aos bookofexamples

Analysis of Structures

Book of Examples2009

University of Duisburg-Essen

Faculty of Engineering

Department of Civil Engineering

Structural Analysis and Construction

Dr. E. Baeck

14.11.2009

Contents

1 Frames 31.1 2d Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Exercise 1: Single Span Girder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Sheets 92.1 Folded Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1.2 Boundary Conditions and Loads . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1

Analysis of Structures - WS09/10

E. Baeck

1

Frames

1.1 2d Frame

In this section a simple 2 dimensional frame should be analysed (see figure 1.1)1. The posts are totallyfixed at their bearings. The load is applied at the upper left corner. The system parameters are given intable 1.1.

We model the frame in parameterized form using symbolic names for the system parameters. The resultsare shown in four windows. Window 1 shows the displacements, window 2 shows the normal forces,window 3 the shear forces and window 4 shows the moments of the frame.

Figure 1.1: Simple 2d Frame

1This example is taken from [3]

3


The system parameters are summarized in the following table.

Symbol ADPL Value Comment

l length 10000 mm frame length or width

h height 4000 mm frame height

E emod 210000 N /mm2 Young’s module, elasticity

ν nue 0.3 Poisson’s ratio

Ap Ap 10.6 cm2 Profiles cross section area

Izz Izz 171 cm4 Profiles moment of inertia

Px Px 1.kN horizontal node load

Py Py -2.kN vertikal node load

Table 1.1: System Parameters

The following listing shows input file for the system analysis.

/cwd,’c:\cm\cm-AoS’ ! setup work directory

/filnam, Frame1new ! setup file name for working files

/prep7 ! starting the preprocessor

/tit, Frame Example 1 ! setup the projects title

! input section for symbolic information

! - geometry

length = 10000.

height = 4000.

! material

emodul = 21000. ! Young’s modul

nue = 0.3 ! Poisson’s ratio

! profiles values: IPB100

Ap = 10.6*1.e+2 ! cross section area

Izz = 171.0*1.e+4 ! moment of inertia

! loads

Px = 1000. ! node load in x-direction

Py =-2000. ! node load in y-direction

! mesh size

es = 500.

E. Baeck

1.1. 2D FRAME Page 5

! creating keypoints (KP))

k,1, 0,0 ! creating key point 1 at x=0 and y=0

k,2, 0,height ! creating key point 2

k,3,length,height ! creating key point 3

k,4,length,0 ! creating key point 4

! creating the lines: the line number is handled implicitly

l,1,2 ! creating line 1 from KP 1 to KP 2



! select the element type

! 1: set number

! 3: beam3

et, 1,3 ! selecting element type for set 1 , beam3

keyopt, 1,6,1 ! setup special setting for beam3

keyopt, 1,9,0

! material values

mp, ex , ,emodul ! setup material parameters in activ set

mp, prxy, ,nue ! which is set 1

! profile values

r,1,Ap,Izz ! setup geometric parameters in set 1

! create the mesh

esize, es ! setup element size using symbolic name

lmesh,all ! mesh all elements along lines

! boundary condition

! - supports

nsel,s,loc,y,0 ! select all nodes with y=0

!d,all,all ! would fix all degrees of freedom in selection

d,all,ux ! fix all x-translation dofs in selection

d,all,uy ! fix all y-translation dofs in selection

d,all,rotz ! fox all z-rotation dofs in selection

nsel,all ! reset node selection

! creating loads

nsel,s,loc,x,0

nsel,r,loc,y,height

f,all,fx,Px ! load on all nodes of selection in x direction

f,all,fy,Py ! load on all nodes of selection in y direction

nsel,all ! reset the node selection

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finish ! close preprocessor section

! calculate the results

/solu ! enter solution section

solve ! starting the solver

finish ! close solution section

! postprocessor section

/post1 ! enter postprocessor section

! prepare the elementtables

etable,ni,smisc,1 ! x-force left node

etable,nj,smisc,7 ! x-force right node

etable,vi,smisc,2 ! y-force left node

etable,vj,smisc,8 ! y-force right node

etable,moi,smisc,6 ! z-moment left node

etable,moj,smisc,12 ! z-moment right node

! setup output windows

/wind,all,off

/wind,1,ltop ! setup left top window

/wind,2,rtop ! setup right top window

/wind,3,lbot ! setup right bottom window

/wind,4,rbot ! setup right bottom window

! set general plot flags

gplot

! create plots

/gcmd,1,pldisp,1 ! plot displacements in window 1

/gcmd,2,plls,ni,nj ! plot normal forces in window 2

/gcmd,3,plls,vi,vj ! plot shear forces in window 3

/gcmd,4,plls,moi,moj ! plot moments in window 4

/replot ! update actual view

E. Baeck

1.2. EXERCISE 1: SINGLE SPAN GIRDER Page 7

1.2 Exercise 1: Single Span Girder

As an exercise you can write an ADPL file to analyse a single span girder (see figure 1.2) using theparameter of table 1.2. The single span girder should be explored for hinged and for fixed ends. Theresults (normal forces, shear forces and moments) should be compared with the table values of theliterature. A representation like in section 1.1 should be chosen.2

Figure 1.2: Single Span Girder



l length 10000 mm span length


Ap Ap 10.6 cm2 Profiles cross section area

Izz Izz 171 cm4 Profiles moment of inertia

P Pnode 10 kN vertical load in the middle of the span


2If you write a little report you will get have a grade.

14.11.2009


E. Baeck

2

Sheets

2.1 Folded Sheet

2.1.1 Geometry

In this section a simple 2 dimensional folded sheet should be analysed (see figure 2.1)1.

We model the sheet in parameterized form using symbolic names for the system parameters.

Figure 2.1: Folded Sheet

1This example is taken from [1]

9




l1 Length1 60 mm hole distance 1

l2 Length2 20 mm hole distance 2

w1 Width1 20 mm sheet width part 1

w2 Width2 20 mm sheet width part 2

d1 DHole1 8 mm hole 1 diameter

d2 DHole2 8 mm hole 2 diameter

r1 Radius1 4 mm fillet radius


ν nue 0.3 Poisson’s ratio

t thickn 0.5 mm sheet thickness

p1 press1 5.0 N /mm2 load ordinate at load boundary

p2 press2 50.0 N /mm2 load ordinate at load center


We use the plane82 element with nodes at the corners and in the middle of the edges (see [2]).

Figure 2.2: Elemente Type Plane82

E. Baeck

2.1. FOLDED SHEET Page 11

The following listing shows input file for the system analysis.

/cwd,’c:\cm\cm-AoS’

/filnam, sheet1

/prep7 ! Enter preprocessor section

/tit, angle sheet

! >>

! begin of input section

! o geometry

Length1 = 60. ! sheet length

Length2 = 20.

Width1 = 20. ! sheet width

Width2 = 20.

DHole1 = 8. ! diameter of holes

DHole2 = 8.

Radius1 = 4. ! radius for fillet

thickn = 1.5 ! thickness

! o material

emod = 210000. ! Young’s Modul / E-Module

nue = 0.3 ! Poisson’s ratio

! end of input section

! <<

! element selection

et,1,Plane82 ! we use a plane element for plane stress conditions

keyopt,1,3,3 ! input of thickness using real constant

r,1,thickn ! setup thickness

! material

mp,ex,1,emod ! Young’s module

mp,nuxy,1,nue ! Poisson’s ratio

! modeling section

rect,0.,Length1,-Width1/2.,Width1/2.

rect,Length1 -Width2,Length1,-Width1/2.,-Width1/2. -Length2

cyl4,,,width1/2. ! cylinder area for 1st hole

kwpave,5,6 ! move workplane in the middle of keypoint 5 and 6

! (the workplane discribes the local koordinate system)

cyl4,,,width2/2. ! cylinder area for 2nd hole

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! combine areas

aadd,1,2,3,4 ! sheet without holes and fillet

! first hole area

cyl4,,,DHole1/2. ! hole at origin of workplane

wpave ! shift workplane to previous position

! second hole area

cyl4,,,DHole2/2. ! hole at origin of workplane

! select hole areas

asel,s,,,1,2,1

! and create a component of the areas of holes

cm,holearea,area

! reset selection

allsel

! substract holes area from sheet area

asba,5,holearea

! reset selection

allsel

! create fillet lines

lfill,17,8,Radius1 ! we select the lines with line number

! the fillet is created with given radius

! fillet area

al,12,13,14 ! the fillet area is build using the edge lines

! add all remaining areas

aadd,all ! all areas are combined

E. Baeck

2.1. FOLDED SHEET Page 13

2.1.2 Boundary Conditions and Loads

14.11.2009


E. Baeck

Bibliography

[1] FEM fur Praktiker - Band 1: Grundlagen7. Auflage 2002, expert verlag, Renningen

[2] ANSYS Helpfile

[3] Einfuhrung ANSYS CLASSIC & WORKBENCH – WorkshopUniversitat Dortmund / Fakultat BauwesenLehrstuhl Numerische Methoden und InformationsverarbeitungProf. Dr.-Ing. habil. Franz-Joseph Barthold, 2. Oktober 2006

15

aos bookofexamples

Documents

frame length

d frame page

setup material parameters

frame example

setup file

setup geometric parameters

dimensional frame

key point