Numerical Investigation on the Moment-Rotation Relationship ...Numerical Investigation… Hashem Al Hendi and Mohammad Adeeb Mahmoud - 560 - The Finite Element (FE) method is a widely

Jordan Journal of Civil Engineering, Volume 12, No. 4, 2018

- 558 - © 2018 JUST. All Rights Reserved.

Numerical Investigation on the Moment-Rotation Relationship of

High-Strength Steel Semi-Rigid Connections

Hashem Al Hendi 1) and Mohammad Adeeb Mahmoud 2)

1) Department of Civil Engineering, Applied Science Private University, Amman, Jordan. E-Mail: [email protected]

2) Department of Civil Engineering, Applied Science Private University, Amman, Jordan. E-Mail: [email protected]

ABSTRACT

The significance of this parametric study initiates from the need for further understanding of the behaviour of

semi-rigid connections with high-strength steel components. This research attempted to gain a qualitative

understanding of the influence of the material properties on the response of three types of semi-rigid

connections: flush end-plate, top and seat angle and top and seat with double web angles. Hence, ABAQUS

(v.6.17) software was used to develop three-dimensional (3-D) FE models. The FE models with different

parameters drawn from previous experimental studies were generated in order to evaluate the effectiveness of

this approach. Issues related to the stiffness, strength, sources of deformability, rotational capacity and failure

mechanisms of joints were emphasized. In most cases, the use of HSS angles or HSS end-plate led to significant

increase in moment capacity. Higher initial stiffness values were observed, especially when thick angles and

plates were used. However, a decrease in rotational capacity of HSS joints was encountered.

KEYWORDS: High-strength steel, Finite element analysis, Moment–rotation curve, Flush end-plate, Top and seat angle, Top and seat with double web angles.

INTRODUCTION

The use of high-strength steel (HSS) in construction

has recently provided some challenges to structural

engineers. One such challenge is to minimize the cross-

section dimensions as the material provides higher

strength, which brings great economic benefits. In the

context of the structural Eurocodes, HSS can be defined

as steel with a yield strength over 460 MPa (Wang et al.,

2016). HSS exhibits high yield ratios and limited

deformation capacity when compared to mild steel

grades. This behavior can be particularly important

when structures are designed for abnormal loading

conditions that produce inelastic deformations. In this

situation, both members and connections have to

develop sufficient ductility where the material is

exposed to higher deformation demands.

For the past few decades, extensive research had

been carried out to understand the actual behavior of

semi-rigid connections and to predict connection

moment-rotation behavior by developing and

interrogating an experimental database. Azizinamini

and Radziminski (1989) and Prado et al. (2014)

experimentally evaluated the moment-rotation behavior

of top-seat angle connection with double web angles

(TSACW); Fig.1(a), where simplified models were

proposed to predict the initial stiffness and ultimate

moment. Moreover, Mander et al. (1994) experimentally

studied the behavior of top and seat angle connections Received on 3/6/2017. Accepted for Publication on 6/2/2018.


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(Fig.1 (b)). The experimental results showed that failure

mode, plastic moment capacity and initial stiffness are

very sensitive to how the bolts are oriented and

tightened. On the other hand, Garlock et al. (2003)

aimed at determining how the angle size and bolt gage

length affect the connection stiffness, strength, energy

dissipation capacity of the connection and resistance to

low-cycle fatigue. It was observed that the top and seat

angle connections are capable of exhibiting considerable

strength even after the formation of the yield

mechanism. Flush end-plate connections (Fig.1(c)) have

been tested by Ostrander (1970), where the effect of

geometrical parameters on the connection response was

determined. In addition, Borgsmiller and Murray (1995)

performed experiments on flush , extended stiffened,

extended unstiffened and multi-row extended end-plate

moment connections. They proposed a simplified

method for design of end-plate moment connections

based on two limit states; end-plate yielding and bolt

rupture.

Figure (1): Size parameters for: (a) top- and seat-angle connection with double web-angle, (b) top- and seat-angle connection and (c) flush end-plate connection (Chen, 2011)

(a) (b)

(c)

Numerical Investigation… Hashem Al Hendi and Mohammad Adeeb Mahmoud

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The Finite Element (FE) method is a widely used

numerical method for analyzing structural steel joints

and is also a convenient supplementary method for

obtaining extensive data. It can be used for parametric

studies and investigation of important local effects that

are usually difficult to capture in experiments (Díaz et

al., 2011). Numerical modelling by finite element

analysis of beam-column connections has been carried

out by many researchers. For instance, Citipitioglu et al.

(2002) and Ahmed et al. (2001) proposed a model to

simulate the top and seat angle joint, whereas Kishi et

al. (2001) and Abdalla et al. (2014) studied the moment-

rotation behavior of TSACW using FEM. Taufik and

Xiao (2005) have studied the behavior of angle bolted

connection by applying high-strength steel with shell

element model.

There is very little information about the beam-

column bolted connection with high-strength steel. The

most relevant to this research is the work done by Puthli

et al. (2001) and Moze et al. (2006). They only studied

the effect of HSS by testing simple bolted connections.

Most of the work done is about HSS column members

(Gao et al., 2009; Girão Coelho, Bijlaard and Kolstein,

2009; Shi, Ban and Bijlaard, 2012; Ban et al., 2013;

Wang et al., 2014; Yu et al., 2017). Nevertheless, there

is still need for further investigation of the HSS

connection behavior. Therefore, finite element modeling

was used to carry out the parametric studies based on

computer simulation in this paper.

The main objective of this study is to capture and

monitor the effect of the material properties on the

behavior of three types of semi-rigid connections: flush

end-plate, top and seat angle and top and seat with

double web angles. This study presents a detailed three-

dimensional (3D) approach for the analysis of bolted

connections. Models with different parameters drawn

from previous experimental studies were generated in

order to evaluate the effectiveness of this approach.

Issues related to stiffness, ductility, strength and

rotational capacity were studied by constructing and

analyzing the moment- rotation relationships for the

previously mentioned connections. Also, sources of

deformability and failure mechanisms are illustrated for

each studied case.

This paper is a basic step towards establishing the

requirements for the design of HSS semi-rigid

connections and is also trying to contribute to the

development of a simple and accurate moment-rotation

(M-) relationship for the purpose of structural design

and elastic-plastic analysis.

METHODOLOGY OF FINITE ELEMENT

MODELING

Displacement-based 3D finite element (FE) models

are used to predict the behavior of semi-rigid

connections. Explicit FEA package ABAQUS is used to

establish geometry and mesh and to carry out the 3D FE

analysis. The tests on top and seat with double web

angles, top and seat angle and flush end-plate

connections conducted by Azizinamini and Radziminski

(1989), Mander (1994) and Ostrander (1970) ,

respectively, were used to verify the finite element

model presented in this study. The size parameters of the

test connections were reported by Chen (2011) and

given in Tables 1-3. The simulation methodology is

summarized as follows:

The connection components were modelled by using

the solid element C3D8R available in the element

library of ABAQUS (Díaz et al., 2011), since it is

precise in the constitutive law integration, suitable

for plasticity problems and appropriate for finite

strain and rotation in large displacement analysis

(Kishi et al., 2001). For the 3-D FE models, material

and geometric non-linearities were considered to

obtain the large deformation and local instability

effects.

Half of the connection was modelled due to

symmetry and the boundary conditions of the FE

models were in line with those arrangements of the

test specimens.


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Table 1. Tested specimens by Azizinamini and Radziminski (1989)

Table 2. Tested specimens by J.B. Mander et al. (1994)

Table 3. Tested specimens by Ostrander (1970)

Quadlinear stress–strain curves (Yun and Gardner,

2017) (Fig. 2(a)) were used for modelling the joint

material behavior. This model could successfully

predict the behavior of hot-rolled carbon steels with

a yield plateau over the full strain range up to εu.

However, it is only suitable for certain steel grades

Specimen Column Beam Angle BoltsSection Section Section nbeam ncolumn14S4 W12X96 W14X38 Top Angle lt tt gt gt’ qt rt ptL 6 X 4 X 3/8 292 83 83 10 89 53 32 2 X 2 2 X 1Bottom Angle ls ts gs gs’ qs rs psL 6 X 4 X 3/8 203 10 89 64 89 140 64 2 X 2 2 X 1Web Angle lP lu ll ta gb gc cu cl pb pcL 4 X 3.5 X 3/8 216 71 71 10 51 66 32 32 76 76 1 X 3 1 X 3 8S1 W12X58 W8X21 Top Angle lt tt gt gt’ qt rt ptL 6 X 3.5 X 5/16 152 8 89 51 70 89 64 2 X 2 2 X 1Bottom Angle ls ts gs gs’ qs rs psL 6 X 3.5 X 5/16 152 8 89 51 70 89 64 2 X 2 2 X 1Web Angle lP lu ll ta gb gc cu cl pb pcL 4 X 3.5 X 1/4 140 35 35 6 51 67 32 32 76 76 1 X 2 1 X 214S6 W12X96 W14X38 Top Angle lt tt gt gt’ qt rt ptL 6 X 4 X 1/2 203 13 89 64 89 140 64 2 X 2 2 X 1Bottom Angle ls ts gs gs’ qs rs psL 6 X 4 X 1/2 203 13 89 64 89 140 64 2 X 2 2 X 1Web Angle lP lu ll ta gb gc cu cl pb pcL 4 X 3.5 X 1/4 216 71 71 6 51 66 32 32 76 76 1 X 3 1 X 3 Specimen Column Beam Angle BoltsSection Section Section nbeam ncolumnR1_01 W8X31 W8X21 Top Angle lt tt gt gt’ qt rt ptL 6 X 4 X 3/8 165 10 92 51 64 89 60 2 X 2 2 X 1Bottom Angle ls ts gs gs’ qs rs psL 6 X 4 X 3/8 165 10 92 51 64 89 60 2 X 2 2 X 1No.1 H250X250X9X14 H250X125X6X9 Top Angle lt tt gt gt’ qt rt ptL 100X100X10 145 9 59 59 71 85 0 2 X 1 2 X 1Bottom Angle ls ts gs gs’ qs rs psL 100X100X10 145 9 59 59 71 85 0 2 X 1 2 X 1No.3 H150X150X7X10 H250X125X6X9 Top Angle lt tt gt gt’ qt rt ptL 100X100X10 145 9 61 61 72 85 0 2 X 1 2 X 1Bottom Angle ls ts gs gs’ qs rs psL 100X100X10 145 9 61 61 72 85 0 2 X 1 2 X 1Specimen Column Beam End-plate BoltsSection Section Thicknessgc gt tp dp ct cc pt ll pc lp nt ncTest 5 W8X28 W10X21 12.7 89 89 13 19 13 13 64 127 64 279.4 2 X 1 2 X 1Test 6 W8X28 W10X21 9.5 89 89 10 19 13 13 64 127 64 279.4 2 X 1 2 X 1Test 7 W8X28 W10X21 6.4 89 89 6 19 13 13 64 127 64 279.4 2 X 1 2 X 1


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as given in Table 4. For bolt materials, a proposed

model by Mohamadi-Shooreh and Mofid (2008) was

adopted in this study (Fig. 2(b)). For S690 high-

strength steel, different curves from different studies

(Shi, Zhu and Ban, 2016; H.C. Ho, X. Liu, K.F.

Chung et al., 2017; Qiang et al., 2017) were obtained

and idealized into a single curve that represents all

the obtained data. The isotropic elastic-plastic multi-

linear properties combined with the von Mises yield

criterion was used for the representation of material

non-linearity effects. The classical metal plasticity

model in ABAQUS (Díaz et al., 2011) was used to

define the non-linear behavior of materials. The

nominal stress and nominal strain in the stress–strain

curve of the coupon tests were converted into the

multi-linear curve of true stress () and true plastic

strain (pl). The *ELASTIC and *PLASTIC options

were used to assign the value of Young’s modulus

and the Poisson’s ratio and to define the plastic part

of the stress–strain curve, respectively.

The contact interaction of the connection

components was defined as surface-to-surface

contact, with a small sliding option. ‘Hard contact’

was used for the normal contact behavior with a

friction coefficient of 0.33 in the tangential direction.

The contact pairs between the bolt shank-to-bolt

holes, bolt head-to-components, nuts-to-

components, angles and plates-to-beams and

columns (Fig. 3) were assigned.

Table 4. Steel grades and material properties implemented for Yun (2017) model

Figure (2): Idealized material behavior used in the FEM analysis for: (a) all parts (Yun and Gardner, 2017) and

(b) high-strength bolts (Mohamadi-Shooreh and Mofid, 2008)

Steel Grade E (N/mm²) Fy (N/mm²) Fu (N/mm²) ɛy(%) ɛsh(%) ɛu(%) ɛsh/ɛy Esh (N/mm²) C1S235 210000 235 360 0.11 1.50 20.83 13.40 1616.00 0.33S275 210000 275 430 0.13 1.50 21.63 11.50 1925.00 0.35S355 210000 355 490 0.17 1.74 16.53 10.30 2283.00 0.38S450 210000 440 550 0.21 2.50 12.00 11.90 2895.00 0.41

u

u

Esh

Et

Strain

E

y

y

uu Pshy y

(a) (b)

EPc1u

Cu Cu

StressStress

Strain


- 563 -

Figure (3): The contact pairs between connection components

The tie constraints (Díaz et al., 2011) were applied

to all nodal degrees of freedom along the weld lines

of the flush end-plate to beam. In order to prevent the

local deformation of the beam under concentrated

force, the end of the beam cross-section was coupled

through coupling constraint to the load application

point. No pre-stressing to the bolts was considered.

The following parameters were used for the

generation of the FE mesh; net = 3 (the number of

elements through the thickness), len =7 mm and lef =

25 mm (the length of elements close to the

connection and far from the connection,

respectively). The mesh density for critical zones of

the connections is shown in Fig. 4.

The general-purpose finite element explicit solver,

ABAQUS/ Standard (Díaz et al., 2011) is capable of

handling complicated contact problems as well as

models with large rotations and large deformations

without generating numerical convergence

difficulties. The 3D-FE analysis was continued until

the ratio of the kinetic energy to the internal energy

increased to more than 10% or the reaction force at

the support suddenly dropped (Yu et al., 2008).

Figure (4): The FE mesh density for TSACW

The verification of the semi-rigid FE model

developed in this study was carried out by comparing its

numerical results with those of related experiments

(Azizinamini and Radziminski, 1989; John Mander,

Chen and Pekcan, 1994; Ostrander, 1970), in terms of

load-displacement characteristics, moment-rotation

characteristics and failure modes of the connections.

The approach of sensitivity analysis suggested by Al-

Hendi and Celikag (2015) was adopted for sensitivity of

mesh size, friction and loading speed. 268 FE joint

models were used for sensitivity analysis, where special

attention was paid to loading duration, in order to ensure

a quasi-static response. The M- curves resulting from

FEM and experiment of 8S1 are clearly illustrated in

Fig. 5 (a). This indicates that the M- curves are almost

in very good agreement with the experimental M-

curves. Furthermore, the M- curves resulting from

FEM and experiment of Test 6 are shown in Fig. 5(b).

Here also, it can be seen that the M- curves resulting

from FE simulation is in very good agreement with the

curve from experiment. Moreover, the predicted failure

mode agrees well with the observed failure modes for all

test specimens.


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Figure (5): Moment-rotation curves from experimental and FE models for: (a) 8S1, (b) test 6

EFFECT OF HSS ON THE RESPONSE OF

TSACW

Higher strength angles are applied to top and seat

connections with double web angles by Azizinamini and

Radziminski (1989), where the angles are determined

using S690 high-strength steel grade. The response to

the material change was not consistent through all

models. The moment-rotation comparison for joints

14S6 and 8S1with S275 and S690 is given in Fig. 6.

Model 14S6 with S690 showed a large increase in initial

stiffness and moment capacity. However, a large drop of

the rotational capacity was experienced compared to

S275 steel grade (Fig. 6(a)). Model 8S1 with S690

compared with S275, however, showed a drop in initial

stiffness value, which clarifies the effect of different

angle thicknesses on the overall response of the

connection. Moreover, a higher moment capacity was

achieved by changing the material to S690 HSS

(Fig. 6 (b)). The von Mises stress distribution for 14S6

joint is illustrated in Fig. 7. The deformation at the

ultimate state of both connections considered is similar

and the main differences are observed by comparing the

curve behaviors.

EFFECT OF HSS ON TOP- AND SEAT-ANGLE

CONNECTION

Von Mises stress distributions of top and bottom

seat-joints of N1 and N3 prior to failure show no effect

of HSS on the failure mode of these tests. For R1 test,

the failure (Fig. 8) was shifted from the bolt hole to the

legs of the top and bottom angles.

EFFECT OF HSS ON FLUSH END-PLATE

CONNECTION

Material effect was studied through moment rotation

relationships obtained by FEA. Materials studied

include S355, S450 and S690 HSS. There was no or little

effect of the studied materials on the initial stiffness of

the steel grade compared to S275 mild steel. The S690

HSS has a noticeable effect on the moment capacity of

the connections. The effects discussed are shown in Fig.

9. Deformed shape plots in Fig. 10 show a difference in

failure modes of HSS connections compared to S275

mild steel connections for test 6. The failure of end-plate

occurs for S275, but the failure was shifted to the tension

side bolt when HSS is introduced. However, test 7

shows failure of the end plate for S275 mild steel grade,

0

10

20

30

40

50

0 0.01 0.02 0.03 0.04 0.05

Mom

ent (

kN.m

)

Rotation (rad)

8S1 Experiment8S1 FEM

(a) (b)

0

20

40

60

80

0 0.02 0.04 0.06 0.08

Mom

ent (

kN.m

)

Rotation (rad)

Test 6 ExperimentTest 6 FEM


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while HSS connection exhibited a more uniform stress distribution through end-plate and bolts.

(a) (b) Figure (6): Moment-rotation curves from FE models for: (a)14S6 with S275 and S690,

(b) 8S1 with S275 and S690

(a)

(b)

Figure (7): Von Mises stress distributions of top and seat with double web angles-14S6 joints prior to failure: (a) S275, (b) S690


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(a)

(b)

Figure (8): Von Mises stress distributions of top and bottom seat- R1 joints prior to failure: (a) S275, (b) S690

Figure (9): Moment-rotation curves from FE models for test 7 with S275, S355, S450 and S690

0

10

20

30

40

50

0 0.01 0.02 0.03 0.04 0.05

Mom

ent (

kN.m

)

Rotation (rad)

FEM-Test 7-S275FEM-Test 7-S355FEM-Test 7-S450FEM-Test 7-S690


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(a)

(b)

Figure (10): Von Mises stress distributions of end-plate-test 6 joints prior to failure: (a) S275, (b) S690

CONCLUSIONS

Past research indicates promising results for semi-

rigid connections, since they have good potential to

achieve sufficient strength and ductility. Therefore,

there is a need to develop a moment-rotation (M-)

model for the purpose of structural design and elastic-

plastic analysis. This paper aimed at finding the effects

of the material properties on the response of three types

of semi-rigid connections: flush end-plate, top and seat

angle and top and seat with double web angles. High-

strength angles and end-plates were used to capture the

effects on the moment-rotation (M-) characteristics of

these connections under monotonic loading. The

following conclusions are drawn based on the findings

of the study:

1. The initial stiffness of the FE model is well

predicted, as determined by verification through

comparison with previous experimental results. A

less pronounced effect of higher yield stress on the

initial stiffness of the connection is demonstrated.

Angles that are thicker and higher in strength are

associated with larger values of initial stiffness and

moment capacity.

2. The plastic strain and stress patterns of high-strength

web angle are generally very similar, like those of


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high-strength top and seat angles. The model

presented gives excellent results for significantly

increasing the moment and rotational capacity.

3. The high-strength angles contribute a significant

proportion of the maximum stress distribution, when

the beam and column are formed of mild carbon steel

allowing for an increase in the ultimate moment

capacity.

4. The high-strength end-plate gives significant

proportion of maximum stress distribution, whereas

the beam and column are kept to mild carbon steel.

5. It can be observed that, if the thickness of end-plate

is higher than the thickness of column flange, the

moment capacity of the connection will not be

increased clearly due to excessive deformation of

column flange and web.

6. Thick high-strength end-plate and angled

connections provide additional rotational stiffness

and moment capacity, but the rotation capacity may

be compromised by bolt failure. This type of failure

mode is not acceptable for semi-rigid frame design,

because a large rotation capacity is required to allow

moment re-distribution.

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Documents

Numerical Investigation on the Moment-Rotation Relationship ...Numerical Investigation… Hashem Al Hendi and Mohammad Adeeb Mahmoud - 560 - The Finite Element (FE) method is a widely