example - sofistik · 2.1 model geometry and loads a simple one-span steel frame is presented....

SOFiSTiK AG, Oberschleißheim, 2014

Example

Imperfection Concept

SOFiSTiK Version 2014


SOFiSTiK AG, Oberschleißheim, 2014 1

This manual is protected by copyright laws. No part of it may be translated, copied or

reproduced, in any form or by any means, without written permission from SOFiSTiK AG.

SOFiSTiK reserves the right to modify or to release new editions of this manual. The manual

and the program have been thoroughly checked for errors. However, SOFiSTiK does not

claim that either one is completely error free. Errors and omissions are corrected as soon as

they are detected. The user of the program is solely responsible for the applications. We

strongly encourage the user to test the correctness of all calculations at least by random

sampling.


SOFiSTiK AG, Oberschleißheim, 2014 2

Table of Contents1 Tutorial Description ........................................................................................................ 3

1.1 Intention of this document ....................................................................................... 3

1.2 Stability verification in EN 1993 ............................................................................... 3

2 Example Description ...................................................................................................... 7

2.1 Model geometry and loads ...................................................................................... 7

2.2 Load Combinations ................................................................................................. 9

3 Workflow in SOFiSTiK ...................................................................................................10

Literature ..............................................................................................................................20


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1 Tutorial Description

This document is exceptionally prepared for SOFiSTiK version 2014. The concept is not valid for version 2012.

1.1 Intention of this document

The intention of this document is to introduce shortly the general stability approach based on

imperfections, which is allowed according to EN 1993-1-1. This tutorial will focus only on the

imperfection problem, but not on the design of elements. Design topics will be described in

upcoming future tutorials. A simple steel frame is analysed in this tutorial.

1.2 Stability verification in EN 1993

The stability verification in EN 1993-1-1 is conceptualised in different ways. But the main

purpose is the same – to consider the second-order effects and imperfections. EN 1993-1-1

allows several ways to account for the second-order effects and imperfections. Chapter 5.2.2

(3) says:

“According to the type of a frame and the global analysis, second order effects and

imperfections may be accounted for by one of the following methods:

a) both totally by the global analysis,

b) partially by the global analysis and partially through individual stability checks of

members according to 6.3,

c) for basic cases by individual stability checks of equivalent members according to 6.3

using appropriate buckling lengths according to the global buckling mode of the

structure.” [1]

EN 1993-1-1 chapter 5.2.2 (7) and (8) describes the stability verification for members:

“In accordance with chapter 5.2.2 (3) the stability of individual members should be checked

according to the following:

a) If second order effects in individual members and relevant member imperfections

(see 5.3.4) are totally accounted for in the global analysis of the structure, no

individual stability check for the members according to 6.3 is necessary.

b) If second order effects in individual members or certain individual member

imperfections (e.g. member imperfections for flexural and/or lateral torsional buckling,

see 5.3.4) are not totally accounted for in the global analysis, the individual stability of


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members should be checked according to the relevant criteria in 6.3 for the effects

not included in the global analysis. This verification should take account of end

moments and forces from the global analysis of the structure, including global second

order effects and global imperfections (see 5.3.2) when relevant and may be based

on a buckling length equal to the system length.” [1]

Clear representation of mentioned methods has been published in “Deutscher Stahlbautag

2012; Aachen, 18. Oktober 2012” by Prof. Dr.-Ing. Ulrike KUHLMANN, Dr.-Ing. Hans-Peter

GÜNTHER and Dipl.-Ing. Antonio ZIZZA.

Methods are named:

Method a)

Method b1)

Method b2)

Method c)

And will be represented in the following.

Figure 1: Method a) [2]


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Figure 2: Method b1) [2]

Figure 3: Method b2) [2]


6

Figure 4: Method c) [2]

Figure 5: Summary of Methods [2]


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2 Example Description

A load case imperfection will be defined with TYPE IMP. The load cases of this type allow to use imperfection loads for the definition of load case combinations for the analysis according to the second (third) order theory. These load cases cannot be used for a linear analysis of single load cases with ASE, STAR2 and also not for a superposition of the linear load cases with MAXIMA.

For imperfections the program is capable to handle cubic load distributions directly for a single beam.

2.1 Model geometry and loads

A simple one-span steel frame is presented. Frames are distributed every 5 m. The geometry

and profiles are shown in the Fig. 6. Following cross-sections are set:

Rafter – HEA 200, steel grade S355,

Column – HEA 200, steel grade S355

Figure 6: Frame geometry and cross sections

Considered loads are described in the Tab. 1.


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Table 1: Loads

Nr. Title Action Load Value [kN/m2]

LC 1 Self-weight G (Permanent) Automatically

LC 2 Dead load G (Permanent) 1,00

LC 3 Live load Q (Variable) 2,00

LC 4 Wind load +Y Q (Variable) 1,00

LC 5 Wind load -Y Q (Variable) 1,00

LC 11 Imperfection - -

Following is the graphical representation of loads in [kN/m], imperfection in [mm].

M 1 : 47

X Y

Z

0.423

0.423

0.423

0.423

0.423

0.423

0.423

0.423

0.423

0.423

0.423

0.423

0.423

All loads, Loadcase 1 Self weight , (1 cm 3D = unit) Beam dead load in global Z (Unit=0.500 kN/m ) (Min=-0.423) (Max=-0.423)

m-2.00 0.00 2.00 4.00 6.00

0.0

02.0

04.0

06.0

0

M 1 : 38

X Y

Z

5.00

All loads, Loadcase 2 Dead load , (1 cm 3D = unit) Free line load (force) in global Z (Unit=5.00 kN/m ) (Min=-5.00) (Max=-5.00)

m-1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

0.0

01.0

02.0

03.0

04.0

05.0

0

M 1 : 41

X Y

Z

10.0

All loads, Loadcase 3 Live load , (1 cm 3D = unit) Free line load (force) in global Z (Unit=5.00 kN/m ) (Min=-10.0) (Max=-10.0)

m0.00 2.00 4.00 6.00

0.0

02.0

04.0

06.0

0

M 1 : 34

X Y

Z

5.00

3.75

All loads, Loadcase 4 Wind +Y , (1 cm 3D = unit) Free line load (force) in global Y (Unit=5.00 kN/m ) (Max=5.00)

m-1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00

0.0

01.0

02.0

03.0

04.0

05.0

0

M 1 : 34

X Y

Z

5.00

3.75

All loads, Loadcase 5 Wind -Y , (1 cm 3D = unit) Free line load (force) in global Y (Unit=5.00 kN/m ) (Min=-5.00) (Max=-3.75)

m0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

0.0

01.0

02.0

03.0

04.0

05.0

0

M 1 : 36

X Y

Z

25.0

25.0

25.0

25.0

24.724.7

23.723.7

22.422.4

21.921.9

17.417.4

9.989.98

All loads, Loadcase 11 Imperfection , (1 cm 3D = unit) Beam load imperfection in local z (Unit=20.0 mm ) (Max=25.0)

m-2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00

0.0

01.0

02.0

03.0

04.0

05.0

0

LC 1 LC 2

LC 3 LC 4

LC 5 LC 11


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2.2 Load Combinations

Load combinations will be created with a help of the task “Loadcase Combination Manager”.

The full workflow is presented in the chapter 3 “Workflow in SOFiSTiK”. Here only the

already created combinations will be presented.

A single load case for imperfection is enough. There is no need to introduce 2 load cases for different imperfection signs, because the sign of imperfection could be easily changed/defined directly in the task “Loadcase Combination Manager”.

Table 2: Load Combinations

Nr. Title Combined Load Cases

1001 Load Case 1001 1.35*LC1+1.35*LC2+1.50*LC3+0.9*LC4+1.0*IMP

1002 Load Case 1002 1.35*LC1+1.35*LC2+1.50*LC3+0.9*LC5-1.0*IMP

1003 Load Case 1003 1.35*LC1+1.35*LC2+1.05*LC3+1.5*LC4+1.0*IMP

1004 Load Case 1004 1.35*LC1+1.35*LC2+1.05*LC3+1.5*LC4-1.0*IMP


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3 Workflow in SOFiSTiK

STEP 1

Open the “Loadcase Manager” in SOFiPLUS.

STEP 2

Create a new load case with action type “IMP Imperfection”. One may create as much

separate imperfection load cases, as it is needed for a project.

In background of the dialog “Loadcase Combination Manager” the module called “SOFiLOAD” is used. Please refer to SOFiLOAD Manual for more information.


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STEP 3

Now open the dialog “Line Load” from register “Element Loads”.

STEP 4

Create a new imperfection by selecting load “Class” Imperfection.

“Element Loads” are loads related to elements. Imperfection kind load is an “Element Load” and thus “Element Line Load” should be selected to introduce an imperfection. Please refer to SOFiLOAD Manual for more information, key-words “element load”, “imperfection”.

Here, how the text input of imperfection

looks like: PROG SOFILOAD

HEAD IMPERFECTION LOADS

LC 11 'IMP' 1 GAMU 0 TITL "Imperfection"

LINE SLN 2 WIDE 0 LINE TYPE UZS 5.00000E-03

LINE SLN 1 WIDE 0 LINE TYPE UZS 5.00000E-03

LINE SLN 2 WIDE 0 QUAM TYPE UZS 5.00000E-03

LINE SLN 1 WIDE 0 QUAM TYPE UZS 5.00000E-03

END


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STEP 5

Select the “Type” of imperfection. One may decide between a discrete imperfection (in [mm])

and a relative imperfection (as a factor of a total length).

STEP 6

Select the “Distribution” of imperfection. There are several distribution types such as Linear,

Quadratic and Qubic.


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STEP 7

Give the value of an imperfection.

We defined linear changeable and quadratic imperfections on our example. These should represent a sway imperfection for the frame and bow imperfections for columns.

For a control of imperfections several ways are possible. First, one can control imperfection graphically in module WinGRAF (Fig. 7). Or numerically in Report Browser (Fig. 8).


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Figure 7: Imperfection control in WinGRAF

Figure 8: Imperfection control in Report Browser


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STEP 8

After the system is exported to SSD, one might open the task “Linear Analysis” to run the

linear analysis of load cases. It will be recognized, that imperfection load case is not supplied

for this task. Imperfection is only available in analysis according to the second (third) order

theory. Imperfection can not be used for a linear analysis of single load cases.

The same is, if one uses a text input. If the linear analysis has been chosen (“SYST PROB

LINE”) and all load cases are going to be analysed (“LC NO ALL”), the solver will ignore the

imperfection load case.

Input:

Output:

STEP 9

Open the task “Define Combinations”. It will be recognized as well, that imperfection load case is

not supplied for this task. Even if one wants to create a “Standard Superposition” imperfection

will not be in a selection list, because imperfection is not to be used for a superposition of the

linear load cases with MAXIMA/WinMAX.


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STEP 10

Open the task “Loadcase Combination Manager”. Now the imperfection load case is supplied

for. One may create load combinations including the

imperfection.

There are two ways to create Load Combinations in task “Loadcase Combination Manager”. The user may create them manually (Fig. 9) or automatically (Fig. 10). Automatic Load Combination generator is a tool based on Objective Functions.


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Figure 9: Load Combinations created manually


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Figure 10: Load Combinations created automatically


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STEP 11

Open the task “Analysis of Combined Loadcases” and run the 2nd (3rd) Order Analysis.

Alternatively one may define global/local imperfection in the task “Analysis of Combined Loadcases” directly. Click on “no inclination” tab by load case register column “Inclination”. Define either a global sway imperfection or an imperfection directly from a load case even with scaling possibility.


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Literature

[1] Eurocode 3: Design of steel structures – Part 1-1: General rules and rules for

buildings (EN 1993-1-1)

[2] “Deutscher Stahlbautag 2012; Aachen, 18. Oktober 2012” by Prof. Dr.-Ing. Ulrike

KUHLMANN, Dr.-Ing. Hans-Peter GÜNTHER and Dipl.-Ing. Antonio ZIZZA.

example - sofistik · 2.1 model geometry and loads a simple one-span steel frame is presented....

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