study regarding input data consideration (required

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Study Regarding Input Data Consideration (Required Accelerograms) for Experimental Test of The Optimal

Moment Resisting (MR) Reinforced Concrete (RC) Frame Model on The Seismic Platform

Sococol Ion1*, Mihai Petru2 and Budescu Mihai3

1PhD Student, “Gheorghe Asachi” Technical University of Iasi, Faculty of Civil Engineering and Building Services, Doctoral School, Romania2Lecturer, PhD, “Gheorghe Asachi” Technical University of Iasi, Faculty of Civil Engineering and Building Services, Department of Concrete, Materials, Technology and Management, Romania3Professor Em., PhD, “Gheorghe Asachi” Technical University of Iasi, Faculty of Civil Engineering and Building Services, Associate Professor, Romania

ISSN: 2641-2039 DOI: 10.33552/GJES.2021.08.000692

Global Journal of Engineering Sciences

Research Article Copyright © All rights are reserved by Sococol Ion

This work is licensed under Creative Commons Attribution 4.0 License GJES.MS.ID.000692.

Abstract A significant number of reinforced concrete (RC) frame models have been studied for seismic (ductile) performance purpose through nonlinear

static analyses (using ATENA software). In these conditions, it was chosen the optimal models for experimental test on the seismic platform. In next stage, it was used the existing pushover curves to establish the ground acceleration values for five performance requirements (objectives). Thus, it was generated for each performance requirement an artificial accelerogram with which optimal RC frame model can be tested on the seismic platform. Consequently, it will be possible to study the complex cracking mechanism and failure/ split/ rupture/ expulsion material process of the RC frame model at each experimental test for either performance objective. Also, it will be possible test results superposition proceeding with existing theoretical studies.

Keywords: Static Pushover bilinearization; performance requirements (objectives); response spectra; Fourier spectra

*Corresponding author: Sococol Ion, Doctoral School, Faculty of Civil Engineering and Building Services, “Gheorghe Asachi” Technical University of Iasi, Nr. 1, 700050, Romania.

Received Date: September 25, 2021

Published Date: October 07, 2021

IntroductionComplex analytical studies it were performed with nonlinear

[1-7] static analyses [8-15] for a multitude of pure [16] moment resisting RC frame models (“reduced to ½ scale [17] with the same

inter-axis distances and story height” [11] (see Figure 1 - Figure 5 and Table 1) in order to identify the optimal ductile (and realistic) seismic response [18-25].

Table 1: “Principal characteristics/ variables considered in numerical simulations (analyses performed with ATENA software [13]) of the MR RC frame models from the global seismic response perspective” [11].

NSC CSC LR-RC-C [CS: 15x15 cm] LR-RC-LB LR-RC-TB R-RC-S

MR RC Frame Models - Type 1 [hL=1/8L*; LB-CS: 15x27 cm; TB-CS: 10x20 cm; hs=7 cm] [11]

M_6 C12/15 4ϕ14 4ϕ12 4ϕ10 ϕ6

M_7 C16/20 4ϕ14 4ϕ12 4ϕ10 ϕ6

http://dx.doi.org/10.33552/GJES.2021.08.000692

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Global Journal of Engineering Sciences Volume 8-Issue 4

Citation: Sococol Ion, Mihai Petru, Budescu Mihai. Study Regarding Input Data Consideration (Required Accelerograms) for Experimental Test of The Optimal Moment Resisting (MR) Reinforced Concrete (RC) Frame Model on The Seismic Platform. Glob J Eng Sci. 8(4): 2021. GJES.MS.ID.000692. DOI: 10.33552/GJES.2021.08.000692.

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M_8 C20/25 4ϕ14 4ϕ12 4ϕ10 ϕ6


K_3 C12/15 4ϕ14 4ϕ10 4ϕ10 ϕ6

K_4 C16/20 4ϕ14 4ϕ10 4ϕ10 ϕ6

K_5 C20/25 4ϕ14 4ϕ10 4ϕ10 ϕ6

K_7 C20/25 4ϕ14 4ϕ8 4ϕ8 ϕ6


Z_6 C12/15 4ϕ12+4ϕ8 4ϕ8 4ϕ8 ϕ6

Z_7 C16/20 4ϕ12+4ϕ8 4ϕ8 4ϕ8 ϕ6

Z_8 C20/25 4ϕ12+4ϕ8 4ϕ8 4ϕ8 ϕ6

where: “NSC - Numerical Simulation Code; CSC - Concrete Strength Class; LR - Longitudinal Reinforcement; RC - Reinforced Concrete; C - Col-umns; CS - Cross Section; LB - Longitudinal Beams; TB - Transverse Beams; R - Reinforcement; S - Slabs; hL - longitudinal cross section beams height from the pre-dimensioning stage; hs - slab thickness” [11];*Note: “RC beams height pre-dimensioning from 1/8L; 1/12L and 1/16L conditions; hL=1/16L represents the minimum limitation of the RC beams cross section height in new completing and modifying provisions of the P100-1 [19] technical regulation” [11].

Figure 1: Classification of the pure MR RC frame system types analyzed with ATENA software. 1/8L; 1/12L and 1/16L ratios represent three RC beams cross section height pre-dimensioning conditions. hL=1/16L ratio represents the minimum limitation of the RC beams cross section height in new completing and modifying provisions of the P100-1 [19] Romanian technical regulation.




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Figure 2: “Representation of the general dimensions for the analytical MR RC frame models and specified in Figure 1 with one opening – one bay plan configuration and identical inter-axis distances/ story height” [11]: (a) structural system type 1 with longitudinal rigid RC beams; (c) structural system type 2 with normal RC beams; (e) structural system type 3 with ductile RC beams. Equivalent static forces are applied on the longitudinal direction of the structure for: (b) structural system type 1 with longitudinal rigid RC beams; (d) structural system type 2 with normal RC beams; (f) structural system type 3 with ductile RC beams.




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Figure 3: “Representation of the longitudinal cross section for: (a) structural system type 1 with longitudinal rigid RC beams; (c) structural system type 2 with normal RC beams; (e) structural system type 3 with ductile RC beams. Representation of the transverse cross section for: (b) structural system type 1 with longitudinal rigid RC beams; (d) structural system type 2 with normal RC beams; (f) structural system type 3 with ductile RC beams” [11].




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Figure 4: “Discrete system imitation of the: (a) structural system type 1 with longitudinal rigid RC beams; (b) structural system type 2 with normal RC beams; (c) structural system type 3 with ductile RC beams” [11].




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Figure 5: “Representation of steel reinforcement car case in pure MR RC frame models with : (a) longitudinal rigid RC beams (structural system type 1); (c) normal RC beams (structural system type 2); (e) ductile RC beams (structural system type 3). Representation of structural mesh discretization for pure MR RC frame models with: (b) longitudinal rigid RC beams (structural system type 1); (d) normal RC beams (structural system type 2); (f) ductile RC beams (structural system type 3)” [11].

Thus, it has been reached the input data stage for experimental test on the seismic platform [26] of the optimal (unique) RC frame model.

In these conditions, it was proposed to “generate artificial ac-celerograms” [27-31] (associated with “target spectra” [30-32]) whose PGA values (see Table 6 - column two (from left to right)) reach the absolute acceleration values assigned for each consid-ered performance requirement [33-43] (see Table 5 - column three (from left to right)) [27,32], [44-51].

Thus, it is desired artificial accelerograms implementation in the pre-test stage of experimental study to verify the structural seis-

mic response [18-23], [25,43] in accordance with achieved perfor-mance objectives [52-53] in the post-test stage.

Determination of Spectral Acceleration Values For M_8, K_5, K_7 And Z_8 Moment-Resisting RC Frame Models Depending on Performance Objectives

Analytical study conducted by Sococol et al. [9] demonstrates the superior concrete strength class effectiveness on ductile seis-mic response for MR RC frame structural models. Thus, it was con-sidered valid for the next research stage M_8, K_5, K_7 and Z_8 RC frame models (see Table 2).

Table 2: Lateral force values and lateral peak displacement values “of the moment resisting RC frame models from the global seismic response perspective” [11].

NSC CSC Fu [kN] du [m] F*y [kN] d*

y [m]

MR RC Frame Models - Type 1 [see Table 1] [11]

M_6 C12/15 44.1 0.02247 - -

M_7 C16/20 48.3 0.02348 - -

M_8 C20/25 50.4 0.02338 49.4 0.0162


K_3 C12/15 37.42 0.0251 - -

K_4 C16/20 41.575 0.0273 - -

K_5 C20/25 43.65 0.0277 42.8 0.0188

K_7 C20/25 41.575 0.0329 39.9 0.0186


Z_6 C12/15 29.14 0.094 - -

Z_7 C16/20 29.14 0.06 - -

Z_8 C20/25 31.08 0.071 29.7 0.0319

where: “NSC - Numerical Simulation Code; CSC - Concrete Strength Class” [11]; “Fu - ultimate lateral force corresponding to global system collapse; F*y - lateral force corresponding to global yielding of structure; d*y - displacement corresponding to global yielding of structure; du -ultimate lateral displacement of the structural system” [54].




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In these conditions, it were drawn the “F-d” capacity curves (where: “F” - Base Shear; “d” - horizontal Roof Displacement) (see Figure 6- Figure 9 and Table 2) in order to establish the absolute

spectral accelerations values for this series of RC frame models depending on the performance requirements (objectives) [34-43], [52-53] (see Table 3).

Figure 6: Static Push-Over (SPO) curve representation for Z_8 MR RC frame model [53,55].

Figure 7: Static Push-Over (SPO) curve representation for M_8 MR RC frame model [53,55].

Figure 8: Static Push-Over (SPO) curve representation for K_7 MR RC frame model [53,55].




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Figure 9: Static Push-Over (SPO) curve representation for K_5 MR RC frame model [53,55].

Table 3: Performance objectives (requirements) enumeration [52-53], [55,59].

FO IO LS CP SC

Fully Operational Immediate Occupancy Life Safety Collapse Prevention Side-sway Collapse

Also, it was obtained the ultimate lateral forces “Fu” and later-al displacement requirements “du” of the structural systems [54], [21-25] (see Table 2) following nonlinear static analyses performed with ATENA software [13-14]. Lateral forces “F*y” and lateral dis-placements “d*y” corresponding to the global yielding mechanism [18-22], [25], were obtained after bilinearization process (method, procedure) [19-20] of the pushover curves for equivalent SDOF sys-

tems [53].

Thus, it were established elastic - perfectly plastic fits com-patible with EC8 indications [20] (see Figure 10 - Figure 13) using SPO2FRAG software [55] (where “SPO2FRAG (Static Push-Over to FRAGility) is introduced, a MATLAB® [56] - coded software tool for estimating structure-specific seismic fragility curves of buildings, using the results of static pushover analysis” [53]).

Figure 10: SPO curve (gray line) and bi-linearized elastic-perfectly plastic curve (red line) representation of the Z_8 MR RC frame model. Red curve was bi-linearized according to EC 8 indications [20]) [53,55].




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Figure 11: SPO curve (gray line) and bi-linearized elastic-perfectly plastic curve (red line) representation of the M_8 MR RC frame model. Red curve was bi-linearized according to EC 8 indications [20]) [53,55].

Figure 12: SPO curve (gray line) and bi-linearized elastic-perfectly plastic curve (red line) representation of the K_7 MR RC frame model. Red curve was bi-linearized according to EC 8 indications [20]) [53,55].

Figure 13: SPO curve (gray line) and bi-linearized elastic-perfectly plastic curve (red line) representation of the K_5 MR RC frame model. Red curve was bi-linearized according to EC 8 indications [20]) [53,55].




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In these conditions, it was indicated position of the perfor-mance requirements (Figure 14 - Figure 17) through “RDR” indica-tor (Roof Drift Ratio) (see Equation 1) for each “F-d” capacity curve,

establishing the absolute spectral accelerations values (see Table 4).

Figure 15: “RDR - Base Shear” curve representation for M_8 SPO curve [53,55]; where: RDR is Roof Drift Ratio – see Equation 1.

Figure 14: “RDR - Base Shear” curve representation for Z_8 SPO curve [53,55]; where: RDR is Roof Drift Ratio – see Equation 1.

Figure 16: “RDR - Base Shear” curve representation for K_7 SPO curve [53,55]; where: RDR is Roof Drift Ratio – see Equation 1.




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Figure 17: “RDR - Base Shear” curve representation for K_5 SPO curve [53,55]; where: RDR is Roof Drift Ratio – see Equation 1.

Table 4: Output data analysis for RC frame models [53,55].

NSC MC (I) [Sa] SD MC (IV) [Sa] LSN

Z_8

0.298g - 0.298g 0.000 - 0.000 0.298g FO

0.596g - 0.596g 0.000 - 0.000 0.596g IO

1.058g - 1.061g 0.004 - 0.006 1.059g LS

1.615g - 1.725g 0.086 - 0.133 1.669g CP

1.802g - 1.970g 0.116 - 0.180 1.884g SC

M_8

0.501g - 0.501g 0.000 - 0.000 0.501g FO

0.696g - 0.696g 0.000 - 0.000 0.696g IO

1.663g - 1.668g 0.004 - 0.007 1.666g LS

1.913g - 1.935g 0.015 - 0.023 1.924g CP

2.087g - 2.152g 0.040 - 0.062 2.119g SC

K_5

0.374g - 0.374g 0.000 - 0.000 0.374g FO

0.519g - 0.519g 0.000 - 0.000 0.519g IO

1.447g - 1.451g 0.004 - 0.006 1.449g LS

1.757g - 1.789g 0.023 - 0.036 1.773g CP

1.865g - 1.923g 0.039 - 0.061 1.894g SC

K_7

0.492g - 0.492g 0.000 - 0.000 0.492g FO

1.369g - 1.372g 0.004 - 0.006 1.371g IO

1.719g - 1.765g 0.035 - 0.054 1.742g LS

1.947g - 2.058g 0.072 - 0.112 2.002g CP

1.947g - 2.058g 0.072 - 0.112 2.002g SCwhere: “NSC - Numerical Simulation Code; MC (I) - Median Capacity (Interval); SD - Standard Deviation; MC (IV) - Median Capacity (Implicit Value); LSN - Limit State Name” (see Table 3) [11].

“RDR” (Roof Drift Ratio) can be performed according to Equa-tion 1 [53]:

( )*1

/ neff y ii

RDR hµ δ=

= Γ ⋅ ∑

(1)

where: “RDR - Roof Drift Ratio [%]; hi - denotes the height of the i-th storey [m]; Γeff - effective modal participation factor; µ = δmax/δy - displacement ductility (structural ductility) [18]; *

yδ - equivalent SDOF yield displacement [m]” [53].

In current seismic design norms [19-20], [57] and engineer-ing literature [21-25], [52,58] is practiced performance objectives consideration in different forms (with qualitative implications and quantitative enumeration [59]). Thus, five performance objectives are considered in current research (analytical) study (see Table 3).

Four performance objectives were considered according to SEAOC recommendations [52]. The fifth limit state, labeled “side-sway collapse”, is added by SPO2FRAG [53,55] when the SPO (Stat-




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ic Push-Over) curve exhibits strength degradation in the form of a negative-stiffness branch (this limit state corresponds to dynamic instability) [53,55] (Table 3).

Generation of Target Spectra and Artificial Accelerograms for K_7 Moment Resisting RC Frame Model Depending on Performance Objectives

The principal parameters regarding optimal RC frame model determination for target spectra [30-32] generation process with the corresponding artificial accelerograms [27-31] (depending on performance objectives) are:

• “F-d” capacity curves values (with focused attention on the ul-timate lateral displacements “du” and structural yielding dis-placements “d*

y” [19-20], [53]);

• bilinearized curves [19-20], [53];

• “RDR” (%) values for five performance objectives [52-53];

• MR RC frame deformation mechanisms [19-25] for either lat-eral loading stage or absolute spectral acceleration values “Sa” (see Table 4).

In these conditions, Z_8 MR RC frame model presents optimal results, without inclusion in a legal design norm [19]. Thus, it was performed the generation of the artificial accelerograms [27-31] ac-cording to the performance objectives for K_7 MR RC frame model.

The analytical process of artificial accelerograms generation [27-31] (in correspondence with performance objectives [52-53]) for K_7 moment resisting RC frame model includes the knowledge of the “normalized elastic response spectrum of absolute accelera-tions for horizontal components of the ground motion with Tc=0.7 s” (according to P100-1 [19] norm - Iasi area) (see Figure 18), in addition to knowing the absolute spectral acceleration values for each performance objective (see Table 4 and Table 5).

Table 5: Input data for Target Spectra generation [60].

NSC MC (IV) [Sa] GA SP DR LSN GR

K_7

0.492g 0.1968g

0.05

FO Figure 19(a)

1.371g 0.5484g TB=0.14 s IO Figure 19(b)

1.742g 0.6968g TC=0.70 s LS Figure 19(c)

2.002g 0.8008g TD=3.00 s CP Figure 19(d)

2.002g 0.8008g SC Figure 19(d)

where: “NSC - Numerical Simulation Code; MC (IV) - Median Capacity (Implicit Value); GA - Ground Acceleration; SP - Spectrum Period; DR -

Damping Ratio; LSN - Limit State Name (see Table 3); GR - Graphical Representation” [11].

Figure 18: Representation of the “normalized elastic response spectrum of absolute accelerations for horizontal components of the ground motion in the area characterized by Tc=0.7 s control period” [19].

Thus, it was calculated (with Equation 3) the absolute accelera-tion values necessary for target spectra generation and comparison of these values with subsequently PGA values related to generated artificial accelerograms. An important condition in the comparison process is the proximity of the PGA values in Table 6 to the GA val-

ues in Table 5, preferably being as PGA>GA.

The elastic response spectrum of absolute accelerations for horizontal components of the site ground motion, Se(T)=Sa(T), is defined according to P100-1 norm [19] (see Equation 2):




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,( ) ( )e I e gS T a Tγ β= ⋅ ⋅ (2)

,( ) / ( )g e I ea S T Tγ β= ⋅ (3)

where: “γI,e =1 (importance class of structure III - established in accordance with P100-1 norm [19]; ag - value of the horizontal soil acceleration; β(T) - normalized elastic response spectrum of abso-lute accelerations for horizontal components of the ground motion (see Equation 4)” [19].

0 ( ) 2.5B CT T T Tβ β< < = = (4)

Target spectra generation was performed using SeismoArtif software [60] (where: “SeismoArtif is an application capable of gen-erating artificial earthquake accelerograms matched to a specific target response spectrum using different calculation methods and varied assumptions” [61]). Thus, it was possible to generate artifi-cial compatible accelerograms sets with these spectra (Figure 19).

Figure 19: TS (Target Spectra) for Artificial Accelerograms Generation [60]: (a) TS with Sa=0.492g; (b) TS with Sa=1.371g; (c) TS with Sa=1.742g; (d) TS with Sa=2.002g.

Accelerogram sets compatible with target acceleration spectra (Figure 19), it was generated with (using) MSIMQKE software [62-63].

Graphical representation of these artificial accelerograms and their elastic response spectra, was performed through PRISM soft-ware [64] (where: “PRISM® is a free program for seismic response analysis of structures idealized as single-degree-of-freedom sys-tems. The main features of the program include modification of earthquake records, calculation of response time histories of var-

ious hysteresis models, and generation of elastic and inelastic re-sponse spectra” [65]).

In these conditions, it was generated a number of artificial ac-celerograms (Figure 20 - Figure 24) for K_7 moment resisting RC frame model, depending on performance objectives.

Accelerogram PGA values presented in Table 6, reach the ab-solute acceleration values enumerated (listed) in Table 5. Elastic spectra of these artificial accelerograms are represented in Figure 25, Figure 26, Figure 27, Figure 28, Figure 29, following the form




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(shape) and “Sa” target spectra values (Figure 19).Also, it are pre-sented Power Spectra configuration (Figure 30 - Figure 34) and Fourier Spectra output data shapes to check the harmonic compo-nents that can induce the highest quantities of seismic energy (Fig-

ure 35 - Figure 39).Thus, it were generated artificial accelerograms for either performance objective, necessary for K_7 moment resist-ing RC frame model [12] experimental test on the seismic platform.

Table 6: Output data analysis for Generated Artificial Accelerograms [64-65].

NSC PGA [g] PGV [mm/s] PGD [mm] LSN GR-AA GR-RS GR-PS GR-FS

K_7

0.239 377.218 446.6 FO Figure 20 Figure 25 Figure 30 Figure 35

0.542 988.204 1018.1 IO Figure 21 Figure 26 Figure 31 Figure 36

0.704 1342.09 1361.98 LS Figure 22 Figure 27 Figure 32 Figure 37

0.837 1415.55 1265.63 CP Figure 23 Figure 28 Figure 33 Figure 38

0.873 1370.42 1544.7 SC Figure 24 Figure 29 Figure 34 Figure 39

where: “NSC - Numerical Simulation Code; PGA - Peak Ground Acceleration; PGV - Peak Ground Velocity; PGD - Peak Ground Displacement; LSN - Limit State Name (see Table 3); GR - Graphical Representation; AA - Artificial Accelerogram; RS - Response Spectrum; PS - Power Spectrum; FS

- Fourier Spectrum” [11].

Figure 21: acc_02 accelerogram generated with MSIMQKE software [62] for Target Spectra represented in Figure 19(b) (Graphical representation – PRISM software [64]).

Figure 20: acc_01 accelerogram generated with MSIMQKE software [62] for Target Spectra represented in Figure 19(a) (Graphical representation – PRISM software [64]).

Figure 22: acc_03 accelerogram generated with MSIMQKE software [62] for Target Spectra represented in Figure 19(c) (Graphical representation – PRISM software [64]).

Figure 23: acc_04 accelerogram generated with MSIMQKE software [62] for Target Spectra represented in Figure 19(d) (Graphical representation – PRISM software [64]).




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Figure 26: Response Spectrum for acc_02 represented in Figure 21 [64].




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Figure 31: Power Spectrum for acc_02 represented in Figure 21 [66].






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Figure 36: Fourier Spectrum for acc_02 represented in Figure 21 [66].






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ConclusionIn current research practice exist a major necessity for clear

methodology regarding required accelerograms consideration for experimental moment resisting RC frame structures/ systems/ prototypes/ models in experimental tests on seismic platforms.

In these conditions, it was presented a method of the input data consideration for the experimental test, have as a reference point the performance objectives necessary to be achieved in terms of the global seismic response of the RC frame structure.

Thus, it was considered this form of input data for experimental seismic analysis of the K_7 moment-resisting RC frame model (sys-tem). Basically, it can be verified the theoretical considerations in RC seismo-engineering literature through the real seismic response of the reinforced concrete frame structure.

If artificial accelerograms cannot be used for any technical rea-son, it can be used PGA values for a standard lateral loading proto-col.

AcknowledgementNone.

Conflict of InterestThis research paper is sponsored by “Gheorghe Asachi” Techni-

cal University of Iasi with grant number GI/R16_Drd/2021.

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study regarding input data consideration (required

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