Design notes for seismic design of building accordance to Eurocode 8

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This publication provides a concise compilation of selected rules in the Eurocode 8, together with relevant Cyprus National Annex, that relate to the design of common forms of concrete building structure in the South Europe. Rules from EN 1998-1-1 for global analysis, regularity criteria, type of analysis and verification checks are presented. Detail design rules for concrete beam, column and shear wall, from EN 1998-1-1 and EN1992-1-1 are presented. This guide covers the design of orthodox members in concrete frames. It does not cover design rules for steel frames. Certain practical limitations are given to the scope.

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Design notes for seismic design of building accordance to Eurocode 8

  1. 1. AUTHOR: VALENTINOS NEOPHYTOU BEng (Hons), MScREVISION 1: June, 2013Design notes for seismicdesign of building accordanceto Eurocode 8
  2. 2. ABOUT THIS DOCUMENTThis publication provides a concise compilation of selected rules in the Eurocode 8, together withrelevant Cyprus National Annex, that relate to the design of common forms of concrete buildingstructure in the South Europe. Rules from EN 1998-1-1 for global analysis, regularity criteria, typeof analysis and verification checks are presented. Detail design rules for concrete beam, columnand shear wall, from EN 1998-1-1 and EN1992-1-1 are presented. This guide covers the design oforthodox members in concrete frames. It does not cover design rules for steel frames. Certainpractical 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 knowledgeor willing to contribute either totally a new section about Eurocode 8 or within this section isencouraged.For further details:My LinkedIn Profile:http://www.linkedin.com/profile/view?id=125833097&trk=hb_tab_pro_topEmail: valentinos_n@hotmail.comSlideshare Account: http://www.slideshare.net/ValentinosNeophytou
  3. 3. Valentinos Neophytou BEng, MSc Page 3Fundamental requirements(ΕΝ1998-1-1,cl.2.1 and CYS NA EN1998-1-1,cl NA2.2)1. “No collapse”(ULS):The structure should be design and constructed as follow: Withstand the seismic action without local or global collapse, thus retainingits structural integrity and residual load bearing capacity after the seismicevent (Protection of human life). A design seismic action (for local collapse prevention) with 10% exceedanceprobability in 50 years (mean return period: 475 years).2. “Damage limitation”(SLS):The structure should be design and constructed asfollow: Withstand the seismic action having a larger probability of occurrence thanthe design than the design seismic action, without the occurrence of damageand the associated limitations of use, the cost which would bedisproportionately high in comparison with the cost of the structure itself(damage limitation). Seismic actions are determined for mean return period of TDLR=95 year andprobability of exceedance is PDLR=41%. The corresponding design life ofthe structure is a TL=50 years design life of structures.Importance classes for buildings(ΕΝ1998-1-1,table.4.3 and CYS NA EN1998-1-1,cl NA2.12)ImportanceclassBuildings Importantfactor γIIBuildings of minor importance for public safety, e.g.argricultural buildings, etc.0.8II Ordinary buildings, not belonging in the other categories. 1.0IIIBuildings whose seismic resistance is of importance in viewof the consequences associated with a collapse, e.g. schools,assembly halls, cultural institutions etc.1.2IVBuildings whose integrity during earthquakes is of vitalimportance for civil protection, e.g. hospitals, fire stations,power plants, etc.1.4The level of seismic action is depending on its important andconsequences of failure (Importance classes of building)
  4. 4. Valentinos Neophytou BEng, MSc Page 4Seismic zones(CYS NA ΕΝ1998-1-1,cl.NA 4) 10% probability to be exceeded in 50 years
  5. 5. Valentinos Neophytou BEng, MSc Page 5Ground condition(ΕΝ1998-1-1,cl.3.2.2.1(6) and CYS NA EN1998-1-1,cl NA2.3)Ground condition(ΕΝ1998-1-1,cl.3.2.2.1(6) and CYS NA EN1998-1-1,cl NA2.3) Ground investigation may be omitted for building with importance class of I and II. They alsoomitted for classes III and IV whenever there is adequate information. The construction site and the nature of the supporting ground should normally be free from risks ofground rupture, slope instability and permanent settlements caused by liquefaction or densification inthe event of an earthquake.Type of ground soil(ΕΝ1998-1-1,cl.3.1.2)Ground typeDescription of straigraphic profile Parametersvs,30 (m/s)NSPT(blows/30cm)cu (kPa)A Rock or other rock-like geologicalformation, including at most 5 m of weakermaterial at the surface.>800 - -B Deposits of very dense sand, gravel, or verystiff clay, at least several tens of metres inthickness, characterised by a gradualincrease of mechanical properties withdepth.360-800 >50 >250C Deep deposits of dense or medium densesand, gravel or stiff clay with thickness fromseveral tens to many hundreds of metres.180-360 15-50 70-250D Deposits of loose-to-medium cohesion lesssoil (with or without some soft cohesivelayers), or of predominantly soft-to-firmcohesive soil.<180 <15 <70E A soil profile consisting of a surfacealluvium layer with vs values of type C or Dand thickness varying between about 5 mand 20 m, underlain by stiffer material withvs> 800 m/s.S1 Deposits consisting, or containing a layer atleast 10 m thick, of soft clays/silts with ahigh plasticity index<100(indicative)- 10-20S2 Deposits of liquefiable soils, of sensitiveclays, or any other soil profile not includedin types A – E or S1
  6. 6. Valentinos Neophytou BEng, MSc Page 6vs,30: average value of propagation velocity of S waves in the upper 30m of the soil profiles at shear strainof 10-5or less.NSPT: Standard penetration test blow countcu: Undrained shear strength of soilVertical elastic response spectrum(ΕΝ1998-1-1,cl.3.2.2.3)The vertical listed below: for horizontal structural member spanning 20m or more, for horizontal cantilever components longer than 5m, component of the seismic action should be taken into account if the avg>0.25g (2.5m/s2) in the casesfor horizontal pre-stressed components, for beams supporting columns, in based-isolated structures.Vertical elastic response spectrum(ΕΝ1998-1-1,cl.3.2.2.3)0 ≤ 𝑇 ≤ 𝑇𝐵: 𝑆 𝑣𝑒 𝑇 = 𝑎 𝑣𝑔 ∙ 1 +𝑇𝑇 𝐵∙ 𝜂 ∙ 3,0 − 1 (ΕΝ1998-1-1,Eq. 3.8)𝑇𝐵 ≤ 𝑇 ≤ 𝑇𝐶: 𝑆 𝑣𝑒 𝑇 = 𝑎 𝑣𝑔 ∙ 𝜂 ∙ 3.0 (ΕΝ1998-1-1,Eq. 3.9)𝑇𝐶 ≤ 𝑇 ≤ 𝑇𝐷: 𝑆 𝑣𝑒 𝑇 = 𝑎 𝑣𝑔 ∙ 𝜂 ∙ 3.0𝑇 𝐶𝑇(ΕΝ1998-1-1,Eq. 3.10)𝑇𝐷 ≤ 𝑇 ≤ 4𝑠: 𝑆 𝑣𝑒 𝑇 = 𝑎 𝑣𝑔 ∙ 𝜂 ∙ 3.0𝑇 𝐶 𝑇 𝐷𝑇2(ΕΝ1998-1-1,Eq. 3.11)Damping correction factor η: 𝜂 = 10/ 5 + 𝜉 ≥ 0.55Design ground acceleration on type A ground: ag=γIagRNote: the value of S is not used in the above expression cause the vertical ground motion is not very muchaffected by the underlying ground conditionVertical elastic design spectrum (ΕΝ1998-1-1,cl.3.2.2.5(5)). 0 ≤ 𝑇 ≤ 𝑇𝐵: 𝑆 𝑑 𝑇 = 𝑎 𝑣𝑔 ∙23+𝑇𝑇 𝐵∙2.5𝑞−23(ΕΝ1998-1-1,Eq. 3.13)𝑇𝐵 ≤ 𝑇 ≤ 𝑇𝐶: 𝑆 𝑑 𝑇 = 𝑎 𝑣𝑔 ∙2.5𝑞(ΕΝ1998-1-1,Eq. 3.14)
  7. 7. Valentinos Neophytou BEng, MSc Page 7𝑇𝐶 ≤ 𝑇 ≤ 𝑇𝐷: 𝑆 𝑑 𝑇 = 𝑎 𝑣𝑔 ∙2.5𝑞𝑇𝐶𝑇≥ 𝛽 ∙ 𝑎 𝑣𝑔 (ΕΝ1998-1-1,Eq. 3.15)𝑇𝐷 ≤ 𝑇 ≤ 4𝑠: 𝑆 𝑑 𝑇 = 𝑎 𝑣𝑔 ∙2.5𝑞𝑇 𝐶 𝑇 𝐷𝑇2≥ 𝛽 ∙ 𝑎 𝑣𝑔 (ΕΝ1998-1-1,Eq. 3.5)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 equalto 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 1.0Special provisions: For the vertical component of the seismic action a behaviour factor q up to to 1,5 should generallybe adopted for all materials and structural systems. The adoption of values for q greater than 1,5 in the vertical direction should be justified through anappropriate analysis.
  8. 8. Valentinos Neophytou BEng, MSc Page 8Horizontal elastic response spectrumHorizontal elastic response spectrum(ΕΝ1998-1-1,cl.3.2.2.2)0 ≤ 𝑇 ≤ 𝑇𝐵: 𝑆𝑒 𝑇 = 𝑎 𝑔 ∙ 𝑆 ∙ 1 +𝑇𝑇 𝐵∙ 𝜂 ∙ 2,5 − 1 (ΕΝ1998-1-1,Eq. 3.2)𝑇𝐵 ≤ 𝑇 ≤ 𝑇𝐶: 𝑆𝑒 𝑇 = 𝑎 𝑔 ∙ 𝑆 ∙ 𝜂 ∙ 2.5(ΕΝ1998-1-1,Eq. 3.3)𝑇𝐶 ≤ 𝑇 ≤ 𝑇𝐷: 𝑆𝑒 𝑇 = 𝑎 𝑔 ∙ 𝑆 ∙ 𝜂 ∙ 2.5𝑇 𝐶𝑇(ΕΝ1998-1-1,Eq. 3.4)𝑇𝐷 ≤ 𝑇 ≤ 4𝑠: 𝑆𝑒 𝑇 = 𝑎 𝑔 ∙ 𝑆 ∙ 𝜂 ∙ 2.5𝑇 𝐶 𝑇 𝐷𝑇2(ΕΝ1998-1-1,Eq. 3.5)Damping correction factor η: 𝜂 = 10/ 5 + 𝜉 ≥ 0.55Design ground acceleration on type A ground: ag=γI*agRThe viscous damping ratio of the structureTYPE OF STRUCTURE Damping ration ξ%SteelWelded 2Bolts 4ConcreteUnreinforced 3Reinforced 5Wall Reinforced 6Design spectrum of elastic analysis(ΕΝ1998-1-1,cl.3.2.2.5)0 ≤ 𝑇 ≤ 𝑇𝐵: 𝑆 𝑑 𝑇 = 𝑎 𝑔 ∙ 𝑆 ∙23+𝑇𝑇 𝐵∙2.5𝑞−23(ΕΝ1998-1-1,Eq. 3.13)𝑇𝐵 ≤ 𝑇 ≤ 𝑇𝐶: 𝑆 𝑑 𝑇 = 𝑎 𝑔 ∙ 𝑆 ∙2.5𝑞(ΕΝ1998-1-1,Eq. 3.14)𝑇𝐶 ≤ 𝑇 ≤ 𝑇𝐷: 𝑆 𝑑 𝑇 = 𝑎 𝑔 ∙ 𝑆 ∙2.5𝑞𝑇𝐶𝑇≥ 𝛽 ∙ 𝑎 𝑔 (ΕΝ1998-1-1,Eq. 3.15)𝑇𝐷 ≤ 𝑇 ≤ 4𝑠: 𝑆 𝑑 𝑇 = 𝑎 𝑔 ∙ 𝑆 ∙2.5𝑞𝑇 𝐶 𝑇 𝐷𝑇2≥ 𝛽 ∙ 𝑎 𝑔 (ΕΝ1998-1-1,Eq. 3.5)Design ground acceleration on type A ground: ag=γI*agRLower bound factor for the horizontal spectrum: β=0.2Note: the value of q are already incorporate with an appropriation value ofdamping viscous, however the symbol ηis not present in the above expressions
  9. 9. Valentinos Neophytou BEng, MSc Page 9Horizontal elastic response spectrum(ΕΝ1998-1-1,cl.3.2.2.2)Design spectrum of elastic analysis(ΕΝ1998-1-1,cl.3.2.2.5)Design spectrum Vs Elastic spectrum Parameters of Type 1 elastic response spectrum (CYS NA EN1998-1-1,table 3.2)GroundTypeS TB (s) TC (s) TD (s)A 1.0 0.15 0.4 2.0B 1.2 0.15 0.5 2.0C 1.15 0.20 0.6 2.0D 1.35 0.20 0.8 2.0E 1.4 0.15 0.5 2.0Note: For important structures (γI>1.0), topographic amplification effectsshould be taken into account (Annex A EN1998-5:2004 providesinformation for topographic amplification effects)
  10. 10. Valentinos Neophytou BEng, MSc Page 10The inertial effects of the design seismic action shall be evaluated by taking into account the presence of themasses associated with all gravity loads appearing in the following combination of actions:𝑮 𝒌,𝒋 + 𝝍 𝑬𝒊 𝑸 𝒌,𝒊 (ΕΝ1998-1-1,Eq. 3.17)Where:Combination coefficient for variable action is: 𝜓 𝐸𝑖 = 𝜙 ∙ 𝜓2𝑖 (ΕΝ1998-1-1,Eq. 4.2)Values of φ for calculating 𝝍 𝑬𝒊(CYS NA EN1998-1-1:2004)Type ofVariableactionStorey φCategoriesA-C1RoofStoreys with correlatedoccupanciesIndependently occupied storeys1,00,80,5CategoriesA-F1 1.01those categories are describes in EN 1991-1-1:2002Note: the value of φ is take into account only for calculating the seismic mass.Calculation of seismic mass(EN1998-1-1,cl.3.2.4)Spectrum Type 10≤T≤TBTB≤T≤TCTC≤T≤TDTD≤T≤4s≤4sYESNOElasticresponse spectrumElasticdisplacementresponse spectrumElastic displacement response spectrum (EN1998-1-1,cl.3.2.2.2(6))
  11. 11. Valentinos Neophytou BEng, MSc Page 11Second-order effects (P-Δ effects) need not be taken into account if the following condition is fulfilled in allstoreys:𝜗 =𝑃𝑡𝑜𝑡 ∙𝑑 𝑟𝑉𝑡𝑜𝑡 ∙𝑕≤ 0,10 (ΕΝ1998-1-1,Eq. 4.28)Ptot: is the total gravity load at and above the storey considered in the seismic design situation dr: is thedesign interstorey drift, evaluated as the difference of the average lateral displacements ds at the top andbottom of the storey under consideration and calculated in accordance with 4.3.4.Vtot: is the total seismic storey shear.h: is the interstorey height.Consequences of value of P-Δ coefficient θ on the analysisθ≤0,1 No need to consider P-Δ effects0,1≤θ≤0,2P-Δ effects may be taken into account approximately byamplifying the effects of the seismic actions by11−𝜗0,2≤θ≤0,3P-Δ effects must be accounted for by an analysisincluding second order effects explicityθ≥0,3 Not permittedSecond order effects P-Δ(EN1998-1-1,cl.4.4.2.2)
  12. 12. Valentinos Neophytou BEng, MSc Page 121.Approximately” symmetrical distribution of mass and stiffness in plan (in X-Y)2.A “compact” shape, i.e one in which the perimeter line is always convex, or at least encloses not morethan 5% of total area as show in figure below.3.The floor diaphragms shall be sufficiently stiff in-plane not to affect the distribution of lateral loadsbetween vertical elements. EC8 warn that this should be carefully examined in the branches ofbranched systems, such as L, C, H, I and X plan shapes.3. The ratio of longer side to shorter side in plan does not exceed 4 (λ=Lmax/Lmin<4).4.The geometrical stiffness – lateral torsional response and torsional flexibility should be satisfied bythe following expressions:Lateral torsional response condition:𝑟𝑥 > 3.33𝑒 𝑜𝑥𝑟𝑦 > 3.33𝑒 𝑜𝑦Torsionally rigidity condition: 𝑟𝑥 > 𝐼𝑠𝑟𝑦 > 𝐼𝑠𝐼𝑠 = 𝑙2 + 𝑏2 /12Where the torsional radius rx and ry are:𝑥 𝑐𝑠 =(𝑥𝐸𝐼𝑦 )(𝐸𝐼𝑦 )𝑦𝑐𝑠 =(𝑦𝐸𝐼𝑥)(𝐸𝐼𝑥)CRITERIA FOR REGULARITY IN ELEVATION(EN1998-1-1,cl. 4.2.3.2)CRITERIA FOR REGULARITY IN PLAN (EN1998-1-1,cl. 4.2.3.2)
  13. 13. Valentinos Neophytou BEng, MSc Page 13𝑟𝑥 ≈𝑥 − 𝑥 𝑐𝑠2 𝐸𝐼𝑦 + 𝑦 − 𝑦𝑐𝑒2 𝐸𝐼𝑥)𝐸𝐼𝑦𝑟𝑦 ≈𝑥 − 𝑥 𝑐𝑠2 𝐸𝐼𝑦 + 𝑦 − 𝑦𝑐𝑒2 𝐸𝐼𝑥)𝐸𝐼𝑥5.In multi-storey buildings only approximate definitions of the centre of stiffness and of the torsionalradius are possible. A simplified definition, for the classification of structural regularity in plan andfor the approximate analysis of torsional effects, is possible if the following two conditions aresatisfied:a) all primary members, run without interruption from the foundations to the top of the building.b) The deflected shapes of the individual systems under horizontal loads are not very different.
  14. 14. Valentinos Neophytou BEng, MSc Page 141.All primary members, shall run without interruption from their foundations to the top of the building.2.Mass and stiffness must either remain constant with height or reduce only gradually, without abruptchanges. In the absence of a quantitative definition in EC8, it is recommended that the decrease withheight may be considered gradual if both the mass and stiffness of every storey is between 70% and100% of that of the storey below.3.In framed buildings the ratio of the actual storey resistance to the resistance required by the analysisshould not vary disproportionately between adjacent storeys3.Buildings with setbacks (i.e. where the plan area suddenly reduces between successive storeys) aregenerally irregular, but may be classified as regular if less than limits shown in figure below. Thisshows that the setback at any level on one side may not exceed 10% compared to the level below.Where the setbacks are symmetrical on each side, there is no limit on overall reduction; however, forasymmetrical setbacks, the overall reduction is limited to 30% of the base width. The exception is thatan overall reduction in width of up to half is permissible within the lowest 15% of the height of thebuilding. Note that „overhangs‟ (i.e. inverted pyramid shapes) as opposed to „setbacks‟ are alwaysclassified as highly irregular.CRITERIA FOR REGULARITY IN ELEVATION(EN1998-1-1,cl. 4.2.3.2)
  15. 15. Valentinos Neophytou BEng, MSc Page 15STRUCTURAL ANALYSIS(EN1998-1-1,cl.4.3)CONSEQUENCES OF STRUCTURAL REGULARITY ON SEISMIC ANALYSIS ANDDESIGN (ΕΝ1998-1-1,table 4.1)The structural regularity if the building is play significant role to the following aspects of the seismicdesign: Construction of structural model (planar or spartial model) Method of analysis (response spectrum analysis/lateral force procedure of a modal The value of behaviour factor q (low value of q is for building not regular in elevation)Consequences of structural regularity on seismic analysis and designRegularity Allowed Simplification Behaviour factorPlan ElevationModel Linear-elasticAnalysis (for linear analysis)Yes Yes Planar Lateral force Reference valueYes No Planar Modal Decreased valueNo Yes SpatialbLateral forceaReference valuesNo No Spatial Modal Decreased valueNotes: aThere are also maximum limits on the period of vibration for the lateral forcemethod to be allowed (see equation above)bThe reference behaviour factor is multiplied by 0.8 for buildings with irregularelevations.cTorsionally flexible concrete buildings, defined, are assigned much lower reference qvalues than equivalent concrete buildings which are regular. Certain other buildingswhich are irregular in plan also attract a lowered q valuedSeparate planar model may be used. e It is observed that equivalent linear analysis maynot always be suitable for irregular buildings. Highly irregular buildings.
  16. 16. Valentinos Neophytou BEng, MSc Page 16METHOD OF ANALYSIS(ΕΝ1998-1-1,cl. 4.3.3)Analysis type CriteriaLateral force analysis𝑇1 ≤ 4𝑇𝑐𝑇1 ≤ 2,0𝑠 Regular in plan and elevation Regular in elevation and irregular in plan Fundamental period: Height of building: H<10mResponse spectrummodal Regular in plan and irregular in elevation Irregular in plan and elevation Fundamental period: Not special requirementsNon-linear  High irregular structures
  17. 17. Valentinos Neophytou BEng, MSc Page 17LATERAL FORCE ANALYSIS(ΕΝ1998-1-1,cl 4.3.3.2)Fundamental period (EN1998-1-1,Eq.4.6)T1=CtH3/4(For heights up to 40m)Value of Ct(EN1998-1-1,cl.4.3.3.2.2(3))Ct = 0.085 (for moment resisting steel frames)Ct= 0.075 (for moment resisting concrete frames)Ct= 0.05 (for all other structures)(EN 1998-1-1:2004, cl. 4.3.3.2.2(3))Ct= 0.075/√ΣAc(for concrete/masonry shear wallstructures)(EN 1998-1-1:2004, Eq. 4.7)Ac= Σ[Ai·(0,2+(lwi/H2))](EN 1998-1-1:2004, Eq. 4.8)Fundamental period requirements(EN1998-1-1,Eq.4.6)T1≤4TCT1≤2secIF thisYES NOLATERAL FORCEANALYSISRESPONSE SPECTRUMANALYSISCorrection factor λ(EN1998-1-1,cl.4.3.3.2.2(1Ρ))λ=0.85 if T1≤2TC and more than 2 storeyλ=1.0 in all other caseDesign spectrumSd(T)(EN1998-1-1,cl.3.2.2.5)0≤T≤TBTB≤T≤TcTC≤T≤TDTD≤TSeismic mass(EN1998-1-1,cl.3.2.4)ΣGk,j/g”+”ΣψE,i.Qk,i/g(EN 1998-1-1:2004, Eq.3.17)Base shear(EN1998-1-1,cl.4.3.3.2.2)Fb=Sd(T1).m.λ(EN 1998-1-1:2004, Eq. 4.5)Fi = Fb ∙si ∙ misj ∙ mjHorizontal seismic forces(according to displacement ofthe masses)(EN 1998-1-1:2004, Eq. 4.10)Fi = Fb ∙zi ∙ mizj ∙ mjHorizontal seismic forces(according to height of themasses)(EN 1998-1-1:2004, Eq. 4.11)Displacement (EN1998-1-1,cl.4.3.4)ds=qd.de(EN 1998-1-1:2004, Eq. 4.23)
  18. 18. Valentinos Neophytou BEng, MSc Page 18MODAL RESPONSE SPECTRUM ANALYSIS(ΕΝ1998-1-1,CL 4.3.3.3)MODALRESPONSESPECTRUMANALYSISCriterion1The sum of effective modal masses along each individual seismic actioncomponenet, X, Y or Z, considered in design, of at least 90% of the totalmass, addresses only the magnitude of the base shear captured by themodes taken into account.Criterion2All the modes whose effective modal mass is higher than 5% of the totalmass are taken into account (X,Y or even in Z direction).Spatial analysisMinimum number of modes is:k≥3.√nandPeriod of vibration of mode:Tk ≤0.20seck: is the number of modes taken into accountn: is the number of storey above foundation or the top of a rigidbasement.Tk: is the period of vibration of mode k.Combination ofmodal responses𝐸 𝐸 = Σ𝐸 𝐸𝑖2The response in two vibration modes:Tj≤ 0.9 TiSeismic action effects:EE: is the seismic action affect under consideration (force,displacement, etc)EEi: is the value of this seismic action affect due to the vibrationmode i.
  19. 19. Valentinos Neophytou BEng, MSc Page 19Horizontal components of the seismic actionHorizontal seismicaction is to beactingsimultaneously:X – direction(independent)Y – direction(independent)Structuralresponse spectrumshall be evaluatedseparately:X – direction(independent)Y – direction(independent)Maximum seismicaction calculationMethod 1: Square root of the sum of the squares (SRSS)Method 2: Complete quadratic combination (CQC)Combination of the horizontalcomponents are:(EN1998-1-1,Eq. 4.18&4.19)EEdx„‟±‟‟0,30EEdy0.30EEdx „‟±‟‟EEdyBehaviour factor qIf the structural system or the regularity classification of the buildingin elevation is different in different horizontal directions, the value ofthe behaviour factor q may also be differentVertical component of the seismic actionRules of vertical seismicactionThe effects of vertical action need to be taken into account ONLY for theelements that are listed in the section of “Vertical component of the seismicaction” and their directly associated supporting elements or substructures.Combination of the verticalcomponents are:(EN1998-1-1,Eq.4.20,4.21&4.22)EEdx„‟±‟‟0.30 EEdy „‟±‟‟0,30EEdz0.30EEdx „‟±‟‟ EEdy „‟±‟‟0,30EEdz0.30EEdx „‟±‟‟0.30 EEdy „‟±‟‟EEdzCOMBINATION OF THE SEISMIC ACTIONS(ΕΝ1998-1-1,cl 4.3.3.5)
  20. 20. Valentinos Neophytou BEng, MSc Page 20DISPLACEMENT CALCULATION(EN1998-1-1,cl.4.3.4)Linear analysis case:ds=qd.de ds<Displacement from the elastic spectrum analysisds:is the displacement of a point of the structural system induced by thedesignseismic actionqd: is the displacement behaviour factor, assumed equal to q unlessotherwisespecifiedde:is the displacement of the same point of the structural system, asdetermined bya linear analysis based on the design response spectrum
  21. 21. Valentinos Neophytou BEng, MSc Page 21Rule of masonryinfilled is APPLIED tothe followingstructural systemONLYDCHFramesFrame equivalent dualconcrete systemsSteel or steel-concretecomposite moment resistingframesRule of masonryinfilled is NOTAPPLIED to thefollowing structuralsystem ONLYWallWall-equivalent dualconcrete systemsSteel braced or steel-concretecomposite systemsFor buildings notregular in plan(EN1998-1-1,cl.4.3.6.3.1)Strongly irregular, unsymmetrical or non-uniform arrangements of infills in planshould be avoidedIn the case of severe irregularities in plan due to the unsymmetrical arrangementof the infills (e.g. existence of infills mainly along two consecutive faces of thebuilding), spatial models should be used for the analysis of the structure.Infill panels with more than one significant opening or perforation (e.g. a doorand a window, etc.) should be disregarded in models for analysesWhen the masonry infills are not regularly distributed, but not in such a way as toconstitute a severe irregularity in plan, these irregularities may be taken intoaccount by increasing by a factor of 2,0 the effects of the accidental eccentricityFor buildings notregular in elevation(EN1998-1-1,cl.4.3.6.3.2)If there are considerable irregularities in elevation (e.g. drastic reduction of infillsin one or more storeys compared to the others), the seismic action effects in thevertical elements of the respective storeys shall be increased.Magnification factor, η𝜂 =1 + Δ𝑉𝑅𝑤𝑉𝐸𝑑≤ 𝑞Note: If η< 1.1, there is no need for modification of action effectsMASONRY INFILLED FRAMES(ΕΝ1998-1-1,cl 4.3.6)
  22. 22. Valentinos Neophytou BEng, MSc Page 22ΔVRw: is the total reduction of the resistance of masonry walls in the storeyconcerned, compared to the more infilled storey above it.ΣVEd: is the sum of the seismic shear forces acting on all vertical primaryseismic members of the storey concerned.DCL, DCM, DCHAdditional rules shouldbe taken into account(EN1998-1-1,cl.4.3.6.2)The consequences of irregularity in plan produced by the infills shall be takeninto account.The consequences of irregularity in elevation produced by the infills shall betaken into account.Mechanical properties, method of attachment and possibility of modification.Shear failure of column under shear force induced by the diagonal strut action ofinfillsDamage limitation ofinfills(EN1998-1-1,cl.4.3.6.4)Slenderness ratio: min(Lwall,Hwall)/twall>15To improve both in-plane and out-of-plane integrity and behaviour, include lightwire meshes well anchored on one face of the wall, wall ties fixed to the columnsIf there are large openings or perforations in any of the infill panels, their edgesshould be trimmed with belts and posts
  23. 23. Valentinos Neophytou BEng, MSc Page 23Resistance condition(EN1998-1-1,cl.4.4.2.2)Ed ≤ RdEd:is the design value of the action effect, due to the seismic design situationRd :is the corresponding design resistance of the elementGlobal and localductility condition(EN1998-1-1,cl.4.4.2.3)Soft plastic mechanismΣMRc≥ 1.3 ΣMRbΣMRc:is the sum of the design values of the moments of resistance of the columnsframing thethe joint. The minimum value of column moments of resistance within the rangeof columnaxial forces produced by the seismic design situationΣMRb:is the sum of the design values of the moments of resistance of the beamsframing the jointWhen partial strength connections are used, the moments of resistance of theseconnectionare taken into account in the calculation of ΣMRbNote: 1. This expression is only applied to the building with two or morestoreys, and should be satisfied at all joints.2. The above expression is waived at the top level of multi-storeybuildings.Resistance offoundation(EN1998-1-1,cl.4.4.2.6)Pad/strip/raft foundationEFd=EF,G + γRdΩEF,EγRd: is the overstrength factor, taken as being equal to 1,0 for q ≤3, or as beingequal to 1,2 otherwiseEF,G: is the action effect due to the non-seismic actions included in thecombination of actions for the seismic design situationULTIMATE LIMIT STATE(ΕΝ1998-1-1,cl 4.4.2)
  24. 24. Valentinos Neophytou BEng, MSc Page 24EF,E: is the action effect from the analysis of the design seismic action; and Ω isthe value of (Rdi/Edi) ≤ q of the dissipative zone or element iof the structurewhich has the highest influence on the effect EF under consideration; whereRdi: is the design resistance of the zone or element iEdi: is the design value of the action effect on the zone or element iin theseismic design situation.Note: If Ω=1 =>γRd= 1.4Damage limitation(EN1998-1-1,cl.4.4.3)For non-structuralelements of brittlematerial attached tothe structureFor building havingductile non structuralelementsFor building havingnon-structuralelements fixed in a wayso as not to interferewith structuraldeformationdrv≤0.005h drv≤0.0075h drv≤0.010hdr: is the interstorey drifth: is the storey heightv: is the reduction factorReduction factor of limitation to interstorey drift(CYA NA EN1998-1-1,cl.NA.2.15)Importance class Reduction factor vI 0.5II 0.5III 0.4IV 0.4
  25. 25. Valentinos Neophytou BEng, MSc Page 25Frame systemStructural system in which boththe vertical and lateral loads aremainly resisted by spatial frameswhose shear resistance at thebuilding base exceeds 65% ofthe total shear resistance of thewhole structural systemDual system(frame or wallequivalent)Dual system in which the shearresistance of the frame system atthe building base is greater than50% of the total shear resistanceof the whole structural systemDual system in which the shearresistance of the walls at thebuilding base is higher than 50%of the total seismic resistance ofthe whole structural systemDuctile wallsystem (couple oruncoupled)Structural system in which bothvertical and lateral loads aremainly resisted by verticalstructural walls, either coupledor uncoupled, whose shearresistance at the building baseexceeds 65% of the total shearresistance of the whole structuralsystemStructural system(EN1998-1-1,cl.5.1.2)SPECIFIC RULES FOR CONCRETE BUILDINGS(EN1998-1-1,cl.5)
  26. 26. Valentinos Neophytou BEng, MSc Page 26System of largelightly reinforcedwallsWall with large cross-sectionaldimensions, that is, a horizontaldimension lw at least equal to 4,0m or two-thirds of the height hwof the wallInvertedpendulum systemSystem in which 50% or more ofthe mass is in the upper third ofthe height of the structureTorsionallyflexibleDual or wall system not having aminimum torsional rigidity
  27. 27. Valentinos Neophytou BEng, MSc Page 27Multiplication factor (EN1998-1-1,cl.5.2.2.2(5a))Frames or frame-equivalent dual systems.Structural system au/a1One-storey building 1.1Multistorey, one-bay frames 1.2Multistorey, multi-bayframes or frame-equivalentdual structures1.3Multiplication factor (EN1998-1-1,cl.5.2.2.2(5b))Wall- or wall-equivalentdual systemsStructural system au/a1Wall system with only two uncoupledwalls per horizontal direction 1.0Other uncoupled wall system 1.1Wall-equivalent dual, or coupled wallsystems1.2Multiplication factor (EN1998-1-1,cl.5.2.2.2(6)Building not regular inplanStructural system au/a1One-storey building 1.05Multistorey, one-bay frames 1.1Multistorey, multi-bayframes or frame-equivalentdual structures1.15Multiplication factorαu/a1Behaviour factor qo(EN1998-1-1,cl.5.2.2.2(2))Approximate values ofαu/a1Explicit calculations (Pushover analysis)LIMITαu/a1≤1.5
  28. 28. Valentinos Neophytou BEng, MSc Page 28Behaviour factor qo for DCM structural system(Extract from IStructE Manual to EC8)STRUCTURAL TYPERegularin planNot regular structuresIn planInelevationIn planandelevationFrame system, dual system, coupled wall systemOne storey (au/a1) 3.3 3.15 2.64 2.52Multi-storey,one bay(au/a1)3.6 3.3 2.88 2.64Multi-storey,multi-bay(au/a1)3.9 3.45 3.12 2.76System of coupled walls or wall equivalent dual system 3.6 3.3 2.88 2.64Uncoupled wall system,Large lightly reinforced walls3,0 3.0 2.4 2.4Tosrionally flexible system 2,0 1.6 1.6 1.6Inverted pendulum system 1,5 1.2 1.2 1.2Note: For buildings which are not regular in elevation, the value of qo should be reduced by 20%
  29. 29. Valentinos Neophytou BEng, MSc Page 29Behaviour factors for horizontal seismic actions, q(EN1998-1-1,cl.5.2.2.2)q = qo . kw ≥ 1.5(EN1998-1-1,Eq.5.1)The factor kw(EN1998-1-1,Eq.5.2)Frame and frame –equivalent dual systemkw = 1.0Wall, wall – equivalent andtorsionally flexibleao = Σhwi / Σlwikw = (1+ao) / 30.5≤ kw ≤ 1.0μφ = 2qo – 1 if (T1≥TC)μφ = 1+2(qo – 1)·TC/T! if (T1≤TC)Curvature ductility factor, μφ(EN1998-1-1,cl.5.2.3.4)REINFORCEMENTCLASSBREINFORCEMENTCLASSC1.5 μφ μφ
  30. 30. Valentinos Neophytou BEng, MSc Page 30Importance class/Ductility classI II III IVDCL DCMDCHDCMDCHDCHIgnore “topographicamplification effects”Consider “topographicamplification effects”IFSlopes <15oCliffs height<30mSlopes <15oCliffs height<30mIgnore ConsiderRegular in plan: YESRegular in elevation YESRegular in plan: NORegular in elevation YESRegular in plan: YESRegular in elevation NORegular in plan: NORegular in elevation NOType of soil:A , B ,C ,D, E, S1, S2Type 1 elastic responsespectrum0≤T≤TBTB≤T≤TCTC≤T≤TDTD≤T≤4sLATERALFORCEMODALANALYSISDisplacementds=qd·deP-Δ effectsθ≤0.1 – Ignore0.1≤θ≤0.2 Consider0.2≤θ≤0.3 Considerθ≥0.3 Not PermitedInterstoreydriftdrv≤0.005h - Brittledrv≤0.0075h - Ductiledrv≤0.010h - OtherFrame jointΣMRC≥1.3ΣMRBStorey ≥ 2
  31. 31. Valentinos Neophytou BEng, MSc Page 31Allowable material for primary seismic element(EN1998-1-1,cl.5.4.1.1)Type of material RequirementsConcrete(EN1998-1-1,cl.5.4.1.1(1)P)C16/20 and higherReinforcement steel(EN1992-1-1,Table C.1) Class B or C (ribbed bars)Allowable material for primary seismic element(EN1992-1-1,cl. 2.4.2.4)Type of material Partial factorConcrete(CYS NA EN1992-1-1,Table 2.1γc=1.5Reinforcement steel(CYS NA EN1992-1-1, Table 2.1γs=1.5Design and detail concrete frame with DCM (EN1998-1-1,cl.5.4)
  32. 32. Valentinos Neophytou BEng, MSc Page 32Design and detailing requirements of EC8 – Primary BeamsDetailing rule name Equation CommentsCritical region length(EN1998-1-1,cl.5.4.3.1.2(2))2hwLongitudinal barsρmin, tension side(EN1998-1-1,Eq.5.12)ρmin = 0.5fctm/fykThe minimum amount of steel reinforcement isprovide in order to withstand to the appliedmoment .ρmax, critical regions(EN1998-1-1,Eq.5.11)ρmax= ρ‟+0.0018fcd/(μφεsy,dfyd)The maximum amount of steel reinforcement isprovide in order to ensure that yielding of theflexural reinforcement occurs prior to crushing ofthe compression block.As,min, critical regions bottomAs,min = 0.5 As,topThe minimum area of bottom steel, As,min, is inaddition to any compression steel that may beneeded for the verification of the end section forthe ULS inbending under the (absolutely)maximum negative (hogging) moment from theanalysis for the design seismic action plusconcurrent gravity, MEd.As,min, support bottom As,min = As,bottom-span/4dbL/hc–bar crossing interior joint(EN1998-1-1,Eq.5.50a)𝑑 𝑏𝐿𝑕 𝑐≤7.5 𝑓𝑐𝑡𝑚𝛾 𝑅𝑑 𝑓𝑦𝑑∙1 + 0.8𝑣 𝑑1 + 0.75𝑘 𝐷 𝜌′/𝜌 𝑚𝑎𝑥 Those equationsdeveloped in order to ensure that
  33. 33. Valentinos Neophytou BEng, MSc Page 33dbL/hc–bar crossing exterior joint(EN1998-1-1,Eq.5.50b)𝑑 𝑏𝐿𝑕 𝑐≤7.5 𝑓𝑐𝑡𝑚𝛾 𝑅𝑑 𝑓𝑦𝑑∙ 1 + 0.8𝑣 𝑑the area is sufficient joint region through thebeam column joint where are existing high rate ofchange of reinforcement stress.Transverse barsOutside critical regions:Outside critical regionSpacing, sw(CYS EN 1992-1-1,Eq.9.8)0.75dρw≥0.08√fck/fykCritical regionCritical regionSpacing, s(EN1998-1-1,Eq.5.13)≤min{hw/4, 24dbw, 225mm, 8dbL}Diamter, dbw(EN1998-1-1,cl.5.4.3.1.2(6)P)≥6mmShear designVEd seismic(EN1998-1-1,Fig.5.1)𝑀 𝑅𝑏𝑙 𝑐𝑙𝑔 𝑘 + 𝜓2 𝑞 𝑘VRd,max,seismic(EN1992-1-1,cl.6.2.3)VRd,max=0.3(1-fck/250)·bw·z·fcd·sin2θ1≤cotθ≤2.5Outside critical region, VRd,s,(EN1992-1-1,cl.6.2.3)VRd,s=bw·z·ρw·fywd·cotθ1≤cotθ≤2.5Critical region, VRd,s,(EN1992-1-1,cl.6.2.3)VRd,s=bw·z·ρw·fywd·cotθ1≤cotθ≤2.5
  34. 34. Valentinos Neophytou BEng, MSc Page 34Design and detailing requirements of EC8 – Primary ColumnsDetailing rule name Equation CommentsCross section sides, hc, bc -Critical region length(EN1998-1-1,Eq.5.14)lcr=max{hc,bc,0.45m, lc/6}Longitudinal barsρmin(EN1998-1-1,cl.5.4.3.2.2(1)P)ρmin=0.011. Symmetrical cross-section must besymmetrically reinforced.2. At least one intermediate bar should beprovidealong in each corner in order toensure the integrity of column beam joint.The column end is consider as criticalregion .ρmax(EN1998-1-1,cl. 5.4.3.2.2(1)P)ρmax=0.04dbL ≥{8mm}Bar per each side(EN1998-1-1,cl.5.4.3.2.2(2)P)≥{ 3}Maximum spacing between restrained bars(EN1998-1-1,5.4.3.2.2(11b))≤{200mm}Distance of unrestrained bar from nearest restrainedbar(EN1998-1-1,cl.5.4.3.3(2))≤{150mm}Transverse barsOutside critical regions:
  35. 35. Valentinos Neophytou BEng, MSc Page 35dbw(EN 1998-1-1,cl.5.4.3.2.2(10)P) ≥{6mm ,dbL/4}Spacing, s(EN1992-1-1,cl.9.5.3(3))≤{20dbL,hc,bc,400mm}At lap splices, if dbL>14mm: sw≤(EN1992-1-1,cl.9.5.3(4))≤{12dbL,0.6hc,0.6bc,240mm}Within critical region:dbw,(EN 1998-1-1,cl.5.4.3.2.2(10)P)≥ {6mm, dbL/4}Spacing, s(EN1998-1-1,Eq.5.18)≤{bo/2, 175mm, 8dbL)In critical region at column base:ωwd,(EN19981-1,cl.5.4.3.2.2(9)≥0.08In critical region at column base:aωwd(EN1998-1-1,Eq.5.15)(EN1998-1-1,Eq. 5.16a & 5.17a)(For cross section)≥30μφvdεsy,dbc/bo-0.035an= 1-Σbi2/6bohoas= (1-s/2bo)(1-s/2ho)1. The amount of hoops at the criticalregions should be satisfy be this equation.2. The mechanical volumetric ratio ofconfining hoops within the criticalregions:3. The confinement effectiveness factor,equal to α=αn.αsThe mechanical volumetric ratio of confininghoops within the critical regions:a) For cross section:
  36. 36. Valentinos Neophytou BEng, MSc Page 36(EN1998-1-1,Eq.5.16b& 5.17b)(For circular cross section) an=1as=(1-s/2Do)2𝜔 𝑤𝑑 =2 𝑕 𝑜 + 𝑏 𝑜 + 𝑕 𝑜2 + 𝑏 𝑜2𝑕 𝑜 𝑏 𝑜 𝑠∙ 𝐴 𝑠 ∙𝑓𝑦𝑑𝑓𝑐𝑑≥ 0.08b) For circular cross section with circularhoops:𝜔 𝑤𝑑 =3 𝑕 𝑜 + 𝑏 𝑜𝑕 𝑜 𝑏 𝑜 𝑠∙ 𝐴 𝑠 ∙𝑓𝑦𝑑𝑓𝑐𝑑≥ 0.08Capacity design – beam column jointCapacity design checks at beam-column joints(EN1998-1-1,Eq.4.29)Σ𝛭 𝑅𝑐 ≥ 1,3Σ𝑀 𝑅𝑏 This rule is not apply at:-to a top level of multi-storey building-in single storey buildingAxial load ratioAxial load ratio(EN1998-1-1,cl.5.4.3.2.1(3)P)𝑣 𝑑 = 𝑁𝐸𝑑 /𝐴 𝑐 𝑓𝑐𝑑 ≤ 0.65Shear designShear design(EN1998-1-1,Fig.5.2)𝛾 𝑅𝑑 ∙Σ𝑀 𝑅𝑐,𝑒𝑛𝑑𝑠𝑙 𝑐𝑙VRd,max,seismic(EN1992-1-1,Eq.6.9)VRd,max=0.3(1-fck/250)·bw·z·fcd·sin2θ1≤cotθ≤2.5VRd,s, seismic(EN1992-1-1,cl.6.2.3)VRd,s=bw·z·ρw·fywd·cotθ+NEd(h-x)/lcl1≤cotθ≤2.5
  37. 37. Valentinos Neophytou BEng, MSc Page 37Design and detailing requirements of EC8 – Ductile wallDetailing rule name Equation CommentsWeb thickness, bwo(EN1998-1-1,Eq.5.7)≥ max{150mm, hstorey/20}Critical region length, hcr(EN1998-1-1,Eq. 519a & 5.19b)hcr= max{lw, hw/6}≤2lw≤hsfor n ≤ 6 storey≤2hs for n ≤ 6 storeyBoundary elementsCritical regionLength of the confined boundary element, lc(EN1998-1-1,cl.5.4.3.4.2(6))lc = max{0.15lw,1.5bw} length over whichεcu>0.0035Thickness bw over lc(EN1998-1-1,cl. 5.4.3.4.2(10))bw≥ 0.20m and bw≥ hs/10lc≥ max(2bw,0.2lw)andbw≥ 0.20m and bw≥ hs/15lc≤ max(2bw,0.2lw)Vertical reinforcement:ρmin over Ac=lcbw(EN1998-1-1,cl.5.4.3.4.2(8))ρmin= 0.005ρmaxover Ac(EN1998-1-1,cl. 5.4.3.2.2(1)P)ρmax= 0.04Confining hoops
  38. 38. Valentinos Neophytou BEng, MSc Page 38dbw(EN 1998-1-1,cl.5.4.3.2.2(10)P)Spacing oh hoops (at edges of the wall), sw(EN1992-1-1,cl.9.5.3(4))Spacing oh hoops (at the distance beyond to the edgeof wall), sw(EN1992-1-1,cl. 9.5.3(4))In the part of the section where : 0.02Ac1. Distance of unrestrained bar incompression zone from nearest restrainedbar ≤150mm2. Hoops with dbw≥max{6mm, dbL/4}3. Spacing of hoops, sw≤ min{12dbL, 0.6bwo,240mm) up to a distance of 4bw above orbelow floor beams or slabs or,4. Spacing of hoops,sw≤min{20dbL,bwo,400mm} beyond thatdistance mansion at (3).The transverse reinforcement of the boundaryelements may be determined in accordance withEN1992-1-1 alone, if one of the followingconditions is fulfilled:a. vd≤ 0.15b. vd≤ 0.20 and the q-factor used in theanalysis is reduced by 15%.(EN1998-1-1,cl.5.4.3.4.2(12a&b)).ωwd,(EN19981-1,cl.5.4.3.2.2(9)0.08aωwd(EN1998-1-1,Eq.5.20)xu,(EN1998-1-1,Eq. 5.21)εcu2,c,(EN1998-1-1,cl. 5.4.3.4.2(6)ωv,(EN1998-1-1,cl. 5.4.3.4.1(5a))αωwd≥ 30μφ (vd + ωv)εsy,dbc/bo – 0.035xu = (vd+ωv)·lwbc/boεcu2,c = 0.0035 + 0.1aωwdωv = (Asv/hcbc)fyd/fcdFor walls of rectangular cross-section.Web
  39. 39. Valentinos Neophytou BEng, MSc Page 39Vertical reinforcementρv.min(EN1998-1-1,cl. 5.4.3.4.2(11))εc> 0.002: ρv.min≥0.005In the height of the wall above the critical regiononly the relevant rules of EN1992-1-1:2004regarding vertical, horizontal and transversereinforcement apply.ρv.max ρv.max = 0.04Spacing of vertical bars, sv(EN1992-1-1,cl.9.6.2(3))≤ min{3bwo,400mm}Horizontal reinforcementρh.min(CYS NA EN1992-1-1,cl. 9.6.3(1))ρh.min = max{0.001Ac , 0.25ρv)Spacing of reinforcement, sh(EN1992-1-1,cl. 9.6.3(2))≤ 400mmAxial load ratioNormalised axial load, vd(EN1998-1-1,cl. 5.4.3.4.1(2))≤ 0.4Design momentsDesign moment, MEd(EN1998-1-1,cl.5.4.2.4(4)P)If the hw/lw ≥ 2.0, the moment distribution alongthe height of slender primary seismic wall shall becoveredThe design bending moment diagram along theheight of the wall should be given by anenvelopeof the bending moment diagram from theanalysis, vertically displaced(tension shift). Theenvelope may be assumed linear, if the structuredoes not exhibitsignificant discontinuities ofmass, stiffness or resistance over its height.
  40. 40. Valentinos Neophytou BEng, MSc Page 40Shear resistanceDesign shear force, VEd(EN1998-1-1,cl.5.4.2.4(7))VEd = 1.5·VEd,seismicOutside critical regionVRd,max,seismic(EN1992-1-1,Eq.6.9)VRd,max=0.3(1-fck/250)·bwo·0.8lw·fcd·sin2θ1≤cotθ≤2.5VRd,s(EN1992-1-1,cl.6.2.3)VRd,s = bwo (0.8lw)ρh·fywd·cotθ1≤cotθ≤2.5Critical region in webVRd,max,seismic(EN1992-1-1,Eq.6.9)VRd,max=0.3(1-fck/250)·bwo·0.8lw·fcd·sin2θ1≤cotθ≤2.5VRd,s if as = MEd/VEdlw≥2(EN1992-1-1,cl.6.2.3)VRd,s = bwo (0.8lw)ρh·fywd·cotθ1≤cotθ≤2.5VRd,s if as = MEd/VEdlw≤2(EN1992-1-1,cl.6.2.3)VRd,s = bwo (0.8lw)ρh·fywd·cotθ1≤cotθ≤2.5

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