2C09 Design for seismic and climate change - UPT and... · 2C09 Design for seismic and climate change ... the calculation examples are carried out ... seismic design situation have

2C09

Design for seismic

and climate change

Raffaele Landolfo

Mario D’Aniello European Erasmus Mundus Master Course

Sustainable Constructions

under Natural Hazards and Catastrophic Events 520121-1-2011-1-CZ-ERA MUNDUS-EMMC

European Erasmus Mundus

Master Course


under Natural Hazards

and 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


Master Course




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


Master Course




Introduction

The case study is a six storey residential building

with 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


Master Course




Introduction

Structural plan and configuration of the CBFs

5

Building

description

Normative

references

Materials

Actions

66

22 2

731

6 5

66 2.34 2.332.33 2.52.5

1 2 3

4 5 6

7 8 9

76

24

X Bracings V Bracings

Direction X Direction Y


Master Course




Introduction

composite slabs with profiled steel sheetings are adopted to

resist 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

Building

description

Normative

references

Materials

Actions


Master Course




Introduction

Apart from the seismic recommendations, the structural safety

verifications 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 for

buildings.

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 factors 7

Building

description

Normative

references

Materials

Actions


Master Course




Introduction

It is well known that the standard nominal yield stress fy is the

minimum 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,max of the steel of dissipative

zones satisfies the following expression

fy,max ≤ 1.1gov fy

where fy is 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

Building

description

Normative

references

Materials

Actions


Master Course




Introduction

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

“seismic-qualified” steel 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 gov which can be set equal to 1.

c) the actual yield strength fy,act of 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 , fy being the

nominal yield strength of the steel of dissipative zones.

9

Building

description

Normative

references

Materials

Actions


Master Course




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

Building

description

Normative

references

Materials

Actions

Grade fy ft gM gov E

(N/mm2) (N/mm

2) (N/mm

2)

S235 235 360 gM0 = 1.00

gM1 = 1.00

gM2 = 1.25

1.00 210000 S355 355 510


Master Course




Introduction

Characteristic values of vertical persistent and transient actions

11

Building

description

Normative

references

Materials

Actions

Gk (kN/m2) Qk (kN/m

2)

Storey slab 4.20 2.00

Roof slab 3.60 0.50

1.00 (Snow)

Stairs 1.68 4.00

Claddings 2.00


Master Course




Introduction

Seismic action

A 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

Building

description

Normative

references

Materials

Actions

0 BT T 2.5

1 1d g

B

TS T a S

T q

B CT T T 2.5

d gS T a Sq

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

(3.2)

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

The parameter β is the lower bound factor for the horizontal design

spectrum, whose value should be found in National Annex.

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


Master Course




Introduction

Seismic action

Elastic and design response spectra

13

Building

description

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)

Se, S

d (

m/s

2)

Elastic spectrum

Design spectrum-X braces

Design spectrum-Inverted-V braces

lower bound = 0.2a g


Master Course




Introduction

Combination of actions

In 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,i is the characteristic value of variable action “I”

and ψ2,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

Building

description

Normative

references

Materials

Actions

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

Type of variable actions 2i

Category A – Domestic, residential areas 0.30

Roof 0.30

Snow loads on buildings 0.20

Stairs 0.80


Master Course




Introduction

Masses

In 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

Building

description

Normative

references

Materials

Actions

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

E,i 2i

Type of variable actions 2i Ei

Category A – Domestic, 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


Master Course




Introduction

Seismic weights and masses in the worked example

16

Building

description

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 5.64 427.75

IV 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

I 4261,26 1608,00 4411.33 5.93 449.68


Master Course




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

Basic

principles of

conceptual

design

Plan location

of CBFs and

structural

regularity

Damage

limitation


Master Course





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 the

following 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

Basic

principles of

conceptual

design

Plan location

of CBFs and

structural

regularity

Damage

limitation

66

22 2

731

6 5

66 2.34 2.332.33 2.52.5

1 2 3

4 5 6

7 8 9

76

24

X Bracings V Bracings


Master Course





- The structure has rigid in plan diaphragms.

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

than 4 (31000 mm / 24000 mm = 1.29), where Lmax and Lmin are

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

Basic

principles of

conceptual

design

Plan location

of CBFs and

structural

regularity

Damage

limitation


Master Course





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 setbacks 20

Basic

principles of

conceptual

design

Plan location

of CBFs and

structural

regularity

Damage

limitation


Master Course





damage limitation requirement is expressed by the following

Equation:

drn ≤ h

where:

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

dr is 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 in

the 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

Basic

principles of

conceptual

design

Plan location

of CBFs and

structural

regularity

Damage

limitation


Master Course





According to EN 1998-1 4.3.4, If the analysis for the design seismic

action 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 = qd ×de

where:

ds is the displacement of the structural system induced by the

design seismic action;

qd is the displacement behaviour factor, assumed equal to q;

de is the displacement of the structural system, as determined by a

linear elastic analysis under the design seismic forces.

22

Basic

principles of

conceptual

design

Plan location

of CBFs and

structural

regularity

Damage

limitation


Master Course




Structural analysis and calculation models

In this Tutorial two separate calculation 2D planar models in the

two 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 (beam–to-

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

General

features

Calculation

models and

code

requirements

for X-CBFs

Calculation

models and

code

requirements

for inverted

V-CBFs


Master Course





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 δ

where:

• x is the distance from the centre of gravity of the building, measured

perpendicularly to the direction of the seismic action considered;

• Le is the distance between the two outermost lateral load resisting

systems.

24

x

Le

G

1 0 6e

x.

L

Se

ism

ic a

cti

on

Seismic

resistant

system

General

features

Calculation

models and

code

requirements

for X-CBFs

Calculation

models and

code

requirements

for inverted

V-CBFs


Master Course





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

Se

ism

ic a

cti

on

Seismic

resistant

system

General

features

Calculation

models and

code

requirements

for X-CBFs

Calculation

models and

code

requirements

for inverted

V-CBFs


Master Course





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

General

features

Calculation

models and

code

requirements

for X-CBFs

Calculation

models and

code

requirements

for inverted

V-CBFs


Master Course





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

specified through a storey stability coefficient (θ) given as:

where:

• Ptot is the total vertical load, including the load tributary to gravity

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

situation;

• Vtot is seismic shear at the storey under consideration;

• h is the storey height;

• dr is 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

General

features

Calculation

models and

code

requirements

for X-CBFs

Calculation

models and

code

requirements

for inverted

V-CBFs


Master Course





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

could be neglected, whilst for 0.1 < θ ≤ 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

General

features

Calculation

models and

code

requirements

for X-CBFs

Calculation

models and

code

requirements

for inverted

V-CBFs


Master Course





X-CBFs According to EN 1998-1 6.7.2(2)P, in case of X-CBFs the structural

model 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 with

the braces tilted in one direction and another with the braces tilted in

the opposite direction

29 a)

k 2i kiiG Q

,Ed iF

b)

k 2i kiiG Q

,Ed iF

General

features

Calculation

models and

code

requirements

for X-CBFs

Calculation

models and

code

requirements

for inverted

V-CBFs


Master Course





X-CBFs the diagonal braces have to be designed and placed in such a way

that, 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, respectively 30

General

features

Calculation

models and

code

requirements

for X-CBFs

Calculation

models and

code

requirements

for inverted

V-CBFs

0.05A A

A A

-


Master Course





X-CBFs

The 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,Rd ≥ NEd, 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

General

features

Calculation

models and

code

requirements

for X-CBFs

Calculation

models and

code

requirements

for inverted

V-CBFs

1.3 2.0

being y


Master Course





X-CBFs

the 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 calculated

considering the half brace length, while the out-of-plane ones

considering the entire brace length

32

General

features

Calculation

models and

code

requirements

for X-CBFs

Calculation

models and

code

requirements

for inverted

V-CBFs

Out-of-plane buckling

In-plane buckling

LbLb

LbLb


Master Course





X-CBFs

In 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 Ωi = 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 Ω the minimum over-strength ratio, the values

of all other Ωi should be in the range Ω to 1.25Ω

33

General

features

Calculation

models and

code

requirements

for X-CBFs

Calculation

models and

code

requirements

for inverted

V-CBFs


Master Course





X-CBFs

Once Ω 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

General

features

Calculation

models and

code

requirements

for X-CBFs

Calculation

models and

code

requirements

for inverted

V-CBFs

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


Master Course





X-CBFs In the numerical model, floors are usually simulated by means of

rigid 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 hand

calculations:

35

General

features

Calculation

models and

code

requirements

for X-CBFs

Calculation

models and

code

requirements

for inverted

V-CBFs


Master Course





Inverted V-CBFs Differently from the case of X bracings, Eurocode 8 states that

the model should be developed considering both tension and

compression diagonals

36

General

features

Calculation

models and

code

requirements

for X-CBFs

Calculation

models and

code

requirements

for inverted

V-CBFs


Master Course





Inverted V-CBFs

Differently 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,i is the required strength

37

General

features

Calculation

models and

code

requirements

for X-CBFs

Calculation

models and

code

requirements

for inverted

V-CBFs

,pl Rd EdN N


Master Course





Inverted V-CBFs

Differently 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 Ωi = 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

General

features

Calculation

models and

code

requirements

for X-CBFs

Calculation

models and

code

requirements

for inverted

V-CBFs

2


Master Course





Inverted V-CBFs

39

General

features

Calculation

models and

code

requirements

for X-CBFs

Calculation

models and

code

requirements

for inverted

V-CBFs

Vertical component of the force transmitted by the tension and compression braces:

(1-0.3)Npl,Rd,iseni

qi=Fi/L

FEd,i

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

Axial force diagram L

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

FEd,i+1

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

Npl,Rd,i 0.3Npl,Rd,i

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

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

Npl,Rd,i

MEd,E=(Npl,Rd,i-0.3Npl,Rd,i)(seni)(L/4)

Bending moment diagram

0.3Npl,Rd,i

+

k 2i kiiG Q

VEd,E=(Npl,Rd,i-0.3Npl,Rd,i)(seni)/2 VEd,E=(Npl,Rd,i-0.3Npl,Rd,i)(seni)/2

Shear force diagram

Npl,Rd,i

(Npl,Rd,i - 0.3Npl,Rd,i)(seni)(L/4)


0.3Npl,Rd,i

+

k 2i kiiG Q


Shear force diagram

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

1

qi=Fi/L

FEd,i




FEd,i+1






Master Course





Inverted V-CBFs

40

General

features

Calculation

models and

code

requirements

for X-CBFs

Calculation

models and

code

requirements

for inverted

V-CBFs

Vertical component of the force transmitted by the tension and compression braces:

(1-0.3)Npl,Rd,iseni

qi=Fi/L

FEd,i




FEd,i+1





Npl,Rd,i

MEd,E=(Npl,Rd,i-0.3Npl,Rd,i)(seni)(L/4)


0.3Npl,Rd,i

+

k 2i kiiG Q


Shear force diagram

Npl,Rd,i

(Npl,Rd,i - 0.3Npl,Rd,i)(seni)(L/4)


0.3Npl,Rd,i

+

k 2i kiiG Q


Shear force diagram

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

1

qi=Fi/L

FEd,i




FEd,i+1






Master Course




Verifications

Numerical models for X-CBFs

numerical models of the calculation example with single

diagonals tilted in +X direction (a) and in –X direction (b).

41

Numerical

models and

dynamic

properties

P- effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

a) b)


Master Course




Verifications

Numerical models for inverted V-CBFs

42

Numerical

models and

dynamic

properties

P- effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation


Master Course




Verifications

43

Numerical

models 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


Master Course




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:

“the sum of the effective modal masses for the modes taken into

account 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

Numerical

models and

dynamic

properties

P- effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation


Master Course




Verifications

the coefficient θ 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

Numerical

models and

dynamic

properties

P- effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation


Master Course




Verifications

Circular hollow sections and S 235 steel grade are

used for X braces. The brace cross sections are

class 1.

46

Numerical

models and

dynamic

properties

P- effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

Storey Brace cross section

d x 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


Master Course




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 Ωi, whose maximum

value (Ωmax) must not differ from the minimum one (Ωmin) by more than

25%. .

47

Numerical

models and

dynamic

properties

P- effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

Storey

Brace cross

section

(d x t) Npl,Rd NEd i = Npl,Rd i min

(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


Master Course




Verifications

Verification of beams

48

Numerical

models 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


Master Course




Verifications


49

Numerical

models 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) MEd

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


Master Course




Verifications

Verification of columns

50

Numerical

models 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


Master Course




Verifications


Axial strength checks for columns in + X direction

51

Numerical

models and

dynamic

properties

P- effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

column type “a”

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

NEd=

NEd,G+1.1govNEd,E Npl,Rd

(mm2) (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


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

Numerical

models and

dynamic

properties

P- effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

Storey Brace cross section

d x t d t d/t .502

(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


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

Numerical

models and

dynamic

properties

P- effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

D1 D1D2D2


Master Course




Verifications

Inverted V-CBFs

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

54

Numerical

models and

dynamic

properties

P- effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

Storey Brace 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


Master Course




Verifications

Inverted V-CBFs

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

55

Numerical

models and

dynamic

properties

P- effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

Storey Brace cross

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

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

VI 127x6.3 107.94 1.15 0.56 315.86 245.60 1.29

V 193.7x8 70.15 0.75 0.82 904.70 461.96 1.96

IV 244.5x8 55.07 0.59 0.89 1249.31 622.87 2.01

III 244.5x10 55.53 0.59 0.89 1538.50 756.68 2.03

II 273x10 49.51 0.53 0.92 1777.16 843.92 2.11

I 323.9x10 45.05 0.48 0.93 2155.83 986.84 2.18


Master Course




Verifications

Inverted V-CBFs


56

Numerical

models 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


Master Course




Verifications

Inverted V-CBFs


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

57

Numerical

models and

dynamic

properties

P- effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation

qi=Fi/L

FEd,i

NA



FEd,i+1

ND



NB i

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


Master Course




Verifications

Inverted V-CBFs


Axial strength checks in beams of inverted-V CBFs

58

Numerical

models 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


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


Master Course




Verifications

Inverted V-CBFs


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

59

Numerical

models 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 1.56

V 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


Master Course




Verifications

Inverted V-CBFs


Shear force checks in beams of inverted-V CBFs

60

Numerical

models 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

(mm2) (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


Master Course




Verifications

Inverted V-CBFs


61

Numerical

models 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


Master Course




Verifications

Inverted V-CBFs


62

Numerical

models 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


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


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 γov Rfy

where Rd is the resistance of the connection, Rfy is the plastic

resistance of the connected dissipative member based on the design

yield stress of the material, γov is the material overstrength factor.

In addition, Eurocode 8 introduces an additional capacity design

criterion 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

Numerical

models and

dynamic

properties

P- effects

X-CBFs

Inverted V-

CBFs

Connections

Damage

limitation


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 ν , it was assumed the

recommended value that is ν = 0.5 (being the structure

calculated in the numerical example belonging to class II)

64

Numerical

models and

dynamic

properties

P- effects

Beams

Columns

Connections

Damage

limitation

a)

0.10m

0.04m

max= 0.54%


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 ν , it was assumed the

recommended value that is ν = 0.5 (being the structure

calculated in the numerical example belonging to class II)

65

Numerical

models and

dynamic

properties

P- effects

Beams

Columns

Connections

Damage

limitation

a)

b)

0.10m

0.04m

max= 0.54%

max= 0.54%

Thank you

for your attention

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

Documents

2C09 Design for seismic and climate change - UPT and... · 2C09 Design for seismic and climate change ... the calculation examples are carried out ... seismic design situation have