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### Transcript of 8.3 Combined Bending and Axial Compression · 2018. 9. 27. · Members Subject to Bending 5-1 PART...

• DCT/V2/02-2004 8-3ASI: 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 x-axis

φMsy = design section moment capacity for bending about the minor principal y-axis

N* = design axial compressive force

φNs = design section capacity in compression

φNcx = design member capacity in compression, buckling about the x-axis

φNcy = design member capacity in compression, buckling about the y-axis

8.3.1 Compression and Uniaxial Bending – about the major principal x-axis

For a member subject to uniaxial bending about the major principal x-axis 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 x-axis

φMrx = design section moment capacity (φMs) for bending about the major principal x-axisreduced by axial force (see Section 8.3.1.1)

φMix = design in-plane member moment capacity (φMi) for bending about the major prin-cipal x-axis (see Section 8.3.1.2(a))

φMox = design out-of-plane member moment capacity (φMo) for bending about the majorprincipal x-axis (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 x-axis with kf = 1.0 sub-ject 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 x-axis 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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• 8-4 DCT/V2/02-2004ASI: DESIGN CAPACITY TABLES FOR STRUCTURAL STEEL VOLUME 2: HOLLOW SECTIONS

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 in-plane 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 in-plane and out-of-plane requirements of Sections 8.3.1.1 and 8.3.1.2 need to be satisfied.

(a) In-plane 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) Out-of-plane capacity

φMox = φMbx (Clause 8.4.4.1 of AS 4100)

where φMbx = design member moment capacity for bending about the major principal x-axis.

8.3.1.3 Tables

For RHS, Tables 8-3 to 8-4 list φMsx, φNs and φMrx (comp) - the latter parameter refers to φMrx asnoted in Section 8.3.1.1. Tables 8-5 to 8-6 for SHS refer to these three parameters as φMs, φNs andφMr (comp) respectively. For CHS, Tables 8-1 to 8-2 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 refer-ences 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 y-axis

For a member subject to uniaxial bending about the minor principal y-axis 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 y-axis

φMry = design section moment capacity (φMs) for bending about the minor principal y-axis reduced by axial force (see Section 8.3.2.1)

φMiy = design in-plane member moment capacity (φMi) for bending about the minor principal y-axis (see Section 8.3.2.2)

• DCT/V2/02-2004 8-5ASI: 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 y-axis subject to bend-ing 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 y-axis only the in-plane requirements need to be satisfied.

(a) In-plane 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 8-3 to 8-4 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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• 8-6 DCT/V2/02-2004ASI: 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 y-axes:

≤ 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 8-3 to 8-4 list φNs, φMsx and φMsy. For SHS, Tables 8-5 and 8-6 list these param-eters as φNs and φMs as do Tables 8-1 to 8-2 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 x-axis

φMsy = design section moment capacity for bending about the minor principal y-axis

N * = design axial tension force

φNt = design section capacity in axial tension

8.4.1 Tension and Uniaxial Bending – about the major principal x-axisFor a member subject to uniaxial bending about the major principal x-axis 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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• DCT/V2/02-2004 (iii)ASI: DESIGN CAPACITY TABLES FOR STRUCTURAL STEEL VOLUME 2: HOLLOW SECTIONS

design capacity tables for structural steel

Volume 2: Hollow Sections

second edition

Foreword (iv)Acknowledgements (iv)

Preface (v)Notation (vi)

PART ONEIntroduction 1-1

PART TWOMaterials 2-1

PART THREESection Properties 3-1

PART FOURMethods of Structural Analysis 4-1

PART FIVEMembers Subject to Bending 5-1

PART SIXMembers Subject to Axial Compression 6-1

PART SEVENMembers subject to Axial Tension 7-1

PART EIGHTMembers subject to Combined Actions 8-1

PART NINEConnections 9-1

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DCT/V2/02-2004 8-1ASI: DESIGN CAPACITY TABLES FOR STRUCTURAL STEEL VOLUME 2: HOLLOW SECTIONS

MEMBERS SUBJECT TO COMBINED ACTIONS

PAGE 8.1 General ......................................................................................................................8-2

8.2 Design for Combined Actions..........................................................................8-2

8.3 Combined Bending and Axial Compression ..............................................8-38.3.1 Compression and Uniaxial Bending – about the major principal x-axis ...8-38.3.1.1 Section Capacity......................................................................................................8-38.3.1.2 Member Capacity ....................................................................................................8-48.3.1.3 Tables ..........................................................................................................................8-4

8.3.2 Compression and Uniaxial Bending – about the minor principal y-axis ...8-48.3.2.1 Section Capacity......................................................................................................8-58.3.2.2 Member Capacity ....................................................................................................8-58.3.2.3 Tables ..........................................................................................................................8-5

8.3.3 Compression and Biaxial Bending.....................................................................8-58.3.3.1 Section Capacity......................................................................................................8-58.3.3.2 Member Capacity ....................................................................................................8-68.3.3.3 Tables ..........................................................................................................................8-6

8.4 Combined Bending and Axial Tension..........................................................8-68.4.1 Tension and Uniaxial Bending – about the major principal x-axis ...........8-68.4.1.1 Section Capacity......................................................................................................8-78.4.1.2 Member Capacity ....................................................................................................8-78.4.1.3 Tables ..........................................................................................................................8-7

8.4.2 Tension and Uniaxial Bending – about the minor principal y-axis ...........8-78.4.2.1 Section Capacity......................................................................................................8-88.4.2.2 Tables ..........................................................................................................................8-8

8.4.3 Tension and Biaxial Bending................................................................................8-88.4.3.1 Section Capacity......................................................................................................8-88.4.3.2 Member Capacity ....................................................................................................8-88.4.3.3 Tables ..........................................................................................................................8-8

8.5 Biaxial Bending.......................................................................................................8-98.5.1 Section Capacity......................................................................................................8-98.5.2 Member Capacity ....................................................................................................8-98.5.3 Tables ..........................................................................................................................8-9

8.6 Example ..................................................................................................................8-10

8.7 References.............................................................................................................8-11

TABLES

TABLES 8-1 to 8-6

Design Section Capacities .................................................................................8-12

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

Cover Page from HollowsSectionsFull Contents Page from HollowsSectionsPart 8 Contentscombined bending and axial compression of hollow sections_bk140.pdf