• Author / Uploaded
• djordjeue

Citation preview

Design of aluminium columns Y. F. W. Lai Mitchel MacFarlane, Hong Kong D. A. Nethercot Department of Civil Engineering, University of Nottingham, UK (Received April 1990; revised January 1991) Theoretical results for the buckling of aluminium columns having longitudinal and local transverse welds are presented. These are used to assess the suitability of the procedures given for column design in th~'~raft British Standard for the use of structural aluminium BS 8118. As a result some modifications to these procedures are suggested. Keyword$: aluminium structures, structural design, welding The new draft British code for the design of aluminium structures BS 8118 I, which will replace CP 1182, has recently been circulated for the purpose of inviting public comment. Although the column design curves suggested in Reference 1 are based largely on test data and accurate numerical studies 3, their suitability is still uncertain for some types of member, especially welded columns and/or columns subject to flexural-torsional buckling. This paper presents the results of an extensive comparison between the column design curves of the draft BS 8118 and numerical results obtained by two finite element programs INSTAF and BIAXIAL 4. All comparisons are restricted to 'compact' cross-sections for which no local buckling occurs.

Nomenclature A A*

C,, Cr E L L*

L,r L,. P,

P~c

Pult /5 n n* r

area of cross-section area of heat-affected zone (HAZ) buckling coefficient for flexural buckling buckling coefficient for torsional buckling Young's modulus length of member length of heat-affected zone critical region defined as a distance extending from 0.25L either side of point of maximum curvature when flexural buckling takes place total length within critical region over which heat-affected zone softening occurs ultimate compressive strength given by draft BS 8118 compressive capacity of cross-section calculated compressive strength of member nondimensional maximum compressive strength of member (= Pult/Oo2A) knee factor in Ramberg-Osgood formula knee factor for HAZ in Ramberg-Osgood formula radius of gyration

0141-0296/92/030188-07 © 1992 Butterworth-Heinemann Ltd

188

Eng. Struct. 1992, Vol. 14, No 3

buckling,

columns,

stability,

ro ry radius of gyration about x- and y-axis, respectively h , X, slenderness (L/rx, L/ry) ~ , ~, nondimensionalized slenderness ratio (Xx/r(E/

00.2)m, X,./Tr(E/ao.2)1/2) o a02 a*2 ault w

normal stress 0.2% proof stress 0.2% proof stress of HAZ tensile strength material strength reduction factor for heataffected zone material properties.

Numerical results All of the numerical results presented herein were obtained by using the programs INSTAF for twodimensional response and BIAXIAL for threedimensional response 4. Both programs permit the full load deflection curve to be traced up to collapse utilizing sophisticated finite element approaches 56 ' , which permit the effects of longitudinal and/or transverse welds to be allowed for. Both have been extensively verified against test data and alternative ultimate strength analyses for both aluminium and steel members 4. Results have been obtained for a large number of axially loaded columns, covering the range of different types for which the design approach of Reference 1 is intended. Tables la and lb list the individual cases studied, Alloy types are characterized by the parameter n used in the Ramberg-Osgood representation of the stress-strain curve, with the HAZ (heat affected zone) material being assumed to possess properties corresponding to 0"2 = 0.500.2 and n* = 10. All columns were assumed initially bowed about the minor axis in the form of a half sine wave with a maximum amplitude of L/IO00.

Column design procedure of draft BS 8118 The factored axial resistance of a column, Pc, which is

Design of aluminium columns: Y. F. W. Lai and D. A. Nethercot Table la Class

List of theoretical column curves (nonwelded and longitudinally welded columns) Theoretical curve

n

A' A

Type of cross -

Program used

Principal results

Gult Gult/GO'2 ..................................................................... A

C-A-I C-A-2

1.17

C-B-I C-B-2 C - B - 3 C-B-4 C-B-5 C-B-6

1.17

C

C-C-I C-C-2

1.08 1.17

D

C- D- I C-D-2

I .17

E

C - E- I C-E-2

I .49 1.61

F

C-F-I

G

25

(I}

0.0 0.0

I III

INSTAF BIAXlAL

Figure

0.1 0.3 0.5 0.1 0.3 0.5

III

BIAXIAL

Figure 2

50 25

0.0 ').0

II IV

INSTAF BIAXIAL

Figure 4

25

0.3 0.5

IV

BIAXIAL

Figure 5

10 8.4

0.0 0.0

I III

INSTAF BIAXIAL

Figure 6

1.61

8.4

0.3

III

BIAXlAL

Figure 7

C-G-I C-G-2

1.36 1.95

13 6

0.0

IV

BIAXlAL

Figure 8

0.0

C-H-1

1.95

9

0.1

...................................................................... B

H

25

I~

lqOmm

10ram

Figure 3

~ ~

I- 80mm~l "~ ~

lOmm mm

{w) BIAXIAL

11mm 7mm

(iH)

IV

~I 10mm

(It)

...................................................................... Table lb

, . 3 - -3...

I

Figure 9

Type of cross-section

List of theoretical column curves (transversely welded columns)

Theoretical curve reference C-TW- 1 C-TW-2 C-TW-3 C-TW -4 C-TW-5 C-TW-6 C-TW-7 C-TW-8 C-TW-9 C-TW-IO C-TW- 11

O'ult

n

L*/L

Type of crosssection (see Table 1 (a))

Program used

Principal results

1.17

25

I

INSTAF

Figure 10

1.17 1.17 1 17 1.17

25 25 25 25

I I I III

INSTAF INSTAF INSTAF BIAXIAL

Figure Figure Figure Figure

1.17

25

0.1 0.2 0.3 1.0 0.0 0.05 0.1 at both ends L* = 50 mm at mid-height L* = L L* = 0 L* = 30 mm at both ends

III

BIAXIAL

Figure 15

00.2

influenced by the compressive proof stress of the material 00.2, the area, HAZ effects, slenderness and the degree of end fixity, thickness of the plate elements and torsional properties of the cross-section, is given by

P~=P,~C~

(1)

where Psc = basic axial capacity and Cc = reduction factor for overall flexural buckling. In determining Psc due account must be taken of HAZ effects, so that

Psc=GO.2[A--~

(1 - w)A*]

(2)

11 12 13 14

in which the second term in the square brackets allows for the reduction in strength due t o the presence of HAZ material. The value of Cc is given as a function of a nondimensional slenderness parameter )] = (L/r)(ao.2/250)m by the set of five column curves provided in Figure 5.9 of Reference 1; selection of the appropriate curve for a particular column type will be discussed later. For a column liable to fail due to torsional instability 7, the reduction factor for torsional buckling Cr replaces Co. Cr is determined from Figure 5.10 of Reference 1, in which the four curves are the upper four curves for flexural buckling. The design of columns containing localized transverse welds is covered in Appendix 5A of Reference 1. The effect on buckling strength is assumed to depend solely on the value of LJLcr, in which Lw is the length of HAZ and L~r defines that part of the column containing

Eng. Struct.

1992,

Vol. 14, No 3

189

Design of aluminium columns: Y. F. W. Lai and D. A. Nethercot Table 2

Factors used in selection of column curve in Reference 1

systematic comparisons against the 29 sets of numerical results of Table 1.

Extent of HAZ

Column curve 1 and class A columns

Lw/Lc,

Design approach

0

Ignore presence of transverse welds Design column as if it consisted wholly of HAZ material

>0.2

(Psc = a(~2A) 0 < Lw/Lcr < 0.2

Table 3

Interpolate between the above t w o cases based on actual Lw/Lc, value

Figure i shows how for the two sets of numerical results corresponding to the most favourable class of member curve 1 represents a safe and reasonable design basis over the whole range of slenderness considered. For the torsionally weaker narrow flange section III the design curve is more conservative, particularly at medium and high slenderness. For stocky columns the use of the squash load P~, = %2 A means that the beneficial effects of the continuously rising material stress-strain curve are not utilized.

Factors used in selection of column curve in Reference 1

Column curve 1 and class B and C columns Oult/O0.2

Alloy type Cross-section Welding

high n (H) yl/Y2* < 1.2 symmetric (s) nonwelded (NW)

O'ult/O'0.2 > 1.2 low n(L) Yl/Y2 > 1.2 aysymmetric (A) welded (W)

* y l and y2 are perpendicular distances from the axis of buckling to the further and nearer extreme fibres, respectively

Table 4

Six cases of longitudinally welded members - three each with symmetrically and non symmetrically arranged welds - are covered in Figures 2 and 3. Residual stresses have been included in all cases except for unsymmetrical welds and A*/A = 0.5. Design curve 2 is safe for all but a few cases of very stocky members; even there it overestimates strength by only a few per cent. However, as slenderness increases the design

Allocation of cases to column design curves I

Class (see Table 1) A B C D E F G H

Condition

Draft BS 8 1 1 8 allocation

Proposed allocation

H-S-NW H-S-W H-A-NW H-A-W L-S-NW L-S-W L-A-NW L-A-W

1 2 2 3 3 4 4 5

1 2 2 3 2 3 3 4

1.0

~"-,~"'-~/~ " ~ , 0.5

0.0

l

I

l

I

I

I

I

I

l

I

0.5

0.0

Lw undergoing the largest curvatures. Three cases are identified as indicated in Table 2. Reference 1 does not recognise the possibility of the HAZ not extending over the full depth of the cross-section. For end-welded columns for which the welds extend for less than 0.05L the effect of transverse welds may be neglected. In all cases it is, however, necessary to ensure that the axial load does not exceed the crosssectional capacity Psc = %.2A. All the column curves are described by a P e r r y - R o b e r t s o n type of equation with the selection for a particular column being based on the factors listed in Table 3. Assessment on the basis of Table 3 permits the columns to be graded into eight classes according to the combinations of these conditions present and thus to be rated according to the number of weakening conditions as indicated in Table 4. The higher the rating number the weaker is that class of column.

c-A-2 ~B, Ax, A, i

I

I

l

I

I

I .0

I

I

i

1.5

ix or Y Figure 1 Comparison between design column curve 1 and theoretical column curves (class A columns). ( ), theoretical curves; ( - - - ) , draft BS 8 1 1 8

....

1.0

-~

__ _

/

---~ ~

\ , ~

I 0.0

C-B-2

-~- ~.--.~ -.~ - " ~

_

0.0

C-B-I

I

I

I

I

i

l

t

l

0.5

i

I .0

l

J

i

I

I

l

I

I

I .5

Comparison between design column curves of draft BS 8118 and numerical results

Figure 2 Comparison between design column curve 2 and

The accuracy of the column design approach described in the previous section has been assessed b y means of

theoretical column curves (class B columns, with symmetric longitudinal welds). ( ) theoretical curves (biaxial); ( - - - ) , draft BS 8 1 1 8

190

Eng. Struct. 1992, Vol. 14, No 3

Y

Design of aluminium co/umns: Y. F. W. Lai and D. A. Nethercot

1.0 ____. 0.2). ( ), theoretical curves (INSTAF); ( - - - ) draft BS 8118

Eng. Struct. 1992, Vol. 14, No 3

I

I

I

0.5

-2×

192

I

- ) , draft BS 8118

\

0.5

0.0

I

Figure 11 Comparison with transversely welded column curves obtained by INSTAF program (LwlLcr = O.1). ( ), theoretical

C-TW-1 {L*IL = 0.1 )\X , ~ C - T W - 2 (L*IL =0.2),\ C-TW-3(L*/L=0.3) \ -

I

x

column curve 5 and theoretical column curves (class H columns). ( ), theoretical curve; ( - - - ) , draft BS 8118 between

I

I .0

Y

Figure 9 Comparison

C-TW-6 (L*/L=O.05)

\

0.5

0.0 0.0

\

I

1.0

I

I

I

I

I

I

I

I

1.5

~v

Figure 12 Comparison with

welded column curves by INSTAF program (end-welded columns). ( ), theoretical curves (INSTAF); ( - - - ) , draft BS 8118 obtained

transversely

Design of a/uminium co/umns: Y. F. W. Lai and D. A. Nethercot

Proposed design improvements

simply that the cross-sectional capacity /'st of such members is still, of course, only O'~.2 and that for stocky columns only a relatively small part of the total longitudinal stress is due to bending. Thus members failing by 'squash' as well as those for which little bending occurs will have their strength overpredicted due to the optimistic value of P=, used in the design process. For slender members, in common with several other cases considered herein, the design method of Reference 1 is conservative since the allowance made for HAZ does not reduce in an appropriate way. For columns welded only at their ends Reference 1 proposed neglecting any reductions in strength. Figure 12 shows this to be clearly unsafe over much of the range. A simple procedure to correct this is given in the next section. When failure is due to torsional buckling and the extent of HAZ present is sufficient for case ii of Table 2 to apply, Figure 13 shows the use of Cr in place of Cc to be reasonable. Figure 14 shows that for an endwelded column, limiting the strength on the basis of P=c calculated for the HAZ material would provide the basis for a satisfactory design treatment.

Nonwelded

or

longitudinally welded(2t)

The results presented in Figures 1 - 9, corresponding to the 29 cases of nonwelded or longitudinally welded columns listed in Table la, suggest that the number and spread of design curves proposed in Reference 1 is too great. Generally speaking the proposals for the more favourable cases are satisfactory,_ if rather too conservative at higher slendernesses 0~ > 1.0), while those requiring the use of curves 4 and 5 are much too conservative over the whole range of slendernesses. Table 4 therefore suggests an alternative allocation of cases using just 4 column curves. For classes A - D the allocation is as before; classes E - H all move up one curve, with the lowest curve 5 being dropped.

Transversely welded The proposed method distinguishes between the 2 cases (1) P*_< P*, in which P * = o*A is the elastic limit for pure compression (2) P*> P*

1.0 k

\

C-TW-8 (L* = 50 mm

~/at

mid-height)

J~xC-TW-9(L*=L)

",.,,

0.5

0.0 0.0

I

I

I

I

I

I

I

I

I

I

0.5

I

I

I

(i)

I

/

1.0

I

P = 1 - (1 - w)A*/A

I

(ii)

Figure 13 Comparison with transversely welded column curves obtained by BIAXIALprogram (centrally-welded columns). ( theoretical curves; ( - - - ) , draft BS 8118

-

-

-

-

~

-~\

"~ ~" ~ , , ~

'~C-TW-11

When longitudinal welds are also present they should be allowed for when determining P=c and thus Pc*.

Conclusions

(L* = 30 m m

at both ends)

___.S"

m

0.0

1

0.0

I

I

I

I

0.5

I

I

I

I

I

1.0

I

I

I

I

I

If condition (i) is not satisfied the column is designed as if it consisted of wholly HAZ material.

),

C-TW-10 (L*=0)

~'~~N

o.,_

The HAZ is located near the ends within a distance of 0.25L of the supports. The column is designated 'end-welded' and may be designed as if it were nonwelded subject to an upper limit given by

1.5

Y

1.0

For the first case HAZ effects may be neglected. For the second two variants are recognised:

I

I

1.5

Figure 74 Comparison with transversely welded column curves obtained by BIAXIAL program (centrally-welded columns). ( ), theoretical curves; ( - - - ) , draft BS 8118 (modified in case of end-welded column)

I

A series of numerical results for the flexural and flexural-torsional buckling of various types of aluminium column have been presented. The cases considered were selected to cover the full range of effects taken into account in allocating column types to design curves by the draft BS 8118. Detailed comparisons between the numerical results and the appropriate column curves have revealed that The strength of most types of column is safely predicted by the method of the draft code. For asymmetric cross-sections or material with au,/%.2 > 1.2 underestimates of strength are possible, especially for columns of intermediate slenderness.

Eng. Struct. 1992, Vol. 14, No 3

193

Design of aluminium columns: Y. F. W. Lai and D. A. Nethercot

.

•

As a general rule the reductions in load carrying capacity obtained by passing through the different categories A - H appears to be too great. Some upward revision of the lower design curves coupled with some re-allocation of classes would appear to be justified. Suggestions for improvements to the treatment of transversely welded columns, particularly when the welds are located at the column ends, have been provided.

Acknowledgments This work forms part of a project funded by R.A.R.D.E.; the authors are grateful for assistance and comments on the studies reported herein by Mr D. Webber and Dr P. S. Bulson.

194

Eng. Struct. 1992, Vol. 14, No 3

References 1 British Standards Institution Draft, British Standard BS 8118, 'Code of practice for the design of aluminium structures', 1985 2 British Standards Institution, CP 118: 1969, 'The structural use of aluminium' 3 Hong, G. M. 'Aluminium column curves', Aluminium structures. design and construction, R. Narayanan Ed., Elsevier Applied Science Publishers, 1987, pp. 40-49 4 Lai, Y. F. W. and Nethercot, D. A., 'Strength ofaluminium members containing local transverse welds', Engineering Structures, (in press) 5 E1 Zanaty, M. H. Murray, D. W. and Bjorhovde, R. 'Inelastic behaviour of multistorey steel frames,' University of Alberta, Canada, 1980 6 El Khenfas, M. A. and Nethercot, D. A., 'Ultimate strength analysis of steel beam-columns subjected to biaxial bending and torsion', Res. Mechanica, 1989, 28, (1-4), 307-360 7 Nethercot, D. A. 'Aspects of column design in the new UK structural aluminium code', Aluminium structures: advances, design and construction, R. Narayanan, Ed., Elsevier Applied Science Publishers, 1987, pp 50-59