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1. The sign convention for internal forces is illustrated below Internal forces and transverse displacements are computed using numerical integration of the distributed loads on the frame elements A corrected trapezoidal integration method is implemented so that the internal force and transverse displacement data match the known internal forces and joint displacements at both ends of each frame element Internal forces and displacements computed with a smaller increment length dx are more accurate In general a value of dx equal to one percent to ten percent of the typical frame element length is sufficiently accurate 7 14 Stress Check 7 14 1 Section Modulus and Torsion Shear Constant The section properties required for elastic frame analysis are Ax Asy Asz Jxx lyy and Izz as described section 7 4 To compute stresses from the frame element end forces the following section properties are required Section Area Ax e Section Shear Area Asy and ASZ e Section Modulus Sy and Sz and e Torsion Shear Constant C The units of Sy Sz and C are length cubed like in or mm Referring to the text and figures of section 7 4 the section moduli and torsional shear constants may be found as follows Circular Tube outer radius Ro inner radius Rj e Sy Sz lyy Ro Izz Ro C Jxx Ro 21 of 33 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 22 of 33 Square Tu
2. nD number of joints with prescribed Displacements nD lt nR nE number of frame Elements nF number of joints with point Forces or concentrated moments nI number of joints with extra joint mass or Inertia nJ number of Joints nL number of static Load cases nM number of Modes to be calculated nP number of frame elements with concentrated point loads nR number of joints with Reaction forces nT number of frame elements with Temperature changes nU number of uniformly distributed loads nW number of trapezoidally distributed loads p the roll angle of the frame element in degrees pan the pan rate of the view point during animation Px concentrated point load in the local x direction Py concentrated point load in the local y direction Pz concentrated point load in the local z direction Rx 1 reaction force in the global X direction 0 free Ry 1 reaction force in the global Y direction 0 free RZ 1 reaction force in the global Z direction 0 free RXX 1 reactoin moment about the global X axis 0 free Ryy 1 reaction moment about the global Y axis 0 free R2z 1 reaction moment about the global Z axis 0 free r r radius of rigid joint sphere around joint i shear 1 include shear deformations 0 do not shift shift factor for non definite stiffness matrices tol tolerance for finding mode shapes 1 e 4 Ty temperature change on the local y face of the element Ty te
3. 1 Install a good plain text editor for Windows NotePad or jEdit or gvim A tutorial for gvim is here Alternatively you may use NotePad 2 Download the Frame3DD ZIP archive Frame3DD_VERSION_win32 zip and save it to your Desktop 3 If the ZIP archive was not automatically unzipped double click the icon to extract it to your Desktop 4 Recommended Put the Frame3DD directory in your path and set the PATH and FRAME3DD_OUTDIR environment variables To do this right click My Computer gt Properties gt Advanced gt Environment Variables Set a new user variable name PATH with variable value S HOMEPATH Desktop Frame3DD Set a new user variable name FRAME3DD_OUTDIR with variable value HOMEPATH Desktop Frame3DD temp The Desktop Frame3DD temp folder should already exist Detailed information on how to set environment variables in Windows is here if you need it 5 Open a command prompt window Start gt All Programs gt Accessories gt Command Prompt change to the directory of example files and run an example as follows chdir HOMEPATH Desktop Frame3DD examples frame3dd exE 3dd exE out Alternatively you may double click on the frame3dd program icon and enter the Input Data file name and Output Data file name when prompted as follows Please enter the input data file name examples exE 3dd Please enter the output data file name examples exE out Some run time information will be displayed on the Command Prompt
4. Read the User Manual and Reference this file Download Frame3DD and save the Frame3DD folder to your Desktop more details below Optionally obtain a copy of Gnuplot for your operating system more details below Open a terminal go to the Frame3DD directory and run the program on one of the examples using a command like Pune frame3dd examples exE 3dd examples exE out 5 Open the Output Data file using a good text editor and view the Output Data 6 Plot the structural configuration the deformed structural shape and mode shapes by starting Gnuplot and typing gnuplot gt cd Desktop Frame3DD examples gnuplot gt load exE plt Observe a series of plots by hitting the Return or Enter key between plots If a dynamic analysis was performed you will enjoy an animation of selected mode shapes Continue to hit the Return or Enter key until the last plot is displayed 2 Input Data and Output Data The Input Data file is a plain text file and must adhere to the format described below Several examples are given at http frame3dd sourceforge net When writing your own input files note the following points e Comments may be placed anywhere in the file and are helpful in organizing the Input Data A comment begins with one of the following four characters and continues to the end of the line All commas in the Input Data are ignored Floating point numbers must be entered as 1 234 1234 or 1 234e3 Arithmetic express
5. frame3dd c frame analysis frame3dd_io c input output functions eig c generalized eigenvalue analysis ldl_dcmp c LDL decomposition lu_demp c LU decomposition coordtrans c coordinate transformation nrutil c dynamic memory allocation In addition to the recommended method using SCons see above Frame3DD can also be compiled directly with the GNU gcc compiler the Apple Xcode gcc compiler the DJGPP gcc compiler the LCC win32 compiler and the MinGW gcc compiler Using GCC the command to compile is gcc O o frame3dd main c frame3dd c frame3dd_io c ldl_dcmp c lu_demp c coordtrans c eig c nrutil c lm 13 Exit code index When Frame3DD exits it returns an integer value to the system calling Frame3DD An exit code of 0 zero indicates error free completion Prior to exiting with a non zero exit code Frame3DD writes a diagnostic error message to stderr Exit code values have the following meanings error free completion unknown error error with the command line options see Section 11 above error with the command line option for shear deformation s error with the command line option for geometric stiffness g ee ooo BWNrFO 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 error with the command line option for lumped mass l error with the command line option for modal analysis method m error with the command line option for modal analysis tolerance
6. is not adequately small and geometric stiffness effects are not included in the analysis try including the effects of geometric stiffness by changing the geometric stiffness variable geom in the Input Data file to 1 or by using the gOn command line option Conversely if the RMS relative equilibrium precision is not adequately small and geometric stiffness effects are included in the analysis try neglecting the effects of geometric stiffness by changing the geometric stiffness variable geom in the Input Data file to O or by using the gOff command line option Natural frequencies and mass normalized mode shapes of the lower modes may be obtained using a generalized Jacobi sub space iteration procedure or a Stodola iteration procedure Jacobi subspace iterations are stopped when the frequency convergence error is less than the specified frequency convergence tolerance The frequency convergence error is defined here as 23 of 33 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 error fN i FN i 1 fN i where e fN i is the highest natural frequency computed at iteration i e fN i 1 is the highest natural frequency computed at iteration i 1 9 Input Data Format Click here to download an Input Data template template 3dd or copy and paste the text below The first line of the Input Data file must be a one line title of your analysis It is recommended to write the system of units
7. 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 Polar Moments of Inertia depend on the shape of the cross section For sections with a circular cross section Jxx lyy Izz For sections with a solid rectangular cross section width b depth d b lt d Ixx Qdb where Q 1 3 0 2244 d b 0 1607 Q 1 3 0 224 db 0 161 0 35 0 3 0 25 L 10 100 d b For more details see page 271 of Timoshenko and Goodier 1951 For open sections made up of thin plates length b thickness t Jxx Z bit 3 For closed single box sections made up of thin plates length b thickness t Ixx 4A2 3 bi ti where A is the area enclosed by the box Restraints to warping deformation are not considered in the analysis 7 4 4 Bending Effects The bending moments of inertia lyy and zz are the principle bending moments of inertia for the cross section 7 4 5 Cross Section Properties of Circular Tube Square Tube Rectangular Tube and I shaped Sections Z SSS HELL SSS 2 f Circular Tube Square Tube Rectangular Tube Circular Tube outer radius Ro inner radius Rj Ax Ro RP e Asy ASZ Ax 1 124235 0 055610 Ri Ro 1 097134 Ri Ro 0 630057 Ri Ro 0 5 e Asy Asz Ax 1 06124 0 59546 Ri Ro 2 14 of 33 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc f
8. 1 locations and loads local y axis xz1 1 xz2 2 wz1 1 wz2 1 locations and loads local z axis M nW xxl nW xx2 nW wxl nW wx2 nW xl and x2 start and end locations xyl nW xy2 nW wyl nW wy2 nW wl and w2 start load and end load xzl nW xz2 nW wzl nW wz2 nW 0 lt xl lt x2 lt L nP number of concentrated interior point loads local elmnt X load Y load 2Z load x loc n point loads in member coordinates M 1 Px 1 Py 1 Pz 1 x 1 x distance from coordinate J1 M nP Px nP Py nP Pz nP x nP 0 lt x lt L nT number of frame elements with temperature changes local elmnt coef y depth z depth deltaTy deltaTy deltaTz deltaTz deg C mm mm deg C deg C deg C deg C M 1 a l hy 1 hz 1 Ty 1 Ty 1 Tz 1 Tz 1 M nT a nT hy nT hz nT Ty nT Ty nT Tz nT Tz nT nD number of prescribed displacements nD lt nR global jnt X displ Y displ Z displ xX rot n Y rot n Z rot n mm mm mm radian radian radian J 1 Dx 1 Dy 1 Dz 3 Dxx 1 Dyy 1 Dzz 1 J nD Dx nD Dy nD Dz nD Dxx nD Dyy nD Dzz nD End Static Load Case 2 repeat up to 30 static load cases dynamic analysis data nM number of desired dynamic modes if nM is set to 0 zero the remaining Input Data may be omitted Mmethod 1 Subspace Jacobi iteration 2 Stodola matrix iteration method lump 0 consistent mass matrix 1 lumped mass matrix tol frequency c
9. 1 the shear stress in the local y axis on average is abs Vy1 Asy abs Txx1 C At end 1 the shear stress in the local z axis on average is abs Vz1 Asz abs Txx1 C And likewise for end 2 8 Numerical Details Frame3DD imposes no limit on the number of degrees of freedom Dynamic memory allocation is accomplished by the public domain routines found in Press W H et al Numerical Recipes In C Cambridge England Cambridge University Press 1991 Frame3DD analyzes the response to temperature loads alone prior to solving for the response to the combination of temperature loads and mechanical loads In this way temperature loads may be used to simulate the effect of pre tension in structures which can provide geometric stiffness For each load case Frame3DD carries out the following nine steps Assemble the structural stiffness matrix for the un stressed structure Compute the joint displacements due to temperature loads using a linear elastic analysis Compute frame element end forces from the displacements due to temperature loads Assemble the structural stiffness matrix again ON 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 If goemetric stiffness effects are to be considered the assembly process makes use of the axial frame element forces arising from the temperature loads Compute the joint displacements due to mechanical loads Add the joint displa
10. There should be no need to install another editor A tutorial for vim is here Download the Frame3DD ZIP archive Frame3DD_VERSION linux zip and save it in your Desktop If the ZIP archive was not automatically unzipped double click the icon to extract it to your Desktop Recommended Put the Frame3DD directory in your path and set the FRAME3DD_OUTDIR location To do this double click the Home icon on the Desktop and select View gt Show Hidden Files If you have a file called bashrc in your home directory open it with a double click Copy and paste the following ten lines into the beginning of bashre for Frame3DD http frame3dd sourceforge net add Frame3DD executable directory to the path export PATH SPATH SHOME Desktop Frame3DD create a Frame3DD output directory if d tmp frame3dd_temp_ USER then mkdir tmp frame3dd_temp_ USER echo creating tmp frame3dd_temp_S USER for Frame3DD fi specify the Frame3DD output directory export FRAME3DD_OUTDIR tmp frame3dd_temp_ USER Save and exit the editor If you have a file named cshrc in your home directory open it with a double click Copy and paste the following ten lines into the beginning of cshrc for Frame3DD http frame3dd sourceforge net add Frame3DD executable directory to the path set path path home Desktop Frame3DD create a Frame3DD output directory if d tmp frame3dd_temp_ user then mkdir tmp frame3dd_temp_ use
11. convention for frame element end forces is shown in the figure below The double headed arrows adhere to the right hand rule Z Mz The mathematical signs of the member end forces are relative to the local x y z axes of the frame element and designate the direction of the force along those axes A positive Nx at joint 1 of the member is compressive while a negative Nx at joint 2 is also compressive The opposite is true for tension The Output Data lists a t or a c along with the axial forces Nx in order to help clarify whether the end force is putting the frame element into tension or compression A frame element with positive My at joint 1 and a negative My at joint 2 has positive curvature in the x z plane A frame element 19 of 33 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 with negative Mz at joint 1 and a positive Mz at joint 2 has positive curvature in the x y plane 7 13 Internal Frame Element Forces and Transverse Displacements Frame3DD optionally generates output data files listing the internal axial force shear forces torsion and bending momements and transverse displacements for each frame element These quantities are tabulated at user specified increments of length dx along the local x axis of each frame element If the x axis increment dx is specified as a value of 1 then the calculation of internal frame element forces and transverse displacements is skipped O
12. frame element joint for each frame element 1 the starting 2 the ending matrix indicated which joints have reactions 0 the joint has no reaction in that degree of freedom 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 1 the joint does have a reaction in that degree of freedom EAIJ a 10xB containing the section and modulus properties of each frame el row 1 Ax cross section area for each frame el row 2 Asy shear area y directionfor each frame el row 3 Asz shear area z directionfor each frame el row 4 Jxx torsional moment of inertia x axis for each frame el row 5 Iyy bending moment of inertia y axis for each frame el row 6 Izz bending moment of inertia z axis for each frame el row 7 E elastic modulus for each frame el row 8 G shear modulus for each frame el row 9 p roll angle for each frame el row 10 d mass density for each frame el P a 6xJ matrix containing the components of the external forces and moments applied to each joint row 1 Joint Force in X direction for each joint row 2 Joint Force in Y direction for each joint row 3 Joint Force in Z direction for each joint row 4 Joint Moment about X axis for each joint row 5 Joint Moment about Y axis for each joint row 6 Joint Moment about Z axis for each joint U a 3xB matrix containing the unif dist load on each frame element row 1 uniform distributed load along the lo
13. in the global X direction Fy Joint load in the global Y direction FZ Joint load in the global Z direction G Shear modulus of elasticity of frame element i gX gravitational acceleration in the global X direction gY gravitational acceleration in the global Y direction gZ gravitational acceleration in the global Z direction geom 1 include geometric stiffness effects 0 do not hy cross section dimension in the local y coordinate dir hz cross section dimension in the local z coordinate dir Iy Moment of inertia for bending about the local y axis Iz Moment of inertia for bending about the local z axis J Joint number J1 Joint 1 of a frame element J2 Joint 2 of a frame element JMs extra mass of a joint for translational motion JMx extra rotatory inertia of a joint about global x coord dir JMy extra rotatory inertia of a joint about global y coord dir JMz extra rotatory inertia of a joint about global z coord dir JX Torsional moment of inertia of a frame element lump 1 use lumped mass matrix 0 use consistent mass matrix M Member number Mxx Joint Moment about the global X axis Myy Joint Moment about the global Y axis Mzz Joint Moment about the global Z axis m list of modes to match in dynamic condensation Mmethod the modal analysis method 1 Subspace Jacobi 2 Stodola nA number of mode shapes to Animate must be less than 20 nc number of joints for matrix Condensation
14. less the rigid radii on each end All joints are fully moment resisting Semi rigid connections may be modeled through the use of short frame elements at the ends of longer members X For two dimensional planar structures the global X direction is horizontal and the global Y direction is vertical For three dimensional structures the global X and Y directions are horizontal and the global Z direction is vertical Joint numbers should be assigned in a systematic way moving from one end of the structural system to the opposite end Support conditions are modeled by fixing the degrees of freedom collocated with reaction forces By default displacements at the fixed degrees of freedom are zero Optionally displacements at the fixed degrees of freedom may be prescribed as a type of loading Elastic support conditions may be modeled by additional elements with the desired flexibility Static reaction forces at the fixed degrees of freedom are computed and are appended to the Output Data file 7 3 Numbering of Frame Element Starting Joints and Ending Joints Coordinate transformations in 3D are not unique and depend upon the sequence of rotations In some cases the orientation of an element within a structure may not be obvious if the element has rotated by more than 90 degrees in going from the local system to the global system For this reason it can be helpful to define end joints in a way that requires rotations of less than 90 degrees about an
15. like sudo apt get install gnuplot or by using the package manager GUI installed on your system 2 Start Gnuplot in the Terminal with the command gnuplot 3 Display the plots of your structure using Gnuplot with a command like gnuplot gt load MyResultsA plt where MyResultsA out is the name of of the Output Data file specified when running Frame3DD 4 Hit the Return key in the Terminal window to see the sequence of plots and animations until the gnuplot gt prompt returns Or hit CTRL C to stop the plots at the current plot 5 To save the current plot as a PostScript file in the Frame3DD examples directory use the saveplot script included in the Frame3DD examples directory gnuplot gt load saveplot gnuplot gt cp my plot ps PlotFileA ps 6 After finishing with your plots you can exit Gnuplot by typing gnuplot gt quit 3 1 2 Installing from source for Linux or Unix The following instructions work on Ubuntu 8 10 9 10 and should work with minor changes on any other recent Linux or Unix system 1 Ensure you have Python SCons and GCC installed on your system On Debian based systems it should suffice to 3 2 4 of 33 sudo apt get install build essential scons If you would like to build the Microstran viewer ensure that the package libsoqt dev4 is installed on your system sudo apt get install libsoqgt dev4 Download the Frame3DD source code tarball frame3dd VERSION tar bz2 and save it in your home directory
16. t error with the command line option for modal analysis shift f 9 error with the command line option for pan rate p 10 error with the command line option for matrix condensation r 11 error in opening the Input Data file 12 error in opening the temporary cleaned input data file for writing 13 error in opening the temporary cleaned input data file for reading 14 error in opening the Output Data file 15 error in creating the path for temporary output data files 16 error in creating the temporary output data file path name 17 error in opening the CSV spread sheet output data file 18 error in opening the M matlab output data file 19 error in opening the interior force output data file for writing 20 error in opening the interior force output data file for reading 21 error in opening the undeformed mesh ouput data file 22 error in opening the deformed mesh ouput data file 23 error in opening the plotting script file for writing first static load case plots 24 error in opening the plotting script file for appending second and higher static load case results 25 error in opening the plotting script file for appending modal plots 26 error in opening the plotting script file for appending modal animations 27 error in opening the modal mesh data file 28 error in opening the modal mesh animation data file 29 error in opening the mass data debugging file MassData txt 30 cubic curvefit sy
17. temporary output directory The additional output files will then appear in the folder you have specified 3 How to install and run Frame3DD Compiled executable programs are updated with some regularity Frame3DD installation packages are available for download for Linux for OS X and for Windows operating systems as ZIP archives These installation ZIP archives include 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 3 of 33 A copy of the GPL license LICENSE txt The executable program frame3dd for the selected operating system Linux OS X or Windows This manual doc user manual html Some general information README txt Some Windows specific issues README win32 txt The Matlab interface code matlab A summary of recent updates to the program ChangeLog txt A set of example Input Data files examples A separate Windows installer includes a Microstran viewer module for Frame3DD The date stamp at the beginning of the manual corresponds to the release date of the code 3 1 Linux For Linux you may install Frame3DD from a ZIP archive or you may compile for Linux or Unix from the source code The following instructions install Frame3DD to the Desktop but other directories may be substituted if so desired 3 1 1 Installing from the ZIP archive for Linux I 2 3 4 6 Linux and Unix systems have good plain text editors pre installed vim gedit nano
18. window and the results of your Frame3DD analysis will have been appended to the end of the exE out Output Data file Data files used primarily for plotting are stored in the Desktop Frame3DD temp folder 6 You may view Output Data files and edit Input Data files using a good plain text editor NotePad jEdit gvim ora spreadsheet program GoogleDocs OpenOffice 7 Run your own Frame3DD analyses within the Command Prompt window using a command like frame3dd MyFrame 3dd MyResultsA out Use Gnuplot to view the graphical output Download the MS Windows version of Gnuplot and save it to your Desktop Navigate to Desktop gt Gnuplot gt bin and right click on wgnuplot to create a shortcut to your Desktop Clicking on the wgnuplot icon on the Desktop will start Gnuplot To load the plot into Gnuplot first change directory to to location of your output files by clicking on the ChDir button at the top of the Gnuplot window and navigating to Desktop gt Frame3DD gt examples 5 Display the plots of your structure using Gnuplot with a command like AWN gnuplot gt load MyResultsA plt 11 09 2010 11 18 AM Frame3DD User Manual 7 of 33 http frame3dd svn sourceforge net viewvc frame3 where MyResultsA out is the name of of the Output Data file specified when running Frame3DD 6 Click OK to see the next plot or Cancel to stop with the current plot 7 To save the current plot as a PostScript file in the Frame3DD exa
19. 1 amp 3295 RAAG ANNNeOek NA 1727772 N O07107 The header information for each frame element contains the element number column B the element s end joints columns C and D the end joint coordinates columns E J and the number of x axis increments for the frame element column K The data for this part of the header information is preceded with a character to facilitate parsing of this data file The last header character prior to the the internal force data is a character again to facilitate parsing of the data In the figure above nx is 181 K 10 indicating that the following element data is tabulated at 181 increments along the local x axis The data in this file is sufficient to plot the undeformed mesh the deformed mesh and plots of internal forces torisons and 20 of 33 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 moments super imposed upon the structural mesh The sign convention for internal forces and transverse displacements is as follows Positive internal axial force Nx is tensile Positive internal shear forces Vy and Vz are in the positive y and z directions on positive x surfaces Positive internal torsion Tx is counter clockwise about the positive x axis Positive bending moments My and Mz produce positive curvature bending deformation in the x z and x y planes Positive transverse displacements Dy and Dz are in the positive y and z directions
20. 3DD User Manual http frame3dd svn sourceforge net viewvc frame3 gravitational acceleration for self weight loading mm s 2 global gX gY gZ mm s 2 mm s 2 mm s 2 gx gY gZ nF number of loaded joints global joint X load Y load Z load X mom Y mom Z mom N N N N mm N mm N mm J 1 Fx 1 Fy 1 Fz 1 Mxx 1 Myy 1 Mzz 1 J nF Fx nF Fy nF Fz nF Mxx nF Myy nF Mzz nF nU number of uniformly distributed element loads local elmnt X load Y load Z load uniform member loads in member coordinates N mm N mm N mm M 1 Ux 1 Uy 1 Uz 1 M nU Ux nU Uy nU Uz nU nW number of trapezoidally distributed element loads local start stop start stop elmnt loc n loc n load load mm mm N mm N mm M 1 xxl 1 xx2 2 wx1 1 wx2 1 locations and loads local x axis xyl 1 xy2 2 wyl 1 wy2 1 locations and loads local y axis xz1 1 xz2 2 wz1 1 wz2 1 locations and loads local z axis M nW xxl nW xx2 nW wxl nW wx2 nW xl and x2 start and end locations xyl nW xy2 nW wyl nW wy2 nW wl and w2 start load and end load xzl nW xz2 nW wzl nW wz2 nW 0 lt xl lt x2 lt L nP number of concentrated interior point loads local elmnt X load Y load Z load x loc n point loads in member coordinates M 1 Px 1 Py 1 Pz 1 x 1 x distance from coordinate J1 M nP Px nP Py nP Pz nP x nP 0 lt x lt L nT number of frame elements with tem
21. 3DD matlab path In Windows you can add the Frame3DD directory to your matlab path with the matlab commands path getenv USERPROFILE Desktop Frame3DD path path getenv USERPROFILE Desktop Frame3DD matlab path The matlab interface function frame 3dd m executes the system command frame3dd on Linux or OS X frame3dd exe on Windows to compute the solution 1 The Matlab file for your problem first sets up the various matrices defining the problem for analysis and calls frame_3dd m A Matlab version of Example A illustrates how to analyze problems using the Matlab interface to Frame3DD 8 of 33 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 9 of 33 Matlab versions of the other examples are forthcoming frame_3dd m writes a Frame3DD input data file called IOdata FMM frame_3dd m calls a system command to run the executable program frame3dd in the input data file IOdata FMM The executable program frame3dd writes the Output Data to IOdata OUT and also writes IOdata_out m containing the Output Data An m file containing the Output Data is written whenever the frame3dd executable is run on a file ending in FMM whether or not the analysis is initiated by frame_3dd m 5 frame_3dd m runs Odata_out m containing the matrices D R F L and Ks 6 frame_3dd m returns D R F L and Ks to the Matlab workspace or to your Matlab function Pw This m function
22. 9 6051 51 973 4 45839 40 3 38 859 29 1157 32 7562 30 885 49 172 2 6572 41 4 5 39A 19 N34 71 AZRA 43 797 4473214 49N47 Modal analysis results are not yet written to the CSV formatted output file 6 FrameEd Frame_Ed is a Windows GUI for the 20020103 version of Frame3DD Jan 3 2002 The zip file FrameEd zip includes e the GUI executable Frame_Ed exe the frame analysis executable Frame3d exe for the 20020103 version e an example input file exG 3dd for the 20020103 version e a template for the Input Data file ex2002 3dd for the 20020103 version Differences between the 2002 and the current versions of Frame3DD are e The 2002 version does not support comments in the Input Data e The 2002 version does not support multiple load cases e The 2002 version does not support roll angles for frame element orientation e The 2002 version uses the Jacobi method for modal analysis e The 2002 version requires specification of joint masses and inertias for every joint e The 2002 version does not support panning of the animation e The 2002 version uses Guyan reduction for matrix condensation to match the first mode Source code for FrameEd is not currently available and development on this GUI is no longer active 7 Structural Modeling 7 1 Units The Output Data is formatted using floating point display not scientific notation To obtain the greatest number of significant 11 of 33 11 09 2010 11 18 AM Frame3D
23. Ax Cross sectional area of a prismatic frame element The x axis is along the element length in local coordinates Asy Shear area in the local y axis of a prismatic frame element Asz Shear area in the local z axis of a prismatic frame element BMs extra mass on a frame element not including self mass Cmethod matrix condensation method O none 1l static 2 Guyan 3 dynamic cx 1 retain X d o f in condensed system at joint J 0 don t cy 1 retain Y d o f in condensed system at joint J 0 don t cz 1 retain Z d o f in condensed system at joint J 0 don t CXX 1 retain X axis rotation at joint J 0 don t cyy 1 retain Y axis rotation at joint J 0 don t Czz 1 retain Z axis rotation at joint J 0 don t Dx Prescribed displacement in the global X direction Dy Prescribed displacement in the global Y direction Dz Prescribed displacement in the global Z direction Dxx Prescribed rotation in the global X direction Dyy Prescribed rotation in the global Y direction Dzz Prescribed rotation in the global Z direction d mass density of a frame element 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 dx x axis increment for frame element internal force data E Modulus of elasticity of a frame element exagg_modal Exaggeration factor for the modal displacements in the plot exagg_ static Exaggeration factor for the static displacements in the plot Fx Joint load
24. D User Manual http frame3dd svn sourceforge net viewvc frame3 digits in the output use units of force and length such that the modulus of elasticity occupies three to five figures before the decimal point For example if the frame to be analyzed is made of steel or aluminum use units of kips 1000 pounds and inches or Newtons millimeters and tonne or MegaNewtons meters and kilotonnes It is recommended to write the units used in your analysis in the title of the analysis and throughout the Input Data files as is done in the example Input Data files 1 inch 25 4 millimeter 0 0254 meter 1 kip 4 448 221 6 Newton 0 004 448 221 6 MegaNewton 1 kip square inch 6 894 757 28 Newton square millimeter 6 894 757 28 MegaNewton square meter 1 kip cubic inch 0 027 679 904 593 tonne cubic millimeter 27 679 904 593 kilotonne cubic meter 1 deg F 1 8 deg C 7 2 Joints Coordinates Support Conditions and Reactions Joint positions are specified by locations in a three dimensional Cartesian coordinate system Each joint has six coordinates three translations in the global X Y and Z directions and three rotations about the global X Y and Z axes Optionally joints may be modeled as rigid within a sphere of radius r The effects of finite joint sizes are modeled approximately in the calculation of the frame element stiffness through the use of an effective beam length which is the joint to joint length of the frame element
25. DD examples gnuplot gt load MyResultsA plt where MyResultsA out is the name of of the Output Data file specified when running frame3dd Hit the Return key in the Terminal window to see the sequence of plots and animations until the gnuplot gt prompt returns To save the current plot as a PDF file in the Frame3DD examples directory use the saveplot_osx script included in 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 6 of 33 the Frame3DD examples directory gnuplot gt load saveplot_osx gnuplot gt cp my plot pdf PlotFileA pdf 5 After finishing with your plots you can exit Gnuplot by typing gnuplot gt quit 3 2 2 Compiling the source on OS X 1 Install the Xcode Developer Tools for your version of OS X as described above 2 Download the Frame3DD source code tarball frame3dd VERSION tar bz2 and save it in your home directory 3 Unpack the source code enter the source directory and build the code as follows gcc 0 o frame3dd main c frame3dd c frame3dd_io c 1ldl_demp c lu_demp c coordtrans c eig c nrutil 3 3 Windows For Microsoft Windows you may install Frame3DD from a ZIP archive you may use a binary installer which may sometimes be out of date or you may compile from the source code The following instructions install Frame3DD to the Desktop but other directories may be substituted if so desired 3 3 1 Installing from the ZIP archive for Windows
26. Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 1 of 33 User manual and reference for Frame3DD A Structural Frame Analysis Program Department of Civil and Environmental Engineerin Edmund T Pratt School of Engineerin Duke University Box 90287 Durham NC 27708 0287 FRAME3DD Version 0 20100105 Frame3DD is a program for the static and dynamic structural analysis of two and three dimensional frames and trusses with elastic and geometric stiffness Frame3DD is preferably executed from the command prompt Windows or shell Linux or terminal OS X as follows with filenames changed as required frame3dd inputfile 3dd outputfile txt Frame3DD reads a plain text Input Data file containing joint coordinates frame element geometry material moduli fixed joints prescribed displacements load information and optionally mass information if a modal analysis is to be carried out Frame3DD appends results to a plain text Output Data file Results from the most recent analysis are appended to the end of the Output Data file Each section of the Output Data gives the date and time of the analysis recapitulates the input information gives joint displacements in global coordinates frame element end forces in local coordinates reactions in global coordinates and natural frequencies and mode shapes in global coordinates Frame3DD writes a Gnuplot script file used for viewing deformed frames and dynamic m
27. Open a Terminal unpack the source code enter the source directory and build the code as follows tar jxvf frame3dd VERSION tar bz2 cd frame3dd VERSION scons If you have root privileges install build frame3dd to usr local bin sudo scons install or you may install frame3dd in another system directory if your choosing such as sudo scons install INSTALL PREFIX usr bin If you do not have root privileges you can run Frame3dd directly from the build tree export LD_LIBRARY_PATH frame3dd VERSION build export PATH SPATH frame3dd VERSION build Copy one of the frame3dd VERSION examples 3dd files e g exE 3dd into your home directory make sure you have write privileges for the file and run one of the examples frame3dd exE 3dd exE out Mac OS X 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 5 of 33 For OS X running on an Intel processor you may install Frame3DD from a ZIP archive or you may compile from the source code The following instructions install Frame3DD to the Desktop but other directories may be substituted if so desired 3 2 1 Installing from the ZIP archive for OS X PUNE 1 Install a good plain text editor for OS X jEdit or Vim A tutorial for Vim is here Alternatively you may use TextEdit Download the Frame3DD ZIP archive Frame3DD_VERSION_osx zip and save it in your Desktop If the ZIP archive was not automatically unzipped doub
28. al for all three dimensional plots Another more customary coordinate transformation process is also implemented in the software In the alternative coordinate transformation process the frame element is first rotated about the global Z axis then about the global Y axis then rolled about the local x axis If the roll angle is zero this transformation results in a frame element with no cross axis bending due to loads are applied in the global Y direction In the code this type of transformation is called Y axis is vertical For a derivation of the alternative coordinate transformation method refer to section 8 3 of the textbook Matrix Analysis of Structures by A Kassimali 16 of 33 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 17 of 33 By allowing the frame element to be rolled about its local x axis during the stiffness matrix assembly process cross axis bending effects may be included Issues related to rolling of cross sections and cross axis bending are important for three dimensional structural systems or planar structures with out of plane deformation such as grillages For planar structures with deformations only in the plane these issues do not arise In addition these issues do not arise for three dimensional structures made entirely of elements for which lyy izz i e square and circular cross sections To reiterate in 2D frames the roll angle p does not matter and can be s
29. ation When geometric stiffness effects are included the solution is obtained iteratively using a quasi Newton Raphson method K D i dD i F K D i D i D i 1 D i dD i where e D i is the displacement vector at iteration i K D i is the secant stiffness matrix at displacements D i e F is the applied load vector e dD i is the incremental displacement vector at iteration i and e D i 1 is the displacement vector at iteration i 1 At each Newton Raphson iteration the relative equilibrium error is displayed to the screen This error is the root mean square of F K D i D i divided by the root mean square of F Newton Raphson iterations stop when this error is less than the convergence tolerance The convergence tolerance is specified as the convergence tolerance for the modal analysis The default value is 0 00001 The accuracy of the final solution is checked using a global equilibrium check and the equilibrium error is reported The RMS relative equilibrium precision is the root mean square of internal frame element forces and external applied loads at every un restrained degree of freedom normalized by the root mean square of the applied loads This equilibrium error is typically less than one part in one billion when geometric stiffness effects are neglected If an analysis has an RMS relative equilibrium precision larger than 0 001 the results should not be trusted If the RMS relative equilibrium precision
30. ations for section properties should therefore be used whenever available Some tabulated section properties are provided below 7 4 6 Cross Section Properties Of Some Common Steel Sections Structural Steel Steel W section beams 1 Steel W section beams 2 Steel S section beams Steel Angles 1 Steel Angles 2 Steel Channels 15 of 33 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 e Aluminum beam e Aluminum Channels 7 4 7 Cross Section Properties Of Some Standard Wood Sections Ax Asy Asz JXX Iyy Izz in 2 in 2 in 2 in 4 in 4 in 4 2x3 3 750 2 500 2 500 1 776 1 953 0 708 2x4 5 250 3 500 3 500 2 875 6 359 0 984 2x5 6 750 4 500 4 500 3 984 11 390 1 266 2x6 8 250 5 500 5 500 5 099 20 800 1 547 2x8 10 850 7 233 7 233 7 057 47 630 2 039 2x10 13 880 9 253 9 253 9 299 98 930 2 602 2x12 16 880 11 253 11 253 11 544 178 000 3 164 2x14 19 880 13 253 13 253 13 790 290 800 33127 7 5 Approximate Properties of Structural Materials Thermal Modulus Young s Shear Expansion Mass per Modulus Modulus Coefficient Density Density E G a d E d N mm 2 N mm 2 deg C T mm 3 mm 2 s 2 Steel A36 200000 79300 11 7e 6 7 85e 9 2 55e13 Boron Fiber Epoxy 106000 38000 30 0e 6 2 00e 9 5 30e13 Carbon Fiber Epoxy 83000 30000 30 0e 6 1 54e 9 5 39e13 Aluminum 2024 T4 73100 28000 23 2e 6 2 78e 9 2 63e13 Aluminum 6061 T6 68900 26000 23 6e 6 2 70e 9 2 55e13 Kevlar Fiber Epoxy 40000 50000 30 0e 6 1 40e 9 2 86e13 G
31. be outer dimension b x b wall thickness t e Sy Sz lyy b 2 Izz b 2 e C 2t b t Rectangular Tube outer dimension a x b wall thickness t e Sy lyy b 2 Sz Izz a 2 e C 2 t a t b t sections depth d width b flange thickness t web thickness w Sy lyy d 2 e Sz Izz b 2 e C sxx 1 28 t assuming t gt w Note Commercial sections have rounded corners Manufacturer specifications for cross sectional properties account for the fact that the corners of the cross sections are rounded Manufacturer specifcations for section properties should therefore be used whenever available Some tabulated section properties are provided in section 7 4 7 14 2 Axial Stress Given the section properties Ax Sy and Sz the axial stresses at the ends of frame elements may be bounded as follows At end 1 of a frame element the maximum bending plus axial tensile stress in the frame element is no greater than Nx1 Ax abs Myy1 Sy abs Mzzi Sz At end 2 the maximum bending plus axial tensile stress in the frame element is no greater than Nx2 Ax abs Myyz2 Sy abs Mzz2 Sz A c indicator on Nx values in the Frame3DD Output Data file indicates compression A t indicator on Nx values indicates tension 7 14 3 Shear Stress Given the section properties Asy Asz and C the axial stresses at the ends of frame elements may be approximated as follows At end
32. ble Such structural configurations can not carry static loads Furthermore the numerical methods used in computing the natural frequencies and mode shapes presume that the stiffness matrix is invertible A numerical trick called frequency shifting overcomes this difficulty Presuming the mass matrix M is invertible and given a sufficiently large positive scalar value s the matrix K s M is invertible even if the stiffness 18 of 33 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 matrix K is not invertible So for the purpose of computing the natural frequencies of frames with rigid body modes K is replaced by K s M The desired natural frequencies are shifted by an amount equal to the shift variable s and are shifted back after the natural frequencies and mode shapes are found The mode shapes are un changed by this shifting If natural frequencies are computed as nan not a number try increasing the value of the frequency shift variable either in the Input Data file or using the f command line option Structural models that are partially restrained or unrestrained should not include geometric stiffness effects A Sturm check is carried out to determine if any eigen values were missed If a dynamic analysis is not to be performed simply set the nM variable the number of desired modes to zero 0 If nM is set to zero Frame3DD will stop reading the Input file at this p
33. cal element x axis row 2 uniform distributed load in the local element y axis row 3 uniform distributed load in the local element z axis D a 6xJ matrix of prescribed displacements at the reaction DoF s row 1 prescribed joint displ in the X direction for each joint row 2 prescribed joint displ in the Y direction for each joint row 3 prescribed joint displ in the Z direction for each joint row 4 prescribed joint rot n about the X axis for each joint row 5 prescribed joint rot n about the Y axis for each joint row 6 prescribed joint rot n about the Z axis for each joint OUTPUT DATA AP dP dP AP AP AP AP AP AP AP BO GP cP AP AP AP AP AP AP AP DP GP GP AP AP AP AP ADP AP AP AO GO V AP P GP AP AP AP AP DP GP OP D a 6xJ matrix of the deflections and rotations of each joint R a 6xJ matrix of the reaction forces and moments F a 12xB matrix of the end forces of each frame element L a 1xB vector of the length of each frame element Ks a 6Jx6J matrix of the structural stiffness matrix The Frame3DD executable program frame3dd on Linux or OS X frame3dd exe on Windows and the matlab interface function frame_3dd m must be saved to directories within your Matlab path To display the or modify the matlab path use the matlab command path In Linux and OS X you can add the Frame3DD directory to your matlab path with the matlab commands path getenv HOME Desktop Frame3DD path path getenv HOME Desktop Frame
34. cements due to mechanical loads to the joint displacements due to temperature loads Compute frame element end forces from the displacements due to the combined temperature and mechanical loads If geometric stiffness effects are to be considered carry out quasi Newton Raphson iterations to converge upon the displacements that satisfy equilibrium The assembly process makes use of the axial frame element forces arising from the combined temperature and mechanical loads 9 Compute the RMS relative equilibrium error ON au Solutions of the matrix equation K d f make use of LDL decomposition back substitution with sparse matrix short cuts and iterative improvement for enhanced speed and accuracy When the program is executed various solution errors are displayed to the screen and are written to the Output Data file Iterative improvements to the LDL back substitution make use of a quasi Newton Raphson method K dD i F K D i D i 1 D i dD i where D i is the displacement vector at iteration i K is the stiffness matrix F is the applied load vector dD i is the incremental displacement vector at iteration i and D i 1 is the displacement vector at iteration i 1 At each LDL back substitution iteration the equilibrium error is displayed to the screen as the RMS equilibrium precision This error is the root mean square of dD i Iterations are stopped when this error decreases by less than ten percent in an iter
35. d itself is available from http www sourceforge net projects frame3dd Last update Last updated 11 09 2010 11 08 06 see full revision log 33 of 33 11 09 2010 11 18 AM
36. e been appended to the end of the exE out Output Data file Data files used primarily for plotting are stored in the Desktop Frame3DD temp folder 6 You may run Frame3DD examine the analysis results visualize the results using Gnuplot and edit Input Data files as described above 3 3 3 Compiling the source on Windows 1 Install a GCC compatible compiler such as the DJGPP gcc compiler the LCC win32 compiler or the MinGW compiler 2 Download the Frame3DD source code tarball frame3dd VERSION tar bz2 and save it in your home directory 3 Unpack the source code enter the source directory and build the code as follows gcc 0 o frame3dd main c frame3dd c frame3dd_io c 1ldl_demp c lu_demp c coordtrans c eig c nrutil 4 Matlab Interface Frame3DD may optionally be executed from within Matlab on any platform via the Matlab interface function frame 3dd m function D R F L Ks frame_3dd XYZ JTS RCT EAIJ P U D D R F L Ks frame 3dd XYZ JTS RCT EAIJ P U D Solve a a three dimensional frame analysis problem INPUT DATA XYZ a 4xJd row row row row JTS a 2xB row row RCT a 6xJ matrix containing the XYZ coordinate of each joint 1 X axis coordinate for each joint Y axis coordinate for each joint Z axis coordinate for each joint N e Ww oll rigid radius for each joint matrix indicating which 2 joints each frame element connects joint for each
37. eadsheet program may be read by Matlab or may be read by your own program for further post processing or visualization An example of the first several lines of an internal force data file is shown here In this example the x axis increment dx has a length of 10 mm A B G D E F G H J 1 FRAME3DD ANALYSIS RESULTS http frame3dd sf net VERSION 20100105 2 _ Example B a pyramid shaped frame static and dynamic analysis N mm ton 3 MyResultsA if02 4 Mon Jan 11 11 20 59 2010 5 LOAD CASE 2 of 3 6 FRAME ELEMENT INTERNAL FORCES local z FRAME ELEMENT TRANSVERSE DISPLACEMENTS local E 9 Elmnt jl J2 X1 Yl Zl X2 Y2 Z2 10 1 2 1 1200 900 o 0 0 1000 EEE x Nx Vy Vz Tx My Mz Dx Dy Dz 12 QO 100 41 4 1321 91 7254 1096 50 30000 8 147 19 0 0 0 13 10 100 40 4 1321 90 7485 1096 50 29088 4 105 75 0 00076 0 02544 0 0088 14 20 100 38 4 1321 89 7715 1096 50 28185 9 64 323 0 00152 0 04809 0 01118 15 30 100 36 4 1321 88 7946 1096 50 27293 1 22 892 0 00229 0 06800 0 05867 16 40 100 35 4 1321 87 8176 1096 50 26410 1 18 5390 0 00305 0 08520 0 13280 17 50 100 33 4 1321 86 8407 1096 50 25536 8 59 9701 0 00381 0 09975 0 23266 18 60 100 32 4 1321 85 8638 1096 50 24673 3 101 401 0 00457 0 11169 0 35736 19 70 100 30 4 1321 84 8868 1096 50 23819 6 142 832 0 00533 0 12105 0 50603 20 80 100 29 4 1321 83 9099 1096 50 22975 7 184 264 0 00610 0 12789 0 67780 21 an 1AN D7 A 1271 e7 072970 1ANA GN 2914
38. ection Properties Cross sectional properties of frame elements are specified in a local coordinate system in which the x axis of the local coordinate system is oriented along the axis of the frame element The local y axis and z axis are aligned with the principle directions of the shape of the cross section 7 4 1 Axial Effects Ax is the cross sectional area of the frame element which is given as the cross sectional area of the material perpendicular to the local x axis 7 4 2 Shear Effects Shear strains in frame elements are distributed in a relatively complicated manner over the cross section Shear areas are effective cross sectional areas corresponding to a uniform distribution of shear strain over the cross section The shear area values Asy and Asz fully account for the non uniform distribution of shear strain in the cross section For slender frame elements in which the span to depth ratio is greater than 10 shear deformations contribute only slightly to the overall structural deformation For stocky frame elements in which the span to depth ratio is less than 5 shear deformations contribute significantly to the overall structural deformation The shear area formulas below for circular square and rectangular cross sections provide accurate approximations of the exact values of these variables Regardless of the section shape the shear areas Asy and Asz are less than the cross section area Ax 7 4 3 Torsion Effects 13 of 33 11
39. element linear and nonlinear static and dynamic analysis of structural elements an addendum A bibliography 1996 1999 Engineering Computations vol 17 no 3 pp 274 351 2000 William McGuire Richard H Gallagher and Ronald D Ziemian Matrix Structural Analysis 2nd ed John Wiley 1999 ISBN 0471376515 W D Pilkey Weize Kang and Uwe Schramm New structural matrices for a beam element with shear deformation Finite Elements in Analysis and Design vol 19 pp 25 44 1995 William H Press Saul A Teukolsky William T Vetterling Brian P Flannery Numerical Recipes in C The Art of Scientific Computing Cambridge University Press 1993 ISBN 0521431085 J S Przemieniecki Theory of Matrix Structural Analysis Dover Press 1985 ISBN 0486649482 Robert E Sennett Matrix Analysis of Structures Waveland Press 2000 ISBN 1577661435 S Timoshenko and J N Goodier Theory of Elasticity 2nd ed McGraw Hill 1951 Ansel C Ugural and Saul K Fenster Advanced Strength and Applied Elasticity 3rd ed Prentice Hall 1995 ISBN 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 013137589X About this document Authors Henri P Gavin P E Ph D Department of Civil and Environmental Engineering Duke University Box 90287 Durham NC 27708 0287 John Pye Dept of Engineering Australian National University SOURCEFORGE NET Source code for this document as well as Frame3d
40. et to 0 zero for all frame elements For frame elements with doubly symmetric sections e g circular or square the roll angle p does not matter and can be set to 0 zero For 3D frames made of non circular or non square sections and all frame elements are aligned with the global X Y or Z axes then the roll angle p might matter but p would probably be either 0 or 90 degrees Again for planar structures with no out of plane bending which lie in the global X Y Y Z or X Z planes and for structures made entirely of bars with lyy lzz the roll angle p may be set to zero Coordinate transformations do not currently consider the effect of finite joint sizes and are based on joint to joint lengths of each frame element 7 7 Connections All connections in a Frame3DD analysis are moment resisting Internal hinges may be modeled using a short element with low values of Jxx lyy and Izz Many connections are more realistically modeled as having some flexibility Such semi rigid connections may be modeled through the inclusion of short frame elements with appropriate section and material properties to model the behavior of the connection Frame elements may be considered infinitely rigid within a sphere of a specified radius r around a joint The effects of finite joint sizes are modeled approximately in the calculation of frame element stiffness through the use of an effective beam length which is the joint to joint length of the frame element
41. et viewvc frame3 10 of 33 A 8 c D E z G H 1 FRAME3DD version 20090101 http frame3dd sf net gt 2 GPL Copyright C 1992 2009 Henri P Gavin 3 _FRAME3DD is distributed in the hope that it will be useful but with no warranty 4 For details see the GNU Public Licence http www fsf org copyle ft gpl html 5 Example B a pyramid shaped frame static and dynamic analysis 6 Thu Jan 107 59 50 2009 7 __ CSV formatted results of Frame3DD analysis 8 9 Load Cas Displace End Forc Reactions a0 First Row T 21 28 38 11 Last Row 1 25 35 42 12 First Row 2 49 56 66 13 Last Row 2 53 63 70 14 First Row 3 77 84 94 15 Last Row 3 81 91 98 16 17 LOAD CASE 1 OF 3 18 19 JOINT DISPLACEMENTS global 20 Joint X dsp Y dsp Z dsp X rot Y rot Z rot 21 1 0 10231 0 3640 1 4532 0 00243 0 00065 6E 07 L 77 2 I This example has three load cases Displacements for load case 1 start at row 21 and end at row 25 Frame element end forces for load case 1 start at row 28 and end at row 35 Reaction forces for load case 1 start at row 38 and end at row 42 Displacements for load case 2 start at row 49 and end at row 53 Frame element end forces for load case 2 start at row 56 and end at row 63 Reaction forces for load case 2 start at row 66 and end at row 70 Displacements for load case 3 start at row 77 and end at row 81 Frame element end forces for load case 3 start at row 84 and end at row 91 Reaction forces f
42. frame element Section 8 below describes how thermal pre stress loads are analyzed before the response to mechanical loads is analyzed 7 10 Dynamic Modal Analysis The Frame3DD analysis will optionally include a dynamic analysis for natural modes of vibration Dynamic properties may be obtained for the un stressed or the stressed structure by either neglecting or including geometric stiffness effects The mass may be modeled using either the consistent mass matrix or the lumped mass matrix The natural frequencies and mode shapes of the structural frame may be computed from the stiffness and mass matrices using either the Stodola method or the Jacobi method The solution method and the convergence tolerance for these iterative methods is specified in the Input Data file If a dynamic modal analysis is to be carried out the Input Data file must also specify the mass density of each frame element additional mass carried by the frame element and extra mass or inertia carried by the joints A specified set of modes may be animated within Gnuplot Frame3DD has the capability of computing the natural frequencies and mode shapes of frames that are fully restrained partially restrained or completely un restrained Partially restrained frames have up to six independent rigid body modes A completely un restrained frame has six independent rigid body modes The stiffness matrix for partially restrained and completely unrestrained structures is not inverti
43. he same load case Whenever the average axial strain in a frame element connection Nx EAx exceeds 0 001 0 1 in magnitude a warning message is displayed indicating the strain level and the element in question Most structural materials yield at strains between 0 1 and 0 2 When this warning message is displayed the structure is likely in an overloaded condition and the loads should be reduced Note that this check for overloaded elements provides an approximate stress check A more complete stress check would compute the composite axial shear torsion and bending stresses and strains within each element Such a check requires additional cross section information the section moduli and the section dimensions as described in sections 7 13 and 7 14 below The static stability of many structures depends upon a level of prestress within the structure In such goemetrically non linear analyses pre stressed structres may be modeled by specifying a uniform temperature cooling in all pre tensioned elements The value of the temperature change corresponding to a desired pre stress tension force depends on the stiffness of the components of the structural system and may be determined with a few iterations As an initial guess set the temperature change to be T a E Ax where T is the value of the desired pre stress tension of the frame element a is the coefficient of thermal expansion E is the elastic modulus and Ax is the cross section area of the
44. input data formatting error in load data 101 number of static load cases must be greater than zero 102 number of static load cases must be less than 30 121 input data formatting error in joint load data joint number out of range 131 input data formatting error in uniformly distributed load data number of uniform loads is greater than the number of frame elements 132 input data formatting error in uniformly distributed load data frame element number out of range 140 input data formatting error in trapezoidally distributed load data too many trapezoidally distributed loads eeoeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eee 8 8 ee Ww N 31 of 33 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 32 of 33 14 L5 141 input data formatting error in trapezoidally distributed load data frame element number out of range 142 input data formatting error in trapezoidally distributed load data x1 lt 0 143 input data formatting error in trapezoidally distributed load data x1 gt x2 144 input data formatting error in trapezoidally distributed load data x2 gt L 150 input data formatting error in internal concentrated load data number concentrated loads greater than number of frame elements 151 input data formatting error in internal concentrated load data frame element number out of range 152 input data formatting error in internal concentrated load data x l
45. interface to Frame3DD is currently capable of static analyses It does not yet implement the following features of Frame3DD Matlab functions for graphical display of the results gravity loading point forces applied between the joints of a frame element temperature loads multiple load cases modal analysis matrix condensation Adding these features would require editing the matlab inteface function frame_3dd m 5 Spreadsheet Interface Input Data for Frame3DD may be read and written using spreadsheet programs excel GoogleDocs OpenOffice Gnumeric Any of the Frame3DD example Input Data files may be opened with a spreadsheet program When editing an Input Data file with a spreadsheet program save it in CSV format with a CSV filename extension When run on a CSV file Frame3DD writes results as plain text to the named Output Data file and also writes results of the static analyses to a spreadsheet with a filename ending in CSV For example running Frame3DD as follows frame3dd MyFrame CSV MyResultsA out results in the two Output Data files MyResultsA out and MyResultsA_out CSV These CSV files may be viewed edited pre processed and post processed with a spreadsheet program The results spreadsheet file includes an index table specifying the row numbers of each type of result Sections of an example results spreadsheet are shown below 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge n
46. into the title The title must not contain the or the characters as these characters are used for parsing the Internal Force data file Template Input Data file for Frame3DD 3D structural frame analysis N mm ton this template indicates units of Newton millimeter and tonne other units may be specified as desired joint data nJ number of joints joint X coord Y coord Z coord radius mm mm mm mm J 1 x 1 y 1 z 1 r l J nJ x nJ y nJ z nJ r nJ reaction data nR number of joints with reactions joint X Y Z XX YY ZZ O free 1 fixed J 1 Rx 1 Ry 1 Rz 1 Rxx 1 Ryy 1 Rzz 1 J nR Rx nR Ry nR Rz nR Rxx nR Ryy nR Rzz nR frame element data nE number of frame elements elmnt j1 j2 AX Asy Asz JX Iy Iz E G roll density mm 2 mm 2 mm 2 mm 4 mm 4 mm 4 MPa MPa deg tonne mm 3 M 1 J1 1 J2 1 Ax 1 Asy 1 Asz 1 Jx 1 Iy 1 Iz 1 E 1 G 1 p 1 d l M nE J1 nE J2 nE Ax nE Asy nE Asz nE Jx nE Iy nE Iz nE E nE G nE p nE d nE shear 1 Do 0 Don t include shear deformation effects geom 1 Do 0 Don t include geometric stiffness effects exagg_static exaggeration factor for static mesh deformations dx length of x axis increment for frame element internal force data mm if dx is 1 then internal force calculations are skipped load data nL number of static load cases 1 30 Begin Static Load Case 1 24 of 33 11 09 2010 11 18 AM Frame
47. ions such as 1 234 10 3 or 6 sin pi 2 are not allowed in the Input Data unless the Matlab interface is used To write your own Input Data file it may be helpful to start with an example that resembles the system you would like to analyze Carefully compare the graphical output of the example the Input Data file the Output Data file and the Input Data format with the variable definitions at the end of this page You may edit Input Data files using a good plain text editor vim jEdit nano gedit Linux NotePad Windows etc using the Matlab interface or using spreadsheet programs GoogleDocs OpenOffice Gnumeric or Excel Details regarding the Matlab interface to Frame3DD are here Details regarding the spreadsheet interface to Frame3DD are here It might take a few tries to get your Input Data just right Frame3DD checks the Input Data for errors prior to analyzing the system and where possible displays descriptive diagnostic messages when errors are found with the Input Data Frame3DD generates several additional output files used in plotting deformed frames By default these output files are sent to a temporary file folder On OS X Linux and Unix the location of this folder defaults to the tmp directory On Windows the location of this folder defaults to C WINDOWS Temp If you would like your output files to be sent to another location you can set the environment variable FRAME3DD_OUTDIR with the path to your desired
48. it Input Data files using your plain text editor jEdit Vim TextEdit or a spreadsheet program GoogleDocs OpenOffice If you use Apple s TextEdit make sure you are in Plain Text mode SHIFT APPLE T or Format gt Make Plain Text Run your own Frame3DD analyses within the Terminal window using a command like frame3dd MyFrame 3dd MyResultsA out Use Gnuplot to view the graphical output From you Mac s Administrator account first install Xcode then install MacPorts and finally install Gnuplot To install Xcode go to the Apple Developer Connection ADC join ADC to create an account log in and then click on Downloads gt Developer Tools and browse for the version of Xcode for your version of OS X For OS X 10 4 Tiger install Xcode 2 5 Developer Tools For OS X 10 5 Leopard install Xcode 3 1 4 Developer Tools For OS X 10 6 Snow Leopard install Xcode 3 2 1 Developer Tools Make sure the Unix Development option is selected if installing Xcode 3 1 4 or 3 2 1 To install MacPorts for your version of OS X 10 4 Tiger 10 5 Leopard or 10 6 Snow Leopard follow these instructions To install Gnuplot open a terminal and type sudo port install gnuplot If this is your first MacPorts package installation it will take several minutes to complete Visualize your Frame3DD analysis output Open a Terminal window Applications gt Utilities gt Terminal and gnuplot gnuplot gt cd Desktop Frame3
49. lass Fiber Epoxy 22000 80000 30 0e 6 1 97e 9 1 12e13 Magnesium AM1000A 44800 17500 25 2e 6 1 80e 9 2 49e13 Douglas Fir 12400 4600 30 0e 6 0 50e 9 2 48e13 Note e These material properties are approximate e Properties of Douglas Fir vary naturally by 15 percent e Properties of Fiber Epoxy composites depend on the volume fraction and orientations of the fibers The values above correspond to volume fractions of roughly 50 percent MatWeb lists properties of other materials 7 6 Frame Element Coordinate Transformation When a frame element is placed into the structure it is translated and rotated and optionally rolled about its local x axis The default coordinate transformation process starts with the frame element s centroidal axis placed along the global X axis and the principle axes of the cross section the local y and z axes aligned with the global Y and Z axes The global Y and Z axes must coincide with the principle axes of the cross section To place the frame element in the structure first it is rotated about the global Y axis then about the global Z axis then rolled or spun about the local x axis If the roll angle p is zero this process results in a transformation for which loads in the global Z direction will cause no cross axis bending In this code this type of coordinate transformation is called Z axis is vertical and is selected primarily for the sake of visualization with Gnuplot in which the Z axis is vertic
50. le click the icon to extract it to your Desktop Recommended Put the Frame3DD directory in your path and set the FRAME3DD_OUTDIR location To do this open your profile file using your good text editor Using TextEdit open a Terminal Applications gt Utilities gt Terminal and type open a TextEdit profile Using jEdit File gt Open and type profile in the File Name text entry bar Using Vim File gt Open and select profile from your home directory Copy and paste the following ten lines into the beginning of profile for Frame3DD http frame3dd sourceforge net add Frame3DD executable directory to the path export PATH SPATH SHOME Desktop Frame3DD create a Frame3DD output directory if d tmp frame3dd_temp_ USER then mkdir tmp frame3dd_temp_ USER echo creating tmp frame3dd_temp_S USER for Frame3DD fi specify the Frame3DD output directory export FRAME3DD_OUTDIR tmp frame3dd_temp_ USER save and exit the editor Open a Terminal Applications gt Utilities gt Terminal change to the directory of example files and run an example cd Desktop Frame3DD examples frame3dd exE 3dd exE out Some run time information will be displayed on the Terminal and the results of your Frame3DD analysis will have been appended to the end of the exE out Output Data file Data files used primarily for plotting are stored in the tmp frame3dd_temp_ USER directory You may view Output Data files and ed
51. less the rigid radii on each end To analyze a structure as a truss with this software specify Jxx lyy and Izz to be much smaller than they would be normally but not zero If the shear forces and bending moments in the structural elements are small then the structural model represents a truss approximation of the actual structure Shear deformation effects and geometric stiffness effects should not be incorporated if Jxx lyy and Izz are made very small See Frame3DD example A 7 8 Shear Deformation Geometric Stiffness and Buckling The Frame3DD analysis will optionally include the effects of shear deformation and or geometric stiffness The geometric stiffness matrix includes the effects of axial forces on bending and warping torsional behaviors When both shear deformations and geometric stiffness effects are included the geometric stiffness matrix includes shear deformation effects If shear deformation effects are not to be included simply set the shear variable to zero 0 If shear deformation effects are neglected then the values for the shear areas Asy and Asz are not used in the calculations Any non zero value for Asy and Asz will do To determine the buckling load of a structure include geometric stiffness effects and increase the loads until the stiffness matrix ceases to be positive definite Additionally you may compute the fundamental natural frequency of the structure and observe how the fundamental frequency decreases wi
52. mperature change on the local y face of the element 28 of 33 11 09 2010 11 18 AM Frame3DD User Manual 29 of 33 http frame3dd svn sourceforge net viewvc frame3 Tz2 temperature change on the local z face of the element Tz temperature change on the local z face of the element Ux uniform distributed load in the local X direction Uy uniform distributed load in the local Y direction Uz uniform distributed load in the local Z direction wxl starting value for trapezoidally distributed loads in the local x direction wx2 stopping value for trapezoidally distributed loads in the local x direction wyl starting value for trapezoidally distributed loads in the local y direction wy2 stopping value for trapezoidally distributed loads in the local y direction wzl starting value for trapezoidally distributed loads in the local z direction wz2 stopping value for trapezoidally distributed loads in the local z direction xxl distance along a frame element for starting trapezoidally distributed loads in the x direction XX2 distance along a frame element for stopping trapezoidally distributed loads in the x direction xyl distance along a frame element for starting trapezoidally distributed loads in the y direction xy2 distance along a frame element for stopping trapezoidally distributed loads in the y direction xzl distance along a frame element for starting trapezoidally distributed loads in the
53. mples folder use the saveplot_w32 script included in the Frame3DD examples folder gnuplot gt gnuplot gt load saveplot_w32 copy my plot ps PlotFileA ps 3 3 2 Installing from the binary installer 1 Install a good plain text editor for Windows NotePad or jEdit or gvim A tutorial for gvim is here Alternatively you may use NotePad w N environment variables To do this right click My Computer gt Properties gt Advanced gt Environment Variables Set a new user variable name PATH with variable value PROGRAMFILES Frame3DD Set a new user variable name FRAME3DD_OUTDIR with variable value WHOMEPATH Desktop Frame3DD temp You will need to create this Temp folder Desktop Frame3DD temp before running Frame3DD Detailed information on how to set environment variables in Windows is here if you need it 4 Copy one or more of the example files eg exE 3dd from your PROGRAMFILES FRAME3DD examples folder into your Desktop folder Download and run the binary installer frame3dd VERSION exe Recommended Put the Frame3DD directory in your path and set the PATH and FRAME3DD_OUTDIR 5 Open a command prompt window Start gt All Programs gt Accessories gt Command Prompt change to the directory of example files and run an example chdir HOMEPATH Desktop frame3dd exE 3dd exE out Some run time information will be displayed on the Command Prompt window and the results of your Frame3DD analysis will hav
54. ocation less than O or grater than L 160 input data formatting error in thermal load data number thermal loads greater than number of frame elements 161 input data formatting error in thermal load data frame element number out of range 162 input data formatting error in thermal load data frame element number out of range 171 input data formatting error in prescribed displacement data prescribed displacements may be applied only at coordinates with reactions 200 memory allocation error 201 error in opening an output data file saving a vector of floats 202 error in opening an output data file saving a vector of ints 203 error in opening an output data file saving a matrix of floats 204 error in opening an output data file saving a matrix of doubles 205 error in opening an output data file saving a symmetric matrix of floats 206 error in opening an output data file saving a symmetric matrix of doubles Enhancements projected for future versions A GPL able GUI Oo FrameEd is a Windows GUI for the 20020103 version of Frame3DD Jan 3 2002 See above O Work has been done on a Qt GUI Fall 2004 A Microstran Viewer interface is in the works here Summer 2008 A Google sketchup interface is in the works here and possibly here Summer 2008 Wood truss analysis and design software that makes use of Frame3DD is in development here Winter 2010 Consistent mass matrix including the effects of shear defo
55. ode shapes If the Output Data is written to a file called MyResultsA out the Gnuplot script is written to a file called MyResultsA plIt Graphical output may be viewed by starting Gnuplot and typing load MyResultsA pIt Frame3DD can consider multiple static load cases in a single analysis Separate output data files list the internal axial force shear forces torsion and bending moments along each frame element for each static load case Frame3DD may optionally interface with Matlab and with spreadsheet programs Frame3DD is free open source software you may redistribute it and or modify it under the terms of the GNU General Public License GPL as published by the Free Software Foundation The software is distributed in the hope that it will be useful but without any warranty without even the implied warranty of merchantability or fitness for a particular purpose See LICENSE txt for details Contents Getting started Input Data and Output Data How to install and run Frame3DD 1 Linux 2 Mac OS X 3 Windows Matlab Interface Spreadsheet Interface FrameEd Structural Modeling Qe So On 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 2 of 33 8 Numerical Details 9 Input Data Format 10 Variable Definitions 11 Command line options 12 Source code 13 Exit code index 14 Enhancements projected for future versions 15 References 1 Getting started
56. oint If nM is set to zero there is no need to provide numerical values for the quantities after the nM variable 7 11 Matrix Condensation Reduced order stiffness and mass matrices may be computed via a static condensation Guyan reduction or dynamic condensation The condensed mass and stiffness matrices are saved as text files called Kc and Mc The Guyan reduction method is generalized so that the condensed matrices match the fundamental frequency of the original structure exactly The dynamic condensation method is a pseudo inverse modal matrix method and the resulting condensed mass and stiffness matrices may be ill conditioned The pseudo inverse of the modal matrix is computed using a regularization method which somewhat improves the conditioning of the condensed mass and stiffness matrices 7 12 End Force Sign Convention The frame element end forces listed in the Output data file adhere to a sign convention determined by the local coordinate system of the frame element The local coordinate system of the frame element has its origin at joint 1 of the frame element The local x axis lies along the element from joint 1 to joint 2 The local y and z axes are aligned with the principle axes of the frame element cross section The frame element end forces are designated as Nx Vy Vz for the axial force and end shears in the local y and z directions and Tx My Mz for the torsional moment and bending moments about the local y and z axes The sign
57. on for Gnuplot output 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 30 of 33 z force X Y Z plotting 1 On off On lumped mass matrix or Off consistent mass matrix f value modal frequency shift for unrestrained structures m J s modal analysis method J Jacobi Subspace or S Stodola t value convergence tolerance for modal analysis p value pan rate for mode shape animation r value matrix condensation method 0 1 2 or 3 e Examples Display help information and exit frame3dd h Suppress screen output frame3dd i InFile o OutFile q Include shear deformation over riding the Input Data file value frame3dd i InFile o OutFile sOn Include geometric stiffness and set deformed mesh exaggeration value over riding Input Data file values frame3dd i InFile o OutFile e100 gOn Use consistent mass matrix set deformed mesh exaggeration value set the animation pan rate over riding Input Data file values and force 3D plotting in Gnuplot frame3dd i InFile o OutFile l0Off e100 p3 4 z 12 Source code The source code is written in ANSI C and is extensively commented The source code includes functions for frame analysis LDL decomposition LU decomposition Newton Raphson iteration sub space iteration Stodola iteration Sturm eigen value check static condensation Guyan reduction and dynamic condensation file name description main c main driver routines
58. onvergence tolerance approx le 4 shift frequency shift factor for rigid body modes make 0 for pos def K exagg_modal exaggerate modal mesh deformations 26 of 33 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 27 of 33 extra joint inertia data nI number of joints with extra joint mass or rotatory inertia jnt mass XX inertia YY inertia ZZ inertia tonne tonne mm 2 tonne mm 2 tonne mm 2 J 1 JMs 1 JMx 1 JMy 1 JMz 1 5 global coordinates J nI JMs nI JMx nI JMy nI JMz nI extra frame element mass data nX number of frame elements with extra mass elmnt extra mass tonne M 1 BMs 1 M nX BMs nE mode shape animation data nA number of modes to be animated list of modes to be animated sorted in increasing order anim 0 anim nA pan pan rate of the animation 0 no panning matrix condensation data Cmethod matrix condensation method 0 none l static 2 Guyan 3 dynamic nc number of condensed joints jnt X Y Z XX YY ZZ 1 condense 0 don t J 1 cx 1 cy 1 cz 1 cxx 1 cyy 1 czz 1 J nC cx nC cy nC cz nC cxx nC cyy nC czz nC m 1 m 2 m 3 list of modes matched in dynamic condensation if Cmethod 1 only mode m 1 is matched 10 Variable Definitions a Coefficient of thermal expansion 1 degree anim List of modes to be animated by mode number
59. or load case 3 start at row 94 and end at row 98 For any Frame3DD CSV results file the spreadsheet cells containing the result row numbers are given in the following table Load Case 1 First Row Last Row joint Displacements e a0 ea Frame Element End Forces D l0 D 11 3 Load Case 2 First Row Last Row Frame Element End Forces D 12 S D 13 Reaction Forces E12 EB Load Case 3 First Row Last Row Frame Element End Forces D 14 D 150 let cetera 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 The columns of the spreadsheet results file are arranged as follows Displacement results are in columns A through G A B E D E F G F 18 19 JOINT DISPLACEMENTS global 20 Joint X dsp Y dsp Z dsp X rot Y rot Z rot 21 1 0 10231 0 3640 1 4532 0 00243 0 00065 6E 07 22 n n n n n n Frame element end force results are in columns A through H A B c D E F G H 25 BEAM END FORCES local A 27 Beam joint Nx Vy Vz TXX Myy Mzz 28 1 1 51 0162 0 0174 0 3470 3 7671 61 0322 6 98192 29 1 2 51 016 0 01740 0 34699 3 76713 59 3415 7 86974 30 2 1 58 5714 0 02283 0 3205 2 51591 60 9668 4 4747 E 31 2 3 58 571 0 0228 0 32046 2 5159 57 8686 4 8709 32 3 1 38 4099 0 0105 0 4001 3 76838 59 716 7 0299 Reaction results are in columns A through G A B C D E F G H 36 REACTIONS global 37 Joint Fx Fy Fz Mxx Myy Mzz 38 1 0 0 0 0 0 0 39 2 33 8149 25 3394 28 5874 2
60. perature changes local elmnt coef y depth z depth deltaTy deltaTy deltaTz deltaTz deg C mm mm deg C deg C deg C deg C M 1 a l hy 1 hz 1 Ty 1 Ty 1 Tz 1 Tz 1 e M nT a nT hy nT hz nT Ty nT Ty nT Tz nT Tz nT nD number of prescribed displacements nD lt nR global jnt X displ Y displ Z displ X rot n Y rot n Z rot n mm mm mm radian radian radian J 1 Dx 1 Dy 1 Dz 3 Dxx 1 Dyy 1 Dzz 1 J nD Dx nD Dy nD Dz nD Dxx nD Dyy nD Dzz nD End Static Load Case 1 Begin Static Load Case 2 gravitational acceleration for self weight loading mm s 2 global gX gY gZ mm s 2 mm s 2 mm s 2 gX gY gZ nF number of loaded joints global 25 of 33 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 joint X load Y load Z load X mom Y mom Z mom N N N N mm N mm N mm J 1 Fx 1 Fy 1 Fz 1 Mxx 1 Myy 1 Mzz 1 J nF Fx nF Fy nF Fz nF Mxx nF Myy nF Mzz nF nU number of uniformly distributed element loads local elmnt X load Y load Z load uniform member loads in member coordinates N mm N mm N mm M 1 Ux 1 Uy 1 Uz 1 M nU Ux nU Uy nU Uz nU nW number of trapezoidally distributed element loads local start stop start stop elmnt loc n loc n load load mm mm N mm N mm M 1 xxl 1 xx2 2 wx1 1 wx2 1 locations and loads local x axis xyl 1 xy2 2 wyl 1 wy2
61. r echo creating tmp frame3dd_temp_ user for Frame3DD endif specify the Frame3DD output directory setenv FRAME3DD_OUTDIR tmp frame3dd_temp_ user Save and exit the editor Open a Terminal window Right click on an open part of the Desktop and select Open Terminal Change to the directory containing the Frame3DD example files and run an example as follows cd Desktop Frame3DD examples frame3dd exE 3dd exE out Some run time information will be displayed on the Terminal and the results of your Frame3DD analysis will have been appended to the end of the exE out Output Data file Data files used primarily for plotting are stored in the tmp frame3dd_temp_ USER directory You may view Output Data files and edit Input Data files using a good plain text editor vim gedit nano ora 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 spreadsheet program GoogleDocs OpenOffice Gnumeric For example to read or edit the Input Data file Double click the Home icon on the Desktop navigate to the directory of your data files right click on the Data File and select the editor of your choice Run your own Frame3DD analyses within the Terminal window using a command like frame3dd MyFrame 3dd MyResultsA out Use Gnuplot to view the graphical output 1 Gnuplot is commonly pre installed on Linux systems If it is not you may install it only if you have root privileges using a command
62. rame3 e Jxx 1 2 n Ro Ri ixx lyy 1 4 n Rof Ri Square Tube outer dimension b x b wall thickness t Ax b b 2t Asy ASZ Ax 2 08334 0 70154 t b 8 00313 t b 12 22572 t b 0 5 Asy Asz Ax 2 1186 1 9900 t b 2 Jxx b t t Izz lyy 1 12 b b 2t Rectangular Tube outer dimension a x b wall thickness t Ax ab a 2t b 2t Asy Ax 1 14766 0 28187 t b 0 96199 b a 2 17742 t a 1 a gt b Asy Ax 1 10498 1 98518 t a 8 74762 t a 0 99548 b a 0 69146 tb a 5 36255 b a 1 b gt a Asz Ax 1 10498 1 98518 t b 8 74762 t b 0 99548 a b 0 69146 ta b 5 36255 a b 1 a gt b Asz Ax 1 14766 0 28187 t a 0 96199 a b 2 17742 t b 1 b gt a Jxx 2 t a t b t a b 2t lyy 1 12 ab a 2t b 2t Izz 1 12 ab a 2t b 2t sections depth d width b flange thickness t web thickness w Z SSws SSS SS SS SS SS SS Wv b Ax bd d 2t b w Asy 1 64 bt Asz dw Jxx 1 3 2b dw lyy 1 12 bd b w d 2t Izz 1 12 2 t b d 2t w Note Commercial sections have rounded corners Manufacturer specifications for cross sectional properties account for the fact that the corners of the cross sections are rounded Manufacturer specifc
63. rmation on rotatory inertia Dynamic time history analysis with the HHT alpha method Spectral modal superposition Member end joint releases Linearly tapered frame elements Sparse matrix storage and sparse matrix solvers your recommendations send me an e mail References This software was developed using methods described in the following texts The two primary sources are the texts by A Kassimali and S Przemieniecki Other relevant books and articles are I 2 3 mue 10 I 12 13 15 16 Howard G Allen Background to Buckling McGraw Hill 1980 ASIN 0070841004 Klaus Jurgen Bathe Finite Element Procedures Prentice Hall 1995 ISBN 0133014584 Arthur P Boresi Richard J Schmidt and Omar M Sidebottom Advanced Mechanics of Materials John Wiley amp Sons 1993 ISBN 0471551570 Raymond W Clough and Joseph Penzien Dynamics of Structures McGraw Hill 1993 ASIN 0070113920 J P Den Hartog Advanced Strength of Materials Dover Press 1987 ISBN 0486654079 Thomas J R Hughes The Finite Element Method Linear Static and Dynamic Finite Element Analysis Dover Press 2000 ISBN 0486411818 Aslam Kassimali Matrix Analysis of Structures Brooks Cole 1999 ISBN 0534206700 Jaroslav Mackerle Finite element linear and nonlinear static and dynamic analysis of structural elements a bibliography 1992 1995 Engineering Computations vol 14 no 4 pp 347 440 1997 Jaroslav Mackerle Finite
64. rting location for a trapezoidal load must be greater than 0 and less than the stopping location of the trapezoidal load The stopping location for a trapezoidal load must be greater than the starting value of the trapezoidal load and less than the length of the frame element Fixed end forces computed from trapezoidal loads include the effects of shear deformation when shear deformation effects are incorporated e Thermal Loads Thermal loads assume a linear temperature gradient through cross sections Thermal loads are specified by values for the coefficient of thermal expansion the depth of the section in the local y direction the depth of the section in the local z direction and the temperature changes on the y surface the y surface the z surface and the z surface Thermal loads are applied over the entire frame element e Prescribed Displacements Static joint displacements and rotations may be prescribed only at reaction degrees of freedom Static joint displacements and rotations are specified in the structure s global X Y Z coordinate system Up to thirty static load cases may be anlayzed by specifying the variable nL in the Input Data file and by specifying the seven types of loads for each load case as shown in Frame3DD example A and Frame3DD example B More than one load of the same type on the same element or joint may be specified For example one or more trapezoidally distributed loads may be applied to the same frame element in t
65. s of point forces and concentrated moments applied to joints in the directions of the structure s global X Y Z coordinate system e Uniformly Distributed Loads 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 Uniformly distributed static loads may be applied in the local element coordinate system over the entire length of a frame element Uniformly distributed loads are specified as values of the load per unit length applied to the frame element in the local x direction the local y direction and the local z direction e Frame Element Point Loads Concentrated static force loads may be applied to frame elements between the joints Up to ten frame element point loads may be specified per frame element These loads are specified as values of point forces applied to the frame element in the directions of the frame element s local coordinate system at a distance x from joint J1 of the frame element e Trapezoidally Distributed Loads Trapezoidally distributed loads may be applied over a partial span of frame elements Up to ten trapezoidal loads may be specified per frame element Trapezoidally distributed loads have components in the local x direction the local y direction and the local z direction Trapezoidally distributed loads are specified by the distances along the local x axis where the loading starts and stops and by the value of the load at the starting location and the stopping location The sta
66. stem matrix for element deformation is not positive definite 31 non positive definite structural static stiffness matrix error in eigen problem analysis 40 error in input data file 41 input data formatting error in the joint data joint number out of range 51 input data formatting error in the frame element data frame element number out of range 52 input data formatting error in the frame element data joint number out of range 53 input data formatting error in the frame element data negative section value 54 input data formatting error in the frame element data cross section area is 0 zero 55 input data formatting error in the frame element data shear area and shear modulus are 0 zero 56 input data formatting error in the frame element data torsional moment of inertia is 0 zero 57 input data formatting error in the frame element data bending moment of inertia is 0 zero 58 input data formatting error in the frame element data modulus value is non positive 59 input data formatting error in the frame element data mass density value is non positive 60 input data formatting error in the frame element data frame element starts and stops at the same joint 61 input data formatting error in the frame element data frame element has length of zero 71 input data formatting error with the shear variable specifying shear deformation 72 input data formatting error with the geom variable specifying geome
67. th increased loading In principle the fundamental frequency is zero when the loads are at the buckling load If geometric stiffness effects are included in the analysis and if the loads are close to the buckling load of the structure then it is recommended to put two or three joints along each frame element i e divide each frame element into three or four segments Including these extra joints is strongly recommended if a buckling analysis is to be performed Whenever geometric stiffness effects are included the analysis is non linear and superposition does not hold In most cases the geometric stiffness matrix lies between the un stressed stiffness matrix and the tangent stiffness matrix 7 9 Loads Seven types of static loads may be specified e Gravity Loads Uniformly distributed gravity loads may be applied to each frame element in a structural model Gravity loads are specified in terms of the three componenets of gravitational acceleration in the structure s global X Y Z coordinate system The magnitude of the gravity load applied to a frame element is the product of the frame element s mass density its cross sectional area and the structure s gravitational acceleration resultant The direction of the gravity load is the same as the direction of the gravitational acceleration resultant e Joint Loads Concentrated static force loads and concentrated static moments may be applied to individual joints These loads are specified as value
68. therwise a separate internal force output file is written for each load case For frame elements of length shorter than dx internal forces and displacements are calculated at x 0 and x L If the Frame3DD analysis Output Data file is named MyResultsA out then the internal force output data files are automatically named MyResultsA ifO1 for load case 1 MyResultsA ifO2 for load case 2 and so on The internal force output data contains a section for each frame element Each section has eleven columns as follows column A x x axis data with a user specified x axis increment dx column B x Nx frame element axial force along the local x axis Vy frame element shear force in the local y direction Vz frame element shear force in the local z direction Tx frame element torsion about the local x axis My frame element bending moments about the local y axis D column C column D column E column F My column G Mz frame element bending moments about the local z axis column H Dx frame element axial displacement in the local x direction column I Dy frame element transverse displacement in the local y direction column J Dz frame element transverse displacement in the local z direction column K Rx frame element twist rotation about the local x axis The data in the frame element internal force data file is tab delimitted The frame element internal force data file may be plotted with Gnuplot may be read by a spr
69. tric stiffness 73 input data formatting error with the exagg_static variable specifying static mesh exageration 74 input data formatting error with the dx variable specifying the length of the internal force x axis increment 80 input data formatting error in reaction data number of joints with reactions out of range 81 input data formatting error in reaction data joint number out of range 82 input data formatting error in reaction data reaction data is not 1 one or O zero 83 input data formatting error in reaction data specified joint has no reactions 84 input data formatting error in reaction data under restrained structure 85 input data formatting error in reaction data fully restrained structure 86 input data formatting error in extra joint inertia data joint number out of range 87 input data formatting error in extra beam mass data frame element number out of range 88 input data formatting error in mass data frame element with non positive mass 90 input data formatting error in matrix condensation data number of joints with condensed degrees of freedom are less than the total number of joints 91 input data formatting error in matrix condensation data joint number out of range 92 input data formatting error in matrix condensation data mode number out of range 94 input data formatting error in matrix condensation data number of condensed degrees of freedom greater than number of modes 100
70. y axis Coordinate transformations in 2D are unique and these potential ambiguities are not a concern For 3D structures the following recommendations can help in avoiding ambiguous coordinate transformations Frame elements connect pairs of joints Each frame element has a starting joint element joint 1 J1 and an ending joint element joint 2 J2 as described in the Input Data format In principle either joint of the frame element could be joint J1 and either joint could be J2 The assignment of J1 and J2 to the frame element should not affect the results However to avoid confusion in certain 3D models the following guidelines are recommended In general joint JL of the frame element should have more negative coordinates than joint J2 of the element 12 of 33 11 09 2010 11 18 AM Frame3DD User Manual http frame3dd svn sourceforge net viewvc frame3 More specifically specifying element joint 1 location as x1 y1 z1 and element joint 2 location as x2 y2 z2 If x1 x2 then x1 should be less then x2 Joint J2 should be toward the more positive side of the X axis e If x1 x2 and y1 y2 then y1 should be less then y2 Joint J2 should be toward the more positive side of the Y axis e If x1 x2 and yl y2 and z1 z2 then z1 should be less then 22 Joint J2 should be toward the more positive side of the Z axis The figure below attempts to illustrate the application of these guidelines J2 7 4 Frame Element Cross S
71. z direction xzZ2 distance along a frame element for stopping trapezoidally distributed loads in the z direction x x coordinate of a joint in global coordinates y y coordinate of a joint in global coordinates Zz y coordinate of a joint in global coordinates xP distance from J1 to the concentrated point load 11 Command line options Frame3DD is executed from within a terminal or command prompt window e Frame3DD may be run with interactive prompting for file names by typing frame3dd e Frame3DD may be run without command line options by typing frame3dd InFile OutFile e Frame3DD may be run with command line options by typing frame3dd i InFile o OutFile OPTIONS where opTrons over rides values in the Input Data file and includes one or more of the following InFile OutFile On Off On Off value the input data the output data print this help display program display program data check only suppress screen write stiffness suppress writing of On On file name described in the manual file name message and exit website version website the output data output except for and mass matrices Er version or tgr include geometric stiffness or Off brief help info and exit and exit reviews the input data warning messages to files named Ks Kd Md for sign of axial forces include shear deformation or Off neglect neglect level of deformation exaggerati

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