外挂混凝土墙板对钢框架结构自振周期的影响

2018-09-26 11:31马俊李元齐
湖南大学学报·自然科学版 2018年5期

马俊 李元齐

摘要:外挂混凝土墙板是装配式钢结构建筑、甚至普通钢框架结构建筑的主要围护墙体材料,对结构自振周期的影响不容忽视.在对各国规范中钢框架结构基本自振周期计算方法进行归纳的基础上,基于已有的一栋带蒸压轻质加气混凝土墙板足尺钢框架结构模型试验数据和一栋带预制装配式混凝土墙板钢框架教学楼实测数据,分析了相关规范计算方法的适用性.结果表明,考虑墙体的经验公式对带外挂混凝土墙板钢框架结构自振周期的估计较为准确.基于40栋带外挂混凝土墙板钢框架结构自振周期实测数据,提出了带外挂混凝土墙板钢框架结构自振周期经验公式.公式以结构高度为自变量,基本自振周期为结构高度的幂函数,公式计算结果离散度较小,与实测结果吻合较好,可供设计人员参考.

关键词:钢框架;外挂混凝土墙板;自振周期;经验公式

中图分类号:TU391 文献标志码:A

Effect of Exterior Concrete Wall Panels on Natural Period of

Steel Frame Structures

MA Jun1,2?偉j , LI Yuanqi1

(1. College of Civil Engineering, Tongji University, Shanghai 200092, China;

2. China Construction Eighth Engineering Division Co, Ltd, Shanghai 200122, China)

Abstract: Exterior concrete wall panels are becoming one of the main building envelope materials for steel frame structures in china, and the effect of exterior concrete wall panels on natural period of steel frames should be realized in the design stage. The formulas for fundamental natural period of steel frame buildings in codes of some countries are summarized, and the feasibility of these formulas for steel frames with exterior concrete wall panels is evaluated by comparing the empirical results with the test data of a full-scale steel frame structure with ALC panels and with the field measured data of a steel frame school building with precast concrete wall panels, the results show that empirical formulas considering the effect of wall materials are most reasonable. Based on the field measured natural periods of steel frames with exterior concrete wall panels, the empirical formula for estimating fundamental natural period of steel frame structures with exterior concrete wall panels is put forward. The structural height is adopted as independent variable in the empirical formula, and the fundamental natural period is a power function of the structural height. The results obtained from the empirical formula have little discreteness and agree well with the field measured data. The empirical formula may serve engineering designers as a reference.

Key words: steel frames; exterior concrete wall panel; natural periods; empirical formulas

鋼框架结构自振周期是钢框架结构抗震设计中的重要参数,其取值关系到地震作用、基底剪力等参数的计算.为了满足空间功能分隔和外部围护等建筑功能要求,钢框架建筑中通常具有大量围护墙体材料.墙体的存在增强了钢框架结构的侧向刚度,减小了结构的自振周期[1-2].各国规范在计算钢框架结构自振周期时均考虑了墙体的影响,但在实际应用中,由于墙体材料不同和墙体的安装、布置方式非常灵活,墙体对钢框架自振周期的影响程度很难进行统一描述.

随着我国墙改政策的实施和工业化建筑的推广,外挂混凝土墙板已逐步成为钢框架结构的主要围护墙体材料.外挂混凝土墙板的材料性质和安装方式与传统的填充墙截然不同,对结构自振周期的影响也有别于传统墙体.然而,已有研究主要集中在砖或混凝土砌块砌体填充墙对钢框架结构自振周期的影响,对于采用外挂混凝土墙板的钢框架结构自振周期取值还缺乏相关研究,设计过程中也缺少相关依据[3-4].因此,有必要研究外挂混凝土墙板对钢框架结构自振周期的影响,提出合理的自振周期计算公式.

本文首先对国内外规范中钢框架结构基本自振周期的计算方法进行归纳,随后采用规范中计算方法对已完成的一栋带蒸压轻质加气混凝土墙板足尺钢框架结构试验模型和一栋带预制装配式混凝土墙板钢框架教学楼的基本自振周期进行计算,并将计算结果与试验结果进行对比,分析了规范计算方法对带外挂混凝土墙板钢框架结构的适用性.基于收集到的40栋已有的带外挂混凝土墙板钢框架结构自振周期实测数据,提出了带外挂混凝土墙板钢框架结构基本自振周期经验公式,供设计人员参考.

1 1 规范中钢框架基本自振周期计算方法

国内外规范[5-19]中的钢框架结构基本自振周期计算方法主要包括经验公式法和瑞利公式法.经验公式在实测数据基础上经统计分析后归纳而成,已经包含了墙体影响.根据是否在表达式中明确考虑墙体布置影响,经验公式可分为忽略和考虑墙体布置两类形式.瑞利公式法是基于结构质量和刚度的动力计算方法,计算结果通常需要采用周期折减系数进行修正,以考虑墙体对自振周期的影响.

%1.1 1.1经验公式

1.1.1忽略墙体布置的经验公式

在实测数据基础上,多数规范建议了基于结构特征参数的钢框架结构基本自振周期经验公式.这些经验公式大体上可分为基于结构高度、基于建筑楼层数、基于结构高度和底部宽度三类,部分规范中建议了多个基本自振周期经验公式.

第一类基本自振周期经验公式以钢结构建筑的高度作为自变量.澳大利亚规范[5]、意大利规范[6]、瑞士规范[7]、韩国规范[8]和我国台湾规范[9]中,钢框架结构基本自振周期是结构高度的函数,如下:

T1=αhβ. (1)

式中:T1为结构基本自振周期,s;h为结构高度,m;α和β是经验公式系数,取值根据各国规范有所不同.澳大利亚规范中,α和β分别取为0.137 5和0.75,意大利、瑞士、韓国和我国台湾规范中,钢框架结构的α和β分别取为0.085和0.75.

第二类基本自振周期经验公式以建筑楼层数作为自变量.我国《建筑结构荷载规范》(GB 50009—2012)[10]和《高层民用建筑钢结构技术规程》(JGJ 99—98)[11]中,钢框架结构基本自振周期是建筑楼层数的线性函数,如下所示:

T1=λN. (2)

式中:N是建筑楼层数;λ是经验公式系数.对于高层钢结构建筑,文献[10]中,λ取为0.1~0.15;文献[11]中,λ取为0.1.

第三类基本自振周期经验公式是结构高度和沿作用力方向结构宽度的函数.法国规范[12]、西班牙规范[13]、埃及规范[14]、印度规范[15]中建议了该类经验公式,如下所示,

T1=αhd. (3)

式中:h为结构高度,m;d是沿作用力方向的结构宽度,m;α是经验公式系数.法国规范和西班牙规范中,α取为0.1;埃及和印度规范中,α取为0.09.

国内外规范中的钢框架结构基本自振周期经验公式大致分为以上三类,同时,部分国家规范中建议了多个不同形式的经验公式.

美国ASCE7—10[16]中分别建议了基于结构高度和建筑楼层数的经验公式.当框架结构承担全部地震作用时,可采用基于结构高度的经验公式计算钢框架结构的基本自振周期:

T1=0.0724h0.8. (4)

同时,对于总层数在12层以下且各层层高不小于3 m的钢框架结构,可采用基于建筑楼层数的经验公式计算钢框架结构的基本自振周期:

T1=0.1N. (5)

日本规范[17]中同时建议了基于结构高度和建筑楼层数的经验公式:

T1=(0.02+0.01αh)h, (6)

T1=(0.1±0.03)N. (7)

式(6)中,基本自振周期是结构高度的函数,αh是采用钢结构建造的楼层高度与结构总高度之比.式(7)中,基本自振周期是建筑楼层数的函数,经验公式系数根据墙体和支撑的布置进行调整.

1.1.2考虑墙体布置经验公式

部分国家规范中明确考虑了墙体布置对结构自振周期的影响.欧洲规范[18]和新西兰规范[19]建议采用式(8)~式(11)计算高度在40 m以内的带填充墙的钢框架结构基本自振周期,

T1=Cth0.75, (8)

Ct=0.075/Ac, (9)

Ac=∑[Ai·(0.2+(lwi/h))2]. (10)

式中:Ct是针对填充墙布置的修正系数;Ac是首层填充墙有效面积,m2;Ai是首层第i片填充墙的有效截面积,m2;lwi是沿水平力作用方向填充墙长度,m;h是结构高度,m.同时,墙体长高比lwi/h需小于等于0.9.

欧洲规范和新西兰规范均用修正系数Ct考虑了填充墙布置对结构自振周期的影响.值得注意的是,规范中仅考虑了底层填充墙的影响,对于其余楼层中的填充墙则没有具体考虑.

%1.2 1.2瑞利公式

除了经验公式方法,国内外规范中还推荐使用瑞利公式来计算钢框架结构的基本自振周期.瑞利公式如下所示:

T=2π∑ni=1Wid2ig∑ni=1Fidi. (11)

式中:Wi是第i层的重力荷载,kg;Fi是第i层所受水平力,N;di是相应的第i层弹性变形,m.

为了便于使用,部分规范中给出了简化的瑞利公式.我国《高层民用建筑钢结构技术规程》(JGJ 99—98)针对质量和刚度沿高度分布比较均匀的钢结构建筑,建议了考虑非结构构件影响的简化瑞利公式:

T1=1.7ξTun. (12)

式中:un是将各层重力荷载作为楼层集中水平力后按弹性静力方法计算得到的顶层侧移,m;ξT是考虑非结构构件影响的修正系数,宜取为0.9.

欧洲、新西兰和瑞士规范中给出的简化瑞利公式如下:

T1=2Δ. (13)

式中:Δ是将各层重力荷载作为水平荷载后得到的结构顶点弹性水平位移,m.

日本规范针对质量和刚度分布均匀的结构,建议了基本自振周期的简化瑞利公式:

T1=δ5~δ5.7. (14)

式中:δ是将各层重力荷载作为水平荷载后得到的结构顶点弹性水平位移,cm.δ/5适用于单自由度系统,δ/5.7对应多自由度系统.

瑞利公式基于结构动力计算,考虑了材料性质、构件截面等参数影响.经验公式则基于实测数据,考虑了墙体作用等动力计算中不能考虑的不确定因素.实际应用中,许多国家规范将经验公式计算结果作为基本自振周期上限值,避免地震力设计值过度降低.譬如:美国规范规定基本自振周期取值不得大于经验公式计算值;我国台湾规范规定基本自振周期取值不得大于经验公式值的1.4倍;澳大利亚规范规定基底剪力设计值不得小于根据自振周期经验公式计算值所得基底剪力计算值的80%.

2 2 各国规范基本自振周期计算方法对比

为了分析规范计算方法对带外挂混凝土墙板钢框架结构的适用性,根据规范中建议公式,对已有的一栋带蒸压轻质加气混凝土墙板钢框架结构试验模型和一栋带预制装配式混凝土墙板钢框架教学楼的基本自振周期进行了计算,并将计算结果与试验和实测结果进行对比.

%1.3 2.1带蒸压轻质加气混凝土墙板钢框架结构

2.1.1结构介绍

带蒸压轻质加气混凝土墙板钢框架结构试验模型为日本防灾科学技术研究所完成的足尺4层钢框架结构[20].试验模型如图1所示,结构的标准层平面图及外立面布置如图2所示.钢框架结构X向1跨,Y向2跨,平面尺寸为10 m×6 m,结构总高度为14.375 m,其中底层层高3.875 m,其余楼层层高3.5 m.钢框架结构中框架柱均采用截面为RHS-300×9的方钢管,框架梁截面尺寸见表1.外挂混凝土墙板采用125 mm厚蒸压轻质加气混凝土墙板,墙板在结构的X向两侧和Y向沿B轴一侧满布布置,在Y向沿A轴一侧未布置墙板.蒸压轻质加气混凝土墙板安装方式:采用摇摆工法,墙板通过内置螺栓和导向角钢连接到钢框架,连接构造如图3所示.摇摆工法使墙板具有随动变形性能,墙板能适应主体结构在各种外力作用下的变形.实际工程中,蒸压轻质加气混凝土外挂墙板的连接方式主要有外墙竖装时的摇摆工法、滑动工法、固定工法,以及外墙横装时的摇摆工法和固定工法[21].

该钢框架结构在模拟振动台上进行了不同激励幅度的振动台试验.当输入地震波为5%、10%、12.5%、20%的JR鹰取波时,基于测得的加速度时程数据,采用单输入多输出的ARX模型对该结构的模态参数进行了识别,结构基本自振周期识别结果依次为0.810 4 s、0.820 3 s、0.830 6 s、0.825 8 s[22].对不同激励幅度下的基本自振周期试验结果取平均值,得到钢框架模型的基本自振周期为0.82 s.

2.1.2各国规范基本自振周期计算结果对比

对于忽略墙体经验公式,除澳大利亚规范外,根据其余规范计算得到的基本自振周期计算结果均小于试验值,误差范围约为24%~66%.基于结构高度的经验公式计算结果误差多数在25%左右,但是日本规范的计算结果误差较大,约为48%.基于结构楼层数的基本自振周期计算结果变化范围较大,误差范围为27%~66%.基于结构高度和底部宽度的经验公式计算结果误差分别为36%和29%.值得注意的是,我国规范中建议的基于建筑楼层数的经验公式误差范围为27%~51%,与试验结果相差偏大.

对于考虑墙体布置经验公式,欧洲规范和新西兰规范的计算结果与试验结果非常接近,误差仅为11%.与忽略墙体经验公式计算结果相比,考虑墙体布置经验公式的计算结果与试验结果更加接近.

对于瑞利公式方法,基于简化瑞利公式的基本自振周期计算结果均大于试验结果.我国《高层民用建筑钢结构技术规程》(JGJ 99—98)中的建议公式由于考虑了非结构构件的影响,修正后的基本自振周期计算结果与试验结果最为接近,但对于修正系数的取值仍需进一步研究.

%1.4 2.2带预制装配式混凝土墙板钢框架教学楼

2.2.1结构介绍

带预制装配式混凝土墙板钢框架教学楼为日本名古屋大学东山校区的IB电子情报馆.建筑外观如图4所示,标准层平面图如图5所示,结构体系为纯钢框架.钢框架结构X向11跨,Y向3跨,平面尺寸60 m×15.2 m,结构总高度41.1 m,建筑楼层数10层.钢框架结构中框架柱采用方钢管,框架梁采用H型钢,截面尺寸见文献[23].外挂混凝土墙板采用150 mm厚预制装配式混凝土墙板,墙板沿结构四周满布布置.

该钢框架教学楼建成后,进行了多次环境激励.基于环境激励下的结构振动加速度,采用随机减量技术对结构模态参数进行了识别,结构基本自振周期识别结果为1.0 s[23].

对于忽略墙体经验公式,根据规范计算得到的基本自振周期计算结果误差范围为0~123%.基于结构高度的经验公式计算结果误差范围为23%~123%,其中澳大利亚规范的计算结果误差较大,为123%.基于结构楼层数的基本自振周期计算结果误差范围为0%~50%,其中我国规范下限值和美国规范的计算结果与实测结果吻合.基于结构高度和底部宽度的经验公式计算结果误差为5%,与实测结果接近.

对于考虑墙体布置经验公式,欧洲规范和新西兰规范的计算结果与实测结果一致,较好地预测了钢框架教学楼的基本自振周期.

对于瑞利公式方法,基于简化瑞利公式的基本自振周期计算结果大于实测结果.我国《高层民用建筑钢结构技术规程》(JGJ 99—98)中的建議公式考虑了非结构构件的影响,修正后的基本自振周期计算结果误差为3%,与实测结果接近.欧洲规范、新西兰规范和日本规范由于未考虑非结构构件对结构自振周期的影响,基本自振周期计算结果误差分别为34%和18%.

通過上述两栋钢框架结构基本自振周期实测值与规范计算结果的对比可知,对于带外挂混凝土墙板钢框架结构,欧洲规范和新西兰规范建议的经验公式中由于考虑了墙体布置的影响,结构基本自振周期计算值最接近真实值;美国、意大利等国家规范中基于结构高度的经验公式与法国、西班牙等国家规范中基于结构高度和宽度的经验公式未明确考虑墙体类型、布置等影响,需对经验公式系数进行修正;基于结构楼层数的经验公式计算结果范围较大;基于瑞利公式的计算结果大于实测结果,需用考虑非结构构件影响的修正系数予以修正.

3 3 带外挂混凝土墙板钢框架自振周期

%1.5 3.1带外挂混凝土墙板钢框架自振周期实测数据

本文收集了40栋已有的带外挂混凝土墙板钢框架结构建筑或足尺试验模型,结构自振周期实测数据见表4,表中同时给出了结构的长、宽、高、楼层数、激励方式以及外挂混凝土墙板类型、建筑用途、数据来源等信息.表中结构体系为钢框架,外挂混凝土墙板主要为预制装配式混凝土墙板和蒸压轻质加气混凝土墙板,建筑高度为4~70 m,建筑楼层数为2~20层.

%1.6 3.2自振周期计算公式回归分析

基于实测数据,采用非线性回归技术,建立带外挂混凝土墙板钢框架结构的基本自振周期经验公式.经验公式形式参考各国规范中建议公式,以高度、宽度等结构特征参数作为自变量,形式见表5.基于楼层数的经验公式由于结果离散性较大,因此表中未列出该类公式形式.非线性回归分析采用最小二乘法对实测数据进行统计回归,回归结果见表5.对于回归结果,采用相关系数和模型效率EF对回归效果进行评价,评价公式如下:

r=∑ni-=1(xi-x-)(yi-y-)∑ni=1(xi-x-)2·∑ni=1(yi-y-)2. (15)

式中:xi和yi为待回归数据和回归值;x-和y-为均值.

EF=[∑ni=1(yi-y-)2-∑ni=1(yi-y^i)2]∑ni=1(yi-y-)2. (16)

式中:yi为待回归数据;y-为待回归数据均值;y^i为对应的回归值.

4 4结 论

本文研究了外挂混凝土墙板对钢框架结构自振周期的影响,主要结论如下:

1)对于带外挂混凝土墙板钢框架结构,考虑墙体布置的经验公式计算结果与实际结构基本自振周期最为接近,基本自振周期经验公式宜考虑墙体布置.

2)忽略墙体布置经验公式中,基于结构高度的经验公式与基于结构高度和宽度的经验公式需对公式系数进行修正;基于结构楼层数的经验公式计算结果离散性较大.

3)瑞利公式计算结果大于实际结构基本自振周期,需用考虑非结构构件影响的修正系数对计算结果予以修正.

4)基于带外挂混凝土墙板钢框架结构自振周期实测数据,采用非线性回归技术,建议了考虑外挂混凝土墙板影响的钢框架结构基本自振周期经验公式,经验公式以结构高度作为自变量,可供设计人员参考.

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