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Transcript of 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
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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
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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
l,2,3 ! creating line 2 from KP 2 to KP 3
l,3,4 ! creating line 3 from KP 3 to KP 4
! 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
The system parameters are summarized in the following table.
Symbol ADPL Value Comment
l length 10000 mm span length
E emod 210000 N /mm2 Young’s module, elasticity
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
Table 1.2: System Parameters
2If you write a little report you will get have a grade.
14.11.2009
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]
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The system parameters are summarized in the following table.
Symbol ADPL Value Comment
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
E emod 210000 N /mm2 Young’s module, elasticity
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
Table 2.1: System Parameters
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
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
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