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A practical approach for estimating the floor deformability in existing RC buildings: evaluation of the effects in the structural response and seismic fragility

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Abstract

A study is presented on the evaluation of the floor deformability in the existing RC buildings and the related effects on the structural behaviour and the seismic fragility are investigated. In particular, the study of the seismic behaviour of existing RC buildings is strictly related to the initial assumptions made by practitioners on the numerical model, which usually assume the floor as rigid, according to a criterion of reducing time and computational efforts. Nevertheless, this hypothesis can provide unrealistic responses, with effect of obtaining not conservative results in the vulnerability estimation. In a view of practitioners’ necessities, a new numerical practical procedure is developed, in order to provide an a priori definition about the effective floor deformability of three-dimensional finite element models. This procedure has been tested on a couple of real existing RC school buildings, modelled with several numerical configurations and accounting for the presence of all elements that constitute the entire buildings (floor system, infill panels and elements of retrofit). Based on the evaluation of structural response and seismic fragility, some interesting observations have been provided, with the aim to define and to prevent the possible errors by assuming the floor as rigid.

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Abbreviations

β :

Standard deviation of fragility curves

\({\bar{\delta }}\) :

Mean of the horizontal displacements in the pushing direction in a storey

δ* :

Difference between the minimum displacements obtained in the torsion case

\(\delta_{min}^{*}\) :

New minimum nodal displacement in the torsion case

δi :

Horizontal displacement of the ith node in the pushing direction in a storey

δ i,new :

New nodal displacements of the generic node in the torsion case

δ min,L :

Normalized minimum nodal displacement to left

δ min,R :

Normalized minimum nodal displacement to right

δ R :

Roof displacement

θ :

Angle of torsion

θ i :

Interstorey drift ratio

θ y :

Yielding rotation of hinge

θ u :

Ultimate rotation of hinge

λ :

In-plane displacement ratio

σ m :

Compression strength of masonry

As :

Area of section strut for the slab model

Cat:

Soil category

COVdisp :

Coefficient of variation of all nodal displacements in a storey

Ec,slab :

Elastic modulus of slab material

Es,strut :

Elastic modulus of strut material for the slab model

E w :

Vertical elastic modulus of masonry

E wθ :

Diagonal elastic modulus of masonry

Ec :

Elastic modulus of concrete

Es :

Elastic modulus of reinforcement steel

f′cm :

Mean compressive strength of in situ concrete

Fh :

Resultant of horizontal forces in a storey

f′ym :

Mean tensile strength of steel rebars

ftp :

Tensile strength of masonry

G:

Dead loads

Gc :

Shear modulus of slab material

Gw :

Shear modulus of masonry

H1 :

Height of the first storey

H2 :

Height of the second storey

J:

Inertia moment of slab section

Kslab :

In-plane stiffness of slab

Kstrut :

Axial stiffness of the strut element for the slab model

L′:

Slab dimension orthogonal to seismic action

L1,2,…N :

Partial length of the bays

Li :

Progressive distance of the generic node from the reference system

Ls :

Length of strut for the slab model

LTot :

Total length of the structure

M (Tdir,push):

Participating mass of the main vibration mode of building in the pushing direction

NL :

Nominal life

Nmode,push :

Number of the main vibration mode in the pushing direction

NNodes :

Number of nodes to consider in graphs of Fig. 3

NNodes,TOT :

Total number of in-plane nodes

NRes-frame,⊥ :

Number of frames along the transverse direction to the force applied

Q:

Live loads

R:

Retrofitted model

Sa,50 :

Median of fragility curves

Sa (T*):

Spectral acceleration of the SDOF equivalent oscillator

Sa (T1):

Spectral acceleration of the first period

T:

Natural period

T* :

Period of the SDOF equivalent oscillator

Tdir,push :

Period of the main vibration mode in the pushing direction

Top:

Topography category

UC :

Usage class

ux, uy, θz :

Planar movements in the plane X–Y

Vb :

Base shear

X:

In-plane minimum displacement

X1,2…N :

Intermediate displacements between X and Y, normalized to X

Y:

In-plane maximum displacement

3D:

Three-dimensional

B1:

Building 1

B2:

Building 2

BF:

Bare-frame model

CY:

Construction year

DIAPH:

Rigid floor model

DOF:

Degree of freedom

DV:

Decision variable

EDP:

Engineering demand parameter

FE:

Finite element

FLEX:

Flexible floor model

IDA:

Incremental dynamic analysis

IF:

Infill-frame model

IM:

Intensity measure

IO:

Immediate occupancy

LS:

Life safety

MAF:

Mean annual frequency

MDOF:

Multi degree of freedom

MSA:

Multiple stripes analyses

NC:

Near-collapse

PBEE:

Performance based earthquake engineering

RC:

Reinforced concrete

SDOF:

Single degree of freedom

SF:

Shear failure

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Authors and Affiliations

  1. Department DICATECh, Polytechnic University of Bari, Via Orabona, 4, 70126, Bari, Italy

    Sergio Ruggieri, Francesco Porco & Giuseppina Uva

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  1. Sergio Ruggieri
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  2. Francesco Porco
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  3. Giuseppina Uva
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Correspondence to Sergio Ruggieri.

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Ruggieri, S., Porco, F. & Uva, G. A practical approach for estimating the floor deformability in existing RC buildings: evaluation of the effects in the structural response and seismic fragility. Bull Earthquake Eng 18, 2083–2113 (2020). https://doi.org/10.1007/s10518-019-00774-2

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