To describe the effects of cracking of concrete and yielding of steel on the distribution of bending moments. To explain methods of elastic structural analysis which allow for these effects and for local buckling of the structural steel section, and to discuss lateral-torsional buckling in continuous composite beams.
RELATED WORKED EXAMPLES
Worked example 10.3: Design of a continuous composite beam
SUMMARY
Elastic analysis for internal moments and forces in continuous composite beams is of more general application than plastic analysis. Redistribution is permitted to allow for cracking of concrete and yielding of steel in the negative moment regions. The extent of the redistribution depends on the classification of cross-sections at internal supports and the assumptions made concerning the flexural rigidity in hogging bending.
For a cross-section in Class 3 or Class 4, stresses should be calculated by elastic theory using an effective width for the concrete flange. Account may be taken of creep of concrete in compression by means of an appropriate modular ratio.
The typical pattern of bending moments in a continuous beam results in the lower flange being in compression over internal supports. As the upper flange of the steel section is restrained by the concrete slab, lateral buckling of the compression flange is accompanied by distortion of the cross-section. Account can be taken of the distortional stiffness to reduce the effective slenderness for lateral-torsional buckling.
Bending moments in continuous composite beams at the ultimate limit state (ULS) may be determined by elastic analysis or, subject to certain conditions, rigid-plastic analysis. The latter method is discussed in the previous lecture, Continuous composite beams I. Elastic analysis has the advantage of more general application and may also be more convenient to use as this approach is also required to check the serviceability limit state (see lectures Composite beams - Design for serviceability part 1 and part 2).
In composite building structures, no consideration of temperature effects is normally necessary in verifications for ULS. Similarly, the effects of shrinkage may be neglected, except in analysis involving Class 4 sections. These effects, therefore, are not considered in this lecture.
This lecture concerns beams in which the steel section is either continuous over simple supports or is jointed by rigid connections.
In general, elastic analysis requires that the relative stiffnesses of adjacent spans be known. As the stiffnesses depend on the second moment of area of cross-sections, it is necessary to know the effective width of the concrete flange and the modulus of elasticity of concrete relative to that of steel (the modular ratio).
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