EUROCODESBuilding the Future Building the Future in the Euro-Mediterranean Area Design of buildings for earthquake resistance, according to Eurocode 8-Part 1 (concrete & masonry buildings) Workshop - 27-29 November 2006, Varese, Italy EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area STRUCTURE OF EN 1998-1:2004 1 2 3 4 5 6 7 8 9 10 General Performance Requirements and Compliance Criteria Ground Conditions and Seismic Action Design of Buildings Specific Rules for Concrete Buildings Specific Rules for Steel Buildings Specific Rules for Steel-Concrete Composite Buildings Specific Rules for Timber Buildings Specific Rules for Masonry Buildings Base Isolation Workshop - 27-29 November 2006, Varese, Italy EUROCODES Building the Future Fundamental features of good structural layout • Clear structural system. • Simplicity & uniformity in geometry of structural system. • Symmetry & regularity in plan. • Significant torsional stiffness about vertical axis. • Geometry, mass & lateral stiffness: regular in elevation. • Redundancy of structural system. • Effective horizontal connection of vertical elements at all floor levels. Workshop - 27-29 November 2006, Varese, Italy Building the Future in the Euro-Mediterranean Area EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area Clear structural system • System of: – plane frames continuous in plan, from one side of the plan to the opposite, w/o offsets or interruption in plan, or indirect supports of beams, and/or – (essentially) rectangular shear walls, arranged in two orthogonal horizontal directions. Workshop - 27-29 November 2006, Varese, Italy EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area Symmetry - regularity in plan • • Lateral stiffness & mass ~symmetric w.r.to two orthogonal horizontal axes (full symmetry → response to translational horizontal components of seismic action will not include any torsion w.r.to the vertical axis). Lack of symmetry in plan often measured via “static eccentricity”, e, between: – centre of mass of storey (centroid of overlying masses, CM) and – centre of stiffness (CS, important during the elastic response). • One of Eurocode 8 criteria for regularity in plan: e x ≤ 0 .3 rx ; – “torsional radius” rx (ry) = √ratio of: • torsional stiffness of storey w.r.to CS, to • storey lateral stiffness in y (x) direction, orthogonal to x (y). e y ≤ 0 .3 r y • CS, CR & rx, ry: unique & independent of lateral loading only in single-storey buildings: ( xEI y ) ( yEI x ) ∑ (x 2 EI y + y 2 EI x ) ∑ (x 2 EI y + y 2 EI x ) ∑ ∑ x CS = ; y CS = ; rx = ry = ( ) ( ) EI EI ( ) EI ∑ y ∑ (EI x ) ∑ y ∑ x Another Eurocode 8 criterion for regularity in plan: compact outline in plan, enveloped by convex polygonal line. Re-entrant corners in plan don’t leave area up to convex polygonal envelope >5% of area inside outline. T-, U-, H-, L-shaped etc. plan: floors may not behave as rigid diaphragms, but deform in horizontal plane (increased uncertainty of response). Workshop - 27-29 November 2006, Varese, Italy • • regularity in plan (cont’d) Torsional response → difference in seismic displacements between opposite sides in plan. Collapse of building due to its torsional response about a stiff shaft at the corner (Athens. Italy .27-29 November 2006. 1999 earthquake).EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area Symmetry . Workshop . larger local deformation demands on side experiencing the larger displacement (“flexible side”). Varese. to vertical axis w/ T > T of lowest (~)purely translational natural mode → accidental torsional vibrations w.to vertical axis by transfer of vibration energy from the response in the lowest translational mode to the torsional one → significant & unpredictable horizontal displacements at the perimeter. • Avoided through Eurocode 8 criterion for regularity in plan: 2 2 2 2 – “torsional radii” rx (better rmx: rmx = rx + e x ) & ry (rmy: rmy = ry + e y ) > – radius of gyration of floor mass in plan ls = √ ratio of: • polar moment of inertia in plan of total mass of floors above w.r.to vertical axis • (~)Purely torsional natural mode w.r. Varese.to floor CM. Italy . ry ≥ l s Workshop .EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area High torsional stiffness w.r.27-29 November 2006.r. to • total mass of floors above 2 2 For rectangular floor area: l s = ( l + b ) / 12 rx ≥ l s . EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area High torsional stiffness w. (b) drawbacks due to restraint of floors & difficulties of foundation at the corners.27-29 November 2006. Varese. (c) sensitive to failure of individual walls Workshop . Italy .to vertical axis (cont’d) Means of providing torsional stiffness about a vertical axis: Shear walls or strong frames at the perimeter Arrangements of shear walls in plan: (a) preferable.r. Workshop . . Italy Bottom: Kobe (JP) 1995. stiffness: regular in elevation Building the Future Collapse of upper or intermediate storeys w/ reduced plan dimensions or stiffness Top left: Kalamata (GR) 1986. top right: Kocaeli (TR) 1999.EUROCODES Building the Future in the Euro-Mediterranean Area Geometry. Varese. mass.27-29 November 2006. mass & lateral stiffness: regular in elevation (cont’d) L1 − L 2 ≤ 0.50 L L3 + L1 ≤ 0. Italy Eurocode 8 criteria for regularity in elevation in buildings w/ setbacks .10 L1 L3 + L1 ≤ 0.20 L1 L − L2 ≤ 0.30 L L1 − L 2 ≤ 0.20 L Workshop .EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area Geometry.27-29 November 2006. Varese. especially in buildings long in plan: In-plane bending of long floor diaphragms in building with two strong walls at the 2 ends → intermediate columns overloaded. • Avoid systems w/ few large walls per horizontal direction.EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area Redundancy of structural system • Provide large number of lateral-load resisting elements & alternative paths for earthquake resistance. compared to results of design w/ rigid diaphragm Vb áu V b d á1Vb d Eurocode 8: Bonus to system redundancy: qo proportional to αu/α1 : 1st yielding anywhere global plastic mechanism Vbd =design base shear äto p Workshop .27-29 November 2006. Italy . Varese. due to internal patios. • Cast-in-situ reinforced concrete is the ideal structural material for earthquake resistant construction. • Vertical elements of lateral-force resisting system should be connected together. Varese. may disrupt continuity of force path. Workshop .EUROCODES Building the Future Continuity of floor diaphragms Building the Future in the Euro-Mediterranean Area • Need smooth/continuous path of forces. wide shafts or stairways. especially if such openings are next to large shear walls near or at the perimeter. compared to prefabricated elements joined together at the site: the joints between such elements are points of discontinuity.27-29 November 2006. via combination of floor diaphragms & beams: – at all horizontal levels where significant masses are concentrated. from the masses where they are generated due to inertia. • Floor diaphragms should have sufficient strength to transfer the inertia forces to the lateral-load-resisting system & be adequately connected to it. Italy . and – at foundation level. • Large openings in floor slabs. etc. to the foundation. Collapse of precast concrete industrial building. Collapse of buildings w/ precast concrete floors inadequately connected to the walls (Spitak. Workshop . 1999). Italy . 1988). Armenia.EUROCODES Building the Future Continuity of floor diaphragms (cont’d) Building the Future in the Euro-Mediterranean Area Floors of precast concrete segments joined together & w/ structural frame via few-cm-thick lightly reinforced cast-in-situ topping.27-29 November 2006. w/ floors poorly connected to lateral-load-resisting system (Athens. Varese. or waffle slabs w/ thin lightly reinforced top slab: Insufficient. 08g) for superstructure of base-isolated buildings. (Or: Foundation elements .including piles .EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area EC8 DESIGN CONCEPTS FOR SAFETY UNDER DESIGN SEISMIC ACTION 1. Design for energy dissipation (normally through ductility): q>1.EC7 (Ductility Class “Low”– DCL) Only: • • for Low Seismicity (NDP. Varese.3ΣMRb in frames): • Local ductility: ¾ Plastic hinges detailed for ductility capacity derived from q-factor. Workshop .27-29 November 2006. recommended: PGA on rock ≤0. 2. ¾ Brittle failures prevented by overdesign/capacity design • Capacity design of foundations & foundation elements: ¾ On the basis of overstrength of ductile elements of superstructure.5 for overstrength.5 • Global ductility: ¾ Structure forced to remain straight in elevation through shear walls. design only according to EC2 . Italy .designed & detailed for ductility) Design w/o energy dissipation & ductility: q≤1. bracing system or strong columns (ΣMRc>1. • For given period. that would develop if the SDoF system was linear-elastic. expressed as ratio to the yield displacement. inelastic spectrum relates: – ratio q = Fel/Fy of peak force. of elastic SDoF system.EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area Force-based design for energy-dissipation & ductility. δy : displacement ductility factor. • Basis of force-based design for ductility: – inelastic response spectrum of SDoF system having elastic-perfectly plastic F-δ curve. provided that integrity of members & of the whole is not endangered. (“behaviour factor”) to – maximum displacement demand of the inelastic SDOF system. in monotonic loading. Fy. μδ = δmax/δy Workshop . to its yield force. to meet no-(life-threatening-)collapse requirement under Design Seismic action: • Structure allowed to develop significant inelastic deformations under design seismic action. T. Italy . δmax.27-29 November 2006. Varese. Fel. and either plastic hinging at wall & column base or rotations at the foundation. involving: plastic hinging at all beam ends. Workshop . and either plastic hinging at column bottoms.27-29 November 2006. Varese. Italy è è è aaaa aaaa aaaa è è è Hto t è aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaaa aaaaa aaaaa è aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaa aaaaa aaaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa .EUROCODES ä Building the Future Building the Future in the Euro-Mediterranean Area Control of inelastic seismic response: Soft-storey mechanism avoided • Soft-storey collapse mechanism to be avoided via proper structural layout ä aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaa aaaa aaaa è è è è è aaaa aaaa aaaa aaaa aaaa aaaa è è è è è aaaa aaaa aaaa aaaa aaaa aaaa è è è è è aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa Hst èst aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa −Strong-column/weak beam frame w/ beamsway mechanism. involving: plastic hinging at all beam ends. or rotations at the foundation. aaaa aaaa aaaa Hto t è aaaa aaaa aaaa è è è aaaa aaaa aaaa aaaa aaaa aaaa è è è aaaa aaaa aaaa aaaa aaaa aaaa è è è aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa ä è è è è è aaaa aaaa aaaa aaaa aaaa aaaa è è è è è aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa aaaa −Wall-equivalent dual frame. with beamsway mechanism. Varese. Ed. They are designed and detailed to provide the required ductility & energy-dissipation capacity.EUROCODES Building the Future in the Euro-Mediterranean Area Control of inelastic seismic response via capacity design • • Not all locations or parts in a structure are capable of ductile behaviour & energy dissipation. regions and mechanisms capable of ductile behaviour & energy dissipation. “Capacity design” provides the necessary hierarchy of strengths between adjacent structural members or regions & between different mechanisms of load transfer within the same member. q) Workshop . Italy . The rest stay in the elastic range. “dissipative zones” are dimensioned to provide a design value of ULS force resistance. from the analysis: Building the Future • • E d ≤ Rd • Normally linear analysis is used for the design seismic action (by dividing the elastic response spectrum by the behaviour factor. Before their design & detailing for the required ductility & energy-dissipation capacity. at least equal to the design value of the action effect due to the seismic design situation. to ensure that inelastic deformations will take place only in those members. The regions of members entrusted for hysteretic energy dissipation are called in Eurocode 8 “dissipative zones”. Rd.27-29 November 2006. EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area EC8-PART 1: FOR ALL MATERIALS: • For Dissipative Structures (except masonry): • Two Ductility Classes (DC): ¾DC H (High). 1. Italy . member detailing. Varese. • Differences in: ¾q-values (usually q > 4 for DCH. ¾DC M (Medium). capacity design against brittle failure modes) Workshop .27-29 November 2006.5 <q <4 for DCM) ¾Local ductility requirements (ductility of materials or section. provided that: ¾Their total contribution to lateral stiffness ≤ 15%.27-29 November 2006. • Designer free to assign elements to the class of “secondary seismic elements”. • Required to remain elastic under deformations due to design seismic action. ¾Regularity classification does not change.EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area EC8-PART 1: FOR ALL MATERIALS: • "Secondary seismic elements": • Their contribution to resistance & stiffness for seismic actions neglected in design (& in linear analysis model. Italy . Varese. too). Workshop . Italy . Varese.EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area CONCRETE & MASONRY BUILDINGS • Yield-point stiffness in analysis (50% of uncracked section EI): • Reduction in design seismic forces vis-a-vis use of full section EI • Increase of displacements for drift-control & P-Δ effects (governs sizes of frame members). Workshop .27-29 November 2006. 27-29 November 2006. Building the Future Workshop . with overstrength factor of 1.EUROCODES Building the Future in the Euro-Mediterranean Area Implementation of EC8 seismic design philosophy • Damage limitation (storey drift ratio < 0. • Detailing of plastic hinge regions. • Member verification for the Ultimate Limit State (ULS) in bending under the “design seismic action”. Italy . with elastic spectrum reduced by the behaviour factor q.5-1%) under the damage limitation earthquake (~50% of “design seismic action”). on the basis of the value of the curvature ductility factor that corresponds to the q-factor value. Varese. using 50% of uncracked gross section stiffness.3 on beam strengths. • Capacity design of members and joints in shear. • In frames or frame-equivalent dual systems: Fulfilment of strong column/weak beam capacity design rule. Concrete (& masonry): – Elastic stiffness = 50% of uncracked gross-section stiffness. steel or composite frames: damage limitation check governs member sizes. Workshop . In concrete. Recommended for ordinary buildings: 10%/10yrs (95yr EQ).27-29 November 2006.EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area EC8-PART 1: DAMAGE LIMITATION CHECK • • • • • • Seismic action for “damage limitation”: NDP. – < 1% for nonstructural elements not present or not interfering w/ structural response (: damage limitation for structure). Varese.5% for brittle nonstructural elements attached to structure. Italy . ~50% of “design seismic action” (475yr EQ).75% for ductile nonstructural elements attached to structure. – <0. Interstorey drift ratio calculated for “damage limitation” action via “equal displacement rule” (elastic response): – <0. • Before their design & detailing for the required ductility & energydissipation capacity.are designed & detailed to provide the required ductility & energy-dissipation capacity. Ed. Italy . q) E d ≤ Rd Workshop . Varese. at least equal to the design value of the action effect due to the seismic design situation.EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area ULS Verification of dissipative zones • The regions of members entrusted for hysteretic energy dissipation called in Eurocode 8 “dissipative zones” . “dissipative zones” are dimensioned to provide a design value of ULS force resistance. Rd. from the analysis: • Normally linear analysis is used for the design seismic action (by dividing the elastic response spectrum by the behaviour factor.27-29 November 2006. in concrete buildings: γc=1. Workshop . Varese.27-29 November 2006. (i. Italy .e.5.EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area NDP-partial factors for materials in ULS: • Recommended: • Use same values as for persistent & transient design situations γs=1.15). 27-29 November 2006.3 Beam & column flexural capacities at a joint in Capacity Design rule column 1 column 1 beam 1 beam 2 beam 1 beam 2 column 2 column 2 Workshop . Italy . Varese.EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area Strong column/weak beam capacity design rule in frames or frameequivalent dual systems (frames resist >50% of seismic base shear) above two storeys (except at top storey joints): ∑ M Rc ≥ γ Rd ∑ M Rb • Overstrength factor γRd on beam strengths γRd = 1. Edi the seismic action effect there from the elastic analysis and γRd=1. Rdi/Edi is the minimum value of MRd/MEd in the two orthogonal principal directions at the lowest cross-section of the vertical element where a plastic hinge can form in the seismic design situation. i. • For individual spread footings of columns of concentric braced frames. or – The ground and the foundation system are designed for their ULS under seismic action effects from the analysis multiplied by γRd(Rdi/Edi)≤q. Means: – The ground and the foundation system are designed for their ULS under seismic action effects from the analysis derived for q=1. for eccentric braced frames.Rd/MEd among all seismic links of the frame. remain elastic while inelasticity develops in the superstructure.27-29 November 2006. γRd(Rdi/Edi) =1.Rd/NEd among all diagonals which are in tension in the particular seismic design situation. Workshop .Rd/VEd and Mpl. Italy . Varese. i. lower than the q-value used for the design of the superstructure.5.2 • For individual spread footings of walls or columns of moment-resisting frames.EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area Seismic design of the foundation • • Objective: The ground and the foundation system should not reach its ULS before the superstructure. Rdi/Edi is the minimum value of Npl.e. • For common foundations of more than one elements. Rdi/Edi is the minimum value of Vpl.4. where Rdi force capacity in the dissipative zone or element controlling the seismic action effect of interest.e. EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area STRUCTURE OF EN19981:2004 1 2 3 4 5 6 7 8 9 10 General Performance Requirements and Compliance Criteria Ground Conditions and Seismic Action Design of Buildings Specific Rules for Concrete Buildings Specific Rules for Steel Buildings Specific Rules for Steel-Concrete Composite Buildings Specific Rules for Timber Buildings Specific Rules for Masonry Buildings Base Isolation Workshop . Italy . Varese.27-29 November 2006. 3). Varese. – Plastic hinge regions (beam ends.27-29 November 2006. • DC (H) High q= 4-4.5 x system overstrength factor (≈1. • The aim of the design is to control the inelastic seismic response: – Structural layout & relative sizing of members ensures beam-sway mechanism. Italy . base of columns) are detailed to sustain inelastic deformation demands related to behaviour factor q: – μδ=q if Τ>Τc – μδ=1+(q-1)Tc/T if Τ≤ Τc Workshop .EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area Seismic Design Philosophy for RC buildings according to Eurocode 8 • Ductility Classes (DC) – Design based on energy dissipation and ductility: • DC (M) Medium q=3 x system overstrength factor (≈1.3). 25fyk Workshop .95 ≤ 1. Italy .EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area Material limitations for “primary seismic elements” Ductility Class Concrete grade Steel class per EN 19921-1.27-29 November 2006. Varese.0. Table C1 longitudinal bars Steel overstrength: No limit DC L (Low) No limit B or C DC M (Medium) ≥ C16/20 B or C only ribbed No limit DC H (High) ≥ C16/20 only C only ribbed fyk. qo. Workshop . Varese. ¾ Buildings irregular in elevation: behaviour factor q = 0.5 2 3 Lateral-load resisting structural system Inverted pendulum system* Torsionally flexible structural system** Uncoupled wall system (> 65% of seismic base shear resisted by walls. ** : at any floor: radius of gyration of floor mass > torsional radius in one or both main horizontal directions (sensitive to torsional response about vertical axis).EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area Basic value. of behaviour factor for regular in elevation concrete buildings DC M 1. value of normalized axial loadνd in combination(s) of the design seismic action with the concurrent gravity loads ≤ 0.3). or with energy dissipation at base of a single element (except one-storey frames w/ all columns connected at the top via beams in both horizontal directions in plan & with max. Italy .27-29 November 2006. ¾ Wall or wall-equivalent dual systems: q multiplied (further) by (1+aο)/3 ≤ 1.8qo. (aο: prevailing wall aspect ratio = ΣHi/Σlwi). more than half by uncoupled walls) not belonging in one of the categories above Any structural system other than those above DC H 2 3 4αu/α1 3αu/α1 4.5αu/α1 * : at least 50% of total mass in upper-third of the height. 1 for: one-storey frame or frame-equivalent dual systems.3 for: multi-storey multi-bay frame or frame-equivalent dual systems. = 1. wall-equivalent dual systems & coupled wall systems.5. Varese. direction.2 for: one-bay multi-storey frame or frame-equivalent dual systems.top displacement curve from pushover analysis. ¾ αu: seismic action at development of global global plastic mechanism • • • • • • αu/α1≤ 1. Vbd =design base shear äto p • for buildings irregular in plan: default value = average of default value of buildings regular in plan and 1. αu/α1 in behaviour factor of buildings designed for ductility: due to system redundancy & overstrength V b áu V b d á1Vb d 1st yielding anywhere mechanism.3 for buildings regular in plan: = 1.EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area Normally: αu & α1 from base shear . = 1.27-29 November 2006. and wall systems w/ > 2 uncoupled walls per direction.0 for wall systems w/ just 2 uncoupled walls per horiz. ¾ α1: seismic action at 1st flexural yielding anywhere. = 1. default values given between 1 to 1.0 Workshop . Italy . against pre-emptive shear failure Workshop . Italy .EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area Capacity design of members.27-29 November 2006. Varese. o ( x ) • in DC H γRd=1. ∑ Rd. bj − min ⎜1.d (x) = l cl ⎞ ⎛ M ⎟ + M Rd. bi min ⎜1.d ( x ) = − ⎡ ⎛ ∑ M Rd.0. Workshop .d ( x i ) .bj min⎜1. ⎜ ∑ M Rd.reversal of V accounted for. b ⎠i ⎝ l cl ⎞ ⎤ ⎟ ⎥ ⎟ ⎥ ⎠j⎦ + Vg + ψq. depending on: ζ i = max V i. Beams Building the Future in the Euro-Mediterranean Area ⎡ ⎛ ∑ M Rd. c + ⎢ γ Rd M Rd. ⎜ ∑ M Rd.c ⎞ ⎛ ∑ M Rd.27-29 November 2006.b ⎟ ⎜ ∑ M Rd. Italy min V i. ⎟ ⎥ γ Rd ⎢M Rd. Varese.bi min⎜1.d ( x i ) • in DC M γRd=1. b ⎢ ⎝ ⎣ min Vi.b ⎟ ⎥ ⎢ ⎝ ⎠ ⎝ ⎠j⎦ i ⎣ + Vg+ψq.EUROCODES Building the Future I.c ⎞ ⎤ − + ⎟ + M Rd. c ⎟ ⎜ ∑ M Rd.o (x) maxVi.2 . 1 Workshop .c1 Rd. c1 min ⎜ 1. ⎜ ∑M ⎢ Rd. c ⎝ ⎠1 h cl ⎞ ⎤ ⎟ ⎥ ⎟ ⎥ ⎠2 ⎦ • in DC H γRd=1. Varese. Columns − = γ Rd VCD − + + M Rd M .EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area II. c ⎝ ⎣ ⎛ ⎞ M ⎟ + M Rd.3. • in DC M γRd=1.c1 Rd.c2 hcl hcl Capacity-design shear in (weak or strong) columns: γ Rd V CD.c 2 Capacity-design shear in column which is weaker than the beams: + VCD = γ Rd _ + M Rd M + . Italy . ∑ Rd.27-29 November 2006. c = ⎡ ⎛ ∑ M Rd. b ⎢ M Rd. c2 min ⎜ 1. b ⎜ ∑M ⎟ Rd. V’Ed. Varese.5 V Ed DC H squat walls (hw/lw ≤ 2): Over-design for flexural overstrength of base w. MRdo: design flexural resistance at base section.to analysis MEdo: design moment at base section (from analysis).to analysis & for increased inelastic shears Se(T): ordinate of elastic response spectrum TC: upper limit T of const.27-29 November 2006. region T1: fundamental period.EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area Eurocode 8: Over-design in shear. ⎛ V M ε= Ed ' VEd ⎛ Se (TC ) ⎞ Rdo ⎞ ⎜ ⎟ ⎟ = ⎜ γ Rd + 0. Italy .r. by factor ε: V Ed DC M walls: ε = ' = 1 . γRd=1. spectral acc.1 ⎜ q ≤q ⎟ ⎜ ⎟ M Edo ⎠ ⎝ ⎝ Se (T1 ) ⎠ 2 2 Workshop . Walls ε= DC H slender walls (hw/lw > 2): Ed ' V Ed ⎛ M Rdo = γ Rd ⎜ ⎜M ⎝ Edo ⎞ ⎟ ⎟≤q ⎠ Over-design for flexural overstrength of base w.r. by multiplying shear forces from the analysis for the design seismic action.2 V III. base/2 design envelope magnified shear diagram 2 h 3 w shear diagram from analysis Vwall. Italy response (after plastic hinging at the base) . Varese.EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area Design shear forces in “ductile wall” of dual structural systems per Eurocode 8 Vwall. base 1h 3 w To account for increase in upper storey shears due to higher mode inelastic Workshop . top>Vwall.27-29 November 2006. 1αωw): Lpl≈0. ft/fy: 1.08-1. • Derivation: – Relation between μφ & Lpl/Ls (Lpl: plastic hinge length. Italy .3Ls & for (safety) factor 2: Lpl=0.15) increase μφ-demand by 50% Workshop . columns & walls (for EC2 confinement model: ε*cu=0. Tc: T at upper limit of constant spectral acceleration region. μδ= q if T1≥Tc. Then: μφ ≈ 2μδ-1 • For steel B (εu: 5-7. qo : q-factor unreduced for irregularity in elevation (multiplied w/ MEd/MRd at wall base).15Ls .0035+0. – Relation q-μδ-T : μδ= 1+(q-1)Tc/T1 if T1<Tc. – Relation of Lpl & Ls for typical RC beams.27-29 November 2006.5%.5Lpl/Ls). Varese.EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area • • μφ=2qo-1 μφ =1+2(qo-1)Tc/T1 – – – DETAILING OF DISSIPATIVE ZONES FOR CURVATURE DUCTILITY FACTOR μφ CONSISTENT w/ q-FACTOR if T1≥Tc if T1<Tc T1: fundamental period of building. Ls: shear span) & μδ (: top displacement ductility factor) in buildings staying straight due to walls or strong columns: μδ =1+3(μφ-1)Lpl/Ls(1-0. v/fcd – Columns meeting strong-column/weak-beam rule (ΣMRc>1. ductile walls): – Confining reinforcement (for walls: in boundary elements) with (effective) mechanical volumetric ratio: αωwd =30μφ(νd+ων)εydbc/bo-0. ω=ω’ (columns.3ΣMRb). Varese. εyd=fyd/Es. – DC H strong columns (ΣMRc>1. • Members w/o axial load & w/ unsymmetric reinforcement (beams): – Max.0018/μφ εyd Workshop . bo: width of confined core. • ων: mechanical ratio of longitudinal web reinforcement =ρνfyd. provided w/ full confining reinforcement only at (building) base. • bc: width of compression zone.EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area MEANS TO ACHIEVE μφ IN PLASTIC HINGES • Members w/ axial load & symmetric reinforcement. mechanical ratio of tension steel: ω ≤ ω’+0.3ΣMRb) also provided w/ confining reinforcement for 2/3 of μφ in all end regions above base. Italy .27-29 November 2006.035 • νd=Nd/bchfcd. but to transform seismic energy to potential energy (uplift of masses) & energy dissipated in the soil by rigid-body rocking. or lack-of-fixity at base wall cannot be designed for energy dissipation in plastic hinge at the base. Varese. ¾ Due to its dimensions. etc. ¾ Designed & detailed to dissipate energy only in flexural plastic hinge just above the base. Large lightly-reinforced wall (only for DC M): ¾ Wall with horizontal dimension lw≥ 4m.to rest of structural system.r. expected to develop limited cracking or inelastic behaviour.EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area • • TYPES OF DISSIPATIVE WALLS Ductile wall: ¾ Fixed at base. to prevent rotation there w. Italy .27-29 November 2006. Workshop . to ensure that plastic hinge develops only at the base: Typical moment diagram in a concrete wall from the analysis & linear envelope for its (over-)design in flexure according Eurocode 8 Workshop .EUROCODES Building the Future in the Euro-Mediterranean Area Strong column/weak beam capacity design not required in wall.or wall-equivalent dual systems (>50% of seismic base shear in walls) Building the Future But: design of ductile walls in flexure.27-29 November 2006. Varese. Italy . 5 for DC M [(1. times: 1.2 MRd/MEd)2+0.27-29 November 2006.0035+0. • MRd: design flexural resistance at base. • In plastic hinge zone: boundary elements w/ confining reinforcement of effective mechanical volumetric ratio: αωwd=30μφ(νd+ων)εydbc/bo-0.1(qSe(Tc)/Se(T1))2]1/2 < q for DC H • MEd: design moment at base (from analysis). • Se(T): ordinate of elastic response spectrum. so that cantilever relation between q & μφ can apply: • Wall provided with flexural overstrength above plastic hinge region (linear moment envelope with shift rule). • Design in shear for V from analysis. region • T1 fundamental period.0035 Workshop . Varese.EUROCODES Building the Future DESIGN & DETAILING OF DUCTILE WALLS Building the Future in the Euro-Mediterranean Area • Inelastic action limited to plastic hinge at base.1αωw & εcu=0. spectral acc. • Tc: upper limit T of const. Italy .035 over part of compression zone depth: xu=(νd+ων)εydbc/bo where strain between: ε*cu=0. On the other hand. Æ special (less demanding) dimensioning & detailing. q=2 – fundamental period T1<0. of walls / floor area & significant uplift of masses). Italy . • have shown satisfactory performance in strong EQs.EUROCODES Building the Future LARGE LIGHTLY REINFORCED WALLS Building the Future in the Euro-Mediterranean Area • Wall system classified as one of large lightly reinforced walls if. if just one wall. supporting together >20% of gravity load above (: sufficient no. large lightly reinforced walls: • preclude (collapse due to) storey mechanism. Workshop . • minimize nonstructural damage.27-29 November 2006. • If structural system does not qualify as one of large lightly reinforced walls. • Rationale: For large walls. minimum reinforcement of ductile walls implies: • very high cost. all its walls designed & detailed as ductile walls.5 s for fixity at base against rotation (: wall aspect ratio low) • Systems of large lightly reinforced walls: Æ only DC M (q=3). • flexural overstrength that cannot be transmitted to ground. Varese. in horizontal direction of interest: – at least 2 walls with lw>4 m. Varese. to minimise flexural • Shear verification for V from analysis times (1+q)/2 ~2: – If so-amplified shear demand is less than (design) shear resistance w/o shear reinforcement: No (minimum) horizontal reinforcement.27-29 November 2006. Workshop . crack width limited by deformation-controlled nature of response (vs.EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area DESIGN & DETAILING OF LARGE LIGHTLY REINFORCED WALLS overstrength. • If inclined cracking occurs. force-controlled non-seismic actions covered in EC2). Italy . even w/o min horizontal steel. • Vertical steel tailored to demands due to M & N from analysis – Little excess (minimum) reinforcement. mainly at construction joints). Reason: • Inclined cracking prevented (horizontal cracking & yielding due to flexure. g +ψ 2 q (4) ∑ M Rb l cl ± V o .min.26fctm/fyk.dfyd)(1) 2Φ14 (308mm2) As.min. 5 ) yd (1 + 0 . 0. 8 ν d ) f ctm 6 .75 ) f yd ρ max ρ max f ≤ 6 .5hw Longitudinal bars (L): 0. hw .s. 8 ν d ) ctm f yd - Transverse bars (w): 0. top & bottom As. 8ν d ) ctm f yd Building the Future in the Euro-Mediterranean Area DCL hw 0. 24dbw.2 ∑ M Rb l cl ± V o .5As. 5 (1 + 0 .08(fck(MPa))1/2/fyk(MPa)(0) 6mm 8dbL.bar crossing interior joint(3) dbL/hc . critical regions(1) As. 24dbw.25 (1 + 0 . outside critical regions(5) VRd.0018fcd/(μφεsy. critical regions bottom As.s. 225mm 4 6dbL.min. 25 (1 + 0 .s=bwzρwfywdcotθ.5VEmax Workshop . seismic(4) VRd.s=bwzρwfywdcotθ (5).13%(0) 0.bar anchored at exterior joint(3) (i) outside critical regions spacing sw≤ ρw≥ (ii) in critical regions: dbw≥ spacing sw≤ - f ≤ 7 .5: inclined bars at angle ±α As=0. with 1≤cotθ≤2. critical regions(5) 1 .04 - “critical region” length ρmin. top-span As. with cross-section As/direction & stirrups for 0.8ν d ) f ctm ≤ ≤ ρ' ρ' f (1 + 0 . h w . Italy .min.max=0. g +ψ 2 q (4) As in EC2: VRd.5 VRd.s=bwzρwfywd (θ=45o) As in EC2: VRd. with 1≤cotθ≤2.5 If VEmax/(2+ζ)fctdbwd>1: If ζ≡VEmin/VEmax(6) <-0.bottom-span/4(0) 7 .5 As in EC2: VRd.75d 0. with 1≤cotθ≤2. 5 (1 + 0 .27-29 November 2006. tension side ρmax.top(2) As.5VEmax/fydsinα to beam axis.EUROCODES Building the Future Detailing & dimensioning of primary seismic beams (secondary as in DCL) DCH DCM 1. Varese.top-supports/4 0. supports bottom dbL/hc .5fctm/fyk ρ’+0.3(1-fck(MPa)/250)bwozfcdsin2θ (5).max seismic (5) VRd. 175mm 4 Shear design: From the analysis for the “seismic design situation” VEd. is in addition to any compression steel that may be needed for the verification of the end section for the ULS in bending under the (absolutely) maximum negative (hogging) moment from the analysis for the “seismic design situation”. (3) hc is the column depth in the direction of the bar. As. Varese. MEd. for the algebraically minimum value of the axial load in the “seismic design situation”. Workshop . d-d1. (1) μφ is the value of the curvature ductility factor that corresponds to the basic value. (4) At a member end where the moment capacities around the joint satisfy: ∑MRb>∑MRc. VEmaxis the absolutely largest of the two values. MRb is replaced in the calculation of the design shear force. The Table gives the value recommended in EC2.minare the algebraically maximum and minimum values of VEd resulting from the ± sign.27-29 November 2006.EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area (0) NDP (Nationally Determined Parameter) according to EC2. Italy Footnotes . VEd. νd = NEd/Acfcd is the column axial load ratio.9d or to the distance between the tension and the compression reinforcement. qo. (6) VEmax. VE. and is taken positive in the calculation of ζ. by MRb(∑MRc/∑MRb) (5) z is the internal lever arm. the sign of VEmin is determined according to whether it is the same as that of VEmax or not. of the behaviour factor used in the design (2) The minimum area of bottom steel. with compression taken as positive.Table on detailing & dimensioning primary seismic beams (previous page) . taken equal to 0.min. 27-29 November 2006. 0.5(1-νd)]bwozfcdsin2θ. 2.bc).6m.2%(0) 4%(0) 8mm 2 DCL Building the Future in the Euro-Mediterranean Area Cross-section sides. bc). 175mm - - 0. 0. or uniaxial with (Mz/0.(5).5 Workshop .(8). N) ≤ 0. with 1≤cotθ≤2.bc).035 6mm.25m. bc ≥ “critical region” length (1) ρmin ρmax dbL≥ bars per side ≥ Spacing between restrained bars distance of unrestrained to nearest restrained bar Outside critical regions: dbw≥ Spacing sw ≤ sw in splices ≤ Within critical regions:(2) dbw≥ (3) sw≤ (3).7.3 ∑ M l cl ends Rc (11) 1 .55 ≤ 0. lc/5 0.max seismic (12).dbc/bo-0.7.1(1) 1. bc). dbL/4 20dbL.1Nd/Acfyd. Italy .08 30μφνdεsy. dbL/4 8dbL.4(fyd/fywd)1/2dbL 6dbL. bo/3.dbc/bo-0. (13) VRd.s seismic (12). lc/5 Longitudinal bars (L): 1% 4% 3 ≤150mm ≤200mm ≤150mm Transverse bars (w): DCM max(hc. 125mm 0.(5).3∑MRb≤∑MRc No moment in transverse direction of column Truly biaxial. (14) (10) 6mm. (13). hv/10 if θ=Pδ/Vh>0.(6).12 0. min(hc. 0.3(1-fck(MPa)/250)min[1.s=bwzρwfywdcotθ+NEd(h-x)/lcl(13) with 1≤cotθ≤2.035 1. N).6m.65 Shear design: 1 . Varese. (My/0. 0. hc.EUROCODES Building the Future Detailing & dimensioning of primary seismic columns (secondary as in DCL) ≥ DCH 0.08 30μφ*νdεsy.(7) In critical region at column base: ωwd≥ αωwd≥ (4).(9) Capacity design check at beam-column joints: Verification for Mx-My-N: Axial load ratio νd=NEd/Acfcd VEd seismic(11) VRd.1 ∑ M l cl ends Rc (11) From the analysis for the “seismic design situation” As in EC2: VRd. 240mm 6mm.5max(hc. 400mmm 12dbL.5 As in EC2: VRd.(4) ωwd≥ (5) αωwd≥ (4).6min(hc. bo/2.max=0. (1+νd).25.(6). 0. (12) z is the internal lever arm. (4) Index c denotes the full concrete section and index o the confined core to the centreline of the hoops. (5) ωwd is the ratio of the volume of confining hoops to that of the confined core to the centreline of the hoops. computed as α = αsαn.9d or to the distance between the tension and the compression reinforcement. (b) of the ground storey in twostorey buildings with axial load ratio νd not greater than 0. VEd. are taken with their most unfavourable value in the seismic design situation for the shear verification (considering both the demand. qo.27-29 November 2006. and the capacity. for bending within a plane parallel to the side of interest. MRc is replaced by MRc(∑MRb/∑MRc). the requirements on dbw. αn = 1 for circular hoops and αn=1-{bo/[(nh-1)ho]+ho/[(nb-1)bo]}/3 for rectangular hoops with nb legs parallel to the side of the core with length bo and nh legs parallel to the one with length ho. Workshop . and (d) in one-out-of-four columns of plane frames with columns of similar size. sw apply over a distance from the end section not less than 1. where: αs = (1-s/2bo)(1-s/2ho) for hoops and αs = (1-s/2bo) for spirals. (10) The capacity design check does not need to be fulfilled at beam-column joints: (a) of the top floor. (3) For DCH: In the two lower storeys of the building. (8) Note (1) of the Table for the beams applies. The Table gives the value recommended in EC2. (13) The axial load. (7) For DCH: at column ends protected from plastic hinging through the capacity design check at beam-column joints. and its normalized value. (9) For DCH: The requirement applies also in the critical regions at the ends of columns where plastic hinging is not prevented. times fyd/fcd. μφ*is the value of the curvature ductility factor that corresponds to 2/3 of the basic value.EUROCODES Building the Future (0) NDP (Nationally Determined Parameter) according to EC2. (6) α is the “confinement effectiveness” factor. at the ends of columns where plastic hinging is not prevented because of the exemptions listed in Note (10) below. the transverse reinforcement in critical regions of columns with axial load ratio νd not greater than 0. νd. (1) hv is the distance of the inflection point to the column end further away. of the behaviour factor used in the design. Italy Footnotes . (c) if shear walls resist at least 50% of the base shear parallel to the plane of the frame (wall buildings or wall-equivalent dual buildings). lc is the column clear length. (2) For DCM: Ιf a value of q not greater than 2 is used for the design. VRd). because of the exceptions listed in Note (10) below.d= fyd/Εs.5 times the critical region length. (14) x is the compression zone depth at the end section in the ULS of bending with axial load. μφ* is taken equal to μφ defined in Note (1) of the Table for the beams (see also Note (9) below). bois the smaller side of this core.Table on detailing & dimensioning primary seismic columns (previous page) Building the Future in the Euro-Mediterranean Area . Varese. taken equal to 0. d-d1. NEd. εsy.3 in all columns.2 may just follow the rules applying to DCL columns. (11) At a member end where the moment capacities around the joint satisfy: ∑MRb<∑MRc. 2% No boundary elements. dbL/4 min(20dbL. 250mm) Min(3bwo. but with required ρv≥0. αωwd.dbw/bo-0.2%. bwo≥ critical region length.2% Web: 0. Varese.5% wherever εc>0. 200mm.0035 200mm.25ρv)(0) 8mm bwo/8 min(25dbh.confining hoops (w) (2): dbw≥ spacing sw≤(3) ωwd≥(2) αωwd≥(3).035 as is critical region.2%(0) - 0.EUROCODES Detailing & dimensioning of ductile walls (cont’d next page) DCH DCM max(150mm.08 6mm.thickness bw over lc ≥ . elsewhere ρv≥0. bwo 400mm)(0) - 30μφ(νd+ ων)εsy.1%. design moments from linear envelope of maximum moments From analysis for “seismic MEd from analysis for the “seismic design situation”. 2 hstorey) if wall > 6 storeys Boundary elements: 0.15lw.35 ≤0. if lc≤ max(2bw. 1. hstorey/20) ≥ max(lw. ωwd reduced by 50% elsewhere ρv≥0. lw/5).max dbν≥ dbv≤ spacing sv≤ .(4) b) storey above critical region c) over the rest of the wall: . length over which εc> 0. 250mm) 0. hstorey) if wall ≤6 storeys ≤ min(2lw.2%(0) if ρL over Ac=lcbw >2%: apply DCL rule for ρL>2% 0.vertical reinforcement: ρmin over Ac=lcbw ρmax over Ac .2%.5% 4% 8mm min(25dbh. Italy .length lc from edge ≥ .horizontal bars: ρhmin dbh≥ dbh≤ spacing sh≤ axial load ratio νd= NEd/Acfcd Design moments MEd: where ρL>2% 0. Hw/6) (1) ≤ min(2lw. 250mm) 400mm ≤0. hst/10.2% 4% 8mm bwo/8 min(25dbv.min ρv.27-29 November 2006.5% wherever εc>0.vertical bars (v): ρv. shifted up by the design situation” “tension shift” al Workshop . ρv≥0. 400mm) 0. hst/15.5bw.2% max(0.4 If Hw/lw≥2. if lc>max(2bw. hcr≥ DCL - a) in critical region: .12 (0) Building the Future Building the Future in the Euro-Mediterranean Area Web thickness. lw/5) 0. 0. 25fyd.s=bwo(0. 1.1⎜q S (T ) ⎟ ≤ q Edo⎠ ⎝ ⎝ e 1 ⎠ Design shear force in walls of dual systems with Hw/lw>2.3 f ctd − Ed Ac 0. ρh from VRd. with 1≤cotθ≤2.s in critical region.s=VRd. web reinforcement ratios.min.EUROCODES Building the Future Detailing & dimensioning of ductile walls (cont’d from previous page) DCH Shear design: DCM DCL Building the Future in the Euro-Mediterranean Area Multiplicative factor ε on the if H /l ≤2(5): ε=1.0 ⎛ 0.5 40% of EC2 value As in EC2 As in EC2: VRd.8lw)ρh fywdcotθ with 1≤cotθ≤2.s: (ii) if αs<2: ρh from VRd.8lw)ρh fywdcotθ with 1≤cotθ≤2. for z between Hw/3 and Hw: (7) VRd.5 As in EC2: VRd.max in critical region VRd.5 − ⎟εVEd⎜ w ⎟ − VEd(z) = ⎜ ⎜H ⎟ ⎜ Hw ⎟ ⎝ 3⎠ ⎝ w 4⎠ ⎝ ⎠ From analysis for “seismic design situation” As in EC2: VRd.5 Workshop .min at construction joints (9).8lw)ρh fywdcotθ with 1≤cotθ≤2.5 VRd.0025 .2 M ⎟ + 0.8lwbwo) VRd.5 f cd f yd As in EC2: VRd.3(1-fck(MPa)/250)bwoxfcd N 1. f yd + 1.(11) ε=1. Varese. ρh.c+bwoαs(0. Italy .27-29 November 2006. (6): w w analysis for “seismic design 2 2 situation”: ⎛ MRdo⎞ ⎛ Se(TC ) ⎞ ⎟ ⎜ ⎟ ε= ⎜ ⎜1.3(1-fck(MPa)/250)bwo(0.5z ⎞ ⎛H ⎞ ⎟εVEd(0) + ⎜1. ρν (i) if αs=MEd/VEdlw≥2 : ρν=ρv.2MRdo/MEdo≤q w w shear force V’Ed from the if H /l >2(5).s: (8) ρv from: (9) Resistance to sliding shear: via bars with total area Asi at angle ±φ to the horizontal (10) ρv.3(fydfcd)1/2)+ 0.max=0.5 ε=1.8lw)fcdsin2θ.75lw)ρhfyhd ρνfyvd ≥ ρhfyhd-NEd/(0.75z 1⎞ ⎛ 1.s outside critical region VRd.s=bwo(0.max outside critical region VRd.s=bwo(0.s =Asifydcosφ+ Asvmin(0. Table on detailing & dimensioning ductile walls (previous pages) ⎧ NEd ⎫ 0. if the minimum value is negative (tension). (6) Se(T1) is the value of the elastic spectral acceleration at the period of the fundamental mode in the horizontal direction (closest to that) of the wall shear force multiplied by ε. MRdo is the design value of the flexural capacity at the wall base for the axial force NEd from the analysis for the same “seismic design situation”.05/γc is the design value of the (5%-fractile of) tensile strength of concrete. The Table gives the value recommended in EC2. (4) μφ is the value of the curvature ductility factor that corresponds to the product of the basic value qo of the behaviour factor times the value of the ratio MEdo/MRdo at the base of the wall (see Note (5)). the waiver applies also if this value of the wall axial load ratio is νd≤0.0.27-29 November 2006. 35 1+ fck ⎥⎜1+ f 0 .15. VRd. (10) Asv is the total area of web vertical bars and of any additional vertical bars placed in boundary elements against shear sliding. (1) lw is the long side of the rectangular wall section or rectangular part thereof. (6) of the Table for columns apply for the confined core of boundary elements.2 ⎞ 1/ 3 ⎪ ⎡180 ⎪ 1/ 3 ⎜ ⎟ ⎢ (100 + VRd.c=0.c (in kN) is given by: Footnotes . x is the depth of the compression zone. NΕd in kN. (2) For DC M: If for the maximum value of axial force in the wall from the analysis for the “seismic design situation” the wall axial load ratio νd= NEd/Acfcd satisfies νd ≤ 0. the DCL rules may be applied for the confining reinforcement of boundary elements.c = ⎨min ρL ) . hstorey is the storey height.d= fyd/Εs. (8) For bw and d in m.2 1/ 6 ⎤⎛ 0. VRd. . (5) MEdois the moment at the wall base from the analysis for the “seismic design situation”. εsy. Workshop . 15 ⎬bwd ck ⎟ A γ d d ⎥ c ⎪ ⎪ ⎠ ⎦⎝ ⎣ c ⎩ ⎢ ⎭ NEd is positive for compression and its minimum value from the analysis for the “seismic design situation” is used. (9) The minimum value of the axial force from the analysis for the “seismic design situation” is used as NEd (positive for compression). (5). Se(Tc) is the spectral acceleration at the corner period TC of the elastic spectrum. Varese.2 but the value of q used in the design of the building is not greater than 85% of the q-value allowed when the DC M confining reinforcement is used in boundary elements.EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area (0) NDP (Nationally Determined Parameter) according to EC2. Hwis the total height of the wall. fck in MPa. (7) A dual structural system is one in which walls resist between 35 and 65% of the seismic base shear in the direction of the wall shear force considered. z is distance from the base of wall. ωνd is the mechanical ratio of the vertical web reinforcement. (3) Notes (4). ρL denoting the tensile reinforcement ratio. Italy (11) fctd=fctκ. Italy . Varese.EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area STRUCTURE OF EN1998-1:2004 1 2 3 4 5 6 7 8 9 10 General Performance Requirements and Compliance Criteria Ground Conditions and Seismic Action Design of Buildings Specific Rules for Concrete Buildings Specific Rules for Steel Buildings Specific Rules for Steel-Concrete Composite Buildings Specific Rules for Timber Buildings Specific Rules for Masonry Buildings Base Isolation Workshop .27-29 November 2006. thickness.EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area MASONRY BUILDINGS Mainly for regions of rather low-seismicity. aspect ratio in plan & deviation of plan from rectangular envelope. as function of PGA. instead of single values) other than those per EC6 alone. Nationally Determined Parameters (NDPs) for national flexibility: • Allowable type of masonry units & of perpend joints • Min. horizontal area of walls. no. – max height of openings relative to wall length. – max. Varese. – Max. – Max. • Max. difference of mass & wall X-section between adjacent storeys. strength of masonry units & mortar. slenderness (height-to-thickness). • Geometric limitations for shear walls: – min. • q-factor values for all types of masonry buildings (ranges given. PGA for use of unreinforced masonry w/ EC6 alone. Workshop . Italy .27-29 November 2006. or w/ EC8. of storeys & min. • Conditions for design w/o detailed calculations (rules for “simple masonry buildings”): – Max. 5) Confined masonry.5 .1g): q=1.05% & ρv> 0.15g): q (NDP) = 1. Reinforced masonry.5 (recommended: q=1.27-29 November 2006. Workshop .3 (recommended: q=2). w/ ρh> 0. w/ horizontal RC belts (As>200mm2) at <4m centres (not recommended for PGA at site > 0. Italy • .5 Unreinforced masonry.2.5). w/ horizontal RC belts > 0.08% (plus vertical steel w/ As>200mm2 at <5m centres & at wall intersections or free edges): q (NDP) =2. Varese.15 m (As>300mm2 or 1%) at <4 m centres and similar vertical ones at <5 m centres & at wall intersections & edges of large openings: q (NDP) = 2 .EUROCODES Building the Future Building the Future in the Euro-Mediterranean Area MASONRY BUILDINGS (cont’d) Types of masonry for EQ-resistance: • • • Unreinforced masonry per EC6 alone (not recommended for PGA at site > 0.5 .3 (recommended: q=2.15x0.
Report "Design of Buildings for Earthquake Resistance According to Eurocode 8 - Part 1"