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- 1. Design notes for seismic assessment of existing structure in accordance to EUROCODE 8-PART 3 VALENTINOS NEOPHYTOU BEng (Hons), MSc REVISION 1: January, 2014
- 2. ABOUT THIS DOCUMENT This publication provides a concise compilation of selected rules in the Eurocode 8 Part 1 & 3, together with relevant Cyprus National Annex, that relate to the seismic design of common forms of concrete building structure in the South Europe. Rules from EN 1998-3 for global analysis, type of analysis and verification checks are presented. Detail design check rules for concrete beam, column and shear wall, from EN 1998-3 are also presented. This guide covers the assessment of orthodox members in concrete frames. It does not cover design rules for steel frames. Certain practical limitations are given to the scope. Due to time constraints and knowledge, I may not be able to address the whole issues. Please send me your suggestions for improvement. Anyone interested to share his/her knowledge or willing to contribute either totally a new section about Eurocode 8-3 or within this section is encouraged. For further details: My LinkedIn Profile: http://www.linkedin.com/profile/view?id=125833097&trk=hb_tab_pro_top Email: valentinos_n@hotmail.com Slideshare Account: http://www.slideshare.net/ValentinosNeophytou
- 3. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Limit state Mean return period in years TR = 2475 (Vary Rare Earthquake) Near Collapse (NC) TR = 475 (Rare Earthquake) TR = 225 (Frequent Earthquake) Significant Damage (SD) TR = 2475 (Vary Rare Earthquake) FUNDAMENTAL REQUIREMENT – LIMIT STATE (LS) (EN1998-3,cl.2.1) Combination Probability of of action and exceedance in Description performance 50 years levels The structure is heavily damaged, with low 2% 2475/NCS residual lateral strength and stiffness, although vertical elements are still capable of sustaining vertical loads. Most non- 10% 475/NC structural components have collapsed. Large permanent drifts are present. The structure is near collapse and would probably not 20% 225/NC survive another earthquake, even of moderate intensity. The structure is significantly damaged, with 2% 2475/SD some residual lateral strength and stiffness, and vertical elements are capable of sustaining vertical loads. Non-structural TR = 475 (Rare Earthquake) 10% Valentinos Neophytou BEng (Hons), MSc 475/SD components are damaged, although partitions and infills have not failed out-of- Page 3 of 61
- 4. Design notes for Seismic Assessment to Eurocode 8 - Part 3 plane. Moderate permanent drifts are TR = 225 (Frequent Earthquake) present. The structure can sustain after20% 225/SD shocks of moderate intensity. The structure is likely to be uneconomic to repair. TR = 2475 (Vary Rare Earthquake) The structure is only lightly damaged, with 2% 2475/DL structural elements prevented from significant yielding and retaining their strength and stiffness properties. Non- Damage Limitation (DL) TR = 475 (Rare Earthquake) 10% 475/DL structural components, such as partitions and infills, may show distributed cracking, but the damage could be economically TR = 225 (Frequent Earthquake) repaired. Permanent drifts are negligible. 20% 225/DL The structure does not need any repair measures. Note 1: TR values above same as for new buildings. National authorities may select lower values, and require compliance with only two limitstates. Note 2: The acceptable performance level for ordinary buildings of importance should be “Significant Damage” which is roughly equivalent with the “No Collapse” in EN1998-1. Note 3: The National Authorities decide whether all three Limit States shall be checked, or two of them, or just one of them. Note 4: The performance levels for which the three Limit States should be met are chosen either nationally through the National Annex to this part of Eurocode 8, or by the owner if the country leaves the choice open. Valentinos Neophytou BEng (Hons), MSc Page 4 of 61
- 5. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Performance Levels and Limit States Valentinos Neophytou BEng (Hons), MSc Page 5 of 61
- 6. Design notes for Seismic Assessment to Eurocode 8 - Part 3 PERFORMANCE REQUIREMENTS AND COMPLIANCE CRITERIA (EN1998-1-1,cl.2.1) Return-period ground motion in TR years Value of the exponent, k Importance factor based on reference seismic action k=3 −1/𝑘 𝛾𝐼 = 𝑇 𝐿𝑅 𝑇𝐿 𝑃𝐿 𝑃 𝐿𝑅 −1/𝑘 𝛾𝐼 = Importance factor based on reference probability of exceeding the seismic action Mean return period EN19981-1,cl.2.1(4) 𝑇𝑅 = − EN19981-1,cl.2.1(4) 𝑇𝐿 𝑙𝑛 1 − 𝑃 𝑅 EN19981-1,cl.2.1(4) EN1998-1-1,cl.2.1(1) Typical values and relationships of reference probabilities of exceedance and corresponding return periods for a specific site. Probability of exceedance PR Time span TL Mean return period TR 20% 10 years 45 years 10% 10 years 95 years 20% 50 years 224 years 10% 50 years 475 years 5% 50 years 975 years 10% 100 years 949 years 5% 100 years 1950 years Valentinos Neophytou BEng (Hons), MSc Page 6 of 61
- 7. Design notes for Seismic Assessment to Eurocode 8 - Part 3 REDUCED DESIGN LIFE OF THE BUILDING (EN1998-1,cl.2.1) By reducing the remaining lifetime of the building is reduced the design ground acceleration Valentinos Neophytou BEng (Hons), MSc Page 7 of 61
- 8. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Peak ground acceleration attenuation relationships for the European area proposed by Ambraseys et al. (1996) Valentinos Neophytou BEng (Hons), MSc Page 8 of 61
- 9. Design notes for Seismic Assessment to Eurocode 8 - Part 3 SEISMIC ZONATION MAP (CYS NA EN1998-1) The seismic building code of Cyprus includes seismic zonation based on ground acceleration values with 10% probability of exceedance in 50 years, i.e., 475years mean return period. Five zones (1-5) are defined with PGA ranging from 0.075g to 0.15g. In a recent revision of the code (2004), three seismic zones are defined. Valentinos Neophytou BEng (Hons), MSc Page 9 of 61
- 10. Design notes for Seismic Assessment to Eurocode 8 - Part 3 REQUIRED INPUT DATA – CHECK LIST (EN1998-3,cl3.1, 3.2 & Annex A.2) Check Description of identification Parameter Results/Comment tick √ I II Identification of “new” importance class III IV Does the building design using any the Prior 1994 previous seismic code? After 1994 Construction date of building Date Column Present of peeling cracks If YES, provide Beam Wall Valentinos Neophytou BEng (Hons), MSc Page 10 of 61
- 11. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Slab Sign of steel Physical condition of reinforced concrete deterioration Column Beam elements and presence of any degradation, Wall due to carbonation, steel corrosion, etc. Slab Vertical at mid-span Beams Diagonal at ends Are there any significant cracks on structural members Diagonal at ends (joints) Columns Mid-span Diagonal at ends (joints) Walls Mid-span Measure crack width of basement walls Settlement of structure due to weak foundation Valentinos Neophytou BEng (Hons), MSc If YES provide the crack width If YES provide which side of the building have been settled Page 11 of 61
- 12. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Are there any presents of cracks of infill walls at the connection points Is there any present of strengthening to the structural members If YES provide where If YES provide where Regular in plan Identification of the structural regularity Regular in elevation Continuity of load paths between lateral resisting elements. Column supported on beam Missing any structural member Frame system Dual system Frame-equivalent dual system Type of structural system Wall equivalent dual system Torsionally flexible system Inverted pendulum system Identification of the lateral resisting system Valentinos Neophytou BEng (Hons), MSc Moment frame/wall system in X direction Page 12 of 61
- 13. Design notes for Seismic Assessment to Eurocode 8 - Part 3 in both directions. Moment frame/wall system in Y direction Distribution of infill walls Regular in plan Identification of the type of building Raft foundation foundation Pad foundation Pile foundation Strip foundation Is there any building attached? Attached YES/NO If YES measure the gap between them Change of existing usage. Variable If YES re-assess the variable load Re-assessment if imposed Installation of any further load (i.e. actions/permanent load. Permanent antenna, board) If YES re-assess the permanent load Solid slab Thickness/dimensions Flat slab Thickness/dimensions Type of slab Valentinos Neophytou BEng (Hons), MSc Page 13 of 61
- 14. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Waffle slab Thickness/dimensions Ribbed slab Thickness/dimensions Beams Depth and width of concrete elements Columns Walls Width of flanges in T-beams Possible eccentricities between beams and columns axes at joints. Is there any asymmetric setbacks at all storeys Is there any effects of short columns Is there any structural member run with interruption from their foundation to top? If exist, measure the width If eccentricities exist check if YES provide the distance (check if e ≤ bc / 4). If YES provide the distance from the previous storey YES / NO YES / NO Is the ground floor is soft storey (pilotis) YES / NO Identification of the ground conditions. A Valentinos Neophytou BEng (Hons), MSc Page 14 of 61
- 15. Design notes for Seismic Assessment to Eurocode 8 - Part 3 B C D E Column Beam Amount of longitudinal steel in beams, Slab columns and walls. Wall Valentinos Neophytou BEng (Hons), MSc Page 15 of 61
- 16. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Column Beam Amount and detailing of confining steel in critical regions and in beam-column joints. Slab Valentinos Neophytou BEng (Hons), MSc Page 16 of 61
- 17. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Wall Amount of steel reinforcement in floor slabs contributing to the negative resisting bending moment of T-beams. Column Seating and support conditions of Beam horizontal elements. Slab Valentinos Neophytou BEng (Hons), MSc Page 17 of 61
- 18. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Wall Column Beam Depth of concrete cover. Slab Wall Valentinos Neophytou BEng (Hons), MSc Page 18 of 61
- 19. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Column Beam Lap-splices for longitudinal reinforcement. Slab Wall Concrete strength. Column Beam Valentinos Neophytou BEng (Hons), MSc Page 19 of 61
- 20. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Slab Wall Column Beam Steel yield strength, ultimate strength and ultimate strain. Slab Wall Valentinos Neophytou BEng (Hons), MSc Page 20 of 61
- 21. Design notes for Seismic Assessment to Eurocode 8 - Part 3 DEFINITION OF KNOWLEDGE LEVEL (EN1998-3,cl.3.3.2) Knowledge level KL2 The overall structural geometry and The overall structural geometry and member sizes are known either: member sizes are known either: member sizes are known either: (a) from survey or (a) from an extended survey or (a) from a comprehensive survey or (b) from original outline (b) from outline construction (b) from the complete set of outline construction drawings used for both drawings used for both the original construction drawings used for both the the original construction and any construction and any subsequent original construction and any subsequent subsequent modifications. Geometry Knowledge level KL1 The overall structural geometry and Factors modifications. modifications. In case (b), a sufficient sample of In case (b), a sufficient sample of In case (b), a sufficient sample of both dimensions of both overall geometry dimensions of both overall geometry Knowledge level KL3 overall geometry and member sizes should and member sizes should be and member sizes should be checked be checked on site; if there are significant checked on site; if there are on site; if there are significant discrepancies from the outline significant discrepancies from the discrepancies from the outline construction drawings, a fuller outline construction drawings, a construction drawings, a fuller dimensional survey is required. fuller dimensional survey should be dimensional survey is required. performed. The structural details are not known The structural details are known either from detailed construction drawings either from extended in-situ from comprehensive in-situ inspection or and may be assumed based on inspection or from incomplete from a complete set of detailed simulated design in accordance with Details The structural details are known detailed construction drawings. construction drawings. Valentinos Neophytou BEng (Hons), MSc Page 21 of 61
- 22. Design notes for Seismic Assessment to Eurocode 8 - Part 3 usual practice at the time of In the latter case, limited in-situ In the latter case, limited in-situ construction; inspections in the most critical inspections in the most critical elements In this case, limited inspections in elements should be performed to should be performed to check that the the most critical elements should be check that the available information available information corresponds to the performed to check that the corresponds to the actual situation. actual situation. No direct information on the Informationonthemechanicalproperti Informationonthemechanicalpropertiesofth mechanical properties of the esoftheconstructionmaterialsis econstructionmaterialsis available either construction materials is available, available either from extended in- from comprehensive in-situ testing or either from original design situ testing or from original design from original test reports. In this latter specifications or from original test specifications. In this latter case, case, limited in-situ testing should be reports. Default values should be limited in-situ testing should be performed. assumed in accordance with performed. assumptions correspond to the actual situation. Otherwise, more extensive in-situ inspection is required. Materials standards at the time of construction, accompanied by limited in-situ testing in the most critical elements. Valentinos Neophytou BEng (Hons), MSc Page 22 of 61
- 23. Design notes for Seismic Assessment to Eurocode 8 - Part 3 KNOWLEDGE LEVELS (EN 1998-3,cl.3.3.1) Knowledge levels (EN 1998-3,cl.3.3.1) Geometry: The properties of the structural system, and of such non-structural elements (e.g. masonry infill panels) as may affect structural response Details: These include the amount and detailing of reinforcement in reinforced concrete, connections between steel members, the connection of floor diaphragms to lateral resisting structure, the bond and mortar jointing of masonry and the nature of any reinforcing elements in masonry Material: The mechanical properties of the constituent materials Choose the knowledge level based on the factors above Limited knowledge KL1 Normal knowledge KL2 Full knowledge KL3 DETAILS DETAILS DETAILS Simulated design in accordance with relevant practice and From limited in-situ inspection From incomplete original detailed construction drawings with limited in-situ inspection or From extended in-situ inspection From original detailed construction drawings with limited in-situ inspection or From comprehensive insitu inspection MATERIALS MATERIALS Default values in accordance with standards of the time of construction and From limited in-situ testing From original design specifications with limited in- situ testing or From extended in-situ testing Valentinos Neophytou BEng (Hons), MSc MATERIALS From original test reports with limited in- situ testing or From comprehensive insitu testing Page 23 of 61
- 24. Design notes for Seismic Assessment to Eurocode 8 - Part 3 LEVEL OF INSPECTION (EN1998-3,cl.3.4.4) YES Is the Knowledge level KL1 ? Details & Materials Does the spot check agree with the drawings/ assumptions ? Note: if the masonry infill walls are considered in the model, certain sampling and testing for shear and compressive strength and for Elastic Modulus make sense NO NO YES Inspection: 20% detail check Testing: 1 sample per floor (beam/column,wall) Is the Knowledge level KL2 or KL3 ? KL2 KL3 Details YES Details Does the spot check agree with the drawings/ Are the drawing available? Does the spot check agree with the drawings/ Are the drawing available? NO YES Limited Extended Limited Comprehesive Inspection: 20% detail check Inspection: 50% detail check Inspection: 20% detail check Inspection: 80% detail check Materials Material properties are derived either from original specification or through in Specifictions situ sampling NO Materials Material properties are derived either past test reports or through in situ sampling Sampling Test Reports Limited Extended Limited Comprehesive Testing: 1 sample per floor (beam/column,wall) Testing: 2 sample per floor (beam/column,wall) Testing: 1 sample per floor (beam/column,wall) Testing: 3 sample per floor (beam/column,wall) Valentinos Neophytou BEng (Hons), MSc Sampling Page 24 of 61
- 25. Design notes for Seismic Assessment to Eurocode 8 - Part 3 SELECTED KNOWLEDGE LEVEL RELATED TO COST/PROCESS OF INSPECTION Low cost/process LIMITED KNOWLEDGE LEVEL Medium cost/process NORMAL KNOWLEDGE LEVEL High cost/process FULL KNOWLEDGE LEVEL SELECTED KNOWLEDGE LEVEL RELATED TO COST SAVING OF RETROFITTING High cost LIMITED KNOWLEDGE LEVEL Medium cost NORMAL KNOWLEDGE LEVEL Low cost FULL KNOWLEDGE LEVEL Valentinos Neophytou BEng (Hons), MSc Page 25 of 61
- 26. Design notes for Seismic Assessment to Eurocode 8 - Part 3 VALUES OF CONFIDENCE FACTOR (EN1998-3,cl.3.3.1) CONFIDENCE FACTOR (CF) (EN1998-3,cl.3.3.1(4)) Limited knowledge KL1 Normal knowledge KL2 Full knowledge KL3 CF=1.4 CF=1.2 CF=1.0 Note: If the existing member has been strengthened the “Confidence factor” (CF) is applied only on its old material. Note: The “Confidence factor” (CF) is applied to each old materials (steel, concrete, infill masonry). ANALYSIS TYPE (EN1998-3,cl.3.3.1) ANALYSIS TYPE (EN1998-3,cl.3.3.1(4)) YES Lateral force (LF) or Modal Response Spectrum (MRS) (More conservative) Valentinos Neophytou BEng (Hons), MSc Is the Knowledge level KL1 ? NO Lateral force (LF) or Modal Response Spectrum (MRS) Or Non-linear analysis (Pushover/Time history) (Less conservative) Page 26 of 61
- 27. Design notes for Seismic Assessment to Eurocode 8 - Part 3 LATERAL FORCE ANALYSIS REQUIREMENTS (LFA) (EN1998-1-1cl. & EN1998-3,cl.4.4.2) HORIZONTAL ELASTIC RESPONSE SPECTRUM (ΕΝ1998-1-1,cl.3.2.2.2) 0 ≤ 𝑇 ≤ 𝑇 𝐵: 𝑆 𝑒 𝑇 = 𝑎 𝑔 ∙ 𝑆 ∙ 1 + 𝑇 𝑇𝐵 ∙ 𝜂 ∙ 2,5 − 1 (ΕΝ1998-1-1,Eq. 3.2) 𝑇 𝐵 ≤ 𝑇 ≤ 𝑇 𝐶 : 𝑆 𝑒 𝑇 = 𝑎 𝑔 ∙ 𝑆 ∙ 𝜂 ∙ 2.5 (ΕΝ1998-1-1,Eq. 3.3) 𝑇 𝐶 ≤ 𝑇 ≤ 𝑇 𝐷 : 𝑆 𝑒 𝑇 = 𝑎 𝑔 ∙ 𝑆 ∙ 𝜂 ∙ 2.5 𝑇𝐶 𝑇 𝐷 ≤ 𝑇 ≤ 4𝑠: 𝑆 𝑒 𝑇 = 𝑎 𝑔 ∙ 𝑆 ∙ 𝜂 ∙ 2.5 𝑇𝐶 𝑇𝐷 𝑇2 (ΕΝ1998-1-1,Eq. 3.4) 𝑇 (ΕΝ1998-1-1,Eq. 3.5) Damping viscous: ξ=5% Damping correction factor η: 𝜂 = 10/ 5 + 𝜉 ≥ 0.55 Design ground acceleration on type A ground: ag=γI*agR Parameters of Type 1 elastic response spectrum (Large magnitude M>5.5Hz) (CYS NA EN1998-1-1,table 3.2) Ground Type A B C D E S TB (s) TC (s) TD (s) 1.0 1.2 1.15 1.35 1.4 0.15 0.15 0.20 0.20 0.15 0.4 0.5 0.6 0.8 0.5 2.0 2.0 2.0 2.0 2.0 Valentinos Neophytou BEng (Hons), MSc Page 27 of 61
- 28. Design notes for Seismic Assessment to Eurocode 8 - Part 3 VERTICAL ELASTIC RESPONSE SPECTRUM (ΕΝ1998-1-1,cl.3.2.2.3) The vertical component of seismic action is taken into account if the design ground acceleration in the vertical direction, avg, exceeds 0.25g, and even then only in the following cases: for horizontal structural member spanning 20m or more, for horizontal cantilever components longer than 5m, for beams supporting columns, in based-isolated structures. 0 ≤ 𝑇 ≤ 𝑇 𝐵 : 𝑆 𝑣𝑒 𝑇 = 𝑎 𝑣𝑔 ∙ 1 + 𝑇 𝑇𝐵 ∙ 𝜂 ∙ 3,0 − 1 (ΕΝ1998-1-1,Eq. 3.8) 𝑇 𝐵 ≤ 𝑇 ≤ 𝑇 𝐶 : 𝑆 𝑣𝑒 𝑇 = 𝑎 𝑣𝑔 ∙ 𝜂 ∙ 3.0 (ΕΝ1998-1-1,Eq. 3.9) 𝑇 𝐶 ≤ 𝑇 ≤ 𝑇 𝐷 : 𝑆 𝑣𝑒 𝑇 = 𝑎 𝑣𝑔 ∙ 𝜂 ∙ 3.0 𝑇𝐶 𝑇 𝐷 ≤ 𝑇 ≤ 4𝑠: 𝑆 𝑣𝑒 𝑇 = 𝑎 𝑣𝑔 ∙ 𝜂 ∙ 3.0 𝑇𝐶 𝑇𝐷 𝑇2 (ΕΝ1998-1-1,Eq. 3.10) 𝑇 (ΕΝ1998-1-1,Eq. 3.11) Damping viscous: ξ=5% Damping correction factor η: 𝜂 = 10/ 5 + 𝜉 ≥ 0.55 Design ground acceleration on type A ground: ag=γI*agR Design ground acceleration in vertical direction: avg = avg/ag*agR*γI Note: the value of S is not used in the above expression cause the vertical ground motion is not very much affected by the underlying ground condition Parameters values of vertical elastic response spectra (Large magnitude M>5.5Hz) (CYS NA EN1998-1-1,cl NA2.8) Spectrum avg/ag TB (s) TC (s) TD (s) Type 1 0.90 0.05 0.15 1.0 Valentinos Neophytou BEng (Hons), MSc Page 28 of 61
- 29. Design notes for Seismic Assessment to Eurocode 8 - Part 3 COMBINATION OF SEISMIC MASS (EN 1998-1-1,cl.3.2.4) Storey φ Roof 1,0 Storeys with correlated occupancies 0.8 Independently occupied storeys 0.5 Type of Variable action Categories A-C1 Categories A-F1 1.0 Category Specific Use ψ2 A Domestic and residential 0.3 B Office 0.3 C Areas for Congregation 0.6 D Shopping 0.6 E Storage 0.8 F Traffic < 30 kN vehicle 0.6 G Traffic < 160 kN vehicle 0.3 H Roofs 0 Snow, altitude < 1000 m 0 Wind 0 Values References 𝜓Ei = 𝜙 ∙ 𝜓2i ΕΝ1998-1-1,Eq. 4.2 Requirements Combination coefficient for variable action Combination of seismic mass Requirements Gk,j + 𝜓Ei Qk,i Values ΕΝ1998-1-1,Eq. 3.17 References ST = 1.0 (S = S * ST) If γI > 1.0 (i.e. III & IV) Amplification factor for Slopes <15o EN1998-5, Annex A Cliffs height <30m ST = 1.2 (S = S * ST) Valentinos Neophytou BEng (Hons), MSc EN1998-5, Annex A Page 29 of 61
- 30. Design notes for Seismic Assessment to Eurocode 8 - Part 3 If γI > I (i.e. III & IV) for Slopes 15o ≤ slope ≤ 30o Cliffs height <30m ST = 1.4 (S = S * ST) If γI > 1.0 (i.e. III & IV) for Slopes slope > 30o EN1998-5, Annex A Cliffs height <30m (Bisch etal, 2011 – Lisbon) Requirements Values References YES / NO ΕΝ1998-1-1,table 4.1 Regular in elevation YES ΕΝ1998-1-1,table 4.1 Ground acceleration 0.10-0.25g Regular in plan Spectrum type TYPE 1 (Large magnitude M>5.5Hz) CYS NA EN1998-1-1:Seismic zonation map EN1998-1-1,cl.3.2.2.2(2)P A,B,C,D,E Ground type Normally type B or C can be used EN1998-1-1,cl.3.1.2(1) normal condition Lower bound factor for the horizontal λ = 0.85 if T1 ≤ 2TC and more than 2 design spectrum storey EN1998-1-1,cl.4.3.3.2.2(1Ρ) λ=1.0 in all other case Damped elastic response spectrum Fundamental period Valentinos Neophytou BEng (Hons), MSc ξ = 5% T1≤4Tc T1≤2,0s EN1998-1-1,cl.3.2.2.2(1)P EN1998-1-1,cl.4.3.3.2.1(2) Page 30 of 61
- 31. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Accidental eccentricity See table below Fb=Sd(T1).mass.λ Base shear Horizontal seismic forces (according EN1998-1-1,cl.4.3.2 (EN1998-1-1,cl.4.3.3.2.2) Fi = Fb ∙ to height of the masses) zi ∙ mi zj ∙ mj (EN 1998-1-1:2004, Eq. 4.11) 𝐹𝑖 = 𝛿 ∙ 𝐹𝑖 (Fi see above) Accidental torsional effects 3D EN1998-1-1,cl.4.3.3.2.4(1) Where: 𝛿 = 1 + 0.6 If the accidental torsional effects as 𝑥 𝐿𝑒 𝑀 𝑎𝑖 = ∓𝑒 𝑎𝑖 ∙ 𝛿𝐹𝑖 shown in table below (EN199811,cl.4.3.2(1)P) is not taken into Where: 2D 𝑒 𝑎𝑖 = ∓0.10𝐿 𝑖 (regular in plan) Where account the following rules can be use 𝛿 = 1 + 1.2 EN1998-1-1,cl.4.3.3.2.4(2) 𝑥 𝐿𝑒 Accidental torsional effect (EN1998-1-1,cl.4.3.2) Asymmetric distribution of Percentage of accidental eccentricity Geometry of model (3D/2D) mass (i.e. infill walls) (Regular/Irregular) 5% 3D Regular 10% 3D Irregular 20% 2D - Requirements Values References Torsional moment Valentinos Neophytou BEng (Hons), MSc 𝑀 𝑎𝑖 = ∓𝑒 𝑎𝑖 ∙ 𝐹𝑖 For eai see the table above EN1998-1-1,cl.4.3.3.3.3(1) Page 31 of 61
- 32. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Load case name Direction and Eccentricity % Eccentricity EQXA X Dir + Eccen. Y As above EQYA X Dir – Eccen. Y As above EQXB Y Dir + Eccen. X As above EQYB Y Dir – Eccen. X As above Reference structure Period T1 Exact formula for Single Degree of Freedom Oscillator. Mass M lumped at top of a vertical cantilever of height H. Cantilever mass MB = 0. T1 = 2π Exact formula for Single Degree of Freedom Oscillator. Vertical cantilever of height H and of total mass MB. T1 = 2π Exact formula for Single Degree of Freedom Oscillator. Mass M lumped at top of a vertical cantilever of height H and of total mass MB. T1 = 2π MH 3 3EI 0.24MB H 3 3EI M + 0.24MB H 3 3EI Approximate Relationship (Eurocode 8). Ct = 0,085 for moment resisting steel space frames Ct = 0,075 for eccentrically braced steel frames Ct = 0,050 for all other structures T1 = Ct H 3/4 H building height in m measured from foundation or top of rigid basement. Approximate Relationship (Eurocode 8). d : elastic horizontal displacement of top of building in m under gravity T1 = 2 d loads applied horizontally. Valentinos Neophytou BEng (Hons), MSc Page 32 of 61
- 33. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Modal Response Spectrum Analysis requirements (MRSA) (EN1998-1-1cl. & EN1998-3,cl.4.4.2) Requirements Values Horizontal elastic response spectrum As above – see LFA Vertical elastic response spectrum As above – see LFA Amplification factor As above – see LFA Seismic mass As above – see LFA Requirements Values YES/NO Structural model Ground acceleration Spectrum type ΕΝ1998-1-1,table 4.1 2D/3D Regular in elevation ΕΝ1998-1-1,table 4.1 NO Regular in plan References EN1998-1-1,cl.4.2.3.1(3)P 0.10-0.25g TYPE 1 (Large magnitude M>5.5Hz) CYS NA EN1998-1-1:Seismic zonation map EN1998-1-1,cl.3.2.2.2(2)P A,B,C,D,E Ground type Normally type B or C can be used EN1998-1-1,cl.3.1.2(1) normal condition ξ = 5% Accidental eccentricity EN1998-1-1,cl.3.2.2.2(1)P See table below Damped elastic response spectrum EN1998-1-1,cl.4.3.2 ΣMx ≥ 90% of total mass ΣMy ≥ 90% of total mass Effective modal modes Mx ≥ 5% of total mass EN1998-1-1,cl.4.3.3.1(3) Mxy ≥ 5% of total mass k ≥3.√n Minimum number of modes (if eigenvalue analysis capture) k: is the number of modes EN1998-1-1,cl.4.3.3.1(5) n: is the number of storey Valentinos Neophytou BEng (Hons), MSc Page 33 of 61
- 34. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Tk ≤ 0.20sec Tk: is the period of vibration of mode k Period of vibration EN1998-1-1,cl.4.3.3.1(5) At least one natural period should be below 0.20s Fundamental period Tj ≤ 0.9 Ti SRSS Tj ≥ 0.9 Ti CQC EN1998-1-1,cl.4.3.3.2.1(2) 𝑀 𝑎𝑖 = ∓𝑒 𝑎𝑖 ∙ 𝐹𝑖 3D For eai see the table EN1998-1-1,cl.4.3.3.3.3(1) below 𝑀 𝑎𝑖 = ∓𝑒 𝑎𝑖 ∙ 𝛿𝐹𝑖 Torsional moment Where: 2D 𝑒 𝑎𝑖 = ∓0.10𝐿 𝑖 (regular in EN1998-1-1,cl.4.3.3.2.4(2) Where plan) 𝛿 = 1 + 1.2 𝑥 𝐿𝑒 Accidental torsional effect (EN1998-1-1,cl.4.3.2) Percentage of accidental eccentricity Asymmetric distribution of mass Geometry of model (3D/2D) (i.e. infill walls) (Regular/Irregular) 5% 3D Regular 10% 3D Irregular 20% 2D - Valentinos Neophytou BEng (Hons), MSc Page 34 of 61
- 35. Design notes for Seismic Assessment to Eurocode 8 - Part 3 q – factor approach analysis requirements (ΕΝ1998-1-1,cl.3.2.2.2) Design spectrum of elastic analysis (ΕΝ1998-1-1,cl.3.2.2.5) 0 ≤ 𝑇 ≤ 𝑇 𝐵: 𝑆 𝑑 𝑇 = 𝑎 𝑔 ∙ 𝑆 ∙ 𝑇 𝐵 ≤ 𝑇 ≤ 𝑇 𝐶: 𝑆 𝑑 𝑇 = 𝑎 𝑔 ∙ 𝑆 ∙ 2 3 + 𝑇 𝑇𝐵 ∙ 2.5 𝑞 2 −3 (ΕΝ1998-1-1,Eq. 3.13) 2.5 𝑇 𝐶 ≤ 𝑇 ≤ 𝑇 𝐷: 𝑆 𝑑 𝑇 = 𝑎 𝑔 ∙ 𝑆 ∙ (ΕΝ1998-1-1,Eq. 3.14) 𝑞 2.5 𝑇 𝐶 𝑞 𝑇 ≥ 𝛽 ∙ 𝑎𝑔 (ΕΝ1998-1-1,Eq. 3.15) 𝑇 𝐷 ≤ 𝑇 ≤ 4𝑠: 𝑆 𝑑 𝑇 = 𝑎 𝑔 ∙ 𝑆 ∙ 2.5 𝑞 𝑇𝐶 𝑇𝐷 𝑇2 ≥ 𝛽 ∙ 𝑎𝑔 (ΕΝ1998-1-1,Eq. 3.5) Design ground acceleration on type A ground: ag=γI*agR Lower bound factor for the horizontal spectrum: β=0.2 A value of q =1.5 for concrete structures (regardless of the structural system) A value of q = 2.0 for steel structures (regardless of the structural system) Parameters of Type 1 elastic response spectrum (Large magnitude M>5.5Hz) (CYS NA EN1998-1-1,table 3.2) Ground Type A B C D E S TB (s) TC (s) TD (s) 1.0 1.2 1.15 1.35 1.4 0.15 0.15 0.20 0.20 0.15 0.4 0.5 0.6 0.8 0.5 2.0 2.0 2.0 2.0 2.0 Valentinos Neophytou BEng (Hons), MSc Page 35 of 61
- 36. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Vertical elastic design spectrum (ΕΝ1998-1-1,cl.3.2.2.5(5)) The vertical component of seismic action is taken into account if the design ground acceleration in the vertical direction, avg, exceeds 0.25g, and even then only in the following cases: for horizontal structural member spanning 20m or more, for horizontal cantilever components longer than 5m, for beams supporting columns, in based-isolated structures. . 0 ≤ 𝑇 ≤ 𝑇 𝐵 : 𝑆 𝑑 𝑇 = 𝑎 𝑣𝑔 ∙ 2 𝑇 𝐵 ≤ 𝑇 ≤ 𝑇 𝐶 : 𝑆 𝑑 𝑇 = 𝑎 𝑣𝑔 ∙ 2.5 𝑇 𝐶 ≤ 𝑇 ≤ 𝑇 𝐷 : 𝑆 𝑑 𝑇 = 𝑎 𝑣𝑔 ∙ 3 + 𝑇 𝑇𝐵 ∙ 2.5 𝑞 2 −3 (ΕΝ1998-1-1,Eq. 3.13) (ΕΝ1998-1-1,Eq. 3.14) 𝑞 2.5 𝑇 𝐶 𝑞 𝑇 ≥ 𝛽 ∙ 𝑎 𝑣𝑔 (ΕΝ1998-1-1,Eq. 3.15) 𝑇 𝐷 ≤ 𝑇 ≤ 4𝑠: 𝑆 𝑑 𝑇 = 𝑎 𝑣𝑔 ∙ 2.5 𝑞 𝑇𝐶 𝑇𝐷 𝑇2 ≥ 𝛽 ∙ 𝑎 𝑣𝑔 (ΕΝ1998-1-1,Eq. 3.5) Design ground acceleration on type A ground: ag=γI*agR Design ground acceleration in vertical direction: avg = avg/ag*agR*γI For the vertical component of the seismic action the design spectrum is given by expressions (3.13) to (3.16), with the design ground acceleration in the vertical direction, avg replacing ag, S taken as being equal to 1,0 and the other parameters as defined in 3.2.2.3. Parameters values of vertical elastic response spectra (CYS NA EN1998-1-1,cl NA2.8) Spectrum avg/ag TB (s) TC (s) TD (s) Type 1 0.90 0.05 0.15 1.0 Special provisions: For the vertical component of the seismic action a behaviour factor q up to to 1,5 should generally be adopted for all materials and structural systems. Valentinos Neophytou BEng (Hons), MSc Page 36 of 61
- 37. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Requirements Values Amplification factor As above – see LFA Seismic mass As above – see LFA Analysis requirements As above – see MRSA Accidental eccentricity As above – see MRSA Regular in plan As above – see MRSA Regular in elevation As above – see MRSA Structural model As above – see MRSA Ground acceleration As above – see MRSA Spectrum type As above – see MRSA Ground type As above – see MRSA Damped elastic response spectrum As above – see MRSA Accidental eccentricity As above – see MRSA Effective modal modes As above – see MRSA Minimum number of modes As above – see MRSA Fundamental period As above – see MRSA Torsional moment As above – see MRSA Accidental torsional effect As above – see MRSA Valentinos Neophytou BEng (Hons), MSc Page 37 of 61
- 38. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Linear Analysis - Requirements from EN1998-3 (EN1998-3,cl.4.4.2(1)P) Requirements Values Ductile mechanism (flexure) Brittle mechanism (Shear) Demand Capacity Demand Capacity (Di) (Ci) (Di) (Ci) Acceptability of linear model (for checking of ρi = From analysis. Use mean values of properties Di Ci Verifications (if LM accepted) values) In term of strength. Use mean values of properties. If ρi < 1: from analysis strength. Verifications (if LM accepted) If ρi > 1: from Ratio between demand and capacity In term of EN1998-3cl.4.4.2(1)P From analysis. strength. Use mean values of properties divided by CF In term of equilibrium with strength of ductile e/m. Use mean values Use mean values of properties divided by CF and by partial factor of properties multiplied by CF. Dseismic : is bending moment at the end member due to the seismic action and the concurrent gravity load. Cgravity : is the corresponding moment resistance, calculated on the basis of the axial force due to gravity load alone and using mean-value properties of old material from in-situ test. Note: ρi=Dseismic/Cgravity Valentinos Neophytou BEng (Hons), MSc Page 38 of 61
- 39. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Value of the ratio ρmax/ρmin ρmax/ρmin = 2.5 (EN1998-3,cl.4.4.2(1P) Valentinos Neophytou BEng (Hons), MSc Page 39 of 61
- 40. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Combination of seismic action (EN1998-1-1cl. & EN1998-3,cl.4.4.2) Seismic load combination for “Modal Analysis/Pushover” SEISMIC 1. DL + ψEiLL + EQX + 0.3EQY SEISMIC 2. DL + ψEiLL + EQX – 0.3EQY SEISMIC 3. DL + ψEiLL - EQX + 0.3EQY SEISMIC 4. DL + ψEiLL - EQX – 0.3EQY SEISMIC 5. DL + ψEiLL + EQY + 0.3EQX SEISMIC 6. DL + ψEiLL + EQY – 0.3EQX SEISMIC 7. DL + ψEiLL - EQY + 0.3EQX SEISMIC 8. DL + ψEiLL - EQY – 0.3EQX Seismic load combination for “Lateral force Analysis/Pushover” SEISMIC 1. DL + ψEiLL + EQXA + 0.3EQY SEISMIC 2. DL + ψEiLL + EQXA – 0.3EQY SEISMIC 3. DL + ψEiLL - EQXA + 0.3EQY SEISMIC 4. DL + ψEiLL - EQXA – 0.3EQY SEISMIC 5. DL + ψEiLL + EQYA + 0.3EQX SEISMIC 6. DL + ψEiLL + EQYA – 0.3EQX SEISMIC 7. DL + ψEiLL - EQYA + 0.3EQX SEISMIC 8. DL + ψEiLL - EQY – 0.3EQX SEISMIC 9. DL + ψEiLL + EQX + 0.3EQY SEISMIC 10. DL + ψEiLL + EQX – 0.3EQY SEISMIC 11. DL + ψEiLL - EQX + 0.3EQY SEISMIC 12. DL + ψEiLL - EQX – 0.3EQY SEISMIC 13. DL + ψEiLL + EQY + 0.3EQX SEISMIC 14. DL + ψEiLL + EQY – 0.3EQX SEISMIC 15. DL + ψEiLL - EQY + 0.3EQX SEISMIC 16. DL + ψEiLL - EQY – 0.3EQX Valentinos Neophytou BEng (Hons), MSc Page 40 of 61
- 41. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Non-linear Analysis – Pushover Analysis requirements (EN1998-1-1cl. & EN1998-3,cl.4.4.2) Requirements Values References Regular in plan YES/NO ΕΝ1998-1-1,table 4.1 Regular in elevation YES/NO ΕΝ1998-1-1,table 4.1 2D/3D EN1998-1-1,cl.4.3.3.1(9&10)P Structural model Ground acceleration Spectrum type CYS NA EN1998-1-1:Seismic 0.10-0.25g zonation map TYPE 1 (Large magnitude M>5.5Hz) EN1998-1-1,cl.3.2.2.2(2)P A,B,C,D,E Ground type Normally type B or C can be used EN1998-1-1,cl.3.1.2(1) normal condition Cracked elements 50% of the stiffness EN1998-1-1,cl.4.3.1(7) Material properties Use mean values EN1998-1-1,cl.4.3.3.4.1(4) Seismic action Apply to the ∓ direction EN1998-1-1,cl.4.3.3.4.1(7)P Lateral Force Analysis Lateral loads derived from or EN1998-1-1,cl.4.3.3.4.2.2(1) Modal Response Spectrum Analysis Determination of the period for SDOF 𝑇 = 2𝜋 𝑚∙ 𝑑𝑦 𝐹𝑦 EN1998-1-1,Eq.B.7 Determination of the Target displacement for SDOF 𝑇 𝑑 𝑒 = 𝑆 𝑒 (𝑇) 2𝜋 2 EN1998-1-1,Eq.B.8 Accidental torsional effect (EN1998-1-1,cl.4.3.2) Percentage of accidental eccentricity Geometry of model (3D/2D) Valentinos Neophytou BEng (Hons), MSc Asymmetric distribution of mass in plan Page 41 of 61
- 42. Design notes for Seismic Assessment to Eurocode 8 - Part 3 (i.e. infill walls) (Regular/Irregular) 5% 3D Regular 10% 3D Irregular 20% 2D - Valentinos Neophytou BEng (Hons), MSc Page 42 of 61
- 43. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Non linear Analysis - Requirements from EN1998-3 (EN1998-3,cl.4.4.2(1)P) Requirements Values Ductile mechanism (flexure) Brittle mechanism (Shear) Demand Ratio between demand Capacity Demand Capacity (Di) (Ci) (Di) (Ci) and capacity From analysis. In term of From analysis. In term of strength. EN1998-3cl.4.4.2(1)P Use mean deformation. Use mean Use mean values of values of Use mean values values of properties divided by properties in of properties properties in CF and by partial model. divided by CF. model. factor. Plastic hinges X & Y – direction (check separately) ∑ M Rc > ∑ M Rb , then plastic hinges will likely develop in beams and, Case 1: At beams consequently, only the beams should be considered for the evaluation of ρmax and ρmin. ∑ M Rc < ∑ M Rb , then plastic hinges will likely develop in columns and, Case 2: At Columns thereby, only the columns should be considered for the evaluation of ρmax and ρmin. Lateral load (EN1998-1-1,cl. 4.3.3.4.2.2(1)) Load pattern Description A “uniform pattern”, corresponding to uniform unidirectional lateral Uniform load pattern accelerations (i.e. Φi = 1) . It attempts to simulate the inertia forces in a potential soft-storey mechanism, limited in all likelihood to the bottom storey, with the lateral drifts concentrated there and the storeys above moving laterally almost as a rigid body. Valentinos Neophytou BEng (Hons), MSc Page 43 of 61
- 44. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Uniform load pattern A “modal pattern”, simulating the inertia forces of the1st mode in the horizontal direction in which the analysis is carried out. This pattern is meant to apply in the elastic regime and during the initial stages of the plastic mechanism development, as well as in a full-fledged beam-sway mechanism Modal load pattern Modal load pattern Valentinos Neophytou BEng (Hons), MSc Page 44 of 61
- 45. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Capacity curve (EN1998-1-1,cl. 4.3.3.4.2.3(1)) Relation between base shear force and the control displacement Capacity curve (for each analysis see below) 1. Pushover curve ends until a terminal point at 1.5 times the “target displacement”. Procedure for determination of the target displacement for nonlinear static (pushover) analysis (EN1998-1,cl.Annex B) Requirements Values Φi = 1 References Uniform pattern EN1998-1,cl.B.1 Normalized displacement Φi = Modal pattern Calculated from Modal analysis Natural period T calculated from linear elastic analysis - Normalized lateral forces 𝐹 𝑖 = 𝑚 𝑖 Φi EN1998-1,Eq.B.1 Mass of an equivalent SDOF 𝑚∗ = Valentinos Neophytou BEng (Hons), MSc 𝑚𝑖 𝜙𝑖 = 𝐹𝑖 EN1998-1,Eq.B.2 Page 45 of 61
- 46. Design notes for Seismic Assessment to Eurocode 8 - Part 3 𝑚∗ Γ= Transformation factor 𝑚 𝑖 Φi = 2 𝐹𝑖 𝐹𝑖 2 𝑚𝑖 𝐹 𝑏 = 𝑆d(𝑇1) ⋅ 𝑚 ⋅ λ Base shear EN1998-1,Eq.B.3 EN1998-11,cl.3.2.2.2 Force of SDOF 𝐹∗ = 𝐹𝑏 Γ EN1998-1,Eq.B.4 Displacement of SDOF 𝑑∗ = 𝑑𝑛 Γ EN1998-1,Eq.B.5 ∗ 𝑑𝑦 = 2 Yield displacement of the idealised SDOF system 𝑑𝑚 ∗ 𝐸 𝑚∗ − ∗ 𝐹𝑦 Note: The maximum displacement of structure is EN1998-1,Eq.B.6 taken from the roof level at the node of centre of mass. The top of a penthouse should not be considered as the roof. 𝑇 = 2𝜋 Period 𝑚∗ ∙ 𝑑 𝑦 ∗ 𝐹𝑦 EN1998-1,Eq.B.7 Elastic acceleration response spectrum, Se(T*) See section above “LFA” Target displacement of the structure with period T* 𝑑 𝑒𝑡 Valentinos Neophytou BEng (Hons), MSc ∗ 𝑇∗ = 𝑆𝑒(𝑇) 2𝜋 ∗ - 2 EN1998-1,Eq.B.8 Page 46 of 61
- 47. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Target displacement Short period range EN1998-1,cl.B.5 (T* < Tc) 𝐹𝑦 ∗ 𝑚∗ 𝐹𝑦 ∗ 𝑚∗ ≥ 𝑆 𝑒 𝑇∗ 𝑑 𝑡 ∗ ≥ 𝑑 𝑒𝑡 ∗ < 𝑆 𝑒 𝑇∗ 𝑑 𝑡∗ = 𝑞𝑢 = 𝑑 𝑒𝑡 ∗ 𝑞𝑢 1+ 𝑞𝑢 −1 𝑇𝐶 𝑇∗ ≥ 𝑑 𝑒𝑡 ∗ 𝑆 𝑒 𝑇 ∗ 𝑚∗ 𝐹𝑦 ∗ Target displacement EN1998-1,cl.B.5 Medium and long period range (T* ≥ Tc) 𝑑 𝑡 ∗ = det ∗ = 𝑆𝑒(𝑇)∗ Valentinos Neophytou BEng (Hons), MSc 𝑇∗ 2 2𝜋 (≤3det*) Page 47 of 61
- 48. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Target displacement of dt =Γdt* MDOF EN1998-1,Eq.B.13 Torsional effects (EN1998-1-1,cl.4.3.3.4.2.7) Requirements 2D/3D Description References This rule applied to the following structural system: Torsionally flexible structural type (i.e. rx < Is see EN1998-1-1,cl.4.2.3.2, or, a structure with a predominantly torsional 1st or 2nd mode of vibration in one of the Torsional effects requirements 3D model two orthogonal horizontal direction). - Displacement at the stiff/strong EN1998-11,cl.4.3.3.4.2.7(1)P side are under estimated compared to the flexible weak side in plan (i.e. is the side which developed smaller displacement under static load parallel to it) shall be increased 𝑀 𝑎𝑖 = ∓𝑒 𝑎𝑖 ∙ 𝛿𝐹𝑖 Where: Torsional effects requirements 2D model (regular 𝑒 𝑎𝑖 = ∓0.10𝐿 𝑖 (see table above) in plan) Where 𝑥 𝛿 = 1 + 1.2 𝐿𝑒 EN1998-11,cl.4.3.3.2.4(2) EN1998-1EN1998-1- 1,cl.4.3.3.4.2.7(3) 1,cl.4.3.2(1)P Procedure for determine the increased displacement of strong/stiff side Procedure for determine the increased displacement of strong/stiff side can be found in the Designer’s Guide to EN1998-1 and EN1998-5 in p. 57 Valentinos Neophytou BEng (Hons), MSc Page 48 of 61
- 49. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Number of Analysis required (Pushover) X & Y – main directions Y - direction “modal” towards (+) positive Y “modal” towards (-) negative X “modal” towards (-) negative Y “uniform” towards (+) positive X “uniform” towards (+) positive Y “uniform” towards (-) negative X Analysis number X – direction “modal” towards (+) positive Directions “uniform” towards (-) negative Y Valentinos Neophytou BEng (Hons), MSc Page 49 of 61
- 50. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Modeling Aspects (EN1998-1-1,cl.4.3.1) Requirements Secondary elements Material properties Lateral components Values References The strength and stiffness of secondary seismic elements, against lateral actions may in general be EN1998-3,cl.4.3(3)P neglected in the analysis Use mean values of material properties All lateral components should be connected by horizontal diaphragms EN1998-3,cl.4.3(5)P EN1998-1-1,cl.4.3.1(3) Floor diaphragms may taken as being rigid in their planes, mass and moments inertia may be lumped at the centre of gravity. Neglect the rigid diaphragm assumption for the following cases: Floor diaphragms 1. not compact configuration and plan view far from rectangular. EN1998-1-1,cl.4.3.1(4) 2. large openings in floor slabs, due to internal patios or stairways. 3. large distance between strong and stiff vertical elements compared to the transverse dimension of the diaphragm. Structural Criteria for regularity are play significant role to the regularity type of modeling and analysis EN1998-1-1,cl.4.3.1(5) No use of the modification for un-crack cross-section (50% EI). Not OK in displacement-based assessment Crack analysis (unconservative for displacement demands). OK in EN1998-1-1,cl.4.3.1(6&7) force-based design of new buildings (conservative for force Infill walls which contribute significally to the lateral Infill walls stiffness and resistance of the building should be taken EN1998-1-1,cl.4.3.1(8) into account Valentinos Neophytou BEng (Hons), MSc Page 50 of 61
- 51. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Foundation The deformability of the foundation shall be taken into account in the model Valentinos Neophytou BEng (Hons), MSc EN1998-1-1,cl.4.3.1(9) Page 51 of 61
- 52. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Seismic assessment of Reinforced Concrete buildings (EN1998-3,Annex A) Partial factors Requirements Values References γs = 1.15 CYS EN1992-1-1,table 2.1 γc = 1.5 CYS EN1992-1-1,table 2.1 Permanent action γG = 1.35 EN1990,cl.6.4.3.2 Variable action γQ = 1.5 EN1990,cl.6.4.3.2 Partial factor for steel reinforcement Partial factor of concrete Limit State of near collapse (NC) Requirements Values Factor for structural References 𝛾 𝑒𝑙 = 1.5 (primary members) element EN1998-3,cl.A.3.2.2(1) 𝛾 𝑒𝑙 = 1.0 (secondary members) primary/secondary Ratio moment/shear at the end section 𝐿 𝑣 = 𝑀/𝑉 EN1998-3,cl.A.3.2.2(1) 𝑣= Design axial force Mechanical reinforcement ratio of the tension and 𝑁 𝑏 ∙ ∙ 𝑓𝑐 EN1998-3,cl.A.3.2.2(1) Mechanical ratio 𝜔= ׳ 𝜌1 + 𝜌 𝑣 𝑓 𝑦𝐿 𝑓𝑐 compression of Valentinos Neophytou BEng (Hons), MSc of tension fc : uniaxial (cylindrical) longitudinal concrete strength (MPa) reinforcement Page 52 of 61
- 53. Design notes for Seismic Assessment to Eurocode 8 - Part 3 longitudinal Mechanical ratio reinforcement, ω,ω׳ 𝜔= 𝜌2 𝑓 𝑦𝐿 𝑓𝑐 of compression longitudinal reinforcement Modulus of Elasticity 𝐸 𝑐𝑚 (as for new members) Concrete compressive 𝑓𝑐 𝑚 = 22 10 EN1998-3,cl.A.3.2.2(1) 𝑓𝑦𝑤 = Stirrup Yield strength Ratio of transverse 𝜌 𝑠𝑥 = steel parallel to the direction x of loading Confinement effectiveness factor capacity 𝑓𝑦 𝐶𝐹 𝐴 𝑠𝑥 𝑏 𝑤 ∙ 𝑠 EN1998-3,cl.A.3.2.2(1) sh : stirrup spacing 𝑠 𝑎 = 1− 2𝑏 𝑜 𝑠 1− 2 𝑜 Total chord rotation 𝜃 𝑢𝑚 EN1992-1-1,table 3.1 𝑓𝑐 𝐶𝐹 𝑓𝑐 = strength 0.3 𝑏𝑖2 1− 6 𝑜 ∙ 𝑏 𝑜 EN1998-3,cl.A.3.2.2(1) Elastic plus inelastic part See the equation below: Beams & Columns (elastic plus inelastic part 1 = 0.016 ∙ 0. 3 𝑣 𝛾 𝑒𝑙 Total chord rotation capacity For cold-work brittle 𝑚𝑎𝑥 0.01; 𝜔׳ 𝑓 𝑚𝑎𝑥 0.01; 𝜔 𝑐 𝐿𝑣 𝑚𝑖𝑛 9; 𝜃 𝑢𝑚 = 0.58 ∙ 𝜃 𝑢𝑚 Walls: 0.35 25 𝑓 𝑦𝑤 𝑎𝜌 𝑠𝑥 𝑓𝑐 1.25100𝜌 𝑑 EN1998-3,cl.A.3.2.2(1) 𝜃 𝑢𝑚 = 𝜃 𝑢𝑚 1.6 EN1998-3,cl.A.3.2.2(1) 𝜃 𝑢𝑚 = 𝜃 𝑢𝑚 1.2 EN1998-3,cl.A.3.2.2(3) steel Members without 0.225 detail for earthquake resistance Total chord rotation capacity Valentinos Neophytou BEng (Hons), MSc Plastic part Page 53 of 61
- 54. Design notes for Seismic Assessment to Eurocode 8 - Part 3 See the equation below: Beams & Columns (elastic plus inelastic part 𝜃 𝑢𝑚 𝑝𝑙 1 = 0.0145 ∙ 0. 25 𝑣 𝛾 𝑒𝑙 𝑚𝑎𝑥 0.01; 𝜔׳ 𝑚𝑎𝑥 0.01; 𝜔 0.3 𝑓𝑐 𝐿𝑣 𝑚𝑖𝑛 9, 0.2 𝛾 𝑒𝑙 = 1.8 (primary members) Factor for structural element primary/secondary 𝛾 𝑒𝑙 = 1.0 (secondary members) Total chord rotation capacity Walls: 𝜃 𝑢𝑚 𝑝𝑙 Members without detail for 𝜃 𝑢𝑚 = earthquake resistance 𝜃 𝑢𝑚 𝑓 𝑦𝑤 𝑎𝜌 𝑠𝑥 𝑓𝑐 1.275100𝜌 𝑑 EN1998-3,cl.A.3.2.2(2) EN1998-3,cl.A.3.2.2(2) EN1998-3,cl.A.3.2.2(2) 𝜃 𝑢𝑚 𝜃 𝑢𝑚 𝑝𝑙 , 𝜃 𝑢𝑚 = 1.2 1.2 EN1998-3,cl.A.3.2.2(3) If 𝑙 𝑜 < 𝑙 𝑜𝑢 ,𝑚𝑖𝑛 Total chord rotation capacity 𝑝𝑙 25 𝜃 𝑢𝑚 2.0 𝜃 𝑢𝑚 = For cold-work brittle steel = 0.6 ∙ 𝜃 𝑢𝑚 0.35 𝑝𝑙 = 𝜃 𝑢𝑚 => EN1998-3,cl.A.3.2.2(4) 𝑙𝑜 𝑝𝑙 𝑙 𝑜𝑢 ,𝑚𝑖𝑛 Requirements for lamping zone of longitudinal bars Actual lamping ratio 𝜌 = 2𝜌 (at the zone of EN1998-3,cl.A.3.2.2(4) overlapping) 𝑎1 = 1 − 𝑠 1 − 𝑠 𝑛 𝑟𝑒𝑠𝑡𝑟 ∙ ∙ 2𝑏 𝑜 2 𝑜 𝑛 𝑡𝑜𝑡 nrestr : number of lapped longitudinal bars Minimum lamping length laterally restrained by a stirrup corner or cross-tie. EN1998-3,cl.A.3.2.2(4) ntot : total number of lapped longitudinal bars along the cross-section perimeter. 𝑙 𝑜𝑢 ,𝑚𝑖𝑛 = 𝑑 𝑏𝑙 ∙ 𝑓 𝑦𝐿 1.05 + 14.5𝑎1 𝜌 𝑠𝑥 Valentinos Neophytou BEng (Hons), MSc 𝑓𝑦 𝑤 𝑓𝑐 ∙ 𝑓𝑐 Page 54 of 61
- 55. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Shear strength 𝐴𝑐 = 𝑏 𝑤 𝑑 Area of cross section Concrete compressive 𝑓𝑐 = strength 𝑓𝑐𝑘 𝛾𝐶 EN1992-1-1,cl.3.1.6(1) 𝛾 𝑒𝑙 = 1.15 (primary members) Factor for structural element EN1998-3,cl.A.3.3.1(1) EN1998-3,cl.A.3.3.1(1) 𝛾 𝑒𝑙 = 1.0 (secondary members) primary/secondary Contribution of 𝑉 𝑤 = 𝜌 𝑤 𝑏 𝑤 𝑧𝑓𝑦 𝑤 Rectangular transverse reinforcement 𝑉𝑤 = Circular to shear resistance Shear resistance after flexural EN1998-3,cl.A.3.3.1(1) yielding, 𝜋 𝐴 𝑠𝑤 𝑓 𝐷 − 2𝑐 2 𝑠 𝑦𝑤 EN1998-3,cl.A.3.3.1(1) EN1998-3,cl.A.3.3.1(1) See below: as controlled by stirrups 𝑉𝑅 = 1 − 𝑥 𝑚𝑖𝑛 𝑁; 0.55𝐴 𝑐 𝑓𝑐 + 1 − 0.05𝑚𝑖𝑛 5; 𝜇∆𝑝𝑙 𝛾 𝑒𝑙 2𝐿 𝑣 ∙ 0.16𝑚𝑎𝑥 0.5; 100𝜌 𝑡𝑜𝑡 1 − 0.16𝑚𝑖𝑛 5; 𝐿𝑣 𝑓𝑐 𝐴 𝑐 + 𝑉 𝑤 Shear resistance as controlled by web crushing (diagonal EN1998-3,cl.A.3.3.1(2&3) See below: compression) Before flexural yielding (𝜇∆𝑝𝑙 = 0), or after flexural yielding (cyclic 𝜇∆𝑝𝑙 > 0) Walls 𝑉 𝑅,𝑚𝑎𝑥 = 0.85 1 − 0.06𝑚𝑖𝑛 5; 𝜇∆𝑝𝑙 𝛾 𝑒𝑙 1 + 1.8𝑚𝑖𝑛 0.15; + 0.25𝑚𝑎𝑥 1.75; 100𝜌 𝑡𝑜𝑡 Columns 𝑁 𝐴 𝑐 𝑓𝑐 1 − 0.2𝑚𝑖𝑛 2; 𝐿𝑣 1 𝑓𝑐 𝑏 𝑤 𝑧 Lv / h ≤ 2 after flexural yielding (cyclic 𝜇∆𝑝𝑙 > 0 Valentinos Neophytou BEng (Hons), MSc Page 55 of 61
- 56. Design notes for Seismic Assessment to Eurocode 8 - Part 3 𝑉 𝑅,𝑚𝑎𝑥 = 4/7 1 − 0.02𝑚𝑖𝑛 5; 𝜇∆𝑝𝑙 𝛾 𝑒𝑙 1 + 0.45 100𝜌 𝑡𝑜𝑡 𝑚𝑖𝑛 40; 𝑓𝑐 𝑏 𝑤 𝑧 𝑠𝑖𝑛2𝛿 where: 𝑡𝑎𝑛𝛿 = /2𝐿 𝑣 Beam column joint Requirements Values 𝛾 𝑅𝑑 = 1.2 Overstrength factor Shear force acting of the joint Interior joint Exterior joint References EN1998-11,cl.5.5.2.3(2) 𝑉𝑗 𝑑 = 𝛾 𝑅𝑑 𝐴 𝑠1 + 𝐴 𝑠2 𝑓 𝑦𝑑 − 𝑉 𝐶 𝑉𝑗 𝑑 = 𝛾 𝑅𝑑 𝐴 𝑠1 𝑓 𝑦𝑑 − 𝑉 𝐶 𝑉𝑗 𝑑 = 𝜂𝑓𝑐𝑑 1 − Shear capacity of joint 𝑣𝑑 𝑏 𝜂 𝑗 𝑗𝑐 Where 𝑓𝑐𝑘 250 See above (NC) EN1998-11,cl.5.5.2.3(2) EN1998-11,cl.5.5.3.3(2) 𝜂 = 0.6 1 − Shear strength Valentinos Neophytou BEng (Hons), MSc EN19983,cl.A.3.3.1(1) Page 56 of 61
- 57. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Limit State of Significant Damage (SD) Requirements Values References 𝜃 𝑢𝑚 = 𝜃 𝑢𝑚 ∙ Chord rotation capacity 3 4 EN19983,cl.A.3.2.3(1) Shear strength (Beams & Columns) The verification against the exceedance of these two LS is not required, unless these two LS are the only ones to be checked. In that case NC requirements applies. Beam column joint Requirements Values References The verification against the exceedance of these two limit state SD and DL is not required, unless these two LS are only ones to be checked. In that case NC requirements applies. Limit State of Damage Limitation (DL) Requirements Values References Design shear resistance (EC2) 𝑣 𝑚𝑖𝑛 = 0.035𝑘 3/2 𝑓𝑐𝑘 0.5 Value of vmin Design compressive Compressive stress in the 𝜍 𝑐𝑝 = concrete from axial load Reinforcement ratio for 𝜌𝐼 = longitudinal reinforcement EN1992-1-1,cl.3.1.6(1) 𝑁 𝐸𝑑 ≤ 0.2𝑓𝑐𝑑 𝐴𝑐 EN1992-1-1,cl.6.2.2(1) 𝐴 𝑠𝑖 𝑏𝑤 𝑑 ≤ 0.02 EN1992-1-1,cl.6.2.2(1) 𝑘1 = 0.44 Coefficient factor k1 𝑘 = 1+ Coefficient factor k Shear 𝑓𝑐𝑘 𝛾𝐶 𝑓𝑐𝑑 = strength 𝑉 𝑅𝑑,𝑐 = EN1992-1-1,cl.5.5(4) 200 ≤ 2,0 𝑑 𝐶 𝑅𝑑 ,𝑐 𝑘 100𝜌 𝐼 𝑓𝑐𝑘 Valentinos Neophytou BEng (Hons), MSc EN1992-1-1,cl.6.2.2(1) 1.3 EN1992-1-1,cl.6.2.2(1) + 𝑘1 𝜍 𝑐𝑝 EN1992-1-1,cl.6.2.2(1) Page 57 of 61
- 58. Design notes for Seismic Assessment to Eurocode 8 - Part 3 𝑉 𝑅𝑑,𝑐𝑚𝑖𝑛 = 𝑣 𝑚𝑖𝑛 + 𝑘1 𝜍 𝑐𝑝 𝑏 𝑤 𝑑 𝑎𝑣 = 1 when My > LvVRd.c 𝑎𝑣 = 0 Tension shift, αv when My < LvVRd.c Chord rotation 𝑧 = 𝑑 − 𝑑׳ 𝑧 ≈ 0.95𝑑 𝑧 = 0.8 Lever arm, z - Lever arm, z (for rectangular wall section) 𝜀𝑦 = Strain , εy 𝜃𝑦 = 𝜑𝑦 𝑓𝑦 𝐸𝑠 EN1998-3,cl.A.3.2.4(2) 𝜀 𝑦 𝑑 𝑏𝐿 𝑓𝑦 𝐿𝑣 + 𝑎𝑣 𝑧 + 0.0014 1 + 1.5 + 3 𝐿𝑣 𝑑 − 𝑑𝑐𝑓 6 ׳ Note: Beams/Columns 𝜀𝑦 = 𝜀𝑦 𝑙𝑜 𝑙 𝑜𝑦 ,𝑚𝑖𝑛 for 𝑙 𝑜 < 𝑙 𝑜𝑦 ,𝑚𝑖𝑛 and 𝑀𝑦 = 𝑀𝑦 𝜃𝑦 = 𝜑𝑦 𝑙𝑜 𝑙 𝑜𝑦 ,𝑚𝑖𝑛 for 𝑙 𝑜 < 𝑙 𝑜𝑦 ,𝑚𝑖𝑛 𝜀 𝑦 𝑑 𝑏𝐿 𝑓𝑦 𝐿𝑣 + 𝑎𝑣 𝑧 + 0.0013 + 3 𝑑 − 𝑑𝑐𝑓 6 ׳ Note: Walls of rectangular, T or 𝜀𝑦 = 𝜀𝑦 barbelled section 𝑙𝑜 𝑙 𝑜𝑦 ,𝑚𝑖𝑛 for 𝑙 𝑜 < 𝑙 𝑜𝑦 ,𝑚𝑖𝑛 and 𝑀𝑦 = 𝑀𝑦 𝑙𝑜 𝑙 𝑜𝑦 ,𝑚𝑖𝑛 for 𝑙 𝑜 < 𝑙 𝑜𝑦 ,𝑚𝑖𝑛 Alternative expressions Beams 𝜃𝑦 = 𝜑𝑦 Columns Valentinos Neophytou BEng (Hons), MSc 𝑑 𝑏𝐿 𝑓𝑦 𝐿𝑣 + 𝑎𝑣 𝑧 + 0.0014 1 + 1.5 + 𝜑𝑦 3 𝐿𝑣 8 𝑓𝑐 Note: Page 58 of 61
- 59. Design notes for Seismic Assessment to Eurocode 8 - Part 3 𝑀𝑦 = 𝑀𝑦 𝜃𝑦 = 𝜑𝑦 Walls of rectangular, T or 𝑙𝑜 𝑙 𝑜𝑦 ,𝑚𝑖𝑛 for 𝑙 𝑜 < 𝑙 𝑜𝑦 ,𝑚𝑖𝑛 𝑑 𝑏𝐿 𝑓𝑦 𝐿𝑣 + 𝑎𝑣 𝑧 + 0.0013 + 𝜑 𝑦 3 8 𝑓𝑐 Note: barbelled section 𝑀𝑦 = 𝑀𝑦 𝑙𝑜 𝑙 𝑜𝑦 ,𝑚𝑖𝑛 for 𝑙 𝑜 < 𝑙 𝑜𝑦 ,𝑚𝑖𝑛 Requirements for lamping zone of longitudinal bars Actual lamping ratio (at the 𝜌 = 2𝜌 Lap length Minimum length of lap EN1998-3,cl.A.3.2.4(3) 𝑙 𝑜 ≥ 15𝑑 𝑏𝐿 zone of overlapping) EN1998-3,cl.A.3.2.4(4) 𝑙 𝑜𝑦 ,𝑚𝑖𝑛 = 0.3𝑑 𝑏𝐿 𝑓 𝑦𝐿 𝑓𝑐 splice for existing concrete members EN1998-3,cl.A.3.2.4(3) fc and fyL are derived from the mean values multiplied by the CF Shear strength The verification against the exceedance of these two LS is not required, unless these two LS are the only ones to be checked. In that case NC requirements applies. Beam column joint Requirements Values References The verification against the exceedance of these two limit state SD and DL is not required, unless these two LS are only ones to be checked. In that case NC requirements applies. Valentinos Neophytou BEng (Hons), MSc Page 59 of 61
- 60. Design notes for Seismic Assessment to Eurocode 8 - Part 3 Summary table Limit State (LS) Member Damage Limitation Significant damage Near Collapse (DL) (SD) (NC) 𝜃 𝑠𝑑 ≤ 0.75𝜃 𝑢 ,𝑚 −𝜍 𝜃 𝑠𝑑 ≤ 𝜃 𝑢,𝑚 −𝜍 𝜃 𝑠𝑑 ≤ 0.75𝜃 𝑢𝑚 𝜃 𝑠𝑑 ≤ 𝜃 𝑢𝑚 Ductile primary (flexural) Ductile secondary 𝜃 𝑠𝑑 ≤ 𝜃 𝑦 (flexural) (shear) 𝑉 𝐸,𝐶𝐷 ≤ 𝑉 𝑅𝑑.𝐸𝐶2 𝑎𝑛𝑑 𝑉 𝐸,𝐶𝐷 ≤ 𝑉 𝑅𝑑 ,𝐸𝐶8 ; 𝐽𝑜𝑖𝑛𝑡: 𝑉 𝐶𝐷 ≤ 𝑉 𝑅𝑑𝑗𝐸𝐶 8 1.15 𝑉 𝐸,𝐶𝐷 ≤ 𝑉 𝑅𝑑.𝐸𝐶2 𝑎𝑛𝑑 𝑉 𝐸,𝐶𝐷 ≤ Brittle primary 𝑉 𝑅𝑑 ,𝐸𝐶8 ; 𝐽𝑜𝑖𝑛𝑡: 𝑉 𝐶𝐷 ≤ 𝑉 𝑅𝑑𝑗𝐸𝐶 8 1.15 Brittle secondary (Shear) θE, VE: chord-rotation & shear force demand from analysis; VE,CD : from capacity design; θy: chord-rotation at yielding θum: expected value of ultimate chord rotation under cyclic loading, calculated using mean strengths for old materials divided by the confidence factor and nominal strengths for new materials. θu,m-σ: mean-minus-sigma ult. chord rotation =θum /1.5, or =θy+θplum/1.8 VRd, VRm: shear resistance, w/ or w/o material safety & confidence factor VR,EC8: shear resistance in cyclic loading after flex. yielding Valentinos Neophytou BEng (Hons), MSc Page 60 of 61
- 61. Design notes for Seismic Assessment to Eurocode 8 - Part 3 GENERAL CONSEQUENCE OF USE EUROCODE 8-PART 3 1. PERFORMANCE REQUIREMENT & CRITERIA 2. APPLICABILITY CONDITIONS OF THE FOUR ANALYSIS METHODS 3. TYPE OF VERIFICATIONS FOR DUCTILE AND BRITTLE MODES OF BEHAVIOUR AND FAILURE 4. COLLECTION OF INFORMATION FOR THE ASSESSMENT AND ITS IMPLICATIONS 5a. CONCRETE STRUCTURES 5b. STEEL OR COMPOSITE STRUCTURES Valentinos Neophytou BEng (Hons), MSc 5c. MASONRY BUILDINGS Page 61 of 61

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