Castellated Beams

Proc. Instn. Ciu. Engrs, Part 1,1991, W,June, 521-536 PAPER 9513

STRUCTURAL BUILDING AND

BOARD

Castellated beams P. R. KNOWLES, MA, MPhil, MICE, FIHT* The process of castellation was patented in 1939. Applied mainly to rolled sections for use as beams, it has been for many years a significant feature in steel construction. The Paper describes the steps leading up to the invention and the early attempts to devise methods of calculating the load carrying capacity and deflexion of castellated beams. Both elastic and plastic methods of analysis are examined, the basis and use of interactive design charts is explained, and the requirements of BS 5950 are outlined.

Notation notional web area for shear deflexion calculation area of tee. beam flange width depth of castellated section serial depth of original section shear modulus notional second moment of area for deflexion calculation second moment of area through anopening constant related to tee constant related to tee bending moment on tee maximum permitted bending moment plastic moment of tee positive bending moment ontee negative bending moment on tee axial force on tee squash load of tee shear force on tee maximum permitted shear shear failure load of tee shear force on upper tee shear force on lower tee elastic section modulus of beam at opening length of horizontal cut forming castellation castellation dimension castellation dimension depth of web between fillets sum of stressesf, andf, stress in tee from bending moment onbeam Written discussion closes 15 August 1991 ;for further details see p. ii. *Principal, Peter KnowlesDelivered and Associates by ICEVirtualLibrary.com to: IP: 192.168.39.63 On: Tue, 28 Sep 2010 12:38:20

521

KNOWLES

f,

stress in tee from shear forceonbeam

h

distance betweencentroids of tees spacing of openings material design strength web thickness angle of sloping side of castellation to horizontal

p

py t

9

Castellated beams Innovations in civil and structural engineering are not common; the invention of the castellated beam was the result of a rare flash of inspiration which occurred to a designer faced with an apparently insoluble problem. 2. Fifty years ago, on 4 January 1939, British Patent number 498281 was granted to Geoffrey Murray Boyd, at that time living at 11 Burwood Avenue, Hayes, Kent, for a specification related to improvements in built-up structural members ‘of the kind comprising two parts with pairs of projections extending towards one another and welded along a line of sinuous or toothed nature’. The rather involved phraseology of the specification refers, in fact, to what isnow known as a castellated steel section, although at the time of the patent application it was called the Boyd beam.’ 3. The basis of the beam’s method of construction, described by a writer in The Shipbuilder’ as ‘both simple and ingenious’, had occurred to Boyd in 1935 when he was working in Buenos Aires, Argentina, as a structural engineer for the British Structural Steel Company,the South American subsidiary of Dorman Long. He was faced with the problem of designing a beam for a monorail hoist. The maximum beam flange width was, of necessity, restricted by the width of the hoist opening, but the choice of rolled beams in stock was such that the only ones available within the restricted flange width were insuficiently stiff for the required span. Boydwas musing on the possibility of strengthening a beam by welding another below it-a rathercrude solution-when he thought of cuttingand welding the beam web in such a way as toincrease its depth and, consequently, its stiffness. An experiment with a cardboard model quickly showed the feasibility of the idea, and thus the Boyd beam was invented. Much development work was, understandably, still required. 4. The patent specification is concerned not only with a simple castellation of rolled beams but also with techniques of tapering, of forming Z-shaped sections from channels and of forming cruciform and star-shaped sections for use as columns. Applications are claimed for ships, aircraft and vehicles as well as for buildings. In the specification, the use of flame cutting and welding is stressed. Various geometries of castellation opening are discussed, based on the angle of the sloping sides and the length of the horizontal portion. It was, however, the Boyd beam type C which went into general use and whose geometry has become the standard for castellated beams in theUnited Kingdom (Fig. 1). The depth of cut c is half the serial depth D , of the original section. Therefore, the depth of the castellated beam D , = D + O.5Ds z 1.5DS, where D is the actual depth of the original section. 5. For various reasons, one of which was the 1939-1945 World War and another Boyd’s position as a Civil Servant, he was unable to exploit his invention commercially. Boyd therefore assigned his patent rights to the Appleby Frodingham branch of the United Steel Companies Limited, which marketed steelwork 522

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CASTELLATED BEAMS

1

P

t

D

[

[

:

, b L a , b L a 1

1

1

l

t

/Web

@

C

+ (b)

Fig. 1 . ( a ) Universal beam cut along web; (b) two halves welded together to form castellated beam

fabricated in accordance with the Boyd principles as Appleby Frodingham Castellated Construction. Regrettably, the inventor’s name was superseded by a more cumbersome but nevertheless descriptive word meaning ‘castle-like or battlemented’, a clear reference to thetoothed appearance of the flame-cut section before welding. The extended patent expired many years ago, allowing castellated sections to be produced freely by any steelwork fabricator. Thefact remains, however, that, with the exception of the Lirska beam in which the depth of the original section is further increased by a plate welded between the castellated teeth (Fig. 2), no significant improvement has been made to Boyd’s original concept.

l

L

Fig. 2. Extended (Litska) castellated beam Delivered by ICEVirtualLibrary.com to: IP: 192.168.39.63 On: Tue, 28 Sep 2010 12:38:20

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KNOWLES

Design considerations 6. Designers have long laboured under the difficulty of not having a generally accepted design method for castellated beams. The inventor did producesafe load charts (Fig. 3), whichwere based on what was then considered theprudent BOYD BEAMS

Shear:

Max. reaction = 1/1.52 of max. safe reaction on original beam at 5 t /in2 on web Bending: Max. extreme fibre stress 8 t /In2 Deflexion: Not exceeding L1325. € = 12000 t /m2

with uniformly distributed loads

Lateral support assumed adequate

Span: ft 10 X 4% BB 15 X 4 % (6 25 Ibs Means. Boyd Beam 15 X 4% 25Ibs made from BSB 10 X 4'12 (ir 25 Ibs Copyright by G. M. Boyd.

Fig. 3. Safe load chartfor Boyd beam Delivered by ICEVirtualLibrary.com to: 524

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Type 'c' openings

CASTELLATED BEAMS

Fig.4. Panel deformation in shear assumption that the beam properties to be used in calculation should be those minimum values obtained for the portions above and below the opening in the web; in effect, two tee sections. Subsequent testing has shown that this apparently safe procedure is not correct;stresses and, in particular, deflexions can be seriously underestimated. The reason lies in the flexibility of the region at each opening, which, deforming in shear (Fig. 4), produces stresses and deflexions whichaugment those producedby simple beam action. Elastic stress distribution 7. Elastic analysis of a beam with openings in the web has been carried out by a number of methods which include finite difference3 and finite element4 techniques. However, a simple analogy in which the castellated beam is considered to be a Vierendeel girder with points of contraflexure at the mid-line of the openings and at mid-height of the web posts (Fig. 5), and with the shear force at the centre-line of the opening divided equally between top and bottom tees,is an attractive substitute structure whichis statically determinate. The stress at the tee-to-post junction can thenbe calculated. 8. Experimental verification of the validity of the Vierendeel analysis has been reported from many sources. A detailed summary is given in Kerdal and Nethercot,’ but it must be pointed out that many of these tests have the weakness that they have been carried out on sections whose castellation profiles are significantly different from those of current UK standard type. Early tests in the UK were on British Standard beams, which became obsolete many years ago, and most of the tests were on beams of small size. It may be concluded that further tests on castellated universal beams of intermediate or larger size could usefully be carried out. 9. At each hole, bending and shear are transmitted by the top and bottom tees. On the assumptions of Vierendeel action, the longitudinalstress at the junction of tee and post (A-A in Fig. 6 ) consists of two components: the component due to bending f, ; the component due to shear f,. The total longitudinal stress f =f, +f,.If the tee properties are area A , and elastic section modulus Z,, then for applied bending moment M and shear force V

f, = M / A , h = K , M

%,/2Z, = K, V Deliveredf vby=ICEVirtualLibrary.com to: IP: 192.168.39.63 On: Tue, 28 Sep 2010 12:38:20

525

KNOWLES

where

K,

=

1/A,h

K , = a/2Z, In calculations, the smallerof the two values of Z , is used. The section constants K , and K , have been tabulated.'j 10. On examination, K , will be seen to be approximately equal to the reciproZ at an opening cal of the castellated beam elastic modulus

I = 2[A, x(h/2)'] = A , h2/2 (neglecting the small valueof I for each tee about its own centroidal axis).

I (C)

Fig. 5. Vierendeel analogy: ( a ) castellated beam; ( b ) equivalent Vierendeel girder; (c)location of points of contraflexure Delivered by ICEVirtualLibrary.com to: 526

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C A S T E L L A T E DB E A M S

(b)

(4

(C)

Fig. 6. Stresses at junction of tee and post (A-A): ( a )direct stress due to bending f, ; (b)bending stress due toshear fv (c) combined stressf

Therefore, the Vierendeel analysis gives a flange stress larger than that found by using the minimum elastic section modulus. 11. If maximum elastic stress be the design criterion then it will be necessary, in design, to check the sum of stresses at each cross-section A-A (Fig. 6) along the length of the castellated beam, unless the point of maximum stress is immediately apparent. Properties K , and K , are not known until a beam has been selected; direct design is not possible, and a trial and error process is needed. Some assistance can be gained from published material: load tables have been calculated for uniformly distributed and central point loads on a range of spans for all the universal beams.6 For certain load cases, use can be made of the results in figure 6 of reference 6. 12. For other load cases, interaction curves are available which are based on the linear interaction between shear force and bending. In the absence of bending moment, the shearforce which can be carried by the beam, in terms of the bending stress generated by the shear force, is limited by the material strength p y . The maximum shear force V is then given by v0

= P&

Similarly, in the absence of shear force, the maximum bending moment MO = P y K l 13. For any general combination of bending moment M and shear force V, the resulting sum of bending stresses must not exceed the material design strength py

Interaction curves (Fig. 7) have been plotted for all castellated universal beams, with X and y axes (l/K2) and (l/K,) respectively. A cornbination(M/p,) and (VIP,) which lies on, or nearer to the origin than, the interaction line for a particular beam is a combination which produces a maximum stress not greater than the allowable stress for that beam material. It will, of course, be necessary to examine combinations of bending moment and shear to determine the worst case. The interaction curves can also be used to check the stress in an existing beam. 14. The shear stress caused by the shear force in the tee webs will also interact with the stress in combined bending, and therefore a check Delivered by ICEVirtualLibrary.com to: should be made of the IP: 192.168.39.63 On: Tue, 28 Sep 2010 12:38:20

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KNOWLES

Section (458 X 127 X 48) (ex 305 X 127 X 48 UB) (381 X 146 X 43) (ex 254 X 146 X 43 UB) (458 X 102 X 33) (ex 305 X 102 X 33 UB) (381 X 102 X 28) (ex 254 X 102 X 28 UB)

2

0

liK,

4

Viallowable stress

6 mm2 X 10'

8

Fig. 7. Interaction chart for elastic design

resulting equivalentstress if design is on an elastic basis. It will generally befound, however, that this combination is not critical.

Deflexion 15. Thecalculation of deflexionwas, ashasalready been explained,based initially on considering a castellated beam as a conventional beam having an unperforated web with a second moment of area equal to the minimum valuefor the castellated beam. This simplification, however, leadsto anunderestimate of the real deflexion by a significant amount. An early improvement,which resulted from a series of tests carried outby United Steel,7 was to apply a correction factor to the deflexion calculated using the minimum second momentof area, based ontests on small beams loaded at the quarter points. The calculated elastic deflexion was multiplied by a factor

c = 1 + (2OImi,/L2) where Iminis the second momentof area through an opening (in4)and L is the span (in). Converting to metric C=1

+ (0~031011,iJZ?)

Later tests produced a revised formula, incorporating the width B and depthD , of the beam. Inits metricated version,this becomes C = 0.94

+ 0.03l5(BDc/L)

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CASTELLATED BEAMS

16. The obvious drawback is that these formulae are derived from a very small number of tests on relatively small beams of a now obsolete pattern, none of which exceeded 375 mm in depth. Nevertheless, as suggested in the 1958 United Steel report,* data for a range of sizes and spans ‘could readily be obtained from beams in production in the workshops. These could be set up on improvised supports on theshop floor, loaded by dead weights and the deflection measured by dial gauges’. The conclusion from the tests was that shear deflexion will be greatest on heavily loaded short-span beams, where the increase in deflexion may be as much as 40%. This is, in fact, less serious than the effect on longer spans, for which the increase, although perhaps only 10%, will be added to an absolute value which is already large. 17. The increased deflexion of a castellated beam is the consequence of its low resistance to shearing deformation (Fig. 4). Calculation of the deflexion caused by shear can be made for each panel of the beam, assuming Vierendeel type action, and the results summed to provide the total shear deflexion. Analysis of the shear deflexion of an individual panel of a castellated beam is contained in reference 6, Appendix 2. The total shear deflexion of the beam can then be found by summation of each panel deflexion; a tedious task for hand calculation if the beam has more than a small number of openings. However, a good approximation can be made by considering an analogous beam with a continuous solid web and thus constant section values Ifictand Afis,. The first of these is used the normal way to find the bending deflexion y, =K w L ~ J E I ~ ~ ~ ~

where K is the relevant elastic factor for the type of loading, and Ificlmay conveThe shear deflexion niently be taken as the minimum second moment of area lmin. is calculated using the relationship

where A is the total shear deflexion between panels 1 and n ; n is the panel number; is the panel shear in panel i ; G is the shear modulus; and p is the spacing of openings. Now

v

is the bending moment at panel n. Therefore, the total shear deflexion at a panel in a simply supported castellated beam, with panel 1 adjacent to a support, is equal to the bending moment at that panel divided by CAfic1.The physical property Afictis analogous to the web area of a conventional beam; its derivation is set out in reference 6. The value of Afic1has been tabulated for each castellated section.6

Webs 18. The capacity of the web will be limited by failure in (a) shear yield in the web

( b ) shear yield at the weld (c) buckling (d)bearing. Delivered by ICEVirtualLibrary.com to: IP: 192.168.39.63 On: Tue, 28 Sep 2010 12:38:20

529

KNOWLES lnflll

/

k’45”

T Fig. 8. Infill plate at a point of concentrated load or reaction (Note: It is normal practice to$ll hole completely) Shear yield 19. Some qualitative appreciation of the effects of shear force can be gained by considering average stresses in weband weld (a) at a web post gross web area = tD, = 1.5D, t average shear stress = V/1.5DSt (b) at a hole gross web area = t X 0.5D, average shear stress = V/O,5D, t (c) at a weld area of weld = 2at = 0.250, t shear force = Vp/h = V(1.08DJ.40,) average shear stress = 0.77V/0.25DSt

= 0.67V/Ds t

= 2.0V/D,t

= 0.77V

= 3.0V/Ds t

Comparing these values, it appears that failure in shear yield will occur at a weld. In fact, the effect of welding is to increase the strength of the material in the weld area so that the joint is lesslikely to be a critical factor.’ Buckling 20. Because the web of a castellated beam consists of a series of relatively isolated posts separated by the openings, there is a general possibility of a post buckling in a lateral torsion mode. This mode has been investigated by Aglan and Redwood”but they observe that, for beams of standard British castellation profile, yield of the web at theweld should occur before a lateral torsional buckle forms. At points where there is concentrated load or reaction, the web may fail by conventional interactive buckling, a condition which may be checked using the same assumptions as those for solid web beams, namely (a) that the web acts as a column of slenderness 2.5d/t for which the compressive strength can be obtained from the appropriate column curve (b) that the compressive capacity of the web post is the compressive strength multiplied by the minimum cross-sectional area of the post at theweld.

Tests have shown that Delivered these are by safeICEVirtualLibrary.com assumptions.” to: 530

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C A S T E L L A T E DB E A M S

21. It is important to appreciate that shear force is assumed to be transmitted across the opening in a castellated beam by equal division between top and bottom tees.At the end of a beam, therefore, halfof the shear force passing through the lower tee does not exert a compressive buckling load on the end post, and so the end post can resist an external reaction equal to twice its compressive capacity. If the web capacity is inadequate for the applied load or reaction infill, plates may be weldedinto the appropriate openings in order to increase the loaded area at the beam centre-line, a conventional 45 degree spread of load being assumed (Fig. 8). Bearing 22. The dispersion of concentrated loads or reactions is assumed to be complete at the nearer root radius, and so the web bearing strength of a castellated beam is identical to thatof its parent section.

Plastic design 23. Plastic design of castellated beams may be interpreted in two ways (a) with the castellated beam as part of a continuous structure (b) with the beam simply supported, collapsing by the formation of either a parallelogram mechanism or by plastic extension and contraction of the bottom and topchords respectively.

24. The first condition cannot be safely recommended to designers because of the imponderable nature of the beam’s reaction to rotation, which may be accompanied by premature web-post buckling in a torsional mode. However, plastic design of a simple beam, showing collapse at only one hinge position, is possible.” Nevertheless, it will still be necessary to ensure that web and flanges remain stable up tothe formation of the plastic hinge. The two basic modes of plastic collapse of a castellated beam are (a) plastic extension and compression of the lower and upper tees respectively

in a region of high bending moment (b) parallelogram action of plastic hinge at the corners of an opening in a region of high shear force (Fig. 9). The location of both the opening which is critical (at which the collapse mechanism forms) and the corresponding load factor is complicated by the need to consider the response of an unsymmetrical tee section to three stress resultants: axial force N caused by the applied external bending moment; bending moment M ; shear force V caused by the applied external shear force.13 For each of these stress resultants actingalone, a tee has limiting values

and, adopting theVon Mises yieldcriterion V, = (web area of tee) X p,,/ J 3 to: Delivered by ICEVirtualLibrary.com IP: 192.168.39.63 On: Tue, 28 Sep 2010 12:38:20

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KNOWLES

Yield in tension /

Fig. 9. Plastic collapse: (a) in region of high bending moment; ( b ) in region of high shear force 25. For a tee under combined factored stress resultants M , N and V , failure surfaces can be derived which give the set of ratios NIN,, M / M p and V J V , at which failure occurs. A two-dimensional interaction diagram illustrating this is shown in Fig. 10. The significant aspect of the diagram is that for fixed values of the ratios N I N , and VlV, , the value of the associated ratio M / M p is dependent on the sign of M . The line A-A in Fig. 10 illustrates this point: for a given magnitude and sign of N and V , the positive value of M I M , is not equal to thecorresponding value of the negative ratio of M I M , . The interaction relationship shows the computational difficulty of locating the critical point in a beam, where the load factor is smallest. If it is assumed that shear stress is not a significant interactive component, thesurface can be reduced to the single curve for V/V, = 0. 26. With this simplified relationship, consideration can be given to a typical bay in which collapse has occurred at the root of the four tees surrounding a hole. Noting that for a given compressive axial force, the moment capacity of a tee is greater for positive (compression in the tee flange) than negative bending implies that thepoint of inflexion is not central (Fig.11).

M+

M+

=

V,X

M-

=

V,y

+M-

= V,(X

+ y ) = V,(a)

and similarly for the lower pair of tees

+

532

M +ICEVirtualLibrary.com M - = V,(a) Delivered by to: IP: 192.168.39.63 On: Tue, 28 Sep 2010 12:38:20

BEAMS

-1.2'

'

-0.8

I

-0.4

I

0

1

0.4

I

I

0.8

A

Fig. 10. Interaction diagram for bending, shear and axial force on tee

The totalshear across the opening

V=V,+r/; Therefore 2(M+ + M - ) = Va

In the limiting case of zero bending moment acting at the openingunder consideration, thereby producing a parallelogram failure, there is no axial force N in the

Fig. 11. Forces in tee atDelivered collapseby ICEVirtualLibrary.com to: IP: 192.168.39.63 On: Tue, 28 Sep 2010 12:38:20

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KNOWLES

tees, the pointof contraflexure is on the openingcentre-line, and M+ =M_ =Mp

The maximum shear force for this condition,V,,, , can be found from M+

+ M _ = 2Mp = V,,,a/2

The interaction curve for the individual tees of a castellated beam can be transformed into a curve for the combined tees, forming the beam by a transformation based on S --

-

M++M-

SF,,, M

2Mp -

N

BM,,, N p where M is the applied bending moment; S is the applied shear force; BM,,, and SF,,, are the maximum values of bending moment or shear force acting alone which the beam can resist. 27. Interaction charts have been prepared for the range of castellated beams6 Their use permits atrial section to be readily checked to determine its adequacy to carry a given factored loading. For concentrated loads, afew trials are necessary to find the critical combination of shear force and bending moment, although the locations which require checking are usually obvious. The common case of uniformly distributed loading can be simplified by comparing a typical beam strength curve with the general uniformly distributed loading curve as shown in Fig. 12. From this it can be seen that a section adequate in shear is inadequate in bending

Applied uniformly distributed load MIml,, = [l - (S~S,,,)I2

Strength ratio MIBM,,,

or moment ratio MIM,,,

1 .o

Fig. 12. Beam strengthDelivered comparedbywith applied unijormly to: distributedload ICEVirtualLibrary.com 534

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C A S T E L L A T E DB E A M S

Table I . Castellated beams withcompact tee stalks

I

Grade 43 Castellated

Original

305 254 203 203

X X X X

127 X 146 X 133 X 133 X

Grade 50

48 43 30 25

Castellated 305

381

X

305

X

305

X

X

133 X 30

146 X 43 133 X 30 133 X 25

by a small amount (about 5%). Therefore, a trial section can be selected from the table of ultimate bending and shear force capacities that have a bending moment capacity alittle larger than the maximum applied bending moment on the beam.

Design to BS 5950 28. The application of BS 595014 to castellated beams requires a consideration of width to thickness ratios so that the section can be correctly classified for local buckling (clause4.15.5.3).Compression flange outstands are unchangedby castellation, andtherefore fall into thesame class astheparent section. The only castellated beams with semi-compact flanges are in grade 50 steel: 381 X 146 X 31 (ex 254 X 146 X 31 UB) and 305 X 133 X 25 (ex 203 X 133 X 25 UB). The remainder areplastic or compact. 29. However, the expansion of universal beams has an important effect on the web depth to thickness ratio in two respects.

( a ) Between openings, the web slenderness d/t is increased by a factor of about 1.5. (b) At an opening, the beam consists of two tee sections, the webs (stalks) of which are unsupported attheir lower edges.

All web posts are at least semi-compact, but many have d/t > 63(275/fy)''2 (BS 5950, clause 3.6.2) and therefore will have to be checked for shear buckling. The classification of the tee chord downstand is not clear: should it be treated as a tee stalk or as partof a web?On the former assumption, calculation of the slenderness ( A / t )ratio of the stalk shows that only afew sections are compact(see Table 1); the remainder are semi-compact. 30. From these considerations it is clear that true plastic design of castellated beams is possible onlyfor a very small number of sections; the remainder mustbe designedon an elastic basis, assemi-compact sections, usingthe net section properties with due allowance for secondary Vierendeel effects of shear at the openings and for the local effects of point loads, if any, at any point in the beam (clause 4.15.3.2).

Conclusion 31. Fifty years after their invention, castellated beams continueto meet a need for an efficient element to provide for moderately loaded longer spans, as they have useful apertures for the passageof services and an attractive appearance. The design of the beams for simply supported structures by elastic methods is wellDeliveredon by their ICEVirtualLibrary.com to: structures is inevitable documented. Some restriction use in continuous IP: 192.168.39.63 535 On: Tue, 28 Sep 2010 12:38:20

KNOWLES giventheproblems of slendernesswhichlead t o restrictedrotationcapacity. of their use is to be encouraged. Experimental work to determine the limits

References 1 . PATENT SPECIFICATION. Improvements in built-up structural members. HMSO, 1939, Jan.

4, Patent Specification 498,281. 2. A new method of girder construction. Shipbldr Mar. Eng. Bldr, 1949, Oct., 682-683. 3. MANDEL A. J. et al. Stress distribution in castellated beams. J . Struct. Diu. Am. Soc. Ciu. Engrs, 1971,97(7),1947-1967. 4. SRIMANI S. L. and DAS.Finite element analysis of castellated beams. Computers Structs, 1978,9, Aug., 169-174. 5. KERDAL D. and NETHERCOT D. A. Failure modes for castellated beams. J . Constr. Steel Res. 1984,4259-315. 6. KNOWLES P. R. Design of castellated beams. CONSTRADO, Croydsn, 1985 (for use with BS 5950 and BS 449). 7. UNITEDSTEEL COMPANIES. Properties and strengths of castella beams. Defection characteristics. United Steel Companies, Rotherham, 1960, Aug., Report D.TS.6/262/2. Properties and strengths of castella beams. Furthertests. 8. UNITEDSTEELCOMPANIES. Research and Development Department, Swinden Laboratories, 1958, July, Report D.GE. 71/262/1. 9. HOSAINM. U. and SPIERSW. G. Failure of castelated [sic] beams due to rupture of welded joints. Acier, Stahl, Steel, 1971,36 (l), Jan., 34-40. 10. AGLAN A. A. and REDWOOD R. G. Web buckling in castellated beams. Proc. Instn Ciu. Engrs, Part 2,1974,57, June, 307-320. 1 1 . OKULW T. and NETHERCOT D. A. Web post strength in castellated beams. Proc. Instn Ciu. Engrs, Part 2, 1985,79, Sept., 533-557. 12. HALLEUX P. Limit analysis of castellated beams. Acier,Stahl,Steel, 1967, 32, Mar., 133-144. 13. SHERBOURNE A. N.and O ~ ~ T R J. O van. M Plastic analysis of castellated beams, 1. Interaction ofmoment, shear and axial force. Computers Structs,1972,2,79-109. 14. BRITISH STANDARDS INSTITUTION. Structural use of steelwork in building. Part 1 : Code of practice for design in simple and continuous construction: hot rolled sections. BSI, London, 1985, BS 5950.

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