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On the quantification of local deformation demands and adequacy of linear analysis procedures for the seismic assessment of existing steel buildings to EC8-3

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Abstract

The application of performance-based design and assessment procedures requires an accurate estimation of local component deformation demands. In the case of steel moment-resisting frames, these are usually defined in terms of plastic rotations. A rigorous estimation of this response parameter is not straightforward, requiring not only the adoption of complex nonlinear structural models, but also of time-consuming numerical integration calculations. Moreover, the majority of existing codes and guidelines do not provide any guidance in terms of how these response parameters should be estimated. Part 3 of Eurocode 8 (EC8-3) requires the quantification of plastic rotations even when linear methods of analysis are used. Therefore, the aim of the research presented in this paper is to evaluate different methods of quantifying local component demands and also to answer the question of how reliable are the estimates obtained using the EC8-3 linear analysis procedures in comparison to more accurate nonlinear methods of analysis, particularly when the linear analysis applicability criterion proposed by EC8-3 is verified. An alternative methodology to assess the applicability of linear analysis is proposed which overcomes the important limitations identified in the EC8-3 criterion.

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Abbreviations

L :

Member length

q :

Uniformly distributed gravity load

V :

Point load applied at the top of the simplified cantilever system

d :

Displacement of the free node of the simplified cantilever system

d 2 :

Displacement of node 2

d L/2 :

Displacement at the mid-span

M E :

Bending moment due to earthquake load

M E+Q :

Bending moment due to combined earthquake and gravity loads

N E+Q :

Axial force due to combined earthquake and gravity loads

N pl :

Axial capacity of the member

M pl :

Plastic bending moment

M y :

Yielding bending moment

M 2 :

Bending moment at node 2

L ph :

Plastic hinge length

Φ u :

Ultimate member curvature

Φ y :

Yielding member curvature

x :

Abscissa of the cross-section within the member length L

Φ(x):

Member curvature at abscissa x

Φ pl (x):

Plastic member curvature at abscissa x

θ pl :

Plastic rotation

θ el :

Elastic rotation

θ t :

Total rotation

x Ls :

Abscissa of the point of contraflexure

δ 2 :

Distance between the member deflection at x Ls and the tangent to the member axis at node 2

x * :

Distance of the intersection point between the tangent to the member axis at node 2 and the perpendicular that intersects the member deflection at x Ls to node 2

θ 1 :

Member chord rotations at node 1

θ 2 :

Member chord rotations at node 2

θ 1a :

Contribution of the deflection at x Ls with respect to the initial member configuration to the member chord rotations at node 1

θ 2a :

Contribution of the deflection at x Ls with respect to the initial member configuration to the member chord rotations at node 2

θ 1b :

Contribution of the nodal rotation to the member chord rotations at node 1

θ 2b :

Contribution of the nodal rotation to the member chord rotations at node 2

d y :

Relative transverse displacements of the sections at nodes 1 and 2, neglecting the contribution of the axial deformation of the member

θ y :

Yielding chord rotation

θ y,ASCE41 :

Yielding chord rotation quantified using the ASCE41-13 approach

θ :

Inter-storey drift sensitivity coefficient

DCR :

Demand-to-capacity ratio

m :

ASCE41-13 member capacity factor that defines the acceptance criteria for linear procedures

k :

ASCE41-13 knowledge factor

θ D :

Deformation demands obtained from structural analysis, defined in terms of plastic rotations by EC8-3 for steel structures

θ C :

Deformation capacity, defined in terms of plastic rotations by EC8-3 for steel structures

CF :

EC8-3 confidence factor

E :

Modulus of elasticity of steel

I :

Moment of inertia of the member cross-section

Q f :

Quantity whose level of error is under evaluation

Q R :

Quantity used as reference to estimate the level of error associated to Q f

ΔQ :

Local error of quantity Q f with respect to quantity Q R

RMSE :

Root mean square error

n :

Number of element sections or number of stories

m i :

Masses at storey i

h i :

Heights of the masses m i above the level of application of the seismic action

T :

Period of vibration of the structure

e :

Exponent that is function of the period of vibration of the structure

mDCR i :

Maximum DCR within a floor i

\(\overline{DCR}_{i}\) :

Mean DCR within a floor i

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Acknowledgments

This work has been performed within the framework of the research project ‘Development and calibration of seismic safety assessment methodologies for existing buildings according to the Eurocode 8—Part 3’ funded by the Portuguese Foundation of Science and Technology (FCT).

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Authors and Affiliations

  1. Department of Civil Engineering, Faculty of Engineering, University of Porto, Porto, Portugal

    Miguel Araújo & José Miguel Castro

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  1. Miguel Araújo
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Correspondence to José Miguel Castro.

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Araújo, M., Castro, J.M. On the quantification of local deformation demands and adequacy of linear analysis procedures for the seismic assessment of existing steel buildings to EC8-3. Bull Earthquake Eng 14, 1613–1642 (2016). https://doi.org/10.1007/s10518-016-9897-4

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