tu8_design and verification of a steel concentrically-braced

8/9/2019 TU8_Design and Verification of a Steel Concentrically-braced

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European Erasmus Mundus

Master Course

Sustainable Constructions

under Natural Hazardsand Catastrophic Events

List of Tutorials

1. Design and verification of a steel moment

resisting frame

2. Design and verification of a steel concentric

braced frame

3. Assignment: Design and verification of a steel

eccentric braced frame

2


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Design and verification of a steel Concentric

Braced Frames

1. Introduction

2. General requirements for Concentric Braced

Frames

3. Damage limitation

4. Structural analysis and calculation models

5. Verification

3


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Introduction

The case study is a six storey residential buildingwith a rectangular plan, 31.00 m x 24.00 m. The

storey height is equal to 3.50 m with exception of

the first floor, which is 4.00 m high

4

Building

description

Normative

references

Materials

Actions


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Introduction

Structural plan and configuration of the CBFs

5

Building

description

Normative

references

Materials

Actions

6

6

22 2

731

6 5

6

6 2.34 2.332.33 2.52.5

1 2 3

4 5 6

7 8 9

7

6

24

X Bracings V Bracings

Direction X Direction Y


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Introduction

composite slabs with profiled steel sheetings are adopted toresist the vertical loads and to behave as horizontal rigid

diaphragms.

The connection between slab and beams is provided by

ductile headed shear studs that are welded directly through

the metal deck to the beam flange.

6

Buildingdescription

Normative

references

Materials

Actions


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Introduction

Apart from the seismic recommendations, the structural safetyverifications are carried out according to the following

European codes:

- EN 1990 (2001) Eurocode 0: Basis of structural design;

- EN 1991-1-1 (2002) Eurocode 1: Actions on structures - Part

1-1: General actions -Densities, self-weight, imposed loads for

buildings;

- EN 1993-1-1 (2003) Eurocode 3: Design of steel structures -

Part 1-1: General rules and rules for buildings;

- EN 1994-1-1 (2004) Eurocode 4: Design of composite steel

and concrete structures - Part 1.1: General rules and rules forbuildings.

In EU specific National annex should be accounted for design.

For generality sake, the calculation examples are carried out

using the recommended values of the safety factors7

Buildingdescription

Normative

references

Materials

Actions


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Introduction

It is well known that the standard nominal yield stress fy is theminimum guaranteed value, which is generally larger than the actual

steel strength.

Owing to capacity design criteria, it is important to know the maximum

yield stress of the dissipative parts.

This implies practical problems because steel products are not usually

provided for an upper bound yield stress.

Eurocode 8 faces this problem considering 3 different options:

a) the actual maximum yield strength fy,maxof the steel of dissipative

zones satisfies the following expression

fy,max1.1ovfy

where fyis the nominal yield strength specified for the steel grade and

gov is a coefficient based on a statistic characterization of steel

products.

The Recommended value is 1.25 (EN1998-1 6.2.3(a)), but the

designer may use the value provided by the relevant National Annex.8

Buildingdescription

Normative

references

Materials

Actions


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Introduction

b) this clause refers to a situation in which steel producers provide a

seismic-qualifiedsteel grade with both lower and upper bound value

of yield stress defined.

So if all dissipative parts are made considering one seismic steel

grade and the non-dissipative are made of a higher grade of steel

there is no need for govwhich can be set equal to 1.

c) the actual yield strength fy,actof the steel of each dissipative zone is

determined from measurements and the overstrength factor is

computed for each dissipative zone as gov,act= fy,act / fy , fybeing the

nominal yield strength of the steel of dissipative zones.

9

Buildingdescription

Normative

references

Materials

Actions


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Introduction

In general at design stage the actual yield stress of the material is not

known a-priori. So the case a) is the more general.

Hence, in this exercise we use it.

10

Buildingdescription

Normative

references

Materials

Actions

Grade fy ft M ov E

(N/mm2) (N/mm

2) (N/mm

2)

S235 235 360 gM0= 1.00

gM1= 1.00

gM2= 1.25

1.00 210000S355 355 510


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Introduction

Characteristic values of vertical persistent and transient actions

11

Buildingdescription

Normative

references

Materials

Actions

Gk(kN/m2) Qk(kN/m

2)

Storey slab 4.20 2.00

Roof slab 3.600.50

1.00 (Snow)

Stairs 1.68 4.00

Claddings 2.00


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Introduction

Seismic actionA reference peak ground acceleration equal to agR= 0.25g (being g

the gravity acceleration), a type C soil and a type 1 spectral shape

have been assumed.

The design response spectrum is then obtained starting from the

elastic spectrum using the following equations

12

Buildingdescription

Normative

references

Materials

Actions

0 BT T 2.51 1d gB

TS T a S T q

B CT T T 2.5

d gS T a S q

C DT T T

2.5 Cg

d

g

Ta S

q TS T

a

DT T 2

2.5 C Dg

d

g

T Ta S

q TS T

a

S= 1.15, TB= 0.20 s , TC= 0.60 s and TD= 2.00 s.

The parameter is the lower bound factor for the horizontal design

spectrum, whose value should be found in National Annex.

= 0.2 is recommended by the code (EN1998-1.2.2.5)


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Introduction

Seismic actionElastic and design response spectra

13

Buildingdescription

Normative

references

Materials

Actions

behaviour factor q was assigned according to EC8 (DCH concept)

as follows:

4

2.5

q for X-CBFs

q for inverted V-CBFs

0

1

2

3

4

5

6

7

8

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

T(s)

S

e,

S

d(

m/s2)

Elastic spectrum

Design spectrum-X braces

Design spectrum-Inverted-V braces

lower bound = 0.2ag


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Introduction

Combination of actionsIn case of buildings the seismic action should be combined with

permanent and variable loads as follows:

where Gk,i is the characteristic value of permanent action I(the self

weight and all other dead loads), AEd is the design seismic action(corresponding to the reference return period multiplied by the

importance factor), Qk,iis the characteristic value of variable action I

and 2,i is the combination coefficient for the quasi-permanent value

of the variable action I,which is a function of the destination of use

of the building

14

Buildingdescription

Normative

references

Materials

Actions

k,i k,i Ed2,i" " " "G Q A

Type of variable actions 2i

Category ADomestic, residential areas 0.30

Roof 0.30

Snow loads on buildings 0.20

Stairs 0.80


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Introduction

MassesIn accordance with EN 1998-1 3.2.4 (2)P, the inertial effects in the

seismic design situation have to be evaluated by taking into account

the presence of the masses corresponding to the following

combination of permanent and variable gravity loads:

where is the combination coefficient for variable action i,which takes into account the likelihood of the loads Qk,i to be not

present over the entire structure during the earthquake, as well as a

reduced participation in the motion of the structure due to a non-rigid

connection with the structure.

15

Buildingdescription

Normative

references

Materials

Actions

k,i k,iE,i" "G Q

E,i 2i

Type of variable actions 2i Ei

Category ADomestic, residential areas 0.30 0.50 0.15

Roof 0.30 1.00 0.30

Snow loads on buildings 0.20 1.00 0.20

Stairs 0.80 0.50 0.40


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Introduction

Seismic weights and masses in the worked example

16

Buildingdescription

Normative

references

Materials

Actions

Storey Gk Qk Seismic Weight Seismic Mass

(kN) (kN) (kN) (kN/m2) (kN s

2/m)

VI 3195,63 1326,00 3519.03 4.73 358.72

V 3990,72 1608,00 4196.23 5.64 427.75IV 4087,66 1608,00 4276.87 5.75 435.97

III 4106,70 1608,00 4283.01 5.76 436.60

II 4187,79 1608,00 4353.15 5.85 443.75

I4261,26 1608,00

4411.33 5.93 449.68


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General requirements for CBFs

Basic principles of conceptual design- structural simplicity: it consists in realizing clear and direct paths for

the transmission of the seismic forces

- uniformity: uniformity is characterized by an even distribution of the

structural elements both in-plan and along the height of the building.

- symmetry : a symmetrical layout of structural elements is envisaged

- redundancy: redundancy allow redistributing action effects and

widespread energy dissipation across the entire structure

- bi-directional resistance and stiffness: the building structure must be

able to resist horizontal actions in any direction

- torsional resistance and stiffness: building structures should possess

adequate torsional resistance and stiffness to limit torsional motions- diaphragmatic behaviour at storey level: the floors (including the roof)

should act as horizontal diaphragms, thus transmitting the inertia forces

to the vertical structural systems

- adequate foundation: the foundations have a key role, because they

have to ensure a uniform seismic excitation on the whole building.

17

Basicprinciples of

conceptual

design

Plan location

of CBFs andstructural

regularity

Damage

limitation


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CBFs are mainly located along the perimeter of the building.There is the same number of CBF spans in the 2 main direction of the

plan.

Hence, the building is regular in-plan because it complies with thefollowing requirements (EN 1998-1 4.2.3.2):

- The building structure is symmetrical in plan with respect to two

orthogonal axes in terms of both lateral stiffness and mass distribution.

- The plan configuration is compact; in fact, each floor may be delimited

by a polygonal convex line. Moreover, in plan set-backs or re-entrant

corners or edge recesses do not exist.18

Basicprinciples of

conceptual

design

Plan location


regularity

Damage

limitation

6

6

22 2

731

6 5

6

6 2.34 2.332.33 2.52.5

1 2 3

4 5 6

7 8 9

76

24


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- The structure has rigid in plan diaphragms.

- The in-plan slenderness ratio Lmax/Lminof the building is lower

than 4 (31000 mm / 24000 mm = 1.29), where Lmaxand Lminare

the larger and smaller in plan dimensions of the building,

measured in two orthogonal directions.

- At each level and for both X and Y directions, the structural

eccentricity eo (which is the nominal distance between the

centre of stiffness and the centre of mass) is practically

negligible and the torsional radius r is larger than the radius of

gyration of the floor mass in plan

19

Basicprinciples of

conceptual

design

Plan location


regularity

Damage

limitation


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Regularity in elevation

- All seismic resisting systems are distributed along the building

height without interruption from the base to the top of the

building.

- Both lateral stiffness and mass at every storey practically

remain constant and/or reduce gradually, without abrupt

changes, from the base to the top of the building.

- The ratio of the actual storey resistance to the resistance

required by the analysis does not vary disproportionately

between adjacent storeys.

- There are no setbacks20

Basicprinciples of

conceptual

design

Plan location


regularity

Damage

limitation


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damage limitation requirement is expressed by the followingEquation:

drn h

where:is the limit related to the typology of non-structural elements;

dris the design interstorey drift;

h is the storey height;

n is a displacement reduction factor depending on the

importance class of the building, whose values are specified inthe National Annex. In this Tutorial n= 0.5 is assumed, which is

the recommended value for importance classes I and II

(the structure calculated in the numerical example belonging to

class II).

21

Basicprinciples of

conceptual

design

Plan location


regularity

Damage

limitation


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According to EN 1998-1 4.3.4, If the analysis for the design seismicaction is linear-elastic based on the design response spectrum (i.e.

the elastic spectrum with 5% damping divided by the behaviour

factor q), then the values of the displacements ds are those from

that analysis multiplied by the behaviour factor q, as expressed by

means of the following simplified expression:

ds= qdde

where:

ds is the displacement of the structural system induced by the

design seismic action;

qdis the displacement behaviour factor, assumed equal to q;

deis the displacement of the structural system, as determined by a

linear elastic analysis under the design seismic forces.

22

Basicprinciples of

conceptual

design

Plan location


regularity

Damage

limitation


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Structural analysis and calculation models

In this Tutorial two separate calculation 2D planar models in thetwo main plan directions have been used, one in X direction and

the other in Y direction. This approach is allowed by the EC8 (at

clause 4.3.1(5)), since the examined building satisfies the

conditions given by EN 1998-1 4.2.3.2 and 4.3.3.1(8)

Modelling assumptions:

for the gravity load designed parts of the frame (beamto-

columns connections, column bases) have been assumed as

perfectly pinned, but columns are considered continuous

through each floor beam.Masses are considered as lumped into a selected master-joint

at each floor, because the floor diaphragms may be taken as

rigid in their planes

The models of X-CBFs and inverted V-CBFs need different

assumption for the braced part.23

Generalfeatures

Calculation

models and

code

requirementsfor X-CBFs

Calculation

models and

code

requirements

for inverted

V-CBFs


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In 3D model, in order to account for accidental torsional effects the

seismic effects on the generic lateral load-resisting system are

multiplied by a factor

where:

xis the distance from the centre of gravity of the building, measured

perpendicularly to the direction of the seismic action considered;

Leis the distance between the two outermost lateral load resisting

systems.24

x

Le

G

1 0 6e

x.

L

Seismicactio

n

Seismic

resistant

system

Generalfeatures

Calculation

models and

code


Calculation

models and

code

requirements

for inverted

V-CBFs


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In planar models, If the analysis is performed using two planar models,

one for each main horizontal direction, torsional effects may be

determined by doubling the accidental eccentricity as follows:

25

x

Le

G

1 1 2e

x.

L

Seism

icaction

Seismic

resistant

system

Generalfeatures

Calculation

models and

code


Calculation

models and

code

requirements

for inverted

V-CBFs


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An important aspect to be taken into account is the influence of second

order (P-) effects on frame stability. Indeed, in case of large lateral

deformation the vertical gravity loads can act on the deformed

configuration of the structure so that to increase the level the overall

deformation and force distribution in the structure thus leading to

potential collapse in a sidesway mode under seismic condition

26

Generalfeatures

Calculation

models and

code


Calculation

models and

code

requirements

for inverted

V-CBFs


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According to EN 1998-1, 4.4.2.2(2) second-order (P-) effects are

specified through a storey stability coefficient () given as:

where: Ptotis the total vertical load, including the load tributary to gravity

framing, at and above the storey considered in the seismic design

situation;

Vtotis seismic shear at the storey under consideration;

his the storey height;

dris the design inter-storey drift, given by the product of elastic inter-

storey drift from analysis and the behaviour factor q(i.e. de q).

27

tot r

tot

P d

V h

Generalfeatures

Calculation

models and

code


Calculation

models and

code

requirements

for inverted

V-CBFs


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Frame instability is assumed for 0.3. If 0.1, second-order effects

could be neglected, whilst for 0.1 < 0.2, P-effects may be

approximately taken into account in seismic action effects through the

following multiplier:

Differently from MRFs, for CBFs it is common that the storey stability

coefficient is < 0.1, owing to the large lateral stiffness of this type of

structural scheme.

Hence, CBFs are generally insensitive to P-Delta effects

28

1

1

Generalfeatures

Calculation

models and

code


Calculation

models and

code

requirements

for inverted

V-CBFs


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X-CBFsAccording to EN 1998-1 6.7.2(2)P, in case of X-CBFs the structuralmodel shall include the tension braces only, unless a non-linear

analysis is carried out. Then, the generic braced bay is ideally

composed by a single brace (i.e. the diagonal in tension).

Generally speaking, in order to make tension alternatively developing in

all the braces at any storey, two models must be developed, one withthe braces tilted in one direction and another with the braces tilted in

the opposite direction

29a

k 2i kiiG Q

,Ed iF

b

k 2i kiiG Q

,Ed iF

Generalfeatures

Calculation

models and

code


Calculation

models and

code

requirements

for inverted

V-CBFs


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X-CBFsthe diagonal braces have to be designed and placed in such a waythat, under seismic action reversals, the structure exhibits similar lateral

load-deflection response in opposite directions at each storey

where A+ and A- are the areas of the vertical projections of the cross-

sections of the tension diagonals (Fig. 4.6) when the horizontal seismic

actions have a positive or negative direction, respectively30

Generalfeatures

Calculation

models and

code


Calculation

models and

code

requirements

for inverted

V-CBFs

0.05A A

A A

-


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X-CBFsThe diagonal braces have also to be designed in such a way

that the yield resistance Npl,Rd of their gross cross-section is

such that Npl,RdNEd, where NEd is calculated from the elastic

model illustrated in Fig. 4.5 (Section 4.4.2).

In addition, the brace slenderness must fall in the range

31

Generalfeatures

Calculation

models and

code


Calculation

models and

code

requirements

for inverted

V-CBFs

1.3 2.0

beingy


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X-CBFsthe restraint effect of the diagonal in tension has been taken into

account in the calculation of the geometrical slenderness of X-

diagonal braces. This effect halves the brace in-plane buckling

length, while it is taken as inefficient for out-of-plane buckling

Hence, the geometrical in-plane slenderness is calculatedconsidering the half brace length, while the out-of-plane ones

considering the entire brace length

32

Generalfeatures

Calculation

models and

code


Calculation

models and

code

requirements

for inverted

V-CBFs

Out-of-plane buckling In-plane buckling

L b

Lb


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X-CBFsIn order to force the formation of a global mechanism, which

means maximizing the number of yielding diagonals, clause

6.7.4(1) of the EC8 imposes that the ratios i = Npl,Rd,i/NEd,i ,

which define the design overstrength of diagonals, may not vary

too much over the height of the structure.

In practical, being the minimum over-strength ratio, the values

of all other ishould be in the range to 1.25

33

Generalfeatures

Calculation

models and

code


Calculation

models and

code

requirements

for inverted

V-CBFs


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X-CBFsOnce has been calculated, the design check of a beam-

column member of the frame is based on Equation

In case of columns, axial forces induced by seismic actions are

directly provided by the numerical model.

This does not apply to beams

34

Generalfeatures

Calculation

models and

code


Calculation

models and

code

requirements

for inverted

V-CBFs

, , ,( ) 1.1pl Rd Ed Ed G ov Ed EN M N Ng


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X-CBFsIn the numerical model, floors are usually simulated by means ofrigid diaphragms. In such a way the relative in-plane

deformations are eliminated and the numerical model gives null

beam axial forces.

it is possible to calculate the beam axial forces by simple handcalculations:

35

Generalfeatures

Calculation

models and

code


Calculation

models and

code

requirements

for inverted

V-CBFs


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Inverted V-CBFsDifferently from the case of X bracings, Eurocode 8 states thatthe model should be developed considering both tension and

compression diagonals

36

Generalfeatures

Calculation

models and

code


Calculation

models and

code

requirements

for inverted

V-CBFs


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Inverted V-CBFsDifferently from X-CBFs, in frame with inverted-V bracing

compression diagonals should be designed for the compression

resistance in accordance to EN 1993:1-1 (EN 1998-1 6.7.3(6)).

This implies that the following condition shall be satisfied the

following condition:

where is the buckling reduction factor (EN 1993:1-1 6.3.1.2

(1)) and NEd,iis the required strength

37

Generalfeatures

Calculation

models and

code


Calculation

models and

code

requirements

for inverted

V-CBFs

,pl Rd EdN N


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Inverted V-CBFsDifferently from the case of X-CBFs, the code does not impose

a lower bound limit for the non-dimensional slenderness , while

the upper bound limit ( ) is retained.

Also in this case it is compulsory to control the variability of the

over-strength ratios i = Npl,Rd,i/NEd,i in all diagonal braces.

However, it should be noted that, differently from the case of X-

CBFs, the design forces NEd,i are calculated with the model

where both the diagonal braces are taken into account

38

Generalfeatures

Calculation

models and

code


Calculation

models and

code

requirements

for inverted

V-CBFs

2


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Inverted V-CBFs

40

Generalfeatures

Calculation

models and

code


Calculation

models and

code

requirements

for inverted

V-CBFs

Static balance of horizontal forces:FEd,i= (1+0.3)(Npl,Rd,(i+1)cos(i+1)-Npl,Rd,icosi)

qi=Fi/L

Npl,Rd,(i+1)cos(i+1)

Axial force diagram

Npl,Rd,(i+1)0.3Npl,Rd,(i+1)

0.3Npl,Rd,(i+1)cosi+1)

Npl,Rd,i 0.3Npl,Rd,i

Npl,Rd,(i+1)cos(i+1)+qiL/2


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Verifications

Numerical models for inverted V-CBFs

42

Numericalmodels and

dynamic

properties

P-effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation


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Verifications

43

Numericalmodels and

dynamic

properties

P-effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

T1= 0.874s;M1= 0.759 T2= 0.316s;M2=0.161

Dynamic properties in X direction

T1= 0.455s;M1= 0.765 T2= 0.176s;M2=0.156

Dynamic properties in Y direction


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Verifications

The effects of actions included in the seismic design situation

have been determined by means of a linear-elastic modal

response spectrum analysis.

The first two modes have been considered because they satisfy

the following criterion:

thesum of the effective modal masses for the modes taken intoaccount amounts to at least 90% of the total mass of the

structure.

Since the first two vibration modes in both X and Y direction

may be considered as independent (being T2 0.9T1, EN 1998-1, 4.3.3.3.2) the SRSS (Square Root of the Sum of the Squares)

method is used to combine the modal maxima

44

Numericalmodels and

dynamic

properties

P-effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation


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Verifications

the coefficient are lesser than 0.1 for both X-CBFs

and inverted V-CBFs.

Hence, the structure is not sensitive to second order

effects that can be neglected in the calculations.

This result is generally common for CBFs

45

Numericalmodels and

dynamic

properties

P-effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation


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under Natural Hazards

and Catastrophic Events

Verifications

Circular hollow sections and S 235 steel grade areused for X braces. The brace cross sections are

class 1.

46

Numericalmodels and

dynamic

properties

P-effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

StoreyBrace cross section

dx t

d t d/t .502

(mm x mm) (mm) (mm) -

VI 114.3x4 114.3 4 28.58 50.00

V 121x6.3 121 6.3 19.21 50.00

IV 121x8 121 8 15.13 50.00

III 121x10 121 10 12.10 50.00

II 133x10 133 10 13.30 50.00

I 159x10 159 10 15.90 50.00


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Verifications

The circular hollow sections are suitable to satisfy both the slenderness

limits (1.3 < 2.0) and the requirement of minimizing the variation

among the diagonals of the overstrength ratio i, whose maximum

value (max) must not differ from the minimum one (min) by more than

25%. .

47

Numericalmodels and

dynamic

properties

P-effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

Storey

Brace crosssection

(dx t) Npl,Rd NEd i= Npl,Rd imin (x 100)(mm x

mm)(kN) (kN)

NEd min

VI 114.3x4 178.10 1.90 326.65 180.65 1.81 16.70

V 121x6.3 171.08 1.82 533.45 325.70 1.64 5.71

IV 121x8 173.22 1.85 667.40 430.74 1.55 0.00

III 121x10 176.29 1.88 820.15 517.46 1.58 2.29

II 133x10 159.31 1.70 907.10 576.19 1.57 1.61

I 159x10 136.57 1.45 1099.80 650.07 1.69 9.19


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Verifications

Verification of beams

48

Numericalmodels and

dynamic

properties

P-effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

IPE 360

IPE 360

IPE 360

IPE 360

IPE 360

IPE 360

IPE 360

IPE 360

IPE 360

IPE 360

IPE 360

IPE 360


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Verifications


49

Numericalmodels and

dynamic

properties

P-effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

Storey Section NRd NEd,G NEd,E NEd=NEd,G+1.1govNEd,E NRd(kN) (kN) (kN) (kN) NEd

VI IPE 360 156.05 265.96 9.70

V IPE 360 281.34 479.51 5.38

IV IPE 360 2580.85 0.00 372.07 634.15 4.07

III IPE 360 446.98 761.82 3.39

II IPE 360 497.72 848.29 3.04

I IPE 360 540.90 921.90 2.80

Storey NEd,G NEd,E

NEd=

NEd,G+1.1govNEd,E MEd,G MEd,E

MEd=

MEd,G+1.1govMEd,E MN,Rd MRd(kN) (kN) (kN) (kNm) (kNm) (kNm) (kNm) M

Ed

VI

0.00

78.02 132.98 64.28

0.00

64.28 361.75 5.63

V 218.70 372.74 86.27 86.27 361.75 4.19

IV 326.71 556.83 86.27 86.27 355.97 4.13

III 409.53 697.99 86.27 86.27 331.14 3.84

II 472.35 805.06 86.27 86.27 312.31 3.62

I 510.16 869.51 86.27 86.27 300.98 3.49


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Master Course




Verifications

Verification of columns

50

Numericalmodels and

dynamic

properties

P-effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

HE 180 A

HE 240 B

HE 240 M

HE 240 B

HE 240 M

HE 180 A

HE 180 A

HE 240 B

HE 240 M

HE 240 B

HE 240 M

HE 180 A

HE 180 A

HE 240 B

HE 240 M

HE 240 B

HE 240 M

HE 180 A

(a) (a)(b) (b)X

Z


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Master Course




Verifications


Axial strength checks for columns in + X direction

51

Numericalmodels and

dynamic

properties

P-effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

column type a

Storey Section A Nl,Rd NEd,G NEd,E

NEd=

NEd,G+1.1govNEd,E Nl,Rd(mm ) (kN) (kN) (kN) (kN) NEd

VI HE180A 4530 0.59 1608.15 103.77 0.00 103.77 9.12

V HE180A 4530 0.59 1608.15 237.62 91.03 392.76 2.41

IV HE240B 10600 0.75 3763.00 372.52 253.90 805.26 3.52

III HE240B 10600 0.75 3763.00 507.15 465.92 1301.24 2.18

II HE240M 19960 0.77 7085.80 646.06 716.86 1867.85 2.94

I HE240M 19960 0.71 7085.80 786.00 994.39 2480.80 2.03

column type b

VI HE180A 4530 0.59 1608.15 92.33 91.03 247.47 3.82

V HE180A 4530 0.59 1608.15 214.20 253.90 646.94 1.46

IV HE240B 10600 0.75 3763.00 338.31 465.92 1132.41 2.50

III HE240B 10600 0.75 3763.00 461.08 716.86 1682.87 1.68

II HE240M 19960 0.77 7085.80 586.39 994.39 2281.19 2.40

I HE240M 19960 0.71 7085.80 710.44 1341.94 2997.59 1.68


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Master Course




Verifications

Inverted V-CBFs

Similarly to the X-bracing, for the inverted-V braces circular hollow

sections and S235 steel grade are used. The adopted brace cross

sections belong to class 1

52

Numericalmodels and

dynamic

properties

P-effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

StoreyBrace cross section

dx td t d/t .50

2

(mm x mm) (mm) (mm) -

VI 127x6.3 127 6.3 20.16 50.00

V 193.7x8 193.7 8 24.21 50.00

IV 244.5x8 244.5 8 30.56 50.00

III 244.5x10 244.5 10 24.45 50.00

II 273x10 273 10 27.30 50.00

I 323.9x10 323.9 10 32.39 50.00


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Master Course




Verifications

Inverted V-CBFs

Because of the presence of vertical loads and the different

deformations of columns, the brace axial force is slightly different for

braces D1 and D2

53

Numericalmodels and

dynamic

properties

P-effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

D1 D1D2D2


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Master Course




Verifications

Inverted V-CBFs

Inverted V-braces (D1 members) design checks in tension

54

Numericalmodels and

dynamic

properties

P-effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

StoreyBrace cross

section (d x t)Npl,Rd NEd, D1

i=Npl,Rd i (x 100)

(mm x mm) (kN) (kN) NEd d,D1

VI 127x6.3 561.65 245.60 2.29 2.04

V 193.7x8 1097.45 461.96 2.38 6.00

IV 244.5x8 1395.90 622.87 2.24 0.00

III 244.5x10 1722.55 756.68 2.28 1.58

II 273x10 1941.10 843.92 2.30 2.63

I 323.9x10 2317.10 986.84 2.35 4.77


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56/66


Master Course




Verifications

Inverted V-CBFs


56

Numericalmodels and

dynamic

properties

P-effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

HE 320 B

HE 320 M

HE 360 M

HE 450 M

HE 500 M

HPE 550 M

HE 320 B

HE 320 M

HE 360 M

HE 450 M

HE 500 M

HPE 550 M


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Master Course




Verifications

Inverted V-CBFs


Axial forces due to the seismic effects in beams of inverted-V CBFs

57

Numericalmodels and

dynamic

properties

P-effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

qi=Fi/L

NA

Axial force diagram

Npl,Rd,(i+1) 0.3Npl,Rd,(i+1)

ND

Npl,Rd,i 0.3Npl,Rd,i

NB

NC

Storey Npl,Rd qi NA NB NC ND

(kN) (kN/m) (kN) (kN) (kN) (kN)VI 561.65 79.209 0.00 237.63 237.63 0.00

V 1097.45 75.563 365.58 592.27 336.36 109.67

IV 1395.90 42.090 714.33 840.60 340.57 214.30

III 1722.55 46.067 908.59 1046.79 410.78 272.58

II 1941.10 30.822 1121.21 1213.67 428.83 336.36

I 2317.10 27.473 1263.46 1345.88 461.46 379.04


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Master Course




Verifications

Inverted V-CBFs


Axial strength checks in beams of inverted-V CBFs

58

Numericalmodels and

dynamic

properties

P-effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

Storey Section A Npl,Rd NEd,G NEd,E=NA

NEd =NEd,G+NEd,E Npl,Rd

(mm ) (kN) (kN) (kN) (kN) NEd

VI HE320 B 16130 5726.15

0.00

475.25 475.25 12.05

V HE320 M 31200 11076.00 928.63 928.63 11.93

IV HE360 M 31880 11317.40 1181.17 1181.17 9.58

III HE450 M 33540 11906.70 1457.57 1457.57 8.17

II HE500 M 34430 12222.65 1642.50 1642.50 7.44

I HE550 M 35440 12581.20 1807.34 1807.34 6.96


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Master Course




Verifications

Inverted V-CBFs


Combined bending-axial force checks in beams of inverted-V CBFs

59

Numericalmodels and

dynamic

properties

P-effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

Storey Section NEd MEd,G MEd,E MEd MRd MRd(kN) (kNm) (kNm) (kNm) (kNm) MEd

VI HE320 B 475.25 41.90 447.83 489.73 762.90 1.56V HE320 M 928.63 58.13 875.05 933.19 1574.43 1.69

IV HE360 M 1181.17 58.35 1113.02 1171.38 1771.10 1.51

III HE450 M 1457.57 58.62 1373.48 1432.10 2247.51 1.57

II HE500 M 1642.50 59.24 1547.74 1606.98 2518.37 1.57

I HE550 M 1807.34 61.28 1946.36 2007.64 2816.22 1.40


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Master Course




Verifications

Inverted V-CBFs


Shear force checks in beams of inverted-V CBFs

60

Numericalmodels and

dynamic

properties

P-effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

Storey Section A Av Vpl,Rd VEd,G VEd,E VEd Vpl,Rd(mm

2) (mm

2) (kN) (kN) (kN) (kN) VEd

VI HE320B 16130 5172.75 1060.20 27.93 149.28 177.21 5.98

V HE320M 31200 9450.00 1943.01 38.75 291.69 330.44 5.88

IV HE360M 31880 10240.00 2098.78 38.90 371.01 409.91 5.12

III HE450M 33540 11980.00 2455.41 38.08 457.83 496.90 4.94

II HE500M 34430 12950.00 2654.22 39.49 515.91 555.41 4.78

I HE550M 35440 13960.00 2861.23 40.62 648.79 689.41 4.15


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Master Course




Verifications

Inverted V-CBFs


61

Numericalmodels and

dynamic

properties

P-effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

HE 180 A

HE 180 A

HE 240 M

HE 240 M

HE 320 M

HE 320 M

HE 180 A

HE 180 A

HE 240 M

HE 240 M

HE 320 M

HE 320 M

HE 180 A

HE 180 A

HE 240 M

HE 240 M

HE 320 M

HE 320 M


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Master Course




Verifications

Inverted V-CBFs


62

Numericalmodels and

dynamic

properties

P-effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

Storey Section A Npl,Rd NEd,G NEd,E NEd=NEd,G+1.1govNEd,E Npl,Rd(mm

2) (kN) (kN) (kN) (kN) NEd

VI HE180A 4530 0.59 1608.15 94.72 0.00 94.72 9.99

V HE180A 4530 0.59 1608.15 225.44 182.06 674.27 1.40

IV HE240M 19960 0.77 7085.80 384.77 527.24 1684.50 3.26

III HE240M 19960 0.77 7085.80 534.95 984.00 2960.71 1.85

II HE320M 31200 0.85 11076.00 694.41 1535.70 4480.22 2.10

I HE320M 31200 0.81 11076.00 847.88 2139.46 6122.07 1.46


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Master Course




Verifications

Connections

Connections have to satisfy the requirements given in EN 1998-1 6.5.5.

In particular, the following connection overstrength criterion must be

applied:

Rd

1.1 ov

Rfy

where Rdis the resistance of the connection, Rfyis the plastic

resistance of the connected dissipative member based on the design

yield stress of the material, ovis the material overstrength factor.

In addition, Eurocode 8 introduces an additional capacity designcriterion for bolted shear connections. Indeed, the design shear

resistance of the bolts should be at least 1.2 times higher than the

design bearing resistance.

63

Numericalmodels and

dynamic

properties

P-effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation


64/66


Master Course




Verifications

In the calculation example ductile non-structural elements have

been hypothesized. Hence, the intestorey drift limit to be

satisfied is equal to 0.75%h. Moreover, for what concerns the

displacement reduction factor , it was assumed the

recommended value that is = 0.5 (being the structure

calculated in the numerical example belonging to class II)

64

Numericalmodels and

dynamic

properties

P-effects

Beams

Columns

Connections

Damage

limitation

a)

0.10m

max= 0.54%


65/66


Master Course




Verifications

In the calculation example ductile non-structural elements have

been hypothesized. Hence, the intestorey drift limit to be

satisfied is equal to 0.75%h. Moreover, for what concerns the

displacement reduction factor , it was assumed the

recommended value that is = 0.5 (being the structure

calculated in the numerical example belonging to class II)

65

Numericalmodels and

dynamic

properties

P-effects

Beams

Columns

Connections

Damage

limitation

b)

0.04m

max= 0.54%


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http://steel.fsv.cvut.cz/suscos

tu8_design and verification of a steel concentrically-braced

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