钢筋混凝土细长柱结构精细化分析模型及动力二阶效应研究
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摘要
当结构承受竖向荷载时,已变形的结构或杆件中会产生P-Δ和P -δ两类二阶效应。人们对细长柱的静力二阶效应研究较多,但对动力二阶效应的研究则相对较少,且大都限于P-Δ效应的研究。本文针对钢筋混凝土细长柱精细化模型和动力二阶效应进行了一些探讨和研究,主要内容如下。
论文基于柔度法理论和纤维模型,建立了能精确考虑P-Δ效应和P -δ效应的新单元模型,且实现了P-Δ效应和P -δ效应的分离计算,从而为采用同一单元模式研究动力二阶效应规律及P -δ效应对P-Δ效应的影响提供了可能。通过数值验证和对比分析,该精细化分析模型准确、高效。
建立了考虑梁柱节点剪切变形的拉—压杆模型,提出了考虑梁柱节点核心区剪切变形的新方法,该方法能全面反映梁柱节点区的受力机理。通过与试验结果及其他方法得到的节点核心区剪应力应变关系曲线进行对比,本论文提出的定参方法与试验结果更接近。
在单质点体系的动力二阶效应研究部分,本论文首先推导了同时考虑P-Δ和P -δ效应的侧向刚度折减系数计算公式;提出了考虑动力二阶效应的通用反应谱法和规范反应谱法,通过数值计算,验证了理论公式的可靠性和准确度;同时,分析了P -δ效应在静力和动力分析下在整体二阶效应中所占的比重,明确了动力二阶效应与静力二阶效应的区别及影响因素,除稳定系数外,结构周期和地震动的频谱特性等都对动力二阶效应有显著影响;论文将竖向地震动对结构水平响应的影响视为变轴力对水平地震响应的影响,建立了在水平和竖向地震动同时作用下考虑结构二阶效应的运动方程,通过参数分析明确了竖向地震动对动力二阶效应的影响因素;论文研究了不同非线性程度引起的动力二阶效应大小,分析了材料非线性对结构动力二阶效应的影响,探讨了采用折减刚度来考虑材料非线性影响的可能性;最后,本论文还设计了5组试件,完成了不考虑和考虑二阶效应的静力推覆试验、单独水平地震作用和水平、竖向地震同时作用下的振动台试验,通过对试验结果的分析,验证了理论公式的准确性。
在多质点体系的动力二阶效应研究部分,针对现有程序和规范中考虑结构二阶效应的方法,分析了其存在的问题,特别是对考虑二阶效应的等效水平力方法和“虚柱法”进行了讨论;本论文从理论上说明了无论静力还是动力分析,都可以采用虚柱法来近似地考虑剪切型或弯曲型结构的P—Δ效应;并提出了两种考虑动力二阶效应的简化方法(振型分解反应谱法和底部剪力法),与数值计算结果对比表明,这两种方法是可行的和合理的。
Under vertical loading, two categories of second-order effects exist in deformed structure, i.e. P -Δeffect and P -δeffect. There are many studies on static second-order effects; however, the researches towards dynamic second-order effects are less concerned, in addition, the related studies are limited to P -Δeffect aspect. This paper has inquired into the refined analysis models of RC slender column structure and dynamic second-order effects. The main contents are as follow.
According to flexibility method theory method and fiber model, a new refined model has been established, which not only accurately evaluates P -Δeffect and P -δeffect but also realizes separate calculations of them. As a result, it is entirely possible to study on the law of dynamic second-order effects and the influence from P -δeffect on P -Δeffect through using same element model. And the refined model is proved accurate and efficient by numerical validation and comparative analysis.
The strut-and-tie model has been introduced due to the shear deformation of beam-column joint, and a new method has been put forward which shows the transferring shear force mechanism of beam-column joint core. The paper has compared the shear stress-strain relationship curves of beam-column joint core resulted from other methods with those from experimental results, it finds that the results based on the new method is more closed to the experimental results.
In the part of studies on the dynamic second-order effects of SDOF system are carried out step by step: firstly, in the light of structures’P -Δeffect and P -δeffect, the calculation formula for reduction coefficient of lateral stiffiness is deduced under horizontal earthquake loading. Based on these, the formulas of general and standard response spectrum with dynamic second-order effects were offered, the reliability and accuracy of theoretical formula were validated by numerical calculation. Secondly, the proportion of P -δeffect accounts for second-order effects is achieved through static and dynamic analyses, the distinction between static and dynamic second-order effects and the factors influencing the two are confirmed, and structural period and frequency spectrum characteristic of ground motion have significant impacts on the two except stability factors. Thirdly, the impact of vertical ground motion on structures’horizontal response is regarded as that of varied-axial-force on horizontal seismic response in this paper, the motion equation in which structural second-order effects is counted has been established as horizontal and vertical earquake take effect simultaneously, the factors of vertical ground motions influencing structural dynamic second-order effecs have been figured out by parametric analysis. Fourthly, the different degrees of material nonlinear on dynamic second-order effects were investigated; furthermore, the possibility of adopting stiffness reduction to assess the impact of material nonlinear was discussed. Finally, 5 groups of specimens have been designed; plate loading test with and without second-order effects and shaking table test under horizontal earquake or horizontal and vertical earthquake in combination have been completed, the results indicate that the methods for considering the dynamic second-order effects are appropriate and accurate.
In the part of study on dynamic P -Δeffect of MDOF system, the problems existing in the methods of designed programs and criterions considering P -Δeffect are analyzed, particularly, the method of equivalent horizontal force regarding second-order effect and“fictitious column”method are discussed. This paper is theoretically showed that the fictitious column method can be used to calculate the P -Δeffect of shearing and flexural structure approximately in static and dynamic analyses; moreover, the two simplified methods with P -Δeffect were presented: modal analysis response spectrum method and equivalent base shear method, the two methods are proved practical and reasonable by comparing the calculated numerical results.
论文基于柔度法理论和纤维模型,建立了能精确考虑P-Δ效应和P -δ效应的新单元模型,且实现了P-Δ效应和P -δ效应的分离计算,从而为采用同一单元模式研究动力二阶效应规律及P -δ效应对P-Δ效应的影响提供了可能。通过数值验证和对比分析,该精细化分析模型准确、高效。
建立了考虑梁柱节点剪切变形的拉—压杆模型,提出了考虑梁柱节点核心区剪切变形的新方法,该方法能全面反映梁柱节点区的受力机理。通过与试验结果及其他方法得到的节点核心区剪应力应变关系曲线进行对比,本论文提出的定参方法与试验结果更接近。
在单质点体系的动力二阶效应研究部分,本论文首先推导了同时考虑P-Δ和P -δ效应的侧向刚度折减系数计算公式;提出了考虑动力二阶效应的通用反应谱法和规范反应谱法,通过数值计算,验证了理论公式的可靠性和准确度;同时,分析了P -δ效应在静力和动力分析下在整体二阶效应中所占的比重,明确了动力二阶效应与静力二阶效应的区别及影响因素,除稳定系数外,结构周期和地震动的频谱特性等都对动力二阶效应有显著影响;论文将竖向地震动对结构水平响应的影响视为变轴力对水平地震响应的影响,建立了在水平和竖向地震动同时作用下考虑结构二阶效应的运动方程,通过参数分析明确了竖向地震动对动力二阶效应的影响因素;论文研究了不同非线性程度引起的动力二阶效应大小,分析了材料非线性对结构动力二阶效应的影响,探讨了采用折减刚度来考虑材料非线性影响的可能性;最后,本论文还设计了5组试件,完成了不考虑和考虑二阶效应的静力推覆试验、单独水平地震作用和水平、竖向地震同时作用下的振动台试验,通过对试验结果的分析,验证了理论公式的准确性。
在多质点体系的动力二阶效应研究部分,针对现有程序和规范中考虑结构二阶效应的方法,分析了其存在的问题,特别是对考虑二阶效应的等效水平力方法和“虚柱法”进行了讨论;本论文从理论上说明了无论静力还是动力分析,都可以采用虚柱法来近似地考虑剪切型或弯曲型结构的P—Δ效应;并提出了两种考虑动力二阶效应的简化方法(振型分解反应谱法和底部剪力法),与数值计算结果对比表明,这两种方法是可行的和合理的。
Under vertical loading, two categories of second-order effects exist in deformed structure, i.e. P -Δeffect and P -δeffect. There are many studies on static second-order effects; however, the researches towards dynamic second-order effects are less concerned, in addition, the related studies are limited to P -Δeffect aspect. This paper has inquired into the refined analysis models of RC slender column structure and dynamic second-order effects. The main contents are as follow.
According to flexibility method theory method and fiber model, a new refined model has been established, which not only accurately evaluates P -Δeffect and P -δeffect but also realizes separate calculations of them. As a result, it is entirely possible to study on the law of dynamic second-order effects and the influence from P -δeffect on P -Δeffect through using same element model. And the refined model is proved accurate and efficient by numerical validation and comparative analysis.
The strut-and-tie model has been introduced due to the shear deformation of beam-column joint, and a new method has been put forward which shows the transferring shear force mechanism of beam-column joint core. The paper has compared the shear stress-strain relationship curves of beam-column joint core resulted from other methods with those from experimental results, it finds that the results based on the new method is more closed to the experimental results.
In the part of studies on the dynamic second-order effects of SDOF system are carried out step by step: firstly, in the light of structures’P -Δeffect and P -δeffect, the calculation formula for reduction coefficient of lateral stiffiness is deduced under horizontal earthquake loading. Based on these, the formulas of general and standard response spectrum with dynamic second-order effects were offered, the reliability and accuracy of theoretical formula were validated by numerical calculation. Secondly, the proportion of P -δeffect accounts for second-order effects is achieved through static and dynamic analyses, the distinction between static and dynamic second-order effects and the factors influencing the two are confirmed, and structural period and frequency spectrum characteristic of ground motion have significant impacts on the two except stability factors. Thirdly, the impact of vertical ground motion on structures’horizontal response is regarded as that of varied-axial-force on horizontal seismic response in this paper, the motion equation in which structural second-order effects is counted has been established as horizontal and vertical earquake take effect simultaneously, the factors of vertical ground motions influencing structural dynamic second-order effecs have been figured out by parametric analysis. Fourthly, the different degrees of material nonlinear on dynamic second-order effects were investigated; furthermore, the possibility of adopting stiffness reduction to assess the impact of material nonlinear was discussed. Finally, 5 groups of specimens have been designed; plate loading test with and without second-order effects and shaking table test under horizontal earquake or horizontal and vertical earthquake in combination have been completed, the results indicate that the methods for considering the dynamic second-order effects are appropriate and accurate.
In the part of study on dynamic P -Δeffect of MDOF system, the problems existing in the methods of designed programs and criterions considering P -Δeffect are analyzed, particularly, the method of equivalent horizontal force regarding second-order effect and“fictitious column”method are discussed. This paper is theoretically showed that the fictitious column method can be used to calculate the P -Δeffect of shearing and flexural structure approximately in static and dynamic analyses; moreover, the two simplified methods with P -Δeffect were presented: modal analysis response spectrum method and equivalent base shear method, the two methods are proved practical and reasonable by comparing the calculated numerical results.
引文
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