3 D seismic analysis of multi-storey wood frame construction

In seismic design of multi-storey wood frame buildings, force reduction factors have been mainly evaluated through twodimensional (2D) dynamic analysis on the basis of "rigid floors symmetric behavior" assumption. In this paper, results from a 3D non-linear time-history dynamic analysis are presented for a sample wood-frame building, symmetric. The building has been designed in Vancouver (B.C., Canada) according to the provisions of the Canadian Building Code, and then analyzed using a 3D dynamic analysis program which included a pinching hysteresis model fitted to the test data obtained on full-size nailed shear wall specimens. The analyses are performed for several Vancouver area based accelerograms and several historical quakes and repeated for flexible and rigid floors to study the effect of diaphragm flexibility on seismic performance. For each building and each accelerogram, the Peak Ground Acceleration (PGAu) producing the "near collapse" ultimate state has been determined. The influence of flexibility of floor diaphragms has been then quantified in terms of reduction of PGAu in respect to the reference "rigid/symmetric" case. INTRODUCTION Most seismic design codes contain action reduction factors (ARF) to be used to evaluate the forces to be accounted for when designing the structure using a simple elastic global analysis. ARF then reflects the capability of a structure to dissipate energy through inelastic behavior, and survive even exceptional earthquakes without complete collapse. In fact any code's objective is the building to resist the foreseen quake for that area. It is evident that behind this idea there is an assumption of acceptable risk for the community. Because resistance against earthquakes results from a combination of hazard and vulnerability, to take into account the relevant uncertainties (according to semi-probabilistic approach philosophy), appropriate safety coefficients are considered in the codes both for the design action and the design resistance. Therefore under these assumptions the easiest way to assess the appropriateness of an ARF value for a particular building type is just to refer to the definition of ARF: "ARF is the factor to be used in calculating design inertia forces so that a structure designed linearly elastic using the code strength values can survive the design quake intensity, even if heavily damaged, but without its compete collapse.", and apply the following procedure. • Design the structure using the ARF according to the seismic code, and the resistant system according to the relevant codes (seismic and “static” codes). At the end of this step the resistant system will be completely anticipated. • Model the building mechanical behaviour on the base of its mechanical characteristic (obtained by tests, and scaled to 5% percentile based on COV and test mean value, using additional safety coefficients eventually provided by the code for the earthquake load combination). • Using a suitable non-linear analysis programme capable of following the displacement history of the building under a quake in the time domain, determine the PGAu that the building will survive without exceeding a given “near collapse” failure limit (for example based on a maximum inter-storey drift, or a rupture in joints or in timber elements). 1 Professor, Dept. of Civil Engineering, Florence University, S. Marta 3 I-50139 Florence ario@dicea.unifi.it 2 Research Fellow, Dept. of Civil Engineering, Florence University, S. Marta 3 I-50139 Florence mfollesa@tiscalinet.it 3 Group Leader, Wood Engineering Department, Forintek Canada Corp., 2665 East Mall, B.C. Canada V6T 1W5 erolk@van.forintek.ca Figure 1a,b: “Florence” hysteresis model fitting plywood shear-walls test. • Compare this PGAu against PGAcode prescribed by the code. • Finally, if PGAu > PGAcode the previously chosen design ARF value is adequate. • This procedure must be repeated for a series of earthquakes suitable for the design site, in order to have a global picture according to different possible inputs. Note that this metodology does not need a definition of yielding limit, but uses only the definition of ultimate inter-storey drift limit. A lower yelding limit may be introduced to control damage in moderate earthquakes. If the design code values for materials strength are artificially low, the structure will be over-designed and consequently it will resist a greater PGA resulting in a greater margin between PGAu and PGAcode. Therefore this margin itself involves some kind of calibration of acceptable risk and becomes a matter for code writers (Ceccotti & Foschi, 1998). Using this methodology for multistory wood frame shear walls, these factors have been previously evaluated through two-dimensional (2D) dynamic analysis on the basis of "rigid floors symmetric behavior" assumption (Ceccotti &Karacabeyli, 2000). The possible dynamic interaction between the floor deformability and the walls deformability has not be taken into account: under quake exitation a long building can deform along its length and some walls are more deformed than others, so that some walls can reach the near-collapse inter-storey drift while others not. Accordingly, the PGA producing the near-collapse state in a long building with deformable floors can be different from the PGA that produces the same effect in a building with rigid floors, where all walls are deforming in the same way. This is even more likely to happen in the case of non-simmetric buildings. MATERIALS AND METHODS Modeling joints The pinching hysteresis model was previously developed at the University of Florence (Ceccotti& Vignoli, 1989) for the semirigid connections. This is a fitting model as shown in figure 1a & b. The model needs to be calibrated to test data. It is a piece-linear model and therefore is not extremely precise. From an energy point of view however, the representation obtained with the model is reasonable (fig 2, max error 15%). Preliminary test results on shaking table, figure 3a,b,c,&d) validated its ability in detecting the PGAu that is the most important parameter to be determined using this model. Figure 2: Differences in energy dissipation according to Figure 1.