钢筋混凝土框架结构层刚度比限制方法研究
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摘要
众所周知,结构抗震性能的好坏,除取决于总体的承载力、变形和耗能能力外,还与结构是否存在局部的抗震薄弱部位关系甚大。结构薄弱部位的形成,往往是由于刚度突变和屈服强度比突变所造成的。
框架结构某个楼层层高的突然增大,往往会引起刚度和承载力的突变,导致该楼层区域的应力剧增和塑性变形集中,甚至严重破坏或倒塌。本文主要是研究钢筋混凝土框架结构由于层高变化引起结构竖向刚度突变的规律及其对抗震性能的影响,并提出框架结构楼层侧向刚度比限制方法的建议。
论文对目前存在的有关结构楼层侧向刚度比计算的三种方法进行了分析、对比,分别在建筑的底部、中部和上部等不同部位变化楼层层高,设计了九个结构算例,进行了多遇地震作用下的弹性计算、罕遇地震作用下的静力弹塑性分析和动力弹塑性时程分析。
考虑到实际工程中结构层高在底层变化的情况较多,本文共进行了三个10层框架结构振动台模型试验,这三个模型的原形结构底层层高分别是5.4m、6.8m、7.8m,二～十层层高均为3.6m,按1:10几何缩尺比例设计。模型一、二、三的竖向配重分别为500.78kN、511.72kN和517.82kN,在重力荷载作用下的应力、应变与实际结构相近,输入地震波加速度峰值1:1。为了全而、直观地认识层高不同变化引起楼层侧向刚度突变的框架结构在地震作用下的反应特征、破坏形态和破坏机理,本次试验模型一、二共进行了单向地震输入的动力反应测试和双向地震输入的倒塌两个阶段试验,模型三因在单向地震作用下已经破坏,故只进行了一个阶段试验。
通过详细计算分析,特别是三个振动台模型试验的研究,取得了以下创新性的研究成果:
1)首次通过振动台模型试验研究及计算分析表明:钢筋混凝土框架结构应采用楼层剪力和层间位移比方法限制楼层侧向刚度比,以避免结构在强震作用下出现软弱层造成该楼层整体破坏甚至倒塌;若采用层间位移角比法或等效剪切刚度比法限制楼层侧向刚度比,对于因楼层层高突变引起的框架结构侧向刚度突变情况是偏于不安全的,不能有效地防止结构在强震作用下出现软弱层。
2)在国内首次进行了钢筋混凝土框架结构振动台模型在双向地震作用下的倒塌试验,获得了按规范设计的钢筋混凝土框架结构在强震作用下的抗震性能及破坏、倒塌模式。
3)当钢筋混凝土框架结构楼层侧向刚度比按楼层剪力和层间位移比法计算不满足规范限值时,为避免罕遇地震作用下结构软弱层发生严重的塑性变形集中,应提高该软弱层的承载能力。现行规范规定将薄弱层地震剪力乘以1.15的增大系数。本文研究表明,在某些情况下乘以1.15的增大系数是不能避免结构在罕遇地震作用下发生塑性变形集中。当结构薄弱层屈服强度系数小于其相邻上、下楼层屈服强度系数平均值的65%时,应乘以≥1.25的增大系数,或直接提高该薄弱层屈服强度,使该层屈服强度系数不小于其相邻上、下楼层屈服强度系数平均值的80%。
4)楼层屈服强度系数ξ_y反映了结构中楼层受剪承载力与按罕遇地震作用标准值计算的楼层弹性地震剪力的相对关系,是影响结构弹塑性变形的主要因素,结构弹塑性层间位移主要取决于楼层屈服强度系数的大小及其沿房屋高度的分布情况。对于ξ_y沿房屋高度分布不均匀的结构,ξ_y最小或相对较小的楼层在罕遇地震作用下往往率先屈服,并出现较大的弹塑性层间位移,其他各层的层间位移则相对较小。
5)按国家现行有关规范要求设计的钢筋混凝土框架结构,梁端负弯矩承载力计算时应考虑有效翼缘宽度范围内的楼板与梁协同工作,控制梁、柱相对刚度比(模型一是1:4.1)和梁的截面尺寸不能过大,同时要求结构楼层侧向刚度比满足限制条件,最终结构是可以设计成梁铰屈服机制(整体屈服机制)的。
6)对于竖向刚度不规则的钢筋混凝土框架结构,进行弹性设计时,有时仅进行振型分解反应谱法计算是不够的,还应采用弹性时程法进行补充验算。
It is well known that the structure's seismic behavior depends on the total bearing capacity, deformation and dissipation energy capacity,it also has great relationship with the existence of the partial weakness position.The formation of the structure's weakness position always due to the discontinuity of stiffness and the yield strength ratio.
The enlargement of the storey height of a frame structure can lead to the discontinuity of stiffness and bearing capacity, it may cause the stress of the storey increased and the plastic deformation concentrated, or even destroyed or collapsed.In this article,the author focused on the discipline of vertical stiffness sudden change and the influence on seismic behavior which due to the change of storey height in a reinforced concrete frame structure, and also give suggestions on controlling methods of storey lateral stiffness ratio in frame structure.
The article analyses and compares the three ways on the calculations of storey lateral stiffness ratio that existed.It designed nine structural models according to the bottom, centeral and upper parts with various storey height.These examples are designed to evaluate the seismic performance of buildings based on the elastic calculation under frequent earthquake, the static ealstoplastic analysis and dynamic elastoplastic time-history analysis under rare earthquake.
In consideration of the complexity of the change in first storey height in in real construction cases, we did three tests of ten-storey frame structure shaking table model, the bottom storey height of the prototype of the three models are 5.4m,6.8m,7.8m. the storey height from 2 to 10 are all 3.6m, and was designed under the scale of 1:10. The vertical additional weight of Model 1,2,3 are 500.78kN、511.72kN and 517.82kN respectively, the stress and strain under gravity load is close to the actual structure, the input peak acceleration of earthquake wave is 1:1. In order to have a clear and general knowledge of the characteristic of earthquake response, fracture morphology and failure mechanism under earthquakes in frame structure which has sudden change in lateral stiffness due to the change of storey height, Model 1 and 2 conducted two stages to test the dynamic response under uni-directional seismic input and the collapse under bi-direction seismic input. Due to the the damage of model 3 under the uni-directional earthquake,model 3 only conducted one stage test.
Through detailed calculations and analysis, especiallly on the three tests of shaking table model, We get the following creative results.
1. Based on the calculation and analysis of the shaking table tests, it proved that we should use storey shear and the inter-storey drift ratio to impose restrictions on storey lateral stiffness ratio of the reinforced concrete frame structure,to avoid emerging soft storey or even the whole storey's damage or collapse under severe earthquake; The adaption of inter-story drift angle ratio and equivalent shear stiffness ratio to control the storey lateral stiffness ratio is not safe in condition of the sudden changes of lateral rigidity in frame structure due to the changes of storey height. It can't prevent the soft storey under strong shock.
2. The first nationwide collapse experiment of the reinforced concrete frame structure shaking table model under bidirection earthquake action shows themodels of earthquake resistance, damage and collapse of reinforced concrete frame structure under strong shocks directly.
3. When the results of storey lateral stiffness ratio of the in reinforced concrete frame structure calculated by the method of storey shear and storey displacement ratio are not in the range of the limited value, it is necessary to enhance the bearing capacity of the soft storey to avoid causing serious plastic deformation concentration under rare earthquake action. The present standard stipuated of the earthquake shear of soft storey is multiplied by 1.15. In this article, it indicated that in certain circumstances, multiplied by the amplification factors of 1.15 can not avoid plastic deformation concentration in the condition of rare earthquake. When the yield strength coefficient of structure's soft storey is smaller than that of its neighboring storey mean value 65%, we should multiply the amplification coefficient which is equal or bigger than 1.25 or enhance the yield strength of the soft storey directly to make sure that the yield strength coefficient is not smaller than its neighboring storey mean value 80%.
4. Storey yield strength coefficientξ_y reflects the relative relationship between the shearbearing capacity and the elastic seismic shears of the storey under rare earthquake actions. It is the main factor of the effection on the eastoplastic deformation in structure. The structure's elastoplastic story displacement is mainly depends on the storey yield strength coefficient and the distribution of along the building's height. Regarding the structure which it'sξ_y distributesnon-uniformed, itsξ_y is the storey which has the smallestξ_y or relatively smaller always takethe lead to yield and present big elastoplasticity storey displacement under rare earthquake actions, the storey displacements of others are relatively smaller.
5. For the reinforced concrete frame structure, when it is designed according to the national present code, the computation of the moment bearing capacity at the end of beam should take the teamwork of the floor of effective flange width scope and the beam into consideration, If we take the control of the beam-to-column stiffness ratio (model 1 is 1: 4.1) and make sure the cross section of the beam is not too big, with the storey lateral stiffness ratio in the limitation ranges.it is possible to be designed into the mechanisms of beam's plastic hingle yielding( the mechanisms of overall yielding).
6. For the reinforced concrete frame structure with irregularity of vertical stiffness, when it comes to the elastic design, it is not enough to use the method of response spectrum only, using the elastic time-history method to check the calculation is necessary in some cases.
框架结构某个楼层层高的突然增大,往往会引起刚度和承载力的突变,导致该楼层区域的应力剧增和塑性变形集中,甚至严重破坏或倒塌。本文主要是研究钢筋混凝土框架结构由于层高变化引起结构竖向刚度突变的规律及其对抗震性能的影响,并提出框架结构楼层侧向刚度比限制方法的建议。
论文对目前存在的有关结构楼层侧向刚度比计算的三种方法进行了分析、对比,分别在建筑的底部、中部和上部等不同部位变化楼层层高,设计了九个结构算例,进行了多遇地震作用下的弹性计算、罕遇地震作用下的静力弹塑性分析和动力弹塑性时程分析。
考虑到实际工程中结构层高在底层变化的情况较多,本文共进行了三个10层框架结构振动台模型试验,这三个模型的原形结构底层层高分别是5.4m、6.8m、7.8m,二～十层层高均为3.6m,按1:10几何缩尺比例设计。模型一、二、三的竖向配重分别为500.78kN、511.72kN和517.82kN,在重力荷载作用下的应力、应变与实际结构相近,输入地震波加速度峰值1:1。为了全而、直观地认识层高不同变化引起楼层侧向刚度突变的框架结构在地震作用下的反应特征、破坏形态和破坏机理,本次试验模型一、二共进行了单向地震输入的动力反应测试和双向地震输入的倒塌两个阶段试验,模型三因在单向地震作用下已经破坏,故只进行了一个阶段试验。
通过详细计算分析,特别是三个振动台模型试验的研究,取得了以下创新性的研究成果:
1)首次通过振动台模型试验研究及计算分析表明:钢筋混凝土框架结构应采用楼层剪力和层间位移比方法限制楼层侧向刚度比,以避免结构在强震作用下出现软弱层造成该楼层整体破坏甚至倒塌;若采用层间位移角比法或等效剪切刚度比法限制楼层侧向刚度比,对于因楼层层高突变引起的框架结构侧向刚度突变情况是偏于不安全的,不能有效地防止结构在强震作用下出现软弱层。
2)在国内首次进行了钢筋混凝土框架结构振动台模型在双向地震作用下的倒塌试验,获得了按规范设计的钢筋混凝土框架结构在强震作用下的抗震性能及破坏、倒塌模式。
3)当钢筋混凝土框架结构楼层侧向刚度比按楼层剪力和层间位移比法计算不满足规范限值时,为避免罕遇地震作用下结构软弱层发生严重的塑性变形集中,应提高该软弱层的承载能力。现行规范规定将薄弱层地震剪力乘以1.15的增大系数。本文研究表明,在某些情况下乘以1.15的增大系数是不能避免结构在罕遇地震作用下发生塑性变形集中。当结构薄弱层屈服强度系数小于其相邻上、下楼层屈服强度系数平均值的65%时,应乘以≥1.25的增大系数,或直接提高该薄弱层屈服强度,使该层屈服强度系数不小于其相邻上、下楼层屈服强度系数平均值的80%。
4)楼层屈服强度系数ξ_y反映了结构中楼层受剪承载力与按罕遇地震作用标准值计算的楼层弹性地震剪力的相对关系,是影响结构弹塑性变形的主要因素,结构弹塑性层间位移主要取决于楼层屈服强度系数的大小及其沿房屋高度的分布情况。对于ξ_y沿房屋高度分布不均匀的结构,ξ_y最小或相对较小的楼层在罕遇地震作用下往往率先屈服,并出现较大的弹塑性层间位移,其他各层的层间位移则相对较小。
5)按国家现行有关规范要求设计的钢筋混凝土框架结构,梁端负弯矩承载力计算时应考虑有效翼缘宽度范围内的楼板与梁协同工作,控制梁、柱相对刚度比(模型一是1:4.1)和梁的截面尺寸不能过大,同时要求结构楼层侧向刚度比满足限制条件,最终结构是可以设计成梁铰屈服机制(整体屈服机制)的。
6)对于竖向刚度不规则的钢筋混凝土框架结构,进行弹性设计时,有时仅进行振型分解反应谱法计算是不够的,还应采用弹性时程法进行补充验算。
It is well known that the structure's seismic behavior depends on the total bearing capacity, deformation and dissipation energy capacity,it also has great relationship with the existence of the partial weakness position.The formation of the structure's weakness position always due to the discontinuity of stiffness and the yield strength ratio.
The enlargement of the storey height of a frame structure can lead to the discontinuity of stiffness and bearing capacity, it may cause the stress of the storey increased and the plastic deformation concentrated, or even destroyed or collapsed.In this article,the author focused on the discipline of vertical stiffness sudden change and the influence on seismic behavior which due to the change of storey height in a reinforced concrete frame structure, and also give suggestions on controlling methods of storey lateral stiffness ratio in frame structure.
The article analyses and compares the three ways on the calculations of storey lateral stiffness ratio that existed.It designed nine structural models according to the bottom, centeral and upper parts with various storey height.These examples are designed to evaluate the seismic performance of buildings based on the elastic calculation under frequent earthquake, the static ealstoplastic analysis and dynamic elastoplastic time-history analysis under rare earthquake.
In consideration of the complexity of the change in first storey height in in real construction cases, we did three tests of ten-storey frame structure shaking table model, the bottom storey height of the prototype of the three models are 5.4m,6.8m,7.8m. the storey height from 2 to 10 are all 3.6m, and was designed under the scale of 1:10. The vertical additional weight of Model 1,2,3 are 500.78kN、511.72kN and 517.82kN respectively, the stress and strain under gravity load is close to the actual structure, the input peak acceleration of earthquake wave is 1:1. In order to have a clear and general knowledge of the characteristic of earthquake response, fracture morphology and failure mechanism under earthquakes in frame structure which has sudden change in lateral stiffness due to the change of storey height, Model 1 and 2 conducted two stages to test the dynamic response under uni-directional seismic input and the collapse under bi-direction seismic input. Due to the the damage of model 3 under the uni-directional earthquake,model 3 only conducted one stage test.
Through detailed calculations and analysis, especiallly on the three tests of shaking table model, We get the following creative results.
1. Based on the calculation and analysis of the shaking table tests, it proved that we should use storey shear and the inter-storey drift ratio to impose restrictions on storey lateral stiffness ratio of the reinforced concrete frame structure,to avoid emerging soft storey or even the whole storey's damage or collapse under severe earthquake; The adaption of inter-story drift angle ratio and equivalent shear stiffness ratio to control the storey lateral stiffness ratio is not safe in condition of the sudden changes of lateral rigidity in frame structure due to the changes of storey height. It can't prevent the soft storey under strong shock.
2. The first nationwide collapse experiment of the reinforced concrete frame structure shaking table model under bidirection earthquake action shows themodels of earthquake resistance, damage and collapse of reinforced concrete frame structure under strong shocks directly.
3. When the results of storey lateral stiffness ratio of the in reinforced concrete frame structure calculated by the method of storey shear and storey displacement ratio are not in the range of the limited value, it is necessary to enhance the bearing capacity of the soft storey to avoid causing serious plastic deformation concentration under rare earthquake action. The present standard stipuated of the earthquake shear of soft storey is multiplied by 1.15. In this article, it indicated that in certain circumstances, multiplied by the amplification factors of 1.15 can not avoid plastic deformation concentration in the condition of rare earthquake. When the yield strength coefficient of structure's soft storey is smaller than that of its neighboring storey mean value 65%, we should multiply the amplification coefficient which is equal or bigger than 1.25 or enhance the yield strength of the soft storey directly to make sure that the yield strength coefficient is not smaller than its neighboring storey mean value 80%.
4. Storey yield strength coefficientξ_y reflects the relative relationship between the shearbearing capacity and the elastic seismic shears of the storey under rare earthquake actions. It is the main factor of the effection on the eastoplastic deformation in structure. The structure's elastoplastic story displacement is mainly depends on the storey yield strength coefficient and the distribution of along the building's height. Regarding the structure which it'sξ_y distributesnon-uniformed, itsξ_y is the storey which has the smallestξ_y or relatively smaller always takethe lead to yield and present big elastoplasticity storey displacement under rare earthquake actions, the storey displacements of others are relatively smaller.
5. For the reinforced concrete frame structure, when it is designed according to the national present code, the computation of the moment bearing capacity at the end of beam should take the teamwork of the floor of effective flange width scope and the beam into consideration, If we take the control of the beam-to-column stiffness ratio (model 1 is 1: 4.1) and make sure the cross section of the beam is not too big, with the storey lateral stiffness ratio in the limitation ranges.it is possible to be designed into the mechanisms of beam's plastic hingle yielding( the mechanisms of overall yielding).
6. For the reinforced concrete frame structure with irregularity of vertical stiffness, when it comes to the elastic design, it is not enough to use the method of response spectrum only, using the elastic time-history method to check the calculation is necessary in some cases.
引文
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[4-10]MEDHEKAR M S.KENNEDY D J L.Displacement-based seismic design of buildings-theory.Engineering Structures,2000,22:201-209.
[4-11]FAJFAR P.Capacity spectrum method based on inelastic demand spectra Earthquake Engineering and Structural Dynamics,1999,28:979-993.
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[5-1]吕西林.复杂高层建筑结构抗震理论与应用.北京:科学出版社,2007。
[5-2]龚思礼.建筑抗震设计手册.北京:中国建筑工业出版社,2002。
[5-3]闫熙臣,高小旺.钢筋混凝土框架结构抗震评估的新方法.工程抗震与加固改造,2007,29(1):103-105。
[5-4]聂祺.高层钢筋混凝土结构非线性动力时程分析研究。中国建筑科学研究院博士学位论文,2009。
[5-5]Subbaraj K,Dokainish M A.A Survey of Direct Time-Integration Methods In Computational Structural Dynamics.1.Explicit Methods[J].Computer& Structure,1989,32(6):1371-1386.
[5-6]Houboult J C.A Recurrence Matrix Solution for the Dynamic Response of Elastic Aircraft[J].Journal of Aeronaut Science,1950,17:540-550.
[5-7]Newmark N M.A Method of Computation for Structural Dynamics[J].Journal of the Engineering Mechanic Division,1959,85(3):249-260.
[5-8]Wilson E L.A computer program for the dynamic stress analysis of underground structures[R].SESM Report No.68-1,University of California,Berkeley 1968.
[5-9]Hilber H.M,Hughes T J R.,Taylor R L.Improved numerical dissipation for time integration algorithms in structural dynamics[J].Earthquake engineering and structural dynamics,1977,5:283-292.
[5-10]Hilber H.M,Hughes T J R.Collocation,dissipation and "overshoot"for time integration schemes in structural dynamics[J].Earthquake engineering and structural dynamics,1978,6:99-117.
[5-11]Chung J,Hulbert G M.A time integration algorithm for structural dynamics with improved numerical dissipation:The Generalized-α Method[J].Journal of Applied Mechanic,1993,60(2):371-375.
[5-12]钟万勰.结构动力方程的精细时程积分法[J].大连理工大学学报,1994,34(2):131-136.
[5-13]Prestandard and commentary for the seismic rehabilitation of buildings.FEMA356,357,Nov.2000.
[5-14]李志山,容柏生.高层建筑结构件罕遇地震作用下的弹塑性时程分析研究.第十九届全国高层建筑结构学术会议论文,2006。
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[6-2]中华人民共和国行业标准.《建筑抗震试验方法规程》JGJ101-96。
[6-3]尚晓江.高层建筑混合结构弹塑性分析方法及抗震性能的研究.中国建筑科学研究院博士学位论文,2008。
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[7-2]ABAQUS/CAE User's Manual,Version 6.5,2006.
[8-1]高立人,方鄂华,钱稼茹.高层建筑结构概念设计.北京:中国计划出版社,2005。