Earthq..docx

The Objective from this chapter is to provide Sufficient information for the effective modelling of reinforced concrete and steel structures, for the purposes of assessment and design under earthquake motion. When it comes to the structural response to static loads, few issues remain unsolved. While, on the other hand, seismic action and response of structures needs knowledge from several sub-disciplines in engineering, such as engineering seismology, geotechnical, structural analysis and computational mechanics. To perform a reliable seismic analysis of structural systems, a conceptual framework is required. The framework includes the essential components:      

Ground motion and load modelling Structural modelling Foundation and soil modelling Method of analysis Performance levels Output for assessment

Modelling of input quantities, such as ground motions and gravity loads, is a critical step in the earthquake response analysis of structures. To perform dynamic analysis either response spectra or time histories of earthquake ground motion may be employed

Several types of loads may be applied to a structure during its lifetime, including primarily dead and live actions. Dead loads may be modelled reliably through Gaussian and exhibit low coefficients of variation. Live loads exhibit higher variability and their statistical representation depends significantly on the type of live load considered. In addition, when an earthquake hits a structure, it is unlikely that all live loads would be at their respective maximum value. Load combination models are an important part of the definition of actions on structures. Dead loads considered in static and dynamic analyses are due to the own weight of the structure as well as partitions, finishes and any other permanent fixtures. Live loads are non-permanent and represent the use and occupancy. Seismic codes provide characteristic values of design values. Lateral loads, such as wind and earthquakes occur only occasionally. Seismic loads are generated by the mass of the structure when accelerated by earthquake ground motion, making these loads a function of the characteristics of both earthquake and structure. When calculating seismic loads, the weight of the structure does not correspond to the full dead and live load, since this would be overconservative in view of the low probability of an earthquake occurring while the structure is at maximum live load. Some live loads may not be rigidly fixed to the supporting system and do not necessarily move in phase with the rest of the structure. So, it is necessary to define percentages of dead and live loads when considering the tributary seismic weight WEq and corresponding mass MEQ.. The approach is implemented in seismic codes as follows:

Where Weq is the seismic weight, p1 and p2 are percentages of the dead and live loads(DL and LL). It is often recommended by codes to assume p1 as unity and p2 and varying between about 0.15 and 0.3. Seismic codes may also recommend the use of different p2 values for the roof level in buildings or ignore some types of live loads. The tributary seismic weight at each storey of the analytical model of the RC frame is calculated as the sum of the total dead loads due to the self-weight of the structure and 30% of live loads on the slab. For multi-storey buildings, the evaluation of the term p1DL in equation (4.1) should include the weight of the floor system, finishes, partitions, beams and columns one-half storey above and below a floor for fixed-base rigid foundations.

SEISMIC LOAD COMBINATIONS Dead, live and earthquake loads should be combined to perform response analysis of structural systems. Loads acting on structures during earthquakes are generally combined as follows:

Where L is the total load, gama are load factors for dead loads DL, live loads LL, and for earthquakes EQ. The values of gama factors and the number of different combinations depend on the limit states employed to assess the structural performance. Lower gama factors are used for loads that are unlikely to vary significantly from the specified characteristic value. In particular, gamaL factors are generally 20-30% greater than gamaD because LLs exhibit higher uncertainty than DLs. Combination coefficient Big gamaL are often used to account the likelihood of certain live loads not being present over the whole structure during the occurrence of the earthquake:

Where values of Big gamaL are less than unity. These Big gamaL factors may also account for a reduced participation of masses in the motion due to the non-rigid connection between a structure and its contents. The design spectrum bay be multiplied by the importance factor gama1, which is used both for equivalent static and dynamic(multi-modal spectral) analysis.

The rationale for multiplying the seismic loads EQ by gama1 is that the return period of the design earthquake for critical structures is longer than normal-use structures. Commonly used load combinations for building structures are summarised:

A portion of the snow load is included in seismic combinations because a significant amount of ice can build up on roofs.