非定常梁与框架分析外文翻译资料

Analysis of Indeterminate Beams and Frames

The individual members that compose a steel or timber structure are fabricated or cut separately and joined together by rivets, bolts, welds, or nails. Unless the joints are specially designed for rigidity, they are too flexible to transfer moments of significant magnitude from one member to another. In contrast, in reinforced concrete structures as much of the concrete as is practical is placed in one single operation. Reinforcing steel is not terminated at the ends of a member but is extended through the joints into adjacent members. At construction joints, special care is taken to bond the new concrete to the old by carefully cleaning the latter, by extending the reinforcement through the joint, and by other means. As a result, reinforced concrete structures usually represent monolithic, or continuous, units. A load applied at one location causes deformation and stress at all other locations. Even in precast concrete construction, which resembles steel construction in that individual members are brought to the job site and joined in the field, connections are often designed to provide for the transfer of moment as well as shear and axial load, producing at least partial continuity

The effect of continuity is most simply illustrated by a continuous beam, such as shown in Fig. 12. 1a. With simple spans, such as provided in many types of steel construction, only the loaded member CD would deform, and all other members of the structure would remain straight. But with continuity from one member to the next through the support regions, as in a reinforced concrete structure, the distortion caused by a load on one single span is seen to spread to all other spans, although the magnitude of deformation decreases with increasing distance from the loaded member. All members of the six-span structure are subject to curvature, and thus also to bending moment, as a result of loading span CD.

Similarly, for the rigid-jointed frame of Fig. 12. 1b, the distortion caused by a load on the single member GH spreads to all beams and all columns, although, as before, the effect decreases with increasing distance from the load. All members are subject to bending moment, even though they may carry no transverse load.

If horizontal forces, such as forces caused by wind or seismic action, act on a frame, it deforms as illustrated by Fig. 12. Ic. Here, too, all members of the frame forces act only on the left side, the amount of distortion is seen to be the same for all corresponding members, regardless of their distance from the points of loading, in contrast to the case of vertical loading. A member such as EH, even without a directly applied transverse load, will experience deformations and associated bending moment.

In statically determinate structures, such as simple-span beams,the deflected shape and the moments and shears depend only on the type and magnitude of the loads and the dimensions of the member. In contrast, inspection of the statically indeterminate structures in Fig. 12. 1 shows that the deflection curve of any member depends not only on the loads but also on the joint rotations, whose magnitudes in turn depend on the distortion of adjacent, rigidly connected members. For a rigid joint such as joint H in the frame shown in Fig. 12. 1b or c. all the rotations at the near ends of all members framing into that joint must be the same. For a correct design of continuous beams and frames. it is evidently necessary to determine moments, shears, and thrusts considering the effect of continuity at the joints.

The determination of these internal forces in continuously reinforced concrete structures is usually based on elastic analysis of the structure at factored loads with methods that will be described in Sections 12.2 through 12.5. Such analysis requires knowledge of the cross-sectional dimensions of the members Member dimensions are initially estimated during preliminary design, which is described in Section 12.6 along with guidelines for establishing member proportions. For checking the results of more exact analysis, the approximate methods of Section 12.7 are useful. For many structures, a full elastic analysis is not justified, and the ACI coefficient method of analysis described in Section 12.8 provides an adequate basis for design moments and shears.

Before failure, reinforced concrete sections are usually capable of considerable inelastic rotation at nearly constant moment, as was described in Section 6.9. This permits a redstribution of elastic moments and provides the basis for plastic analysis of beams, frames, and slabs. Plastic analysis will be developed in Section 12.9 for beams and frames and in Chapters 14 and 15 for slabs.

LOADING

The individual members of a structural frame must be designed for the worst combination of loads that can reasonably be expected to occur during its useful life. Internal moments, shears, and thrusts are brought about by the combined effect of dead and live loads, plus other loads, such as wind and earthquake, as discussed in Section 1.7.While dead loads are constant, live loads such as floor loads from human occupancy can be placed in various ways, some of which will result in larger effects than others.In addition, the various combinations of factored loads specified in Table 1. 2 must be used to determine the load cases that govern member design. The subject of load placement will be addressed first.

Placement of Loads

In Fig. 12.2a only span CD is loaded by live load. The distortions of the various frame members are seen to be largest in, and immediately adjacent to, the loaded span and to decrease rapidly with increasing distance from the load. Since bending moments are proportional to curvatures, the moments In more remote members are correspondingly smaller than those in, or close to, the loaded span. However, the loading s

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