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  • Delft, University of Technology Engineering office of Public works Rotterdam

    Interaction between plate and column buckling Master Thesis

    Name: Alex van Ham Student number: 1306138 Email: vanham.alex@gmail.com

    12-1-2012

  • Alex van Ham Interaction between plate and column buckling 12 januari 2012

    3

    Graduation Committee

    Chairman prof. ir. F.S.K. Bijlaard

    Department of Structural Engineering, Steel Structures

    Faculty of Civil Engineering and Geosciences

    Delft University of Technology

    Committee members ir. R. Abspoel

    Department of Structural Engineering, Steel Structures

    Faculty of Civil Engineering and Geosciences

    Delft University of Technology

    dr. ir. P.C.J. Hoogenboom

    Department of Structural Engineering, Structural Mechanics

    Faculty of Civil Engineering and Geosciences

    Delft University of Technology

    External committee member ir. J.H. Reusink

    Senior consultant Bridges and Steel Structures

    Engineering office Public Works Rotterdam

    Secretary ir. L.J.M. Houben

    Department of Structural Engineering, Road and Railway Engineering

    Faculty of Civil Engineering and Geosciences

    Delft University of Technology

  • Alex van Ham Interaction between plate and column buckling 12 januari 2012

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    Preface This master thesis has been written as the final part of my study Civil Engineering at Delft

    University of Technology. My master is at the department of Structural Engineering and the

    specialization is Steel and Timber Structures. Also an honours track has been done to include

    courses on both Concrete Structures and Structural Mechanics.

    My master thesis project is done at the Engineering Office of Public Works Rotterdam. They

    offered me the opportunity to study the subject of plate buckling in steel structures. Their

    main question at the Engineering Office was to provide insight in the Eurocode on plate

    buckling (NEN-EN1993-1-5) and how it should be applied. This resulted in a tool which can

    be used to check class 4 steel cross-sections. This question is combined with the subject of the

    interaction of plate and column buckling which is a theoretical study.

    I would like to thank the entire MSc graduation committee for their input and feedback.

    Alex van Ham

    Rotterdam, January 2012

  • Alex van Ham Interaction between plate and column buckling 12 januari 2012

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    Abstract Dimensioning and verification of steel structures is often governed by the demands for

    stability and the plastic capacity of the material is not fully utilized. There are a several forms

    of instability such as column buckling, lateral-torsional buckling and plate buckling.

    Interaction of plate and column buckling has not been extensively studied before and that is

    the main subject of this master thesis. In present verification codes in The Netherlands it is

    allowed to separately calculate the effects of both and then combine them in a certain way.

    Question is whether this is indeed correct. Analytical calculations have been done on an I-

    column to derive the theoretical buckling load combining the effects of plate and column

    buckling. In general the interaction is very small but for uneconomic cross-sections with a

    large area of the web compared to the area of the flange this interaction can be large. The

    numerical answer is not very relevant because the post-buckling behaviour of plate and

    column buckling is totally different but the knowledge gained is more important. The most

    important conclusion from the analytical calculation is that interaction is only present when

    the number of half sine waves in the web is equal to the number of half sine waves in the

    entire column.

    Also calculations have been performed using a finite element method. Many cross-sections

    have been considered and the general trend is that the bearing capacity according to the

    verification regulations are closely related to the results from the finite element analysis. For a

    certain type of cross-section the results are significantly different compared to the verification

    regulations. This is for uneconomic cross-sections with a large area of the web compared to

    the area of the flange. The difference can be up to 20% of the bearing capacity. This type of

    cross-sections is not used very often because these would be very uneconomic but the

    verification regulations overestimate the bearing capacity. In general a designer is free to

    design any sort of structure. After that the structure should be verified for structural safety

    using the regulations. These regulations should either provide the correct verification

    regulations or inform that a certain type of structure is outside the scope of the regulations.

    Neither is done in the current verification regulations. A formula is developed to calculate the

    reduced bearing capacity for this type of cross-sections.

    A probabilistic design has been done on an economic and an uneconomic type of cross-

    section. The required safety was reached for the economic cross-section ( ) but for the uneconomic cross-section ( ) the safety was not reached. No general conclusions may be drawn because only two situations have been investigated but the difference is

    striking. It confirms the unsafe nature of the verification regulations for the uneconomic

    cross-sections.

    A design recommendation has been made on how to design a class 4 cross-section. It is

    shown that it is not efficient to add longitudinal stiffeners to the web when verification

    regulations of the effective cross-section method are used. Only the effective area of the web

    is increased which is in general small and for bending moments also close to the centre of

    gravity.

    A design tool has been developed which checks class 4 cross-sections according to the

    verification regulations in NEN-EN1993-1-5. The tool can check I cross-sections as well as a

    box or a cross-section. Longitudinal stiffeners to the web, through decks and concrete toppings can be added.

  • Alex van Ham Interaction between plate and column buckling 12 januari 2012

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    Table of Contents Graduation Committee ............................................................................................................... 3

    Chairman ................................................................................................................................ 3

    Committee members .............................................................................................................. 3

    External committee member .................................................................................................. 3

    Secretary ................................................................................................................................. 3

    Preface ........................................................................................................................................ 5

    Abstract ...................................................................................................................................... 7

    Table of Contents ....................................................................................................................... 9

    Chapter 1: Introduction ............................................................................................................ 15

    General introduction ............................................................................................................. 15

    Objectives ............................................................................................................................. 15

    Thesis outline ....................................................................................................................... 16

    Chapter 2: Buckling ................................................................................................................. 19

    Buckling ............................................................................................................................... 19

    Rayleigh method .................................................................................................................. 23

    Conventions in thesis ........................................................................................................... 23

    Bernoulli assumptions ...................................................................................................... 23

    Economic design .............................................................................................................. 23

    Coordinate system ............................................................................................................ 23

    Derivation column buckling ................................................................................................. 24

    Derivation lateral torsional buckling .................................................................................... 26

    Derivation plate buckling ..................................................................................................... 29

    Chapter 3: Plate buckling in Eurocode ..................................................................................... 31

    Effective cross-section method ........................................