1、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 conti
2、nuity 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
3、for the layout and externally for the fenestration. Rigid 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
4、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 vertic
5、al 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 include the following stages: 1. Estimation of gravity load forces in girders
6、 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 an
7、d 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 s
8、izes 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 method
9、s 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 BEHAVIOR The horizontal stiffness of a rigid frame is governed mainly by the bending resistan
10、ce 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 doub
11、le 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
12、 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 F
13、ig. 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 associ
14、ated 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 storie
15、s, 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 o
16、f 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 mome
17、nts 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.
18、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.
