8.3 Combined Bending and Axial Compression · 2018. 9. 27. · Members Subject to Bending 51 PART...
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DCT/V2/022004 83ASI: DESIGN CAPACITY TABLES FOR STRUCTURAL STEEL VOLUME 2: HOLLOW SECTIONS
8.3 Combined Bending and Axial CompressionIn this section:
φ = 0.9 (Table 3.4 of AS 4100)
φMsx = design section moment capacity for bending about the major principal xaxis
φMsy = design section moment capacity for bending about the minor principal yaxis
N* = design axial compressive force
φNs = design section capacity in compression
φNcx = design member capacity in compression, buckling about the xaxis
φNcy = design member capacity in compression, buckling about the yaxis
8.3.1 Compression and Uniaxial Bending – about the major principal xaxis
For a member subject to uniaxial bending about the major principal xaxis and axial compression,the following condition must be satisfied:
M*x ≤ min.[φMrx; φMix; φMox]
where φ = 0.9 (Table 3.4 of AS 4100)
M*x = design bending moment about the major principal xaxis
φMrx = design section moment capacity (φMs) for bending about the major principal xaxisreduced by axial force (see Section 8.3.1.1)
φMix = design inplane member moment capacity (φMi) for bending about the major principal xaxis (see Section 8.3.1.2(a))
φMox = design outofplane member moment capacity (φMo) for bending about the majorprincipal xaxis (see Section 8.3.1.2(b))
8.3.1.1 Section Capacity
The value of φMrx must be determined at all points along the member and the minimum value usedto satisfy Section 8.3.1.
φMrx = φMsx (Clause 8.3.2 of AS 4100)
Alternatively, for RHS and SHS to AS 1163, which are compact about the xaxis with kf = 1.0 subject to bending and compression
φMrx = 1.18φMsx ≤ φMsx (Clause 8.3.2 of AS 4100)
For RHS and SHS to AS 1163, which are compact about the xaxis with kf < 1.0 subject to bendingand compression
φMrx = φMsx ≤ φMsx (Clause 8.3.2 of AS 4100)
where λw = the element slenderness of the web (Clause 6.2.3 of AS 4100)
=
λwy = the web yield slenderness limit (Table 6.2.4 of AS 4100)
= 40 for RHS and SHS considered in this publication.
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8.3.1.2 Member Capacity
This section only applies to members analysed using an elastic method of analysis. Where there issufficient restraint to prevent lateral buckling, only the inplane requirements of Sections 8.3.1.1and 8.3.1.2 need to be satisfied. If there is insufficient restraint to prevent lateral buckling, then boththe inplane and outofplane requirements of Sections 8.3.1.1 and 8.3.1.2 need to be satisfied.
(a) Inplane capacity
φMix = φMsx (Clause 8.4.2.2 of AS 4100)
For braced and sway members, the above value of φNcx is calculated using an effective length factor (kex) equal to 1.0 (i.e. Lex = L), unless a lower value of kex has been calculated for a braced member,provided that N* ≤ φNcx where the value of φNcx in this inequality is calculated using the correctvalue of kex.
Clause 8.4.2.2 of AS 4100 also provides a higher tier method for evaluating Mi which is dependenton the ratio of the member’s end bending moments. Due to the variable nature of these end bendingmoments, the further consideration of this higher tier method is beyond the scope of this publication.
(b) Outofplane capacity
φMox = φMbx (Clause 8.4.4.1 of AS 4100)
where φMbx = design member moment capacity for bending about the major principal xaxis.
8.3.1.3 Tables
For RHS, Tables 83 to 84 list φMsx, φNs and φMrx (comp)  the latter parameter refers to φMrx asnoted in Section 8.3.1.1. Tables 85 to 86 for SHS refer to these three parameters as φMs, φNs andφMr (comp) respectively. For CHS, Tables 81 to 82 list φNs, φMs and the relationship to φMr (i.e.the design section moment capacity reduced by compression). Designers should evaluate n =N*/φNs, then use it to calculate the value of φMrx and ensure that it is less than or equal to thedesign section capacity φMsx. For specific hollow sections, the 8 Series tables also provide references to other tables (e.g. φMb (for RHS only), φNcx and φNcy) to evaluate φMix and φMox.
8.3.2 Compression and Uniaxial Bending – about the minor principal yaxis
For a member subject to uniaxial bending about the minor principal yaxis and axial compression,the following condition must be satisfied:
M *y ≤ min. [φMry;φMiy]
where φ = 0.9 (Table 3.4 of AS 4100)
M *y = design bending moment about the minor principal yaxis
φMry = design section moment capacity (φMs) for bending about the minor principal yaxis reduced by axial force (see Section 8.3.2.1)
φMiy = design inplane member moment capacity (φMi) for bending about the minor principal yaxis (see Section 8.3.2.2)

DCT/V2/022004 85ASI: DESIGN CAPACITY TABLES FOR STRUCTURAL STEEL VOLUME 2: HOLLOW SECTIONS
8.3.2.1 Section Capacity
The value of φMry must be determined at all points along the member and the minimum value isused to satisfy Section 8.3.2:
φMry = φMsy (Clause 8.3.3 of AS 4100)
Alternatively, for RHS and SHS to AS 1163, which are compact about the yaxis subject to bending and compression:
φMry = 1.18φMsy ≤ φMsy (Clause 8.3.3 of AS 4100)
8.3.2.2 Member Capacity
This section only applies to members analysed using an elastic method of analysis. For bendingabout the minor principal yaxis only the inplane requirements need to be satisfied.
(a) Inplane capacity
φMiy = φMsy (Clause 8.4.2.2 of AS 4100)
For braced and sway members, the above value of φNcy is calculated using an effective length factor(key) equal to 1.0 (i.e. Ley = L), unless a lower value of key has been calculated for a braced member,provided that N* ≤ φNcy where the value of φNcy in this inequality is calculated using the correctvalue of key.
Clause 8.4.2.2 of AS 4100 also provides a higher tier method for evaluating Mi which is dependenton the ratio of the member’s end bending moments. Due to the variable nature of these end bendingmoments, the further consideration of this higher tier method is beyond the scope of this publication.
8.3.2.3 Tables
For RHS, Tables 83 to 84 list φMsy, φNs and φMry. Designers should evaluate n = N*/φNs, then useit to calculate the value of φMry and ensure that it is less than or equal to the design sectioncapacity φMsy. For specific hollow sections, the 8 Series tables also provide references to othertables (e.g. φNcy) to evaluate φMiy.
8.3.3 Compression and Biaxial BendingFor a member subject to biaxial bending and axial compression, both the conditions defined inSections 8.3.3.1 and 8.3.3.2 must be satisfied.
8.3.3.1 Section Capacity
≤ 1 (Clause 8.3.4 of AS 4100)
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86 DCT/V2/022004ASI: DESIGN CAPACITY TABLES FOR STRUCTURAL STEEL VOLUME 2: HOLLOW SECTIONS
Alternatively, for RHS and SHS to AS 1163, which are compact about both the x and yaxes:
≤ 1 (Clause 8.3.4 of AS 4100)
where γ = 1.4 + ≤ 2.0
φMrx and φMry are calculated using the alternatives presented in Sections 8.3.1.1 and 8.3.2.1.
8.3.3.2 Member Capacity
≤ 1 (Clause 8.4.5.1 of AS 4100)
where φMcx = lesser of φMix and φMox (see Section 8.3.1.2)
and φMiy is calculated using the alternative presented in Section 8.3.2.2.
8.3.3.3 Tables
For RHS, Tables 83 to 84 list φNs, φMsx and φMsy. For SHS, Tables 85 and 86 list these parameters as φNs and φMs as do Tables 81 to 82 for CHS. As noted in Sections 8.3.1.3 and 8.3.2.3,the parameters φMrx, φMry, φMix, φMiy and φMoy can also be calculated from these tables.
8.4 Combined Bending and Axial TensionIn this section:
φ = 0.9 (Table 3.4 of AS 4100)
φMsx = design section moment capacity for bending about the major principal xaxis
φMsy = design section moment capacity for bending about the minor principal yaxis
N * = design axial tension force
φNt = design section capacity in axial tension
8.4.1 Tension and Uniaxial Bending – about the major principal xaxisFor a member subject to uniaxial bending about the major principal xaxis and axial tension, thefollowing conditions must be satisfied:
M*x ≤ min. [φMrx; φMox]

design capacitytables for
structural steel
Volume 2: Hollow Sectionssecond edition
CHS  Grade C250/C350 (to AS 1163)RHS  Grade C350/C450 (to AS 1163)SHS  Grade C350/C450 (to AS 1163)
AUSTRALIAN STEEL INSTITUTE (ABN) / ACN (94) 000 973 839
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AS 4
100
1998
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DCT/V2/022004 (iii)ASI: DESIGN CAPACITY TABLES FOR STRUCTURAL STEEL VOLUME 2: HOLLOW SECTIONS
design capacity tables for structural steel
Volume 2: Hollow Sections
second edition
TABLE OF CONTENTS
Foreword (iv)Acknowledgements (iv)
Preface (v)Notation (vi)
PART ONEIntroduction 11
PART TWOMaterials 21
PART THREESection Properties 31
PART FOURMethods of Structural Analysis 41
PART FIVEMembers Subject to Bending 51
PART SIXMembers Subject to Axial Compression 61
PART SEVENMembers subject to Axial Tension 71
PART EIGHTMembers subject to Combined Actions 81
PART NINEConnections 91
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DCT/V2/022004 81ASI: DESIGN CAPACITY TABLES FOR STRUCTURAL STEEL VOLUME 2: HOLLOW SECTIONS
MEMBERS SUBJECT TO COMBINED ACTIONS
PAGE 8.1 General ......................................................................................................................82
8.2 Design for Combined Actions..........................................................................82
8.3 Combined Bending and Axial Compression ..............................................838.3.1 Compression and Uniaxial Bending – about the major principal xaxis ...838.3.1.1 Section Capacity......................................................................................................838.3.1.2 Member Capacity ....................................................................................................848.3.1.3 Tables ..........................................................................................................................84
8.3.2 Compression and Uniaxial Bending – about the minor principal yaxis ...848.3.2.1 Section Capacity......................................................................................................858.3.2.2 Member Capacity ....................................................................................................858.3.2.3 Tables ..........................................................................................................................85
8.3.3 Compression and Biaxial Bending.....................................................................858.3.3.1 Section Capacity......................................................................................................858.3.3.2 Member Capacity ....................................................................................................868.3.3.3 Tables ..........................................................................................................................86
8.4 Combined Bending and Axial Tension..........................................................868.4.1 Tension and Uniaxial Bending – about the major principal xaxis ...........868.4.1.1 Section Capacity......................................................................................................878.4.1.2 Member Capacity ....................................................................................................878.4.1.3 Tables ..........................................................................................................................87
8.4.2 Tension and Uniaxial Bending – about the minor principal yaxis ...........878.4.2.1 Section Capacity......................................................................................................888.4.2.2 Tables ..........................................................................................................................88
8.4.3 Tension and Biaxial Bending................................................................................888.4.3.1 Section Capacity......................................................................................................888.4.3.2 Member Capacity ....................................................................................................888.4.3.3 Tables ..........................................................................................................................88
8.5 Biaxial Bending.......................................................................................................898.5.1 Section Capacity......................................................................................................898.5.2 Member Capacity ....................................................................................................898.5.3 Tables ..........................................................................................................................89
8.6 Example ..................................................................................................................810
8.7 References.............................................................................................................811
TABLES
TABLES 81 to 86
Design Section Capacities .................................................................................812
PART 8
NOTE: SEE SECTION 2.1 FOR THE SPECIFIC MATERAL STANDARD (AS 1163) REFERRED TO BY THE SECTION TYPE AND
STEEL GRADE IN THESE TABLES
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