土木工程毕业设计外文翻译最终中英文

7 Rigid-Frame Structures

A rigid-frame high-rise structure typically comprises parallel or orthogonally arranged bents consisting of columns and girders with moment resistant joints. Resistance to horizontal loading is provided by the bending resistance of the columns, girders, and joints. The continuity of the frame also contributes to resisting gravity loading, by reducing the moments in the girders.

The advantages of a rigid frame are the simplicity and convenience of its rectangular form.Its unobstructed arrangement, clear of bracing members and structural walls, allows freedom internally for the layout and externally for the fenestration. Rig id frames are considered economical for buildings of up to' about 25 stories, above which their drift resistance is costly to control. If, however, a rigid frame is combined with shear walls or cores, the resulting structure is very much stiffer so that its height potential may extend up to 50 stories or more. A flat plate structure is very similar to a rigid frame, but with slabs replacing the girders As with a rigid frame, horizontal and vertical loadings are resisted in a flat plate structure by the flexural continuity between the vertical and horizontal components.

As highly redundant structures, rigid frames are designed initially on the basis of approximate analyses, after which more rigorous analyses and checks can be made. The procedure may typically inc lude the following stages:

1. Estimation of gravity load forces in girders and columns by approximate method.

2. Preliminary estimate of member sizes based on gravity load forces with arbitrary increase in

sizes to allow for horizontal loading.

3. Approximate allocation of horizontal loading to bents and preliminary analysis of member

forces in bents.

4. Check on drift and adjustment of member sizes if necessary.

5. Check on strength of members for worst combination of gravity and horizontal loading, and

adjustment of member sizes if necessary.

6. Computer analysis of total structure for more accurate check on member strengths and drift,

with further adjustment of sizes where required. This stage may include the second-order P-Delta effects of gravity loading on the member forces and drift..

7. Detailed design of members and connections.

This chapter considers methods of analysis for the deflections and forces for both gravity and horizontal loading. The methods are included in roughly the order of the design procedure, with approximate methods initially and computer techniques later. Stability analyses of rigid frames are discussed in Chapter 16.

7.1 RIGID FRAME BEHA VIOR

The horizontal stiffness of a rigid frame is governed mainly by the bending resistance of the girders, the columns, and their connections, and, in a tall frame, by the axial rigidity of the columns. The accumulated horizontal shear above any story of a rigid frame is resisted by shear in the columns of that story (Fig. 7.1). The shear causes the story-height columns to bend in double curvature with points of contraflexure at approximately mid-story-height levels. The moments applied to a joint from the columns above and below are resisted by the attached girders, which also bend in double curvature, with points of contraflexure at approximately mid-span. These deformations of the columns and girders allow racking of the frame and horizontal deflection in each story. The overall deflected shape of a rigid frame structure due to racking has a shear configuration with concavity upwind, a maximum inclination near the base, and a minimum inclination at the top, as shown in Fig. 7.1.

The overall moment of the external horizontal load is resisted in each story level by the couple resulting from the axial tensile and compressive forces in the columns on opposite sides of the structure (Fig. 7.2). The extension and shortening of the columns cause overall bending and associated horizontal displacements of the structure. Because of the cumulative rotation up the height, the story drift due to overall bending increases with height, while that due to racking tends to decrease. Consequently the contribution to story drift from overall bending may, in. the uppermost stories, exceed that from racking. The contribution of overall bending to the total drift, however, will usually not exceed 10% of that of racking, except in very tall, slender,, rigid frames. Therefore the overall deflected shape of a high-rise rigid frame usually has a shear configuration.

The response of a rigid frame to gravity loading differs from a simply connected frame in the continuous behavior of the girders. Negative moments are induced adjacent to the columns, and positive moments of usually lesser magnitude occur in the mid-span regions. The continuity also causes the maximum girder moments to be sensitive to the pattern of live loading. This must be considered when estimating the worst moment conditions. For example, the gravity load maximum hogging moment adjacent to an edge column occurs when live load acts only on the edge span and alternate other spans, as for A in Fig. 7.3a. The maximum hogging moments adjacent to an interior column are caused, however, when live load acts only on the spans adjacent to the column, as for B in Fig. 7.3b. The maximum mid-span sagging moment occurs when live load acts on the span under consideration, and alternate other spans, as for spans AB and CD in Fig. 7.3a.

The dependence of a rigid frame on the moment capacity of the columns for resisting horizontal loading usually causes the columns of a rigid frame to be larger than those of the corresponding fully braced simply connected frame. On the other hand, while girders in braced frames are designed for their mid-span sagging moment, girders in rigid frames are designed for the end-of-span resultant hogging moments, which may be of lesser value. Consequently, girders in a rigid frame may be smaller than in the corresponding braced frame. Such reductions in size allow economy through the lower cost of the girders and possible reductions in story heights. These benefits may be offset, however, by the higher cost of the more complex rigid connections.

7.2 APPROXIMATE DETERMINATION OF MEMBER FORCES CAUSED BY GRA VITY LOADSIMG

A rigid frame is a highly redundant structure; consequently, an accurate analysis can be made only after the member sizes are assigned. Initially, therefore, member sizes are decided on the basis of approximate forces estimated either by conservative formulas or by simplified methods of analysis that are independent of member properties. Two approaches for estimating girder forces due to gravity loading are given here.

7.2.1 Girder Forces—Code Recommended V alues

In rigid frames with two or more spans in which the longer of any two adjacent spans does not exceed the shorter by more than 20 %, and where the uniformly distributed design live load does not exceed three times the dead load, the girder moment and shears may be estimated from Table

7.1. This summarizes the recommendations given in the Uniform Building Code [7.1]. In other cases a conventional moment distribution or two-cycle moment distribution analysis should be made for a line of girders at a floor level.

7.2.2 Two-Cycle Moment Distribution [7.2].

This is a concise form of moment distribution for estimating girder moments in a continuous multibay span. It is more accurate than the formulas in Table 7.1, especially for cases of unequal spans and unequal loading in different spans.

The following is assumed for the analysis:

1. A counterclockwise restraining moment on the end of a girder is positive and a clockwise

moment is negative.

2. The ends of the columns at the floors above and below the considered girder are fixed.

3. In the absence of known member sizes, distribution factors at each joint are taken equal to 1

/n, where n is the number of members framing into the joint in the plane of the frame.

Two-Cycle Moment Distribution—Worked Example. The method is demonstrated by a worked example. In Fig, 7.4, a four-span girder AE from a rigid-frame bent is shown with its loading. The fixed-end moments in each span are calculated for dead loading and total loading using the formulas given in Fig, 7.5. The moments are summarized in Table 7.2.

The purpose of the moment distribution is to estimate for each support the maximum girder moments that can occur as a result of dead loading and pattern live loading. A different load combination must be considered for the maximum moment at each support, and a distribution made for each combination.

The five distributions are presented separately in Table 7.3, and in a combined form in Table 7.4. Distributions a in Table 7.3 are for the exterior supports A and E. For the maximum hogging

moment at A, total loading is applied to span AB with dead loading only on BC. The fixed-end moments are written in rows 1 and 2. In this distribution only .the resulting moment at A is of interest. For the first cycle, joint B is balanced with a correcting moment of - (-867 + 315)/4 = - U/4 assigned to M BA where U is the unbalanced moment. This is not recorded, but half of it, ( - U/4)/2, is carried over to M AB. This is recorded in row 3 and then added to the fixed-end moment and the result recorded in row 4.

The second cycle involves the release and balance of joint A. The unbalanced moment of 936 is balanced by adding -U/3 = -936/3 = -312 to M BA (row 5), implicitly adding the same moment to

the two column ends at A. This completes the second cycle of the distribution. The resulting maximum moment at A is then given by the addition of rows 4 and 5, 936 - 312 = 624. The distribution for the maximum moment at E follows a similar procedure.

Distribution b in Table 7.3 is for the maximum moment at B. The most severe loading pattern for this is with total loading on spans AB and BC and dead load only on CD. The operations are similar to those in Distribution a, except that the T first cycle involves balancing the two adjacent joints A and C while recording only their carryover moments to B. In the second cycle, B is balanced by adding - (-1012 + 782)/4 = 58 to each side of B. The addition of rows 4 and 5 then gives the maximum hogging moments at B. Distributions c and d, for the moments at joints C and D, follow patterns similar to Distribution b.

The complete set of operations can be combined as in Table 7.4 by initially recording at each joint the fixed-end moments for both dead and total loading. Then the joint, or joints, adjacent to the one under consideration are balanced for the appropriate combination of loading, and carryover moments assigned .to the considered joint and recorded. The joint is then balanced to complete the distribution for that support.

Maximum Mid-Span Moments. The most severe loading condition for a maximum mid-span sagging moment is when the considered span and alternate other spans and total loading. A concise method of obtaining these values may be included in the combined two-cycle distribution, as shown in Table 7.5. Adopting the convention that sagging moments at mid-span are positive, a mid-span total; loading moment is calculated for the fixed-end condition of each span and entered in the mid-span column of row 2. These mid-span moments must now be corrected to allow for rotation of the joints. This is achieved by multiplying the carryover moment, row 3, at the left-hand end of the span by (1 + 0.5 D.F. )/2, and the carryover moment at the right-hand end by -(1 + 0.5 D.F.)/2, where D.F. is the appropriate distribution factor, and recording the results in the middle column. For example, the carryover to the mid-span of AB from A = [(1 + 0.5/3)/2] x 69 = 40 and from B = -[(1+ 0.5/4)/2] x (-145) = 82. These correction moments are then added to the fixed-end mid-span moment to give the maximum mid-span sagging moment, that is, 733 + 40 + 82 = 855.

7.2.3 Column Forces

The gravity load axial force in a column is estimated from the accumulated tributary dead and live floor loading above that level, with reductions in live loading as permitted by the local Code of Practice. The gravity load maximum column moment is estimated by taking the maximum difference of the end moments in the connected girders and allocating it equally between the column ends just above and below the joint. To this should be added any unbalanced moment due to eccentricity of the girder connections from the centroid of the column, also allocated equally between the column ends above and below the joint.

第七章框架结构

高层框架结构一般由平行或正交布置的梁柱结构组成，梁柱结构是由带有能承担弯矩作用节点的梁、柱组成。具有抗弯能力的梁、柱和节点共同作用抵抗水平荷载。连续框架可降低梁的跨中弯矩而有利于抵抗重力荷载。

框架结构有简捷和便于采用矩形体系的优点。由于这种布置形式没有斜支撑和结构墙体，因此，没有不便利之处，内部可以自由布置，外部可以自由设计门、窗。框架结构对于25层以内的建筑是经济的，超过25层由于要限制其位移而花费的代价高，显得很不经济。如果框架与剪力墙及芯筒相结合，刚度能够大幅度提高，可以建造50层以上的建筑。板柱结构与框架结构非常相似，不同之处仅是用板代替了梁。和框架结构一样，板柱结构是通过其水平和竖向构件之间的连续抗弯作用来抵抗水平和竖向荷载。

对于高次超静定框架结构，应根据近似分析进行初步设计，随后进行精确分析和校核。分析过程一般包括以下几步:

1．按近似方法确定梁和柱所受重力荷载;

2．初步确定在重力荷载作用下构件的截面尺寸，考虑水平荷载的作用进行构件截面尺寸的任意调整;

3．将水平荷载分配到各梁柱结构上，对这些结构构件的内力进行初步分析;

4．检验位移并对构件截面尺寸做必要的调整;

5．按最不利的重力荷载和水平荷载组合检验构件强度，做必要的构件截面尺寸调整; 6．为了更精确地验算构件强度和位移，利用计算机对结构进行整体分析，需要时则近一步调整构件截面尺寸。这一阶段中应包括考虑重力荷载对构件内力和位移产生的Ρ一△二阶效应;

7．构件和节点的详细设计。

本章讨论在重力和水平荷载作用下结构的变形和内力分析方法。这些方法基本上按照设计过程中的次序介绍，首先是近似法，然后介绍计算机分析技术。框架结构的稳定性分析将在第十六章中讨论。

7.1框架结构的性能

框架结构的侧向刚度主要取决于梁、柱及节点的抗弯能力，在较高的框架中主要取决于

柱子的轴向刚度。作用于框架任一层间的水平集中剪力由该层柱子的抗剪能力抵抗(图7.

1)。剪力使框架结构每层的柱产生双曲率弯曲，其反弯点大约在层高的中间部位。上、下柱引起的作用于节点处的弯矩由相邻梁承担，该梁、柱的变形引起框架的整体变形，使各层间产生水平位移。在水平推力作用下结构的整体变形和剪力图如图7. 1所示，其凹面朝向风荷载作用方向，最大倾角在基底附近，最小倾角在顶端。

外部水平荷载产生的总弯矩由各层间两个边柱中的轴向拉、压力组成的力矩抵抗(图7.2 )。柱子的伸、缩引起结构的整体弯曲变形，并产生相应的水平位移。因为转角沿建筑高度累加，所以整体弯曲变形引起的层间位移随高度增加而增加，而剪切变形引起的层间位移随高度的增加而减小。其结果在建筑的最顶部整体弯曲对层间位移的贡献会大大超过剪切变形对层间位移的贡献。但是，整体弯曲变形对总位移的贡献与剪切变形对总位移的贡献之比不会超过10％，除非在极高或细长的框架中。因此，高层框架结构变形型式为剪切型。

从梁的连接受力性能来看，高层建筑采用的刚性节点连续的框架不同于一般简单连接的普通框架。梁在柱边附近产生负弯矩，跨中正弯矩值常常很小。这种连续性能使梁中最大弯矩对活荷载的作用方式非常敏感。如果能够估计出产生最不利弯矩的因素，则必须加以认真的考虑。例如，重力荷载作用下梁在边柱附近产生的最大负弯矩只会在活荷载作用于边跨和相间跨时才能发生，如图7.3a中的A点。而梁在内柱附近产生的最大负弯矩只会在活荷载作用于相邻跨时才能发生，如图7.3a中的B点。当活荷载作用于本跨和相间跨时，梁的跨中正弯矩最大，如图7. 3a中的AB和CD跨。

框架的尺寸取决于柱子在水平荷载作用·下的抗弯强度，这往往会使框架柱的截面尺寸大于相应全对角支撑简单连接框架的柱截面尺寸。另外，框架支撑结构中的梁被设计为只具有跨中正弯矩，而框架结构的梁则被设计为端部为负弯矩和跨中为正弯矩，跨中弯矩值较小。因此，框架结构中梁的截面尺寸会小于相应的框架支撑结构中梁的截面尺寸。梁截面的减小将会降低其造价，有时可以降低层高，经济效益明显。但是，由于刚性节点的处理相当复杂，

代价较高，使上述经济优势被削弱。

7.2重力荷载作用下构件内力的近似计算

框架结构是多次超静定结构，因此，只有在确定了构件截面尺寸后才能进行精确分析。所以，在初步设计阶段，可根据传统的公式和不考虑构件特征值的简化分析法近似确定构件中的内力，以此为基础确定构件的截面尺寸。下面将讨论在重力荷载作用下构件内力计算的两种方法。

7.2.1梁的内力—规范推荐值

对于两跨以上的框架结构，当任何相邻两跨中的长跨不超过短跨的20%跨度，同时设计均布活荷载不超过3倍的恒载时，梁的弯矩和剪力可以按表7.1确定。表中各数值是根据统一建筑规范【7.1】中的推荐值给出。对于其它情况，可按照楼面连续梁采月传统弯矩分配法或两次循环弯矩分配法进行分析确定。

7.2.2弯矩分配法【7.2】

弯矩分配法用于计算多跨连续梁的弯矩是非常便利的形式。该方法的计算结果比表7.1中的推荐公式计算结果更精确，特别是对于不等跨和荷载变化较大的情况。

弯矩分配法的分析假定如下:

1．梁端约束弯矩以反时针方向为正，顺时针方向为负;

2．被分析的梁与上、卞柱的连接为固接;

3．当构件尺寸尚未确定时，每个节点的分配系数取1/n，n是框架平面内连接在各节点上的构件总数。

两次循环弯矩分配实例.

现以一个实例具体说明两次循环弯矩分配的过程。在图7.4中表示出一个取自框架单榻结构的中跨连续梁AE和作于其上的荷载。恒载和全部荷载作用下每跨的固端弯矩采用图7.5中的公式计算。这些弯矩值汇总于表7.2 中。

弯矩分配的目的是为了确定每个支座处梁在恒载和标准活荷载作用下可能产生的最大弯矩。计算梁在支座处最大弯矩时必须考虑不同的荷载组合，而每种荷载组合作用都应进行一次计算。

表7.3分别给出了5组弯矩分配，表7.4给出的是混合形式。表7. 3中a组分配为边支座A和E。为了求出A点的最大负弯矩。在AB跨施加全部荷载，在BC跨只布置恒载。固端弯矩列于1、2行。这组分配主要是为了求出A点的结果。第一循环分配，节点B由修正弯矩-(-867+315 )/ 4=-U4平衡指定为MBA，U是不平衡弯矩。这些计算可不作记录，而将修正弯矩的一半即(-U/4)/2传于MAB。将此值记录在第3行，同时与固端弯矩相力盯，结果写在第4行。

第二循环包括节点A的释放和平衡。通过加上-U/3=-936/3 =-312(MBA第5行)来平衡原有的不平衡弯矩936，这也隐含地说明对节点A处的两个柱端增加了同样大小的弯矩。弯矩分配的第二循环到此完成，节点A处最终的最大弯矩为第4、5行数值之和，即936-31=624。节点E处的最大弯矩分配应遵循同样的方式。

表7.3中b组分配是针对B节点的最大弯矩。最不利的荷载作用方式是BC作用全部荷载，CD跨只有恒载。计算过程类似于a组分配，但首次循环应平衡两相间节点A和C，同时仅将它们的传递弯矩记录在节点B。第二次循环，将-(-1012+782)/4=58与节点B两边值分别相加，以此平衡节点B。将第4、5行的弯矩相加后就得出节点B的两端最大负弯矩。节点C和D的弯矩分配即c组和d组分配按照b组分配的同样的方式进行。

全部运算过程可以一同列于表7，4中，表中首先记录每个节点处相应于恒载和全部荷载的固端弯矩。选择合理的荷载组合，将所关心的节点两侧相邻节点加以平衡，然后将传递弯矩分配于所关心的节点并记录。平衡该节点，完成这个支座的分配。

最大跨中弯矩

与跨中最大正弯矩出现的相应最不利荷载条件即为该跨和相间各跨均作用全部荷载。该值计算的最简便方法是将两次循环弯矩分配组合起来，如表7.5所示。采用跨中正弯矩为正号的规则就可以计算各跨为固端条件时全苟祠苛载在跨中产生的弯矩，并记录在第2行的跨中一列。实际结构的节点处应该能够转动，所以需要对跨中弯矩加以修正。修正的方法是:将该跨左端第3行的传递弯矩乘以(1+0.5D.F.)/2，右端的传递弯矩乘以-(1+0. 5D.F. )/2，其中D.F.为合理性分配系数，这些结果记录在跨中一列上。例如，从A传递给AB跨中的弯矩为〔（1+0.5/3)/2〕×69=40，从B传给AB跨中的弯矩为-〔（1+0.5/4）/2〕×(-145)=85。

这些修正弯矩与固端情况下的跨中弯矩相加就得到了最大跨中正弯矩，即733+40+82=855。

7.2.3柱的内力

重力荷载使柱子中产生的轴向力可以采用每层间的恒载和活荷载叠加值进行计算，如果当地现行规范许可，则应对活荷载加以折减。重力荷载作用下使柱子中产生的最大弯矩的计算应取与该柱相连的梁端弯矩的最大差值均等地分配于上、下柱端节点，同时，还应加上由于柱轴心到梁节点的偏心引起的不平衡弯矩，这个不平衡弯矩也应均等地分配于上、下柱端节点。