Effect of Structural Uncertainties on Seismic Performance of RC Frames.

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Presentation
Submitted by
Md. Saniul Haque Mahi
Effect of Structural Uncertainties on
Seismic Performance of RC Frames.

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Introduction
Since the prediction of the seismic response of a structure is highly uncertain, a probabilistic approach is needed, not only for the determination of
the seismic hazard, but also for the estimation of the seismic response parameters.
Uncertainties
Aleatoric uncertainties
(related only to the
random nature of earthquakes)
Epistemic uncertainties
(related to the physical properties of the
structure and its modeling parameters.)
Past Studies
1. Estevaand Ruiz: uncertainties in the mechanical and geometrical properties of structural elements probably do not contribute importantly to
the variations in the calculated structural failure rates.
2. Aslani and Miranda: the effect of modeling (epistemic) uncertainties is negligible in the range of low seismic intensities, but the influence of
uncertainty increases with increasing earthquake intensity.

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DESCRIPTION OF THE EXAMPLE STRUCTURES AND THE SEISMIC LOADING
The effects of the modeling uncertainties on the seismic response parameters were estimated for three RC frame buildings. The first structure is an
older three-storey asymmetric RC frame building.
1. Plan dimensions: 9.7 X 10 m.
2. Storey Height : 3 m
3. Monolithic slabs depth : 15 cm.
4. The strength of the concrete: 26.5 MPa
5. The strength of the steel reinforcement : 459 MPa
6. The modulus of concrete elasticity : 29 GPa.
7. The masses and corresponding mass moments of inertia : 65.5 t m2 and 1196 t m2 for the first two storeys, and 64.1 t m2 and 1254 t m2 for
the top storey, respectively.
Fig. 2. Elevation and plan view of the older three-storey building, showing the typical cross sections of the columns and beams.
(D. Celarec, M. Dolšek / Engineering Structures)
Description of the example structures and the seismic loading

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The second structure, called the contemporary three-storey building, has the same plan and elevation geometry as the older three-storey building, but
its structural elements have appropriately modified reinforcement details and dimensions. In the design process, the dimensions of the weak square
columns and of the strong rectangular column C6 were increased to 35X35 cm and 35X85 cm, respectively. The dimensions of the beam section were
changed to 35X45 cm.
1. The masses and corresponding mass moments of inertia: 96.3 t m2 and 1667 t m2 for the first two storeys, and 94.4 t m2 and 1634 t m2 for
the top storey.
2. The strength of the concrete: 333 MPa
3. The strength of the steel reinforcement : 400 MPa
4. The modulus of concrete elasticity : 31 GPa
Fig. 3. The dimensions and typical reinforcement of the columns and beams for the contemporary three-storey building, which was designed according to EC8.
(D. Celarec, M. Dolšek / Engineering Structures)

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The third structure which was used in the study was a four storey RC frame building, with plan symmetry in one direction (Fig. 4).
1. Plan dimensions: 10 X 10 m.
2. Storey Height : first storey 3.5m and upper three storeys are 3 m
3. Monolithic slabs depth : 15 cm.
4. The strength of the concrete: 42 MPa
5. The strength of the steel reinforcement : 580 MPa
6. The modulus of concrete elasticity : 34 GPa.
7. The masses and corresponding mass moments of inertia : 83 t m2 and 1770 t m2 for the first storey, 86 t m2 and 1908 t m2 for the second
and third storeys, and 87 t m2 and 1983 t m2 for the top storey.
The load-bearing structure consists of nine columns, whose dimensions, except for the strongest column D, are 40X40 cm. Column D, which is located
in the middle of the floor plan, is somewhat stronger (45X45 cm). All the beams have a height of 45 cm, and a width of 30 cm.
Fig. 4. Elevation and plan view of the contemporary four-storey building, showing the typical cross-sections of the columns and beams.
(D. Celarec, M. Dolšek / Engineering Structures)

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Random variables
In order to incorporate selected physical and modelling uncertainty into the structural models, the following input parameters were identified as
uncertain:
• the strength of the concrete and steel reinforcement,
• the mass of the structure,
• the effective slab width and
• the parameters which describe the characteristic rotations in the plastic hinges, i.e. the yield (Y) and ultimate (NC) rotation.
Based on the identification of uncertainties for this study, the input model parameters were defined by means of eight random variables, each representing
an individual model parameter.
Table 1: The uncertain input parameters of the structural models, the corresponding coefficients of variation and the probability distribution.

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The seismic response parameters
Sensitivity analysis
Fig. 6. Tornado diagrams for the older three-storey building. The results are presented for two response parameters (Dnc, ag,nc).
(D. Celarec, M. Dolšek / Engineering Structures)
 The horizontal bars in the tornado diagrams are shown in two colours. The red (dark) bars are related to the lower values of the random variables
(i.e. the 16th fractiles), whereas the blue (bright) bars are associated with the upper values of the random variables (i.e. the 84th fractiles).
 The positive X direction is the critical direction in which the minimum displacement (Dnc) and acceleration capacities (ag,nc) are obtained.
 The seismic response parameters Dnc and ag,nc of the deterministic model of the older three storey building amounted to 0.13 m and 0.36 g,
respectively.

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Fig. 8. Tornado diagrams for (a) the contemporary three-storey building and (b) the contemporary four-storey building. The results are presented for two response
parameters (Dnc, ag,nc). (D. Celarec, M. Dolšek / Engineering Structures)
 The contemporary structures suffered more damage in the beams whereas the columns have sufficient strength and rotation capacity to be able to
remain in the elastic region except for sections at the base of the 1st storey.
 Variations in the ultimate rotations of the plastic hinges in the beams (ϴub) can have a substantial impact on the seismic response parameters and are in
the case of two selected structures even more important than the ultimate rotations in the columns (ϴuc) (see Fig. 8a and b).
 The contemporary three-storey building Dnc amounts to 0.39 m. Three times higher than that observed in the case of the older three storey building.

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Conclusion
The results of the sensitivity analysis reveal the relatively significant impact of modelling uncertainties on the seismic response parameters. It was
shown that the uncertain parameter which has the greatest affect on the seismic response parameters can vary from structure to structure, since the
structural collapse mechanism depends on the design process.
The seismic performance of the older three-storey building is controlled mostly by the ultimate rotation of the plastic hinges in the columns (ϴuc)
whereas in the case of the contemporary buildings the ultimate rotation of the beams (ϴub) has the greatest affect on the seismic response parameters.
This was an expected result, since the contemporary buildings were designed according to capacity design principles, which means that the structural
damage is concentrated mostly in their beams whereas in the case of the old structure the damage is concentrated in the columns.
The uncertain parameters which in the case of this study were of lesser importance are
• the mass of the structure,
• the concrete strength,
• the yield rotation in the columns and
• the effective slab width.
In the case of this study, this means that neglecting the modelling uncertainties led to unsafe design, since the results of the analyses show that the
predicted median seismic capacity of the example structures, given in terms of the peak ground acceleration may be reduced in a great quantity.

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Thank You