## Seismic response analysis of three-storey building considering the epistemic uncertainties

- The structure was designed for gravity loads only and was conceived as representative of older construction in Southern Europe countries without sufficient earthquake resistance. This structure was also pseudo-dynamically tested within a SPEAR project at ELSA Laboratory, Ispra.
- The plan and elevation of structure:

- The plan and 3D view of structural model generated with PBEE toolbox. Slab effective widths are considered for determination of stiffness and strength of beams.

- The moment-rotation relationship of a plastic hinge in columns and beams and pushover curve for deterministic structural model.

- Following model parameters were identified as source of epistemic uncertainty.

Variable COV Distribution Reference Concrete strength 0.20 Normal Melchers (1999) Steel strength 0.05 Lognormal JCSS (2000) Mass 0.10 Normal Ellingwood (1980) Mass centre 0.10 Normal Assumed value Eff. Slab width 0.20 Normal Haselton (2006) Yield rotation: - columns
- beams

0.36

0.36

Lognormal

LognormalPanagiotakos (2001) Ultimate rotation: - columns
- beams

0.40

0.60

Lognormal

Lognormal

Peruš (2001)

Panagiotakos (2001)

- The contributions of individual random variables to overall seismic capacity (displacement and acceleration capacity) were determined by a simple sensitivity analysis. Tornado diagrams illustrate the results of sensitivity analysis in positive X direction.

- The pushover and IN2 curves with NC limit state points for the set of 20 structural models and the deterministic structural model. The results are presented for the analysis in positive X direction.
- Comparison of damage in columns and beams in structural models for two models, which have, among all of the structural models, the smallest and the highest displacement capacity, respectively.

## Fragility curves with consideration of epistemic uncertainties

- The method for the determination of fragility parameters involves a nonlinear static analysis of a set of structural models, which is defined by utilizing Latin Hypercube Sampling (the LHS method), and nonlinear dynamic analyses of equivalent single-degree-of-freedom (SDOF) models. The set of structural models captures the epistemic uncertainties, whereas the aleatory uncertainty due to the random nature of the ground motion is, as usual, simulated by a set of ground motion records.
- The pushover curves corresponding to the set of structural models, the pushover curve corresponding to the deterministic model, and the so-called median pushover curve. The highlighted points indicate the DL, SD and NC limit-states.
- Damage to the structure for the NC limit state in a) the deterministic model (top displacement=0.51 m), b) model No.17, corresponding to the minimum NC top displacement (0.18 m), and c) model No.9, corresponding to the maximum NC top displacement (0.96 m). The pushover curves for all three models are presented, as well as a schematic visualization of the damage in the plastic hinges of the beams and columns.
- The fragility curves for the three limit state and for incorporating only aleaotry or both, aleatory and epistemic uncertainties

## Approximate IDA curves

- A web application for prediction of approximate IDA curves of reinforced concrete structures was recently developed. It enables determination of the approximate 16th, 50th and 84th fractile response of a reinforced concrete structures. The approximate IDA curves are predicted by performing the n-dimensional linear interpolation based on the response database of the SDOF system, which was computed for a selected set of ground motion records and for selected discrete values of the six parameters, which were defined in order to describe the period, damping and the force-displacement relationship of the structure. The developed application enables quadrilateral idealization of the pushover curve including the strength degradation. In order to demonstrate the use of the web application the seismic response of the four storey reinforced concrete structure is predicted.
- The four-linear force-displacement relationships and corresponding pushover curves of the four storey frame building
- Comparison between the approximate and “exact” fractile IDA curves for the two intensity measures and engineering demand parameters

## Progressive IDA of an eight-storey frame

- Progressive incremental dynamic analysis introduces the precedence list of ground motion records aiming of selecting the most representative ground motions from a set of ground motions. Therefore, the IDA curves are computed progressively, starting from the first ground motion record in the precedence list. After an acceptable tolerance is achieved, the analysis can be terminated. Such approach facilitates practical application of incremental dynamic analysis, especially, if the number of ground motions in a set of ground motions is large.
- The precedence list of ground motion records is determined for an eight storey frame, which is not typical first-mode dominated structure. The results indicate that the sufficiently accurate seismic response of an eight-storey frame can be determined with the first twelve to fifteen ground motion records from the precedence list of ground motions, which consisted of ninety-eight ground motion records.
- The pushover curve and the idealized force-displacement relationship which is used to determine the precedence list of ground motion records
- The comparison between the “original” and “selected” 16th, 50th and 84th fractile IDA curve for the first five subsets records (s=5), i.e. the first fifteen ground motion records from the precedence list of ground motion records, which consisted of 98 ground motion records

## Seismic response analysis of four-storey building

- The structure was designed according to previous versions of Eurocodes 2 and 8 (C25/30, S500, q=5) and pseudo-dynamically tested at ELSA Laboratory, Ispra. For references and more details see OS Modeler examples of applications.
- The plan, elevation and typical reinforcement in columns and beams.

- Ground motion record

- Pushover curve with indicated damage at near collapse limit state in plastic hinges of columns and beams

- Top displacement time history – calculated response versus experiment
- L-test (ag=0.12 g)

- H-test (ag=0.45 g)

- L-test (ag=0.12 g)
- Base shear time history – calculated response versus experiment
- L-test (ag=0.12 g)

- H-test (ag=0.45 g)

- L-test (ag=0.12 g)
- IDA curve with indicated damage in columns and beams (e.g. yield rotation)

## Seismic response analysis of ICONS frame

- The frame had been designed to reproduce the design practice in European countries about forty to fifty years ago (C16/20, FeB22k, design base shear coefficient 0.08) and pseudo-dynamically tested at ELSA Laboratory in Ispra. For references and more details see OS Modeler examples of applications.

- Elevation and typical reinforcement

- Ground motion record

- Pushover curves for different lateral loads

- Third storey drift time history – calculated response versus experiment for B475 (ag=0.22 g) and B975 test (ag=0.29 g)

- Third storey shear time history – calculated response versus experiment B475 (ag=0.22 g) and B975 test (ag=0.29 g)