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.     

Determination of a model partial safety factor for unreinforced masonry walls under buckling

The design/verification method in the Eurocodes is based on the partial safety concept. Eurocode 6 suggests a constant partial safety factor for the material γ_M for all design/verification problems, without consideration of model uncertainty in the design/verification formula. In the following, a model partial safety factor is determined for the problem of unreinforced masonry walls mainly subjected to vertical loading. For that purpose, the newly proposed formula for EC 6, annex G will be considered [1–3]. In order to cover all aspects in tests and to use the results for design purposes, several methods have been included in EN 1990 Annex D for design based on test data. In this study, the recommended methods in Annex D of EN 1990 for resistance of the material are used to extract the partial safety factors. A database including more than 119 experimental tests on unreinforced masonry shear walls is used to compare the model prediction and the test results and to determine the model partial safety factor.     

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.     

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.     

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.     

Analysis and comparison of the NDPs of various national annexes of Eurocode 6 / Analyse und Vergleich der NDPs verschiedener nationaler Anhänge zu Eurocode 6

In the national annexes of Eurocode 6, the individual European Member States can define values for nationally determined parameters in various places or add regulations which are not in contradiction to the current European provisions. Consequently – despite a harmonized Eurocode 6 – the normative regulations of the individual Member States differ more or less. However, in the sense of practicability of the standards in Europe, it should be the aim to develop a European standard which is as uniform as possible and which has not to be applied in significantly different ways due to the national regulations. In order to better understand the interests of the other Member States for future generations of standards and to derive potentials of harmonization, the values of the Nationally Determined Parameters (NDPs) of various Member States are compared in this paper. In this context, the extent of the deviations between the different national annexes is examined and on this basis a possible potential of harmonization is identified.     

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.     

Shear resistance of reinforced masonry beams with and without additional concrete or prestress

This article investigates the transferability of the Simplified Modified Compression Field Theory (SMCFT) [2], which is known in reinforced concrete design and included in the fib Model Code for Concrete Structures 2010 (Volume 3) [1], to reinforced or prestressed masonry beams (RM beams) with or without an additional layer of concrete. The investigation for this work is the obsolete shear design concept that has been used until now for reinforced masonry under shear loading, which does not adequately reflect the actual load‐bearing behaviour of significant areas of masonry. The fundamentals of the SMCFT are explained and the transferability of the theory to RM beams is examined, taking into account in particular the different material properties of masonry compared to reinforced concrete. A first approach for future application is represented by the equations presented here for the determination of the shear force capacity of RM beams. The verification is performed through a comparison of the shear resistances determined experimentally (exp.) and by calculation (calc.).     

Load‐bearing capacity of slender unreinforced masonry compression members under biaxial bending

Dedicated to Prof. Dr.‐Ing. Carl‐Alexander Graubner on the occasion of his 60th birthday Masonry members have to resist vertical loads and bending moments about the weak axis due to rotation of adjacent slabs. If the compression member is part of the bracing system, there are also bending moments about the strong axis. This paper deals with the load‐bearing capacity of biaxially eccentrically compressed unreinforced compression members with rectangular cross‐sections. For linear‐elastic material, the principles of an analytical model is presented, which considers geometrical and physical (cracking) non‐linearity. The deflections of the wall can be determined by using moment‐curvature relations, making possible the analytical analysis of compression members considering the effects of 2nd order theory. For a non‐linear stress‐strain relation, the calculation of the load carrying capacity of rectangular compression members under biaxial bending is complex and has to be determined numerically. The good accordance of the results of the analytical model with the numeric calculations is also shown for various eccentricities. In addition, a simplified proposal for the calculation of the load‐bearing capacity of biaxially eccentrically compressed unreinforced compression members is shown. The proposal is based on the load‐bearing capacity of uniaxially eccentrically compressed unreinforced compression members. Therefore it is possible to use the proposal considering existing models, for example according to Eurocode 2 or 6.     

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.     

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.     

Influence of material spatial variability on required safety factors for masonry walls in compression

Since masonry is one of the oldest and most traditional construction types, corresponding safety concepts are usually based on experience instead of being calibrated by structural reliability methods. For this reason, reliability analyses of masonry structures are needed to check if safety factors should be adjusted. Masonry is a non‐homogenous material. Because of that, it is very important to consider the spatial variability of material properties when assessing the reliability of masonry walls. Therefore, it is useful to know if and to what extent spatial variability increases or decreases the reliability of masonry walls and the required safety factors. The influence of spatial variability depends on the length of a wall due to the capability of load redistribution. Also, it is affected by the governing failure mode, which depends on the slenderness of the wall, and can be local compression or stability failure. This paper demonstrates the effect of spatial variability on the load‐bearing capacity of masonry walls in terms of mean value, scatter and design value. For this purpose, walls of varying length and slenderness were analysed with and without the consideration of spatial variability by performing Monte Carlo simulations. Based upon that, safety factors were determined which are required to meet the target reliability defined by EN 1990.     

Shear capacity of brick masonry with partially supported slab

In order to investigate the influence of a partially supported slab on the in‐plane shear resistance of masonry walls, six shear tests on full scale walls were performed at the Chair of Structural Concrete of the University of Kassel in cooperation with ”Arbeitsgemeinschaft Mauerziegel“. The walls were made of large chamber clay masonry units and the depths of the partially supported slabs were different. The large chamber units are typically used for thermally insulated exterior walls, with the slabs only being partially supported. The influence of this constellation is not taken into account in shear capacity assessment according to the current version of Eurocode 6 for Germany. This article describes the test results and provides a comparison with Eurocode 6. In addition, the results of older shear tests on masonry walls made of vertically perforated units with eccentric load application were used.     

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.     

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.     

Extended conditions of application of DIN EN 1996‐3/NA for high walls

According to Eurocode 6, unreinforced masonry walls can be designed using different verification methods, whereby the simplified calculation methods are contained in Part 3 of DIN EN 1996 [1]. If the associated application limits and boundary conditions are fulfilled, a large part of the usual problems occurring in masonry construction can be dealt with without great effort. A limiting condition for the application of the simplified calculation methods is a maximum clear wall height of h = 2.75 m or h = 12 ? t. Changes in user requirements for modern buildings with masonry walls nowadays often require greater wall heights, wherefore a verification according to the general rules from DIN EN 1996‐1‐1/NA [2] is necessary. This means a considerably higher effort for the structural engineer. A considerable amount of calculations was done to verify whether the results of the simplified calculation methods are also valid for greater wall heights. The results were transferred into a consistent standardization proposal with regard to extended application limits of DIN EN 1996‐3/NA, which is contained in a new draft Amendment A3 for the National Application Document for Germany.     

Investigation of the seismic performance of modern masonry buildings during the Emilia Romagna earthquake series

The article presents the investigation of the seismic behaviour of a modern URM building located in the municipality of Finale Emilia in province of Modena, Northern Italy. The building is situated in the centre of the series of the 2012 Northern Italy earthquakes and has not suffered any damage during the earthquake series in 2012. The observed earthquake resistance of the building is compared with predicted resistances based on linear and nonlinear design approaches according to Eurocode. Furthermore, probabilistic analyses based on nonlinear calculation models taking into account scattering of the most relevant input parameters are carried out to identify their influence to the results and to derive fragility curves.     

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.