UPPC梁的开裂截面惯性矩及挠度计算研究

为满足无粘结部分预应力混凝土(UPPC)梁正常使用极限状态的设计要求, 必须合理估算使用荷载下构件的挠度。由于预应力筋与其周围混凝土没有粘结, 加之部分预应力混凝土梁的中性轴随外荷载而动, 开裂截面形心轴及开裂截面惯性矩也跟着变, 这给UPPC梁的挠度计算带来了困难。该文建立了一个UPPC梁的开裂截面惯性矩计算方法, 在此基础上, 可以按Branson方法很容易地计算出截面有效惯性矩。该有效惯性矩与按《混凝土设计规范》(GB50010-2010)方法所得的有效惯性矩较接近, 前者与后者之比在0.89~1.10。计算挠度与3个不同研究者的试验对比表明所建立方法是正确的并具有较广泛的适用性, 可用于无粘结预应力筋为纤维复合材料的混凝土梁, 而目前的混凝土结构设计规范方法则无法应用于此类构件。     

钢筋增强超高韧性水泥基复合材料(RUHTCC)梁弯曲性能影响的几何参数分析

具有超高韧性新型随机PVA短纤维增强的水泥基复合材料(UHTCC)代替传统的具有准脆性应力软化特征的混凝土或纤维混凝土材料制作的钢筋(RUHTCC)受弯梁,可提高承载力,改善构件的延性,并具有良好的损伤演变能力,被认为是一种抗震性能较好的新型构件形式。除了配筋率和UHTCC拉压材料性能外,截面几何尺寸是影响其弯曲性能的一个重要因素。基于受弯理论分析和试验验证,采用该理论公式对截面几何尺寸(截面高度、宽度以及面积)的影响规律进行了系列分析。结果发现:对承载力,梁高度比宽度影响明显,而对承载力提高幅度和变形而言,随梁高的增加而减小,梁宽没有影响;对裂缝控制来说,只要梁下边缘的极限拉应变小于UHTCC材料的极限拉应变,截面尺寸的变化几乎不影响裂缝宽度的大小。并进一步针对RUHTCC梁的受弯设计提出了一些设计建议。     

钢筋增强超高韧性水泥基复合材料受弯构件理论分析

使用超高韧性水泥基复合材料(Ultra High Toughness Cementitious Composite,简称UHTCC)取代普通混凝土可以有效控制裂缝宽度,阻止外界不利因素进入混凝土和钢筋,极大降低钢筋腐蚀的可能性,从而可以显著提高钢筋混凝土结构耐久性。UHTCC是在单轴拉伸状态下具有应变硬化特性的超高韧性材料,能够稳定地分担部分拉力。为了对钢筋增强超高韧性水泥基复合材料受弯结构构件进行更加合理的设计以节约钢材,在设计中应该考虑受拉区UHTCC拉伸承载能力。开展了钢筋增强超高韧性水泥基复合材料受弯构件的研究工作,先后完成了受弯理论分析、无腹筋长梁实验研究、试验研究与理论分析验证对比、裂缝控制分析、承载力简化计算方法等方面研究。该文依据UHTCC单轴拉伸状态下的应变硬化特性、单轴压缩状态的双直线模型以及平截面假定,进行了钢筋增强超高韧性水泥基复合材料受弯构件的理论分析,包括正截面受弯各阶段内力分析、界限配筋梁受压区高度的确定、加载至破坏整个过程的弯矩-曲率关系的确定以及跨中挠度的计算。     

CFRP筋体外预应力加固T形截面混凝土梁短期挠度计算方法

通过静力试验和理论分析,研究CFRP筋体外预应力加固T形截面混凝土梁在短期荷载作用下的使用性能,探讨短期挠度计算方法。结果表明,CFRP筋体外预应力加固梁的荷载-跨中挠度曲线呈三折线变化;跨中截面混凝土和CFRP筋的平均应变在梁体开裂之前沿截面高度基本呈线性变化,开裂后,CFRP筋的平均应变明显小于梁底混凝土的应变。基于试验结果,计算开裂刚度折减系数和CFRP筋粘结特征系数,考虑二次效应的影响,运用有效惯性矩法建立了CFRP筋体外预应力加固T形截面混凝土梁的短期挠度计算公式,可供实际工程设计 参考。     

考虑压-拉薄膜效应的围框约束RC板极限抗力分

合理估算大变形条件下梁板构件的极限抗力,对工程设计计算具有重要意义。传统的RC （reinforced concrete）板极限抗力一般由小变形条件下的受压薄膜效应得到,然而RC板构件的灾变断裂大部分出现在大挠度阶段,因此考虑压-拉薄膜效应的极限抗力分析尤为重要。该文将RC板从加载到断裂全过程分为板端受压上升段、混凝土开裂下降段和钢筋拉伸上升段,根据正截面抗弯的钢筋混凝土弹塑性模型得到基于受压薄膜效应的荷载-挠度全曲线。利用经典的挠曲线微分方程并引入抗弯刚度软化系数对挠度进行修正,结合能量原理推导出大变形条件下基于受拉薄膜效应的RC板极限抗力,进一步得到考虑压-拉薄膜效应的荷载-挠度全曲线。计算结果表明,考虑压-拉薄膜效应的RC板极限抗力分析方法可以更合理地预测荷载-挠度全过程,计算结果与相关试验吻合良好,为合理评估RC板的极限承载力提供参考。     

考虑压-拉薄膜效应的围框约束RC板极限抗力分析

合理估算大变形条件下梁板构件的极限抗力,对工程设计计算具有重要意义。传统的RC(reinforced concrete)板极限抗力一般由小变形条件下的受压薄膜效应得到,然而RC板构件的灾变断裂大部分出现在大挠度阶段,因此考虑压-拉薄膜效应的极限抗力分析尤为重要。该文将RC板从加载到断裂全过程分为板端受压上升段、混凝土开裂下降段和钢筋拉伸上升段,根据正截面抗弯的钢筋混凝土弹塑性模型得到基于受压薄膜效应的荷载-挠度全曲线。利用经典的挠曲线微分方程并引入抗弯刚度软化系数对挠度进行修正,结合能量原理推导出大变形条件下基于受拉薄膜效应的RC板极限抗力,进一步得到考虑压-拉薄膜效应的荷载-挠度全曲线。计算结果表明,考虑压-拉薄膜效应的RC板极限抗力分析方法可以更合理地预测荷载-挠度全过程,计算结果与相关试验吻合良好,为合理评估RC板的极限承载力提供参考。     

钢纤维混凝土梁压、弯组合作用下的承载力分析

钢纤维混凝土开裂后.钢纤维能在开裂面上提供一定的拉应力.这类似钢筋混凝土中受拉钢筋的作用.与钢筋混凝土不同,钢纤维混凝土开裂面上的拉应力随裂缝宽度的增加而逐渐降低.本文通过四点弯曲试验得到钢纤维混凝土梁开裂截面上钢纤维拉应力与裂缝宽度曲线,然后以此为基础对轴力、弯矩组合作用下的钢纤维混凝土梁的承载能力进行分析,得到钢纤维混凝土梁在轴力和裂缝宽度作用下的抗弯承载力计算公式.最后用得到的计算公式做出钢纤维混凝土梁在极限承载状态下的N-M相关曲线.计算分析表明,钢纤维混凝土梁开裂后,开裂面上的应力重分布会使截面的抗弯力臂增大.从而提高截面的抗弯承载力.并且开裂截面的抗弯能力也随轴压力的增大而有明显提高.这就从理论上解释了受压钢纤维梁开裂后的抗弯承载力不但没有降低,反而有所提高的现象.     

预应力连续组合梁负弯矩区抗弯承载力分析

预应力钢-混凝土连续组合梁具有承载力高、变形小等诸多优点,作为一种新型的横向承重构件,在工程中得到了广泛的使用。其负弯矩区承载能力计算与变形分析是其设计的关键,目前规范还是空白。因此,有必要对其刚度、变形及抗弯承载力进行研究。该文基于换算截面法,引入混凝土参与受拉工作的程度系数,确定了组合梁截面抗弯刚度,进而推出了预应力钢-混凝土连续组合梁负弯矩区的弹性抗弯承载力计算公式;基于简化塑性理论,得到了负弯矩区的极限抗弯承载力计算方法;研究表明连续组合梁能够显著提高截面刚度与减少开裂。该文公式计算结果与实测值均吻合较好,满足工程精度要求。     

基于二阶理论的弹性约束变截面悬臂梁刚度与稳定性分析

从计入二阶效应的挠曲微分方程出发,对惯性矩沿轴向二次变化的变截面Bernoulli-Euler梁在弹性约束下的刚度和稳定性进行了分析,推导了在弹性约束下变截面悬臂梁在复合载荷作用下的挠度和稳定性的精确表达式,给出轴向压力引起的挠度影响系数。在极端情况下,该文公式可相应退化为根部固支的变截面梁及等截面梁之刚度与稳定表达式。将该文的计算结果与用ANSYS软件密分单元的计算结果进行分析比较,分析比较结果验证了该文推导的刚度和稳定性表达式的正确性,该文方法可广泛应用于弹性约束下变截面悬臂梁的刚度和稳定性分析。     

带翼缘剪力墙截面曲率分析及延性的计算

通过对非对称截面带翼缘剪力墙的弯矩-曲率分析,分别计算了翼缘受拉和翼缘受压方向的截面屈服曲率和极限曲率,分析了轴压比、纵筋配筋率、腹板竖向分布钢筋配筋率、翼缘宽度与腹板高度比、混凝土强度、配箍特征值、腹板截面高厚比对截面曲率的影响,并结合受压区高度的变化详细阐述了截面曲率随各影响因素的变化规律。通过对4941个工况下计算结果的回归分析,建立了带翼缘剪力墙截面屈服曲率和极限曲率的简化计算公式,并进一步推导了曲率延性和位移延性的计算公式。通过与试验结果的比对,验证了计算公式的准确性。该文公式不仅将翼缘受拉和翼缘受压状态进行了区分,并择取了影响截面曲率的关键因素,可为带翼缘剪力墙的变形能力计算以及基于位移的抗震设计提供依据。     

碳纤维增强压弯构件弹塑性失稳解析解

基于计算压弯构件弹塑性失稳的Je■ek法,推导了在轴压和弯矩共同作用下拉压侧粘贴碳纤维片材后矩形截面柱绕强轴失稳时极限荷载的计算公式,通过与有限元解进行对比,表明该解析解是正确的,它为构件弹塑性屈曲的基础理论研究提供了一个新的分析方法。计算结果表明,构件横截面进入塑性的区域越大,这种碳纤维的增强效果越为明显,可见,表面粘贴碳纤维对提高构件弹塑性极限荷载是十分有效的。     

Moment curvature relationship of reinforced concrete sections under combined bending and normal force

The modelling of tension stiffening effects is important for the verification of serviceability limit states of reinforced or prestressed concrete structures or even for the computation of the stability limit state of particular classes of slender concrete structures (bridge piles, towers, masts, etc.). The case of pure bending has received extensive analytical and experimental consideration, but little attention has been paid, up to now, to the case of combined bending and normal force. A series of tests on rectangular reinforced concrete beams submitted to bending and constant compressive normal force is reported in this paper. The moment-curvature relationships are evaluated and compared with the prediction of two theoretical models. The first model is the CEB model proposed by Favre and Koprna. It is a simplified model which refers to the uncracked and fully cracked stiffnesses in pure bending only. The second model is a proposition made by the authors which takes into account the tension stiffening effects, the variation in position of the neutral axis as a function of the eccentricity of the normal force, and the non-linear behaviour of concrete in compression.     

Neutral axis depth and moment redistribution in FRP and steel reinforced concrete continuous beams

The neutral axis depth is considered the best parameter for quantifying the moment redistribution in continuous concrete beams, as exemplified in various design codes worldwide. It is therefore important to well understand the variation of neutral axis depth against moment redistribution. This paper describes a theoretical investigation into the neutral axis depth and moment redistribution in concrete beams reinforced with fibre reinforced polymer (FRP) and steel bars. A finite element model has been developed. The model predictions are in favourable agreement with experimental results. Three types of reinforcement are considered, namely, glass fibre, carbon fibre and steel. Various levels of reinforcement ratio are used for a parametric evaluation. The results indicate that FRP reinforced concrete continuous beams exhibit significantly different response characteristics regarding the moment redistribution and variation of neutral axis depth from those of steel reinforced ones. In addition, it is found that the code recommendations are generally unsafe for calculating the permissible moment redistribution in FRP reinforced concrete beams, but the neglect of redistribution in such beams may be overconservative.     

Stress analysis of functionally gradient beam using effective principal axes

The mechanical model is established for the functionally gradient material (FGM) beam with rectangular cross section. A new method of effective principal axes is put forth, based on which the normal stress formula is derived for the FGM beam. The method is verified to be correct by the retrogression of it to the centroidal principal axes method of the traditional beam made of homogeneous elastic material. For several different loading cases, the␣effects of the non-homogeneity parameter on the distribution of the normal stress and on the position of the neutral axis are discussed. It is indicated that, with the increase of the absolute value of the non-homogeneity parameter, the normal stress at the more rigid region in the cross section increases, the normal stress at the less rigid region decreases, and the neutral axis moves toward the more rigid region.     

Effective Tension Active Cross-Section of Reinforced Concrete Beams After Cracking

In the design of concrete structures, estimation of the deflection of the structural members under the service loads is often a critical factor. Strains and displacements are linked to the tension stiffening effect, which is not quantified in the standards. The CEB-FIP model code proposes an interesting simplified method for evaluating the concrete tension stiffening effect on reinforced concrete behavior. One of the parameters which enables the mechanical contribution of the concrete to be quantified is the effective tensile active section of the reinforced concrete beams. In this paper, a new method for calculating the effective tensile active section A _ct.ef is proposed. The calculation is based on an analytical model of stress distribution in the full depth of the concrete section. An experimental study on several reinforced concrete beams is reported. The results show that the new proposed model enhances the accuracy of the beam deflection predictions significantly.     

An elasticity solution of functionally graded beams with different moduli in tension and compression

In this study, we analytically solved the problem of a functionally graded beam with different moduli in tension and compression under the action of uniformly distributed loads. By determining the location of the unknown neutral layer of the beam, we first established a simplified mechanical model based on complete partition of tension and compression. Using boundary conditions and continuity conditions of the neutral layer, we obtained an elasticity solution of the problem, in which grade functions of tensile and compressive moduli of elasticity are assumed to be two different exponential expressions while Poisson's ratio is unchanged. The numerical results and comparison also verified the validity of the analytical solution. By changing the grade parameters of the material, the stress and displacement of the beam in three cases, i.e., the tensile modulus is greater than, equal to, or less than the compressive modulus, are discussed, respectively. The result shows that due to the introduction of bimodular effect and functional grade of materials, the maximum tensile and compressive bending stresses may not take place at the bottom and top of the beam, which should be given more attention in the analysis and design of structures made of functionally graded materials with bimodular effect.     

Timoshenko阻尼转轴的涡动不平衡响应

考虑系统的质量不平衡和材料的阻尼作用，应用Timoshenko梁理论和Hamilton原理，建立转轴的空间运动方程，它包含了剪切变形、旋转惯性、陀螺效应、动不平衡和内粘性阻尼与材料迟滞阻尼的影响。数值分析了系统的动力学响应和特性，由不平衡质量产生的强迫振动和材料阻尼引起的自激振动导致转轴产生复杂的涡动变形。     

大曲率圆弧深拱平面弹性稳定分析

大曲率拱中,截面形心轴与中性轴不重合,其截面抗弯惯性矩与不考虑曲率影响的截面面积二阶矩有一定的差别;当截面尺寸相对拱弧长来说较大时,此时拱为深拱,剪切变形的影响不能忽略。基于此认识,提出了考虑曲率、剪切变形影响的深拱平面弹性稳定分析方法,讨论了圆弧拱在径向均布荷载作用下的面内稳定问题,导出了临界荷载计算公式,比较了不同理论结果的差别,给出了弹性失稳与塑性屈曲的临界系数和临界圆心角,得出了一些重要结论。     

钢筋活性粉末混凝土简支梁受弯力学性能试验与计算

活性粉末混凝土（RPC）与普通混凝土（OC）相比,具有超高的强度、高韧性和优异的耐久性,其构件承载力与刚度计算方法必然不同于普通混凝土构件。该文对4根钢筋活性粉末混凝土简支梁开展受弯性能足尺试验,获得了梁的开裂弯矩、极限弯矩及荷载-跨中位移曲线,揭示了RPC简支梁受弯变形特征与破坏模式,推导了钢筋RPC简支梁的开裂弯矩与正截面受弯承载力计算公式。结果表明：钢纤维RPC极限压应变为4394 με~5200 με,开裂应变为690 με~820 με,均远大于普通混凝土;由于添加了钢纤维,公式推导时必须考虑RPC拉区拉应力的影响,推导所得开裂弯矩、正截面受弯承载力及刚度公式计算值与试验值吻合较好,计算公式具有较高的精度,可用于钢筋RPC梁的设计计算。