1

Seismic Retrofitting of a Building using the EC8-3

Paulo Marques Baptista de Carvalho nº56562

Abstract - The document assess and retrofits

two reinforced concrete structure buildings in a

seismic event, using the EC8-3, leading to a

reinforcement of the structure as a whole and a

local retrofit. The methodology used in the

structural assessment is displacement based.

Key words - Seismic, EC8-3, structure,

assessment, retrofit, concrete.

1. Introduction

The standard EN1998-3 or EC8-3 [1] proposes a

methodology to assess the capacity of an

existing building to perform well in a seismic

event. This document studies the particular case

of a building with a structure of reinforced

concrete. The EC8-3 uses a displacement based

approach to assess the structural behaviour,

which evaluate the capacity of the members of

the structures sustain the displacements induced

by an earthquake.

2. Seismic assessment of a concrete

structure

A. Displacement based design

The displacement based design is an approach

towards the design of structures, which focuses

in the displacements that a structure can

withstand rather than the sections resistance

from a lateral loading. This is more suited for a

seismic design because the seismic action is a

displacement imposed to the structure

foundation, which leads to by P-Δ effects,

instead of lateral forces that mobilizes the

section resistance. A displacement based

approach checks the member capacity

deformation, by other means, the capacity of

still carrying the vertical loads in a deformed

configuration.

The stiffness of a concrete element decay in the

various cycles of load, leading to a point where

enhancement of force carried by the element is

very small, although still show the capability to

deform (see figure 1) - the ductility. In a force

based design the ductility of the structure is

taken into account by the behaviour factors, in

the EC8-1 [2] “q”, equal to the whole structure -

the global ductility. In a displacement based

design, like it’s proposed in the EC8-3, the

ductility is also taken in account in the element

level - local ductility.

A linear analysis to assess the structure is

suitable, because the Newmarck [3] equal

displacement principle, this states that the

ultimate displacement of two structures with

similar stiffness and mass with linear elastic

behaviour have the same limit displacement

using a linear elastic or non linear analysis.

Figure 1 - Moment curvature relation of a concrete

member, adapt from [4]

This method of analysis can be performed in a

certain range of natural frequencies [4] that

includes the majority of the reinforced concrete

buildings, and for the structures that don´t have

concentration of plastic hinges in few members

[3] .The members stiffness is the key factor for

the purpose of displacement evaluation. The

concrete elements show a decreasing of stiffness

higher than the 50% of elastic stiffness proposed

in [2], so it’s used the effective stiffness. The

method is proposed in [1] is the secant stiffness

in the point where the first fibre of a concrete

section yields, using an approximation of the

concrete element to an elastic-perfectly-plastic

behaviour (present in figure 1 in traced lines)

this can be obtained by the following expression

proposed in [1].

(1)

Where:

My and θy are the yield moment and rotation, respectively

Lv is the shear span MEd/VEd

2

B. Assessment of concrete structures by EC8-

3

The EC8-3 sets for Portugal the limit state (LS)

named Significant Damage (SD) to fulfil; this

state corresponds to a probability of exceedance

of 10% in 50 years or a return period of 475

years. In other countries can be checked a lower

limit state named Near Collapse (NC) with a

higher return period. It´s presented other LS

with a higher level of protection, the limit state

of Damage Limitation (DL) with a return period

of 225 years, which corresponds to a probability

of exceedance of 20% in 50 years.

The seismic ground acceleration is the same

presented in [2], including the foundations type

soil, and with two types of earthquake indicated

in the national annex, the type 1 and type 2,

with an equal division of the country by zones.

The standard [1] indicates a series of data to

collect from the structure members and the

minimum tests of the materials. This divides in

three types of information to collect: geometry

of the members of the structure, details that

consists in the amount of reinforcement and its

details and the materials mechanic properties.

This data leads to three levels of information

named Knowledge Levels (KL) that correspond

to a confidence factor (CF) used like a safety

factor. The KL1, KL2 and KL3 leads to a CF of

1,35, 1,20 and 1,00 respectively. The

information to retrieve to indentify and reach

the KLs is presented in 3.3 and 3.4 of [1].

The prerequisites to the use of each type of

structural analysis are the same presented in [2],

but if the inspection leads to a KL1 the analysis

needs to be linear, by lateral loads or using a

modal response spectrum. To use a linear

analysis is needed to fulfil another condition,

which is the formation plastic hinges spread

evenly throughout the structure. This is

checked, for each section, by the parameter ρi

present in the expression (2) that relates the

demand (Di) with the capacity (Ci) of the section

using the flexure moments.

(2)

(3)

The capacities values need to be calculated

excluding the possibility of plastic hinge

formations in the column or beams and vice-

versa. In the whole structure, for each element,

the relation express in (3) must be smaller than

the value 2 to 3, varying by country.

The EC8-3 in the annex A proposes a set of

expressions, suitable to evaluate the rotations

capacities and shear resistance of the elements.

The expression (4) used to predict the ultimate

rotation capacities was made and calibrated

based in various tests to columns, beams and

walls [5]. In this expressions ω ω´ are the

mechanical percentages of longitudinal

reinforcement in tension and compression,

respectively, υ axial force normalized to the

section resistance. The parameter ρsx and ρd are

the steel ratio of transverse reinforcement and

diagonal reinforcement respectively, α is a

factor considering the confinement given by

expression (A2) of [1] and γel is the safety factor

with the value 1,5 for primary elements and 1,0

for secondary ones. The average mechanical

properties of the materials divided by the

corresponding CF are presented by fc for the

concrete and fyw for the steel in stirrups.

(4)

The elastic part of the rotation of an element is

presented in the expression (5) and like (4) was

calibrated by tests [5]. The first member of this

expression takes in to account the possibility of

the shear cracking prior to the moment of yield,

the second it’s inherent to the shape of the

element, and the third considers the anchorage

tension in the longitudinal steel bars.

For

columns

and

beams

(5a)

For walls

(5b)

The yield curvature in (5) is represented by Øy,

av is equal to 1 if shear cracking occurs before

the section reaches the yield moment, or else is

0. The parameters z and h are respectively the

3

length or the internal lever arm and the depth of

the section. The medium yield stress is

represented by fy and dbl is the medium

diameter, both from the longitudinal

reinforcement.

The limits state of severe damage (SD)

demanded by the rotations should be inferior to

3/4 of the ultimate rotation. For the state of

damage limitation (LD) the elements should

remain elastic.

The shear resistance of a section is decresed in

its plastic phase [5] and based in testing the

EC8-3 gives the following expression (6) to the

shear resistance. The web concrete crushing

resistance through shear in all walls elements or

in columns with a relation Lv to height less or

equal to 2,0 is taken equal to the value given by

(7). In expressions (6) and (7) x is the depth of

the compression zone, N the axial force (only in

compression else zero) and Ac the area of the

section, μΔpl

equal to , ρtot the

total longitudinal reinforcement ratio, Vw the

transverse reinforcement shear resistance

contribution and bw the web width. The safety

factor is equal to 1,15 to primary elements and

1,0 for secondary ones.

1−0,05min(5; ∆ 0,16 0,5;100 1−0,16

5; + (6)

1,8 0,15; 1+0,25 1,75;100 1−0,2

2;

(7)

The assessment of the beam column joint is

made like a fragile mechanism and is checked

like in the design of new buildings presented in

[2], for structures of high ductility (DCH) [1].

3. Assessment and retrofitting of a

building using the EC8-3

The practical assessment of a structure will be

made in two similar buildings, which leads to

two retrofitting strategies, a reinforcement of a

structure as a whole, and a local retrofitting one.

The structure in analysis is an office building

located in the town of Faro in Portugal. The

structure has 6 floors above ground without

basements, with a height between floors of

2,8m. The thickness of the slab floors is 0,18m,

with the exceptions of the zones near the stairs

which have 0,22m (see figure 2). The concrete

used in the structure was a B25 (actual C20/25),

and the steel used in reinforcement an A400.

The foundation is made by footings connected

by foundation beams.

Assessment of building A

The first structure to be assess is the building A

which was designed using the standards in use

in the 1960´s in Portugal, for the actions it was

used the Regulamento de Solicitações em Edi

fícios e Pontes (RSEP) [6] and for the design of

the concrete elements the Regulamento de

Estruturas de Betão Armado (REBA) [7]. The

detailing of the structure was made considering

low seismic actions comparing with the actual

practice, with the vertical loads prevailing in

comparison with the lateral loads. The survey

and the testing of the materials, geometry and

the details of the elements of the structure leads

to a KL2, with a confidence factor of 1,2. The

location of the vertical elements and the beams

are displayed in the figure 2 and in figure 3 the

detailing and dimensions of wall elements.

After the inspection to the building materials the

average mechanical properties found is

presented in the table 2.

Table 1 – Average mechanical properties of building

materials after inspection

Material Type Tension (MPa) E

(GPa)

concrete C20/25 28(comp.); 2,8(tens.) 30

steel A400 500 200

Soil

found. Type B (EC8-1) 0,650 0,070

4

Figure 2 – Location of the vertical elements and beams in the type floor of building A

Figure 3 – Dimensions and details of wall elements NC and

PA

Figure 4 – Detail of anchorage in a corner joint (at left),

detail of lap splice in a column and joint with at least 2

stirrups through the joint (at right)

The sections of the columns and its details are

presented in table 4. The walls elements were

light reinforced based on a low seismic action as

presented in figure 3. The beam sections that

connect to the vertical elements are presented in

tables 5 and 6. The detailing of corner joints

were made with special care with the anchorage

of longitudinal reinforcement of the beams (see

figure 4). The lap splices were located in

sections with low strains and with a proper

length to a good transfer of tensions (figure 4).

The vertical loads in a seismic event were

considered in compliance with the EC0 [8] and

EC1-1-1 [9] according to the building use,

except in the top floor where to take in to

account the live loading in the seismic mass was

used the same combination factor of the floors

below. The live load in the top floor is taken

equal to the indicated in [6] because is higher

than the indicated in [9] for floors of use H, and

because was the original value in design.

Table 2 – Vertical loads and combinations factors

Floor

Load (kN/m2)

φ2 (EC0)

Perm. Live

1-5 4,5 3,0 (type B EC1)

0,3

6 1,5 1,0

1-5 Perimeter beams 9,0 kN/m

The seismic reference acceleration is presented

in the table 3.

5

Table 3 – Zone and seismic acceleration in accordance with

the EC8-1

Local Type action Zone agR (m/s2) γI ag (m/s2)

Faro

1 1.2 2,0

1,0

2,0

2 2.3 1,7 1,7

The foundation was modelled by springs for the

rotations by the horizontal directions and in

translation in the vertical direction, using the

Memoria LNEC nº 353 [10]

The stiffness of each element is estimated by

(1), using the limits of strain, presented in 3.1.7

and 3.2.7 of EC2-1-1 [11], for the concrete and

steel respectively, in the calculus of the yield

moment and curvature of each section. For

beams and columns the Lv was taken equal to

half the length.

Table 4 – Dimensions and details of sections of columns

sections

Dimensions Details

Element x(m) y(m) Ver. Hor.

P1_floor 0 to 2 0,30 0,30 4ϕ12

ϕ6//0,15

P2_floor 0 to 2 0,50 0,30 6ϕ16

P3_floor 0 to 2 0,55 0,30 6ϕ16

P4_floor 0 to 2 0,30 0,45 4ϕ16

P5_floor 0 to 2 0,50 0,50 4ϕ16+8ϕ12

P1 and

P4_floor 2 to 4 0,30 0,30 4ϕ12

P2 and P3 floor

2 to 4 0,35 0,30

4ϕ12(P2)

6ϕ12(P3)

P5 floor 2 to 4 0,40 0,40 12ϕ12

P1-P5 floor 4

to 6 0,30 0,30 4ϕ12

P6 0,30 0,40 4ϕ12

In the walls the value of Lv was taken equal to

2/3 of the whole height of the wall because it´s

the point of the resulting force of a triangular

shape force distribution. The stiffness in the

beams varies from 12-18% in the 1 to 5 floors,

and from 8-14% in the top floor, of the gross

section without cracking.

Table 5 – Dimensions and details of beams in floors 1-5

Flo Ele. h(m) b(m) Top

rein.

Bot.

rein. Sitr.

1-5

V1_A

0,55 0,30

4ϕ12 4ϕ12 ϕ6//0,20

V1_B 4ϕ12 2ϕ12 ϕ6//0,20

V2_A

0,50 0,30

2ϕ16+

2ϕ12

2ϕ16+

2ϕ12 ϕ6//0,20

V2_B 4ϕ16+

2ϕ12 2ϕ12 ϕ8//0,15

VA_1 2ϕ12 2ϕ12 ϕ6//0,20

VA_2 3ϕ16+

2ϕ12 2ϕ12 ϕ6//0,20

VA_4 6ϕ16 2ϕ12 ϕ6//0,20

VB_1 2ϕ12 4ϕ12 ϕ8//0,15

VB_2 2ϕ16+

2ϕ12 2ϕ12 ϕ8//0,15

VB_3 7ϕ16 2ϕ12 ϕ8//0,15

Table 6 - Dimensions and details of beams in floor 6

Flo Ele. h(m) b(m) Top

rein.

Bot.

rein. Sitr.

6

V1 0,55 0,30 2ϕ12+

1ϕ10

2ϕ12+

1ϕ10 ϕ6//0,20

V2_A

0,50 0,30

2ϕ12 4ϕ12 ϕ6//0,20

V2_B 2ϕ16+

2ϕ12 2ϕ12 ϕ6//0,20

VA_1 2ϕ12 2ϕ12 ϕ6//0,20

VA_2 3ϕ12 2ϕ12 ϕ6//0,20

VA_4 5ϕ12 2ϕ12 ϕ6//0,20

VB_1

and 2 2ϕ12 3ϕ12 ϕ6//0,20

VB_3 5ϕ12 2ϕ12 ϕ8//0,20

In the columns the value of the stiffness

decreases in height caused by the decreasing of

vertical loads. The wall type elements (NC e

PA) have a low stiffness in comparison to the

gross elastic stiffness, because the lack of

reinforcement. The secant stiffness is presented

in the table 7 for two representative columns

and in the table 8 for the wall elements.

6

Table 7 – Percentage of elastic stiffness of the gross section

of columns and walls

Floor Ele. By “x” By “y” Ele. By “x” & ”y”

1

P2

22% 18%

P5

15%

2 19% 16% 14%

3 19% 18% 16%

4 14% 14% 13%

5 13% 13% 15%

6 9% 9% 10%

Table 8 - Percentage of elastic stiffness of the gross section

of walls

Ele By “x” By “y”

PA Secon. 16%

NC 13% 7%

The beams, because of the design for the

vertical loads, have low reinforcement in the

lower face in interior joints, this leads to a low

capacity (see table 9) to the positive flexural

moments caused by an earthquake. The

evaluation to the parameter ρi presented in (2)

and (3) leads to the conclusion that in some

beams the value of (3) is larger than the

permitted, as presented in table 9, although is

not considered inhibitory to the use of an elastic

analysis in the assessment. The evenly spread of

the plastic hinges is granted because even

considering in the sections where ρi is larger a

hinge in the model, this don’t modify in a

significant manner the deformation of the

structure as a whole. The columns, although

light reinforced, at a section level, never have a

ρi lower 2, and in a element level, the value

given by (3) is never higher than 1,5.

Table 9 – Parameter ρi , for the beam V2, in the alignment B

and interior sections, with a seismic action in y direction

Floor ρi_B _- ρi_B _+ ρmax/ρmin

1 1,01 5,24 5,2

2 4,63 4,63 4,1

The combination of the seismic action is made

by 4.3.3.5.1 [2] , and the type of seismic action

that leads to larger deformations is the type 1.

The analysis show that there´s no need to

considerer second order effects. The limit state

checked in Portugal is the severe damage (SD),

and in the next paragraphs, the structure will be

assessed to this limit state for a seismic action of

type 1.

The assessment to the seismic actions leads to 4

elements in which the rotation surpasses the

ultimate rotation to check in the limit state SD

as presented in figure 5.

There´s also a large number of sections where

(as seen in figures 5 and 6) yield rotation is

reached, this is relevant because in the plastic

phase the shear strength lowers.

The shear demand of the elements is calculated

on the basis of capacity design and the shear

resistance by (8) in the elements that reaches a

yielding point. In the remain sections the shear

verification is made by [11].

Figure 5 – Location of the sections that reaches the yield

rotation (in orange) and where reaches the ultimate rotation

for a LS of SD (in red), for a seismic action in the y

direction in the frame 1

Figure 6 - Location of the sections that reaches the yield

rotation (in orange) for a seismic action in the x direction in

the frame B

Table 10 – Rotation at the base of the element NC

θy_base_xx (rad)

(5b)

θed_base_xx

(rad)

θy_base_yy (rad)

(5b)

θed_base_yy

(rad)

0,008 0,007 0,0063 0,0058

The low horizontal reinforcement of the

columns in combination with a post yield phase

leads to a large number of columns that the

shear capacity is lower than the demand as seen

in figures 7 and 8. The number of sections of

beams, with shear deficiencies, is lower than the

number of sections in columns, due to the good

shear reinforcement to the vertical loads.

Although, the sections where yielding take place

7

have shear resistance problems in particular the

sections that connect to the elements PA and

NC which have large deformations.

The walls PA and NC, though they don´t enter

in plastic phase, have a deficit of shear

resistance due to a low transverse

reinforcement. This is presented in the table 10

and figure 9. The shear resistance is calculated

by [11], because the sections in the base remain

in elastic phase.

The foundations of the walls, even using the

springs, don’t sustain the demands. This fact

leads to the conclusion that the deformability of

the structure is higher than the assessed.

The assessment of the structure indicates a

deformation problem in the y direction. Based

on the analysis is also imperative to enhance the

shear resistance of a great number of elements,

including the walls elements.

Figure 7 - Elements that lacks shear resistance (in red) for a

seismic action in the x direction, for the frame 1

Figure 8 - Elements that lacks shear resistance (in red) for a

seismic action in the x direction, for the frame B

Figure 9 – Shear behaviour of the wall NC, resistances by

EC2-1-1 [11]

Table 11 – Capacity of the footing of the wall NC

dir MEd_xx

(kNm)

MEd_ yy

(kNm)

MRd_yy

(kNm)

MRd_xx

(kNm)

x 2103,9 11112,0 3611 6259

y 4592,0 4791,1

The enumerated facts lead to a retrofitting

strategy of the structure as a whole, by the

inclusion of new walls.

The assessment of the beam column joint and

the secondary elements is not made because it

will not interfere in the choice of the retrofitting

strategy, and will be assessed in the structure

with the reinforced that is made.

B. Retrofit solution for building A

The inclusion of new walls to diminish the

deformation in the y direction is mandatory,

because is the direction with the column P4 with

deformation problems and the larger number of

elements to reinforce because of the shear. The

addition of walls in the x direction will be

checked in its cost/benefit relation. One other

objective is to eliminate the torsion in the 3 first

modes of vibration.

The first solution to be considered was the

execution of two walls in the perimeter frames,

between the columns P4 and orientated by y

direction, this was called solution 1, as

presented in figure 10. Another solution is

analysed, derived of the solution 1, this solution

adds another pair of walls orientated by x in the

perimeter frames including the column P3,

between the alignment 3 and 5, this one is called

solution 2 (figure 10).

0

1

2

3

4

5

6

0 1000 2000 3000 4000

Floor

V(kN)

Wall (NC)

VRd,s x

VEd x

VR,max x

VRd,s y

VEd y

VR,max y

8

Figure 10 - Location of the reinforcement walls in solution

1(left) and solution 2 (right)

To check if the elastic foundation has a great

influence in the results of the analysis and to

simulate the foundation of the reinforcement

walls by micro-piles was tested the solution 2

with fixed foundations. The comparative

analysis of the solutions, although decreasing

deformations from the solution 1 to 2 and 2

fixed, leads to small differences between the

numbers of elements to reinforce. In none of the

cases the yield point is reached in the base of

any walls, so the shear resistance is given by

[EC2]. The evaluation of the solutions on a wall

element is showed in figure 16.

Figure 11 – Shear in wall element for the solutions of

reinforcement

The similar number of beams and columns to

retrofit to shear forces and the same retrofit to

be made in the walls elements (figure11) leads

to the conclusion that is no need to execute the

additional walls in the solution 2, so from now

on the results showed are referred to the chosen

solution, the solution 1.

The assessment of the beams and columns

shows that the plastic hinge can be formed in

the columns, this need to be considered in the

evaluation of the demand in the joints. An

example of evaluation of a joint is presented in

table 12.

Table 12 – Shear evaluation of beam VA column P3 joint

Flo. b(m) h(m) ν Vc(kN)

Vjhd (EC8-1)

(kN)

VRd (kN)

(10)

1 0,3 0,55 0,26 129,8 766,7 826,0

2 0,3 0,55 0,20 74,5 822,1 912,1

3 0,3 0,35 0,23 64,3 465,1 510,6

4 0,3 0,35 0,14 36,1 363,1 583,0

5 0,3 0,30 0,05 24,8 236,4 527,4

6 0,3 0,30 0,00 0,00 88,6 557,4

Table 13 – Shear evaluation to the column P6 for a seismic

action in the y direction

Flo. Pos. VR(kN)(8) VEd(kN)

1

base 90,0 52,4

top 89,0 53,6

2

base 85,4 68,3

top 84,6 68,5

3

base 80,7 82,1

top 79,5 82,2

4

base 75,4 79,1

top 74,1 79,2

5

base 69,7 65,2

top 68,6 65,3

6

base 63,9 57,1

top 62,3 57,2

Although the prescriptive detailing measures of

DCH structures are not reached in the joints, the

0

1

2

3

4

5

6

0 500 1000 1500 2000 2500

Floor

V(kN)

Shear x in NC

VEd sol.

type 1

VEd sol type

2

VEd sol.

Type 2 fixed

VRd,s EC2

9

main mechanism for a good behaviour of a

joint, the crushing the concrete in diagonal, is

verified.

The secondary elements considered were the

columns P3 in both directions and the column

P3 and wall PA in y direction. This type of

elements has only problems in shear resistance

and in only one element, the column P6, showed

in table 13.

The design of the reinforcement wall (PA_R) is

made like a wall in a new building [5], and by

the construction dispositions of the EC8-1. The

ductility taken into account is a medium

ductility (DCM), using a “q” factor of 3 units.

The flexure and shear actions on these walls are

presented in figure 17.

The construction dispositions in the first two

floors, granting the ductility and the

confinement of the corner elements, are

presented in figure 13 and table 14.

Even with the addition of the walls PA_R there

is still need to reinforce the original walls (NC

and PA) as presented in figure 11, as well as

some beams and columns. This retrofit will be

made by carbon fibres reinforced polymers

(CFRPs), using sheets from the company S&P,

with 240g/m2.

Figure 12- Moment and shear in the reinforcement walls

PA_R

Figure 13 - Dispositions of reinforcement of the wall PA_R

Table 14 - Dispositions of the wall PA_R by [2] and

resistances

lw(m) bw(m) hcr (m) lc_min(m) lc_adop(m)

6,15 0,4 2,8 0,925 0,95

νd ωv μϕ s_min(mm) s_adop(mm)

0,06 0,057 5,0 128 125

αn αs α MRd (kNm) VRd (kN)

0,642 0,743 0,477

21184 5465 ωw_x ωw_y ωwd

0,064 0,044 0,044

The original wall elements do not enter in

plastic phase in the bottom sections, according

to [1] the expression (9) is used to calculate the

FRPs contribution to shear resistance for a fully

warped element; for sheets sf equal to wf.

(9)

The value of the referred expression is to be

summed to the shear resistance given by the

EC2-1-1.

The original walls will be retrofitted by fully

warped by one layer the FRP sheets (see figure

14) to be applied in a various number of floors

(see figure 17).

Figure 14 - Construction disposition of jacketing of the

walls (top) and columns (bottom) with CFRPs sheets

0

1

2

3

4

5

6

0 5000 10000 15000 20000

Floor

M(kNm)

MEd wall PA_R

MEd_model

MEd_envel_EC8

0

1

2

3

4

5

6

0 1000 2000 3000 4000 5000 6000

Floor

V(kN)

VEd wall PA_R

VEd_model

VEd_envel_

EC8

10

Table 15 – Shear resistance of the CFRP per layer of sheet

in walls

Ele. θ (º) β(º) R(cm)

ffdd

(MPa)

ffdd,e,W

(MPa)

VRd,f

(kN)

PA

22 90 3,0

1270 1514 2425

NC_dir x 1269 1515 2581

NC_dir y 1281 1498 1333

The columns with lack of shear resistance to

shear demands will also be fully warped by

FRPs sheets (figure 17), but in this case the

elements reaches the yield rotation, so the

contribution to the shear resistance is calculated

through the expression (10) proposed in [1]. The

enhancement of shear resistance by the FRP is

to be added to the transverse reinforcement

value (Vw) in the expression (6). These values

are presented in table 16.

(9)

Table 16 - Shear resistance of the CFRP per layer of sheet in

columns

Ele. bw(m) d (m) fu (N/mm2) Vw,f(kN)

P1 flo.0-1 0,300 0,265

4500

74,9

P2 flo.2-4 0,300 0,315 89,0

P2 flo.2-4 0,500 0,465 74,9

P5 flo.0-1 0,500 0,465 131,4

P5 flo.2-4 0,400 0,365 103,1

P6 flo.2-4 0,300 0,365 103,1

The beams sections, even with a good amount

of transverse reinforcement, at the connection

with the walls (original and PA_R) where

yielding takes place, need a shear

reinforcement. The reinforcement made is an

application in “U” shape of FRPs sheets (see

figure 18), the shear resistance contribution of

the FRP is calculated by the expression (9). This

value is to be added to the original resistance of

the stirrups in expression (8), as applied in the

columns. In figure 16 is presented an example

of the shear behaviour of a beam, considering

the degradation of the shear resistance in the

plastic hinge length considered by 0,7 meters

calculated by (A.9) of [1].

Figure 15- Construction disposition of “U” shaped jacketing

of the beams with CFRPs sheets

Figure 16 – Shear evaluation of beam VB between P5 (left

to right) and PA wall

Table 17 - Shear resistance of the CFRP per layer of sheet in

beams

Ele. θ (º) β(º) R(cm)

ffdd

(MPa)

ffdd,e,U

(MPa)

VRd,f

(kN)

V1_B

22 90 3,0

662 606 218

VB&C_3 677 614 197

The reinforcement will be applied in the VB and

VC in the extension of 2,5 m, as presented in

figure 21 and in 0,7 m in the connection of the

wall PA_R. The shear resistance contribution of

the FRPs is presented in table 17.

The execution of all reinforcements in the

building A is presented in figure 17.

C. Assessment and retrofit of building B

The building B is similar to the building A in

terms of location, use and vertical loadings.

The major difference is the wall element NC1

(location in figure 18), the dimensions and

details are presented in figure 19. The element

NC2 has the same dimensions as NC in the

building A but with a 0,30m thickness, the

details are similar with NC1. The differences for

building A in the columns details are presented

in table 18.

0

50

100

150

200

250

300

0 1 2 3 4

V(kN)

L(m)

Shear beam VB VRd_EC2

VEd_envolv

ente

sismo+cqp VRd_rot.

Plástica eq

(37)

11

Figure 17 – Location reinforcements of building A

Figure 18 – Location of vertical elements and beams in building B

The beams have an increase of transverse

reinforcement; the beams of type VA in align. 2

and V1 align. B and C to ϕ8//0,15 and VB&C

align. 1 to ϕ8//0,20, to this is added in all

interior supports the double amount of inferior

longitudinal reinforcement. There was an

increased care in the detail of the beam column

joints with a decreasing of spacing of stirrups of

the columns in half. This is executed in a height

of 0,5m bellow and after the joint, as well as

through the joint.

To not underestimate the global deformation of

the structure, the springs of the wall elements

were calibrated in the model so that the supports

didn´t take loads superior to their capacity. The

limit state to be checked is also the severe

damage(SD).

12

Table 18 – Details of columns in building A

Flo. column Asw

1 e 2

P1 ϕ6//0,125

P2 -P6 ϕ 8/0,125

2 e 3 P1-P6 ϕ 6//0,125

4 e 5 P1-P6 ϕ 6//0,15

Figure 19 – Dimensions and details of wall (NC1) of

building B

The deformation assessment of the structure

leads to the conclusion that none of the sections

reaches the ultimate rotation (see figure 26).

The structure B, in comparison with structure A,

has fewer sections where the yield rotation is

reached; this can be seen in figure 20. The

beams sections which rotations are higher than

the yield limit, are located at the connection to

the walls elements.

The shear assessment shows that the columns

with a lower capacity than the demand are

located between the 2nd

and 4th

floor (see figure

20). The lower number of elements, in relation

to the building A, that reaches a plastic phase,

and the increasing of horizontal reinforcement,

leads to a minor number of elements with a

shear resistance deficit. The beams sections with

lack of shear resistance are again in most cases

located in the connection to the wall elements.

An example of beam behaviour to shear is

presented in figure 22, the figure indicates a

length of the shear problem only in the length of

the plastic hinge. The wall elements have a

shear resistance problem in the lower floors as

presented in figures 20 and 21, this occurs even

with a larger horizontal reinforcement.

The secondary elements are considered to be the

P3 in the y direction and P6 in both directions.

The elements don´t have rotations larger than

the limit of LS of SD, but the element P6

between floor 2 and 4 need to be reinforced to

shear forces.

Figure 20 – Location of the sections that reaches the yield

rotation (in orange) for a seismic action in the y direction in

the frame 1, in building B

Figure 21 - Shear behaviour of the wall NC 2, resistances by

EC2-1-1

0

1

2

3

4

5

6

0 1000 2000 3000 4000

Floor

V(kN)

SHEAR NC2

VRd,s x

VEd x

VRd,max x

VRd,s y

VEd y

VRd,max y

13

Figure 22 - Shear evaluation of beam VB between P5 (left to

right) and PA wall in building B

The beam columns joints do not have the

concrete in the diagonal crushed, as presented in

table 19. Again, the prescriptive measures to be

fulfil in accordance to [2] for DCH structures

are not achieved, even with a significant

increasing of horizontal reinforcement through

the joint. However because the crushing of the

concrete in the diagonal is prevented, the joint

resistance is verified.

Because there is not a generalized deformation

problem and the number of elements to

reinforce to shear is relatively low, the

retrofitting strategy chosen is a local one, which

leads to a reinforcement only to the elements

with lack of shear resistance.

Table 19 – Beam column joint evaluation

flo b(m) h(m) ν Vc(kN)

Vjhd (EC8-1)

(kN)

VRd (kN)(10)

1 0,3 0,55 0,26 129,8 916 826

2 0,3 0,55 0,20 74,5 787 912

3 0,3 0,35 0,23 64,3 412 511

4 0,3 0,35 0,14 36,1 322 583

5 0,3 0,30 0,05 24,8 209 527

6 0,3 0,30 0,00 0,00 85 557

The reinforcements should be executed with the

same material (CFRP) used in building A,

applied with the same reinforcement techniques,

used in the original columns, beams and walls.

All the reinforcements needed are presented in

figure 29.

Figure 23 - Locations of the reinforcements in building B

0

100

200

300

0 2 4

V(kN)

L(m)

Shear VB

VRd_EC2

VEd_envol

vente

sismo+cqp

14

4. Conclusions

The EC8-3 gives the engineers a guide to assess

the structural behaviour of old structures by

evaluate the deformation capacity, instead of the

strength of the members. Also summarizes and

proposes in the annexes ways to assess the

member’s deformations capacities and shear

resistances, as well as the retrofitting of

elements.

The standard promotes a good survey and

testing of the building, which leads to minor

security factors less penalizing to the

assessment. The methodology of evaluation is

made on the basis of deformation, although if it

is used an elastic analysis, the evaluation of the

brittle mechanisms is made by capacity, this

leads to high shear demands that old structures

are likely not meant to sustain. It´s not granted

that in an earthquake this demands are reached,

so this leads to the conclusion that the EC8-3

promotes the use of non-linear analysis. The

beam-column joints are obliged to comply with

the prescriptive measures of structures of high

ductility, which very few old structures will

fulfil, even structures design by modern codes.

In a retrofitting strategies that reinforce the

structure as a whole, if the foundation of the

new wall elements is made by shallow

foundation without basements, it is very

difficult to extract the total potential of this

solution, because the uplift of the foundation.

References:

[1] CEN, Eurocode 8: Design of structures for

earthquake resistance - Part 3: Assessment

and retrofitting of buildings, Brussels:

CEN, 2005.

[2] CEN, Eurocode 8 - Design of structures for

earthquake resistance - Part 1 : General

rules, seismic actions and rules for

buildings, Brussels: CEN, 2004.

[3] Appleton, J., Estruturas de Betão Vol. II,

Alfragide: Edições Orion, 2013.

[4] Priestley, M. J. N., Calvi, G. M. ,

Kowalsky, M. J., Displacement-Based

Seismic Design of Structures, Pavia: IUSS

Press, 2007.

[5] Fardis, M. N., Seismic Design, Assessment

and Retrofitting of Concrete Buildings,

London New York: Springer, 2009.

[6] Regulameno de Solicitações em Edifícios e

Pontes -decreto lei 44041 de 18 Novembro

1961, Lisboa: Impresa Nacional, 1961.

[7] Regulamento de Estruturas de Betão

Armado decreto lei 47723 20 de Maio de

1967, Lisboa: Impresa Nacional, 1967.

[8] CEN, Eurocode - Basis of structural

design, Brussels: CEN, 2002.

[9] CEN, Eurocode 1: Actions on structures

Part 1-1:General actions Densities, seft

weight, imposed loads for buildings,

Brussels: CEN, 2002.

[10] Castro, G., "Deformabilidade das

fundações e sua consideração no cálculo

de estruturas Memória Laboratório

Nacional de Engenharia Civil:353",

LNEC, Lisboa, 1970.

[11] CEN, Eurocode 2 - Design of concrete

structures Part 1-1: General rules and

rules for buildings, Brussels: CEN, 2004.