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Second-order Direct Analysis Method to Code of Practice for the Structural Use of Steel 2011
Dr. Y.P. Liu & NIDA Research Team
The Hong Kong Polytechnic University
24 May 2013
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Contents
2
• Second-Order Analysis vs. First-Order Analysis
• What’s NIDA
• General Procedures & Settings
• Most Frequently Asked Questions
• New Features
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Second-Order Analysis vs. First-Order Analysis
3
First-Order Linear Analysis & Design
Apply Loads
Responses
Design Check
Des
ign
Flow Linear
AnalysisIgnore(1) P-& P-Effects; (2) Imperfection; …
(1) Effective Length; or(2) Amplify Moment
Consider P-& P-Effects, Imperfection, Material Yield etc.
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Second-Order Analysis vs. First-Order Analysis
4
Second-Order Direct Analysis & Design
Apply Loads
Responses
Design Check
Des
ign
Flow Nonlinear
AnalysisConsider (1) P-& P-Effects; (2)Imperfection; …
Real Structure Behavior
Section Capacity Check Only
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Second-Order Analysis vs. First-Order Analysis
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Apply Loads
Responses
Design Check
Linear Analysis
Ignore(1) P-& P-Effects; (2) Imperfection; …
Approximate Behavior
(1) Effective Length; or(2) Amplify Moment
Indirect
First-Order Analysis(Conventional Method)
Apply Loads
Responses
Design Check
Nonlinear Analysis
Consider (1) P-& P-Effects; (2) Imperfection; …
Real Behavior Section Capacity Check Only
Direct
Second-Order Analysis(Innovative Method)
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Second-Order Analysis vs. First-Order Analysis
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• No need to assume effective length;
• Frame classification is not needed;
• More safer and more economic;
• Wider applications (performance-based seismic design, load &
construction sequences, structural fire engineering, progressive
collapse analysis, …);
• Recommended in modern design codes (Eurocode3, LRFD, New
GB50017);
Advantages of Direct Analysis:
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Second-Order Analysis vs. First-Order Analysis
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Effective Length = ? 500kN500kN
5m
3m
4m
152x152x30UC grade S275(43)
120x120x10L grade S275(43)
Pin Supports
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Second-Order Analysis vs. First-Order Analysis
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When under snow loads, snap-through buckling may take place.
Effective Length = ?
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Major Concerns of Direct Analysis
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P- Effect (frame sidesway)
P- Effect (member curvature)
Imperfection P- P-
P P
The P- and P- Effects
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Initial Imperfection
10
No perfect structure exists in the world. Realistic imperfections should be included in the second-order analysis.
(1) Frame Imperfection (out‐of‐plumbness)a) Notional horizontal force (0.5% vertical forces)b) First eigen‐value bucking mode (H/200)
(2) Member Imperfection (out‐of‐straightness, residual stresses)a) Perry‐Robertson formulae (Linear analysis only)b) Initial member bowing (e.g. L/500)
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Second-Order Analysis vs. First-Order Analysis
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Without Imperfection With Imperfection
Axial Shortening Axial Shortening + Bending
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Second-Order Analysis vs. First-Order Analysis
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Imperfection Shape Deformed Shape
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What’s NIDA – Nonlinear Integrated Design & Analysis
13
NIDA is specially developed for second-order direct analysis.
BD Pre-accepted Structural Programme Reference – S0844 (NIDA 9.0)
NIDA has been used for the structural design of many projects.
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What’s NIDA – Nonlinear Integrated Design & Analysis
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Analysis Capabilities of NIDA :
• First-Order Linear Analysis
• Second-Order Nonlinear Analysis
• Eigenvalue Buckling Analysis
• Modal Analysis
• Response Spectrum Analysis
• Time History Analysis
Daily Design (ULS, SLS)
Elastic Buckling Load Factor, cr
Natural Frequency & Vibration Mode
Seismic Design
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What’s NIDA – Nonlinear Integrated Design & Analysis
15
Analysis Capabilities of NIDA :
• First-Order Linear Analysis
• Second-Order Nonlinear Analysis
• Eigenvalue Buckling Analysis
• Modal Analysis
• Response Spectrum Analysis
• Time History AnalysisAdvanced beam-column elements;Robust numerical methods;Meet code requirements;
Advanced beam-column elements;Robust numerical methods;Meet code requirements;
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What’s NIDA – Nonlinear Integrated Design & Analysis
16
Conventional Straight Element:
Lxev sin00
Innovative Curved Element (NIDA):– One Element per Member
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What’s NIDA – Nonlinear Integrated Design & Analysis
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Buckling Curve = Member Imperfection
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What’s NIDA – Nonlinear Integrated Design & Analysis
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1)()(
cz
zzz
cy
yyy
y MPPM
MPPM
ApP
Taking both global frame and local member imperfection into account, only section capacity check is needed.
Global stability;Member stability; Effective Length
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What’s NIDA – Nonlinear Integrated Design & Analysis
19
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General Procedures & Settings in NIDA
20
Second-Order Analysis Procedure:• Create Model (Node, Member, Material, Section, Boundary
Condition, End Condition, Load Case, Load Combination, …), or Import from SAP2000/Etabs/Staad/Strand7/GSA/PKPM or DXF/Revit;
• Check Member Imperfection Associated with Section;• Create Analysis Cases (ULS & SLS) with Consideration of Frame
Imperfection;
• Check Maximum Section Capacity Factors < 1;
• Check Building Drift and Member Deflection by Code;
• Export Results & Prepare Design Report
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General Procedures & Settings in NIDA
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Member Imperfection
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General Procedures & Settings in NIDA
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• To determine global imperfection (shape, magnitude);
• To determine the direction of member imperfection.
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General Procedures & Settings in NIDA
23
H/200
Global Imperfection(Geometry Approach)
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General Procedures & Settings in NIDA
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Global Imperfection(Notional Force Approach)
= 0.5%
Limitation: regular structures
Direction: worst direction
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Most Frequently Asked Questions
25
Q1: About Elastic Buckling Load Factor– Why cr is very small ?
• Local member buckling (large axial force, high slenderness ratio);
• End releases (moment release with torsional release);
• Inconsistent unit system (”N,mm” – MPa / kPa);
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Most Frequently Asked Questions
26
Q1: About Elastic Buckling Load Factor– Why cr is different from other software ?
• Generally the difference of cr from different software is very small due to same linear theory background;
• Improperly consider end releases in many software;
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Most Frequently Asked Questions
27
Q2: Why second-order analysis diverges ? • Load increment is too large (reduce load size, check deflection
and strengthen the location with large deflection, change
numerical method);
Large Load Step
Linear Analysis
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New Features
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1. Design procedure for every member
Double click the dialog to open it by external editor tool such as “Notepad.exe”.
• Section classification;• Design strength reduced by plate thickness;• Web shear buckling;• Torsional resistance;• Lateral-torsional buckling; • Section capacity check;
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New Features
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2. Imperfection of Combined Member– An individual member
A member divided into 4 elements
Imperfection for each element
Imperfection for combined member
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New Features
30
2. Imperfection of Combined Member (Cont’d)– A member with intermediate members
Imperfection of all elements along z-axis as a single member
Imperfection of each element along y-axis
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New Features
31
3. Nonlinear Spring Element
Connect 2 nodes
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New Features
32
3. Nonlinear Spring Element (Cont’d)
To model right-angle couplers of scaffold system (Application)
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New Features
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4. Nonlinear Support Spring5. Node Local Axes6. More steel design codes7. More response spectrum functions8. More functions of time history analysis9. Many improvements …
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More NIDA Products
34
I. Nida x Revit 2012 – Link to BIM
• Export from Revit to create a new NIDA model;
• Import from NIDA to create a new Revit model;
• Export from Revit to update an existing NIDA model;
• Export from NIDA to update an existing Revit model;
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More NIDA Products
35
I. Nida x Revit 2012 – Link to BIM (Cont’d)
Revit Model
NIDA Model
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More NIDA Products
36
II. RCD 2013 – RC & Composite Section DesignRCD 2013 is advanced and technology-leading cross-section analysis anddesign software, a product of NIDA family.
Updates from RCD 2009: New User Interface (Ribbon); Multi-Documents Supported; Composite Sections Supported; Many Improvements …
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Features of RCD 2013
More NIDA Products
Capable for analysis of arbitrary composite, RC and built-up steel sections;more faster & powerful
Over 50 common shapes for direct use!Automatically mesh into fibers
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Features of RCD 2013
More NIDA Products
New core-engine and results viewer
Only 2.3s for this section!
Two dimensional curve
3D View for Yield Surface Output PDF Report
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More NIDA Products
39
III. NIDA-MNN (Special version for Moving Node Net)– Large deflection analysis of net made of polygonal and line elements with internal nodes moving along their sides
Flexible Barriers: widely used as protection systems against natural hazards, such as rockfalls, landslides and debris flows.
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More NIDA Products
40
III. NIDA-MNN (Cont’d)
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More NIDA Products
41
III. NIDA-MNN (Cont’d)
Model – Sliding Cable
Cable
Tie rod
Tie beam
Movable Node
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More NIDA Products
42
III. NIDA-MNN (Cont’d)
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More NIDA Products
43
IV. NIDA-TMS (Special version)– Large deflection analysis of Tensioned Membrane Structure
Amphitheatre in Hong Kong Science Park Phase 2
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More NIDA Products
44
IV. NIDA-TMS (Cont’d)
CHS 508x25
Cable ()
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