Zur Querkraftbemessung bei Kreisquerschnitten: Teil 2: Bauteile mit Querkraftbewehrung

Shear Design of Girders with circular Sections, Part 2: Girders with shear Reinforcement Continuing part 1 of the contribution a method is derived to design reinforced concrete beams with circular sections and usual stirrups against shear forces. It is valid for the cracked state and bases on the theoretical shear flow resolved in radial and tangential components as well as deviation forces that arise due to the circular shape of the stirrups. The method uses the design principles of DIN 1045‐1 and supplements the shear resistances of the tensile and of the compressive strut with a reducing efficiency factor that accounts for the increases of stirrup and concrete stresses compared to rectangular sections. An arch mechanism models the positive effect of compressive axial forces. The method is verified to experimental data taken from the literature.     

Bemessungshilfen und Konstruktion bei geneigten Querkräften

Design Methods and Detailing for RC Beams with Inclined Shear Forces The shear‐resistant design of reinforced concrete (RC) beams with rectangular cross sections and inclined shear forces (biaxial shear) is presented. Equations for the shear resistances provided by the tensile strut and by the compressive strut are derived according to the design concepts of DIN 1045‐1 and EC 2. They are verified to experimental data and elaborated to gain design charts. Examples show the practical applications. Existing detailing provisions for the anchorage of stirrups and the horizontal displacement in the tensile force of the bending reinforcement can directly be applied to cases of biaxial shear, if the rotations of the neutral axis and of the resultant strut‐and‐tie system are taken into account.     

Zur Querkraftbemessung bei Kreisquerschnitten. Teil 1: Bauteile ohne Querkraftbewehrung

Shear Design of Girders with circular Sections: Part 1: Girders with no shear Reinforcement. The shear resistances acc. to DIN 1045‐1 are not valid for girders with circular sections. The “Normenausschuß Bauwesen” (NABau) recommends using an equivalent rectangular cross section. Verifications to experimental data show that in cases of axisymmetrically reinforced girders with no shear reinforcement this assumption conservatively underestimates actual resistances. However, results pronouncedly scatter. Thus, a practical design method is derived for circular sections that bases on the concepts of DIN 1045‐1 and takes into account the well accepted factors of influence like geometry parameters, the longitudinal reinforcement ratio or the concrete strength. It incorporates the positive effects of compressive axial forces by an additive term. The approach is statistically evaluated and verified to experimental data.     

Stahlbetonträger mit zweiachsiger Querkraftbeanspruchung

Reinforced Concrete Beams subject to biaxial Shear Forces: strut‐and‐tie models, experiment and design approach Spatial strut‐and‐tie models are developed for the design of reinforced concrete beams subject to biaxial shear forces. They are derived from a resolution of the vector of the resultant shear force and valid for beams with rectangular cross sections. The models consist of tensile struts of stirrups and longitudinal bars, compressive concrete struts directed to each separate area of the longitudinal reinforcement in the cracked part of the cross section as well as compressive struts stiffening the stirrups. They are qualitatively verified by experiments and further elaborated to derive design charts for the design of the stirrups. An example shows the practical application of the charts.     

Querkraftbemessung von bügel‐ oder wendelbewehrten Bauteilen mit Kreisquerschnitt

Für bügel‐ oder wendelbewehrte Stahlbetonbauteile mit Kreisquerschnitt – mit oder ohne zusätzlich drückenden Normalkräften – werden aus dem speziellen inneren Schubfluss die Spannungen in Bügeln und im geneigten Druckfeld abgeleitet und in Widerstandsgleichungen zur Querkraftbemessung umgesetzt. Die Gleichungen besitzen die bekannte Form aus DIN 1045‐1 bzw. EC2 und sind erweitert durch einen so genannten Wirksamkeitsfaktor, welcher die Widerstände gegenüber Rechteckquerschnitten auf rund 75% herabsetzt. Alternativ zur bekannten Gleichungsart wird eine additive Widerstandsform aus Betontraganteilen, Fachwerkwirkung und Sprengwerk für die maßgebende Zugstrebentragfähigkeit vorgeschlagen. Eine umfangreiche Versuchsserie verifiziert die Ansätze und zeigt Einzeleffekte von Bügelspannungen, Bewehrungsgrad und Bügelaktivierung sowie Wendel‐ und Normalkrafteinflüsse. Shear Design of Members with Circular Sections Reinforced by Stirrups or Spirals For RC members with circular sections the stresses within stirrups or spiral reinforcements as well as within the inclined compression field are derived from the specific inner shear flow and elaborated to gain equations for the shear resistances. The equations use the established scheme of DIN 1045‐1 or EC 2 extended by an efficiency factor reducing resistances compared to rectangular sections to about 75%. Alternatively, an additive approach for the resistance of the tensile strut is proposed. It sums up from concrete contributions, strut‐and‐tie actions as well as arch contributions introduced by axial forces. Both approaches are verified to experimental data taken from extensive test series. The characteristics of stirrup stresses and stirrup activation as well as effects from the shear reinforcement ratio, the use of inclined spirals and axial forces are presented.     

Aussteifung von Gebäudehüllen durch randverklebte Glasscheiben

Stabilisation of building envelopes by the use of circumferential glued glass panels. The pursuit of maximum transparency with increasingly filigree bearing structures fuels the possibility of using the glazing as a load bearing element that is able to transmit both lateral and in plane forces. Space grid structures with rectangular glass panes seem to be very capable for this purpose. In this case the linear bars are normally pin‐joint at nodes to minimise both cross sections and erection cost. It is common to triangulate space grid structures with rods or prestressed steel cables. These bracings could be omitted if the stiffening forces would be transmitted by the glazing. In the here considered system the glass panes are used as shear panels to stabilize the envelope. Therefore, the panes are glued to the space grid members along their perimeter. Details were designed and the load bearing behaviour of the connections and the glass elements were investigated and design rules developed. These rules consider the shear interaction in laminated glass elements, and the interaction of in plane and out of plane loads.     

框架柱双向受剪承载力计算方法比较

结合7根不等肢配箍矩形截面钢筋混凝土框架柱双向受剪承载力试验数据,综合比较和评价3种计算不等肢配箍矩形截面框架柱双向受剪承载力计算方法。将三者计算值与试验结果对比,表明运用上述3种方法计算矩形截面框架柱双向受剪承载力均偏于安全,其中三折线简化法所计算的受剪承载力更接近试验值。     

Plastische Tragfähigkeit von semi‐kompakten Querschnitten aus Stahl

Plastic capacity of semi‐compact cross‐sections made of steel. Semi‐compact cross‐sections are those that are defined as class 3 cross‐sections according to EN 1993‐1‐1. In the code their cross‐section capacity is defined as pure elastic resulting in a discontinuity at the border to the plastic resistances of class 2 sections. The current paper investigates the plastic cross‐section capacities of semi‐compact sections. Axial compression, minor and major axis bending as well as their interaction were investigated. Experimental and numerical tests were carried out. Based on the results several design proposals were developed and statistically evaluated according to EN 1990.     

Computation of major axis shear deformations in wide flange steel girders and columns

Shear deformations in the clear span region of wide flange girders and columns can often be responsible for a significant portion of the lateral flexibility of steel moment resisting frames. To include shear deformation in the analysis of such structures, the shear modulus of the material and the effective shear area of the various cross sections are required. The effective shear area is often defined in terms of a sectional form factor, κ, which is equal to the total cross sectional area divided by the effective shear area. Structural engineering literature provides several formulas for computing the form factor for a variety of cross sectional shapes, including wide flange beams. When applying these formulas to sections in the AISC section database, however, it was found that the results varied considerably, particularly for jumbo sections. The purpose of the work reported in this paper was to determine which of the existing formulas is most accurate when applied to all sections in the database. A special virtual work based finite element analysis procedure was developed for this purpose. The results of the analysis indicate that a simple empirical formula for determining the form factor may be applied with sufficient accuracy in most situations. Because the analysis of rectangular sections provides insight into the wide flange beam problem, a detailed discussion of the computation of the form factor for rectangular sections is also provided.     

Analytical solution for deep rectangular structures subjected to far-field shear stresses

Underground structures located in seismic areas have to support the static loads transferred from the surrounding ground under normal working conditions, as well as the loads imposed by any seismic event. Typically underground structures have cross section dimensions much smaller than the wave length of ground peak velocities, in which case inertial forces can be neglected and the structure can be designed using a pseudo-static analysis, where the seismic-induced loads or deformations can be approximated by a far-field shear stress or strain. Current close-form solutions for deep rectangular structures subjected to a far-field shear stress are approximations that do not consider all the relevant variables. An analytical solution is presented in this paper for deep rectangular structures with a far-field shear stress. Complex variable theory and conformal mapping have been used to develop the solution, which is applicable to deep rectangular structures in a homogeneous, isotropic, elastic medium. The solution shows that the deformations of the structure depend on the relative stiffness between the structure and the surrounding ground, and on the shape of the structure. The analytical solution has been verified by comparing its predictions with results from a finite element method and from previously published data.     

A non-linear theory for the behaviour of thin-walled sections subject to combined bending and torsion

Thin-walled steel sections are extensively used in modern building either as purlins or as sheeting rails. Comparatively little is known about the effects of position and orientation with respect to the shear centre of the loading on the stability of such sections. The governing differential equations for the non-linear elastic behaviour of thin-walled sections subject to combined bending and torsion are developed in the paper. They include the non-linear contribution resulting from the movement of the point of application of the load. This is shown to have a significant influence on the behaviour of the member when the loads are inclined to the principal axes, as in the case of an asymmetrical section subject to gravity loading. Furthermore, it is shown that load resultants which pass through the shear centre but which are inclined to the principal axes of the section do not produce pure bending. They induce torsional moments in the section which are not accounted for in traditional theories. A finite-difference method is used to solve the equations, and the validity of the theory is assessed by comparing the results with those obtained from experiment.     

考虑地震作用矩形截面框架柱双向受剪承载力

通过5根无箍筋和7根有箍筋矩形截面钢筋混凝土框架柱试验,研究不同加载角度时,低周往复斜向水平荷载作用下,矩形截面框架柱双向受剪的破坏机理和计算方法.结果表明,不能用单向剪切理论计算矩形截面框架柱双向受剪承载力的原因,主要是矩形截面框架柱双向受剪时,斜裂缝开展迅速,部分混凝土提前退出工作,导致轴压力对混凝土强度的提高作用...     

主应力轴旋转下(b=0.5)原状软黏土孔压特性

采用浙江大学空心圆柱扭剪仪(ZJU-HCA),对杭州原状软黏土进行固结不排水主应力轴旋转试验,探讨剪应力变化、初始剪应力水平高低及主应力轴正向和逆向旋转对黏土孔隙水压力(简称孔压)发展的影响。试验中保持平均主应力不变,中主应力系数b=0.5。试验结果表明:定向剪切产生的孔压主要受剪应力控制;用双重屈服面理论得到孔压系数,结合孔压线性拟合结果发现,若初始剪应力低于峰值剪应力,体积屈服面函数不受主应力轴旋转影响;若初始剪应力接近峰值剪应力,主应力轴开始旋转时的孔压上升速率相对较高,但后期孔压反而会下降;纯主应力轴旋转过程中的孔压上升速率主要受初始剪应力大小控制。主应力轴正向旋转较逆向旋转产生的孔压小;主应力轴逆向旋转相对正向旋转对整个剪切过程的孔压发展有较大影响。     

Vorgespannte Bodenplatten – ein brachliegendes Potential

Prestressed Foundations Slabs Continuous slabs proves to be an attractive foundation system. Foundation slabs can be used to withstand the loading and simultaneously form a tight and continuous element between foundation soil and the building. Foundation slabs are highly stressed structural elements, which require large bending and shear resistance. Thus hugh cross‐sections and large bending and shear reinforcement is needed. A prestressing reinforcement will be ideal to resist especially the high loading. Prestressing is an activ reinforcement element in contrast to the mild reinforcement. The pretensioned part of the steel cause forces, which cause deflection forces due to the curvature of the tendon geometry. Thoses forces will be able to match the individual loading directly and then distribute them continuously over the unloaded slab area. The load bearing system, caused by the deflection loads of the prestressing forces reduces the stresses within the structural element. Consequently slender cross‐section and less amount of mild reinforcement is needed. Additionally the compression stresses due to prestressing forces reduce the cracking and enlarge the tightness of the foundation slab.     

Wölbkrafttorsion von Durchlaufträgern mit konstantem Querschnitt unter Berücksichtigung sekundärer Schubverformungen

Warping torsion of continuous beam with constant cross‐section considering shear deformation. The analogy between the theory of warping torsion and second order theory of a bending member with tensile force is also valid, if shear‐deformations in both cases are additionally included. On the basis of this analogy the three‐moment equation for continuous beam with constant cross‐section is given. It is demonstrated, that shear‐deformations for open sections can normally be neglected but must be encluded in the case of hollow‐sections. It is also shown, that for these sections warping‐torsion occurs only in ranges of discontinuity, but causes stresses which are in the same order as the stresses of primary torsion.     

应力主轴循环旋转对砂土变形特性的影响(英文)

采用香港科技大学的空心圆柱扭剪仪进行了应力主轴固定单调剪切和应力主轴循环旋转两种不同路径的排水试验。通过应力主轴固定单调剪切试验分析了所制作砂样的初始各向异性特性。在应力主轴循环旋转试验中,控制施加在试样上的3个有效主应力的大小不变,仅应力主轴在0°～180°循环旋转。着重分析了4个应变分量及体应变随应力主轴循环旋转周数的变化关系、剪应力剪应变关系以及所施加的剪应力水平和有效球应力在应力主轴循环旋转过程中对砂土变形特性的影响。     

低矮小开口剪力墙自由振动问题的半解析解

针对低矮小开口剪切型剪力墙,研究基于直接模态摄动法原理的结构动力特性的半解析分析方法。首先把低矮小开口剪力墙视为变截面的剪切型悬臂结构,依据连续系统动力分析原理建立剪切型剪力墙自由振动分析的变系数微分方程;然后利用等截面剪切型悬臂结构模态函数的解析解和直接模态摄动法原理,考虑剪力墙中小开口对系统特征值和主模态所带来的影响,并进行修正;最后应用Ritz变换,将低矮小开口剪力墙的自振特性分析问题转化为一组非线性代数方程的求解问题,进而求得该类剪力墙自振特性的近似半解析解。算例结果表明,该方法对以剪切变形影响为主的低矮小开口剪力墙动力分析简便有效。     

＜形、L形、T形截面剪力墙配筋研究

为解决<形、L形、T形截面剪力墙配筋设计,参考《复杂截面剪力墙配筋研究》,采用混凝土单轴受压简化应力—应变曲线和应变线性分布的平截面假定,积分计算剪力墙正截面承载力.通过不同纵筋形心位置矩形截面剪力墙正截面承载力骨架曲线比较分析,指出将纵筋设计于边缘构件中不够经济合理.通过<形、L形、T形截面剪力墙承载力骨架曲线分析,并与ACI 318-99,BS 8110-97和GB 50010-2002国内外规范比较,说明本文方法比较安全、可靠、合理.最后通过算例,将本文配筋方法应用于<形、L形、T形截面剪力墙配筋设计,揭示了目前某些软件针对<形、L形、T形截面剪力墙所采取的分段设计方法不够安全合理的隐患.     

Flexural behaviour of stainless steel oval hollow sections

Structural hollow sections are predominantly square, rectangular or circular in profile. While square and circular hollow sections are often the most effective in resisting axial loads, rectangular hollow sections, with greater stiffness about one principal axis than the other, are generally more suitable in bending. Oval or elliptical hollow sections (EHS) combine the aesthetic external profile of circular hollow sections with the suitability for resisting flexure of rectangular sections, whilst also retaining the inherent torsional stiffness offered by all tubular sections. This paper examines the structural response of recently introduced stainless steel oval hollow sections (OHS) in bending and presents design recommendations. In-plane bending tests in the three-point configuration about both the major and minor axes were conducted. All tested specimens were cold-formed from Grade 1.4401 stainless steel and had an aspect ratio of approximately 1.5. The full moment-rotation responses of the specimens were recorded and have been presented herein. The tests were replicated numerically by means of non-linear finite element (FE) analysis and parametric studies were performed to investigate the influence of key parameters, such as the aspect ratio and the cross-section slenderness, on the flexural response. Based on both the experimental and numerical results, structural design recommendations for stainless steel OHS in bending in accordance with Eurocode 3: Part 1.4 have been made.     

不同应力路径下砾石土力学特性的宏细观研究

 利用空心圆柱仪对砾石土进行三轴压缩、扭剪、三轴–扭剪联合3种单调加载路径试验以及应力主轴旋转路径试验。通过设计新型加载路径,实现应力主轴在不同应力水平下往复旋转,并在旋转时保持广义剪应力不变。试验结果表明,随着应力水平的增加,主轴旋转产生的广义剪应变呈现先增大、后减小、再增大的规律;主轴旋转会造成试样强度明显下降,内摩擦角显著减小,其破坏时刻的应力圆位于三轴–扭剪联合加载路径应力圆的内部。对三轴压缩和扭剪2种路径试验进行离散元细观分析,发现扭剪力作用下试样会形成水平滑动面。最后,对应力主轴旋转造成试样强度下降的原因进行分析和讨论。