## Methods of analysis

At the ultimate limit state (ULS) the type of analysis should be appropriate to the problem being considered. The following are commonly used:

■ Linear elastic analysis.

■ Linear elastic analysis with limited redistribution.

■ Plastic analysis.

At the serviceability limit state (SLS) linear elastic analysis may be used. Linear elastic analysis may be carried out assuming:

■ Cross-sections are uncracked and remain plane (i.e. may be based on concrete gross sections).

■ Linear stress-strain relationships.

■ The use of mean values of elastic modulus.

For ULS, the moments derived from elastic analysis may be redistributed provided that the resulting distribution of moments remains in equilibrium with the applied actions. In continuous beams or slabs with /ck < 50 MPa the minimum ratio of the redistributed moment to the moment in the linear analysis, S, is 0.70 where Class B or Class C reinforcement is used or 0.80 where Class A reinforcement is used.

Within the limits set, coefficients for moment and shear derived from elastic analysis may be used to determine forces in regular structures (see Appendix B).

The design of columns should be based on elastic moments without redistribution. <5.2.7>

Plastic analysis may be used for design at ULS provided that the required ductility <5.6.2> can be assured, for example, by:

■ Limiting xu / d (to < 0.25 for concrete strength classes < C50/60).

■ Using Class B or C reinforcement.

■ Ensuring the ratio of moments at intermediate supports to moments in spans is between 0.5 and 2.0.

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