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1、6.4 Analysis of Rigid Reinforced Concrete Frame Structures,Rigid Frame Behavior 框架结构性能,(a) Forces and deformations caused by external shear (b) Forces and deformations caused by external moment,框架总体剪切变形,框架总体弯曲变形,Rigid Frame Behavior 框架结构性能,Rigid Frame Behavior,The shear causes the storey-height colu
2、mns to bend in double curvature with inflection points反弯点 at approximately mid-storey-height levels. The moments applied to a joint from the columns above and below are resisted by the attached girders, which are also bent in double curvature, with inflection points at approximately mid-span.,Rigid
3、Frame Behavior,These deformations of the columns and girders allow racking of the frame and horizontal deflection in each storey. The overall deflection shape总体变形 of a rigid frame structure due to racking has a shear configuration剪切变形 with concavity凹度 upwind, a maximum inclination near the base, and
4、 a minimum inclination at the top,框架总体剪切变形,Rigid Frame Behavior,The overall moment of the external horizontal load is resisted in each storey level by the couple 力偶 resulting from the axial tension and compressive forces in the columns on opposite sides of the structure. The extension and shortening
5、 of the columns cause overall bending 总体弯曲 and associated horizontal displacement of the structure.,框架总体弯曲变形,Rigid Frame Behavior,Because of the cumulative rotation up the height, the storey drift 层间位移 due to overall bending increases with height, while that due to racking tends to decrease. Consequ
6、ently the contribution to the storey drift from overall bending may, in the uppermost level, exceed that from racking.,框架总体弯曲变形,The contribution of overall bending to the total drift, however, will usually not exceed 10% of that racking except very tall, slender, rigid frames. Therefore the overall
7、deflection shape of a high-rise rigid frame usually has a shear configuration,Rigid Frame Behavior,The response of a rigid frame to gravity loading Negative moments are induced adjacent to the columns, and positive moments of usually lesser magnitude occur in the mid-span regions.,Rigid Frame Behavi
8、or,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,Approximate Determination of Member Forces Caused by Gravity Loading: Floor Frame Substructure Method分层力矩分配法,For building frame
9、s with a regular outline, not involving unusual asymmetry of loading or shape, the influence of sideway caused by vertical loads can be neglected.框架的侧移忽略不计 Moments due to vertical loads are determined with sufficient accuracy by dividing the entire frame into simple subframes,Approximate Determinati
10、on of Member Forces Caused by Gravity Loading: Floor Frame Substructure Method分层力矩分配法,Each of subframes consists of one continuous beam, plus the top and bottom columns framing into that particular beam. The far ends of the columns are considered fixed柱端设为固定端,Approximate Determination of Member Forc
11、es Caused by Gravity Loading: Floor Frame Substructure Method分层力矩分配法,Only two cycles are carried out in the analysis. Moments transferred from one floor to another floor are small. Hence, the moments for each floor are separately calculated.每层梁上的竖向荷载对本层梁及与本层梁相连的柱产生弯矩,分层法计算步骤及要点,1.选择某榀框架作为计算单元,2.计算梁柱
12、线刚度以及节点处分配系数 1）对于现浇框架，要考虑梁有效截面惯性矩的调整； 2）柱端设为固定端； 3）底层柱固定在基础顶面，可以视为固定端，其它层柱要 考虑到实际有柱端转动，故上层各柱线刚度乘以0.9修 正系数； 4）梁和底层柱的传递系数(carry-over factor)按远端(far ends of members)固定，取1/2；上层各柱的传递系数取1/3。,3. 统计各层梁上竖向荷载(Gravity Loading)设计值，并计算梁的固端弯矩(fixed-end moment)。 4. 按前面规定的分配系数(distribution factor)和传递系数(carry-over f
13、actor)，采用力矩分配法(Moment Distribution Method)对每一层框架分别进行计算。 5. 求得每层内力后，将同属于上下两层的柱弯矩值进行叠加，作为原框架该柱的最终弯矩，梁的弯矩仅属于本层，不需叠加。 6.得到框架最终弯矩图后，根据节点静力平衡可求得梁跨中弯矩，支座剪力以及柱剪力和轴力。,例题,The gravity load axial force in a column is estimated from the accumulated tributary dead and live floor loading above that level, with red
14、uctions in live loading 活荷载折减as permitted by design code.,The resistance to moments at any floor or roof leve is estimated by taking the maximum difference of the end moments in the connected girders and distributing the moment between columns immediately above and below the given floor in proportio
15、n to the relative column stiffness.,6层,5层,2-4层,1层,Approximate Determination of Member Forces Caused by Horizontal Loading,Allocation of Loading Between Columns Assumption ：floor slabs are rigid in plane For a symmetric structure subjected to symmetric loading Total external shear at a level will be
16、distributed between the columns in proportion to their shear rigidities抗侧刚度 (D0) at that level. The shear rigidity of a column is,linear rigidity of column,height of the storey,Approximate Determination of Member Forces Caused by Horizontal Loading,Inflection Point Method反弯点 法 The inflection points of all members, columns and girders, are located midway between joints except that of the ground floor.对上层柱，假定各柱上下转角相等，则柱上下端弯矩相等，反弯点在柱中央 The inflection points of the ground floor co
