大跨度门式起重机刚性支腿对结构刚度的影响分析外文文献翻译、中英文翻译、外文翻译
大跨度门式起重机刚性支腿对结构刚度的影响分析外文文献翻译、中英文翻译、外文翻译,跨度,起重机,刚性,结构,刚度,影响,分析,外文,文献,翻译,中英文
18
大跨度门式起重机刚性支腿对结构刚度的影响分析
官保华，甄圣威，曾庆敦
( 华南理工大学 土木与交通学院，广东 广州 510640)
摘要: 利用有限元软件对某公司设计的 83 m 跨度 A5 型门式起重机的刚度进行分析，求得的主梁挠度超出《通用门式起重机》( GB/ T14406 － 93) 的规定，且结构产生较大的侧向位移． 通过对刚性支腿结构设计进行修改，使得主梁最大挠度下降 69. 2% ，侧向位移下降 62. 6% ．
关键词: 门式起重机; 刚性支腿; 吊车梁; 侧偏
中图分类号: TU32 文献标志码: A 文章编号: 1007-7162( 2011) 04-0083-04
随着船海工业的发展，大跨度、大吨位吊车的应用越来越广泛，以满足造船业生产的灵活性和建造大型船只时对吊装吨位的需求． 箱型梁有刚度大和抗偏扭性能好等诸多优点［1］，使之广泛运用于大跨度吊车梁中． 由于吊车梁对容许挠度有严格的规定［2 － 3］，超出此规定不但会影响吊车的正常使用，且由于主梁振幅较大，将大大降低疲劳使用寿命，所以对主梁的刚度验算显得尤为必要． 通过对文献［4 － 8］的调研发现，对门吊鲜有关于侧向刚度的研究报道，仅文献［8］提及了造船门式起重机门架反变位技术，但未进行深入的理论研究． 由于大跨度门吊多采用一刚一柔两条支腿的形式，由结构力学［9］分析可以发现，这种结构在受竖向力作用后必然会发生侧偏，这种侧偏对结构是非常不利的，这一点将在后面的论述中详细说明． 在发现设计不满足规范要求后就盲目地加大结构尺寸、提高结构刚度的做法显然是不明智的，也是不经济的，应首先考虑通过结构上的优化改造来达到预期效果． 本文通过对门式起重机刚性支腿的设计改造，在不增加建造成本，不改变门吊净空的基础上，不但使主梁的刚度满足规范要求，而且极其明显地改变了门式起重机侧偏位移较大的情况，充分说明了刚性支腿在门式起重机结构上所起的作用．
1 门式起重机的结构形式
本文以某公司设计的 ME150 + 110 /25 － 83A5 型门式起重机为例，设计最大起重量 200 t，主梁跨度 83 m，高达 55 m，梁高 5 m 且由双梁构成． 根据《起重机设计手册》［10］，当梁跨度大于 30 m 时，采用一个刚性支腿一个柔性支腿相结合的结构形式，可以减小因超静定产生的水平支反力，故其中一侧可设置为刚性支腿，与水平梁采用固定式连接; 另一侧设置为柔性支腿，采用球铰与主梁连接． 刚性支腿下端宽 1. 25 m，上端宽 5 m． 其结构简图如图 1 所示．
图 1 门式起重机原始设计示意图
由结构力学的分析易知，图 1 所示结构在主梁受到竖向荷载后，主梁除会产生向下挠曲以外，还会 产生向右的沿着梁轴向的侧偏． 小量的侧偏是允许的，但当侧偏较大时，不但会影响门吊的正常使用， 而且存在安全隐患，甚至可能由于倾斜过大导致门 吊的整体倾覆．
2 有限元模型及计算结果
本文对图 1 所示龙门吊车结构使用通用有限元软件 ANSYS，依据原设计图纸建立整体模型． 对组成梁与支腿的各板件选用 shell63 单元，各加劲肋和轨道则选用 beam188 单元． 不考虑细部的螺栓连结和外围辅助配套设施( 如栏杆、扶梯等) 对结构响，建立有限元模型如图 2 所示
图 2 龙门吊车结构的有限元模型
吊车的额定起重量为 200 t，小车分上下两部，上部小车自重 40 t，下部小车自重 45 t． 主梁钢材采用 Q345B，两支腿钢材均采用 Q235B．
通过结构力学［9］中的影响线理论求得主梁挠度的最不利载荷位置如图 3 所示． 荷载则通过计算出的轮压以集中力的形式加到轨道位置上．
下小车轮压:
P1 = αβγQP1max = 1. 05 × 1. 13 × 1. 4 × 182 =302. 32( kN) ;
上小车轮压:
P2 = αβγQP2max = 1. 05 × 1. 13 × 1. 4 × 175 × 2 =81. 4( kN) ．
其中，根据规范［3］，取动力系数 α = 1. 05，对于箱形结构，荷载增大系数 β = 1. 13，吊车竖向荷载分项系数γQ = 1. 4． P1max 、P2max 是下、上小车的主钩轮压．
图 3 主梁挠度最不利荷载布置图
在结构自重和吊车满载起吊的条件下，同时考
虑最不利工况，计算结果如下:
主梁最大挠度( 如图 4 所示) 为
δ = 260. 9 mm． ( 1)
主梁沿轴向的侧偏位移( 如图 5 所示) 为
U = 492. 8 mm． ( 2)
根据《通用门式起重机》( GB / T14406 － 93 ) ［2］ 第 4. 2. 8 条，起重机的静态刚性规定为: 对于 A5 型起重机，起重机的额定起重量与小车自重在主梁跨中( 或挠度最大处) 引起的垂直静挠度不应大于
S /800，其中 S 为起重机主梁的跨度．
图 4 主梁挠度图
图 5 吊车侧向位移图
由此可知，该吊车梁的许用垂直静挠度为
［δ］= 83 000 mm /800 = 103. 75 mm， ( 3)
通过如下比较:
δ = 260. 9 mm ＞［δ］= 103. 75 mm． ( 4)
可见，主梁挠度已远超过了《通用门式起重机》的静态刚性规定．
通过对有限元计算的分析发现，门式吊机顶部， 即主梁发生了多达 0. 49 m 的沿梁轴向的侧向位移， 为了了解这个位移带来的危害，下面将先分析如此 大位移产生的原因．
3 计算结果分析
前面已经介绍过，对于图 1 所示的结构，在主梁受到竖向荷载作用时，结构必然会产生向右的侧偏， 这是由它的结构形式所决定的．
此外，观察图 1 中刚性支腿，其结构形式为非对称结构，其左侧边线为垂直地面，而右侧边线为斜直线． 刚性支腿上表面与主梁用螺栓及电焊连接，在受载后接触面上内力可近似看成均匀分布的面载，方向竖直向下; 下表面受到的是支座反力，由于吊车轮与轨道接触面积较小，故可将其视为集中荷载，如图
6 所示． 考虑刚性支腿的结构形式，这两个力的合力并非在同一条直线上，在这两个荷载作用下，结构会产生一个顺时针的力偶，如图 6 中顺时针旋转箭头所示．
显然，当仅有这个顺时针弯矩存在时，主梁会产 生一个向右的侧向位移和向下的弯曲，分别如图 6 中水平和竖直箭头所示，根据结构力学的叠加原理， 它将另外增加主梁在正常工作时的侧偏和跨中挠 度． 因此这个弯矩的存在对结构是不利的，以下称其 为“不利弯矩”，故最好能消除这个弯矩对结构的不 利影响．
图 6 吊车原设计受力分析简图
在本文的实例中，由于这个不利弯矩的存在，一方面使得主梁跨中挠度超过规范要求; 另一方面侧偏量多达 0. 49 m，在正常使用过程中表现为很大幅度的晃动，起吊物将随其晃动，因此当吊车放下起吊物时难以实现精确定位． 而造船用起重机常常需要将起吊的构件或设备精确地吊放在安装位置，以备焊接或栓紧． 因此，晃动对吊车的正常工作是十分不利的．
同时，此不利弯矩增加了刚性支腿与主梁连接处螺栓的应力水平，加之吊车晃动的影响，将明显降低螺栓的疲劳寿命．
由于结构存在上述种种问题，因此需对结构的设计进行修改．
4 设计修改
第 2 节通过有限元计算发现，某公司原设计的大型门式起重机存在跨中挠度和侧偏过大的问题， 并在第 3 节中分析了其产生的机理，得出了必须修改设计的结论．
加大结构尺寸，提高结构刚度虽可立竿见影，但会造成资源的浪费、工期的延长，考虑到生产的商业性和结构设计中“安全可靠，经济合理”的基本原则，这种方法在非必要的情况下不应采取，而应优先考虑结构优化．
由第 3 节的分析发现，不利弯矩的存在增加了结构跨中挠度和侧偏量，故只需消除不利弯矩的作用便可起到改变结构性能的作用． 不利弯矩是由刚性支腿的摆放方式不合理引起的，因此改变刚性支腿的摆放方式将是行之有效的方法，不但可以消除不利弯矩的影响，甚至将其不利的影响变为有利，进一步减小主梁原本的挠度和侧偏．
综上所述，参照文献［8］的思路，将翻转刚性支 腿的摆放位置如图 7 所示，在刚性支腿上部面力和下部集中力的合力作用下，产生一个逆时针的力偶， 如图 7 中逆时针旋转箭头所示，与图 6 中的力偶方向恰恰相反． 在这个力偶的单独作用下，一方面，主梁将产生向上的挠曲，如图 7 中向上的箭头所示，可以抵消一部分正常工作时主梁的下挠; 另一方面，主梁会产生向左的沿梁轴向的侧偏，如图 7 中水平向左的箭头所示，可以抵消部分的结构固有侧偏． 故不利弯矩在经过改造后可以变为对结构有利的弯矩．
图 7 吊车结构优化受力图
为了验证结构优化后的效果，在有限元软件中按上述思想修改计算模型，只需按图 7 修改刚性支腿的摆放方式，其他参数均保持不变． 经计算得到主梁跨中挠度与侧偏量如下:
主梁跨中挠度为
δ' = 80. 27 mm ＜ 103. 75 mm，
主梁跨中挠度下降了 69. 2% ，满足《通用门式起重机》GB / T14406 － 93［2］中对主梁刚度的要求． 而且有较大的刚度富余，仍有较大可优化的空间．
主梁的侧偏位移为
U' = 184 mm，
相对于优化前的 492. 8 mm 下降了 62. 6% ，效果十
分明显．
根据上述的分析和计算结果告知起重机生产厂家，厂家同意按上述结构优化方案修改原 ME150 + 110 /25 － 83A5 型门式起重机的设计并按修改后的设计生产起重机． 广东某船务工程有限公司购买了多台经结构优化后的此类吊车，迄今为止一直安全稳定运营，取得了良好的经济和社会效益．
5.结论
本文通过通用有限元软件 ANSYS 对某公司设计的 ME150 + 110 /25 － 83A5 型门式起重机进行整体分析，发现该设计存在如下问题:
首先，主梁跨中挠度过大，刚度不能满足规范要求; 其次，结构在受力时，主梁在其轴线方向上有较大的侧偏，影响结构的稳定．
通过对吊车结构产生侧偏的机理分析，得出了刚性支腿不合理的摆放方式是造成结构侧偏的主要原因． 刚性支腿的合理摆放会产生一个有利于结构的弯矩，不但可以减小主梁的跨中挠度，而且可以减小结构在受载后的固有侧偏位移，充分体现了刚性支腿在门式起重机结构中所起的作用．
参考文献:
［1］ 方子帆，陈永清，魏友霖，等． 大跨度箱形吊车梁的强度分析及结构改进［J］． 三峡大学学报，2007，29( 2) :141-143．
［2］ 大连起重机器厂． GB/ T14406-93，通用门式起重机［S］．北京: 中国标准出版社，1993．
［3］ 中华人民共和国建设部． GB50017-2003，钢结构设计规范［S］． 北京: 中国计划出版社，2003．
［4］ 刘标，程文明，栗园园． 铰接式支腿箱梁门式起重机有限元分析［J］． 起重运输机械，2010( 4) : 47-49．
［5］ 许海翔，李鸣，李振林． 基于虚拟样机的门式起重机安全分析［J］． 起重运输机械，2010( 7) : 40-44．
［6］ 阎少泉． 造船门式起重机结构型式及性能比较［J］． 科技创新与生产力，2010( 12) : 94-95，99．
［7］ 陈进，樊艳，侯沂，等． 大型双梁桁架门式起重机钢结构设计与研究［J］． 中国工程机械学报，2009，7 ( 1 ) : 63-67．
［8］ 肖海江． 造船门式起重机门架反变位技术的应用［J］．机械工程师，2009 ( 4) : 155-156．
［9］ 朱慈勉． 结构力学［M］． 北京: 高等教育出版社，2004．
［10］ 张质文． 起重机设计手册［M］． 北京: 中国铁道工业出版社，1998．
Analysis of the Influence of Long-span Gantry Cranes' Rigid Legs on Structure Stiffness
Gan Bao-hua，Zhen Sheng-wei，Zeng Qing-dun
( School of Civil Engineering and Transportation，South China University of Technology，Guangzhou 510640，China)
Abstract: Finite software was used to research the A5 Gantry Cranes designed by a company，whose span was 83
m． The research results indicate that the deflection of girder oversteps the formulations of General purpose gantry cranes ( GB / T14406-93) ，coupled with a big lateral displacement． After a simple modification of the structure de- sign for the rigid legs，the deflection of girder and the lateral displacement have reduced by 69． 2% and 62． 6% ， respectively．
Key words: gantry crane; rigid leg; crane beam; laterodeviation
Analysis on the Influence of Rigid Legs of Long-span Gantry Crane on Structural Stiffness
Guan Baohua，Saint Vincent Yan，Chung On
( School of Civil Engineering and Communications, South China University of Technology, Guangzhou, Guangdong510640)
Summary: Using finite element software to design a company83 mSpan spanA5Stiffness analysis of type gantry crane，The deflection of the main beam obtained exceeds《General gantry crane》( G B / T 14406 － 93)Provisions，And the structure produces large lateral displacement．Modification of Rigid Leg Structure，The maximum deflection of the main beam decreases69. 2% ，Lateral displacement62. 6% ．
Key words: Gantry crane; Rigid leg; Crane beam; Side deviation
Middle Chart Classification Number:TU32 Document symbol codeA :1 Number of articles:1007-7162(2011)04-0083-04
With the development of ship-sea industry, large-span and large-tonnage cranes are more and more widely used to meet the flexibility of shipbuilding industry and the demand for hoisting tonnage when building large ships． The box girder has many advantages such as high stiffness and good deflection resistance［1］，It is widely used in large span crane beams． Because the crane beam has strict requirements for allowable deflection［2 － 3］，Exceeding this regulation will not only affect the normal use of the crane，Because of the large amplitude of the main beam, the fatigue life will be greatly reduced, so it is necessary to check the stiffness of the main beam． Adoption of the text－ It is found that the lateral stiffness of the door crane is reported,Only literature[8] has mentioned the reverse displacement technology of gantry crane in shipbuilding, but has not carried on the thorough theoretical research． Because the long span door crane is mostly in the form of one rigid and one flexible two legs, the structure mechanics［9］It can be found that this kind of structure will inevitably have side deviation after being subjected to vertical force, which is very unfavorable to the structure, which will be explained in detail in the following discussion． It is obviously unwise and uneconomical to blindly increase the size and stiffness of the structure after finding that the design does not meet the requirements of the code, so we should first consider the optimal transformation of the structure to achieve the desired results． In this paper, through the design and modification of the rigid leg of the gantry crane, on the basis of not increasing the construction cost and not changing the clearance of the gantry crane, the stiffness of the main beam not only meets the requirements of the code, but also obviously changes the large side displacement of the gantry crane. The function of the rigid leg in the gantry crane structure is fully explained．
4 Structure of gantry crane
This article is designed by a companyME150+110/25-83 A5Example of type gantry crane，Design Maximum Weight200 t,Main girder span83 m,Up to55 m,Beam height5 mAnd made of double beams．Basis《Crane Design Manual》［10］，When the beam span is greater than 30 mTime，Using a rigid leg combined with a flexible leg can reduce the horizontal support reaction caused by statics, so one side can be set as a rigid leg and fixed connection with the horizontal beam; The other side is provided with a flexible leg, which is connected with the main beam by ball hinge． Lower end width of rigid leg 1.25 m,Upper width m .5A schematic diagram of the structure 1as shown．
Chart1 Original design of gantry crane
From the analysis of structural mechanics，Chart1After the main beam is subjected to vertical load, the main beam will not only produce downward flexure, but also produce lateral deflection to the right along the． A small amount of side deviation is allowed, but when the side deviation is large, it will not only affect the normal use of the door crane， And there are safety risks, even because of the tilt too large to cause the overall overturning of the door crane．
5 Finite element model and calculation results
In this paper, the diagram1General finite element software for gantry crane structureAN S Y S,Build the whole model according to the original design drawing． Selection of each plate forming the beam and legshell63Units, stiffeners and tracksbeam188Unit． Bolt connections and peripheral ancillary facilities without consideration of details( such as railings, escalators, etc) The finite element model is established as shown in the diagram2 as shown
Chart2 Finite element model of gantry crane structure
The rated lifting weight of the crane is200 t,The car is divided into two parts，Weight of upper car40 t,Weight of lower car45 t.Main girder steelQ 345B,Both leg steel are usedQ 235B.
Through structural mechanics［9］The most unfavorable load position of the main beam deflection is obtained by the influence line theory as shown in the diagram3 as shown． The load is added to the track position in the form of concentrated force by calculating the wheel pressure．
Lower Car Wheel Pressure:
P1 = αβγQPmax 1= 1. 05 × 1. 13 × 1. 4 × 182 =302.32(k N);
Car wheel pressure:
P2 =αβγQPmax 2 = 1. 05 × 1. 13 × 1. 4 × 175 × 2 =81.4(k N)...
Of which，According to specifications［3］，Dynamic coefficient α= 1. 05，For box structure，Load increase coefficient β= 1. 13，γ of sub-coefficient of vertical load of craneQ = 1. 4． Pm a x 1 P; andm a x 2Next、Main wheel pressure on the trolley．
Chart3 Main girder deflection worst load layout
Under the condition of structure weight and crane full load lifting，At the same time
Considering the most unfavorable working conditions, the calculation results are as follows:
Maximum deflection of main girder( Figure 14 as shown) For
δ= 260. 9 m m. ( 1)
Lateral deflection of main girder along axial direction( Figure 15 as shown) For
m m. U =492.8 ( 2)
According to General Gantry Crane(GB /T14406) Annex － 93 ) ［2］ Section 1428. . The static rigidity of the crane is specified as: For exampleA5Crane, rated lifting weight and car weight in the main girder span( Or maximum deflection) The resulting vertical static deflection should not be greater than
S /800，Of whichSSpan for crane girder．
Chart4 deflection of main girder
Chart5 Lateral Displacement Map of Crane
From this we can see，The allowable vertical static deflection of the crane beam is
[δ]=83 000 mm /800 = 103. 75 mm, ( 3)
Through the following comparison:
δ= 260. 9 m m ＞［δ］= 103. 75 m m. ( 4)
It can be seen that the deflection of the main girder has far exceeded the general gantry crane》Static Rigid Provisions．
Based on the finite element analysis, it is found that the top of the gantry crane， That's when the main beam. m 049lateral displacement along the beam axis， In order to understand the harm caused by this displacement, we will first analyze the causes of such a large displacement．
6 Analysis of results
I've already introduced，For the diagram1Structure shown，When the main beam is subjected to vertical load, the structure will inevitably produce a lateral deviation to the right， This is determined by its structural form．
In addition，Observation map1Medium Rigid Leg，Its structure form is asymmetric structure, its left side line is vertical ground, and the right side line is oblique straight line． The upper surface of the rigid leg is connected with the main beam by bolt and electric welding. The internal force on the contact surface after loading can be regarded as a uniformly distributed surface load, and the direction is vertical and downward; The lower surface is subjected to support reaction, which can be regarded as concentrated load because of the small contact area between the lifting wheel and the track, as shown in the figure
6 as shown． Considering the structural form of the rigid leg, the resultant force of the two forces is not in the same straight line, and under these two loads, the structure will produce a clockwise couple，Figure 16Central clockwise rotation arrow．
Obviously, when only this clockwise moment exists, the main beam will produce a lateral displacement to the right and a downward bending，Figure 16 Medium horizontal and vertical arrows, according to the superposition principle of structural mechanics， It will also increase the lateral deflection and midspan deflection of the main girder during normal operation． Therefore, the existence of this moment is unfavorable to the structure, hereinafter referred to as "unfavorable moment ", so it is best to eliminate the adverse effects of this moment on the structure．
Chart6 Analysis of Force in the Original Design of Crane
In the example of this paper, due to the existence of this unfavorable bending moment, on the one hand, the mid-span deflection of the main beam exceeds the specification requirement; On the other hand, as much as0. 49 m,In the normal use of the performance of a very large amount of sloshing, lifting objects will shake with it, so when the crane put down the lifting object is difficult to achieve accurate positioning． Ship-building cranes often require lifting components or equipment precisely in the mounting position for welding or fastening． Therefore, sloshing is very unfavorable to the normal operation of the crane．
At the same time, this unfavorable moment increases the stress level of the bolt at the connection between the rigid leg and the main beam, and the influence of the crane sloshing will obviously reduce the fatigue life of the bolt．
Because of the above problems, the design of the structure needs to be modified．
5 Design changes
Section 12The section is found by finite element calculation，A large gantry crane originally designed by a company has problems of midspan deflection and excessive side deflection， and in3The mechanism of its production is analyzed in the section，It is concluded that the design must be modified．
Increasing the size of the structure and increasing the stiffness of the structure can be an immediate result, but it will lead to the waste of resources and the extension of the construction period. Considering the commercial production and the basic principles of "safety, reliability and reasonable economy" in the structural design, this method should not be adopted if it is not necessary, but should give priority to the optimization of the structure．
by3Section analysis findings，The existence of unfavorable bending moment increases the deflection and lateral deflection of the structure, so it can change the structure performance only by eliminating the unfavorable bending moment． The unfavorable moment is caused by the unreasonable arrangement of the rigid leg, so it will be an effective method to change the arrangement of the rigid leg, which can not only eliminate the influence of the unfavorable moment, but also turn the adverse effect into advantage. Further reduce
the original deflection and side deflection of the main beam．
As a result, referring to the ideas [8] in the literature, the position of the inverted rigid leg is shown in the figure7as shown，A counterclockwise couple is produced under the combined force of the upper surface force and the lower concentrated force of the rigid leg， Figure 17Rotate the arrow counterclockwise，Figure II6In the opposite direction． On the one hand, under the sole action of this couple, the main beam will produce upward flexure，Figure 17The arrow up in the middle，Can offset part of the normal operation of the main beam deflection; On the other hand，The main beam will produce a lateral deviation to the left along the axial direction of the beam，Figure 17An arrow pointing horizontally to the left can offset part of the structure's intrinsic lateral bias． Therefore, the unfavorable bending moment can be changed into favorable bending moment after modification．
Chart7 Optimization of Crane Structure
In order to verify the effect of structural optimization, the calculation model is modified according to the above idea in finite element software，Just click7Modify the placement of rigid legs, other parameters remain unchanged． The mid-span deflection and side deflection of the main beam are calculated as follows:
Medium deflection of main girder
δ' = 80. 27 mm <103.9 75 mm,
The midspan deflection of the main girder decreases692%. to meet the General Gantry CraneGB /T14406-93［2］Requirements for stiffness of main girder． And has the bigger rigidity surplus, still has the bigger may optimize the space．
The lateral displacement of the main beam is
m m, U'=184
Relative to pre-optimization4928 mm. Down626%. The effect is ten
Obviously．
According to the above analysis and calculation results to inform the crane manufacturer，The manufacturer agrees to modify the above structure optimization planME150+110/25-83 A5Type gantry crane design and production of crane according to modified design． Guangdong Shipping Engineering Co., Ltd. has purchased a number of structural optimization of such cranes, so far has been safe and stable operation，Good economic and social benefits have been achieved．
5.Conclusion
In this paper, general finite element softwareANSYSDesigned for a companyME150+110/25-83 A5Holistic analysis of type gantry crane，It is found that the design has the following problems:
First of all, the midspan deflection of the main beam is too large and the stiffness can not meet the requirements of the code; Secondly, when the structure is subjected to force, the main beam has a large side deviation in the direction of its axis，Impact on structural
stability．
Based on the analysis of the mechanism of side deviation of crane structure, it is concluded that the unreasonable placement of rigid leg is the main cause of side deviation． The reasonable placement of the rigid leg will produce a favorable bending moment, which can not only reduce the mid-span deflection of the main beam, but also reduce the inherent lateral deflection of the structure after loading. It fully reflects the role of the rigid leg in the gantry crane structure．
References:
[1] Fang Zifan, Chen Yongqing, Wei Youlin, et al． Strength Analysis and Structural Improvement of Long-span Box Crane Beam[J].Journal of the Three Gorges University，
收藏