Investigation of the seismic out‐of‐plane behaviour of unreinforced masonry walls

The structural stability of unreinforced masonry (URM) walls has to be guaranteed not only under static (permanent and live) loads but also under earthquake loads. Loads transverse to the plane (out‐of‐plane) often have a decisive influence on the load‐bearing capacity. In practical applications, simplified methods from codes, guidelines and literature are often used to analyse and evaluate the out‐of‐plane capacity of load‐bearing and non‐load‐bearing URM walls. The results of these simplified methods can be significantly conservative and inaccurate since essential influencing effects are neglected. For many existing buildings, the simplified methods underestimate the capacity, which leads to cost‐intensive retrofitting and strengthening measures or complete replacement by other wall systems. In order to realistically estimate the out‐of‐plane capacity, parameters such as wall geometry, boundary conditions, vertical loads and especially dynamic effects (e.g. inertia forces) have to be taken into account. In this paper, non‐linear time history simulations are presented to investigate the influence of these effects. The numerically determined maximum acceptable earthquake acceleration is compared with results from simplified analysis models. The comparison shows that the out‐of‐plane capacity is significantly higher than the values predicted by simplified models. Finally, several initial experimental seismic tests conducted on the shaking table of the TU Kaiserslautern are presented, together with the planned extensive experimental test program on the out‐of‐plane capacity of masonry walls.     

Reliability of masonry walls subjected to in‐plane loading: A slip failure along head joints / Zuverlässigkeit von Mauerwerkswänden bei Belastung in der Ebene: Versagen entlang der Stoßfugenflucht

Masonry structures are a sustainable, economical and traditionally widely used type of construction. However, current masonry design codes are rather conservative, so there is a growing need for revision i.e. calibration of safety factors to improve the allocation of material resources. In this paper, we investigate the probability of occurrence of slip failure along head joints (perpends) in masonry subjected to in‐plane loading. An appropriate limit state function is established and the masonry material properties and loads are defined as random variables in order to simulate likelihood of occurrence of a slip failure regime along the head joints. Furthermore, an example of masonry wall with probabilistic analysis outcomes using Monte Carlo simulation is presented and recommendations for further work are provided.     

Simplified design concept for slender masonry walls / Vereinfachter Stabilitätsnachweis knickgefährdeter Mauerwerkswände

The verification of safety against buckling of unreinforced masonry walls according to the accurate design procedure of EN 1996‐1‐1 Appendix G is based on semi‐empirical approaches, which do not always realistically describe the load‐bearing behaviour. This statement is also supported by an objection of the country Denmark concerning the load capacity function which is regulated in Appendix G. Using new findings about the effects of non‐linear material behaviour in case of stability failure this article investigates fundamental questions about the buckling behaviour of masonry walls and transfers these into a simple practical structural design proposal. As a result, the load capacity function can be considerably simplified, the influence of creep can be integrated and the number of input parameters can be reduced.     

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.     

Loadbearing capacity of infill masonry walls considering the deformation‐based membrane effect

According to currently valid codes, it is not possible to determine the loadbearing capacity of unreinforced infill walls considering the deformation‐based membrane effect by incorporating the exact support conditions. One reason for this is the lack of a validated calculation procedure, which in addition to the equilibrium conditions also realistically represents the compatibility conditions of these systems. In the present paper, therefore, a new non‐linear analytical calculation procedure is presented. The main focus of the analysis of walls subject to area loading is the incorporation of the support conditions and thus the consideration of the deformation‐based membrane compressive force. Through generalised formulation and a standardised notation of the determination equations, different material behaviours and various support conditions can be taken into account with few parameters. On the action side, both lighter loading like wind loads and heavier loading like explosion loads can be considered. Through the implementation of the partial factor concept, it is possible to comply with the requirements of European codes and thus ensure the applicability of the analysis model.     

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.     

Masonry buildings at the borderline to high‐rise – Part 2 / Mauerwerksbauten an der Hochhausgrenze – Teil 2

For the verification of framing shear walls of masonry, the decisive combination of actions derives from the interaction of vertical and horizontal actions. In this article, a method based on simple truss models is extended for the transfer of horizontal actions. It is demonstrated how the required verifications of load‐bearing safety can be performed with the results of the structural calculation. As an example, the application of the method for a seven‐storey building with calcium silicate blockwork or Poroton brick masonry is described.     

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.     

Bracing systems in masonry buildings. Part 1: Simple application of FE programs / Aussteifungssysteme im Mauerwerksbau. Teil 1: Einfache Anwendung von FE‐Programmen

Due to the low tensile strength of masonry perpendicular to the bed joint, masonry wall panels have non‐linear material properties. Assuming simple elastic constitutive laws, this article presents two modelling variants, which consider the lack of tensile strength in a simple manner. Both variants are investigated for their advantages and disadvantages. In a second part of the article, the application of the methods will be illustrated through the example of a four‐storey building.     

Experimental determination of the load‐bearing capacity of a reinforced perforated brick facade

For a new multi‐storey car park over the Central Bus Station (ZOB) in Kiel, a perforated clinker brick veneer facade not conforming to standards was planned. The design and technical characteristics of the facade have already been described in the article by Medzech and Schrade in this issue [1]. This article deals with the experimental investigations carried out to obtain a project‐related one‐off approval (ZiE). These experiments contain in particular large tests on storey‐height wall sections, which were subjected to eccentric compressive loading and partly to horizontal loads representing wind action. Supplementary small tests on unreinforced and reinforced masonry served to determine the bending capacity, the anchoring capacity of the reinforcement and the load‐bearing capacity of the wall anchors in the masonry. Due to the special facade construction with special bricks for the project, wall anchors, reinforcement bar couplers and unique test set‐ups had to be developed for the specific project.     

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.     

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.