Journal of Constructional Steel Research Volume 62 issue 9 2006 [doi 10.1016_j.jcsr.2006.01.004] Tadeh Zirakian; Hossein Showkati -- Distortional buckling of castellated beams.pdf

8/10/2019 Journal of Constructional Steel Research Volume 62 issue 9 2006 [doi 10.1016_j.jcsr.2006.01.004] Tadeh Zirakian;

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Journal of Constructional Steel Research 62 (2006) 863871www.elsevier.com/locate/jcsr

Distortional buckling of castellated beams

Tadeh Zirakian, Hossein Showkati

Department of Civil Engineering, Engineering Faculty, Urmia University, P.O. Box: 165-57159, Urmia, Iran

Received 15 August 2005; accepted 3 January 2006

Abstract

In previous studies of the structural behavior of castellated steel beams, different possible failure modes of these extensively used structural

members have been identified and investigated. On the other hand, during the past 25 years or so, a proliferation of research work has beenundertaken on the distortional buckling of steel members. Nonetheless, no studies are found in the literature on the distortional buckling of

castellated beams. Accordingly, tests of six full-scale castellated beams are described, in which the experimental investigation of distortional

buckling was the focus of interest. In addition to the test strengths, the accurate critical loads of the beams have been obtained using some

extrapolation techniques, and ultimately a comparison has been made between the obtained test loads and some theoretical predictions.c 2006 Elsevier Ltd. All rights reserved.

Keywords: Distortional bucklings; Castellated steel beams; Experimental investigation; Buckling loads; Theoretical predictions

1. Introduction

Modern techniques of fabricating steel members allow for

welded I-beams to be easily fabricated and it is often eco-nomical to produce such beams with equal flanges and slender

unstiffened webs using standard hot-rolled beams. Castellated

beams are such structural members, which are made by flame

cutting a rolled beam along its centerline and then rejoining

the two halves by welding so that the overall beam depth is in-

creased by 50% for enhanced structural performance against

bending. Therefore, application of these structural members

may lead to substantial economies of material. Basically, the

reasons for fabricating castellated beams are as follows:

(a) the augmentation of section height that results in the

enhancement of moment of inertia, section modulus,

stiffness, and flexural resistance of the section;(b) decreasing the weight of the profile which, in turn, reduces

the weight of the whole structure and economizes on

construction work;

(c) optimum utilization of the existing profiles;

(d) no need to plate girders; and

(e) the passage of services through the web openings.

Corresponding author.E-mail addresses: [email protected](T. Zirakian),

[email protected] (H. Showkati).

The widespread use of castellated beams as structural

members in multistory buildings, commercial and industrial

buildings, warehouses and portal frames, has prompted several

investigations into their structural behavior. As a resultof various theoretical and experimental studies reported in

the literature over the last three decades, different failuremodes (i.e. the Vierendeel collapse mechanism, buckling of

a web post, web weld failure, etc.) have been identified andinvestigated. In addition to earlier research concerned with

the in-plane behavior of castellated beams, lateral-torsional

buckling of these members was studied by Nethercot andKerdal in 1982 [5], in which they provided quantitative

data on the lateral-torsional buckling strength of castellatedsections, and the similarity in behavior of castellated and

plain-webbed beams was shown. Furthermore, web buckling ofcastellated beams was studied theoretically and experimentally

by Redwood et al. In some cases [8,10] flexural deformationof the web posts was shown through the measurement of web

strains.On the other hand, distortional buckling of steel I-section

beams was identified in some of the relatively early work on

lateral stability. Apart from the early work, systematic studiesof distortional buckling have only been attempted during the

past 25 years or so, particularly due to the advent of digitalcomputers for accurate modeling of the phenomenon. The

majority of the work in the open literature has originated

from Australian research, mostly by M.A. Bradford et al.

0143-974X/$ - see front matter c

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864 T. Zirakian, H. Showkati / Journal of Constructional Steel Research 62 (2006) 863871

Notation

The following symbols are used in this paper:

A = 2.95+ 4.070w 1.143w2;b =

flange width;

B = 1;Cbs = equivalent moment factor for beams which

accounts for the effects of moment gradient and

end conditions of the beam [3];

Cw = warping section constant;E = Youngs modulus of elasticity;Fy = yield stress;G = shear modulus of elasticity;h = overall cross-sectional height;Ir = 1 (Iy/Ix );Ix ,Iy= second moments of area about thex ,y axes;J

= torsional constant;

L = length;M = bending moment;MI = inelastic buckling moment;Mpx = full plastic moment;Myz = elastic uniform bending buckling moment;P,Pcr= buckling load;PElastic= elastic lateral buckling load;PInelastic= inelastic lateral buckling load;PMassey= extrapolated buckling load using Massey Plot;PModified= extrapolated buckling load using Modified

Plot;

PSouthwell = extrapolated buckling load using Southwell

Plot;PTest= test strength (maximum test load);r = radius of the gable-shaped web-flange junction;s = web thickness;t = flange thickness;w = (/L)ECw/G J;x,y = cross-sectional principal axes;m = moment modification factor [6]; = ratio of end moments; and = lateral deflection.

The phenomenon has generally been investigated in two

lateral-distortional (Fig. 1) and restrained distortional

(Fig. 2) modes of buckling, beside the two well-known local

and lateral-torsional buckles. A review paper on the work

undertaken prior to the early 1990s was published by Bradfordin 1992 [1]. Since then, extensive studies have been performed

and different analytical models have also been proposed in this

respect. In general, lateral-distortional buckling takes place in

intermediate length members with slender webs as a result of

the interaction between the two local and lateral buckles, and is

characterized by simultaneous distortion and lateral deflection

of the cross-section. In fact, web distortion allows the flangesto deflect laterally with different angles of twist, reduces the

effective torsional resistance of the member, and consequently

reduces the resistance to buckling [7]. Restrained distortional

Fig. 1. Lateral-distortional buckling.

Fig. 2. Restrained distortional buckling.

buckling also happens due to applied restraints against rigid

cross-sectional movements of one of the flanges.

Ultimately, according to the authors knowledge, despite the

considerable volume of research on the structural behavior of

castellated beams and the distortional buckling of steel I-section

beams, distortional buckling of castellated steel beams has

remained untouched. Thus, experimental work reported in this

paper was undertaken with the aim of experimentally verifying

distortion in castellated sections. Six full-scale beam tests have

been conducted and, despite the experimental investigation ofthe phenomenon, comparison has also been made between

the acquired experimental buckling loads and some theoretical

predictions.

2. Test program

2.1. Test specimens

In all, six tests were performed. These were on castellated

steel beams fabricated from the hot-rolled IPE12 and

IPE14 profiles in accordance with the German so-called

Estahl Standard. The specimens were designed in three 3600,

4400, and 5200 mm lengths and two types of cross-sectionalspecifications. A typical configuration of the expanded beam

and the notation adopted are shown in Fig. 3, and the test

arrangement is shown inFig. 4.The cross-sectional dimensions

are given inTable 1, using the nomenclature defined inFigs. 3

and 4. Further, the measured overall cross-sectional heights

of the specimens, given in the table, are the averages of the

recorded values at the 1/4, 1/2, and 3/4 points of the beams.

The test specimens were labeled such that the height and

length of each specimen could be identified from the label. For

example, the label C180-3600 indicates that the overall cross-

sectional height and nominal length of the test specimen are 180

and 3600 mm, respectively.


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T. Zirakian, H. Showkati / Journal of Constructional Steel Research 62 (2006) 863871 865

Table 1

Test beam dimensions

Original hot-rolled profile Test specimen Nominalh (mm) Measuredh (mm) b(mm) t (mm) s (mm) r (mm) L(mm)

IPE12 C180-5200 180 176.67 64 6.3 4.4 7 5200

C180-4400 180 176.33 64 6.3 4.4 7 4400

C180-3600 180 176.33 64 6.3 4.4 7 3600

IPE14 C210-5200 210 211.67 73 6.9 4.7 7 5200C210-4400 210 210.25 73 6.9 4.7 7 4400

C210-3600 210 206.50 73 6.9 4.7 7 3600

Fig. 3. Beam and opening geometry.

Fig. 4. Test arrangement.

2.2. Test setup

In general, the tests were carried out on simply supported

castellated beams with central concentrated load and an

effective lateral brace at the mid-span of the top compression

flange.Figs. 4and5give a good indication of the setup.Loading was by means of a 608 kN jack with a hydraulic

system, and load was applied through a 100 100 100 mmsteel cube placed on the top compression flange of the beam.

The steel cube was fixed against lateral movements by means

of two restricting plates placed at both its sides and the contact

surfaces between the cube and the plates were well lubricated

to avoid any friction during downward movement of the cube

during the loading process. The loading point configuration is

shown inFig. 6. Due to the influence of the shear developed

between the contact surfaces of the cube and the flange, lateraldeflections, twists, and rotations of the top compression flange

were effectively prevented at the mid-span. As was observed,

lateral deflections of the top flange were mostly prevented and

any small deflections were recorded. The rotations of the top

flange, on the other hand, were limited to some extent and were

especially evident when buckling took place at the two adjacent

spans, while the twists were fully prevented.The end supports consisted of two 1.16 m long supporting

columns erected on a base plate which, in turn, was linked to

Fig. 5. Overall view of the test setup.

Fig. 6. Loading point configuration.

a steel deck by four bolts. The two supporting columns were

joined by an intermediate cylindrical member, which could

rotate around its axis by means of two ball-bearings located

at its two ends. The test specimens were initially placed on the

cylindrical member at each end and additional restraints against

lateral deflections and twists were applied later at an average

distance of 165 mm from the axis of the end supports. The

bracing system included two restricting members, each with

two ball-bearings, which were tied to the supporting columns at

two sides of the specimen. The ball-bearings could freely roll


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Fig. 7. Configuration of end restraints.

on the rectangular plates tightly attached to the two sides of the

specimen.Fig. 7shows the configuration of the end restraints.

In addition, at the end supports, appropriate stiffeners were

designed and welded to the web and the two flanges to ensure

that shear and web crippling problems would be avoided at

these locations.

2.3. Instrumentation

Considering the test setup, the two lateral-distortional and

restrained distortional modes of instability were expected to

occur at the two laterally unbraced adjacent spans and the mid-point, respectively. Accordingly, the lateral deflections and web

strains were measured at the mid-length (1/2 point) and mid-

distance between the center and end support (1/4 point). The

lateral deflections were measured at the three top flange, mid-

point, and bottom flange levels of section height using three

displacement transducers, which were fixed on a board in a

plane perpendicular to the plane of the web. In addition, two

strain gauges were stuck vertically to both sides of the web

between adjacent openings at the mid-height point in order

to record the developed strains of the web. Fig. 8 shows the

measurement details at the two measurement locations.

The load applied by the jack was monitored by a 100 kN

capacity ring load cell at the mid-span and the load cell was

instrumented by a displacement transducer with 0.001 mm

accuracy.

2.4. Test procedure

During the tests, the load was applied in a step-by-step

manner and, using a Kyowa UCAM-20PC type data logger,

the applied load and the readings of transducers and strain

gauges were monitored and consequently recorded at regular

intervals. Consistent with all the tests, unloading took place

when the lateral deflections were large at the two laterally

unbraced adjacent spans. Fig. 9 shows a typical beam which has

Fig. 8. Measurement details.

Fig. 9. Buckled shape (C210-4400).

undergone lateral buckling and, as is seen, the buckling mode

is a complete sine wave.

As mentioned before, castellated beams were fabricated

from the hot-rolled IPE12 and IPE14 profiles, so two tensile

coupons were generally taken from each CIPE12 and CIPE14

fabricated profile: one from the flange and one from the web.

Tension test results are given inTable 2.

3. Test results

3.1. Experimental verification of distortion

All of the test beams underwent lateral buckling which took

place at the two laterally unbraced adjacent spans. However,

considering the test setup, distortion was expected to occur

at the two laterally unbraced and the restrained mid-length

regions. Therefore, with respect to the main objective of

this research, which was the revelation and verification of

any possible distortion, proper measurements were made at

the two 1/2 and 1/4 points where the beam was prone to

undergo restrained distortional and lateral-distortional modes

of buckling, respectively. Furthermore, it should be pointed out


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Table 2

Summary of tension test results

Fabricated profile Tensile coupon taken from Yield stress (MPa) Ultimate stress (MPa)

CIPE12 Flange 279.31 894.35

Web 233.93 892.23

CIPE14

Flange 280.29 1002.91

Web 332.03 671.16

Fig. 10. Web deformations (C180-3600).

that web-post buckling did not occur in any case. Fig. 10shows

the longitudinal web deformations of a typical test beam.

1/2 point: At this point, a concentrated load was applied onthe top effectively braced compression flange, so that the web

was subjected to significant compressive stresses, and thus it

might become unstable and deflect out-of-plane while pulling

the tension flange as it buckled. The result would be a web with

a distorted shape, and indeed a restrained distortional or web

lateral mode of buckling would occur [4]. On the other hand,

distortional behavior of the web at the mid-span was influenced

by various factors such as the initial geometric imperfections,

interaction of the two distortional modes, interaction between

the buckling behaviorsof the two adjacent spans, web openings,

etc., so that, in some cases, a complex distortional behavior

was observed at this point. Overall, web distortion at the mid-

span has been revealed through the measurements. InFig. 11,unequal discrepancies in the amounts of lateral deflection of the

three section-height points are observed clearly, which indicates

that the three points have not remained on a straight line just

because of flexural deformation or distortion of the web. In

Fig. 12, on the other hand, flexural deformation or distortion

of the web is represented by divergence of the strains in the

gauges mounted on each side of the web at the mid-height

point. Ultimately, in Fig. 13 distortion of the web during the

loading process is shown in a typical beam, which has been

drawn on the basis of values of lateral deflections measured

at the three section-height points. In spite of the little lateral

displacement of the top restrained flange, it is observed clearly

Fig. 11. Loaddeflection curves (C210-3600).

Fig. 12. Loadstrain curves (C210-3600).

that, by continuation of the loading process, the web has been

distorted.

1/4 point: Similarly to the 1/2 point measurements and therespective analyses of the experimental data obtained, web

distortion is revealed and verified through the loaddeflection

(Fig. 14) and loadstrain (Fig. 15) curves. InFig. 16, distortion

of the web during the loading process is shown in a typical

beam, which has been drawn on the basis of values of lateral

deflections measured at the three section-height points. In the

figure, it is observed clearly that lateral deflection of the cross-

section has been accompanied by web distortion, and this

has become more pronounced by continuation of the loading

process. Finally, as an example, the distorted shape of the web

has been shown with a little exaggeration inFig. 17at a loading

level of 18.61 kN and, in addition to presenting the trendline,


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Fig. 13. Distortional behavior of web at the 1/2 point (C210-3600).

Fig. 14. Loaddeflection curves (C180-3600).

Fig. 15. Loadstrain curves (C180-3600).

which was fitted by using a least-squares-method regression

analysis, the respective second-order polynomial that was

obtained is also shown in the figure. As a result, through

revealing the web distortion that has occurred simultaneously

Fig. 16. Distortional behavior of the web at the 1/4 point (C180-3600).

Fig. 17. Distorted shape of the web (C180-3600).

with the lateral instability of the beam, the occurrence of lateral-distortional (or simply distortional) buckling is confirmed.

3.2. Test strengths and the extrapolated buckling loads

As was previously mentioned, failure of the beam became

evident when the lateral deflections were large and, after a

certain amount of loading (test strength or maximum test load),

the applied load indeed did not increase and consequently

unloading took place. These loads were considered to be

an inaccurate measure of the critical load, and extrapolation

techniques were used to obtain the critical loads. These are the

so-called Southwell, Modified, and Massey Plots, which were

developed for elastic buckling. Here, considering the inelastic

buckling behavior of the specimens, the inelastic buckling loads

representing the strength of the beam were extrapolated with

the assumption that these methods may be used for inelastic

buckling [2]. The Southwell Plot graphs /P against , where

is the lateral deflection. The Modified Plot [9], on the other

hand, graphs P against , while the Massey Plot graphs

/P2 against . The critical load may be obtained from the

relevant straight lines of best fit from these. As an example,

Figs. 18 through 20 provide the Southwell, Modified, and

Massey Plots for test specimen C210-5200. Table 3 provides

the maximum test loads and the critical loads obtained using

the three extrapolation techniques.


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Table 3

Test strengths, extrapolated buckling loads, and theoretical predictions

Test specimen PTest (kN) PSouthwell(kN) PModified(kN) PMassey (kN) PElastic (kN) PInelastic (kN)

C180-5200 25.92a 20.60 14.48

C180-4400 15.63 16.72 16.01 17.68 31.96 18.55

C180-3600 21.58 22.94 22.68 22.94 55.45 23.85

C210-5200 24.90 26.88 25.86 27.74 35.48 22.77C210-4400 39.94b 42.19 41.94 40.82 56.07 28.91

C210-3600 37.22 40.32 39.46 40.82 97.44 35.11

a Due to the influence of initial geometric imperfections and interaction between the buckling behaviors of the two adjacent spans, failure of the beam has occurred

at a higher load than the expected amount. This was quite evident in loaddeflection curves of the 1/4 point, where the beam has suddenly undergone large lateral

deflections in the opposite direction to the pre-buckling direction of deflection.b Because of some frictional restraint at the loading point, which was observed during the test, the test strength is high compared to those for the other C210

beams.

Fig. 18. Southwell Plot.

Fig. 19. Modified Plot.

The average discrepancy between the maximum test and

the extrapolated buckling loads obtained using the Southwell

technique is about 7%. This, on the other hand, is about 4%

for the Modified technique, while for the Massey technique

the average discrepancy is about 8%. As is seen, the smallest

Fig. 20. Massey Plot.

discrepancy between the test strengths and the extrapolated

buckling loads is found in the case of the Modified technique.

4. Comparison with theoretical predictions

According to the authors knowledge, except for a few rules

for beams on seats and for beams with partial torsional restraint

provided in the Australian AS4100 code, no explicit formulas

are found that account for the effect of distortional buckling

in I-section beams. Accordingly, comparison is made between

the experimental results and theoretical predictions of some

equations developed for elastic and inelastic lateral buckling.

Elastic lateral buckling: The elastic lateral buckling loads

of specimens have been calculated using Eq. (1), which is

presented for elastic lateral buckling of a simply supported

beam with a central concentrated load and lateral support at the

center [3]:

Pcr L4 = Cbs Myz (1)

where

Myz=

LE Iy G J

Ir1+ w2 (2)


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Table 4

Some of the quantities used in the calculations of buckling loads

Test specimen MeasuredL a (mm) Iy (mm4) Ix (mm

4) J(mm4) Cw (mm6) Mpx (kN mm) Cbs

C180-5200 4880.0 275 415.50 6874 632.32 15 327.38 1997 355 990 19 552.04 4.315

C180-4400 4073.5 275 579.02 6845 584.37 15 317.73 1989 391 872 19 506.11 4.545

C180-3600 3271.0 275 579.02 6845 584.37 15 317.73 1989 391 872 19 506.11 4.865

C210-5200 4875.0 447 860.63 12 499 300.38 22 835.26 4689 635 514 29 608.14 4.613C210-4400 4060.0 447 856.48 12 310 323.36 22 786.11 4624 819 449 29 357.98 4.877

C210-3600 3269.5 447 845.75 11 818 606.42 22 656.34 4455 818 612 28 700.97 5.207

a Measured length between the end restraints of the specimens.

Ir= 1 (Iy/Ix ) (3)

w = L

ECw

G J(4)

and, for the upper flange loading case,

Cbs=A(= 2.95+ 4.070w 1.143w2)

B(= 1) . (5)

In theoretical calculations, the Youngs modulus Eand theyield stress Fy were taken as 206.01 GPa and 235.44 MPa,

respectively, and the shear modulus G was taken as 0.385E.

The values of the actual L between the end restraints, Iy , Ix ,

J, Cw, Mpx , and Cbs , used in calculating the buckling loads

of the beams are given in Table 4. It should be pointed out

that, in both the elastic and inelastic cases, all cross-sectional

properties have been calculated for the cross-section at the

center of a castellation. The predicted elastic buckling loads

are given inTable 3, and as is seen, the disparity between the

experimental and theoretical results increases markedly as the

span length decreases, since instability is dominated by yielding

rather than by elastic buckling. In addition, the influence of

initial geometric imperfections, distortion, web openings, and

other factors should also be taken into consideration.

Inelastic lateral buckling:Using an approximate equation(6)

suggested by Nethercot and Trahair [6] for predicting the

inelastic buckling momentsMIof statically determinate simply

supported I-beams with unequal end moments MandM, the

inelastic lateral buckling loads of the test beams have been

obtained by calculating MIfor a beam length of half the span

under a linear moment diagram that increases from zero to the

mid-span value with m = 1.75, the value for this momentdiagram:

MIMpx

= 0.7+ 0.3(1 0.7Mpx /mMyz )(0.61 0.3 + 0.072)

mMyzMpx

. (6)

The predicted inelastic lateral buckling loads of the beams

are also given in Table 3. Considering the inelastic buckling

behavior of the beams, good predictions are generally provided

compared with those for elastic buckling, in spite of the

influence of some factors that were not considered in theoretical

calculations, including initial geometric imperfections, the

virtual distribution of residual stresses, web distortion,

interactions between adjacent segments, etc.

As a consequence, considering the differences between the

behavior of the beams in reality and that of the theoretically

conceived perfect beams, agreement between the test loads and

the theoretically predicted inelastic lateral buckling loads is

quite satisfactory.

5. Conclusions

In spite of extensive studies on various failure modes of

castellated beams and, on the other hand, the considerable

volume of research on the distortional buckling of steel I-

section beams, the distortional buckling of castellated beamshas remained untouched. Accordingly, a series of six tests on

full-scale simply supported castellated beams with a centrally

concentrated load and an effective lateral brace at the mid-

span of the compression flange was performed, mainly with

the aim of experimentally verifying the web distortion in these

structural members.

Considering the test setup, the two well-known lateral-

distortional and restrained distortional modes of instability

were expected to occur at the two adjacent segments and mid-

length point, respectively, so that appropriate measurements

were made at the 1/4 and 1/2 points of the specimens.

All of the test beams underwent lateral buckling, which wasaccompanied by web distortion. In fact, web distortion was

revealed and demonstrated through the experimentally acquired

loaddeflection and loadstrain curves at both measurement

locations. As a consequence, the occurrence of the lateral-

distortional mode of buckling was confirmed.

In addition to the test strengths, using the Southwell,

Modified, and Massey extrapolation techniques, the accurate

critical loads were obtained. On the average, the discrepancy

between the test strengths and the extrapolated buckling loads

was found to be 7% for the Southwell Plot, 4% for the Modified

Plot, and 8% for the Massey Plot. The smallest discrepancy was

found in the case of the Modified Plot.

Ultimately, comparison was made between the experimentalresults and the theoretical predictions of the elastic and inelastic

lateral buckling loads. Considering the inelastic buckling

behavior of the beams, agreement between the test and the

theoretically obtained inelastic lateral buckling loads was quite

satisfactory, in spite of the disparities between test and theory.

Acknowledgments

The test program was supported by a grant from the Iranian

Ministry of Sciences, Researches, and Technology specified

for the postgraduate research. The funding was provided as

a result of great efforts made by Dr. Mirzayee, the Head


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of the Engineering Faculty of Urmia University, which are

gratefully acknowledged. Further, the experiments would not

have been possible without the help of the laboratory technician

Jaafar Azimzadeh. The authors are also grateful to Professor

M.A. Bradford, Professor N.S. Trahair, Professor T.M. Roberts,

Professor B.W. Schafer, Dr. Z. Vrcelj, Dr. H.R. Ronagh, and

Pedro Simao for their great help in providing articles andpresenting constructive comments regarding this research.

References

[1] Bradford MA. Lateral-distortional buckling of steel I-section members.

J Construct Steel Res 1992;23:97116.

[2] Bradford MA, Wee A. Analysis of buckling tests on beams on seat

supports. J Construct Steel Res 1994;28:22742.

[3] Chen WF, Lui EM. Structural stability (theory and implementation). New

York: Elsevier Science Publishing Co.; 1987.

[4] McCormac JC. Structural steel design; LRFD method. 2nd ed. New York:

HarperCollins; 1995.

[5] Nethercot DA, Kerdal D. Lateral-torsional buckling of castellated beams.

The Struct. Eng. 1982;60B(3):5361.

[6] Nethercot DA, Trahair NS. Inelastic lateral buckling of determinate

beams. J Struct Div, ASCE 1976;102(ST4):70117.

[7] Ng MLH, Ronagh HR. An analytical solution for the elastic lateral-

distortional buckling of I-section beams. Adv Struct Eng 2004;7(2):

187200.

[8] Redwood R, Demirdjian S. Castellated beam web buckling in shear. J

Struct Eng, ASCE 1998;124(10):12027.

[9] Trahair NS. Deformations of geometrically imperfect beams. J Struct Div,

ASCE 1969;95(ST7):147596.

[10] Zaarour W, Redwood R. Web buckling in thin webbed castellated beams.

J Struct E ng, ASCE 1996;122(8):8606.

Documents

Journal of Constructional Steel Research Volume 62 issue 9 2006 [doi 10.1016_j.jcsr.2006.01.004] Tadeh Zirakian; Hossein Showkati -- Distortional buckling of castellated beams.pdf