Static web moment connections

J. Construct. Steel Research 10 (1988) 8%131

Static Web Moment Connections

W. F. C h e n Department of Structural Engineering, School of Civil Engineering, Purdue University, West Lafayette, Indiana 47907, USA & E. M. L u i Department of Civil Engineering, Syracuse University, Syracuse, New York 13244, USA

ABSTRACT In a web connection, the beam is framed into the column web with the action of the beam moment causing bending of the column about its weak axis. The analysis and design of this type of connection is comparably more difficult than that for flange connections, because the maximum strength of the connection assemblage may be limited by the formation of plastic hinges in the column or in the beam, by the formation of a yield line type of mechanism in the column web, by the development of local buckling of the column flanges and web, and by the fracture of material of the assemblage. This paper primarily deals with these limiting factors with much emphasis in the connection moment and rotation capacities as well as its elastic stiffness under working load.

1 INTRODUCTION In the preceding article, the behavior, test highlights and design recommendations for flange moment connections under monotonically applied loads have been discussed. In this paper, another type of m o m e n t connection referred to as web moment connection will be discussed. A w e b m o m e n t connection is one which connects a beam to the web of the column as depicted in Fig. 1. U n d e r an unbalanced joint moment, the column will b e n d a b o u t its weak axis. 89 J. Construct. Steel Research 0143-974X/88/$03.50 © 1988 Elsevier Science Publishers Ltd, England. Printed in Great Britain

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The analysis and design of this type of connection is comparably more difficult than that for flange connections for the following reasons: (1) Theoretically the maximum strength of the connection assemblage corresponds to the state when plastic hinges form in the column or in the beam. However, for web moment connections there exist other factors that limit this maximum strength. For example, if the beam flanges that are welded to the column web are much narrower than the distance between column fillets, a yield line type of mechanism may form in the column web plate before the formation of plastic hinges in the column or beam. Other limiting factors that prevent the attainment of the plastic limit load based on a simple plastic theory include local buckling of the column flanges and web, and fracture of material of the assemblage. If the loading of the beam and column is such that it exceeds the load required for the formation of a yield line mechanism or local buckling, stiffening of the column must be considered. (2) Even after the connection has been properly designed and detailed, the erection of such assemblage in the field may be arduous because of the space restrictions imposed by the column flanges. This paper will deal primarily with the first consideration. Emphasis will be placed on the strength and rotation capacity of the connection as well as its elastic stiffness under working load. Although web connections are used quite often today in steel frames, a thorough knowledge of their behavior remains relatively unknown. Questions often posed are: 1. Can the connection attain its plastic limit load without premature failure? 2. Can the connection exhibit enough ductility to permit moment redistribution? 3. Does it have sufficient elastic stiffness under working loads? 4. What criteria govern the need for providing stiffeners for the column? 5. What are the limiting factors that a designer should be aware of? 6. What effect does column axial load have on the performance of such connections? 7. What connection media (welding, bolting, or a combination of both) should be used? 8. If welding is used, how should the beam flange or beam flange connection plates be connected to the column? Should they be welded to the column flanges or would merely welding to the column web be sufficient?

92

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To answer these questions, a systematic study of these web connections, both theoretically and experimentally, is imperative. The purpose of this paper is to investigate and discuss the behavior of some specific beam-tocolumn web connections. Theoretical analyses using simple plastic theory, yield line theory and finite element method will be presented. The results of these theoretical predictions will be checked against experimental results based on full-scale connection tests carried out at Lehigh University. 1

2 BACKGROUND Previous research on web beam-to-column moment connections is scanty. Static testing of early web connections under symmetric loading was reported by Graham e t al. 2 in which four-way beam-to-column m o m e n t connection tests were conducted. Research on unsymmetric web connections under repeated and reversed loading was reported by Popov and Pinkney. 3 Additional tests on web connection assemblages under cyclic loading were also reported. 4'5 Because of the lack of full-scale testing conducted on such connections, the understanding of these web connections is very limited. In order to acquire a better knowledge on the behavior of web m o m e n t connections, a testing program of these moment-resisting steel beam-to-column web connections was initiated at Lehigh University 6 in the mid seventies under the guidance of the American Iron and Steel Institute and the Welding Research Council. The main aim of this program is to provide theoretical predictions and experimental results on web moment connections under static loading using welding, bolting and a combination of welding and bolting as connection media. The experimental study of web moment connections was divided into two distinct phases of activity: (1) pilot test program; and (2) full scale test program. A brief description of these programs is given as follows. A comprehensive report on these types of connection tests is given elsewhere, v.8

3 PILOT TEST P R O G R A M The pilot test program consists of a series of preliminary tests to investigate the column web strength, column web behavior and failure modes of simulated web connections under the action of beam moment. Instead of using a W-section for the beam, two moment plates simulating the tension and compression flanges of a beam were used. These plates were welded to column sections using four different attachment details (Figs 2 and 3). A

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compressive force was loaded on one plate and a tensile force was loaded on the other to simulate the bending moment of a beam acted upon the column. The aim of these pilot tests was to provide the necessary criteria such as m e m b e r sizes, connection geometry and stiffener requirements for the design of full-scale specimens. Additional objectives of these tests were: 1. To study the behavior and ultimate strength of the column web under the action of concentrated flange forces representing the beam moment. 2. To study different methods of attaching the beam flanges to the column web. 3. To study the stiffener requirements on the side of the column opposite the beam. The test setup for the pilot tests is shown in Fig. 4. The column was placed horizontally on two supports and loaded at two points by means of a spreader beam. The two supports are the compression plates of each

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representative of a typical lower story of a multi-story building. For each column section, four different geometries of attaching the simulated flange plates were employed. These geometries are shown in Figs 2 and 3. The thickness of the plates were designed so that the theoretical ultimate load could be reached without yielding of the plates. The theoretical ultimate load is the load at which plastic hinges are formed in the column. The two column shapes and the plates attached to them were made of A572 Grade 50 steel. The purpose of Test A was to simulate a narrow beam flange plate so that the bending of the column web could be observed as well as the pattern and associated strength of any yield line mechanism which might occur. As the beam flange width increases, a point is reached at which bending of the web is not predominant and the yield line mechanism theoretically cannot form. Test B was such a case that the flange plate spans the distance between the column fillets so that a column web yield line mechanism cannot form. The intent of this test was to see whether the maximum plastic hinge load could be attained or whether shear punch of the column web would occur at a lower load level. Tests C and D simulate the case of a beam flange plate having a width equal to the clear distance between column flanges. These tests represent the case where a beam flange is so wide that the use of a narrower flange connection plate is necessary to connect the beam flanges to the column web. Test C had the flange plate fillet welded to the column web and flanges whereas Test D had the flange plate fillet welded to the column flanges only. Because of space restrictions, a detailed discussion of these pilot tests will not be attempted here. Interested readers should refer to the papers by Chen and Rentschler9 and Rentschler et al. 1o for a thorough discussion of the tests. Some important observations which are useful to guide the design of full-scale specimens are given here as follows: 1. For Test A in which the flange plates were groove welded to a narrow portion of the column web, a yield line type of mechanism could not be developed in the column web because of fracture of column web material at the ends of the tension plates. 2. For Test B in which the flange plates were groove welded to the full width of the column web, the theoretical plastic hinge mechanism of the column could not be attained because of fracture of column web material at the ends of the tension plates. 3. For Tests A and B, out-of-plane deformations of column flanges and web were quite significant. These deformations, if coupled by high axial forces in the column, may cause local buckling. No significant out-of-plane deformations of the column flanges and web were observed for Tests C and D.

Static web moment connections

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4. For Test C in which the flange plates were fillet welded to the column flanges and web, and Test D in which the flange plates were fillet welded to the column flanges only, sufficient elastic stiffness and adequate strength were observed. No premature failure occurred but check against possible shear yielding of the flange plate adjacent to the flange weld should be made. The load-deflection behavior of Tests C and D was very similar. This is attributed to the fact that only a small portion of plate force" was carried by the column web. A significant portion (90%) of the plate force was carded by the column flanges.

4 FULL-SCALE TEST PROGRAM Following the pilot test program was the design and test of four full-scale web moment connections. The test set-up for the full-scale specimens is shown in Fig. 1. Each assemblage consists of an 18-ft (5.5 m) long column and a beam approximately 5-ft (1.5 m) long framed into one side of the column web at mid-height. These tests were designed for unsymmetrical loads because it was felt that this loading would be more critical than the symmetrically loaded case. It should be noted from Fig. 1 that the column is subjected to an axial force and the connection is subjected to the combined action of shear and bending moment. It is the objective of this study to investigate the behavior of the connection under these severe loading conditions. Four full-scale specimens using welds, bolts and a combination of welds and bolts were designed according to the AISC Specification (1969). The connections were proportioned to resist the moment and shear generated by the full factored load. Since the loading condition resembled a gravity type of loading (dead load plus live load), the load factor used was 1.7. Thus, the stresses used in proportioning welds, shear plates, and top and bottom moment plates were then equal to 1-7 times those given in Section 1.5--Allowable Stresses of the AISC Specification (1969) (see AISC Manual~2). For the full-scale specimens, the column size used was W14 × 246 and the beam section used was W27 × 94. These sections were chosen to simulate actual beam-to-column web connections in a multi-story steel frame. The length of the column was 18 ft (5.5 m). The beam lengths (measured from point of application of load to centerline of column web) varied for the four specimens. Each connection was designed to resist Mp (Mp = plastic moment capacity of the section) and approximately 0-81 Vp (V~ = beam load required to cause shear yielding of the beam web) at the beam-tocolumn juncture.

98

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The specimens were fabricated using ASTM A572 Grade 50 steel. This steel was selected because of its availability at the time of the tests. In addition, there is a narrower margin between the yield and ultimate stresses than for lower strength steels. Thus, if the connection behavior is adequate for A572 steel, the results could be assumed to apply to lower grade steels. In connections in which some of the elements were bolted, ASTM A490 bolts designed as bearing-type connection having an allowable stress of 40 ksi (276 MN/m 2) were used. Standard holes having a diameter of (1.6 mm) larger than the bolt diameter were used. The bolts were installed by the turn-of-nut method. A hardened washer was used under the element (nut or bolt head). Joint surfaces and nut rotation from snug tight condition were in accordance with the AISC provisions. In connections in which the elements were welded, E70XX low hydrogen electrodes are used. In determining the size of fillet weld, the design shear stress on the effective throat was 1.7 times 21 ksi (145 MN/m2). Defects were checked by ultrasonic methods before load testing. Procedures for welding followed those outlined in the AWS code. 13 The four specimens were designated as 14-1, 14-2, 14-3 and 14-4. Specimens 14-1 and 14-2 are flange-welded web-bolted connections, Specimen 14-3 is a fully-bolted connection and Specimen 14-4 is a fully-welded connection.

5 B E H A V I O R AND TEST H I G H L I G H T S OF T H E FULLY-WELDED CONNECTION

The connection detail for the fully-welded specimen 14-4 is shown in Fig. 5. The beam flanges were connected to the column by means of flange m o m e n t plates. These plates, equal in thickness to the beam flanges, were fillet welded to the column flanges and web. The beam flanges were groove welded to these m o m e n t plates. The beam web was groove welded to the shear plate to transfer beam shear. The web shear plate was fillet welded to both the column web and flange moment plates. The beam web was welded to the web shear plate after being held in position by three ~ in (19 mm) A307 erection bolts. The critical section for this connection is at the column flange tips with a beam span (distance between point of application of load and centerline of column) length of 56 in (1422 mm). The purpose of this test was to provide a control against which the behavior of other specimens can be compared. Figure 6 shows the load-deflection behavior of this connection. This connection exhibits a linear elastic slope up to a beam load of approximately 150 kips (667 kN) after which the stiffness starts to reduce due to local

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Static web m o m e n t connections

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yielding in the assemblage. The testing was terminated when large beam deflection and other deformations due to local buckling were observed. The load started to fall off from its peak value due to out-of-plane deformation of the beam compression flange and the vertical web connection plate. The beam deflection at the end of testing was 3.22 in (82 mm). A photo showing Connection 14-4 at the conclusion of the test is shown in Fig. 7. During the test vertical cracks were noted in the area of the groove weld connecting the tension flange to the flange moment plate in the region where the flange widened to a width equal to the distance between the inside faces of the column flanges. These cracks when first noticed were of a length equal to ~ of the plate thicknesses and grew to a length equal to about :-',of the plate thickness. These cracks also extended laterally across the flange for approximately ~ in (13 mm) along the back-up bar adjacent to the beam flange groove weld. From the load-deflection (V-A) curve, it is concluded that this connection possesses the necessary strength, ductility and stiffness required for a m o m e n t connection in a plastically designed structure. A more detailed discussion of this connection is given elsewhere. 81° This fully-welded connection is considered to be adequately designed because it has sufficient strength and ductility. It also exhibits a linear elastic stiffness until local yielding and buckling occur in the subassemblage element resulting in a reduction in stiffness. The maximum test load attained is above the predicted plastic moment load if this load is evaluated at the column centerline. Although cracks are observed at the weld of the tension flange, no failure due to fracture is observed. Stiffening is not required for this connection since the column web deformation is not significant.

6 B E H A V I O R AND TEST H I G H L I G H T S OF T H E F L A N G E - W E L D E D WEB-BOLTED CONNECTIONS In the full-scale test program, two connections were designed as flangewelded web-bolted connections. They were designated as 14-1 and 14-2, respectively. In these connections, beam shear is carried by high-strength bolts rather than by welds as in Connection 14-4. Connection 14-1 is shown in Fig. 8. The beam flanges were groove welded to the flange m o m e n t plates which in turn were fillet welded to the column flanges and web. A one-sided shear plate bolted with seven ~ in (22 mm) diameter A490 bolts was used to resist beam shear. This shear plate was fillet welded to both the column web and flange moment plates. Round holes ~ in (1.6 ram) greater than the bolt diameter were used in the web plate and beam web. The flange moment plates were ~ in (19 mm) thick which is the

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thickness of the beam flanges. The web shear plate is ~ in (13 mm) thick, which is the beam web thickness. The critical section for this connection is at the column flange approximately 8 in (203 mm) from the centerline of the column web. Thus, the beam span is about 56 in (1-4 m) long. Specimen 14-2 is shown in Fig. 9. The beam flanges were groove welded directly to the column web. The beam web was connected to the column web by means of two structural angles which are fillet welded to the beam web and bolted to the column web by eight q in (19 mm) diameter A490 bolts. The angles are 3~ in x 3½in x ~-in (89 mm x 89 mm x 9.5 mm) and the holes " (21 mm) diameter. The critical section for this connection is at the are ~':~ in centerline of the column giving a beam span equal to the length of beam of 48 in (1.2 m). The purpose of Test 14-1 was to examine the connection behavior when beam flanges are welded to flange moment plates and beam web is bolted to shear plate. The purpose of Test 14-2 was to examine connection behavior when both the beam flanges and beam web are connected to the column web directly by wdlding and bolting, respectively. Figure 10 shows the load-deflection curve for Test 14-1. The connection exhibits a linear elastic slope until at approximately 150 kips (667 kN) when the effect of yielding causes a reduction in stiffness. The maximum test load attained was 273 kips (1214 kN) when failure occurred. Failure of this specimen was due to tearing of the entire width of the tension flange moment plate in the region of the transverse groove weld as shown in Fig. 11. Failure was instantaneous with no early warning of tearing prior to the last load increment. Because of this instantaneous failure, the beam load dropped to zero immediately at failure with no opportunity to trace the unloading curve for the connection. The load-deflection curve for Test 14-2 is shown in Fig. 12. The curve shows a definite linear elastic slope up to a load of about 100 kips (445 kN). Then a reduction in stiffness was observed when local yielding of the assemblage elements occurs. Yielding and out-of-plane deformation of the column web was the primary cause of the non-linear behavior of the V-A curve. The maximum test load for this specimen is 205 kips (912 kN). The failure of this specimen was indicated by two related events. First, at a beam load of 195 kips (867 kN), the column web fractured on one side of the beam tension flange where the beam was welded to the column web. The fracture did not completely penetrate the column web but caused a redistribution of stress in the beam tension flange. The fracture caused an increase in stress (and strain) on the portion of the beam still intact with the column web. Ultimate failure then occurred at a load of 205 kips (912 kN) when the portion of weld still connecting the beam flange to the column web fractured. Since failure was not instantaneous, the load did not drop

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off immediately, but no further loading was attempted. Figures 13 and 14 show respectively the fracture in the region of the beam flange-to-column web groove weld and the extent of yielding and out-of-plane deformation of the column web at the conclusion of testing. In Fig. 14 the beam tension flange is in the lower part of the photograph. A more thorough discussion of these flange-welded web-bolted connections can be found elsewhere. 1.~,11 Based on the test results of these two connections, the following conclusions can be made regarding the behavior of the connections: 1. For Connection 14-1, adequate elastic stiffness was obtained until local yielding occurs which reduces the stiffness. The maximum load reached was 99% of the predicted load if the critical section was taken at the centerline of the column web. Although this connection gives enough strength, fracture at the weld of the tension flange limits its ductility. This fracture is due to stress concentration at the top of the tension flange and may be remedied by changing the geometry of the flange moment plate. This will be discussed in the future. 2. For Connection 14-2, significant yielding and out-of-plane deformation of the column web due to the beam flange force reduced the stiffness of the connection even in the working load range. This out-ofplane movement of the column web and the resultant reduction in connection stiffness was particularly noticeable in Connection 14-2

Static web moment connections

Fig. 13. Tearing at tension flange-column web junction of connection 14-2.

Fig. 14. Column web yielding of connection 14-2.

107

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W. F. Chen, E. M. Lui

because the beam was attached only to the column web. Care must therefore be taken if such connections are used in design. In order to limit the column web deformation, column stiffening must be considered. Column stiffening may also be used in reducing stress concentration which causes the ultimate failure due to fracture.

7 B E H A V I O R AND TEST HIGHLIGHTS OF T H E F U L L Y - B O L T E D CONNECTION

Figure 15 shows the joint details for this connection. The beam flanges were bolted to the top and bottom moment plates by ten I-in. (25.4 mm) diameter A490 high-strength bolts. The moment plates were fillet welded to the column flanges and web. This connection was designed as a bearing-type connection with a hole 1 &in (27 mm) in diameter. The beam shear was transferred to a one-sided web shear plate by means of seven ~-in (22 mm) diameter A490 high-strength bolts in ~ i n (24 mm) diameter holes. The web shear plate was fillet welded to the column web and to the top and bottom m o m e n t plates. The thickness of the web shear plate is ~ in (13 mm). The critical section for this connection is taken as the outer row of flange bolts. The beam span is thus 70 in (1.8 m). The purpose of this test was to investigate the behavior of fully-bolted connections and to examine how the behavior of Connection 14-1 is changed when the beam flanges are bolted and not welded to the flange m o m e n t plates. The load-deflection curve for this specimen is shown in Fig. 16. Two distinct linear slopes were observed in the elastic range. The first linear slope extends up to a load of about 90 kips (400 kN), then followed by a shallower second linear slope up to a load of approximately 200 kips (890 kN). The occurrence of the second linear slope was due to slip of the bolts into the bearing. This p h e n o m e n o n was also observed in fully-bolted flange m o m e n t connections as described in the preceding paper. After this second linear slope, the connection lost its stiffness gradually due to local yielding of the assemblage elements. The load reached a value of approximately 300 kips (1334 kN) when a tear developed in the tension flange connection plate (Fig. 17). No further loading was attempted and the connection was completely unloaded. From the V-A curve, it can be concluded that this connection is not proper for plastically designed structures because of the significant reduction in stiffness in the working load range due to bond slip and the inadequate ductility due to fracture in the tension flange. For a more complete dis-

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-__/_

z

< 0 J
/

/

~P.v

/

600

400

/

200

#

l

I

I

2 BEAM

I

l

3 4 D E F L E C T I O N (A)

dl 5

I

I

6

7

¢m

Fig. 16. Load~leflection curve for fully bolted connection 14-3.

Fig. 17. Tearing of flange plate of connection 14-3.

Static" web moment connections

111

cussion of this connection, the readers are referred to the paper by Rentschler e t al.1 and Chen and Lui. s Although this fully-bolted connection exhibits adequate strength, care must be exercised in using such connections because the reduction in stiffness in the working load range and inadequate rotational capacity are very undesirable. Since the reduction in stiffness is due to bolt slippage and inadequate ductility is due to premature fracture, it is felt that if the connections are designed as friction-type rather than bearing-type together with column stiffening, these shortcomings can be eliminated.

8 A N A L Y T I C A L PREDICTIONS OF V-A B E H A V I O R In this section, three analytical schemes which one can use to predict the behavior of web moment connections will be discussed. They are: (1) simple plastic analysis, (2) yield line analysis and (3) finite element analysis.

8.1 Simple plastic analysis The use of simple plastic analysis to predict the plastic limit load of the connection assemblage shown in Fig. 1 is straightforward. If the plastic hinge is formed in the beam, the plastic limit load is PP -

lb

(1)

where Zxb is the plastic section modulus of the beam about the strong axis, Fyb is the yield stress of the beam, lb is the length of beam measured from the point of application of load to the location of the plastic hinge. If plastic hinges are formed in the column (Points X and Y in Fig. 1), the plastic limit load is

pp

2ZycFy¢ -

t

(2)

where Zyc is the plastic section modulus of the column about the weak axis considering the effect of axial force, Fyc is the yield stress of the column, ! is the length of beam measured from the point of application of load to the centerline of the column. The plastic limit load of the connection assemblage is the smaller of the two calculated in eqns (1) and (2).

8.2 Prediction of elastic joint stiffness Besides predicting the plastic limit load an analyst or a designer may be interested in assessing the elastic stiffness of the connection assemblage.

112

W. F. ('hen, E. M. Lui

The stiffness of a connection is best described by its load-deflection behavior. The overall load deflection behavior of the connection assemblage shown in Fig. 1 can be predicted by considering that the deflection is comprised of four components: 1. 2. 3. 4.

The deflection due to bending of the beam, Ab (Fig. 18(a)) The deflection due to beam shear deformation, A~ (Fig. 18(b)) The deflection due to joint rotation, Am(Fig. 18(c)) The deflection due to out-of-plane deformation of the column web, Aw (Fig. 18(d)).

The total deflection A at the point of application of load V is therefore A =

A b q'- A s -'1- A4~ -'l- A w

(3)

Generally speaking, there are two types of column web moment connections distinguished by the method in which the beam flanges are attached to the column. They are shown in Fig. 19. Type A has the beam flanges attached to either the column flanges alone or a combination of the column flanges and the column web by means of a flange connection plate. Type B has the beam flanges attached directly to the column web alone. The various deflection components for Type A and Type B connections will be investigated as follows: (1) Bending deformation Ab. The deflection A~ due to bending upon application of the beam load V is given as Ab -

Vl 3

3El

(4)

where I is the length of beam measured from column flange tip for Type A connection and from column web centerline for Type B connection, E is the modulus of elasticity, I is the moment of inertia of beam. Note that Ab is independent of the type of connection. (2) Shear deformation A~. For a beam of length l, the shear deformation can be written as

As -

Vl AwG

(5)

where Aw is the area of the web of the beam and G is the shear modulus. In writing eqn (5), it has been assumed that the shear force is carried by the beam web only and that beam web buckling does not occur. (3) Deflection due to joint rotation. Referring to Fig. 18(c), a joint rotation of the connection will cause a rigid body rotation of the beam.

Static web m o m e n t connections

I 13

iiII IIII

I

|| IF-' II II II II

~r

Ab

(a)

IIII i iiII I

I,

'il

~ / -

'

I|

I'

(b)

(c)

L A w

T

II (d)

Fig. 18. Deflection components of web moment connections.

114

W, F. Chen. E. M. Lui

( • ) Type

A

Web

Connection

( b ) Type

B

Web

Connection

Fig. 19. Web connection types.

Thus, if the joint rotates through an angle 0 (measured in radians), the deflection at the far end of the beam is

A+ = Ol

(6)

in which l is the length of the beam measured from the column web centerline (for both Type A and Type B web connections). The value of 0 is a function of the weak axis moment of inertia of the column, m o m e n t applied by the beam to the column, length of the column and end conditions of the column. It can be obtained from the analysis of a structural system using computer techniques or by conventional techniques such as m o m e n t distribution or slope deflection. (4) Deflection due to out-of-plane deformation of column web Aw. For Type A web connection, this deflection component is small because of the flange connection plate attachment to the column flanges which have high in-plane bending stiffnesses. The magnitude of this deflection component is a function of beam depth, flange plate and stiffener thickness, and to a smaller degree, column web thickness. The computation of this deflection component is very hard to arrive at

Static web moment connections

115

from a rigorous theoretical formulation of connection parameters because of the complex geometry of the connection and the non-uniform stress distributions in the flange connection plate at or near the column web. In an attempt to obtain a rational prediction of this column web displacement, simplified models together with assumptions are utilized in the following discussion. To facilitate modeling and discussion, this Type A web connection is subdivided into three cases. (i) Case 1--the flange connection plate is welded to both the column web and flanges and a stiffener is provided opposite the flange connection plate. (ii) Case 2--same as Case 1 except that no stiffener is provided. (iii) Case 3---the flange connection plate is welded to the column flanges only and no stiffener is provided. (i) Case 1 modeling. The model for Type A--Case 1 web connection is shown in Fig. 20. The column stiffener is modeled as a fixed-ended beam acted upon by a percentage of the beam flange force in the form of a uniformly distributed load. The uniform load wm acting on this fictitious beam is given by II W m = ( 0 " 5 0 -- 0 " 2 0 0 / ) W

(7)

in which a is the ratio of the width of beam flange to the clear distance between column flanges, w is the total uniform load from the beam flange force. This can be calculated from the beam bending m o m e n t at the column web divided by the center-to-center distance between beam flanges and then divided by the clear distance between column flanges. The deflection due to this uniform load Wmis composed of two values, the shear deflection 8ws and the bending deflection &~. The shear deflection is

GA

(s)

where Vomis (Wmlc)/2, lc is the clear distance between column flanges, G is shear modulus, A is bc tc, b~,t~ are depth and thickness of the stiffener (see Fig. 20). The bending deflection is

Wm/4 8, b- 384E--------I

(9)

116

W. F. Chen, E. M. Lui IC

thickness

- tc

.~

,i[

bC

/

Y1

l

LI Ic Loading

Wm

V°m[ ~ ~ V o

m

Shear

Moment

Fig. 20. SchematicrepresentationofflangeconnectionplateforTypeACase lconnections.

where Wmis that fraction of uniform load from the beam flange that goes to the stiffener as defined in eqn (7). lc is the clear distance between column flanges, E is the modulus of elasticity of flange connection plate, I is ,4, (6 b~. (ii) Case 2 modeling. The model for Type A - - C a s e 2 is shown in Fig. 21. This model is similar to the Case 1 model except now the flange connection plate rather than the stiffener is modeled as the fixed-ended beam. The uniform load acting on the fictitious beam is taken as 90% of w since the load that is transferred to the column flanges was shown by Rentschler tl to be about at least 90% of the total load from the beam flange force. Thus, the

117

Static web moment connections

Ic

thickness

-

tc II/~-fJ

r

,//

/

/

\

I_

Ic

J-

-I _1

Loading

W

V°~

V°

Shear

Moment Fig. 21. Schematic representation of flange connection plate for Type A Case 2 connections.

components of deflections due to shear and bending can be calculated by eqns (8) and (9) respectively with w~ replaced by 0.90 w. (iii) Case 3 modeling. The flange plate deformation due to force in the flange connection plate for Type A--Case 3 connection is shown in Fig. 22. As in Case 2, the flange connection plate is modeled as a fixed-ended beam. However, in this case, all the beam flange force will be transferred to the column flanges. So, in calculating the shear and bending deformations, the total uniform load w from the beam flange force is used in eqns (8) and (9). Upon comparison of column web deflections calculated using the above approach and those from a finite element analysis, it was shown n that the error is a function of t~. For large a, the theoretical approach overestimates

118

W. F. Ctlen. E. M. Lui

,

[ I I I I

Ic

/

/ I

thickness = t c

(a)

[

\\

(b)

Fig. 22. Flange plate deformation due to force in flange connection plate for Type A Case 3 connections.

the deflections whereas for small c~, this approach underestimates the deflections. This is due to the assumption of uniform stress distribution for the beam flange force at the column web while in actuality, the stress is highly non-uniform. For Type B web connection in which the beam flange is welded to the column web only, the column web alone has to carry the beam flange force if no stiffener is present. Because of the low out-of-plane stiffness of the web, large deformation of the column web will result. This deformation is particularly significant if the column web is thin. In order to reduce this deformation, a stiffener has to be provided opposite the beam flange. In the following discussion, a procedure which can be used to compute the column

";tatic web moment connections

119

web deflection for this type of connection (Type B) with stiffeners will be shown. The three assumptions used in the procedure are: (a) The stiffener is assumed to be a beam fixed at both ends and loaded by the beam flange force. (b) The points where the stiffener is attached to the column flanges do not rotate and displace. (c) The stress distribution in the beam flange at the column web is assumed to be uniform. And, as a further idealization, the uniform load is replaced by two concentrated loads placed at the quarter points of the loaded portion of the beam (Fig. 23). With these assumptions, the column web deflection can be calculated by superimposing the two deflection components: the deflection due to shear 8w~and the deflection due to bending &~b. The shear deflection is given as:

=

(lO)

GA

where V0 is total applied load from beam flange, lsh is shear span length (Fig. 23), G is shear modulus, A = b~t~ where b~, t~ are depth and thickness of the stiffener (see Fig. 23). The deflection due to bending of the stiffener is computed from: 8wb

V0 ls2 12 Etls

(

1.5als-

,,sh)

( 11 )

--2--

where V0 is total applied load from beam flange, l~h is shear span length, l~ is span length, a is l~ - l~h,I is ~ (ts b3), E is modulus of elasticity of the stiffener. The deflections computed using the above procedure was compared to the finite element solution" and was shown that the procedure overpredicts the deflection for columns with thick webs and underpredicts the deflection for columns with thin webs. This is due to the assumptions made and the model used in the procedure to make the problem tractable. Recall that column web deflection is only one of the four components that contributes to the total beam deflection, error that may result from the computation of this component will not affect the overall result significantly. Rentschler" has shown that although the accuracy of this deflection component is in error in some cases, the technique described above provides a sufficiently accurate prediction which yields a good prediction of the overall deflection.

120

W. F. Chen, E. M. Lui

I6

thickness

-t s

/

L- Lo,o

I I'~

I

] /A

i ~ S.E^. 2

MOMENT

Fig. 23. Schematic representation of Type B stiffener used for column web deflection calculations.

A comparison between the theoretical predicted strength of the connections using simple plastic theory and tests are shown in Figs 6, 10, 12 and 16 for Connections 14-4, 14-1, 14-2 and 14-3, respectively. In these figures, the symbol Vmpdesignates the beam shear required to cause the formation of plastic hinges in the subassemblage. For Connections 14-4, 14-1 and 14-3, two values of Vmp are shown. The larger Vmp corresponds to the shear required to produce plastic moment at the critical section and the smaller Vmp

Static web m o m e n t connections

121

corresponds to the shear required to produce plastic m o m e n t at the column web. The critical section for Connections 14-1 and 14-4 is at the juncture of the beam flange and the flange connection plates. The critical section for Connection 14-3 is at the outer row of flange bolts. The critical section for Connection 14-2 is at the column web. As a result, there is only one Vmp value for Connection 14-2. As can be seen from the figures, unless fracture occurs as in the case for Connections 14-1 and 14-2, Vmpevaluated based on the assumption that the formation of plastic hinge is at the column web gives a lower bound to the strength of the connections. Also shown in these figures are the elastic stiffness of the connections evaluated using the four displacement components of eqn (3) and the measured rotation at the top of the column. For Connection 14-4, it can be seen that the theoretically predicted stiffness gives a reasonable representation of the actual stiffness of the connection. The slight deviation of the test curve from the theoretical curve is due to items such as local yielding of the column web and beam flanges, loss of column stiffness due to axial load and the effect of column shear deformation. For Connection 14-1, a good correlation between the theoretically predicted stiffness and test results is observed in the linear elastic range. However, for Connection 14-2, a noticeable deviation of the test curve from the predicted stiffness is observed. This is attributed to the significant deformation of the column web which was not considered in the theoretical predictions. By taking into account the effect of column web deformation measured during the test, a shallower slope was constructed. It is seen that good correlation is obtained between the predicted stiffness and the test curve in the linear elastic range. For Connection 14-3, Fig. 16 shows that the predicted stiffness compares well with the test curve before any bolt slippage occurs. The second shallower slope of the test curve is due to bolt slippage and is not predicted by the analysis outline earlier.

8.3 Yield line analysis The yield line analysis is an energy approach to structural problems. By assuming that all the external work done on a system is dissipated as internal work in the formation of a yield line mechanism in the system, an upper bound solution to the actual collapse or limit load that would produce the actual failure mechanism can be obtained. The yield line approach has been used previously by Abolitz and Warner ~4 for brackets welded to column webs, by Blodgett ~5 for welding rolled section to box columns, by StockwelP 6 for column webs with welded beam connections and by Kapp 17 for web connection in direct tension.

122

W. F. ('hen, E. M. Lui

In predicting the load corresponding to the formation of a mechanism in the column web, the following assumptions are made: (a) The prescribed mechanism is as shown in Fig. 24. (b) All lines in the assumed yield line pattern are stressed to Fy, the yield strength of the column material. (c) The web surface enclosed by lines (1) and (2) remains planar. (d) The yield line hinge rotations are small. (e) The effect of shear on yielding of material is negligible. With the above assumptions in mind, the expression for internal work along the yield lines can be written as: W, = --~--

-(~ + --~ t+

+ 2a ]

T

where b is width of flange plate, d is distance between flanges, a is one-half of the value of the distance between column fillets minus flange width, t is thickness of column web, ~ is deflection under the flange plate. The expression for external work is

W~ = 2Pyl~

(13)

where Pyl is force in one flange required to cause theyield line mechanism. Equating eqn (12) with eqn (13) and canceling A, the force Pyl can be written as

P" = a

~+--~- t+

+~a

(14)

For a given combination of beam and column with specified yield stress, all variables in the right-hand side of eqn (14) are known, Py~ can therefore be determined easily. The use of the yield line analysis to predict the failure load is particularly suitable for web m o m e n t connections for which the beam flanges are connected to the web of the column alone with no backup stiffeners. It has been demonstrated in the pilot test program by Chen and Rentschler 9 that the failure load evaluated using the yield line theory correlates well with the experiments. 8.4 Finite element analysis The use of finite element method to analyze web moment connections has been reported by Rentschler, u and Patel and Chen. ~s Rentschle? ~gave a detailed discussion of a finite element approach to the analysis of web m o m e n t connections. The program used was SAP IV. This is

Static web moment connections

123

Z t = Web

6t

d/2

d/t

6t

Thickness

t

~

I

,l J

T

®

®

Fig. 24. C o l u m n w e b yield line m e c h a n i s m .

a general-purpose finite element program for use in static or dynamic analysis of elastic structures. The two elements that were used extensively in the analyses are the quadrilateral flat plate bending element and the quadrilateral plane stress element. In addition to these two elements, beam bending elements are used to transfer forces into the connections in regions far from the detail under consideration. Stiff linear spring elements are used to introduce displacements into the structural models. Two types of web m o m e n t connections: Type A and Type B (Fig. 19) were analyzed separately.

Finite element analysis of Type A web Based on the finite element analyses, H the following conclusions that pertain to Type A web connections can be drawn:

124

W. F. Chen, E. M. Lui

(1) The stress distribution in the flange connection plate at the transition with the beam flange is highly non-uniform. The stress is the highest at the edges and the lowest at the center of the plate. (2) The stress non-uniformity decreases when column stiffening is provided. (3) Stress concentrations increase as a increases where o~is the ratio of the width of beam flange to the clear distance between column flanges. (4) An increase in column stiffener thickness reduces the magnitude of stress concentrations in the flange connection plate. (In practice, a thicker stiffener plate is often used to facilitate welding.) (5) For connections with large a (e.g. >0.6), a reduction in stress concentration will result if the flange connection plate is extended past the column flange tip. (6) For Case 1 web connection, 55-75% of the beam flange force enters the column flanges through the connection plate (Fig. 20). For Case 2 the percentage is 89-97 (Fig. 21) and for Case 3,100% of the flange connection plate force goes directly to the column flanges (Fig. 22). (7) The horizontal shear stress distribution along the junction of the column flanges and the flange connection plate is not uniform. The peak varies from the column flange tip to the junction of the column flange and the column web as a decreases. (8) Extending the flange plate does not reduce the peak shear stress in the flange connection plate significantly, but it levels out the distribution by attracting more of the beam flange force to the column flange. This effect is more pronounced for connections with smaller o~values than for those with larger a values. (9) An increase in column stiffener thickness will reduce the amount of beam flange force from the flange connection plate entering the column flanges as shear. (10) An increase in column stiffener thickness tends uniformly to increase the amount of beam flange force going to the column web.

Finite element analysis of Type B web connections The results of the finite element studies on Type B web connections are summarized as follows: (1) For a constant column web thickness and a constant flange plate force, the deflection of the column web decreases as the tension flange width increases for connections without stiffening. (2) The stress in the beam flange where it joins the column web is highly non-uniform. (3) The stress concentrations in the beam flange at the column web are

125

Static web moment connections

greater for a column with a smaller web thickness for connections with the same a value and with no stiffening. For columns with the same web thickness, the stress concentration is greater for connections with larger a values. (4) For column with stiffening, the stress concentration increases with decreasing web thickness, regardless of o~. For constant web thickness, the stress concentration increases with increasing o~. (5) The use of column stiffening can reduce column web deflection and alleviate the shear punch problem. (Tearing of the column web by the action of the tensile or compressive beam flange force.)

Non-linearfinite element analysis. The discussion so far has been centered on a linear elastic analysis of web moment connections. A non-linear analysis using NONSAP was reported by Patel and Chen ~8and will be discussed in the following. The main purpose of this non-linear analysis is to investigate the stress distributions in the flange connection plate in the regions near the column C/1//1/lll/ll

D

Flee or Pertly fixed

p.

~ 2

i

C~/~

~

~f

~

~'

~ ~'~t~

B

Fixed,

D

2 3 3 nodes 2, 208 elements I I

]

',x.°- i i f "!~.AJ~A i J I I \/~-~/

I I III

I I I IIII I I I IIII I

Fig. 25. Typical free body and finite element mesh for flange connection plate and beam flange.

126

W. F. Chen, E. M. Lui

web and column flange tip as well as at the junction of flange connection plate and beam flange. The flange connection plate was isolated by means of a suitable free-body to make a convenient finite element model. Plane stress isoparametric finite elements were used. The structural model and mesh layout is shown in Fig. 25. Due to symmetry, only half of the plate was modeled. Only welded connections are examined but the junction at the flange connection plate and the column web can be modeled as fullywelded, partially-welded or no weld. Besides investigating stress distributions, the fracture behavior of the flange connection plate was examined. Here, the von Mises yield criterion was used to describe the initial yielding of the material and the maximum shear stress criterion was used to describe fracture. Seven hypothetical connection assemblages comprising of actual wide flange beams and columns were considered. As far as loading is concerned, the beam flange was loaded in a tensile manner. The load was applied at the end of a beam flange at nodal points sufficiently far from the junction of beam flange and flange connection plate to cause a uniform tensile stress in the beam flange. The most important finding of this analysis is that welding the flange connection plate all around the column web and flanges is not necessary. Partial welding with welds joint about 30--40% of the width of the flange connection plate and column web near the center is sufficient to provide the necessary strength. Although the stiffness of the connection is reduced somewhat, the effect is not significant for most connections. 9 S U M M A R Y , CONCLUSIONS AND DESIGN R E C O M M E N D A T I O N S Test results of the four full-scale specimens have been discussed in the previous sections. As far as strength is concerned, Connections 14-1, 14-3 and 14-4 all achieved load levels beyond the plastic m o m e n t load if the critical section is taken at the centerline of the column web. The use of column web centerline as critical section rather than the true critical section is acceptable since most design and analysis of beams use span lengths from center to center of columns. Connection 14-2 attains only 65% of the plastic limit load and shows a significant reduction in stiffness in the working load range due to out-of-plane deformation of the column web. This out-of-plane deformation can be reduced if the following measures are taken: (1) use a wider m o m e n t plate and weld it to the column flanges so that both the column flanges and web can take part in carrying the beam bending forces; or (2) use a back-up stiffener on the other side of the column to increase the stiffness of the column web. The use of a back-up stiffener can also help to

Static web moment connections

127

alleviate stress concentration at the tension flange tip that brings about failure by fracture of the column web. With regard to stiffness, Connections 14-1 and 14-4 both give satisfactory results. Connection 14-2 gives inadequate stiffness due to severe column web deformation; the remedy for this has been given in the above paragraph. Connection 14-3 exhibits two linear elastic slopes prior to the start of local connection yielding. The second shallower elastic slope is due to minor slips of the bolted flange plates into bearing. If a designer considers that this decrease in stiffness in the working load range is undesirable, he can remedy this by designing the connection as a friction-type rather than a bearingtype. Experiment on flange moment connection (Test C8 described in the preceding article) has shown that such friction-type connections give adequate stiffness for most practical purposes. Besides strength and stiffness, another important ingredient that a m o m e n t connection must have is ductility or rotation capacity at plastic limit load. Other than the Control Test 14-4, all the other connections failed prematurely by fracture at or near the plastic limit load. The lack of deformation capacity at the maximum or ultimate load for these connections is considered unsatisfactory. This is because redistribution of moments which is very important in plastic design and in seismic-resistant design is not possible if the connection does not exhibit enough ductility. With regard to this, the rest of this section will be devoted to the discussion of methods to prevent such premature fracture failure. Before proceeding to the discussion of remedies to the problem, it is of utmost importance to investigate the cause of the problem. Here, the question asked is why the fracture occurred? Figure 26 shows the stress distributions at three sections of a typical web m o m e n t connection in which the beam flanges are welded to a m o m e n t plate which in turn are welded to the column web and inside of the column flanges. The stress distribution across the width of the moment plate in Section A-A is shown in Fig. 26(a). Note that the stresses at the region of the column flange tips are much higher than the stresses away from the tips. This non-uniform stress distribution is attributed to the fact that lesser restraint is imposed on the part of the moment plate away from the column flanges. In other words, the part of the moment plate which is not attached to the column flanges is more flexible. Hence, the stresses are lower. The part of the m o m e n t plate that is attached directly to the column flanges by welding has more restraint, so the stresses are much higher. The phenomenon in which stress tends to migrate to region of higher stiffness is referred to as the shear lag effect. Another reason for the non-uniformity is that no back-up stiffener is used. The result is that the welds to the column web are

128

W. F, Chen. E. M. Lui

A I I

C

"1. . . .

I I I

,I

,,

I IA

Nominal Elastic Applied Stress

L

I

(a)

(b)

(c)

Fig. 26. Stress distribution: (a) longitudinal stresses on Section A-A; (b) longitudinal stresses on Section B-B; (c) shear stresses on Section C-C.

not fully effective near its center. At some distance away from the beam flange to m o m e n t plate juncture (Section B-B) a uniform longitudinal stress distribution across the width of the beam flange is observed (Fig. 26(b)). The longitudinal stresses in the moment plate introduce strains in the transverse and through-thickness direction because of the Poisson effect. Since the m o m e n t plate is attached to the column flanges, restraint is introduced and this causes tensile stresses in the transverse and throughthickness direction. As a result of this, triaxial tensile stresses are present along Section A - A , and they are at their maximum values at the intersections of Section A - A and C-C (Fig. 26). If this triaxial state of tensile stresses is sufficiently high, fracture will occur. This probably explains why Connections 14-1 and 14-3 failed prematurely before enough ductility was obtained.

129

Static web moment connections

(a)

~

I

.

Use Thicker

Plate

t \

\\\\\\I

l\\\\x\

\\\I

I\ \\

I\\

.~~:~ I..F=

\ \\

(c)

\',\\',I

=:

......

t

Extended Connection

Plate

| \ \ \

INNN\NNN\

(d)

\

\1

~=:=f.~___.r~ .7.= : = = ___= ~

Tapered Connection

Plate

r~ \ \ \

I \ \ \ \ \ \ \ \

(e)

\1

Extended end Filleted Connection Plates

Fig. 27. Possible approaches, for use individually or in combination, for improving performance of tension flangeconnections to column web. 19

To preclude such failure and to improve ductile action, the following suggestions were given by Driscoll and Beedle. 19 (1) Use oversized m o m e n t plates (Fig. 27(a)) to reduce the nonuniformity of tensile stresses across the plate. (2) Use a back-up stiffener (Fig. 27(b)). Limited finite element analyses '1 indicate that the stress concentration at the flange tip is reduced by at least one-third when such a back-up stiffener plate is used. (3) Use an extended connection plate so as to move beam flange butt welds away from the welds to the column flanges to avoid intersecting welds and associated residual stresses (Fig. 27(c)). (4) Use a tapered plate to decrease the stress concentration at the critical section (Fig. 27(d)).

130

W. F. Chen, E. M. Lui

(5) Provide a reduced width in the m o m e n t plate between the connection to the beam flange and the connection to the column flanges at some distance away from both connections (Fig. 27(e)). The above suggested connection geometries should be examined in more detail. The results of these additional tests will undoubtedly aid the designer in improving connection performance, especially the rotation capacity of such web m o m e n t connections.

REFERENCES 1. Rentschler, G. P., Chen, W. F. & Driscoll, G. C., Tests of beam-to-column web moment connections, Journal of the Structural Division 106(ST5) Proc. Paper No. 15386 (1980) 1005-22. 2. Graham, J. D., Sherbourne, A. M., Khabbaz, R. N. & Jensen, C. D., Welded interior beam-to-column connections, AISC Publication A.I.A. File No. 13-C, 1959. 3. Popov, E. P. & Pinkney, R. B., Cyclic yield reversal in steel building connections, Journal of the Structural Division, ASCE, Proc. Paper No. 6441, 95(ST3) (1969) 327-53. 4. Kajima Construction Company, Load test of beam-to-column connections of steel frames for Nusautaura building, Part I, Part II and Part III, D jakarta, 1964. 5. Kato, B., Design criteria of beam-to-column joint panels, New Zealand Natural Society for Earthquake Engineering Bulletin, 7(1) (1974). 6. Rentschler, G. P. & C h e n , W. F., Test program of moment-resistant steel beam-to-column web connections, Fritz Engineering Laboratory Report No. 405.4, Lehigh University, Bethlehem, PA, May 1975. 7. Chen, W. F. & Lui, E. M., Steel beam-to-column moment connections, Part I: flange moment connections, Solid Mechanics Archives, 11(4) (1986) 1-61. 8. Chen, W. F. & Lui, E. M., Steel beam-to-column moment connections, Part II: web moment connections, Solid Mechanics Archives, 12(1) (1987). 9. Chen, W. F. & Rentschler, G. P., Tests and analysis of beam-to-column web connections, Proceedings of the ASCE Specialty Conference on Method of Structural Analysis held at the University of Wisconsin-Madison, August 22-25, 1976, pp. 957-76. 10. Rentschler, G. P., Chen, W. F. & Driscoll, G. C., Beam-to-column web connection details, Journal of the Structural Division, ASCE, Proc. Paper No. 16880, 108(ST2) (1982) 393--409. 11. Rentschler, G. P., Analysis and Design of Steel Beam-to-Column Web Connections, Ph.D. Dissertation, Department of Civil Engineering, Lehigh University, Bethlehem, PA, 1979. 12. AISC Manual of Steel Construction, Specification for the Design, Fabrication and Erection of Structural Steel for Buildings, 7th Edition, American Institute of Steel Construction, New York, 1970. 13. AWS D1.0-69, Code for Welding in Building Construction, 9th Edition, American Welding Society, New York, 1969.

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14. Abolitz, A. L. & Warner, M. E., Bending under seated connections, AISC Engineering Journal, 2(1) (1965) 1-5. 15. Blodgett, O. W., Design of Welded Structures, James F. Lincoln Arc Welding Foundation, Cleveland, Ohio, 1966, p. 3.6-6. 16. Stockwell, F. W., Jr, Yield line analysis of column webs with welded beam connections, AISC Engineering Journal, 11(1) (1974) 12-17. 17. Kapp, R., Yield line analysis of a web connection in direct tension, AISC Engineering Journal 11(2) (1974) 38--41. 18. Patel, K. V. & Chen, W. F., Nonlinear analysis of steel moment connections, Journal of Structural Engineering, ASCE, 110(8)(1984) 1861-74. 19. Driscoll, G. C. & Beedle, L. S., Suggestions for avoiding beam-to-column web connection failure, A ISC Engineering Journal 19(1) (1982) 16-19.