双周期标准化的弹塑性反应谱研究
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摘要
首先对考虑P-△效应、承受冲击荷载和简谐荷载作用下单自由度(SDOF)体系的动力响应进行了研究,分析了弹性、安定、塑性荷载作用下不同滞回模型(理想弹塑性滞回模型EPP、双折线弹塑性强化模型ELH、剪切滑移滞回模型SSP和理想双线性弹性模型BI)SDOF体系的能量和位移反应,考察了阻尼、耗能能力和二阶效应对结构反应的影响。结果显示：二阶效应的存在,减小了弹性荷载区间和安定荷载区间,增大了输入能和最大位移,对耗能能力提出更高的要求,其影响是不利的；后期刚度的存在,可以弥补二阶效应带来的不利影响；对于弹性体系,阻尼耗能贡献明显,基本占到总耗能能力的1/2,而在弹塑性体系中,主要的耗能能力来自于滞回耗能,阻尼耗能作用并不大；二阶效应的存在,进一步凸显了滞回耗能的地位。
鉴于结构非线性反应分析的复杂性,各国均用地震力调整系数R对依据弹性反应谱计算的弹性地震力折减来获得弹塑性体系的地震力。本文利用弹塑性动力时程分析程序,对四类场地共计370条地震波作用下的理想弹塑性单自由度体系和剪切型多自由度(MDOF)体系进行分析,获得了不同延性、周期的地震力调整系数,结果显示：横轴采用Tga和TgR标准化的R谱很好地保留了其特征周期处的峰值特性；考虑二阶效应的R谱要小于不考虑二阶效应的R谱；将根据单自由体系获得的R谱直接用于多自由度体系会偏于不安全,可以通过系数RM对其进行相应修正,以适用不同楼层体系(Rμ,MDOF=Rμ,SDOF×RM);RM随楼层数的增加而减小,RM受周期影响。
通过建立弹塑性动力放大系数βμ谱,可以进一步简化弹塑性地震力计算,与利用R调整弹性地震力相比,由于仅需要拟合一个谱,其精度和可信性更高。根据对理想弹塑性单自由度体系的分析,二阶效应对βμ有着明显的影响,大致使地震力增大1+2μθ倍。阻尼比对βμ谱的影响与场地类别关系不大。其中阻尼对弹性βe谱的影响与二阶.效应系数无关,随阻尼比增大,βe值越小；对塑性βμ谱的影响与延性无关,随二阶效应系数增大,阻尼影响增强。阻尼比对βe的影响要大于对βμ的影响,但随着二阶系数的增大,对两者的影响趋近。
根据弹塑性位移放大系数cd谱可较方便地估算结构在地震动作用下的非弹性最大位移,以实现基于性能的抗震设计目标,动力分析的结果表明：长周期结构满足等位移准则；二阶效应的存在会增大弹塑性最大位移,二阶效应越大,影响越大,这种影响在特征周期处最为明显,特别是在TgR处。
曲率延性和位移延性分别从截面和杆件层面反应结构的延性,分析了两个层次延性的关系。对折减系数的研究显示：滞回模型中弹性阶段和后期强化阶段间曲线过渡段的存在能够增大折减系数,特别是延性小时。采用双折线模型来进行分析会偏于安全；基于位移延性的分析结果具有更好的稳定性,在相同计算精度的要求下,对杆件单元划分数的要求也更低。
Dynamic analysis of single-degree-of-freedom (SDOF) systems under impact and harmonic loads considering P-Δeffect are studied. Energy and displacement response of SDOF system under elastic, shakedown and plastic loads are analyzed. The hysteretic models are elastic-perfectly plastic (EPP), elastic-linearly-hardening (ELH), shear-slipped (SSP) and bilinear-elastic (BIL) model. The influence of damping ratio, energy dissipation capacity and P-Δeffect on structural responses are studied. It is found that the P-Δeffect reduces the elastic limit and shakedown loads, and enlarges input energy and maximum displacement. Post yield stiffness ratio can make up for the adverse impact of the P-Δeffect. Damping is very important for elastic system in dissipating energy and almost half of total energy is due to the damping. While for elasto-plastic systems, hysteretic energy plays the most important role, especially when considering P-Δeffect.
Due to the complexity of nonlinear dynamic analysis, the seismic force modification factor R is commonly used to reduce elastic seismic force to get the strength demand. Based on elastic-plastic time-history earthquake analysis of EPP hysteretic SDOF system and MDOF system, total 370 earthquake records belonging to 4 site are used to calculate the structural response. Results indicate that peak feature of R spectra around characteristic periods are well retained with lateral axis being normalized by Tga and TgR. Seismic force modification factors becomes smaller when considering P-Δeffect. Using R of SDOF system for MDOF structure is dangerous. RM factor is introduced to consider MDOF effect (Rμ,MDOF=Rμ,SDOF×RM).RM decreases with increase of the number of stories. RM is presented for different periods.
By using inelastic response spectra, seismic force of elasto-plastic system can be obtained more easily. The direct method has more accuracy than the indirect method. Inelastic response spectra between systems with and without considering P-Δeffect are different. The effects of damping ratio on elastic and inelastic spectra are independent on sites. Elastic spectra decreases with the increase of damping ratio. Damping effects on elastic spectra and inelastic spectra have little relation to P-Δeffect and ductility, respectively. Elastic spectra are more sensitive to damping ratio than inelastic spectra. The influence of damping ratio on inelastic spectra is larger for system considering P-Δeffect.
Inelastic displacement ratio Cd is studied to estimate the maximum inelastic displacement according to the maximum elastic displacement. It is found that the equal displacement rule is applicable for long period region. Maximum inelastic displacement of structure considering the P-Δeffect is larger than those without P-Δeffect. The influence of P-Δeffect is significant for structure with period being equal to characteristic periods, especially when period being equal to TgR.
The relation between sectional ductility and member ductility is studied. Strength reduction factors based on curvature ductility and displacement ductility are analyzed. Curved segment in the moment-curvature relationship between elastic stage and hardening stage is proved to be favorable. The responses can be conservatively predicted using the simple bilinear-elastic model. The results based on displacement ductility are more stable. Larger element number of structures is required to guarantee calculation precision when the analysis is based on curvature ductility than on displacement ductility.
鉴于结构非线性反应分析的复杂性,各国均用地震力调整系数R对依据弹性反应谱计算的弹性地震力折减来获得弹塑性体系的地震力。本文利用弹塑性动力时程分析程序,对四类场地共计370条地震波作用下的理想弹塑性单自由度体系和剪切型多自由度(MDOF)体系进行分析,获得了不同延性、周期的地震力调整系数,结果显示：横轴采用Tga和TgR标准化的R谱很好地保留了其特征周期处的峰值特性；考虑二阶效应的R谱要小于不考虑二阶效应的R谱；将根据单自由体系获得的R谱直接用于多自由度体系会偏于不安全,可以通过系数RM对其进行相应修正,以适用不同楼层体系(Rμ,MDOF=Rμ,SDOF×RM);RM随楼层数的增加而减小,RM受周期影响。
通过建立弹塑性动力放大系数βμ谱,可以进一步简化弹塑性地震力计算,与利用R调整弹性地震力相比,由于仅需要拟合一个谱,其精度和可信性更高。根据对理想弹塑性单自由度体系的分析,二阶效应对βμ有着明显的影响,大致使地震力增大1+2μθ倍。阻尼比对βμ谱的影响与场地类别关系不大。其中阻尼对弹性βe谱的影响与二阶.效应系数无关,随阻尼比增大,βe值越小；对塑性βμ谱的影响与延性无关,随二阶效应系数增大,阻尼影响增强。阻尼比对βe的影响要大于对βμ的影响,但随着二阶系数的增大,对两者的影响趋近。
根据弹塑性位移放大系数cd谱可较方便地估算结构在地震动作用下的非弹性最大位移,以实现基于性能的抗震设计目标,动力分析的结果表明：长周期结构满足等位移准则；二阶效应的存在会增大弹塑性最大位移,二阶效应越大,影响越大,这种影响在特征周期处最为明显,特别是在TgR处。
曲率延性和位移延性分别从截面和杆件层面反应结构的延性,分析了两个层次延性的关系。对折减系数的研究显示：滞回模型中弹性阶段和后期强化阶段间曲线过渡段的存在能够增大折减系数,特别是延性小时。采用双折线模型来进行分析会偏于安全；基于位移延性的分析结果具有更好的稳定性,在相同计算精度的要求下,对杆件单元划分数的要求也更低。
Dynamic analysis of single-degree-of-freedom (SDOF) systems under impact and harmonic loads considering P-Δeffect are studied. Energy and displacement response of SDOF system under elastic, shakedown and plastic loads are analyzed. The hysteretic models are elastic-perfectly plastic (EPP), elastic-linearly-hardening (ELH), shear-slipped (SSP) and bilinear-elastic (BIL) model. The influence of damping ratio, energy dissipation capacity and P-Δeffect on structural responses are studied. It is found that the P-Δeffect reduces the elastic limit and shakedown loads, and enlarges input energy and maximum displacement. Post yield stiffness ratio can make up for the adverse impact of the P-Δeffect. Damping is very important for elastic system in dissipating energy and almost half of total energy is due to the damping. While for elasto-plastic systems, hysteretic energy plays the most important role, especially when considering P-Δeffect.
Due to the complexity of nonlinear dynamic analysis, the seismic force modification factor R is commonly used to reduce elastic seismic force to get the strength demand. Based on elastic-plastic time-history earthquake analysis of EPP hysteretic SDOF system and MDOF system, total 370 earthquake records belonging to 4 site are used to calculate the structural response. Results indicate that peak feature of R spectra around characteristic periods are well retained with lateral axis being normalized by Tga and TgR. Seismic force modification factors becomes smaller when considering P-Δeffect. Using R of SDOF system for MDOF structure is dangerous. RM factor is introduced to consider MDOF effect (Rμ,MDOF=Rμ,SDOF×RM).RM decreases with increase of the number of stories. RM is presented for different periods.
By using inelastic response spectra, seismic force of elasto-plastic system can be obtained more easily. The direct method has more accuracy than the indirect method. Inelastic response spectra between systems with and without considering P-Δeffect are different. The effects of damping ratio on elastic and inelastic spectra are independent on sites. Elastic spectra decreases with the increase of damping ratio. Damping effects on elastic spectra and inelastic spectra have little relation to P-Δeffect and ductility, respectively. Elastic spectra are more sensitive to damping ratio than inelastic spectra. The influence of damping ratio on inelastic spectra is larger for system considering P-Δeffect.
Inelastic displacement ratio Cd is studied to estimate the maximum inelastic displacement according to the maximum elastic displacement. It is found that the equal displacement rule is applicable for long period region. Maximum inelastic displacement of structure considering the P-Δeffect is larger than those without P-Δeffect. The influence of P-Δeffect is significant for structure with period being equal to characteristic periods, especially when period being equal to TgR.
The relation between sectional ductility and member ductility is studied. Strength reduction factors based on curvature ductility and displacement ductility are analyzed. Curved segment in the moment-curvature relationship between elastic stage and hardening stage is proved to be favorable. The responses can be conservatively predicted using the simple bilinear-elastic model. The results based on displacement ductility are more stable. Larger element number of structures is required to guarantee calculation precision when the analysis is based on curvature ductility than on displacement ductility.
引文
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