PowerPoint by Dr Fong - The Hong Kong Institute of Steel Construction

Second-order Direct Analysis Method to Codeof Practice for the Structural Use of Steel 2011Alfred FongYoung Members Group (YMG)Hong Kong Institute of Steel Constriction

• What?• Why?• When?• How?2

3Commonly used analysis and design method

First-order Linear Analysis MethodWhen can I use first-order linear analysis method ??4

First-order Linear Analysis Method• Elastic Critical Load factor• 1) Deflection method- For sway buckling mode of a geometrically regular andrectangular frame• 2) Eigenvalue analysis5

First-order Linear Analysis Method• Effective LengthEffective length of idealized columns6

Effective Length• How to define the buckling effective length7

First-order Linear Analysis Method• Effective Length• Moment Amplification for sway frames• Maximum slenderness ratio

What is Buckling?Buckling behavior9

Second-order Analysis and Design Method‣ P-δ Moment- Member initial imperfectionPerfect member10

Second-order Analysis and Design Method‣ P-δ Moment- Member initial imperfectionMember Imperfection11

Second-order Analysis and Design Method‣ P-δ Moment- Member initial imperfection + Member deformation under loadUse effective length and buckling reduction factor in linear analysis12

Second-order Analysis and Design Method‣ P-Δ Moment-Structural global imperfection13

Second-order Analysis and Design Method‣ Structural global imperfection• Shape of imperfection• 1) Notional horizontal force method- Suitable for regular structures• 2) Elastic buckling mode- Applicable for all structures• Value of imperfection• Storey height/20014

Second-order Analysis and Design Method‣ P-Δ Moment-Structural global imperfection+ Nodal geometric change0.5V 0.5V 0.5VV V V0.5H HUse in Moment Amplification factor in linear analysis15

Second-order Analysis and Design Method‣ Structural global imperfection16

17Commonly Used Analysis and Design Method

Second-order Analysis and Design Method• What’s second-order INDIRECT (P-∆) analysis?Effective lengthBuckling reduction factor18

Second-order Analysis and Design Method• What’s second-order DIRECT (P-∆-δ) analysis?19

Second-order Analysis and Design Method• What do I NEED for second-order direct analysis?• Member imperfection• Frame imperfect20

Second-order Analysis and Design Method• Section capacity check

Comment questions• Second-order direct analysis ONLY used in HK Steel Code?22

Comment questionsRecommended by many design codes23

Comment questions• Second-order direct analysis ONLY used in HK Steel Code?• Second-order analysis gives a more economic/conservativedesign?• Can I add the reaction forces from each load cases?• Anything miss in linear analysis?24

25Snap-through buckling problem

Conclusion• What?• Why?• When?• How?26

Thank youYoung Members Group (YMG)Hong Kong Institute of Steel Constriction (HKISC)27