Seismic assessment of buildings accordance to Eurocode 8 Part 3

Design notes for seismic assessment of existing structure in accordance to EUROCODE 8-PART 3

VALENTINOS NEOPHYTOU BEng (Hons), MSc REVISION 1: January, 2014

ABOUT THIS DOCUMENT

This publication provides a concise compilation of selected rules in the Eurocode 8 Part 1 &

3, together with relevant Cyprus National Annex, that relate to the seismic design of

common forms of concrete building structure in the South Europe. Rules from EN 1998-3

for global analysis, type of analysis and verification checks are presented. Detail design

check rules for concrete beam, column and shear wall, from EN 1998-3 are also presented.

This guide covers the assessment of orthodox members in concrete frames. It does not cover

design rules for steel frames. Certain practical limitations are given to the scope.

Due to time constraints and knowledge, I may not be able to address the whole issues.

Please send me your suggestions for improvement. Anyone interested to share his/her

knowledge or willing to contribute either totally a new section about Eurocode 8-3 or within

this section is encouraged.

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Design notes for Seismic Assessment to Eurocode 8 - Part 3

Valentinos Neophytou BEng (Hons), MSc Page 3 of 61

FUNDAMENTAL REQUIREMENT – LIMIT STATE (LS)

(EN1998-3,cl.2.1)

Limit state Mean return

period in years

Probability of

exceedance in

50 years

Combination

of action and

performance

levels

Description

Near

Collapse (NC)

TR = 2475

(Vary Rare

Earthquake)

2% 2475/NCS

The structure is heavily damaged, with low

residual lateral strength and stiffness,

although vertical elements are still capable

of sustaining vertical loads. Most non-

structural components have collapsed. Large

permanent drifts are present. The structure

is near collapse and would probably not

survive another earthquake, even of

moderate intensity.

TR = 475

(Rare

Earthquake)

10% 475/NC

TR = 225

(Frequent

Earthquake)

20% 225/NC

Significant

Damage (SD)

TR = 2475

(Vary Rare

Earthquake)

2% 2475/SD

The structure is significantly damaged, with

some residual lateral strength and stiffness,

and vertical elements are capable of

sustaining vertical loads. Non-structural

components are damaged, although

partitions and infills have not failed out-of-

TR = 475

(Rare

Earthquake)

10% 475/SD



TR = 225

(Frequent

Earthquake)

20% 225/SD

plane. Moderate permanent drifts are

present. The structure can sustain after-

shocks of moderate intensity. The structure

is likely to be uneconomic to repair.

Damage

Limitation

(DL)

TR = 2475

(Vary Rare

Earthquake)

2% 2475/DL

The structure is only lightly damaged, with

structural elements prevented from

significant yielding and retaining their

strength and stiffness properties. Non-

structural components, such as partitions

and infills, may show distributed cracking,

but the damage could be economically

repaired. Permanent drifts are negligible.

The structure does not need any repair

measures.

TR = 475

(Rare

Earthquake)

10% 475/DL

TR = 225

(Frequent

Earthquake)

20% 225/DL

Note 1: TR values above same as for new buildings. National authorities may select lower values, and require compliance with only two limit-

states.

Note 2: The acceptable performance level for ordinary buildings of importance should be “Significant Damage” which is roughly equivalent with

the “No Collapse” in EN1998-1.

Note 3: The National Authorities decide whether all three Limit States shall be checked, or two of them, or just one of them.

Note 4: The performance levels for which the three Limit States should be met are chosen either nationally through the National Annex to this

part of Eurocode 8, or by the owner if the country leaves the choice open.



Performance Levels and Limit States



PERFORMANCE REQUIREMENTS AND COMPLIANCE CRITERIA

(EN1998-1-1,cl.2.1)

Return-period ground motion in TR years

Value of the exponent, k k = 3 EN19981-1,cl.2.1(4)

Importance factor based on

reference seismic action 𝛾𝐼 =

𝑇𝐿𝑅

𝑇𝐿 −1/𝑘

EN19981-1,cl.2.1(4)

Importance factor based on

reference probability of

exceeding the seismic action

𝛾𝐼 = 𝑃𝐿

𝑃𝐿𝑅 −1/𝑘

EN19981-1,cl.2.1(4)

Mean return period 𝑇𝑅 = −𝑇𝐿

𝑙𝑛 1 − 𝑃𝑅 EN1998-1-1,cl.2.1(1)

Typical values and relationships of reference probabilities of exceedance and corresponding

return periods for a specific site.

Probability of exceedance PR Time span TL Mean return period TR

20% 10 years 45 years









REDUCED DESIGN LIFE OF THE BUILDING

(EN1998-1,cl.2.1)

By reducing the remaining

lifetime of the building is reduced

the design ground acceleration



Peak ground acceleration attenuation relationships for the European area proposed by

Ambraseys et al. (1996)



SEISMIC ZONATION MAP

(CYS NA EN1998-1)

The seismic building code of Cyprus includes seismic zonation based on ground acceleration values

with 10% probability of exceedance in 50 years, i.e., 475years mean return period. Five zones (1-5)

are defined with PGA ranging from 0.075g to 0.15g. In a recent revision of the code (2004), three

seismic zones are defined.



REQUIRED INPUT DATA – CHECK LIST

(EN1998-3,cl3.1, 3.2 & Annex A.2)

Description of identification Parameter Results/Comment

Check

tick

√

Identification of “new” importance class

I

II

III

IV

Does the building design using any the

previous seismic code?

Prior 1994

After 1994

Construction date of building Date

Present of peeling cracks If YES, provide

Column

Beam

Wall



Slab

Physical condition of reinforced concrete

elements and presence of any degradation,

due to carbonation, steel corrosion, etc.

Sign of steel

deterioration

Column

Beam

Wall

Slab

Are there any significant cracks on

structural members

Beams

Vertical at mid-span

Diagonal at ends

Columns

Diagonal at ends (joints)

Mid-span

Walls

Diagonal at ends (joints)

Mid-span

Measure crack width of basement walls If YES provide the crack width

Settlement of structure due to weak

foundation If YES provide which side of the building have been settled



Are there any presents of cracks of infill

walls at the connection points If YES provide where

Is there any present of strengthening to the

structural members If YES provide where

Identification of the structural regularity

Regular in plan

Regular in elevation

Continuity of load paths between lateral

resisting elements.

Column supported on beam

Missing any structural member

Type of structural system

Frame system

Dual system

Frame-equivalent dual system

Wall equivalent dual system

Torsionally flexible system

Inverted pendulum system

Identification of the lateral resisting system Moment frame/wall system in X direction



in both directions. Moment frame/wall system in Y direction

Distribution of infill walls Regular in plan

Identification of the type of building

foundation

Raft foundation

Pad foundation

Pile foundation

Strip foundation

Is there any building attached? Attached YES/NO

If YES measure the gap between them

Re-assessment if imposed

actions/permanent load.

Variable

Change of existing usage.

If YES re-assess the variable load

Permanent

Installation of any further load (i.e.

antenna, board)

If YES re-assess the permanent load

Type of slab

Solid slab Thickness/dimensions

Flat slab Thickness/dimensions



Waffle slab Thickness/dimensions

Ribbed slab Thickness/dimensions

Depth and width of concrete elements

Beams

Columns

Walls

Width of flanges in T-beams If exist, measure the width

Possible eccentricities between beams and

columns axes at joints.

If eccentricities exist check if YES provide the distance (check

if e ≤ bc / 4).

Is there any asymmetric setbacks at all

storeys If YES provide the distance from the previous storey

Is there any effects of short columns YES / NO

Is there any structural member run with

interruption from their foundation to top? YES / NO

Is the ground floor is soft storey (pilotis) YES / NO

Identification of the ground conditions. A



B

C

D

E

Amount of longitudinal steel in beams,

columns and walls.

Column

Beam

Slab

Wall



Amount and detailing of confining steel in

critical regions and in beam-column joints.

Column

Beam

Slab



Wall

Amount of steel reinforcement in floor

slabs contributing to the negative resisting

bending moment of T-beams.

Seating and support conditions of

horizontal elements.

Column

Beam

Slab



Wall

Depth of concrete cover.

Column

Beam

Slab

Wall



Lap-splices for longitudinal reinforcement.

Column

Beam

Slab

Wall

Concrete strength.

Column

Beam



Slab

Wall

Steel yield strength, ultimate strength and

ultimate strain.

Column

Beam

Slab

Wall



DEFINITION OF KNOWLEDGE LEVEL

(EN1998-3,cl.3.3.2)

Factors Knowledge level KL1 Knowledge level KL2 Knowledge level KL3

Geometry

The overall structural geometry and

member sizes are known either:

(a) from survey or

(b) from original outline

construction drawings used for both

the original construction and any

subsequent modifications.

In case (b), a sufficient sample of

dimensions of both overall geometry

and member sizes should be

checked on site; if there are

significant discrepancies from the

outline construction drawings, a

fuller dimensional survey should be

performed.



(a) from an extended survey or

(b) from outline construction

drawings used for both the original

construction and any subsequent

modifications.

In case (b), a sufficient sample of

dimensions of both overall geometry

and member sizes should be checked

on site; if there are significant

discrepancies from the outline

construction drawings, a fuller

dimensional survey is required.



(a) from a comprehensive survey or

(b) from the complete set of outline

construction drawings used for both the

original construction and any subsequent

modifications.

In case (b), a sufficient sample of both

overall geometry and member sizes should

be checked on site; if there are significant

discrepancies from the outline

construction drawings, a fuller

dimensional survey is required.

Details

The structural details are not known

from detailed construction drawings

and may be assumed based on

simulated design in accordance with

The structural details are known

either from extended in-situ

inspection or from incomplete

detailed construction drawings.

The structural details are known either

from comprehensive in-situ inspection or

from a complete set of detailed

construction drawings.



usual practice at the time of

construction;

In this case, limited inspections in

the most critical elements should be

performed to check that the

assumptions correspond to the actual

situation. Otherwise, more extensive

in-situ inspection is required.

In the latter case, limited in-situ

inspections in the most critical

elements should be performed to

check that the available information

corresponds to the actual situation.

In the latter case, limited in-situ

inspections in the most critical elements

should be performed to check that the

available information corresponds to the

actual situation.

Materials

No direct information on the

mechanical properties of the

construction materials is available,

either from original design

specifications or from original test

reports. Default values should be

assumed in accordance with

standards at the time of construction,

accompanied by limited in-situ

testing in the most critical elements.

Informationonthemechanicalproperti

esoftheconstructionmaterialsis

available either from extended in-

situ testing or from original design

specifications. In this latter case,

limited in-situ testing should be

performed.

Informationonthemechanicalpropertiesofth

econstructionmaterialsis available either

from comprehensive in-situ testing or

from original test reports. In this latter

case, limited in-situ testing should be

performed.



KNOWLEDGE LEVELS

(EN 1998-3,cl.3.3.1)

Knowledge levels

(EN 1998-3,cl.3.3.1)

Limited knowledge

KL1

Geometry: The properties

of the structural system, and

of such non-structural

elements (e.g. masonry infill

panels) as may affect

structural response

Normal knowledge

KL2

Full knowledge

KL3

Details: These include the amount and

detailing of reinforcement in reinforced

concrete, connections between steel

members, the connection of floor

diaphragms to lateral resisting structure,

the bond and mortar jointing of masonry

and the nature of any reinforcing

elements in masonry

Material: The mechanical

properties of the constituent

materials

Choose the

knowledge level

based on the

factors above

DETAILS

Simulated design in

accordance with relevant

practice

and

From limited in-situ

inspection

DETAILS

From incomplete original

detailed construction

drawings with limited in-situ

inspection

or

From extended in-situ

inspection

DETAILS

From original detailed

construction drawings with

limited in-situ inspection

or

From comprehensive in-

situ inspection

MATERIALS

Default values in

accordance with standards

of the time of construction

and

From limited in-situ testing

MATERIALS

From original design

specifications with limited

in- situ testing

or

From extended in-situ

testing

MATERIALS

From original test reports

with limited in- situ testing

or

From comprehensive in-

situ testing



LEVEL OF INSPECTION

(EN1998-3,cl.3.4.4)

Extended

Inspection: 20% detail

check

Testing: 1 sample per

floor (beam/column,wall)


check

Is the Knowledge

level

KL1 ?

YES

NO

Is the Knowledge

level

KL2 or KL3 ?

KL2


check

Limited

Does the spot check agree

with the drawings/ Are the

drawing available? YES NO

KL3





ExtendedLimited

Material properties are

derived either from original

specification or through in

situ samplingSpecifictions Sampling

Details

Materials

Comprehesive


checkInspection: 20% detail

check

Limited


with the drawings/ Are the

drawing available? YES NO





ComprehesiveLimited

Material properties are

derived either past test

reports or through in situ

samplingTest Reports Sampling

Details

Materials


with the drawings/

assumptions ?

YES

Details & Materials

NO

Note: if the masonry infill

walls are considered in

the model, certain

sampling and testing for

shear and compressive

strength and for Elastic

Modulus make sense



SELECTED KNOWLEDGE LEVEL RELATED TO COST/PROCESS OF

INSPECTION

Low cost/process

Medium cost/process

High cost/process

LIMITED KNOWLEDGE LEVEL

NORMAL KNOWLEDGE LEVEL

FULL KNOWLEDGE LEVEL

SELECTED KNOWLEDGE LEVEL RELATED TO COST SAVING OF

RETROFITTING

High cost

Medium cost

Low cost

LIMITED KNOWLEDGE LEVEL

NORMAL KNOWLEDGE LEVEL

FULL KNOWLEDGE LEVEL



VALUES OF CONFIDENCE FACTOR

(EN1998-3,cl.3.3.1)

CONFIDENCE FACTOR

(CF)

(EN1998-3,cl.3.3.1(4))

Limited knowledge

KL1

Normal knowledge

KL2

Full knowledge

KL3

CF=1.4 CF=1.2 CF=1.0

Note: If the existing member has been strengthened the “Confidence factor” (CF) is applied only on its old

material.

Note: The “Confidence factor” (CF) is applied to each old materials (steel, concrete, infill masonry).

ANALYSIS TYPE

(EN1998-3,cl.3.3.1)

Is the Knowledge

level

KL1 ?

YES NO

Lateral force (LF)

or

Modal Response Spectrum

(MRS)

(More conservative)

Lateral force (LF)

or

Modal Response Spectrum

(MRS)

Or

Non-linear analysis

(Pushover/Time history)

(Less conservative)

ANALYSIS TYPE

(EN1998-3,cl.3.3.1(4))



LATERAL FORCE ANALYSIS REQUIREMENTS (LFA)

(EN1998-1-1cl. & EN1998-3,cl.4.4.2)

HORIZONTAL ELASTIC RESPONSE SPECTRUM

(ΕΝ1998-1-1,cl.3.2.2.2)

0 ≤ 𝑇 ≤ 𝑇𝐵: 𝑆𝑒 𝑇 = 𝑎𝑔 ∙ 𝑆 ∙ 1 +𝑇

𝑇𝐵∙ 𝜂 ∙ 2,5 − 1 (ΕΝ1998-1-1,Eq. 3.2)

𝑇𝐵 ≤ 𝑇 ≤ 𝑇𝐶: 𝑆𝑒 𝑇 = 𝑎𝑔 ∙ 𝑆 ∙ 𝜂 ∙ 2.5 (ΕΝ1998-1-1,Eq. 3.3)

𝑇𝐶 ≤ 𝑇 ≤ 𝑇𝐷: 𝑆𝑒 𝑇 = 𝑎𝑔 ∙ 𝑆 ∙ 𝜂 ∙ 2.5 𝑇𝐶

𝑇 (ΕΝ1998-1-1,Eq. 3.4)

𝑇𝐷 ≤ 𝑇 ≤ 4𝑠: 𝑆𝑒 𝑇 = 𝑎𝑔 ∙ 𝑆 ∙ 𝜂 ∙ 2.5 𝑇𝐶𝑇𝐷

𝑇2 (ΕΝ1998-1-1,Eq. 3.5)

Damping viscous: ξ=5%

Damping correction factor η: 𝜂 = 10/ 5 + 𝜉 ≥ 0.55

Design ground acceleration on type A ground: ag=γI*agR

Parameters of Type 1 elastic response spectrum (Large magnitude M>5.5Hz)

(CYS NA EN1998-1-1,table 3.2)

Ground

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

A 1.0 0.15 0.4 2.0

B 1.2 0.15 0.5 2.0

C 1.15 0.20 0.6 2.0

D 1.35 0.20 0.8 2.0

E 1.4 0.15 0.5 2.0



VERTICAL ELASTIC RESPONSE SPECTRUM

(ΕΝ1998-1-1,cl.3.2.2.3)

The vertical component of seismic action is taken into account if the design ground acceleration in the vertical

direction, avg, exceeds 0.25g, and even then only in the following cases:

for horizontal structural member spanning 20m or more,

for horizontal cantilever components longer than 5m,

for beams supporting columns,

in based-isolated structures.

0 ≤ 𝑇 ≤ 𝑇𝐵: 𝑆𝑣𝑒 𝑇 = 𝑎𝑣𝑔 ∙ 1 +𝑇

𝑇𝐵∙ 𝜂 ∙ 3,0 − 1 (ΕΝ1998-1-1,Eq. 3.8)

𝑇𝐵 ≤ 𝑇 ≤ 𝑇𝐶: 𝑆𝑣𝑒 𝑇 = 𝑎𝑣𝑔 ∙ 𝜂 ∙ 3.0 (ΕΝ1998-1-1,Eq. 3.9)

𝑇𝐶 ≤ 𝑇 ≤ 𝑇𝐷: 𝑆𝑣𝑒 𝑇 = 𝑎𝑣𝑔 ∙ 𝜂 ∙ 3.0 𝑇𝐶

𝑇 (ΕΝ1998-1-1,Eq. 3.10)

𝑇𝐷 ≤ 𝑇 ≤ 4𝑠: 𝑆𝑣𝑒 𝑇 = 𝑎𝑣𝑔 ∙ 𝜂 ∙ 3.0 𝑇𝐶𝑇𝐷

𝑇2 (ΕΝ1998-1-1,Eq. 3.11)

Damping viscous: ξ=5%

Damping correction factor η: 𝜂 = 10/ 5 + 𝜉 ≥ 0.55


Design ground acceleration in vertical direction: avg = avg/ag*agR*γI

Note: the value of S is not used in the above expression cause the vertical ground motion is not very much

affected by the underlying ground condition

Parameters values of vertical elastic response spectra (Large magnitude M>5.5Hz)

(CYS NA EN1998-1-1,cl NA2.8)

Spectrum avg/ag TB (s) TC (s) TD (s)

Type 1 0.90 0.05 0.15 1.0



COMBINATION OF SEISMIC MASS

(EN 1998-1-1,cl.3.2.4)

Type of Variable action Storey φ

Categories A-C1

Roof 1,0

Storeys with correlated occupancies 0.8

Independently occupied storeys 0.5

Categories A-F1

1.0

Category Specific Use ψ2

A Domestic and residential 0.3

B Office 0.3

C Areas for Congregation 0.6

D Shopping 0.6

E Storage 0.8

F Traffic < 30 kN vehicle 0.6

G Traffic < 160 kN vehicle 0.3

H Roofs 0

Snow, altitude < 1000 m 0

Wind 0

Requirements Values References

Combination coefficient for variable

action 𝜓Ei = 𝜙 ∙ 𝜓2i ΕΝ1998-1-1,Eq. 4.2

Combination of seismic mass Gk,j + 𝜓Ei Qk,i ΕΝ1998-1-1,Eq. 3.17


Amplification factor

ST = 1.0 (S = S * ST)

If γI > 1.0 (i.e. III & IV)

for Slopes <15o

Cliffs height <30m

EN1998-5, Annex A

ST = 1.2 (S = S * ST) EN1998-5, Annex A



If γI > I (i.e. III & IV)

for Slopes 15o ≤ slope

≤ 30

o Cliffs

height <30m

ST = 1.4 (S = S * ST)

If γI > 1.0 (i.e. III & IV)

for Slopes slope > 30

o

Cliffs height <30m

EN1998-5, Annex A

(Bisch etal, 2011 – Lisbon)


Regular in plan YES / NO ΕΝ1998-1-1,table 4.1

Regular in elevation YES ΕΝ1998-1-1,table 4.1

Ground acceleration 0.10-0.25g CYS NA EN1998-1-1:Seismic

zonation map

Spectrum type TYPE 1

(Large magnitude M>5.5Hz) EN1998-1-1,cl.3.2.2.2(2)P

Ground type

A,B,C,D,E

Normally type B or C can be used

normal condition

EN1998-1-1,cl.3.1.2(1)

Lower bound factor for the horizontal

design spectrum

λ = 0.85 if T1 ≤ 2TC and more than 2

storey

λ=1.0 in all other case

EN1998-1-1,cl.4.3.3.2.2(1Ρ)

Damped elastic response spectrum ξ = 5% EN1998-1-1,cl.3.2.2.2(1)P

Fundamental period T1≤4Tc

T1≤2,0s EN1998-1-1,cl.4.3.3.2.1(2)



Accidental eccentricity See table below EN1998-1-1,cl.4.3.2

Base shear

Fb=Sd(T1).mass.λ

(EN1998-1-1,cl.4.3.3.2.2)

Horizontal seismic forces (according

to height of the masses)

Fi = Fb ∙zi ∙ mi

zj ∙ mj

(EN 1998-1-1:2004, Eq. 4.11)

Accidental torsional effects

If the accidental torsional effects as

shown in table below (EN19981-

1,cl.4.3.2(1)P) is not taken into

account the following rules can be

use

3D

𝐹𝑖 = 𝛿 ∙ 𝐹𝑖

(Fi see above)

Where:

𝛿 = 1 + 0.6𝑥

𝐿𝑒

EN1998-1-1,cl.4.3.3.2.4(1)

2D

(regular in plan)

𝑀𝑎𝑖 = ∓𝑒𝑎𝑖 ∙ 𝛿𝐹𝑖

Where:

𝑒𝑎𝑖 = ∓0.10𝐿𝑖

Where

𝛿 = 1 + 1.2𝑥

𝐿𝑒

EN1998-1-1,cl.4.3.3.2.4(2)

Accidental torsional effect

(EN1998-1-1,cl.4.3.2)

Percentage of accidental

eccentricity Geometry of model (3D/2D)

Asymmetric distribution of

mass

(i.e. infill walls)

(Regular/Irregular)

5% 3D Regular

10% 3D Irregular

20% 2D -


Torsional moment 𝑀𝑎𝑖 = ∓𝑒𝑎𝑖 ∙ 𝐹𝑖

For eai see the table above EN1998-1-1,cl.4.3.3.3.3(1)



Load case name Direction and Eccentricity % Eccentricity

EQXA X Dir + Eccen. Y As above

EQYA X Dir – Eccen. Y As above

EQXB Y Dir + Eccen. X As above

EQYB Y Dir – Eccen. X As above

Reference structure Period T1

Exact formula for Single Degree of Freedom Oscillator. Mass M lumped at

top of a vertical cantilever of height H. Cantilever mass MB = 0. T1 = 2π MH3

3EI

Exact formula for Single Degree of Freedom Oscillator. Vertical cantilever

of height H and of total mass MB. T1 = 2π 0.24MBH3

3EI

Exact formula for Single Degree of Freedom Oscillator. Mass M lumped at

top of a vertical cantilever of height H and of total mass MB. T1 = 2π M + 0.24MB H3

3EI

Approximate Relationship (Eurocode 8).

Ct = 0,085 for moment resisting steel space frames Ct = 0,075 for

eccentrically braced steel frames

Ct = 0,050 for all other structures

T1 = CtH3/4

H building height in m measured

from foundation or top of rigid

basement.

Approximate Relationship (Eurocode 8).

d : elastic horizontal displacement of top of building in m under gravity

loads applied horizontally.

T1 = 2 d



Modal Response Spectrum Analysis requirements (MRSA)

(EN1998-1-1cl. & EN1998-3,cl.4.4.2)

Requirements Values

Horizontal elastic response spectrum As above – see LFA

Vertical elastic response spectrum As above – see LFA

Amplification factor As above – see LFA

Seismic mass As above – see LFA


Regular in plan YES/NO ΕΝ1998-1-1,table 4.1

Regular in elevation NO ΕΝ1998-1-1,table 4.1

Structural model 2D/3D EN1998-1-1,cl.4.2.3.1(3)P


zonation map



Ground type

A,B,C,D,E


normal condition

EN1998-1-1,cl.3.1.2(1)

Damped elastic response spectrum ξ = 5% EN1998-1-1,cl.3.2.2.2(1)P

Accidental eccentricity See table below EN1998-1-1,cl.4.3.2

Effective modal modes

ΣMx ≥ 90% of total mass

ΣMy ≥ 90% of total mass EN1998-1-1,cl.4.3.3.1(3)

Mx ≥ 5% of total mass

Mxy ≥ 5% of total mass

Minimum number of modes

k ≥3.√n

(if eigenvalue analysis capture)

k: is the number of modes

n: is the number of storey

EN1998-1-1,cl.4.3.3.1(5)



Period of vibration

Tk ≤ 0.20sec

Tk: is the period of vibration of mode

k EN1998-1-1,cl.4.3.3.1(5)

At least one natural period should be

below 0.20s

Fundamental period Tj ≤ 0.9 Ti SRSS

EN1998-1-1,cl.4.3.3.2.1(2) Tj ≥ 0.9 Ti CQC

Torsional moment

3D

𝑀𝑎𝑖 = ∓𝑒𝑎𝑖 ∙ 𝐹𝑖

For eai see the table

below

EN1998-1-1,cl.4.3.3.3.3(1)

2D

(regular in

plan)


Where:

𝑒𝑎𝑖 = ∓0.10𝐿𝑖

Where

𝛿 = 1 + 1.2𝑥

𝐿𝑒

EN1998-1-1,cl.4.3.3.2.4(2)


(EN1998-1-1,cl.4.3.2)



Asymmetric distribution of mass

(i.e. infill walls)

(Regular/Irregular)

5% 3D Regular

10% 3D Irregular

20% 2D -



q – factor approach analysis requirements

(ΕΝ1998-1-1,cl.3.2.2.2)

Design spectrum of elastic analysis

(ΕΝ1998-1-1,cl.3.2.2.5)

0 ≤ 𝑇 ≤ 𝑇𝐵: 𝑆𝑑 𝑇 = 𝑎𝑔 ∙ 𝑆 ∙ 2

3+

𝑇

𝑇𝐵∙

2.5

𝑞−

2

3 (ΕΝ1998-1-1,Eq. 3.13)

𝑇𝐵 ≤ 𝑇 ≤ 𝑇𝐶: 𝑆𝑑 𝑇 = 𝑎𝑔 ∙ 𝑆 ∙2.5

𝑞 (ΕΝ1998-1-1,Eq. 3.14)

𝑇𝐶 ≤ 𝑇 ≤ 𝑇𝐷: 𝑆𝑑 𝑇 = 𝑎𝑔 ∙ 𝑆 ∙2.5

𝑞 𝑇𝐶

𝑇

≥ 𝛽 ∙ 𝑎𝑔 (ΕΝ1998-1-1,Eq. 3.15)

𝑇𝐷 ≤ 𝑇 ≤ 4𝑠: 𝑆𝑑 𝑇 = 𝑎𝑔 ∙ 𝑆 ∙2.5

𝑞 𝑇𝐶𝑇𝐷

𝑇2

≥ 𝛽 ∙ 𝑎𝑔 (ΕΝ1998-1-1,Eq. 3.5)


Lower bound factor for the horizontal spectrum: β=0.2

A value of q =1.5 for concrete structures (regardless of the structural system)

A value of q = 2.0 for steel structures (regardless of the structural system)

Parameters of Type 1 elastic response spectrum (Large magnitude M>5.5Hz)

(CYS NA EN1998-1-1,table 3.2)

Ground

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

A 1.0 0.15 0.4 2.0

B 1.2 0.15 0.5 2.0

C 1.15 0.20 0.6 2.0

D 1.35 0.20 0.8 2.0

E 1.4 0.15 0.5 2.0



Vertical elastic design spectrum

(ΕΝ1998-1-1,cl.3.2.2.5(5))

The vertical component of seismic action is taken into account if the design ground acceleration in the

vertical direction, avg, exceeds 0.25g, and even then only in the following cases:

for horizontal structural member spanning 20m or more,

for horizontal cantilever components longer than 5m,

for beams supporting columns,

in based-isolated structures.

. 0 ≤ 𝑇 ≤ 𝑇𝐵: 𝑆𝑑 𝑇 = 𝑎𝑣𝑔 ∙ 2

3+

𝑇

𝑇𝐵∙

2.5

𝑞−

2

3 (ΕΝ1998-1-1,Eq. 3.13)

𝑇𝐵 ≤ 𝑇 ≤ 𝑇𝐶: 𝑆𝑑 𝑇 = 𝑎𝑣𝑔 ∙2.5

𝑞 (ΕΝ1998-1-1,Eq. 3.14)

𝑇𝐶 ≤ 𝑇 ≤ 𝑇𝐷: 𝑆𝑑 𝑇 = 𝑎𝑣𝑔 ∙2.5

𝑞 𝑇𝐶

𝑇

≥ 𝛽 ∙ 𝑎𝑣𝑔 (ΕΝ1998-1-1,Eq. 3.15)

𝑇𝐷 ≤ 𝑇 ≤ 4𝑠: 𝑆𝑑 𝑇 = 𝑎𝑣𝑔 ∙2.5

𝑞 𝑇𝐶𝑇𝐷

𝑇2

≥ 𝛽 ∙ 𝑎𝑣𝑔 (ΕΝ1998-1-1,Eq. 3.5)


Design ground acceleration in vertical direction: avg = avg/ag*agR*γI

For the vertical component of the seismic action the design spectrum is given by expressions (3.13) to

(3.16), with the design ground acceleration in the vertical direction, avg replacing ag, S taken as being

equal to 1,0 and the other parameters as defined in 3.2.2.3.

Parameters values of vertical elastic response spectra

(CYS NA EN1998-1-1,cl NA2.8)

Spectrum avg/ag TB (s) TC (s) TD (s)

Type 1 0.90 0.05 0.15 1.0

Special provisions:

For the vertical component of the seismic action a behaviour factor q up to to 1,5 should generally

be adopted for all materials and structural systems.



Requirements Values

Amplification factor As above – see LFA

Seismic mass As above – see LFA

Analysis requirements As above – see MRSA

Accidental eccentricity As above – see MRSA

Regular in plan As above – see MRSA

Regular in elevation As above – see MRSA

Structural model As above – see MRSA

Ground acceleration As above – see MRSA

Spectrum type As above – see MRSA

Ground type As above – see MRSA

Damped elastic response spectrum As above – see MRSA

Accidental eccentricity As above – see MRSA

Effective modal modes As above – see MRSA

Minimum number of modes As above – see MRSA

Fundamental period As above – see MRSA

Torsional moment As above – see MRSA

Accidental torsional effect As above – see MRSA



Linear Analysis - Requirements from EN1998-3

(EN1998-3,cl.4.4.2(1)P)

Requirements Values

Ratio between demand and

capacity

EN1998-3cl.4.4.2(1)P

Ductile mechanism (flexure) Brittle mechanism (Shear)

Demand

(Di)

Capacity

(Ci)

Demand

(Di)

Capacity

(Ci)

Acceptability of linear model

(for checking of ρi =D i

C i values)

Verifications (if LM accepted)

From

analysis.

Use mean

values of

properties

In term of

strength.

Use mean values

of properties.

If ρi < 1: from

analysis In term of

strength.

Use mean values

of properties

divided by CF and

by partial factor

Verifications (if LM accepted)

From

analysis.

In term of

strength.

Use mean values

of properties

divided by CF

If ρi > 1: from

equilibrium with

strength of

ductile e/m.

Use mean values

of properties

multiplied by

CF.

Dseismic : is bending moment at the end member due to the seismic action

and the concurrent gravity load.

Cgravity : is the corresponding moment resistance, calculated on the basis of

the axial force due to gravity load alone and using mean-value properties

of old material from in-situ test.

Note: ρi=Dseismic/Cgravity



Value of the ratio

ρmax/ρmin

(EN1998-3,cl.4.4.2(1P)

ρmax/ρmin = 2.5



Combination of seismic action

(EN1998-1-1cl. & EN1998-3,cl.4.4.2)

Seismic load combination for “Modal Analysis/Pushover”

SEISMIC 1. DL + ψEiLL + EQX + 0.3EQY

SEISMIC 2. DL + ψEiLL + EQX – 0.3EQY

SEISMIC 3. DL + ψEiLL - EQX + 0.3EQY

SEISMIC 4. DL + ψEiLL - EQX – 0.3EQY

SEISMIC 5. DL + ψEiLL + EQY + 0.3EQX

SEISMIC 6. DL + ψEiLL + EQY – 0.3EQX

SEISMIC 7. DL + ψEiLL - EQY + 0.3EQX

SEISMIC 8. DL + ψEiLL - EQY – 0.3EQX

Seismic load combination for “Lateral force Analysis/Pushover”

SEISMIC 1. DL + ψEiLL + EQXA + 0.3EQY

SEISMIC 2. DL + ψEiLL + EQXA – 0.3EQY

SEISMIC 3. DL + ψEiLL - EQXA + 0.3EQY

SEISMIC 4. DL + ψEiLL - EQXA – 0.3EQY

SEISMIC 5. DL + ψEiLL + EQYA + 0.3EQX

SEISMIC 6. DL + ψEiLL + EQYA – 0.3EQX

SEISMIC 7. DL + ψEiLL - EQYA + 0.3EQX


SEISMIC 9. DL + ψEiLL + EQX + 0.3EQY

SEISMIC 10. DL + ψEiLL + EQX – 0.3EQY

SEISMIC 11. DL + ψEiLL - EQX + 0.3EQY

SEISMIC 12. DL + ψEiLL - EQX – 0.3EQY

SEISMIC 13. DL + ψEiLL + EQY + 0.3EQX

SEISMIC 14. DL + ψEiLL + EQY – 0.3EQX

SEISMIC 15. DL + ψEiLL - EQY + 0.3EQX




Non-linear Analysis – Pushover Analysis requirements

(EN1998-1-1cl. & EN1998-3,cl.4.4.2)


Regular in plan YES/NO ΕΝ1998-1-1,table 4.1

Regular in elevation YES/NO ΕΝ1998-1-1,table 4.1

Structural model 2D/3D EN1998-1-1,cl.4.3.3.1(9&10)P


zonation map



Ground type

A,B,C,D,E


normal condition

EN1998-1-1,cl.3.1.2(1)

Cracked elements 50% of the stiffness EN1998-1-1,cl.4.3.1(7)

Material properties Use mean values EN1998-1-1,cl.4.3.3.4.1(4)

Seismic action Apply to the ∓ direction EN1998-1-1,cl.4.3.3.4.1(7)P

Lateral loads derived from

Lateral Force Analysis

or

Modal Response Spectrum Analysis

EN1998-1-1,cl.4.3.3.4.2.2(1)

Determination of the period

for SDOF 𝑇 = 2𝜋

𝑚 ∙ 𝑑𝑦

𝐹𝑦 EN1998-1-1,Eq.B.7

Determination of the

Target displacement for

SDOF

𝑑𝑒 = 𝑆𝑒(𝑇) 𝑇

2𝜋

2

EN1998-1-1,Eq.B.8


(EN1998-1-1,cl.4.3.2)



Asymmetric distribution of mass in

plan



(i.e. infill walls)

(Regular/Irregular)

5% 3D Regular

10% 3D Irregular

20% 2D -



Non linear Analysis - Requirements from EN1998-3

(EN1998-3,cl.4.4.2(1)P)

Requirements Values

Ratio between demand

and capacity

EN1998-3cl.4.4.2(1)P

Ductile mechanism (flexure) Brittle mechanism (Shear)

Demand

(Di)

Capacity

(Ci)

Demand

(Di)

Capacity

(Ci)

From analysis.

Use mean

values of

properties in

model.

In term of

deformation.

Use mean values

of properties

divided by CF.

From analysis.

Use mean

values of

properties in

model.

In term of strength.

Use mean values of

properties divided by

CF and by partial

factor.

Plastic hinges

X & Y – direction (check separately)

Case 1: At beams

∑ M Rc > ∑ M Rb , then plastic hinges will likely develop in beams and,

consequently, only the beams should be considered for the evaluation of

ρmax and ρmin.

Case 2: At Columns

∑ M Rc < ∑ M Rb , then plastic hinges will likely develop in columns and,

thereby, only the columns should be considered for the evaluation of ρmax

and ρmin.

Lateral load

(EN1998-1-1,cl. 4.3.3.4.2.2(1))

Load pattern Description

Uniform load pattern

A “uniform pattern”, corresponding to uniform unidirectional lateral

accelerations (i.e. Φi = 1) . It attempts to simulate the inertia forces in a

potential soft-storey mechanism, limited in all likelihood to the bottom

storey, with the lateral drifts concentrated there and the storeys above

moving laterally almost as a rigid body.



Uniform load pattern

Modal load pattern

A “modal pattern”, simulating the inertia forces of the1st mode in the

horizontal direction in which the analysis is carried out. This pattern is

meant to apply in the elastic regime and during the initial stages of the

plastic mechanism development, as well as in a full-fledged beam-sway

mechanism

Modal load pattern



Capacity curve

(EN1998-1-1,cl. 4.3.3.4.2.3(1))

Capacity curve (for each

analysis see below)

Relation between base shear force and the control displacement

1. Pushover curve ends until a terminal point at 1.5 times the

“target displacement”.

Procedure for determination of the target displacement for nonlinear static (pushover) analysis

(EN1998-1,cl.Annex B)


Normalized displacement

Φi = 1 Uniform pattern

EN1998-1,cl.B.1

Φi = Modal pattern

Calculated from Modal analysis

Natural period T calculated from linear elastic analysis -

Normalized lateral forces 𝐹𝑖 = 𝑚𝑖Φi EN1998-1,Eq.B.1

Mass of an equivalent

SDOF 𝑚∗ = 𝑚𝑖𝜙𝑖 = 𝐹𝑖 EN1998-1,Eq.B.2



Transformation factor Γ =

𝑚∗

𝑚𝑖Φi2 =

𝐹𝑖

𝐹𝑖

2

𝑚𝑖

EN1998-1,Eq.B.3

Base shear 𝐹𝑏 = 𝑆d(𝑇1) ⋅ 𝑚 ⋅ λ EN1998-1-

1,cl.3.2.2.2

Force of SDOF 𝐹∗ =𝐹𝑏

Γ EN1998-1,Eq.B.4

Displacement of SDOF 𝑑∗ =𝑑𝑛

Γ EN1998-1,Eq.B.5

Yield displacement of the

idealised SDOF system

𝑑𝑦∗ = 2 𝑑𝑚

∗ −𝐸𝑚

∗

𝐹𝑦∗

Note: The maximum displacement of structure is

taken from the roof level at the node of centre of mass.

The top of a penthouse should not be considered as the

roof.

EN1998-1,Eq.B.6

Period 𝑇 = 2𝜋 𝑚∗ ∙ 𝑑𝑦

∗

𝐹𝑦 EN1998-1,Eq.B.7

Elastic acceleration

response spectrum, Se(T*)

See section above “LFA” -

Target displacement of the

structure with period T*

𝑑𝑒𝑡

∗ = 𝑆𝑒(𝑇)∗ 𝑇∗

2𝜋

2

EN1998-1,Eq.B.8



Target displacement

Short period range

(T* < Tc)

𝐹𝑦∗

𝑚 ∗ ≥ 𝑆𝑒 𝑇∗ 𝑑𝑡

∗ ≥ 𝑑𝑒𝑡∗

𝐹𝑦

∗

𝑚 ∗ < 𝑆𝑒 𝑇∗ 𝑑𝑡

∗ =𝑑𝑒𝑡

∗

𝑞𝑢 1 + 𝑞𝑢 − 1

𝑇𝐶

𝑇∗ ≥ 𝑑𝑒𝑡∗

𝑞𝑢 =𝑆𝑒 𝑇

∗ 𝑚∗

𝐹𝑦∗

EN1998-1,cl.B.5

Target displacement

Medium and long period

range (T* ≥ Tc)

𝑑𝑡∗ = det

∗ = 𝑆𝑒(𝑇)∗ 𝑇∗

2𝜋

2

(≤3det*)

EN1998-1,cl.B.5



Target displacement of

MDOF dt =Γdt

* EN1998-1,Eq.B.13

Torsional effects

(EN1998-1-1,cl.4.3.3.4.2.7)

Requirements 2D/3D Description References

Torsional effects

requirements 3D model

This rule applied to the following

structural system:

Torsionally flexible structural type (i.e.

rx < Is see EN1998-1-1,cl.4.2.3.2, or, a

structure with a predominantly torsional

1st or 2

nd mode of vibration in one of the

two orthogonal horizontal direction).

- Displacement at the stiff/strong

side are under estimated compared

to the flexible weak side in plan

(i.e. is the side which developed

smaller displacement under static

load parallel to it) shall be

increased

EN1998-1-

1,cl.4.3.3.4.2.7(1)P

Torsional effects

requirements

2D model

(regular

in plan)


Where:

𝑒𝑎𝑖 = ∓0.10𝐿𝑖

(see table above)

Where

𝛿 = 1 + 1.2𝑥

𝐿𝑒

EN1998-1-

1,cl.4.3.3.2.4(2)

EN1998-1-

1,cl.4.3.3.4.2.7(3) EN1998-1-

1,cl.4.3.2(1)P

Procedure for determine the increased displacement of strong/stiff side

Procedure for determine the increased displacement of strong/stiff side can be found in the Designer’s

Guide to EN1998-1 and EN1998-5 in p. 57



Number of Analysis required (Pushover)

X & Y – main directions

Directions X – direction Y - direction

Analysis number

“modal” towards (+) positive “modal” towards (+) positive Y

“modal” towards (-) negative X “modal” towards (-) negative Y

“uniform” towards (+) positive X “uniform” towards (+) positive Y

“uniform” towards (-) negative X “uniform” towards (-) negative Y



Modeling Aspects

(EN1998-1-1,cl.4.3.1)


Secondary

elements

The strength and stiffness of secondary seismic

elements, against lateral actions may in general be

neglected in the analysis

EN1998-3,cl.4.3(3)P

Material properties Use mean values of material properties EN1998-3,cl.4.3(5)P

Lateral components All lateral components should be connected by

horizontal diaphragms EN1998-1-1,cl.4.3.1(3)

Floor diaphragms

Floor diaphragms may taken as being rigid in their

planes, mass and moments inertia may be lumped at

the centre of gravity.

Neglect the rigid diaphragm assumption for the

following cases:

1. not compact configuration and plan view far

from rectangular.

2. large openings in floor slabs, due to internal

patios or stairways.

3. large distance between strong and stiff vertical

elements compared to the transverse dimension

of the diaphragm.

EN1998-1-1,cl.4.3.1(4)

Structural

regularity

Criteria for regularity are play significant role to the

type of modeling and analysis EN1998-1-1,cl.4.3.1(5)

Crack analysis

No use of the modification for un-crack cross-section

(50% EI). Not OK in displacement-based assessment

(unconservative for displacement demands). OK in

force-based design of new buildings (conservative

for force

EN1998-1-1,cl.4.3.1(6&7)

Infill walls

Infill walls which contribute significally to the lateral

stiffness and resistance of the building should be taken

into account

EN1998-1-1,cl.4.3.1(8)



Foundation The deformability of the foundation shall be taken into

account in the model EN1998-1-1,cl.4.3.1(9)



Seismic assessment of Reinforced Concrete buildings

(EN1998-3,Annex A)

Partial factors


Partial factor for steel

reinforcement

γs = 1.15 CYS EN1992-1-1,table 2.1

Partial factor of concrete γc = 1.5 CYS EN1992-1-1,table 2.1

Permanent action γG = 1.35 EN1990,cl.6.4.3.2

Variable action γQ = 1.5 EN1990,cl.6.4.3.2

Limit State of near collapse (NC)


Factor for structural

element

primary/secondary

𝛾𝑒𝑙 = 1.5 (primary members)

EN1998-3,cl.A.3.2.2(1)

𝛾𝑒𝑙 = 1.0 (secondary members)

Ratio moment/shear at

the end section 𝐿𝑣 = 𝑀/𝑉

EN1998-3,cl.A.3.2.2(1)

Design axial force 𝑣 =𝑁

𝑏 ∙ 𝑕 ∙ 𝑓𝑐 EN1998-3,cl.A.3.2.2(1)

Mechanical

reinforcement ratio of

the tension and

compression of

𝜔׳ = 𝜌1 + 𝜌𝑣 𝑓𝑦𝐿

𝑓𝑐

Mechanical ratio

of tension

longitudinal

reinforcement

fc : uniaxial (cylindrical)

concrete strength (MPa)



longitudinal

reinforcement, ω,ω׳

𝜔 =𝜌2𝑓𝑦𝐿

𝑓𝑐

Mechanical ratio

of compression

longitudinal

reinforcement

Modulus of Elasticity

(as for new members) 𝐸𝑐𝑚 = 22

𝑓𝑐𝑚10

0.3

EN1992-1-1,table 3.1

Concrete compressive

strength 𝑓𝑐 =

𝑓𝑐𝐶𝐹

EN1998-3,cl.A.3.2.2(1)

Stirrup Yield strength 𝑓𝑦𝑤 =𝑓𝑦

𝐶𝐹

Ratio of transverse

steel parallel to the

direction x of loading

𝜌𝑠𝑥 =𝐴𝑠𝑥

𝑏𝑤 ∙ 𝑠𝑕

sh : stirrup spacing

EN1998-3,cl.A.3.2.2(1)

Confinement

effectiveness factor 𝑎 = 1 −

𝑠𝑕

2𝑏𝑜 1 −

𝑠𝑕

2𝑕𝑜 1 −

𝑏𝑖2

6𝑕𝑜 ∙ 𝑏𝑜 EN1998-3,cl.A.3.2.2(1)

Total chord rotation

capacity

Elastic plus inelastic part

See the equation below: Beams & Columns (elastic plus inelastic part

𝜃𝑢𝑚 =1

𝛾𝑒𝑙0.016 ∙ 0. 3𝑣

𝑚𝑎𝑥 0.01; 𝜔׳

𝑚𝑎𝑥 0.01; 𝜔 𝑓𝑐

0.225

𝑚𝑖𝑛 9;𝐿𝑣

𝑕

0.35

25 𝑎𝜌 𝑠𝑥

𝑓𝑦𝑤𝑓𝑐

1.25100𝜌𝑑


capacity Walls: 𝜃𝑢𝑚 = 0.58 ∙ 𝜃𝑢𝑚 EN1998-3,cl.A.3.2.2(1)

For cold-work brittle

steel 𝜃𝑢𝑚 =

𝜃𝑢𝑚

1.6 EN1998-3,cl.A.3.2.2(1)

Members without

detail for earthquake

resistance

𝜃𝑢𝑚 =𝜃𝑢𝑚

1.2

EN1998-3,cl.A.3.2.2(3)


capacity Plastic part



See the equation below: Beams & Columns (elastic plus inelastic part

𝜃𝑢𝑚𝑝𝑙 =

1

𝛾𝑒𝑙0.0145 ∙ 0. 25𝑣

𝑚𝑎𝑥 0.01; 𝜔׳

𝑚𝑎𝑥 0.01; 𝜔

0.3

𝑓𝑐0.2 𝑚𝑖𝑛 9,

𝐿𝑣

𝑕

0.35

25 𝑎𝜌 𝑠𝑥


1.275100𝜌𝑑

Factor for structural element

primary/secondary

𝛾𝑒𝑙 = 1.8 (primary members) EN1998-3,cl.A.3.2.2(2)

𝛾𝑒𝑙 = 1.0 (secondary members)

Total chord rotation capacity Walls: 𝜃𝑢𝑚𝑝𝑙 = 0.6 ∙ 𝜃𝑢𝑚

𝑝𝑙 EN1998-3,cl.A.3.2.2(2)

For cold-work brittle steel 𝜃𝑢𝑚 =𝜃𝑢𝑚

2.0 EN1998-3,cl.A.3.2.2(2)

Members without detail for

earthquake resistance 𝜃𝑢𝑚 =

𝜃𝑢𝑚

1.2 , 𝜃𝑢𝑚 =

𝜃𝑢𝑚𝑝𝑙

1.2 EN1998-3,cl.A.3.2.2(3)

Total chord rotation capacity If 𝑙𝑜 < 𝑙𝑜𝑢 ,𝑚𝑖𝑛 =>

𝜃𝑢𝑚𝑝𝑙 = 𝜃𝑢𝑚

𝑝𝑙 𝑙𝑜

𝑙𝑜𝑢 ,𝑚𝑖𝑛

EN1998-3,cl.A.3.2.2(4)

Requirements for lamping zone of longitudinal bars

Actual lamping ratio

(at the zone of

overlapping)

𝜌 = 2𝜌 EN1998-3,cl.A.3.2.2(4)

Minimum lamping

length

𝑎1 =1 − 𝑠𝑕

2𝑏𝑜∙

1 − 𝑠𝑕

2𝑕𝑜∙𝑛𝑟𝑒𝑠𝑡𝑟

𝑛𝑡𝑜𝑡

nrestr : number of lapped longitudinal bars

laterally restrained by a stirrup corner or

cross-tie.

ntot : total number of lapped longitudinal

bars along the cross-section perimeter.

EN1998-3,cl.A.3.2.2(4)

𝑙𝑜𝑢 ,𝑚𝑖𝑛 =𝑑𝑏𝑙 ∙ 𝑓𝑦𝐿

1.05 + 14.5𝑎1𝜌𝑠𝑥


∙ 𝑓𝑐



Shear strength

Area of cross section 𝐴𝑐 = 𝑏𝑤𝑑 EN1998-3,cl.A.3.3.1(1)

Concrete compressive

strength 𝑓𝑐 =

𝑓𝑐𝑘𝛾𝐶

EN1992-1-1,cl.3.1.6(1)

Factor for structural

element

primary/secondary

𝛾𝑒𝑙 = 1.15 (primary members) EN1998-3,cl.A.3.3.1(1)

𝛾𝑒𝑙 = 1.0 (secondary members) EN1998-3,cl.A.3.3.1(1)

Contribution of

transverse reinforcement

to shear resistance

Rectangular 𝑉𝑤 = 𝜌𝑤𝑏𝑤𝑧𝑓𝑦𝑤

EN1998-3,cl.A.3.3.1(1) Circular 𝑉𝑤 =

𝜋

2

𝐴𝑠𝑤

𝑠𝑓𝑦𝑤 𝐷 − 2𝑐

Shear resistance after

flexural yielding, as

controlled by stirrups

See below: EN1998-3,cl.A.3.3.1(1)

𝑉𝑅 =1

𝛾𝑒𝑙 𝑕 − 𝑥

2𝐿𝑣𝑚𝑖𝑛 𝑁; 0.55𝐴𝑐𝑓𝑐 + 1 − 0.05𝑚𝑖𝑛 5; 𝜇∆

𝑝𝑙

∙ 0.16𝑚𝑎𝑥 0.5; 100𝜌𝑡𝑜𝑡 1 − 0.16𝑚𝑖𝑛 5;𝐿𝑣

𝑕 𝑓𝑐𝐴𝑐 + 𝑉𝑤

Shear resistance as controlled

by web crushing (diagonal

compression)

See below: EN1998-3,cl.A.3.3.1(2&3)

Walls

Before flexural yielding (𝜇∆𝑝𝑙 = 0), or after flexural yielding (cyclic 𝜇∆

𝑝𝑙 > 0)

𝑉𝑅,𝑚𝑎𝑥 =0.85 1 − 0.06𝑚𝑖𝑛 5; 𝜇∆

𝑝𝑙

𝛾𝑒𝑙 1 + 1.8𝑚𝑖𝑛 0.15;

𝑁

𝐴𝑐𝑓𝑐 1

+ 0.25𝑚𝑎𝑥 1.75; 100𝜌𝑡𝑜𝑡 1 − 0.2𝑚𝑖𝑛 2;𝐿𝑣

𝑕 𝑓𝑐𝑏𝑤𝑧

Columns Lv / h ≤ 2 after flexural yielding (cyclic 𝜇∆𝑝𝑙 > 0



𝑉𝑅,𝑚𝑎𝑥 =4/7 1 − 0.02𝑚𝑖𝑛 5; 𝜇∆

𝑝𝑙

𝛾𝑒𝑙 1 + 0.45 100𝜌𝑡𝑜𝑡 𝑚𝑖𝑛 40; 𝑓𝑐 𝑏𝑤𝑧 𝑠𝑖𝑛2𝛿

where:

𝑡𝑎𝑛𝛿 = 𝑕/2𝐿𝑣

Beam column joint


Overstrength factor 𝛾𝑅𝑑 = 1.2 EN1998-1-

1,cl.5.5.2.3(2)

Shear force acting of the

joint

Interior

joint

𝑉𝑗𝑕𝑑 = 𝛾𝑅𝑑 𝐴𝑠1 + 𝐴𝑠2 𝑓𝑦𝑑 − 𝑉𝐶

EN1998-1-

1,cl.5.5.2.3(2) Exterior

joint

𝑉𝑗𝑕𝑑 = 𝛾𝑅𝑑𝐴𝑠1𝑓𝑦𝑑 − 𝑉𝐶

Shear capacity of joint

𝑉𝑗𝑕𝑑 = 𝜂𝑓𝑐𝑑 1 −𝑣𝑑

𝜂𝑏𝑗𝑕𝑗𝑐

Where

𝜂 = 0.6 1 −𝑓𝑐𝑘250

EN1998-1-

1,cl.5.5.3.3(2)

Shear strength See above (NC) EN1998-

3,cl.A.3.3.1(1)



Limit State of Significant Damage (SD)


Chord rotation capacity 𝜃𝑢𝑚 = 𝜃𝑢𝑚 ∙3

4

EN1998-

3,cl.A.3.2.3(1)

Shear strength (Beams & Columns)

The verification against the exceedance of these two LS is not required, unless these two LS are the

only ones to be checked. In that case NC requirements applies.

Beam column joint


The verification against the exceedance of these two limit state SD and DL is not required, unless

these two LS are only ones to be checked. In that case NC requirements applies.

Limit State of Damage Limitation (DL)


Design shear resistance (EC2)

Value of vmin 𝑣𝑚𝑖𝑛 = 0.035𝑘3/2𝑓𝑐𝑘

0.5 EN1992-1-1,cl.6.2.2(1)

Design compressive

strength 𝑓𝑐𝑑 =

𝑓𝑐𝑘𝛾𝐶

EN1992-1-1,cl.3.1.6(1)

Compressive stress in the

concrete from axial load 𝜍𝑐𝑝 =

𝑁𝐸𝑑

𝐴𝑐 ≤ 0.2𝑓𝑐𝑑 EN1992-1-1,cl.6.2.2(1)

Reinforcement ratio for

longitudinal reinforcement 𝜌𝐼 =

𝐴𝑠𝑖

𝑏𝑤𝑑≤ 0.02 EN1992-1-1,cl.6.2.2(1)

Coefficient factor k1 𝑘1 = 0.44 EN1992-1-1,cl.5.5(4)

Coefficient factor k 𝑘 = 1 + 200

𝑑≤ 2,0 EN1992-1-1,cl.6.2.2(1)

Shear 𝑉𝑅𝑑 ,𝑐 = 𝐶𝑅𝑑 ,𝑐𝑘 100𝜌𝐼𝑓𝑐𝑘 1.3 + 𝑘1𝜍𝑐𝑝 EN1992-1-1,cl.6.2.2(1)



𝑉𝑅𝑑 ,𝑐𝑚𝑖𝑛 = 𝑣𝑚𝑖𝑛 + 𝑘1𝜍𝑐𝑝 𝑏𝑤𝑑

Tension shift, αv

𝑎𝑣 = 1 when My > LvVRd.c

𝑎𝑣 = 0 when My < LvVRd.c

Chord rotation

Lever arm, z 𝑧 = 𝑑 − 𝑑׳ 𝑧 ≈ 0.95𝑑

Lever arm, z

(for rectangular wall

section)

𝑧 = 0.8𝑕 -

Strain , εy 휀𝑦 =

𝑓𝑦

𝐸𝑠 EN1998-3,cl.A.3.2.4(2)

Beams/Columns

𝜃𝑦 = 𝜑𝑦

𝐿𝑣 + 𝑎𝑣𝑧

3+ 0.0014 1 + 1.5

𝑕

𝐿𝑣 +

휀𝑦

𝑑 − 𝑑׳

𝑑𝑏𝐿𝑓𝑦

6 𝑓𝑐

Note:

휀𝑦 = 휀𝑦𝑙𝑜

𝑙𝑜𝑦 ,𝑚𝑖𝑛for 𝑙𝑜 < 𝑙𝑜𝑦 ,𝑚𝑖𝑛

and

𝑀𝑦 = 𝑀𝑦𝑙𝑜

𝑙𝑜𝑦 ,𝑚𝑖𝑛 for 𝑙𝑜 < 𝑙𝑜𝑦 ,𝑚𝑖𝑛

Walls of rectangular, T or

barbelled section

𝜃𝑦 = 𝜑𝑦


3+ 0.0013 +

휀𝑦

𝑑 − 𝑑׳


6 𝑓𝑐

Note:

휀𝑦 = 휀𝑦𝑙𝑜

𝑙𝑜𝑦 ,𝑚𝑖𝑛for 𝑙𝑜 < 𝑙𝑜𝑦 ,𝑚𝑖𝑛

and



Alternative expressions

Beams

Columns

𝜃𝑦 = 𝜑𝑦


3+ 0.0014 1 + 1.5

𝑕

𝐿𝑣 + 𝜑𝑦


8 𝑓𝑐

Note:





Walls of rectangular, T or

barbelled section

𝜃𝑦 = 𝜑𝑦


3+ 0.0013 + 𝜑𝑦


8 𝑓𝑐

Note:



Requirements for lamping zone of longitudinal bars

Actual lamping ratio (at the

zone of overlapping) 𝜌 = 2𝜌 EN1998-3,cl.A.3.2.4(3)

Lap length 𝑙𝑜 ≥ 15𝑑𝑏𝐿 EN1998-3,cl.A.3.2.4(4)

Minimum length of lap

splice for existing concrete

members

𝑙𝑜𝑦 ,𝑚𝑖𝑛 = 0.3𝑑𝑏𝐿

𝑓𝑦𝐿

𝑓𝑐

fc and fyL are derived from the mean

values multiplied by the CF

EN1998-3,cl.A.3.2.4(3)

Shear strength

The verification against the exceedance of these two LS is not required, unless these two LS are the

only ones to be checked. In that case NC requirements applies.

Beam column joint


The verification against the exceedance of these two limit state SD and DL is not required, unless

these two LS are only ones to be checked. In that case NC requirements applies.



Summary table

Member

Limit State (LS)

Damage Limitation

(DL)

Significant damage

(SD)

Near Collapse

(NC)

Ductile primary

(flexural) 𝜃𝑠𝑑 ≤ 𝜃𝑦

𝜃𝑠𝑑 ≤ 0.75𝜃𝑢 ,𝑚−𝜍 𝜃𝑠𝑑 ≤ 𝜃𝑢 ,𝑚−𝜍

Ductile secondary

(flexural) 𝜃𝑠𝑑 ≤ 0.75𝜃𝑢𝑚 𝜃𝑠𝑑 ≤ 𝜃𝑢𝑚

Brittle primary

(shear) 𝑉𝐸,𝐶𝐷 ≤ 𝑉𝑅𝑑 .𝐸𝐶2 𝑎𝑛𝑑 𝑉𝐸,𝐶𝐷 ≤

𝑉𝑅𝑑 ,𝐸𝐶8

1.15; 𝐽𝑜𝑖𝑛𝑡: 𝑉𝐶𝐷 ≤ 𝑉𝑅𝑑𝑗𝐸𝐶 8

Brittle secondary

(Shear)

𝑉𝐸,𝐶𝐷 ≤ 𝑉𝑅𝑑 .𝐸𝐶2 𝑎𝑛𝑑 𝑉𝐸,𝐶𝐷 ≤𝑉𝑅𝑑 ,𝐸𝐶8

1.15; 𝐽𝑜𝑖𝑛𝑡: 𝑉𝐶𝐷 ≤ 𝑉𝑅𝑑𝑗𝐸𝐶 8

θE, VE: chord-rotation & shear force demand from analysis;

VE,CD : from capacity design; θy: chord-rotation at yielding

θum: expected value of ultimate chord rotation under cyclic loading, calculated using mean

strengths for old materials divided by the confidence factor and nominal strengths for new

materials.

θu,m-σ: mean-minus-sigma ult. chord rotation =θum /1.5, or =θy+θpl

um/1.8

VRd, VRm: shear resistance, w/ or w/o material safety & confidence factor

VR,EC8: shear resistance in cyclic loading after flex. yielding



GENERAL CONSEQUENCE OF USE EUROCODE 8-PART 3

1.

PERFORMANCE

REQUIREMENT

&

CRITERIA

2.

APPLICABILITY

CONDITIONS OF THE

FOUR ANALYSIS

METHODS

4.

COLLECTION OF

INFORMATION FOR THE

ASSESSMENT AND ITS

IMPLICATIONS

5b.

STEEL OR COMPOSITE

STRUCTURES

5a.

CONCRETE

STRUCTURES

5c.

MASONRY BUILDINGS

3.

TYPE OF VERIFICATIONS

FOR DUCTILE AND

BRITTLE MODES OF

BEHAVIOUR AND

FAILURE

Seismic assessment of buildings accordance to Eurocode 8 Part 3

Design

design notes

design rules

design check rules

rare earthquakethe structure

reduced design life

dlthe structure

reference seismic actionk

rare earthquake tr