Home

Karamba Manual

image

Contents

1. gt 2An Eigen mode 7 is the solution to the matrix equation C z A Z which is called the gt special eigen value problem Where C is a matrix Z a vector and A a scalar that is a number called eigen value The whole thing does not necessarily involve statical structures Eigen modes and eigen values are intrinsic properties of a matrix When applied to structures then C stands for the stiffness matrix whose number of rows and columns corresponds to the number of degrees of freedom of the statical system g is an eigen mode as can be computed with Karamba Vibration modes 7 of structures result from the solution of the generalized Eigenvalue problem This has the form C z w M g In a structural context M is the mass matrix which represents the effect of inertia The scalar w can be used to compute the eigen frequency f of the dynamic system from the equation f w 2n In the context of structural dynamics eigen modes are also called normal modes or vibration modes If the eigenfrequency has a low value this means that the vibration takes a long time for one cycle to complete In the limit when f 0 this means that the static system leaves its initial state of equilibrium and never returns In other words the system gets unstable As the value of f goes towards zero so does the speed of vibration This means that inertia forces do not play an important role So if someone is interested whether a given statical system is stable
2. v y a 2 7 i of E Figure 32 The Tension Compression Eliminator component These are the available input parameters 9This component was devised and programmed by Robert Vierlinger The following section is based on his written explanations 41 Iter The removal of tensile or compressive elements works in an iterative fashion The procedure stops either when no changes occur from one step to another or if the the maximum number of iterations Tter is reached Ind Indices of the elements that may be removed in the course of the procedure By default the whole structure is included LC You can specify a special load case to consider The default is 0 which means that the superposition of all loads is taken Compr If true then only members under compression will be kept Ohter wise only members under tension will Survive This value is false by default Like in ESO and BESO elements selected for removal are assigned a negligible stiffness 5 19 Eigen modes of structures The Eigen modes of a structure describe the shapes to which it can be deformed most easily in ascending order The first mode is the one which can be achieved most easily The higher the mode number the more force has to be applied Eigen modes find application in two areas of the engineering discipline First in structural dynamics second in stability analysis which involves the determination of buckling loads P
3. 39 Model Slider O 0 232 d i AddRatio Ind LC Links max disp Model Charact ContElemAdd MinDist MaxDist Bidir BESO Designer Info Slider 00 126 Slider 0 200 Figure 31 The BESO component in action Ratio the target ratio of active elements to all participating elements The resulting structure may slightly deviate from this ratio This is due to additional boundary conditions like grouping of elements or distance relations between added or removed elements which can be imposed by the user Ind Indices of elements that take part in the BESO design process If none are specified BESO is carried out for the entire model LC index of load case to be considered Zero is the index of the first load case Links Sometimes it is desirable to remove or add patches of elements as a whole Feed a two dimensional tree into the Links plug The element indices in each leaf define one group Activation and deactivation of groups works as follows If a group contains an element that qualifies for activation the entire group is added In case of group elements that qualify for removal the ranking value of all other group members is checked The group stays active as long as all other elements ranking value is twice as high as the current limit value for deactivation Charact Sets the element ranking criteria by number as described belo
4. There are two ways for defining a material in Karamba Either select a material by type from a data base see section 5 11 or set each material property manually see below 5 10 1 Material properties definition The component MatProps lets one directly define material properties see fig 24 These are e Young s Modulus E e Shear modulus G e specific weight gamma e yield stress fy Figure 24 The definition of the properties of two materials via the MatProps compo nent In addition to these user defined materials can be given a name via the input plug Name for identification in later stages of calculation 5 10 2 Material stiffness The stiffness i e resistance of a material against deformation is characterized by its Young s Modulus or modulus of elasticity E The higher its value the stiffer the material Table 3 lists E values for some popular building materials For composite materials like in the case of rods made from glass fiber and epoxy it is necessary to defer a mean value for E by material tests Karamba expects the input for E to be in kilo Newton per square centimeter kN cm 31 type of material E kN em steel 21000 aluminum 7000 reinforced concrete 3000 glass fiber 7000 wood spruce 1000 Table 3 Young s Modulus of materials If one stretches a piece of material it not only gets longer but also thinner it contracts laterally In case of steel for example la
5. A 36 5 15 The Dissemble component 2 0088 37 paa at esi whee A 37 o 39 ee eee 41 a age eee eee eee ee 42 5 19 1 Eigen modes in structural dynamics 43 5 19 2 Eigen modes in stability analysis 43 5 19 3 The EigenMode component 43 5 20 Hints on reducing computation time 45 6 Utility Components 45 6 1 Nearest Neighbor 0 4 45 6 2 Remove duplicate lineS 45 6 3 Remove duplicate points 45 ia 46 7 Trouble shooting 46 7 1 Karamba does not work for unknown reason 46 Ra 47 1 3 Karamba does not work after reinstalling Grasshoper 48 7 4 Predefined displacements take no effect 48 o Aa is Ed Un IN 48 7 6 Icons in Karamba toolbar do not show up 48 A ee ee o ee ds 48 7 8 Component in old definition reports a run time error 48 7 9 Other problemsS 00000004 49 8 Version history 49 8 1 Version 0 9 06 released on June 6 2011 49 8 2 Version 0 9 007 released on September 7 2011 1 Introduction Karamba is a Finite Element plug in for the Rhino plug in Grasshopper It lets you interactively calculate the response of three dimensional beam structures under the action of external loads Karamba is fully embedded in the parametric environment of Grasshopper This makes it easy to combine parameterized geometric
6. LCase the PreDisp component will act like a simple support with fixed degrees of freedom equal to zero E NS Endrotation 060 000 z x Figure 14 Left Deflection of a beam under predefined displacements at its end supports Right PreDisp component for setting displacement condition at left support The Trans and Rot input plugs expect vectors They define nodal translations and rotations in global coordinates Translations are to be given in meter rotations in degree The X component of the rotation vector describes a rotation about the global X axis A positive value means that the node rotates counter clockwise if the X Axis points towards you Analog definitions apply to rotations about the global Y and Z axis Karamba is based on the assumption of small deflections Thus be aware that large 4The term displacement as used throughout this manual includes translations and rota tions 5In order to find out the index of a specific node enable the tag checkbox in the ModelView component See section 5 1 1 on how to predefine the index of specific nodes 18 prescribed displacements and rotations give rise to incorrect results which can nevertheless be used for shape finding In order to approximate effects due to large displacements apply them in several steps e g see example FixedFixedBeam ghx Displacements can only be prescribed if the corresponding displacement degree of freedom is
7. concrete wood and aluminum Upper and lowercase letters may be arbitrarily mixed spaces get removed prior to searching the data base A means that the rest of the line is comment There exist different types of steel concrete etc The generic term concrete will result in the selection of an everyday type of concrete a C25 30 according to Euro code More specific descriptions may be given Have a look at the data base in order to get an overview This data base by default resides in Rhinoceros 4 0 Plug ins Grasshopper Karamba MaterialProperties csv The extension csv stands for comma separated value The file can be opened with any text editor and contains the table entries separated by semicolons It is preferable however to use OpenOffice or Excel both can read and write csv files because they render the data neatly formatted see fig 26 Make sure to have a and not a set as your decimal separator The setting may be changed under Windows via regional settings in system settings All lines in the table that start with are comments Feel free to define your own materials A B C D E F G 1 E G gamma fy 2 family type kN cm2 kN cm2 kN m3 kN cm2 3 Steel Steel 21000 8076 78 5 23 5 4 Steel 235 21000 8076 78 5 23 5 5 Steel 5275 21000 8076 78 5 27 5 6 Steel 5355 21000 8076 78 5 36 7 Steel st37 2 21000 8076 78 5 24 8 Figure 26 Partial view of the default da
8. 20 design iterations The ESO component expects a model to be plugged into its left side The number if design iterations Iter determines the number of design iterations the higher this number the less beams will be removed per iteration and the longer the computation time The ratio of the number of beams to be removed to the initial number of elements is set by the value in RRatio Its value is expected to be 0 lt RRatio lt 1 Sometimes one only wants to optimize certain regions of a structure In such a case on can feed a list of beam indexes into the Ind plug of the ESO component This will limit the application of the ESO procedure to these elements If no input is given here then all beams of a model will be included in optimization by default Karamba implements the ESO method in a basic way The only criteria for element removal is the mean value of the axial force of the beams over all 38 load cases If the number of iterations is selected too low then it may occur that single beams get disconnected from the main structure and they seem to fly The reason for this lies in the fact that Karamba applies a so called soft kill approach for thinning out the structure elements are not removed but simply given small stiffness values This ensures that structural response can be calculated under all circumstances At the end of the ESO procedure those beams that were given small stiffness are set inactive This may cause kinemat
9. WN ah if ANNY WN ANN HAN INN WS HNN TIL MIN WII MN A MINA WAN MIM VAAN WN WANN INN YVAN i WANN i NWN y WIN J NWANNN AAN ASN ANN AKIN VAAN AAAI WANN ALZAN WIN WIN WAW AN Figure 34 Undeflected geometry upper left corner and the first nine eigen modes of the structure 44 5 20 Hints on reducing computation time Karamba spends most of its time solving for the deflections of a model The time needed depends on the number of degrees of freedom n of the statical system and how many connections exist between the nodes In the theoretical case that each node is connected to all others computation time grows with n If each node is connected to Nneigh Others and the overall structure has a main axis along which it is oriented i e there are no connections between distant nodes then computational effort increases approximately with 0 5 Ts Ne aigh Karamba makes use of multiple processors so having more than one saves time Using trusses instead of beams more than halves computation time When doing optimization with Galapagos the continuous display updates slow down things considerably For better performance disable the preview of all Components or minimize the Rhino window 6 Utility Components 6 1 Nearest Neighbor Assume you have a list of points and want to have a network that connects each point with a predefined number of its nearest neighbors or to points that lie within a given distance or both
10. a structure This kind of calculation works also in cases of moveable structures rigid body modes if present correspond to the first few eigen modes Figure 12 shows the geometry developed above with supports added at the endpoints of the structure The Karamba Ensemble Support component takes as input either the inde l or the coordinates of the point or a list 3In order to find out the index of a specific node enable the tag checkbox in the ModelView component See section on how to predefine the index of specific nodes 15 three trans laliong pra to ai E gt y wo fs Figure 11 Metaphor for the six degrees of freedom of a body in three dimensional space B A J Assembie Render Settings Toad case Selection ondion Tx Ty Tz Rx Ry Rz 000000 Figure 12 Define the position of supports by node index or position with indexes or positions of points to which it applies Six small circles on the component indicate the type of fixation The first three correspond to translations in global x y and z direction the last three boxes stand for rotations about the global x y and z axis Filled circles indicate fixation which means that the corresponding degree of freedom is zero The state of each box can be changed by clicking on it The string output of the component lists node index or nodal coordinate an array of six binaries corresponding to its six degrees of freedoms and the nu
11. assembly New options in the ModelView component Bending moments shear and normal forces can be displayed along the beam axis The corresponding output of the ModelView component consists of meshes and curves and thus lends itself to further pro cessing In addition to strains it is now also possible to visualize stresses and level of material utilization All color plots now also work with superimposed load cases The Mesh output was reorganized Instead of one big mesh a list of meshes with one entry per beam is now generated The input plug Colors can be used to customize the colors used for plotting stress strain and utilization Id on the input side lets you select parts of the model for display Regular expressions may be used to enable visibility for multiple groups of beams Two new output plugs Legend C and Legend T can be used to show a legend for the color plots There is an option for displaying local beam axes The new Orien tate Beam component gives the user control over the orientation of beams Besides circular profiles there are now also box I and trapezoid profiles available The results output for displacements cross section forces and inter nal energies was reorganized There are now separate output plugs for bending and translational components A configuration file allows to customize the appearance colors number formats etc of K
12. input plugs that define the cross section geometry there are the Mat Family and Name plug 36 e Mat accepts a material definition It defaults to Steel S235 e Family Each cross section belongs to a family When doing cross section optimization Karamba selects only profiles that belong to the same family as the original section e Name an identifier supposed to be unique for each cross section Enable CroSec names in ModelViews RenderSettings submenu in order to view them 5 15 The Dissemble component Y x Figure 29 Model is dissolved into its ingredients It is sometimes necessary to put apart existing models in order to reassem ble them in different configurations The Dissemble component can be used for dissolving a statical model into its ingredients see figure 29 Be aware of the fact that index references of loads or supports to nodes will remain unaltered Mixing them with incompatible geometries results in errors or unexpected results The lines output plug lists only lines that coincide with active elements This allows for example to extract the structural parts that remain after evolutionary structural optimization see below 5 16 Evolutionary structural optimization Evolutionary structural optimization ESO constitutes a method of topol ogy optimization which was pioneered by Y M Xie and G P Steven The underlying principle is simple One starts from a given volume ma
13. models Karamba and optimization algorithms like Galapagos 2 Disclaimer Although being tested thoroughly Karamba probably contains errors there fore no guarantee can be given that Karamba computes correct results Use of Karamba is entirely at your own risk Please read the licence agreement that comes with Karamba in case of further questions 3 Installation These are the prerequisites for installing Karamba e Rhino 4 0 with Service Release 8 or 9 e Grasshopper Build 0 8 0051 In case you do not possess Rhino 4 download a fully featured free trial version of from http www rhino3d com download html Grasshopper which is free can be found at http www grasshopper3d com Other versions of Grasshopper than that mentioned above may cause prob lems We will try to keep up with Grasshoppers future development by pro viding corresponding Karamba versions Check the download area of the Karamba web site for corresponding information Invoke KarambaSetup msi and choose the folder where Grasshopper is installed when asked for an installation path This is usually something like C Programs Rhinoceros 4 0 Plug ins Grasshopper Besides other things a folder named Karamba will be created there which contains the license agreement a readme file pre fabricated cross section and material tables and the configuration file karamba ini The config file can be edited with any text editor It contains key value p
14. removed from the statical system This means you have to click on the corresponding button in the Conditions section of the PreDisp component The first three buttons stand for translations the last three for rotations Only those components of the Trans and Rot vectors take effect which correspond to activated conditions 5 6 Loads Currently Karamba supports three kinds of loads point mesh and gravity loads An arbitrary number of point or mesh loads and one gravity load may be combined to form a load case of which again an arbitrary number may exist Figure 15 shows the definition of loads with the help of Gravity and Point load components On the bottom of the ModelView component there is a drop down list unfold it by clicking on the Load case Selection menu header which can be used to select single load cases for display Select all in order to view all existing load definitions of all load cases simultaneously Use the force slider to scale to size of the load symbols double clicking on its knob lets you change the value range and its current value D J Render settings Strain Tags o Length Subdivision m 0100 Faces Cross section 15 00 Render Color Margin wwo Load case selection Figure 15 Simply supported beam with three loads and three load cases 19 5 6 1 Point loads The component Karamba Ensemble Point Load lets you define point loads The
15. 2 1068 02 1068 02 3 18e 02 5298 02 7410 02 953e 02 1 16e 01 1 e The Curve plug delivers the axes of the deformed structure as inter polated 3 degree nurb splines Use the Length Subdivision slider to set the number of interpolation points e Legend C and Legend T provide lists of colors and strings which can be fed into Grasshoppers Legend component see fig 8 The numbers on the right side of the Legend correspond to the lower limit that the corresponding color represents The number of color shades can be set in the karamba ini file 5 3 1 The Display Scales submenu Figure 9 Local axes of cantilever composed of two beam elements The Display Scales submenu contains check boxes and sliders to en able disable and scale displacements load symbols support symbols and 13 local coordinate systems The displacement scale influences the display and the output at the model plug It has no effect on stresses strains etc The colors of the local coordinate axes red green blue symbolize the local X Y and Z axis 5 3 2 Display of cross section forces and moments 16 45 Figure 10 Moment My green about the local beam Y Axis and shear force V blue in local Z direction The section forces sub menu lets you plot section
16. In that case the Nearest Neighbor component will be the right choice It outputs lists of connection lines and a corresponding connectivity diagram Be aware of the fact that these lists will probably contain duplicate lines But this is no big problem see below 6 2 Remove duplicate lines When you have a list of lines that you suspect of containing duplicate lines then send it through this component and out comes a purified list of ones of a kind The input plug LDist determines the limit distance for nodes to be considered as identical Lines of length less than LDist will be discarded 6 3 Remove duplicate points Does essentially the same as the component described above only with points instead of lines 45 6 4 Line line intersection This component takes a list of lines as input and mutually tests them for intersection Output plug IP delivers a list of intersection points LSS returns all the line segments including those which result from mutual inter section 7 Trouble shooting 7 1 Karamba does not work for unknown reason This is the recommended procedure 1 2 If a component turns red read its runtime error message In case that more than one item is plugged into an input check the incoming data via a panel component Sometimes flattening the input data helps The dimension of input lists must be consistent For diagnosis plug them into a Panel component which will show the dimension
17. PARAMETRIC STRUCTURAL MODELING Ka User Manual for Version 0 9 007 written by Clemens Preisinger contributions by Justin Diles and Robert Vierlinger September 7 2011 Contents 1 Introduction 2 _ Disclaimer 3_ Installation ES al Quick start Usage 5 1 Define the model geometry 5 1 1 The LineloBeam component 5 1 2 The IndloBeam component 5 1 3 The ConToBeam component 5 2 The Assemble component 5 3 The ModelView component 5 3 1 The Display Scales submenul 5 3 2 Display of cross section forces and moments 5 3 3 Render settings 5 4 upports a 2 052 ee 5 6 1 Point loads 5 6 2 Mesh loads 5 6 3 Gravity loads ee aoe ee ee ee ee ee eo bn re De et 5 8 1 Section forces 5 8 2 Elastic energy 5 8 3 Nodal displacements 5 9 How to change beam properties 5 9 1 Bending stiffness 5 9 2 Activation status of beams 5 9 3 Height and wall thickness of cross sections 5 9 4 Changing the default material 5 10 MaterlalS 5 10 1 Material properties definition O 0 10 10 11 13 14 14 15 18 19 20 21 23 23 26 26 27 28 28 28 30 30 30 31 31 5 10 2 Material stiffness 0 00000 a a 31 5 10 3 Specific weight 32 a ee a a ee Ge a 32 33 oe RA 34 5 13 Cross sections oaoa aaa a 35 ecm www we
18. View uses to scale the loads Its default value is 1 0 Each item in the list applies to a load case If the number of items in this list and the number of load cases do not match then the last number item is copied until there is a one to one correspondence The second option for scaling displacements can be used in the course of form finding operations The model plug at the right side of the ModelView outputs the displaced geometry which can be used for fur ther processing Selecting item all on the drop down list for the selected load case results in a superposition of all load cases with their corresponding scaling factor Looking at figure 18 one immediately notices that only beam center axes are shown In order to see the beams in a rendered view activate the Cross section checkbox on the ModelView component in Menu This results in an image such as in figure 19 a The mesh of the rendered image is available 24 1 e z z a E b s Figure 19 Rendered images of the beam Left Only deflections enabled Right Deflec tions and strains enabled at the Mesh output of the model view Two sliders control the mesh size of the rendered beams First Length Subdivision determines the size of sections along the middle axis of the beams Second Faces Cross section controls the number of faces per cross section Figure 20 Mesh of beams under dead weight with Render Color Margin set to 5 It is instru
19. airs and is pretty self descriptive If all goes well you will notice upon starting Grasshopper that there is a new category called Karamba on the component panel It consists of eight subsections see figure 1 In case you do not see any icons select Draw All Components in Grasshoppers View menu If you consistently get an fem karambaPINVOKE exception see section for how to solve that issue Grasshopper No document File Edit View Arange Solution Window Help Params Math Sets Vector Curve Surface Mesh Intersect Transform W Figure 1 Category Karamba on the component panel These are the subsections which show up in the Karamba category e Algorithms components for the calculation of statical models e Cross Section contains components to create and select cross sec tions for beams Ensemble lets you create models e Loads components for applying external forces Materials components for the definition of material properties e Params classes of objects that make up the statical model Results for the retrieval of calculation results e Utils contains some extra geometric functionality that is not directly linked to creating a model but makes certain things easy e ZZZ Depricated holds components which changed from an earlier version of Karamba to the current They will be removed in some future version In order to make definitions based on old versions work corr
20. ality of the data Another method is to enable Draw Fancy Wires in the View menu Differently outlined connection lines signify different dimensionality of the data that flows through them If no results show check whether preview is enabled on the ModelView component If the Analyze component reports a kinematic structure do the follow ing e Check the supports for forgotten support conditions e Start to fix all degrees of freedom on your Supports until the Analyze component reacts Introduce additional supports Plug the model into the EigenModes component The first eigen modes will be the rigid body modes you forgot to fix e If the first few eigen modes seemingly show an undeflected struc ture there might be beams in the system that can rotate about 46 their longitudinal axis Enable Local Axes in the ModelView component and move the slider for scaling Deformation in order to check this e Turn trusses into beams by activating their bending stiffness Be aware of the fact that a node has to be fixed by at least three trusses that do not lie in one plane Remember that trusses have no torsional or bending stiffness and thus can not serve to fix the corresponding rotations on a beam that attaches to the same node e Check whether an element has zero area height or Young s mod ulus 7 2 fem karambaPINVOKE exception On some computers the analysis component of Karamba refuses to work and thro
21. aramba The Assemble component renders the mass of the structure in kilo gram When analyzing eigen modes of a structures also eigen values are avail able 50
22. ba can be used to analyze the response of structures of any scale It is based on two assumptions First deflections are small as compared to the size of the structure Second materials do behave in a linear elastic manner i e a certain increase of deformation is always coupled to the same increase of load Real materials behave differently they weaken at some point and break eventually If you want to calculate structures with large deflections you either have to increase the load in several steps and update the deflected geometry as described in section or live with the fact that the results somewhat deviate from the real response Figure 27 Simply supported beam For typical engineering structures the assumptions mentioned above suffice for an initial design In order to get meaningful cross section dimensions limit the maximum deflection of the structure 34 Figure shows a simply supported beam of length L with maximum deflection A under a single force at mid span The maximum deflection of a building should be such that people using it do not start to feel uneasy As a rough rule of thumb try to limit it to A lt L 300 If your structure is more like a cantilever A lt L 150 will do This can always be achieved by increasing the size of the cross section If deflection is dominated by bending like in figure it is much more efficient to increase the height of the cross section than its area see section 5 9 3 Make sure to inclu
23. ctive to see which parts of a beam are under tension or com pression Activate the Strain checkbox in menu Render Settings in order to display the strains in longitudinal beam direction Red like brick means compression blue like steel tension Strain is the quotient between the increase of length when loaded and the initial length of a piece of mate rial Compressive strain is negative tensile strain positive In some models there may exist small regions with high strains with the rest of the structure having comparatively low strain levels This results in a strain rendering that is predominantly white and not very informative With the slider Render Color Margin of the Render Settings Menu you can set the percentage 25 of maximum tensile and compressive strain at which the color scale starts Compressive strain values beyond that level appear yellow excessive tensile strains pink see figure 20 5 8 Results 5 8 1 Section forces The S Force component retrieves axial forces N and resultant bending mo ments M for all elements and load cases See fig 21 for the definition of N and M The order of element results corresponds to the order of beams Thus the data can be used for cross section design Figure 21 Normal force N and resultant moment M at cross section with local coordi nate axes XYZ Figure 22 shows a simply supported beam with two load cases presented in one picture The beam consists of two e
24. d there are lots of examples on the web site which can be easily customized according to ones own needs So casual users can do without reading further 5 Usage 5 1 Define the model geometry First thing to do when setting up a statical model is to define its geometry In Rhino a given geometry consists of a collection of entities like points lines and surfaces For Karamba a given geometry consists of straight beams with physical properties e g cross section material The next three subsections explain how to create them 5 1 1 The LineToBeam component Figure 3 shows how Karambas LineToBeam component takes two lines as input finds out how they connect and outputs beams as well as a set of unique points which are their end points Points count as identical if their common distance is less than that given in LDist the default value being 0 005 m The LineToBeam component accepts only straight lines as ge ometric input Therefore polylines and the like need to be exploded into segments first in E o a o E v ist E Figure 3 The LineToBeam component that turns two lines into beams All coordinates are in meter In order to be of immediate use the beams come with a number of default values see string output in figure 3 active means that it will be included in the static model Teh default cross section is a circular profile of diameter 10 cm with a wall thickness of 0 33 cm The default material is ste
25. de all significant loads dead weight live load wind when checking the allowable maximum deflection For a first design however it will be sufficient to take a multiple of the dead weight e g with a factor of 1 5 This can be done in Karamba by giving the vector of gravity a length of 1 5 In case of structures dominated by bending collapse is preceded by large deflections see for example the video of the collapse of the Tacoma Narrows bridge at which also gives an impression of what normal shapes are see also example Bridge ghx with the EModes component enabled So limiting deflection automatically leads to a safe design If however compressive forces initiate failure collapse may occur without prior warning The phenomenon is called buckling In Karamba it makes no difference whether an axially loaded beam resists Compressive or tensile loads it either gets longer or shorter and the absolute value of its change of length is the same In real structures the more slender a beam the less compressive force it takes to buckle it An extreme example would be a rope As a rule of thumb limit the slenderness which is approximately the ratio of free span to diameter of compressed elements to 1 100 5 13 Cross sections Karamba offers four basic types of cross section e circular tube the default e hollow box section e filled trapezoid section e I profile The dimensions of each of these may be defined manually or by referenc
26. de up from structural elements on predefined supports and with preset loads acting on it Calculating the structural response will show that there are regions which carry more of the external load than others Now one removes a number of 37 those elements that are least strained and thus least effective in the struc ture Again the response of the now thinned out structure is determined and under utilized elements removed and so on This iterative procedure stops when a target volume or number of remaining structural elements is reached Render Color Margin 100 00 9 M Toad case Selection all Figure 30 Triangular mesh of beams before left and after application of ESO Karamba uses the absolute value of normal force of the beams as an indicator of their effectiveness This means that it renders incorrect results in case of structures dominated by bending Figure shows the ESO component which can be found in the subsection algorithms at work On the left side one can see the initial geometry which is a triangular mesh derived from a surface see example ESOWall ghx for details There exist two load cases with loads acting in the plane of the structure in horizontal and vertical direction respectively Three corner nodes of the structure are held fixed The right picture shows the optimized structure with 55 of initial beams removed in the course of
27. des movability in one direction A node that is not attached to a support has three translational degrees of freedom Thus there must be three truss elements that do not lie in one plane for a node to be fixed in space 5 9 2 Activation status of beams When set to true this option excludes the corresponding beam from further calculations until it is reset to true 5 9 3 Height and wall thickness of cross sections Height which in case of circular tubes is equivalent to the outer diameter D and wall thickness of a cross section determine a beams axial and bending stiffness Karamba expects both input values to be given in centimeter The cross section area is linear in both diameter and thickness whereas the moment of inertia grows linearly with thickness and depends on D So in case of insufficient bending stiffness it is much more effective to increase a beams height or diameter than increasing its wall thickness If a cross section hight D is given but no wall thickness t then Karamba assumes t D 30 by default 5 9 4 Changing the default material Steel is the default material of all elements The default grade is S235 which means that it yields at fy 23 5 kN m The next section shows how to define materials with arbitrary properties or how to select predefined materials from a data base Feed these into the Mat input plug of the ModifyBeam component in order to override the default values 30 5 10 Materials
28. e subsection gathers all the necessary information and creates a statical model from it see figure 6 In case that some beams were defined by node indexes then these will refer to the list of points given at the Pt input plug The output plug Mass renders the mass of the structure in kilogram When being plugged into a panel the model prints basic information about itself number of nodes beams and so on At the end of the list the characteristic length of the model is given which is calculated as the distance 10 Deform Scale Ml LC Index Colors Line li B liS K Ka 2 E 5 P A lt l Figure 6 The Assemble component gathers data and creates a model from it between opposing corners of its bounding box 5 3 The ModelView component The ModelView component of the Ensemble subsection can be used to check the current state of a statical model see figure 6 When adding a ModelView to the definition it is a good idea to turn off the preview of all other components so that they do not interfere Clicking on the black menu headings unfolds the ModelView and unveils additional widgets for tuning the model display Each of these will be explained further below The range and current value of the sliders may be set by double clicking on the knob Model def Model b v v 5 3 E gt E lt gt Cross section Strain Oo Stress 0 Utilization O Node tags Length Subdivisi
29. e to a cross section table see section 7 35 Figure 28 Cantilever with four different kinds of cross section For each type of cross section there exist two ways of attaching them to beams e The first works analogously to the ModifyBeam component on the left side it takes a list of beams as input attaches a cross section of given properties and output them on the right side Alternatively cross sections can be defined as autonomous entities which may be plugged into the Assemble component see fig 28 They know about the beams they belong to by their Beam Id property This is a list of strings containing beam identifiers or regular expres sions Upon assembly all beam identifiers are compared to all Beam Id entries of a cross section In case of correspondence the cross sec tion is attached to the beam So this second method for attaching cross sections to beams overrules the first method Components of the first kind have names ending with Beam those of the second kind have names with Profile at their back 5 14 Cross section properties definition Fig shows a cantilever with cross section properties defined by means of beam identifiers The beam axis always coincides with the center of gravity of a cross section Changing e g the upper flange width of an I section therefore results in a slight movement of the whole section in the local Z direction Apart from the
30. e is an empty string Beams that meet at a common point are connected rigidly in the statical model like they were welded together The Info output plug informs about the number of removed nodes and beams 5 1 2 The IndToBeam component Sometimes the initial geometry is already given as a set of points and two lists of node indexes with one entry for each start and end point of beams re spectively In such a case it would be cumbersome to convert this information into geometric entities only for feeding it into the Line ToBeam component which reverses the previous step The IndexToBeam component see figure ia ME o w ir IM le ao E Figure 4 The IndexToBeam component lets you directly define the connectivity informa tion of beams accepts a list of pairs of node indexes and produces beams with default properties from it This speeds up model generation considerably for there is no need to compare nodes for coincident coordinates 5 1 3 The ConToBeam component In Grasshopper meshing algorithms result in topological connectivity dia grams With the help of the ConToBeam component these may be directly converted to beam structures see figure 5 Figure 5 The ConToBeam component turns connectivity diagrams into sets of beams 5 2 The Assemble component In order to calculate the behavior of a real world structure one needs to define its geometry loads and supports The component Assemble from the Ensembl
31. ectly they remain part of Karamba for the time being The colors of Karambas icons have a special meaning black or white designates the entity or entities on which a component acts Products of components get referenced by a blue symbol This guide assumes that you have some basic knowledge of Rhino and Grasshopper In case you need introductory material regarding Grasshopper it is probably a good idea to download the Grasshopper Primer from the Grasshopper web site 4 Quick start Creating a statical model in Karamba consists of six basic stepg see fig Figure 2 Basic example of a statical model in Karamba 1 Create wire frame or point geometry for the structural model with Rhino or GH 2 Convert wire frame or point geometry to Karamba beams 3 Define which points are supports and which receive loads Optional Define custom beam cross sections and multiple load cases 4 Assemble the Karamba structural model with points beams supports and loads 5 Analyze the Karamba structural model 6 View the analyzed model Deflections can be scaled stress strain etc can be observed and multiple load cases can be viewed together or This step by step procedure was devised and formulated by Justin Diles separately Mesh representations of beams can be refined to the desired resolution Karamba is intended to provide an intuitive approach to statical model ing All its components come with extensive help tags an
32. el 78 5 aluminum 27 0 fir wood 3 2 snow loose 1 2 snow wet 9 0 water 10 0 Table 1 Specific weights of some building materials In order to find out the index of a specific node enable the tag checkbox in the ModelView component See section on how to predefine the index of specific nodes Longest list principle means that if the input consists of lists of different length then the longest one determines the length of all the others They get blown up by adding their last element for as many times as required 20 loads type kN m life load in dwellings 3 0 life load in offices 4 0 snow on horizontal plane 1 0 cars on parking lot no trucks 2 5 trucks on bridge 16 7 Table 2 Loads for typical scenarios By default point loads will be put into load case zero Any positive number fed into the LCase plug defines the load case to which the corresponding load will be attributed A value of 1 signals that the load acts in all existing load cases 5 6 2 Mesh loads The Mesh load component can be used to transform surface loads into equiv alent nodal loads This lets you define life loads on floor slabs moving loads on bridges see example Bridge ghx in the examples collection on the Karamba web site snow on roofs wind pressure on a facade etc Figure left side shows a simply supported beam and a mesh which consists of two rectangular faces Each face covers one half of the beam span The orange arrows s
33. el of grade S235 The first beam corresponds to the first item in the list of input lines and so on The order in which points appear in the output node list is random by default However it is sometimes advantageous to identify certain points by their list index in order to put loads on them or to define supports This can be achieved by feeding a list of coordinates into the Points plug They will be placed at the beginning of the output nodes list So in order that the end points of the structure in figure 3 have index O and 1 it is necessary to input a list of points with coordinates 0 0 0 and 8 0 0 There are four more input plugs on the LineToBeam component e New If this plug has the value False only those lines will be added to the structure that start and end at one of the points given in the input points list e Remove If this option has the value True the Line ToBeam component checks for lines that lie on each other and merges such duplicates into one This prevents an error that is hard to detect by visual inspection alone Two lines on the same spot mean double member stiffness in the statical model LDist sets the limit distance for two points to be merged into one Lines of length less than that value will be discarded Id takes a list of strings as identifiers for beams If the number of items in this list is less than the number of beams then the last Id applies to the surplus beams The default valu
34. es to each node when active Element ids displays the beam identifiers CroSec names shows the cross section name used for each beam 5 4 Supports Without supports a structure would have the potential to freely move around in space This is not desirable in case of most buildings The current version of Karamba does statical calculations This means that there must always be enough supports so that the structure to be calculated can not move without deforming Thus rigid body modes are prohibited When defining the supports for a structure one has to bear in mind that in three dimensional space a body has six degrees of freedom DOFs three translations and three rotations see figure 11 The structure must be supported in such a way that none of these is possible without invoking a reaction force at one of the supports Otherwise Karamba will refuse to calculate the deflected state Sometimes you get results from moveable structures although you should not The reason for this lies in the limited ac curacy of computer calculations which leads to round off errors Sometimes one is tempted to think that if there act no forces in one direction consider e g a plane truss then there is no need for corresponding supports That is wrong What counts is the possibility of a displacement Bad choices of support conditions constitute a source of errors that is hard to track Later on it will be shown how to calculate the eigen modes of
35. forces and moments as curves meshes and with or without values attached All generated curves and meshes get appended to the ModelViews curve and Mesh output The graphical representation is oriented according to the local coordinate axes of the beam and takes the un deflected geometry as its base The index of bending moments indicates the local axis about which they rotate for shear forces it is the direction in which they act see also fig 21 Customize the mesh colors vie karamba ini The slider Length Subdivision in sub menu Render Settings controls the number of interpolation points 5 3 3 Render settings The Render Settings menu contains checkboxes for displaying different aspects of a model e When activated Cross section Strain Stress and Utilization re sult in a rendered view of the model Utilization is the ratio between the stress at a point and the yield stress of the corresponding material Shear is neglected for calculating strains stresses and utilization Do not be disappointed that the colors do not change when switching from 14 strain to stress to utilization The color range starts at the minimum value and stretches to the maximum In case the model consists of one material the zone of highest strain will also be the zone of highest stress and material utilization Use a legend component see below to get additional information out of color plots Node tags attaches node index
36. ic structures if unconnected beams exist in the optimized result 5 17 Bi directional evolutionary structural optimization The bidirectional evolutionary structural optimization BESO method car ries the ideas behind ESO one step further Instead of always removing structural parts it also reactivates elements during optimization This takes account of the fact that an element which got removed in an early stage of optimization may gain importance later on The default procedure as used in karambas BESO component consists of the following steps 1 Deactivate all participating elements by setting their Young s Modulus to a very small value 2 Calculate the structural response for given loads and rate the elements according to a user defined criteria 3 Activate a predefined number of the highest ranking elements 4 Recalculate the structural response and rank elements 5 Deactivate a predefined number of the lowest ranking elements 6 If the target number of active elements is reached stop the iteration otherwise proceed to step two Figure 31 shows the BESO component Here the meaning of each input parameter Model receives the model to be optimized Iter the target number of BESO iterations the more iterations the better the results and the more time consuming the optimization 8This component was devised and programmed by Robert Vierlinger The following section is based on his written explanations
37. le pieces As M is always rendered positive the maximum at the end points is unambiguously given Under gravity normal forces in a beam may change sign In such a case Karamba returns that N which gives the maximum absolute value Let us take a look at the output in fig In load case zero both elements return zero normal force because there acts no external axial load The maximum moment of both elements is 2 k Nm For a simply supported beam under a mid point transverse load the maximum moment occurs in the middle and turns out to be M F L 4 1 kN 8 m 4 2 kNm The axial force of 3 kN in load case one flows to equal parts into both axial supports It causes tension 1 5 kN in the left element and compression 1 5 kN in the right one 5 8 2 Elastic energy In mechanics energy is equal to force times displacement parallel to its di rection Think of a rubber band if you stretch it you do work on it This work gets stored inside the rubber and can be transformed into other kinds of energy You may for example launch a small toy airplane with it then the elastic energy in the rubber gets transformed into kinetic energy When stretching an elastic material the force to be applied at the beginning is zero and then grows proportionally to the stiffness and the increase of length of the material The mechanical work is equal to the area beneath the 27 curve that results from drawing the magnitude of the applied force over its co
38. lements and has a total length of eight meters In load case zero a vertical force of magnitude 1kN acts vertically downwards in the middle of the beam Load case one consists of a point load of 3kN directed parallel to the un deformed beam axis The results at the output plugs N and M in fig 22 are a three dimensional trees that hold the beams Normal force in kilo Newton kN and resultant bending Moment in kilo Newton times meter kNm respectively There is only one model fed into the S Force component thus the first index is zero The second index refers to the load case the first two lists contain results for load case zero the last two for load case one Index three corresponds to the element indices in the model Tensile normal forces come out positive compressive normal forces have negative sign The resultant moment yields always positive values as it is the length of the resultant moment vector in the plane of the cross section 26 Figure 22 Simply supported beam under axial and transversal point load List of Nor mal forces and moments for all elements and all load cases Karamba currently computes section forces at the endpoints of elements and returns their maximum values In case of zero gravity the maximum values of M and N occur at the endpoints With gravity switched on these maxima may lie inside the elements In order to get a good approximation of the maximum cross section forces divide the elements in litt
39. lutionary structural optimization There are two new components that allow to define Materials the Material component groups material properties the MaterialSelect component lets you chose predefined materials from a data base in csv format that can be easily extended via Excel or OpenOffice A new ModifyBeam component accepts them as input The new subsection results contains two components for retrieving an elements normal force resultant bending moment internal bending en ergy and internal axial deformation energy A third component outputs nodal displacements i e translations and rotations Analysis has a new output plug called Energy which returns the elastic energy stored in the structure It is a measure for the overall stiffness the larger its value the more flexible the structure All output of the Analysis component now comes for each load case separately An error in the NearestNeighbor component was removed The subsection ZZ 7Z deprecated now holds all components that changed in previous versions and will be removed in future They are kept for the time being so that definitions based on previous versions of Karamba remain valid Version 0 9 007 released on September 7 2011 Beams can be given an identifier This makes it sometimes easier to attach properties to them and set their visibility 49 The result of multiple Line2Beam components can be plugged into an
40. mber of load case to which it applies Supports apply to all load cases by default From the support conditions in figure 12 one can see that the structure is a simply supported beam green arrows symbolize locked displacements in the corresponding direction The translational movements of the left node 16 a at b Hs Figure 13 Influence of support conditions undeflected and deflected geometry Left All translations fixed at supports Right One support moveable in horizontal direction are completely fixed At the right side two supports in y and z direction suffice to block translational movements of the beam as well as rotations about the global y and z axis The only degree of freedom left is rotation of the beam about its longitudinal axis Therefore it has to be blocked at one of the nodes In this case it is the left node where a purple circle indicates the rotational support The displacement boundary conditions may influence the structural re sponse significantly Figure 13 shows an example for this when calculating e g the deflection of a chair Support its legs in such a way that no excessive constraints exist in horizontal direction otherwise you underestimate its de formation The more supports you apply the stiffer the structure and the smaller the deflection under given loads Try changing support conditions in PortalFrame ghx in the examples on the karamba web site and observe how the maximum deflecti
41. mponent of the force vector is at right angle to the mesh face the Y component acts horizontally if the mesh face X axis is not parallel to the global Z axis Otherwise the Y component of the force is parallel to the global Y axis This means a surface load with components only in X direction acts like wind pressure global The force vector is oriented according to the global coordinate system This makes the surface load behave like additional weight on the mesh plane global proj The force vector is oriented according to the global co ordinate system The corresponding surface load is distributed on the area that results from projecting the mesh faces to global coordinate planes In such a way the action of snow load can be simulated GBR SARE 777 7777 Wh a b c Figure 17 Orientation of loads on mesh a local b global c global projected to global plane 22 The input plug Mesh accepts the mesh where the surface load shall be applied Its vertices need not correspond to structure nodes The mesh may have any shape In order to define the structure nodes where equivalent point loads may be generated plug a list of their coordinates into the Pos plug These need to correspond with existing nodes otherwise the Assembly component turns red Offending nodes will be listed in its run time error message Set the LCase input to the index of the load case in which the surface load shall act I
42. n values of structures see figure and NModesWall ghx in the examples section on the Karamba web site as used for buckling anal ysis i e without inertia effects The input parameters are a model the index of the first eigen mode to be computed and the number of desired eigen modes The model which comes out on the right side lists the com puted eigen modes as load cases Thus they can be superimposed using the ModelView component for form finding or structural optimization All loads which were defined on the input model get discarded The determination of eigen shapes can take some while in case of large structures or many modes to be calculated The number of different eigen modes in a structure equals the number of degrees of freedom In case of beams there are six degrees of freedom per node with only trusses attached a node possesses three degrees of freedom 43 Figure 33 Left 14 eigen mode with strain display enabled Right EigenMode component in action Figure 34 shows the first nine eigen modes of a triangular beam mesh that is fixed at its lower corners In the upper left corner of figure 34 one sees the undeflected shape The higher the index of an eigen mode the more folds it exhibits The eigen values represent a measure for the resistance of a structure against being deformed to the corresponding eigen form Values of zero or nearly zero signal rigid body modes
43. ndexing of load cases starts with zero 1 is short for all load cases For input plugs Vec Mesh and LCase the longest list principle applies 5 6 3 Gravity loads Each load case may contain zero or one definition for the vector of gravity In this way one can e g simulate the effect of an earthquake by applying a certain amount of gravity in horizontal direction For Vienna which has medium earthquake loads this amounts to approximately 14 of gravity that a building has to sustain in horizontal direction In areas with severe earthquake loads this can rise to 100 The gravity component applies to all active beams in the statical model The gravity vector defines the direction in which gravity shall act A vector of length one corresponds to gravity as encountered on earth 5 7 Analysis With geometry supports and loads defined the statical model is ready for fur ther processing The Analysis component computes the deflection for each load case and adds this information to the model Whenever the Analysis component reports an error turns red despite the fact that the Assemble component works it is probably a good idea to check the support conditions Figure shows a deflected beam The analysis component not only computes the model deflections but also outputs the maximum nodal dis placement in meter the maximum total force of gravity in kilo Newton and the structures internal deformation energy from each load ca
44. ndoning bending stiffness reduces computation time by more than half for each node with only trusses attached Karamba bases deflection calculations on the initial undeformed geom etry Some structures like ropes are form active This means that when a rope spans between to points the deformed geometry together with the axial forces in the rope provide for equilibrium This effect is not taken into account in Karamba In Karamba only the bending stiffness of the rope which is very small keeps it from deflecting indefinitely One way to circumvent this lies in using a truss instead of a beam element The second possibility would be to reduce the specific weight of the rope to zero see further below The third possibility would be to start from a slightly deformed rope geometry and apply the external loads in small steps where the initial geometry of each step results from the deformed geometry of the previous one 29 Trusses only take axial forces Therefore they do not prevent the nodes they are connected to from rotating In case that only trusses attach to a node Karamba automatically removes its rotational degrees of freedom Otherwise the node could freely rotate which is a problem in static calcu lations AS soon as one beam connects to a node the node has rotational degrees of freedom Bear this in mind when the Analysis component turns red and reports a kinematic system Transferring only axial forces means that a truss reduces a no
45. nent to set the beam properties according to your choice Figure shows how this can be done by inserting it in front of the Assemble component By default the ModifyBeam component leaves all incoming beams unchanged Negative values for input properties take no effect The size of the lists of input data is scaled to match the number of input beams by copying their last item Several ModifyBeam components may act consecutively on the same beam 5 9 1 Bending stiffness Beams resist normal force and bending Setting the Bending plug of the ModifyBeam component to false disables bending stiffness and turns the 28 Q a gt 3 o Figure 23 Modification of the default beam properties corresponding beam into a truss There exist reasons that motivate such a step e Connections between beams that reliably transfer bending and normal force are commonly more expensive than those that carry normal force only The design of connections heavily depends on the kind of material used rigid bending connections in wood are harder to achieve than in steel Yet rigid connections add stiffness to a structure and reduce its deflection Therefore you are always on the safe side if you use truss elements instead of beams For beams with small diameter compared to their length the effect of bending stiffness is negligible compared to axial stiffness Just think of a thin wire that is easy to bend but hard to tear by pulling e Aba
46. on m E UA Faces Cross section 8 00 Render Color Margin 100 00 y l Figure 7 Partial view of a model The ModelView component features five plugs on its left side e Model expects the model to be displayed e LC Factor can be used to scale individual load cases see further 11 below e LC Index lets one select the visible load case see example EMod esWall ghx The value in LC Index will be added to the load case selected in the drop down list of ModelView If the resulting number is larger than the number of available load cases the ModelView turns red If the resulting value is smaller than O all load cases are superimposed The possibility of using a number slider for selecting load cases makes life easier in case that there are many of them Colors Color plots for stresses strains etc use a color spectrum from blue to white to red by default One can customize the color range by handing over a list of RGB values to the Colors plug There have to be at least three colors given The first color is used for values below the last color for values above the current number range The remaining colors get evenly distributed over the number range The Grasshopper component Gradient can be used to generate the list of colors see fig 8 e Id This plug lets one select those parts of a model which shall be displayed It expects a list of strings The default value is an empt
47. on changes In order to arrive at realistic results introduce supports only when they reliably exist By default the size of the support symbols is set to approximately 1 5 m The slider with the heading Support on the ModelView component lets you scale the size of the support symbols Double click on the knob of the Slider in order to set the range of values 17 5 5 Predefined displacements Supports as described above are a special case of displacement boundary condition They set the corresponding degree of freedom of a node to zero The more general PreDisp component lets you preset arbitrary displacements at nodes Figure 14 shows a beam with prescribed clockwise rotations at both end points See also example FixedFixedBeam ghx The PreDisp component resembles the Support component to a large de gree Nodes where displacement conditions apply can be selected via node index or nodal coordinates The size of the list fed into the Pos Ind plug determines the number of displacement conditions All other input will be truncated or blown up by copying its last list item Input plug LCase lets you set the index of the load case in which displace ments shall have a specified value The default value is 1 which means that the displacement condition is in place for all load cases It is not pos sible to have displacement boundary active in one load case and completely disabled in others For load cases not mentioned in
48. or not can leave out the mass matrix and solve the special eigenvalue problem instead of the general one which is easier 42 5 19 1 Eigen modes in structural dynamics If you hit a drum on its center the sound you hear originates from the drum skin that vibrates predominantly according to its first normal mode When things vibrate then the vibration pattern and frequency depend on their stiffness and support conditions the distribution of mass and where you hit them Imagine a drum with a small weight placed on it the weight will change the sound of the drum The same is true when you hit the drum near its boundary instead of in the center You will excite the drums eigen modes differently 5 19 2 Eigen modes in stability analysis An unstable structure can be thought of as a statical system that vibrates very slowly leaves its initial state of equilibrium and never comes back This is why inertia forces do not play a role in the calculation of buckling shapes Otherwise the phenomina of vibration and buckling are very similar The loads placed on a structure together with the eigen modes determine the actual way a structure buckles The Euler cases describe the buckling modes of beams subject to different support conditions The more degrees of freedoms fixed at the boundary the higher the load at which a beam buckles 5 19 3 The EigenMode component Karambas EigenMode component allows to calculate eigen modes and cor responding eige
49. rresponding displacement In case of linear elastic materials this gives a rectangular triangle with the final displacement forming on leg and the final force being its other leg From this one can see that for equal final forces the elastic energy stored in a material decreases with decreasing displacements which corresponds to increasing stiffness The structure of the results list returned from the E Energy component resembles that of the S Force component described above Instead of normal force and moment the work of normal force and moment on each beam are given 5 8 3 Nodal displacements The Disp component lists the displacements of each node for all load cases Again two trees with three dimensions form its output These dimensions correspond to Model LoadCase Node The data for each node at the output plugs Trans and Rot consists of three values each three translations and three rotations All of them are given in the global coordinate system in meter and radiant A positive rotation say about the global X axis means that the node rotates counter clockwise for someone who looks at the origin of the coordinate system and the X axis points towards him or her 5 9 How to change beam properties By default Karamba assumes the cross section of beams to be steel tubes with a diameter of 10 cm and a wall thickness of 0 33 cm When two beams meet they are rigidly connected like they were welded together Use the ModifyBeam compo
50. se see section 5 8 2 for details on work and energy These values can be used to rank structures in the course of a structural optimization procedure the more efficient a structure the smaller the max 23 Model Q Deform Scale E Model E v Mesh v LC Index 2 Curve Ay sees Deformation 22 95 Loads E 22 Supports E D LoadCase 0 Figure 18 Deflection of simply supported beam under single load in mid span imum deflection the amount of material used and the value of the internal elastic energy Real structures are designed in such a way that their de flection does not impair their usability See section 5 12 for further details Maximum deflection and elastic energy both provide a benchmark for struc tural stiffness yet from different points of view the value of elastic energy allows to judge a structure as a whole The maximum displacement returns a local peak value When activating the preview property of the Analysis component the un deflected structure shows up In order to view the deflected model use the ModelView component and select the desired load case in the menu Load case Selection There exist two options for scaling the deflection output First there is a slider entitled Deformation in the menu Display Scales that lets you do quick fine tuning on the visual output Second option the input plug LC Factor which accepts a list of numbers that Model
51. se get attached to points either by node index or node position Feed a corresponding list of items into the Pos Ind plug quite analogous to the Support component A point load is given as a vector Its components define the force components in global x y and z direction The number of point loads generated follows from the longest list principle applied to all input The output of the force component has to be connected to the corresponding plug of the assembly Plugging a point load into a panel component gives the following information Node index where the load gets applied force vector and number of the load case to which it belongs Karamba expects all force definitions to be in kilo Newton kN On earth the mass of 100kg corresponds to a weight force of roughly 1kN The exact number would be 0 981kN but 1kN is normally accurate enough Table contains the specific weight of some everyday materials Rules of thumb numbers for loads can be found in table Do not take these values too literally For example the snow load varies strongly depending on the geo graphical situation Loads acting along lines or on a specified area can be approximated by point loads All you need to do is estimate the area or length of influence for each node and multiply it with the given load value The Mesh load component see next section automates this task for surface loads type of material N m reinforced concrete 25 0 glass 25 0 ste
52. ta base underlying the MatSelect component The file path to the materials data base can be changed in two ways first right click on the component and hit Select file path to material definitions in the context menu that pops up Second plug a panel with a file path into Path Relative paths are relative to the directory where your definition lies 5 11 1 Theoretical background of stiffness stress and strain As mentioned in section 5 7 strain is the quotient between the increase of length of a piece of material when loaded and its initial length Karamba 33 can visualize strains as color plots in order to do this activate the strain checkbox in the ModelView component Usually one uses the greek letter e for strains Strain induces stress in a material Stress has the meaning of force per unit of area From the stress in an beam cross section one can calculate the normal force that it withstands by adding up integrating the product of area and stress in each point of the cross section Stress is normally symbolized by the greek letter o Linear elastic materials show a linear dependence between stress and strain The relation is called Hooke s Law and looks like this o Bb e E stands for Young s Modulus which depends on the material and depicts its stiffness Hooke s law expresses the fact that the more you deform something the more force you have to apply 5 12 Tips for designing statically feasible structures Karam
53. teral strain amounts to 30 of the longitudinal strain In case of beams with a large ratio of cross section height to span this effect influences the displacement response In common beam structures however this effect is of minor importance The shear modulus G describes material behavior in this respect It is included in the MaterialProps component for completeness Currently Karamba does not take account of this property 5 10 3 Specific weight The value of gamma is expected to be in kilo Newton per cubic meter k N m This is a force per unit of volume Due to Earths gravitational acceleration a g 9 81 kg m s and according to Newtons law f m a a mass m of one kilogram acts downwards with a force of f 9 81N For calculating deflections of structures the assumption of f 10N is accurate enough Table 1 gives specific weights of a number of typical building mate rials The weight of materials only takes effect if gravity is added to a load case see section 5 6 3 5 11 Material selection v 2 Ss a o MatSelect File path to the location of the cross section table 0 Plug ins Gra Figure 25 Selection of material definitions by type 32 The MatSelect component in the menu subsection Material lets you select materials by name via the input plug Name which expects a string or list of strings see fig 25 The data base currently holds properties for steel
54. value is added to the load case index selected on the drop down list If the sum is negative all load cases will be displayed 7 6 Icons in Karamba toolbar do not show up Sometimes it happens that Karambas component panels do not display any component icons Select menu item View Show all components in order to make them show up 7 7 Error messages upon loading definitions saved with outdated Karamba versions When loading definitions based on outdated Karamba version a pop up win dow will inform you that IO generated x messages Normally this can be ignored It may happen however that very old Karamba components do not load In this case put their Current versions in place 7 8 Component in old definition reports a run time error On some components the order of input plugs changed over time e g the Assemble component They will turn red when loaded and the runtime error message will state that one object can no be cast to some other object In this case replace the old component with a new one and reattach the input plugs accordingly 48 1 9 Other problems In case you encounter any further problems please do not hesitate to contact us at karamba bollinger grohmann schneider at or via the karamba group at http www grasshopper3d com group karamba xg_source activity 8 Version history 8 1 8 2 Version 0 9 06 released on June 6 2011 Robert Vierlinger contributed a component for bidirectional evo
55. w e 0 absolute value of normal force e 1 bending energy 40 e 2 deformation energy stored in an element which is equal to the sum of bending and axial deformation energy 3 specific deformation energy i e elastic energy stored in an ele ment per unit of volume this prevents big elements from outscoring small ones ContElemAdd In some cases it makes sense to activate only such el ements that connect to either supports or previously added elements Set ContElemAdd to true to enable that option MaxDist sets the upper threshold distance for the end points of neighbor ing elements to count as connected if option ContElemAdd is enabled MinDist sets a limit on the minimum distance between the end points of active and elements to be newly added This prevents clustering and spatial overlap between elements BiDir if set to False the algorithm performs pure growth until the desired ratio of active to participating elements is reached A value of True makes the algorithm activate twice the amount of elements say 2 n in each step needed to achieve the target element ratio in the desired number of iteration steps After recalculation the n lowest ranking elements get deactivated again for compensation 5 18 Elimination of tension or compression members The Tension Compression Eliminator component removes elements from a model based on the sign of their axial force y
56. ws a fem karambaPINVOKE exception This may be due to left overs from previous Karamba installations which were not removed properly during the installation procedure In such a case precede as follows e Uninstall Karamba completely via settings Software e Make sure that everything was removed Go to folder Rhinoceros 4 0 Plug ins Grasshopper remove files karamba gha karamba dll KD TreeDLL dll and libiomp5md dll by hand if they still exist This is plan b if the above does not help e Start Grasshopper e Type GrasshopperDeveloperSettings in the Rhino Window and hit EN TER e Toggle the status of the Memoryload GHA assemblies using COFF byte arrays option e Restart Rhino Plan c is to post a help request to the karamba group at grasshopper3d com group karamba xg_source activity 47 7 3 Karamba does not work after reinstalling Grasshoper Upon installing Grasshopper some files of the Karamba package may get erased on some systems Try to reinstall Karamba 7 4 Predefined displacements take no effect Check whether you disabled the correct degrees of freedom in the Condi tions section of the PreDisp component 7 5 The ModelView component consistently displays all load cases simultaneously If the ModelView component does not seem to react to selections done with the drop down list for load cases check the value in the LC Index input plug Remember that its
57. y string which means that all of the model shall be visible As one can see in fig it is possible to input regular expressions These must start with the character 2 and adhere to the conventions of regular expressions as defined for C7 The identifier of each beam of the model is compared to each item of the given string list In case a list entry matches the beam identifier the beam will be displayed Fig contains four examples of Id lists The first would limit visibility to beam A the second to beam B The third is a regular expression which matches beams A or C The fourth matches beams A to OS There are five output plugs on the ModelView component e Model is essentially the model which was fed in on the left side When there are results available from a statical calculation deflections are scaled and added to the node coordinates so that it contains the deformed geometry e From the Mesh output plug you can get the mesh of the rendered model for further processing In fact it is a list of meshes with each 12 o Colors ME Legend ld Mode fg detiioce Lc Factor G Mesh Lo LC Index 3 Curves 3 Legend T Length Subdivision m 044 E z Render Color Margin 5 O Figure 8 Color plot of strains with custom color range item corresponding to one element strainimm m 201e 01 180e 01 159e 01 138e 01 116e 01 9530 02 7418 02 5 29e 02 3188 0
58. ymbolize the equivalent nodal forces One can see that the equivalent force in the middle of the beam is twice as large as those at the supports The procedure for calculating nodal forces from surface loads consists of the following steps First Karamba calculates the resultant load on each face of the given mesh Then the resultant loads of each face get evenly distributed among their corresponding vertices The second step consists of distributing the vertex loads among the nodes of the structure this is done by considering the distance between the vertices and structure nodes where the mesh load shall apply Each vertex transfers its load to the nearest such node In case that there are several nodes at equal distance the vertex load gets evenly distributed among them Differences of distance of less than 5mm are neglected From the algorithm described above one can see that a crude mesh may lead to a locally incorrect distribution of loads The right side of figure shows what data the Mesh load component 21 Ly Figure 16 Simply supported beam loaded with three forces that approximate an evenly distributed surface load on a mesh collects The input plug Vec expects a vector or list of vectors that define the surface load Its physical units are kilo Newton per square meter kN m2 The orientation of the load vector depends on the checkbox selected under Orientation see also figure 17 local to mesh X co

Download Pdf Manuals

image

Related Search

Related Contents

Samsung SGH-U900 Наръчник за потребителя  AT-DL5HD 取扱説明書    Bedienungsanleitung OL2092EU - Halogen  Mitel ACD 2000 User's Manual  LE CAHIER JURIDIQUE  

Copyright © All rights reserved.
Failed to retrieve file