Method .1 Design Section Moment Capacity

2 Therefore, substituting qV v for V max and rearranging the equation gives

5.2 Design Section Moment and Web Capacities

5.2.2 Method .1 Design Section Moment Capacity

The design section moment capacity (qMs) is determined from Clauses 5 . 1 and 5 . 2 . 1 of AS 4100 using:

qMs = qfy Ze

where q = 0 . 9 (Table 3 . 4 of AS 4100 ) fy = yield stress used in design

Ze = effective section modulus (see Section 3 . 2 . 2 . 2 )

For RHS, design section moment capacities are listed for bending about both principal axes.

These actions are split into two separate tables – the type (A) table for bending about the x-axis (e.g. Table 5 . 2 - 2 ( 1 )(A) for Grade C 450L0 (C450PLUS®) RHS lists qMsx) which is immediately followed by the type (B) table for bending about the y-axis (e.g. Table 5 . 2 - 2 ( 1 )(B) for Grade C 450L0 (C450PLUS®) RHS lists qMsy). Due to SHS being doubly-symmetric, the SHS tables (i.e. Tables 5 . 2 - 3 and 5.2-4 ) only consider design section moment capacities about the x-axis.

For RHS bending about the x-axis, the design member moment capacity (qMb) equals the design section moment capacity (qMs) for members which have full restraint against flexural-torsional buckling (see Section 5 . 1 . 3 ). For SHS bending about the x-axis and RHS bending about the y-axis, flexural-torsional buckling does not normally occur so qMb equals qMs (refer section 5.1.3).

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5.2.2.2 Segment Length for Full Lateral Restraint (FLR)

The Tables only consider RHS bending about the major principal x-axis to be susceptible to flexural-torsional buckling. For such sections, a beam segment with full or partial restraint at each end may be considered to have full lateral restraint if its length satisfies Clause 5 . 3 . 2 . 4 of AS 4100 , i.e.

FLR ) ry ( 1800 + 1500 `m) bf bw

¤² ¥

¦´ 250 fy

²²

´´

where FLR = maximum segment length for full lateral restraint ry = Iy

²²

´´ (see Tables 3 . 1 - 3 and 3.1-4 )

The FLR values listed in the (A) series tables of Tables 5 . 2 - 1 and 5.2-2 (for RHS) are calculated using `m = - 1 . 0 which is the most conservative case. However, `m = - 0 . 8 may be used for segments with transverse loads (as in the case of the (A) series tables in Tables 5 . 1 - 3 and 5.1-4 for RHS). Alternatively, `m may be taken as the ratio of the smaller to larger end moments in the length (L) for segments without transverse loads (positive when the segment is bent in reverse curvature).

5.2.2.3 Design Torsional Moment Section Capacity

The design torsional moment section capacity (qMz ) listed in the 5 . 2 Table series is determined in accordance with (a) and (b) as noted below.

(a) Although AS 4100 makes no provision for the design of members subject to torsion it is nevertheless considered appropriate to provide torsional capacities for hollow sections in the Tables. Hollow sections perform particularly well in torsion and their behaviour under torsional loading is readily analysed by simple procedures. An explanation of torsional effects is provided in Refs. [ 5 . 1 , 5 . 2 ].

The general theory of torsion established by Saint-Venant is based on uniform torsion. The theory assumes that all cross-sections rotate as a body around the centre of rotation.

When the applied torsional moment is non-uniform, such as when the torsional load is applied midspan between rigid supports or when the free warping of the section is restricted, then the torsional load is shared between uniform and non-uniform torsion or warping. However, in the case of hollow sections, the contribution of non-uniform torsion is negligible and sections can be treated as subject to uniform torsion without any significant loss of precision in analysis.

(b) For hollow sections, torsional actions can be considered using the following formulae:

Strength Limit State M*z ) qMz qMz = q0 . 6fyC

where M*z = design torsional moment

q = 0 . 9 (based on shearing loads and Table 3 . 4 of AS 4100 ) qMz = design torsional section moment capacity

fy = yield stress used in design

C = torsional section modulus (see 3 . 1 Table series) Serviceability Limit State

The angle of twist per unit length e (in radians) can be determined from the following formula:

e = M*z

where G = shear modulus of elasticity, GJ 80 x 103 MPa J = torsional section constant (see 3 . 1 Table series).

The method for determining the constants C and J is detailed in Section 3 . 2 . 1 . 1 .

Part 5

MEMBERS SUBJECT TO BENDING

Part 5

MEMBERS SUBJECT TO BENDING

5.2.2.4 Design Shear Capacity of a Web

Designers must ensure that the design shear force (V*) ) qVv along the beam.

RHS and SHS generally have non-uniform shear stress distributions along their webs.

Consequently, the design shear capacity of a web (qVv) for most RHS/SHS in the Tables are primarily determined from Clauses 5 . 11 . 3 and 5 . 11 . 4 of AS 4100 and is calculated as the lesser of:

qVv = qVw (Clause 5 . 11 . 4 of AS 4100 )

and qVv = 2qVu 0.9 fvm*

fva*

²²

´´

(Clause 5 . 11 . 3 of AS 4100 )

Also, for CHS:

qVv = 0 . 324fyAe (Clause 5 . 11 . 4 of AS 4100 ) Where q = 0 . 9 (Table 3 . 4 of AS 4100 )

Vw = 0 . 6fy (d – 2t) 2t Vu = Vw for d1

t fy

250

²²

´´)82 and applies for all ATM RHS/SHS in the Tables

= _vVw for d1 t

fy 250

²²

´´82 and _v is evaluated from Clause 5 . 11 . 5 of AS 4100 f*va = average design shear stress in the web

f*vm = maximum design shear stress in the web fy = yield stress used in design

Ae = effective sectional area of CHS in shear

= Ag (i.e. gross cross-section of CHS provided there are no holes larger than those required for fasteners, or that the net area is greater than 0 . 9 times the gross area) d = full depth of section

t = thickness of section d1 = d – 2t

The ratio of maximum to average design shear stress in the web (f *vm / fva* ) for bending about the x-axis is calculated [ 5 . 3 ] using:

fvm*

fva* = 3 2 bd 2 3 bd where d = full depth of section

b = full width of section

Note: For bending about the y-axis, b and d are interchanged in the calculation of the maximum to average design web shear stress ratio. Non-uniform shear stress governs when d / b > 0 . 75 .

For calculating the web area, the web depth has been taken as d – 2t (or b – 2t when appropriate) for RHS/SHS and 0 . 6 times the gross cross-section area ( 0 . 6 Ag) for CHS.

5.2.2.5 Design Web Bearing Capacities

Designers must ensure that the design bearing force (R*) )qRb at all locations along a beam where bearing forces are present.

The design bearing capacity (qRb) is calculated in accordance with Clause 5 . 13 of AS 4100 and taken as the lesser of:

qRby = q2_pbbtfy and qRbb = q2_cbbtfy

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

qRby = design web bearing yield capacity (Clause 5 . 13 . 3 of AS 4100 ) qRbb = design web bearing buckling capacity (Clause 5 . 13 . 4 of AS 4100 ) t = thickness of section

fy = yield stress used in design

bb = bs + 5rext + d5

bs = actual length of bearing (see Figure 5 . 2 (b)) d5 = flat width of web (see Figure 5 . 2 (a)) rext = outside corner radius (see Section 3 . 2 . 1 . 2 ) _p = 0.5

ks 1 1< _pm2 1kks

< 1< _pm2 0.25 kv2

²²

´´

à à _pm = 1

ks0.5 kv ks = 2rext

t <1 kv = d5

_c = member slenderness reduction factor determined from Clause 5 . 13 . 4 of AS 4100 . This is equal to the design axial compression capacity of a member with area twbb with _b = 0 . 5 , kf = 1 . 0 and slenderness ratio, Le/r = 3 . 5d5/t.

Part 5

MEMBERS SUBJECT TO BENDING

(b) Interior Force

(c) End Force (a) Section

d d5 = d - 2rext

rext

bb =bbf + 2bbw

bbf =bs + 5rext

bbw= rext

bbf bs

2.5 11 1

bbw bbw

bb =bbf + bbw

bbf =bs + 2.5rext bbw=

rext

bbf

2.5 11 1 bbw

2 d5

d5 2

Figure 5.2: Dispersion of force through flange, radius and web of RHS/SHS

Part 5

MEMBERS SUBJECT TO BENDING

(b) For end bearing such that bd < 1.5d5 (see Figure 5 . 2 (c)) bb = bs2.5rextd5

2 _p = 2ks2<ks

_c = member slenderness reduction factor determined from Clause 5 . 13 . 4 of AS 4100 . This is equal to the design axial compression capacity of a

member with area twbb with _b = 0 . 5 , kf = 1 . 0 and slenderness ratio, Le/r = 3 . 8d5/t.

Tables 5 . 2 - 1 to 5 . 2 - 4 list values qRby and qRbb in terms of qRby/bb and qRbb/bb respectively for RHS/SHS. In both the interior and end bearing cases, the critical web bearing failure mode (i.e. web bearing yield design capacity or web bearing buckling design capacity) is shown in bold. Additionally, the terms 5rext (= 2 x 2 . 5rext for interior bearing), 2 . 5rext (for end bearing), bbw (see Figures 5 . 2 (b) and (c)) and Le/r are also listed in these tables. For the same section range, the RHS listings in this table series consider shear and bearing forces for flexure about the x-axis (the (A) series tables) which is then immediately followed by the (B) series tables for flexure about the y-axis.

Method .1 Design Section Moment Capacity

Moment Ampliﬁcation for First-Order Elastic Analysis

SERVICEABILITY LIMIT STATE MAXIMUM DESIGN LOADS