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.     

弯曲型支撑-框架的假想荷载法

为避免在钢结构设计中逐一去确定框架柱的计算长度,该文提出了一种应用于弯曲型支撑框架的假想荷载法。将假想荷载作用于框架楼层,配合二阶弹性分析,考虑材料非线性、残余应力和初始几何缺陷,研究了多种几何和荷载条件下的弯曲型支撑框架模型,分析了一系列模型的极限承载力,提出了统一的假想荷载系数以及假想荷载的近似公式,无论是有水平荷载或无水平荷载,无论是等截面还是变截面,其结果与有限元结果都符合较好。     

On Biaxially Loaded Internal Cracks

The initiation of fracture is studied for an internally cracked large plate. The cracked plate is subjected to biaxial loading with different ratios of the normal load to the lateral load. The initiation of crack propagation is predicted by using a strain based mechanism of fracture. It is shown that the normal load required for fracturing a linear elastic material drops significantly when the lateral load increases beyond a critical value.     

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.     

弱横梁人字撑结构的弹塑性抗侧性能

人字撑结构是多高层钢结构建筑常用的抗侧力结构,然而在强烈地震作用下,这种支撑结构的拉压支撑会在两者交汇的横梁处形成一竖向不平衡力,可能导致支撑架横梁形成塑性铰、结构的抗侧能力快速下降。许多现行规范要求支撑架的横梁应具备承受这一竖向不平衡力作用的能力,但是实际人字撑结构可能不能满足这一要求,因此有必要对弱横梁人字撑结构的抗侧性能进行研究。该文对不同支撑长细比下(20~150),不同横梁的强度(0.3倍,0.5倍,0.8倍,1.0倍横梁强度)人字撑结构的弹塑性抗侧性能进行了分析。对弱横梁人字撑结构的整体抗侧性能、拉压支撑分别的抗侧性能、超强系数和极限承载力等主要性能指标进行了分析,同时提出了弱横梁人字撑结构塑性抗侧曲线的近似计算方法和超强系数的计算方法。该文的研究有助于充分了解弱横梁人字撑结构的弹塑性抗侧性能,为它的实际应用提供参考。     

Finite element analysis of vickers indentation cracking processes in brittle solids using elements exhibiting cohesive post-failure behaviour

The cracking processes during the indentation test of brittle solids is simulated by means of the finite element method (FEM) using elements exhibiting cohesive post-failure behaviour and alumina as the model material. The results show that at low indentation loads, median cracks could nucleate at full loading but Palmqvist cracks only nucleate in the unloading stage and that they may not join up even after full unloading. Such cracks are stable as they are embedded in a region of high hydrostatic compression throughout the indentation test. At high indentation loads, both median and Palmqvist cracks nucleate early during the loading stage and coalesce to form a half-penny crack on further loading. Although the cracks are embedded in a region of high hydrostatic compression during loading, an annular tensile region eventually develops in between the cracked material beneath the indenter and the surrounding uncracked material during the unloading stage of the macro-indentation. This not only provides the driving force for existing cracks to grow but also new crack systems to form. The present work shows that for brittle solids with negligible plastic deformation, the mismatch in elastic recovery between the cracked and uncracked bodies on unloading plays an important role in indentation fracture processes.     

Masonry buildings at the borderline to high‐rise – Part 1 / Mauerwerksbauten an der Hochhausgrenze – Teil 1

The interaction of vertical and horizontal loads is the decisive combination of actions for multi‐storey buildings with masonry shear walls in most cases. This article presents a simple and clear method, which can be used with modern open floor plans to verify a favourable load transfer of the vertical actions for masonry walls. The method is extended in the second part of the article to be published in one of the coming issues of the journal Mauerwerk for horizontal actions and explained with an example.     

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.     

Fracture experiments on through wall cracked elbows under in-plane bending moment: Test results and theoretical/numerical analyses

Fracture assessment of pipe bends or elbows with postulated through wall crack is very essential for leak-before-break qualification of primary heat transport system piping of nuclear power plants. The methodology for fracture assessment of cracked elbows is still in developing stage. Any new development in theoretical aspect requires experimental validation. However, fracture test data on cracked elbows is not so abundant as straight pipes. The earlier experiments on cracked elbows were focused mainly on the determination of limit load. Other fracture parameters e.g. crack growth, crack initiation load or crack opening displacement were not reported in the open literature. Against this backdrop, a comprehensive experimental and theoretical program on component integrity has been initiated at Reactor Safety Division (RSD) of Bhabha Atomic Research Center (BARC), India. Under this program, a number of fracture tests have been carried out on elbows with through wall circumferential/axial cracks subjected to in-plane closing/opening bending moment. These test data are then thoroughly analysed numerically through non-linear finite element analyses, analytically through limit load comparison and also through comparison of crack initiation loads by finite element and R6 methods. These test data may be utilized in future for validation of new theoretical developments in the integrity assessment of through wall cracked elbows.     

Plastic collapse load prediction and failure assessment diagram analysis of cracked circular hollow section T‐joint and Y‐joint

This paper concerns the validation of standard safety assessment procedure given in BS 7910 for cracked circular hollow section T‐joint and Y‐joint, using the finite element (FE) results. A robust and efficient FE mesh generator is developed to produce the 3D models of the cracked joints and to calculate the elastic J‐integral (J_e) and elastic–plastic J‐integral (J_ep) values of the crack respectively. In order to verify its accuracy and convergence, the plastic collapse loads (P_c) obtained from experimental tests and FE predictions are compared; they agree very well with each other. It is also found from experimental tests that the plastic collapse loads (P_c) predicted using the BS 7910 reduction factor (F_AR) are safe and conservative. Subsequently, the failure assessment diagrams (FADs) of five cracked T‐joints and three cracked Y‐joints are constructed using the FE results, following the J‐integral method, which is classified as Level 3C in BS 7910. Thereafter, a comparison between the constructed FAD curves and the standard Level 2A curve is carried out, and it is observed that the safety assessment results using the standard Level 2A curve might be unsafe because some parts of the constructed FAD curves fall inside of the standard one. A penalty factor of 1.15 working on both the elastic–plastic J‐integral and plastic collapse load (P_c) is proposed to move all the constructed FAD curves just outside of the standard Level 2A curve.     

超高层结构设计的经济性及相关问题的研究

提高超高层结构设计的经济性可从三方面入手:降低结构所受的水平荷载、提高结构体系的抗侧效率和选择合理的设计指标。首先,为了降低结构所受的水平荷载,可通过选择合理的建筑体型和设置减振装置来降低结构所受的风荷载和采用消能减震的方法以及选用比强度、比刚度大的材料来降低结构所受的地震作用。其次,为了提高结构体系的抗侧效率,应尽可能使结构布置支撑化、周边化、巨型化和伸臂桁架化。最后,建议对超高层设计中的一些规定指标作进一步研究,在满足安全性的前提下进一步提高结构设计的经济性。     

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 investigation of masonry arches exposed to horizontal impact / Experimentelle Untersuchungen von Mauerwerksbögen unter Horizontalanprall

Abstract: Arch bridges still form a large part of the bridge stock in German‐speaking countries and in Europe. In general, they have a high loadbearing capacity for vertical loads. However, only a limited number of research investigations into the capacity of these bridges to resist horizontal impact have been carried out. In this paper we describe static and dynamic tests for the evaluation of the loadbearing capacity of masonry arches exposed to horizontal loads in transverse direction. Furthermore, a simple engineering model is developed for such load cases.     

Confined Masonry subjected to Lateral Loads / Eingefasstes Mauerwerk unter Plattenbeanspruchung

Just as with shear stress on the edges of masonry walls, prestressing through the confinement and restraint of all four sides of the wall improves the load‐carrying capacity under lateral loads. The extra load arising from prestressing leads to increased flexural strength of the masonry. The confinement of the edges results in relatively smaller span moments. In this case, the torsional stiffness of the reinforced concrete frame is important. This is determined by the frame itself as well as by its integration within the building. As a supplement to [4], an examination of panel loading was also performed within the guidelines of a research project at the TU Dresden, Chair for Structural Design, on behalf of the Federal Office for Building and Regional Planning on the subject of “Confined Masonry as an Option for Increasing the Load‐Carrying Capacity of Stiffening Walls”[9]. The various influences are to be initially researched on the basis of various analytical observations and a small numerical study. A thorough, experimentally‐based clarification of the load‐carrying capacity of the panels was not possible within the framework of the research project.     

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.     

Bracing systems in masonry buildings / Aussteifungssysteme im Mauerwerksbau

In this article, an FE analysis model suitable in engineering practice for masonry bracing walls acting as deep beams without tensile strength is compared with simple models based on trusses. The results of both processes are compared through the example of a four‐storey building of Poroton masonry.     

Demountable prototype house – from facade to water tap

In connection with climate development, our buildings, both existing and newbuild, have to be intensively investigated regarding their energy balance and use of resources. An energy‐efficient dry building system capable of being recycled is important for new building today. This is the starting point for the project ReDeMaM (recyclable – demountable – highly energy‐efficient – massive – prototype house), to investigate whether appropriate systems are already available on the market and to what extent these are compatible with each other. The end result should be a prototype house, which includes all necessary elements including finishings with the objective of being capable of being dismantled, reused and recycled. The research project is supported by the research initiative Zukunft Bau (future building) and is currently underway at the Chair of Structural Design at the TU Dresden.     

用Rayleigh-Ritz法求含裂纹偏心柱的弹性挠度

本文采用Ｒａｙｌｅｉｇｈ－Ｒｉｔｚ能量变分法,计算分析了两端铰支含裂纹偏心受压柱的弹性挠度,其中重点研究了裂纹对最大挠度的影响。首先选取三角函数级数作为柱挠度的试函数;然后分别计算弹性体系的弯曲变形能和裂纹引起的变形能增量及外力势能,进而得到体系的总势能;最终根据势能驻值条件确定挠度系数,从而得到一个在裂纹截面满足变形协调条件的挠度级数解。文中还以含Ⅰ型裂纹箱形截面偏心柱为例,具体地应用上述解分析了裂纹对柱最大挠度的影响。数值结果表明,用上述级数解的首项进行工程近似计算具有良好的精度。     

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.