[Eng]Tutorial Input of Buckling Lengths

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Input of Buckling Lengths

Tutorial


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All information in this document is subject to modification without prior notice. No part or this

manual may be reproduced, stored in a database or retrieval system or published, in any form or

in any way, electronically, mechanically, by print, photo print, microfilm or any other means

without prior written permission from the publisher. SCIA is not responsible for any direct or

indirect damage because of imperfections in the documentation and/or the software.

Copyright 2008 SCIA. All rights reserved.


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Table of contents

1 Ways of input and work with buckling lengths................................................................4

1.1 Keeping pre-set and by program calculated values so called default on the member...4

1.1.1 View of results............................................................................................................6

1.2 Buckling system so called BC*.....................................................................................8

1.2.1 Sway setting..............................................................................................................131.2.2 Advantage of BC*system.........................................................................................14

1.3 Input of user buckling data on particular member so called. BB*...............................16

1.3.1 Options for BB* setting............................................................................................18

2 Calculation according to the implemented method........................................................25

2.1 References...................................................................................................................25

2.2 Example of simple 2D frame.......................................................................................26


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1 WAYS OF INPUT AND WORK WITH BUCKLING LENGTHS

1.1 Use the pre-set and by-program-calculated values for the member (called default)

Example_frame_XYZ_01

A new structure is created.

Fig. 1 Example: frame XYZ

Every member has pre-set buckling and relative lengths, which are called default. Thesettings can be found in member properties (fig. 2). The program analyses the structure and

creates a buckling system. It means that all member nodes in one line are recognized. If the

members satisfy the following conditions, then the program will connect them into one buckling

system.

1)Members have to be straight

2) LSS of members have to be of the same orientation

Note:

Members can be of different cross-sections. If a member is a non-straight polygon, the program

will connect the whole polygon into one buckling system. The number of fields depends on thenumber of nodes in the polygon.

Afterwards the program identifies, in which direction (y-y/z-z) the nodes are fixed/free. The

distance between fixed nodes is equal to system length L.


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The default settings depend on the

material the member is made of. In case

that there are two members of the same

orientation and of different material, then

the program takes the x-axis of the

member LCS and the material of the first

member in the LCS. See Example:

different materials. Furthermore, the

program evaluates default settings in

particular services (steel, concrete,

timber).

Fig. 2 Default system setting

In this case service Steel and Setup (fig. 3).

Fig. 3 Default setup in service Steel

Sway type for whole structure.Max. ratio k- is the maximum value of the buckling coefficient

in the whole structure. This value is there because of the following reason - when the calculation

of buckling coefficient by method implemented in program failed and the program determines

value greater than 10, then it is automatically set to max. value 10.

To check manually how the program has recognized the fixed and free nodes you can display

system lengths for calculation of buckling lengths.


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- for the whole structure or selected part of it (fig.4).

Fig. 4 Setting for displaying of system lengths for calculation

If the user now starts the calculation, program performs it according to the implemented method.

For description of method see below.

1.1.1 View of results:This can be done in particular services (steel, concrete and other) or through icon (fig.5).


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Fig. 5 View of results

The other option is through new button buckling coefficient(fig.6), which appears in the window

of member properties after the calculation. Basically, results can be viewed from any point in

Scia Engineer.

Fig. 6 Buckling coefficient


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Fig. 7 Displaying of results

1.2 Buckling system - called BC*

If user disagrees with calculated values or with the position of fixed and free nodes, it is possible

to use the option for creation of a user buckling systems. By clicking on button with three dots in

window of member properties (see fig.8), buckling data and buckling system (e.g. BC1) are

automatically created.

Fig. 8 Creating buckling system BC1

The system was created for member B31, but it is also automatically assigned to member B227

(fig.9), because the conditions for systems composition were satisfied (this have been already

described in point 1.1).


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In window of buckling data (see fig.8), there can

be also seen free and fixed nodes according to

directions yy and zz (full triangles), as evaluated

by the program.

If user enters the library of buckling data

through member properties, the filteringaccording to number of fields is activated

automatically. In this example number of parts is

2. The program has connected members B31 and

B227 into one system, because the requirements

from point 1.1 were met. Next, there is

information about material, from which buckling

system was created. It indicates the relation

where to find the default (see fig. 3).

By clicking on button Edit in this dialogue the

menu for editing of buckling system is opened

(fig.10).

Fig. 9 Automatic assigning to member

Fig. 10 Base menu Buckling and relative lengths

These default settings are loaded depending on the material of which the buckling system was

created.


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Fig. 11 Default settings for whole structure, from which data for creation of bucklingsystem BC* are read

Note:

Changes of settings in particular services are not applied to the already created systems. They

are used only for new ones and for default calculation.

In Base settings the user can define buckling systems relations. When coefficients ky, kz are set

to Calculate, then the relations of system lengths L have to be defined (fig.12).

Fig. 12 Setting of buckling systems relations

Setting:

Zz=zz: system lengths zz are independent. User can define them separately for zz and yy

systems.


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Fig. 13 Buckling data zz=zz

There is no option for input of freedom/fixity of nodes in zz and yy directions (fig.13 and 14).

If setting is zz=yy, it will be the same for the both directions.

The same properties are valid for yz torsional flexural buckling and for lt lateral torsional

buckling.

Independency of all elements is achieved by setting (see fig.15).

Fig. 15 Setting of element independency


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In case that settings are made according to fig. 16, the user will define the value of the factor

between fixed nodes directly.

Fig. 16 Setting for input of buckling coefficients between fixed nodes

In case that settings are made according to fig. 17, the user will input the buckling length

between fixed nodes directly.

Fig. 17 Setting for input of buckling length between fixed nodes


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1.2.1 Sway setting

The last setting in this dialogue is the sway type setting.

a) Sway setting for one node. WhenAcc. to Base settings is kept, program will consider these

settings for the whole buckling system.

b) Sway setting for whole buckling system BC*. WhenAcc. to Steel>Beams>Setup is set,

program will consider these settings for whole structure.

c) Sway setting for whole structure


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1.2.2 Advantage of BC* systema) Filtering according to number of fields

When user enters library through member properties, all buckling systems are shown.

b) User can return to default settings anytime and create buckling system again.

c) Easy input on other members, only systems with same number of parts are offered.


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d) Simple searching in structure through filters.

E.g. it finds all members which have assigned BC1

e) Automatic saving into buckling system library.


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There are options for editing, saving and reading.

1.3 Input of user buckling data on particular member so called BB*In particular services for checks (concrete, steel, timber), there is an option for input of buckling

data directly at the particular member. These data are called additional data (fig. 13).

By double-click onMember buckling data, user fills in a basic dialogue which can be changed

anytime afterwards. After clicking OK, these data are assigned to the member.


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Another option for input is through the action button that can be found in the property window

of each member.

Note:

If the user defines buckling data from service Concrete, then it will not be possible to add them

to cross-section which has steel material assigned etc.


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1.3.1 Options for BB* setting1.3.1.1 From standard analysisa) If member has assigned the buckling system Default, program will take system lengths for

buckling calculation from this default setting.

b) If member has assigned the buckling system BC* with edited free/fixed nodes, then the

program will take system lengths for calculation of buckling lengths from this new setting.


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c) If buckling length ratio or buckling length is set to be defined manually for particular parts of

the buckling system, the program will ignore this manual input and perform calculation

according to the implemented method.

1.3.1.2 Default value from library managerWhen the member has assigned the buckling system BC*, then all factors, including manually

defined, are read from this buckling system.


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1.3.1.3 User inputTo perform calculation from standard analysis byimplemented method on selected member,ky and kz factors have to be set to Calculate. The user can also set buckling systems relations for

selected member.


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System lengths are taken from the default settings, or if there is assigned any buckling system

BC*, then from the buckling calculation.

The user can input the buckling length ratio manually:


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Sway settingSetting of sway type for particular nodes or for whole member. Again there are three levels of

setting.

a) Sway type can be defined for particular nodes. If the basic setting is kept, the program will

consider this setting for the whole member.

b) For the whole member with BB* assigned. When Acc. to Steel>Beam>Setup is selected, the

program will consider this setting for the whole structure.


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c) When Acc. to Steel>Beam>Setup is selected, the program will consider this setting in

particular services.

The advantage of this method is that the data can be copied as additional data. Values, whichwere defined manually, remain constant and recalculation of other values is performed. E.g. on

member B26 the buckling coefficients were set manually by the user as ky and kz = 2.


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After copying of additional data, the values of ky and kz remain fixed and the recalculation is

performed according to the classic formula.

Calculation will be carried out according to the following formula:

Lz . kz = lz

Lz is system length

kz is buckling length ratiolz is buckling length


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If the user inputs the buckling length directly, then the buckling length will remain fixed.

Note:

Terms BC* and BB* are the default names for particular ways of input in Scia Engineer. Names

can be edited according to the user requirements. For easier orientation in the text, the default

names are used.

2 CALCULATION ACCORDING TO THE IMPLEMENTED METHOD

The program performs calculation from the standard analysis for calculation of factors

approximate formulas are used. These formulas are listed in [1], [2] and [3].

a) for non-sway structure:

b) for sway structure:

L system length

E Youngs modulus of elasticity

I moment of inertiaCi stiffness in node I

Mi moment in node I

Fi rotation in node I

Approximate values of Mi and i are determined using internal forces and deformations,

calculated from load cases, which generate shapes of deformations similar to the buckling shape

(see [4], pp. 113 a [5], pp. 112). Load cases used for that purpose contain unit loads which

generate horizontal displacements of structure. The applied approach gives satisfactory results

for frame structures with perpendicular rigid or semi-rigid beam connections. Results are onlyrecommended and it is up to the user to evaluate their relevancy.

2.1 References

[1] Handleiding moduul STACO VGI Staalbouwkundig Genootschap Staalcentrum

Nederland 5684/82

[2] Newmark N.M. A simple approximate formula for effective end-fixity of columns

J.Aero.Sc. Vol.16 Feb.1949 pp.116

[3] Stabiliteit voor de staalconstructeur uitgave Staalbouwkundig Genootschap- 26 -

[4] Rapportnr. BI-87-20/63.4.3360 Controleregels voor lijnvormige constructie

elementen IBBC Maart 1987

[5] Staalconstructies TGB 1990 Basiseisen en basisrekenregels voor overwegend


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statisch belaste constructies NEN 6770, December 1991

2.2 Example of simple 2D frame:

Program generates two load cases in the background:

LC1 - beams are subject to load in LCS gy = 1 N/m, gz= -100 N/m and columns in global

coordinate system Qx = 1000 N/m and Qy = 1000 N/m

LC2 - beams are subject to load in LCS gy = -1 N/m, gz= -100 N/m and columns in globalcoordinate system Qx = -1000 N/m and Qy = -1000 N/m

Based on obtained deformations and moments, the program determines the buckling length ratio.

In this example, only a 2D problem was considered.


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Buckling length ratio calculated by the program:

Buckling length ratio calculated manually:


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Documents

[Eng]Tutorial Input of Buckling Lengths