Serbian Association for Earthquake Engineering (SUZI-SAEE)

May 25, 2022

1

From the first to the second generation of Eurocode 8

for the seismic design of concrete buildings –
with emphasis on wall systems

Michael N. Fardis
University of Patras, Greece
Vice-Chairman, CEN/TC250: ”Structural Eurocodes”
 Organization of the presentation
2

• Overview of the provisions of Eurocode 8 for the design

of new RC buildings, focusing on the evolution from the
current to the new generation.
• More detailed discussion of walls and wall-systems.
• Example application to 6(+2)-storey wall-system building.
 Eurocodes started

ENVs (pre-standards) started

Publication of ENVs

Conversion of ENV to EN

Publication of the 1st generation of the Eurocodes

Deadline to withdraw conflicting National Standards

Commission’s Mandate: 2nd generation of Eurocodes

Grant agreements for Phases 1 to 4 of drafting

Final EN-Drafts from all 4 Phases complete

National Comments to 2nd generation of Eurocodes

Formal Voting on 2nd generation of Eurocodes

1975 1990 1992 1998 2007 20102012-14 2014-21 2022 2020-24 2021-25

Deadline to withdraw 1st generation Eurocodes

2028
3

Timeline of the various generations of Eurocodes

General objectives of second generation:
• Reduce number of Nationally Determined Parameters. 4

• Enhance “Ease of use” by:

• Improving clarity;
• Simplifying routes through the Eurocodes;
• Limiting, where possible, alternative application rules;
• Avoiding/removing rules of little practical use in design.
• Fill voids – expand scope.
• Consolidate; produce shorter, succinct texts.
• Ensure stability for the users.

De-facto development:
• Updating of content according to State-of-the-Art.
New elements in the 2nd generation of Eurocodes
Structural
5

Assessment & retrofitting of existing structures

safety,
EN1990 serviceability
durability

Robustness of structures
Actions
EN1991 (loadings) on
structures

EN1992 EN1993 EN1994

concrete steel composite (steel-concrete) Material
CEN TS & EN Eurocodes:
EN1995 EN1996 EN1999
structural glass design &
timber masonry aluminium
detailing
Fibre-Reinforced membrane
Polymer structures structures
Horizontal,
EN1997 EN1998
service
geotechnical seismic
Eurocodes
 Eurocode 8 Parts
1st generation 2nd generation 6

EN1998-1 General rules, seismic EN1998-1-1 General rules, seismic

actions, rules for buildings action
EN1998-2 Bridges EN1998-1-2 Rules for new buildings
EN1998-3 Assessment and EN1998-2 Bridges
retrofitting of buildings
EN1998-4 Silos, tanks, pipelines EN1998-3 Assessment and retrofitting
of buildings and bridges
EN1998-5 Foundations, retaining EN1998-4 Silos, tanks and pipelines,
structures, geotechnical towers, masts and
aspects chimneys
EN1998-6 Towers, masts, chimneys EN1998-5 Geotechnical aspects,
foundations, retaining and
underground structures
 EN 1998-1:2004 General rules, seismic actions,
rules for buildings 7

1. General
2. Performance Requirements and Compliance Criteria
3. Ground Conditions and Seismic Action
4. Design of Buildings
5. Specific Rules for Concrete Buildings
6. Specific Rules for Steel Buildings
7. Specific Rules for Steel-Concrete Composite Buildings
8. Specific Rules for Timber Buildings
9. Specific Rules for Masonry Buildings
10.Base Isolation
Annex A (Informative): Elastic Displacement Response Spectrum
Annex B (Informative): Determination of Target Displacement for
Nonlinear Static (Pushover) Analysis
Annex C (Normative): Design of the Slab of Steel-Concrete Composite
Beams at Beam-Column Joints in Moment Resisting Frames
 prEN1998-1-1:2022 General rules, seismic action
Annex A (I) European Hazard Maps 8

4 Basis of design Annex B (N) Alternative identification of site

4.1 Performance requirements categories
4.2 Consequence classes Annex C (N) Site-specific elastic response
4.3 Limit states and associated seismic actions spectra
4.4 Primary and Secondary members Annex D (N) Criteria for selection and
4.5 Compliance criteria for new structures scaling of input motions
5 Site conditions and seismic action Annex E (N) Determination of target
5.1 Site conditions displacement and limit-state spectral
5.2 Seismic action acceleration by non-linear response-history
6 Modelling, analysis and verification analysis of equivalent sdof model
6.2 Modelling Annex F (I) Simplified reliability-based
6.3 Seismic action verification format
6.4 Force-based approach Annex G (N) Design of fastenings to
6.5 Non-linear static analysis concrete in seismic design situation
6.6 Response-history analysis Annex M (N) Material or product properties
6.7 Verification to limit states in EN 1998-1-1
6.8 Structures equipped with antiseismic devices
7 Deformation criteria and strength models
7.2 Reinforced concrete structures
7.3 Steel and composite-steel structures
7.4 Timber structures
 prEN1998-1-2:202X Rules for new buildings
4. Basis of design Annex A (I) Characteristics of earthquake resistant
5. Modelling and structural buildings and in plan regularity
9

analysis Annex B (I) Natural eccentricity and torsional radius

6. Verification of structural Annex C (N) Floor accelerations for ancillary elements
elements to limit states Annex D (N) Buildings with energy dissipation
7. Ancillary elements systems
8. Base isolated buildings Annex E (N) Seismic design of connections for steel
buildings
9. Buildings with energy
Annex F (N) Steel lightweight structures
dissipation systems
Annex G (N) Design of composite connections in
10. Specific rules for concrete
dissipative composite steel-concrete moment resisting
buildings frames
11. Specific rules for steel Annex H (I) Seismic design of exposed and embedded
buildings column base connections
12. Specific rules for Annex I (N) Design of the slab of steel-concrete
composite steel–concrete composite beams at beam-column joints in moment
buildings resisting frames
13. Specific rules for timber Annex J (I) Drift limits for eccentrically loaded
buildings unreinforced masonry piers
14. Specific rules for masonry Annex K (I) Simplified evaluation of drift demands on
buildings infilled frames
15. Specific rules for Annex L (N) Load-deformation relationships of
aluminium buildings dissipative timber components for non-linear analyses
4. Basis of design
4.1. Building classification prEN1998-1-2:202X Rules for new buildings
4.2. Seismic actions
4.3. Compliance criteria 10

4.4. Characteristics of earthquake resistant buildings

5. Modelling and structural analysis
5.1. Modelling
5.2. Minimum design eccentricity in buildings
5.3. Methods of analysis
6. Verification of structural elements to limit states
6.2. Verification of Significant Damage (SD) limit state
6.3. Verification to other limit states
10. Specific rules for concrete buildings
10.1 Scope
10.2. Basis of design and design criteria
10.3. Materials requirements
10.4. Structural types, behaviour factors, limits of seismic action and limits of drift
10.5. Beams
10.6. Columns
10.7. Beam-column joints
10.8. Ductile walls
10.9. Large walls
10.10. Flat slabs
10.11. Provisions for anchorages and laps
10.12. Provisions for concrete diaphragms
10.13. Prestressed concrete
10.14. Precast concrete structures
10.15. Design and detailing of foundations
 Limit States in prEN1998-1-1:2022
Limit State Facility operation Structural condition 11

Operational Continued use; any damage Only slight damage to structure and
(OP) SLS may be repaired later infills/partitions
Damage Safe, but normal use Light structural damage (localised bar yielding,
Limitation temporarily interrupted; concrete cracking or spalling). Insignificant
(DL) SLS permanent drift. Structure retains full
resistance with minor decrease in stiffness;
infills/partitions have distributed cracks
Significant No threat to life during event; Significant structural damage or moderate
Damage emergency / temporary use permanent drifts; sufficient capacity for gravity
(SD) ULS only; repair feasible, but loads; infills or partitions damaged but not
maybe uneconomic collapsed
Near Unsafe for emergency use; Heavy structural damage, or large permanent
Collapse life safety during earthquake drifts, or infills/partitions collapsed; strength
(NC) ULS almost ensured, not (barely) sufficient for gravity loads
guaranteed (falling debris)
Performance-based design of new buildings in EN1998-
1:2004 and EN1998-1-1:2022, EN1998-1-2:202X 12

Two-(and-a-half)performance levels design:

• ULS design of the structure (for ductility) for Significant
Damage; in Importance Class II or Consequence Class CC2
(ordinary) buildings, this is done for the “Reference seismic
action” (475yr return period).
• SLS verification of infills/partitions for Damage Limitation under
a frequent (~100 years) earthquake.
• (implicit) Collapse Prevention under a very strong/rare, but
unspecified, earthquake thanks to Capacity Design.
 EN 1998-1:2004 Recommended Importance classes & factors for buildings
Building type (nationally determined parameter - NDP) γI (NDP)
I Minor importance for public safety (warehouses, agricultural buildings) 0.8 13

II Ordinary (residential or office buildings, small buildings) 1

III Major consequences of collapse: Grandstands, large buildings, schools, 1.2
assembly halls, cultural facilities
IV Of vital importance for civil protection: hospitals, fire stations, power plants 1.4

EN1998-1-1:2022 & -1-2:202X: Recommended Consequence Classes (CC),

performance factors γLS,CC and return periods TLS,CC for the seismic action at four
Limit States

Building type γLS,CC (NDP) TLS,CC [years] (NDP)

(NDP) DL (& OP) SD NC DL (& OP) SD NC
CC1 see I above 0.4 0.8 1.2 50 250 800
CC2 see II above 0.5 1 1.5 60 475 1600
CC3a see III above 0.5 1.2 1.8 60 800 2500
CC3b see IV above 0.6 1.5 2.2 100 1600 5000

 The performance factor γLS,CC multiplies 475yr seismic action of CC2, like the
importance factor
 “Reference Seismic Action” and “Reference Return
Period” in EN1998-1:2004 and prEN1998-1-1:2022 14

The seismic action for which new structures of Importance Class II

or Consequence Class CC2 (ordinary) are designed for Significant
Damage is called “Reference seismic action”.
 Its mean return period is termed “Reference return period” and is
a nationally determined parameter (NDP) with recommended value
475 years (ie, 10% probability of exceedance of Reference seismic
action” in 50 years).
EN1998-1:2004: Standard Ground types
15
 EN1998-1-1:202X: Standard Ground types
medium 16

Ground class stiff soft

stiffness
Depth class vs,H (m/sec) 400-800 250-400 150-250

H800 (m)
very shallow H800 ≤ 5m A A E
shallow 5m < H800 ≤ 30m B E E
intermediate 30m < H800 ≤ 100m B C D
deep H800 > 100m B F F
 Representation of the seismic action by the Elastic
Response Spectrum for 5% damping. 17

 Seismic action defined in terms of Elastic Response Spectrum for 5%

viscous damping.
 Same spectrum applies to the two orthogonal independent horizontal
components of the seismic action; a different one for the vertical.
 The shapes of the spectra depend on ground type.
 The spectra of the “reference seismic action” on Ground of Type A (rock):
 In EN1998-1:2004 are defined in terms of:
 the Peak Ground Acceleration” (PGA) on rock, ag,R.
 In prEN1998-1-1:2022 in terms of the Spectral Acceleration on rock:
 at the constant-acceleration plateau of the spectrum, Sα,ref, and
 at 1 sec period, Sβ,ref.
 Zonation maps in the National Annex to EN1998-1:2004 give ag,R;
 Those of EN1998-1-1:202X will give Sα,ref and Sβ,ref, or just Sα,ref with Sβ,ref
taken equal to 20%, 30% or 40% of Sα,ref, for Sα,ref ≤2.5m/s2, 2.5m/s2<Sα,ref
≤5m/s2 or 5m/s2<Sα,ref, respectively (“low”, “moderate” and “high”
seismicity, according to prEN1998-1-1:2022).
EN1998-1:2004 Two recommended elastic spectral shapes
• Depending on the most significant contributions to the hazard at a site:
• Type 1 - High and moderate seismicity regions (Ms > 5,5 ) 18

• Type 2 - Low seismicity regions (Ms  5,5 ); near field earthquakes

Type 1 Type 2

Ground Type S TB (s) TC (s) TD (s) S TB (s) TC (s) TD (s)

A 1,0 0,15 0,4 2,0 1,0 0,05 0,25 1,2
B 1,2 0,15 0,5 2,0 1,35 0,05 0,25 1,2
C 1,15 0,2 0,6 2,0 1,5 0,1 0,25 1,2
D 1,35 0,2 0,8 2,0 1,8 0,1 0,3 1,2
E 1,4 0,15 0,5 2,0 1,6 0,05 0,25 1,2
4 5 D
E D Type 1 - Ms > 5,5 E

Se/ag
Se/ag

C 4 C
3
B
B
Type 2 - Ms  5,5
3
A A
2
2

1
1

0 0
0 1 2 3 0 1 2 3 4
T (s) 4 T (s)
prEN1998-1-1:2022 -Annex A (I)
475yr short-period 5%-damped 19

Spectral acceleration on Rock

prEN1998-1-1:2022 -Annex A (I)
475yr 1 sec 5%-damped
Spectral acceleration on Rock 20
EN1998-1-1:2022: Horizontal elastic response spectrum Se (T)
0  T  TA: 21

T A  T  T B:

T B  T  TC

TC  T  TD:

T  TD:

FA=2.5

   , )] s
EN1998-1-1:2022 Nonlinear amplification of spectral values
22

Ground Fα Fβ
type
H800, vs,H
H800, vs,H available Default value Default value
available
A 1,0 1,0 1,0 1,0
B , ) , )

C , ) , )

D , ) , )

E , ) , )

1,25
F 0,9 ,
, ) , , )

, ,
, Sα,RP, Sβ,RP in m/s2, vs,H in m/s
 Elastic design w/ force reduction and ductility
• 5%-damped elastic spectrum reduced by (prescriptive) 23

behaviour factor q, (depends on material, type, layout,

regularity & redundancy of structural system):
• Global ductility:
• One-to-one correspondence between q
& global displacement ductility factor, μ
• Inelastic spectra of SDOF system
(Vidic, Fajfar, Fischinger 1994):
 If T1 ≥ TC: μ = q
 If T1 < TC: μ = 1+(q-1)TC/T1

TC T1
 Buildings of any material in EN1998-1:2004 or
EN1998-1-2:202X
 Three Ductility Classes (DC): (except in masonry buildings):
24

DCH (High), DCM (Medium), DCL (Low) in EN1998-1:2004;

DC3, DC2, DC1 in EN1998-1-2:202X.
• Differences in:
behaviour factor q:
• usually q > 4 in DCH/DC3;
• 1.5 < q <4 in DCM/DC2
• q=1.5 (usually) in DCL/DC1.
Local ductility requirements
• ductility of materials or section,
• member detailing,
• capacity design against brittle failure modes.
 Heightwise irregular buildings: q-factor reduced by 20%.
 Buildings of any material in EN1998-1-2:202X
 Behaviour factor q for the reduction of the elastic spectrum 25

in force-based design split in three factors:

q = qsqRqD

• qs= 1.5 for (member and material) overstrength;

• qR ≥ 1 for redundancy of structural system;
• qD ≥ 1 for ductility (:capacity to deform inelastically
and dissipate energy in cyclic loading).
Column capacity design in ductile frames of any material
• Strong column/weak beam capacity design to avoid soft-story mechanisms: 26

• Required by EN1998-1:2004 in primary columns of DCH or DCM frames (in

RC buildings also in frame-equivalent dual systems) of over two stories.
• In EN1998-1-2:202X:
• Limited to DC3 RC frames and frame-equivalent systems of two or more stories
– except in 25% of the columns per frame and at the ground story of two-story
buildings with axial load ratio less than 0.3.
• In DC2 RC frames and frame-equivalent dual systems:
• Moment resistances at the ends of the n columns where plastic hinges may
form (index i) should meet at every storey the condition

( , : minimum column plastic rotation capacity in storey,

de,top: displacement of the top from linear analysis)
 EN 1998-1:2004
Basic value qo of behavior factor- regular in elevation RC buildings
27

Lateral-load resisting structural system DC L DC M DC H

Inverted pendulum system* 1.5 1.5 2
Torsionally flexible structural system** 1.5 2 3
Uncoupled wall system (>65% of base shear 1.5 3 4u/1
taken by walls; >half by uncoupled walls) not
belonging in one of the categories above
Any structural system other than above 1.5 3u/1 4.5u/1
*Inverted pendulum system: if ≥ 50% of total mass in upper-third of the height, or all
energy dissipation takes place at the base of a single element (except one-story
frames with all columns connected at the top via beams in both horizontal directions in
plan and with max. value of normalized axial load in seismic design situation νd ≤ 0.3).
** Torsionally flexible structural system: If, at any floor:
radius of gyration of floor mass > torsional radius in one or both main horiz. directions
(sensitive to torsional response about vertical axis).
Buildings irregular in elevation: behavior factor q = 0.8qo;
 EN 1998-1:2004: αu/α1 in q-factor of buildings for system
redundancy & overstrength
28

Normally:
αu & α1 from base shear-top displacement
curve of a pushover analysis.
• αu: seismic action at development of global mechanism;
• α1 : seismic action at 1st flexural yielding anywhere.
• αu / α1 ≤ 1.5;
• default values for buildings regular in plan:
= 1.0 for wall systems w/ just 2 uncoupled walls per horiz. direction;
= 1.1 for: one-story frame or frame-equivalent dual systems, or
wall systems w/ > 2 uncoupled walls per direction;
= 1.2 for: (one-bay multi-story frame or frame-equivalent dual systems),
wall-equivalent dual systems or coupled wall systems;
= 1.3 for: multi-story multi-bay frame or frame-equivalent dual systems.

•for buildings irregular in plan:

default value = average of default value of buildings regular in plan and 1.0
 EN 1998-1-2:202X
Basic value of behaviour factor- regular in elevation RC buildings
qo
29

qR qD
DC2 DC3 DC2 DC3
Frame or multi-story, multi-bay frames or
1,3 2,5 3,9
frame- frame-equivalent dual structures
1,3 2,0
equivalent dual multi-story, one-bay frames 1,2 2,3 3,6
structures one-story frames 1,1 2,1 3,3
Wall- or wall- wall-equivalent dual structures 1,2 1,3 2,3 3,6
equivalent dual coupled walls structures 1,2 1,4 2,0 2,5 3,6
structures uncoupled walls structures 1,0 1,3 2,0 3,0
large walls structures -- -- 3,0
Flat slab structures 1,1 1,2 -- 2,0 --
Inverted pendulum system 1.0 1.5 1.5 1.5 1.5
Buildings irregular in elevation or torsionally flexible systems:
behaviour factor q = 0.8qo;
 Restrictions in the use of DCs and structural systems
depending on seismicity 30

• EN 1998-1:2004
• Other than for low seismicity (475yr PGA at the ground surface >1
m/sec2, i.e., 475yr constant spectral acceleration of elastic spectrum
at surface >2.5m/sec2) DCL not recommended.

• EN 1998-1-2:202X
• If 475yr constant spectral acceleration of elastic spectrum at ground
surface (times 0.6, 1.25 or 1.6 for CC1, CC3a, CC3b, respectively) is:
• >2.5 m/sec2:
• frame or dual structures should be designed for DC 2 or 3;
• >5 m/sec2:
• flat slab frames should not be used,
• frame structures should be designed for DC3,
• wall structures for DC2.
Capacity-design shear, beams or columns -weak or strong
31

EN1998-1:2004
EN1998-1-2:202X
 DCM γRd=1.0,
 DC2 or 3: γRd=1.1
 DCH γRd=1.2

EN 1998-1:2004
 in DC M γRd=1.1 EN1998-1-2:202X
 in DC H γRd=1.3  DC2 or 3: γRd=1.1
 EN 1998-1:2004
Ductility of plastic hinges by detailing them for a target 32

curvature ductility factor μφ derived from the q-factor

•μφ=2qo-1 if T1≥Tc
•μφ =1+2(qo-1)Tc/T1 if T1<Tc
–T1: fundamental period of building,
–Tc: T at upper limit of constant spectral acceleration region,
– qo: q-factor unreduced for irregularity in elevation
(multiplied with MEd/MRd at a wall base).
• For steel class B (εu: 5-7.5%, ft/fy: 1.08-1.15) increase μφ-demand by
50%
 EN 1998-1:2004 Means for achieving μφ in plastic hinges
• Base of columns, ductile walls (symmetric reinforcement ω=ω’): 33

– Confining reinforcement (for walls: in boundary elements) with (effective)

mechanical volumetric ratio:
αωwd =30μφ(νd+ων)εydbc/bo-0.035
νd=Nd/bchfcd; εyd=fyd/Es;
bc: width of compression zone; bo: width of confined core;
ων: mechanical ratio of longitudinal web reinforcement =ρνfyd,v/fcd
– DC H columns not meeting the strong-column/weak-beam rule
(ΣMRc<1.3ΣMRb), should have full confining reinforcement at the end
regions of all stories, not just at the (building) base;
– DC H strong columns (ΣMRc>1.3ΣMRb) are also provided w/ confining
reinforcement for μφ corresponding to 2/3 of qo at the end regions of every
story.
• Beams:
– Max. mechanical ratio of tension steel: ω ≤ ω’+0.0018/μφ εyd
EN 1998-1-2:202X: Ductility of plastic hinges through
chord-rotation ductility factor μθ derived from q-factor
34

Ratio of:
• Chord rotation at SD LS
(average of:
 plastic ultimate chord-
rotation, θupl, &
 chord-rotation at
yielding, θy,
divided by safety factor of
~1.6) to
• chord-rotation at yielding, θy

should not be smaller than the

ductility-based component qD
of the behaviour factor used
in design.
EN1998-1-1:2022: Member chord rotation at yielding, θy
(Chord rotation at the end of a member, θ:
35

angle between normal to end section and chord

connecting member ends at the displaced position).
θy = sum of:
1. flexural component @ at yield curvature φy:
 φy(Ls+z)/3 if 45o-cracking of member precedes
flexural yielding of its end section (shear force at flexural
yielding, My/Ls> shear strength w/o shear reinforcement);
 φyLs/3 if it doesn’t
2. shear deformation,
- beams/rect. columns: 0.0019(1+h/1.6Ls)
- walls/box sections: 0.0011(1+h/3Ls)
- circular columns : 0.0025max[0; 1-Ls/8D]
3. fixed-end-rotation due to slippage of tension bars from
their anchorage outside the member length;
at yielding of the end section: θslip,y = φydbLfy/8√fc (MPa)
EN1998-1-1:2022: Ultimate plastic chord rotation capacity
of members w/ rect. compression zone 36

 DC =1, 2, 3 for DC!, DC2 or DC3;

 aw,r = 1 for rect. walls, aw,r=0 in all other cases;
 anr =1 in T-, H-, U-, box sections, anr=0 for rectangular sections;
 1=(1fy1+vfyv)/fc mech. steel ratio in entire tension zone (flange & web);
 2=2fy2/fc mechanical reinforcement ratio for compression zone;
 Ls/h=M/Vh: shear-span-to-depth ratio at section of maximum moment;
 =N/bhfc ; b: width of compression zone, N: axial force, >0 for compression;
 s=Ash/bwsh: ratio of transverse steel in direction of bending;
 : confinement effectiveness factor:  s h  s h   bi 2 / 6 
sh: centreline spacing of stirrups,   1  1   1 
bo, ho: confined core dimensions to centreline of hoop;  2bo  
2ho  
bo ho 
bi: axial spacing on section perimeter of longitudinal bars (index: i) engaged by stirrup or X-tie.
 EN1992-1-1:2004 –
Shear resistance of members with shear reinforcement 37

Variable strut inclination model: 1<cotθ<2.5, 22°<θ<45°

If VEd > VRdc,min

VEd  VRd,s= ρwbwzfywd(cot+cotα)sinα,
VEd  VRd,max=bwzfcd/(cot+tan), =0.6 (1– fck/250)
VRdc,min=[CRd,ck(100lfck)1/3+k1cp]bwd,
37
k=1+√(200/d(mm))2,
l=Asl/bwd: tension steel ratio, cp=NEd/Ac mean axial stress in section,
Recommended values: CRd,c=0.18/gC, k1=0.15
 EN1998-1:2004 – Members with shear reinforcement
DCL DCM DCH
All members VRd,c,min CRd,ck(100lfck)1/3+k1cp)bwd 38

Frame beam VRd,c 0

VRd,s ρwbwzfywdcot ρwbwzfywd
VRd,max 0.3(1– fck/250) bwzfcd sin2θ 0. 3(1– fck/250) bwzfcd
Frame VRd,c 0
column VRd,s ρwbwzfywdcot
VRd,max 0.3(1– fck/250) bwzfcd sin2θ
Wall other VRd,c 0
than below VRd,s ρwbwzfywdcot ρwbwzfywd
VRd,max 0.3(1– fck/250) bwzfcd sin2θ 0.12(1– fck/250) bwzfcd
VRd,c 0 VRd,c,min
Wall w/ Ls/h <2 VRd,s ρwbwzfywdcot ρwbwzfywdcot
VRd,max 0.3(1– fck/250) bwzfcd sin2θ 0.12(1– fck/250) bwzfcd sin2θ

,
Ls/h <2:
 prEN1992-1-1:202X –
Shear resistance of members with shear reinforcement 39

Strain-dependent variable strut inclination model: 1<cotθ<2.5, 22°<θ<45°

VEd  VRd,max=bwzfcd/(cot+tan),
: tensile strain @ right angles to struts,

, + ,
: (elastic) longitudinal strain at (cracked) section mid-depth

• Shear resistance to concentrated load at short distance Ls to

support (angle of compr. stress field θ<β=atan(h/Ls)):
 prEN1998-1-1:2022 – consistent with new approach in
Eurocode 2 40

Estimation of inelastic longitudinal strain at section mid-depth:

• In plastic hinges (“critical region(s)” @ member end(s)):
 From moment from linear analysis with design spectrum (elastic divided by
q), back-multiplied by q:

𝒄𝒄 𝒄
• Outside plastic hinges (outside “critical region(s)”):
 From moment and behavior factor q from linear analysis with design
spectrum (elastic divided by q), without multiplying by q.

• Squat members (angle of compression field θ<β=atan(h/Ls))

 41

Member prescriptive detailing in

EN1998-1:2004 vs EN1998-1-2:202X
 EN1998-1:2004 - Beam longitudinal reinforcement
DC H DC M DC L
“critical region” length at member end 1.5h h 42

min =As,min/bd at the tension side 0.5fctm/fyk (1) 0.26fctm/fyk (1), 0.13% (2)
max =As,max/bd in critical regions (2) '+0.0018fcd/(ydfyd) (3) 0.04
As,min, top and bottom bars 214 (308mm2) -
As,min, top bars in the span 0.25As,top-supports -
As,min, bottom bars in critical regions 0.5As,top (4) -
As,min, bottom bars at supports 0.25As,bottom-span (2)
anchorage length for diameter dbL (5) lbd =atr[1-0.15(cd/dbL-1)](dbL/4)fyd/(2.25fctdapoor) (6),(7),(8),(9)
(1) fctm (MPa)=0.3(fck(MPa))2/3: mean tensile strength of concrete; fyk (MPa): nominal yield stress of
longitudinal bars
(2) NDP (Nationally Determined Parameter) per EC2; value recommended in EC2 is given here
(3) ': steel ratio at the opposite side of the section; : curvature ductility factor corresponding to
basic value of behavior factor, qo, applicable to the design; yd = fyd/Εs.
(4) This As,min is additional to the compression steel from the ULS verification of the end section in
flexure under the extreme hogging moment from the analysis for the seismic design situation.
(5) Anchorage length in tension reduced by 30% if bar end extends by ≥5dbL beyond a bend≥ 90o.
(6) cd: concrete cover of anchored bar, or one-half the clear spacing to nearest parallel anchored
bar if it is smaller
(continued next slide)
 EN1998-1:2004 - Beam longitudinal reinforcement (cont’d)
(continued from previous slide)
(7) atr = 1-k(nwAsw-As,t,min)/As ≥ 0.7, with Asw: cross-sectional area of tie-leg within the cover of the 43

anchored bar; nw: number of such tie legs over the length lbd; k = 0.1 if the bar is at a corner of
a hoop or tie, k = 0.05 otherwise; As = πdbL2/4 and As,t,min is specified in EC2 as equal to
0.25As.
(8) fctd=fctk,0.05/gc = 0.7fctm/gc = 0.21fck2/3/gc : design value of 5%-fractile tensile strength of concrete.
(9) apoor = 1.0 if the bar is in the bottom 0.25 m of the beam depth, or (in beams deeper than 0.6
m) ≥ 0.3 m from the beam top; otherwise, apoor = 0.7.

EN1998-1:2004 - Beam transverse reinforcement

DC H DC M DC L
outside critical regions
spacing, sh 0.75d
w =Ash/bwsh  (0.08√fck(MPa))/fyk(MPa) (1)
in critical regions
diameter, dbw 6 mm
spacing, sh  6dbL (2), h/4, 24dbw, 175mm 8dbL (2), h/4, 24dbw, 225mm -
(1) NDP (Nationally Determined Parameter) per EC2; value recommended in EC2 is given here
(2) dbL: minimum diameter of all top and bottom longitudinal bars within the critical region.
 prEN1998-1-2:202X - Beam longitudinal reinforcement
DC 3 DC 2 DC 1
“critical region” length at member end h 44

Such that moment resistance

min =As,min/bd at the tension side 0.5fctm/fyk (1)
exceeds cracking moment
fck ≤ 25 MPa '+0.013-0.002fyk/100 '+0.015-0.002fyk/100
max =As,max/bd
in critical 25 <fck(MPa)<50 '+0.026-0.004fyk/100 '+0.028-0.004fyk/100 -
regions (2)
fck ≥ 50 MPa '+0.035-0.005fyk/100 '+0.037-0.005fyk/100
As,min, bottom bars at supports 0.25As,bottom-span (2)
(1) fctm (MPa)=0.3(fck(MPa))2/3 if fck50 MPa, fctm (MPa)=1.1(fck(MPa))1/3 if fck>50 MPa; fyk (MPa):
nominal yield stress of longitudinal steel.
': steel ratio at the opposite side of the section; fyk in MPa.
prEN1998-1-2:202X - Beam transverse reinforcement
DC 3 DC 2 DC 1
outside critical regions
spacing, sh 0.75d
w =Ash/bwsh  (0.08√fck(MPa))/fyk(MPa) (1)
in critical regions
spacing, sh  8dbL (2), h/4, 24dbw 12dbL (2), h/4, 30dbw -
(1) Value may be reduced by 10 or 20%, when ductility class B or C steel is used, respectively.
(2) dbL: minimum diameter of all top and bottom longitudinal bars within the critical region.
 EN1998-1:2004 - Column longitudinal reinforcement
DC H DC M DC L 45

min = As,min/Ac 1% 0.1Nd/Acfyd, 0.2% (1)

max = As,max/Ac 4% 4% (1)
diameter, dbL 8mm
number of bars per side 3 2
spacing along the perimeter of bars
150mm 200mm -
restrained by a tie corner or hook
Axial load ratio in seismic design
0.55 0.65 1.00
situation 
distance along perimeter of unrestrained
150mm
bar to nearest restrained one
lap splice length (2) l0 =1.5[1-0.15(cd/dbL-1)]atr(dbL/4)fyd/(2.25fctd) (3), (4), (5)

(1) NDP (Nationally Determined Parameter) per EC2; value recommended in EC2 is given here
(2) Anchorage length in tension reduced by 30% if bar end extends by ≥ 5dbL past a bend ≥ 90o.
(3) cd: minimum of: concrete cover of lapped bar and 50% of clear spacing to adjacent lap splice.
(4) atr =1-k(2nwAsw-As,t,min)/As, with k = 0.1 for bars at a corner of a hoop or tie, k = 0.05 otherwise;
Asw: cross-sectional area of a column tie; nw: number of ties in the cover of the lapped bar over
the outer third of the length l0; As = πdbL2/4 and As,t,min is specified in EC2 as equal to As.
(5) fctd=fctk,0.05/gc = 0.7fctm/gc = 0.21fck2/3/gc : design value of 5%-fractile of concrete tensile strength.
 EN1998-1:2004 - Column transverse reinforcement
DC H DC M DC L
critical region length(1)  1.5hc, 1.5bc, 0.6m, Hcl/5 hc, bc, 0.45m, Hcl/6 hc , b c , 46

Outside the critical regions

diameter, dbw  6mm, dbL/4
spacing, sw  20dbL, hc, bc, 400mm
at lap splices of bars
12dbL, 0.6hc, 0.6bc, 240mm
with dbL>14mm, sw
In critical regions (2)
diameter, dbw  (3) 6mm, 0.4√(fyd/fywd)dbL 6mm, dbL/4
spacing, sw  (3), (4) 6dbL, bo/3, 125mm 8dbL, bo/2, 175mm as outside critical regions
mechanical ratio wd(5) 0.08 -
effective mechanical ratio
30*dyd bc/bo - 0.035 -
awd (4), (5), (6), (7)

In the critical region at the base of the column (at the connection to the foundation)
mechanical ratio wd 0.12 0.08 -
effective mechanical ratio
30dydbc/bo -0.035 -
awd (4), (5), (6), (8), (9)
(1) hc, bc, Hcl: column sides and clear length.
(2) For DC M: Ιf a value of q ≤ 2 is used in design, transverse reinforcement in critical regions of
columns with axial load ratio d ≤ 0.2 may follow rules for DCL columns.
(continued next slide)
EN1998-1:2004 - Column transverse reinforcement (cont’d)
(continued from previous slide) 47

(3) For DC H: In the two lower stories of the building, the requirements on dbw, sw apply over a
distance from the end section not less than 1.5 times the critical region length.
(4) Index c denotes full concrete section; index o the confined core to centreline of perimeter
hoop; bo is the smaller side of this core.
(5) wd: volume ratio of confining hoops to confined core (to centerline of perimeter hoop) times
fywd/fcd.
(6) a = (1-s/2bo)(1-s/2ho)(1-{bo/[(nh-1)ho]+ho/[(nb-1)bo]}/3): confinement effectiveness factor of
rectangular hoops at spacing s, with nb legs parallel to the side of the core with length bo and
nh legs parallel to the side of length ho.
(7) For DCH: at column ends protected from plastic hinging through the capacity design check at
beam-column joints, * is the value of the curvature ductility factor that corresponds to 2/3 of
the basic value, qo, of the behavior factor applicable to the design; at the ends of columns
where plastic hinging is not prevented, because of the exemptions from the application of the
strong column-weak beam rule, * is taken equal to  defined in Note (8) (see also Note (9));
yd= fyd/Εs.
(8) : curvature ductility factor corresponding to basic value, qo, of behavior factor
(9) For DCH: The requirement applies also in the critical regions at the ends of columns where
plastic hinging is not prevented, because of the exemptions from the application of the strong
column-weak beam rule.
 prEN1998-1-2:202X - Column longitudinal reinforcement
DC 3 DC 2 DC 1
min = As,min/Ac 1% 0.1Nd/Acfyd, 0.2%
48

max = As,max/Ac 4% 4% (1)

diameter, dbL 12 mm

number of bars per side 3 2
spacing along the perimeter of bars restrained by a tie corner or hook 200mm 250mm -
Axial load ratio in seismic design situation  0.55 0.65 1.00
distance along perimeter of unrestrained bar to nearest restrained one 150mm

prEN1998-1-2:202X - Column transverse reinforcement

DC 3 DC 2 DC 1
critical region length (1)  hc, bc, 0.45m, Hcl/6 hc, bc
Outside critical regions
diameter, dbw  dbL/4
spacing, sw  15dbL, hc, bc, 300mm
at lap splices of bars with dbL>14mm, sw 9dbL, 0.6hc, 0.6bc, 180mm
In critical regions
diameter, dbw  6mm, dbL/4
spacing, sw (2) 8dbL, bo/2, 175mm 9dbL, bo/2, 200mm as at bar laps w/ dbL>14mm
mechanical ratio wd  (3) 0.08 0.05 -
(1) hc, bc, Hcl: column sides and clear length.
(2) Index o denotes confined core to axis of perimeter hoop; bo is the smaller side of this core.
(3) wd: volume ratio of confining hoops to confined core (to axis of perimeter hoop) times fywd/fcd
 EN1998-1:2004 - Walls
DC H DC M DC L
 max(lw, Hw/6) (2)
critical region height, hcr
 min(2lw, hstorey) if wall 6 stories - 49

 min(2lw, 2hstorey) if wall > 6 stories

Boundary elements
a) in critical height region:
- length lc from wall edge  0.15lw, 1.5bw, part of the section where c >0.0035 -
- thickness bw over lc  0.2m; hst/15 if lcmax(2bw, lw/5), hst/10 otherwise -
- vertical reinforcement:
min over Ac = lcbw 0.5% 0.2% (1)
max over Ac 4% (1)
spacing along perimeter of
bars restrained by tie corner 150mm 200mm -
or cross-tie hook
- confining hoops (index w)(3)
diameter, dbw  6mm, 0.4√(fyd/fywd)dbL 6mm, wherever L>
spacing, sw  (4) 6dbL, bo/3, 125mm 8dbL, bo/2, 175mm 2% in section:
wd  (3) 0.12 0.08 as over rest of
the wall (see
awd  (4), (5) 30(d+)ydbw/bo - 0.035 case b below)
b) over the rest of the wall Wherever in the section c>0.2%: v,min = 0.5%; elsewhere: 0.2%
height: In parts of the section where L > 2%:
- distance of unrestrained bar in compression zone to nearest
restrained bar  150mm;
- hoops with dbw  max(6mm, dbL/4), spacing sw  min(12dbL,
0.6bwo, 240mm) (1) till distance 4bw above or below floor slab
/beam; sw  min(20dbL, bwo, 400mm) (1) beyond that distance
 EN1998-1:2004 - Walls (cont’d)
(1) NDP (Nationally Determined Parameter) per EC2; the value recommended in EC2 is given 50

here
(2) lw: long side of rectangular wall section or rectangular part thereof; Hw: total height of wall;
hstory: story height.
(3) (In DC M only) The DCL rules apply to the confining reinforcement of boundary elements, if:
under the maximum axial force in the wall from the analysis for the seismic design situation,
the wall axial load ratio d= NEd/Acfcd is  0.15; or, if d  0.2 but the q-value used in the design
is  85% of the q-value allowed when the DC M confining reinforcement is used in boundary
elements.
(4) Notes (4), (5), (6) of Table for EN1998-1:2004 columns apply to the confined core of boundary
elements.
(5) : value of the curvature ductility factor corresponding to the product of the basic value qo of
the behavior factor times the ratio MEdo/MRdo of the moment at the wall base from the analysis
for the design seismic action to the design value of moment resistance at the wall base for the
axial force from the same analysis; yd= fyd/Εs; vd: mechanical ratio of vertical web
reinforcement.
 EN1998-1:2004 - Walls (cont’d)
DC H DC M DC L
Web 51

thickness, bwo  max(150mm, hstorey/20) -

vertical bars (index: v):
(1)
v =Asv/bwosv  0.2%, but 0.5% wherever in the section c>0.002 0.2%
v =Asv/bwosv  4%
dbv  8mm -
dbv  bwo/8 -
spacing, sv  min(25dbv, 250mm) min(3bwo, 400mm)
horizontal bars (index: h):
h,min 0.2% max(0.1%, 0.25v) (1)
dbh  8mm -
dbh  bwo/8 -
spacing, sh  min(25dbh, 250mm) 400mm

v,min at construction joints (6) max(0.25%; 1.3 f ctd  N Ed / Ac ) -

f yd  1.5 f cd f yd

(6) NEd: minimum axial load from the analysis for the seismic design situation (positive for
compression); fctd=fctk,0.05/gc = 0.7fctm/gc = 0.21fck2/3/gc : design value of 5%-fractile tensile
strength of concrete.
 prEN1998-1-2:202X - Walls
DC 3 DC 2 DC 1
critical region height, hcr lw, Hw/6, 2lw, hstory if wall 6 stories, 2hstory if >6 stories - 52
Boundary elements
a) in critical height region:
- length lc from wall edge  0.15lw, 1.5bw -
- thickness bw over lc  0.2m; hst/15 if lc2bw, lw/5; hst/10 otherwise -
- vertical reinforcement:
diameter, dbL 12 mm
number of bars per side 3 – every other one engaged by hoop or cross-tie -
min over Ac = lcbw 1% 0.2%, 0.5fctm/fyk (1)
max over Ac 4% (1)
spacing (along perimeter) of bars
200mm 250mm -
restrained by tie corner or X-tie
- confining hoops (index w): wd  0.08 0.05 -
b) over the rest of the wall height: As in the web (see below)
Web
thickness, bwo  150mm, hstory/20, lw/40 -
vertical bars (index: v):
v =Asv/bwosv  0.25%; 0.5% wherever in the section c>0.002 0.2%, 0.5fctm/fyk (1)
v =Asv/bwosv  4%
spacing in critical region, sv  250mm 300mm 3bwo, 400mm(1)
horizontal bars (index: h):
h,min 0.25% 0.5fctm/fyk, v/4 (1)
spacing in critical region, sh  250mm 300mm 400mm(1)
 53

Types of walls in Eurocode 8:

• Ductile walls for moderate or high seismicity

• Large, lightly reinforced walls for low or moderate

seismicity
 Two types of dissipative RC walls
• Ductile walls: 54

– Fixed at the base, to prevent rotation there with respect to rest of

structural system.
– Designed & detailed to dissipate energy only in flexural plastic
hinge just above the base.
• Large lightly-reinforced walls (only in DCM, DCL in EN
1998-1:2004)
– Walls with horizontal dimension lw ≥ 4m, expected to develop limited
cracking or inelastic behavior during design seismic action, but to
transform seismic energy to potential energy (uplift of masses) & to
energy radiated back into the soil by rigid-body rocking, etc.
– Large X-sectional length, lack-of-fixity at the base or connection
with transverse walls prevent plastic hinging at the base of such
walls and hence energy dissipation in plastic hinges.
 Ductile Walls – EN1998-1:2004
Over-design in shear, by multiplying shear forces from linear analysis for 55

design seismic action, V’Ed, by factor ε, accounting for overstrength of

plastic hinge at the base and higher modes after plastic hinging there:
DC M walls:

DC H squat walls (hw/lw ≤ 2):

Over-design for flexural overstrength of the base w.r.to analysis
MEdo: design moment at base section (from analysis),
MRdo: design flexural resistance at the base section,
γRd=1.2

DC H slender walls (hw/lw > 2):

Over-design for flexural overstrength of the base
w.r.to analysis & for increased inelastic shears
Se(T): ordinate of elastic response spectrum
TC: upper limit period of constant spectral acceleration region
T1: period of mode with the largest participating mass in direction of VEd
 Ductile Walls – prEN1998-1-2:202X
Design shear forces: 56

V’Edw(z): from the combination of shears in all modes from the analysis;
V’Edw,1(z): shear in mode with largest participating mass in direction of VEd

DC 2 walls:

DC 3 walls:

MEdo: design moment at base section (from the analysis),

MRdo: design flexural resistance at base section,
γRd=1.2
0.1 in lower-third of wall height;
= 0.05 in middle-third;
= 0.25 in upper-third.
Se(T): ordinate of elastic response spectrum
TC: upper limit period of constant spectral acceleration region
T1: period of mode with the largest participating mass in direction of VEd
 Design shears in “dual” structural systems
57

To account for increase in the upper story shears due to higher mode
inelastic response (after plastic hinging at the base)
 Ductile walls: Overdesign in bending
• Strong column/weak beam capacity design not required in wall or wall- 58

equivalent dual systems (ie, if walls resist >50% of seismic base shear)
• But: ductile walls over-designed in flexure for linear envelope of moments
from the analysis, to ensure that plastic hinge develops only at the base:

M Edw

h cr
M 'E d w

M 'E d w ,b a s e

EN1998-1:2004 (envelope anchored M R d w ,b a s e

@ base to moment from the analysis)
g R d M R d w ,b a s e

prEN1998-1-2:202X (envelope anchored

@ base to 1.2 x Moment resistance there)
Ductile walls: Detailing for ductility
• In plastic hinge zone (“critical region” over one-sixth of wall height):
59

boundary elements:
• EN1998-1:2004: effective mechanical volumetric ratio of confining
reinforcement:
αωwd=30μφ(νd+ω)εydbc/bo-0.035
over at least length of compression zone: xu=(νd+ωv)lwεydbc/bo
where strain is between: ε*cu=0.0035+0.1αωw & εcu=0.0035

lc

b0 b = bw

lw
Examples of large walls
60
 Large lightly reinforced concrete walls
• Wall system classified as one of large lightly reinforced walls if, in horizontal 61

direction of interest:
– At least 2 walls with lw>4 m, supporting together >20% of gravity load above
(: sufficient no. of walls / floor area & significant uplift of masses); if one wall: q=2
– Fund. period T1<0.5s for fixity at the base against rotation (: low wall aspect ratio)
• Systems of large lightly reinforced walls:
– q=3;
– special (less demanding) dimensioning & detailing.
• Rationale: For large walls, minimum reinforcement of ductile walls implies:
– very high cost;
– flexural overstrength that cannot be transmitted to ground.
On the other hand, large lightly reinforced walls:
– preclude (collapse due to) story mechanism,
– minimize nonstructural damage,
– have shown satisfactory performance in strong EQs.
• If structural system does not qualify as one of large lightly reinforced walls,
all its walls designed & detailed as ductile walls.
Design/detailing of large lightly reinforced walls -EC8
• Vertical steel tailored to demands due to M & N from 62

analysis
– Little excess (minimum) reinforcement, in order to
minimize flexural overstrength.
• Shear verification for V from analysis times (1+q)/2 ~2:
– If so-amplified shear demand is less than (design) shear
resistance without shear reinforcement:
No (minimum) horizontal reinforcement. Reason:
• Inclined cracking prevented (horizontal cracking &
yielding due to flexure mainly at construction joints);
• If inclined cracking occurs, crack width limited by
deformation-controlled nature of response (vs. force-
controlled non-seismic actions covered in EC2), even
without min horizontal steel.
 Non-rectangular walls in Eurocode 8
• Modelling, dimensioning and detailing only as vertical prismatic 63

members.
• “Composite wall sections consisting of connected or intersecting
rectangular segments (T-, L-, U-, I- or similar sections) should be
taken as integral units, consisting of a web or webs parallel, or
approximately parallel, to the direction of the acting seismic shear
force and a flange or flanges normal, or approximately normal, to it.”
• In the calculation of moment resistance and in analysis (for the
properties of the cracked cross-section), the effective flange width
on each side of a web ….”.
• Modelling with “shell” FE and dimensioning/detailing for ductility as
planar members:
• Not covered.
• Adopt DCL (DC1) with q=1.5?
• Strain limits given in prEN1998-1-1:2022 apply only for the
calculation of the ultimate curvature of prismatic members.
prEN1998-1-1:2022: Ultimate strains in members in cyclic flexure
• Before spalling:
Concrete: 0.0035   cu  18.5 / h ( mm )   0.01
2
• Steel: εsu=0.4εu,k , 64

• After spalling:
• Steel: εsu=(4/15)εu,k1 3db / sh 1 0.75exp(0.4Nbars,compression 
• Concrete: , , ,
• for rect. compression zone:  cu ,c   cu  0.04 a w f yw / f c

• for circular sections:  cu ,c   cu  0.07 a w f yw / f c

• for triangular compression zone:  cu ,c   cu  0.12 a w f yw / f c

 w: ratio of transverse reinforcement in direction of bending (or minimum in two
transverse directions for biaxial bending); fyw: its yield stress,
 : confinement effectiveness factor:  s h  s h   bi 2 / 6 
  1  1   1 
– rectangular sections:  2b2o  2ho  bo ho 
 sh 
– circular sections & circular hoops:   
 2 D 
1 
 o  sh 
– circular sections & spiral reinforcement:   1  
s : centerline spacing of stirrups,
h
 2 Do 
Do: confined core diameter to centreline of hoop.
Earthquake damage to walls
65
Collapse of open-ground-story building with walls
66
Ground story collapse in open-ground-story building with walls
67
Ground story collapse in open-ground-story building with walls
68
Shear failures
69
 70

Shear
failures
 Shear
failures
71
Shear failures
72
 73

Sliding shear at
construction joint
 74

Flexural
& shear
failure
 A special case:
The thin, tall, high-axial-load walls in 75

Chile, Viña del Mar & Concepción

(photos courtesy Patricio Bonelli & Rodolfo Saragoni)
76

76
77
Typical L-, C- and T- walls
78
 Typical walls
79

Walls in a basement
80

80
81
82
83
84
85
86

86
87
88
89
 90

Basement walls
Horizontal failure strip in basement walls
91
Horizontal failure strip in basement walls
92
 93

Edge of
basement walls
Edge of basement walls at horizontal failure strip
94
 EUROCODE 8
Application of 1st Generation Eurocodes to design of
95

6-storey RC Wall-system building with two basements

APPLICATION OF EN-EUROCODE 8 PART 1
FOR THE SEISMIC DESIGN OF
MULTISTOREY CONCRETE BUILDINGS

MICHAEL N. FARDIS, GEORGIOS TSIONIS

Vertical section along Y axis
96
D C B A
 Framing plan of typical floor
97

1 2 3 4 5 6

SLAB

X
D
 Framing plan of basements
1 2 3 4 5 6 98

SLAB

D
 Foundation plan view
99

1 2 3 4 5 6

FOUNDATION
 Design specifications
100

• Concrete: C25/30
• Steel class: S500
• Finishings: 2 kN/m2
• Live loads: 2 kN/m2
• No masonry infills.
• Importance Class ΙΙ (γΙ=1)
• Type 1 Spectrum on Ground Category B
• Design PGA (on rock) ag = 0.25g
• Ductility Class M (Medium)
 Behaviour factor(s)
• Regular in plan and in elevation, no matter the two basements 101

• Structural system, on the basis of the base shear taken by walls

• Vw,Χ=0.648V0Χ=> Wall-equivalent dual system (almost a wall system)

qx=qo,xkw=3.0αu/α1kw=3.0x1.2x1.0=3.6.
0.8
Se(T)
• Vw,Υ=0.923V0Υ=> Wall system Sd,x(T)
Sd,y(T)
0.6

Spectral acceleration (g)

qy=qo,ykw=3.0x1.0=3.0
0.4

0.2

0.0
0 1 2 3 4
Period (sec)
 Periods from Rayleigh quotient
- T1x = 0.85 sec, 102

- T1y = 0.68 sec.

Spectral values Sd(T1)=αgS 2.5(Tc/T1)/q

- Sd(T1x) = 0.25g×1.2×2.5×0.50/0.85/3.6 = 0.12 g along Χ,
- Sd(T1y) = 0.25g×1.2×2.5×0.50/0.68/3.0 = 0.18 g along Υ.

Base shear for lateral force procedure

- Fbx = λ m Sd(T1x) = 0.85×22939×0.12 = 2340 kN,
- Fby = λ m Sd(T1y) = 0.85×22939×0.18 = 3510 kN.
Storey masses, loads for lateral force method, torsional moments
due to accidental torsion
103

zimi eaXifXi eaYifYi MSRSS

story zi (m) mi (ton) fi/Vb fXi (kN) fYi (kN)
(tonm) (kNm) (kNm) (kNm)
6 19 373.2 7090 0.27 622 933 444. 1413. 1482

5 16 390.6 6249.8 0.23 548 822 392. 1246. 1306

4 13 390.6 5078.1 0.19 446 668 318. 1012. 1061

3 10 390.6 3906.2 0.15 343 514 245. 778. 816

2 7 390.6 2734.4 0.10 240 360 171. 545. 571

1 4 402.7 1610.8 0.06 141 212 101. 321. 337

Sum: 2338.3 26669.2 1 2340 3510

 Natural modes
Τ3 < T1, Τ2: Mode Period (sec) mx (%) my (%) 104

Not
1 0.86 53.3 0.0
torsionally
flexible 2 0.68 0.0 53.5
3 0.49 0.1 0.0

T1 = 0.86 s 4 0.22 11.4 0.0

5 0.16 0.0 21.1
6 0.12 0.3 0.0

Τ2 = 0.69 s 7 0.10 6.2 0.0

8 0.08 0.0 17.8
9 0.07 15.9 0.0
10 0.06 3.8 0.0
sum 91.1 92.3
Τ3 = 0.49 s
Interstorey drift ratio under Serviceability (Damage limitation) action
105

20 direction X
direction Y
15

10
Height (m)

0
0.0 0.1 0.2 0.3 0.4

-5

-10
Drif t ratio (%)
Seismic shears (left) and moments (right) due to EX+0.3EY. Frame A

106

1 2 3 4 5 6

C
Seismic shears (left) and moments (right) due to EX+0.3EY. Frame B

107

1 2 3 4 5 6

C
Seismic shears (left) and moments (right) due to EX+0.3EY. Frame C

108

1 2 3 4 5 6

C
Seismic shears (top) and moments (bottom) in basement wall D

109

1 2 3 4 5 6

D
Seismic shears (left) and moments (right) due to EY+0.3EX. Frame 1
1 2 3 4 5 6

110

D
Seismic shears (left) and moments (right) due to EY+0.3EX. Frame 2
1 2 3 4 5 6

111

D
Seismic shears (left) and moments (right) due to EY+0.3EX. Frame 3
1 2 3 4 5 6

112

D
Seismic shears (left) and moments (right) due to EY+0.3EX. Wall W3

113

1 2 3 4 5 6

D
Seismic shears (left) & moments (right) in X (left) or Y (right) of Wall W5
1 2 3 4 5 6

A 114

D
Gravity loads shears (top) and moments (bottom) in basement wall 1

115

1 2 3 4 5 6

D
 116

1 2 3 4 5 6

Gravity loads shears (top row) & moments (2nd row)

in basement walls A (top) or D (bottom)
B

D
 117

(Sample) Dimensioning & detailing of

beams at ULS & SLS
 Frame 2, Story 5, Beams B27, B28: ULS design of longitudinal bars
Beam B28, clear length: 6.6 m, section: T, depth h: 0.5 m, width bw: 0.3 m, flange thickness hf: 0.18 m
Location max bar compression maxMEd req. steel beam bars prov. steel design moment118
2 2
Ø (mm) flange width (m) (kNm) area (mm ) continuous added area (mm ) resistance (kNm)
left end (C2), top 14 0.30 202.5 1182 2Ø14 4Ø14 1204 † 213.0
‡
left end, bottom 14 0.72 -12.2 591 2Ø14 - 616 116.6
midspan, bottom - 2.68 101.7 526 2Ø14 2Ø14 616 ‡, § 118.8
†
right end (C7), top 24 0.30 164.5 934 2Ø14 2Ø16 1120 193.3
‡
right end, bottom 24 1.14 44.8 467 2Ø14 - 462 88.7
†: Provided top reinforcement includes 250 mm2 from the slab per m of an effective tension flange width which
extends beyond each side of a supporting column by 4hf at interior joints or 2hf at exterior ones.
‡: Additional bottom mid-span bars extended: 2Ø14 to the left end; 1Ø14 to the right end
§: Additional bottom mid-span bars extended across C7 to the left end of beam B27: 1Ø14.
Beam B27, clear length: 6.6 m; section: T; depth h: 0.5 m; width bw: 0.3 m; flange thickness hf: 0.18 m
Location max bar compression maxMEd req. steel beam bars prov. steel design moment
Ø (mm) flange width (m) (kNm) area (mm ) continuous added area (mm2) resistance (kNm)
2

left end (C7), top 24 0.30 185.0 1065 2Ø14 2Ø16 1120 † 193.3
left end, bottom 24 1.14 23.8 533 2Ø14 - 616 §, ‡ 117.7
midspan, bottom - 2.68 100.3 519 2Ø14 2Ø14 616 ‡ 118.8
†
right end (C12) top 14 0.30 183.4 1055 2Ø14 3Ø14 1050 182.6
‡
right end, bottom 14 0.72 6.5 528 2Ø14 - 616 116.6
†: Provided top reinforcement includes 250 mm2 from the slab per m of an effective tension flange width which
extends beyond each side of a supporting column by 4hf at interior joints or 2hf at exterior ones.
‡: Additional bottom mid-span bars extended: 1Ø14 to the left end; 2Ø14 to the right end
§: Additional bottom mid-span bars of beam B28 extended across C7 to the left end of beam B27: 1Ø14.
 Frame 2, Story 5, Beams B27, B28: SLS checks per EC2: Stress
limits; crack width <wmax=0.3 mm; steel area for crack control
Beam B28 119

Location for characteristic loads G+Q for quasi-permanent loads G+ψ2Q steel area/crack control
moment steel concrete moment concrete crack spacing crack width minimum provided
(kNm) stress/fyk stress/fck (kNm) stress/fck (mm) (mm) (mm2) (mm2)
left end top 125.8 0.628 0.348 107.4 0.297 324.8 0.26 214 923
midspan bottom 79.0 0.605 0.084 67.4 0.071 283.2 0.22 75 615
right end top 70.4 0.441 0.220 59.9 0.188 498.3 0.28 380 709
Beam B27
Location for characteristic loads G+Q for quasi-permanent loads G+ψ2Q steel area/crack control
moment steel concrete moment concrete crack spacing crack width minimum provided
(kNm) stress/fyk stress/fck (kNm) stress/fck (mm) (mm) (mm2) (mm2)
left end, top 94.8 0.527 0.271 80.6 0.231 423 0.24 386 709
midspan bottom 77.9 0.596 0.083 66.4 0.070 283 0.22 75 615
right end, top 103.6 0.542 0.291 88.5 0.248 358 0.25 239 769
 Frame 2, Story 5, Beams B27, B28: - Capacity design of beams in
shear - ULS dimensioning of transverse reinforcement
Sums of beam/column design moment resistances around joint, ∑MRd,b / ∑MRd,c for maxN (kNm) 120

Beam Beam end and direction of MRd,b vector:

Left end, +y Left end, -y Right end, +y Right end, -y
28 213 / 220.7 (C2) 116.6 / 220.7 (C2) 321.6 / 527.5 (C7) 311 / 527.5 (C7)
27 321.6 / 527.5 (C7) 311 / 527.5 (C7) 116.6 / 215.8 (C12) 182.6 / 215.8 (C12)
Beam 28
Left end section: maxVEd = 148.9 kN, minVEd = 54.9 kN,  = minVEd/maxVEd = 0.37
Right end section: maxVEd = 128.1 kN, minVEd = 34.1 kN,  = minVEd/maxVEd = 0.27
Region length design shear (kN) max tie provided ties strut shear resistance (kN)
(m) seismic non-seismic spacing, mm No. Ø, mm s, mm angle VRd,s VRd,max
left end 0.50 135.8 127.2 112 6 8 110 22o 399.6 416.2
central 5.60 122.8 107.4 330 18 8 330 22o 133.2 416.2
right end 0.50 115.0 109.6 112 6 8 110 22o 399.6 416.2
Beam 27
Left end section: maxVEd = 142.2 kN, minVEd = 50.6 kN,  = minVEd/maxVEd = 0.36
Right end section: maxVEd = 132.4 kN, minVEd = 40.8 kN,  = minVEd/maxVEd = 0.31
Region length design shear (kN) max tie provided ties strut shear resistance (kN)
(m) seismic non-seismic spacing, mm No. Ø, mm s, mm angle VRd,s VRd,max
o
left end 0.50 138.5 129.2 112 6 8 110 22 399.6 416.2
o
central 5.60 125.5 109.5 330 18 8 330 22 133.2 416.2
o
right end 0.50 111.0 107.6 112 6 8 110 22 399.6 416.2
Beam framing plan -roof (longitudinal bars: left-hand-side, ties: right-hand-side)

121
1 2 3 4 5 6

Roof
Beam framing plan –Level 5 (longitudinal bars: left-hand-side, ties: right-hand-
side)
1 2 3 4 5 122 6

Level 5
 Beam framing plan –Level 4(longitudinal bars: left-hand-side, ties: right-hand-
side)
1 2 3 4 5 6123

Level 4
Beam framing plan –Level 3(longitudinal bars: left-hand-side, ties: right-hand-
side)
1 2 3 4 5 6
124

Level 3
Beam framing plan –Level 2(longitudinal bars: left-hand-side, ties: right-hand-
side)
1 2 3 4 5 125
6

Level 2
Beam framing plan –Level 1(longitudinal bars: left-hand-side, ties: right-hand-
side)
1 2 3 4 5 6
126

Level 1
Beam framing plan –Level 0(longitudinal bars: left-hand-side, ties: right-hand-
side) 1 2 3 4 5 6

127

Level 0
Beam framing plan –Level -1(longitudinal bars: left-hand-side, ties: right-hand-
1 2 3 4 5 6
side)
128
A

Level -1
 129

Dimensioning & detailing of columns

at ULS
 Column reinforcement
Column vertical bars steel critical height in critical height in critical height of all In basement lapping
ratio at column ends at the column columns except at the or outside the at floor 130

(%) - superstructure base - Level 1 column base - Level 1 critical height level (m)
C1, C6 4Ø18+6Ø14 1.08 0.6 m Ø8/90 mm Ø6/110 mm Ø6/170 mm 0.60
C2, C5 4Ø18+8Ø14 1.07 0.7 m Ø8/90 mm Ø6/110 mm Ø6/170 mm 0.60
C3, C4 4Ø18+8Ø14 1.07 0.7 m Ø8/95 mm Ø6/110 mm Ø6/170 mm 0.60
C7, C10 4Ø18+8Ø14 1.0 0.7 m Ø8/90 mm Ø6/110 mm Ø6/170 mm 0.60
C8, C9 4Ø18+8Ø14 1.0 0.7 m Ø8/110 mm Ø6/110 mm Ø6/170 mm 0.60
C11, C16 4Ø18+6Ø14 1.08 0.6 m Ø8/90 mm Ø6/110 mm Ø6/170 mm 0.60
C12, C14 4Ø18+8Ø14 1.07 0.7 m Ø8/90 mm Ø6/110 mm Ø6/170 mm 0.60
C13, C15 4Ø18+8Ø14 1.07 0.7 m Ø8/95 mm Ø6/110 mm Ø6/170 mm 0.60
 Column reinforcement
131

4Φ18 + 8Φ14

4Φ18 + 6Φ14
1 2 3 4 5

SLAB

4Φ18 + 8Φ14
 Column C12 - Check of slenderness for negligible 2nd-order effects
Story Combination Column direction z Column direction y
of actions slenderness column slenderness column 132

per EN1990 limit actual eff. l0 (m) sufficient size (m) limit actual eff. l0 (m) sufficient size (m)
6 Eq.6.10a 184.4 8.0 1.61 0.70 179.8 17.1 1.48 0.30
Eq.6.10b 186.5 8.0 1.61 0.70 181.9 17.1 1.48 0.30
5 Eq.6.10a 133.2 7.9 1.60 0.70 124.8 17.1 1.48 0.30
Eq.6.10b 135.2 7.9 1.60 0.70 126.8 17.0 1.48 0.30
4 Eq.6.10a 109.1 7.9 1.60 0.70 109.2 17.2 1.49 0.30
Eq.6.10b 110.8 7.9 1.60 0.70 111. 17.1 1.48 0.30
3 Eq.6.10a 94.1 7.9 1.61 0.70 94.9 17.3 1.50 0.30
Eq.6.10b 95.8 7.9 1.61 0.70 96.5 17.3 1.50 0.30
2 Eq.6.10a 83.0 8.0 1.61 0.70 84.9 17.5 1.52 0.30
Eq.6.10b 84.4 8.0 1.61 0.70 86.5 17.5 1.52 0.30
1 Eq.6.10a 75.0 11.1 2.24 0.70 69.8 23.6 2.04 0.30
Eq.6.10b 76.6 11.1 2.24 0.70 71.0 23.6 2.04 0.30
0 Eq.6.10a 65.1 8.0 1.62 0.70 67.5 16.6 1.44 0.30
Eq.6.10b 66.3 8.0 1.62 0.70 68.7 16.6 1.44 0.30
-1 Eq.6.10a 47.1 7.1 1.43 0.70 47.8 15.4 1.33 0.30
Eq.6.10b 48.0 7.1 1.43 0.70 48.6 15.4 1.33 0.30
 Column C12 - Normal stress resultants in seismic design situation
from the analysis, for ULS dimensioning of vertical reinforcement
Story 6 Column Base Column Top
Combination of actions My (kNm) Mz (kNm) N (kN) My (kNm) Mz (kNm) N (kN) 133
EN1990 Eq.6.10a -26.5 -82.5 252.9 28.9 96.6 231.6
EN1990 Eq.6.10b -25.2 -78.2 237.9 27.4 91.7 219.8
G+ψ2Q+E:+X,+Y/maxN 99.5 -3.8 190.4 170.2 121.6 174.7
G+ψ2Q+E:-X,+Y/maxN -134.7 -3.8 190.4 -131.9 121.6 174.7
G+ψ2Q+E:+X,-Y/maxN 99.5 -105.5 190.4 170.2 6.6 174.7
G+ψ2Q+E:-X,-Y/maxN -134.7 -105.5 190.4 -131.9 6.6 174.7
G+ψ2Q+E:+X,+Y/minN 99.5 -3.8 148.0 170.2 121.6 132.3
G+ψ2Q+E:-X,+Y/minN -134.7 -3.8 148.0 -131.9 121.6 132.3
G+ψ2Q+E:+X,-Y/minN 99.5 -105.5 148.0 170.2 6.6 132.3
G+ψ2Q+E:-X,-Y/minN -134.7 -105.5 148.0 -131.9 6.6 132.3
Story 5 Column Base Column Top
Combination of actions My (kNm) Mz (kNm) N (kN) My (kNm) Mz (kNm) N (kN)
EN1990 Eq.6.10a -24.4 -71.7 507.5 24.5 70.1 486.2
EN1990 Eq.6.10b -23.1 -68.0 477.5 23.2 66.5 459.4
G+ψ2Q+E:+X,+Y/maxN 102.3 1.0 394.6 139.5 94.7 378.9
G+ψ2Q+E:-X,+Y/maxN -134.6 1.0 394.6 -107.0 94.7 378.9
G+ψ2Q+E:+X,-Y/maxN 102.3 -96.0 394.6 139.5 -1.8 378.9
G+ψ2Q+E:-X,-Y/maxN -134.6 -96.0 394.6 -107.0 -1.8 378.9
G+ψ2Q+E:+X,+Y/minN 102.3 1.0 284.7 139.5 94.7 269.0
G+ψ2Q+E:-X,+Y/minN -134.6 1.0 284.7 -107.0 94.7 269.0
G+ψ2Q+E:+X,-Y/minN 102.3 -96.0 284.7 139.5 -1.8 269.0
G+ψ2Q+E:-X,-Y/minN -134.6 -96.0 284.7 -107.0 -1.8 269.0
Column C12 - Normal stress resultants in seismic design situation from
the analysis, for ULS dimensioning of vert. reinforcement (cont’d)
Story 4 Column Base Column Top
134
Combination of actions My (kNm) Mz (kNm) N (kN) My (kNm) Mz (kNm) N (kN)
EN1990 Eq.6.10a -23.9 -72.1 761.9 24.1 72.5 740.7
EN1990 Eq.6.10b -22.7 -68.4 716.9 22.8 68.7 698.8
G+ψ2Q+E:+X,+Y/maxN 114.3 2.1 598.4 150.1 97.6 582.6
G+ψ2Q+E:-X,+Y/maxN -146.0 2.1 598.4 -118.1 97.6 582.6
G+ψ2Q+E:+X,-Y/maxN 114.3 -97.7 598.4 150.1 -1.5 582.6
G+ψ2Q+E:-X,-Y/maxN -146.0 -97.7 598.4 -118.1 -1.5 582.6
G+ψ2Q+E:+X,+Y/minN 114.3 2.1 421.5 150.1 97.6 405.7
G+ψ2Q+E:-X,+Y/minN -146.0 2.1 421.5 -118.1 97.6 405.7
G+ψ2Q+E:+X,-Y/minN 114.3 -97.7 421.5 150.1 -1.5 405.7
G+ψ2Q+E:-X,-Y/minN -146.0 -97.7 421.5 -118.1 -1.5 405.7
Story 3 Column Base Column Top
Combination of actions My (kNm) Mz (kNm) N (kN) My (kNm) Mz (kNm) N (kN)
EN1990 Eq.6.10a -24.1 -69.7 1016.3 23.9 70.4 995.1
EN1990 Eq.6.10b -22.8 -66.2 956.2 22.6 66.8 938.2
G+ψ2Q+E:+X,+Y/maxN 119.4 1.8 801.6 148.6 93.4 785.8
G+ψ2Q+E:-X,+Y/maxN -151.3 1.8 801.6 -117.0 93.4 785.8
G+ψ2Q+E:+X,-Y/maxN 119.4 -94.3 801.6 148.6 0.0 785.8
G+ψ2Q+E:-X,-Y/maxN -151.3 -94.3 801.6 -117.0 0.0 785.8
G+ψ2Q+E:+X,+Y/minN 119.4 1.8 558.8 148.6 93.4 543.1
G+ψ2Q+E:-X,+Y/minN -151.3 1.8 558.8 -117.0 93.4 543.1
G+ψ2Q+E:+X,-Y/minN 119.4 -94.3 558.8 148.6 0.0 543.1
G+ψ2Q+E:-X,-Y/minN -151.3 -94.3 558.8 -117.0 0.0 543.1
Column C12 - Normal stress resultants in seismic design situation from
the2analysis,
G+ψ for ULS-151.3
Q+E:-X,-Y/minN dimensioning
-94.3 of558.8
vert. reinforcement
-117.0 0.0 (cont’d)
543.1
Story 2 Column Base Column Top
Combination of actions My (kNm) Mz (kNm) N (kN) My (kNm) Mz (kNm) N (kN) 135

EN1990 Eq.6.10a -20.7 -75.4 1270 22.6 71.7 1249

EN1990 Eq.6.10b -19.6 -71.5 1195 21.5 68.1 1177
G+ψ2Q+E:+X,+Y/maxN 121.8 -6.3 1001 137.5 87.6 986
G+ψ2Q+E:-X,+Y/maxN -149.3 -6.3 1001 -107.5 87.6 986
G+ψ2Q+E:+X,-Y/maxN 121.8 -93.7 1001 137.5 7.5 986
G+ψ2Q+E:-X,-Y/maxN -149.3 -93.7 1001 -107.5 7.5 986
G+ψ2Q+E:+X,+Y/minN 121.8 -6.3 699 137.5 87.6 683
G+ψ2Q+E:-X,+Y/minN -149.3 -6.3 699 -107.5 87.6 683
G+ψ2Q+E:+X,-Y/minN 121.8 -93.7 699 137.5 7.5 683
G+ψ2Q+E:-X,-Y/minN -149.3 -93.7 699 -107.5 7.5 683
Story 1 Column Base Column Top
Combination of actions My (kNm) Mz (kNm) N (kN) My (kNm) Mz (kNm) N (kN)
EN1990 Eq.6.10a -26.8 -31.6 1531 20.6 45.3 1503
EN1990 Eq.6.10b -25.4 -30.0 1440 19.6 43.0 1416
G+ψ2Q+E:+X,+Y/maxN 117.4 5.1 1199 102.7 50.1 1178
G+ψ2Q+E:-X,+Y/maxN -152.9 5.1 1199 -75.4 50.1 1178
G+ψ2Q+E:+X,-Y/maxN 117.4 -47.1 1199 102.7 10.0 1178
G+ψ2Q+E:-X,-Y/maxN -152.9 -47.1 1199 -75.4 10.0 1178
G+ψ2Q+E:+X,+Y/minN 117.4 5.1 852 102.7 50.1 831
G+ψ2Q+E:-X,+Y/minN -152.9 5.1 852 -75.4 50.1 831
G+ψ2Q+E:+X,-Y/minN 117.4 -47.1 852 102.7 10.0 831
G+ψ2Q+E:-X,-Y/minN -152.9 -47.1 852 -75.4 10.0 831
Column C12 - Normal stress resultants in seismic design situation from
the analysis, for ULS dimensioning of vert. reinforcement (cont’d)
Story 0 Column Base Column Top
Combination of actions My (kNm) Mz (kNm) N (kN) My (kNm) Mz (kNm) N (kN) 136

EN1990 Eq.6.10a -32.2 -21.1 2029 37.0 21.8 2007

EN1990 Eq.6.10b -30.6 -20.0 1910 35.1 20.6 1892
G+ψ2Q+E:+X,+Y/maxN -7.9 -7.8 1531 71.0 19.7 1515
G+ψ2Q+E:-X,+Y/maxN -34.8 -7.8 1531 -22.0 19.7 1515
G+ψ2Q+E:+X,-Y/maxN -7.9 -20.2 1531 71.0 9.2 1515
G+ψ2Q+E:-X,-Y/maxN -34.8 -20.2 1531 -22.0 9.2 1515
G+ψ2Q+E:+X,+Y/minN -7.9 -7.8 1182 71.0 19.7 1166
G+ψ2Q+E:-X,+Y/minN -34.8 -7.8 1182 -22.0 19.7 1166
G+ψ2Q+E:+X,-Y/minN -7.9 -20.2 1182 71.0 9.2 1166
G+ψ2Q+E:-X,-Y/minN -34.8 -20.2 1182 -22.0 9.2 1166
Story -1 Column Base Column Top
Combination of actions My (kNm) Mz (kNm) N (kN) My (kNm) Mz (kNm) N (kN)
EN1990 Eq.6.10a -7.0 -5.3 2537 18.6 13.2 2516
EN1990 Eq.6.10b -6.6 -5.1 2391 17.7 12.5 2373
G+ψ2Q+E:+X,+Y/maxN 12.7 6.3 1866 29.8 17.9 1850
G+ψ2Q+E:-X,+Y/maxN -21.9 6.3 1866 -5.1 17.9 1850
G+ψ2Q+E:+X,-Y/maxN 12.7 -13.4 1866 29.8 -0.4 1850
G+ψ2Q+E:-X,-Y/maxN -21.9 -13.4 1866 -5.1 -0.4 1850
G+ψ2Q+E:+X,+Y/minN 12.7 6.3 1524 29.8 17.9 1508
G+ψ2Q+E:-X,+Y/minN -21.9 6.3 1524 -5.1 17.9 1508
G+ψ2Q+E:+X,-Y/minN 12.7 -13.4 1524 29.8 -0.4 1508
G+ψ2Q+E:-X,-Y/minN -21.9 -13.4 1524 -5.1 -0.4 1508
Column C12-Sum of beam design moment resistances around joints with
column, ∑MRd,b (kNm), for capacity design in shear & strong column/weak
beam design Story Location Direction of MRd vector 137

+y -y +z -z
6 Top 197.6 197.6 88.0 145.3
Base 274.4 255.3 116.6 182.6
5 Top 274.4 255.3 116.6 182.6
Base 293.0 255.3 116.6 181.1
4 Top 293.0 255.3 116.6 181.1
Base 293.0 255.3 116.6 181.1
3 Top 293.0 255.3 116.6 181.1
Base 293.0 255.3 88.0 163.5
2 Top 293.0 255.3 88.0 163.5
Base 245.2 197.6 76.8 160.5
1 Top 245.2 197.6 76.8 160.5
Base 175.9 175.9 191.4 223.3
0 Top 175.9 175.9 191.4 223.3
Base 141.8 141.8 216.8 217.0
-1 Top 141.8 141.8 216.8 217.0
Base 0.0 0.0 0.0 0.0
Column C12- Design moment resistance, MRd,c (kNm) - values for minN/maxN
Story Location Direction of MRd vector
138

+y -y +z -z
6 top 259.3/319.6 -259.3/-319.6 92.3/96.9 -92.3/-96.9
base 314.0/322.8 -314.0/-322.8 94.0/98.6 -94.0/-98.6
5 top 338.3/358.4 -338.3/-358.4 106.7/117.2 -106.7/-117.2
base 341.3/361.1 -341.3/-361.1 108.3/118.7 -108.3/-118.7
4 top 363.0/390.6 -363.0/-390.6 119.7/134.4 -119.7/-134.4
base 365.7/392.8 -365.7/-392.8 121.1/135.6 -121.1/-135.6
3 top 384.9/416.2 -384.9/-416.2 131.3/148.3 -131.3/-148.3
base 387.2/417.9 -387.2/-417.9 132.6/149.3 -132.6/-149.3
2 top 404.1/435.0 -404.1/-435.0 141.7/159.0 -141.7/-159.0
base 406.1/436.2 -406.1/-436.2 142.8/159.8 -142.8/-159.8
1 top 421.0/447.0 -421.0/-447.0 151.0/166.5 -151.0/-166.5
base 423.1/448.0 -423.1/-448.0 152.2/169.1 -152.2/-169.1
0 top 446.5/454.1 -446.5/-454.1 166.1/169.8 -166.1/-169.8
base 447.2/454.0 -447.2/-454.0 166.6/169.2 -166.6/-169.2
-1 top 454.1/445.2 -454.1/-445.2 170.1/156.3 -170.1/-156.3
base 454.1/443.8 -454.1/-443.8 169.5/155.7 -169.5/-155.7
 Column C12 - Dimensioning of transverse reinforcement between the
column end regions, for the ULS in shear (for maxN or minN)
Story design shear, VEd provided ties strut angle shear resistance (kN)
(kN) Ø no. legs spacing VRd,s VRd,max
139

y z (mm) y z (mm) y z y z y z
§ ‡ o o
6 for maxN 87. 43. 6 3 5 170 22 22 363. 219. 545. 490.
for minN 87. 41. 22o 22o 349. 214. 545. 490.
5 for maxN 66. 24. 6 3§ 5‡ 170 22o 22o 412. 236. 545. 490.
for minN 66. 23. 22o 22o 382. 225. 545. 490.
4 for maxN 66. 23. 6 3§ 5‡ 170 22o 22o 461. 252. 545. 490.
for minN 67. 22. 22o 22o 415. 236. 545. 490.
3 for maxN 66. 22. 6 3§ 5‡ 170 22o 22o 510. 268. 545. 490.
for minN 66. 22. 22o 22o 448. 247. 545. 490.
2 for maxN 66. 20. 6 3§ 5‡ 170 22o 22o 549. 284. 556. 490.
for minN 66. 20. 22o 22o 482. 259. 545. 490.
1 for maxN 39. 14. 6 3§ 5‡ 170 22o 22o 523. 273. 545. 490.
for minN 39. 14. 22o 22o 460. 252. 545. 490.
0 for maxN 35. 14. 6 3§ 5‡ 170 26o 22o 626. 327. 626. 490.
for minN 35. 13. 23o 22o 575. 298. 575. 490.
-1 for maxN 17. 10. 6 3§ 5‡ 170 29o 22o 676. 354. 676. 490.
for minN 17. 10. 26o 22o 622. 325. 624. 490.
§: The value 3 applies for the number of legs , if a si ngle cros s-tie connect s the two central bars of
the short sides; if a diam on d tie is us ed around all four central bars of the four sides, instead of
orthogonal s traight cross -ties, then the number is 3.9.
‡ : The value 3 applies for the num ber of legs, if a single cross-tie connects the two central bars of
the long s ides; if a diamond tie is u sed around all four central bars, instead of orthogonal s traight
cross-ties, then the number is 4.65.
 Column C12 -Confinement reinforcement at column ends (for maxN)
Story required ωwd required aωwd stirrups provided ωwd provided aωwd
(for DC M) (for DCM) legs Ø (mm) spacing (mm) 140

base top base Top y z base top base top base Top base top
6 0.00 0.00 0.000 0.000 3§ 5‡ 6 6 110 110 0.174 0.174 0.055 0.055
5 0.00 0.00 0.000 0.000 3§ 5‡ 6 6 110 110 0.174 0.174 0.055 0.055
4 0.00 0.00 0.000 0.000 3§ 5‡ 6 6 110 110 0.174 0.174 0.055 0.055
3 0.00 0.00 0.000 0.000 3§ 5‡ 6 6 110 110 0.174 0.174 0.055 0.055
2 0.00 0.00 0.000 0.000 3§ 5‡ 6 6 110 110 0.174 0.174 0.055 0.055
1 0.08 0.00 0.136 0.000 3§ 5‡ 8 6 90 110 0.379 0.174 0.133 0.055
0 0.00 0.00 0.000 0.000 3§ 5‡ 6 6 170 170 0.113 0.113 0.025 0.025
-1 0.00 0.00 0.000 0.000 3§ 5‡ 6 6 170 170 0.113 0.113 0.025 0.025
§: The value 3 applies for the number of legs , if a si ngle cros s-tie connect s the two central bars of
the short sides; if a diam on d tie is us ed around all four central bars of the four sides, instead of
orthogonal s traight cross -ties, then the number is 3.9.
‡ : The value 3 applies for the num ber of legs, if a single cross-tie connects the two central bars of
the long s ides; if a diamond tie is u sed around all four central bars, instead of orthogonal s traight
cross-ties, then the number is 4.65.
Column C12- Capacity design factor for the design of column's footing
Combination of actions MRdy (kNm) MEdy (kNm) aCDy MRdz (kNm) MEdz (kNm) aCDz aCD
141
G+ψ2Q+E:+X,+Y/maxN 448.0 117.4 4.58 169.1 2.1 33.35 3.0
G+ψ2Q+E:-X,+Y/maxN 448.0 152.9 3.52 169.1 2.1 33.35 3.0
G+ψ2Q+E:+X,-Y/maxN 448.0 117.4 4.58 169.1 47.1 3.59 3.0
G+ψ2Q+E:-X,-Y/maxN 448.0 152.9 3.52 169.1 47.1 3.59 3.0
G+ψ2Q+E:+X,+Y/minN 423.1 117.4 4.33 152.2 5.1 30.0 3.0
G+ψ2Q+E:-X,+Y/minN 423.1 152.9 3.32 152.2 5.1 30.0 3.0
G+ψ2Q+E:+X,-Y/minN 423.1 117.4 4.33 152.2 47.1 3.23 3.0
G+ψ2Q+E:-X,-Y/minN 423.1 152.9 3.32 152.2 47.1 3.23 3.0
 142

Dimensioning & detailing of walls at

ULS
 Design envelopes of wall W1: moments (left), shears (right)
20 from analysis
design envelope 143

16 from analysis
20
design envelope
12
Height (m)

16

8 12

Height (m)
4 8

0 4
0 4000 8000 12000
Bending moment (kNm) 0
0 500 1000 1500 2000 2500
Shear force (kN)
Wall W1 reinforcement
(left half of section) 144
 Design envelopes of wall W3: moments (left), shears (right)
20 from analysis
145
design envelope
16
20 from analysis
12 design envelope
16
Height (m)

8
12
4

Height (m)
8
0
0 1000 2000 3000 4000 5000 4
-4
0
-8 0 500 1000 1500
-4
Bending moment (kNm)
-8

Shear force (kN)

Wall W3 reinforcement (left half of section)
146
 20 from analysis 20 from analysis
design envelope design envelope
16 16
Design envelopes of 12
147

12
wall W5–X (left), Y

Height (m)
Height (m)

8 8
(right) direction:
4 moments (top), shears 4

0 (below) 0
0 5000 10000 15000 0 500 1000 1500 2000
-4 20 -4 from analysis
20 from analysis
design envelope -8 design envelope
-8 16
16

Bending moment12
(kNm) 12 Bending moment (kNm)

Height (m)
Height (m)

8 8

4 4

0 0
0 1000 2000 30000 400 800 1200
-4 -4

-8 -8

Shear force (kN) Shear force (kN)

 Wall W5 - Geometry; M, V at floor level from analysis for design
seismic action; N due to G+ψ2Q
Cross-section: U. Flanges: 1.80 m, web: 3.60 m, end stubs: None 148

Total/Critical height: 25.0m/3.60 m, flange/web thickness: 0.25 m/0.25 m

Storey My (kNm) Vy (kN) Mz (kNm) Vz (kN) N (kN)
6-Top 0 ±610 0.0 ±75 294
6-Base ±1830.0 ±610 ±226 ±75 294
5-Base ±2148 ±376 ±291 ±78 588
4-Base ±2257 ±564 ±430 ±101 882
3-Base ±3111 ±788 ±714 ±142 1176
2-Base ±5509 ±1113 ±1189 ±192 1470
1-Base ±11369 ±1609 ±1739 ±169 1806
0-Base ±3832 ±2512 ±147 ±625 2100
-1-Base ±2697 ±399 ±674 ±274 2394
W5 - Design Story
+My, +Mz
My (kNm)
-2187
Vy (kN)
1207
Mz (kNm)
-164
Vz (kN)
115
N (kN)
0.0
envelopes of 6-top
-My, +Mz
+My, -Mz
2187
-2187
-1207
1207
-164
167
115
-110
0.0
0.0
moments and -My, -Mz
+My, +Mz
2187
-3975
-1207
1207
167
-447
-110
115
0.0
294
149

magnified 6-base
-My, +Mz
+My, -Mz
3977
-3975
-1207
1207
-447
431
115
-110
294
294
shears -My, -Mz
+My, +Mz
3977
-5763
-1207
1463
431
-728
-110
119
294
588
-My, +Mz 5766 -1463 -728 119 588
5-base
+My, -Mz -5763 1463 699 -115 588
-My, -Mz 5766 -1463 699 -115 588
+My, +Mz -7551 1573 -1010 154 882
-My, +Mz 7555 -1572 -1010 154 882
4-base
+My, -Mz -7551 1573 966 -149 882
-My, -Mz 7555 -1572 966 -149 882
+My, +Mz -9339 1682 -1294 216 1176
-My, +Mz 9344 -1682 -1294 216 1176
3-base
+My, -Mz -9339 1682 1231 -209 1176
-My, -Mz 9344 -1682 1231 -209 1176
+My, +Mz -11127 1670 -1582 292 1470
-My, +Mz 11133 -1670 -1582 292 1470
2-base
+My, -Mz -11127 1670 1492 -283 1470
-My, -Mz 11133 -1670 1492 -283 1470
+My, +Mz -11365 2414 -1792 255 1806
Corresponding MRd at base: 11590 6194 at νd = 0.065
-My, +Mz 11373 -2414 -1792 255 1806
Corresponding MRd at base: 11590 6194 at νd = 0.065
1-base
+My, -Mz -11365 2414 1685 -251 1806
Corresponding MRd at base: 11590 4279 at νd = 0.065
-My, -Mz 11373 -2414 1685 -251 1806
Corresponding MRd at base: 11590 4279 at νd = 0.065
+My, +Mz -11360 2514 -1387 1135 2100
-My, +Mz 11378 -2510 -1387 1135 2100
0-base
+My, -Mz -11360 2514 1395 -784 2100
-My, -Mz 11378 -2510 1395 -784 2100
+My, +Mz -6794 2125 -217 1135 2394
-My, +Mz 6848 -2125 -217 1135 2394
-1-base
+My, -Mz -6794 2125 826 -784 2394
-My, -Mz 6848 -2125 826 -784 2394
 Wall W5 - Design in shear, for diagonal tension and compression
(neglecting short-shear-span effects)
floor location amplification design shear horizontal bars strut shear resistance
150

factor for shear maxVEd (kN) Ø Legs spacing sh (mm) angle (kN)
(mm) max provided VRd,s VRd,max
6 web 1.5 1208 8 2 200 200 22o 1573 2234
flanges 1.5 116 8 2×2 200 200 22o 1573 2234
o
5 web 1.5 1463 8 2 200 200 22 1573 2234
flanges 1.5 120 8 2×2 200 200 22o 1573 2234
4 web 1.5 1573 8 2 200 200 22o 1573 2234
flanges 1.5 154 8 2×2 200 200 22o 1573 2234
3 web 1.5 1683 8 2 200 185 22o 1701 2234
flanges 1.5 216 8 2×2 200 185 22o 1573 2234
o
2 web 1.5 1670 8 2 200 185 22 1701 2234
flanges 1.5 292 8 2×2 200 185 22o 1573 2234
1 web 1.5 2415 8 2 200 115 24o 2428 2428
flanges 1.5 256 8 2×2 200 115 22o 1573 2234
0 web - 2514 8 2 200 105 25o 2516 2516
flanges - 1136 8 2×2 200 105 22o 1573 2234
o
-1 web - 2125 8 2 200 145 22 2170 2234
flanges - 1136 8 2×2 200 145 22o 1573 2234
Wall W5 - Vertical, horizontal, hoop reinforcement (whole story and
base of story above); steel added at construction joints
Floor Boundary elements: dimensions & reinforcement Web reinforcement added
location size (m) vertical bars hoops ωwd location vertical horizontal steel @ 151
Ø no Ø s req. prov. Ø sv Ø sh joint
(mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm2)
6 corners 0.25×0.25 18 4 8 105 0.0 0.32 web 8 200 8 200 -
edges 0.15×0.25 18 4 8 105 0.0 0.46 flanges 8 200 8 200 -
5 corners 0.25×0.25 18 4 8 110 0.0 0.30 web 8 200 8 200 -
edges 0.15×0.25 18 4 8 110 0.0 0.43 flanges 8 200 8 200 -
4 corners 0.25×0.25 20 4 8 110 0.0 0.30 web 8 200 8 200 -
edges 0.15×0.25 20 4 8 110 0.0 0.43 flanges 8 200 8 200 -
3 corners 0.25×0.25 20 5 8 110 0.0 0.30 web 8 200 8 185 -
edges 0.15×0.25 20 5 8 110 0.0 0.26 flanges 8 200 8 185 -
2 corners 0.25×0.25 20 6 8 105 0.0 0.24 web 8 200 8 185 -
edges 0.25×0.25 20 6 8 110 0.0 0.24 flanges 8 200 8 185 -
1 corners 0.4×0.25, 18 10 8 105 0.0 0.24 web 8 200 8 115 -
0.55×0.25
edges 0.4×0.25 20 6 8 110 0.0 0.24 flanges 8 200 8 115 -
0 corners 0.4×0.25, 18 10 8 105 0.0 0.24 web 8 200 8 105 -
0.55×0.25
edges 0.4×0.25 20 6 8 110 0.0 0.24 flanges 8 200 8 105 -
-1 corners 0.4×0.25, 18 10 8 105 0.0 0.24 web 8 200 8 150 -
0.55×0.25
edges 0.4×0.25 20 6 8 110 0.0 0.24 flanges 8 200 8 150 -
-2 corners 0.4×0.25, 18 10 8 105 0.0 0.24 web 8 200 8 150 -
0.55×0.25
edges 0.4×0.25 20 6 8 110 0.0 0.24 flanges 8 200 8 150 -
Wall W5 reinforcement (left half of section) & biaxial moment resistance diagram

152

10000

Bending moment Mz (kNm)

5000

-5000

-10000
-20000 -10000 0 10000 20000

Bending moment My (kNm)

 153

(Sample) Dimensioning & detailing of

basement walls and footings
 Perimeter Frame 1, basement storeys - Foundation beams B20, B21, B22 -
ULS design of longitudinal bars (multiplier of seismic internal forces: 1.4).
Beam B20, clear length: 7.0 m; section: asymmetric I; depth h: 6.3 m; width bw: 0.3 m;
flange thickness (top) hf: 0.18 m; (bottom) hf: 0.30 m 154
Location compression maxMEd req. steel flange bars lateral side bars design moment
2
flange width (m) (kNm) area (mm ) no. Ø area (mm2) Ø/s mm area (mm2/m) resistance (kNm)
left end (D), top 1.00 670 379. 4Ø18 1018. Ø10/130 2×604 11420
left end, bottom 0.72 466 379. 8Ø18 2036. Ø10/130 2×604 13792
mid-length, top 1.49 200 379. 2Ø18 509. Ø10/130 2×604 10246
right end (C11) top 1.00 1157 379. 2Ø18 509. Ø10/130 2×604 10245
right end, bottom 0.51 2697 379. 8Ø18 2036. Ø10/130 2×604 13792
Beam B21, clear length: 5.0 m; section: asymmetric I; depth h: 6.3 m; width bw: 0.3 m;
flange thickness (top) hf: 0.18 m; (bottom) hf: 0.30 m
Location compression maxMEd req. steel flange bars lateral side bars design moment
2
flange width (m) (kNm) area (mm ) no. Ø area (mm2) Ø/s mm area (mm2/m) resistance (kNm)
left end (C11), top 1.00 400 379. 2Ø18 509. Ø10/130 2×604 10245
left end, bottom 0.72 1551 379. 8Ø18 2036. Ø10/130 2×604 13792
mid-length, bottom 1.28 432 379. 8Ø18 2036. Ø10/130 2×604 14038
right end (W1), top 1.00 2941 379. 2Ø18 509. Ø10/130 2×604 10245
right end, bottom 0.72 4936 379. 8Ø18 2036. Ø10/130 2×604 13792
Beam B22, clear length: 5.0 m; section: asymmetric I; depth h: 6.3 m; width bw: 0.3 m; flange
thickness (top) hf: 0.18 m; (bottom) hf: 0.30 m
Location compression maxMEd req. steel flange bars lateral side bars design moment
2
flange width (m) (kNm) area (mm ) no. Ø area (mm2) Ø/s mm area (mm2/m) resistance (kNm)
left end (W1), top 1.00 1807 379. 2Ø18 509. Ø10/130 2×604 10245
left end, bottom 0.51 3190 379. 8Ø18 2036. Ø10/130 2×604 13573
mid-length, top 1.49 366.8 379. 2Ø18 509. Ø10/130 2×604 10246
right end (C1), top 1.00 477.5 379. 4Ø18 1018. Ø10/130 2×604 11420
right end, bottom 0.72 278.9 379. 8Ø18 2036. Ø10/130 2×604 13792
 Perimeter Frame 1, basement stories – Found.beams B20, B21, B22 - SLS
checks per EC2: Stress limits; crack width<0.3 mm; steel area for crack control
Beam B20
Location for characteristic loads G+Q for quasi-permanent loads G+ψ2Q steel for crack control
155

moment steel concrete moment concrete crack spacing crack width minimum provided
(kNm) stress/fyk stress/fck (kNm) stress/fck (mm) (mm) (mm2) (mm2)
left end, top 114.7 0.006 0.001 102.1 0.001 252.5 0.00 893 1018
midspan, top 165.9 0.001 0.001 146.8 0.001 0.0 0.00 174 509
right end bottom 889.4 0.034 0.010 770.0 0.009 200.2 0.01 1863 2036
whole span, web 877.8 0.02
Beam B21
Location for characteristic loads G+Q for quasi-permanent loads G+ψ2Q steel for crack control
moment steel concrete moment concrete crack spacing crack width minimum provided
(kNm) stress/fyk stress/fck (kNm) stress/fck (mm) (mm) (mm2) (mm2)
left end, bottom 671.8 0.026 0.008 575.6 0.006 412.1 0.01 1863 2036
midspan bottom 332.0 0.007 0.002 294.9 0.001 200.2 0.01 1867 2036
right end bottom 1115.3 0.043 0.013 997.4 0.011 200.2 0.01 1863 2036
whole span, web 877.8 0.03
Beam B22
Location for characteristic loads G+Q for quasi-permanent loads G+ψ2Q steel area/crack control
moment steel concrete moment concrete crack spacing crack width minimum provided
(kNm) stress/fyk stress/fck (kNm) stress/fck (mm) (mm) (mm2) (mm2)
left end bottom 759.1 0.043 0.013 691.3 0.012 412.1 0.02 1861 2036
midspan top 298.1 0.001 0.001 249.2 0.001 0.0 0.00 174 509
right end top 110.0 0.005 0.001 99.3 0.001 252.5 0.00 893 1018
whole span, web 877.8 0.03
 Perimeter Frame 1, basement stories - Foundation beams B20, B21, B22 - ULS
design of transverse reinforcement (multiplier of seismic internal forces: 1.4).
Beam 20
156
Region length design shear (kN) max tie provided ties strut shear resistance (kN)
(m) seismic non-seismic spacing, mm No. Ø, mm s, mm angle VRd,s VRd,max
Left half (D) 3.50 562.5 1897 250 15 10 250 22o 3654 5535
Right half (C11) 3.50 1995 1864 250 15 10 250 22o 3654 5535
Beam 21
Region length design shear (kN) max tie provided ties strut shear resistance (kN)
(m) Seismic non-seismic spacing, mm No. Ø, mm s, mm angle VRd,s VRd,max
Left half (C11) 2.50 134.7 134.1 250 11 10 250 22o 3654 5535
Right half (W1) 2.50 1960 1567 250 11 10 250 22o 3654 5535
Beam 22
Region length design shear (kN) max tie provided ties strut shear resistance (kN)
(m) seismic non-seismic spacing, mm No. Ø, mm s, mm angle VRd,s VRd,max
Left half (W1) 2.50 1705.4 85.0 250 11 10 250 22 3654 5535
Right half (C1) 2.50 1139.7 -529.7 250 11 10 250 22 3654 5535
Reinforcement & strip footing of basement wall-and-foundation beam

157
 Footing F12 of column C12 – Geometry; design forces at center of footing's
base - Soil bearing pressure and capacity per EC7
Footing depth h:0.70 m; footing plan dimensions : //y by = 2.00 m, //z bz = 2.00 m
158
overburden depth:0.0 m column cross-sectional dimensions: //y cy = 0.70 m, //z cz = 0.30 m
column axis eccentricity://y ay = 0 m, //z az = 0 m
Combination of actions capacity design Ntot My ey/by Vy Mz ez/bz Vz soil bearing
magnification (kN) (kNm) (kN) (kNm) (kN) pressure capacity
factor (kPa) (kPa)
DA3 EN1990 Eq.(6.10a)* - 2632 -5 0.001 8 6 0.001 6 661 1276
DA3 EN1990 Eq.(6.10b)* - 2471 -5 0.001 8 6 0.001 5 620 1276
G+ψ2Q+E:+X,+Y/maxN 3.0 2278 26 0.012 40 56 0.006 23 590 1673§
G+ψ2Q+E:-X,+Y/maxN 3.0 2278 33 0.012 29 56 0.007 23 592 1677§
G+ψ2Q+E:+X,-Y/maxN 3.0 2278 26 0.010 28 47 0.006 14 588 1674§
G+ψ2Q+E:-X,-Y/maxN 3.0 2278 33 0.010 17 47 0.007 14 590 1679§
G+ψ2Q+E:+X,+Y/minN 3.0 1252 26 0.023 40 56 0.010 23 334 1669§
G+ψ2Q+E:-X,+Y/minN 3.0 1252 33 0.023 29 56 0.013 23 336 1674§
G+ψ2Q+E:+X,-Y/minN 3.0 1252 26 0.019 26 47 0.010 14 332 1671§
G+ψ2Q+E:-X,-Y/minN 3.0 1252 33 0.019 15 47 0.013 14 334 1677§
*: The most unfavourable outcome of the application of Eqs.(6.10a) or (6.10b) applies.
 Footing F12 of column C12 – ULS design in shear, punching shear and
flexure
Combination of actions shear stress vEd & resistance (kPa) punching shear at distance av 159

section //y section //z resistance max stress critical resistance

VEdy/bzd VEdz/byd vRd,c maxvEd distance av (m) (2d/av)vRd (kPa)
EN1990 Eq.(6.10a) * 12.1 214.4 340.9 679 0.3 1299
EN1990 Eq.(6.10b) * 11.4 201.0 340.9 636 0.3 1299
G+ψ2Q+E:+X,+Y/maxN 10.8 196.0 340.9 598 0.3 1299
G+ψ2Q+E:-X,+Y/maxN 10.9 196.0 340.9 599 0.3 1299
G+ψ2Q+E:+X,-Y/maxN 10.8 194.0 340.9 596 0.3 1299
G+ψ2Q+E:-X,-Y/maxN 10.9 194.0 340.9 597 0.3 1299
G+ψ2Q+E:+X,+Y/minN 5.9 110.8 340.9 327 0.3 1299
G+ψ2Q+E:-X,+Y/minN 6.0 110.8 340.9 328 0.3 1299
G+ψ2Q+E:+X,-Y/minN 5.9 108.7 340.9 325 0.3 1299
G+ψ2Q+E:-X,-Y/minN 6.0 108.7 340.9 326 0.3 1299
Maximum bending moments Reinforcement
vertical section //bz vertical section //by bar //by //bz
MEdy/bz Combination MEdz/by Combination dia.(mm) spacing No. spacing No.
(kNm/m) (kNm/m) (mm) (mm)
132.0 EN1990 Eq.(6.10a) 230.5 EN1990 Eq.(6.10a) 12 130 15 120 16

*: The most unfavourable outcome of the application of Eqs.(6.10a) or (6.10b) applies.

Footing reinforcement
1 2 3 4 5 6

160
A

Depth of footings 0.7m FOUNDATION

Top face of all foundation elements flush with top surface of RC slab,
playing the role of tie-beams and bottom diaphragm of box foundation.
EUROCODES
161

Thank you !