Bulletin of Earthquake Engineering (2024) 22:4477–4513
https://doi.org/10.1007/s10518-024-01931-y
ORIGINAL ARTICLE
Comparative application to RC buildings of the two
generations of Eurocodes and proposals for seismic design
Michael N. Fardis1
· Telemachos B. Panagiotakos2
Received: 23 February 2024 / Accepted: 8 May 2024 / Published online: 22 May 2024
© The Author(s), under exclusive licence to Springer Nature B.V. 2024
Abstract
Three concrete buildings with six storeys above ground and two basements have been
designed in detail according to the first generation of Eurocodes 2 (including structural fire
design) and 8, as well as the official drafts of their second generation counterparts as of the
end of 2023. In one horizontal direction the buildings have a wall-, frame-equivalent-dualor frame-lateral-load-resisting system; in the other, the first two buildings have a wall-system and the third a wall-equivalent-dual. The design seismic action is in all cases according
to the current generation Eurocode 8, scaled to a peak ground acceleration on rock of 0.2
or 0.3 g. Seismic design is for ductility class (DC) Medium (M) of the current generation
or DC 3 of the new one, which have the same behaviour factors, q, in all structural systems
considered; so, in each building seismic action effects from the analysis are the same for
the two Eurocode generations. All designs are assessed through nonlinear response history analysis (NLRHA), carried out according to the pertinent Eurocode 8 rules. Designs
according to the second generation meet the performance goals of Eurocode 8 much better
and transparently than with the first generation, but use markedly larger steel quantities and
indeed often unnecessarily so, especially for confining reinforcement—which sometimes
comes out in quantities that cannot be placed. Proposals are made for a more rational linkage of local ductility demands with the q-factor and implemented in alternative second
generation designs. Minor changes to the new generation’s design/detailing rules for ductile walls are also proposed and implemented in these alternative designs; they prove only
partially effective in resolving certain deadlocks originating from poorly justified detailing
rules that produce unnecessary and counterproductive wall flexural overstrengths. The new
generation Eurocode 8 lacks design rules for the free height of ductile walls within rigid
basements, which is a weak link, very likely to fail under the high shear force which balances the wall’s moment resistance at the top of the rigid basement. NLRHA confirms that
the alternative provisions proposed for second generation Eurocode 8 give more cost-effective designs than the first generation, with better overall performance at about the same or
even lower cost.
Keywords Eurocode 8 · Nonlinear response history analysis · RC buildings · Seismic
design · Seismic performance
Extended author information available on the last page of the article
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1 Introduction
Structural design codes aim at balancing safety and serviceability with economy. Society
may not be conscious of the safety level aimed at by codes—which is often difficult to
quantify and of relative, rather than absolute, value—but is aware of the average cost level
implied and accepts it, expecting it to drop with every new generation of codes thanks to
advancements in knowledge. Moreover, the imperatives of sustainable use of resources,
minimization of C
­ O2-emissions and energy savings (e.g., the requirement for high LEED
certification of new buidings) put nowadays pressure on engineers to design structures that
meet codes with less materials. New codes should support designers in that task.
The construction sector and the structural design profession do not welcome radical
change in design codes. They expect their revision to take place gradually, incrementally
and at frequent time-intervals. In this respect, 18 years between the dates of withdrawal
of standards conflicting to the first two generations of Eurocodes (2010 to 2028) is a long
period and, naturally, brings major advancements in State-of-the-Art. It is the duty of
experts and organisations who develop the second generation to let European society and
citizens enjoy the fruits of this advancement. And, indeed, this is happening, but unavoidably leads to longer texts and, often, major differences from the first generation. Nevertheless, as the first generation of Eurocodes has not fully penetrated yet design practice, it is
hoped that radical change in some Eurocodes will not unduly incovenience the construction industry and the design profession. Provided, of course, that the second generation
will promote cost-effective and easily implementable solutions. It is noted that ease-of-use
is not limited to clarity, ease of navigation and consistency of code contents; it concerns
also ease of implementation—constructability. However, in the absense of systematic trial
applications, this cannot be taken for granted.
As soon as all second generation Eurocodes needed for the design of a certain type of
structure with a specific material reach their final draft stage, they should be applied alongside their counterparts in the previous generation to design typical structures, in order to
check cost-effectiveness and ease-of-use/implementation of the new generation. This has
been done for earthquake resistant concrete buildings at least, during the work for the first
generation of Eurocodes before its drafts were final (e.g., Fardis and Panagiotakos 1997;
Panagiotakos and Fardis 1998, 2004). The present work aspires to contribute to a similar
effort for concrete buildings designed for earthquake and all other relevant actions according to the current drafts of the second generation, namely FprEN1992-1-1:2023 (CEN/
TC250/SC2 2023a) for concrete structures, FprEN1991-1-2:2023 (CEN/TC250/SC1
2023b) and FprEN1992-1-2:2023 (CEN/TC250/SC2 2023b) for their structural fire design
and FprEN1998-1-1:2023 (CEN/TC250/SC8 2023a), prEN1998-1-2:2022 (CEN/TC250/
SC8 2022) for seismic design, as well as their counterparts of the first generation: EN19921-1:2004 (CEN 2004a), EN1991-1-2:2002 (CEN 2002), EN1992-1-2:2004 (CEN 2004b)
and EN1998-1:2004 (CEN 2004c). It is hoped that there is still time for Part 1–2 of Eurocode 8 to take into account the findings and main conclusions of this work.
The rules of both generations of Eurocodes—called herein Generation 1 and Generation 2—have been implemented in a computational platform for fully-automated, cloudbased detailed design of concrete buildings, including assessment of seismic performance
with nonlinear response-history analysis (NLRHA). The scope covers Ultimate Limit State
(ULS) design for resistance and ductility for seismic and non-seismic actions, Serviceability Limit State (SLS) design for quasi-permanent or frequent actions and fire rating of elements under the three types of fire defined in Eurocodes. It covers columns of rectangular,
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circular, L- or T-section, beams and foundation beams with or without flanges at top and/
or bottom, walls of rectangular, L-, or U-section, beam-column connections, rectangular
footings and the underlying soil, and storey- or multi-storey-deep perimeter walls of basements. Any layout in plan or elevation is treated.
Strong interdependency of different phases of detailed design of the same or different members or member types in Eurocode 8 prevents sequential, member-by-member, seismic design.
A single, integrated module for the design of the entire building (all members and member
types) in one shot is essential. This is convenient for users but a major challenge for the programmer. Needless to say, design by hand calculations, without a computer code is impossible,
even for the simplest building (a single-storey building, with one-bay-per direction).
2 The example buildings for the application: definition, analysis
and design
Three versions of a building are designed. All have six storeys above ground and two basements below, larger in-plan than the six storeys above (see Figs. 1, 2, 3 and 4).
• A version called “Wall” building has in both horizontal directions a (uncoupled) wall
system. It has been intentionally chosen essentially the same—with minor increase in
the size of perimeter columns—as the building used as example in Bisch et al (2012)
and Fardis et al (2015).
• At the other extreme, a version termed “Frame” building has a frame system in one
horizontal direction, and a wall-equivalent dual (at the margin of a frame-equivalent
dual one) in the other.
• The intermediate version, called for convenience “Dual” building, has a wall-equivalent
dual system in one direction and a (uncoupled) wall system in the other.
The “Wall” building has 300 × 600 mm rectangular perimeter columns (300 × 500 mm at
corners), 500 mm-square interior ones, four 4 m-long rectangular ductile walls and a U-shaped
one with a 3.6 m-long web and two 1.8 m-long flanges (Fig. 2). One of the objectives of the
two other building configurations is to apply both Eurocode generations to vertical members of
various cross-sectional shapes. So, the “Frame” building has 600 mm-diameter circular interior
columns, 600 × 600 × 300 mm L-shaped corner columns and 1100 × 600 × 300 mm T-shaped
perimeter columns (with the 1100 mm flange on the perimeter); its ductile walls are rectangular, 1.7 m-long on the perimeter and 1.6 m- or 2.4 m-long near the centre in plan. The “Dual”
building has columns similar to those of the “Frame” building, two 3 m-long rectangular ductile walls on the perimeter, two 3.2 × 1.3 m L-shaped ones near the centre and a U-shaped wall
nearby with a 3.2 m-long web and 1.3 m-long flanges; the three interior walls do not qualify as
walls in the weak direction, as their section is compact in that direction (see Figs. 3 and 4). All
walls of the three buildings are 300 mm-thick.
Slabs are 180 mm thick, beams are 500 mm deep and 300 mm wide. Basement perimeter walls are 250 mm thick, with 1.15 m wide and 300 mm deep foundation strips. The
six columns closest to the perimeter have a concentric 2 m-square, 1 m deep footing.
In the “Dual” or “Wall” buildings the two columns closest to the centre in plan and the
three nearby walls are supported on a 7 × 9 m, 0.8 m-deep common footing, centred at
the point of application of the resultant of vertical forces and moments at the bottom of
the common footing under the gravity loads acting in the seismic design situation. In the
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Fig. 1 Elevation of typical building
“Frame” building these two closest to the centre columns have a 1.5 m-square footing,
the two 1.6 m long rectangular a 2.5 × 1 m one and the 2.4 m long wall a 3.5 × 1 m footing, all 1 m-deep. A lightly reinforced concrete slab between the perimeter footing strip
and the footings inside the plan provides horizontal connection and rigid diaphragm
action at the level of the foundation.
Member sizes are kept the same across all design options and Eurocode 8 versions
considered, as well as in all storeys. Only the reinforcement is optimized in each case
and at each member, within the constraints posed by the Eurocodes.
The building is assumed to be in an environment of moderate humidity and water saturation without deicing salts or airborne chlorides but with possible freezing, corresponding to exposure class XC3, X0 and XF1 for carbonation, chloride-induced corrosion and
freeze–thaw cycles, respectively. Exterior parts below grade and foundations are taken to
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Fig. 2 Framing of basement and of typical storey above ground in “Wall” building
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Fig. 3 Framing of basement and of typical storey above ground in “Dual” building
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Fig. 4 Framing of basement and of typical storey above ground in “Frame” building
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be in contact with natural soil, corresponding to exposure class XA1 for chemical attack.
Concrete class is C30/37, the minimum recommended in the pertinent annex of EN19921-1 in either generation of Eurocodes for all these—quite mild—exposure conditions.
A 50 year design life is specified, for which the Structural Class recommended in
EN1992-1-1:2004 is S4. Under these conditions, and with the 10 mm deviaton of cover
recommended in both generations of EN1992-1-1, Generation 1 gives a nominal cover of
reinforcing bars of 35 mm. To maintain the same cover in Generation 2, exposure resistance class to carbonation is chosen to be XRC 3. The exposure resistance class for chloride-induced corrosion does not affect cover if exposure class to chlorides is X0. If moderate water saturation without deicing salts but with airborne chlorides (exposure class
XD1) had been specified alongside exposure resistance class to chlorides XRDS 2, the
cover required by EN1992-1-1 in Generation 2 wouldn’t have increased any further. However, exposure class XD1—which is quite moderate for chlorides–would have required a
cover of 45 mm according to EN1992-1-1:2004, heavily penalizing the effectively confined
core in the 300 mm thick concrete members of the present applications. It is noted that
FprEN1992-1-1:2023 repeats in Informative Annex P the EN1992-1-1:2004 approach to
durability and cover and allows adopting it nationally, instead of the more elaborate new
approach of Generation 2. It is noted that the requirements and the approach for durability
can seriously impact the density of confinement reinforcement for earthquake resistance,
as cover controls the volume of the effectively confined core of moderately thin members.
As the present work focuses on differences in the design and detailing rules of Generations 1 and 2 of the Eurocodes for concrete buildings, design to either one should use the
same design seismic action effects from the analysis, no matter the different definition of
the design seismic action in the two generations. So, the design to Generation 2 uses the
same seismic action effects as design to Generation 1, derived from the Type 1 Spectrum
recommended in EN1998-1:2004 for buildings of ordinary importance on Ground Category B (stiff soil). Two values of the design peak ground acceleration on rock (PGA) are
used: 0.2 and 0.3 g. Ductility Class Medium (DC M) is used for Generation 1 of Eurocode
8 and Ductility Class 3 (DC 3) for Generation 2. All structural systems used in the three
version of the building have the same q-factors across the two generations:
• 3.0 for wall systems,
• 3.6 for wall-equivalent dual
• 3.9 for frame- or frame-equivalent dual systems.
It is noted that design to DC M has dominated so far application of Generation 1 of
Eurocode 8 in practice, as Ductility Class H (DCH) is much harder to apply, especially to
ductile walls. In Generation 2 DC 2 differs from DC 3 more in the values of behaviour factors than in the design and detailing rules; so, DC 3 appears to be more attractive for future
application, not only for high seismicity, but for moderate as well. Therefore, for concrete
buildings, DC M and DC 3 seem to be the core of the respective generations of Eurocode 8.
Table 1 summarizes the rules of the two generations for design in DC M and 3.
Tables 2, 3 and 4 give an overview of detailing provisions for beams, columns or ductile
walls, respectively, in these two Ductility Classes.
Further specifications for the design of the buildings are as follows:
• Steel is grade 500 and Class C.
• The characteristic value of live loads on slabs is 2 kN/m2 while floor finishings and partitions are taken to add another 2 kN/m2 of uniform floor loads.
13
Generation 2-DC 3
Concrete class
≥ C16/20
≥ C20/25
Steel grade and class
400 to 600, B or C
400 to 700, B or C
Any ULS, according to EN1992-1-1:2004
Factor included in design compression
1.0
min(1; 40/fck (MPa))1/3
strength fcd
ULS in shear, according to EN1992-1-1:2004
Angle θ of compression field to member axis 1.0 ≤ cotθ ≤ 2.5
ν = 0.6 (1– fck(MPa)/250)
Reduction factor on fcd in compression field
ν = 1/[1 + 110(εx + (εx + 0.001)cot2θ)]; simplification ν = 0.5
due to longitudinal tensile strain εx at section mid-depth
Shear resistance
min[0.5νfcdbwzsin2θ; ρwfywdbwzcotθ + zN/2lV]a
min[0.5νfcdbwzsin2θ; ρwfywdbwzcotθ + zN/2lV]a
If shear span lV = M/V ≥ zcotθ
If shear span lV = M/V < zcotθ
min[0.5νfcdbwzsin2θ; νfcdbwzsin2θ(cotθ-lV/z) + ρwfywdbwlV + zN/2lV]a
Design for the ULS in shear in the seismic design situation, according to EN1998-1:2004 or FprEN1998-1-1:2023
Factor on strength νfcd of compression field
1.0
1/1.6
Factor γRd on moment resistance of plastic hinge(s) for capacity design shears
Beams
1.0
1.1
Columns
1.1
Walls
1.2
Moment resistance of beam’s end sections in seismic design situation
Slab width on each side of supporting column 2hf or 0 at end columns with or without crossbeam,
25% of clear span, but not beyond slab’s transverse half-span or edge
or wall contributing to tension chord of
plus 2hf at interior ­columnsb
beam
Column design axial force due to design seismic action
Amplification factor on axial force from
1.0
2.0
analysis
Materials
Generation 1-DC M
Table 1 General rules for ULS design in Ductility Class M of Generation 1 of the Eurocodes and 3 of Generation 2
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Generation 1-DC M
Generation 2-DC 3
13
w
w
–
Se(T1) and Se(TC): elastic spectral acceleration at the fundamental and the corner period; q: behaviour factor in the horizontal direction of the shear force
lw: longest dimension of wall section along the seismic shear force considered; Hw: total height of wall, from the top of a rigid basement or the foundation
d
c
hf: thickness of slab serving as flange of a beam
bw and z: width of web and internal lever arm of member subjected to shear; ρw and fywd: ratio and design strength of transverse reinforcement
1.1MRd(z = 0)/Htot,basement
b
a
Design shear in basement of total height
Htot,basement
Design shear in slender wall of dual system
(
)
(
) (
) (
)
VEd (z) = 0.75z∕Hw − 0.25 𝜀(0)VE (0) + 1.5 − 1.5z∕Hw 𝜀 Hw ∕3 VE Hw ∕3 for Hw/3 ≤ z ≤ Hw
w
w
w
Axial load ratio in seismic design situation
≤ 0.65
≤ 0.55
N/Acfcd
Design of ductile walls for the ULS in flexure or shear in the seismic design situation, according to EN1998-1:2004 or FprEN1998-1-1:2022
Axial load ratio in seismic design situation
≤ 0.4
≤ 0.35
N/Acfcd
Design moment at elevation z above basement Linear envelope of moments from analysis for seismic Linear envelope of moments from analysis for seismic design situdesign situation, ME(z)
top, MEd(z), before shifting up by “tension
ation and of γRd × moment resistance at wall base, MRd(z = 0);
shift” 0.5zcotθ
γRd = 1.2
√(
)2
( ( ) ( ))2
Amplification factor ε(z) at elevation z on
ε(z) = 1.5
ε(z) =
𝛾Rd MRd (z = 0)∕ME (z = 0) + m(z) qSe TC ∕Se T1 d
shear force VE(z) of slender wall (Hw/lw > 2)
from analysis for design seismic ­actionc
m(z) = 0.1 if z ≤ H /3; 0.05 if H /3 ≤ z ≤ 2H /3; 0.25 if 2H /3 < z ≤ H
Table 1 (continued)
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b
φy: yield curvature (at steel yielding, in section analysis); fym = 1.15fyk, fywm = 1.15fywk: mean yield stress of reinforcement (MPa); fcm(MPa) = fck(MPa) + 8
g
b, h: section width and depth; bo, ho: width and depth of confined core, defined by centreline of perimeter hoop
Value may be reduced by 10 or 20%, if ductility class B or C steel is used, respectively
h
f
dbL: minimum diameter of all top and bottom longitudinal bars within critical region
Nationally Determined Parameter according to FprEN1992-1-1:2022; the choice recommended therein is given
e
d
in Generation 1: μϕ: curvature ductility factor corresponding to basic value of behaviour factor applicable; εyd = fyd/Εs
ρ’: steel ratio at opposite side of section
≥ 0.08√fck(MPa)/fyk(MPa) f
No limit
Such that (θy + θupl/2)/1.35 ≥ qθy/1.5; with θy = φy(lV + z)/3 + 0.001
9(1 + h/1.6lV) + φydbLfym/8√fcm; g
θupl = 0.0205 min(9; lV)0.35 min(50; fcm)0.1(ρ’/ρ)0,2524aρhfywm/fcm g
where: a = (1−sh/2bo) (1−sh/2ho) (1−bo/6ho−(ho−hf)/3bo) h
8dbL e, h/4, 24 dbw
8dbL, h/4, 24 dbw, 225 mm
0.75 d
dbL/4 d, 6 mm
–
–
0.5fctm/fyk; sufficient for moment resistance ≥ cracking moment
ρ’ + 0.015-fyk/50000 if fck ≤ 25 MPa; ρ’ + 0.028−fyk/25000 if
25 < fck(MPa) < 50; ρ’ + 0.035−fyk/20000 if fck ≥ 50 MPa
6 mm
0.25 As,bottom-span
0. 5 As,top
0.25 As,top-supports
2Φ14 (308 ­mm2)
ρ’ + 0.0018fcd/(μϕεydfyd) c
0.5fctm/fyka
h
Generation 2-DC 3
fctm (MPa) = 0.3(fck(MPa))2/3 (fctm(MPa) = 1.1(fck(MPa))1/3 for fck > 50 MPa in Generation 2): mean tensile strength of concrete; fyk(MPa): nominal yield stress of bars
C
b
a
Mean effective mech. ratio of ties aρhfywm/fcm, in critical
regions
Steel ratio of ties ρh = Ash/bwsh d
Outside critical region
In critical regions
Spacing of ties, sh ≤
Tie diameter dbw ≥
Transverse reinforcement
As,bottom at supports ≥
As,bottom in critical regions ≥
As,top in span ≥
As top and bottom ≥
ρ = As/bd in critical regions ≤
ρ = As/bd at tension side ≥
Longitudinal reinforcement
Critical region length at beam end
Generation 1-DC M
Table 2 Detailing of beams in Ductility Class M of Generation 1 of the Eurocodes and 3 of Generation 2
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Table 3 Detailing of columns in Ductility Class M of Generation 1 of the Eurocodes and 3 of Generation 2
Generation 1-DC M
Critical region length at column ends
Longitudinal reinforcement
Steel ratio ρ = As/Ac
Number of bars per side
Spacing of bars which are restrained by tie
corner or hook
Unrestrained bars between
Number
two restrained ones
Distance to
restrained bar
Lap splice length
Transverse reinforcement
Tie spacing sw ≤
In critical regions
Outside critical region
At lap splices outside
Tie diameter dbw ≥
In critical regions
Outside critical region
Design value of tie mechan. volume ratio in
critical regions ωwd ≥ b
Design value of effective mech. volume ratio,
aωwd, in critical region over basement top ≥ e
Mean value of effective mech. volume ratio of
ties, aρwfywm/fcm, in critical regions
a
b
c
Generation 2-DC 3
≥ h, b, 0.45 m, Hcl/6 a
≥ 1%
≤ 4%
≥3
≤ 200 mm
–
≤ 150 mm
≤1
1.5 × anchorage
length
1.2 × anchorage length
8dbL, bo/2, 175 mm
20dbL, h, b, 400 mm
if dbL > 14 mm, 60%
of values outside
critical region
6 mm, dbL/4
6 mm, dbL/4
–
30μϕνdεydb/bo
−0.035
No limit
15dbL, h, b, 300 mm
dbL/4
0.05
–
So that (θy + θupl/2)/1.35 ≥ qθy/1.5
with c θy = φy(lV + z)/3 + 0.0019(
1 + h/1.6lV) + φydbLfym/8√fcm
θupl = 0.0205 min(9;lV)0.35
min(50;fcm)0.1(ρ’/(ρtotρ’))0.250.2N/bhfcm24aρhfywm/fcm
where: a = (1−sw/2bo) (1−sw/2ho)
(1−bo/(3(nb−1)ho)−ho/
(3(nh−1)bo)) d
h, b, Hcl: column sides and clear length
ωwd: volume ratio of confining hoops to confined core (to centerline of perimeter hoop) times fywd/fcd
See footnote (7) of previous table
d
a: confinement effectiveness of rectangular hoops at spacing sw, with nb legs parallel to side of core with
length bo and nh legs parallel to side of length ho
e
μϕ: curvature ductility factor corresponding to basic value, qo, of behaviour factor; εyd = fyd/Εs
• Any masonry infills present are assumed not to interact structurally with the structural
system.
• Calcareous aggregates are considered for concrete with maximum grain size 16 mm;
• For creep calculations:
• Relative humidity 70%,
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• Normal hardening cement,
• Average temperature of concrete during maturing: 20 °C,
• Age of beams’ concrete at loading by permanent loads of floors: 10 days,
• Soil is taken to be clay with:
• Design value of undrained shear strength cud = 500 kPa (reduced to 450 kPa in the
seismic design situation),
• Design value of friction angle φd = ­20o,
• Design value of drained cohesion cd = 50 kPa,
• Weight density 21 kN/m3.
These properties are consistent with the characterisation as Ground type B per EN19981:2004 for the definition of the seismic action at the top of the ground.
• Ground surcharge for soil bearing capacity calculations is taken to be 25 kN/m2,
• Additional concrete cover for bars in concrete cast against prepared ground is taken as
40 mm;
• Chi-factor for calculation of design seismic action effects on the ground according to
FprEN1998-5:2023: 1.25.
Gravity loads on floors are applied on beams or perimeter basement walls as uniform
line loads, with magnitude determined by elastic Finite Element Analysis of the slabs of
each floor, considered to be continuous over beams, columns or walls, with the supporting
nodes taken as vertically fixed but free to rotate about horizontal axes.
Linear elastic analysis is carried out separately for permanent and imposed gravity
loads, the horizontal components of the design seismic action and their accidental eccentricities (always considered, even though they are in most cases smaller than the natural
ones). Response spectrum modal analysis is used for the 5%-damped horizontal design
spectrum of Generation 1 of Eurocode 8. Prismatic elements are used to model members,
with their length within the connections to other members taken as rigid. Beams are modelled with constant effective slab width along their elastic length, as specified in Eurocode
2. Perimeter walls of the basement are modelled as horizontal prismatic elements with centreline at the level of the basement’s roof (bottom of the ground storey); they have intermediate modelling nodes at a spacing Lj of (about) 1 m, connected vertically to Winkler
springs placed at the underside of the strip footing and modelling the vertical compliance
of soil. This connection is implemented through fictitious elements with horizontal stiffness as vertical cantilevers equal to the in-plane shear stiffness of the associated part of
the wall, GtLj/h, where h and t are height and thickness of the perimeter wall. If these
fictitious elements have also thickness t, their cross-sectional dimension Hj in the plane of
the wall is determined from the condition 3EtHj3/(12h3) = GtLj/h (E and G are the Elastic
and Shear Moduli of concrete). The horizontal elements connecting the modelling joints at
the level of the roof of the basement have the vertical cross-section of the perimeter wall
(6.4 m-deep. 0.25 m-wide, with a 1.15 m-wide footing strip at the bottom and the effective
slab width according to Eurocode 2 at the top). The default value of 50% the uncracked
gross section stiffness allowed in both generations of Eurocode 8 is used in all these linearelastic analyses.
Table 5 lists values of variables or parameters from the linear-elastic analysis for the
design of the buildings. The characterisation as “Wall”, “Dual” or “Frame” reflects the
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if N/Acfcd > 0,15 in seismic design situation
Spacing, sw ≤
Design mech.vol. ratio ωwd
Design effective mech. volume ratio, aωwd ≥
if N/Acfcd ≤ 0,15
≤ 4bw from end section sw ≤
> 4bw from end section sw ≤
Boundary elements above critical height
Length lc from wall edge ≥
Distance of unrestrained bar to restrained
Confining hoops diameter, dbw ≥
Confining hoops
Diameter, dbw ≥
Mean effective mech. volume ratio aρwfywm/fcm
Spacing of vert. bars restrained by tie corner or hook
Unrestrained bars between two restrained
Boundary elements in critical height
Length lc from wall edge ≥
Thickness bw over lc ≥
Vertical bar ratio over boundary element area Ac = lcbw
Critical region height, hcr
≤1
≥ 1%
9dbL, 6bw, 180 mm
15dbL, bw, 300 mm
12dbL, 0.6b.o, 240 mm
20dbL, bwo, 400 mm
Wherever ρL > 2%
≤ 150 mm
6 mm, dbL/4
–
–
–
–
6 mm
So that (θy + θupl/2)/1,35 ≥ qθy/1,5; with
θy = φy(lV + z)/3 + 0,0011(1 + h/3lV) + φydbLfym/8√fcm;
θupl = 0.012 min(9;lV)0,35 min(50;fcm)0,1(ρ/(ρtot-ρ))0,25 0.2N/bwlwfcm ­24aρwfywm/fcm
where: a = (1-sw/2bo) (1-sw/2lco) (1-bo/(3(nb-1)lco)-lco/(3(nh-1)bo))
0.15lw, 1.5bw, part of section where εc > 0.0035
0.2 m; hstorey/15 if lc ≤ max(2bw, lw/5), hstorey/10 otherwise
≥ 0.5%
≤ 4%
≤ 200 mm
–
≤ 150 mm
8dbL, bw/2, 175 mm
≥ 0.08
30μϕ(νd + ων)εydbw/bwo −0.035
6 mm, dbL/4
No limit
Number
Distance to restrained
Generation 2-DC 3
≥ Hw/6 and ≥ lw, but ≤ 2lw and ≤ hstorey if ≤ 6 storeys, ≤ 2hstorey if > 6 storeys
Generation 1-DC M
Table 4 Detailing of ductile walls in Ductility Class M and 3 of Generations 1 and 2 of the Eurocodes (note (1) is footnote (4) of Table 2)
4490
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Horizontal bars
Thickness, bwo ≥
Vertical bars
Hoop spacing sw ≤
Table 4 (continued)
12dbL, 0.6bwo, 240 mm
20dbL, bwo, 400 mm
150 mm, hstorey/20, lw/40
where εc ≤ 0,002, ρv = Asv/bwosv ≥
0.2%
where εc > 0,002, ρv = Asv/bwosv ≥
0.2%
Ratio ρv = Asv/bwosv ≤
4%
Spacing in critical height, sv ≤
400 mm
Spacing above critical height, sv ≤ 400 mm
Ratio ρh = Ash/bwosh ≥
0.2%
Spacing in critical height, sv ≤
400 mm
Spacing above critical Height, sv ≤ 400 mm
> 4bw from end sections
≤ 4bw from end sections
Generation 1-DC M
0.5fctm/fyk a, 0.25%
250 mm
250 mm
0,5fctm/fyk a, 0.25%
0,5fctm/fyk a, 0.5%
–
–
Generation 2-DC 3
Bulletin of Earthquake Engineering (2024) 22:4477–4513
4491
13
13
0.81
0.71
0.78
“Dual”
“Frame”
0.67
0.87
0.62
0.55
0.7
0.5
0
0
0
0.64
0.09
1.62
along Y
along X
Torsion
Translation in X
Translation in Y
Natural eccentricity (m)
Lowest periods (s)
“Wall”
Building
Table 5 Seismic design parameters from the linear elastic analysis of the buildings
12.8
13.3
13.2
in X
14.4
12.3
19.0
in Y
torsional radii (m)
10.18
10.35
10.13
46.5
18.5
68
in X
80
57
91
in Y
radius of gyra- Base shear in
tion (m)
walls (%)
3.9
3.9
3.0
in X
3.0
3.6
3.0
in Y
Behaviour
factor in DC
M or 3
4492
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Bulletin of Earthquake Engineering (2024) 22:4477–4513
4493
lateral load resisting system of the buildings in the X-direction; in the Y-direction the first
two are wall systems and the third one is wall-equivalent dual.
Perimeter walls in the basement are designed as deep beams spanning between consecutive vertical members. As there is no specific rule in Generation 2 of Eurocode 8 for the
design shear in basement storeys of ductile walls, its value in the Generation 2 designs of
such storeys is taken equal to the ratio of the wall’s design moment resistance at the top
of the basement to the height of the basement storey (but not less than the shear from the
analysis).
All designs aim to minimize the quantity of reinforcement within the constraints posed
by the version of Eurocode 8 applied. To this end, provided reinforcement is tailored to the
required one, without packaging members in groups with the same reinforcement. Small
bar diameters are chosen, to reduce anchorage and lap-splice lengths and help meet the
crack width limit in SLS design to Eurocode 2 without increasing the tension reinforcement area beyond what is required to design for the ULS in flexure. Moreover, decisions
and choices are made automatically by the computer code, following the same approach in
all design cases considered and leaving no room for users’ bias to affect the comparison.
3 Discussion of design outcomes
Design results are summarized and compared in Figs. 5, 6, 7, 8, and 9. These figures
address two more options for Generation 2 of Eurocode 8, Altern(ative) 1 and 2, to be
introduced soon. Figures 5 and 6 depict the total quantities of steel and concrete and the
steel content per unit volume in the various types of building members. The total amount
of steel is markedly larger in Generation 2 designs, especially in “Frame” and “Dual”
buildings. “Frame” buildings come out as overall less costly in Generation 1 and “Wall”
ones in Generation 2. It is noted, though, that design of the “Wall” building to Generation 2
Eurocodes for a seismic action with PGA on rock of 0.3 g violates two rules of prEN19981-2:2022. To meet these rules the size of few members should be increased:
• The cross-section of corner columns at ground storey by about 25%, to meet the upper
limit of axial load ratio in the seismic design situation (cf rules on “Column design
axial force due to design seismic action” in Table 1). We will see later that, according
to NLRHA, this violation does not adversely affect performance of the columns concerned.
• The thickness of the long web of the U-shaped wall at ground storey and the basements and of the two other interior walls at the basements only, by as much as 50%,
to provide the required resistance of the inclined compression field (cf rules on compression field under “ULS in shear according to EN1992-1-1:2004” or “Design for
the ULS in shear in the seismic design situation, according to EN1998-1:2004 or
FprEN1998-1-1:2023” in Table 1). These violations were not corrected by increasing wall thickness, because this would had been ineffective, as the minimum vertical
reinforcement rules would increase the moment resistance of the wall further and
lead to a vicious cycle.
13
Bulletin of Earthquake Engineering (2024) 22:4477–4513
4494
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
90
m3 concrete
80
60
50
"Dual" buildings
40
"Frame" buildings
tn steel
70
"Wall" buildings
30
20
10
"Frame" building 0.3g
"Frame" building 0.2g
"Dual" building 0.3g
"Dual" building 0.2g
"Wall" building 0.3g
All
Foongs
Foundaon- & e
beams
Beams (w/o slab)
Walls
"Wall" building 0.2g
0
Columns
650
600
550
500
450
400
350
300
250
200
150
100
50
0
Fig. 5 Total quantity of concrete and steel reinforcement in the designs (excluding slabs)
200
180
160
140
120
100
Overall
Beam tot
Beam T
Overall
Beam tot
Beam T
Beam L
Column L
Overall
Beam tot
Beam T
Beam L
Wall tot
Steel content - "Frame" building, agR: 0.30g
240
220
EN1998-1:2004
prEN1998-1-2:2022
200
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
180
160
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
140
Overall
Overall
Beam tot
Beam T
Beam L
0
Wall tot
20
0
Wall T
40
20
Wall L
60
40
Column tot
80
60
Column T
100
80
Column L
100
Beam tot
120
Beam T
120
prEN1998-1-2 altern.2
Beam L
140
prEN1998-1-2:2022
prEN1998-1-2 altern.1
Wall tot
160
Steel content -
kg steel/m3 concrete
180
kg steel/m3 concrete
200
Wall tot
0
Wall T
20
0
Wall L
20
Column tot
40
Column T
60
40
Column L
80
60
220
EN1998-1:2004
100
80
240
Beam L
Column L
Overall
Beam tot
Beam T
prEN1998-1-2 altern.2
Wall T
120
prEN1998-1-2:2022
prEN1998-1-2 altern.1
Wall T
140
EN1998-1:2004
prEN1998-1-2 altern.2
Steel content - "Dual" building, agR: 0.30g
Wall L
160
220
Wall L
180
240
Column tot
200
Steel content - "Dual" building, agR: 0.20g
Column tot
220
kg steel/m3 concrete
240
Beam L
0
Wall tot
20
0
Wall T
40
20
Wall L
60
40
Column tot
80
60
Column T
100
80
Column L
100
prEN1998-1-2:2022
prEN1998-1-2 altern.1
Wall tot
120
EN1998-1:2004
Wall T
140
Wall L
180
Column tot
prEN1998-1-2 altern.2 160
Column T
120
prEN1998-1-2:2022
prEN1998-1-2 altern.1
Column T
140
EN1998-1:2004
Steel content - "Wall" building, agR: 0.30g
Column T
160
200
kg steel/m3 concrete
180
220
kg steel/m3 concrete
200
Steel content - "Wall" building, agR: 0.20g 240
Column L
220
kg steel/m3 concrete
240
Fig. 6 Amount of reinforcement per cubic meter of concrete (L: longitudinal, T: transverse)
To compare cost-effectiveness, Figs. 7, 8 and 9 show on the left-hand-side the average
and on the right-hand-side the maximum value per member group of the two most challenging demand-to-capacity indices of the design:
• In Fig. 7 the demand-to-capacity ratio is the average and the maximum ratio of
the target ductility factor of q/1.5 in Generation 2 of Eurocode 8 to the design
13
4495
Bulletin of Earthquake Engineering (2024) 22:4477–4513
1.4 Average EC8's-Duclity-target-to-SD-LS-Capacity-rao - "Wall" building, agR: 0.20g 2.4 Maximum EC8's-Duclity-target-to-SD-LS-Capacity-rao - "Wall" building, agR: 0.20g
1.3
2.2
1.2
2
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2:2022
1.1 EN1998-1:2004
1.8
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
1 prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
1.6
0.9
1.4
0.8
1.2
0.7
0.6
1
0.5
0.8
0.4
0.6
0.3
0.4
0.2
0.2
0.1
0
0
1.4
Average EC8's-Duclity-target-to-SD-LS-Capacity-rao - "Dual" building, agR: 0.20g 2.4 Maximum EC8's-Duclity-target-to-SD-LS-Capacity-rao - "Dual" building, agR: 0.20g
1.3
2.2
1.2
2
EN1998-1:2004
prEN1998-1-2:2022
EN1998-1:2004
prEN1998-1-2:2022
1.1
1.8
1
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
1.6
0.9
1.4
0.8
0.7
1.2
0.6
1
0.5
0.8
0.4
0.6
0.3
0.4
0.2
0.2
0.1
0
0
1.4 Average EC8's-Duclity-target-to-SD-LS-Capacity-rao - "Frame" building, agR: 0.20g 2.4 Maximum EC8's-Duclity-target-to-SD-LS-Capacity-rao - "Frame" building, agR: 0.20g
1.3
2.2
1.2
2
EN1998-1:2004
prEN1998-1-2:2022
EN1998-1:2004
prEN1998-1-2:2022
1.1
1.8
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
1
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
1.6
0.9
1.4
0.8
1.2
0.7
0.6
1
0.5
0.8
0.4
0.6
0.3
0.4
0.2
0.2
0.1
0
0
1.4 Average EC8's-Duclity-target-to-SD-LS-Capacity-rao - "Wall" building, agR: 0.30g 2.4 Maximum EC8's-Duclity-target-to-SD-LS-Capacity-rao - "Wall" building, agR: 0.30g
1.3
2.2
1.2
2
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2:2022
1.1 EN1998-1:2004
1.8
1 prEN1998-1-2 altern.1
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
prEN1998-1-2 altern.2
1.6
0.9
1.4
0.8
1.2
0.7
0.6
1
0.5
0.8
0.4
0.6
0.3
0.4
0.2
0.2
0.1
0
0
1.4
Average EC8's-Duclity-target-to-SD-LS-Capacity-rao - "Dual" building, agR: 0.30g 2.4 Maximum EC8's-Duclity-target-to-SD-LS-Capacity-rao - "Dual" building, agR: 0.30g
1.3
2.2
1.2
2
EN1998-1:2004
prEN1998-1-2:2022
EN1998-1:2004
prEN1998-1-2:2022
1.1
1.8
1
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
1.6
0.9
1.4
0.8
1.2
0.7
0.6
1
0.5
0.8
0.4
0.6
0.3
0.4
0.2
0.2
0.1
0
0
1.4 Average EC8's-Duclity-target-to-SD-LS-Capacity-rao - "Frame" building, agR: 0.30g2.4 Maximum EC8's-Duclity-target-to-SD-LS-Capacity-rao - "Frame" building, agR: 0.30g
1.3
2.2
1.2
2
EN1998-1:2004
prEN1998-1-2:2022
EN1998-1:2004
prEN1998-1-2:2022
1.1
1.8
1
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
1.6
0.9
1.4
0.8
1.2
0.7
0.6
1
0.5
0.8
0.4
0.6
0.3
0.4
0.2
0.2
0.1
0
0
Column base ground floor Columns above ground Wall base ground floor Walls upper floors
Beams
Y-dir.
X-dir.
Y-dir.
X-dir.
Y-dir.
X-dir.
Y-dir.
X-dir.
Y-dir.
X-dir.
Y-dir.
X-dir.
Y-dir.
X-dir.
Y-dir.
X-dir.
.
Column base ground floor Columns above ground Wall base ground floor Walls upper floors
Beams
Fig. 7 Mean and maximum ratio per superstructure member group of q/1.5 to design value of the corresponding capacity per prEN1998-1-2:2022 at the SD Limit State (nb: horizontal axis legends at figure bottom apply to all levels)
value of ductility factor capacity at the Significant Damage (SD) Limit State, ie, to
(1 + 0.5θupl/θy)/1.35, see rules on mean effective mechanical volumetric ratio of ties
at the last row of Tables 2 and 3 and row 9 under “Boundary elements in critical
height” in Table 4. (For Generation 1 of Eurocode 8 the design value of ductility
13
Bulletin of Earthquake Engineering (2024) 22:4477–4513
0.3
0.2
0.1
0
0.9
0.8
0.7
0.6
Average design-shear-to-shear-resistance-rao - "Dual" building, agR: 0.20g
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.5
0.4
0.3
0.2
0.1
0
0.9
0.8
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Average design-shear-to-shear-resistance-rao - "Frame" building, agR: 0.20g
0.7
EN1998-1:2004
prEN1998-1-2:2022
0.6
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.5
0.4
0.3
0.2
0.1
0
0.9
Average design-shear-to-shear-resistance-rao - "Wall" building, agR: 0.30g
0.8
0.7
EN1998-1:2004
prEN1998-1-2:2022
0.6
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.5
0.4
0.3
0.2
0.1
0
0.9
0.8
Average design-shear-to-shear-resistance-rao - "Dual" building, agR: 0.30g
0.7
EN1998-1:2004
prEN1998-1-2:2022
0.6
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.5
0.4
0.3
0.2
0.1
0
0.9
Average design-shear-to-shear-resistance-rao - "Frame" building, agR: 0.30g
0.8
0.7
EN1998-1:2004
prEN1998-1-2:2022
0.6
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.5
0.4
0.3
0.2
0.1
strainindependent
straindependent
strainindependent
straindependent
strainindependent
Superstructure columns
X-dir.
Y-dir.
straindependent
strainindependent
straindependent
strainindependent
straindependent
0
Basement columns Superstructure beams Basement beams
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
Maximum design-shear-to-shear-resistance-rao - "Dual" building, agR: 0.20g
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
Maximum design-shear-to-shear-resistance-rao - "Frame" building, agR: 0.20g
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
Maximum design-shear-to-shear-resistance-rao - "Wall" building, agR: 0.30g
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
Maximum design-shear-to-shear-resistance-rao - "Dual" building, agR: 0.30g
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
Maximum design-shear-to-shear-resistance-rao - "Frame" building, agR: 0.30g
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
Superstructure columns
X-dir.
Y-dir.
Basement columns Superstructure beams
strainindependent
0.4
EN1998-1:2004
straindependent
prEN1998-1-2 altern.2
strainindependent
prEN1998-1-2 altern.1
0.5
Maximum design-shear-to-shear-resistance-rao - "Wall" building, agR: 0.20g
straindependent
0.6
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
strainindependent
prEN1998-1-2:2022
straindependent
EN1998-1:2004
strainindependent
0.7
straindependent
Average design-shear-to-shear-resistance-rao - "Wall" building, agR: 0.20g
0.8
strainindependent
0.9
straindependent
4496
Basement beams
Fig. 8 Mean (left) and maximum (right) ratio per frame member group of the design shear to the design
shear resistance according to the Eurocode (nb: horizontal axis legends at figure bottom apply to all levels)
factor capacity at the SD Limit State is taken equal to (1 + θupl/θy)/1.35, because in
EN1998-1:2004 detailing aims at a ductility factor of 1 + θupl/θy). Results are summarized for:
•
•
•
•
64 base sections of ground storey columns;
704 column ends above the base of the ground storey;
312 beam ends in floors above ground level;
4 base sections of the ground storey in each horizontal direction where the vertical
member of a “Frame” or “Wall” building is considered as a wall and 12 such sections in each “Dual” building;
13
4497
Bulletin of Earthquake Engineering (2024) 22:4477–4513
Average design-shear-to-shear-resistance-rao - "Wall" building, agR: 0.20g
1.2
1
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
2
1.8
1.6
1.4
1.2
0.8
0.4
0.2
Y-dir.
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
1.4
1.2
Basement
X-dir.
storeys
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
strainindependent
straindependent
strainindependent
straindependent
strainindependent
straindependent
straindependent
straindependent
strainindependent
storey
Y-dir.
Y-dir.
0.4
0.2
1
Y-dir.
2
1.8
EN1998-1:2004
prEN1998-1-2:2022
1.6
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
1.4
straindependent
straindependent
Basement
X-dir.
storeys
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
strainindependent
storey
Y-dir.
strainindependent
ground
strainindependent
straindependent
straindependent
straindependent
Above
X-dir.
Y-dir.
Maximum design-shear-to-shear-resistance-rao - "Frame" building, agR: 0.20g
1.2
0.8
storey
strainindependent
Ground
X-dir.
strainindependent
storeys
strainindependent
straindependent
straindependent
Basement
X-dir.
strainindependent
storey
Y-dir.
strainindependent
ground
strainindependent
Above
X-dir.
Y-dir.
straindependent
straindependent
strainindependent
storey
strainindependent
straindependent
strainindependent
straindependent
Ground
X-dir.
Average design-shear-to-shear-resistance-rao - "Frame" building, agR: 0.20g
1.2
straindependent
0
0
Y-dir.
1
0.6
0.8
0.6
0.4
0.4
0.2
0.2
Y-dir.
2
straindependent
Basement
X-dir.
storeys
Maximum design-shear-to-shear-resistance-rao - "Wall" building, agR: 0.30g
strainindependent
storey
Y-dir.
strainindependent
ground
straindependent
strainindependent
Above
X-dir.
Y-dir.
straindependent
strainindependent
storey
straindependent
strainindependent
Ground
X-dir.
straindependent
straindependent
0
strainindependent
storeys
Average design-shear-to-shear-resistance-rao - "Wall" building, agR: 0.30g
strainindependent
Basement
X-dir.
straindependent
straindependent
storey
Y-dir.
strainindependent
ground
strainindependent
Above
X-dir.
Y-dir.
straindependent
strainindependent
storey
straindependent
strainindependent
Ground
X-dir.
straindependent
strainindependent
straindependent
0
Y-dir.
1.8
1.2
1
EN1998-1:2004
prEN1998-1-2:2022
1.6
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
1.4
1.2
0.8
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
1
0.6
0.8
0.6
0.4
0.4
0.2
0.2
Y-dir.
2
1.8
prEN1998-1-2:2022
1.6
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
1.4
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
1.2
storeys
strainindependent
straindependent
straindependent
Basement
X-dir.
Maximum design-shear-to-shear-resistance-rao - "Dual" building, agR: 0.30g
EN1998-1:2004
0.8
storey
Y-dir.
strainindependent
ground
strainindependent
Above
X-dir.
Y-dir.
straindependent
straindependent
strainindependent
storey
strainindependent
Ground
X-dir.
straindependent
strainindependent
storeys
0
straindependent
straindependent
straindependent
Basement
X-dir.
Average design-shear-to-shear-resistance-rao - "Dual" building, agR: 0.30g
strainindependent
storey
Y-dir.
strainindependent
ground
strainindependent
Above
X-dir.
Y-dir.
straindependent
strainindependent
storey
straindependent
strainindependent
Ground
X-dir.
straindependent
strainindependent
straindependent
0
Y-dir.
1
0.6
0.8
0.6
0.4
0.4
0.2
0.2
0
Y-dir.
2
1.8
1.2
1
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
Basement
X-dir.
straindependent
storeys
EN1998-1:2004
prEN1998-1-2:2022
1.4
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
strainindependent
storey
Y-dir.
strainindependent
ground
straindependent
strainindependent
Above
X-dir.
Y-dir.
straindependent
strainindependent
storey
straindependent
straindependent
strainindependent
Ground
X-dir.
Maximum design-shear-to-shear-resistance-rao - "Frame" building, agR: 0.30g
1.6
1.2
0.8
strainindependent
storeys
straindependent
straindependent
straindependent
Basement
X-dir.
Average design-shear-to-shear-resistance-rao - "Frame" building, agR: 0.30g
strainindependent
storey
Y-dir.
strainindependent
ground
strainindependent
Above
X-dir.
Y-dir.
straindependent
straindependent
strainindependent
storey
strainindependent
Ground
X-dir.
straindependent
strainindependent
0
straindependent
Y-dir.
1
0.6
0.8
0.4
0.6
0.4
0.2
0.2
0
Y-dir.
Y-dir.
Y-dir.
Basement
X-dir.
straindependent
strainindependent
storey
Y-dir.
straindependent
straindependent
straindependent
ground
strainindependent
Above
X-dir.
strainindependent
storey
strainindependent
Ground
X-dir.
strainindependent
storeys
straindependent
straindependent
straindependent
Basement
X-dir.
strainindependent
storey
Y-dir.
strainindependent
ground
strainindependent
Above
X-dir.
straindependent
straindependent
strainindependent
storey
strainindependent
Ground
X-dir.
straindependent
strainindependent
straindependent
0
strainindependent
1.4
ground
0.6
0.2
1
Above
X-dir.
Y-dir.
0.8
0.4
1.2
storey
Maximum design-shear-to-shear-resistance-rao - "Dual" building, agR: 0.20g
1
0.6
1.4
straindependent
1.6
EN1998-1:2004
Ground
X-dir.
1.8
0.8
1.4
2
strainindependent
storeys
0
strainindependent
Basement
X-dir.
Average design-shear-to-shear-resistance-rao - "Dual" building, agR: 0.20g
strainindependent
straindependent
straindependent
storey
Y-dir.
strainindependent
ground
strainindependent
Above
X-dir.
Y-dir.
straindependent
strainindependent
storey
straindependent
strainindependent
Ground
X-dir.
straindependent
strainindependent
straindependent
0
1.4
prEN1998-1-2 altern.2
0.6
0.2
1
prEN1998-1-2:2022
prEN1998-1-2 altern.1
0.8
0.4
1.2
EN1998-1:2004
1
0.6
1.4
Maximum design-shear-to-shear-resistance-rao - "Wall" building, agR: 0.20g
straindependent
1.4
storeys
Y-dir.
Fig. 9 Mean (left) and maximum (right) ratio per wall group of design shear to design shear resistance
according to the Eurocode
• 20 base sections in storeys above the ground storey per horizontal direction in which
a vertical member of a “Frame” or “Wall” building is considered as a wall and 60
such sections in each “Dual” one.
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4498
• In Fig. 8 for beams or columns and Fig. 9 for walls, the average and the maximum of
the ratio of the design shear force to the corresponding shear resistance (Biskinis and
Fardis 2020), at the following locations:
•
•
•
•
•
•
•
•
•
•
192 columns above ground level;
64 basement columns;
468 beam sections above ground level;
312 beam sections in basements;
8 ground storey walls in the X-direction in each “Frame” or “Wall” building and 32
such walls in each “Dual”;
40 ground storey walls in the Z-direction in each “Dual” or “Wall” building or 32 of
them per “Frame” one;
40 walls above ground storey in the X-direction in each “Frame” or “Wall” building
and 120 such walls in each “Dual” building;
200 walls above the ground storey in the Z-direction in each “Dual” or “Wall” building or 160 of them in each “Frame” building;
16 interior basement walls in the X-direction in each “Frame” or “Wall” building
and 48 such walls in each “Dual” one;
48 interior basement walls in the Z-direction in each “Dual” or “Wall” building or
32 of them per “Frame” building.
The closer to 1.0 the demand-to-capacity ratios in Figs. 7, 8 and 9 are, the better is the
cost-effectiveness of the design.
Figure 7 shows that essentially all “Frame” or “Wall” buildings designed to EN19981:2004 easily provide the target ductility factor of q/1.5 in the critical height of walls, but
have difficulty doing so at practically every “critical region” of a column—despite the
relaxed target ultimate chord rotation of (θy + θupl)/1.35 in EN1998-1:2004. “Dual” buildings designed to prEN1998-1-2:2022 have a similar difficulty in the dominant direction of
their walls (the Y-direction). Similar is the situation in beams designed to prEN1998-12:2022. Figure 6 demonstrates, though, the high costs incurred in the columns of “Dual” or
“Frame” buildings to achieve the confinement required for this detailing. In fact, in some
cases confining reinforcement is so dense and at such diameters that it seems surreal. We
will come back to the issue of unfeasibility of the confinement required to achieve the target ductility factor in critical regions of columns.
Two distinct cases are presented in Figs. 8 and 9 for ULS design in shear:
• Design independent of the magnitude of the longitudinal strain at section mid-depth, or
• Design dependent on this strain.
Design according to Generation 1 of the Eurocodes belongs to the first case, as the
reduction factor on the strength of the compression field, ν, does not depend on longitudinal strain (see second row in “ULS in shear, according to EN1992-1-1” in Table 1);
FprEN1992-1-1:2023 belongs to it as well, as it allows using a constant value ν = 0.5. The
second case is relevant only to design according to FprEN1992-1-1:2023, FprEN1998-11:2023 and prEN1998-1-2:2022.
Overall, shear-demand-to-resistance ratios in Figs. 8 and 9 are most often higher in the
strain-independent approach than in the strain-dependent one, suggesting that the former
gives, in general, lower resistance than the later; in other words, the approximation does
not appear to be safe-sided. A closer look suggests that the gap between the two approaches
widens in the maximum values of shear-demand-to-resistance ratios per group of frame
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Bulletin of Earthquake Engineering (2024) 22:4477–4513
4499
members in Fig. 8, compared to the average ratio of the group, but closes in the groups
of walls in Fig. 9. In fact, the average ratios in Fig. 8 are about the same in strain-independent and strain-dependent shear design. The same can be said for the maximum ratios
in Fig. 9. This may imply that the approximate, strain-independent approach reflects on
average relatively well the spectrum of possible strain values in frame members, whereas,
the large maximum longitudinal strains in their plastic hinges may reduce shear resistance
well below the level to which the approximate approach has been calibrated. By contrast,
in walls, the longitudinal strains associated with the most critical shear situations seem to
be close to those presumed in the strain-independent approach, while those encountered on
average are lower.
The magnitude of shear-demand-to-resistance ratios in Figs. 8 and 9 is consistent with
the design goals, except for:
• The large values of maximum ratios—around 1.2—for beams in Fig. 8. Those in superstructure beams may be justified by the sheer number of such beams and by roundingup the tie spacing required in one or two of them to a higher multiple of 5 mm. Those
in basement beams may be due to similar reasons, along with their wide tie-spacing due
to negligibly small seismic shears and to detailing according to EN1992-1-1 instead of
Eurocode 8.
• The large values—average ones about 1.2, maximum ones of 1.4 or higher—in the
ground or basement storeys of the single wall in the X-direction of “Wall” buildings
designed for a PGA of 0.3 g. These values are due to a web thickness which is insufficient at these locations for the resistance of the inclined compression field. For reasons
explained before, this deficiency has not been corrected through a local increase in web
thickness.
Figures 10 and 11 concern beam-column joints reinforced horizontally and vertically
through extension of the corresponding column reinforcement into the part of the column
which falls within the joint.
For the left-hand and middle part of Fig. 10 shear resistance is calculated according to
FprEN1998-1-1:2023 and (Fardis 2021); for the right-hand part it is determined according to EN1998-1:2004. As prEN1998-1-2:2022 does not have rules for the calculation of
the design shear in joints, the latter is always determined according to the provisions of
EN1998-1:2004 for DC H joints (i.e., as 1,2-times the largest among the two faces of the
joint design yield force of the beam’s top plus bottom reinforcement, minus the column’s
shear force), except that in design to prEN1998-1–2:2022 the yield force of the beam’s
top reinforcement is neglected at exterior joints, because the outside face of such a joint is
free of horizontal forces and the seismic axial force in the column which is critical for the
joint’s shear resistance (the tensile one) is associated with a sagging beam moment at the
inside. As the impact of the Eurocode 8 generation on performance and likelihood of failure of interior joints in the left-hand parts of Fig. 10 is minor, the dramatic effect on exterior joints in the middle figures is attributed to the different way design shear is calculated
for Generation 2.
Design resistance of the joint is calculated for the purposes of the right-hand part of
Fig. 10 according to the provisions of EN1998-1:2004 for DC H joints. Comparison of the
results in this part to their counterparts in the left-hand and middle part of Fig. 10 (i.e., to
those referring to joints of EN1998-1:2004 design) suggests that the provisions of EN19981:2004 for the shear resistance of DC H joints may not be safe-sided.
13
Bulletin of Earthquake Engineering (2024) 22:4477–4513
Average design-shear-demand/shear-resistance
per EN1998-1:2004 in buildings designed to
EN1998-1:2004 with column reinforcement
1.4 extended in the joint
1.2
prEN1998-1-2:2022
prEN1998-1-2 alt.1 or 2
1.2
60
50
70
50
90
80
Frame building 0.3g
0
Frame building 0.2g
0
Dual building 0.3g
10
0
Dual building 0.2g
10
Wall building 0.3g
20
10
Wall building 0.2g
30
20
Frame building 0.3g
30
20
Frame building 0.2g
30
Dual building 0.3g
40
Dual building 0.2g
Frame building 0.3g
Exterior joints
50
40
Wall building 0.3g
Interior joints
60
40
Wall building 0.2g
% of joints with column reinforcement
extended in buildings designed to EN19981:2004 , failing shear-resistance-check of
EN1998-1:2004
70
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 alt.1 or 2
60
Wall building 0.2g
Frame building 0.3g
Frame building 0.2g
Wall building 0.2g
80
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 alt.1 or 2
100
Frame building 0.3g
70
% of exterior joints with column
reinforcement extended, failing
shear-resistance-check of
FVprEN1998-1-1:2023
90
Frame building 0.2g
80
100
% of interior joints with column
reinforcement extended, failing shearresistance-check of FVprEN1998-1-1:2023
Dual building 0.3g
0
Dual building 0.2g
0
Wall building 0.3g
0.2
0
Frame building 0.3g
0.2
Frame building 0.2g
0.4
0.2
Dual building 0.3g
0.4
Dual building 0.2g
0.6
0.4
Wall building 0.3g
0.8
0.6
Wall building 0.2g
0.8
0.6
90
Exterior joints
1
1
0.8
100
Interior joints
Frame building 0.2g
1.6
Dual building 0.3g
1
1.4
1.8
Dual building 0.3g
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 alt.1 or 2
1.2
Average design-shear-demand/
shear-resistance per FVprEN1998-11:2023 in exterior joints with
column reinforcement extended in
EN1998-1:2004
joint
1.6
Dual building 0.2g
1.4
1.8
Wall building 0.3g
Average design-shear-demand/shear-resistance
per FVprEN1998-1-1:2023 in interior joints with
the column reinforcement extended in the joint
Wall building 0.3g
1.6
Wall building 0.2g
1.8
Dual building 0.2g
4500
Fig. 10 Joints with column reinforcement extended in them: (top) average of ratio of shear demand per
EN1998-1:2004 to shear resistance per FprEN1992-1-1:2023 and FprEN1998-1-1:2023 (left and middle) or
per EN1998-1:2004 (right); (bottom) percent of joints in building where shear demand exceeds resistance
Figure 11 concerns the simplified verification of beam-column joints using values in
a table contained in prEN1998-1-2:2022 and refers to the version of the three buildings
which have been designed to Generation 2 of Eurocode 8. The applicability ratios in the
left-hand part suggest that the bounds and restrictions set by prEN1998-1-2:2022 for verification of joints using the table are very tight, and the scope of the simplified approach very
narrow. With the reservation that the population of joints where this type of verification
can be applied is small, the low failure rates at the right-hand part of Fig. 11 suggest that
this approach may not be safe-sided.
Summing up the discussion of the outcomes of the designs, two problem areas have
emerged:
• The very high cost and the constructability problem associated with confinement of
all critical regions so that the design value of their chord-rotation ductility factor at
the Significant Damage (SD) Limit State (LS) matches the part of the behaviour factor
reflecting ductility and system redundancy; and
• The difficulty to verify the ULS in shear at basements and ground storeys of ductile
walls which take a large share of the base shear.
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20
Interior joints
15
Exterior joints
% of joints failing
Table-based
verificaon per
prEN1998-1-2:2022
15
10
10
5
Interior joints
5
Exterior joints
Dual building 0.2g
Wall building 0.3g
Wall building 0.2g
Frame building 0.3g
Frame building 0.2g
Dual building 0.3g
Dual building 0.2g
Wall building 0.3g
0
Wall building 0.2g
0
Frame building 0.3g
25
20
Frame building 0.2g
30
% of joints meeng applicability
criteria of Table-based verificaon
per prEN1998-1-2:2022
Dual building 0.3g
35
Fig. 11 Percent of joints in buildings designed to prEN1998-1-2:2022 where Table-based verification per
prEN1998-1-2:2022 is applicable and percent of this group where the check is met
Proposals for modifications of prEN1998-1–2:2022 to address the first issue are presented next. The second issue will be revisited after assessing the designs carried out so far
using nonlinear response history analysis.
4 The link between global behaviour factor and member ductility
factor ‑proposed modifications to rules of generation 2 of eurocode
8
Concrete buildings typically have fundamental period in the velocity-controlled range of
the spectrum. So the equal-displacement rule applies in good approximation and the global
displacement ductility factor demand, μ, is on average about equal to the global behaviour
factor, q. In an ideal sidesway plastic mechanism plastic hinges develop at both ends of all
beams; vertical members remain straight up their full height thanks to a rotation at the base
(often in a plastic hinge there). Then, the demand value of chord rotation ductility factor,
μθ, at member ends where plastic hinges develop is equal to the global displacement ductility factor, μ. Non-simultaneous formation of plastic hinges throughout the structure, as well
as height- or plan-wise non-uniform distribution of inelastic chord rotation demands are
reflected in the redundancy-dependent component of the behaviour factor. On this basis,
prEN1998-1-2:2022 requires all critical regions of primary seismic members in concrete
buildings to have a chord-rotation capacity at the SD LS at least equal to the product of the
redundancy- and ductility-dependent components of the global behaviour factor times the
chord rotation at yielding of the corresponding member end. The rule establishes for the
first time in Eurocode 8 the connection of the ductility factor for which plastic hinges are
detailed to the global behaviour factor. Regions expected to remain elastic during any inelastic response by virtue of capacity design are not excluded from application of the rule.
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FprEN1998-1-1:2023 specifies the chord-rotation capacity of members at the SD LS
to be equal to the chord rotation at yielding of the member end plus 50% of the ultimate
plastic chord-rotation at that end, divided by a partial factor, which is a NDP; prEN1998-12:2022 recommends for this NDP a value of 1.26 for concrete members with circular section or 1.35 for all others. The latter value gives the following relation between μθ and q:
𝜇𝜃 = 1.8q−1
(1)
In EN1998-1:2004 the chord-rotation capacity of members at the SD LS is equal to the
chord rotation at yielding of the member’s end plus the ultimate plastic chord-rotation at
that end—instead of 50% in FprEN1998-1-1:2023; this gives:
𝜇𝜃 = q
(2)
from which a set of gross approximations referring to a typical member—not to the specific one being detailed for ductility—gives the required curvature ductility factor, μφ:
𝜇𝜑 = 2q−1
(3)
For the range of q-factor values of interest (3 to 3.9), Eq. (2) gives μθ-values in the same
range, whereas Eq. (1) values from 4.4 to over 6. In large columns (with low shear-spanratio, lV, and compression reinforcement ratio, ρ’, as low as one-quarter of the total, ρtot)
ductility factors in that latter range require confining reinforcement ratios, ρh, beyond the
limits of validity of the expression for θupl at the last line of Table 3 to the available test
results.
More important than the issue of practical implementation of Eq. (1) through detailing
is the following conceptual problem. Equation (2)—which is essentially Eq. (1) without
safety factors or margins—presumes using a bilinear envelope or skeleton curve for the
(generalised) force–deformation relation of members with elastic stiffness consistent with
that used in the elastic seismic analysis of the structure with the reduced-by-q response
spectrum. Therefore, the ductility factor should be computed using as normalising deformation, not the real chord rotation at yielding, θy, given near the lower right-hand corner of
Tables 2 and 3, but the chord rotation derived from the yield moment using as secant stiffness to the yield point the elastic stiffness used in the elastic analysis of the building with
the design spectrum of the seismic action, which in the present case and commonly, is the
default value of one-half the flexural stiffness of the uncracked section allowed in EN19981:2004 and the drafts of the Generation 2 of Eurocode 8. In fact, that approach has been
followed for EN1998-1:2004, namely for the calibration of Eq. (3) and of the detailing
rules derived from it (Fardis et al 2005). The fictitious ductility factor derived from this
proxy stiffness is on average about double the real one.
To mitigate the problem of excessively high confinement in critical regions of
frame members to meet Eq. (1) at all of them, two alternatives to the current content of
prEN1998-1–2:2022 have been considered:
• “Alternative 1”: To keep using the real chord rotation at yielding, θy, given for beams
or columns near the lower right-hand corner of Tables 2 and 3, as normalising deformation in the ductility factor, but limit the application of Eq. (1) and the verification
of member deformations at the SD LS to frame member ends expected to develop
plastic hinges, i.e., to column ends framing into stronger beams and to beam ends
framing into stronger columns. This option reduces by about 50% the extra cost and
the extent of the constructability problem in the building.
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Bulletin of Earthquake Engineering (2024) 22:4477–4513
4503
• “Alternative 2”: To keep the application of Eq. (1) and verification of member deformations at the SD LS at all critical regions of frame members, but to use as normalising deformation for μθ not the chord rotation at yielding, θy, given in the last line of
Tables 2 and 3, but the chord rotation derived from the yield moment using as secant
stiffness to the yield point the elastic stiffness used in the elastic seismic analysis
of the building—in the present case, one-half the flexural stiffness of the uncracked
section.
Both alternatives were supplemented with measures to mitigate the problems with
the shear resistance of ductile walls identified so far, as follows:
(1) Removal of the overstrength factor of 1.2 multiplying the design moment resistance
at the base of ductile walls, for the purposes of the design moment envelope and the
shear magnification factor.
(2) Reduction of the minimum vertical reinforcement ratio in boundary elements within
the critical height of ductile walls from 1 to 0.5%—as in EN1998-1:2004.
(3) Setting the minimum compression field inclination in the web of ductile walls equal
to that of the line connecting the centroids of tension and compression chords at the
wall’s top and bottom sections in a storey, in order to:
• Avoid considering part of the slab reinforcement as web reinforcement of the
wall;
• Reduce the tension shift of the wall’s moment diagram with respect to that
obtained from the minimum inclination given in FprEN1992-1-1:2023;
• Push the compression field inclination into a range of values which favours the
field’s strength and the wall’s shear resistance.
Figures 5 and 6 show drastically reduced quantities of steel for both “Alternatives”.
“Alternative 2” meets Eq. (1) at all critical regions—not just where plastic hinging is
expected, like “Alternative 1”—and reduces steel to the level of designs with Generation 1. “Frame” buildings designed to either “Alternative” are overall less costly than
“Dual” or “Wall” ones.
Figure 7 shows certain missing of ductility targets in “Alternative 1”; in columns or
walls this is limited to levels above the base, i.e., to locations where plastic hinging is
unlikely—if not impossible. Thanks to the change in yield deformation, “Alternative 2”
easily meets ductility targets everywhere, at about the same cost as for Generation 1.
Concerning shear in frames or walls, Figs. 8 and 9 show a minor deterioration in
achieving the targets for few cases of upper storey columns or basement walls for both
“Alternatives”, but an improvement in certain ground storey walls.
For shear in joints, there is a minor loss in meeting targets due to the reduction
in transverse reinforcement of the critical regions of columns brought about by both
“Alternatives”, but this does not change the overall satisfactory picture.
Summing up, “Alternative 2” entails few minor modifications in prEN1998-1-2:2022
which bring cost and constructability to levels of the current Generation 1, but at a major
improvement in seismic performance, at least as measured by the achievement of targets
set by Generation 2 of Eurocode 8. However, the improvement in performance needs to be
confirmed by the results of the nonlinear response history analyses described next.
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Bulletin of Earthquake Engineering (2024) 22:4477–4513
5 Assessment of the designs through nonlinear response history
analyses
The 24 different building designs have been assessed by carrying out nonlinear responsehistory analysis (NLRHA) in 3D under seven historic ground motion pairs of horizontal
records, obtained from the Engineering Strong Motion (ESM) Database—https://​esm-​db.​
eu/#/​rexel according to Iervolino et al (2010, 2011). Table 6 lists the earthquakes and the
main features of the records used. The site classification is compatible with Ground Category B and the magnitude, depth and mechanism with the seismicity of Southern Europe.
Figure 12 displays:
• The individual elastic response spectra,
• The average of the seven spectra per horizontal direction,
• The target spectrum (Type 1 recommended spectrum in EN1998-1:2004 for ground
category B),
• The lower bound of 0.9 × target spectrum set by EN1998-1:2004 for the average spectra
(the one set by FprEN1998-1-1:2023 being 0.75 × target spectrum),
• The upper bound of 1.3 × target spectrum set for the average spectra by FprEN1998-11:2023, and
• The lower bound of 0.5 × target spectrum set for the individual spectra by FprEN19981-1:2023.
The limits refer to the period range from 20% of the shortest to 1.5-times the longest
fundamental period of the three buildings in the horizontal direction considered (0.14 to
1.22 s in X, 0.125 to 1.3 s in Y). All spectra in Fig. 12 are for 5% viscous damping and the
target one is scaled to a PGA on rock of 0.25 g.
The code used for NLRHA is OPENSEES (McKenna et al 2000, 2010). The model
used for each building is the same regarding geometry, loads, masses, member connectivity and rigid offsets as in the elastic analysis for design, except that, for members
above the basements, beam elements capable of developing inelastic hinges at the ends
and a generalized hysteretic law are used according to (Neuenhofer and Filippou 1997,
Scott and Fenves 2006 and Scott and Ryan 2013). Their elastic flexural stiffness was
computed from the yield moments and chord rotations at yielding of the two ends (average of the stiffness values at the two ends obtained by connecting yield points in sagging and hogging or positive and negative bending). Members in the basements were
modelled as uncracked. Yield moments were computed from section analysis at yielding at the centroid of the tension chord. For the designs to EN1998-1:2004 chord rotations at yielding or ultimate were obtained according to Annex A of EN1998-3:2005
(CEN 2005), which are those of (Biskinis and Fardis 2010a, 2010b) and are slightly
different from those used in designs according to prEN1998-1-2:2022 and the two
“Alternatives”, which are those of FprEN1998-1-1:2023 and (Grammatikou et al 2018a,
2018b)—(see last row of Tables 2 and 3 for expressions for these rotations applying to
members with rectangular section. Calculation of all properties employed mean values
of steel and concrete strength, as given in the Eurocodes of the generation being considered. Coupling between the two orthogonal transverse directions in column or walls
was neglected. A bilinear skeleton or envelope curve was employed, with 5% hardening ratio. A multilinear model was adopted for the cyclic behaviour, with unloading to
the horizontal (deformation) axis with the stiffness of the elastic branch of the skeleton
13
15.9
6.6
6.6
6.5
6.1
6.1
7.8
7.8
Corinth, GR, 24/02/1981
Central Italy, 30/10/2016
Aegio, GR, 15/06/2015
L’Aquila, IT, 06/04/2009
L’Aquila, IT, 06/04/2009
Turkey-Syria, 06/02/2023
Turkey-Syria, 06/02/2023
6.2
2.9
8.3
8.3
20
20
Depth (km)
Mw
Seismic event
Normal
Normal
Normal
Normal
Strike-slip
Strike-slip
Normal
Mechanism
Accumoli Madonna delle coste (MZ102)
Aegio (AIGA)
AGQ
AGV
Pazarcik Kahramanmaras (KHMN)
NAR
Korinthos (KORA)
station
Table 6 Features of historic ground acceleration records used in NLRHA
B
B
B
B
B
B
B
Ground
category
17.4
23.6
5
4.9
25.5
25.6
30.2
Epicentral
distance (km)
0.372
0.498
0.446
0.657
0.519
0.589
0.24
PGA (g’s)
0.73
1.0
1.0
1.28
0.74
0.88
1.27
X
0.71
0.97
1.44
0.75
0.86
0.83
1,1
Y
Scale factor
Bulletin of Earthquake Engineering (2024) 22:4477–4513
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Bulletin of Earthquake Engineering (2024) 22:4477–4513
Fig. 12 5%-damped elastic response spectra of individual records used in NLRHA, with their averages per
horizontal direction compared to target spectra for ground category B in EN1998-1:2004 and a PGA on
rock of 0.25 g and to bounds set by EN1998-1:2004 and FprEN1998-1:2023.
curve and bilinear reloading to the extreme past point on the skeleton curve in the direction of reloading (to model pinching). The position of the corner (turning point) of
pinching was chosen for each member so that the area enclosed by the pinched hysteresis loops reflects the hysteretic energy dissipation in the member at the corresponding
peak displacement amplitude, depending on the geometric and mechanical features of
the member and its reinforcement according to (Grammatikou et al 2022); the concurrent operation of global viscous damping at 5% of critical was taken into account in this
calculation. All properties needed for the NLRHA are automatically calculated at the
end of the design face and transferred to OPENSEES for the NLRHA. P-Δ effects were
taken into account.
Seismic performance of individual members was assessed using mean values of material properties, separately for:
• Flexure, through the maximum value during the response of the ratio of chord-rotation
demand to the concurrent value of (θy + 0.5θupl)/1.35—or (θy + 0.5θupl)/1.26 for circular
columns (see Fig. 13)
• Shear, through the maximum value during the response of the ratio of shear force
demand to the concurrent value of shear resistance/1.6—or/1.5 for circular columns,
with shear resistance determined according to FprEN1998-1-1:2023 (Biskinis & Fardis
2020) taking into account the effect of longitudinal strains (see Figs. 14 and 15).
Concerning flexure (Fig. 13):
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Bulletin of Earthquake Engineering (2024) 22:4477–4513
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.8
0.7
0.6
Average end-rotaon-demand-to-SD-LS-capacity-rao -"Wall" building, agR: 0.20g 1.2 Maximum end-rotaon-demand-to-SD-LS-capacity-rao - "Wall" building, agR: 0.20g
1.1
EN1998-1:2004
prEN1998-1-2:2022
1
0.9
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.8
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Average end-rotaon-demand-to-SD-LS-capacity-rao - "Dual" building, agR: 0.20g 1.2 Maximum end-rotaon-demand-to-SD-LS-capacity-rao - "Dual" building, agR: 0.20g
1.1
1
EN1998-1:2004
prEN1998-1-2:2022
EN1998-1:2004
prEN1998-1-2:2022
0.9
EN1998-1:2004
prEN1998-1-2:2022
0.8
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.7
0.6
0.5
0.3
0.4
0.2
0.3
0.2
0.1
0.1
0
0
0.8 Average end-rotaon-demand-to-SD-LS-capacity-rao - "Frame" building, agR: 0.20g 1.2
Maximum end-rotaon-demand-to-SD-LS-capacity-rao -"Frame" building, agR: 0.20g
1.1
0.7
EN1998-1:2004
prEN1998-1-2:2022
1
EN1998-1:2004
prEN1998-1-2:2022
0.6
0.9
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.8
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.5
0.7
0.4
0.6
0.5
0.3
0.4
0.2
0.3
0.2
0.1
0.1
0
0
0.8 Average end-rotaon-demand-to-SD-LS-capacity-rao - "Wall" building, agR: 0.30g 1.2 Maximum end-rotaon-demand-to-SD-LS-capacity-rao - "Wall" building, agR: 0.30g
1.1
0.7
1
EN1998-1:2004
prEN1998-1-2:2022
EN1998-1:2004
prEN1998-1-2:2022
0.9
0.6
prEN1998-1-2 altern.1
0.5
prEN1998-1-2 altern.2
0.4
0.6
EN1998-1:2004
prEN1998-1-2:2022
0.5
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.4
0.3
0.2
0.1
0
0.8
Average end-rotaon-demand-to-SD-LS-capacity-rao -"Frame" building, agR: 0.30g
0.7
0.6
EN1998-1:2004
prEN1998-1-2:2022
0.5
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.4
0.3
0.2
0.1
Column base ground floor Columns above ground Wall base ground floor Walls upper floors
X-dir.
Y-dir.
X-dir.
Y-dir.
X-dir.
Y-dir.
X-dir.
Y-dir.
X-dir.
0
1.2 Maximum end-rotaon-demand-to-SD-LS-capacity-rao -"Frame" building, agR: 0.30g
1.1
1
EN1998-1:2004
prEN1998-1-2:2022
0.9
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Beams
Y-dir.
Average end-rotaon-demand-to-SD-LS-capacity-rao - "Dual" building, agR: 0.30g
0.7
X-dir.
0
0.8
Y-dir.
0.1
X-dir.
0.2
Y-dir.
0.3
0.8
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1.2 Maximum end-rotaon-demand-to-SD-LS-capacity-rao - "Dual" building, agR: 0.30g
1.1
1
EN1998-1:2004
prEN1998-1-2:2022
0.9
0.8
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
X-dir.
prEN1998-1-2 altern.2
0.4
Y-dir.
prEN1998-1-2 altern.1
0.5
Column base ground floor Columns above ground Wall base ground floor Walls upper floors
Beams
Fig. 13 Mean and maximum ratio per member group of chord rotation from NLRHA to design value of
corresponding capacity specified in prEN1998-1-2:2022 for the SD LS (nb: horizontal axis legends at figure bottom apply to all levels)
13
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Bulletin of Earthquake Engineering (2024) 22:4477–4513
• Designs to prEN1998-1-2:2022 have excellent flexural performance.
• “Alternative 2” came out slightly worse at column or wall ground floor bases than
design to prEN1998-1-2:2022.
• EN1998-1:2004 came out worse, often much worse, than prEN1998-1-2:2022, especially in columns. In fact, a few columns of the “Dual” or “Wall” buildings designed
to EN1998-1:2004 for a PGA of 0.3 g came out as deficient.
It is worth noting that, the corner columns of “Wall” buildings designed to
prEN1998-1-2:2022 or its two “Alternatives” for a PGA of 0.3 g, which were found in
the design stage to violate at the ground storey the upper limit of axial load ratio, perform very well in flexure according to the NLRHA analyses of these buildings.
Concerning shear (Figs. 14 and 15):
• In every design analysed all frame members perform very well, but designs to
EN1998-1:2004 systematically less so.
• Performance of frame members is slightly worse in the “Alternatives” to prEN19981-2:2022, than in designs to prEN1998-1-2:2022 itself—especially in “Alternative
2”.
• Walls of “Dual” or “Wall” buildings designed to EN1998-1:2004 exhibit acute shear
deficiencies almost throughout their height. Except possibly in “Frame” buildings, the
shear amplification factor of 1.5 severely underestimates post-elastic shear magnification in DC M ductile walls of EN1998-1:2004.
• Walls of prEN1998-1-2:2022 design have satisfactory shear performance in the superstructure; the “Alternative” ones even better.
• NLRHA does not confirm the few shear deficiencies identified in the design phase at
certain ground storey walls of prEN1998-1-2:2022 design.
• The basement storeys of all “Dual” or “Wall” buildings designed to prEN1998-12:2022 exhibit severe deficiencies in shear; those designed to one of the “Alternatives”
to prEN1998-1-2:2022, much less so, thanks to their lower flexural overstrength at the
base of the ground storey.
• Shear deficiencies in the basements of “Wall” buildings designed to prEN1998-12:2022 and in those of the “Dual” one for a PGA of 0.3 g well exceed the partial safety
factor of 1.6 built in the design shear resistance. These walls are expected to fail in
shear in the basement under the design seismic action. By contrast, the shear deficiencies in the basements of all “Dual” or “Wall” buildings designed to one of the “Alternatives” to prEN1998-1-2:2022 can be covered by the partial factor of 1.6. To prevent
such failures, the width of the web of deficient walls can be increased in the basement
storeys in proportion to their shear deficit, without changing anything else in the rest of
the building.
Summing up, Nonlinear Response History Analyses carried out in accordance with the
provisions of Eurocode 8 confirm the overall qualitative assessment which is based on the
degree of satisfaction of design targets for ductility of critical regions and shear resistance
of members in the design phase. However, in the light of the NLRHA results problems
identified in that previous phase turn out to be less acute or have even disappeared; this
point concerns in particular shear in storeys of ductile walls above ground.
13
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Bulletin of Earthquake Engineering (2024) 22:4477–4513
0.5
Average shear-demand-to-shear-resistance-ratio
"Wall" building, agR: 0.20g
0.4
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.3
0.2
1.2
1.1
1
0.9
0.8
0.7
0.6
Maximum shear-demand-to-shear-resistance-ratio
"Wall" building, agR: 0.20g
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.5
0.4
0.3
0.1
0.2
0.1
0
0.5
Average shear-demand-to-shear-resistance-ratio
"Dual" building, agR: 0.20g
0.4
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.3
0
1.2
1.1
1
0.9
0.8
0.7
0.6
Maximum shear-demand-to-shear-resistance-ratio
"Dual" building, agR: 0.20g
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.5
0.2
0.4
0.3
0.1
0.2
0.1
0
0.5
Average shear-demand-to-shear-resistance-ratio
"Frame" building, agR: 0.20g
0.4
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.3
0
1.2
1.1
Maximum shear-demand-to-shear-resistance-ratio
"Frame" building, agR: 0.20g
1
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.9
0.8
0.7
0.6
0.5
0.2
0.4
0.3
0.1
0.2
0.1
0
0.5
Average shear-demand-to-shear-resistance-ratio
"Wall" building, agR: 0.30g
0.4
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.3
0
1.2
1.1
Maximum shear-demand-to-shear-resistance-ratio
"Wall" building, agR: 0.30g
1
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.9
0.8
0.7
0.6
0.5
0.2
0.4
0.3
0.1
0.2
0.1
0
0.5
Average shear-demand-to-shear-resistance-ratio
"Dual" building, agR: 0.30g
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.4
0.3
0
1.2
1.1
Maximum shear-demand-to-shear-resistance-ratio
"Dual" building, agR: 0.30g
1
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.9
0.8
0.7
0.6
0.5
0.2
0.4
0.3
0.1
0.2
0.1
0
0.5
Average shear-demand-to-shear-resistance-ratio
"Frame" building, agR: 0.30g
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
0.4
0.3
0
1.2
1.1
Maximum shear-demand-to-shear-resistance-ratio
"Frame" building, agR: 0.30g
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
1
0.9
0.8
0.7
0.6
0.5
0.2
0.4
0.3
0.1
0.2
0.1
0
Superstructure
beams
Basement columns
Superstr. columns Ydir.
Superstr. columns Xdir.
Superstructure
beams
Basement columns
Superstr. columns Ydir.
Superstr. columns Xdir.
0
Fig. 14 Mean or maximum ratio per frame member group of shear from NLRHA to shear resistance per
Eurocode 8
13
Bulletin of Earthquake Engineering (2024) 22:4477–4513
Above ground storey Basement storeys
Ground storey
Y-dir.
X-dir.
Y-dir.
X-dir.
Y-dir.
X-dir.
Y-dir.
X-dir.
Y-dir.
X-dir.
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
Above ground storey Basement storeys
Maximum shear-demand-to-shear-resistance-rao
"Frame" building, agR: 0.20g
Y-dir.
X-dir.
Ground storey
Y-dir.
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
X-dir.
Y-dir.
X-dir.
Y-dir.
Ground storey
X-dir.
Y-dir.
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
4.2
4
3.8
3.6
3.4
3.2
3
2.8
2.6
2.4
2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
Above ground storey Basement storeys
Maximum shear-demand-to-shear-resistance-rao
"Dual" building, agR: 0.20g
Y-dir.
Above ground storey Basement storeys
Average shear-demand-to-shear-resistance-rao
"Frame" building, agR: 0.20g
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
Ground storey
4.2
4
3.8
3.6
3.4
3.2
3
2.8
2.6
2.4
2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
Y-dir.
X-dir.
Y-dir.
Ground storey
X-dir.
Y-dir.
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
Maximum shear-demand-to-shearresistance-rao
"Wall" building, agR: 0.20g
Y-dir.
Y-dir.
X-dir.
Above ground storey Basement storeys
Average shear-demand-to-shear-resistance-rao
"Dual" building, agR: 0.20g
X-dir.
3
2.8
2.6
2.4
2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
Y-dir.
Ground storey
X-dir.
3
2.8
2.6
2.4
2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
X-dir.
Y-dir.
EN1998-1:2004
prEN1998-1-2:2022
prEN1998-1-2 altern.1
prEN1998-1-2 altern.2
4.2
4
3.8
3.6
3.4
3.2
3
2.8
2.6
2.4
2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
X-dir.
Average shear-demand-to-shear-resistance-rao
"Wall" building, agR: 0.20g
X-dir.
3
2.8
2.6
2.4
2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
X-dir.
4510
Above ground storey Basement storeys
Fig. 15 Mean and maximum ratio per wall group of shear from NLRHA to design shear resistance per
Eurocode
6 Conclusions
The three six-storey-plus-two-basements concrete buildings designed in detail to Generation 1 of Eurocodes 2 (including structural fire design) and 8, and to the official drafts of
their Generation 2 counterparts at the end of 2023, have in one horizontal direction a wall-,
frame-equivalent-dual- or frame-lateral-load-resisting system, while in the other direction
the first two buildings have a wall system and the third one a wall-equivalent dual. The
design seismic action is always according to Generation 1 of Eurocode 8, scaled to a PGA
on rock of 0.2 or 0.3 g. As DC M is used for Generation 1 and DC 3 for Generation 2,
which have the same behaviour factors, q, in each one of the structural systems considered,
seismic action effects from the analysis are the same for the two Eurocode generations.
This has allowed to focus on the impact of the different design and detailing provisions
for concrete buildings in the two generations of Eurocodes 2 and 8. All designs have been
13
Bulletin of Earthquake Engineering (2024) 22:4477–4513
4511
assessed through Nonlinear Response History Analysis (NLRHA), carried out according to
the pertinent Eurocode 8 provisions.
Designs according to the draft of Generation 2 at the end of 2023 were found to meet
the performance goals of Eurocode 8 much better and more transparently than for Generation 1. However, this comes at the cost of larger steel quantities, and indeed most often
unnecessarily so, especially for confining reinforcement—which sometimes comes out in
surreal quantities that cannot be placed. To address this issue, proposals have been made
for a more rational linkage of the local ductility demands with the q-factor and the effective
elastic stiffness used in the analysis. If this change is accepted, critical regions of beams
and columns may be subject to prescriptive detailing rules alone, without explicit verification of their ductility capacity. Implementation of these proposals in alternative Generation
2 designs shows marked reduction in steel quantity at no loss in seismic performance, i.e,
superior cost-effectiveness.
Minor changes to the design and detailing rules of Generation 2 for ductile walls have
also been proposed and implemented in these alternative designs. However, they proved
only partly effective in resolving certain deadlocks, which originate from poorly justified
detailing provisions producing unnecessary and counterproductive flexural overstrengths
in such walls. To improve further on this issue, it may be necessary for Generation 2 of
Eurocode 8 to introduce its own National Determined Parameters (NDP) for the minimum
web reinforcement (vertical and horizontal) of ductile walls and recommend for them
much lower values than those recommended in Generation 2 of Eurocode 2. It may seem
unconventional to relax a detailing provision when dealing with a more challenging action
environment, as in design for moderate or high seismicity, instead of low, which does not
require full application of Eurocode 8. Nevertheless, the likelihood of shear failure of ductile walls and its consequences for the safety of the building and its occupants may make
the reasons for the high minimum web reinforcement recommended in Generation 2 of
Eurocode 2 look unimportant. Reduction of the minimum web reinforcement (vertical and
horizontal) recommended for ductile walls in earthquake resistant buildings below what is
recommended in Generation 2 of Eurocode 2 may render wall- and wall-equivalent-dual
systems of Generation 2 competitive to frame- or frame-equivalent systems—currently
they are not.
Generation 2 of Eurocode 8 does not have special design provisions for the free height
of ductile walls within rigid basements, which turns out to be a weak link in the buiding,
very likely to fail under the high shear force which builds up in it to balance the wall’s
moment resistance at the top of the rigid basement. It is vital to add such provisions, by reinstating those of Generation 1 and indeed improving/refining them.
Beam/column joints of Generation 2 designs having horizontal and vertical reinforcement not less than that of the critical region at the top of the column below appear to have a
low likelihood to fail, lower than that of their counterparts of Generation 1, which currently
do not require explicit verification of shear resistance. This finding may justify omitting
explicit verification of Generation 2 beam/column joints in shear, if their horizontal and
vertical reinforcement is not less than in the critical region at the top of the column below.
The proposals made for verification of the ductility capacity of critical regions of beams
and columns and of the shear strength of beam/column joints will improve ease-of-use of
Generation 2 of Eurocode 8 for concrete buildings.
The results of NLRHA confirm that the alternative provisions proposed for Generation
2 of Eurocode 8 lead to better overall performance at markedly lower cost, about the same
or even less than that of design to Generation 1. Problems identified in the design phase
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Bulletin of Earthquake Engineering (2024) 22:4477–4513
turn out to be less acute in the light of NLRHA, or have even disappeared; this point concerns in particular shear in storeys of ductile walls above ground.
Funding The authors declare that no funds, grants, or other support were received during the preparation of
this manuscript.
Data availability The datasets generated during and/or analysed during the current study are available from
the corresponding author on reasonable request.
Declarations
Conflict of interests The authors have no relevant financial or non-financial interests to disclose.
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Authors and Affiliations
Michael N. Fardis1
· Telemachos B. Panagiotakos2
* Michael N. Fardis
fardis@upatras.gr
1
Department of Civil Engineering, University of Patras, 26504 Patras, Greece
2
DENCO Structural Engineering, Marousi, Athens, Greece
13