, an upper limit value for the utilisation factor α_6,fi for the simplified method is summarised in tables.     

Minimum vertical load on masonry walls – a realistic view / Mindestauflast auf Mauerwerkswänden – eine realitätsnahe Betrachtung

To transfer bending moments in building components consisting of a material without tensile strength always requires a simultaneously acting normal force. Accordingly, masonry walls exposed to horizontal loads (e.g. wind) require a minimum vertical load, so that the resultant stress at the mid‐height of the wall remains the same within the cross‐section. As part of the A2 amendment to DIN EN 1996‐3/NA, this verification of walls subjected to low vertical loads, such as outer walls on the top floor exposed to high wind load was implemented in the National Annex. Part 3 of DIN EN 1996‐3 includes a similar standard regulation for verification of the minimum vertical load, which is based on an arch effect within the wall cross‐section. Based on this technical background and taking into account the main influencing parameters, a verification model is presented here which realistically describes the load‐bearing behaviour of unreinforced masonry walls subjected primarily to bending. Apart from the bending moments due to wind load, an initial eccentricity of the wall as well as second order effects due to wall deformations also have to be taken into account. In addition, a simple approximation equation is provided for the practical determination of the required minimum vertical load.     

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.     

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.     

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.     

Shear tests on highly thermal insulating clay unit masonry walls with thin layer mortar

The paper presents the results of a series of 6 shear tests on full scale highly thermal insulating clay unit masonry walls. The walls consisted of units with large voids filled with mineral wool with a thermal conductivity of λ = 0,07 W/(m · K). The aim of the investigations was the verification of the in‐plane‐shear resistance of this type of thermal insulating clay unit masonry in addition to the tests reported in [1]. The current design rules for clay unit masonry in DIN EN 1996‐1‐1/NA are rather conservative compared to the test results for thermal insulating units.     

Determination of partial resistance factors for unreinforced masonry shear walls

Partial safety factors for resistance applied in the design equation of semi‐probabilistic formats can be obtained from the evaluation of a test database. These partial safety factors are influenced by two factors, the material uncertainty and the model uncertainty. This topic is covered in a former publication [1]. It includes the determination of a partial factor for the model uncertainty of unreinforced masonry shear walls. In this study the authors examine the next step, and calculate the partial factor of resistance applying the same method, as recommended i n EN 1990 – Annex D. In addition to the Coefficient of Variation (COV) for the model uncertainty, the calculation of the resistance partial factor considers deviations in geometry, as well as loading and material properties. The influence of the material uncertainty on structural performance is considered in the calculation by means of a weighted average of all COV values for various types of material properties, based on the number of relevant failure modes in the test database. In the last step, the resistance partial factors for models defined in DIN EN 1996‐1‐1/NA and DIN EN 1996‐1‐1/NA – Annex K are calculated by applying the probabilistic methods recommended in EN 1990 – Annex D and the model bias.     

Analysis of rectangular cross sections under double eccentric compression stress

Double eccentrically loaded cross‐sections with failing tension zone occur both in foundation engineering and in masonry building. The case of walls or columns loaded with double eccentricity by a normal force was no longer covered under the global safety concept of DIN 1053‐1 and is thus not normally considered in practice. With the transition to the semi‐probabilistic safety concept, verification of the cross‐section at the limit state of loadbearing capacity is performed near or at the failure state. This also made it necessary as part of the introduction of EN 1996‐1‐1 to introduce a verification for double eccentrically loaded cross‐sections. The present article considers the non‐linear stress distribution in double eccentrically loaded cross‐sections and the resulting position of the neutral axis. The described process is numerically robust and can be implemented with little effort for the analysis of masonry as an Excel spreadsheet.     

Shear tests on full scale storey‐height specimens constructed with thermally insulating clay unit masonry with thin‐layer mortar

The paper presents results of a series of 6 in‐plane shear tests on storey‐height clay unit masonry panels [1] with thin‐layer mortar, carried out in addition to previous test campaigns [2], [3], and [4]. The walls were constructed with unfilled thermally insulating clay units with a thermal conductivity of λ = 0.09 W/(m · K). The current design rules for clay unit masonry according to DIN EN 1996‐1‐1/NA [5] are conservative compared to the presented test results for thermally insulating clay unit masonry.     

Design according to Eurocode 6 in practice

For the structural design of masonry according to Eurocode 6 with the associated German national annex, the simplified method and the further simplified calculation method in Annex A are available. These procedures provide tools that can be used in practice to design standard cases quickly and easily. One feature of the verification of masonry walls under compressive loading is that no bending moments in the walls have to be determined as part of the determination of section forces and moments since the verification of the load‐bearing capacity of the wall is based solely on the acting vertical force. The effects of floor end restraint and buckling are dealt with by simple equations. One new feature of verification according to Eurocode 6 is that the effect of partially supported floors on the load‐bearing capacity of the wall can be included directly. The code is compact and simple to use and the further simplified calculation method is predestined for verification by manual calculation.     

Numerical investigation of lateral earth pressure for unreinforced masonry walls

For the design of unreinforced masonry walls under lateral earth pressure according to DIN EN 1996‐3 [1], the active earth pressure is used, which is less than the earth pressure at rest. For the consideration of active earth pressure, a sufficient deflection of the wall is needed. It is unknown whether the deflections in reality are large enough to justify a reduction of the active earth pressure. Therefore a numerical model has been developed which considers the load‐bearing behaviour of masonry walls, with several boundary conditions being considered to estimate the effective earth pressure.     

Out‐of‐plane bending moments in masonry walls – Analysis of different calculation methods

In the course of the revision of EN 1996‐1‐1, a new proposal has been made for the calculation of internal forces in frame‐type structures for the determination of bending moments due to slab rotation. In addition to a stiffness reduction for masonry walls in conjunction with the special features of partially supported slabs, which is already usual in Germany, the calculated ever‐present minimum loadbearing capacity of a wall is also increased due to a reduction of the maximum applied load eccentricity. Another major change is the direct implementation of wind loads in the method to determine the internal forces. To ensure that these changes do not lead to a safety deficit or an uneconomic reduction of the loadbearing capacity compared with the current situation, the results of extensive comparative calculations are presented. In addition, it is examined whether the proposal could conflict with further investigations to extend the conditions for application of the simplified design procedures according to EN 1996‐3. It is shown that the new draft provides similar results to the current method and that there are no concerns about its application. Also, the investigations to extend the conditions for application of the simplified calculation methods can be based on the new proposal without concerns.     

Characterization of uncertainty (probabilistic models) in verification of unreinforced masonry shear wall / Charakterisierung der Unschärfe (probabilistische Modelle) beim Nachweis von Wandscheiben aus unbewehrtem Mauerwerk

The model uncertainty has significant role in determination of safety factor. Eurocode has been considered partial factor covering uncertainties in the resistance model. Moreover, the model uncertainty has important role in full probabilistic verification. A stochastic analysis may yield to realistic results, only if the uncertainties have been involved in the calculation, properly. The uncertainty in predicted load‐carrying model may be identified by comparing the observed (experimental records) load‐carrying behaviour with the predicted value. Some general recommendations for considering uncertainty in probabilistic verifications are available in literature. In this study, the deviation of predicted values according to DIN EN 1996‐1‐1/NA model of masonry shear wall from test results has been derived. The best‐fitted distribution with associated statistical parameters (type of distribution, mean and coefficient of variation) has been proposed for uncertainty model. The uncertainty models have been compared with recommendations in the literature.     

Practical application of a non‐linear earthquake analysis according to DIN EN 1998‐1 / Praktische Anwendung einer nichtlinearen Erdbebenanalyse nach DIN EN 1998‐1

Seismic safety verification can be performed by maintaining constructive rules or by calculation. Verification by calculation can be performed with a linear simplified or linear multi‐modal response spectrum analysis. Alternatively, a non‐linear quasi‐static verification is also possible according to DIN EN 1998‐1, which was not available in DIN 4149. In this article, the non‐linear quasi‐static earthquake verification according to DIN EN 1998‐1 is presented in practice, using the example of a building in Mittenwald/Germany. The verification has been checked and accepted by an independent building supervision report.