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Seismic assessment of an innovative eccentrically braced frame with shape memory alloy

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Abstract

Strong earthquake impacts the structure and creates plastic hinges in some parts of the structure. Performance and serviceability of structure are significant after the earthquake, so it is necessary to decrease residual deformations created by the earthquake. In modern design, the plastic behavior of the structure is concentrated in some members, called fuse members. If the residual deformation of fuse members is decreased, the residual displacement of the structure is decreased. The eccentrically braced frame with vertical link (V-EBF) is a very ductile structure, and the link beam plays as a fuse member. The present study tries to use shape memory alloy (SMA) to decrease the residual deformation of the link beam. Eight and twelve-story V-EBF (with and without SMA rods) were designed. The design method includes the design of the structure for design earthquake, the design of SMA rods based on the properties of the link beam, and the design of all members except link beams and SMA rods for forces and moments of link beams and SMA rods. Designed structures were analyzed by OpenSees software. Pushover, time history, and incremental dynamic analysis were done, and the effect of SMA rods was investigated in the performance of designed structures, so the ratio of ultimate shear to yield base shear, residual displacements, and drifts was investigated in this study. Time history analysis showed that using SMA rods decreases residual displacement considerably, and the residual displacement of the frame equipped with SMA rods is more uniform than the frame without SMA rods. And using SMA rods decreases maximum inter-story residual drift. The analysis showed that using SMA rods often increases the spectral acceleration of the first mode at the collapse threshold. The ratio of ultimate base shear to yield base shear increases when V-EBF is equipped with SMA rods. SMA rods will be effective if the seismic requirements and design methodology are met.

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Abbreviations

V-EBF:

Eccentrically braced frame with vertical link

SMA:

Shape memory alloy

IDA:

Incremental dynamic analysis

EBF:

Eccentrically braced frame

AISC:

American Institute of Steel Construction

MRF:

Moment resistance frame

DBE:

Design basis earthquake

CBF:

Concentrically braced frame

BRB:

Buckling restraint brace

IDA:

Incremental dynamic analysis

\({M}_{bot}\) :

Bottom bending moment of link beam

\({M}_{top}\) :

Top bending moment of link beam

k :

The lower moment to upper moment ratio of the link beam

\(V\) :

Shear force of link beam

\({V}_{u}\) :

Link beam shear at the instant of shear strength drop

e :

Link beam length

\({e}_{0}\) :

The length of the link beam in the borderline of shear and shear–flexural behavior

\({V}_{y}\) :

Expected yield shear

\({M}_{y}\) :

Expected yield moment

\({F}_{ye}\) :

Expected yield stress

\({F}_{y}\) :

Nominal yield stress

Z :

Plastic section module

\({K}_{1V}\) :

Tangent shear stiffness of first segment in four-linear shear capacity curve of link beam

\({K}_{2V}\) :

Tangent shear stiffness of second segment in four-linear shear capacity curve of link beam

\({K}_{3V}\) :

Tangent shear stiffness of third segment in four-linear shear capacity curve of link beam

\({K}_{4V}\) :

Tangent shear stiffness of forth segment in four-linear shear capacity curve of link beam

\({K}_{1M}\) :

Tangent moment stiffness of first segment in four-linear moment capacity curve of link beam

\({K}_{2M}\) :

Tangent moment stiffness of second segment in four-linear moment capacity curve of link beam

\({K}_{3M}\) :

Tangent moment stiffness of third segment in four-linear moment capacity curve of link beam

\({K}_{4M}\) :

Tangent moment stiffness of fourth segment in four-linear moment capacity curve of link beam

G :

Shear modulus of elasticity

Aw :

Link web area

E :

Modulus of elasticity

\(I\) :

Moment inertia

\({V}_{y1}\) :

Shear force at the end of first segment of four-linear shear capacity curve

\({V}_{y2}\) :

Shear force at the end of second segment of four-linear shear capacity curve

\({V}_{y3}\) :

Shear force at the end of third segment of four-linear shear capacity curve

\({M}_{y1}\) :

Bending moment at the end of first segment of four-linear moment capacity curve

\({M}_{y2}\) :

Bending moment at the end of second segment of four-linear moment capacity curve

\({M}_{y3}\) :

Bending moment at the end of third segment of four-linear moment capacity curve

\({F}_{s}^{AM}\) :

The austenite-to-martensite starting axial force

\({F}_{f}^{AM}\) :

The austenite-to-martensite finishing axial force

\({F}_{s}^{MA}\) :

The martensite-to-austenite starting axial force

\({F}_{s}^{MA}\) :

The martensite-to-austenite finishing axial force

R :

The response modification factor of the structure

\({\Delta }_{lSMA}\) :

The axial deformation of the SMA part of the rod

\(L\) :

Sums of SMA and non-SMA element length after rotation

\({L}_{0}\) :

Sums of SMA and non-SMA element length before rotation

\({L}_{0SMA}\) :

SMA element length before rotation

\({L}_{SMA}\) :

SMA element length after rotation

\({\theta }_{r}\) :

Residual rotation of the link

F :

The amount of force required to return a link to zero rotation

\({\delta }_{rSMAt}\) :

Tensile SMA rod displacement at the moment of residual rotation of \({\theta }_{r}\)

\({\delta }_{rSMAc}\) :

Compressive SMA rod displacement at the moment of residual rotation of \({\theta }_{r}\)

\({\varepsilon }_{rSMAt}\) :

Tensile SMA rod strain at the moment of residual rotation of \({\theta }_{r}\)

\({\varepsilon }_{rSMAc}\) :

Compressive SMA rod strain at the moment of residual rotation of \({\theta }_{r}\)

\({\sigma }_{t}\) :

Tensile stress of SMA rod corresponding to \({\varepsilon }_{rSMAt}\)

\({\sigma }_{c}\) :

Compressive stress of SMA rod corresponding to \({\varepsilon }_{rSMAc}\)

\({A}_{SMA}\) :

The area of the SMA section

\(\alpha\) :

The angle of the rod with vertical axis

\({R}_{y}\) :

The ratio of the expected yield stress to the specified minimum yield stress

ATC:

Applied Technology Council

\({\Delta }_{y}\) :

Displacement of the structure yield

ASCE:

American Society of Civil Engineers

Ω :

The ratio of ultimate base shear to first yield base shear

\({T}_{0}\) :

Fundamental period of structure

\({S}_{T1}\) :

The spectral acceleration of the first mode of each record

\({S}_{a}\) :

Spectral failure acceleration

\(\overline{{S }_{a}}\) :

Median of failure spectral accelerations

\({\beta }_{tot}\) :

Standard deviation

Φ:

Function of lognormal cumulative destruction

FEMA:

Federal Emergency Management Agency

CP:

Collapse prevention

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  1. School of Civil Engineering, University of Tehran, Tehran, Iran

    Mehdi Ghassemieh & Amir Reza Ghavami

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  1. Mehdi Ghassemieh
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Correspondence to Mehdi Ghassemieh.

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Ghassemieh, M., Ghavami, A.R. Seismic assessment of an innovative eccentrically braced frame with shape memory alloy. Innov. Infrastruct. Solut. 8, 335 (2023). https://doi.org/10.1007/s41062-023-01300-9

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