Shear effect on seismic behaviour of masonry walls

Firstly, a finite element numerical model for nonlinear dynamic analysis of masonry walls is briefly presented. The model can simulate the main nonlinear effects of masonry and reinforced concrete. It is simple and intended to the engineering application. A macro model of masonry is adopted for simulation its behaviour in compression and for cracks modelling in tension. Two constitutive models are implemented to describe the shear resistance of the masonry wall: One that does not take the effect of the shear failure of masonry (Model 1), and second which takes into account shear failure of masonry (Model 2). By using the numerical model, the shear effect of masonry on the behaviour of two‐storey unreinforced and confined masonry walls exposed to harmonic base acceleration was investigated. The height to length ratio of the walls and the quality of masonry are varied. Analysis results for Model 1 and Model 2 are significantly different. Model 1 gives a significantly higher load bearing capacities of masonry. It was concluded that the shear effect of masonry significantly depends on the type of the masonry walls (unreinforced, confined), the quality of the masonry and height to length ratio of masonry walls.     

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.     

Application of the partial safety concept for complex non‐linear calculations through the example of Friedrichswerder Church in Berlin

Non‐linear analysis of special structures is routine practice in every engineering design office. Current code provisions provide no sufficient regulations or clear procedures on how to use partial safety factors in non‐linear analyses. The present paper introduces some specific problems of masonry structures from practice. Limit state functions of vertically loaded masonry walls were investigated. A reliability study shows that the decisive case of verification can be obtained by considering a special combination of material parameters. The study also indicates the importance of considering a partial factor for the elastic modulus to account for stability failure. This proposed procedure has been applied to a practical example, the Friedrichswerder Church. The stability of the church has been checked with many FEM models at the macro level.     

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.     

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.     

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.     

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.     

Experimentelle und analytische Untersuchung des out‐of‐plane‐Verhaltens von unbewehrten Mauerwerkswänden unter Erdbebenbelastung

Experimental and analytical investigation of the seismic out‐of‐plane behavior of unreinforced masonry walls In addition to the vertical and horizontal load‐bearing in‐plane, masonry must also withstand out‐of‐plane loads that occur in earthquake scenarios. The out‐of‐plane behavior of unreinforced masonry walls depends on a variety of parameters and is very complex due to the strong non‐linearity. Current design methods in German codes and various international codes have not been explicitly developed for out‐of‐plane behavior and contain considerable conservatism. In the present work, shaking‐table experiments with heat‐insulating masonry walls have been conducted to investigate the out‐of‐plane behavior of vertical spanning unreinforced masonry walls. As shown in previous numerical investigations, important parameters are neglected in existing design and analysis models and the out‐of‐plane capacity is underestimated significantly. In the conducted experiments the results of these numerical investigations are verified. Furthermore, the development of an analytical design model to determine the force‐displacement relationship and the out‐of‐plane load‐bearing capacity considering all significant parameters is presented.     

In-plane behavior of perforated brick masonry walls

This paper reports the results of experimental and theoretical research conducted on perforated brick masonry walls under in-plane loading. The walls?? structural behavior depends strongly on their specific features, e.g. geometry, mechanical properties of the masonry material, brick arrangement and loading conditions. The experimental program was designed to study the incidence of brick arrangement in the spandrels and piers, and of the acting vertical load on the failure mode and load-bearing capacity of the walls. Six specimens of brick masonry wall with a central opening were submitted to a constant vertical load and a monotonic horizontal force that was gradually increased until the kinematic mechanism condition was reached. The object of the theoretical research was to develop a simplified analytical model for describing the kinematic mechanism of the walls. The results of the experiments indicate that brick arrangement strongly influences the failure mode and load-bearing capacity of the walls. Proper a priori assessment of the failure mode of walls becomes fundamental to an accurate evaluation of their load-bearing capacity using the proposed model.     

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.     

Monte Carlo homogenized limit analysis model for randomly assembled blocks in-plane loaded

A simple rigid-plastic homogenization model for the limit analysis of masonry walls in-plane loaded and constituted by the random assemblage of blocks with variable dimensions is proposed. In the model, blocks constituting a masonry wall are supposed infinitely resistant with a Gaussian distribution of height and length, whereas joints are reduced to interfaces with frictional behavior and limited tensile and compressive strength. Block by block, a representative element of volume (REV) is considered, constituted by a central block interconnected with its neighbors by means of rigid-plastic interfaces. The model is characterized by a few material parameters, is numerically inexpensive and very stable. A sub-class of elementary deformation modes is a-priori chosen in the REV, mimicking typical failures due to joints cracking and crushing. Masonry strength domains are obtained equating the power dissipated in the heterogeneous model with the power dissipated by a fictitious homogeneous macroscopic plate. Due to the inexpensiveness of the approach proposed, Monte Carlo simulations can be repeated on the REV in order to have a stochastic estimation of in-plane masonry strength at different orientations of the bed joints with respect to external loads accounting for the geometrical statistical variability of blocks dimensions. Two cases are discussed, the former consisting on full stochastic REV assemblages (obtained considering a random variability of both blocks height an length) and the latter assuming the presence of a horizontal alignment along bed joints, i.e. allowing blocks height variability only row by row. The case of deterministic blocks height (quasi-periodic texture) can be obtained as a subclass of this latter case. Masonry homogenized failure surfaces are finally implemented in an upper bound FE limit analysis code for the analysis at collapse of entire walls in-plane loaded. Two cases of engineering practice, consisting on the prediction of the failure load of a deep beam and a shear wall arranged with random texture are critically discussed. In particular, homogenization results are compared with those provided by a heterogeneous approach. Good agreement is found both on the failure mechanism and on the distribution of the collapse load.     

Current developments in fire protection – Changeover to design and classification according to the Eurocode / Aktuelle Entwicklungen im Brandschutz – Umstellung auf die Bemessung und Klassifizierung nach europäischen Normen

The European requirements for fire safety design and testing of structural masonry members are already the governing requirements in many cases. In principle, both the European and the German classification may be used according to the Bauregelliste. However, the latter may only be used when European classification of a member or construction material is not possible because the appropriate European standards do not exist. The European standards do not differ fundamentally from the German standard DIN 4102‐2. One significant difference is that according to the DIN 4102‐2, it was required to carry out two tests with the most unfavourable result governing, while according to the European standard, only one test is required. According to the EN Standard, the tests for fire resistance and the reaction to fire are carried out separately. There are other differences related to the pressure in the furnace as well as the use of plate thermocouples instead of jacketed thermocouples. Fire safety design of masonry is carried out in accordance with EC 6‐1‐2 and the National Annex. Only the members not regulated in the EC 6‐1‐2, e.g. pre‐cast masonry members, non‐load‐bearing walls, lintels, connections and joints, should be designed and checked according to the revised DIN 4102‐4.     

Shear tests on external clay unit masonry walls / Monolithische Ziegelaußenwände unter Schubbeanspruchung

Monolithic external walls are commonly made of thermally insulated clay blocks that do not require any additional external thermal insulation such as an external thermally insulated composite system (ETICS). To reduce thermal bridge losses, the support length (a) of the slab on the wall is shorter than the wall thickness (t): a < t. The influence on the shear capacity of the respective masonry walls has not yet been tested and analysed. The paper presents the results of shear tests on monolithic external walls with a reduced support length under static‐cyclic and pseudo‐dynamic loading. The test results will be compared with the shear resistance calculated according to DIN EN 1996 with consideration of the German National Annex and the results according to the relevant Technical Approval.     

Gründerzeitliche Mauerwerksbauten unter Erdbebeneinwirkung – Tragverhalten im Widerspruch zur aktuell angewandten Nachbemessung

Historic masonry buildings under earthquakes – Load‐bearing behaviour in contradiction to the currently applied methods of analysis The stability of historic masonry buildings must be guaranteed not only under normal conditions, but also during natural disasters. The seismic assessment of the masonry buildings of the Gründerzeit (1840–1918) in Vienna is a central topic in the qualitative and constructive assessment. Although masonry construction has been used for many centuries, the realistic evaluation of the load‐bearing behaviour is still a complex challenge. The methods of analysis according to current regulations are only insufficiently able to reflect the real load‐bearing behaviour and the possible activation of global failure mechanisms. As a result, the simplified verification is often difficult to calculate for many historic buildings, and questionable reinforcement measures are taken to compensate, even though the buildings have already experienced several earthquakes and survived most of them without damage. The present work deals with the approaches of current methods of analysis and aims to identify problem points and to compare them with time history analysis, which is supported by a powerful material model based on test series. It is shown that the conventional analysis for the historic masonry buildings without consideration of the interaction and load transfer effects as well as the characteristic construction methods only partially reflect the real load‐bearing behaviour. The work is intended to be a contribution to the technical expert discussions on the seismic safety of historic buildings and to stimulate the discussion on the formulation of realistic methods of analysis.     

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.     

Predicting laser weld reliability with stochastic reduced‐order models

Laser welds are prevalent in complex engineering systems and they frequently govern failure. The weld process often results in partial penetration of the base metals, leaving sharp crack‐like features with a high degree of variability in the geometry and material properties of the welded structure. Accurate finite element predictions of the structural reliability of components containing laser welds requires the analysis of a large number of finite element meshes with very fine spatial resolution, where each mesh has different geometry and/or material properties in the welded region to address variability. Traditional modeling approaches cannot be efficiently employed. To this end, a method is presented for constructing a surrogate model, based on stochastic reduced‐order models, and is proposed to represent the laser welds within the component. Here, the uncertainty in weld microstructure and geometry is captured by calibrating plasticity parameters to experimental observations of necking as, because of the ductility of the welds, necking – and thus peak load – plays the pivotal role in structural failure. The proposed method is exercised for a simplified verification problem and compared with the traditional Monte Carlo simulation with rather remarkable results. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Bemessung von Fensterbrüstungen aus Mauerwerk unter Ansatz der Biegezugfestigkeit

Design of masonry window parapets considering flexural tensile strength Parapet masonry is often neglected in design. However, if verification is explicitly necessary, this is often economically feasible only on the basis of flexural tensile strength. For this application, two design methods are presented with which parapet masonry can be designed as a freestanding wall considering the flexural tensile strength. In addition to a general method based on linear‐elastic stress‐strain relationship of the masonry, which is applicable to both fully and partially supported slabs, a second approach is presented, which takes into account an existing slab edge shell and thus applies especially for parapet masonry with reduced bearing length. Both methods can also be used to design freestanding walls with minor adjustments. Finally, the permissible height of a parapet made of brickwork is determined exemplarily for various applications and indicated in tabular form depending on the acting wind load.     

Tragfähigkeitserhöhung bei Mauerwerk durch textilglasgitterverstärkte Mörtelfugen

Increase of the vertical load carrying capacity of masonry due to mortar bed joints with textile glass mesh reinforcement From a structural point of view, one of the most important material parameters in the construction sector is the vertical compressive strength of masonry, which consists of the compressive strength of the bricks as well as of the mortar bed. The interaction between the bricks and the mortar beds is the main reason for compression failures of masonry walls. A close analysis of the deformation behavior of the two components shows that different transverse strains in the contact surface between the bricks and the mortar are the main cause for compression failures. However, the load‐bearing capacity of masonry walls can be increased by using some reinforcement in the mortar beds which counteracts lateral expansion. The impact of textile glass mesh reinforcement on the load‐bearing capacity of masonry was analyzed in a test program on masonry columns with different numbers of textile glass mesh reinforced mortar beds. The results of the analyses show that the load‐bearing capacity of the columns rises with an increased ratio of reinforcement, regardless of the type of bricks used. From the ratio of the height of the reinforcement layers to the thickness of the wall it can be deduced that a higher degree of reinforcement has a positive effect on the load‐bearing capacity of the masonry. On this basis, an increase of the strength and load‐bearing capacity of masonry walls is formulated to be on the safe side.     

The two‐shearfield test – A suitable method for the empirical shear capacity design of masonry / Der Zweifeld‐Schubversuch – Eine praxistaugliche Methode zur versuchsgestützten Bemessung der Schubtragfähigkeit von Bestandsmauerwerk

The investigations [1] demonstrate that the two‐shearfield test is a suitable method for the determination of the shear capacity of masonry. The testing equipment is mounted directly on the wall in order to retain realistic boundary conditions like stiffness, load and prior damage. The behaviour factor q and the capacity curves of certain masonry walls can be directly obtained from the experimental results and realistic material behaviour in earthquake design can be represented. In particular, existing masonry can be assessed realistically with methods like the response spectrum, the push‐over and the capacity spectrum by using the two‐shearfield test.