偏心支撑钢框架的高等分析及基于性能的塑性设计方法研究
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摘要
针对现行钢结构分析与设计方法的不足，强调了钢框架高等分析方法的重要性。偏心支撑钢框架兼顾了纯框架结构和中心支撑钢框架结构的优点，刚度大、延性好，受力性能合理，罕遇地震作用下具有良好的抗震性能。目前对于钢框架高等分析方法的研究很多，但对于偏心支撑钢框架的高等分析方法研究较少。此外，《建筑抗震设计规范》中关于偏心支撑钢框架的规定大多来源于美国规范，对采用我国钢材的耗能梁性能研究较少，不利于准确评估偏心支撑钢框架的性能。
现阶段对于偏心支撑钢框架的设计，先由弹性分析求出基底剪力和各楼层的侧向力，再计算出耗能梁所受的剪力，通过耗能梁的设计原理确定截面的大小；根据耗能梁的内力和规范中的相关放大系数，确定其余构件截面的大小。然而，基于弹性分析所设计的结构，直接运用于罕遇地震下的非弹性分析中，可能无法满足预期的破坏模式和相关规范的要求。
针对以上关于高等分析方法和偏心支撑钢框架所存在的不足，本文研究内容主要包括以下几方面：
（1）基于截面组合法和截面弹簧刚度理论，提出了一种有分布荷载作用时考虑单元跨内塑性铰的钢框架高等分析方法。该方法利用稳定函数考虑几何非线性和剪切变形、在初始屈服方程中考虑残余应力、折减弹性模量法考虑初始缺陷的影响等。此外，当单元上有分布荷载作用时，在可能出现屈服的两端和跨内分别假想有一个零长度的弹簧考虑截面在不同受力时的刚度，得到仅使用一个单元/杆件就能准确模拟跨内塑性铰的钢框架高等分析方法；
（2）基于串联弹簧模型在单元端部同时考虑材料非线性和半刚性连接的影响，并在有分布荷载作用时，提出了一种准确模拟跨内塑性铰的半刚性钢框架的高等分析方法；
（3）现行规范中对翼缘宽厚比的限制过于严格，许多轧制型钢很难作为耗能梁使用。与已有试验对比，校正有限元分析方法的准确性。为了重新评估该值，基于Q235钢材设计70个不同翼缘宽厚比和长度的耗能梁模型，并在往复荷载下进行有限元分析。结果表明，对剪切型耗能梁和弯曲型耗能梁，可考虑将翼缘宽厚比放宽至10235/fy，并得到相应的破坏模式、超强系数及力-位移曲线等；
（4）基于Q235钢材设计50个不同加劲肋间距、厚度和布置方式的耗能梁模型、36个不同轴力作用下的耗能梁模型，通过有限元分析研究往复荷载作用下各种因素对不同长度耗能梁性能的影响，得到了一种耗能梁的优化设计方法；
（5）根据耗能梁有限元分析所得的多线性力-位移曲线，在单元两端分别假定有三个零长度的转动子弹簧和三个零长度的平动子弹簧来模拟弯矩和剪力的影响，中间单元始终处于弹性状态，并结合截面组合法理论所推导的考虑单元应变强化的屈服方程，得到了耗能梁的高等分析模型。此外，基于该模型还考虑了半刚性连接的影响。耗能梁以外构件的分析模型与普通单元的高等分析模型相同，由此提出了偏心支撑钢框架的高等分析方法；
（6）基于预先确定结构在非弹性变形下的目标位移和屈服机理，并结合建筑抗震设计规范，提出了纯框架结构和D型、K型和V型偏心支撑框架基于性能的塑性设计方法。该方法还根据罕遇地震作用下能量平衡原理得到结构的基底剪力和各楼层的剪力值，并考虑耗能折减系数η的影响。分析结果表明，使用该方法对不同抗震设防烈度下的各种结构设计时，无需进行复杂的计算和迭代，就能满足多遇地震及罕遇地震下的预定功能；
（7）根据偏心支撑钢框架基于性能的塑性设计方法，设计某三十层的偏心支撑钢框架，采用基于性能的抗震设计方法对其进行评估。将结构的性能目标选为D，并选择合适的地震波，再根据相关规范确定各构件的性能指标，从层间位移角和构件变形两方面对结构进行评估。
The advantage of advanced analysis method has been emphasized due to the insufficientof current analysis and design method for steel structure. Eccentrically braced frames (EBFs),which combine the advantages of moment resisting frames (MRFs) and concentrically bracedframes (CBFs), can exhibit both adequate ductility and lateral stiffness during rare earthquake.Advanced analysis of steel frames has been a subject of extensive research over the pastdecade, but little research has been done in the EBFs. In the Code for Seismic Design ofBuildings, the design method about EBFs are mainly derived from AISC, few studies focus onthe mechanical properties of links that use Q235or Q345steel, so the performance of links inEBFs can’t be well predicted.
In the current design method of EBFs, the elastic static analysis is utilized to distributebase shear and storey shear force along the height, then shear force and sizes of all the linkshave been obtained, so the other members can be determined by using the links and relativeamplification factors. However, when the structures designed by current elastic static analysisundergo large inelastic deformations under rare earthquakes, the yield mechanisms andinterstory drift may not meet the expected requirements.
According to the current disadvantages of advanced analysis and EBFs, this papercontains following subjects:
(1) Based on the section assemblage concept and section spring stiffness, an advancedanalysis method for steel frames using element with internal plastic hinge is proposed. In theproposed method, the stability function is used to consider the geometric nonlinearity andshear deformation, and the residual stress is considered in the initial yield function. Also, thereduced tangent modulus method is used to consider the influence of initial imperfection. Theelement subjected to distributed loads is derived by assuming a spring with zero-length at theend and internal of an element to consider the cross-sectional stiffness. It is demonstrated thatthe plastic hinge at the internal of the element can be well predicted, based on the proposedmethod, by only using one element per member.
(2) An advanced analysis method for semi-rigid steel frames using element with internal plastic hinge is also proposed. Element with springs-in-series at each end is presented toconsider the effect of semi-rigid connections and material nonlinearity. Based on the proposedmethod, it is demonstrated that internal plastic hinge can be also well predicted by only usingone element for the members subjected to distributed loads.
(3) Flange width-thickness ratio of links is so conservative in the current specificationthat many rolling sections cannot be used as links. In order to reevaluate the value,70linksare conducted to investigate the effect of different flange width-thickness ratio and length,which are all based on the Q235steel. The finite element model, verified by usingexperimental data during cyclic loading, indicates that the flange width-thickness ratio can berelaxed to10235/fy for shear links and flexural links. Also, the failure modes, overstrengthfactors and hysteresis curves can be obtained.
(4)50links are also conducted to investigate the influence of stiffeners spacing,stiffeners thickness and placing on side(s), and36links are designed to consider the effect ofaxial loads. Finite element analysis is used to investigate the influencing factors on therotation capacity of links during cyclic loading. Then an optimum and practical designmethod of links with varying length is proposed.
(5) According to the multilinear force-displacement curves of links obtained by finiteelement analysis, and yield functions derived by using section assemblage concept andaccounting for strain hardening, the advanced analytical model of links is proposed by usingthree rotational subprings and three translational subsprings elements with zero-length,respectively, at each element end to simulate the flexural and shear yielding behavior andstrain hardening effect, and the inner element should be constrained to remain elasticallyunder any condition. Moreover, semi-rigid connection is also considered based on the linksmodel. For the other elements in EBFs, a spring with zero-length is provided at each end toconsider yielding on the cross-sectional level, it is as same as the conventional model. So asimple and practical advanced analysis method for EBFs is proposed.
(6) Based on the pre-selected target drift and yield mechanism under the inelastic seismicbehaviors and the Code for Seismic Design of Buildings, performance-based plastic design (PBSD) methods for moment resisting frame, D-, K-and V-EBF are proposed. In the PBSDmethods, the base shear and lateral force distribution are derived from modified energybalance equation under rare earthquake, and the reduced energy dissipation coefficient η isalso important to the proposed method. Numerical analysis shows that the frames withdifferent seismic precautionary intensity designed by the proposed method can exhibitexpected functions under frequent and rare earthquake without complicated iteration andcalculation.
(7) A30-storey K-EBF designed by the proposed PBPD method is evaluated by theperformance-based seismic design method. The performance objective D is selected for thisEBF, and three earthquake records meet the specification requirement are chosen. Thecomponent performance levels, based on related specifications, are defined to consider theeffect of inelastic deformations. Both interstory drift and component deformations areincluded in the acceptance criteria.
现阶段对于偏心支撑钢框架的设计，先由弹性分析求出基底剪力和各楼层的侧向力，再计算出耗能梁所受的剪力，通过耗能梁的设计原理确定截面的大小；根据耗能梁的内力和规范中的相关放大系数，确定其余构件截面的大小。然而，基于弹性分析所设计的结构，直接运用于罕遇地震下的非弹性分析中，可能无法满足预期的破坏模式和相关规范的要求。
针对以上关于高等分析方法和偏心支撑钢框架所存在的不足，本文研究内容主要包括以下几方面：
（1）基于截面组合法和截面弹簧刚度理论，提出了一种有分布荷载作用时考虑单元跨内塑性铰的钢框架高等分析方法。该方法利用稳定函数考虑几何非线性和剪切变形、在初始屈服方程中考虑残余应力、折减弹性模量法考虑初始缺陷的影响等。此外，当单元上有分布荷载作用时，在可能出现屈服的两端和跨内分别假想有一个零长度的弹簧考虑截面在不同受力时的刚度，得到仅使用一个单元/杆件就能准确模拟跨内塑性铰的钢框架高等分析方法；
（2）基于串联弹簧模型在单元端部同时考虑材料非线性和半刚性连接的影响，并在有分布荷载作用时，提出了一种准确模拟跨内塑性铰的半刚性钢框架的高等分析方法；
（3）现行规范中对翼缘宽厚比的限制过于严格，许多轧制型钢很难作为耗能梁使用。与已有试验对比，校正有限元分析方法的准确性。为了重新评估该值，基于Q235钢材设计70个不同翼缘宽厚比和长度的耗能梁模型，并在往复荷载下进行有限元分析。结果表明，对剪切型耗能梁和弯曲型耗能梁，可考虑将翼缘宽厚比放宽至10235/fy，并得到相应的破坏模式、超强系数及力-位移曲线等；
（4）基于Q235钢材设计50个不同加劲肋间距、厚度和布置方式的耗能梁模型、36个不同轴力作用下的耗能梁模型，通过有限元分析研究往复荷载作用下各种因素对不同长度耗能梁性能的影响，得到了一种耗能梁的优化设计方法；
（5）根据耗能梁有限元分析所得的多线性力-位移曲线，在单元两端分别假定有三个零长度的转动子弹簧和三个零长度的平动子弹簧来模拟弯矩和剪力的影响，中间单元始终处于弹性状态，并结合截面组合法理论所推导的考虑单元应变强化的屈服方程，得到了耗能梁的高等分析模型。此外，基于该模型还考虑了半刚性连接的影响。耗能梁以外构件的分析模型与普通单元的高等分析模型相同，由此提出了偏心支撑钢框架的高等分析方法；
（6）基于预先确定结构在非弹性变形下的目标位移和屈服机理，并结合建筑抗震设计规范，提出了纯框架结构和D型、K型和V型偏心支撑框架基于性能的塑性设计方法。该方法还根据罕遇地震作用下能量平衡原理得到结构的基底剪力和各楼层的剪力值，并考虑耗能折减系数η的影响。分析结果表明，使用该方法对不同抗震设防烈度下的各种结构设计时，无需进行复杂的计算和迭代，就能满足多遇地震及罕遇地震下的预定功能；
（7）根据偏心支撑钢框架基于性能的塑性设计方法，设计某三十层的偏心支撑钢框架，采用基于性能的抗震设计方法对其进行评估。将结构的性能目标选为D，并选择合适的地震波，再根据相关规范确定各构件的性能指标，从层间位移角和构件变形两方面对结构进行评估。
The advantage of advanced analysis method has been emphasized due to the insufficientof current analysis and design method for steel structure. Eccentrically braced frames (EBFs),which combine the advantages of moment resisting frames (MRFs) and concentrically bracedframes (CBFs), can exhibit both adequate ductility and lateral stiffness during rare earthquake.Advanced analysis of steel frames has been a subject of extensive research over the pastdecade, but little research has been done in the EBFs. In the Code for Seismic Design ofBuildings, the design method about EBFs are mainly derived from AISC, few studies focus onthe mechanical properties of links that use Q235or Q345steel, so the performance of links inEBFs can’t be well predicted.
In the current design method of EBFs, the elastic static analysis is utilized to distributebase shear and storey shear force along the height, then shear force and sizes of all the linkshave been obtained, so the other members can be determined by using the links and relativeamplification factors. However, when the structures designed by current elastic static analysisundergo large inelastic deformations under rare earthquakes, the yield mechanisms andinterstory drift may not meet the expected requirements.
According to the current disadvantages of advanced analysis and EBFs, this papercontains following subjects:
(1) Based on the section assemblage concept and section spring stiffness, an advancedanalysis method for steel frames using element with internal plastic hinge is proposed. In theproposed method, the stability function is used to consider the geometric nonlinearity andshear deformation, and the residual stress is considered in the initial yield function. Also, thereduced tangent modulus method is used to consider the influence of initial imperfection. Theelement subjected to distributed loads is derived by assuming a spring with zero-length at theend and internal of an element to consider the cross-sectional stiffness. It is demonstrated thatthe plastic hinge at the internal of the element can be well predicted, based on the proposedmethod, by only using one element per member.
(2) An advanced analysis method for semi-rigid steel frames using element with internal plastic hinge is also proposed. Element with springs-in-series at each end is presented toconsider the effect of semi-rigid connections and material nonlinearity. Based on the proposedmethod, it is demonstrated that internal plastic hinge can be also well predicted by only usingone element for the members subjected to distributed loads.
(3) Flange width-thickness ratio of links is so conservative in the current specificationthat many rolling sections cannot be used as links. In order to reevaluate the value,70linksare conducted to investigate the effect of different flange width-thickness ratio and length,which are all based on the Q235steel. The finite element model, verified by usingexperimental data during cyclic loading, indicates that the flange width-thickness ratio can berelaxed to10235/fy for shear links and flexural links. Also, the failure modes, overstrengthfactors and hysteresis curves can be obtained.
(4)50links are also conducted to investigate the influence of stiffeners spacing,stiffeners thickness and placing on side(s), and36links are designed to consider the effect ofaxial loads. Finite element analysis is used to investigate the influencing factors on therotation capacity of links during cyclic loading. Then an optimum and practical designmethod of links with varying length is proposed.
(5) According to the multilinear force-displacement curves of links obtained by finiteelement analysis, and yield functions derived by using section assemblage concept andaccounting for strain hardening, the advanced analytical model of links is proposed by usingthree rotational subprings and three translational subsprings elements with zero-length,respectively, at each element end to simulate the flexural and shear yielding behavior andstrain hardening effect, and the inner element should be constrained to remain elasticallyunder any condition. Moreover, semi-rigid connection is also considered based on the linksmodel. For the other elements in EBFs, a spring with zero-length is provided at each end toconsider yielding on the cross-sectional level, it is as same as the conventional model. So asimple and practical advanced analysis method for EBFs is proposed.
(6) Based on the pre-selected target drift and yield mechanism under the inelastic seismicbehaviors and the Code for Seismic Design of Buildings, performance-based plastic design (PBSD) methods for moment resisting frame, D-, K-and V-EBF are proposed. In the PBSDmethods, the base shear and lateral force distribution are derived from modified energybalance equation under rare earthquake, and the reduced energy dissipation coefficient η isalso important to the proposed method. Numerical analysis shows that the frames withdifferent seismic precautionary intensity designed by the proposed method can exhibitexpected functions under frequent and rare earthquake without complicated iteration andcalculation.
(7) A30-storey K-EBF designed by the proposed PBPD method is evaluated by theperformance-based seismic design method. The performance objective D is selected for thisEBF, and three earthquake records meet the specification requirement are chosen. Thecomponent performance levels, based on related specifications, are defined to consider theeffect of inelastic deformations. Both interstory drift and component deformations areincluded in the acceptance criteria.
引文
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