FUSEIS Design Guide

Research Programme of the Research Fund for Coal and Steel Steel RTD

Contract No: RFSR-CT-2008-00032

FUSEIS Dissipative Devices for Seismic Resistant Steel Frames

Design Guide

Authors: I. Vayas, Ph. Karydakis, D. Dimakogianni, G. Dougka (NTUA) C. A. Castiglioni, A. Kanyilmaz (PMIL) L. Calado, Jorge M. Proença, M. Espinha (IST) B. Hoffmeister, T. Rauert (RWTH) D. Kalteziotis (SIDENOR)

March 2012

Table of Contents 1 Introduction ................................................................................................................ 1 2 FUSEIS 1 ..................................................................................................................... 1

2.1 Description of FUSEIS 1 ....................................................................................... 1 2.2 Conceptual design ................................................................................................. 3

2.2.1 General .......................................................................................................... 3 2.2.2 FUSEIS 1-1 .................................................................................................... 4 2.2.3 FUSEIS 1-2 .................................................................................................... 4

2.3 Preliminary design ................................................................................................. 5 2.4 Design for linear elastic analysis ........................................................................... 8

2.4.1 Dissipative element verifications .................................................................... 9 2.4.2 Connection verifications ............................................................................... 10 2.4.3 Non-dissipative element verifications ........................................................... 11

2.5 Design for non - linear static analysis .................................................................. 11 2.6 Design for non - linear dynamic analysis ............................................................. 12

3 FUSEIS 2 ................................................................................................................... 13 3.1 Description of FUSEIS 2 ..................................................................................... 13 3.2 Rules for the design of buildings ......................................................................... 14 3.3 Design of the fuse devices for bending ............................................................... 15

3.3.1 Bending resistance ....................................................................................... 15 3.3.2 Flange plate ................................................................................................. 15 3.3.3 Longitudinal reinforcement ........................................................................... 16

3.4 Elastic bending stiffness (Initial Flexural Bending Stiffness) ................................ 17 3.5 Design of the fuse devices for shear ................................................................... 17

3.5.1 Shear resistance .......................................................................................... 17 3.5.2 Shear stiffness ............................................................................................. 17

3.6 Design of the non-dissipative connecting elements............................................. 17 3.6.1 Design of the bolted connection ................................................................... 18 3.6.2 Design of the welded connection ................................................................. 18

3.7 Additional detailing remarks ................................................................................ 18 3.7.1 Design of the transverse reinforcement ....................................................... 18 3.7.2 Design of the shear connection .................................................................... 19 3.7.3 Design of the reinforced zone of the beam .................................................. 19

3.8 Ductility of the structures with fuse devices / Proposal for q factor ...................... 19 3.8.1 Low Ductility ................................................................................................. 19 3.8.2 Medium Ductility ........................................................................................... 20

Appendix 1 - Algorithm for the elastic-plastic analysis ............................................... 21

FUSEIS Dissipative Devices for Seismic Resistant Steel Frames Page 1

Design Guide

1 Introduction Opposite to concrete building frames, the lateral stability and hence the seismic safety of steel buildings may be obtained by a large variety of structural systems, Indeed, due to the monolithic nature of concrete, beam – to – column joints are generally rigid so that concrete buildings constitute 3D - frames with or without shear walls. This is not the case in steel buildings, where the designer has the freedom to form the connections as rigid or flexible and put additional bracing systems or shear walls. Therefore a 3D-frame action is one of the options for seismic resistant steel structures, others being listed in Table 1.1. Modern seismic codes allow for inelastic deformations in dissipative zones during design earthquakes, accepting damage to a certain extend in the relevant structural parts. As past experience shows, repair works are needed after strong earthquakes, either less or larger than the design one. Structural systems that are easily repairable-replaceable, while maintaining the benefits of high ductility, are therefore beneficial in seismic regions. Therefore innovation in developing new seismic resistant systems is highly appreciated. The scope of this research project was the development and study of two such innovative systems that are introduced in the present Guide. Table 1.1 shows existing structural systems and evaluates them in respect to stiffness and ductility as well as the two new systems, named FUSEIS1 and FUSEIS2. Their main advantage is that inelastic deformations are strictly concentrated and controlled in zones that constitute easily replaceable fuses.

Table 1.1: Structural systems for steel frames Stiffness Ductility Dissipative

zones Moment resisting frames 0 ++ Beam ends Concentric braced frames ++ 0 Tension braces Eccentric braced frames + ++ Beam links INERD concentric braced frames

+ ++ Pins

BRB concentric braced frames ++ ++ BRB braces Steel shear walls + + Steel plates Composite shear walls ++ 0 Shear wall FUSEIS 1 + + FUSEIS 1

beams or pins FUSEIS 2 0 ++ FUSEIS 2

beams Based on the experimental and analytical research carried out during the project this Design Guide gives all necessary information for conceptual design, analysis and design of building frames with FUSEIS systems, retaining the format of Eurocode 8.

2 FUSEIS 1

2.1 Description of FUSEIS 1 (1) FUSEIS 1 is an innovative seismic resistant system composed of two closely spaced strong columns, rigidly connected to multiple beams. The beams run from column to column (FUSEIS 1-1) or alternatively are interrupted and connected by short pins (FUSEIS 1-2) (Figure 2.1).


Design Guide

Figure 2.1: FUSEIS 1-1 and FUSEIS 1-2 systems

(2) The system resists lateral loads as a vertical Vierendeel beam, mainly by bending of the beams and axial forces of the columns. The dissipative elements of the system are the beam sections in FUSEIS 1-1 or the pins in FUSEIS 1-2. These elements are not generally subjected to vertical loads, as they are placed between floor levels.

(3) The seismic resistance of a building may be obtained by appropriate provision of a number of such systems in the relevant directions (Figure 2.2). When beam-to-column connections of the laterally supported building are formed as simple (hinges), this system provides alone the seismic resistance of the building. When the connections are rigid or semi-rigid, it works in combination with the overall moment resisting frame. In both cases the beam-to-system columns connections should be formed as simple (hinges), since the system is not intended to consist a gravity load carrying part of the structure.

Figure 2.2: Provision of FUSEIS 1 system in a building


Design Guide

(4) Aiming to minimise damage at the foundation locations pinned connections at the column bases are proposed. At high multi-storey buildings the column bases may be pinned or fixed, analytical investigations showed that the difference in the response was not significant.

(5) The fuses-to-column joints are formed as rigid to enable the Vierendeel action and are designed to have sufficient overstrength in order to achieve energy absorption only in the fuses. Bolted end-plate connections which enable an easy replacement of the beams should be used.

(6) The advantages of FUSEIS 1 can be summarized as following: a) Inelastic deformations are strictly limited to the dissipative elements (beams or pins) b) The dissipative elements are easily replaceable if they are plastically deformed or damaged

after a strong seismic event, since they are small and are not part of the gravity loading resistant system.

c) The dissipative elements can be positioned in small areas of the building and do not interrupt the architectural plan as braced do.

d) The dissipative elements can constitute visible parts of the building indicating its seismic resistant system.

e) Sequential plastifications may be allowed for by appropriate selection of the sections of the dissipative elements

2.2 Conceptual design

2.2.1 General (1) Fuse beams may have closed sections (RHS or CHS) or open sections (I- or H- sections). Considering a typical floor height of 3,4 m, four or five beams may be placed per storey. The beam height depends on the required stiffness with the provision to leave the necessary vertical spacing between them. RHS-sections are more beneficial to open sections due to their larger flexural and torsional rigidities and strength.

(2) Beam or pin sections may vary between floors, following the increase of storey shear from the top to the base of the building. Beams or pins may also vary within the floor, either in respect to their cross-sections or to the distances ln.

(3) Columns may be of open or closed section. Open sections are more beneficial, since they offer an easier connection to the beams. When closed sections are used, a T-section can be welded to it to offer the advantage of easier connection.

a )SHS variable lengths b) SHS variable sections c) PINS variable lengths d) PINS variable sections

Figure 2.3: Modification of beam or pin properties within a floor


Design Guide

(4) In order to avoid excessive overstrength of the dissipative elements, the steel of these beams shall have in accordance with the EC 8 – rules a maximum value of:

yovy ff 1,1max, (2.1)

where: γov =1,25 fy = nominal value of the yield strength It is advisable to use S 235 steel for the beams. In this instance, eq. (2.1) yields fy,max = 323 ΜPa. The value of fy,max shall be referred to in the design drawings.

2.2.2 FUSEIS 1-1 (1) The dissipative elements are the FUSEIS beams. To allow the plastic hinge to form away from the connection area and protect the beam to column connections against early fracture, beam flanges should be reduced near the ends – RBS(Figure 2.4). Constant, tapered or radius cut shapes are possible to reduce the cross sectional area. FEMA 350, FEMA 351 and EC8 Part 3 provide the recommendations for the design of the RBS members (Table 2.1).

a) IPE sections b) CHS (circular hollow sections) c) RHS (rectangular) or SHS (square)

Figure 2.4: RBS sections of beams

Table 2.1: Geometry of RBS radius cut FEMA350 /351 EC8, Part3

a=0,50-0,70*bf a=0,60*bf

b=0,65-0,85*db b=0,75*db

c ≤ 0,25*bf g ≤ 0,25*bf

r = (4c2 + b2)/8c r = (4g2 + b2)/8g

(2) In order to ensure the formation of the plastic hinge at the RBS-section, the connection should be capacity designed in respect to the RBS strength. As an alternative, the connection region could be strengthened by means of additional plates (Figure 2.5).

Figure 2.5: Strengthening of the connection area

2.2.3 FUSEIS 1-2 (1) The device consists of short pins and two receptacle beams. The pins may be circular if the receptacle beams are hollow or rectangular if the receptacle beams are I or H. The dissipative elements are the FUSEIS pins (Figure 2.6).


Design Guide

Figure 2.6: Fuseis 1-2

(2) Aiming to lead the plastic hinge formation away from the contact area between the face plate of the receptacles and the pins, the pins diameter should be weakened in the middle (similar to the RBS sections). In order to keep contact area away from the end of the plates, ensuring triaxial stress conditions, pin’s diameter decrease starts away from the plate’s face and the edges of the plate hole are smoothed (Figure 2.7). To facilitate the mounting and dismounting of the fuse by adjusting their lenth, the ends could be screwed with inverse directions.

Figure 2.7: Circular Pin Fuse with weakened middle part and screwed ends

2.3 Preliminary design (1) As previously mentioned, the FUSEIS – 1 system works as a vertical Vierendeel beam. Considering hinges at the midpoints of beams and columns between the fuses beams and, the internal moments and forces for horizontal loading in the elastic state may be derived from statics as following (Figure 2.8): Columns

L

MN ov

c

(2.2)

2storey

c

VV

(2.3)

42

hVhVM storey

cc

(2.4)

Beams

22

hVMM storey

cb

(2.5)

L

hV

L

MV storey

bb

2/ (2.6)

where: Mov = overturning moment of the frame Vstorey = storey shear L = axial distance of columns h = axial distance of FUSEIS beams Equations (2.2) - (2.6) show that within a storey the shears and moments of columns and beams remain constant, while the axial forces of columns moments increase linearly from the top to the base.


Design Guide

Figure 2.8: Theoretical internal forces and moments in beams and columns

(2) At the ultimate limit state all beams reach, as the dissipative elements of the system, their moment capacity. Therefore, the storey shear that may be transferred is equal to:

storey

Rdbstorey h

MV ,2

(2.7)

where the summation refers to the beams at the relevant storey and Mb,Rd = design moment resistance of FUSEIS beams hstorey= storey height

(3) When the FUSEIS beams are provided with RBS-sections at distance lRBS, Equation (2.7) may be written as (Figure 2.9):

RBSstorey

RdRBSplstorey l

L

h

MV ,,2

(2.8)

where

yRBSplRdRBSpl fWM ,,, = design moment resistance of RBS FUSEIS beam section

lRBS / lpin = axial distance between RBS sections / pin net length L = axial distance of FUSEIS columns

(4) If the total base shear of the building is VB, the number of systems to be used for a preliminary design is equal to:

storey

B

V

Vm

(2.9)

The column sections are chosen primarily from stiffness consideration in order to limit 2nd order effects. However, for m equal FUSEIS systems the columns have to resist at least an axial force


Design Guide

Lm

MN ov

Edc ,

(2.10)

(5) The cross sections for beams and columns of the system as well as the required number of systems cannot be estimated from strength criteria alone. The deformations shall be also controlled in order to limit second order effects. The relevant Code provisions require for buildings that the interstorey drift sensitivity coefficient (Equation (2.11) is limited to θ ≤ 0,1, if second order effects are ignored. In any case it shall be θ < 0,3.

storeytot

rtot

hV

dP

(2.11)

The symbols in eq. (2.11) are: Ptot = total gravity load at and above the storey considered in the seismic design situation dr = design interstorey drift = difference of top and bottom displacements Vtot = seismic storey shear hstorey = storey height

Alternatively, the interstorey drift sensitivity coefficient θ can be calculated more accurately by a linear buckling analysis through the factor αcr, the factor by which the design loading would have to be increased to cause elastic instability in a global mode. The analysis is carried out under conditions of constant gravity loads (1,00G + 0,30φQ) and produces the buckling modes. The modes that move the building at x and y directions are chosen and the correspondent αcr values are calculated. To take into consideration the inelastic displacements of the building αcr is divided by the q factor (Equation (2.12)).

cr

q

(2.12)

The interstorey drift sensitivity coefficient is limited to θ ≤ 0,1, if second order effects are ignored. If 0,1 < θ < 0,2, the second-order effects may approximately be taken into account by multiplying the relevant seismic action effects by a factor equal to 1/(1 - θ). If 0,2 < θ < 0,3 a second order analysis is required. In any case it shall be θ < 0,3. The interstorey drift sensitivity coefficient θ is calculated for both directions with a maximum value θ=0,104>0,10, as a result the seismic action effects have to be multiplied by 1,12.

(6) At global inter-storey drift rotations θgl of the frame during seismic loading, the dissipative elements, beams or pins, exhibit larger plastic rotations than θgl. Indeed the frame kinematics indicate that the local plastic rotations are equal to (Figure 2.8):

gln

p l

l

(2.13)

where: θp = plastic rotation of the fuse beam/pin l = axial distance of columns ln = axial distance between plastic hinges – net length of beams/pins

(7) Equation (2.13) shows that in FUSEIS 1-2 where ln is much smaller than l, the pin rotations may be considerable. This results in catenary action of the pins due to pin elongations at large rotation (3rd order effects) that has been proven to be beneficial to the overall response.


Design Guide

2.4 Design for linear elastic analysis (1) For the design of steel buildings with FUSEIS 1 EN 1993-1 and EN 1998 apply. The following rules are additional to those given in these codes.

(2) The conventional method for determining the seismic effects for building frames is the modal response spectrum analysis, using a linear-elastic model of the structure and a design spectrum. The design spectrum shall be defined in accordance with Eurocode 8. The maximum q-factor to be used is 5.

(3) Frames with FUSEIS 1 shall be designed so that the fuseis beams/pins, are able to dissipate energy by the formation of plastic bending mechanisms. The rules given hereafter are intended to ensure that yielding, will take place in the fuseis beams/pins prior to any yielding or failure elsewhere. The system beams/pins shall be designed to resist the forces of the most unfavourable seismic combination.

(4) In linear analysis the displacements induced by the design seismic action shall be calculated on the basis of the elastic deformations of the structural system through the expression:

s ed q d (2.14a)

where ds = displacement of a point of the structural system induced by the design seismic action q = qμ the behavior factor that may be taken equal to the displacement ductility factor (μd) if T1≥TC de = displacement of the same point of the structural system, as determined by a linear analysis based on the design response spectrum.

Usually the limitation of inter storey drift defines the design of a structure with the FUSEIS1 system, whereas the capacity ratios of the dissipative elements (Ω) are low. The calculation of the design inter–storey drift based on ds is therefore conservative. A reduction factor (qΩ) equal to the capacity ratio of the fuseis beams/pins may be employed as follows:

s ed q q d (2.15b)

For non-linear analysis, static or dynamic, the displacements induced by the seismic action are those obtained from the analysis.

(5) The non-dissipative elements, the fuseis beams/pins-to-columns connections, the system columns and the receptacle beams (FUSEIS 1-2), should be designed taking into account the section overstrength Ω and the material overstrength factor γov.

(6) In the current state of the art, a spatial model representing the 3-D structure is used. The following modelling guidelines may be followed:

a) The FUSEIS elements shall be represented by appropriate beam-column FE-elements. b) Rigid zones shall be provided from column centers to column faces to exclude non-existent

beam flexibilities. c) The net beam length shall be subdivided to 5 zones (Figure 2.9) that represent the full

sections (ends – middle) and the RBS-sections, and the net length of the pin fuses shall be subdivided to 3 zones that represent the full section at the ends and the weakened section in the middle. In this manner, the true system flexibility and strength will be accounted for.

d) The remaining structural elements shall be represented as usually by appropriate Finite elements.

e) Beam-to-column joints will be represented as rigid, semi-rigid or hinged in accordance to the connection detailing.


Design Guide

Figure 2.9: Modeling of FUSEIS 1-1 system

2.4.1 Dissipative element verifications (1) The dissipative elements of the system, beams or pins, shall be verified to resist the internal forces and moments as determined from the structural analysis.

(2) The moment capacity shall be verified as following:

0,1,,

RdRBSpl

Ed

M

M

(2.16)

where: MEd = design bending moment Mpl,RBS,Rd = design moment, plastic, resistance of RBS section

(3) The shear resistance shall be verified in accordance to:

1,,

, Rdplb

EdCD

V

V

(2.17)

where:

RBS

RdRBSplEdCD l

MV ,,

,

2

(2.18)

VCD,Ed = capacity design shear force Vb,pl,Rd = design shear resistance of beam section

(4) It should be noted that the influence of shear should be accounted for in determining Mpl,RBS,Rd. This is the case when the ratio between acting shear and shear resistance is:

5,0,,

, Rdplb

EdCD

V

V

(2.19)

The combination of Equations (2.18) and (2.19) gives that the influence of shear should be accounted for if:

, , ,

,

4 4

/ 3pl RBS Rd pl RBS

RBSb Rd v

M Wl

V A

(2.20)

Equation (2.19) is seldom fulfilled due to the fact that Av refers to the full section while Wpl,RBS to the reduced beam section. In order to avoid the interaction between shear and moments, the flanges should be reduced so that equation (2.20) is fulfilled.


Design Guide

(5) The beam end moment resistance shall be verified in accordance with:

0,1,,

, Rdplb

EdCD

M

M

(2.21)

where:

RdRBSplRBS

bEdCD M

l

lM ,,,

= capacity design bending moment

Mb,pl,Rd = design bending moment of beam section

(6) Lateral torsional buckling verifications for the FUSEIS beams are generally not necessary due to their small length.

2.4.2 Connection verifications (1) Bending moment resistance

21,, ,max MMM EdconCD

(2.22)

where:

RdRBSplRBS

bov M

l

lM ,,1 1,1

(2.23)

buov MM ,2 1,1 (2.24)

where:

ubplbu fWM ,,

y

actyov f

f , or

γov =1,25 if the actual yield strength of the beam is known or not

lb = net beam length lRBS = axial distance of RBS sections fy,act = actual yield strength of the beam fu = ultimate strength of the beam Wpl,b =plastic moment of the beam section at beam end

(2) Shear force

RBS

RdRBSplovEdconCD l

MV ,,

,,

21,1

(2.25)

(3) If RBS sections are not used and alternatively the connection region is strengthened by means of additional plates, the strengthened area and the connection shall have a capacity design moment equal to:

bunet

bCDcon M

l

lM ,,

(2.26)

where:


Design Guide

lb = net beam length

lnet = net un-strengthened beam length

ubplbu fWM ,,

The design shear of the connection may be calculated from:

b

CDconCDcon l

MV ,

,

2

(2.27)

(4) It should be added that both alternatives have been experimentally proved to be effective in ensuring the plastic hinge formation away from the connection (Figure 2.10).

Figure 2.10: Plastic hinges with RBS sections and end strengthening of the beam

2.4.3 Non-dissipative element verifications (1) The FUSEIS columns and the receptacle beams (FUSEIS 1-2) shall be verified to resist the capacity design action effects as following:

EEdovGEdEdCD NNN ,,, 1,1 (2.28)

EEdovGEdEdCD MMM ,,, 1,1 (2.29)

EEdovGEdEdCD VVV ,,, 1,1 (2.30)

where: NEd,G= axial forces in columns due to the non-seismic actions included in the combination of actions for the seismic design situation NEd,E

= axial forces in columns due to the design seismic action γov =1,25

iEd

iRdRBSpli M

M

,

,,,minmin

= minimum value of the relevant ratios for all FUSEIS beams in

the building.

2.5 Design for non - linear static analysis (1) The structural model used for elastic analysis shall be extended to include the response of structural elements beyond the elastic state and estimate expected plastic mechanisms and the distribution of damage.

(2) Since the ductile elements are the FUSEIS beams/pins, potential plastic hinges shall be inserted at the ends of their reduced parts. The nonlinear properties for IPE, SHS, CHS and pin sections that derived from experimental and analytical investigations are given in Table 2.2.

(3) Additional potential plastic hinges may be inserted at the ends of the composite beams, the columns and the system columns to check if they also behave inelastic during the seismic event. The hinge properties shall be calculated according to the provisions of relevant codes (e.g. FEMA-356).


Design Guide

Table 2.2: Non-linear hinge parameters for IPE,SHS,CHS & Pins HINGE PROPERTIES (αpl=shape factor)

IPE SHS CHS PIN

Point M/SF Rot./SF M/SF Rot./SF M/SF Rot./SF M/SF Rot./SF

E- -0,6 -45 -0,4 -30 -0,2 -30 -0,5 -150

D- -0,6 -40 -0,4 -25 -0,2 -25 -0,5 -100

C- - αpl -40 - αpl -25 - αpl -25 -2,5 -100

B- 1 0 -0,6 0 -1 0 -2 0

A 0 0 0 0 0 0 0 0

B 1 0 0,6 0 1 0 2 0

C αpl 40 αpl 25 αpl 25 2,5 100

D 0,6 40 0,4 25 0,2 25 0,5 100

E 0,6 45 0,4 30 0,2 30 0,5 150

ACCEPTANCE CRITERIA

IPE SHS CHS PIN

IO 15 5 6 30

LS 25 12 10 45

CP 35 18 16 60

2.6 Design for non - linear dynamic analysis (1) In order to define time-dependent response of steel buildings when designed according to the provisions of the European Codes under real earthquake conditions, non - linear dynamic analyses shall be performed.

(2) For the dissipative elements of the structure the nonlinear hinge properties of Table 2.2 shall be assigned at their ends.

(3) For the non-dissipative elements the hinge properties shall be calculated according to the provisions of relevant codes (e.g. FEMA-356).

(4) The non-linear dynamic analysis provides the capability to restrict damage after a seismic event by evaluating and eliminating the residual drifts of the structure. If the fuseis system is appropriately designed it can work as a self-centering system, with practically zero residual drifts. When combined with moment resisting frame (MRF) action the deformations are concentrated in the fuseis system and the rest of the structure remains elastic, while the moment frame action helps the structure return to its initial state. On the contrary, when simple beam-to-column connections are used, the structure is not able to return at the end of the seismic event.

(5) Additionally for FUSEIS 1-2 the plastic rotations are considerable due to the small pin length. Nonlinear Time history analyses shall be used to determine the damage index for variable amplitude cycles by the Palgrem – Miner law of damage accumulation:

....2

2

1

1 ff N

n

N

nD

(2.31)

Failure occurs when D≥1. The number of cycles to be sustained by the system is dictated by low-cycle fatigue considerations, which deal with the deformation and strain histories rather than the stress histories (high - cycle fatigue). The following procedure is based on the assumption that the receptacle beams remain rigid. This results in higher values of pin drifts than the actual and consequently the introduction of a safety factor for the determination of the pin’s damage index is not required.


Design Guide

The damage index of a building with pin fuses shall be determined with the following steps: a) For the storey with the maximum interstorey drift the number of cycles that a pin can sustain

is calculated approximately as follows:

φpin= φfr · L

lpin (2.32)

where, φpin = pin drift φfr = frame interstory drift lpin = pin net length L = axial distance of FUSEIS columns

b) The drift ranges Δφ = φpin,max+ φpin,min per cycle are applied at the experimental fatigue curve and the number of the correspondent cycles N is calculated from the equation of the experimental fatigue curve (Figure 2.11):

log Δφ = - 1

3 (log N)-0,30 (2.33)

Figure 2.11: Fatigue curves for pin fuses

3 FUSEIS 2

3.1 Description of FUSEIS 2 (1) This document presents guidelines for the design of structures with FUSEIS2 devices. All the remaining checks that are not covered in this guide should be referred to the relevant EN.

(2) FUSEIS2 devices are seismic fuses for steel and composite steel-concrete moment resisting frames that provide good seismic performance and easiness in repair work.

(3) The FUSEIS2 fuse devices have the following main characteristics:

a) consist in a cross-sectional weakening located at the beam ends at a certain distance from the beam-to-column connections, avoiding this way potential brittle failures at the welds;

-1.4

-1.3

-1.2

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.00.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

log

Δφ

log N

log Δφ13

log N 0,30


Design Guide

b) act as dissipative seismic fuses, forcing the plastic hinge to develop at the fuse device trough concentration of inelastic behaviour, preventing the spreading of damage into the beams and columns;

c) concentrate all the damage efficiently and are easily replaceable, so that repair work after an earthquake is limited to replacing the fuses by new ones;

d) have a simple detail and calculation procedure and are easy to manufacture.

(4) The devices are made by introducing a discontinuity on the composite beams of a moment resisting frame and assembling the two parts of the beam through steel plates bolted or welded to the web and flange of the beam. The configuration of the device on a typical beam-to-column connection is shown in the following Figure 3.1.

a) bolted device b) welded device Figure 3.1: FUSEIS 2 system

(5) The damage and energy dissipation may only occur due to inelastic behaviour of the replaceable parts. To assure that irreplaceable parts remain undamaged, these have to be designed to be elastic when the device achieves its resistant capacity.

(6) The zones marked as reinforced beam consist in a reinforcement of the composite beam with additional steel plates welded to both webs and lower flange along a certain length.

(7) The bending resistance of the devices is obtained by defining the value of the capacity ratio α of the fuse, given by:

α = MRd ,fuse

Mpl, Rd, beam (3.1)

where, MRd ,fuse is the design resistant moment of the fuse device;

Mpl, Rd, beam is the design plastic moment of the composite cross-section of the beam at the

unreinforced zone.

3.2 Rules for the design of buildings (1) The design of a building with FUSEIS2 devices should be in compliance with the disposals of the relevant EN, in particular with EN1993-1-8.

(2) The fuse devices should be included at the beam ends of all the beams that belong to the primary earthquake resistant system.

(3) When designing a building, the cross-sections of the relevant structural elements should be first pre-designed for the same building but without fuses, considering the relevant limit states.


Design Guide

(4) With the design resistant values of the pre-designed composite beams Mpl,Rd,beam, the resistant moment of the fuses MR , may be computed through Equation (3.1), by choosing a lower bound for the value of the capacity ratio α, based on the desired seismic performance of the devices.

(5) It is recommended that the value of α should remain between 0,50 and 0,80. One should notice that higher values of α provide higher resistant capacities, energy dissipation and stiffness. On the other hand, lower values of α are more efficient to prevent the spreading of damage to the irreplaceable parts of the structure.

(6) The fuses devices should be classified according to the classification of joints of EN1993-1-8 (5.2) for both strength and stiffness. In the code provisions, the variables that are defined for the joints should be replaced by the same variables defined for the fuses, in the relevant expressions. Most of the fuses will be classified as partial strength, semi-rigid joints and be modelled according to the provisions of part 5.1 of the same code.

3.3 Design of the fuse devices for bending

3.3.1 Bending resistance (1) Since the fuse plates may buckle at hogging rotations, the bending behaviour of the fuses is asymmetric in most of the cases. Therefore, there is the need of computing both sagging and hogging resistant moments of the fuse, MR , and MR , , respectively.

(2) The buckling behaviour of the fuse plates may be controlled by the geometric slenderness, given by:

λ = L0

tfuse (3.2)

where, L0 is the free buckling length of the fuse; tfuse is the thickness of the plate considered.

(3) The free buckling length L is given by the horizontal distance between - the bolt rows on each side of the gap on the fuse section for bolted devices; - the end of the lap welds on each side of the gap on the fuse section for welded devices. This distance should be the same for the web and for the flange plates.

(4) Assuming a plastic distribution of forces and to take into account for bending-shear interaction, the contribution of the web plates of the fuse to the bending resistance should be neglected.

(5) The bending resistance of the fuse device should be obtained through an elastic-plastic analysis considering an adequate value for α.

3.3.2 Flange plate (1) The dimensions of the flange plate of the fuse device control the resistant bending moment of the cross-section of the fuse and is therefore dependent on the value of the capacity ratio of the device.

(2) Assuming that the plastic neutral axis is coincident with the centre of gravity of the longitudinal reinforcement, the area of the flange plate may be estimated in pre-design by the expression:


Design Guide

Af,fuse = MRd, fuse

+

fyd · z (3.3)

where,

M Rd, fuse+ is the sagging resistant moment of the fuse device;

fyd is the design yield strength of the structural steel according to EN1993-1-1;

z is the lever arm between the flange plate and the centre of gravity of the rebar layers.

(3) The hogging resistance of the fuse MRd,fuse- should be obtained through an elastic-plastic analysis

on the cross section with a modified constitutive relationship for the flange plate σmod,b(ε), given by:

σmod,b(ε) = min σt ε ; σb ε (3.4)

where σt ε is the stress-strain relationship obtained through experimental tensile tests or according to the Annex C.6 of EN1993-1-5; σb ε is the buckling stress-strain relationship given by

σb ε = fyd

λf · √2ε (3.5)

where λf is the geometric slenderness of flange plate.

3.3.3 Longitudinal reinforcement (1) The longitudinal reinforcement should be computed to remain elastic when the maximum resistant moment is developed by the fuse.

(2) In order to avoid yielding of the rebars, their area has to be computed so that the plastic neutral axis lies between the upper and lower rebar layers of the slab. It is recommended to provide the upper rebar layer with the double of the area of the lower layer.

(3) One should notice that only the rebars that are located within the effective width of the concrete flange of the composite beams at the sections adjacent to the fuse should be accounted for the bending resistance. The effective widths should be computed according to EN1993-1-8 (7.6.3) and EN1994-1-1 (5.4.1.2).

(4) The position of the plastic neutral axis should be obtained by an elastic-plastic analysis on the cross section with the material properties obtained experimentally or as defined in Annex C.6 of EN1993-1-5. An example of an algorithm to solve the elastic-plastic problem may be found in Annex I.

(5) The non-yield condition should be verified by imposing the plastic curvature χ to the cross-section of the device at sagging, assuming that the ultimate strain of the structural steel ε is developed at the flange plate. The verification consists in performing an elastic-plastic analysis and checking that the strains on both rebar layers ε are lower than the yield strain of the material ε according to EN1993-1-1.

(6) The plastic curvature is given by χp=L0θp, where θp is the plastic rotation as defined in 6.6.4(3)

of EN1998-1. In order to achieve a good behaviour the structural steel should be very ductile, matching the ductility requirements of 3.2.2(1) of EN1993-1-1.


Design Guide

(7) The following total longitudinal rebar quantity A , is recommended to be used as a first iteration at a pre-design stage:

Asl ,total = 7 · Af ,fuse · fyd

fsd

(3.6)

where, Af, fuse is the area of the cross-section of the flange plate of the fuse;

fsd is the design yield strength of the reinforcement steel according to EN1992-1-1.

(8) The length of the gap on the concrete slab should be detailed to assure that the plastic rotation θp is developed without contact of the concrete parts.

(9) After determining Asl,total and Af,fuse the sagging and hogging bending resistances may be

computed and the new values of the capacity ratios α+ and α- should be determined.

3.4 Elastic bending stiffness (Initial Flexural Bending Stiffness) (1) The bending stiffness of the fuses is obtained by dividing the yield moments My,fuse with the yield rotations θp of the fuse for both sagging and hogging.

(2) The yield moments should be obtained by an elastic analysis considering that the flange plate is in yielding. The design yield stress fydof the steel of the flange plate should be used for sagging and the design yield stress at buckling fyd,b for hogging:

fyd,b= min fyd; σb εy (3.7)

(3) The yield rotations θ are obtained by the Equations χ L θ , assuming that cross-sections remain plane and regarding the strains diagram on the fuse at yielding for both sagging and hogging.

3.5 Design of the fuse devices for shear

3.5.1 Shear resistance (1) The web plates should be considered alone for the shear resistance of the fuse.

(2) The resistance of the web plates should be computed according to EN1993-1-1 (6.6.6), considering a shear area A equal to the area of the cross-section of the web plates. Special attention should be given to the verification of shear buckling, as specified in EN1993-1-5 (5).

3.5.2 Shear stiffness (1) Shear deformability may be neglected for common spans in buildings.

3.6 Design of the non-dissipative connecting elements (1) The connection between the fuse plates and the steel beam should be rigid and have full strength.

(2) Based on the disposals of EN1998-1 (6.5.5(3)), the following expression should be used for the design force that shall be considered on non-dissipative connections between each fuse plate and the corresponding connected part of the beam: FEd = 1,1· γov · A · fu (3.8)


Design Guide

where, A is the tensile resistant area of the fuse plate under consideration which should be taken as the net cross section for bolted fuses and as the gross cross section for welded fuses; γov is the overstrength factor according to of EN1998-1 (6.2 (3)a)). The recommended value is 1,25;

fu is the ultimate tensile strength of the steel of the fuse plate according to EN1993-1-1 (Table 3.1);

(3) All the disposals of EN1993-1-8 that are not mentioned here should also be verified.

3.6.1 Design of the bolted connection (1) The bolts that connect the fuse plates to the beam should be designed to remain elastic when the fuse develops its maximum moment. Despite being replaceable parts, irrecoverable deformations on the bolts could compromise the unbolting process when trying to replace the fuse plate and so, these should remain elastic and be treated as non-dissipative elements.

(2) The following expression should be satisfied for non-dissipative bolted connections:

Fv,Rd > FEd

n (3.9)

where, Fv,Rd is the shear resistance per shear plane according to EN1993-1-8 (Table 3.4) computed with the

yield strength of the bolts fyd;

FEd is the design force of the non-dissipative connections; is the number of bolts used to transmit the shear forces.

(3) The bolts should be pre-loaded and designed to behave as type B shear connections according to of EN1993-1-8 (3.4 and 3.9).

3.6.2 Design of the welded connection (1) In order to avoid brittle failures of the welds that connect the fuse plates to the beam, these should be designed to guarantee that the maximum stresses developed by the fuse can be transmitted safely to the beam.

(2) The following expression should be satisfied for non-dissipative welded connections:

Fw,Rd > FEd (3.10)

where Fw,Rd is the design resistance of the total length of the fillet weld according to EN1993-1-8 (4.5.3.3

(1) ) computed with the yield strength of the welds fyd;

FEd is the design force of the non-dissipative connections.

3.7 Additional detailing remarks (1) The detailing rules not mentioned in this guide should be done considering the provisions of the relevant EN.

(2) In particular, and regarding the detailing of the concrete slab of the composite beam, special attention should be given to the provisions of EN1998-1 (Annex C).

3.7.1 Design of the transverse reinforcement


Design Guide

(1) The transverse reinforcement of the beam flange of the composite beam should be computed according to the provisions of EN1994-1-1 and EN1998-1.

(2) In particular, they should be designed taking into account the shear resistance of the shear connectors and the axial forces on the concrete flange and on the steel profile, according to the design procedures of EN1994-1-1 (6.6.6).

3.7.2 Design of the shear connection (3) The shear connection should be designed according to the provisions of EN1994-1-1 and EN1998-1 for full shear connection.

3.7.3 Design of the reinforced zone of the beam (1) The reinforcement of the composite beam with additional welded steel plates prevents the spreading of plasticity near the high concentration of stresses due to the transmission of forces near the fuse device.

(2) For beams with bolted devices, the thickness of the reinforcement plates should be sufficient to avoid the ovalization of the holes on the beam with bolted devices, to avoid the enhancement of difficulties in the replacing operation of the fuse.

(3) For beams with welded devices, the thickness of the plates should take into account the damage produced by the unwelding and welding processes inherent of the replacement operations.

(4) The resistance of the reinforced cross-section of the composite beam should be checked for the relevant ULS at the critical sections.

(5) The width of the flange reinforcement plate should be larger than the width of the flange plate of the fuse.

(6) The reinforced beam should be provided with a length of at least the height of the steel profile in both directions of the fuse.

(7) As a recommendation, the area of the reinforcing flange plates and the area of both web plates should at least be equal to the area of the flange and web of the steel profile, respectively.

3.8 Ductility of the structures with fuse devices / Proposal for q factor

3.8.1 Low Ductility The structure provides low ductility when the plasticity is only observed at the beam ends of the structure. According to the pushover analysis, the behavior factor obtained with such a local plastic mechanism is close to 1.

Yet, since the fuse devices get plasticized, the behavior of the structure under seismic actions can be satisfactory thanks to the energy dissipation in the fuse devices. Moreover, due to the limited horizontal deflections, the second order effects also become negligible.


Design Guide

Figure 3.2: Local plastic mechanism – Low ductility

3.8.2 Medium Ductility In order to increase the global ductility of the structure, the plastic hinges must be allowed at the column bases to form a global plastic mechanism. In this case, the behavior factor obtained as a result of such a global mechanism is around 3. Also, due to the larger horizontal deflections observed in the structure, the second order effects may gain importance and are to be checked. Also in this case, since the columns at the base show plastic behavior, another method of reparation of damaged columns become an issue.

Figure 3.3: Local plastic mechanism – Medium ductility

0

100

200

300

400

500

600

700

800

900

0 0,05 0,1 0,15 0,2 0,25Base Reaction (KN)

Displacement of Top Joint (m)

Pushover Curve (Local Plastic Mechanism)

0

200

400

600

800

1000

1200

0 0,1 0,2 0,3 0,4 0,5 0,6

Base Reaction (KN)

Displacement of Top Joint (m)

Pushover Curve (Global Plastic Mechanism)


Design Guide

Appendix 1 - Algorithm for the elastic-plastic analysis The following procedure is recommended to solve the equilibrium equations. The resistance model is shown in the following figure.

The approach consists in computing the bending moment of the cross-section of the fuse for each imposed curvature, based on the stress-strain relationship of the materials.

As input, two files should be created, one with the strain-strain relationships for tension and compression for both rebar and structural steel.

Another input file should include the fibre layout on a table with information about the

coordinate of each fibre j in respect to a chosen origin, the area Aj of each element and the material

type. The index "f" refers to the flange fibre. The value of the admissible error - adm_error - should be as small as possible without compromising computational efficiency

1) Initialization at instant : χi=0

2) εf = εinitial

3) εj = εf + χi zj

4) Read corresponding stress-strain relationship of the material from file: σ(εj)

5) Compute force on each fibre: Rj = Aj · σ(εj)

6) If |∑ Rjj | >adm_error → go back to step 2) and make εf = εf ± Δε The sign of Δε depends on the sign of ∑ Rjj .

7) If | ∑ Rj|j <adm_error → compute bending moment: Mi = ∑ · Rjj · zj

8) Save pair of values (Mi , χi)

9) Go back to 1) and proceed to next curvature at instant i+1: χi+1=χi+Δχ

The value of Δχ is constant depends on the level of accuracy needed. A value below of 1,0 is recommended.

FUSEIS Design Guide

Documents

Transcript of FUSEIS Design Guide