Cyclic Performance of Moment Resisting Welded Connections with RBS

Built by Iranian Profiles

Parham Memarzadeh, Mohammad Davarpanah

Department of Civil Engineering, Najafabad Branch, Islamic Azad University,

Najafabad, Iran

ABSTRAST: Reduced Beam Section (RBS) connections have been developed in

order to provide a reliable and more ductile performance. Iranian National

Provisions (INP) in Part 10 prescribes recommendations for the design of RBS

members. However, the effectiveness of these recommendations for Iranian

profiles is dubious, due to limited Iranian research in this field. Numerical study

was performed on various RBS connections designed according to INP-10 in

order to evaluate the proposed values of geometrical characteristics of the RBS.

Finite element models of the RBS connections were analyzed under cyclic loading

and the results are compared with the expected results and also with those

obtained from the analysis of connections designed according to FEMA 350. The

study confirms the need for readjustment of the geometrical characteristics of the

RBS in order to apply to Iranian profiles.

1. Introduction

Since 1994 Northridge earthquake, a bulk of research have been performed to

replace better connections for new steel moment frame and to enrich poor moment

connections for exiting steel moment frames. The prior and post-Northridge

laboratory observations have also demonstrated the inherent disability of the

conventional moment connections to develop enough ductility (Engelhard et al.

1993).

Since the Northridge earthquake, a number of various studies have been carried

out in order to improve the seismic performance of the conventional welded

connections. One of the most promising ways to modify the behavior of the

conventional moment frame is to soften a portion of beam flanges near the column

face (Plumier 1997; Engelhard et al. 1998). The connection softening may be

accomplished by trimming circular selectors from the beam flanges near the

column. This solution known as reduced beam section (RBS) method, leads

plastic hinges toward the beam span away from column face, resulting in the

reduction of stress concentration at the interface of beam and column. However,

as the result of reducing beam section within a sensitive zone, the beam becomes

more prone to buckling. Previous testing on the RBS moment connections (EC 8

2005; Plumier 1994; Chen et al. 1997) highlighted the effectiveness of the new

approach in the post-Northridge design era. The reduced beam section (RBS),

allows controlled yielding of the beam by moving the plastic hinge region at the

beam – in a short distance from the column’s face – protecting the connection

from any type of failure. Various shapes cutouts are possible (constant, tapered or

radius cut) to reduce the cross sectional area. Extensive experimental and

analytical projects have been conducted demonstrating that the radius cut behaves

with the highest rotational capacity. Recommendations for the design and

detailing of the RBS member were prescribed in FEMA 350 (2000) and FEMA

351(2000) regarding the location and reduction rate of RBS, based on the local

performance of tested beam to column assemblies. Several researches were

investigating the influence of the RBS technique, most of them including US

profiles and type of connections (Adan and Reaveley 2004; Deylami and Moslehi

Tabar 2008; Moon et al. 2009).

Although the RBS technique is widely investigated in the US, there is poor

existing data using the Iranian National Provisions (INP 2014). INP profiles and

types of moment connection that are widely used in Iran are not investigated in the

same level. For this reason, the INP (2014) in Part 10 recommended RBS

geometrical parameters are in need of further research in order to be applied with

the appropriate level of reliability.

2. Comparison of presented parameters for reduced beam section between

FEMA 350 and INP

Effective parameters in the study of presents are shown in fig. 1 including radius

of the cuts in both top and bottom flanges at the RBS (R), depth of the flange cut

(c), length of the RBS (b) and distance of the beginning of the RBS from the

column face (a). comparison of presented parameters for RBS connection between

FEMA 350 (2000) and Iranian National Provisions (INP 2014) will be discussed

according to table (1) the only difference between presented parameters in the two

regulations is the amount of parameter C (depth of the flange cut), which is the

most important parameter for the reduced beam section.

FIG. 1. RBS connection detail.

Table 1. Geometrical characteristics of the reduced beam section.

FEMA 350 Iranian National

Provisions (INP)

𝑎 ≅ (0.5 ~ 0.75)𝑏𝑓 𝑎 ≅ (0.5 ~ 0.75)𝑏𝑓

𝑏 ≅ 0.65~0.85)𝑑𝑏 𝑏 ≅ 0.65~0.85)𝑑𝑏

𝑐 ≅ (0.2 ~ 0.25)𝑏𝑓 𝑐 ≅ (0.1~ 0.25)𝑏𝑓

𝑅 =4𝑐2 + 𝑏2

8𝑐 𝑅 =

4𝑐2 + 𝑏2

8𝑐

3. Design of specimens

To design a RBS connection with radius cut the recommended relations between

FEMA350 and Iranian National Provisions used.

Design steps are:

Step 1: Determine the length and location of the beam flange reduction, based on

the following:

𝑎 ≅ (0.5 ~ 0.75)𝑏𝑓 (1)

𝑏 ≅ 0.65~0.85)𝑑𝑏 (2)

Where a and b are as shown in Figure 1, and bf and db are the beam flange width

and depth respectively.

Step 2: Determine the depth of the flange reduction, c, according to the following:

I) Assuming the amount of parameter (c) being at minimum according to

FEMA350 (2000) and INP (2014):

According to FEMA 350

𝑐 = 0.2𝑏𝑓 (3)

According to INP (2014)

𝑐 = 0.1𝑏𝑓 (4)

II) Calculating ZRBS:

𝑍𝑅𝐵𝑆 = 𝑍𝑏 − 2 × 𝑐 × 𝑡𝑓 × (𝑑𝑏 − 𝑡𝑓) (5)

III) Calculating MF:

𝑀𝑓 = 𝑀𝑝𝑟 + 𝑉𝑝 × (𝑆ℎ −𝑑𝑐

2) (6)

IV) If 𝑀𝑓 < 𝐶𝑝𝑟 × 𝑅𝑦 × 𝑍𝑟𝑏𝑠 × 𝐹𝑦 the design is acceptable. If Mf is greater than

the limit, increase, c. The value of c should not exceed 0.25 bf.

Hence, the analysis for the finite element parametric study considering 6 models,

are summarized in Table 2. The material properties for the beams was obtained

from three- point bending coupon tests performed for this study. The resulting

values were as follows: Young's modulus E = 210000 𝑁

𝑚𝑚2 , yield stress f𝑦 =

240 𝑁

𝑚𝑚2 and ultimate stress f𝑢 = 370 𝑁

𝑚𝑚2 .

Table 2. General specifications of the models

Models Beam Column

Reduce parameters

(mm)

Designed according

to

a b c FEMA 350 INP

ORC1 IPE300 IPB300 - - - - -

RBS1 IPE300 IPB300 0.5bf 0.65db 0.2bf *

RBS2 IPE300 IPB300 0.5bf 0.65db 0.1bf *

ORC2 IPE360 IPB400 - - - - -

RBS3 IPE360 IPB400 0.625bf 0.75db 0.2bf *

RBS4 IPE360 IPB400 0.625bf 0.75db 0.1bf *

4. Finite element modelling

In the present project, the finite element package ABAQUS (1997) was used to

predict the structural behavior of RBS moment connections subjected to cyclic

loading The subassemblies were modelled using four node thin shell elements

with reduced integration (element S4R in ABAQUS). Fig. 2 shows a typical finite

element meshing used in this study. As observed in Fig. 2 a more refined mesh

was applied at the regions near the RBS. The cyclic displacement amplitude

followed the loading protocol in the AISC Seismic Provisions (AISC 2002),

which is the same as the SAC loading protocol 1997 (SAC 1997). The loading

protocol is shown in Fig. 3.

FIG. 2. View of the finite element mesh of the RBS connection

FIG. 3. Loading protocol [14]

5. Finite elements modeling results validation by experimental model

To verify the analytical models, we modeled the conventional connection tested

by Pachoumis and colleagues (2010) shown in Fig. 4, there is a close agreement

between the experimental results obtained by Pachoumis and colleagues and our

numerical results.

(a)

(b)

FIG. 4. Comparison between the experimental and numerical hysteretic

results, (a) experimental sample, (b) finite elements sample of the current

study

6. Description of model analysis

6.1 Stress distribution

The Von Misses stress distributions for 0.05 rad inter story drift angle are shown

in Fig. 5 for all models. It can be seen that concentrated stress for RBS models

designed according to FEMA 350 (2000) occurs in beams, for RBS models

designed according to Iranian National Provisions (INP, 2014) and ordinary rigid

connection (ORC) occurs in connection.

a b c

d e f

Fig. 5. Von Misses distribution (a) ORC1, (b) RBS1, (c) RBS2, (d) ORC2, (e)

RBS3, (f) RBS4.

6.2. PEEQ

The PEEQ index is defined as the plastic equivalent strain (PEEQ) divided by

the yield strain 𝜀𝑦 of the beam material, which represents the local strain demand

[16]. The plastic equivalent strain is defined as:

𝑃𝐸𝐸𝑄 = √2

3𝜀𝑖𝑗𝜀𝑖𝑗 (7)

where εij is the component of plastic strain in the direction specified by i and j.

The plastic equivalent strain (PEEQ) distributions for 0.05 rad inter story drift

angle are shown in Fig. 6 for all models. It can be seen that concentrated strain for

all types of RBS models occurs in beams and for ordinary rigid connection

(ORC), it occurs in connection. Also models designed according to FEMA 350

(2000) showed more appropriate behavior compared with those designed

according to Iranian National Provisions.

a b c

d e f

FIG.6. PEEQ index (a) ORC1, (b) RBS1, (c) RBS2, (d) ORC2, (e) RBS3, (f)

RBS4

To access the effect of the parameters on the ductile fracture potential of the

models of the various connection configurations, the Rupture Index (RI) was

computed from the finite element analysis results. The RI is defined as the ratio of

the equivalent plastic strain (PEEQ) index to the ductile fracture strain εf ,

multiplied by the material constant a i.e.

𝑅𝐼 = 𝛼𝑃𝐸𝐸𝑄

𝜀𝑦⁄

𝜀𝑓= 𝛼

𝑃𝐸𝐸𝑄𝜀𝑦

⁄

𝑒𝑥𝑝(1.5 𝑝

𝑞)

(7)

Where p and q are equal to the hydrostatic pressure and Von Misses stress,

respectively, with:

𝑃 = −1

3 𝜎𝑖𝑗 (8)

𝑞 = √3

2 𝑆𝑖𝑗𝑆𝑖𝑗 (9)

Values of the RI were used to evaluate and compare the potential for ductile

fracture of different locations in a finite element model or between two different

models at the same location. Research by Hancock and Makenzie (1976) has

shown that this criterion for evaluating the potential for ductile fracture to be

accurate. Fig. 7 indicates that the reduced beam section connection (RBS) has a

lower RI, and thus fracture potential, compared to ordinary rigid connection

(ORC) to a similar condition. The cause for the higher value of the RI in the ORC

connection is due to the larger plastic strains that develop in the connection region

near the column face. As it can be seen in Fig. 9 the RBS1 and RBS3 designed

according to FEMA 350 has minimum value of RI to compare with other

connection.

FIG.7. Effect of connection type on Rupture Index

6.3. Cyclic behavior

Moment-plastic rotation hysteretic responses of all models are shown in Fig. 8.

The moment was measured at the column face and the total beam rotation was

computed by dividing the total beam tip displacement by the distance to the

column face.

As it can be observed, all models have suitable hysteretic behavior. Hysteretic

curves show that the strength of the connection is reduced due to beam local

buckling. However, this strength degradation is not so important, since after the

buckling, the strength of connection in all models is still more than plastic

moment capacity of beams. Therefore, this connection can be classified as a full

strength connection. As it can be observed from the hysteretic curves, all models

have reached to 0.04 rad rotation, and the strength of connection at 0.04 rad

rotation is more than 80% of the beam plastic moment capacity, (0.8 Mp).

Consequently, this connection satisfies the criteria of AISC Seismic Provisions

(2005) for special moment frame systems.

a b c

d e f

FIG.8. Hysteresis response of beam (a) ORC1, (b) RBS1, (c) RBS2, (d)

ORC2, (e) RBS3, (f) RBS4.

6.4 Connection stiffness classification

The connections could be classified using moment-joint rotation curves. The

joint rotation is considered as the summation of connection rotation and panel

zone rotation.

Secant stiffness is computed using moment-joint rotation curves of models.

Secant stiffness is defined as:

𝐾𝑠 = 𝑀𝑆 𝜃𝑆⁄ (10)

𝑀𝑆 = 𝐹𝑦 × 𝑆 (11)

where Fy is the yield stress of steel, and S is beam section modulus.

𝜃S = joint rotation corresponding to MS obtained from moment-joint rotation

curves.

According to AISC (2005) Specifications for Structural Steel Buildings, if

KL/EI > 20 the connections can be considered as fully restrained. Where, L and

EI are length and bending rigidity of the beam respectively. Values of secant

stiffness and KL/EI are presented in Table 3 for all models. The value of L in this

table is considered as equal to the length of beam in the frame between two

columns which is twice the beam length in each side of column in selected

subassemblies.

As it can be seen in Table 3, all models are full restrained connection and also

Secant stiffness magnitude in RBS1 and RBS3 connections designed according to

FEMA 350 is bigger than that in other connections.

Table 3. Stiffness classification of connections.

Models MS

(kN.m)

𝜽𝑺

(Rad)

Ks

(kN.m) I (m4) L(m) KsL/EI

ORC1 133 0.00144 92.361 83.6e-6 5 26.31

RBS1 86 0.00123 69.918 53.4e-6 5 31.17

RBS2 114 0.00128 89.062 72.1e-6 5 29.45

ORC2 216 0.00146 147.945 162.7e-6 5 21.65

RBS3 174 0.00126 138.095 109.8e-6 5 30.72

RBS4 213 0.00131 162.595 135.1e-6 5 28.65

7. Conclusions

In this paper, the results obtained from modeling by ABAQUS computer

program were provided:

(1) In the RBS connection designed according to FEMA 350 (2000), plastic

deformations take place significantly in the beam.

(2) As shown in hysteretic curves, this connection is a full strength connection.

(3) This connection can be used in special moment frame (SMF) systems.

(4) All values of KL/EI are greater than 20; therefore, this type of connection is a

fully restrained connection.

(5) Specimens RBS1 and RBS3, which were not designed according to designed

according to Iranian National Provisions, exhibited excellent performance when

subjected to cyclic loading. The key parameters for the design of an RBS with

radius cut that were adopted by INP (2014) in part 10 should be readjusted in

order to be more safely applicable to Iranian profiles.

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