J, Rondal, K,·G, WOrker D. Dutta, J. Wardenier, N

CONSTRUCTION WITH HOLLOW STEEL SECTION

Edited by: Comite International pour le Developpement et l'Etude de la Construction Tubulaire

Authors: Jacques Rondal, University of Liege Karl-Gerd WOrker, Consulting engineer Dipak Dutta, Chairman of the Technical Commission CIDECT Jaap Wardenier, Delft University of Technology Noel Yeomans, Chairman of the Cidect Working Group "Joints behaviour and Fatigue-resistance"

J. Rondal, K.-G. WOrker, D. Dutta, J. Wardenier, N. Yeomans

.. Verlag TUV Rheinland

Die Deutsche Bibliothek - CIP Einheitsaufnahme

Structural stability of hollow sections I [Comite International pour le Developpement et l'Etude de la Construction Tubulaire). J. Rondal ... - Koln: VerI. TUV Rheinland, 1992

(Construction with hollow steel sections) Dt. Ausg. u.d.T.: Knick- und Beulverhalten von Hohlprofilen (rund und rechteckig). - Franz. Ausg. u.d.T.: Stabilite des structures en profils creux ISBN 3-8249-0075-0

NE: Rondal, Jasques; Comite International pour le Developpement et I'Etude de la Construction Tubulaire

ISBN 3-8249-0075-0

© by Verlag TUV Rheinland GmbH, Koln 1992 Entirely made by: Verlag TUV Rheinland GmbH, Koln Printed in Germany 1992

Preface

The objective of this design manual is to present the guide lines for the design and calculation of steel structures consisting of circular and rectangular hollow sections dealing in particular with the stability of these structural elements. This book describes in a condensed form the global, local and lateral-torsional buckling behaviour of hollow sections as well as the methods to determine effective buckling lengths of chords and bracings in lattice girders built with them. Nearly all design rules and procedures recommended here are based on the results of the analytical investigations and practical tests, which were initiated and sponsored by CIDECT. These research works were carried out in the universities and institutes in various parts of the world. The technical data evolving from these research projects, the results of their evaluation and the conclusions derived were used to establish the "European buckling curves" for circular and rectangular hollow sections. This was the outcome of a cooperation between ECCS (European Convention for Constructional Steelwork) and CIDECT. These buckling curves have now been incorporated in a number of national standards. They have also been proposed for the buckling design by Eurocode 3, Part 1: "General Rules and Rules for Buildings", which is at present in preparation. Extensive research works on effective buckling lengths of structural elements of hollow sections in lattice girders in the late seventies led in 1981 to the publication of Monograph No. 4 "Effective lengths of lattice girder members" by CIDECT. A recent statistical evaluation of all data from this research programme resulted in a recommendation for the calculation of the said buckling length which Eurocode 3, Annex K "Hollow section lattice girder connections" (Draft October 1991) also contains. This design guide is the second of a series, which CIDECT will publish in the coming years: - Design guide for circular hollow section (CHS) joints under predominantly static loading. - Structural stability of hollow sections. - Design guide for rectangular hollow section joints under predominantly static loading. - Design guide for hollow section columns susceptible to fire. - Design guide for circular and rectangular hollow section joints under fatigue loading. The first book of this series has already been published early 1991 in three languages (english, french and germ an). The remaining three design manuals are now in preparation. All these publications are intended to make architects, engineers and constructors familiar with the simplified design procedures of hollow section structures. Worked-out examples make them easy to understand and show how to come to a safe and economic design. Our sincere thanks go to the authors of this book, who belong to the group of well known specialists in the field of structural applications of hollow sections. We express our special thanks to Dr. Jacques Rondal of the University of Liege, Belgium as the main author of this book. We thank further Mr. D. Grotmann of the Technical University of Aix-Ia-Chapelle for numerous stimulating suggestions. Finally we thank all CIDECT members, whose support made this book possible.

Dipak Dutta Chairman of the Technical Commission CIDECT

5

Quadrangular vierendee! columns

6

Contents Page

Introduction ........................................................... 9

1

1.1 1.2 1.3 1.4

2

3

3.1 3.2 3.3

4

4.1

5

5.1 5.2 5.2.1 5.2.2 5.2.2.1 5.2.2.2

6

6.1 6.2 6.2.1 6.2.2 6.2.3 6.3

7

7.1 7.2 7.3

8

8.1 8.2

8.3

General . ....................................................... 10

Limit states ..................................................... 10 Limit state design ................................................ 10 Steel grades .................................................... 11 Increase in yield strength due to cold working . . . . . . . . . . . . . . . . . . . . . . . . .. 11

Cross section classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13

Members in axial compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19

General ........................................................ 19 Design method .................................................. 19 Design aids ..................................................... 25

Members in bending .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 27

Design for lateral-torsional buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 27

Members in combined compression and bending . . . . . . . . . . . . . . . . . . . .. 28

General ........................................................ 28 Design method .................................................. 28 Design for stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 28 Design based on stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 30 Stress design without considering shear load .......................... 31 Stress design considering shear load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 32

Thin-wailed sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 34

General ........................................................ 34 Rectangular hollow sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 34 Effective geometrical properties of class 4 cross sections . . . . . . . . . . . . . . . .. 34 Design procedure ................................................ 36 Design aids ..................................................... 37 Circular hollow sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 38

Buckling length of members in lattice girders . . . . . . . . . . . . . . . . . . . . . . .. 40

General ........................................................ 40 Effective buckling length of chord and bracing members with lateral support .. 40 Chords of lattice girders, whose joints are not supported laterally . . . . . . . . . .. 40

Design examples .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 43

Design of a rectangular hollow section column in compression . . . . . . . . . . . .. 43 Design of a rectangular hollow section column in combined compression and uni-axial bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 43 Design of a rectangular hollow section column in combined compression and bi-axial bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 45

7

8.4 Design of a thin-walled rectangular hollow section column in compression ... 47 8.5 Design of a thin-walled rectangular hollow section column in concentric

compression and bi-axial bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 49

9 Symbols ....................................................... 51

1 0 References ............... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 53

CIDECT - International Committee for the Development and Study of Tubular Structures ............................................................. 55

8

Introduction

it is very often considered that the problems to be solved while designing a steel structure are only related to the calculation and construction of the members and their connections. They concern mainly the static or fatigue strength and the stability of the structural members as well as the load bearing capacity of the joints. This point of view is certainly not correct as one cannot ignore the important areas dealing with fabrication, erection and when necessary, protection against fire. It is very important to bear in mind that the application of hollow sections, circular and rectangular, necessitates special knowledge in all of the above mentioned areas extending beyond that for the open profiles in conventional structural engineering. This book deals with the aspect of buckling of circular and rectangular hollow sections, their calculations and the solutions to the stability problems. The aim of this design guide is to provide architects and structural engineers with design aids based on the most recent research results in the field of application technology of hollow sections. It is mainly based on the rules given in Eurocode 3 (final draft) "Design of Steel Structures, Part 1: General Rules and Rules for Buildings" and its annexes [1, 2]. Small differences can be found when compared to some national standards. The reader will find in reference [3] a review of the main differences existing between Eurocode 3 (final draft) and the codes used in other countries. However, when it is possible, some indications are given on the rules and recommendations in the codes used in Australia, Canada, Japan and United States of America as well as in some european countries.

Lift shaft with tubular frames

9

1 General

1.1 Limit states

Most design codes for see I structures are, at the present time, based on limit state design. Limit states are those beyond which the structure no longer satisfies the design performance requirements. Limit state conditions are classified into - ultimate limit state - serviceability limit state Ultimate limit states are those associated with collapse of a structure or with other failure modes, which endanger the safety of human life. For the sake of simplicity, states prior to structural collapse are classified and treated as ultimate limit states in place of the collapse itself. Ultimate limit states, which may require consideration, include: - Loss of equilibrium of a structure or a part of it, considered as a rigid body - Loss of load bearing capacity, as for example, rupture, instability, fatigue or other agreed

limiting states, such as excessive deformations and stresses Serviceability limit states correspond to states beyond which specified service criteria are no longer met. They include: - Deformations or deflections which affect the appearance or effective use of the structure

(including the malfunction of machines or services) or cause damage to finishes or non­structural elements

- Vibration which causes discomfort to people, damage to the building or its contents or which limits its functional effectiveness

Recent national and international design standards recommend procedures proving limit state resistance. This implies, in particular for stability analysis, that the imperfections, mechanical and geometrical, which influence the behaviour of a structure significantly, must be taken into account. Mechanical imperfections are, for example, residual stresses in structural members and connections. Geometrical imperfections are possible pre­deformations in members and cross sections as well as tolerances.

1.2 Limit state design

In the Eucrocode 3 format, when considering a limit state, it shall be verified that:

R r:(-yF·F)~- (1.1)

I'M where I'F = Partial safety factor for the action F I'M = Partial safety factor for the resistance R F = Value of an action R = Value of a resistance for a relevant limit state

I'F . F = Fd is called the design load while R/I'M = Rd is deSignated as the design resistance. It is not within the scope of this book to discuss in detail these general provisions. They can be taken from Eurocode 3 and other national codes, which can sometimes show small deviations from one another. As for example, the calculations in the recent US-codes are made with cJ> = 11'YM·

10

1.3 Steel grades

Table 1 gives the grades of the generally used structural steels with the nominal minimum values of the yield strength fv' range of the ultimate tensile strength fu and elongations. The steel grades correspond to the hot-rolled hollow sections as well as to the basic materials for cold-formed hollow sections. The designations of the steel grades in Table 1 are in accordance with ISO 630 [8) as well as EN 10025 [31). They can be different in other standards. For hot­rolled hollow sections (circular and rectangular), the draft of the european code EN 10210, Part 1 [20), 1990 is available.

Table 1 - Steel grades for structural steels

min. yield strength tensile strength min. percentage elongation

steel grade Lo = 5.65 YSo fy (N/mm2) fu (N/mm2)

longitudinal transverse

Fe 360 235 340 ... 470 26 24 Fe 430 275 370 ... 540 24 22 Fe510 355 470 ... 630 22 20

FeE 460' 460 550 ... 720 17 15

• from EN 10 210, Part 1 (20)

Table 2 contains the recommended physical properties valid for all structural steels.

Table 2 - Physical properties of structural steels

modulus of elastiCity:

shear modulus:

poisson co-efficient:

E = 210000 N/mm2 E

G = --- = 81 000 N/mm2 2(1 + v)

v = 0.3

co-efficient of linear expansion: Cl = 12· 10- 6 /°C

density: Q = 7850 kg/m3

1 .4 Increase In yield strength due to cold working

Cold rolling of profiles provides an increase in the yield strength due to strain hardening, which may be used in the design by means of the rules given in Table 3. However, this increase can be used only for RHS in tension or compression elements and cannot be taken into account if the members are subjected to bending (see Annex A of Eurocode 3 [2)). For cold rolled square and rectangular hollow sections, eq. (1.2) can be simplified (k = ?for all cold-forming of hollow sections and n = 4) resulting in:

14t fva = fYb + b + h (fu - fVb) (1.3)

:s; fu :s; 1.2· fyb

Fig. 1 allows a quick estimation of the average yield strength after cold-forming, for square and rectangular hollow sections for the four basic structural steels.

11

Table 3 - Increase of yield strength due to cold-forming of RHS profiles

Average yield strength:

The average yield strength fys may be determined from full size section tests or as follows [19. 32[:

fya = fyb + (k . n . t2f A) . (fu - fyb) (1.2)

where fyb• fu = specified tensile yield strength and ultimate tensile strength of the basic material (Nfmm2)

t = material thickness (mm) A = gross cross-sectional area (mm2) k = co-efficient depending on the type of forming (k = 7 for cold rolling) n = number of 900 bends in the section with an internal radius < 5 t (fractions of 900

bends should be counted as fractions of n) fys = should not exceed fu or 1.2 fyb

The increase in yield strength due to cold working should not be utilised for members which are annealed" or subject to heating over a long length with a high heat input after forming. which may produce softening.

Basic mat.erial: Basic material is the flat hot rolled sheet material out of which sections are made by cold forming.

" Stress relief annealing at more than 5800C or for over one hour may lead to deterioration of the mechanical properties [29)

12

Increase in yield strength fya/fYb

1.20 -.--r-....--.-------,

1. 1 5 +--I--l-\\

rm tICbf

G!J 'yb = 275 N/mm2

+--\t~~~= = 235 N/mm2 1.1 0 = 355 N/mm2

~--'lN~-= 460 N/mm2

1.00 +-..,.-+---r--+--,+-,--+-r-1 o 10 20 30 40 50 60 70 80 90 100

b+h 2t

Fig. 1 - Increase in yield strength for cold-formed square and rectangular hollow sections

2 Cross section classification

Different models can be used for the analysis of steel structures and for the calculation of the stress resultants (normal force, shear force, bending moment and torsional moment in the members of a structure). For an ultimate limit state design, the designer is faced mainly with three design methods (see Fig. 2). The cross section classes 3 and 4 with the procedure "elastic-elastic" differ from each other only by the requirement for local buckling for class 4.

Procedure "plastic-plastic"

Cross section class 1

This procedure deals with the plastic design and the formation of plastic hinges and moment redistribution in the structure. Full plasticity is developed in the cross section (bi-rectangular stress blocks) . .The cross section can form a plastic hinge with the rotation capacity required for plastic analysis. The ultimate limit state is reached when the number of plastic hinges is sufficient to produce a mechanism. The system must remain in static equilibrium.

Procedur.e "elastic-plastic"

Cross section class 2

In this procedure the stress resultants are determined following an elastic analysis and they are compared to the plastic resistance capacities of the member cross sections. Cross sections can develop their plastic resistance, but have limited rotation capacity. Ultimate limit state is achieved by the formation of the first plastic hinge.

Procedure "elastic-elastic"

Cross section class 3

This procedure consists of pure elastic calculation of the stress resultants and the resistance capacities of the member cross sections. Ultimate limit state is achieved by yielding of the extreme fibres of a cross section. The calculated stress in the extreme compression fibre of the member cross section can reach its yield strength, but local buckling is liable to prevent the development of the plastic moment resistance.

Procedure "elastic-elastic"

Cross section class 4

The cross section is composed of thinner walls than those of class 3. It is necessary to make explicit allowances for the effects of local buckling while determining the ultimate moment or compression resistance capacity of the cross section. The application of the first three above mentioned procedures is based on the presumption that the cross sections or their parts do not buckle locally before achieving their ultimate limit loads; that means, the cross sections must not be thin-walled. In order to fulfil this condition, the bIt-ratio for rectangular hollow sections or the d/t-ratio for circular hollow sections must not exceed certain maximum values. They are different for the cross section classes 1 through 3 as given in Tables 4, 5 and 6. A cross section must be classified according to the least favourable (highest) class of the elements under compression andlor bending. Tables 4 through 6 give the slenderness limits bIt or dlt for different cross section classes based on Eurocode 3 [1, 2). Other design codes show slightly different values (compare Tables 8 and 9).

13

cross section class 1 class 2 class 3 class 4 classes

load resistance full plasticity in full plasticity in elastic cross elastic cross capacity the cross section the cross section section section

full rotation restricted rotation yield stress in the local buckling to capacity capacity extreme fibre be taken into

account

stress distribution and rotation I 1f<,~~~ 1f- t ---7'::. - I < fS'---& 'Ls- I -z:; capacity

j ; -Iy -Iy

I I + Iy + Iy + Iy +Iy

procedure for the plastic elastic ( elastic elastic determination of the stress resultants

procedure for the plastic plastic elastic elastic determination of the ultimate resistance capacity of a section

Fig. 2 - Cross section classification and design methods

Table 4 - Limiting d/t ratios for circular hollow sections

€I] t ~

Y .+ y d

z

cross section class compression and/or bending

1 d/t::s 50f2

2 d/t::s 70f2

3 d/t::s 90f2

fy (N/mm2) 235 275 355 460

f=~ fy f 1 0.92 0.81 0.72

f2 1 0.85 0.66 0.51

14

Table 5 - Limiting h,/t·ratlos for webs of rectangular hollow sections

webs: (internal element perpendicular to the axis of bending) $] ""0' h h---h, = h - 3t

t 1 bending

h, = h - 3t

class web subject to web subject to web subject to bending and compression beding compression

stress distribution + Iy + Iy + Iy

in element [B} D~n JJ2]h (compression positive)

I • + Iy • y

1 h,lt s 72e h,lt s 33e when a > 0.5 h,lt s 396e/(13a-1)

when a < 0.5 h,lt s 36ela

2 h,lt s 83e h,lt s 38e when a > 0.5 h,lt s 456e/(13a-1)

when a < 0.5 h,lt s 41.5ela

stress distribution + Iy + + Iy

in element h'/2~ Dl} El} (compression h,/2 positive)

Iy • + Iy </Ily •

3 h,tt s 124 e h,lt s 42e when if; >-1

h,lt s 42 el (0.67 + 0.33 if;)

when if; <-1 h,lt s 62€{1 - if;) -.i( - if;)

e=~ fy 235 275 355 460

fy e 1 0.92 0.81 0.72

15

Table 6 - Limiting b,/t-ratlos for flanges of rectangular hollow sections

flanges: (internal elements parallel to the axis of bending) QJ b, = b - 3t

b1 = b-3t

class section in bending section in compression

stress distribution in ~y I ~y element and cross section -rr=='i'I F~ 1

1 I Fll F"1 (compression positive) 11 11

itJ P 11 11

11 11 11 tb=JJ t::I tk-.=,J] 6:1

-I- -I-

1 b1/t :$ 33f b1/t :$ 42f

2 b1/t:$ 38 f b1/t:$ 42 f

stress distribution in ~y Ify !C::J.!y element and cross section -n Ft - 1

rr===n F, (compression positive) X I I

11 d I1 11 I I tb-=dJ id L!:-=dJ I:d

-I- -I-

3 b1/t :$ 42 f b1/t :$ 42 f

f=~ fy (N/mm2) 235 275 355 460

fy f 1 0.92 0.81 0.72

In Table 7 the bIt, hIt and dlt limiting values for the different cross section classes, cross section types and stress distributions are given for a quick determination of the cross section class of a hollow section. The values for width b and height h of a rectangular hollow section are calculated by using the relationship bIt = b1/t + 3 and hIt = h1/t + 3. For the application of the procedures "plastic-plastic" (class 1) and "elastic-plastic" (class 2), the ratio of the specified minimum tenSile strength fu to yield strength fy must be not less than 1.2.

fuffy 2! 1.2 (2.1)

Further, according to Eurocode 3 [1,2), the minimum elongation at failure on a gauge length 10 = 5.65.../l:\, (where Ao is the original cross section area) is not to be less than 15%. For the application of the procedure "plastic-plastic" (full rotation), the strain Eu comes­ponding to the ultimate tensile strength fu must be at least 20 times the yield strain Ey corresponding to the yield strength fy. The steel grades in Table 1 for hot formed RHS and hot or cold formed CHS may be accepted as satisfying these requirements. Tables 8 and 9 give, for circular hollow sections and for square or rectangular hollow sections respectively, the limiting bIt and hIt ratios, which are recommended in various national codes around the world (3). Table 8 shows that there are significant differences in dlt limits recommended by the national codes, when a circular hollow section is under bending. In particular, this is clear in the case of the recent american code AISC 86. For the concentrically loaded circular hollow sections, the deviations are significantly smaller (less than about 10%). Table 9 shows that the differences in bIt limits for rectangular hollow sections between the national codes are, in general, not as large as those for circular hollow sections.

16

Table 7 - b/t- , h/t- and dlt limits for the cross section classes 1, 2 and 3 with bIt = b,/t + 3 and hIt = h,/t + 3

class 1 2 3

cross section element fy (N/mm2) 235 275 355 460 235 275 355 460 235 275 375 460

RHP compression' compression m 45 41.6 36.6 32.2 45 41.6 36.6 32.2 45 41.6 36.6 32.2

01 RHP bending compression m 36 33.3 29.3 25.7 41 37.9 33.4 29.3 45 41.6 36.6 32.2

011 RHP bending bending m 75 69.3 61.1 53.6 86.0 79.5 70.0 61.5 127 117.3 103.3 90.8

011 CHS compression CO) 50 42.7 33.1 25.5 70.0 59.8 46.3 35.8 90.0 76.9 59.6 46.0

andlor bending []]]]]]J

nIl6n ~

• There is no difference between bIt and hit limits for the classes 1, 2 and 3, when the whole cross section is only under compression.

"'-I

Table 8 - Max. d/t limits for circular hollow sections by country and code

f235 (€ = '\/ ,----f- ; fy in N/mm2)

y

bending

country code axial compression plastic limit (class 2)

Australia ASDR 87164 98.8€2 76.5€2

Belgium NBN B51-002 (08.88) 100€2 70€2

Canada CAN/CSA S 16.1-M89 97.9€2 76.7€2

Germany DIN 18800, Part 1 (11.90) 90€2 70€2

Japan AIJ 80 100€2 -Netherlands NEN 6770, publ. draft (08.89) 100€2 70€2

United BS 5950, Part 1 (1985) 93.6€2 66.7 €2 Kingdom

U.S.A. AISC/LRFD (1986) 96.8€2 61.8 €2

European Eurocode 3 [1) 90€2 70€2 Community

Tabelle 9 - Max. b1/t limits for rectangular hollow sections by country and code

(€ = ~ 2:5' ; fy in N/mm2) y

yield limit (class 3)

129.7 €2

100€2

97.9€2

90€2

100E2

100€2

93.6€2

268€2

90€2

bending

country code axial compresion platic limit yield limit (class 2) (class 3)

Australia ASDR 87164 40.2€* 29.9€ 40.2€* 45.4€* * 45.4€**

Belgium NBN B51-002 (08.88) 42€ 34€ 42€

Canada CAN/CSA-S 16.1-M89 37.6€ 34.2€ 43.6€

Germany DIN 18800, Part 1 (11.90) 37.8€ 37€ 37.8€

Japan AIJ 80 47.8€ - 47.8€

Netherlands NEN 6770, publ. draft (08.89) 42€ 34e 42e

United BS 5950 Part 1 (1985) 42.2e 34.6e 42.2e Kingdom

U.S.A. AISC/LRFD (1986) 40.8e - 40.8e

European Eurocode 3 [1) 42e 38e 42e Community

* for cold formed non-stress relieved hollow sections for hot-formed and cold-formed stress relieved hollow sections

18

3 Members in axial compression

3.1 General

This chapter of the book is devoted to the buckling of compressed hollow section members belonging to the cross section classes 1, 2 and 3. Thinwalled cross sections (class 4) will be dealt with in chapter 6. The buckling of a concentrically compressed column is, historically speaking, the oldest problem of stability and was already investigated by Euler and later by many other researchers (5). At the present time, the buckling design of a steel element under compression is performed by using the so called "European buckling curves" in most european countries. They are based on many extensive experimental and theoretical investigations, which, in particular, take mechanical (as for example residual stress, yield stress distribution) and geometrical (as for example, linear deviation) imperfections in the members into account.

x , .00 ...------.;;;:::---,-------,..----------,

0.75 -t----+--V'<A'If---\

0.25 +----+----+----+----'~::!IiiII

OO+-----+-----~-----+----~ o 0.5 1.0

X 1.5

Fig. 3 - European buckling curves (1)

2.0

A detailed discussion on the differences between buckling curves used in codes around the world is given in reference (3). Both design methods, allowable stress design and limit state design, have been covered. For ultimate limit state design, multiple buckling curves are mostly used (as for example, Eurocode 3 with ao' a, b, c curves, similarly in Australia and Canada). Other standards adopt a single buckling curve, presumably due to the fact that emphasis is placed on simplicity. Differences up to 15% can be observed between the various buckling curves in the region of medium slenderness (A).

3.2 Design method

At present, a large number of design codes exist and the recommended procedures are often very similar. Eurocode 3 [1,2) is referred to in the following. For hollow sections, the only buckling mode to be considered is flexural buckling. It is not required to take account of lateral-torsional buckling, since very large torsional rigidity of a hollow section prevents any torsional buckling.

19

The design buckling load of a compression member is given by the condition;

Nd:5 Nb,Ad

where Nd = Design load of the compressed member (or times working load) Nb,Ad = Design buckling resistance capacity of the member

fy N -,,·A·-b,Ad - 'YM

A is the area of the cross section;

(3,1)

" is the reduction factor of the relevant buckling curve (Fig. 3, Tables 11 through 14) dependent on the non-dimensional slenderness>': of a column;

fy is the yield strength of the material used; 'YM is the partial safety factor on the resistance side (in U,S.A.: 1/'YM = cp)

The reduction factor " is the ratio of the buckling resistance Nb,Ad to the axial plastic resistance Npl,Ad:

Nb,Ad fb,Ad ,,=-- =--Npl,Ad fy,d

N fb,Ad = design buckling stress = ~Ad

f fy,d = design yield strength = -y-

'YM

The non-dimensional slenderness>': is determined by

>.: = ~ (3.2) hE

Ib with h = T (Ib = effective buckling length; i = radius of gyration)

hE = 7r' Vf (UEulerian" slenderness)

E = 210000 N/mm2

Table 10 a - Eulerian slenderness for varlus structural steels

steelgrade Fe 360 Fe 430 Fe 510 Fe E460

fy (N/mm2) 235 275 355 460

AE 93,9 86.8 76.4 67.1

The selection of the buckling curve (a through c in Fig. 3) depends on the cross section type, This is mainly based on the various levels of residual stresses occurring due to different manufacturing processes. Table 10b shows the curves for hollow sections,

20

Table 10b - Buckling curves according to manufacturing process fyb = Yield strength of the basic (not cold-formed) material fya = Yield strength of the material after cold-forming

cross section manufacturing process

(!lISIUt hot-forming

cOld-forming vt _J -; L, t V (fYb used)

z Ca=:! m cold-forming (fya used)

Table 11 - Reduction factor )( - buckling curve ao

>; 0 1 2 3 4 5 6

0.00 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 .10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 .20 1.0000 0.9986 0.9973 0.9959 0.9945 0.9931 0.9917 .30 0.9859 0.9845 0.9829 0.9814 0.9799 0.9783 0.9767 .40 0.9701 0.9684 0.9667 0.9649 0.9631 0.9612 0.9593 .50 0.9513 0.9492 0.9470 0.9448 0.9425 0.9402 0.9378 .60 0.9276 0.9248 0.9220 0.9191 0.9161 0.9130 0.9099 .70 0.8961 0.8924 0.8886 0.8847 0.8806 0.8764 0.8721 .80 0.8533 0.8483 0.8431 0.8377 0.8322 0.8266 0.8208 .90 0.7961 0.7895 0.7828 0.7760 0.7691 0.7620 0.7549

1.00 0.7253 0.7178 0.7101 0.7025 0.6948 0.6870 0.6793 1.10 0.6482 0.6405 0.6329 0.6252 0.6176 0.6101 0.6026 1.20 0.5732 0.5660 0.5590 0.5520 0.5450 0.5382 0.5314 1.30 0.5053 0.4990 0.4927 0.4866 0.4806 0.4746 0.4687 1.40 0.4461 0.4407 0.4353 0.4300 0.4248 0.4197 0.4147 1.50 0.3953 0.3907 0.3861 0.3816 0.3772 0.3728 0.3685 1.60 0.3520 0.3480 0.3441 0.3403 0.3365 0.3328 0.3291 1.70 0.3150 0.3116 0.3083 0.3050 0.3017 0.2985 0.2954 1.80 0.2833 0.2804 0.2775 0.2746 0.2719 0.2691 0.2664 1.90 0.2559 0.2534 0.2509 0.2485 0.2461 0.2437 0.2414 2.00 0.2323 0.2301 0.2280 0.2258 0.2237 0.2217 0.2196 2.10 0.2117 0.2098 0.2079 0.2061 0.2042 0.2024 0.2006 2.20 0.1937 0.1920 0.1904 0.1887 0.1871 0.1855 0.1840 2.30 0.1779 0.1764 0.1749 0.1735 0.1721 0.1707 0.1693 2.40 0.1639 0.1626 0.1613 0.1600 0.1587 0.1575 0.1563 2.50 0.1515 0.1503 0.1491 0.1480 0.1469 0.1458 0.1447 2.60 0.1404 0.1394 0.1383 0.1373 0.1363 0.1353 0.1343 2.70 0.1305 0.1296 0.1286 0.1277 0.1268 0.1259 0.1250 2.80 0.1216 0.1207 0.1199 0.1191 0.1183 0.1175 0.1167 2.90 0.1136 0.1128 0.1120 0.1113 0.1106 0.1098 0.1091 3:00 0.1063 0.1056 0.1049 0.1043 0.1036 0.1029 0.1023 3.10 0.0997 0.0991 0.0985 0.0979 0.0972 0.0966 0.0960 3.20 0.0937 0.0931 0.0926 0.0920 0.0915 0.0909 0.0904 3.30 0.0882 0.0877 0.0872 0.0867 0.0862 0.0857 0.0852 3.40 0.0832 0.0828 0.0823 0.0818 0.0814 0.0809 0.0804 3.50 0.0786 0.0782 0.0778 0.0773 0.0769 0.0765 0.0761 3.60 0.0744 0.0740 0.0736 0.0732 0.0728 0.0724 0.0720

buckling curves

a

b

c

7 8 9

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9903 0.9889 0.9874 0.9751 0.9735 0.9718 0.9574 0.9554 0.9534 0.9354 0.9328 0.9302 0.9066 0.9032 0.8997 0.8676 0.8630 0.8582 0.8148 0.8087 0.8025 0.7476 0.7403 0.7329 0.6715 0.6637 0.6560 0.5951 0.5877 0.5804 0.5248 0.5182 0.5117 0.4629 0.4572 0.4516 0.4097 0.4049 0.4001 0.3643 0.3601 0.3560 0.3255 0.3219 0.3184 0.2923 0.2892 0.2862 0.2637 0.2611 0.2585 0.2390 0.2368 0.2345 0.2176 0.2156 0.2136 0.1989 0.1971 0.1954 0.1824 0.1809 0.1794 0.1679 0.1665 0.1652 0.1550 0.1538 0.1526 0.1436 0.1425 0.1414 0.1333 0.1324 0.1314 0.1242 0.1233 0.1224 0.1159 0.1151 0.1143 0.1084 0.1077 0.1070 0.1016 0.1010 0.1003 0.0955 0.0949 0.0943 0.0898 0.0893 0.0888 0.0847 0.0842 0.0837 0.0800 0.0795 0.0791 0.0756 0.0752 0.0748 0.0717 0.0713 0.0709

21

Table 12 - Reduction factor" - buckling curve "a"

5; 0 1 2 3 4 5 6 7 8 9

0.00 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 .10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 .20 1.0000 0.9978 0.9956 0.9934 0.9912 0.9889 0.9867 0.9844 0.9821 0.9798 .30 0.9775 0.9751 0.9728 0.9704 0.9680 0.9655 0.9630 0.9605 0.9580 0.9554 .40 0.9528 0.9501 0.9474 0.9447 0.9419 0.9391 0.9363 0.9333 0.9304 0.9273 .50 0.9243 0.9211 0.9179 0.9147 0.9114 0.9080 0.9045 0.9010 0.8974 0.8937 .60 0.8900 0.8862 0.8823 0.8783 0.8742 0.8700 0.8657 0.8614 0.8569 0.8524 .70 0.8477 0.8430 0.8382 0.8332 0.8282 0.8230 0.8178 0.8124 0.8069 0.8014 .80 0.7957 0.7899 0.7841 0.7781 0.7721 0.7659 0.7597 0.7534 0.7470 0.7405 .90 0.7339 0.7273 0.7206 0.7139 0.7071 0.7003 0.6934 0.6865 0.6796 0.6726

1.00 0.6656 0.6586 0.6516 0.6446 0.6376 0.6306 0.6236 0.6167 0.6098 0.6029 1.10 0.5960 0.5892 0.5824 0.5757 0.5690 0.5623 0.5557 0.5492 0.5427 0.5363 1.20 0.5300 0.5237 0.5175 0.5114 0.5053 0.4993 0.4934 0.4875 0.4817 0.4760 1.30 0.4703 0.4648 0.4593 0.4538 0.4485 0.4432 0.4380 0.4329 0.4278 0.4228 1.40 0.4179 0.4130 0.4083 0.4036 0.3989 .03943 0.3898 0.3854 0.3810 0.3767 1.50 0.3724 0.3682 0.3641 0.3601 0.3561 0.3521 0.3482 0.3444 0.3406 0.3369 1.60 0.3332 0.3296 0.3261 0.3226 0.3191 0.3157 0.3124 0.3091 0.3058 0.3026 1.70 0.2994 0.2963 0.2933 0.2902 0.2872 0.2843 0.2814 0.2786 0.2757 0.2730 1.80 0.2702 0.2675 0.2649 0.2623 0.2597 0.2571 0.2546 0.2522 0.2497 0.2473 1.90 0.2449 0.2426 0.2403 0.2380 0.2358 0.2335 0.2314 0.2292 0.2271 0.2250 2.00 0.2229 0.2209 0.2188 0.2168 0.2149 0.2129 0.2110 0.2091 0.2073 0.2054 2.10 0.2036 0.2018 0.2001 0.1983 0.1966 0.1949 0.1932 0.1915 0.1899 0.1883 2.20 0.1867 0.1851 0.1836 0.1820 0.1805 0.1790 0.1775 0.1760 0.1746 0.1732 2.30 0.1717 0.1704 0.1690 0.1676 0.1663 0.1649 0.1636 0.1623 0.1610 0.1598 2.40 0.1585 0.1573 0.1560 0.1548 0.1536 0.1524 0.1513 0.1501 0.1490 0.1478 2.50 0.1467 0.1456 0.1445 0.1434 0.1424 0.1413 0.1403 0.1392 0.1382 0.1372 2.60 0.1362 0.1352 0.1342 0.1332 0.1323 0.1313 0.1304 0.1295 0.1285 0.1276 2.70 0.1267 0.1258 0.1250 0.1241 0.1232 0.1224 0.1215 0.1207 0.1198 0.1190 2.80 0.1182 0.1174 0.1166 0.1158 0.1150 0.1143 0.1135 0.1128 0.1120 0.1113 2.90 0.1105 0.1098 0.1091 0.1084 0.1077 0.1070 0.1063 0.1056 0.1049 0.1042 3.00 0.1036 0.1029 0.1022 0.1016 0.1010 0.1003 0.0997 0.0991 0.0985 0.0978 3.10 0.0972 0.0966 0.0960 0.0954 0.0949 0.0943 0.0937 0.0931 0.0926 0.0920 3.20 0.0915 0.0909 0.0904 0.0898 0.0893 0.0888 0.0882 0.0877 0.0872 0.0867 3.30 0.0862 0.0857 0.0852 0.0847 0.0842 0.0837 0.0832 0.0828 0.0823 0.0818 3.40 0.0814 0.0809 0.0804 0.0800 0.0795 0.0791 0.0786 0.0782 0.0778 0.0773 3.50 0.0769 0.0765 0.0761 0.0757 0.0752 0.0748 0.0744 0.0740 0.0736 0.0732 3.60 0.0728 0.0724 0.0721 0.0717 0.0713 0.0709 0.0705 0.0702 0.0698 0.0694

The buckling curves can be described analytically (for computer calculations) by the equation:

" = ,~' but,,:s; 1 cp + Vcp2_>:2

with cP = 0,5 [1 + Cl! (>:- 0,2) + PI

(3.3)

(3.4)

The imperfection factor Cl! (in equation 3.4) for the corresponding buckling curve can be obtained from the following table:

buckling curve ao a

imperfection factor a 0.13 0.21

22

b

0.34

c

0.49 See Tables 11 through 14 for the reduction factor" as a function of X

Table 13 - Reduction factor )( - buckling curve "b"

>; 0 1 2 3 4 5 6 7 8 9

0.00 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 .10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 .20 1.0000 0.9965 0.9929 0.9894 0.9858 0.9822 0.9786 0.9750 0.9714 0.9678 .30 0.9641 0.9604 0.9567 0.9530 0.9492 0.9455 0.9417 0.9378 0.9339 0.9300 .40 0.9261 0.9221 0.9181 0.9140 0.9099 0.9057 0.9015 0.8973 0.8930 0.8886 .50 0.8842 0.8798 0.8752 0.8707 0.8661 0.8614 0.8566 0.8518 0.8470 0.8420 .60 0.8371 0.8320 0.8269 0.8217 0.8165 0.8112 0.8058 0.8004 0.7949 0.7893 .70 0.7837 0.7780 0.7723 0.7665 0.7606 0.7547 0.7488 0.7428 0.7367 0.7306 .80 0.7245 0.7183 0.7120 0.7058 0.6995 0.6931 0.6868 0.6804 0.6740 0.6676 .90 0.6612 0.6547 0.6483 0.6419 0.6354 0.6290 0.6226 0.6162 0.6098 0.6034

1.00 0.5970 0.5907 0.5844 0.5781 0.5719 0.5657 0.5595 0.5534 0.5473 0.5412 1.10 0.5352 0.5293 0.5234 0.5175 0.5117 0.5060 0.5003 0.4947 0.4891 0.4836 1.20 0.4781 0.4727 0.4674 0.4621 0.4569 0.4517 0.4466 0.4416 0.4366 0.4317 1.30 0.4269 0.4221 0.4174 0.4127 0.4081 0.4035 0.3991 0.3946 0.3903 0.3860 1.40 0.3817 0.3775 0.3734 0.3693 0.3653 0.3613 0.3574 0.3535 0.3497 0.3459 1.50 0.3422 0.3386 0.3350 0.3314 0.3279 0.3245 0.3211 0.3177 0.3144 0.3111 1.60 0.3079 0.3047 0.3016 0.2985 0.2955 0.2925 0.2895 0.2866 0.2837 0.2809 1.70 0.2781 0.2753 0.2726 0.2699 0.2672 0.2646 0.2620 0.2595 0.2570 0.2545 1.80 0.2521 0.2496 0.2473 0.2449 0.2426 0.2403 0.2381 0.2359 0.2337 0.2315 1.90 0.2294 0.2272 0.2252 0.2231 0.2211 0.2191 0.2171 0.2152 0.2132 0.2113 2.00 0.2095 0.2076 0.2058 0.2040 0.2022 0.2004 0.1987 0.1970 0.1953 0.1936 2.10 0.1920 0.1903 0.1887 0.1871 0.1855 0.1840 0.1825 0.1809 0.1794 0.1780 2.20 0.1765 0.1751 0.1736 0.1722 0.1708 0.1694 0.1681 0.1667 0.1654 0.1641 2.30 0.1628 0.1615 0.1602 0.1590 0.1577 0.1565 0.1553 0.1541 0.1529 0.1517 2.40 0.1506 0.1494 0.1483 0.1472 0.1461 0.1450 0.1439 0.1428 0.1418 0.1407 2.50 0.1397 0.1387 0.1376 0.1366 0.1356 0.1347 0.1337 0.1327 0.1318 0.1308 2.60 0.1299 0.1290 0.1281 0.1272 0.1263 0.1254 0.1245 0.1237 0.1228 0.1219 2.70 0.1211 0.1203 0.1195 0.1186 0.1178 0.1170 0.1162 0.1155 0.1147 0.1139 2.80 0.1132 0.1124 0.1117 0.1109 0.1102 0.1095 0.1088 0.1081 0.1074 0.1067 2.90 0.1060 0.1053 0.1046 0.1039 0.1033 0.1026 0.1020 0.1013 0.1007 0.1001 3.00 0.0994 0.0988 0.0982 0.0976 0.0970 0.0964 0.0958 0.0952 0.0946 0.0940 3.10 0.0935 0.0929 0.0924 0.0918 0.0912 0.0907 0.0902 0.0896 0.0891 0.0886 3.20 0.0880 0.0875 0.0870 0.0865 0.0860 0.0855 0.0850 0.0845 0.0840 0.0835 3.30 0.0831 0.0826 0.0821 0.0816 0.0812 0.0807 0.0803 0.0798 0.0794 0.0789 3.40 0.0785 0.0781 0.0776 0.0772 0.0768 0.0763 0.0759 0.0755 0.0751 0.0747 3.50 0.0743 0.0739 0.0735 0.0731 0.0727 0.0723 0.0719 0.0715 0.0712 0.0708 3.60 0.0704 0.0700 0.0697 0.0693 0.0689 0.0686 0.0682 0.0679 0.0675 0.0672

Eurocode 3, Annex D allows the use of the higher buckling curve "ao" instead of "a" for compressed members of I-sections of certain demensions and steel grade FeE 460 (6). This is based on the fact that, in case of high strength steel, the imperfections (geometrical and structural) play a less detrimental role on the buckling behaviour, as shown by numerical calculations and experimental tests on I-section columns of FeE 460. As a consequence hot formed hollow sections using FeE 460 steel grade may be designed with respect to buckling curve "ao" instead of "a".

23

Table 14 - Reduction factor x - buckling curve "c"

>; 0 1 2 3 4 5 6 7 8 9

0.00 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 .10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 .20 1.0000 0.9949 0.9898 0.9847 0.9797 0.9746 0.9695 0.9644 0.9593 0.9542 .30 0.9491 0.9440 0.9389 0.9338 0.9286 0.9235 0.9183 0.9131 0.9078 0.9026 .40 0.8973 0.8920 0.8867 0.8813 0.8760 0.8705 0.8651 0.8596 0.8541 0.8486 .50 0.8430 0.8374 0.8317 0.8261 0.8204 0.8146 0.8088 0.8030 0.7972 0.7913 .60 0.7854 0.7794 0.7735 0.7675 0.7614 0.7554 0.7493 0.7432 0.7370 0.7309 .70 0.7247 0.7185 0.7123 0.7060 0.6998 0.6935 0.6873 0.6810 0.6747 0.6684 .80 0.6622 0.6559 0.6496 0.6433 0.6371 0.6308 0.6246 0.6184 0.6122 0.6060 .90 0.5998 0.5937 0.5876 0.5815 0.5755 0.5695 0.5635 0.5575 0.5516 0.5458

1.00 0.5399 0.5342 0.5284 0.5227 0.5171 0.5115 0.5059 0.5004 0.4950 0.4896 1.10 0.4842 0.4790 0.4737 0.4685 0.4634 0.4583 0.4533 0.4483 0.4434 0.4386 1.20 0.4338 0.4290 0.4243 0.4197 0.4151 0.4106 0.4061 0.4017 0.3974 0.3931 1.30 0.3888 0.3846 0.3805 0.3764 0.3724 0.3684 0.3644 0.3606 0.3567 0.3529 1.40 0.3492 0.3455 0.3419 0.3383 0.3348 0.3313 0.3279 0.3245 0.3211 0.3178 1.50 0.3145 0.3113 0.3081 0.3050 0.3019 0.2989 0.2959 0.2929 0.2900 0.2871 1.60 0.2842 0.2814 0.2786 0.2759 0.2732 0.2705 0.2679 0.2653 0.2627 0.2602 1.70 0.2577 0.2553 0.2528 0.2504 0.2481 0.2457 0.2434 0.2412 0.2389 0.2367 1.80 0.2345 0.2324 0.2302 0.2281 0.2260 0.2240 0.2220 0.2200 0.2180 0.2161 1.90 0.2141 0.2122 0.2104 0.2085 0.2067 0.2049 0.2031 0.2013 0.1996 0.1979 2.00 0.1962 0.1945 0.1929 0.1912 0.1896 0.1880 0.1864 0.1849 0.1833 0.1818 2.10 0.1803 0.1788 0.1774 0.1759 0.1745 0.1731 0.1717 0.1703 0.1689 0.1676 2.20 0.1662 0.1649 0.1636 0.1623 0.1611 0.1598 0.1585 0.1573 0.1561 0.1549 2.30 0.1537 0.1525 0.1514 0.1502 0.1491 0.1480 0.1468 0.1457 0.1446 0.1436 2.40 0.1425 0.1415 0.1404 0.1394 0.1384 0.1374 0.1364 0.1354 0.1344 0.1334 2.50 0.1325 0.1315 0.1306 0.1297 0.1287 0.1278 0.1269 0.1260 0.1252 0.1243 2.60 0.1234 0.1226 0.1217 0.1209 0.1201 0.1193 0.1184 0.1176 0.1168 0.1161 2.70 0.1153 0.1145 0.1137 0.1130 0.1122 0.1115 0.1108 0.1100 0.1093 0.1086 2.80 0.1079 0.1072 0.1065 0.1058 0.1051 0.1045 0.1038 0.1031 0.1025 0.1018 2.90 0.1012 0.1006 0.0999 0.0993 0.0987 0.0981 0.0975 0.0969 0.0963 0.0957 3.00 0.0951 0.0945 0.0939 0.0934 0.0928 0.0922 0.0917 0.0911 0.0906 0.0901 3.10 0.0895 0.0890 0.0885 0.0879 0.0874 0.0869 0.0864 0.0859 0.0854 0.0849 3.20 0.0844 0.0839 0.0835 0.0830 0.0825 0.0820 0.0816 0.0811 0.0806 0.0802 3.30 0.0797 0.0793 0.0789 0.0784 0.0780 0.0775 0.0771 0.0767 0.0763 0.0759 3.40 0.0754 0.0750 0.0746 0.0742 0.0738 0.0734 0.0730 0.0726 0.0722 0.0719 3.50 0.0715 0.0711 0.0707 0.0703 0.0700 0.0696 0.0692 0.0689 0.0685 0.0682 3.60 0.0678 0.0675 0.0671 0.0668 0.0664 0.0661 0.0657 0.0654 0.0651 0.0647

24

3.3 Design aids

The reduction factor for buckling x is equal to 1.0 for x: :s 0.2. When this limit is exceeded, the design resistance must take the buckling reduction factor x into acount. For identical X:, x is independent of the steel grade (yield strength fy) Figures 4 through 7 allow a quick determination of buckling resistance. The diagrams give the

I buckling strength as a function of A = T (buckling length/radius of gyration) with yield

strength of the material as a parameter.

Buckling strength (Nb.Rd • ~M/A) N/mm2

450

400

350

300

250

200

150

100

r-~\ \

IV 0460 Nlmm2

\

" h I 1]1-

50

o o i

o i o

50 i

20

20

100 150

40 i

40 60

200 250,\:1 i

i

60 80 Illd-l) i i

80 100 Illb-l)

Fig. 4 - Buckling curve for hot-formed hollow sections of FeE 460, basis "ao" (see Table 11)

Buckling strength INb.Ad . ~M/A) N/mm2

450

400

350

300 +--+-"<H.

250 +---!""d-'I..-\

IV = 460 Nlmm2 Iv o 355 Nlmm2 IV .0 275 Nlmm2 IV .0 235 Nlmm2

150 +-+-+--t-''''-

100 +-+----+-+-+---"'1 ....

0 50 100 150 200 i i i 0 20 40 60

i i 20 40 60 80

250 ,\:1. i

80 Illd -I)

100 Illb-t)

Fig. 6 - Buckling curves for hollow sections of various steel grades, basis "b" (see Table 13)

Buckling strength (N b.Rd • ~M/A) N/mm2

450

400

350

300

250

200

150

100

50

0

IV : 460 Nlmm2

IV : 355 Nlmm2

IV : 275 Nlmm2

++~---¥V IV : 235 Nlmm2

0 50 100 150 200 i

20 40 60 i i i i 0 20 40 60 80

250,\:+

80 Illd-l)

100 Illb-l)

Fig. 5 - Buckling curves for hollow sections of various steel grades, basis "a" (see Table 12)

Buckling strength (Nb.Rd . ~ MI A) N/mm2

350-=,..----------,

300

250+---t".;~

200++"""<-Y

150 ++--+-~"

IV : 355 Nlmm2 IV : 275 Nlmm2

IV.: 235 Nlmm2

100 ++--+---+-----t"~

50 +-+-+-+--+--+--t-~ __

50 100 150 200 i

o 20 40 60 i i

20 40 60 80

250,\:1 i

i

80 Illd -tl

100 Illb-t)

Fig. 7 - Buckling curves for hollow section of various steel grades, basis "c" (see Table 14)

For circular and square hollow sections the abscissa values I/(d - t) or I/(b - t) can approximately replace the slenderness A. This is precisely valid for t <c d or t <c b.

25

Tubular triangular arched truss for the roof structure of a stadium

26

4 Members in bending

In general, lateral-torsional buckling resistance need not be checked for circular hollow sections and rectangular hollow sections normally used in practice (b/h ~ 0.5). This is due to the fact that their polar moment of intertia It is very large in comparison with that of open profiles.

4.1 Design for laterlal-torsional buckling

The critical lateral-torsional moment decreases with increasing length of a beam. Table 15 shows the length of a beam (of various steel grades) exceeding which lateral­torsional failure occurs. The values are based on the relation:

_I_:s; 113400 . ~ -V 3 + "Iy' h-t fy 1 +"Iy 1 +"Iy

fy = Yield strength in N/mm2 b-t

"Iy = h - t

(4.1)

Equation (4.1) has been established on the basis of the non-dimensional slenderness limit XLT = 0.4 * (see Eurocode 3 (1)), which is defined by the relation:

- ~y ALT= --fCr•LT

(4.2)

where fer. LT is the critical elastic stress for lateral-torsional buckling. Equation 4.1 is based on pure bending of a beam (most conservative loading case) for elastic stress distribution (cross section class 3). However, it is also valid for plastic stress destribution (cross section classes 1 and 2). The lowest value for I/(h - t) is 37.7 (FeE 460) according to Table 15. Assuming a size of 100 x 200 mm, the critical length, for which lateral-torsional buckling can be expected, is:

ICr = 37.7·0.2 = 7.54 m,

This span length can be regarded as quite large for the given size (and full utilization of yield strength for "IF times load).

Table 15 - Limiting I/(h - t) ratios for a rectangular hollow section, below which no lateral-torsional buckling check Is necessary

M( )M I/(h-t) oS /5. 21. 'Yy

fy = 235 N/mm2 fy = 275 N/mm2 fy = 355 N/mm2 fy = 460 N/mm2

'Ut 0.5 73.7 63.0 48.8 37.7

ccb' 0.6 93.1 79.5 61.6 47.5

0.7 112.5 96.2 74.5 57.5

0.8 132.0 112.8 87.4 67.4

b-t bm 0.9 151.3 129.3 100.2 77.3

'Y =--=-y h -t hm 1.0 170.6 145.8 112.9 87.2

• ALT oS 0.4 is also recommended by some other codes [3, 21)

27

5 Members in combined compression and bending

5.1 General

Besides concentrically compressed columns, structural elements are most often loaded simultaneously by axial compression and bending moments. This chapter is devoted to classes 1 , 2 and 3 beam-columns. Thin-walled members (class 4) are considered in chapter 6.

5.2 Design method

5.2.1 Design for stability

Lateral-torsional buckling is not a potential failure mode for hollow sections (see chapter 4). According to Eurocode 3 [1 J the relation is based on the following linear interaction formulae:

NSd + K My,Sd K Mz,Sd < 1 (5.1) Nb,Ad y My,Ad + z Mz,Ad -

where: NSd = Design value of axial compression ('YF times load)

(5.2) Npl A·f

Nb Ad = X - = x --y , 'YM 'YM

X = min (XY' x z) = Reduction factor (smaller of Xy and xz), see chapter 3.2 A = Cross sectional area fy = Yield strength 'YM = Partial safety factor for resistance

My,Sd' Mz,Sd = Maximum absolute design value of the bending moment about y-y or z-z axis according to the first order theory')

fy My,Ad = Wel,y' 'YM by elastic utilization of a cross section (class 3)

fy or My Ad = Wpl Y • - by plastic utilization of a cross section (class 1 and 2)

, ''YM

fy Mz Ad = Wel z . - by elastic utilization of a cross section (class 3).

, ''YM

(5.3)

fy or Mz,Ad = Wpl,z' 'YM by plastic utilization of a cross section (class 1 and 2)

NSd Ky = 1 - --. -N- . P-Y' however Ky :S 1.5

Xy pi (5.4)

_ (WPIY ~ P-y = Ay (2{jM,y - 4) + W - 1 ,however P-y :S 0.9 el,y

(5.5)

11 Increment of bending moments according to the second order theory is considered by determining \. and };z by buckling lengths of whole structural system

28

NSd Kz = 1 - --N- . JI." however Kz ~ 1.5

}{y' pi

- (WPIZ ~ Jl.z = Az (2i3M,z - 4) + W - 1 ,however Jl.z ~ 0.9 el,z

(5.6)

(5.7)

W For elastic sections (class 3) the value wPI,z in the equations (5.5) and (5.7) is taken to be

el,z equal to 1.

i3M,y and i3M,z are equivalent uniform moment factors according to Table 16, column 2, in order to determine the form of the bending moment distribution My and Mz.

Remark 1: For uni-axial bending with axial force, the reduction factor }{ is related to the loaded bending axis, as for example, }{y for the applied My with Mz = O.

Then the following additional requirement has to be fulfilled:

(5.8)

Table 16 - Equivalent uniform moment factors {3M and {3m

1 2 3

moment diagram equivalent uniform moment equivalent uniform moment factor {3M factor {3m

1 edge moments {3M,~ = 1.8 - 0.7 '" {3m,~ = 0.66 + 0.44 "', N

M1~tjJ'M1 however {3m,~ 2: 1 - N Ki

-1 ,;;;tjJ,;;, 1 and {3m,~ 2: 0.44

2 moment from laterat foad {3M,a = 1.3 {3m,a = 1.0

~ {3M,a = 1.4

Ma

~ Ma

3 moment due to combined lateral load plus edge Ma

moments {3M = {3M,~ + AM ({3M,a - (3M,~) '"

s 0.77:

Ma = I max M I due to {3m = 1.0 M1 ~:::JdM lateral load only

> 0.77: Ma

'" AM = I max M I for Ma + Ml • {3m,~ M1 ~ tdM moment diagram {3m =

Ma+ Ml Ma without change of sign

M1~JdM I max M I + I min M I Ma where sign of

moment changes

29

Remark 2: A further design method for the loading case of bending moment and axial compression is available in the literature [21,22,23], which is called "substituting member method" [24, 25]. It is based on the formula for uni-axial bending moment and axial force1), which is used frequently:

NSd ~m' Mysd -"""';;-'--- + . Xy • N pl .Rd My,Rd

-~,..---- :s 1 NSd

1---'x NKi y

where, besides the definitions already described, A· f

NplRd

= __ v , 'YM

11'2. El NI NKi = Ir- = };~ (Eulerian buckling load)

~m = Equivalent uniform moment factor from Table 16, column 3,

(5,9)

~m < 1 , allowed only for fixed ends of a member and constant compression without lateral load My,Rd according to equation (5,3) (elastic or plastic)

Equation (5,9) can be written conservatively in a simplified manner:

NSd ~m' Mysd + ':s 0.9

Xy • Npl,Rd My,Rd (5.9a)

5.2.2 Design based on stress

A compressed member has to be designed on the basis of the most stressed cross section in addition to stability, Axial force, bending moments My and M z and shear force have to be considered simultaneously, According to Eurocode 3 [1], an applied shear force VSd can be neglected, when the following condition is fulfilled:

VSd:S 0,5 Vpl,Rd

where V pl,Rd = Design plastic shear resistance of a cross section

fy = 2t . dm • -- for CHS VS· 'YM

fy = 2t·hm·--­

VS, 'YM

for RHS (bm instead of hm when shear force is parallel to b)

Av = 2t . dm or 2t . hm

1) Corresponding formulae for uni- or bi-axial bending and axial force are given in [21, 23),

30

(5,10)

(5,11 )

(5.12)

Equation (5.10) is satisfied in nearly all practical cases.

V In some other codes [21] the limiting values for V Sd ,Up to which the shear force can be

pl,Ad disregarded, is significantly lower than 0.5.

5.2.2.1 Stress design without considering shear load [1]

The following relationship is valid for plastic design (cross section classes 1 and 2):

~ + _z,Sd <1 (M)'" (M )13 MNy,Ad MNz,Ad-

(5.13)

where Cl = {3 = 2 for CHS

f.I 1.66 h 6 a = tJ = l' _ 1.13 n2 ' owever:$ (5.14)

NSd NSd n=--=---

Npl,Ad fy A·-

with (5.15)

'YM

MNy,Ad and MNz,Ad are the reduced plastic resistance moments taking axial forces into account. These reduced moments are described by the relations given below.

For rectangular hollow sections:

MNy,Ad = 1.33 Mpl,y,Ad (1 - n), however:$ Mpl,y,Ad

(1 - n) MNz,Ad = Mpl,z,Ad 0.5 + h

m • t/A ' however :$ Mpl,z,Ad

For square hollow sections: MN,Ad = 1,26 Mpl,Ad (1 - n), however :$ Mpl,Ad

For circular hollow sections: MN,Ad = 1,04' Mpl (1 - n1.7), however:$ Mpl

(5.16)

(5.17)

(5.18)

(5.19)

For circular hollow sections, the following exact and simple equation [23] is also valid instead of the equation (5.19):

M~~:d :$ cos (~~. i) where MSd = VM~,Sd + M~,Sd\

VSd But the shear force must be limited to -V--:$ 0.25

pl,Ad

(5.20)

(5.21)

For elastic design the following simple linear equation can be applied instead of the equation (5.13):

(5.22)

where fYd = f/'YM

This equation can also be used, as a lower bound, but more simple to use, for plastic design of cross section classes 1 and 2 instead of the equation (5.13).

31

5.2.2.2 Stress design considering shear load [1J

If the shear load V Sd exceeds 50% of the plastic design resistance of the cross section V pl.Rd'

the design resistance of the cross section to combinations of moment and axial force shall be calculated using a reduced yield strength for the shear area, where:

red. fy = (1 - e) fy

'1 = (2 VSd _1)2 Vpl•Rd

V pl.Rd is according to equation (5.11) or (5.12).

For circular hollow section: AT = 2A 71"

For rectangular hollow section:

- shear load parallel to depth: AT = b ~h h

- shear load parallel to width: AT = b ~b h

(5.23)

(5.24)

For circular hollow section, the following exact but simple equation can be given taking also the shear force into account [23]:

V pl,Rd is according to the equation (5.11). MSd is according to the equation (5.21). No reduction for fy as shown in the equation (5.23) has to be made.

32

(5.25)

(5.26)

(5.27)

Uni-planar tubular broken-off truss

Tubular supports for a canvas roof construction

33

6 Thin-walled sections

6.1 General

The optimisation of the buckling behaviour of hollow sections leads, for a constant value of cross sectional area, to profiles of large dimensions and small thicknesses (large moment of inertia). Small thicknesses (relative to outer dimensions) can cause failure, before reaching yield strength in the outer fibres, by local buckling. The unavoidable imperfections of the profiles involve an interaction between local buckling in the cross section and flexural buckling in the column. This decreases the resistance to both types of buckling. By keeping within the dlt or bIt limits for the respective cross section classes given in Tables 4, 5 and 6, it is not required to check locall:>uckling. Only when exceeding the dlt or bIt limits for class 3 sections, does the influence of local buckling on the load bearing capacity of the structural members have to be taken into account. The cross section thus involved shall be classified as class 4 (see Fig. 2). It should be noted that the phenomenon of local buckling can become more critical by applying and utilizing higher yield strength, so that smaller bIt ratios have to be selected (see Tables 4 and 5, last line). Eurocode 3 [1] takes account of local buckling by the determining the load bearing capacity using effective cross section dimensions, which are smaller than the real ones. In the structures, which are dealt with in this book, circular hollow sections with a dlt ratio higher than the limiting values given in Table 4 are seldom used; in general, dlt values are 50 at the highest. In consequence, this chapter is mainly devoted to class 4 square and rectangular hollow sections.

6.2 Rectangular hollow sections

6.2.1 Effective geometrical properties of class 4 cross sections

The effective cross section properties of class 4 croSs sections are based on the effective widths of the compression elements. The effective widths of flat compression elements shall be obtained using Table 17. The plate buckling reduction facor e shall be calculated by means of the relations given in Table 18. Forthe sake of simple calculation, the equation (6.2) and (6.1) are described in Fig. 8 (e = f(~))andFig.9(ka = f(1/.-)). In order to determine the effective width of a flange element, the stress ratio 1/.- used in Table 17 shall be based on the properties of the gross (not reduced) cross section. To calculate the effective depth (hell) of web elements, the effective area of the compressed flange (bell' t) but the gross area of the webs (h . t) has to be used. This simplification allows a direct calculation of effective widths. Strictly speaking, an exact calculation of the effective width of a web element requires an iterative procedure. Under bending moment loading it is possible that the effective (reduced) width becomes valid only for one flange. This results in a mono-symmetrical cross section with a corresponding shift of the neutral axis. As a consquence, the effective section modulas has to be calculated with reference to the new neutral axis.

Note: Eurocode 3 [1,2] is not consistent regarding the definition of a so-called "thin-walled profile" .

34

Table 17 - Effective widths and buckling factors for thin-wailed rectangular hollow sections

stress distribution (compression positive) b, = h - 3t or b - 3t

+ +

al rmnlll 111111111 a2

t="=J b 1 ~

a 1 llIID::-rrrnnm a 2

Ebl~

ali~·(t·1 belt- L~<QJJjJJ a 2 b 1 .1

>/; = U2/U' + 1 +1>>/;>0 0

buckling factor 4.0

3.2 7.81 ---

k. 1.05 - >/;

Alternatively: for 1 ~ >/; ~ - 1

k = 16 • V(1 + lW+0 .. 112(1->/;)2\(1 +>/;)

Plate buckling reduction factor p

1.0

0.9 \ -1--- k' Ap-0.22

_. o=~

-- --~i'-..

'r--... r--....

0.8

0.7

0.6

0.5

OA

0.3

0.2

0.1 I

o o 0.2 OA 0.6 0.8 1.0 1.2 lA 1.6 1.8 2.0

Non-d1mensional slenderness Xp

Fig. 8 - Plate buckling reduction faktor Q

effective width beff

beff = Q' b,

be' = 0.5 beff

be2 = 0.5 beff

beff = Q' b,

2beff be' = 5 _ >/;

be2 = beff - be'

>/; U2

U,

beff = Q • be

be' = OAbeff

be2 = 0.6beff

0>>/;>-1 - 1

7.81 - 6.29>/; + 9.78if;2

Buckling factor Ka

60

55

50

45

40

35

30

~ -~

.... \

I'\. f'\.

23.9

r-....

-1>>/;>-2

5.98 (1 - >/;)2

(6.1)

25

20

15

10 I

" j l't---I I I I T-

-2 -1 o + 1

Stress ratio y..

Fig. 9 - k. vs. >/;

35

Table 18 - Plate buckling reduction factor e

>:p - 0.22 e = :s; 1.0

h~ where >:p' the non-dimensional slenderness of the flat compression element, is given by:

- , r:-::' b,lt hp = V fylfE = 28.4 f -v'i\ where fE is the critical plate buckling stress and kG is the plate buckling factor (see Table 17 and Fig. 9)

with f = ~ and fy = yield strength in N/mm2

Reference [2) considers that the influence of the internal corner radius need not to be taken into account provided that:

r:s; 5t

r b:S; 0.15 , These conditions are fulfilled by practically all actually produced square and rectangular hollow sections.

(6.2)

(6.3)

The b,lt limit above which local buckling needs to be taken into account according to Tables 8 and 9 is bIt> 42 f for a uniformly compressed flange. However equation (6.2) in Table 18 for an identically loaded flange gives ~p > 0.673; this results in b,lt > 38.2 f, some what smaller than the 42 f above. It is well known, that the equation (6.3) for plate buckling gives conservative results. On account of this, possible local buckling of thin-walled sections has to be considered first, when the b,lt limits given in Tables 5 through 7 are exceeded.

6.2.2 Design procedure

When the effective geometrical properties of a class 4 cross section, e. g. effective area Aell, effective radius of gyration iell, effective section modulus Well, have been calculated, it is easy to check the stability and the resistance. Indeed, it is just necessary to use these effective properties in place of the geometrical properties of the gross section in class 3 calculations. For dimensioning thin-walled cross section, equation (5.21) is replaced by the relation:

Aell · fyd

fy with f =-yd 'YM

(6.4)

Hollow sections have two axes of symmetry and therefore there is no shift of the neutral axis when the cross section is subject to uniform compression. This leads to an important simplification of class 4 beam-column equations, because additional bending moments due to this shift do not exist in the case of structural hollow section. The use of effective geometrical properties of thin-walled sections is recommended in the codes of the most countries around the world. Only in the japanese code, the load bearing capacity of a thin-walled rectangular hollow section is given by the smaller of the maximum plate buckling load and global buckling load. At last, as shown in reference [10). the lateral-torsional buckling can also be disregarded for thin-walled hollow sections of class 4.

36

6.2.3 Design aids

For practical application, the transition from the cross section class 3 to class 4 is of special imporance showing the bIt limits, below which local buckling can be disregarded. With e = 1, the equation (6.2) leads to the limit Xp S 0.673. Fig. 10 gives - on base of the depth or width-to-thickness ratio and of the ku coefficient (Table 17) as well as of the yield strength fy - the possibility of a quick check of the zone where no allowance for local buckling is necessary. The area to the left of the curves belongs to cross section class 3, while that to the right covers class 4, all of them lying in the elastic range. When bIt limits given by the curves are exceeded (local buckling), the plate buckling reduction factor e according to the equation (6.2) has to be determined.

Kar-__ .-_~IV,IN_I_mm_2_1_=~4~60 __ 35~5~2~7~5_27035

50+---+----~--~~L-~~~

40+---+-----+--.~~~~~-~ -no local buckling 30+--------~-.~Y-~---~

23.9 +----+_---+~~~f.----L..=.::.c.c.:.;~~'------j

20+---+-~~~~~~~-~~-~

10+--~~~~-~--~--~-~

4+--~~~---+_--~LC~0~m~pr~es~sio~n-~

O+-----+-----~----~----~--~

Q

1.00

0.90

0.80

0.70

0.60

0.50

0.40

0.30

0.20

0.10

0

IV = 235 N/mm2

Iv = 275 N/mm2

Iv = 355 N/mm2

Iv = 460 N/mm2

25 50 75 100

!:l or .!'.!. 125 150 0 10 20 30 40 50 60 70 80

b,/t

t t w:a Fig. 10- b,1t or h,1t limits, below which local

buckling can be disregarded Fig. 11 - Plate buckling curves

r-r'~I12\t I I I

v+- + +v hml=h-t

~: IJI-, i I heff/2+ t __ + _ -=u beff/2 + tU' zU bell/2 + t

~

o

bm =b-t beff/2 + t beff/2 +t ~ n zn heff/2+t I -, 171

hm~ : - -,- - f l t; : ---I 1 -il I I -+ I I I I I I I

8v hm=h-t yr-'+I I V hm=h-t

f V: -I I v 1 [: 1 i : J I __ I -----1 f I __ . _ I

I. '.z I heff12 + t I. ._: z ~ ~

@ CS) Fig. 12 - Effective RHS cross section under axial force N and bending moments My, Mz

37

b1/t Plate buckling reduction factor e vs. Yk for various structural steel grades is drawn in

Fig. 11 (see equation 6.3). • Effective geometrical values for the cross sections of class 4 can be calculated by means of the formulae given in Table 19. The notations in Table 19 are explained in Fig. 12.

Table 19 - Effective geometrical properties

axial force:

= 2t(belf + helf + 41)

V'--(h-elf + 21-)2 (3-hm - he---'If - 21)' = 0.289 hm 3 - ---

hm belf + helf + 41

V (belf + 21)2 (3bm - belf - 21)' = 0 289 b 3 - ---. m bm belf + helf + 41

6.3 Circular hollow sections

For thin-walled circular hollow sections, it is more difficult to judge the local buckling behaviour, especially the interaction between global and local buckling, than in the case of plates. This is due to the local instability behaviour of cylindrical shells, their high susceptibility to imperfections and sudden reduction of load bearing capacity without reserve [23]. Local buckling has also to be considered for CHS, when the d/t limits for the cross section 3 are exceeded (see Tables 4 and 7).

38

Circular hollow sections, which are applied in practice, do not or seldom, possess d/t ratios exceeding those given in Tables 4 and 7; in general d/t s 50. In cases, where thin-walled circular hollow sections are applied, the procedure of substituting the yield strength fy in the already mentioned formulae by the real buckling stresses' for a short cylinder, can be used. These buckling stresses can be calculated by the procedure shown in [26] or [27]. The procedures in both cases are simple; however, there is no equation describing the buckling stress explicitly.

• O"u in (26); O"XS,RK in (27)

39

7 Buckling length of members in lattice girders

7.1 General

Chord and bracing members of a welded lattice girder are partially fixed at the nodes, although the static calculation of the forces in the members is carried out assuming the joints to be hinged. As a consequence of this partial restraint, a reduction of the system length I is made to obtain the effective buckling length lb.

7.2 Effective buckling length of chord·and bracing members with lateral support

The buckling of hollow sections in lattice girders has been treated in [14, 15,28). Based on this, Eurocode 3 [1, 2 - Annex K] recommends the buckling lengths for hollow sections in lattice girders as follows:

Chords: - in-plane: Ib = 0.9 x system length between joints - out-of-plane: Ib = 0.9 x system length between the later supports

Bracings: - in- and out-of-plane: Ib = 0.75 x system length between jOints.

When the ratio of the outer diameter or width of a bracing to that of a chord is smaller than 0.6, the buckling length of the bracing member can be determined in accord with Table 20. The equations given are only valid for bracing members, which are welded on the chords along the full perimeter length without cropping or flattening of the ends of the members. Due to the fact that no test results are, at present time, available on fully overlapped joints, the equation given in Table 20 cannot be applied to this type of joint.

Fully overlapped joints

In both of the last cases, a buckling length equal to the system length of the bracing member has to be used.

7.3 Chords of lattice girders, whose jOints are not supported laterally

The calculation is difficult and lengthy. Therefore, it is convenient to use a computer. For laterally unsupported truss chords the effective buckling length can be considerably smaller than the actual unsupported length. References [12, 15) give two calculation methods for the case of compression chords in lattice girders without lateral support. Both methods are based on an iterative melhod and require the use of a computer. However, in order to facilitate the application for commonly encountered cases (laterally restrained in direction), 64 design charts have been drawn and appear as appendices in CIDECT Monograph no. 4 [15). The effective buckling length of a bottom chord loaded in compression (as for example, by uplift loading) depends on the loading in the chord, the torsional rigidity of the truss, the

40

bending rigidity of the pulins and the purlin to truss connections. For detailed information, reference is given to [12, 15]. For the example given in the following figure, the buckling length of the unsupported bottom chord can be reduced to 0.32 times the chord length L.

IPE 140

~

~1lJ139.7X4

I IlJ 60x 3

IlJ 139.7x4

buckling length bottom chord Ib = - 0.32 L

Lateral buckling of laterally unsupported chords

Table 20 - Buckling length of a bracing member in a lattice girder

do: outer diameter of a circular chord member :t d,: outer diameter of a circular bracing member d, d, b, be: external width of a square chord member {3=- or - or-

b,: external width of square bracing member do bo be

for ail {3: Ibli =:; 0.75

Ib when {3 < 0.6, in general 0.5 =:; T =:; 0.75

calculate with:

chord: CHS ( d2 y25 bracing: CHS Ibli = 2.20 I. ~e (7.1)

chord: SHS ( d2 y25 bracing: CHS Ibli = 2.35 I . ~e (7.2)

chord: SHS ( b2 y25 bracing: SHS Ibli = 2.30 I . ~e (7.3)

41

La.ttice girder of square hollow sections supported by a cabie construction

Genera! view of a RHS roof structure

42

8 Design examples

8.1 Design of a rectangular hollow section column in compression

Nsd ~ 1150 kN

I

/ 1 I I

I Ib,y 0 I I ~8m

\ I \ : \ _-.--1 t ,-, y- y

Fig. 13 - Column under concentric compression

A column is to be designed using a rectangular hollow section 300 x 200 x 7.1 mm. hot­formed with a yield strength of 235 N/mm2 (steel grade Fe 360). The length of the column is 8 m. It has hinged support at both ends. An intermediate support at the middle of the column length exists against buckling about the weak axis y-y. Given: Concentric compression (design load) NSd = 1150 kN

buckling length: Ib.y = 8 m Ib,z = 4 m

steel grade: Fe 360; fy = 235 N/mm2

geometric properties: A = 67.7 cm2; iy = 11.3 cm; iz = 8.24 cm

b, 300 - 3·71 max' t = 7.1' = 39.25 < 42 (compare with Tab. 5 and 6)

800 400 Ay = 11.3 = 70.8; Az = 8.24 = 48.6 < Ay

- 70.8 Ay = 93.9 = 0.754 (see Tab. lOa)

)(y = 0.821 (Tab. 12. buckling curve "a")

Acc. to equation (3.1):

Nb.Ad = 0.821 ·6770· ~~; . 10- 3 = 1187 kN > 1150 kN. Therefore column okay.

8.2 Design of a rectangular hollow section column in combined compression and uni­axial bending

60kNm

, ,+-u t 18kNm

z-z My,sd

Fig. 14 - Column under combined compression and uni-axial bending

43

given: hot-formed rectangular hollow section column 300 x 200 x 8 mm compression NSd = 800 kN bending moment My.Sd = 60 kNm or 18 kNm at both ends buckling length Ib,y = Ib.z = 8.0 m steel grade Fe 430; fy = 275 N/mm2

geometric properties: A = 75.8 cm2; iy = 11.2cm; iz = 8.20 cm Wy = 634 cm3 ;

Wpl,y = 765 cm3;

Wz = 510 cm3

Wpl,z = 580 cm3

b1

t

h1 t

:~::: = 22 ] 8 = 34.5

< 38 . 0.92 = 35 for class 2 cross section of Fe 430 (Tables 5 and 6)

a) Calculation for flexural buckling:

800 Ay = 11.2 = 71.4;

800 Az = 8.2 = 97.6

- 71.4 Ay = 86.8 = 0.823 (see Tab. 10a);

- 97.6 Az = 86.8 = 1.124

Xy = 0.782 (see Tab. 12, buckling curve "a"); Xz = 0.580

Acc. to Table 16: {3M,y = 1.8 - 0.7 . 0.3 = 1.59 (With 1/; = !~ = 0.3)

. 765 - 634 Acc. to equation (5.5): /Ly = 0.823 (2 . 1.59 - 4) + 634 = - 0.468 < 0.9

. (- 0.468)' 800.103

Acc. to equation (5.4): Ky = 1 - 0.782. 7580 . 275 = 1.23 < 1.5

Calculation for the stability about y-y axis acc. to equation (5.1):

_ --=8:...:0....:.0_ . ....:.1-=..03_._1:....:. . .:....1 _ 1.23·60· 106• 1,1 + = 0.540 + 0.386 = 0.926 < 1.0

0.782·7580·275 765· 103 • 275

Calculation for buckling about z-z axis:

NSd :s Nb,z,Rd

235 '10- 3

800 < 0.580 . 7580 . 1.1 = 939 kN. Therefore column okay.

b) Calculation for the load bearing capacity

60 - 18 Shear load V: Vy,Sd = 8 = 5.25 kN

44

275 '10- 3 Acc. to equation (5.11): Vpl y Rd = 2· 8 (300 - 8)' _ rn

" v3·1.1 VySd 5.25

-V-- = 674 = 0.008 < 0.5 pl,y,Rd

The shear load can be disregarded.

Acc. to equation (5.13): My,Sd :s 1.0 MNy,Rd

My,Sd = 60 kNm (max)

= 674 kN

Acc. to equation (5.16): MNy,Rd - 1 33 . 765 . 103. 275 (1 _ 800· 103

. 1.1 ) - . 1 .1 7580 . 275

= 147· 106 Nmm

= 147 kNm

My•Sd 60 -M-- = 147 = 0.41 < 1.0. Therefore column okay.

Ny,Rd

8.3 Design of a rectangular hollow section column in combined compression and bi-axial bending

1000 kN

60kNm 2 ~ 50kNm

'}mV / ,J""y z

{ffl \ =5.6m +- 300

\ -~ y I ~ \

1 t -25 kNm GU z -z My,sd y-y MZ,sd

Fig. 15 - Column under combined compression and bi-axial bending

Given: Hot formed rectangular hollow section column 300 x 200 x 8.8 mm The length of the column is 8 m. Both ends of the columns have hinged support about the strong axis z-z and fixed support at the foot end about the weak axis y-y,

Compression NSd = 1000 kN

Bending moment My,Sd = 60 kNm Mz,Sd = 50 kNm

Steel grade: Fe510; fy = 355 N/mm2

Buckling length: Ib,y Ib,z

Geometric properties: A Wy Wpl,y iy

=8m = 0.7, 8,0 = 5.6 m

= 82,9 cm3

= 689 cm3 ;

= 834cm3; = 11.2 cm;

Wz = 553cm3

Wpl,z = 632 cm3

iz = 8,16 cm

max ~1 = ~1 = 300 ~,~. 8,8 = 31,0,., 38'0.81 = 31

The cross section just satisfies the requirements for the class 2 of Fe510 (Tables 5 and 6),

45

a) Calculation for the global buckling acc. to equation (5.1)

800 560 Ay = 11.2 = 71.4 Az = 8.16 = 68.6

- 71.4 - 68.6 Ay = 76.4 = 0.935 Az = 76.4 = 0.898

Xy = 0.711 (= Xmin) X z = 0.735 (buckling curve "a")

355 Acc. to equation (5.2): Nb,y,Rd = 0.711 ·8290' U .10- 3 = 1902 kN (= min Nb,Rd)

355 Nb,z,Rd = 0.735' 8290 . U . 10- 3 = 1966 kN

355 Acc. to equation (5.3): Mpl.y,Rd = 834.103 • U . 10-6 = 269 kNm

355 Mpl,z.Rd = 632.103

• U . 10-6 = 204 kNm

Acc. to :rab. 16: f3M,y

Acc. to equation (5.5): J.ty = 1.8 (834 ~ = 0.935 (2 '1.8 - 4) + 689 - 1) = - 0.164 < 0.9

Acc. to equation (5.4): Ky (- 0.164) 1000

= 1 - 1902 = 1.09 < 1.5

Acc. to Tab. 16: f3M,z = 1.8 - 0.7(- 0.5) = 2.15

Acc. to equation (5.7): J.tz (632 ~ = 0.898 (2' 2.15 - 4) + 553 - 1) = 0.412 < 0.9

Acc. to equation (5.6): Kz - 1 - 0.412 ·1000 - 0790 15 - 1966 -. <.

1000 1.09' 60 0.79' 50 Finally. acc. to equation (5.1): 1902 + 269 + 204 = 0.526 + 0.243 + 0.194

= 0.963< 1.0

b) Calculation for load bearing capacity

46

In order to obtain sufficient load bearing capacity of the cross section the "elastic" equation (5.22) is applied conservatively (all values in kN and mm):

1000 + 60· 103

+ 50' 103 = 0.340 + 0.245 + 0.255

8290' 0.355 689· 103 • 0.355 553· 103 • 0.355 = 0.84 < 1.0

If this calculation would not have led to a satisfactory result (that means > 1.0). then the calculation must be carried out using equation (5.13). The assumption to neglect shear load in equations (5.13) and (5.22) is V Sd :S 0.5 V pl,Rd' see equation (5.10) [1.2).

The shear resistance acc. to equation (5.12) is decisive in this case:

355 Vpl z Rd = 2 . 8.8 (200 - 8.8) Jii

" v3·1.1 = 627 kN

. 10-3

VSd = 508~025 = 9.4 kN

V V Sd = 0.Q15 < 0.5. Therefore shear is not critical.

pl.Rd

8.4 Design of a thin-walled rectangular hollow section column In compression

z· z

Fig. 16 - Thin-walled column under concentric compression

Given: Cold-for-med rectangular hollow section column 400 x 200 x 4 mm (acc. to ISO 4019 [17)) The length of the column is 10 m. Both ends of the column have hinged support about the strong axis z-z and fixed supports at both ends about the weak axis y-y.

Steel grade: Fe 430, fy = 275 N/mm2 (basic hot rolled strip)

Buckling length: Ib,y = 10 m

10 Ib,z ="2 = 5m

NSd = 500 kN

Cross sectional area A = 46.8 cm2

1. Calculation of average increased yield strength after cold-forming . 14·4

Acc. to equation (1.3): fya = 275 + 400 + 200 (430 - 275)

= 289 N/mm2 < 1.2 . 275 = 330 N/mm2

2. Cross section classification

. h, 400 - 3 . 4 ] Long side: t- = 4 = 97 ~35

b > 42 275 = 38.8 (Tables 5 and 6)

. , 200-3'4 Short side: t- = 4 = 47

The cross section is thin-walled (class 4) and the calculation shall be made using effective width. According to Fig. 8, the limit for plate buckling: Xp, limit = 0.673 (>::p acc. to equation (6.2) with e = 1.0).

Non-dimensional slenderness taking yield strength of the basic material fYb acc. to equation (6.3):

X - 97 = 1.85> 0.673 P.y - 28.4' V4 V235/275

47 Xp Z = V4' = 0.90 > 0.673

, 28.4' 4 V235/275

47

Non-dimensional slenderness taking average increased yield strength fya (289 N/mm2) after cold-forming:

- 97 Ap.y = 28.4' V4y235/289' = 1.89> 0.673

- 47 Ap z = . fA' = 0.92> 0.673

. 28.4 . v4 y235/289'

In all cases, the cross section belongs to class 4.

3. Effective geometric values

a) With yield strength of the basic material fYb (275 N/mm2) and Ka = 4 (simple compression):

Qy = 0.476 1 . Qz = 0.840 J acc. to equation (6.2)

hell = 0.476 (400 - 3· 4) = 184.7 mm 1 acc. to Tab. 17 bell = 0,840 (200 - 3· 4) = 157.7 mm J

~ell.y = 17.50 cm acc. to Tab. 19 Aell = 28.69 cm

2 ]

lell.z = 8.76 cm

b) With average increased yield strength after cold forming (fya = 289 N/mm2)

Qy = 0.468 1 . Qz = 0.827 J acc. to equation (6.2)

hell = 0.468 (400 - 3· 4) = 181.6 mm 1 bell = 0.827 (200 - 3 . 4) = 155.5 mm J acc. to Tab. 17

Aell = 28.25 cm2

iell.y = 17.60 cm iell.z = 8.33 cm

4. Design for global buckling

a) With yield strength of the basic material (fYb = 275 N/mm2):

• Strong axis

1000 Ay = 17.5 = 57.1

};y = ~~:~ = 0.66 (see Tab. 10a)

Xy = 0.806 (acc. to Tab. 13, curve "b")

275 Nb.Rd = 0.806 . 2869 . TI = 578 kN (see equation (3.1))

• Week axis

500 = 8.76 = 57.1

57.1 066 = 86.8 = . X z = 0.806 (acc. to Tab. 13, curve "b")

0.275 Nb.Rd = 0.806 . 2869 . -1-.1- = 582 kN

48

b) With average increased yield strength after cold-forming (289 N/mm2):

AE = 93.9 y235/289' = 84.7 (see Tab. 10a)

• Strong axis

1000 Ay = 17.6 = 56.8

~y = ~::~ = 0.67 > 0.2

Xy = 0.743 (acc. to Tab. 14, curve "c")

0.289 Nb•Ad = 0.743·2825· -1.-1- = 551 kN

• Weak axis

500 = 8.33 = 60.0

60 = 84.7 = 0.71

X z = 0.719 (acc. to Tab. 14, curve "c")

0.289 Nb•Ad = 0.719·2825· -1.-1- = 534 kN

Conclusion: . Assuming both criteria (basic and average increased yield strength, the design com­pressive load (= 500 kN) lies lower than the calculated lead bearing capacity. The calculated values for the strong and weak axis differ by a small margin from each other. An economic selection of the cross section has been made.

8.5 Design of a thin-wailed rectangular hollow section column in concentric com­pression and bi-axlal bending

250 kN

12.5kNm ~ -12.5kNm

'i~B"'~E( J ! 25 kNm 1 t 12.5 kNm

z-z My,sd y -y MZ,sd

Fig. 17 - Thin·walled column under combined compression and b-axial bending

Given: Cold-formed rectangular hollow section column 400 x 200 x 4 mm. Concentric compression NSd = 250 kN

Bending moments: My•Sd = 25 kNm and 12.5 kNm at the ends of the column Mz.Sd = 12.5 kNm and - 12.5 kNm at the ends of the column

49

Under bending moment the yield strength of the basic material is always to be assumed even for cold-formed profiles. The strain hardening of cold-formed section is desregarded.

Steel grade: Fe430; fy = fy,b = 275 N/mm2 Column system length I = 10 m Buckling lengths: Ib,y = 10 m

10 Ib,z =""2 = 5m

From design example 8.4:

Xy = 0.806 --> >':y = 0.~6 Xz = Xmin = 0.806 --> Az = 0.66 hell = 184.7 mm bell = 157.9 mm Aell = 28.69 cm2

iell,y = 17.5 cm iell,z = 8.76 cm

Ratio of the end moments:

= 12.5 _ 05 .fy 25 - .

-12.5 .fz =~= -1.0

f3M,y = 1.45]

f3M,z = 2.50

Further effective geometric values acc. to Tab. 19:

Oy = 5.2 mm Oz = 20.3 mm Well.y = 482.2 cm3

Well.z = 219.9 cm3

acc. to Tab. 16, second column

Acc. to equation (5.5): /l-y

Acc. to equation (5.4): Ky

= >':y (2f3M•y - 4) = 0.66 (2' 1.45 - 4) = - 0.726 < 0.9

- 0.726·250· 103

= 1 - 0.806.2869. 275 = 1.256 <1.5

Acc. to equation (5.7): /l-z

Acc. to equation (5.6): Kz

= 0.65 (2 . 2.50 - 4) = 0.65 < 0.9

0.65·250· 103

= 1 - 0.811 .2869. 275 = 0.746 < 1.5

Calculation to check stability acc. to equation (5.1):

250000 . 1.1 1.256 . 25 . 106 • 1.1 0.746 . 12.5 . 106 • 1.1 + +

0.806·2869· 275 482.2' 103 • 275 219.9' 103 • 275

= 0.432 + 0.260 + 0.170 = 0.862 < 1.0

Calculation to check maximum stress at the foot end acc. to equation (5.22):

250 . 103 • 1.1 25 . 106 • 1.1 12.5 . 106 • 1.1 + +

2869· 275 482.2' 103 • 275 219.9' 103 .275

= 0.348 + 0.207 + 0.227 = 0.782 < 1.0

Conclusion: The cross section 400 x 200 x 4 mm satisfies the requirements.

50

9 Symbols

A, Ao Gross area of the cross section Aelf Effective area of the cross section CHS Circular hollow section E Modulus of elasticity F Calculated value of an action G Shear modulus I Moment of inertia lelf Effective moment of inertia Ky, Kz Amplification co-efficient for a beam-column (see equations 5.1, 5.4, 5.6) MN•Ad Reduced design plastic resistance moment allowing for the axial force MSd Design value of the bending moment Nb,Ad Design value of the buckling resistance of a compression member Npl,Ad Plastic design value of the resistance of a compression member NSd Design value of the axial force R Resistance RHS Rectangular hollow section V pl.Ad Plastic design shear resistance V Sd Design value of the shear force W Section modulus Welf Effective section modulus Wpl Plastic section modulus

b, h External width of RHS b1, h1 Width of a flat element (see Tab. 6) bm Average width of RHS (b - t) hm Average width of RHS (h - t)

d External diameter of CHS fE Critical plate buckling stress fu Ultimate tensile strength of the basic material of a hollow section fy Tensile yield strength fya Average design yield strength of a cold-formed section fyb Tensile yield strength of the basic material of a hollow section

fyd Design yield strength ( = ~:) fCr,LT Critical stress (elastic) for lateral buckling h External depth of RHS

Radius of gyration ielf Effective radius of gyration k. Buckling factor (see Tab. 18) I, L Length Ib Effective buckling length r Internal corner radius for RHS t Wall thickness

51

y Strong axis of the cross section z Weak axis of the cross section

a Co-efficient of linear expansion (see Tab. 1) ex Imperfection co-efficient of the buckling curves ex, (3 Exponents of the criterion for the resistance of a beam-column (3M Equivalent uniform moment factor (see Tab. 16) "Yy Ratio of the width minus thickness to depth minus thickness of RHS "YM Partial safety factor for the resistance {j Shift of the neutral axis of a thin-walled section fu Ultimate strain fy Yield strain }.. Slender.ness of a column }..E Eulerian slenderness >.: Non-dimensional slenderness of a column >':LT Non-dimensional slenderness of a flat plate for lateral-torsional buckling >':p Non-dimensional slenderness of a flat plate /A-y' /A-z Co-efficient used for a beam-column (see equations 5.5 and 5.7) v Poisson's ratio e Density e Reduction factor of the yield strength to take account of the shear force and effective

width x Reduction factor for buckling curves (see Fig. 3) 1/; Stress or moment ratio (see Tab. 17)

52

10 References

(1) EC3: Eurocode no. 3, Design of Steel Structures, Part I - General Rules and Rules for Buildings. Commission of the European Communities, volume 1, chapters 1 to 9, November 1990 (Draft).

(2) EC3: Eurocode no. 3, Design of Steel Structures, Part 1 - General Rules and Rules for Buildings. Commission of the European Communities, volume 2 - annexes, July 1990 (Draft).

(3) SSRC: Stability of Metal Structures - A World View. Structural Stability Research Council, 2nd Edition, 1991.

(4) Sherman, D. R.: Inelastic Flexural Buckling of Cylinders. Steel Structures - Recent Research Advances and their Applic.ation to Design, International Conference, Budva, M. N. Pavlovic editor, Elsevier, London, 1986.

(5) Johnston, B. G.: Column Buckling Theory - Historic Highlights. A. S. C. E., Journal of the Structural Division, Vol. 109, no. 9, September 1983.

(6) EC3: Eurocode no. 3, Design of Steel Structures, Part 1 - General Rules and Rules for Buildings. Annex D - The Use of Steel Grade FeE 460, Commission of the European Communities, Report EC3 - 90-CI-D3Rev, July 1990.

(7) Beer, H., and Schulz, G.: The European Buckling Curves, International Association for Bridge and Structural Engineering, Proceedings of the International Colloqium on Column Strength, Paris, November 1972.

(8) Austin, W.J.: Strength and Design of Metal Beam-Columns, A. S. C. E. Journal of the Structural Devision, Vol. 87, no. 4, April 1961.

(9) Chen, W. F., and Atsuta, T.: Theory of Beam-Columns, Volume 1: In-Plane Behaviour and Design. MC.Graw Hill, New-York, 1976.

(10) Rondal, J., and Maquoi, R.: Stabilite des poteaux en profils creux en acier, Soditube, Notice 1117, Paris, Mai 1986.

(11) Ellinas, C. P., and Croll, J. G. A.: Design Loads for Elastic-Plastic Buckling of Cylinders under Combined Axial and Pressure Loading, Proceedings of the BOSS '82 Confe­rence, Boston, August 1982.

(12) CIDECT: Construction with Hollow Steel Sections, ISBN 0-9510062-07, December 1984.

(13) Grimault, J. P.: Longueur de flambement des treillis en profils creux soudes sur membrures en profils creux, Cidect report 3E-3G-80/3, January 1980.

(14) Rondal, J.: Effective Lengths of Tubular Lattice Girder Members, Statistical Tests, Cidect report 3K - 88/9, August 1988.

(15) Mouty, J.: Effective Lengths of Lattice Girder Members, Cidect, Monograph no. 4,1980.

(16) ISOIDIS 657-14: Hot-rolled steel Sections; Part 14: Hot formed structural hollow sections - Dimensions and sectional properties, Draft Revision of Second edition ISO 657: 14-1982.

(17) ISO 4019: Cold-finished steel structural hollow sections - Dimensions and sectional properties, 1 st edition, 1982.

(18) ISO 630: Structural Steels, 1st edition, 1980.

53

(19) IIW XV - 701/89: Design Recommendations for hollow section joints - Predominantly statically loaded, 2nd Edition, 1989, International Institute of Welding.

(20) prEN 10210: Hot finished structural hollow section of non-alloy and fine grained structural steels Part 1: Technical delivery requirements, 1991. Part 2: Tolerrances, dimensions and sectional properties (in preparation).

(21) DIN 18800, Teil1: Stahlbauten, Bemessung und Konstruktion, November 1990. Teil2: Stahlbauten, Stabilitatsfalle, Knicken von Staben und Stabwerken, November

1990.

(22) ECCS-CECM-EKS: European Recommendation for Steel Structures - 2E, March 1978

(23) Dutta, D., und WOrker K.-G.: Handbuch Hohlprofile in Stahlkonstruktionen, Verlag TUV Rheinland·GmbH, Koln 1988.

(24) Roik, K., und Kindmann, R.: Das Ersatzstabverfahren - Tragsicherheitsnachweise fOr Stabwerke bei einachsiger Biegung und Normalkraft, Der Stahlbau 5/1982.

(25) Roik, K., und Kindmann, R.: Das Ersatzstabverfahren - eine Nachweisform fOr den einfeldrigen Stab bei planmaBig einachsiger Biegung mit Druckkraft, Der Stahlbau 12/1981.

(26) European Convention for Constructional Steelwork (ECCS-EKS): Buckling of Steel shells, European Recommendations (section 4.6 als selbstandige Schrift), 4th Edition, 1988.

(27) DIN 18800, Teil4: Stahlbeton, Stabilitatsfalle, Schalenbeulen, November 1990.

(28) Sedlacek, G., Wardenier, J .. , Dutta. D., und Grotmann, D.: Eurocode 3 (draft), Annex K - Hollow section lattice girder connections, October 1991.

(29) prEN 10219-1, 1991: Cold formed structural hollow section of non-alloy and fine grain structural steels, Part 1 - Technical delivery conditions, ECISS/TC 10/SC 1, Structural Steels: Hollow Sections.

(30) Boeraeve, P., Maquoi, R., und Rondal, J.: Influence of imperfections on the ultimate carrying capacity of centrically loaded columns, 1 st International Correspondence Conference "Design Limit States of Steel Structures", Technical University of Brno, Czechoslovakia, Brno, 1983.

(31) EN 10025: Hot-rolled products of non-alloy structural steels, Technical delivery conditions, March 1991.

(32) European Convention for Constructional Steelwork: ECCS-E6-76, Appendix no. 5: Thin walled cold formed members.

Acknowledgements for photographs:

The authors express their appreciation to the following firms for making available the photographs used in this Design Guide: British Steel plc. Mannesmannrohren-Werke A.G. Mannhardt Stahlbau IIva Form Valexy

54

[~I Comlt. Intematlonal pou, I. DOvaloppement et I'~tude de la Construction Tubulal",

International Committee for the Development and Study of Tubular Structures

CIDECT founded in 1962 as an international association joins together the research resources of major hollow steel section manufacturers to create a major force in the research and application of hollow steel sections worldwide.

The objectives of CIDECT are:

o to increase knowledge of hollow steel sections and their potential application by initiating and participating in appropriate researches and studies

o to establish and maintain contacts and exchanges between the producers of the hollow steel sections and the ever increasing number of architects and engineers using hollow steel sections throughout the world.

o to promote hollow steel section usage wherever this makes for good engineering practice and suitable architecture, in general by disseminating information, organizing congresses etc.

o to co-operate with organizations concerned with practical design recommen­dations, regulations or standards at national and international level.

Technical activities

The technical activities of CIDECT have centred on the following research aspects of hollow steel section design:

o Buckling behaviour of empty and concrete-filled columns o Effective buckling lengths of members in trusses o Fire resistance of concrete-filled columns o Static strength of welded and bolted jOints o Fatigue resistance of joints o Aerodynamic properties o Bending strength o Corrosion resistance o Workshop fabrication

The results of CIDECT research form the basis of many national and international design requirements for hollow steel sections.

55

CIDECT, the future

Current work is chiefly aimed at filling up the gaps in the knowledge regarding the structural behaviour of hollow steel sections and the interpretation and imple­mentation of the completed fundamental research. As this proceeds, a new complementary phase is opening that will be directly concerned with practical, economical and labour saving design.

CIDECT Publications

The current situation relating to CIDECT publications reflects the ever increasing emphasis on the dissemination of research results.

Apart from the final reports of the CIDECT sponsored research programmes, which are available at the Technical Secretariat on demand at nominal price, CIDECT has published a number of monographs concerning various aspects of design with hollow steel sections. These are available in English, French and German as indicated.

Monograph No. 3 - Windloads for Lattice Structures (E, F,G) Monograph No. 4 - Effective Lengths of Lattice Girder Members (E, F, G) Monograph No. 5 - Concrete-filled Hollow Section Columns (E, F) Monograph No. 6 - The Strength and Behaviour of Statically Loaded Welded

Connections in Structural Hollow Sections (E) Monograph No. 7 - Fatigue Behaviour of Hollow Section Joints (E, G)

A book "Construction with Hollow Steel Sections", prepared under the direction of CIDECT in English, French, German and Spanish, was published with the sponsor­ship of the European Community presenting the actual state of the knowledge acquired throughout the world with regard to hollow steel sections and the design methods and application technologies related to them.

In addition, copies of these publications can be obtained from the individual members given below to whom technical questions relating to CIDECT work or the design using hollow steel sections should be addressed.

The organization of CIDECT comprises:

o President: J. C. Ehlers (Federal Republic of Germany) Vice-President: C. L. Bijl (The Netherlands)

o A General Assembly of all members meeting once a year and appOinting an Executive Committee responsible for adiministration and executing of esta­bished policy

o Technical Commission and Working Groups meeting at least once a year and directly responsible for the research and technical promotion work

56

o Secretariat in Dusseldorf responsible for the day to day running of the orga­nization.

Present members of CIDECT are: (1992)

o Altos Hornos de Vizkaya S.A., Spain o British Steel PLC, United Kingdom o Hoesch Rohr AG, Federal Republic of Germany o ILVA Form, Italy o IPSCO Inc., Canada o Laminoirs de Longtain, Belgium o Mann.esmannrohren-Werke AG, Federal Republic of Germany o Mannstadt Werke GmbH, Federal Republic of Germany o Nippon Steel Metal Products Co. Ltd., Japan o Rautaruukki Oy, Finland o Sonnichsen AIS, Norway o Tubemakers of Australia, Australia o Van Leeuwen, The Nietherlands o Valexy, France o Verenigde Buizenfabrieken (VBF), The Netherlands o VOEST Alpine Krems, Austria

Cidect Research Reports can be obtained through:

Mr. D. Dutta Office of the Chairman of the CIDECT Technical Commission clo Mannesmannrohren-Werke AG Mannesmannufer 3 D-4000 Dusseldorf 1 Federal Republic of Germany

Telephone: (49) 2111875-3480 Telex: 8 581 421 Telefax: (49) 2111875-4689

Care has been taken to ensure that all data and information herein is factual and that numerical values are accurate. To the best of our knowledge, all information in this book is accurate at the time of publication. CIDECT, its members and the authors assume no responsibility for errors or misinterpretation of the information contained in this book or in its use.

57