## Stiffness of composite sections

In structural elements in which there is concrete in compression, the effective equivalent steel section is calculated assuming that the concrete in compression is uncracked. This is reflected in the value for the modular ratio n =EJEcm = 7. In structural elements in which the concrete is in tension, the effective equivalent steel section is calculated neglecting the concrete in tension and considering only the reinforcement. As a result, the stiffness of the section can be different, depending on the sign of the seismic action effect. For example, in composite beams with a slab under positive (sagging) bending, the second moment of area/, ('moment of inertia') of the effective equivalent steel section involves all steel components (steel profile plus slab rebars) and the concrete (in compression). Under negative moments,

Clauses 7.4.2(1), 7.4.2(2), 7.4.2(3), 7.4.2(4), 7.4.2(5)

the second moment of area /2 involves only the steel profile and the rebars of the slab. As, in addition, the effective width of the slab is different for positive (sagging) and negative (hogging) moments, /, and I2 are generally different./, and I2 could be equal if and only if the equivalent section of concrete of the slab is equal to the sections of the rebars, both sections being computed with their respective effective widths under sagging and hogging bending and both sections having their centre at the same level.

For composite beams with a slab, the effective width of a slab needed to compute /, (for the sagging moment) and I2 (for the hogging moment) are defined in Table 7.5 I of EN 1998-1.

The different values of /, and /2 raise a practical problem in the analysis of a structure, as Clauses there are zones in structural elements which are subjected to positive bending, with other 7.7.2(2), zones subjected to negative bending. The structural model for the analysis has to allocate the 7.7.2(3), values /, and I2 to these zones, which implies more elements in the model and difficulty in 7.7.2(4)

defining the length of sagging and hogging zones. Fortunately, a simpler alternative is provided in Eurocode 8, which allows computation of an 'equivalent' second moment of area I , which is constant for the entire span. Clauses 7.7.2(3) and 7.7.2(4) define 7eq for beams and (EI)C for columns, respectively.

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