The code recognizes that a certain number of elements can be considered as not to be part of the seismic-resisting system of the building and be designed as “secondary seismic members”.

Accordingly, the corresponding strengths and stiffness of these elements against seismic actions must be neglected. The main advantage is that secondary elements can be designed for gravity loads only, following the provisions of Eurocode 2. This will allow for slender sections, and, consequently, fewer structural constraints. A typical example is the case of shallow beams, which could hardly be designed as primary elements due to the poor resulting joint dimension.

The choice of the secondary elements however cannot be arbitrary, but needs to comply with the following conditions:

• the total contribution to the lateral stiffness of all secondary elements should not exceed 15% of that of the primary elements.
• In any case, the choice of the secondary elements cannot change the classification of the structure from irregular to regular.
• Lastly, secondary members and their connections shall be designed to maintain the support of gravity loading when subjected to the displacements caused by the most unfavourable seismic design condition.

The fulfilment of the first two requirements can easily be verified by comparing the behaviour of the finite element model, including and excluding the secondary members’ stiffness. The last condition instead, requires the definition of specific load combinations for checking the flexural and shear resistance of the secondary members under the imposed seismic displacements.

The whole process can readily be implemented in VIS, using a unique model analyzed in “SAP2000” or “ETABS”.

The present SAP2000 model represents a 5-story reinforced concrete building, to be designed according to Eurocode 8 as a ductility class medium structure.

The seismic resisting system is in this case different in the two principal horizontal directions:

• in the X direction, a set of primary ductile moment frames are employed;
• while in the Y direction, a shear wall system is adopted.

The horizontal floor diaphragms are made by one-way ribbed slabs, oriented along the global X direction and supported by beams at each span. In order to limit the total depth of the interior beams to the depth of the slab, they have been considered as secondary seismic elements. Let’s now see how we can justify this assumption.

The first thing to do is set up the two alternatives stiffness scenarios:

• the first, called “Full Stiffness”, will include all the elements;
• the second, called “Primary Stiffness”, will exclude the contribution of the secondary elements.

This will allow us to compare the results of both cases, and check the code requirements in terms of stiffness and regularity.

Different stiffness scenarios can easily be created in SAP2000 using a simple “single-stage” staged construction analysis.

Before defining the analysis, we need to create the necessary “property sets” that will be assigned to the different elements. Appropriate stiffness modifiers are defined for beams, columns, and walls, to represent the effect of cracking. Then, a set of flexural end releases, specific for the secondary elements, is also created.

At this point we are ready to define the analysis:

• as mentioned, the “Full Stiffness” analysis will include all the elements, assigning them the corresponding stiffness modifiers;
• the “Primary Stiffness” analysis will instead apply the flexural releases to the secondary elements and the stiffness modifiers to the primary elements.

We can now use these two cases as the reference stiffness for all the other analysis:

• the “Primary Stiffness” is associated with the modal and the response spectrum analysis used for the design of the primary elements.

The reference spectrum is reduced by the appropriate behaviour factor, chosen in accordance with the structural system and the ductility class of the building.

• The “Full Stiffness” is instead associated with all the static load cases and to the modal and response spectrum analysis used for the design of the secondary elements.

In this case, the applied spectrum is the full reference spectrum, since the internal forces in these elements must correspond to the effective maximum seismic displacements.

The last required step is the definition of the design load combinations.

Different seismic combinations must be defined for primary and secondary elements, using the appropriate response spectrum analysis. We are now ready to run the analysis. By comparing the results of the two-modal analysis, we can readily verify the impact of the secondary elements both in terms of total stiffness contribution and structural regularity. Once the basic requirements have been satisfied, we can proceed with the design of the elements.

Let’s open VIS from the tools menu and start the import process. We first need to select the design load combinations for each limit state. At this stage, as seismic load combinations, we select only those corresponding to the primary elements.Once we have properly filled all the fields, we can move to the dedicated “Secondary Elements” tab. In this section, we can identify the secondary elements and overwrite the corresponding seismic design combinations.

Now that the structure has been imported, we can set the appropriate code parameters and start the design.

VIS will automatically apply the appropriate design rules for primary and secondary elements. Let’s compare, for example, the different design strategies adopted by the program for a primary and a secondary set of beams.

In addition to the strength and service requirements, primary elements are designed to satisfy the capacity design rule and the special detailing provisions included in Eurocode 8. Secondary elements are instead checked against strength and service limit states only, and for the standard detailing provisions defined in Eurocode 2.

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