基于无应力状态法的分段成形梁桥合拢技术的研究(中英文0811)

基于无应力状态法的分段成形梁桥合拢技术的研究
张师定
(青岛华城市政工程设计院，青岛266071）
摘要：本文从桥梁体系转换入手，应用无应力状态控制法理论，剖析现行桥梁合拢体系转换做法的不周；提出成桥设计内力分布应当选择连续结构、桥梁合拢方案必须采取专门技术等新理念；对于连续梁桥，建议采用“顶升-降落”支点法；对于连续刚构桥，笔者建议采用“顶升合拢梁端”法；最后，给出了简化的数字例子。

关键词：桥梁体系转换；桥梁合拢专门技术；无应力状态控制法理论；成桥内力分布
中国已建成许多座跨度超过百米的预应力混凝土梁桥，然而，经多年运营发现，跨中下挠是最突出的问题。

许多学者对此问题进行了深入研究
[1][2][3][4][5]，发现的主要原因有：
(1)混凝土材料的长期收缩徐变的影响；
(2)混凝土材料长期收缩徐变导致预应力损失；
(3)混凝土开裂导致截面刚度变小等。

然而，更为深奥的道理尚未被认识。

笔者从桥梁体系转换入手，应用无应力状态控制理论，透彻剖析现行体系转换做法的不周，提出新的设计理念。

1 现行混凝土梁桥合拢方案
以悬臂浇筑节段施工的三跨预应力混凝土连续箱梁桥为例。

总体合拢顺序：先边跨合拢，解除临时固结落梁后，再中跨合拢。

边跨合拢方案：通过外施劲性骨架锁口，并预张拉合拢束，悬吊架法浇筑合拢段砼。

中跨合拢方案：边跨合拢完成后，通过外施劲性骨架锁口中跨合拢段，并预张拉合拢束，悬吊架法浇筑合拢段砼。

1.1边跨合拢段施工方案
1.1.1 施工准备
首先完成挂篮悬浇段施工和边跨支架现浇段施工。

然后将边跨端挂篮推进至边跨合拢段，中跨端挂篮位置不变。

施工时预先在边跨悬浇块和支架现浇段箱梁处，预留底模和侧模锚固孔，利用挂篮吊带将挂篮底模和侧模锚固在边跨合拢段两侧已完成的箱梁上，作为合拢段施工的底模和侧模。

1.1.2 配重
边跨合拢段施工配重仅在T构端上进行，配重重量为合拢段砼重量的一半，而边跨现浇段不予配重。

配重可以为沙包或水箱等。

1.1.3 合拢段锁口
合拢段锁口采用外施（或内施）劲性骨架，劲性骨架设置在箱梁底板和顶板上，共四组，每组有两根型钢组成。

按照规范规定，在当天温度最低时将型钢焊接在合拢箱梁的预埋钢板上，完成锁定。

1.1.4 合拢束预张拉
(1)精确固定边跨合拢段底模板和外侧模板；
(2)绑扎底、腹板钢筋，安装底、腹板波纹管；
(3)立合拢段内模；
(4)绑扎顶板钢筋和安装波纹管；
(5)穿合拢束。

边跨预张拉合拢束,完成后.开始进行合拢段砼浇筑工作。

1.1.5 合拢段砼施工
合拢段砼浇筑时间选在一天气温较低时进行。

砼施工中配重逐级卸除，且浇注砼的重量与卸除配重的重量相等，使合拢段始终处于相对稳定状态。

1.1.6 预应力筋张拉与落梁
预应力筋张拉需满足一下先决条件：
（1）合拢段强度达到设计强度的95%；
（2）砼弹性模量达到设计的100%；
（3）砼龄期不少于5天。

开始进行预应力束张拉，张拉前拆除合拢段劲性骨架。

张拉顺序为：先底板束，后顶板束；先长束，后短束，并将合拢束补拉到设计吨位。

张拉完毕后进行孔道压浆。

当张拉并锚固纵向预应力束及横向和竖向预应力筋后，拆除两墩上临时固结并落梁，完成体系转换。

张拉完成后拆除边跨合拢段及现浇段的吊架、模板及支架。

1.2中跨合拢段施工方案
1.2.1 施工准备
预先在中跨两个梁块（与合拢段相邻）施工时预留底模和侧模锚固孔，利用挂篮吊带将挂篮底模和侧模锚固在两侧已完成的箱梁上，作为合拢段施工的底模和侧模。

1.2.2 配重
中跨合拢段施工配重在两个悬臂端上同时对称进行，各端配重重量为合拢段砼（包括横隔梁，如果有）重量的一半。

1.2.3 合拢段锁口
要求同1.1.3.
1.2.4 合拢束预张拉
要求同1.1.4.
1.2.5 合拢段砼施工
合拢段砼浇筑时间选在一天气温较低时进行。

砼施工中配重逐级卸除，且浇注砼的重量与卸除配重的重量相等，使合拢段始终处于相对稳定状态。

1.2.6 预应力张拉
要求同1.1.6.
2 无应力状态法理论对合拢方案的要求
桥梁结构往往不是一次形成的，施工过程中往往发生多次体系转换，其成桥行为不一定与一次落架成桥相同[4]。

这样以来，最优受力、目标线形及施工控制（措施）三者间相互影响，使问题复杂化。

秦顺全先生提出无应力状态控制理论与方法[6]来解决此类问题，是桥梁发展的一个里程碑。

【定理1】对于给定的结构，包括其外荷载、结构体系、支承边界条件、单元的无应力长度及无应力曲率，无论其形成过程如何，其最终对应的结构内力和位移是唯一的。

【推论1】结构单元的内力和位移随着结构的加载、体系转换、或斜拉索的张拉而变化，但单元的无应力长度只有人为地调整才会发生变化。

当结构体系和荷载一定时，单元的无应力长度的变化必然唯一地对应一个单元轴力的变化，单元的无应力曲率的变化必然唯一地对应一个单元弯矩的变化。

【定理2】对于上一阶段形成的结构，安装无应力状态下的非合拢性构件后，形成的本阶段结构的结构内力和位移是唯一的，无论非合拢性构件是否一次形成、是否用支架或悬臂拼装。

2.1 合拢方案应遵循的基本原则
预应力混凝土连续梁（刚架）桥设计时，虽然考虑其梁体分段形成，但期望其一期恒载下结构内力状态仍呈连续梁状态，而非悬臂梁（受力不利）状态。

结合无应力状态法的要求，梁体施工过程中必须满足如下条件：
（1）在任一施工阶段，结构各构件受力安全；
（2）安装任一结构构件时，必须保证该构件无应力；
（3）必须采用专门技术措施，保证合拢处弹性曲线连接，使成桥内力状态为设计目标状态；
（4）必须合理设置施工预拱度，保证成桥线形符合设计目标。

注：预拱度设置改变不了结构内力分布，代替不了合理的体系转换措施。

（5）施工方案在安全的前提下，必须经济合理。

2.2 合拢方案中的专门技术措施
依据无应力法理论，要求合拢前的两侧梁端转角必须连续。

其专门技术措施包括：
方案一：跨中合拢前，在两侧梁端施加一对力偶，待跨中合拢后，卸除该力偶。

方案二：跨中合拢前，在两侧梁端各施加一个集中力，使两侧梁端转角连续（消除转角差），待跨中合拢后，卸除该集中力。

方案三：跨中合拢前，分别转动两个支点处的梁体，从而消除两侧梁端转角差，待跨中合拢后，再卸除该扭矩。

方案四：跨中合拢前，分别顶升两个支点处的梁体，从而消除两侧梁端转角差，待跨中合拢后，再卸除该顶力。

2.3 数字例
图2-1 连续梁计算模型与目标成桥线形
图2-2 目标成桥弯矩分布
图2-3 中跨合拢前悬臂状态
以（0.7l+l+0.7l）三跨等截面连续梁（见图2-1）为简单例，比较了不同施工方案典型截面的恒载内力及变形情况，成果见表2-1.
方案一未发生体系转换，其恒载内力状态完全是连续梁（见图2-2）。

方案二类似现行方案，恒载内力为悬臂梁状态，笔者不推荐该方案。

方案三对于合拢前悬臂状态（见图2-3）采用专门技术措施，即“顶升-降落”支点。

对于连续梁桥，笔者建议采用此方案。

方案四对于合拢前悬臂状态（见图2-3）专门技术措施，即顶升合拢梁端。

对于连续刚构桥，笔者建议采用此方案。

表2-1 (0.7l+l+0.7l)三跨连续梁桥的施工方案比较
注1：EI-连续梁抗弯刚度；
注2：q-满跨均布荷载集度；
注3：l-中跨跨度；
注4：表中数值由结构力学求得；
注5：方案四中P值由下式求得。

0.2417Pl2/EI=0.0357ql3/EI
（2-1）
3 现行合拢方案之工艺缺陷及后果
3.1 设计成桥状态内力分布的缺陷
现行发生体系转换的预应力混凝土梁桥，在设计过程中，往往对成桥内力分布的预想不清楚、不科学，往往形成“伪连续”。

例如，本应成桥目标状态为连续梁，而误设计为若干个简支悬臂梁；本应成桥目标状态为连续刚构，而误设计为若干个T构。

3.2设计对体系转换过程考虑不周
对比第1节及第2节内容，发现：现行施工方案的最大缺点是缺失第2节第（3）条的要求，即缺失2.2节专门技术措施，另外，合拢时挂篮自重及配重使梁跨结构受力恶化，并持久影响；后果则是成桥内力状态非连续梁状态，而倾向于悬臂梁状态；跨度越大，则内力差别越明显，跨中下挠度就越大。

悲观的是，发生体系转换的预应力混凝土连续梁（刚构）桥，几乎都没有按第2节的方案去做。

4 结束语
笔者确信，大跨预应力混凝土梁桥存在的设计误区已找到。

从现在起，我们应当创新设计思路：
（1）优化成桥设计内力分布，以真正的连续梁（刚构）内力分布为内力设计
目标；
（2）优化桥梁合拢方案，必须顶升中支点或采取其他措施，使梁合拢端圆顺
连接。

（3）确保实施合理的桥梁合拢方案后，就可以达到优化的成桥目标设计内力
分布。

笔者现在认识到这点，桥梁界必须改良现有的理论与做法，否则，桥梁建成
之日，就是危桥诞生之时。

本文的观点对其他形式桥梁的设计与施工有借鉴作用。

参考文献
[1]许震.大跨预应力混凝土连续刚构桥下挠分析及对策研究[D],重庆交通大
学硕士学位论文，2007.
[2]孙剑川.预应力混凝土连续刚构桥下挠问题研究[D],西南交通大学硕士学
位论文，2010.
[3]刘亚军.预应力混凝土连续刚构桥下挠问题的研究[D],武汉理工大学硕士
学位论文，2010.
[4]张师定.桥梁建筑的结构构思与设计技巧[M],人民交通出版社，2002.
[5]北京市政工程设计院.大跨径预应力混凝土连续刚构桥设计指南[S], 2013.
[6]秦顺全.桥梁施工控制——无应力状态理论与实践[M],人民交通出版社，2007.
张师定，男，工学学士，高级工程师，陕西大荔人，主要研究方向：桥梁与
房屋结构的优化设计及体系转换分析。

青岛华城市政工程设计院总工程师，E-mail：zhangshiding@ 电话：152********.
通讯地址：（266071）青岛市市北区劲松三路277号依山半岛1-1-803#
Study on Closure Technique of Sectional Forming Beam Bridge
Based on Unstressed State Control Method
ZHANG Shi-ding
（Qingdao Achene Municipal Engineering Design Co.,Ltd.,Qingdao 266071,China）
Abstract:Based on unstressed state control method, proceed with bridge system change, shortcoming of present plan of bridge system change is ana-lysed. It is suggested to regard continuous beam/girder as target of internal force distribution under completion stage of bridge, and use special technique of bridge closure, for example, "lift-up/drop-down supports" method for continuous beam bridge;"lift-up adjacent ends" method for continuous girder bridge. Finally,a digital simple example is presented.
Keywords:bridge system change; technique of bridge
closure; unstressed state control method; internal force distribution under completion stage of bridge
There are many pre-stressed concrete beam bridges with span of over 100m ,which built in China.But after running for many years,a large problem has found that deflection at the center of each span is
heavy.Many scholar studied[1][2][3][4][5] deeply on it,and main reasons are as follows:
(1)Influence of concrete shrinkage and creep;
(2)Loss of prestress due to concrete shrinkage and creep;
(3)Decrease of cross section stiffness due to concrete cracking,and etc.
In the author's opinion , there is an important field unfounded now. Starting with bridge system change,based on unstressed state control theory,a new idea with respect to shortcoming of current system change
is presented.
1 Present plan of concrete beam bridge closure
Take it as an ideal example,a pre-stressed concrete boxed-beam bridges with 3 spans, using cast-in-place cantilever method, is as belows.
General sequence of closures:first,close side span .then remove the temporary consolidation device and drop down beam,finally close mid-span.
Plan of side span closure:erect stiff skeleton outside to lock adjacent ends,pre-tension cables for closure,then cast concrete of closure segment with movable suspended scaffolding.
Plan of mid span closure:after side span is closed,erect stiff skeleton outside to lock adjacent ends,pre-tension cables for
closure,then cast concrete of closure segment with movable suspended scaffolding.
1.1 Construction plan of side span closure
1.1.1 Construction preparation
First,cast cantilever segments with movable suspended
scaffolding,as well as cast segments of side span on falsework.Then move the form traveler of side span ahead to closure sector,and hold place of the form traveler of mid span . At the ends of adjacent beams(i.e.both besides of closure segment of side span),have holes reserved for anchoring bottom and vertical form for casting closure segment to fix
on already completed portion of the bridge,use suspended steel belts of form traveler.
1.1.2 Additional weight
At the end of side "T" girder,apply additional weight which value equals to half of closure segment weight,but no additional weight is there at the end of segments of side span on falsework.
Additional weight can be bags filled sands or tanks filled water.
1.1.3 Lock adjacent ends for closure
Erect outside(or inside) stiff skeleton which consists of 4 sets with each set has 2 standard steel tie members ,placed at bottom slab and top slab of box-girder,to lock adjacent ends.According to the requirement of codes,when erecting stiff skeleton on steel plates reserved at completed portion ,air temperature around structure must be lowest during a day.
1.1.4 Pretension of closure tendons
(1)Actually fix bottom form and vertical form of side span closure segment;
(2)Place rebars and corrugated pipes in webs and bottom slab;
(3)Place inside formwork;
(4)Place rebars and corrugated pipes in top slab;
(5)Place closure tendons in corrugated pipes.
Pretension tendons necessary,then pour closure concrete.
1.1.5 Pour closure concrete
When pouring closure concrete ,air temperature around structure must be lower during a day.Additional weight is reduced grade by grade,keep casting concrete weight equal reduced weight,to maintain closure segment under steady state.
1.1.6 Tension of tendons and drop down beam
Tension closure tendons under some conditions:
(1)Closure concrete strength is up 95% of design value;
(2)Elastic modulus of closure concrete is up 100% of design value;
(3)Age of concrete is more than 5d.
Before tensioning,remove stiff skeleton.
Sequence of tension:first,tendons in bottom slab ,second,tendons in top slab;first,long tendons,second,short tendons.
Tension closure tendons pretensioned to design stress.After have tensioned,grout ducts.
After longitudinal ,lateral and vertical tendons have
tensioned,grout ducts,remove the temporary consolidation device of two mid piers and drop down beams,finally close mid-span,so structural system change is finished.
Remove movable traveler,form and falsework.
1.2 Construction plan of mid span closure
1.2.1 Construction preparation
At the ends of adjacent cantilevers(i.e.both sides of closure segment ),have holes reserved for anchoring bottom and vertical form for casting closure segment to fix on already completed portion of the bridge,use suspended steel belts of form traveler.
1.2.2 Additional weight
At each end of adjacent cantilevers,apply additional weight which value equals to half of closure segment weight,include cross-girder if designed.
1.2.3 Lock adjacent ends for closure
Same as 1.1.3.
1.2.4 Pretension of closure tendons
Same as 1.1.4.
1.2.5 Pour closure concrete
When pouring closure concrete ,air temperature around structure must be lower during a day.Additional weight is reduced grade by grade,keep casting concrete weight equal reduced weight,to maintain closure segment under steady state.
1.2.6 Tension of tendons
Same as 1.1.6.
2 Requirement for closure plan based on theory of unstressed state control
Bridge structure is not usually one-step forming.During construction,there are many times of changing structural system.The bridge built in such way does not behave exactly the same way as a
bridge that is built totally on falsework.So,these aspects,for example,optimum internal fore,objective geometric
configuration,monitoring and control of construction,influence with each other,and make it complex.To solve the problem,Mr.Ain-shushuan presented theory and technique[6] of unstressed state control ,which became a landmark in bridge development.
[Theorem 1] When they are set,include external loads,structure systems,structural boundary conditions,lengths and curvatures of elements under unstressed states,internal forces and displacements of final structure is determined.
[Corollary 1] Internal force and displacement of structure changes with changing of external loads,structure systems and tension of cables.Length of an element under unstressed state will change only having been adjusted artificially. When external loads and structure systems are settled,change of element length under unstressed
state corresponds to change of the element axial force;change of element curvature under unstressed state is respond to change of the element bending moment.
[Theorem 2] Having erected a non-closed part under unstressed state on the last stage structure, the new structure’s internal forces and displacements is determined, no matter whether the part is one-step forming or not, no matter the part is built on falsework or suspended scaffolding.
2.1 Principle of plan of bridge closure
During design of prestressed concrete continuous beam (girder) bridge,it is assumed that beam is built in segment,and the internal
force distribution under the weight of bridge self is still same as continuous beam, not cantilevers(bad state).Based on the theory of unstressed state, the best construction technique for a given structure depends mainly on local conditions as below:
(1)At any stage under construction,structure or any portion is safe.
(2)When element or portion of structure is being erected,it must be under unstressed state.
(3)It is necessary to use special technique to make the ends of adjacent cantilevers smoothly joint,thus,the internal fore distribution under completion stage of bridge is near to target of design.
(4)In order to obtain a bridge with the right elevation,the
required camber of the bridge at each construction stage must be calculated. Note: set up of camber cannot change distribution of
internal force,so it cannot take the place of reasonable technique for changing of system.
(5)Construction plan is economical and reasonable as well as safe.
2.2 Special technique of closure plan
Based on the theory of unstressed state,it is necessary to use special technique to make the ends of adjacent cantilevers smoothly joint.The special technique are as below:
Plan 1#:having loaded a bending moment at each end of adjacent cantilevers,then joint ends,finally,cancel the bending moments.
Plan 2#:having loaded a force at each end of adjacent
cantilevers,then joint ends,finally,cancel forces.
Plan 3#:rotate cantilevers at adjacent mid-supports,then joint ends of adjacent cantilevers,finally,cancel the torsion.
Plan 4#:lift-up cantilevers at adjacent mid-supports,then joint ends of adjacent cantilevers,finally,cancel the force.
2.3 Digital example
Fig.2-1 Model of continuous beam and target configuration under complete stage。