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Section Builder: User`s Manual - Georgia Institute of Technology

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1. Pd 7 l Location X_2 5 56605e 002 X_3 1 75000e 001 m Out ol plane stresses Sig_11 0 00000 000 Pa Tau 12 2 21630 003 Tau 13 2 48881 000 Temporary displz of elemerital str sses Elemental Stresses AP INS fol ih Out ol plane stresses Sig 22 0 00000 000 23 0 00000 000 Sig 33 0 00000 000 Cancel ii di me mA CD pee ACCENDI Selected element Figure 1 10 The temporary display of stress levels Interactive definition of sensors It is often convenient to create a permanent record of the warping displacement stress or strain levels at a point of the cross section This can be achieved through the interactive definition of sensors as described in section 8 5 at specific locations of the cross section Once defined these sensors become part of the model definition and as discussed in section 1 4 2 each time the finite element analysis is run warping displacements stresses or strains will be output for each sensor and each loading condition To define a sensor first select the desired element of the model then create a sensor at that location The procedure is as follows 1 Enter the visualization mode select a loading condition and visualize warping displacement stress or strain fields These steps are described in sections 1 5 1 and 1 5 2
2. Cis Css K2 1 5 Ms Cie Cse Cos K3 and a twisting moment shear force problem characterized by the following 3 x 3 stiffness matrix M C34 K V2 E 1 6 V3 C34 C23 C33 E3 The corresponding compliance matrices are E1 01 Sig Sg Sis Sss 556 1 7 K3 Sie S56 See Ms and Ky S44 Soa S34 M S24 S22 S23 V 1 8 E3 S34 S23 S33 V3 for the axial force bending moment and twisting moment shear force problems respectively The axial force bending moment problem If the stiffness matrix of the cross section presents the special structure displayed in eq 1 4 it becomes possible to separately analyze the axial force bending moment and twisting moment shear force problems The former problem is the focus of this section To further simplify the relationship between the axial forces and bending moment and the corresponding sectional strain components eq 1 5 it is convenient to introduce the centroid of the cross section a point of the cross section with coordinates as depicted in fig 1 3 With the help of the centroid the relationship between axial force and axial strain decouples from the relationship between bending moments and curvatures NI e 1 9 1 4 PERFORMING THE FINITE ELEMENT ANALYSIS 11 where Nf N is the axial force ef the axial strain at the centroid and S the axial stiffness The be
3. Visualize the results Third icon Perform finite element analysis Second icon Mesh the section First icon Figure 1 1 The SECTIONBUILDER toolbar 8 CHAPTER 1 INTRODUCTION 1 22 Definition of the beam cross section The definition of the configuration of the beam s cross section involves two main components the two dimensional geometric configuration of the section and the physical properties of the materials of which it is made e The geometric configuration of the cross section can be defined in two alternative manners 1 First parametric shapes can be used as discussed in detail in chapter 2 The following parametric shapes can be defined airfoil sections as described in section 2 1 circular arcs as described in section 2 2 C sections as described in section 2 3 circular cylinders as described in section 2 4 double boxes as described in section 2 5 I sections as described in section 2 6 rectangular boxes as described in section 2 7 rectangular sections as described in section 2 8 circular tubes as described in section 2 9 triangular sections as described in section 2 10 and T sections as described in section 2 11 The various configurations are parametrized and hence each section is readily defined by a small number of input parameters 2 Second more complex sections of arbitrary configuration can be constructed as discussed in chapter 3 The definition process is tailored towards the definition of composite s
4. LEFT_WEB_MATERIAL_NAME LWebMaterialName RIGHT_ WEB MATERIAL NAME RWebMaterialName GTOP REINFORCE MATERIAL NAME RMaterialName 15 DEFINED IN FRAME FxdFrameName MESH_DENSITY md 124 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 11 5 Examples A few examples that describe the construction procedure of this type of section are shown below Example 1 This example shows a T section with skewed flange and top reinforcement Here web height web thick nesses flange widths flange thicknesses flange skew angles materials and mesh density are assigned for constructing this section This example also shows the inverse of the reserve factor field over the cross section under the applied sectional loads Figure 2 91 Example 1 T section Example 2 This example shows a T section with flange reinforcement Here web height web thicknesses flange widths flange thicknesses materials and mesh density are assigned for constructing this section This example also shows the axial stress field over the cross section under the applied sectional loads 2 11 DEFINITION OF T SECTIONS 125 Figure 2 92 Example 2 T section 126 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS Chapter 3 Builder 3 1 Introduction Composite materials have found increasing use in aerospace and civil engineering constructions Typically complex sections are build by laying layers of composite materials in a mold for lower performance structure
5. 1 11 and 1 12 the relationship between the corresponding quantities at the reference point are readily found as N S 2 35 1005 i 1035 H5 27 8 H5 1032 38 1 14 M3 25 e2 e3 S z2 S K3 12 CHAPTER 1 INTRODUCTION The corresponding bending compliance matrix is then found by inversion 2 2 El 1 E Tor H3 e3 H33 2203209 H33 002 zea Hgs co H5 zea H33 N K M i 202 H33 53 H33 H33 p K ze2 H zea H33 H gt 3 1 15 where Ay Identifying the compliance matrices in eqs 1 7 and 1 15 it is possible to compute from the terms of the compliance matrix the various engineering sectional stiffnesses listed below e The centroidal bending stiffnesses Ax Se6 As H33 S55 As H33 Sse As 1 16 where Ag S55 S66 S e The coordinates of the centroid location T2c 33546 53515 d3c 53 516 5 515 1 17 e The azial stiffness i S S11 122016 23915 1 18 1 10 describes bending behavior of the cross section but due to the presence of the cross bending stiffness term H bending in the two planes 71 72 and 7 73 is coupled It is possible to define the principal centroidal axes of bending As illustrated in fig 1 4 the principal centroidal axes of bending 7 7 78 correspond to a planar rotation of orthonormal basis Z by an angle o7 note tha
6. Definition of Split sections s a a oa X Q w ER IR ome w ee WQ 134 CONTENTS Oo Formatted Opb lt ro saa nania x ae amp Qe ee ee we 82 Tees PPP Oe Sw ccc id Detiniton ot Tean sections 2 7 39 puwa x SOEUR SUR NOR GO ROS oa 520 m m W W m Rote sb eR Q b RR UN ea ERS Q Q 02412 2255 03 aes ee Q ORS GEE Dame qe RAE A 20 Debniionob Veon sections 235299334 R3 5 bobo UAE s Yo ev E Yo 5 Jl sapu 2212995009 3 b EGG xem m RON RD ROG X a Ree ow W dodo EAMES e Q ashes del 3o QUQ Q he ee Q Do o0bob x os rc M Q Q oe ded 01 a 4 Material properties 4 1 Definition of material properties eh 4 1 1 The Material properties dialog window a a a ee eee s s e w a 4 12 Ihe Siifness dialog window cis Ro o Ro Rr rU W Q d QQ 4 1 8 The Failure Criterion dialog window gt e s s s e socca we e w eee s ss ee ee ee 4 1 4 The Strength dialog widow 223 264444 De Pew ew ee ee eee eee 4 15 oi OA ee E Salas 0 W d 42 Definition of solid properties lt gt lt sss sasea ak REGE ERR PEE 4 2 1 The Solid material properties dialog 4 2 2 The Layer List dialog window sa ddan 50846 eb eee dee eRe S 5 Mesh density Dl RAP 2 hu dE b a du Kee Oe hee
7. To select an element of the finite element mesh first click the Select Element menu item or toolbar icon then click on the desired element that element will be highlighted as shown in fig 1 11 1 5 VISUALIZING THE RESULTS 23 3 Next click the Create Sensor menu item or toolbar icon to open the interactive sensor definition dialog shown in fig 1 11 an fill in the following information a Sensor name Enter a unique name for the sensor b Sensor type Select Stresses Strains or Warping for the sensor to compute the six stress components the six strain components or the three warping components respectively c Sensor Location Select Middle At Gauss Points or At Corners to locate one sensor at the middle of the element four sensors at each of the four Gauss points of the element or four sensors at the four corners of the element respectively For stresses and strains the Gauss point option provides the most accurate information whereas for warping displacements the four corner option is preferable NET Interactive sensor ae definition dialog H Sensor definition Sensor name Selected SensorForStresses element Sensor type Sensor location Stresses Middle C Strains At Gauss points C Warping C At comers Figure 1 11 The interactive definition of a sensor 1 5 4 The Graphics menu and toolbar The Graphics menu and toolbar shown in fig 1 12 controls the manner in which the requested
8. cross section and the associated principal axes These entries or icons are toggle switches that turn on and off the visualization of the associated quantities In all cases the origin of the axis system i e the reference axis of the beam is indicated by a yellow circle 1 The Princ axes Bending menu item or toolbar icon switches on the visualization of the principal centroidal axes of bending The location of the centroid is given by eq 1 17 and the orientation of the principal centroidal axes by eq 1 20 as illustrated in fig 1 4 Examples are shown in fig 2 10 and fig 2 65 2 The Princ axes Shearing menu item or toolbar icon switches on the visualization of the principal ares of shearing at the shear center The location of the shear center is given by eq 1 31 and the 1 5 VISUALIZING THE RESULTS 21 orientation of the principal axes of shearing at the shear center by eq 1 34 as illustrated in fig 1 6 Examples are shown in fig 2 16 and fig 2 85 3 The Princ axes Inertia menu item or toolbar icon switches on the visualization of the principal axes of inertia at the mass center The location of the mass center is given by eq 1 40 and the orientation of the principal axes of inertia at the mass center by eq 1 44 as illustrated in fig 1 7 Examples are shown in fig 2 11 and fig 2 79 As discussed in section 1 4 1 the complete sectional stress sectional strain relationship given by eq 1 2 often splits into
9. e The shearing stiffnesses about shear center Kh tag K eg K cAxk 1 32 where a 599 za Hg b S33 z2 Hii 93 z kzZ 3k Hii and A 1 ab 2 Eq 1 24 describes the shearing behavior of the cross section but due to the presence of the cross shearing stiffness term shearing in the two planes 71 72 and 71 73 is coupled It is possible to define the principal axes of shearing at the shear center As illustrated in fig 1 6 the principal axes of shearing at the shear center Z 1 15 13 correspond to a planar rotation of orthonormal basis Z by an angle a note that clearly 7 When using the principal axes of shearing at the shear center the twisting moment and shearing forces are fully uncoupled Me H VP KES VE oft 1 33 1 4 PERFORMING THE FINITE ELEMENT ANALYSIS 15 Clearly MF and amp f g since the rotation of the axis system takes place about unit vector 71 The shearing forces V and V are computed with respect to the shear center along axes 7 and 73 respectively Similarly yf and yf are the sectional transverse strains along axes 75 and 75 respectively M Shear center Figure 1 6 Orientation of the principal axes of shearing The following quantities are also provided e The orientation o of the principal axes of shearing at the shear center k k k sin 2a A 608 2o SA 3 1 34 w
10. zk 1 0 Ya Y zk 1 0 1 26 a zk2 1 vfs vfs 0 1 713 Eqs 1 23 and 1 24 relating the sectional forces and strains about the shear center can be recast in a matrix form as He 0 0 KE Ve 0 yia 1 27 0 K33 is 14 CHAPTER 1 INTRODUCTION 1 i Forces and moments Forces and moments applied at the reference point applied at the shear center Figure 1 5 Left figure forces and moments applied at the reference point Right figure forces and moments applied at the shear center Introducing eqs 1 25 and 1 26 the relationship between the corresponding quantities at the reference point are readily found as M 22 2 Kk KE rk KE Ska K Ky 1 K 212 V3 K 55 K5 13 1 28 The corresponding bending compliance matrix is then found by inversion Ky 1 91 Hii zk2 Hii 712 ka Hii Kk Ax 223 Hi Kh Aw xkatka Hii Vo 1 29 a xio Hii KE Ak xpotr3 Hi K Ax t v25 Hii V3 where Ay K Identifying the compliance matrices in eqs 1 8 and 1 29 it is possible to compute from the terms of the compliance matrix the various engineering sectional stiffnesses listed below e The torsional stiffness 1 Hn Ss 1 30 e The coordinates of the shear center HiiS934 vak H11 S24 1 31
11. 2 51 This Z section does not have TRFlgR TRFlg BLFlgR and BLFlg solids shown in fig 2 52 Here the coordinates of the points are also adjusted from the I section 2 If the widths 0 and 0 the section looks like T shape depicted in fig 2 53 This T section does not have BLFlgR BLFlg BRFIgR and BRFlg solids shown in fig 2 54 Here the coordinates of the points are also adjusted from the I section 2 6 DEFINITION OF I SECTIONS 79 Al A2 A3 TLFIgR B2 TRFIgR TLFlg B3 E3 BLFlg BLFIgk E BRFIgR El D3 D2 D1 Figure 2 50 The four zones of the I Section CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS Wort Figure 2 51 Configuration of the Z section 2 6 DEFINITION OF I SECTIONS TRFIgR Figure 2 52 The zones of the Z section 81 82 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS Figure 2 53 Configuration of the T section 2 6 DEFINITION OF I SECTIONS 83 Al C1 aa TLFIgR B2 HA ERE C3 B3 E3 E2 E4 Figure 2 54 The zones of the T section 84 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 6 4 Formatted input The data defined in the above sections will be saved in a specially formatted input file which has the following structure I_ SECTION DEFINITION I_ SECTION NAME IsecName WEB HEIGHT LEFT WEB THICKNESS tw RIGHT_WEB_THICKNESS tw TOP_FLANGE_WIDTH wis TOP FLANGE THICKNESS tu TOP_FLANGE
12. Walls 134 CHAPTER 3 BUILDER 3 3 Definition of Split sections Split is a connector for connecting three walls Three walls Wall A Wall B and Wall C connected with Spilt are depicted in fig 3 8 Split can be constructed at any direction i e one wall can split in two walls or two walls can marge into one wall User has to provide the Wall A connected at position A of Split Wall B connected at position B of Split and Wall C connected at position C of Split information for constructing a Split Before Connection CONNECTED AT A Wall A CONNECTED_AT_B CONNECTED_AT_C After Connection Figure 3 8 Three walls can be connected as above with a Split The detail description of Split is shown in fig 3 9 Basically wall information is used for Split construction Points Ki K1i Mi and i 1 2 3 n are generated from WallA WallB and WallC Points Ki and Mi or Mli are the starting positions at U 0 of various layers of WallA and WallC respectively Similarly points Kli are the final position at U 1 of the layers of WallB Li are the intersection points of the tangents of the layers of WallA at U 0 and WallC at U 0 Lli are the intersection points of the tangents of the layers of WallB at U 1 and WallC at U 0 Here the sum of the layers for WallA and WallB is equal to that of WallC Curves and surfaces are constructed from Ki K1i Li L1i Mi and M1i Solids are generated using the material and mesh
13. an axial force bending moment problem characterized by eq 1 5 and a twisting moment shear force problem characterized by eq 1 6 When this decoupling takes place the Princ axes Bending and Princ axes Shearing entries or icons will display the quantities indicated above If the decoupling does not take place clicking these entries or icons will simply display the origin of the axis system since the corresponding centers and associated principal axes do not exist Visualizing warping stress and strain fields The next six entries or icons control the display of the warping displacement stress and strain fields over the cross section Clicking one of these entries or icons will cause the display of a specific displacement stress or strain component the six actions are mutually exclusive 1 Clicking the Displacements menu item or toolbar icon causes the display of the three dimensional warping displacement of the cross section under the applied sectional loads Examples are shown in fig 2 38 and fig 2 78 2 Clicking the Axial strains menu item or toolbar icon causes the display of the axial strain field over the cross section under the applied sectional loads Examples are shown in fig 2 44 and fig 2 56 3 Clicking the Shear strains menu item or toolbar icon causes the display of the shear strain field over the cross section under the applied sectional loads Examples are shown in fig 2 17 and fig 2 29 4 Clicking the Axial
14. axes 25 and 15 respectively The following quantities are also provided e The orientation o of the principal axes of inertia at the center of mass 33 1 123 20 A gt Gs 205 aK 1 44 where Im ym 2 A A Tg 1 45 e The principal moments of inertia per unit span about center of mass 133 and Le IU IU Im Ip 2 AS pms 33 422 OA 1 46 2 2 Note that the choice the orientation of the principal axis 74 given by eq 1 44 guarantees that axis sm 12 is the axis about which the minimum moments of inertia occurs hence 25 lt mM 1 4 PERFORMING THE FINITE ELEMENT ANALYSIS 17 m i Center of mass Figure 1 7 Orientation of the principal axes of inertia at the center of mass 1 4 2 Three dimensional stresses and strains The geometry of the cross section is described in an orthonormal basis Z 7 72 73 where 71 72 and 73 are three mutually orthogonal unit vectors The plane of the cross section is assumed to coincide with plane 72 73 and the axis of the beam is along unit vector 71 as depicted in fig 1 2 The reference axis of the beam is a line along axis 71 the origin of the coordinate system is at the intersection of the reference axis with the plane of the cross section To compute three dimensional warping displacement stress components or strain components two user defined inputs are
15. b Ste p 2 Displacements Axial strains lt n Displacement Shear strains Y stress and strain fields Axial stresses 95 Shear stresses Reserve Factors u Element selection Select Element Step 3 and Element stresses lt Pi sensor creation Create Sensor lt Loading Loading menu toolbar Figure 1 9 The Loading menu and toolbar Each action can be invoked by selecting a menu item or clicking the corresponding toolbar icon In this figure the menu items and corresponding toolbar icons are shown next to each other to highlight the correspondence 1 The Reference menu item or toolbar icon will show the reference configuration of the cross section no loading condition is selected 2 The First Loading menu item or toolbar icon activates the first loading condition in the list 3 The Next Loading menu item or toolbar icon moves to the next loading condition in the list 1 5 2 Step 2 Selecting the quantities to be visualized The second step of the visualization phase is to select the quantities to be visualized Nine entries or icons in the Loading menu shown in fig 1 9 are used to select the desired quantities to be visualized and these fall into two categories 1 sectional centers and principal axes and 2 the warping stress or strain fields over the cross section Visualizing centers and principal axes The first three entries or icons are used to visualize the centroid shear center and center of mass of the
16. circles used to indicate the locations of the sectional centers and the arrays that represent the principal axes 7 The size of the arrows used to visualize the strain or stress fields can be adjusted using the Data Size or Data Size entries or icons Graphics View Help Zoom In Zoom Out Center Show Model Rotate x arrow gt Rotate X Alt arrow lt Rotate Y arrow Rotate Y Alt arrow v Rotate 2 Page up Graphics Rotate Z down menu 4 Graphics toolbar OOPS D P Translate X arrow gt Translate X arrow lt Translate Y arrow Translate Y arrow v View from x Alt x Food Symbol size Ctr arrow gt Symbol size Ctr arrow lt Data size Ctr arrow Data size Ctr arrow v Background Figure 1 12 The Graphics menu and toolbar Each action can be invoked by selecting a menu item or clicking the corresponding toolbar icon In this figure the menu items and corresponding toolbar icons are shown next to each other to highlight the correspondence 1 6 Installation of SectionBuilder 1 6 1 Directory structure A typical installation of the code features the following five sub directories e SectionBuilder bin This directory contains the executable SecBuild exe and the input file icon seb ico 1 6 INSTALLATION OF SECTIONBUILDER 25 SectionBuilder Demos This directory contains a number of sample input fil
17. dialog tab The Materials dialog tab as described in fig 2 63 defines the materials the rectangular box is made of As shown in fig 2 64 the section is divided into three zones 1 The top reinforcement flange consists of the components labeled TLFIgR and TRFIgR 2 The rectangular box consists of the components labeled TLFlg TRFlg LWeb RWeb BLFlg and BRFlIg 3 The bottom reinforcement flange consists of the components labeled BLFIgR and BRFIgR It is possible to assign material properties as described in section 4 1 or solid properties as described in section 4 2 to each zone of the rectangular box 2 7 DEFINITION OF RECTANGULAR BOXES 93 D1 El F1 Figure 2 64 The three zones of the rectangular box 94 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 7 4 Formatted input The data that defines the rectangular box as described in the above sections will be saved in a specially formatted input file which has the following structure RECTANGULAR BOX DEFINITION GRECTANGULAR BOX NAME HEIGHT OGLEFT WEB THICKNESS tw ORIGHT WEB THICKNESS tw TOP LEFT FLANGE WIDTH wi OTOP LEFT FLANGE THICKNESS tis TOP_LEFT_FLANGE_SKEW_ANGLE our TOP_FLANGE_REINFORCE_THICKNESS ty TOP_RIGHT_FLANGE_WIDTH wre TOP_RIGHT_FLANGE_SKEW_ANGLE our BOTTOM_LEFT_FLANGE_WIDTH wy BOTTOM_LEFT_FLANGE_THICKNESS trt BOTTOM_LEFT_FLANGE_SKEW_ANGLE our BOTTOM_FLANGE_REINFO
18. for various loading cases This file can be viewed using any text editor sva This file contains the information pertaining to the meshing of the cross section This file should not be edited 1 6 4 Installation Procedure Follow the installation procedure for Windows XP 1 2 Extract file SectionBuilder rar to C V Associate the extension seb with the execution of the executable SectionBuilder bin SecBuild exe From a folder s window click Tools gt Folder Options Once the Folder Options dialog is open click tab File Types Click the New icon to Create New Extension dialog type seb and click OK With the new file type seb highlighted in the Registered file types list click Advanced to open the Edit File Type dialog Click Change icon then Browse and point to icon SectionBuilder bin seb ico Next click on New type open under Action then click Browse and point to executable SectionBuilder bin SecBuild exe and click OK Click OK and Close to exit the Folder Options dialog Place a short cut to SectionBuilder bin SecBuild exe on your desktop Verify the installation Go to SectionBuilder Demos Airf and double click on airfi seb this should open the SectionBuilder program 26 CHAPTER 1 INTRODUCTION Chapter 2 Parametric shape configurations Parametric shape configurations have given geometric shapes that are parameterized Parametric shape configurations are defined through the Sections menu item shown in fig 4
19. h k h S SOS s s s Q s s w Q Q w a Q k W Q 88 241 The Rectangular bor dialog 48D 2 5 4 2a s s s s RO us a a E OE 89 2 7 2 The Dimensions dialog tab lt lt saamaa eo ae ee RR E W k ROUX RUE dos d 90 24 44 The Materiale drag tab os doom m EK Qo SE SHR RR dw ox 92 2 1 4 Formatted pub hoe wow ec ow m Rea Pee ee eee ee d 94 ONES IT go y u ee a Pe eee h eee we eee de ee ki Aa amp amp 8 94 2 8 Definition of rectangular sections u e 22 228 o oe e 96 2 8 1 The Rectangular section dialog tab aa siad aa QUQ 44 Q Ie 97 202 The Dimensions dialog tab 2222449 Go aad RR a 98 2 5 9 The Matemale dialog tab c s sea w a Mea k Q h k QUQ Q W UL UQ W RO dog d 99 294 Formatted DH i ri riti Gee M nel RRR SOROR wa a 101 2 95 Exemples sua dad h kus XY Mow a eS Sle eb ee w aras Na Q da Q ads 102 20 of dicular tapes v x s huhu as musu XO uu L ade bow eae 104 29 1 The Circular tube dialog tab 2 644 2 4424 Pee qua dee See eS 105 29 2 The Dimensions dialog tab cd s 4 924 RR 4444 a aaa ee Se ar 106 2 0 4 The Materials dialog tab ca RAR SO REY sus ala OG oe a E RUE W 107 2 04 Popnaatted s s uox 20350 Sos s 39 eee EES EEL Q dedo cR QS ox 108 35 x mco o RRR Gee Rer RRR E ES S AC fex d Q 109 2 10 Definition of triangular sections 4 45 2 DUE S RA P
20. is satisfied aT m joi if o gt 0 oe oC if or lt 0 eat aT ma _ J e if og gt 0 m oC if 02 lt 0 oe T12 4 13 where and are the stresses along the material axes e and e gt respectively and 719 the corresponding shear stress The allowable tensile and compressive stresses along axis are denoted o T and oP respectively Similarly the allowable tensile and compressive stresses along axis are denoted oT and o3 respectively Finally the allowable shear stresses in plane 6i is denoted Tf All these quantities are defined in section 4 1 4 4 Tsai Wu Criterion This criterion is used for transversely isotropic material only At failure the following equation is satisfied s2 182 4 52 82 Fisi Foso 1 where s c1 o210 29 2 s o2 o3T08 and sg T12 T and the stresses along the material axes e and 2 respectively and the corresponding shear stress The allowable tensile and compressive stresses along axis are denoted oT and o respectively Similarly the allowable tensile and compressive stresses along axis are denoted oT and respectively Finally the allowable shear stresses in plane 61 is denoted 7 All these quantities are defined in section 4 1 4 The two coefficients F and F gt 00 of oft of and Fy 08 o37 03 5 Von Mises C
21. left flange dimensions 1 The width wpf of the bottom left flange default value war 2 The thickness tyr of the bottom left flange default value tyr tur 3 The skew angle oir of the bottom left flange positive down measured in degrees default value 0 2 5 DEFINITION OF DOUBLE BOXES 69 4 The thickness tpr of the bottom reinforcement flange this thickness applied to both left and right reinforcements that cannot exist independently of each other default value ty 0 This variable is also used as flag for the presence of the bottom flange reinforcement if ty gt 0 this reinforcement is present Bottom right flange dimensions 1 The width of the bottom right flange default value Were 2 The thickness tpt of the bottom right flange default value tyre ttre 3 The skew angle of the bottom right flange positive down measured in degrees default value 0 70 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 5 3 The Materials dialog tab Double Box Double Box Dimensions Materials Top Flange Material Ro Web Mera Bottom Flange Material Figure 2 42 The Materials dialog tab The Materials dialog tab as described in fig 2 42 defines the materials the double box is made of As shown in fig 2 43 the section is divided into four zones 1 The top reinforcement flange consists of components labeled TLFIgR and TRFIgR 2 The l
22. material properties as described in section 4 1 or solid properties as described in section 4 2 to each zone of the circular tube 108 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 9 4 Formatted input The data defined in the above sections will be saved in a specially formatted input file which has the following structure CIRCULAR_TUBE_DEFINITION CIRCULAR_TUBE_NAME Tubelame GINNER RADIUS R OUTER RADIUS Ro MATERIAL PROPERTY NAME MaterialName IS_DEFINED_IN_FRAME FxdFrameName MESH_DENSITY md 2 9 DEFINITION OF CIRCULAR TUBES 109 2 9 5 Examples A few examples that describe the construction procedure of this type of sections are show below Example 1 This example shows a circular tube section Here inner and outer radii frame material and mesh density are assigned for constructing this section This example also shows the warping displacement of the cross section under the applied sectional loads Figure 2 78 Example 1 Circular Tube Example 2 This example shows also a circular tube section Here inner and outer radii frame materials property and mesh density are assigned for constructing this section This example also shows the principal axes of inertia at the mass center CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 110 a lt HEE oe Figure 2 79 Example 2 Circular Tube 2 10 DEFINITION OF TRIANGULAR SECTIONS 111 2 10 Definition of triangular sect
23. ob airfoil Section 2 loeo x 6o EK S S REDE eee Rob RUE XY Q 3 21 The Ainyoiseckon dialog 8b 225922 9G eee w wad Pee w W 2 1 2 Th Airfoil propie dialog tab ca oa 44444 eee ee eed RR RR 21 3 The Dimensions dialog tab 4 4 54 s X x ox 0 a y s s w a a 2 1344 The dialog tab o acars Lh s apus ERU RR ee RON RR W 2 1 5 Formatted u ean 4402584 444 Bek Se Q ouod d n S e ede ee Q ed LLG SIC os asa a a was Gee SUS W 22 Definition Gf circular arcs uou s s san uw w ox ore a e Y q a wo k 4 S S E sub ROO wx 2 2 1 The Circular Are dialog tabo s oo s os 2 040 w w w w on m dad eee eee ee TS 223 2 The Dimensions dialog tab s 4 444 ese 5 54 8 e ao ee usss a 5 22 4 The Materiais dialog tab u e e gag a 2 vw W 2 24 Formatted mph s se s 6444 54 eR eee SEL de dS SEES 25 Mea pIOS xl oe SERRE AS ES ESSE ERR PEAS EERE S Q 23 Deinition of puke ee la s a u RS RE PSS SEE EE Q ah x 2 41 The C secbonm dialog tab s lt s sa bk w k eee ee BS Q Q Q ww n RR mom d ds 2 32 The Dimenstona dialog taD s sa a a ea d Ma h sa s OR aS 233 The Materigis dialog ccce u sadba a a RET X RUE E Oa E W 2244 Bonuatted u sa s s 39 909 xoxo ESS dedo W S ia qox 3 UL Sg uuu a RR s ITI 2 44 Dennitiom of circu
24. of the materials it is made of Two avenues are available for this step First parametric shapes can be used such as I sections C sections or a variety of commonly used cross section Second more complex sections of arbitrary configuration can be constructed The process of defining the section involves a number a dialog windows described in chapter 2 for the parametric shapes and in chapter 3 for complex sections of arbitrary configuration 2 Second a finite element mesh of this two dimensional problem is created as discussed in section 1 3 Clicking the first icon of the menu shown in fig 1 1 will launch the mesh generation phase of the analysis 3 Next the finite element analysis of the problem is run to compute sectional properties and stress distributions for given sectional loads Clicking the second icon of the menu shown in fig 1 1 will launch the finite element analysis of the section 4 The last step of the process is the visualization of all results Principal axes of bending shearing and inertia are displayed together with the centroid shear center and center of mass Axial and shear stress or strain distributions associated with a given sectional loading can also be visualized Clicking the third icon of the menu will invoke the visualization program a detailed discussion of this topic appears in section 1 5 airf1 seb SecBuild File Edit Sections Builder Geomg Dau eS Materials Analysis Graphics View Help
25. required 1 First sectional loading cases must be defined as described in section 6 1 A loading case consists of an axial force and two transverse shear forces as well as a twisting moment and two bending moments applied to the cross section These 3 forces and 3 moments can be applied at the reference axis at the centroid at the shear center or at an arbitrary point of the cross section 2 Second sensors must be defined as described in section 8 5 These sensors are analogous to their physical counterparts such as strain gauges which provide information about the local strain field Sensors define the location on the cross section where the information will be computed and the type of quantity to be sensed which could be three dimensional warping displacement stress components or strain components For each of the defined loading cases the quantities measured by each of the sensors will be computed and printed A detailed report is printed in an output file with extension sbs as described in section 1 6 3 Warping displacements Under the effect of the applied loading the cross section will deform This deformation is characterized by a three dimensional warping displacement field which features components both in and out of plane of the cross section A typical print out of a warping sensor is shown in Table 1 1 For the sensor named SensorWarping the out of plane warping displacement component as well as the in pla
26. shown in fig 2 84 the section features a single zone 1 The top reinforcement flange consists of the components labeled TWeb TFlg BFlg It is possible to assign material properties as described in section 4 1 or solid properties as described in section 4 2 to the triangular section 2 10 DEFINITION OF TRIANGULAR SECTIONS 115 CU A Bweb gt CL Figure 2 84 The three zones of the triangular section 116 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 10 4 Formatted input The data defined in the above sections will be saved in a specially formatted input file which has the following structure TRIANGULAR SECTION DEFINITION TRIANGULAR SECTION NAME TrialName TOP_WEB HEIGHT hw BOTTOM_WEB_HEIGHT hw WIDTH vw WEB_THICKNESS tw OPEN_SECTION YES NO Q WEB_MATERIAL_NAME twwaterialName f IS_DEFINED_IN_FRAME FxdFrameName MESH_DENSITY md 2 10 DEFINITION OF TRIANGULAR SECTIONS 117 2 10 5 Examples A few examples that describe the construction procedure of this type of section are shown below Example 1 This example shows an open triangular section Here top and bottom web heights width web thickness material frame and mesh density are assigned for constructing this section This example also shows the principal axes of shearing at the shear center tITCUCtePEUd Saar 5 5 3 CIE a SERERE IUE gale n Figure 2 85 Example 1 Triangular Sec
27. skew angle of the top right flange positive up measured in degrees default value ae 0 2 11 DEFINITION OF T SECTIONS 121 2 11 3 The Materials dialog tab T section T section Dimensions Materials Left Web Material Right Web Material Figure 2 89 The Materials dialog tab The Materials dialog tab as described in fig 2 89 defines the materials the T section is made of As shown in fig 2 90 the section is divided into three zones 1 The top reinforcement flange consists of the components labeled TLFIgR and TRFIgR 2 The left portion of the T section consists of the components labeled TLFlg and LWeb 3 he left portion of the T section consists of the components labeled TRFlg and RWeb It is possible to assign material properties as described in section 4 1 or solid properties as described in section 4 2 to each zone of the T section 122 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS Al C1 o BEER B2 m 88 gi B3 D EF Figure 2 90 The three zones of the T section 2 11 DEFINITION OF T SECTIONS 123 2 11 4 Formatted input The data defined in the above sections will be saved in a specially formatted input file which has the following structure T SECTION DEFINITION GT SECTION NAME TsecName WEB HEIGHT OGLEFT WEB THICKNESS tw ORIGHT WEB THICKNESS tw OTOP LEFT FLANGE WIDTH 1 war TOP_LEFT_FLANGE_THICKNESS tar TOP_FLANGE_REINFORCE_THICKNESS ty
28. stresses menu item or toolbar icon causes the display of the axial stress field over the cross section under the applied sectional loads Examples are shown in fig 2 30 fig 2 45 fig 2 66 and fig 2 92 5 Clicking the Shear stresses menu item or toolbar icon causes the display of the shear stress field over the cross section under the applied sectional loads Examples are shown in fig 2 55 and fig 2 73 6 Clicking the Reserve Factors menu item or toolbar icon causes the display of the reserve factor field over the cross section under the applied sectional loads When the menu item or toolbar icon Reserve Factors is pressed the reserve factors are computed over the cross section and the inverse of the reserve factor is displayed Examples are shown in fig 2 72 and fig 2 91 The visualization of the centers and principal axes can be superimposed onto the display of these various fields 1 5 3 Step 3 Interactive definition of sensors The last step of the visualization phase is the optional interactive definition of sensors The last three entries or icons of the Loading menu shown in fig 1 9 are used to that effect two options are possible 1 a temporary display the warping displacement stress or strain levels at a point of the cross section or 2 the interactive definition of sensors Temporary display of warping displacement stress or strain levels It is often important to obtain numerical rather than graphical information
29. 1 and can be of the following type airfoil sections as described in section 2 1 circular arcs as described in section 2 2 C sections as described in section 2 3 circular cylinders as described in section 2 4 double boxes as described in section 2 5 I sections as described in section 2 6 rectangular boxes as described in section 2 7 rectangular sections as described in section 2 8 circular tubes as described in section 2 9 triangular sections as described in section 2 10 or T sections as described in section 2 11 Sections Builder Geometr Airfoil section 1 Circular arc Circular cylinder Circular tube C section Double box I section Rectangular box Rectangular section Triangular section T section Figure 2 1 The section menu 27 28 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 1 Definition of airfoil sections Airfoil sections are parametric configurations with no internal web as depicted in fig 2 2 or with one or two internal webs as shown in fig 2 3 and 2 4 respectively Airfoil sections consist of top and bottom flanges with optional internal webs The section consists of up to three zones to which independent material properties can be assigned t c Figure 2 2 Configuration of the Airfoil Section with no web c 2 Figure 2 3 Configuration of the Airfoil Section with a single web Airfoil sections are defined by means of four dialog tabs 1 The Airfoil section dialog tab
30. 6 x 6 matrix N Ci Ci Cu Cis Cio E1 Vo Cio C22 Cos C24 Cos Cog 2 V3 C23 C33 C34 C35 C36 E3 1 2 M Cia Coa C34 Cas gp ES 0 M3 Cis Cos C35 Cas Css Cse M3 Cie C36 Cse Coe K3 10 CHAPTER 1 INTRODUCTION The three forces V2 and Vs are positive along axes 21 72 and 73 respectively whereas moments M M and Ms are positive about axes 71 72 and 73 respectively as depicted in fig 1 2 Identical sign conventions are used for the three strains 1 2 and and curvatures Kg and respectively The three forces are the resultants of the stress distributions over the cross section the three moments are computed with respect to the origin of the coordinate system i e with respect to the reference axis of the beam as depicted in fig 1 2 e The 6 x 6 sectional compliance matriz S the inverse of the sectional stiffness matrix i e S C7 and hence 5 1 3 It is often the case that the 6 x 6 stiffness matrix defined by eq 1 2 contains a number of vanishing terms and presents the following structure Ni Cu 0 0 0 Ci5 E1 Vo 0 Ca 0 0 E2 Vs C33 C34 0 0 E3 1 4 M 0 Coa C34 Cu 0 0 K1 i M Cis 0 0 0 Css M3 Cig 0 0 0 K3 In such cases the complete problem splits into an axial force bending moment problem characterized by the following 3 x 3 stiffness matrix Cu Cis Cio 1
31. A A s 111 2 10 1 The Triangular sechon name dialog taD o co raa so RR En 112 2 10 2 The Dimensions dialog ss saa soo s W oo xo ee S E 113 2 10 3 The Materiqig dialog tab zz ooo RR ORE x 114 2 104 Input nno gom ow wow b Mob Ek ROO wy m wow Mos e Ree ded eg 3 116 2 10 5 Examples oca doses toe odo LEE OE dede de we eyed 117 2 11 Deneidon of ropa s new 9 i PRESS EES ng W NGA ROB OR A d 118 2 11 1 The T seciton dialog tab 209 u ce cay y II PRAECEDENS RR Bed 119 2 11 2 The Dimensions dialog tab 2 o utia Q Q GS FE RR eumd Rd 120 2 41 3 The Materials dialog tab c Q Coa Rew amp m W depo ee RR ES REX 121 SOLLI 244 EG 43 OR Som DR Re or eee DE x 123 3115 EX pep Loo Qe qe e A AO AC IRURE ee EON EUR dude Net de de Q 124 Builder 127 el TOUOQ Gb 0 a OYE oe ee ele ee eae Bee wee 127 Gla ESARET u u u ee Ra Boe SE eee ee eee Ge be eek Q 127 22 Denion OD Wass 2 nwa asc w SOG SHH A aa WIR Foe kh 08 Q 129 3 21 Wall geometiy u u kuy y eee bebe Q Q W M Se ww ee Oe o3 3 129 32 2 Wall stacking soos s o 44 X X W eS ae ee EON Q h d 129 9 4 0 Formatted inpub xu naa Tad ae 0444 ae eed aden de EUROS ed dG 131 3254 RXSMD IBE oasa ee ex Rag hg x RAE S amp aa aca a CRUCES S gs 132 23
32. Builder path Enter here the complete path to the installation directory for SECTION BUILDER typically the path is C SectionBuilder 178 CHAPTER 8 UTILITY OBJECTS 8 5 Definition of Sensors It is important to obtain numerical information about the displacement stress or strains in the cross section when subjected to a given sectional loads This is achieved by defining sensors at specific location of the cross section Sensor can be defined in two manners Sensors can be defined more expeditiously during the visualization phase of the analysis see section 8 6 8 6 The Sensor dialog window Sensor Sensor name Senso Sensor type m Target object Stresses du Location C Warping Frame name Figure 8 5 The Sensor dialog window The Sensor dialog window defines the sensor with the following data 1 Sensor name Enter a unique name for the sensor 2 Sensor type Select Stresses Strains or Warping for the sensor to compute the six stress components the six strain components or the three warping components respectively 3 Target object To locate the sensor at a point of the cross section it is necessary to specify the solid element on which the sensor is located then its exact position within this solid element By defining the sensor in the visualization phase see section 8 6 it is not necessary to provide this information Enter the name of the solid element on which the sensor will be located 4
33. F CIRCULAR TUBES 105 2 9 1 The Circular tube dialog tab Circular Tube Circular tube Dimensions Materials Section name ube Figure 2 75 The Circular tube dialog tab The Circular tube dialog tab as described in fig 2 75 defines the following data for the circular tube 1 Section name Enter a unique name for the Circular Tube 2 Mesh density Enter the desired mesh density as described in section 5 1 for the finite element discretization 3 Defined in frame The geometry of the circular tube can be defined with respect to a fixed frame as described in section 7 1 allowing translation and rotation of the section as a rigid body 106 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 9 2 The Dimensions dialog tab Circular Tube Circulartube Dimensions Materials Figure 2 76 The Dimensions dialog tab The Dimensions dialog tab as described in fig 2 76 defines the dimensions of the circular tube shown in fig 2 74 The dimensions of the section are defined by two parameters 1 The outer radius Ro of the circular tube required input 2 The inner radius Rr of the circular tube required input 2 9 DEFINITION OF CIRCULAR TUBES 107 2 9 3 The Materials dialog tab Circular Tube Circulartube Dimensions Materials Figure 2 77 The Materials dialog tab The Materials dialog tab as described in fig 2 77 defines the materials the circular tube is made of It is possible to assign
34. LLS 129 3 2 Definition of walls As discussed in section 1 a general beam section is defined as an assembly of interconnected walls see fig 3 1 3 2 1 Wall geometry The geometry of a wall is is defined by an oriented planar curve as shown in fig 3 3 defined in terms of its NURBS representation 2 3 Each point on the curve is associated with a variable 7 the curve is defined between points A and B corresponding to 7 0 and 7 1 respectively Along the curve the unit tangent and normal vectors denoted t and respectively are defined such that points in the direction of increasing values of 7 and unit vectors t correspond to a planar rotation of unit vector 75 273 It now becomes possible to define the upper and lower portion of the wall the upper portion of the wall is located above the curve i e in the direction of n whereas the lower portion of the wall is located below the curve Upper wall Lower wall Figure 3 3 General configuration of a wall 3 2 2 Wall stacking sequence The upper and lower walls consist of a number of layers stacked on top and below the curve respectively Fig 3 3 shows an upper wall consisting of three layers denoted Layeri Layer2 and Layer3 whereas the lower wall consists of layers Layer4 Layer5 and Layer6 Each layer has a specific thickness for instance layers Layer2 and Layer3 are of thickness t gt and ts respectively Layers do not necessarily span the entire
35. Location Enter the coordinates of the location of the sensor within the solid element Here again by defining the sensor in the visualization phase see section 8 6 it is not necessary to provide this information Bibliography 1 LH Abbott and A E Von Doenhoff Theory of Wing Sections Dover Publications Inc New York 1959 2 G E Farin Curves and Surfaces for Computer Aided Geometric Design Academic Press Inc Boston third edition 1992 L Piegl and W Tiller The Nurbs Book Springer Verlag Berlin New Jersey second edition 1997 R M Jones Mechanics of Composite Materials Taylor amp Francis Philadelphia second edition 1999 R M Christensen Mechanics of Composite Materials John Wiley amp Sons New York 1979 ct C S W Tsai and H T Hahn Introduction to Composite Materials Technomic Publishing Co Inc West port CT 1980 179
36. NGLE ow BOTTOM_FLANGE_REINFORCE_THICKNESS ty WEB_MATERIAL_NAME WebMaterialName TOP_REINFORCE_MATERIAL_NAME TopMaterialName BOTTOM_REINFORCE_MATERIAL_NAME BottomMaterialName IS_DEFINED_IN_FRAME FxdFrameName MESH_DENSITY md 2 3 DEFINITION OF C SECTIONS 57 2 3 5 Examples A few examples that describe the construction procedure of this type of section are shown below Example 1 This example shows a C section Here web height web thickness top flange width web material and mesh density are assigned for constructing this section This example also shows the shear strain field over the cross section under the applied sectional loads i ill AAP nt a aa rn CHE T KEEL LL Figure 2 29 Example 1 C Section Example 2 This example shows also a C section with skewed top and bottom flanges Here web height web thickness top flange width top flange thickness flange reinforce thicknesses flange skew angles materials and mesh density are assigned for constructing this section This example also shows the axial stress field over the cross section under the applied sectional loads Example 3 This example shows a reverse L section Here web height web thickness top flange width bottom flange width 0 web material and mesh density are assigned for constructing this section This example also shows principal centroidal axes of bending Example 4 T
37. RCE_THICKNESS ty BOTTOM_RIGHT_FLANGE_WIDTH wore BOTTOM_RIGHT_FLANGE_SKEW_ANGLE ow WEB_MATERIAL_NAME WebMaterialName TOP_REINFORCE_MATERIAL_NAME TopMaterialName BOTTOM_REINFORCE_MATERIAL_NAME BottomMaterialName IS_DEFINED_IN_FRAME FxdFrameName MESH_DENSITY md 2 7 5 Examples A few examples that describe the construction procedure of this type of section are shown below Example 1 This example shows a rectangular box with skewed flanges Here height web thicknesses flange widths flange skew angles materials and mesh density are assigned for constructing this section This example also shows the principal centroidal axes of bending Example 2 This example shows a rectangular box with top and bottom flange reinforcements Here height web thicknesses flange widths flange thickness bottom left flange skew angle materials and mesh density are assigned for constructing this section This example also shows the axial stress field over the cross section under the applied sectional loads 2 7 DEFINITION OF RECTANGULAR BOXES Figure 2 65 Example 1 Rectangular Box Figure 2 66 Example 2 Rectangular Box 95 96 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 8 Definition of rectangular sections Rectangular sections are parametric configurations of the shape depicted in fig 2 67 They consist of a rectangular section possibly reinforced by top and or bottom flanges The section consi
38. SS tia LAYER_MATERIAL MaterialName LAYER_NAME LayerName3 GINITIAL STATION eta0 FINAL STATION etal LAYER_THICKNESS tLayer3 LAYER_MATERIAL MaterialName Similarly add all other layers information here CONNECTED AT 1 WallName QGCONNECTED AT 0 WallName CURVE_NAME CurveName ADD DROP ZONE SIZE delta MESH DENSITY nma 132 CHAPTER 3 BUILDER 3 2 4 Examples A few examples that describe the construction procedure of this type of section are shown below Example 1 This example shows a wall that has five layers Each layer may have different materials Ply add drop is also shown here The mesh density can also be adjusted base on the requirement This example also shows the axial stress field over the cross section under the applied sectional loads Figure 3 6 Example 1 Wall with arbitrary lay ups Example 2 This example mainly shows the connection between two walls Both walls have equal number of layers at the connection The material properties of the layers need to be compatible at the joining position The tangents of the base curves of the walls should also be equal or comparable the angle between them should be less than 10 degrees Both walls may have ply add drop Ply add drop is not allowed at the connection position This example also shows the principal axes of shearing at the shear center 3 2 DEFINITION OF WALLS 133 Figure 3 7 Example 2 Connection between two
39. Section Builder User s Manual Olivier A Bauchau School of Aerospace Engineering Georgia Institute of Technology Atlanta GA USA February 6 2007 Contents 1 2 Introduction 1l Overview of SechonmDaWdeP a a W RR E RU ee 12 Definition of the beard cross section cs sso og eee Q w s s W LA Q Q lt L3 Meshing the Gross sectiol Q 9 amp a bon n RK QUQ Wu e W W VIR RO E OR 1 4 Performing the finite element analysis 11 1 Sectional properties 22e soe em oon hada g Ree E x x0 xeberer ES ee 1 4 2 Three dimensional stresses and Tap Visualizing Che f sulis o cw Q s k h w s 9 k k k kO Que Ee MON 1 5 1 Step 1 Selecting a sectional loading case 1 5 2 Step 2 Selecting the quantities to be visualized 1 2 llle 1 5 8 Step 3 Interactive definition of sensors 15 4 Ihe Graphics menu and toolbar o s ra saa sas dasrda PCR EX s 1 6 Installation of SectionBuilder o ee mm S a x Rd LOL Directory strmeti eue Loo a OX XX ee eee ey JE Poppa BEBE og a a Oe ORE Re oe ee Qua g usus ale Q Q LOS Output les e uos sos aes dob e d Qum m h WOW d a w sisan S S gp ls ES 106 4 Installation Procedure ee Rh GRON Xem eae ee P3 4 Parametric shape configurations 2 1 JDehnition
40. The Circular Arc dialog tab Circular Arc Circular Arc Dimensions Materials Section name 2 Figure 2 13 The Circular Arc dialog tab The Circular Arc dialog tab as described in fig 2 13 defines the following data for the circular arc 1 Section name Enter a unique name for the circular arc 2 Mesh density Enter the desired mesh density as described in section 5 1 for the finite element discretization 3 Defined in frame The geometry of the circular arc can be defined with respect to a fixed frame as described in section 7 1 allowing translation and rotation of the section as a rigid body 40 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 2 2 The Dimensions dialog tab Circular Arc Figure 2 14 The Dimensions dialog tab The Dimensions dialog tab as described in fig 2 14 defines the dimensions of the circular arc shown in fig 2 12 The dimensions of the section are defined by the following parameters 1 The outer radius Ro and inner radius Rr of the circular tube required input 2 The initial angle and final angle of the circular arc both measured in degrees required input Note 0 lt 0 lt 360 0 lt 0p lt 360 and 0 lt Even when 6 0 and 360 the circular arc is still an open circular tube 2 2 DEFINITION OF CIRCULAR ARCS 41 2 2 3 The Materials dialog tab Circular Arc Figure 2 15 The Materials dialog tab The Materials dialog ta
41. The skew angle or of the top flange positive down measured in degrees default value apf 0 4 The thickness tpr of the bottom reinforcement flange this thickness applies to both left and right reinforcements which cannot exist independently of each other default value ty 0 This variable is also used as flag for the presence of the bottom flange reinforcement if ty gt 0 this reinforcement is present 48 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 3 3 The Materials dialog tab C section C section Dimensions Materials Bottom Flange Figure 2 21 The Materials dialog tab The Materials dialog tab as described in fig 2 21 defines the materials the C section is made of As shown in fig 2 22 the section is divided into three zones 1 The top reinforcement flange consists of a single solid labeled 2 The C section it self consists of the solids labeled TFlg Web BF lg 3 The bottom reinforcement flange consists of a single solid labeled BFIgR It is possible to assign material properties as described in section 4 1 or solid properties as described in section 4 2 to each zone of the C section Special Cases 1 If the width 0 the section looks like L shape depicted in fig 2 23 This L shape section does not have TFlgR and TFlg solids shown in fig 2 24 2 If the width 0 the section looks like reverse L shape depicted in fig 2 25 This reverse L shape section does no
42. _SKEW_ANGLE ais TOP_FLANGE_REINFORCE_THICKNESS tea BOTTOM_FLANGE_WIDTH BOTTOM_FLANGE_THICKNESS tyt BOTTOM_FLANGE_SKEW_ANGLE ow BOTTOM_FLANGE_REINFORCE_THICKNESS ty LEFT_WEB_MATERIAL_NAME LWebMaterialName RIGHT_WEB_MATERIAL_NAME RWebMaterialName TOP_REINFORCE_MATERIAL_NAME TopMaterialName BOTTOM_REINFORCE_MATERIAL_NAME BottomMaterialName IS_DEFINED_IN_FRAME FxdFrameName MESH_DENSITY md 2 6 5 Examples A few examples that describe the construction procedure of this type of section are shown below Example 1 This example shows an I section Here web height web thicknesses flange widths flange thicknesses web materials and mesh density are assigned for constructing this section This example also shows the shear stress field over the cross section under the applied sectional loads Example 2 This example shows an I section with top and bottom reinforcements Here web height web thicknesses flange widths flange reinforcement thicknesses materials and mesh density are assigned for constructing this section This example also shows the axial strain field over the cross section under the applied sectional loads Example 3 This example also shows a Z section without any reinforcement Here web height web thicknesses flange widths here wy 0 and 0 materials and mesh density are assigned for constructing this section This example also shows principal centroida
43. a dimensional quantity default value tw2 0 This variable is also used as a flag for the presence of the second web if tw2 0 two webs are present 2 The location bw2 of the intersection of the second web with the lower airfoil profile this is a dimen sional quantity default value tpw2 tw2 3 The thickness t w2 of the left portion of the second web default value tiw2 tta1 4 The thickness trw2 of the right portion of the second web default value trw2 tta2 34 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 1 4 The Materials dialog tab Airfoil Section Airfoil section Airfoil profile Dimensions Materials Material 2 Material 3 Figure 2 8 The Materials dialog tab The Materials dialog tab as described in fig 2 8 defines the materials from which the airfoil section is made As shown in fig 2 9 the section is divided into three zones 1 The front portion of the airfoil consists of the components labeled Flg1U Flg1L and LWeb1 2 The middle portion of the airfoil consists of the components labeled RWeb1 Flg2U Flg2L LWeb2 these components are present in the single and dual web designs only 3 The aft portion of the airfoil consists of the components labeled RWeb2 Flg3U Flg3L TedU and TedL these components are present for the dual web design only It is possible to assign material properties as described in section 4 1 or solid properties as described in sectio
44. able tensile and compressive stresses along axis are denoted a T and cC respectively Similarly the allowable tensile and compressive stresses along axis are denoted 087 and o2 respectively Finally the allowable shear stresses in plane 61 is denoted All these quantities are defined in section 4 1 4 The two coefficients and F gt are Fi 9 e 7 o1 T 0191 2 4 5 and Fy 08 087 03 03 4 6 The last coefficient is Fia o97 03 o TgtC i2 4 7 2 Maximum Strain Criterion This criterion is used for transversely isotropic material only At failure one of the following equations is satisfied aT _ Jf er EQ OX x BE if a lt 0 4 8 aT _ Jf of E2 if lt gt O 2 o8 E if lt 0 4 9 VS 715 G12 4 10 where e and are the strains along the material axes e and e respectively and the corresponding shear strain The allowable tensile and compressive stresses along axis are denoted and c1 respectively Similarly the allowable tensile and compressive stresses along axis are denoted oT and 03 respectively Finally the allowable shear stresses in plane is denoted All these quantities are defined in section 4 1 4 4 1 DEFINITION OF MATERIAL PROPERTIES 157 3 Maximum Stress Criterion This criterion is used for transversely isotropic material only At failure one of the following equations
45. about the warping displacement stress or strain levels at a point of the cross section This can be done by selecting a specific finite element from the model then displaying the stresses or strain at that point The procedure is as follows 22 CHAPTER 1 INTRODUCTION 1 Enter the visualization mode select a loading condition and visualize warping displacement stress or strain fields These steps are described in sections 1 5 1 and 1 5 2 To select an element of the finite element mesh first click the Select Element menu item or toolbar icon then click on the desired element that element will be highlighted as shown in fig 1 10 Next click the Element Stresses menu item or toolbar icon to display the stresses or strain at the center of the element If the warping displacement stress or strain field is presently visualized warping displacement stress or strain levels will be displayed respectively Fig 1 10 illustrate this process while the shear stress field is visualized An element of the mesh is selected and is highlighted as shown on the figure The temporary pop up display gives the three dimensional stress components at the center point of the selected element Once the OK icon is clicked the box disappears and no record is kept of the stress level at that point If a permanent record of the stress level is desired the interactive definition of a sensor should be used as discussed in the next section b
46. as described in section 2 1 1 which defines the name of the section 2 The Airfoil profile dialog tab as described in section 2 1 2 which defines the outer geometry of the section as a NACA four digit series airfoil 3 The Dimensions dialog tab as described in section 2 1 3 which defines the dimensions of the section 4 The Materials dialog tab as described in section 2 1 4 which defines the materials the section is made of 2 1 DEFINITION OF AIRFOIL SECTIONS Figure 2 4 Configuration of the Airfoil Section with two webs 29 30 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 1 1 The Airfoil section dialog tab Airfoil Section Airfoil section Airfoil profile Dimensions Materials Section name Mesh density e l Figure 2 5 The Airfoil section dialog tab The Airfoil section dialog tab as described in fig 2 5 defines the following data for the airfoil section 1 Section name Enter a unique name for the airfoil section 2 Mesh density Enter the desired mesh density as described in section 5 1 for the finite element discretization 3 Defined in frame The geometry of the airfoil section can be defined with respect to a fixed frame as described in section 7 1 allowing translation and rotation of the section as a rigid body 2 1 DEFINITION OF AIRFOIL SECTIONS 31 2 1 2 The Airfoil profile dialog tab Airfoil Section Airfoil section Airfoil profile Dimensions Materials NACA four digi
47. ascending order The layer list shown in fig 4 10 contains the following information 1 The first column of the layer list is the layer index i 2 The second column gives the starting location coordinate rj 3 The next two columns give the material coordinate system orientation angles o and 0 4 The last column gives the name of the material properties as described in section 4 1 the layer is made of The orientation angles and material properties appearing in the last line of the layer list repeat the entries on the previous line Layer list Eta location Beta 0 50000e 000 0 00000 000 Delete Material name Dismiss MatPropB 4 5505 B oran E poxy E Nb Eta Beta Gamma Material 0 00 MatPropT 300 5208 Graphite E poxy 0 13 MatPropT 300 5208 Graphite E poxy 0 25 MatPropScotchply1 002 Glass Epoxy 0 38 MatPropB4 5505 Boron E 0 50 E MatPropB4 5505 Boron Epoxy 0 63 MatPropScotchply1 002 Glass Epoxy 0 75 MatPropT 300 5208 Graphite E poxy 0 88 MatPropT 300 5208 Graphite E poxy MatPropT 300 5208 Graphite E poxy Figure 4 10 The Layer List dialog window The layer list feature 9 entries for this 8 layer stack The layer orientation angles Axes Flag set to Local The two orientation angles 9 and y define the orientation of the material axis system E 21 with respect to the global reference frame Z t1 72 73 Material properties a
48. b as described in fig 2 15 defines the materials the circular arc is made of As shown in fig 2 12 the section consists of a single zone to which it is possible to assign material properties as described in section 4 1 or solid properties as described in section 4 2 42 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 2 4 Formatted input The data that defines the circular arc as described in the above sections will be saved in a specially formatted input file which has the following structure CIRCULAR_ARC_DEFINITION CIRCULAR_ARC_NAME TboxName INNER_RADIUS R OUTER RADIUS Ro THETA INITIAL 6 THETA FINAL 0r MATERIAL_PROPERTY_NAME MaterialName IS_DEFINED_IN_FRAME FxdFrameName MESH_DENSITY md 2 2 DEFINITION OF CIRCULAR ARCS 43 2 2 5 Examples A few examples that describe the construction procedure of this type of section are shown below Example 1 This example shows a circular arc Here the inner and outer radii initial 0 degree and final 180 degrees angular positions of the arc material and mesh density are assigned for constructing this section This example also shows the principal axes of shearing at the shear center Figure 2 16 Example 2 Circular Arc Section Example 2 This example shows a circular arc Here the inner and outer radii initial and final angular positions of the arc material and mesh density are assigned for constructing this section This exampl
49. ded into three zones 1 The top reinforcement flange consists of a single component labeled T FIgR 2 The central portion of the section consists of a single component labeled Core 3 The bottom reinforcement flange consists of a single component labeled BFIgR It is possible to assign material properties as described in section 4 1 or solid properties as described in section 4 2 to each zone of the rectangular section 100 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS Figure 2 71 Solid zones of the rectangular section 2 8 DEFINITION OF RECTANGULAR SECTIONS 101 2 8 4 Formatted input The data defined in the above sections will be saved in a specially formatted input file which has the following structure RECTANGULAR SECTION DEFINITION GRECTANGULAR SECTION NAME TboxNane WIDTH v HEIGHT QCORE MATERIAL NAME 1 CoreMaterialName QOTOP REINFORCE MATERIAL NAME TopMaterialName QBOTTOM REINFORCE MATERIAL NAME BottomMaterialName 15 DEFINED IN FRAME FxdFrameName MESH_DENSITY md 102 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 8 5 Examples A few examples that describe the construction procedure of this type of section are shown below Example 1 This example shows a rectangular section Here width height frame core material and mesh density are assigned for constructing this section This example also shows the inverse of the reserve factor field over the cross section under the a
50. defined with the help of the circular tube predefined section as described in section 2 9 1 Figure 2 34 Configuration of the circular cylinder Circular cylinders are defined by means of three dialog tabs 1 The Cylinder dialog tab as described in section 2 4 1 which defines the name of the section 2 The Dimensions dialog tab as described in section 2 4 2 which defines the dimensions of the section 3 The Materials dialog tab as described in section 2 4 3 which defines the materials the section is made of 2 4 DEFINITION OF CIRCULAR CYLINDERS 61 2 41 The Cylinder dialog tab Cylinder Cylinder Dimensions Materials Section name Figure 2 35 The Cylinder dialog tab The Cylinder dialog tab as described in fig 2 35 defines the following data for the circular cylinder 1 Section name Enter a unique name for the circular cylinder 2 Mesh density Enter the desired mesh density as described in section 5 1 for the finite element discretization 3 Defined in frame The geometry of the circular cylinder can be defined with respect to a fixed frame as described in section 7 1 allowing translation and rotation of the section as a rigid body 62 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 4 2 The Dimensions dialog tab Cylinder Cylinder Dimensions Materials Figure 2 36 The Dimensions dialog tab The Dimensions dialog tab defines the dimensions of the circular cylinder shown in fig 2 34 Th
51. ding Figure 2 10 Example 1 Airfoil Section Example 2 This example shows a NACA 4 digit series airfoil section The section has 2 webs The chord length the location of the webs thickness of the upper lower section and web material properties and mesh density are assigned here This example also shows the principal axes of inertia at the mass center 2 1 DEFINITION OF AIRFOIL SECTIONS Figure 2 11 Example 2 Airfoil Section with T wo Webs 37 38 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 2 Definition of circular arcs Circular arcs are predefined sections presenting the shape shown in fig 2 12 Circular arcs consist of an area included between two circular arcs spanned by a common angle The section consists of a single zone to which material properties can be assigned The circular arc is an open circular tube as shown in fig 2 12 Closed circular tubes can be defined with the help of the circular tube predefined section as described in section 2 9 Figure 2 12 Configuration of the circular arc Circular arcs are defined by means of three dialog tabs 1 The Circular Arc dialog tab as described in section 2 2 1 which defines the name of the section 2 The Dimensions dialog tab as described in section 2 2 2 which defines the dimensions of the section 3 The Materials dialog tab as described in section 2 2 3 which defines the materials the section is made of 2 2 DEFINITION OF CIRCULAR ARCS 39 2 2 1
52. e dimensions of the section are defined by a single parameter 1 The radius R of the cylinder required input 2 44 DEFINITION OF CIRCULAR CYLINDERS 63 2 4 3 The Materials dialog tab Cylinder Figure 2 37 The Materials dialog tab The Materials dialog tab defines the materials the circular cylinder is made of The section is made of a single homogeneous material It is possible to assign material properties as described in section 4 1 to the section 64 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 4 4 Formatted input The data defined in the above sections will be saved in a specially formatted input file which has the following structure CYLINDER DEFINITION CYLINDER_NAME CyldName RADIUS MATERIAL_PROPERTY_NAME MaterialName IS_DEFINED_IN_FRAME FxdFrameName MESH_DENSITY md 2 4 DEFINITION OF CIRCULAR CYLINDERS 65 2 4 5 Examples An example that describes the construction procedure of this type of section is shown below Example 1 This example shows a Circular cylinder Here radius frame definition material and mesh density are assigned for constructing this section This example also shows the warping displacement of the cross section under the applied sectional loads Figure 2 38 Example 1 Cylinder 66 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 5 Definition of double boxes Double boxes are parametric configurations of the shape depicted in fig 2 39 They consis
53. e Loading toolbar 1 First select a sectional loading case as described in section 6 1 This is an essential step because the warping stress or strain fields all depend on the applied loading More details are given in section 1 5 1 2 Second select the quantities to be visualized they fall into two main groups 1 sectional centers and principal axes and 2 the warping stress or strain fields over the cross section More details are given in section 1 5 2 3 Optionally it is also possible to interactively define sensors as described in section 8 5 at specific locations over the cross section as discussed in section 1 5 3 The Graphics toolbar controls the manner in which the requested information is to be visualized and more details are given in section 1 5 4 1 5 1 Step 1 Selecting a sectional loading case The first step of the visualization phase is to select a sectional loading condition as provided by the sectional loads see section 6 1 These user defined loading conditions form a list of loading conditions The first three entries or icons of the Loading menu shown in fig 1 9 are used to navigate this loading list 20 CHAPTER 1 INTRODUCTION Loading Materials Analysi Step 1 Sectional loading Reference lt H selection First loading Next loading b j lu lt B Sectional centers Princ axes Bending aie Princ axes Shearing b amp principal axes Princ axes Inertia
54. e also shows the shear strain field over the cross section under the applied sectional loads CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 44 Figure 2 17 Example 2 Circular Arc Section 2 3 DEFINITION OF C SECTIONS 45 2 3 Definition of C sections C sections are parametric configurations of the shape depicted in fig 2 18 They consist of a C section possibly reinforced by top and or bottom flanges The section consists of up to three zones to which independent material properties can be assigned Note that through the use of fixed frames as described in section 7 1 the C section can be made to look like the following shapes Ll or Wir Wor Figure 2 18 Configuration of the C section C sections are defined by means of three dialog tabs 1 The C section dialog tab as described in section 2 3 1 which defines the name of the section 2 The Dimensions dialog tab as described in section 2 3 2 which defines the dimensions of the section 3 The Materials dialog tab as described in section 2 3 3 which defines the materials the section is made of 46 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 3 1 The C section dialog tab C section Figure 2 19 The C section dialog tab The C section dialog tab as described in fig 2 19 defines the following data for the C section 1 Section name Enter a unique name for the C section 2 Mesh density Enter the desired mesh density as described in secti
55. e stress components and are listed at the sensor location Fig 1 8 shows the sign convention used for the stress computation Sensor SensorStresses Sensor location 12 r3 2 7e 02 4 7e 02 m Out of plane stresses 01 712 713 3 0e 04 0 0e 00 0 0e 00 Pa In plane stresses 02 03 1 7e 10 9 9e 11 1 2e 10 Pa Reserve factors 2 0 04 2 0e 04 Table 1 2 Print out of the three dimensional strains at a sensor location Figure 1 8 Sign convention for the three dimensional stresses acting on a differential element of the beam 1 5 VISUALIZING THE RESULTS 19 Three dimensional strains Under the effect of the applied loading the cross section will deform generating a three dimensional strain field which features both in and out of plane components on the cross section Since the cross section is in plane 75 23 the in plane strain components are and whereas the out of plane strain components are 1 Yi2 and Note that classical beam theory predicts only the the out of plane strain component 1 and the two transverse shearing strains and 713 typically the in plane strain components are ignored because the Euler Bernoulli kinematic assumptions correspond to a rigid body motion of the cross section i e 0 y23 0 and 0 The analysis implemented in SectionBuilder predicts both out of plane and in plane strain comp
56. ed in section 7 1 allowing translation and rotation of the section as a rigid body 120 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 11 2 The Dimensions dialog tab T section T section Dimensions Materials Top left flange Top right flange Figure 2 88 The Dimension dialog window The Dimensions dialog tab as described in fig 2 88 defines the dimensions of the T section shown in fig 2 86 The dimensions of the section are defined by the following parameters Web dimensions 1 The height h of the section required input 2 The thickness tiy of the left part of the web required input 3 The thickness trw of the right part of the web required input Top left flange dimensions 1 The width of the top left flange required input 2 The thickness tur of the top left flange default value tag tiw 3 The skew angle our of the top left flange positive up measured in degrees default value our 0 4 The thickness tir of the top reinforcement flange this thickness applied to both left and right rein forcements that cannot exist independently of each other default value t 0 This variable is also used as flag for the presence of the top flange reinforcement if tir gt 0 this reinforcement is present Top right flange dimensions 1 The width wer of the top right flange default value wire war 2 The thickness fu of the top right flange default value tir trw 3 The
57. ee wee OR A b gef a 6 Applied loading 6 1 Sectional loads 2000 son eee Se eee EES Boe be moe hmm QU e Ee Vea 6 1 1 The Sectional loads dialog window leen 7 Geometric elements 4 1 ot fined Mames 206 9 9x ox Roe lard xS 7 2 The Fixed frame dialog window 4 Tal Worsted 2 0L ix Z t but s 3 9 9 W w W eee ee ERE Reb CR OX ROR DS 8 Utility objects 8 1 Definition of the Include command lee 8 2 The Include command dialog Window 222924443343 Eee s s REOR Rm OR 821 Formatted 2 225499 4A 4 Ron no dem e deed Og cz eU Ae APRESS CARER ME Nae d usc sg 84 The Options dialog window n cst eee badd Dee o hmmm RR seo Denion Gi 21010 E wg eR ace ee eS Ok s 8 6 The Sensor dialog window eee e Q Q Q Q 136 137 138 141 142 144 146 147 149 151 152 154 156 158 159 160 161 162 CONTENTS Chapter 1 Introduction 1 1 Overview of SectionBuilder SECTIONBUILDER analyzes beam cross sections The analysis proceeds in four steps The menu of SEC TIONBUILDER depicted in fig 1 1 reflects these four steps 1 First the configuration of the cross section is defined this step is discussed in section 1 2 The two dimensional geometric configuration of the section must be defined together with the physical prop erties
58. eft portion of the double box itself consists of components labeled TLFlg LWeb and BLFlg 3 The right portion of the double box itself consists of components labeled TRFlg RWeb and BRF lg 4 The top reinforcement flange consists of components labeled BLFlgR and BRFIgR It is possible to assign material properties as described in section 4 1 or solid properties as described in section 4 2 to each zone of the double box 2 5 DEFINITION OF DOUBLE BOXES Figure 2 43 The four zones of the double box 71 72 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 5 4 Formatted input The data defined in the above sections will be saved in a specially formatted input file which has the following structure GDOUBLE BOX DEFINITION GDOUBLE BOX NAME DboxName WEB HEIGHT OGLEFT WEB THICKNESS tw ORIGHT WEB THICKNESS tw FLANGE WIDTH wis TOP_FLANGE THICKNESS tur TOP_FLANGE_SKEW_ANGLE ais TOP_FLANGE_REINFORCE_THICKNESS ty BOTTOM_FLANGE_WIDTH wy BOTTOM_FLANGE_THICKNESS tyr BOTTOM_FLANGE_SKEW_ANGLE ow BOTTOM_FLANGE_REINFORCE_THICKNESS ty LEFT_WEB_MATERIAL_NAME LWebMaterialName RIGHT_WEB_MATERIAL_NAME RWebMaterialName TOP_REINFORCE_MATERIAL_NAME TopMaterialName BOTTOM_REINFORCE_MATERIAL_NAME BottomMaterialName IS_DEFINED_IN_FRAME FxdFrameName MESH_DENSITY md 2 5 5 Examples A few examples that describe the construction procedure of thi
59. erial 2 Material density Enter the density of the material 3 Material type Materials will fall into three categories isotropic orthotropic and transversely isotropic materials 4 5 6 Orthotropic materials possess two orthogonal planes of material property symmetry implying the existence of a third as described in fig 4 4 transversely isotropic materials feature a plane of material isotropy i e properties are identical in all directions in this plane finally isotropic material have identical properties in all directions In each case a material axis system 1 is defined that reflects the existence of various planes of symmetry and or orthotropy 4 1 DEFINITION OF MATERIAL PROPERTIES 153 Orthotropic material two orthogonal planes of material property symmetry exist Planes of 7 implying the existence m of a third symmetry e e e form the material axis system Plane of isotropy e e Transversely isotropic Isotropic material material properties are identical properties identical in all directions in all directions of plane e Figure 4 4 Orthotropic transversely isotropic and isotropic materials 154 CHAPTER 4 MATERIAL PROPERTIES 4 1 2 The Stiffness dialog window Stiffness Young s moduli Shear moduli Poisson s ratio Figure 4 5 The Stiffness dialog window The Stiffness dialog window defines the stiffnesses of the material Fo
60. es a list of files to be included in the definition of a cross section An Include command is defined by a single dialog window the Include command dialog window 8 2 The Include command dialog window Include command Include command name Include123 List of files Browse Cancel Figure 8 1 The Include command dialog window The Include command dialog window defines the Include command with the following data 1 Include command name Enter a unique name for the Include command 2 List of files Enter the complete path and file name of the specific file to be included in the model as shown in fig 8 2 3 Browse Browse your computer to select the desired file as shown in fig 8 3 The way of selecting a file is preferable to spelling out the entire path and file name List of Items File name EZ Insert Delete List of File name C SectionBuilder Materials MATERIAL_SI tpl C SectionBuilder M aterials Old_MATERIAL_US old Cancel Figure 8 2 The List of files dialog window 8 2 THE INCLUDE COMMAND DIALOG WINDOW 175 Look in Materials MATERIAL SI tpl mE MATERIAL US tpl S MATERA Us JN Old_MATERIAL_US old tpl o0 Files of type Template files tpl Cancel Figure 8 3 The Browse dialog window 176 CHAPTER 8 UTILITY OBJECTS 8 2 1 Formatted input The data that defines the include command as described in the above section will be saved in a specially for
61. es illustrating the various types of cross sections that can be defined SectionBuilder Manual This directory contains the user s manual in pdf format The same document can be found online manual SectionBuilder Materials This directory contains materials properties for a number of materials in both international system of units and US units These files should not be edited SectionBuilder Templates This directory contains template files that should not be edited 1 6 2 Input files The following file types are input files for SectionBuilder e sbf These are input files to be executed by SectionBuilder The input files contain the data in the format described in this manual tpl These are input files are template files that should not be edited 1 6 3 Output files The following file types are created by SectionBuilder and contain the results of the analysis bak This file is backup file that duplicates the seb input file html This file echoes the definition of the model in hyper linked format out This file echoes the definition of the cross section and lists potential error and warning messages It can be viewed using any text editor sbp This file contains the sectional stiffness and mass properties computed by SectionBuilder This file can be viewed using any text editor sbs This file contains the three dimensional warping displacements stress components and strain components computed by SectionBuilder
62. ese walls have 2 layers This example also shows the principal axes of inertia at the mass center Figure 3 20 Example 1 Vcon connector with three Walls 148 CHAPTER 3 BUILDER Chapter 4 Material properties To fully define the cross section of a beam both its geometry and material properties must be defined Material properties are defined through the buttons of the Materials menu item shown in fig 4 1 and can be of the following type definition of material properties as described in section 4 1 or definition of solid properties as described in section 4 2 Materials Analysis GrapF Material properties 1 Solid properties Figure 4 1 The Materials menu For the purpose of discretization cross sections are divided in a number of quadrangular areas called solids For instance consider the C section shown in fig 4 2 the section is divided into three solids labeled TFlg Web and BFlg The material properties of each solid must be defined If a solid is made of a single material as depicted in the left portion of fig 4 2 the physical properties of this material must be defined This involve the definition of stiffness mass and strength characteristics of the material as discussed in section 4 1 In other cases the solid could be made of a stack of layered materials as depicted in the right portion of fig 4 2 This is a common occurrence when laminated composites materials are used It is then becomes necessa
63. h density Mesh density is an important parameter that will influence the quality of the finite element computation and consequently the accuracy of the predicted sectional stiffness characteristics and stress distributions Mesh density is controlled by an integer parameter m A characteristic overall dimension D of the section is estimated first next a characteristic finite element dimension is computed as d D m The mesh process then attempts to create finite elements that are approximately of size d The meshing process recognizes the potential presence of layered materials each layer is meshed independently to avoid smearing of the material properties 5 1 Example Consider the C section shown in fig 5 1 Mesh density parameters m 4 8 and 16 used to create the meshes illustrated in the figure Note that for m 4 and 8 a single finite element is used through the thickness of the wall For higher values of m more than two or more finite elements are used through the thickness of the wall Mesh density 8 165 8 E ee peted ehe J OOO eke 3 83 5350707 E EE H Figure 5 1 Mesh density variation effect on the C section z pti tunu tuyuna ar Len Mesh Newekskewenenenevedeqedeqsiedsdedeled sfebsfabafefafasefasaparepayatexexaney HH B H H n density 32 166 CHAPTER 5 MESH DENSITY Chapter 6 App
64. here Kk Kk N2 a E 2 ead 1 35 The principal shearing stiffnesses at the shear center K53 and K z Ko KR 2 _ A Kh Sat ia a 1 36 KS Note that the choice the orientation of the principal axis 15 given by eq 1 34 guarantees that axis 38 75 is the axis along which the minimum shearing stiffness occurs hence lt Sectional masses and moments of inertia The 6 x 6 sectional mass matriz This matrix relates the sectional linear velocities denoted v4 v9 and vs and angular velocities denoted wi w2 and ws to the sectional linear momenta denoted pi p2 and and angular momenta denoted hi hg and ha The relationship between these sectional velocities and sectional momenta takes the form of a symmetric 6 x 6 matrix Dn My Mig Mis Mio Ui p2 Moa Ms Ms v2 _ Mis M3 Ms v3 1 37 hy Mi Mo Maa Mas Mae wy ho Mis Mas Ms Mas Mss w2 h3 Mig M s Ms Mese 16 CHAPTER 1 INTRODUCTION Due to the nature of the problem many of these coefficients vanish and the remaining entries are written as pi moo 0 0 0 M0L3m 0022 Ui pa 0 Moo 0 Mo0L3m 0 0 U2 ps _ 0 0 Moo 0 0 U3 1 38 hy 0 mo0Z3m ThooX2m Ii 0 0 wi MooT3m 0 0 0 I2 Ioa mo0t2m 0 0 0 Ioa w3 where moo is the sectional mass per unit span 2m and 3m the coo
65. his example shows a L section Here web height web thickness top flange width 0 bottom flange width flange reinforce thickness materials and mesh density are assigned for constructing this section This example also shows axial stress field over the cross section under the applied sectional loads Example 5 This example shows a strip section Here web height web thickness top flange width 0 bottom flange width 0 web material and mesh density are assigned for constructing this section This example also shows principal axes of inertia at the mass center 58 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS Figure 2 30 Example 2 C Section 7 Creek LP LOL A BUMS OL OOOCOOOCOO4 siepe Pape pages eres ing Figure 2 31 Example 3 Reverse L Section 2 8 DEFINITION OF C SECTIONS T ZEE 3 Ru Figure 2 32 Example 4 L Section BH bef on HH HH HH HH bef un K3 of HH HH 3 HH un HH HH Figure 2 33 Example 5 Strip Section 59 60 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 4 Definition of circular cylinders Circular cylinders are predefined sections presenting the shape shown in fig 2 34 Circular cylinders consist of a solid circular cylinder The section consists of a single zone to which material properties can be assigned The circular cylinders are solid cylinders as shown in fig 2 34 Hollow circular cylinder or circular tubes can be
66. ibed in section 5 1 for the finite element discretization 4 Defined in frame The geometry of the triangular section can be defined with respect to a fixed frame as described in section 7 1 allowing translation and rotation of the section as a rigid body 2 10 DEFINITION OF TRIANGULAR SECTIONS 113 2 10 2 The Dimensions dialog tab Triangular section Triangular section name Dimensions Materials Web Bottom Flange Figure 2 82 The Dimension dialog window The Dimensions dialog tab as described in fig 2 82 defines the dimensions of the triangular section shown in fig 2 80 The dimensions of the section are defined by the following parameters Web dimensions 1 The height hy of the top web required input 2 The height hy of the bottom web required input 3 The thickness tw of the web required input Top flange dimensions 1 The width w of the section required input 2 The thickness tie of the top flange default value tig tw Bottom flange dimensions 1 The width w of the section required input 2 The thickness tyr of the bottom flange default value tur tw 114 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 10 3 The Materials dialog tab Triangular section Triangular section name Dimensions Materials Figure 2 83 The Materials dialog tab The Materials dialog tab as described in fig 2 83 defines the material the triangular section is made of As
67. igR 2 the C section it self consisting of the solids labeled TFlg Web BF lg and 3 the bottom reinforcement flange consisting of a single solid labeled BFIgR The physical properties of each solid must be defined If a solid is made of a single material the properties of this material can be directly defined as material properties as described in section 4 1 In other cases the solid consists of layered materials such as laminated composites it is then becomes necessary to use the present solid properties that are defined by means of two dialog windows 1 The Solid material properties dialog window as described in section 4 2 1 which defines the name of the solid properties and the axis system to be used 2 The layer List dialog window section 4 2 2 which defines the thickness orientation angle and material for each of the layers 4 2 DEFINITION OF SOLID PROPERTIES 161 4 2 1 The Solid material properties dialog window Solid material properties Solid property name SolPropBox Axes Orientation Local Along U C Global C Along V View layers Cancel OK Figure 4 8 The Solid material properties dialog window The Solid material properties dialog window as described in fig 4 8 defines the following data for the solid properties 1 Solid properties name Enter a unique name for the solid properties 2 Axes Flag This flag can be set to local or global This option will play an imp
68. information is to be visualized 1 The Zoom In and Zoom Out perform the familiar zoom in and zoom out function to focus on a specific portion of the cross section zoom in or obtain an overall view of the entire cross section zoom out 2 The Center menu item or toolbar icon brings the geometric center of the cross section to the center of the graphical window whereas the Show Model menu item or toolbar icon adjusts the zooming level so the entire cross section is visible in the graphical window 3 Although a two dimensional slice of beam is defined in the analysis three dimensional displacement stress and strain fields are computed To allow visualization of stress and strain components it is often necessary to rotate the model in the graphical window The six entries or icons Rotate X Rotate X Rotate Y Rotate Y Rotate Z and Rotate Z rotate the model by 5 degrees about the X Y and Z axes respectively The X Y and Z axes are screen axes 24 CHAPTER 1 INTRODUCTION 4 Similarly the four entries or icons Translate X Translate X Translate Y and Translate Y translate the model by 5 along the X or Y axes respectively 5 The View From X1 menu item or toolbar icon reset the view point so that the structural axis is now perpendicular to the plane of the screen 6 The size of the symbols used in the visualization can be adjusted using the Symbol size or Symbol size entries or icons The symbols are the
69. information of WallA at U 0 and WallB at U 1 Di are the middle points of Ai and Bi Aai and Bbi i 1 2 3 n are generated from the rest of the layers information of WallA at U 0 and WallB at U 1 Ci and Cci are constructed from the upper and lower parts of WallC at U 0 respectively Ei are the intersection points of the tangents of the layers of WallA at U 0 and upper part of WallC at U 0 Fi are the intersection points of the tangents of the layers of WallB at U 1 and lower part of WallC at U 0 Curves and surfaces are constructed using these points Finally solid is defined using the material and mesh properties TRFlgR and TLFlgR are constructed form the pass through layers information of WallA and WallB respectively TRFlg and TLFlg are constructed form the other layers information of WallA and WallB Where as RWeb and LWeb are constructed form the upper and lower parts of WallC information respectively 3 4 DEFINITION OF TCON SECTIONS 139 Figure 3 12 Three walls can be connected as above with a Tcon L Pass Thu Pass Thu Layers Layers Wall A Figure 3 13 Three walls and Tcon in upward direction in detail For downward Tcon shown in fig 3 14 points Ai and Bi i 1 2 3 n are generated from the pass through layers of WallA at U 1 and WallB at U 0 Like before Di are the middle points of Ai and Bi Aai and Bbi i 1 2 3 n are generated from the rest of the layers information
70. ions Triangular sections are parametric configurations of the shape depicted in fig 2 80 They consist of a triangular section which can be open or closed The section consists of a single zone which material properties can be assigned Note that through the use of fixed frames as described in section 7 1 the triangular section can be made into the following shapes A lt gt or h Closed Open section section Figure 2 80 Configuration of the triangular section with open or closed section Triangular sections are defined by means of three dialog tabs 1 The Triangular section name dialog tab as described in section 2 10 1 which defines the name of the section 2 The Dimensions dialog tab as described in section 2 10 2 which defines the dimensions of the section 3 The Materials dialog tab as described in section 2 10 3 which defines the materials the section is made of 112 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 10 1 The Triangular section name dialog tab Triangular section Triangular section name Dimensions Materials Section name Figure 2 81 The Triangular section name dialog tab The Triangular section name dialog tab as described in fig 2 81 defines the following data for the triangular section 1 Section name Enter a unique name for the triangular section 2 Section status Select an open or closed section 3 Mesh density Enter the desired mesh density as descr
71. ions dialog tab Double Box Double Box Dimensions Materials Left wall Web Right wall Bottom left flange Bottom right flange Figure 2 41 The Dimensions dialog tab The Dimensions dialog tab as described in fig 2 5 2 defines the dimensions of the double box shown in fig 2 39 The dimensions of the section are defined by the following parameters Web dimensions 1 The height h of the section required input 2 The thickness tiy of the left part of the web required input 3 The thickness tyw of the right part of the web required input Top left flange dimensions 1 The width wyr of the top left flange required input 2 The thickness tur of the top left flange default value tag tiw 3 The skew angle our of the top left flange positive up measured in degrees default value 0 4 The thickness tir of the top reinforcement flange this thickness applies to both left and right rein forcements that cannot exist independently of each other default value ta 0 This variable is also used as flag for the presence of the top flange reinforcement if tj gt 0 this reinforcement is present Top right flange dimensions 1 The width wire of the top right flange default value wire wur 2 The thickness tr of the top right flange default value t trw 3 The skew angle aire of the top right flange positive up measured in degrees default value ae r 0 Bottom
72. is ply add drop feature gives the freedom for designing a realistic airfoil section after connecting several walls with various connectors i e Tcon Vcon Split etc Two walls with arbitrary lay ups can be connected using GCONNECTED AT 0 and CONNECTED AT 1 command For connecting the initial position of a wall with the final position of another wall QCONNECTED AT 0 command is used On the other hand GCONNECTED AT 1 command is considered for connecting the final position of a wall with the initial position of another wall as depicted in fig 3 5 The number of layers for walls must be equal at the connection The layer thickness and material properties should also be compatible at the connection position of two walls Before Connection Wall A Wall B CONNECTED AT 1 WallB CONNECTED AT O WallA U 0 U 1 U 0 U 1 After Connection Wall A Wall B Figure 3 5 Connection of two Walls 3 2 DEFINITION OF WALLS 131 3 2 3 Formatted input The data defined in the above sections will be saved in a specially formatted input file which has the following structure SECTION DEFINITION WALL SECTION NAME WallName UPPER LOWER_WALL_DEFINITION LAYER_DEFINITION LAYER_NAME LayerName1 GINITIAL STATION eta0 FINAL STATION etal QLAYER THICKNESS tiae LAYER_MATERIAL MaterialName LAYER_NAME LayerName2 INITIAL_STATION eta0 FINAL STATION etal LAYER_THICKNE
73. l axes of bending Example 4 This example shows a Z section with top and bottom reinforcements Here web height web thicknesses flange widths here 0 and wy 0 flange reinforcement thicknesses materials and mesh density are 2 6 DEFINITION OF I SECTIONS 85 EMAXLAXCOILLITITTILIIIITITIZM ri z LII a d u D DA I HIR A VIA dece ded de sik sk se se o fe a AY Y 21 4 U TOP MUNI Figure 2 55 Example 1 I section assigned for constructing this section This example also shows the axial stress field over the cross section under the applied sectional loads Example 5 This example shows a T section with top reinforcement Here web height web thicknesses flange widths here 0 and 0 flange reinforcement thicknesses materials and mesh density are assigned for constructing this section This example also shows the principal axes of inertia at the mass center CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 86 Figure 2 56 Example 2 I section ug ng 8 E Bi i ee DOC CLCE KE 1311 DOO IONE E3 18 EEELEELUELLUEUULUUPEXYNSSCCNSN SUR Hunnununuuuuutuuuuuuuoo0002 t nunmuunuunuunUununoPr 20000020 HHHHUHBUBUDOUU TU uadguuuwogwge we FOX QUOQOE OCOLLTECILULEEERETUT EE EE pat apes age se X UO Figure 2 57 Example 3 Z section 2 6 DEFINITION OF I SECTIONS Figure 2 58 Example 4 Z secti
74. lar cylinders is v w w wa I eee W Q a 24L1 The Cylinder dialog tab 1 2 22 w k h h k UQ OE k Q Q 4 Q 24 2 The Dimensiona dialog tab lt o 4 s a a wor A S Soo ROO EUR RS N 24 49 The Materials dialog tab os u 2 44444 45 o 9o w a w w a a CONTENTS 2414 Formatted so a eA 33e amp Que ee oe ee R E w a 64 BAD Temples so eee RG ee we hee hae W Q 65 2 0 D linition of double BOXxes o msc 4 HE EEE EG SES AUR 2 66 20 1 The Double Box dialog tab i lt ossi s w W w ee BR Q O he 67 2 0 39 Th Dimensions dialog tab 9 o3 8 ee Sw ws 68 2 0 4 The dialog tab 452225255 yc 9 eee ae S Rok US 70 2 5 4 Formatted input 2 00666 2264444444 eee Ro eR ta bees ewe TS 72 2 05 Eomp u ee Ruhe Be Ae Oe ee Pe RSU SG aS 72 20 Detiirtion of sechong o6 zoo 4o ox a ae a BEEP OO PEG Ghee ee 74 2 0 1 The Psec on dialog tab ca cep wa EAA eee 0 b Q O eee ee Q d 75 262 The Dimensions dialog taD s lt s s s gc h aa dna EUR RES Ri 76 203 The Maierigis dialog tab poo oos ee YE P479 ee Pee PX 78 208 FPormaned put Lo 012 pom cR ROROROROR RUEOEOS EEE a a EE RE 9 a Q 84 2 0 5 Exemples ca 42 vio oy W EEE EEE Q dod dod eee a eee ow dde ded 84 2 7 Definition of rectangular boxes s s k
75. length of the curve defining the geometry of the wall In general each layer starts at a given location 7 along the curve and ends at a location nf The left portion of fig 3 4 shows a typical configuration for a stacking sequence layers Layeri Layer2 and Layer5 have the same beginning and end coordinates 7 0 and ny 1 respectively whereas Layer3 features T 1 and nf and Layer4 features n 71 and nf r4 Of course when layers are dropped or added the layers at the further distance from the curve defining the geometry of the wall drop onto the remaining layers as illustrated on the right portion of fig 3 4 An add drop zone length defines the distance over which the layers are allowed to collapse onto a lower position Each layer is characterized by the following parameters 1 the layer name 2 the layer beginning and end coordinates and respectively 3 the layer thickness 4 the material the layer is made of For transversely isotropic materials which are common for fiber reinforced composites are easier to express materials properties as solid properties 130 CHAPTER 3 BUILDER Definition of the Actual stacking sequence configuration n Tl 1 0 n 1 i T Add drop Add drop zone length zone length Figure 3 4 Definition of the stacking sequence and actual configuration of the wall Walls are allowed for ply add drop at any position between U 0 to U 1 as depicted in fig 3 4 Th
76. lied loading 6 1 Sectional loads External loads applied to the cross section are defined defined by means of a load vector and of a moment vector A loading condition is defined by a single dialog window the Sectional loads dialog window 6 1 1 The Sectional loads dialog window Sectional loads f Sectional loads name Ge bendingMomentM3 Scaling factor Applied forces 1 00000 000 Applied moments Applied at centers Applied at point Cancel Figure 6 1 The Sectional loads dialog window The Sectional loads dialog window defines the loading condition with the following data 1 2 Sectional loads name Enter a unique name for the loading condition Scaling factor This scaling factor is a multiplicative factor that will affect both the force and the moment vectors Applied Forces The Applied Forces button allows the definition of the three components of the externally applied force vector As shown in fig 6 2 the three components of force V2 and V3 are acting along the axes 71 t2 and respectively These forces are applied at the origin of the axis system Applied Moments The Applied Moment button allows the definition of the three components of the externally applied moment vector As shown in fig 6 2 the three components of moment M M gt and are acting about the axes 71 and 73 respectively 167 168 CHAPTER 6 APPLIED LOADING Forces and moments applied at the o
77. matted input file which has the following structure INCLUDE_COMMAND INCLUDE_COMMAND NAME IncludeName LIST_OF_FILE_NAMES FileNamei FileName2 FileNameN 8 3 OPTIONS 177 8 3 Options A number of Options can be selected to affect SECTIONBUILDER operations The following can be selected the way in which cross sectional shapes are allowed to be defined the unit system to be used and the installation path of SECTIONBUILDER on the computer 8 4 The Options dialog window Options Shape definition Build shape Parametrized shape Units 6 C US C US N SectionBuilder path Figure 8 4 The Options dialog window The Options dialog window defines the following options 1 Shape definition Select Build shape or parametrized shape The parametrized shapes are those defined in chapter 2 whereas the build shapes refer to the custom shapes discussed in chapter 3 Note that the Build shape option is not available under the academic license 2 Unit system SECTIONBUILDER is not aware of any unit system The user must input all data in a consistent set of units However SECTIONBUILDER will provide unit labels in all output files according to the declared unit system The following unit systems are available a SI international system of units b US US customary system of units c US IN US customary system of units but inches are used instead of feet as the unit of length 3 Section
78. n CONNECTED AT A Z Wall A Vcon EN CONNECTED AT B After Connection Wall A Vcon Wall B Figure 3 18 Two walls can be connected as above with a Vcon The detail description of Vcon is shown in fig 3 19 Basically wall information is used for Vcon con struction Points Pi and Ri i 1 2 3 n are generated from WallA and WallB Points Pi are the starting positions U 0 of various layers of WallA Similarly points Ri are the final positions at U 1 of the layers of WallB Qi are the intersection points of the tangents of the layers of WallA at U 0 WallB at U 1 Curves and surfaces are constructed from Pi Qi and Ri Solids are generated using the material and mesh properties From WallA and WallB properties VconUp and VconLo sections are constructed 3 5 DEFINITION OF VCON SECTIONS 145 Before Connection More Detail CONNECTED AT B Figure 3 19 Two walls and Vcon in detail 146 CHAPTER 3 BUILDER 3 5 1 Formatted input The data defined in the above sections will be saved in a specially formatted input file which has the following structure V_CONNECTOR_DEFINITION V_CONNECTOR_NAME VconName CONNECTED_AT A WallAName QGCONNECTED AT B WallBName 3 5 DEFINITION OF VCON SECTIONS 147 3 5 2 Examples An example that describes the construction procedure of this type of section is shown below Example 1 This example shows a Vcon connector that connects 2 walls Th
79. n 4 2 to each zone of the airfoil section EU i Figure 2 9 The three zones of the airfoil section 2 1 DEFINITION OF AIRFOIL SECTIONS 35 2 1 5 Formatted input The data that defines the airfoil section as described in the above sections will be saved in a specially for matted input file which has the following structure AIRFOIL SECTION DEFINITION GAIRFOIL SECTION NAME TboxName CHORD LENGTH c TOP_AIRFOIL_1_THICKNESS tia NACA_AIRFOIL PROFILE 1 n2 Y TOP_AIRFOIL_2_THICKNESS tia BOTTOM_AIRFOIL_2_THICKNESS tha2 TOP_AIRFOIL_3_THICKNESS tas BOTTOM_AIRFOIL_3_THICKNESS ty TOP WEB 1 LOCATION t GBOTTOM WEB 1 LOCATION t WEB 1 THICKNESS ti RIGHT_WEB_1_THICKNESS t amp TOP_WEB_2_LOCATION tis BOTTOM WEB 2 LOCATION LEFT_WEB_2_THICKNESS t RIGHT_WEB_2 THICKNESS ts AIRFOIL_1_MATERIAL_NAME MaterialName1 AIRFOIL_2 MATERIAL_NAME MaterialName2 AIRFOIL_8_MATERIAL_NAME MaterialName3 IS_DEFINED_IN_FRAME FxdFrameName MESH_DENSITY md 36 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 1 6 Examples A few examples that describe the construction procedure of this type of section are shown below Example 1 This example shows a NACA 4 digit series airfoil section The chord length thickness material properties and mesh density are assigned here This example also shows the principal centroidal axes of ben
80. n frame The geometry of the rectangular box can be defined with respect to a fixed frame as described in section 7 1 allowing translation and rotation of the section as a rigid body 90 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 7 2 The Dimensions dialog tab Rectangular Box Rectangular box Dimensions Materials emg Webs Bottom left flange Bottom right flange Figure 2 62 The Dimensions dialog tab The Dimensions dialog tab as described in fig 2 62 defines the dimensions of the rectangular box as depicted in fig 2 60 Dimensions of the section are defined by the following parameters Web dimensions 1 The height h of the section required input 2 The thickness tiy of the left web required input 3 The thickness trw of the right web required input Top left flange dimensions 1 The width wyr of the top left flange required input 2 The thickness tig of the top flange default value tit tiw 3 The skew angle our of the top left flange positive up measured in degrees default value 0 4 The thickness t of the top reinforcement flange this thickness applies to both left and right rein forcements that cannot exist independently of each other default value ta 0 This variable is also used as flag for the presence of the top reinforcement flange if ti Z 0 the top reinforcement flange is present Top right flange dimensions 1 The width wire of the t
81. n is not necessarily at the centroid and can be anywhere that is convenient A detailed description of the sectional properties is printed in an output file of extension sbp as described in section 1 6 3 This file contains the information detailed in the sections below i Forces and moments applied at the origin Figure 1 2 Sign conventions for the externally applied force and moment components acting on the cross section Sectional stiffness and compliance matrices The following sectional stiffness and compliance matrices are computed e The 4x4 sectional stiffness matrix This matrix relates the sectional axial strain twisting curvature Ki and two bending curvatures k2 and to the axial force Ni twisting moment Mj and two bending moments M gt and M3 The relationship between these sectional strains and sectional stress resultants takes the form of a 4 x 4 matrix Ni Cir Cis Cio Ey M _ Ca Cas K 1 1 M C54 Css Cse Ms Coi Coes K3 e The 6 x 6 sectional stiffness matriz C This matrix relates the sectional axial strain 1 transverse shearing strains and twisting curvatures and two bending curvatures and to the axial force Nj transverse shear forces V2 and V3 twisting moment and two bending moments M and Ms The relationship between these sectional strains and sectional stress resultants takes the form of a symmetric
82. nd 03 c Shear strength In this case o3T o3T 090 and T in view of the isotropy in the plane the subscripts 2 and 3 can be interchanged Furthermore the isotropy of plane gt implies 3 For an isotropic material a single property is required a Tension strength In this case gi oBT g gi qa o3C o and T Th TA c 3 4 1 DEFINITION OF MATERIAL PROPERTIES 159 4 1 5 Formatted input The data that defines materials properties as described in the above section will be saved in a specially formatted input file which has the following structure MATERIAL PROPERTY DEFINITION MATERIAL PROPERTY DEFINITION MaterialName MATERIAL PROPERTY TYPE MaterialType FAILURE_CRITERION_TYPE FailureCriterion MATERIAL DENSITY YOUNG S MODULUS Ej Eo Es POISSON S_RATIO 112 113 vos SHEAR_MODULUS G12 Gis G23 Y ALLOWABLE_TENSILE_STRESS oT 027 027 ALLOWABLE_COMPRESSIVE STRESS oC 03 03 QGQALLOWABLE SHEAR STRESS 775 773 733 160 CHAPTER 4 MATERIAL PROPERTIES 4 2 Definition of solid properties For the purpose of discretization cross sections are divided in a number of quadrangular areas called solids For instance consider the C section shown in fig 2 22 the section is divided into three zones 1 the top reinforcement flange consisting of a single solid labeled TF
83. nding moments are related to the sectional curvatures M3 Ms 3 Ko X 1 10 where 5 M are the bending moments computed with respect to the centroid about axes parallel to 22 and 23 respectively K and the sectional curvatures H and H the bending stiffnesses computed with respect to the centroid about axes parallel to 22 and respectively and H the cross bending stiffness computed with respect to the centroid about axes parallel to 72 and Forces and moments Forces and moments applied at the reference point applied at the centroid Figure 1 3 Left figure forces and moments applied at the reference point Right figure forces and moments applied at the centroid The forces and moments computed with respect to the reference point and the centroid can be related as follows 1 0 0 1 za 1 0 Ms 1 0 Mp 1 11 Ms z2 0 1 Ms M 0 1 Ms Similarly the sectional strains and curvatures with respect to the reference point and the centroid can be related as follows 1 1 Xe2 D gt 1 Xe3 c2 El ko 0 1 0 KS Ks 0 1 0 1 12 K3 0 0 1 0 0 1 Eqs 1 9 and 1 10 relating the sectional forces and strains about the centroid can be recast in a single matrix equation as S 0 0 et 0 H Hs x 1 13 Ms 0 Hs Introducing eqs
84. ne warping displacement components and are listed at the sensor location The displacement components w1 and ws are the components of the displacement vector along unit vectors 21 9 and 73 respectively 18 CHAPTER 1 INTRODUCTION Sensor SensorWarping Sensor location ro 3 1 9e 18 7 4e 02 m Section warping w1 W2 0 0e 00 3 9e 09 4 8e 09 m Table 1 1 Print out of the three dimensional warping displacement at a sensor location Three dimensional stresses Under the effect of the applied loading the cross section will deform generating a three dimensional stress field which features both in and out of plane components on the cross section Since the cross section is in plane 72 73 the in plane stress components are and whereas the out of plane stress components are and as described in fig 1 8 Note that classical beam theory predicts only the the out of plane stress component and the two transverse shearing stresses and typically the in plane stress components are assumed to be negligible i e 95 z 0 0 and 0 The analysis implemented in SectionBuilder predicts both out of plane and in plane stress components A typical print out of a stress sensor is shown in Table 1 2 For the sensor named SensorStresses the out of plane stress components and as well as the in plan
85. nsions Materials rem Reinforcement Thicknesses Figure 2 69 The Dimensions dialog tab The Dimensions dialog tab as described in fig 2 62 defines the dimensions of the rectangular section shown in fig 2 67 The dimensions of the section are defined by the following parameters 1 2 The width w of the section required input The height h of the section required input The thickness of the top reinforcement flange this thickness applies to both left and right rein forcements that cannot exist independently of each other default value ta 0 The thickness t of the top reinforcement flange default value ta 0 This variable is also used as a flag for the presence of the top reinforcement flange if t Z 0 the top reinforcement flange is present The thickness tpr of the bottom reinforcement flange default value ty 0 This variable is also used as a flag for the presence of the bottom reinforcement flange if thr Z 0 the bottom reinforcement flange is present 2 8 DEFINITION OF RECTANGULAR SECTIONS 99 2 8 3 The Materials dialog tab Rectangular section Rectangular section Dimensions Materials Top Flange Material Core Material Bottom Flange Material Figure 2 70 The Materials dialog tab The Materials dialog tab as described in fig 2 70 defines the materials the rectangular section is made of As shown in fig 2 71 the section is divi
86. nstruction procedure of this type of section are shown below Example 1 This example shows a simple Tcon connector that connects 3 walls All walls have 2 layers This example also shows the axial strain field over the cross section under the applied sectional loads Figure 3 15 Example 1 Tcon connector with three Walls Example 2 This example shows the connection among 5 walls using 2 Tcon connectors This example also shows the inverse of the reserve factor over the cross section under the applied sectional loads Example 3 This example shows the connection among 8 walls using 6 Tcon connectors All walls have more than 2 layers and ply add drop is also shown here This example also shows the shear strain field over the cross section under the applied sectional loads 3 4 DEFINITION OF TCON SECTIONS 143 Figure 3 16 Example 2 two Tcon connectors with five Walls Figure 3 17 Example 3 Four Tcon connectors with Eight Walls 144 CHAPTER 3 BUILDER 3 5 Definition of Vcon sections Vcon is a connector for connecting two walls like a V shape Two walls Wall A and Wall B connected with a Vcon are depicted in fig 3 18 Vcon has the same number of layers of walls at the junction It is very useful for the trailing edge construction of an airfoil section User needs to provide the Wall A connected at position A of Vcon and Wall B connected at position B of Vcon information for constructing a Vcon Before Connectio
87. of WallA at U 1 and WallB at U 0 Ci and Cci are constructed from lower and upper parts of WallC at U 1 respectively Ei are the intersection points of the tangents of the layers of WallA at U 1 and lower part of WallC at U 1 Fi are the intersection points of the tangents of the layers of WallB at U 0 and upper part of WallC at U 0 Curves and surfaces are constructed using these points Finally solid is defined using the material and mesh properties TRFIgR and TLFIgR are constructed form the pass through layers information of WallA and WallB respectively TRFlg and TLFlg are constructed form the other layers information of WallA and WallB Where as RWeb and LWeb are constructed form the lower and upper parts of WallC information respectively 140 CHAPTER 3 BUILDER Tcon in Downward direction Wall C z s s 3 Upper Wall U 1 i C3 C2 C1 CO Cc1 Cc2 cc3 Bb3 Figure 3 14 Three walls and Tcon in downward direction in detail 3 4 DEFINITION OF TCON SECTIONS 141 3 4 1 Formatted input The data defined in the above sections will be saved in a specially formatted input file which has the following structure GT CONNECTOR DEFINITION T CONNECTOR NAME TconName QGCONNECTED AT 11 GCONNECTED AT B WallBName QGCONNECTED AT C WallCName GNUMBER OF PASS THROUGH LAYERS NbOfLayers 142 CHAPTER 3 BUILDER 3 4 2 Examples A few examples that describe the co
88. on Figure 2 59 Example 5 T section 87 88 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 7 Definition of rectangular boxes Rectangular boxes are parametric configurations of the shape depicted in fig 2 60 They consist of a rectan gular box possibly reinforced by top and or bottom flanges The section consists of up to three three zones to which independent material properties can be assigned Wir Wort Figure 2 60 Configuration of the rectangular box The dimensions of the various elements of the section are indicated on the figure The three shaded areas correspond to the three zones of three section Rectangular boxes are defined by means of three dialog tabs 1 The Rectangular box dialog tab as described in section 2 7 1 which defines the name of the section 2 The Dimensions dialog tab as described in section 2 7 2 which defines the dimensions of the section 3 The Materials dialog tab as described in section 2 7 3 which defines the materials the section is made of 2 7 DEFINITION OF RECTANGULAR BOXES 89 2 7 1 The Rectangular box dialog tab Rectangular Box Figure 2 61 The Rectangular box dialog tab The Rectangular box dialog tab as described in fig 2 61 defines the following data for the rectangular box 1 Section name Enter a unique name for the rectangular box 2 Mesh density Enter the desired mesh density as described in section 5 1 for the finite element discretization 3 Defined i
89. on 5 1 for the finite element discretization 3 Defined in frame The geometry of the C section can be defined with respect to a fixed frame as described in section 7 1 allowing translation and rotation of the section as a rigid body 2 8 DEFINITION OF C SECTIONS 4T 2 3 2 The Dimensions dialog tab C section C section Dimensions Materials Bottom Flange Figure 2 20 The Dimensions dialog tab The Dimensions dialog tab as described in fig 2 20 defines the dimensions of the C section as depicted in fig 2 18 The dimensions of the section are defined by the following parameters Web dimensions 1 The height h of the web required input 2 The thickness tw of the web required input Top flange dimensions 1 The width wit of the top flange required input 2 The thickness tir of the top flange default value tig tw 3 The skew angle or of the top flange positive up measured in degrees default value ast 0 4 The thickness ttr of the top reinforcement flange this thickness applies to both left and right rein forcements which cannot exist independently of each other default value tty 0 This variable is also used as a flag for the presence of the top flange reinforcement if t gt 0 this reinforcement is present Bottom flange dimensions 1 The width wpr of the bottom flange default value wir 2 The thickness tyr of the bottom flange default value typ tu 3
90. onents A typical print out of a strain sensor is shown in Table 1 3 For the sensor named SensorStrains the out of plane strain components 1 and as well as the in plane strain components 2 and are listed at the sensor location The sign conventions for strain components are consistant with the stresses shown for stresses in fig 1 8 Sensor SensorStrains Sensor location ro 3 2 7e 02 4 7e 02 m Out of plane strains y12 4 2e 07 0 0 00 0 0e 00 In plane strains 723 1 2e 07 3 5e 21 1 2e 07 Reserve factors 2 0e 04 2 0e 04 Table 1 3 Print out of the three dimensional strains at a sensor location 1 5 Visualizing the results The last step of the SectionBuilder process is to visualize the results of the finite element analysis performed in the previous step Clicking the third icon of the SECTIONBUILDER toolbar shown in fig 1 1 enters the visualization mode Some of the results of the finite element analysis such as the sectional stiffness and compliance matrices do not lend themselves to visualization however many of the other computed quantities are most easily interpreted through graphic visualization Visualization of the results is controlled by two menu items and associated toolbars the Loading toolbar shown in fig 1 9 and the Graphics toolbar shown in fig 1 12 Visualization proceeds in three steps controlled by the th
91. op right flange default value wire 2 The thickness of the top right flange equals that of the top left flange 3 The skew angle Qtrf of the top right flange positive up measured in degrees default value 0 Bottom left flange dimensions 1 The width of the bottom left flange default value wy wur 2 The thickness tyr of the bottom left flange default value ty tu 2 7 DEFINITION OF RECTANGULAR BOXES 91 3 The skew angle of the bottom left flange positive down measured in degrees default value Qblf 0 4 The thickness tpr of the bottom reinforcement flange this thickness applied to both left and right reinforcements that cannot exist independently of each other default value ty 0 This variable is also used as a flag for the presence of the bottom reinforcement flange if tj Z 0 the bottom reinforcement flange is present Bottom right flange dimensions 1 The width of the bottom right flange default value 2 The thickness of the bottom right flange equals that of the bottom left flange 3 The skew angle of the bottom right flange positive down measured in degrees default value Qbrf 0 92 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 7 3 The Materials dialog tab Rectangular Box Rectangular box Dimensions Materials Top Flange Material Web Material Bottom Flange Material Figure 2 63 The Materials
92. or the single or dual web design this is the wall thickness for the front portion of the airfoil Airfoil Thickness 1 The top wall thickness 42 of the aft or middle portion of the airfoil for the single or dual web design respectively default value tiaz 2 The bottom wall thickness 542 of the aft or middle portion of the airfoil for the single or dual web design respectively default value tpa 3 The top wall thickness of the aft portion of the airfoil for the dual web design default value tta3 a2 4 The bottom wall thickness 543 of the aft portion of the airfoil for the dual web design default value tba3 Web 1 Dimensions 1 The location 2 1 of the intersection of the first web with the upper airfoil profile this is a dimensional quantity default value 0 This variable is also used as a flag for the presence of the first web if 0 at least one web is present 2 The location zy 1 of the intersection of the first web with the lower airfoil profile this is a dimensional quantity default value zbw1 zwi 3 The thickness of the left portion of the first web default value tiwi tq41 4 The thickness trw1 of the right portion of the first web default value tta2 2 1 DEFINITION OF AIRFOIL SECTIONS 33 Web 2 Dimensions 1 The location of the intersection of the second web with the upper airfoil profile this is
93. ortant role in the definition of the material axes orientation as described in below 3 Layer orientation Layers can be selected to be oriented Along U or Along V Fig 4 9 depicts a typical solid in the cross section with the local axis system 1 v The layers of material can run along the or v axes as illustrated in the left and right portions of the figure respectively v Along v Th Th Ne Il 0 Ns n 0 Figure 4 9 Stacks of layers defining solid properties In the left portion of the figure the layers all run parallel to the axis this corresponds to the Along U option In the right portion of the figure the layers all run parallel to the v axis this corresponds to the Along V option 162 CHAPTER 4 MATERIAL PROPERTIES 4 2 2 The Layer List dialog window Clicking View Layers button of the Name dialog tab as described in fig 4 8 opens the Layer List dialog window shown in fig 4 10 As shown in fig 4 9 solid properties define a stack of layers each layer has its own thickness orientation angles and material The thickness of the layer is determined by non dimensional coordinates 7 and 7 41 Referring to fig 4 9 Layer i extends from coordinate m to coordinate g 4 If the stack features n layers a total of n 1 entries must appear in the layer list the list must start with coordinate 7 0 0 and must end with coordinate 7 41 1 0 the intermediate coordinates must appear in
94. part of the web required input Top left flange dimensions 1 The width of the top left flange required input 2 The thickness tur of the top left flange default value tut tiw 3 The skew angle our of the top left flange positive up measured in degrees default value 0 4 The thickness t of the top reinforcement flange this thickness applies to both left and right rein forcements that cannot exist independently of each other default value ta 0 This variable is also used as a flag for the presence of the top flange reinforcement if tir gt 0 this reinforcement is present Top right flange dimensions 1 The width wire of the top right flange default value wire wyt 2 The thickness fur of the top right flange default value tire trw 3 The skew angle air of the top right flange positive up measured in degrees default value 0 Bottom left flange dimensions 1 The width wpf of the bottom left flange default value war 2 The thickness tyr of the bottom left flange default value tyr tur 3 The skew angle of the bottom left flange positive down measured in degrees default value 0 2 6 DEFINITION OF I SECTIONS 77 4 The thickness tpr of the bottom reinforcement flange this thickness applied to both left and right reinforcements that cannot exist independently of each other default value ty 0 This variable is also used a
95. perties dialog window as described in section 4 1 1 which defined the name of the materials its mass density and type 2 The Stiffness dialog window as described in section 4 1 2 which defines the stiffness coefficients for the material 3 The Failure Criterion dialog window as described in section 4 1 3 which selects a failure criterion 4 The Strength dialog window as described in section 4 1 4 which defines the strength characteristics of the material Material properties for a few standard materials aluminum titanium and steel are available in a template files The material property names are MatPropAluminum MatPropTitanium MatPropSteel for aluminum titanium and steel respectively To use these properties invoke the include command see section 8 1 to include one of the following files C SectionBuilder Materials MATERIAL_SL tpl or C SectionBuilder Materials MATERIAL_US tpl or C SectionBuilder Materials MATERIAL_US_IN tpl for material properties in the SI US or US IN unit systems respectively 152 CHAPTER 4 MATERIAL PROPERTIES 4 1 1 The Material properties dialog window Material properties Material name Mat Prop Steel Material density 7 80000 003 Material type Isotropic Orthotic Transversly isotropic Figure 4 3 The Material properties dialog window The Material properties dialog window defines the following data for the material 1 Material name Enter a unique name for the mat
96. pplied sectional loads SS NL LN eite Y KS Y ANA AI V Figure 2 72 Example 1 Rectangular Section Example 2 This example shows also a rectangular section Here width height frame reinforcement thicknesses composite core materials and mesh density are assigned for constructing this section This example also shows the shear stress field over the cross section under the applied sectional loads 2 8 DEFINITION OF RECTANGULAR SECTIONS 103 Figure 2 73 Example 2 Rectangular Section 104 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 9 Definition of circular tubes Circular tubes are predefined sections presenting the shape shown in fig 2 74 Circular tubes consist of an area included between two circles T he section consists of a single zone to which material properties can be assigned The circular tube is a closed circular tube as shown in fig 2 74 Open circular tubes can be defined with the help of the circular arc predefined section as described in section 2 2 Figure 2 74 Configuration of the circular tube Circular tubes are defined by means of three dialog tabs 1 The Circular tube dialog tab as described in section 2 9 1 which defines the name of the section 2 The Dimensions dialog tab as described in section 2 9 2 which defines the dimensions of the section 3 The Materials dialog tab as described in section 2 9 3 which defines the materials the section is made of 2 9 DEFINITION O
97. properties From WallB and lower part of WallC properties Left lTailLo and RightTailLo sections are generated Left TailUp and Right TailUp sections are generated from WallA and upper part of WallC properties 3 8 DEFINITION OF SPLIT SECTIONS 135 Figure 3 9 Three walls and Split in detail 136 CHAPTER 3 BUILDER 3 3 1 Formatted input The data defined in the above sections will be saved in a specially formatted input file which has the following structure GSPLIT CONNECTOR DEFINITION GSPLIT CONNECTOR NAME SplitName QGCONNECTED AT A WallAName QGCONNECTED AT B WallBName QGCONNECTED AT _C WallCName 3 8 DEFINITION OF SPLIT SECTIONS 137 3 3 2 Examples An example that describes the construction procedure of this type of section is shown below Example 1 This example shows a Split connector that connects 3 walls WallA WallB and WallC have 2 2 and 4 layers respectively Here the sum of the number of layers for WallA and WallB are equal to that of WallC at the connection position This example also shows the principal centroidal axes of bending Figure 3 10 Example 1 Split connector with three Walls 138 CHAPTER 3 BUILDER 3 4 Definition of Tcon sections Tcon is a connector for connecting three walls like a T shape Three walls Wall A Wall B and Wall C connected with Tcon are depicted in fig 3 11 fig 3 12 Tcon has three parts and those are web right flange and left flange The web is construc
98. r an orthotropic material the compliance matrix 4 5 6 takes the following form 1 1 vjg E 0 0 0 71 2 vi E 1 E2 uo s E Eo 0 0 0 02 3 113 V23 E2 1 Es 0 0 0 03 4 1 0 0 0 1 0 0 T33 y ES 0 0 0 0 1 Gi3 0 T13 12 0 0 0 0 0 1 Gi2 T12 The array of strain components is e ea 703 ma V12 4 2 where ei and are the axial strains components along unit vectors i and respectively The orthonormal units vectors i and form the material axis system as illustrated in fig 4 4 the corresponding engineering shear strains components are 713 and The array of stress components is a 01 02 03 T13 712 4 3 where and os are the axial stress components along unit vectors 1 and respectively the corresponding shearing stresses are T23 and In view of eq 4 1 the material stiffness properties are characterized by three distinct Young s moduli E and Es along unit vectors 2 and es respectively three Poisson s ratios v12 v13 and v23 and three shearing moduli Gi3 and G s 1 For an orthotropic material the following nine properties are required a Young s moduli E and Es b Shear moduli G12 Gi3 and c Poisson s ratios v1 v13 and vos 2 For a transversely isotropic material the following five propertie
99. rdinates of the center of mass 125 33 and 53 the components of the sectional mass moments of inertia per unit span and the sectional polar moment of inertia per unit span The following quantities are also provided e The sectional area A e The sectional mass per unit span moo M22 M33 1 39 e The location of the mass center M3 Mis 3m 1 40 moo moo e The mass moments of inertia per unit span about the center of mass I5 22 3 33 22 9 I5 M00 m2 m3 1 41 e The polar moment of inertia per unit span about the center of mass In 152 133 1 42 It is possible to define the principal axes of inertia at the center of mass As illustrated in fig 1 7 the principal axes of inertia at the center of mass 7 77 77 17 correspond to a planar rotation of orthonormal basis Z by an angle o7 about 21 so that 77 t When using the principal axes of inertia at the center of mass the relationship between angular momenta and angular velocities so that uncouples mM 22 _ ym __ mM Ay wi h3 33 mx h3 05 E w3 1 43 Clearly hi and wj since the rotation of the axis system takes place about unit vector 21 The angular momenta A5 and A7 are computed with respect to the center of mass along axes 73 and 73 respectively Similarly w and w3 are the angular velocities about
100. red frame called FXDFRAME INERTIAL is predefined an can be used without being explicitly defined The FXDFRAME INERTIAL frame coincides with the structural axes 7 A fired frame is defined by a single dialog window the Fixed frame dialog window 7 2 The Fixed frame dialog window Fixed frame x Fixed frame name F dFramel Za Origin Orientation Cancel Figure 7 1 The Fixed frame dialog window The Fixed frame dialog window defines the fired frame with the following data 1 Fixed frame name Enter a unique name for the fized frame 2 Origin The location of the fixed frame is defined by the components of the position vector 1 2 x3 of its origin measured is Z see fig 7 2 Note that z must be zero 3 Orientation The orientation of the fixed frame is defined by angle as shown in fig 7 2 Angle is measured in degrees and is positive in the counterclockwise direction 7 2 1 Formatted input The data that defines the fixed frame as described in the above section will be saved in a specially formatted input file which has the following structure 171 172 CHAPTER 7 GEOMETRIC ELEMENTS Fixed Frame e Figure 7 2 Definition of a fixed frame FIXED FRAME DEFINITION GFIXED FRAME NAME FxdFrameName ORIGIN 1 292 T3 ROTATION_ANGLE Chapter 8 Utility objects 173 174 CHAPTER 8 UTILITY OBJECTS 8 1 Definition of the Include command An Include command defin
101. rigin V Figure 6 2 Externally applied force and moment components acting on the cross section 5 Applied at Centers The flag Applied at Centers affect the way in which the previously defined forces and moments are applied to the cross section If the box Applied at centers is checked the axial force is applied at the centroid and the transverse shear forces V2 and V3 are applied at the shear center as depicted in fig 6 3 Axial force i applied at the centroid Transverse forces applied at the shear center Figure 6 3 Externally applied force and moment components acting on the cross section Transverse shear forces are applied at the shear center axial force at the centroid 6 Applied at Point It is sometimes convenient to be able to apply the loads at an arbitrary point of the cross section The Applied at Point button allows the definition of the coordinates oa 134 of point A the point of application of the force vector This option is depicted in fig 6 4 6 1 SECTIONAL LOADS 169 E Forces applied at point A Figure 6 4 Externally applied force and moment components acting on the cross section The forces are applied at point A with coordinates xoa 3a 170 CHAPTER 6 APPLIED LOADING Chapter 7 Geometric elements 7 1 Definition of fixed frames A fixed frame consists of an origin point and an orientation triad that do not vary with time as depicted in fig 7 2 A default fi
102. riterion This criterion is used for isotropic materials only At failure the following equation is satisfied 1 5 51 s2 82 1 1 where s 0 0 s2 02 07 and ss 03 0 oi 03 and are the principal stresses and c T the allowable stress in tension defined in section 4 1 4 Note that since the material is assumed to be isotropic its strength is identical in all directions furthermore its compressive and tensile strengths are assumed to be identical 158 4 1 CHAPTER 4 MATERIAL PROPERTIES 4 The Strength dialog window Strength Tension strength Compression strength Sere Figure 4 7 The Strength dialog window The Strength dialog window defines the strength properties of the material In general nine different strength values can be defined 1 2 Allowable stress in tension o11 and along the material axes and respectively Allowable stress in compression 02 o3 and 02 along the material axes and respectively Allowable shear stress and 733 For an orthotropic material all nine strength properties are required a Tension strength c T 03 and 087 b Compression strength c 03 and o3 c Shear strength and 733 For a transversely isotropic material the following five properties are required a Tension strength c T and cT b Compression strength c a
103. ry to describe the thicknesses of the layers the materials they are made of and the fiber orientation angle This more complex task is done by defining solid properties as discussed in section 4 2 When dealing with solid properties a solid local axis system 71 v is defined This local axis system is necessary to describe the configuration of the stack of layered materials For instance in the right portion of fig 4 2 the layers of material run parallel to unit vector of this local axis system Furthermore this local system will also be used to describe the fiber orientation angle when laminated composite materials are used 149 150 CHAPTER 4 MATERIAL PROPERTIES i Solid local axis system Material Solid properties properties I I Figure 4 2 A C section divided in three solids called TFlg Web and BFlg Left figure the three solids are made of a single material Right figure the three solids are made of a stack of layered materials 4 1 DEFINITION OF MATERIAL PROPERTIES 151 4 1 Definition of material properties The definition of the physical properties of materials involve the definition of material density material stiffness and strength characteristics and the selection of a failure criterion Materials to be defined can be of three distinct types isotropic orthotropic or transversely isotropic materials These properties are defined by means of four dialog windows 1 The Material pro
104. s flag for the presence of the bottom flange reinforcement if ty gt 0 this reinforcement is present Bottom right flange dimensions 1 The width of the bottom right flange default value Were 2 The thickness tpt of the bottom right flange default value tyre ttre 3 The skew angle of the bottom right flange positive down measured in degrees default value Obrf 0 78 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 6 3 The Materials dialog tab l section section Dimensions Materials Top Flange Material Left Web Material Right Web Material Bottom Flange Material Figure 2 49 The Materials dialog tab The Materials dialog tab as described in fig 2 49 defines the materials the I section is made of As shown in fig 2 50 the section is divided into four zones 1 The top reinforcement flange consists of components labeled TLFIgR and TRFIgR 2 The left portion of the I section itself consists of components labeled TLFlg LWeb and BLFlg 3 The right portion of the I section itself consists of components labeled TRFlg RWeb and BRFlg 4 The top reinforcement flange consists of components labeled BLFIgR BRFigR It is possible to assign material properties as described in section 4 1 or solid properties as described in section 4 2 to each zone of the I section Special Cases 1 If the widths wire 0 and 0 the section looks like Z shape depicted in fig
105. s extrusion can be used A typical beam section will be viewed here as a number of interconnected walls as depicted in fig 3 1 The upper flange of the profile consists of Wa111 and Wa112 whereas the lower flange consists of Wa114 and Wa115 The web consists of Wa113 and finally the trailing edge tab consists of Wa116 The web and flanges are connected together by T connectors labeled Tcon1 and Tcon2 The trailing edge tab splits into the upper and lower flanges through a split connector labeled Spliti Finally two walls can be directly connected to each other such as Wa112 and Wa114 near the leading edge of the airfoil Figure 3 1 Airfoil Section construction The definition of sections will involve the following components 1 Walls see section 3 2 2 Split connectors see section 3 3 3 T connectors see section 3 4 4 V connectors see section 3 5 3 1 1 Examples An example that describes the construction procedure of this type of section is shown below Example 1 This example constructs a simple airfoil section of NACA 4 digit series which has one web This section has five walls two Tcon and one Vcon connectors Walll and Wall5 have two layers Wall2 Wall3 and Wall4 127 128 CHAPTER 3 BUILDER have more than two layers with ply add drop Wall2 and Wall4 are connected between them This example also shows the principal centroidal axes of bending Figure 3 2 Example 1 Airfoil Section 3 2 DEFINITION OF WA
106. s are required a Young s moduli F and E b Shear moduli c Poisson s ratios vj and 193 4 1 DEFINITION OF MATERIAL PROPERTIES 155 In this case Es E2 Gig and M2 in view of the isotropy in the gt plane the subscripts 2 and can be interchanged Furthermore the isotropy of plane implies G23 E2 2 1 v23 For an isotropic material the following two properties are required a Young s modulus E b Poisson s ratios v In this case the isotropy of the material implies Es E vis 23 v and Gig E 2 1 v 156 CHAPTER 4 MATERIAL PROPERTIES 4 1 3 The Failure Criterion dialog window Failure Criterion Failure Criterion C Hoffmann Tsai Wu C Maximum Strain C Von Mises C Maximum Stress Figure 4 6 The Failure Criterion dialog window The Failure Criterion dialog window defines the failure criterion to be used for this material type The failure criterion can be selected from the following list 1 Hoffmann Criterion This criterion is used for transversely isotropic material only At failure the following equation is satisfied s Fi28182 82 s Fisi Fos 1 4 4 where 81 s2 o9 031 08 and sg and oz are the stresses along the material axes e and 2 respectively and the corresponding shear stress The allow
107. s described in section 4 1 are defined in the material axis system as described in fig 4 4 A sequence of three planar rotations brings the global reference frame Z to the material axis system as illustrated in fig 4 11 1 The first planar rotation is of magnitude a about axis and brings the reference axis system 7 t T2 13 to the solid local axis system U 71 Angle a is determined by the geometry of the section 4 2 DEFINITION OF SOLID PROPERTIES 163 2 The second planar rotation is of magnitude 0 about axis and brings the solid local axis system v to frame B 71 b2 bs Angle is defined in the layer list Since these first two planar rotations take place about the same axis 21 they can be combined into a single planar rotation of magnitude a 8 about axis 71 The third planar rotation is of magnitude y about axis bs and brings frame B 71 b2 b3 to the material axis system 61 Angle y is defined in the layer list Note that positive angles 8 and y correspond to positive rotations about axes 7 and bs respectively following the right hand rule If the layer is a transversely isotropic material such as a unidirectional layer of composite angle 8 0 and angle y corresponds to the fiber orientation angle Solid local U axis system Reference 2 axis system Material i axis system Figure 4 11 Orientation of the material axis sy
108. s featuring finite elements of decreasing sizes can be created by specifying a mesh density parameter 1 4 Performing the finite element analysis Next the mapped mesh generated in the previous step is used as the basis for a finite element analysis of the section launched by clicking the second icon of the SECTIONBUILDER toolbar shown in fig 1 1 The finite element analysis computes the three dimensional warping deformation field over the cross section Based on this warping field the sectional stiffness and mass matrices are computed as well as three dimensional stresses and strains at any location in the section The predictions of the analysis are summarized in two files the first details the sectional properties as described in section 1 4 1 and the second provides the the three dimensional stresses and strains at user specified location of the cross section as described in section 1 4 2 1 4 PERFORMING THE FINITE ELEMENT ANALYSIS 9 1 4 1 Sectional properties The geometry of the cross section is described in an orthonormal basis Z 71 72 73 where 71 72 and 73 are three mutually orthogonal unit vectors The plane of the cross section is assumed to coincide with plane 22 13 and the axis of the beam is along unit vector 71 as depicted in fig 1 2 The reference axis of the beam is a line along axis 7 the origin of the coordinate system is at the intersection of the reference axis with the plane of the cross section This axis origi
109. s type of section are shown below Example 1 This example shows a double box Here web height web thicknesses flange width web materials and mesh density are assigned for constructing this section This example also shows the axial strain field over the cross section under the applied sectional loads Example 2 This example shows a double box with skewed flanges Here web height web thicknesses flange widths flange thicknesses flange reinforcement thickness flange skew angles materials and mesh density are assigned for constructing this section This example also shows the axial stress field over the cross section under the applied sectional loads 2 5 DEFINITION OF DOUBLE BOXES Figure 2 44 Example 1 Double Box Figure 2 45 Example 2 Double Box 73 74 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 6 Definition of I sections Lsections are parametric configurations of the shape depicted in fig 2 46 They consist of an I section pos sibly reinforced by top and or bottom flanges The section consists of up to four zones to which independent material properties can be assigned Note that through the use of fixed frames as described in section 7 1 the I section can be made to look like the following shapes H sections Wyr Wort Figure 2 46 Configuration of the I section I sections are defined by means of three dialog tabs 1 The l section dialog tab as described in section 2 6 1 which defines the name of the
110. section 2 The Dimensions dialog tab as described in section 2 6 2 which defines the dimensions of the section 3 The Materials dialog tab as described in section 2 6 3 which defines the materials the section is made of 2 6 DEFINITION OF I SECTIONS 75 2 6 1 The I section dialog tab l section section Dimensions Materials Section name Figure 2 47 The I section dialog tab The I section dialog tab as described in fig 2 47 defines the following data for the I section 1 Section name Enter a unique name for the I section 2 Mesh density Enter the desired mesh density as described in section 5 1 for the finite element discretization 3 Defined in frame The geometry of the I section can be defined with respect to a fixed frame as described in section 7 1 allowing translation and rotation of the section as a rigid body 76 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 6 2 The Dimensions dialog tab l section Fsection Dimensions Materials Cots Web Bottom left flange Bottom right flange Figure 2 48 The Dimensions dialog tab The Dimensions dialog tab as described in fig 2 6 2 defines the dimensions of the I section shown in fig 2 46 The dimensions of the section are defined by the following parameters Web dimensions 1 The height h of the section required input 2 The thickness tiy of the left part of the web required input 3 The thickness tyw of the right
111. stem using the Local Axes option The layer orientation angles Axes Flag set to Global The two orientation angles 3 and y define the orientation of the material axis system 1 with respect to the reference axis system Z 71 72 73 Material properties as described in section 4 1 are defined in the material axis system as described in fig 4 4 A sequence of two planar rotations brings the global reference frame Z to the material axis system as illustrated in fig 4 12 1 The first planar rotation is of magnitude 8 about axis 2 and brings the reference axis system Z 71 T2 73 to frame B 71 b2 b3 Angle is defined in the layer list 164 CHAPTER 4 MATERIAL PROPERTIES 2 The second planar rotation is of magnitude y about axis bs and brings frame B 7 bz to the material axis system 1 Note that positive angles 3 and y correspond to positive rotations about axes 7 and bs respectively following the right hand rule It is important to note that in this scheme while the layer orientation depends on the local axis system the determination of the material axis system orientation is independent of that of the local system dd Reference 2 axis system a 2 2 yee Material n 1 axis system Figure 4 12 Orientation of the material axis system using the Global Axes option Chapter 5 Mes
112. sts of up to three three zones to which independent material properties can be assigned w Figure 2 67 Configuration of the rectangular Section Rectangular sections are defined by means of three dialog tabs 1 The Rectangular section dialog tab as described in section 2 8 1 which defines the name of the section 2 The Dimensions dialog tab as described in section 2 8 2 which defines the dimensions of the section 3 The Materials dialog tab as described in section 2 8 3 which defines the materials the section is made of 2 8 DEFINITION OF RECTANGULAR SECTIONS 97 2 8 1 The Rectangular section dialog tab Rectangular section Rectangular section Dimensions Materials Section name um Mesh density 2 Defined in Frame Figure 2 68 The Rectangular section dialog tab The Rectangular section dialog tab as described in section 2 68 defines the following data for the rect angular section 1 Section name Enter a unique name for the rectangular section 2 Mesh density Enter the desired mesh density as described in section 5 1 for the finite element discretization 3 Defined in frame The geometry of the rectangular box can be defined with respect to a fixed frame as described in section 7 1 allowing translation and rotation of the section as a rigid body 98 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 8 2 The Dimensions dialog tab Rectangular section Rectangular section Dime
113. t clearly 7 ij When using the principal centroidal axes of bending the axial forces and bending moments are fully uncoupled 5 MS 5 M H 1 19 Clearly Nf Nf and ef ef since the rotation of the axis system takes place about unit vector 71 The bending moments M and M are computed with respect to the centroid along axes 73 and 25 respectively Similarly amp and are the sectional curvatures about axes 7 and 7 respectively Figure 1 4 Orientation of the principal axes of bending The following quantities are also provided 1 4 PERFORMING THE FINITE ELEMENT ANALYSIS 13 e The orientation aj of the principal centroidal axes of bending HAS AS HS A cos 2a r 22 sin 2a 1 20 where A 22 1 21 e The principal centroidal bending stiffnesses 55 and H HS T 2 A HS T 2 A 1 22 Note that the choice the orientation of the principal axis 73 given by eq 1 20 guarantees that axis 7 is the axis about which the minimum bending stiffness occurs hence HS lt Hi The twisting moment shear force problem If the stiffness matrix of the cross section presents the special structure displayed in eq 1 4 it becomes possible to separately analyze the axial force bending moment and twisting moment shear force problems The latter problem is the focus of this section To further simplify the relationship between the t
114. t have BFlgR and BFlg solids shown in fig 2 26 3 If the widths wig 0 and wy 0 the section looks like a strip depicted in fig 2 27 This strip section does not have TFlgR TFlg BFlgR and BFlg solids shown in fig 2 28 It only has Web 2 8 DEFINITION OF C SECTIONS Figure 2 22 The three zones of the C section 50 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS Figure 2 23 Configuration of the L section 2 8 DEFINITION OF C SECTIONS Figure 2 24 The two zones of the L section 52 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS Figure 2 25 Configuration of the reverse L section 2 8 DEFINITION OF C SECTIONS 53 E2 E4 Figure 2 26 The two zones of the reverse L section 54 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS Figure 2 27 Configuration of the strip section 2 8 DEFINITION OF C SECTIONS B4 E4 Figure 2 28 The zone of the strip section 55 56 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 3 4 Formatted input The data that defines the C section as described in the above sections will be saved in a specially formatted input file which has the following structure C_SECTION DEFINITION QC SECTION NAME CsecName WEB HEIGHT WEB_THICKNESS TOP_FLANGE_WIDTH wis TOP_FLANGE_THICKNESS tur TOP_FLANGE_SKEW_ANGLE aq TOP_FLANGE_REINFORCE_THICKNESS ty BOTTOM_FLANGE_WIDTH wy BOTTOM_FLANGE_THICKNESS tor BOTTOM_FLANGE_SKEW_A
115. t of an double box possibly reinforced by top and or bottom flanges The section consists of up to four zones to which independent material properties can be assigned Note that through the use of fixed frames as described in section 7 1 the double box can be made to look like the following shapes H sections Wor Wort Figure 2 39 Configuration of the double box Double boxes are defined by means of three dialog tabs 1 The Double Boz dialog tab as described in section 2 5 1 which defines the name of the section 2 The Dimensions dialog tab as described in section 2 5 2 which defines the dimensions of the section 3 The Materials dialog tab as described in section 2 5 3 which defines the materials the section is made of 2 5 DEFINITION OF DOUBLE BOXES 67 2 5 1 The Double Box dialog tab Double Box Double Box Dimensions Materials Section name Figure 2 40 The Double Box dialog tab The Double Box dialog tab as described in fig 2 40 defines the following data for the double box 1 Section name Enter a unique name for the double box 2 Mesh density Enter the desired mesh density as described in section 5 1 for the finite element discretization 3 Defined in frame The geometry of the double box can be defined with respect to a fixed frame as described in section 7 1 allowing translation and rotation of the section as a rigid body 68 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 5 2 The Dimens
116. t series Per cent camber Figure 2 6 The Airfoil profile dialog tab The Airfoil profile dialog tab defines the outer aerodynamic profile for the airfoil section This profile is assumed to be one of the profiles defined by the NACA four digit series 1 1 The first digit 1 indicates the airfoil camber in percent of the chord required input integer 1 0 9 2 The second digit 2 indicates the distance from the leading edge to the location of the maximum camber in tenth of the chord required input 2 c 0 9 3 The las two digits 3 indicate the airfoil thickness in percent chord required input 3 00 09 For instance the NACA 2415 airfoil section has 2 percent camber at 0 4 of the chord from the leading edge and is 15 percent thick 32 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 1 3 The Dimensions dialog tab Airfoil Section Airfoi section Airfoil profile Dimensions Materials le ce Web1 Figure 2 7 The Dimensions dialog tab The Dimensions dialog tab as described in fig 2 7 defines the dimensions of the airfoil section The section can feature no web as described in fig 2 2 a single web as described in fig 2 3 or two webs as described in fig 2 4 The dimensions of the section are defined by the following parameters Airfoil Dimensions 1 The chord c of the airfoil section required input 2 The thickness tta1 of the section wall for the no web design required input F
117. ted from the layers of the Wall C Wall C has layers at upper and lower directions Upper direction means layers are stacked at the positive normal direction of the base curve of the wall Whereas lower direction means the layers are stacked at the negative normal direction Right portion of the web RWeb and lower part of the right flange TRFlg are constructed from the upper direction layers of Wall C Where as the left part of the web LWeb and lower portion of the left flange TLFlg is constructed from the lower direction layers of the Wall C The upper portion of the left and right flanges TLFlgR and TRFIgR are constructed from the pass through layers Pass through layers are the common number of layers from the Wall A and Wall B User has to provide the Wall A connected at position A of Tcon Wall B connected at position B of Tcon Wall C connected at position C of Tcon and Number of pass through layers information for constructing a Tcon Before Connection CONNECTED AT B CONNECTED AT A Wall B Wall CONNECTED AT C Wall C After Connection Wall B Tcon Wall A Wall C Figure 3 11 Three walls can be connected as above with a Tcon The detail description of Tcon is shown in fig 3 13 and fig 3 14 Wall information is used for Tcon construction Tcon can be orientated at upward and downward directions For upward Tcon shown in fig 3 13 points Ai and Bi i 1 2 3 n are generated from the pass through layers
118. tion 118 CHAPTER 2 PARAMETRIC SHAPE CONFIGURATIONS 2 11 Definition of T sections T sections are parametric configurations of the shape depicted in fig 2 86 They consist of a T section possibly reinforced by a top flange The section consists of up to three zones to which independent material properties can be assigned Note that through the use of fixed frames as described in section 7 1 the T section can be made into the following shapes L 4 F or T Figure 2 86 Configuration of the T section T sections are defined by means of three dialog tabs 1 The T section dialog tab as described in section 2 11 1 which defines the name of the section 2 The Dimensions dialog tab as described in section 2 11 2 which defines the dimensions of the section 3 The Materials dialog tab as described in section 2 11 3 which defines the materials the section is made of 2 11 DEFINITION OF T SECTIONS 119 2 11 1 The T section dialog tab T section T section Dimensions Materials Section name Mesh density Figure 2 87 The T section dialog tab The T section dialog tab as described in fig 2 87 defines the following data for the T section 1 Section name Enter a unique name for the T section 2 Mesh density Enter the desired mesh density as described in section 5 1 for the finite element discretization 3 Defined in frame The geometry of the T section can be defined with respect to a fixed frame as describ
119. tructures layers of material are stacked in a mold of arbitrary shape ply insertions or drop offs are allowed The resulting unit is called a wall It is then possible to connect several walls to create complex sections of arbitrary configuration The definition of walls is detailed in section 3 2 the following connectors are available split connectors as described in section 3 3 T connectors as described in section 3 4 and V connectors as described in section 3 5 e The physical properties of the materials the section is made of can be defined in two alternative manners 1 Section 4 1 discusses the definition of material properties Three types of materials can be defined isotropic orthotropic and transversely isotropic materials Material stiffness strength and density can be defined and a failure criterion can be selected 2 Section 4 2 discusses the definition of solid properties In this case a layered material structure is defined each layer features its proper material ply thickness and fiber orientation angles 1 3 Meshing the cross section Once the configuration of the cross section has been defined a finite element mesh discretization is created by clicking the first icon of the SECTIONBUILDER toolbar shown in fig 1 1 A mapped mesh of the section is created The meshing process recognizes the potential presence of layered materials each layer is meshed independently to avoid smearing of the material properties Meshe
120. wisting moment and shearing forces and the corre sponding sectional strain components eq 1 6 it is convenient to introduce the shear center of the cross section a point of the cross section of coordinates 2 as depicted in fig 1 5 With the help of the shear center the relationship between twisting moment and twist rate decouples from the relationship between shearing forces and sectional transverse strains My H 1 23 where MF is the twisting moment computed with respect to the shear center the sectional twist rate and H ki the torsional stiffness The shear forces are related to the sectional transverse strains Kp pi Yt K5 Kss 713 where V V gt and Vf V3 are the sectional shearing forces and yE the sectional transverse shearing strains K and KE the shearing stiffnesses computed with respect to the shear center about axes parallel to 22 and 73 respectively and KE the cross shearing stiffness computed with respect to the shear center about axes parallel to 7 and 23 The forces and moments computed with respect to the reference point and the shear center can be related as follows V pr 1 24 1 Tk3 Lk2 ME ME 1 Tk3 Ck2 Mi V 0 1i 0 vE Wels 1 0 Vo 1 25 V3 0 0 1 VE Ve 0 0 1 V3 Similarly the sectional twist rate and transverse strains with respect to the reference point and shear center are related as follows Ky 1 00 KT i 1 00

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