Probabilistic safety assessment of self-centering steel braced frame

doi:10.1007/s11709-017-0384-z

Front. Struct. Civ. Eng.

2018, Vol. 12

Issue (1) : 163-182 https://doi.org/10.1007/s11709-017-0384-z

RESEARCH ARTICLE

Probabilistic safety assessment of self-centering steel braced frame

Navid RAHGOZAR¹(

), Nima RAHGOZAR¹, Abdolreza S. MOGHADAM²

¹. Department of Structural Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
². Structural Engineering Research Center, International Institute of Earthquake Engineering and Seismology (IIEES), Tehran, Iran

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Abstract

The main drawback of conventional braced frames is implicitly accepting structural damage under the design earthquake load, which leads to considerable economic losses. Controlled rocking self-centering system as a modern low-damage system is capable of minimizing the drawbacks of conventional braced frames. This paper quantifies main limit states and investigates the seismic performance of self-centering braced frame using a Probabilistic Safety Assessment procedure. Margin of safety, confidence level, and mean annual frequency of the self-centering archetypes for their main limit states, including PT yield, fuse fracture, and global collapse, are established and are compared with their acceptance criteria. Considering incorporating aleatory and epistemic uncertainties, the efficiency of the system is examined. Results of the investigation indicate that the design of low- and mid-rise self-centering archetypes could provide the adequate margin of safety against exceeding the undesirable limit-states.

Keywords self-centering steel braced frame mean annual frequency safety assessment confidence level margin of safety

Corresponding Author(s): Navid RAHGOZAR

Online First Date: 19 June 2017 Issue Date: 08 March 2018

Cite this article:

Navid RAHGOZAR,Nima RAHGOZAR,Abdolreza S. MOGHADAM. Probabilistic safety assessment of self-centering steel braced frame[J]. Front. Struct. Civ. Eng., 2018, 12(1): 163-182.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-017-0384-z
https://academic.hep.com.cn/fsce/EN/Y2018/V12/I1/163

Fig.1 (a) Configuration of the self-centering system; (b) push and hysteretic curves of the self-centering system, fuse and PT strand components

Fig.2 Outline procedure for PSA of the self-centering steel braced frame

Fig.3 Schematic plan of the PSA procedure: correlation between (a) seismic hazard curve and (b) structural demand and capacity parameters

Tab.1 Performance groups along with considered archetypes

Fig.4 Configurations of self-centering braced frame archetypes (a) space SC-CR; (b) perimeter SC-CR; (c) perimeter and space SC-CR

Fig.5 (a) Configuration and (b) material of post-tensioning strand. (c) Configuration, (d) modeling, (e) and hysteretic behavior of butterfly-shaped fuse [41]

Fig.6 Three design load cases. (a) Inverted triangular; (b) upward triangular; (c) reverse triangular profiles [13]

Tab.2 Design properties of self-centering braced frame archetypes

Tab.3 Brace, beam, and column sections of self-centering archetypes

Fig.7 Nonlinear simulation of self-centering archetypes in OpenSees

Fig.8 (a) Brace with gusset-plate model; (b) details of gusset plate connection

Fig.9 (a) Ground motion hazard curves for the archetypes of PG₁ (A₁, A₂, and A₃); (b) spectral accelerations and median spectrum of far-field FEMA P695 ground motion set.

Fig.10 (a) IDAs of (1) A₁, (2) A₂, and (3) A₃ archetypes under a set of selected ground motions; (b) (1) roof drift ratio, (2) PT axial force versus (2) time and (3) roof drift ratio for the A3 archetype under the scaled horizontal component of Hector Mine earthquake to PGA of 0.27 and 1.91 g

Fig.11 (a) Idealized schematic lateral force-drift ratio of self-centering systems; (b) definition of performance levels and limit-states

Fig.12 Quantified PT yield (LS(1); red plus), fuse fracture (LS(2); green plus), and global collapse (LS(3); black plus) limit-state points (IDR and Sa) for (a) A₁, (b) A₂, and (c) A₃ archetypes

Tab.4 Summary of the pushover and IDA results for self-centering archetypes

Fig.13 (a) Fractile IDA curves and (b) record-to-record uncertainty of (b) maximum inter-story drift (IDR_max) versus Sa (b_DR(IDR_max |Sa)) and (c) Sa versus IDR_max (b_DR(Sa| IDR_max)) for (1) A₁, (2) A₂, and (3) A₃ archetypes

Fig.14 Lognormal and adjusted fragility curves for PT yield, fuse fracture, and global collapse limit states of (a) A₁, (b) A₂, and (c) A₃ archetypes.

Tab.5 Summary of IDA results, safety margin ratios, and confidence levels of self-centering archetypes at defined limit states.

Fig.15 Derivative MAF spectra of PT yield, fuse fracture, and global collapse limit states respecting Sa(d(l_LS)/d(Sa)) for (a) A₁, (b) A₂, and (c) A₃ archetypes

Tab.6 Performance evaluation of self-centering archetypes

Table A1Far-field ground motion record set [44]

The following symbols are used in this paper:

A_PT = cross-sectional area of post-tensioning strands;

a_fs/b_fs = link width ratio;

b_fs = link depth at the end;

b_fs/t_fs = width-to-thickness ratio of fuse link ends;

D_max = maximum spectral acceleration intensity associated with SDC D;

D_min = minimum spectral acceleration intensity associated with SDC D;

E_PT₌ PT modulus of elasticity;

f_yfs = yield strength of the fuse;

f_yPT = yield strength of the post-tensioning strand;

f_PTi = initial post-tensioning stress;

F_PTi = initial post-tensioning force;

f_ufs = fracturing strength of the fuse;

f_UPT = ultimate strength of the post-tensioning strand;

f₅₀ = median IDA curve;

f₁₆ = 16% fractile curve;

f₈₄ = 84% fractile curve;

k= logarithmic slope of the hazard curve;

k₀ = real and positive constant of the prediction of the site seismicity;

K_AB = hardening stiffness;

K_fs = initial fuse stiffness;

K_OA = initial stiffness of the archetype;

K_X = standard normal value of the inverse cumulative distribution index of x;

L_eff = unbraced length of the brace;

L_fs = effective width of the fuse;

L_fs/t_fs = slenderness ratio;

L_PT = length of the post-tensioning strand;

M_fsy = yield moment of the fuse;

M_u = overturning moment;

M_UP = uplift moment of the system;

M_w = moment magnitudes;

M_y = yield moment of the system;

N_fs = number of fuses;

Nl_fs = number of links per fuse;

N_PT = number of post-tensioning strands;

P_D = total gravity load;

R= response modification coefficient;

S_a = spectral intensity at the fundamental period of the archetype;

SC= self-centering ratio;

S_DS = design, 5% damped spectral response acceleration parameter at short period;

S_D1 = design, 5% damped spectral response acceleration parameter at a period of 1 s;

S_MT = spectra intensity at maximum considered earthquake ground motion;

S?_LS = median limit state spectral intensity for the entire ground motion record set;

t= fundamental period of the system;

t_fs = plate thickness of the fuse;

V_fp = shear strength of the fuse;

V_max = maximum lateral strength;

V= design base shear of the system;

X= confidence level;

α= hardening ratio;

β= energy dissipation ratio;

β_C,U = capacity uncertainty;

β_C,R = capacity aleatory randomness;

β_EDP,R = demand aleatory randomness;

β_EDP,R_|16 = demand randomness calculated by 16% fractile;

β_EDP,R_|84 = demand randomness calculated by 84% fractile;

β_EDP,R_|_s = aleatory randomness of demand at each seismic intensity level;

β_Des = design requirement-related uncertainty;

β_MDL = model uncertainty;

β_total,D = test data-related uncertainty;

β_TOT = total uncertainty;

β_total,R = record to record uncertainty;

β_total,U = total epistemic uncertainty;

β_UD = demand uncertainty;

δ_u = ultimate roof drift ratio;

δ_up = system uplift drift;

δ_y,eff = effective yield roof drift ratio;

δ_y = yield drift of the system;

ε_i = initial strain of the post-tensioning strand;

ε_limit = strain limit of the post-tensioning strand;

ε_m = fracture strain of the post-tensioning strand;

ε_target = target strain of the post-tensioning strand;

ε_u = ultimate strain of the post-tensioning strand;

ε_y = yield strain of the post-tensioning strand;

φ= capacity factor;

φ^-¹(x) = inverse cumulative distribution function of the normal variable of x;

γ= demand factor;

γ_m = shear strain of the fuse;

λ^LS = mean annual frequency of exceeding a given limit-state;

λ^P₀ = acceptable risk of occurring a limit state at a given seismic intensity;

λ_x = conﬁdence factor.

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