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the connections are either fully rigid or ideally pinned. In reality, many “rigid” connections in

Conventional analysis and design of steel framework are performed using the assumption that

2. Semi-rigid design of steel frames

nd top seat-angle connection.namely endplate connection a

equations. The present study addresses the FE modeling aspects of two types of connectionsused for a number of studies and the numerical results can be used in assessing the design

ABAQUS model of the problem is validated with the test results, the validated model can be

problem has been overcome using ABAQUS, a general purpose FE software. Once anmoment-rotation curves with varying input parameters, which is quite expensive. The above

model requires a number of experimental investigations to obtainformulation of M-

) model. Thecolumn connections and to formulate the appropriate moment-rotation (M-semi-rigid frames, it is necessary to know the moment-rotation behaviour of actual beam-to-

behaviour of semi-rigid steel bolted connections. To establish the guidelines for the design of

One of the aspects under active research in the area of steel structures is the moment-rotation

1. Introduction

Morris model.

Key words: Beam-to-column connections, Moment-Rotation curves, Semi-Rigid design, Frye-

of high precision finite element models.

revision of design code equations. The present paper also brings out the economic advantage

connection behaviour. Based on such parametric studies, suggestions have been made for the

number of expensive experiments by varying the most influencing parameters that affect the

steel beam-to-column connection test results, the calibrated FE model can be used to mimic

characterization. Once an ABAQUS finite element model of a connection is calibrated with

several features which are readily applicable to the present problem of connection

present paper considers a couple of case studies on steel semi-rigid connection. ABAQUS has

rpose finite element analysis program. Thesimplified with the use of ABAQUS, a general puexperiments is a compulsion for the research to progress. The problem gets enormously

experiments is costly, time consuming and hence uneconomical. On the other hand conducting

continuous process and requires a wide range of experimental studies. Performing number of

Engineering, development of structural design code equations or redeveloping them is a

become a practical tool for engineering analysis and design. In the realm of Structural

ABSTRACT: With the advances in modern computing techniques, finite element analysis has

113.

* Scientists, Structural Engineering Research Centre, CSIR campus, Taramani, Chennai - 600

and V. Marimuthu, S. Arul Jayachandran, S. SeetharamanP. Prabha

MIMICKING EXPENSIVE EXPERIMENTS BY

1

ABAQUS* * * *

θr

θr

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economic advantage for the building contractors and designers.

connections, thereby providing an economic benefit. Semi-rigidities in joints offer a great

rigid connections may facilitate reduction of high-restraint (fixed) moments in rigidleads to simpler, reliable designs and economies in construction [Maggi et al. (2005)]. Semi-

being flexible or semi–rigid (Figure 1). Consideration of real behaviour of the connections

accurate analysis of such structures is desired, it is necessary to consider the connections as

most “pinned” connections offer a small amount of restraint against rotation. Thus, if a more

steel structures permit a certain amount of rotation to take place within the connections, and

2

welded to the beam cross-section and bolted by three rows (one row in compression and two

The test set-up (Figure 2) of endplate connection (Vengadeswaran, 2006) consisting of a plate

4. Experimental Study

studies by systematically varying the parameters.

briefly explains how a numerical model in ABAQUS can be used to carry out parametrictype of connections the number of tests required is a large number. The following section

Normally for a simple connection it requires a minimum of ten tests. Likewise for all the eight

parameters and five for complex connections. Each size parameter needs atleast three tests.systematic change of parameters. Each simple connection has atleast two or three size

in the literature cannot be used to modify the polynomial model as they may not involve

all the other size parameters are kept constant. Hence many of the experimental work reported

number of experimental or numerical parametric studies by varying one size parameter while

rred, that the Frye-Morris model (1975) needs astiffness. From a literature review it is infeStudies show that this analytical model overestimates or underestimates the connection

analytical model is developed by incorporating only few test results, long back in 1975.

typified connections. The problem with the original Frye and Morris model is that theanalytical model (Frye-Morris model, 1975) to predict the moment-rotation behaviour of eight

for the semi rigid design of steel frames. The new IS: 800 (2006) code has suggested an

for steel design. Indian code has made a good attempt to implement a simple design procedure

Explicit formulae for semi-rigid design are generally not presented in many codes of practice

Code IS: 8003. Impediments to the codification of semi-rigid design provisions in Indian

Figure 1. Types of Connections

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Figure 2. Endplate connection

experimental behaviour of the connections.

2007) is carried out using the ABAQUS software (Hibbit et al., 2006) to simulate the

Finite element analysis of endplate connection and top and seat-angle connection (Prabha,

5. Finite element analysis

effected through a central load over the stub column.the bolts are pretensioned as they are high strength friction grip bolts. The load application isconnected to the central stub column formed a typical beam with simply supported ends. All

angles bolted to the beam and column flanges. The overall specimen with two beams

The set-up of top and seat-angle connection (Figure 3) (Raman, 2005) consists of top and seat

rows in tension) of pre-tensioned high strength bolts to the flanges of a central stub column.

3

Figure 3. Top and seat-angle connection

ISMB: 300

ISMB: 300

Stiffener of 8 mm

thick

910 910

HSFG bolts8.8 grade16 mm Φ

ISMB: 300 9 5 0

All dimensions are in mm

HingeRoller

Top angle

Seat angle

Bolt pretension

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bending (Figure 4).

angles and the column flange are discretized across the thickness to consider the effect of direction. As the solid elements do not have rotational degree of freedom, the end-plate,

This element has three degrees of freedom at each node, translations in the nodal x, y, & z

refers to continuum three dimensional 8-noded brick element with reduced order integration.the connecting members including the bolts were modeled using the element C3D8R which

The experimental connection set-up includes beams, stub column, plates, angles and bolts. All

5.1 Finite element modeling

4

end-plate was assumed to be rigid. Frictional (value = 0.3) contact using penalty stiffness but could undergo arbitrary rotation of the bodies. The connection between the beam and the

was considered for all the contacts in the connection which assumed relatively small sliding,

the members caused by pre-tensioning of the bolts. Small sliding surface-to-surface contact

connections. The forces are transferred through friction due to the clamping action betweenfriction grip bolts and the friction between the components are the critical parameters in bolted

on the performance of the connection and its response. The pre-tension of the high strength

Representation of the contacts (Figure 5 and Figure 6) between components has a major effect

5.3 Contact modeling and boundary conditions

in ABAQUS.

et al., 2005) was applied at the center section of the bolt using the pretension option availablestrain considered was 0.12. A pretension force of about 0.7 times the bolt yield stress (Maggi

tensile stresses considered for the bolts were 640 and 800 MPa respectively. The ultimate

High strength friction grip bolts (8.8 grade) were used in this study. The yield and ultimate

were considered as 250 and 420 MPa respectively. The ultimate strain considered was 0.23.

The yield and ultimate tensile stresses for the beams, column end-plate and top seat angles

5.2 Material model

discretisation along the thickness directionFigure 4. Finite element mesh of the end-plate connection showing

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accurate solution is obtained efficiently.

for these parameters, it also continually adjusts them during the analysis to ensure that an

appropriate load increments and convergence tolerances. Not only does it choose the valuesanalysis option of ABAQUS, in which for a nonlinear analysis, it automatically chooses

linear, leading to non-convergence of the solution. It is overcome by using the nonlinear

conditions such as contact and friction considered in the study make the problem highly nonload is applied over the stub column. Different types of material properties and boundary

first step, pretensioning forces are applied to all the bolts. In the second step, uniform pressurethe simply supported condition. The load application has been effected in two load steps. In

surfaces. One of the beam ends is supported by a hinge and the other by a roller to simulate

bolt head, bolt shank, whereas the surfaces interfacing master surfaces are defined as slaveMaster surfaces of contact pair options represent the surfaces of column and beam flanges,

beam/column/angles.Lagrange formulation. Hard constraint is used for the connection of bolt head/nut to theconsidered to be frictionless. The normal contact was considered as hard using augmented

angle connection. The tangential contact between the bolt hole and the bolt shank is

flange in endplate connection and between the beam/column with the angles in top and seat-

formulation was considered for the tangential contact between the end-plate and the column

5

Figure 5. Contacts in endplate connection

bolt head/nut to the beam/columnand column flange

(a) Contact between the end-plate (b) Tie constraint between the

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observed in top and seat-angle connection (Figure 10).

9) for endplate connection. The shear of the top angle bolts and the tearing of seat angle are

plate rupture and (ii) bolt rupture were observed in the tests as well as in FEM analysis (Figurefrom the tests for endplate connection is shown in Figure. 8. Two types of failures (i) end-

correlation of moment rotation curves obtained from the ABAQUS model with that obtained

finite element model and the deformed configuration of both the connections. A goodThe finite element model has been validated with the experimental results. Figure 7 shows the

5.4 Comparison of numerical and experimental results

Figure 6. Contacts in top and seat-angle connection

Tie constraintFriction contact Frictionless contact

6

seat-angle connectionFigure 7. FE model and the deformed configuration of endplate and top

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7

Rotation (radians)

M o m e n t ( k N - m )

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

0

20

40

60

80

100

120

Experiment

Figure 8. Comparison of moment-rotation curves

Abaqus model

(a) bolt rupture

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8

Figure 9. Failure modes – endplate connection

(b) End-plate rupture

from the tests within 12% for endplate connection and 0.2% for top and seat angle connection.obtained. The failure loads obtained from FE analysis compare well with the loads obtained

modified curve is shown in Figure 11. With this modification, a very good correlation is

and the closing of the air gap, this displacement is added to the results of the FE model and theto shear. Since it is known that in first stage, the shear of the top bolt causes a displacement

as shown in Figure 11 as the present ABAQUS model could not capture the load shedding due

load distribution. In the case of the FE analysis this phenomenon takes place more graduallyseat angle connection is due to the bolt fracture in the compression side and the subsequent

connection. The flat plateau that is seen in the Figure 11, for the experimental curve of top andFigure 11 show the relation between moment and the relative rotation for top and seat angle

5.5 Modeling Problem

Figure 10. Failure mode – Top and seat-angle connection

(a) Tearing of seat angle

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9

-1.210.48-0.84-1.7connection is given as K = d

and the standardization factor for the top- and seat-angle(Moment kN-m, Parameters in mm)

(2)(KM)+1.70 x 10(KM)(KM)+ 1.80 x 10= 2.76 x 10

The proposed model based on the finite element study has relationship as

-1.1-0.7-1.5connection is given as K = d

and the standardization factor for the top- and seat-angle(Moment kN-m, Parameters in mm)

(1)+3.31x 10(KM)+7.25x 10=1.63X10

Frye-Morris et al. (1975), has given the moment-rotation relationship as

(1975) procedure are given in Equation 1 and Equation 2 respectively.studies a new model is proposed. The old and the proposed model based on Frye-Morrisinput, using the calibrated FE model presented here. Based on the finite element parametric

design. A number of moment-rotation curves are generated with varying size parameters asunderestimates. Therefore it’s necessary to reassess the connection model for an economic

by design code equation for top and seat-angle connection and in some cases it

connection. The literature (Prabha, 2007) shows the overestimation of the connection stiffness

(2006) have suggested an analytical model to predict the behaviour of different types of

Based on a series of parametric studies, the revised IS (Indian Standard) draft: 800 code

6. Assessment of design code equations

curvesFigure 11. Comparison of M-

θr

θr 3 14

(KM)3 23

(KM)5

ta-0.5

la d b

θr 3 11 3 19 5

ta la d b ag0.07

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moment rotation model is found to be more reliable of the actual connection behaviour.model compares better with the experimental result (1947) (Id No: 16). Hence the proposed

shows the underestimation of connection stiffness by Frye-Morris model and the proposed

e proposed model. The comparison (Figure 12)evaluate the Frye-Morris (1975) model and th

The experimental result presented by R.A. Hechtmann et al (1947) (Test id No: 16) is used to

10

such as ABAQUS, costly experimental studies can be simulated and extensive parametric

model are validated by comparing with the experimental results. Thus, using an FE software

connection are discussed and the ABAQUS, FEendplate connection and top and seat anglecolumn connection experimental studies. The modeling aspects of two connections namelyThe paper briefly explains the use of ABAQUS, FE software in mimicking costly steel beam-

8. Conclusion

economy and also time consumption.consuming. With the above said problems, ABAQUS is more advantageous with respect to

tenders and getting at right time with good workmanship is a tedious process and time

connection requires minimum 23 tests. Also, the procurement of steel sections by inviting parameter. Therefore endplate connection requires minimum 9 tests and the top seat-angle

the first connection is 2 and for the second is 4. Atleast three tests are required for each size

Performing experiments on connections involves high cost. The number of size parameters for

7. Cost analysis of the parametric study

and Frye-Morris (1975) model

Figure 12. Comparison of proposed model with experiment (1947)

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Research Centre (SERC), Chennai, India.This paper is published with the kind permission of the Director, Structural Engineering

10. Acknowledgement

M.E Thesis, Thiagarajar college of Engineering, Madurai, 2006.

Vengadeswaran, S, “Investigations on the Behaviour of Semi-Rigid End-plate connections,”

M.E Thesis, Malnad college of Engineering, Hassan, 2005.

Raman, M, “Analytical & Experimental Investigations on Semi-Rigid Steel Connections,”

college of Engineering, Madurai, 2007.Prabha, P, “Finite Element Analysis of Beam-Column connections,” M.E thesis, Thiagarajar

Constructional Steel Research, Vol.61, pp.689-708, 2005.

Steel Bolted End-plate Connections using Finite Element Modeling,” Journal of

nd L.F.L. Rebeiro, “Parametric Analysis of Maggi, Y.I., R.M. Gonclaves., R.T. Leon., a

Standards, New Delhi, 2006.

IS: 800 Draft, Code of Practice for General Construction in Steel, Bureau of Indian

2006.

Hibbit, Karlsson and Sorenson, ABAQUS User’s Manual, Version 6.6. Pawtucket, USA,

Progress Report No. 1, AISC Research at Lehigh University, Bethlehem, PA, 1947.Hechtman, R.A., and B. G. Johnston, Riveted Semi-Rigid Beam-To-Column connections,

Canadian Journal of Civil Engineering, Vol.2, pp.280-291, 1975.

Frye John, M., and Glenn, A. Morris, “Analysis of Flexibility Connected Steel Frame,”

9. References

societal benefits.

studies carried out for the improvement of codal provisions leading to overall economic and

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