建筑专业毕业设计外文翻译---张弦梁结构的探讨

附录A
张弦梁结构的探讨
摘要：本文就张弦梁结构中的相关问题作一些说明，以及张弦梁结构研究的现状和需要以后研究的问题。

本文还讨论张弦梁结构的影响因素，以及目前找形分析的方法。

关键词：张弦梁结构找形预应力稳定问题
0 引言
张弦梁结构最早是由日本大学M.Saitoh教授提出，是一种区别于传统结构的新型杂交屋盖体系。

张弦梁结构是一种由刚性构件上弦、柔性拉索、中间连以撑杆形成的混合结构体系，其结构组成是一种新型自平衡体系，是一种大跨度预应力空间结构体系，也是混合结构体系发展中的一个比较成功的创造。

张弦梁结构体系简单、受力明确、结构形式多样、充分发挥了刚柔两种材料的优势，并且制造、运输、施工简捷方便，因此具有良好的应用前景。

本文就张弦梁结构的分类，受力机理，张弦梁结构的找形分析，用有限元分析总结了撑杆数目、垂跨比、高跨比、拱的惯性矩、弦的预应力等对张弦梁结构的受力性能的影响，以及结构的稳定性分析。

1、张弦梁结构的受力机理和分类
1.1、张弦梁结构的受力机理
目前，普遍认为张弦梁结构的受力机理为通过在下弦拉索中施加预应力使上弦压弯构件产生反挠度，结构在荷载作用下的最终挠度得以减少，而撑杆对上弦的压弯构件提供弹性支撑，改善结构的受力性能。

一般上弦的压弯构件采用拱梁或桁架拱，在荷载作用下拱的水平推力由下弦的抗拉构件承受，减轻拱对支座产生的负担，减少滑动支座的水平位移。

由此可见，张弦梁结构可充分发挥高强索的强抗拉性能改善整体结构受力性能，使压弯构件和抗拉构件取长补短，协同工
作，达到自平衡，充分发挥了每种结构材料的作用。

所以，张弦梁结构在充分发挥索的受拉性能的同时，由于具有抗压抗弯能力的桁架或拱而使体系的刚度和稳定性大为加强。

并且由于张弦梁结构是一种自平衡体系，使得支撑结构的受力大为减少。

如果在施工过程中适当的分级施加预拉力和分级加载，将有可能使得张弦梁结构对支撑结构的作用力减少的最小限度。

1.2、张弦梁结构的分类
张弦梁结构按受力特点可以分为平面张弦梁结构和空间张弦梁结构。

平面张弦梁结构是指其结构构件位于同一平面内，且以平面内受力为主的张弦梁结构。

平面张弦梁结构根据上弦构件的形状可以分为三种基本形式：直线型张弦梁、拱形张弦梁、人字型张弦梁结构。

直梁型张弦梁结构主要用于楼板结构和小坡度屋面结构，拱形张弦梁结构充分发挥了上弦拱得受力优势适用于大跨度的屋盖结构，人字型张弦梁结构适用于跨度较小的双坡屋盖结构。

空间张弦梁结构是以平面张弦梁结构为基本组成单元，通过不同形式的空间布置所形成的张弦梁结构。

空间张弦梁结构主要有单向张弦梁结构、双向张弦梁结构、多向张弦梁结构、辐射式张弦梁结构。

单向张弦梁结构由于设置了纵向支撑索形成的空间受力体系，保证了平面外的稳定性，适用于矩形平面的屋盖结构。

双向张弦梁结构由于交叉平面张弦梁相互提供弹性支撑，形成了纵横向的空间受力体系，该结构适用于矩形、圆形、椭圆形等多种平面屋盖结构。

多向张弦梁结构是平面张弦梁结构沿多个方向交叉布置而成的空间受力体系，该结构形式适用于圆形和多边形平面的屋盖结构。

辐射式张弦梁结构是由中央按辐射状放置上弦梁，梁下设置撑杆用环向索而连接形成的空间受力体系，适用于圆形平面或椭圆形平面的屋盖结构。

2、张弦梁结构的找形分析
2.1 张弦梁结构的形态定义
张弦梁结构象悬索结构等柔性结构一样，根据张弦梁结构的加工、施工、及受力特点。

通常也将其结构形态定义为零状态、初始态和荷载态。

零状态，是拉索张拉前的状态，实际上是构件加工和放样形态，通常也叫结构放样态。

初始态，是拉索张拉完毕后，结构安装就位的形态，通常也叫预应力状态。

初始态是建筑施工图中明确的结构外形。

（包括在自重作用下）
荷载态，是外荷载作用在初始态结构上发生变形后大平衡态。

如果张弦梁结构的上弦构件按照初始形态给定的几何参数进行加工放样，那么在张拉拉索时，由于上弦构件刚度较弱，拉索的张拉势必会引导撑杆使上弦构件产生向上的变形，当张拉完毕后，结构上弦构件的形状将偏离初始形态，从而不满足建筑设计的要求。

因此，张弦梁结构上弦构件的加工放样通常要考虑张拉产生的变形影响，这也是张弦梁结构需要进行形态定义的原因。

2.2 张弦梁结构找形分析
目前有关文献中找形的方法不外乎有张其林提出的逆迭代法、文献中改进的逆迭代法。

I.逆迭代法的简介
逆迭代法实际上是一种非常自然的思路：既然设计蓝图上的张弦梁几何尺寸是初状态(预应力张拉完毕时结构的状态)的尺寸，那么就可以以此初状态尺寸为近似零状态尺寸建立有限元模型，然后对其施加预应力(预应力值按设计要求)进行张拉，得到近似初状态。

然后将此近似初状态的几何尺寸与设计图中真正的初状态的几何尺寸的差值反向增加到原有限元模型的节点坐标上，作为近似初状态重新建模，并再次进行张拉，如此循环迭代，直到近似初状态与初状态的坐标差值足够小，即可视此近似初状态为初状态，而由之张拉而来的近似零状态为要求的零状态。

如此既可得到零状态几何尺寸(施工人员据此放样)，又可得到初状态的内力、应力分布，从而完成找形工作。

实践证明，只需进行次数不多的迭代，就可达到足够的找形计算精度。

II.改进的逆迭代法
上面提到的逆迭代法是将端部索段断开，，释放该处屋架上下弦的水平约束，
并将该索段的预拉力的水平分量作为外力分别反向作用在屋架上下弦端部，进而一步步逆迭代计算。

这种处理方法固然可以求出零状态的几何参数和初始态预应力分布，但是如果要在此基础上继续进行荷载态的分析，则举步维艰。

因为索切断之后的结构已经转化为静定结构，在这个静定结构上加载分析显然不能反映原先结构的受力特性，特别是此时下弦索内力已不会再随荷载的变化而变化，失去了其原有的作用。

改进的逆迭代法，不是把索段用力张拉来实现，而是在索段中施加一定大小的初应变，使其在变形协调后该索段的内力等于预定值，通过这样的改变使得研究问题可以在此基础上连续进行承受外荷载作用下的分析。

从而弥补了以往预应力张弦梁结构的力学性能研究中未能考虑受力状态改变的缺陷。

具体迭代过程如下：
假定图纸给定的结构初始态坐标表示为{X Y Z}，经过第k次迭代后所得的零状态几何坐标为{X Y Z}初始态坐标为{X Y Z}，位移为{U}。

(1)首先假设当前的几何即为零状态几何，即令{X Y Z}＝{X Y Z}。

(2)在某(些)索段加上初应变(预估)，对几何为{X Y Z}的结构计算得位移{U}
，k＝1
(3)计算{X Y Z}＝{X Y Z}+ {U}，令△＝{X Y Z}一{X Y Z}。

(4)判别△是否满足给定的精度。

若满足，则{X Y Z}即为所求的零状态几何坐标；若不满足，则令{X Y Z}＝{X Y Z}+ △，转第二步，并令 k ＝k+ 1。

(5) 由以上步骤得出零状态的几何参数后，将初应变值赋予该索段求出平衡后所得到的状态即为初始态预应力分布。

此时，应当检验该索段的内力值是否为预定值，如果不是，则应当调整初应变值从步骤(2)重新计算。

3、单榀张弦梁结构性能各影响因素分析
3.1 对单榀张弦梁结构性能各影响因素分析的研究现状
文献[4]通过对撑杆数目、垂跨比、高跨比、梁的截面特性和弦的预应力等参数对单棍张弦梁结构静力性能的影响进行分析，得出以下结论:
(1)、撑杆数目：通过撑杆连接拱和弦的张弦梁结构，受力合理。

但是撑杆数目的增加并不能改善结构的受力性能，文献[4]以一跨度为22.4m的单榻张弦梁为例进行分析，认为该情况下撑杆数超过3个后，受力性能改善效果不再明显，所以撑杆数目以3个为益。

(2)、垂跨比或高跨比的影响：垂跨比是下弦索的垂度和结构跨度的比值价/L),高跨比是上弦梁的矢高和结构跨度的比值切IL)。

随着垂跨比或高跨比的增大，除剪力外，其它内力如梁的弯矩和轴力以及索的最大应力都减小，同时结构的变形也减小，但半跨荷载下的变形幅度小于全跨荷载下的变形幅度，因此，当垂跨比达到某个特定值后，位移反应的不利荷载由全跨荷载转为半跨荷载。

(3)、上弦梁的惯性矩的影响：随着上弦梁的惯性矩的增大，全跨荷载下的变形儿乎没有变化，但半跨荷裁下的变形显著减小，并且全跨荷载下的最大正应力和半跨荷载下的梁的正应力也减小，所以通过增大梁的惯性矩，来提高半跨荷载下的刚度及结构受力性能是有益的。

(4)、梁截面面积的影响：随着梁截面面积的增大，除梁的正应力有所减小外、其它内力及变形几乎没有变化，所以提高梁的面积，对一受力性能的改善是不明显的。

(5)、下弦索的预应力的影响：随着下弦索的预应力的增大，变形显著减小，拱的正应力也趋向于减小，但不明显，所以弦的预应力主要有助于减小变形。

(6)、下弦索的面积的影响：随着下弦索的面积的增大，变形和索的内力显著减小，梁的正应力也趋向于减小，但幅度不大，所以单纯增大弦的面积，虽能提高刚度，但弦的材料强度不能充分利用。

(7)、梁截面型式的影响：梁截面采用工字型截面相比采用钢管截面，从力学角度看，更经济合理。

(8)、张弦梁结构尺寸应在建筑允许的条件下，采用尽可能大的垂跨比;高跨比的
取值要考虑平面外风载的作用大小;选择适当的梁的尺寸和弦的面积，使梁的最大正应力和弦的最大应力同步达到材料极限状态，对弦施加一定的预应力以提高刚度。

文献[5]在对单榀张弦梁的各参数分析的基础上，认为文献[16]中大部分内容比较正确地反映了单榀张弦梁结构的静力性能，但是一些数据所反映的趋势并不合理，并提出了一些新的认识和结论。

(1)、垂跨比或高跨比的影响：文献[5]认为，随着垂跨比或高跨比的增大，梁截面的弯矩不是减小而是显著增加，所以不应该无限制地提高垂跨比和高跨比。

(2)、弦的预应力的影响：文献[4]认为，随着下弦索的预应力的增大，变形显著减小，而文献[5]的计算分析则表明，预应力的增大对于结构变形的影响几乎可以忽略不计，甚至还略有影响;就预应力对张弦梁结构的内力的影响来看，文献[5]认为预应力的增大会导致结构所有内力项都相应增大，对于上弦梁的主要内力弯矩的影响尤为显著。

3.2 对单榀张弦梁结构各因素影响分析的新认识
鉴于以上文献分析，本人觉得还有如下方面影响因素分析：垂跨比＋高跨比、撑杆的布置方式（如斜向布置、竖斜向布置），还有考虑撑杆和拉索的接触分析。

4、结论与展望
本文就张弦梁结构的受力机理和分类作了一定的说明，施工中的找形问题的方法作了介绍，还有介绍了目前文献中有关对张弦梁结构的影响因素及本人觉得还应该考虑的一些因素。

在目前的研究中，还应该考虑的一些问题：
(1)、索单元的数值模型问题。

采用杆单元是不能精确描述索在低应力水平下的状态，选择合适的索单元来进行数值分析是值得讨论的问题。

(2)、对非线性有限元的收敛速度需要做深入的研究。

在结构计算中经常会遇到用非线性有限元计算不收敛的问题。

(3)、对于大跨度张弦梁结构的风致振动、结构的振动特性以及振动控制是目前急需研究的问题，包括风场和风速的模拟、随机振动和藕合问题等
(4)、本文讨论的基本上是单榀平面张弦梁结构，此外，对于空间张弦梁结构比如空间双向、多向张弦梁结构、辐射式张弦梁结构其受力性能，有待更进一步的分析和研究。

(5)、现在的分析都是基于线弹性材料下的几何非线性分析，对于强震等较大荷载作用下的弹塑性分析，有待更进一步的研究。

附录Ｂ
Tring of beam structure
Abstract : This article beam string structure of the relevant issues to make some explanations, and the beam string structure of the status and needs of future research. This paper also discusses beam string of factors, and the current form-finding methods of analysis.
Keywords : String beam structure for stability prestressed.
0 Introduction
String beam structure is the first by the Japanese University Professor M. Saitoh, is a distinguished from the traditional structure of the new hybrid roof systems. String beam structure is a component wind from the rigid, flexible cable, in the middle pole connected to the formation of mixed structural system, its structure is a new self-balancing system is a large-span prestressed structure. Mixed structure is the development of a more successful creations. String simple beam structure, a clear force structure in various forms, and give full play to the two coil material advantages, as well as manufacturing, transport, construction simple convenience, it has a good prospect.
In this paper, beam string structure of the classification, the mechanism of power, beam string structure of the form-finding analysis, Finite element analysis summed up the pole number of vertical cross-ratio, high-ratio, the arch moment of inertia, String of the prestressed concrete beam string structure, the mechanical properties of impact and structural stability analysis.
1, beam string to the stress mechanism and classification of .
1.1, beam string structure of the mechanism of force.
Currently, generally considered beam string structure of the force through the mechanism of the last quarter of prestressed cables were imposed so that wind columns have anti-deflection , the load structure of the final deflection can be reduced, and pole bending to the wind to provide flexibility to support component, improve the structure of mechanical performance. General tighten the use of columns or beams
arch truss arch, under load arch thrust by the level of the last quarter tensile component affordable, reduce the arch bearing the burden. sliding bearings reduce the horizontal displacement. This shows that the beam string structure can take advantage of high-strength cable tensile properties of the strong improvement of the overall structure property, enable bending and tensile Component Component own work together to achieve self-balance, and give full play to each of the role of structural materials.
Therefore, the beam string giving full play to the structure of the cable tension capabilities, but Because of the bending resistance of truss or arch makes the system stiffness and stability has been significantly strengthened. As the string and beam structure is a self-balancing system, support structure makes the force greatly reduced. If in the course of construction to impose proper grading and classification of pre-tension loading, will be possible to make beam string structure of the supporting structure of the force to reduce the minimum.
1.2, beam string structure of the classification
String beam structure by force characteristics can be divided into planar beam string structure and spatial beam string structure.
Plane beam string structure is its structural component in the same plane and the plane to force the main beam string structure. Plane beam string structure based on the shapes of wind component can be divided into three basic forms : linear beam string, the string of arched beams, Text string people beam structure (figure 2).
Straight beam-beam string structure for the main floor structure and the small slope roof structure, String arched beam into full play the wind arch subject to applicable to the advantage of large-span roof structure, Text string people beam structure in the span of two smaller slope roof structure.
String space beam structure is planar beam string structure of the basic components, through different forms of spatial layout formed by String beam structure. Space beam string structure mainly unidirectional beam string structure, a two-way beam string structure, multi-beam string structure, String radiation-beam structure.
Unidirectional beam string structure Since the creation of a support cable vertical
space formed by the edge of the system, ensuring the stability of the plane outside, applied to the rectangular planar roof structure. Bidirectional beam string planar structure due to cross-beam string provide flexibility to support each other, forming a vertical and horizontal space force system, The structure applicable to the rectangular, circular, elliptical and other planar roof structure. Multi-beam string structure is a string planar beams along the direction of a number of cross-space layout from the force system, The structure applicable to the circular and polygon surface roof structure. String radiation-beam structure is centrally placed by the wind radial beam, Beam set up a pole to ring cable connecting the space formed by the power system, applied to planar circular or oval flat roof structure.
2, beam string structure of the form-findi
2.1 beam string structure definition of the form
String beam suspension structure as flexible structure, under String beam processing, construction, and mechanical ually its structure and morphology definition of a state of zero, the initial state and loading state.
Zero state is tensioned cables before the state is actually processing and lofting component form, usually called lofting state structure.
Initial state is tensioned cables after installation of the structure in place in the state, usually called prestressed state. Initial state of construction plans is clearly the structural shape. (Including under the weight)
Load state, the outer load in the initial state structural deformation occurred after the big equilibrium.
If the beam string structure of the wind component to the form in accordance with the initial set of geometric parameters for processing Lofting, Zhang Revised then, because of weaker wind component stiffness, The tensioning cable is bound to guide the pole so that wind upward components produced the deformation, when the tension has been completed, Structure wind component will depart from the shape of the initial form, thereby not satisfied architectural design requirements. Therefore, the beam string structure of the wind component processing lofting normally tensioned to consider the deformation, This string is the need for structural beams form the
definition of reasons.
2.2 beam string structure form
At present the literature to find a method gather there are Zhang Lin put the inverse iteration, literature improved inverse iteration.
I. inverse iteration method was introduced.
Inverse iteration is in fact a very natural idea : Since the design blueprint for the beam string geometry of the early state (pre-stressed tensioned structure of the finished state) the size, it can be the beginning of this approximate size of the state of the state is the size of finite element model, Then the tendons (prestressed value according to design requirements) tensioned, the approximate initial state. Then save the state early approximation of the geometric dimensions and layout of the real state of the early geometric margin increased to reverse the original Limited model coordinates of the nodes, as a state similar to the early re-modeling and re-tensioning, so iterative, Approximate state until the beginning of the early state with the coordinates margin small enough, this approximation can be regarded as the beginning of the early state of the state, and the only tension from the approximate zero state is requiring the zero state. So will be zero state geometry (constructors lofting accordingly), can be the beginning of the state of stress, stress distribution, thus completing form-finding work. Practice has proved that only require a small number of iteration, we can achieve sufficient accuracy to find form.
II. Improved inverse iteration
The above-mentioned inverse iteration method is to end cable disconnected, and the release of the department from top to bottom chord of the roof truss level constraints, The cable will of the Pretension of the level of external components as were reverse role in next roof truss chord end, then gradually reverse an iterative calculation. While this approach can be used to calculate the zero state geometric parameters and initial shapes. But if it is to continue on this basis for the analysis of load state, limping along. Round broken because after the structure had been set into a static structure, In the Static structural loading analysis is obviously not reflect the original structure of the force characteristics, particularly at this time last quarter
REQUEST internal forces will no longer load with the change, which lost its original role.
Improved inverse iteration, instead of having cable tensioned to achieve, but REQUEST to put some of the size of the initial strain.it deformation in the coordination of the internal force cable to a predetermined value. Such changes can be made to study issues on the basis of continuous bear outside under load analysis. Thus compensate for the past prestressed beam string structure of the mechanical properties failed to take into account the changing state of defects.
Specific iterative process as follows :
Drawings to assume that the initial structure of the state coordinates (X Y Z) After k-th iteration after the zero state geometric coordinates () X Y Z coordinates for the initial state (X Y Z) displacement (U).
(1)First, assume that the current state of geometry that is zero geometry, and even if
the (X) = Y Z X Y Z ().
(2) a certain (s) of the cable with the early response (estimates), right geometry - (X
Y Z) structure calculated displacement (U), k = 1
(3)Calculations (X) = Y Z X Y Z (+) (U), △X = (1) Y Z X Y Z ().
(4)whether the discriminant △to meet the precision. If satisfied, then () X Y Z
represents zero for the state of geometric coordinates; If not satisfied, which makes (X) = Y Z X Y Z (+) △, to the second step, and so k = k + 1.
(5)derived from the above steps is the state of geometric parameters, will be given
early strain of the cable sought after balance the state shall be the initial shapes.
At this point, should examine the cable Nalizhi of whether the predetermined value, if not, it should be adjusted from the initial strain steps (2) re-calculated. 3, single load beam string structural performance analysis of the impact of factors
3.1 pairs of single load beam string structure factors affecting the performance analysis of the status quo
The literature [4] by the number of pole pairs, vertical cross-ratio, high-ratio, the beam characteristics of prestressed Polyphonic parameters of single-string stick beam static properties of the analysis, come to the following conclusions :
(1), the number of pole : Pole arch connecting string chords beam structure, reasonable force. However, the increase in the number of pole does not improve the structure, the mechanical properties, the literature [4] in a span of a single fallen 22.4m string beam analysis that the number of pole after more than three, by the effect of behavior will not improve significantly, the pole number to three for benefits.
(2), vertical cross-over or a high cross-over effects : vertical cross-over is the last quarter of the cable sag and span the ratio of price / L), There are high-wind vector high beams span the structure and the ratio of shear IL). With vertical cross-over or a high-ratio increase, in addition to shear, Other internal forces such as the beam moments and axial forces, as well as the largest cable stress are reduced, while the deformation is also decreased. But a half-load of the whole is less than the magnitude of deformation under load - deformation of the range, so when vertical cross-over to a particular value, displacement of the negative reaction from the load-load to full-load half.
(3), the moment of inertia of the beam wind effects : With the wind of the moment of inertia of the beam increases, full-load deformation infants between no change, but the half-a Conference where the deformation decreased significantly, full-load and the maximum stress load and half-beams under the stress decreases. Therefore, passage of the beam increased moment of inertia to enhance cross-half load and stiffness of the structural behavior is useful.
(4), the beam area of impact : With the beam size increases, in addition to the beam have reduced stress, Other internal forces and deformation almost no changes, increases in the beam area, a force of the performance improvement is not obvious. (5), the last quarter of prestressed REQUEST : The impact of cable with the last quarter of prestressed increasing deformation significantly reduced, Arch stress also tend to decrease, but not obvious, the reason the prestressed major help reduce the deformation.
(6), the last quarter of the area REQUEST : The impact of cable with last quarter the size of the increase, the deformation of the internal forces and Solana significantly reduced, Beam stress also tend to decrease, but to a lesser extent, simply increasing
the size of string, can increase stiffness and But the string of material strength to full use.
(7), beam type of impact : beam using H-section steel tube sections than from the mechanical point of view, more economical and reasonable.
(8), beam string structure size of the building should be allowed under the conditions of the greatest possible use of the vertical span; high-value ratio of in-plane to consider the role of wind in size; choosing the appropriate size Polyphonic beam, the area Leung made the greatest stress is the greatest stress Polyphonic simultaneously achieve limit state materials, String of exerting certain prestressed to enhance stiffness.
Literature [5] in the single load beam string of parameters on the basis of the analysis, that the literature [16] Most of the content more accurately reflect the single load beam string structure of the static properties, However, some of the data reflecting the trend and unreasonable, and made some new understanding and conclusions. (1), vertical cross-over or a high cross-over effects : literature [5] that, as vertical cross-over or a high-ratio increase, Beam is not the moment but decreased significantly increased and therefore should not be unlimited increases vertical cross-over and high-Span.
(2), the string of prestressed : literature [4] that, with the last quarter of prestressed cable increases, deformation significantly reduced, and the literature [5] The analysis shows that the increase of prestressed structural deformation of almost negligible, even slightly affected; on the right prestressed beam string structure of the internal forces, literature [5] that the increase of prestressed structure will lead to internal forces of all items have increased correspondingly. For the main beam wind moment of internal forces is particularly significant.
3.2 pairs of single load beam string structure analysis of the factors affecting the new understanding
Given the above analysis of the literature, I think there are implications factors : vertical cross-than + high-ratio, pole of the layout (eg diagonal layout, vertical diagonal layout), and consider the cable pole and contact analysis.
4, conclusions and Prospects
In this paper, beam string structure of the force mechanism and classification of certain note, Construction of the form-finding methods, There on the current literature on the right beam string structure of the factors and I think that should also consider a number of factors.
In the current study, we should also consider some of the problems :
(1), cable element numerical model of the problem. Rod module used is not accurate to describe cable in low stress level in the state, choice of cable element to the numerical analysis is worthy of discussion.
(2), the nonlinear finite element convergence needs to be done in-depth research. Calculation of the structure often encounter nonlinear finite element calculation of convergence problems.
(3), for the long-span beam string of wind-induced vibration, the vibration characteristics and vibration control is an urgent problem, including wind and wind speed simulation, Random vibration coupling problems and
(4), discussed in this paper are basically single load beam string planar structure, in addition, For space beam string structures such as two-way space, multi-beam string structure, the radiation-beam string structure of its mechanical behavior, pending further analysis and research.
(5), the present analysis is based on linear elastic material under the geometric nonlinear analysis, For larger earthquake loads of elastoplastic analysis, pending further study.。