A procedure for creep and shrinkage analysis of frames with low beam stiffness

Adjacent vertical members in tall buildings undergo differential time‐dependent deformations due to creep and shrinkage. These deformations result in differential deflections at floor levels and redistribution of forces. An available practical procedure in the literature to estimate these deformations, taking into account the sequential nature of the loading, utilizes the rate of creep method (RCM) to evaluate the stress transfer between concrete and steel. This procedure is designated as Procedure(RCM) and is prone to errors since the creep recovery of concrete is neglected in RCM. A more accurate procedure designated as Procedure(AEMM) using the age‐adjusted effective modulus method (AEMM) as a stress transfer method, and taking into account the sequential nature of the loading, is proposed. The proposed procedure is more accurate than Procedure(RCM) since creep recovery of concrete is considered in AEMM. Numerical studies are carried out in this paper to compare the results from these two procedures. Copyright © 2007 John Wiley & Sons, Ltd.     

考虑收缩徐变影响的两跨钢-混凝土连续组合梁长期性能预测方法

为量化混凝土翼板收缩徐变对多跨钢-混凝土连续组合梁长期性能的影响,提出相应的预测方法,基于现有两跨连续组合梁长期试验结果对典型的组合梁设计方法进行适用性评述; 在此基础上,基于龄期调整的有效模量法并考虑混凝土的收缩徐变、开裂及组合梁界面相对滑移的综合影响,提出两跨连续组合梁长期中支座弯矩与跨中挠度的计算公式,并采用长期试验结果验证预测方法的可靠性; 进一步对比不同混凝土翼板类型(收缩徐变分布模型)对组合梁长期性能的影响。结果表明:采用龄期调整的有效模量法模拟混凝土徐变特征,考虑收缩产生的附加弯矩,采用折减刚度考虑混凝土开裂与界面滑移的影响,提出的两跨连续组合梁长期性能计算公式,可有效预测组合梁长期中支座弯矩分布与跨中挠度,计算结果与试验结果最大相差25.3%; 混凝土的收缩变形对组合梁长期性能影响显著,当不考虑混凝土收缩变形时,组合梁中支座弯矩与跨中挠度仅分别为试验值的41.1%和60.6%; 组合梁长期性能设计时,应根据楼板类型采用不同的收缩徐变模型,针对钢筋混凝土楼板采用均匀收缩、均匀徐变模型,针对组合楼板采用非均匀收缩、非均匀徐变模型。     

Effect of creep and shrinkage in reinforced concrete frame–shear wall system with high beam stiffness

The behaviour of frames and frame–shear wall systems with regard to creep and shrinkage with high beam stiffness has been largely unexplored until recently since no procedure has been available. For low beam stiffness the most widely used procedure available in literature for determining creep and shrinkage effects in reinforced concrete building frames and frame–shear wall systems designated herein as approximate procedure, AP has been recommended for buildings having flexible slab systems and with a limited number of storeys. Recently an accurate procedure termed Consistent Procedure (CP) has been developed which is applicable to low as well as high beam stiffness and requires no restriction on number of storeys. In this paper, using CP, studies are reported for frame–shear wall systems with high beam stiffness. The effect of introduction of shear walls on load transfer among vertical members considering creep and shrinkage is studied. It is shown that the presence of shear wall alters significantly the load transfer among vertical members. It is also shown that whereas differential vertical deflections between adjacent vertical members are small owing to high stiffness of beams, the load transfer between them can be significant. Copyright © 2003 John Wiley & Sons, Ltd.     

Control of time-dependent effects in steel-concrete composite frames

Studies are presented for the control of time-dependent effects of creep and shrinkage in steel-concrete composite frames with pre-cast concrete slab for both shored and un-shored constructions. A developed hybrid procedure has been used for carrying out the studies. The procedure accounts for creep, shrinkage and progressive cracking in concrete slab panels. Two frames, a single storey and a five storey frame are considered. It is shown that, for both the types of constructions, shored and un-shored, the increase in bending moments and mid-span deflections can be controlled to a significant degree, without putting constraints on design parameters, by simply delaying the time of mobilization of composite action between the pre-cast concrete slab panels and the steel section. It is also found that though there is insignificant effect of type of construction on bending moments, the percentage change in mid-span deflection due to creep and shrinkage is significantly higher for shored construction.     

Effect of concrete creep and shrinkage on tall hybrid-structures and its countermeasures

This paper aims to study the different vertical displacements in tall hybrid-structures and the corresponding engineering measures. First, the method to calculate the different vertical displacements in tall hybrid-structures is presented. This method takes into account the effects of construction process by applying loads sequentially story by story. Based on the concrete creep and shrinkage calculation formula in American Concrete Institute (ACI) code, with the assumption that loads are increased linearly in members, the creep and shrinkage effects of members are analyzed by adopting two parameters named average load-aged coefficient and average age-last coefficient. The effects of steel ratio on members creep are analyzed by age-adjusted module method (AEMM). The effects that core-tube were constructed in advance to outer steel frame were also considered. Then, based on the sample calculation, the measures to effectively reduce the different vertical displacements in hybrid-structures are proposed. This method is simple and practical in the calculation of different vertical displacements in tall and super-tall hybrid-structures. __________ Translated from Journal of Hunan University (Natural Sciences), 2008, 35(1): 1–5 [译自: 湖南大学学报 (自然科学版)]     

结合梁中混凝土收缩徐变引起的次内力分析

根据钢-混凝土结合梁的受力特点,考虑采用有支架施工方法,由力的平衡条件和变形协调条件,分析结合梁中由混凝土收缩徐变引起的内力重分布,以此为基础,进一步提出了连续结合梁内力重分布的计算方法。应用该方法分析了两跨连续结合梁算例,计算了混凝土收缩徐变引起的内力重分布。研究结果表明,混凝土收缩徐变对钢-混凝土结合梁有显著影响,足以使连续结合梁中支座负弯矩区的混凝土产生裂缝。     

Effect of beam stiffness–column reinforcement on creep and shrinkage behaviour of R.C frames

Vertical deflections and load transfer among columns of R.C frames depend on the percentage of reinforcement in columns and stiffness of beams. No systematic studies are available in the literature on the effect of these parameters. Such systematic studies are reported in this paper. The beam stiffness is expressed in terms of a non‐dimensional parameter, designated as stiffness factor, which is the ratio of shear stiffness of beams to axial stiffness of columns. It is shown that depending on stiffness factor and column reinforcement, a column may receive the load from the adjacent columns or transfer the load to the adjacent columns, or may receive the load from one of the adjacent columns and at the same time transfer the load to the other adjacent column. Further, the effect of the creep and shrinkage on column axial forces can be of design significance in the lower and middle portions of buildings. The effect becomes greater with the increase in stiffness factor and difference in percentage reinforcement of the adjacent columns. Copyright © 2007 John Wiley & Sons, Ltd.     

Nachweis der Gebrauchstauglichkeit von Bauteilen aus Stahlbeton nach DIN 1045 und nach EC 2

Design of reinforced concrete members for serviceability after DIN 1045 and after EC 2. Considered are the frequently used members with rectangular cross section in normal strength normal concrete C 20 up to C 50 and one‐sided reinforcement with steel BSt 500. For the calculation of the deflection w, both concrete creep and shrinkage are taken into consideration, for the calculation of the crack width w_k and the stresses σ_c and σ_s the creep only.     

兰州红楼时代广场施工模拟与混凝土收缩和徐变效应分析

在兰州红楼时代广场施工过程模拟的基础上,对主楼高层框架柱与钢筋混凝土筒体的竖向变形及竖向变形差异随时间和空间的变化规律进行分析。在分析中采用时间依存累加模型,在混凝土特性中考虑徐变、收缩和强度增长,并计入部分构件(如加强层伸臂桁架)延时安装对整体模型的影响。并比较不同加载模式、框架梁梁端与核心筒不同连接方式对竖向变形的影响等。分析表明,工程施工完毕时,核心筒筒体徐变变形占总变形的40%以上,并在使用阶段继续增长;徐变收缩增加了高层框架柱的轴力及竖向变形,也使得核心筒墙肢轴向力均有不同程度的减小;采用核心筒与框架梁铰接的形式大大减小了核心筒与周边框架之间因竖向变形差异产生的附加内力,也使得施工期间核心筒与周边框架分别承担竖向荷载的分担率基本保持不变。     

A space-exact beam element for time-dependent analysis of composite members with discrete shear connection

This paper presents a space-exact, time-discretized solution for the time-dependent analysis of composite beams with partial interaction. The time effects considered in this model are creep and shrinkage of the concrete slab. The constitutive model adopted to describe the time effects is linear viscoelasticity with time-dependent coefficients to account for ageing. By using the time-discretized form of the constitutive relations, the equilibrium equations in terms of the displacements at a generic instant are analytically solved. Based on the analytical expressions (exact in space) of the displacements and the internal forces, the space-exact stiffness matrix is deduced for a generic composite beam element. This stiffness matrix can be used in a displacement-based procedure for the time-analysis of continuous composite steel-concrete beams with arbitrary support and loading conditions. The present formulation requires a minimum number of elements depending on the support and loading conditions. The proposed hybrid analytical-numerical method is used to investigate both the short-term and the long-term deflections of simply supported composite beams in order to assess the calculation method proposed in Eurocode EN 1994-1-1 [21]. The effects of creep, shrinkage and degree of shear connection on the deflection of simply supported composite beams are also analyzed. The long-term deflection calculated with the analytical model based on the rules given in EN 1994-1-1 [21] is compared against the one predicted by the proposed model. It is found that EN 1994-1-1 [21] slightly underestimate the long-term deflection. It was also observed that the contribution of shrinkage to the deflection is more significant than suggested in EN 1994-1-1 [21].     

钢框架-钢筋混凝土核心筒体系竖向变形差异的计算

本文研究了钢框架-钢筋混凝土核心简体系在重力荷载下,框架柱与混凝土简体的竖向变形差异问题,在分析中考 虑了混凝土的收缩和徐变以及建筑物室内外温差的影响。采用在整体结构计算模型上分层施加竖向荷载的叠加方法,利 用有限元程序SAP2000进行计算。分析表明,在仅考虑重力荷载和筒体混凝土的收缩和徐变时,高度在150m以上的钢框 架.钢筋混凝土核心简体系平均每3个楼层需要找平2mm以上。此外,混凝土的收缩和徐变以及建筑物室内外温差对框 架柱的轴力有相当大的影响,三者影响的总和占重力荷载作用下钢柱轴力的3％-20％之间。连系梁与框架柱刚接或铰 接,对柱筒竖向变形差异的影响较小,但是对节点的内力影响较大。采用钢管混凝土柱将大大减小柱筒之间的竖向变形差 异。     

不同火灾工况下钢梁-钢管混凝土柱平面框架受火全过程分析

采用多尺度建模方法建立了考虑钢材高温蠕变的三层三跨钢梁-钢管混凝土柱平面框架火灾全过程热-力耦合数值模型,研究不同火灾工况下平面框架经历常温加载、恒载升温、降温和火灾后等不同受火阶段的力学性能。在与已有试验对比验证的基础上,分析了框架经历升温和降温后受火钢梁跨中挠度和受火柱顶轴向变形与升降温时间关系,计算了火灾后框架底层柱底水平荷载P-框架顶层水平位移Δ关系曲线。研究结果表明：钢材的高温蠕变是钢材在热力耦合作用下应变的一部分,计算过程中需要考虑其影响;钢梁在升温过程中由于高温膨胀对框架柱产生外推作用,而进入降温阶段后钢梁产生明显的收缩变形;框架底层三跨同时受火时钢梁跨中挠曲变形最大,受火初期柱顶轴向压缩变形小于膨胀变形;受火后框架水平承载力和初始刚度均随受火区域的增大呈下降趋势。     

Lateral stiffness characteristics of tall reinforced concrete buildings under service loads

This paper presents an analytical method for quantitatively predicting the effects of cracking on the lateral deflection and stiffness characteristics of tall reinforced concrete buildings under service loads. The effects of cracking in tall reinforced concrete buildings can be considered using an element stiffness reduction model. This model determines the probability of cracking occurrence by dividing the area of the moment diagram, S_cr, where the working moment exceeds the cracking moment by the total area of the moment diagram, S. A practical cracking analysis method can be established by integrating the proposed stiffness reduction model with an iterative algorithm and commercial linear finite element analysis package. The proposed method has been validated by good agreement of results between the numerical computation and experimental testing of large‐scale rigid‐frame and wall‐frame structural sub‐assemblages. The effectiveness of the numerical analysis method is also illustrated through a practical 40‐storey reinforced concrete building example. The cracking effects on the lateral deflection and stiffness characteristics of this building were analysed both explicitly and quantitatively. Copyright © 2000 John Wiley & Sons, Ltd.     

Determination of efficient shoring system in RC frame structures

In this paper, systematic analyses, based on a numerical approach introduced in a companion paper, are performed for the shoring systems installed to support applied loads during construction. A rigorous time-dependent analysis provides insight on structural behaviors of reinforced concrete (RC) frame structures with changes in design variables, such as the types of shoring systems, the shore stiffness, and the shore spacing. Time-dependent deformations of concrete, such as creep and shrinkage, and the construction sequences of frame structures are also taken into account to minimize structural instability and to attain an improved shoring system design, as these effects may increase the axial forces delivered to the shores. In addition, the influence of the column shortening effect, generally considered in the design of the tall building structures, is analyzed. From numerous parametric studies, it is concluded that the most effective shoring system for RC frame structures is the 2S1R (two shores and one reshore), regardless of the changes in design variables.     

Earthquake analysis of isotropic asymmetric multistory buildings

Isotropic multistory buildings are the ones characterized by the property: all load‐resisting planar frames have proportional lateral stiffness matrices. In the present paper it is proved that the modal analysis of an N‐story isotropic asymmetric, torsionally coupled, building (a problem of order 3N) can be separated into two independent sub‐problems: (a) a sub‐problem that corresponds to a single‐story asymmetric, torsionally coupled, building (a problem of order 3); and (b) a sub‐problem that corresponds to an N‐story, torsionally uncoupled, planar frame (a problem of order N). It is also demonstrated that the orientation of peak modal seismic forces of the building is independent of the orientation of seismic excitation, which affects only their size. The separation provides a better insight into the structural behavior of asymmetric multistory buildings under earthquake ground motion. Copyright © 2006 John Wiley & Sons, Ltd.     

Untersuchungen zur Drehbettung von biegedrillknickgefährdeten Trägern durch Sandwichelemente

Investigation of the torsional restraint of sandwich panels against lateral torsional buckling of beams. Experimental investigations and parametric FE‐analyses show that the torsional restraint of sandwich panels against lateral torsional buckling of beams can be expressed by a tri‐linear moment‐rotation‐relationship. Formulae are given for different profile types combined with sandwich panels for roof and wall for calculation of the parameters of this relationship. From this moment‐rotation‐relationship, which depends on the lateral load of the beam, the rotational stiffness c_{ϑ A} of the connection is obtained as secant stiffness. The rotational stiffness c_ϑ required for the design against lateral torsional buckling according to DIN 18800 part 2 is governed by c_{ϑ A}. The rotational stiffness values c_{ϑ A} of the connection, which so far were only known for two types of elements, can be calculated with this method for all common types of sandwich panels and different types of constructions.     

Cyclic threshold shear strain in pore water pressure generation in clay in situ samples

The threshold level of the cyclic shear strain required for pore water pressure generation in clay samples is examined through the results of torsional hollow cylinder cyclic shearing tests according to JGS 0543-2009. The study confirms the previous results, namely, that the threshold cyclic shear strain is dependent on the effective consolidation stress and plasticity index (I_p). The average and standard deviations in the estimated threshold strain levels are 0.038?±?0.023% (I_p?<?30, σ′_c?$\leqq$?100?kN/m²), 0.047?±?0.016% (I_p?<?30, σ′_c?>?100?kN/m²), 0.079?±?0.028% (30?$\leqq$?I_p?<?5?0), and 0.143?±?0.041% (I_p?$\geqq$?50). As was found in past research, the levels of threshold strain for pore water pressure generation for clay are larger than those for clean sand. An increase in pore water pressure is only observed when the stiffness is reduced to around 80% of its initial value. This delay occurs because there is a difference between the cyclic threshold strain of the pore water pressure generation, γ_tp, and the cyclic threshold strain of the stiffness degradation, γ_td. Since the test procedure of JGS 0543-2009 is a standard scheme in the practical design process, it is expected that more data will become available in the near future which will allow for further discussions on threshold strain.     

Comprehensive stability design of planar steel members and framing systems via inelastic buckling analysis

This paper presents a comprehensive approach for the design of planar structural steel members and framing systems using a direct computational buckling analysis configured with appropriate column, beam and beam-column inelastic stiffness reduction factors. The stiffness reduction factors are derived from the ANSI/AISC 360-16 Specification column, beam and beam-column strength provisions. The resulting procedure provides a rigorous check of all member in-plane and out-of-plane design resistances accounting for continuity effects across braced points as well as lateral and/or rotational restraint from other framing. The method allows for the consideration of any type and configuration of stability bracing. With this approach, no member effective length (K) or moment gradient and/or load height (C _b ) factors are required. The buckling analysis rigorously captures the stability behavior commonly approximated by these factors. A pre-buckling analysis is conducted using the AISC Direct Analysis Method (the DM) to account for second-order effects on the in-plane internal forces. The buckling analysis is combined with cross-section strength checks based on the AISC Specification resistance equations to fully capture all the member strength limit states. This approach provides a particularly powerful mechanism for the design of frames utilizing general stepped and/or tapered I-section members.     

The in-plane behaviour and FE modeling of a T-joint connection of thin-walled square tubes

The behaviour of square hollow tubes with T-joints subjected to in-plane loading conditions is examined numerically. The stresses in the joint and its stiffness are determined from the finite element (FE) models using 2-D shell and 3-D solid elements. The parameters identifying the joint's stress concentration (ξ_m, ξ_b), and the bending stiffness reduction (α_K) are defined in terms of the ‘thin-wallness’ ratio (the side length to thickness) of the tube. These parameters permit modeling accurately the tubes and the T-connection by simple 1-D beam elements with certain properties modified. The FE models consisting of beam elements are significantly easier to prepare and analyze. The effectiveness of the approach is demonstrated by applying it to a structure with a T-connection and dimensions typical for the agricultural industry. It is shown that such beam models provide accurately all important information of the structural analysis (i.e., the stresses, displacements, reactions forces, and also the natural frequencies) at substantially reduced computational effort in comparison with the complicated FE models built of shell or solid elements.