MEMBERS SUBJECT TO AXIAL COMPRESSION

Section Page

6.1 General 6-2

6.2 Design Section Capacity in Axial Compression 6-2 6.3 Design Member Capacity in Axial Compression 6-2

6.4 Effective Length 6-3

6.5 Example 6-4

6.6 References 6-4

Table Page

Tables 6-1 to 6-6

Design Member Capacities in Axial Compression 6 - 6

See Section 2.1 for the specific Material Standard (AS/NZS 1163) referred to by the section type and steel grade in these Tables.

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6.1 General

Values of the design member capacity in compression (qNc) for buckling about each principal axes for a range of effective lengths (Le) are given in Tables 6 - 1 to 6 - 6 . The design member capacities are determined from Section 6 of AS 4100 . All the Tables for CHS, RHS and SHS are supplemented by graphs of qNc versus Le placed consecutively after the tables for each corresponding grade and section type. All loads are assumed to be applied through the centroid of the section. The column capacity is associated with flexural buckling as torsional buckling is not a common buckling mode for

hollow sections in axial compression.

For RHS only, the Tables in this section have been grouped into two series:

the (A) series for the member buckling about the x-axis, and the (B) series for the member buckling about the y-axis.

The (A) series tables and graphs for each group of sections are immediately followed by the (B) series of tables and graphs for the same group.

6.2 Design Section Capacity in Axial Compression

The design section capacity in compression (qNs) is obtained from Clause 6 . 2 of AS 4100 and is given by:

qNs = qkf An fy

where q = 0 . 9 (Table 3 . 4 of AS 4100 ) kf = form factor (see Section 3 . 2 . 2 . 3 ) An = net area of the cross section

= Ag assuming no penetrations or holes (see 3.1 series Tables in Part 3) fy = yield stress used in design

The design section capacity considers the behaviour of the cross-section only (as in a stub column test), and is affected by the element slenderness of each plate element in the cross-section. The form factor (kf) represents the proportion of the section that is effective in axial compression and is determined from considerations of element slenderness as affected by local buckling, using Clause 6.2.3 and 6.2.4 of AS 4100. See discussion in Section 3.2.2.3.

6.3 Design Member Capacity in Axial Compression

The design member capacity in axial compression accounts for the effect of overall member buckling for the effective length of the member (amongst other factors) and it is obtained from Clause 6 . 3 of AS 4100 and given by:

qNc = q_cNs ) qNs

where q = 0 . 9 (Table 3 . 4 of AS 4100 )

_c = member slenderness reduction factor

The member slenderness reduction factor (_c) depends on the modified member slenderness (hn) and the member section constant (_b). From Clause 6 . 3 . 3 of AS 4100 :

_c = jj 1< 1< 90 jh

¤² ¥

¦´

à à

âô êô

ưô

đô

where j =

h 90

¤² ¥

¦´

1 d

2 h 90

¤² ¥

¦´

hn = Le r

¤² ¥

¦´ kf 250fy h = hn + _a _b _a = 2100 hn<13.5

h2n

<15.3hn2050 d = 0 . 00326 (h– 13 . 5 ) * 0

Part 6

MEMBERS SUBJECT TO AXIAL COMPRESSION

Buckled Shape

Sway Member

Effective length

factor (ke) 0.7 0.85 1.0 1.2 2.2 2.2

Symbols for end restraint conditions

= Rotation fixed, translation fixed

= Rotation free, translation fixed

= Rotation fixed, translation free

= Rotation free, translation free

Figure 6.1: Effective Length Factors for Members with Idealised Conditions of End Restraint Le = effective length of a compression member about the axis of buckling

r = radius of gyration about the axis of buckling

For routine design the above equations need not be used. Table 6 . 3 . 3 ( 3 ) of AS 4100 may be consulted to obtain the value of (_c) directly once hn and _b are evaluated.

Note that the design member capacity equals the design section capacity (i.e. qNc = qNs) when the effective length is zero (i.e. Le = 0 ).

Table T 6 . 1 (which is extracted from Table 6.3.3 of AS 4100) lists values of _b for the sections considered in these Tables.

Table T6.1: Values of Member Section Constant (_b) for Compression Members

Section Residual Stresses Yield Slenderness Limit _b

hey kf = 1.0 kf < 1.0

RHS, SHS CF 40 -0.5 -0.5

CHS CF 82 -0.5 -0.5

6.4 Effective Length

The values of qNc are based on the effective length (Le) of the member. The effective length depends on the member length (L), the rotational and translational restraints at the ends of the member and is determined from the following formula:

Le = keL

The member effective length factor (ke) for use in Clause 6 . 3 . 2 of AS 4100 can be determined using Clause 4 . 6 . 3 of AS 4100 or by a rational frame buckling analysis (Clause 4.7 of AS 4100) . ke is given in Figure 6 . 1 for members with idealised end restraints (from Figure 4.6.3.2 of AS 4100). For braced or sway members in frames, ke depends on the ratio ( a ) of the compression member stiffness to the end restraint stiffness, calculated at each end of the member. Example 2 of Section 4 . 3 in Ref [ 6 . 1 ] provides a sample calculation of ke for columns in an unbraced plane frame.

Part 6

MEMBERS SUBJECT TO AXIAL COMPRESSION

6.5 Example

Design a RHS column, with a length of 5 . 8 m, in Grade C 450 L 0 (C450PLUS®) steel to resist a design axial force, N* = 2400 kN. Assume that for x-axis buckling both ends are pinned (rotation free, translation fixed), while for y-axis buckling one end is rotation free, translation fixed (pinned) and the other end is rotationally and translationally fixed.

Design Data:

N* = 2400 kN Solution:

(i) Determine effective lengths

For x-axis buckling ke = 1 . 0 (Figure 6 . 1 ) Lex = keL = 1 . 0 x 5 . 8 = 5 . 8 m 5 6 . 0 m

For y-axis buckling ke = 0 . 85 (Figure 6 . 1 ) Ley = keL = 0 . 85 x 5 . 8 = 4 . 93 m 5 5 . 0 m

(ii) Select a member

When looking up Tables 6 - 4 ( 1 )(A) and 6-4(1)(B) from bottom to top there are various sections for which N* < qNc. As such there is the possibility that the first sections being sighted are uneconomical. In order to select a more optimal section it may be prudent to summarise a few of the initial listings for qNcx and qNcy based on their respective effective lengths. This is summarised in Table T 6 . 2 for the example being considered.

Table T6.2: Possible C450PLUS® RHS options to resist N* = 2400 kN compression.

Note: shaded values indicate the lightest section in mass (kg/m).

as noted in Table T6 . 2 , adopt a 350 x 250 x 8 . 0 RHS in C 450 L 0 (C450PLUS) as:

qNcx = 2720 kN (Lex = 6 . 0 m in Table 6 - 4 ( 1 )(A))

> N*

qNcy = 2660 kN (Ley = 5 . 0 m in Table 6 - 4 ( 1 )(B)) > N*

6.6 References

[ 6 . 1 ] ASI, “Design Capacity Tables for Structural Steel – Volume 1 : Open Sections”, fourth edition, Australian Steel Institute, 2009.

See Section 1.1.2 for details on reference Standards.

Part 6

MEMBERS SUBJECT TO AXIAL COMPRESSION

Buckling about x-axis with Lex = 6.0 m

Designation Mass

per m qNcx

d b t (kN)

mm mm mm kg/m Le = 6.0m

400 x 200 x 10.0 RHS 88.4 3500 8.0 RHS 71.6 2510 350 x 250 x 16.0 RHS 136 5940 12.5 RHS 109 4780 10.0 RHS 88.4 3720 8.0 RHS 71.6 2720 300 x 200 x 16.0 RHS 111 4440 12.5 RHS 89.0 3610 10.0 RHS 72.7 2970 250 x 150 x 16.0 RHS 85.5 2850

Buckling about y-axis with Ley = 5.0 m

Designation Mass

per m qNcy

d b t (kN)

mm mm mm kg/m Le = 5.0m

400 x 200 x 10.0 RHS 88.4 3050 8.0 RHS 71.6 < N*

350 x 250 x 16.0 RHS 136 5750 12.5 RHS 109 4630 10.0 RHS 88.4 3620 8.0 RHS 71.6 2660 300 x 200 x 16.0 RHS 111 4020 12.5 RHS 89.0 3290 10.0 RHS 72.7 2720 250 x 150 x 16.0 RHS 85.5 < N*

Blank Page

TABLE 6 - 1

Circular Hollow Sections AS/ NZS 1163 Grade C 250 L 0

Moment Ampliﬁcation for First-Order Elastic Analysis

SERVICEABILITY LIMIT STATE MAXIMUM DESIGN LOADS