GLOBAL PERFORMANCE OF STEEL MOMENT RESISTING

FRAMES WITH SEMI-RIGID JOINTS

D. Dubina1, A. Ciutina

1 A. Stratan

1, & F. Dinu

2

1Department of Steel Structures and Structural Mechanics, The “Politehnica” University,

Timisoara, Romania 2Centre of Advanced and Fundamental Technical Studies, Romanian Academy of Science,

Timisoara, Romania

ABSTRACT

Beam-to-column joints have a fundamental importance in case of seismic moment resistant frames,

because dissipative zones must be located at the beam-ends, so that their rotational ductility supply

is strictly related to the detailing of connections. Based on a large numerical study, the present paper

investigates the seismic performance of two series of moment resisting frames with beam-to-

column joints with different configurations. Performance of the analysed structures is expressed in

terms of characteristic failure acceleration, ductility demand, damage indices and the q factor.

KEYWORDS

moment resisting frames, beam-to-column joints, steel frames, semi-rigid joints, rotation capacity,

ductility, damage, earthquake.

1. INTRODUCTION

The use of semi-rigid joints in frames subjected to seismic loads is a matter of controversy. None of

the existing design codes include provisions for their use and, in zones characterised by a high

seismicity, the use of rigid full-strength joints is mandatory.

To ensure that a beam-to-column joint is ductile enough and has the capacity to provide the required

rotations, the related connection must be capable to develop adequate plastic hinge while sustaining

its yield moment capacity.

Due to their higher flexibility, semi-rigid steel frames are prone to increases in inter-storey drifts.

The inter-storey drift condition is related to the serviceability limit state which corresponds to minor

frequent earthquake. The design objective, when building serviceability is checked, is that the

building, including both structural and non-structural components, should suffer no damage and

discomfort of the inhabitants should be minimal. The first requirement, which leads to the

avoidance of damage, is satisfied by ensuring that the structure behaviour during the earthquake

remains in the elastic range. In order to fulfil the second requirement - both non-structural

components damage and discomfort of inhabitants is avoided- it is necessary to provide sufficient

stiffness to prevent significant deformations.

The ultimate limit state of a building in seismic circumstances could be regarded either as damage

limit state or failure limit state.

The damage limit state allows some minor damages to non-structural components due to large local

deformation in certain zones.

The failure limit state pertains to very infrequent severe earthquake ground motions in which both

structural and non-structural damages are expected, but safety of the inhabitants must be

guaranteed. Furthermore, the structure must be able to absorb and dissipate large amounts of

energy. In case of MR frames with semi-rigid partial-resistant beam-to-column connections, the

connection design properties can be expressed in rotational stiffness, moment capacity and plastic

rotation supply. In case of strong seismic motion, the plastic rotation demand for beam-to-column

connection could be greater than the plastic rotation supply, which leads to its damage (partial or

total). This was the situation of most beam-to-column welded connections in multi-storey MR

frames during the Northridge earthquake (Kato B. et al, 1997). The problem in such cases is

whether damaged connections can be recuperated by repairing works or not?

The SAC joint venture project suggests several reparatory design detailing for seismic damaged

welded connections. It is obviously that reparatory detailing can be also proposed for bolted

connections. It is recommendable, of course, to have an initial design of beam-to-column

connections such that both damage and reparatory works to be easy controlled.

Authors’ opinion is that based on the Performance Design Philosophy (Bertero V., 1997), semi-

rigid steel frames could satisfy the required strength and stiffness conditions for “Operational and

Functional” or “Life Safety” performance levels. In terms of rotation capacity of connections, it

means that, if a certain percentage of damage in frame connections can be accepted, a larger

rotation capacity of the connections (related to design) can be considered as a supplementary

ductility supply for the global behaviour of the structure. A parametrical study was developed by

the authors in order to analyse the effects of beam-to-column connection properties on the global

performance of two series of MR frames. The present paper shows the results and the conclusions

of this study.

2. ANALYSED FRAMES

The parametrical study is developed on two frames: a 6 storey – 3 bay frame (C36) made out of

Fe430 steel and a 3 storey – 3 bay frame (C33) made out of Fe360 steel, shown in Figure 1.

The member cross-sectional dimensions and joint properties were obtained by means of an

equivalent static design procedure, using an elasto-plastic analysis.

Different frame typologies have been considered in the study. Member characteristics for the C36

and C33 frames are given in Table 1.

HEB260

HEB260

HEB300

HEB360

HEB360

HEB300IPE300

IPE300

IPE300

IPE300

IPE300

IPE300

4.50 4.504.50

3.00

3.00

3.00

3.00

3.00

3.00

Figure 1. Geometry of the analysed frames

The rigid and semi-rigid joints have been designed according to Annex J of Eurocode 3 [8]. Joint

Table 1. Design values of the section characteristics.

Frame Column Beam Mpl,b,Rd

x106 Nxmm

Mpl,c,Rd

x106 Nxmm

Mpl,c,Rd/

Mpl,b,Rd material

C36 HEB360

HEB300

HEB260

IPE300

157.1

670.8

467.3

320.7

4.27

2.97

2.04

Fe430

C33 HEB240 IPE330 171.8 225.0 1.31 Fe360

configurations are given in Figure 2 and the design values of moment capacity and stiffness in

Table 2. Distinction is made between single-sided and double-sided joint, subjected to unbalanced

moments, as is the case under seismic horizontal forces.

C1 C2 C3 C4

C5 C6

M20/6.6 M20/6.6

Figure 2. Detailing of semi-rigid joints.

Table 2. Joints Characteristics Joint

Type

Mj,Rd

x106 Nxmm

m*

(Mj,Rd/Mpl,b,Rd)

Sj,ini

x1011

Nxmm/rad

Sj

x1011

Nxmm/rad

S*j

C36.1A

C36.1B

C36.1C

153.4

153.4

153.4

0.98

0.98

0.98

0.628

0.561

0.493

0.314

0.281

0.246

8.05

7.21

6.31

C36.2A

C36.2B

C36.2C

133.8

109.3

91.4

0.85

0.70

0.58

0.421

0.340

0.305

0.211

0.127

0.152

5.40

3.26

3.90

C36.3A

C36.3B

C36.3C

153.4

153.4

153.4

0.98

0.98

0.98

1.235

1.274

1.292

0.618

0.640

0.646

15.85

16.41

16.57

C36.4A

C36.4B

C36.4C

153.4

153.4

153.4

0.98

0.98

0.98

1.235

1.274

1.292

0.618

0.640

0.646

15.85

16.41

16.57

C36.5A

C36.5B

C36.5C

219.3

280.8

172.3

1.40

1.79

1.10

1.186

1.509

0.936

0.977

1.509

0.468

25.05

38.70

12.00

C36.6A

C36.6B

C36.6C

280.8

280.8

243.4

1.79

1.79

1.55

C33.1 130.9 0.76 0.501 0.250 4.05

C33.2 74.63 0.43 0.307 0.153 2.48

C33.3 155.8 0.91 1.362 0.681 11.02

C33.4 152.5 0.89 1.362 0.681 11.02

C33.5 140.9 0.82 0.907 0.454 7.34

C33.6 210.4 1.22

A – connections at levels 1-2; B - connections at levels 3-5; C - connections at the roof level

If the web panel of the C2 joints is considered as unstiffened to shear, compared to C4, the drop of

stiffness is very important in the case of unbalanced bending moments. This penalisation is

probably too severe.

The topology of the frames, including the joint distribution, is shown in Figure 3.

The elasto-plastic dynamic analysis has been performed using the DRAIN2DX computer program

and the set of three accelerograms described in Chapter 3.

The main aim of the analysis was to investigate the influence of the different ground motions on the

seismic response of the frames. For this study, a value of 3% inelastic inter-storey drift and two

values of plastic rotation capacities i.e. 0.02 rad. for welded joints and 0.03 rad. for bolted joints

were accepted.

The monotonic plastic rotation capacity of members (p) was computed by DUCTROT computer

program (Gioncu et al, 1997). Plastic rotation capacity of members for cyclic behaviour conditions

(pcor

) has been computed by adjusting the monotonic values by coefficients depending on the

member cross-sectional slenderness and the axial force. A material partial safety factor =1.5 was

used (Gioncu, 1997). Computed values of plastic rotation supply of members are given in Table 3.

Table 3 Plastic rotation supply of members

Frame type member p pcor

C36 IPE300

HEB360

HEB300

HEB260

0.0946

0.1085

0.0926

0.1267

0.054

0.049

0.042

0.065

C33 IPE330

HEB240

0.0934

0.0963

0.053

0.044

In order to assess the structural response to the different ground motions, local and global damage

indexes are computed as follows:

lim.p

p

DLI

;

Li

Li

D

D

DgI

II

2

where: IDL is the local damage index, p is the plastic rotation demand and p.lim is the minimum

guaranteed plastic rotation supply and IDg is the global damage index

C36RIG C36SR1 C36SR2

C36DU1 C36DU2 C36DU3

C36DU4 C36DU5- joint type C1

- joint type C2

- joint type C3

- joint type C4

- joint type C5

- joint type C6 - pined joint

C33RIG C33SR1 C33SR2

C33DU1 C33DU3

C33DU4 C33DU5

Figure 3. Frame typologies

The q-factor is evaluated as the ratio between the ground acceleration leading to failure (u) and that

corresponding to the first yielding (e):

e

uq

The ultimate design limit state multiplier ud may be evaluated as:

),,min( mu

where: is the accelerogram multiplier corresponding to the attainment of 3% inter-storey drift

limit;

is the accelerogram multiplier corresponding to the plastic rotation capacity either in joint

or members;

m is the accelerogram multiplier corresponding to the plastic mechanism.

3. SELECTION AND SCALING OF RECORDS

Three different earthquakes have been chosen to study the dynamic response of the considered

structures. The ground records have been chosen so as to assure a large variety of Control Periods

Tc [7] (considered to be a very significant parameter for an earthquake if it is reported to a structure

with a given eigenperiod):

max

max2SA

SVTC

Table 4 Ground motions characteristics

Record PGA (g) TC

(sec)

EPA

(g)

scaling

factor

scaled

PGA (g)

EPV

(cm/sec)

Incerc-Bucharest NS, March 04, 1977 0.199 1.335 0.240 1.042 0.207 52.18

Kobe NS, 17 Jan 1995 0.836 0.622 0.704 0.355 0.297 97.17

Brienza NS, November 23, 1980 0.21 0.19 0.22 1.155 0.248 9.06

Table 4. gives the values of the most important parameters which characterise the considered

earthquakes (INCERC Bucharest - Romania, 4 March 1977, Kobe NS - Japan, 17 Jan. 1995 and

Brienza NS - Italy, 23 Nov. 1980), and in Fig. 4 are given the spectral accelerations of the same

eatrhquakes with a damping factor of 5%. For comparison, in Tab. 5 are given the fundamental

periods of the resulted structures.

Fig.4 Acceleration response spectra of records.

The scaling of records for structural analysis was done so as to correspond to the same Effective

Peak Acceleration (EPA).

Table 5 Fundamental periods of vibration of the analysed frames.

Frame C36RIG C36DU4 C36SR2 C36DU1 C36DU2 C36DU5 C36SR1 C36DU3

Fund. Period 1.33 1.35 1.47 1.52 1.61 1.63 1.69 1.86

Frame C33RIG C33DU4 C33SR2 C33DU1 C33SR1 C33DU5 C33DU3

Fund. Period 0.95 1.01 1.04 1.09 1.15 1.20 1.31

4. NUMERICAL RESULTS

As it was described in Chapter 2 – Analysed Frames, the parameters that have been monitored were

the Damage Index – ID and the q-Factor. A different parameter that has been taken into account for

results is the Effective Peak Acceleration (EPA) in the failure situation.

Fig. 5 EPA values for C36 frame series -

INCERC 1977 earthquake

Fig. 8 EPA values for C33 frame series -

INCERC 1977 earthquake

Fig. 6 EPA values for C36 frame series – Kobe

NS earthquake

Fig. 9 EPA values for C33 frame series – Kobe

NS earthquake

Fig. 7 EPA values for C36 frame series –

Brienza earthquake

Fig. 10 EPA values for C33 frame series –

Brienza earthquake

This parameter has been introduced in order to see the maximum values of EPA, as frame response,

for each earthquake. These values are computed for each failure criterion type (drift – 3%, rotation

capacity – 0.02 or 0.03 rad and mechanism). In Fig. 5-7 are given the charts with the obtained

values for C36 frame series (for the three earthquakes considered) and the similar values for the

C33 frame series are given in Fig. 8-10. In the charts are also given the mean values for each

criterion. The Global Damage Indices for each earthquake are given in Fig. 11 and Fig. 12 for frame

series C36 and C33 respectively.

Fig. 11 Global Damage Indices C36 frame series

Fig. 12 Global Damage Indices C33 frame series

For a better identification of the global and partial Damage Indices. These values are given in the

Table 6. It is to be noted that the Global Damage Index is not a linear sum of partial indices. Also,

the damage index in joints is computed for the ductility criteria stated in Chapter 2.

Table 6. The Global and Partial (Columns, Beams and Joints) Damage Indices.

Frame Global Damage Indices Frame Global Damage Indices

ID,col ID,beam ID,joint ID,G ID,col ID,beam ID,joint ID,G

INCERC-BUCHAREST NS, MARCH 04, 1977 ROMANIA

C36RIG 0.168 0.397 0 0.384 C33RIG 0.442 0.256 0 0.360

C36DU4 0.162 0.398 0 0.386 C33DU4 0.352 0.192 0.762 0.494

C36SR2 0.125 0 0.710 0.696 C33SR2 0.459 0 0.488 0.478

C36DU1 0.122 0 0.698 0.651 C33DU1 0.428 0 0.505 0.479

C36DU2 0.047 0 0.656 0.651 C33SR1 0.451 0 0.649 0.613

C36DU5 0.018 0.383 0.206 0.348 C33DU5 0.266 0 0.758 0.680

C36SR1 0.049 0 0.661 0.656 C33DU3 0.327 0 0.763 0.690

C36DU3 0.024 0 0.642 0.639

KOBE NS JAPAN

C36RIG 0.027 0.269 0 0.267 C33RIG 0.228 0.281 0 0.258

C36DU4 0.037 0.284 0 0.281 C33DU4 0.318 0.272 0.860 0.543

C36SR2 0.043 0 0.488 0.483 C33SR2 0.263 0 0.646 0.561

C36DU1 0.064 0 0.506 0.499 C33DU1 0.270 0 0.583 0.503

C36DU2 0.011 0 0.564 0.564 C33SR1 0.055 0 0.513 0.501

C36DU5 0.014 0.351 0.207 0.320 C33DU5 0.086 0 0.470 0.440

C36SR1 0.021 0 0.540 0.538 C33DU3 0.166 0 0.743 0.700

C36DU3 0.055 0 0.577 0.568

BRIENZA, 24 NOV. 1980, N-S

C36RIG 0.018 0.314 0 0.311 C33RIG 0.325 0.243 0 0.286

C36DU4 0.018 0.304 0 0.301 C33DU4 0.319 0.206 0.681 0.439

C36SR2 0.021 0 0.758 0.755 C33SR2 0.361 0 0.473 0.437

C36DU1 0.020 0 0.709 0.706 C33DU1 0.378 0 0.547 0.495

C36DU2 0.019 0 0.706 0.703 C33SR1 0.118 0 0.601 0.576

C36DU5 0.020 0.275 0.211 0.257 C33DU5 0.089 0 0.796 0.759

C36SR1 0.022 0.314 0 0.311 C33DU3 0.076 0 0.215 0.199

C36DU3 0.027 0 0.655 0.650

q-Factor values, may be regarded as a measure of global ductility, are given in Fig. 13 and Fig. 14

(frame series C36 and C33 respectively), comprising also the mean values for each earthquake.

They have been computed according to the three failure criteria, but only the minimum values are

represented in the Fig. 13 and Fig. 14.

Fig. 13 q factors for C33 frame series

Fig. 14 q factors for C33 frame series

5. CONCLUSIONS

Previous chapter presents the results obtained by the numerical analysis for the considered frame

series, for three main parameters: failure value of EPA, global damage index and the q-factor. In

order to draw the final conclusions, Table 7 sumarises the qualitative description of the structural

behaviour.

Table 7. Global structural behaviour. Frame series C36/

Types of joints

Output Results Frame series C33/

Types of joints

Output Results Comments

Rigid Frame

(theoretical)

RIG

EPA - high

ID - low

q-fct - high

Rigid Frame

(theoretical)

RIG

EPA - high

ID - low

q-fct - high

Ideal behaviour, but

it remains

theoretical

Real Rigid Frame

(rigid joints)

DU4

EPA - high

ID - high

q-fct - high

Real Rigid Frame

(rigid joints)

DU4

EPA - med-high

ID - high

q-fct - high

High values of

damages. This is the

consequence of real

rigid joints.

Frames with semi-

rigid joints:

(semi-rigid joints)

SR1-SR2

EPA - SR1-medium

- SR2 - med-high

ID - SR1 - low

- SR2 - high

q-fct - SR1 - med -low

- SR2 - high

Frames with semi-

rigid joints:

(semi-rigid joints)

SR1-SR2

EPA - SR1-medium

- SR2 - med-high

ID - SR1 - high

- SR2 - medium

q-fct - SR1 - med -high

- SR2 - medium

Frame behaviour is

influenced by the

joint propreties

Dual frames without

pinned joints

(rigid and SR joints)

DU1 - DU4

EPA - DU1-med.-low

- DU4 - med-high

ID - DU1 - high

- DU4 - high

q-fct - DU1 - medium

- DU4 - high

Dual frames without

pinned joints

(rigid and SR joints)

DU1 - DU4

EPA - DU1 - high

- DU4 - high

ID - DU1 - med-high

- DU4 - med-high

q-fct - DU1 - medium

- DU4 - medium

Frame behaviour is

influenced by the

joint propreties

Dual frames with

pinned joints

(rigid and SR joints)

DU3 - DU5

EPA - DU3-medium

- DU5 - medium

ID - DU3 - medium

- DU5 - high

q-fct - DU3 - low

- DU5 - high

Dual frames with

pinned joints

(rigid and SR joints)

DU3 - DU5

EPA - DU3 - low

- DU5 - low

ID - DU3 - high

- DU5 - high

q-fct - DU3 - low

- DU5 - low

Pinned joints have a

bad influence on

frame behaviour

Tab. 7. (Continued) Global structural behaviour. Horizontal Dual

Frames

(semi-rigid joints)

DU2

EPA - med-low

ID - high

q-fct - low

Intermediar results,

between the two

types of SR frames.

No conclusions for

just a frame

Concluding remarks:

- The perfect rigid frames resulted to have a very good behaviour, but they still remain

unrealisable. The real rigid frames have big damages, damages due to joint degradation mainly.

This may be related to the relatively low value of ductility (plastic rotation capacity of 0.02 rad. and

of 0.03 rad. respectively) that have been considered for computing the damage index in joints. It is

expected to improve the frame performances if the joints rotation capacity could be increased.

- The frames having semi-rigid joints have a good general behaviour. The problem is to find the

right joint properties that “fit” better for the given frame. Anyway, the semi-rigid frames seem to be

an alternative to the classical ones. The only problem is to establish the limits of their use.

- Dual frames with rigid / semi-rigid joints represent an open problem: it seems possibly to find

configurations with improved performances, but further studies are necessary.

- Dual frames with pinned joints in middle span have generally a bad behaviour and they should be

avoided. They have a bad behaviour of all the three parameters monitored.

- The main conclusion of this study is that global performances of MR frames can be controlled by

beam-to column joint properties. We can either improve or get worse frame performances. This

problem is important enough to focus further researches.

6. REFERENCES

Bertero V. (1997): General Report on Codification, Design and Applications, STESSA ’97

Behaviour of Steel Structures in Seismic Areas, Proceedings of the Second International

Conference 3-8 Aug. 1997, Kyoto, Japan.

Gioncu et al. (1997): Simplified Approach for Evaluating the Rotation Capacity of Double T Steel

Sections, STESSA ’97 Behaviour of Steel Structures in Seismic Areas, Proceedings of the Second

International Conference 3-8 Aug. 1997, Kyoto, Japan.

Kato. B. et al (1997): Seismic Damage of Steel Beam-to-Column Rigid Connections in the

Hyogoken-Nanbu Earthquake, STESSA ’97 Behaviour of Steel Structures in Seismic Areas,

Proceedings of the Second International Conference 3-8 Aug. 1997, Kyoto, Japan.

Lungu D. et al (1997): Effective Peak Ground Acceleration (EPA) Versus Peak Ground

Acceleration (PGA) and Effective Peak Ground Velocity (EPV) Versus Peak Ground Velocity

(PGV) for Romanian Seismic Records. Eurocode 8 - Worked examples

Mazzolani F. M. & Piluso V. (1996): Theory and Design of Seismic Resistant Steel Frames.

London: E& FN Spon.

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Rules for Buildings. Brussels: CEN, European Committee for Standardisation.

ENV 1998-1-1, (1993) - second draft - EUROCODE 8: Earthquake Resistant Design of Structures.

Part 1.: General Rules and Rules for Buildings - Seismic Actions and General Requirements for

Structures. Brussels: CEN, European Committee for Standardisation.

SAC Joint Venture (1996). Connection Test Summaries. SAC 96-02. Sacramento, California.