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Floor acts as diaphragm

Floor acts as diaphragm

FIGURE 22.28 Location of bracing systems: (a) exterior braced frames, (b) internal braced core, and (c) bracing arrangements to be avoided.

torsional resistance. Bracing frames should be situated where the center of lateral resistance is approximately equal to the center of shear resultant on plan. Where this is not possible, torsional forces will be induced and they must be considered when calculating the load carried by each braced system.

When core braced systems are used, they are normally located in the center of the building (Figure 22.28b). The torsional stability is then provided by the torsional rigidity of the core brace. For tall building frames, a minimum of three braced bents are required to provide transitional and torsional stability. These bents should be carefully arranged so that their planes of action do not meet at one point so as to form a center of rotation. The bracing arrangement shown in Figure 22.28c should be avoided.

The flexibility of different bracing systems must be taken into account in the analysis, since the stiffer braces will attract a larger share of the applied lateral load. For tall and slender frames, the bracing system itself can be a sway frame and a second-order analysis is required to evaluate the required forces for ultimate strength and serviceability checks.

Lateral loads produce transverse shears, over turning moments and sidesway. The stiffness and strength demands on the lateral system increase dramatically with height. The shear increases linearly, the overturning moment as a second power and sway as a fourth power of the height of the building. Therefore, apart from providing the strength to resist lateral shear and overturning moments, the dominant design consideration (especially for tall buildings) is to develop adequate lateral stiffness to control sway.

For serviceability verification, it requires that both the interstory drifts and the lateral deflections of the structure as a whole must be limited. The limits depend on the sensitivity of the structural elements to shear deformations. Recommended limits for typical multistory frames are given in Table 22.2. When considering the ultimate limit state, the bracing system must be capable of transmitting the factored lateral loads safely down to the foundations. Braced bays should be effective throughout the full height of the building. If it is essential for bracing to be discontinuous at one level, provision must be made to transfer the forces to other braced bays. Where this is not possible, torsional forces may be induced and they should be allowed for in design (see Section 22.3.6).

Figure 22.29 shows an example of a building that illustrates the locations of vertical braced trusses provided at the four corners to achieve lateral stability. Diaphragm action is provided by a lightweight aggregate concrete slab that acts compositely with metal decking and floor beams. The floor beam-to-column connections are designed to resist shear force only as shown in the figure.

FIGURE 22.29 Simple building frame with vertical braced trusses located at the corners. Copyright 2005 by CRC Press

22.4.5 Moment-Resisting Frames

In cases where bracing systems would disturb the functioning of the building, rigidly jointed moment-resisting frames can be used to provide lateral stability to the building, as illustrated in Figure 22.30a. The efficiency of development of lateral stiffness depends on bay span, number of bays in the frame, number of frames, and the available depth in the floors for the frame girders. For buildings with heights not more than three times the plan dimension, the moment frame system is an efficient form. Bay dimensions in the range of 6 to 9 m and structural height up to 20 to 30 stories are commonly used. However, as the building height increases, deeper girders are required to control drift, thus the design becomes uneconomical.

When a rigid unbraced frame is subjected to lateral load, the horizontal shear in a story is resisted predominantly by the bending of columns and beams. These deformations cause the frame to deform in a shear mode. The design of these frames is controlled therefore by the bending stiffness of individual members. The deeper the member, the more efficiently the bending stiffness can be developed. A small part of the frame sidesway is caused by the overturning of the entire frame resulting in shortening and elongation of the columns at opposite sides of the frame. For unbraced rigid frames up to 20 to 30 stories, the overturning moment contributes for about 10 to 20% of the total sway, whereas shear racking accounts for the remaining 80 to 90% (Figure 22.30b). However, the story drift due to overall bending tends to increase with height, while that due to shear racking tends to decrease.

22.4.5.1 Drift Assessment

Since shear racking accounts for most of the lateral sway, the design of such frames should be directed toward minimizing the sidesway due to shear. The shear displacement A in a typical story in a multistory frame, as shown in Figure 22.31, can be approximated by the equation

where A,- is the shear deflection of the ¿th story, E is the modulus of elasticity, Ic, Ig are second moments of area for columns and girders, respectively, h, is the height of the ¿th story, L, is the length of girder in the ¿th story, V, is the total horizontal shear force in the ¿th story, ^(Jc,/hi) is the sum of the column stiffness in the ¿th story, and ^(Ig,/L;) is the sum of the girder stiffness in the ¿th story.

Examination of Equation 22.4 shows that sidesway deflection caused by story shear is influenced by the sum of column and beam stiffnesses in a story. Since for multistory construction span lengths are generally larger than the story height, the moment of inertia of the girders needs to be larger to match the

Lateral load Sidesway of Shear racking Column shortening unbraced frame component component

FIGURE 22.30 Sidesway resistance of a rigid unbraced frame. Copyright 2005 by CRC Press

Lateral load Sidesway of Shear racking Column shortening unbraced frame component component

FIGURE 22.30 Sidesway resistance of a rigid unbraced frame. Copyright 2005 by CRC Press

FIGURE 22.31 Story drift due to (a) bending of columns and (b) bending of girders.

column stiffness, as both of these members contribute equally to the story drift. As the beam span increases, considerably deeper beam sections will be required to control frame drift.

Since the gravity forces in columns are cumulative, larger column sizes are needed in lower stories as the frame height increases. Similarly, story shear forces are cumulative and, therefore, larger beam properties in lower stories are required to control lateral drift. Because of limitations in available depth, heavier beam members will need to be provided at lower floors. This is the major shortcoming of unbraced frames because considerable premium for steel weight is required to control lateral drift as building height increases.

Apart from the beam span, height-to-width ratios of the building play an important role in the design of such structures. Wider building frames allow a larger number of bays (i.e., larger values for story summation terms ^(Ici/hi) and ^(IgJLi) in Equation 22.4 with consequent reduction in frame drift. Moment frames with closed spaced columns that are connected by deep beams are very effective in resisting sidesway. This kind of framing system is suitable for use in the exterior planes of the building.

22.4.5.2 Moment Connections

Fully welded moment joints are expensive to fabricate. To minimize labor cost and to speed up site erection, field bolting instead of field welding should be used. Figure 22.32 shows several types of bolted or welded moment connections that are used in practice. Beam-to-column flange connections can be shop-fabricated by welding of a beam stub to an end plate or directly to a column. The beam can then be erected by field bolting the end plate to the column flanges or splicing beams (Figure 22.32c and d).

An additional parameter to be considered in the design of columns of an unbraced frame is the ''panel zone'' between the column and the transverse framing beams. When an unbraced frame is subjected to lateral load, additional shear forces are induced in the column web panel as shown in Figure 22.33. The shear force is induced by the unbalanced moments from the adjoining beams causing the joint panel to deform in shear. The deformation is attributed to the large flexibility of the unstiffened column web. To prevent shear deformation so as to maintain the moment joint assumption as assumed in the global analysis, it may be necessary to stiffen the panel zone using either a doubler plate or a diagonal stiffener

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