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User Manual for Version 1.0.5

1. 048 30 peewee eee ee E E ee ee 30 Cee ee eee ee ee ee ee ee 33 anar E 34 TEEN 35 TEE 37 6 2 1 Box Profile Circular Profile I Profile and Trapezoid e 38 6 2 2 Shell Cross Section 39 6 2 3 Spring Cross Section 048 40 6 2 4 Beam Joints 0 2 00 2 0 eee 41 6 2 5 Disassemble Cross Section 42 6 2 6 Eccentricitiy on Beam Eccentricity on Cross Section 42 6 2 7 Cross Section Matcher 43 6 2 8 Cross Section Range Selector 44 6 2 9 Cross Section Selector 44 oa 44 AA 46 OS Matera ociosas cs ce A A a a 4T 6 3 1 Material Properties a a a a a a a a a a 47 6 3 2 Material Selection 04 48 6 3 3 Read Material Table from File 48 CA ALO essa a a e e a e E O e e Ea 49 6 4 1 _Point Load aoaaa a 51 6 4 2 Mesh Load 2 2 0404 51 6 4 3 Line Load on Element 54 6 4 4 Pretension Load 048 54 6 4 5 Temperature Load 55 6 4 6 Gravity 56 6 4 7 Point Mass e 56 6 4 8 Prescribed displacements 22 57 6 5 Algorithms 6 5 1 6 5 2 6 5 3 6 5 4 6 5 5 6 5 6 6 5 7 6 6 1 6 6 2 6 6 3 6 6 5 6 6 6 6 6 7 6 6 8 6 6 9 6 7 Export 6 7 1 6 8 Utilities 6 8 1 6 8 2 6 8 3 6 8 4 6 8 5
2. Figure 67 Color plot of strains with custom color range There are five output plugs on the ModelView component e Model is the model which was fed in on the left side e From the def Mesh output plug you can get the mesh of the shells of the deformed model for further processing It is a list of meshes with each item corresponding to one shell e The def Curve plug delivers the axes of the beams of the deformed 76 structure as interpolated 3 degree nurb splines Use the Length Sub division slider to set the number of interpolation points e def Model When there are results available from a statical calculation deflections are scaled and added to the node coordinates of the original model so that it contains the deformed geometry The Display Scales submenu Model Model LC Fact poked def Mesh LC Index def Curves Colors Id def Model Deformation m Reactions m O 0 18 Loads E 00 20 Supports E O 0 11 m Local axes O 0 28 Joints Length Segment m O 0 20 11 50 575 Result orde EA o Node tags g Element tags O Element Ids g Elements m CroSec names O Eccentricities Load values E Figure 68 Local axes of cantilever composed of two beam elements reaction force and moment at support The Display Scales submenu contains check boxes and sliders to enable dis able and scale displacements reaction forces at supports load symb
3. Stacked Stitch Connects beam sets by a preset number of elements that do not intersect each other User Iso Lines Creates iso lines on a model based on user supplied nodal values User Stream Lines Creates stream lines on a model based on user supplied vectors at the nodes 6 Component Reference 6 1 Ensemble The subsection Ensemble of Karamba contains components for handling the basic aspects of a statical model 23 Pt Model Beam Elem Q Support Load a gt CroSec wm o w l Assemble S Disassemble Material IndToBeam a Set Mass LDist Figure 13 Setting the activation state of all elements of a model with a list of boolean values 6 1 1 Activate Element The activation state of an element can be controlled with the Activate Element component see fig 13 This component expects a model and a list of boolean values as input The list of true false values will be mapped to the activation status of the elements in the model true corre sponds to active false to inactive Section 6 5 5 shows how the Activate Element component enables one to view the solution history of the iterative FindForcePath algorithm Karamba sets elements inactive by giving them a very weak material with zero weight 6 1 2 Assemble Model In order to calculate the behavior of a real world structure one needs to define its geometry loads a
4. Scale R4 VT2 TIS wis Figure 70 Approximation of principal strains in a simply supported slab simulated with beam elements under a point load Irregularity of principal strain directions is due to the irregularity of the element grid Karamba includes shell elements from which principal stress lines can be retrieved see sec 6 6 16 In case of single layer grid shells made up of beams the Approximate Principal Strains component can be used to determine the approximate principal strain directions of such structures see fig 70 It works on arbitrary sets of deformed points The calculation of principal strains is based on the assumption of a con tinua When applied to nodes connected with linear elements the result can thus only result in a qualitative picture therefore the term Approximate The Approximate Principal Strains component expects as input a refer ence model input plug Model and the same model in a deformed config uration input plug def Model The deformed model can be the output of a ModelView component Hand over a list of points to the input plug Point where principal strain directions shall be computed For each point in this list the following two steps are applied First those three nodes of the reference model that do not lie on a line and have minimum distance to the given point are determined Second the strains in the sides of the thus found triangle d
5. o LL U c he a e Figure 83 Cantilever analyzed as shell structure directions of second principal normal forces at element centers The Principal Force Directions on Shells component lets you retrieve principal normal forces and moments at element centers see fig 83 All Shells of a model get considered by default Use the input plug Elemids to select a subset Results refer to the selected load case at the nearest upstream ModelView component The order of all result lists corresponds to the order of faces in the mesh used to generate the shell Output plug P lists the coordinates of the element centers where the normal forces and bending moments were cal culated Ni and N2 deliver the first and second principal normal force directions as vectors Their length corresponds to the absolute value of the corresponding quantity in kN m The output plugs M1 and M2 return first and second principal bending moment directions 6 6 14 Principal Moment Lines on Shells Works like the Principal Stress Lines on Shells component see section 6 6 16 Instead of principal stress lines it returns principal moment lines 6 6 15 Principal Stress Directions on Shells This components provides the same results as the Princ Stress 1 2 option of the ShellView component see fig 84 The output plug P renders the positions of the elements centroids V1 and V2 return corresponding vectors f
6. property This is a list of strings con taining element identifiers see or regular expressions that match a group of element identifiers element ids Upon assembly each element id is compared to all Elemids entries of a material In case they match the material is attached to the element An empty string which is the default value signifies that the material shall be applied to all elements 6 3 1 Material Properties Figure 40 The definition of the properties of two materials via the MatProps component and selection of the second Material from the resulting list The component MatProps lets one directly define material properties see fig 40 e Elemids list of identifiers of elements or a regular expression that depicts the elements that shall have the specified material e Young s Modulus E kN cm Al e Shear modulus G kN cm e specific weight gamma kN m e coefficient of thermal expansion alphaT 1 C e yield stress fy kN cm e the name of the material in Name The yield stress characterizes the strength of a material The utilization of cross sections as displayed by the BeamView see section is the ratio of actual stress and yield stress In case of shells utilization is determined as the ratio of Van Mises Stress and yield stress see section 6 6 18 Cross section optimization see section 6 5 7 also makes use of the materials yield stress In case of t
7. represents the longitudinal beam axis y is horizontal z vertically upwards Cross sections with eccentricities can be stored in cross section tables using the GenCS Table component and thus be made reusable in other projects The Eccent Beam component has one additional input plug as compared to the cross section variant ecce glo lets one define beam eccentricities cm with respect to the global coordinate system 6 2 7 Cross Section Matcher D o Ma 2 2 2 D Dp PD E 5 A I Profile o D n 3 3 o o D 2 CroSecRSelect 3 a a Figure 35 The Cross Section Matcher component returns a standard profile for a custom profile Use the Cross Section Matcher component in case you want to find the first profile from a given list that provides equal or higher resistance compared to a given custom profile see fig 35 The CSMatch component takes a cross section and a list of cross sections as input Traversing the list starting from the first element it proceeds until an appropriate profile is found which is returned as the result 43 6 2 8 Cross Section Range Selector The cross section library that comes with Karamba contains roughly 5300 profiles In order to reduce the amount of information the list can be short ened by applying selection criteria on it using the Cross Section Range Select component see fig 36 The input plugs maxH and maxW l
8. It consists of ten subsections see figure 2 In case you do not see any icons select Draw All Components in Grasshoppers View menu The installation can be tested by placing a Karamba License component on the canvas it should not issue a warning or error If not see section for how to solve that issue On Apple machines make sure to have Microsofts NET Framework 4 0 installed These are the subsections which show up in the Karamba category License The License component contained in here delivers informa tion regarding the current type of license and how to get a pro version of Karamba see fig 1 Params containers for Karamba objects like beams loads models 10 Grasshopper No document File Edt View Display Solution Help Params Maths Sets Vector Curve Surface Mesh Koo alo Asz a a Bi 2 00 E Ob Q a LO C Transform Karamba Extra PanelingT 38 A na t y Hi Ed mo KR Ge ip ols g Q AN S LunchBo A q BL Es do STA Bie Ki 22 am lt y As T So e uz Figure 2 Category Karamba on the component panel e Algorithms e Cross Section tions for elements e Ensemble e Export file e Load e Materials e Results e Utils lets you create models to handle and optimize models components for applying external forces for the retrieval of calculation results comp
9. O 00 Length Segment m 1 00 Result Threshold 100 00 Figure 86 Resultant displacement of a shell The ShellView component works like the BeamView component see sec l6 6 8 and controls the display of shell results Figure shows the resultant displacement of a shell You can choose from these rendering options e Cross section shows the upper and lower shell surface and adds them 93 to the output at the Mesh output plug Displacement colors the shell according to the resultant displacement Utilization renders the material utilization of shells The utilization ts calculated as the ratio between yield stress of the material and maximum Van Mises Stress along the shells cross section hight The Van Mises Yield criterion is not applicable to brittle materials like concrete e Princ Stress 1 visualizes the resultant value of the first principal stress in the plane of the shell Princ Stress 2 displays the resultant value of the second principal stress direction would also be a correct result e Van Mises Stress renders the Van Mises Stress Layer of Results sets the shell layer on which results are calculated A value of 1 corresponds to the upper surface 1 to the lower Princ Stress 1 2 Enables disables and scales the vector display of principal stresses in the element centers Use the Result Threshold Sliders in the Display Scales menu of the Mo
10. area that results from projecting the mesh faces to global coordinate planes In such a way the action of snow load can be simulated 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 Set the LCase input to the index of the load case in which the surface load shall act Indexing of load cases starts with zero 1 is short for all load cases 53 b c Figure 46 Orientation of loads on mesh a local b global c global projected to global plane 6 4 3 Line Load on Element local to element O global O global proj a Figure 47 Line loads on a structure consisting of three beam elements defined in local beam coordinate systems Figure shows a tilted structure consisting of three beams under the action of a uniformly distributed load at elements 0 and 2 The load acts parallel to the beams local z axis The components of the load vector are assumed to be given in kilo Newton per meter kN m The input plug Beamids receives a list of the identifier of the beams on which the load shall act See section for how to attach identifiers to beams By default beams are named after their index in the FE model There are three options for the orientation of the load local to element global and global proj Their meaning corresponds to the options available for mesh load
11. may give rise to problems The help text of Grasshopper components does not change dynamically Switching from SI to imperial units leaves the help text of those components already placed on the canvas unaltered The interpretation of the input values however changes Opening a GH definition with Karamba versions with differently set physical units entails the same problem 4 3 Elements Figure 4 Components for creating beam 1 and shell elements 2 Beam and shell elements can be generated based on lines and meshes Give an id name for later reference e g B and S in fig 4 This allows non default cross sections and materials to be assigned to them El ement names need not be unique Karamba provides truss beam and shell elements All geometric input is assumed to be in meters when you use SI units and feet in case of Imperial units 4 4 Materials Materials can be defined by setting their mechanic properties Alternatively materials can be selected from a library of predefined materials that comes with Karamba The Elem ld input plug specifies the names of the elements to which the material shall be attached Leaving Elem Id empty defines 13 Figure 5 left definition of a custom material 1 Right selection of a material from the material library 2 the material for all elements Steel is the default for elements if nothing is given 4 5 Cross Sections Elemlds Height Upper Wi
12. z_ t real Mt force Node x_r real My force Node y_r real Mz force Node z_r if node_ind 0 N N tension is gt O for axial stress real fb if N gt 0 fb N Nrd abs My Myrd abs Mz Mzrd abs Mt Mtrd else fb N Nbrd abs My Myrd abs Mz Mzrd abs Mt Mtrd for shear real fs abs Vy Vyrd abs Vz Vzrd abs Mt Mtrd take the larger of the two real f fb gt fs fb fs update utilization level _ utilization _ utilization gt f _ utilization f if f gt 1 4 _insufficiency f return false 0 5x 1 props gt alpha_y lam_y 0 2 lam_y x lam_y 0 5x 1 props gt alpha_z lam_z 0 2 lam_z lam_z In line 9 the buckling length l is determined The function bucklin gLength starts with the end points of the given beam and procedes to its neighbors until nodes with more than two beams attached are detected The distance between these nodes is taken as the buckling length In lines 13 and 14 the materials yield stress f and Young s Modulus E are 117 determined The critical buckling load of a beam is given as m2 E NS cr 2 in 1 This calculation is done in lines 16 to 18 for the two principal axes of the cross section A variable h acts as a helper M PI represents m The procedure for calculating the design value of the buckling force Nra is taken from Eurocode EN 1993 1 1 2005 paragraph 6 3 1 1 eq
13. 6 8 6 6 8 7 6 8 8 Analyze Analyze Large Deformation Eigen Modes Natural Vibrations 2 2 22282482 4 Force Flow Finder 2 2 2 2 2222482 Tension Compression Eliminator Optimize Cross Section 2 2 2 22 4 6 6 Results Deformation Energy ModelView Nodal DisplacementS l 6 6 4 Approximate Principal Strains Reaction Forces Utilization of ElementSl Beam Displacements 2 2 22848 BeamView Resultant Section Forces ee a a a 6 6 12 Isolines on Shells 048 Seen oa oe oa ae ee ee ee TETTETETT Pee ee gee oe a n Mesh Breps Nearest NeighborS Multi dimensional Nearest Neighbors Remove Duplicate Lines 0220242 Remove Duplicate Points 022 Get Cells from Lines 2 2 20242 Line Line Intersection 2 2 24 2 Element Felting 58 58 59 62 64 64 68 69 73 74 74 79 80 81 81 82 82 85 87 88 90 91 91 91 92 93 93 94 94 95 95 97 97 98 98 98 99 99 6 8 9 Mapper 2 00 a a 100 aa ee ee ee ek eR Be A 101 aaa ee eee eee ee eee ee 102 as ee ee 103 ee ee ee ee ee ee 103 Aaa 104 7 Trouble shooting 105 7 1 Karamba does not work for unknown reason 105 1 2 fem karambaP
14. Load The Mesh load component can be used to transform surface loads into equiv alent node or element loads This lets you define life loads on floor slabs moving loads on bridges see example Bridge ghx in the examples collec tion on the Karamba web site snow on roofs wind pressure on a facade etc Figure 44 left side shows a simply supported beam and a mesh which consists of two rectangular faces Each face covers one half of the beam and has a width of 2 m perpendicular to the beam axis With a distributed load of 1 kN in negative global Z direction a uniformly distributed load of 2 kN m results With the input plug Beamlds groups of elements can be specified on which equivalent loads shall be generated By default all beams of the model are included In case no beam loads shall be included provide an identifier like e g None which does not correspond to an element in the model In order to define structure nodes where equivalent point loads may be generated plug a list of their coordinates into the Pos plug These need to correspond to existing nodes otherwise the Assembly component turns In order to find out the index of a specific node enable the node tag checkbox in the ModelView component See sectionl6 1 5lon how to predefine the index of specific nodes or node position 51 O local to mesh O global O global proj Figure 44 Simply supported beam loaded with line loads that approxima
15. Wissenschaften GmbH amp Co KG Berlin 81 32 40 2012 119
16. are positive in the direction of the local coordinate axes 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 Res S Forcg Figure 79 Simply supported beam under axial and transverse point load List of normal forces shear forces and moments for all elements and all load cases The input plug NPoi sets the number of equidistant points along the beam axis where resultant forces are calculated in order to determine the maximum values for output In case of zero gravity and in the absence of uniform beam loads the maximum values of M and N occur at the endpoints Otherwise these maxima may lie inside the elements The default value of NPoi is three which means that values are checked at the beams end points and in the middle As M is always rendered positive the maximum along an element is unam biguously given Under gravity normal forces in a beam may change sign 36 In such a case Karamba returns that N which gives the maximum absolute value Fig shows the results of a simply supported beam consisting of two elements under two load cases In load case zero both elements return zero normal force because there acts no external axial load The maximum mo ment of both elements is 2 kNm For a simply su
17. 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 curve that results from drawing the magnitude of the applied force over its corresponding displacement In case of linear elastic materials this gives a rectangular triangle with the final displacement forming one 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 axial def energy kNm bending energy kNm Figure 65 Simply supported beam under axial and transversal point load List of axial deformation energy and bending energy for each element and load case The structure of the data tree returned from the D Energy component see fig corresponds to Model Load case Element result In case of Shells the list on the lowest level contains the axial or bending energy of each element of the shell 6 6 2 ModelView The ModelView component of the Results subsection controls the general display properties of the statical model see figure 14 More specific visual prop
18. considerably For better performance disable the preview of all components or minimize the Rhino window A 5 Natural Vibrations and Eigen Modes 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 A 5 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 In this manual eigen modes of a statical system that gt An Eigen mode is the solution to the matrix equation C Z A which is called the gt special eigen value problem Where C is a matrix a vector and A a scalar that is a number called eigen value The whole thing does not necessarily involve statical stru
19. effect Several ModifyBeam components may act consecutively on the same beam Remove Active Height Beam D Thickness bid Id i owo Buckling BklLenY BklLenZ Figure 23 Modification of the default beam properties Bending stiffness Beams resist normal force and bending Setting the Bending plug of the ModifyBeam component to false disables bending stiffness and turns the corresponding beam into a truss There exist reasons that motivate such a step 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 slender beams i e 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 Abandoning 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 31 a rop
20. f 10N is accurate enough Table 3 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 111 case see section 6 4 6 A 1 3 Theoretical Background of Stiffness Stress and Strain As mentioned in section 6 5 1 strain is the quotient between the increase of length of a piece of material when loaded and its initial length Usually one uses the Greek letter e for strains Strain induces stress in a material Stress is 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 EH 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 A 2 Additional Information on Loads 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 fou
21. free can be found at http www grasshopper3d com Karamba comes as 32 bit or 64 bit application Select the version accord ing to the bitness of the Rhino version you want to work with By default Rhinoceros 5 this is the 32 bit version and Rhinoceros 5 64 bit get installed The installation procedure lets you set the physical units used for calcula tion By default Karamba assumes input to be in SI units e g meters for point coordinates You can switch to Imperial units either on installation or later on by editing the karamba ini file Coordinates will then be interpreted to be in feet force in kips material strength in ksi and so on For installation invoke KarambaSetup msi It automatically installs karamba dll and libiomp5md dil to C Windows and all other files to the Compo nents Folder Its location can be easily found by selecting File Special Folders Component Folders from the Grasshopper menu Besides other things a folder named Karamba will be created there containing the li cense agreement a readme file pre fabricated cross section and material tables and the configuration file karamba ini The config file contains gen eral program settings and can be edited with any text editor It contains key value pairs 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
22. group size Maintain Figure 15 The Connected Parts component groups beams into sets of elements that have at least on node in common each 6 1 4 Disassemble Model It is sometimes necessary to pull apart existing models in order to reassemble them in different configurations The DisassembleModel component can be used for decomposing a statical model into its components see figure 16 Loads supports and elements reference the nodes they connect to by their node index regardless whether they were initially defined using coordinates 25 Figure 16 Model is decomposed into its components or node indexes This can be used to change the geometry of a model without altering its topology plug a list of modified Grasshopper points into the Pt plug of an Assemble component along with the objects you get from DisassembleModel and see what happens 6 1 5 Line to Beam Figure shows how Karambas Line TOBeam 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 distance is less than that given in LDist The default value is 0 005 m The Line ToBeam component accepts only straight lines as geometric input Therefore poly lines and the like need to be exploded into segments first 0 w ca o w E Figure 17 The LineToBeam component that turns two lines into beams All coordinate
23. 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 28 shows an example for this when calculating e g the deflection of a chair Support its legs in such a way that no exces sive constraints exist in horizontal direction otherwise you underestimate its deformation The more supports you apply the stiffer the structure and the smaller the deflection under given loads 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 6 2 Cross Section Karamba offers five basic types of cross section e Circular tube the default 37 e hollow box section e filled trapezoid section e I profile e shell cross sections The dimensions of each of these may be defined manually or by reference to a list of cross sections see section 6 2 9 Figure 29 Cantilever with four different kinds of cross section Cross sections are autonomous objects which may be plugged into the Assemble component see
24. 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 Compr If true then only members under compression will be kept Oth erwise only members under tension will survive This value is false by default Elements selected for removal are assigned a negligible stiffness i e a soft kill approach is used 6 5 7 Optimize Cross Section Use the Optimize Cross Section OptiCroSec component for the automatic selection of the most appropriate cross sections of beams and shells It takes into account the cross sections load bearing capacity and optionally limits the maximum deflection of the structure Figure shows a typical set up The initial structure consisted of I sections of type HEA100 which have a height and width of 100 mm They could not sustain the given load The resulting bending stresses would lie way beyond the yield stress of the assumed material which is steel S235 with fy 23 5 kN cm First the OptiCroSec component determines the cross section of each el ement in such a way that their load bearing capacity is sufficient for all load cases In order to achieve this Karamba uses the following procedure 69 Am i l CroSecSelect eh u 1 Og I UM o9 9 q o o A N le x Figure 63 Cross section optimization with the OptiCroSec component on a simply sup ported beam 1 D
25. of a family are ordered starting with your most favorite and descending to the least de sired cross section In the cross section table CrossSectionValues csv that comes with Karamba all families are ranked according to their height The cross section with the smallest height comes first the one with the largest height last When using cross section area as sorting criteria structures of minimum weight and thus approximately cost result See 6 2 11 for how to switch between minimum height and minimum weight design Ordering the profiles by area may lead to structures where the cross section heights vary significantly from one beam to the next In order to check whether a given beam cross section is sufficient Karamba applies a procedure that approximates that for steel according to Eurocode 1993 1 1 It takes account of the normal force biaxial bending torsion and shear force For more details see section It is possible to switch off the influence of buckling for single members or set user defined values for the 1 buckling length see section 6 1 11 The adverse effect of compressive normal forces in a beam can be taken into account In order to do this one needs to determine the buckling length l of an element For this the following simplification which is not always on the safe side is applied Starting from the endpoints of an element proceeding to its neighbors the first nodes are tracked that connect to more than
26. selections done with the drop down list for load cases check the value in the LC Index input plug Remember that its 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 9 The View components do not show rendered meshes stress Strain Supports etc Check whether Shaded Preview is enabled in Grasshoppers Solution menu 7 10 The ModelView component does not display any tags Check whether your Rhino background color is black Some types of tags are printed in black and do not show on a black canvas 108 7 11 Circular cross sections show up as flat stripes when rendered Set the Faces Cross section slider of the ModelView component to a value larger than two such that the displayed result sufficiently corresponds to your idea of roundness 7 12 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 13 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 TO 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 Deprecated com ponen
27. yn A HTA i i a b Figure 53 Hanging models Left Model of Antoni Gaudi for the Temple Expiatori de la Sagrada Fam lia from the internet Right Some of Heinz Islers hanging models from the internet All external loads get applied in steps After each step the model geometry updates to the deflected state The more and the smaller the steps the better the approximation of geometric non linearity The purely incremental method however incurs an unavoidable drift from the exact solution For form finding this error should be negligible in most cases Figure 54 Structure resulting from large deflection analysis with the LaDeform component Figure shows a simply supported beam under the action of uniformly distributed point loads Due to its slenderness axial stiffness by far outweighs bending stiffness Thus the deflected shape corresponds to a string under self weight The LaDeform component has four input plugs 60 Model Inc MaxDisp LocPLoads FindForm Figure 55 Catenary resulting from point loads that do not change their direction when displaced Model model to be deformed LaDeform uses load case 0 for calcu lating the deflected shape Inc number of increments for applying the loads MaxDisp maximum displacement to be reached in meter m When Supplied with a value the incremental deflection in each step is scaled to MaxDisp Inc T
28. 2 family name KN cm2 KN cm2 KN m3 m mC kN cm2 3 Steel Steel 21000 8076 18 5 1 20E 05 4 Steel 5239 21000 8076 78 5 1 20E 05 23 5 3 Steel 275 21000 8076 78 5 1 20E 05 27 5 6 Steel S355 21000 8076 185 1 20E 05 36 T Steel St37 2 21000 8076 78 5 1 20E 05 24 2 H Figure 41 Partial view of the default data base of materials SI units are used irrespec tive of user settings Automatic conversion ensures compatibility with Imperial units list of materials from it These are available at the output plug Material The data base currently holds properties for steel concrete wood and aluminum 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 Eurocode More specific descriptions may be given Have a look at the data base in order to get an overview Material properties specified via table are assumed to be in SI units They get automatically converted when used in the context of Imperial units 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 They render the data neatly formatted see fig 41 Make sure to have a and not a set as your decimal separator In some countries is use
29. 4 6 8 3 Multi dimensional Nearest Neighbors Figure 89 Random points in a unit volume connected to their nearest neighbor in a 5 D setting A nearest neighbor search can be generalized to any number of dimensions Use the Multi dimensional Nearest Neighbors component in case of more than three Fig 89 shows an example with five dimensions Dimensions one to three represent space Dimension four is the shortest distance between 97 each point and the thick red guide line The curve parameter of the guide line at the point where it meets the line of shortest distance acts as fifth dimension Each of the randomly generated points is connected with its nearest neighbor One can see from fig 89 that the resulting line segments align to the guide curve in some way There are three input plugs on the component FromPts expects a list of lists where the rightmost list comprises n values which are the coordinates of the point The FromPts input Specifies points where nearest neighbor connections can start e ToPts expects the same sort of input as FromPts It contains the points where nearest neighbor connections can end e NN number of nearest neighbor connections to be generated for each point in FromPts The output C of the Multi dimensional Nearest Neighbors component is a connectivity diagram 6 8 4 Remove Duplicate Lines When you have a list of lines that you suspect of conta
30. Creates rectangular trapezoid and triangular hollow cross sections Circular Hollow Profile Creates circular hollow cross sections I Profile Creates I shaped cross sections Shell Cross Section Lets you set the height of a shell cross section Spring Cross Section Defines the spring stiffness of an element Trapezoid Profile Creates filled rectangular trapezoid and triangu lar cross sections Beam Joints Adds hinges at the end points of beams Disassemble Cross Section Retrieves properties of a cross section Eccentricity on Beam Sets the eccentricity of a cross section rela tive to the element axis in global coordinates Eccentricity on Cross Section Sets the eccentricity of a cross sec tion relative to the element axis in local beam coordinates Cross Section Matcher Returns for a cross section the best fitting cross section contained in a given list The matched cross section is or better in all mechanical aspects at minimum weight Cross Section Range Selector Lets you select cross sections by country shape family or maximum depth or width 18 Generate Cross Section Table Converts a list of cross sections into a string which can be streamed as a csv file and used aS a cross section table 3 T F J Xx a y 2 RE UN 7 l e he DIDIDE Cross Section Selector Lets you select cross sections by name regular expression or index from a list of cross sections Read Cross Sectio
31. INVOKE exception 0202 106 Lao aaa as As 107 1 4 Karamba does not work after reinstalling Grasshoper 107 A E E eu eee 107 17 06 Karamba seems to get stuck while calculating a modell 108 1 1 Predefined displacements take no effect 108 AA eee 108 MAATTI 108 7 10 The ModelView component does not display any tags 108 7 11 Circular cross sections show up as flat stripes when rendered 109 1 12 Icons in Karamba toolbar do not show up 109 E 109 1 14 Component in old definition reports a run time errory 109 7 15 The Optimize Cross Section component does not work 109 7 16 The Optimize Cross Section component returns wrong results 10 1 17 Other problems e 110 111 Re See ss 111 A 1 1 Material Stiffness 28 111 Ae PHRRER eee ARERR EEE SE Ee 111 A 1 3 Theoretical Background of Stiffness Stress and Strainj112 POENE 112 eee as 112 A 4 Hints on Reducing Computation Time A 5 Natural Vibrations and Eigen Modes A 5 1 Elgen modes in Structural Dynamics A 5 2 Elgen modes in Stability Analysis 2 A 6 Approach Used for Cross Section Optimization 1 Introduction Karamba is a Finite Element program like many others However it has advantages over these programs in several important respects It is easy to use for non experts has been tailored to the needs of architects in the early design p
32. PARAMETRIC STRUCTURAL MODELING NN User Manual for Version 1 0 5 written by Clemens Preisinger March 14 2014 Contents 1 Introduction 1 1 How to obtain a pro or pro student license 2 What s new in version 1 0 5 2 1 Disclaimer 3 Installation 4 Quick start AT SS amp amp bh hh we oo oe ete eee ee HEE eG GG 4 8 Model kee eh ase oe ee ee Re eee eee Ree eee 4 1 Basic Example 4 2 Physical Units 4 3 Elements 4 4 Materials 4 5 Cross Sections 4 6 Supports 4 9 Algorithms Peas 4 11 Results 5 Quick Component Reference 5 1 License 5 6 Load kk 5 2 Algorithms 5 3 Cross Section 5 4 Ensemble 5 5 Export 5 7 Material 2 5 8 Results 5 9 Utilities 6 Component Reference 6 1 Ensemble 6 1 1 6 1 2 Activate Element Assemble Model 11 11 12 13 13 14 14 15 15 15 16 17 17 17 17 18 19 20 20 21 21 22 23 23 24 24 6 1 3 Connected Parts 2 2 222828048 4 25 6 1 4 Disassemble Model 25 6 1 5 Line to Beam 2 2 048 26 6 1 6 Index to Beamj 2 082 058 27 6 1 7 Connectivity to Beamj 8 28 6 1 8 Mesh to Shell 28 6 1 9 Disassemble Beam 29 6 1 10 Make Beam Set
33. 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 2 lists E values for some popular building materials type of material E kN cm steel 21000 aluminum 000 reinforced concrete 3000 glass fiber 1000 wood spruce 1000 Table 2 Young s Modulus of 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 using material tests Karamba expects the input for E to be in kilo Newton per square centimeter kN em If one stretches a piece of material it not only gets longer but also thinner it contracts laterally In case of steel for example lateral 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 A 1 2 Specific Weight The value of gamma is expected to be in kilo Newton per cubic meter kN 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
34. a mass of n kg removed in order to meet the structures target mass in the given Iter number of iterations With Overdrive m there will be m 1 n active elements moved to the pool of inactive elements An evaluation of the structures response follows In a second step m n members get flipped from inactive to active so that the balance is right again This adds a bi directional component to the FFF process which often leads to improved results MinDist In some cases one wishes to limit the number of elements that get added or removed in a certain area MinDist lets you select the minimum distance in meter m between the endpoints of elements that may be changed in one iteration WLimit At the end of the FFF process it often occurs that a small fraction of the elements is much less utilized than the average WLimit lets you remove those elements whose weight is below WLimit times the average weight of elements On the right side of the ForceFlowFinder component these output plugs exist max disp maximum displacement of the resulting model from among all load cases 67 Figure 61 Triangular mesh of beams before a and after b applying the FindForcePath component Model structure with element activation according to the force path found hist a data tree which contains for each iteration step a list of boolean values that signify whethe
35. ams When set to false this option excludes the corresponding beam from further calculations until it is reset to true See section 6 1 1 for an alternative way of setting a beams activation state 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 bend ing 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 in case of full sections and on D in case of hollow sections So in case of insufficient bending stiffness it is much more effective to increase a beams height or diameter than increasing its wall thickness Buckling property for cross section optimization Buckling can be turned off for cross section optimization This lets you Simulate pre tensioned slender elements without having to really pretension 32 them The necessary pretension force is the negative value of the largest compressive axial normal force of all load cases Buckling length in local beam directions For doing cross section optimization it is necessary to know a beams buck ling length Karamba approximates it using the algorithm described in section For cases of system buckling this approximation does not lie on the safe side The input plugs BklLenY and BklLe
36. and the number of load case to which it applies Supports apply to all load cases by default Supports cause reaction forces These can be visualized by activating Reactions in the Display Scales section of the ModelView see section 6 6 2 They show as arrows with numbers in colors green representing forces and purple representing moments The numbers either mean kN in case of forces or kNm when depicting moments The orientation of the moment arrows corresponds to the screw driver convention They rotate about the axis of the arrow anti clockwise when looked at in such a way that the arrow head points towards the observer From the support conditions in figure 27 one can see that the structure is 3In order to find out the index of a specific node enable the node tag checkbox in the ModelView component See section l6 1 5 on how to predefine the index of specific nodes 36 a e b ea Figure 28 Influence of support conditions undeflected and deflected geometry Left All translations fixed at supports Right One support moveable in horizontal direction a simply Supported beam green arrows symbolize locked displacements in the corresponding direction The translational movements of the left node 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
37. ased In order to obtain the pro version download Karamba from either or and in Stall the trial version Then use the Karmba license component right click on the icon to generate a machine id file on the computers where you wish to run Karamba on Send these files to info karamba3d com and buy a license at http www karamba3d com downloads In return you will get a license lic file which turns your Karamba trial into a Karamba pro or pro student ver sion Start Rhino as an administrator right click on the Karamba license component and select Load license file When purchasing a student version either attach a scan of your student ID or send the e mail from your university account More information regarding the pro version can be obtained through the License component see fig 1 Figure 1 The License component Those parts of this manual that apply to the pro trial version only are either blue or have blue section headings 2 What s new in version 1 0 5 e A simplified installation procedure e Iso and stream lines with user supplied values and vectors at mesh vertices unlimited mesh size also in the free version of Karamba e Benchmark examples with known results from literature for the evalua tion of calculation accuracy e Cross section optimization comprises now also shells e Shell elements can be given individual thicknesses Line like shell results can be plotted on th
38. ass plug informs you about the overall mass of the optimized structure Disp and Energy plugs return the maximum displacement and internal energy of the structure after the last cross section design iteration Nonstandard cross sections e g those that you custom design may show local buckling This means they loose their load bearing capacity either before the maximum stress reaches the yield limit in case of elastic design or before they form a yield hinge in case of plastic design Slender I sections or hollow sections with very thin wall thickness may be affected Karamba does not take account of that Consult you local building code on this The aim of the design procedure applied in Karamba is to render plau sible cross section choices It builds upon a range of simplifications e g determination of buckling length interaction of multiple section forces and omits some phenomena that might be decisive e g local buckling of slender sections lateral torsional buckling system buckling 6 6 Results The results category consists of three sections The first contains compo nents that apply to a structure in general Components of the second and third category apply to beams and shells respectively 13 6 6 1 Deformation 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
39. assemble Cross Section component for that see fig 33 6 2 6 Eccentricitiy on Beam Eccentricity on Cross Section ile Eccent Beam E m z Ej a VI O 2 y us T A La LL Fa o Figure 34 Beam positioned eccentrically with respect to the connection line of its two end nodes Cross section forces of beam and truss elements relate to the line that con nects the cross section centroids When a cross section changes chances are 42 high that also the position of its centroid shifts In case of elements predom inantly loaded by bending moments such a shift can normally be neglected In the presence of normal forces however e g when considering columns changes in the centroids position lead to additional bending moments that may be decisive for a members cross section design In Karamba there exist two components that can be used to take care of eccentricities see fig 34 One works on beams the other on cross sections When both variants of definition coincide for an element then they get additively combined This enables one to define families of cross sections of different size with e g the position of their upper sides at one level The definition of a local eccentricity for cross sections with a Eccent CroSec component is straight forward The ecce loc input plug expects a vector that defines the offset with respect to the local beam axes Values are expected in centimeters x
40. c cross section see sec 6 2 1 a shape field which defines the basic cross section type I Esection hollow box section V trapezoid filled section circular tube S spring Sh shell e geometric properties which are used for drawing the cross section e area moments of inertia etc that define the cross sections mechanical behavior The GenCS Table component takes a cross section or a list of cross sec tions as input and returns the equivalent table data as a string The physical units used for output are always metric When plugged into a panel the in formation can be streamed to a file which then constitutes a valid cross section table Karamba reads the data of cross section tables only once So in order that changes in the table take effect restart Grasshopper 45 Figure 38 Transformation of a list of cross sections to a cross section table 2 lb UN Q U G Uv Figure 39 List of cross sections generated from the standard cross section table 6 2 11 Read Cross Section Table from File Predefined cross sections stored in a csv database can be used to gener ate lists of cross sections via the ReadCSTable component see fig 39 It works along the same lines as the ReadMatTable see section component When given no path to a valid csv table ReadCS Table uses the cross section table that comes with Karamba and is situated i
41. cally taken care of All other items need to be included via point masses Be aware of the fact that masses defined with the Point Mass component do not have a weight but inertia only Thus they only show effects in connection with the calculation of natural frequencies The Point Mass component expects a mass in kg at its input plug Mass see fig 50 Nodes where masses shall sit can be identified by supplying node indexes or positions just like for point loads Point masses get displayed as green spheres Their diameters result from the volume calculated as mass divided by density The latter defaults to 7850 kg m steel and can be provided at the input plug rho Figure 50 Vibration mode of beam with point mass in the middle 56 6 4 8 Prescribed displacements Supports as described in section are a special case of displacement boundary conditions 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 shows a beam with prescribed clockwise rotations at both end points The PreDisp component resembles the Support component to a large de gree Nodes where displacement conditions apply can be selected via node index gt or nodal coordinates The Plane plug can be used to define an arbitrarily oriented coordinate system for the application of Support condi tions Input plug LCase lets you set the index o
42. cenarios e g wind from different directions to be created Gravity loads 1 act on the whole Structure The location of point loads 2 can be specified by node index or position Beam loads 3 act on elements given by element identifiers Dis tributed loads on arbitrary meshes 4 get reduced to approximately statically equivalent node and beam loads The direction of gravity and point loads is given by a vector in input plug Vec and refers to the global coordinate sys tem The direction vector of beam and mesh loads can be specified relative to the global or local relating to the element or mesh coordinate system 4 8 Model After defining Elements supports loads and optionally cross sections and materials the statical model can be assembled see fig 9 Elements get rigidly connected in case they attach to the same node 4 9 Algorithms Karamba offers several different ways of evaluating a structural model The Analyze component calculates the response of a model under external 15 Pt Elem Support Load CroSec Material Set LDist Figure 10 The model can be evaluated in several ways Left analysis of structural re sponse under loads Right calculation of eigen modes loads The numerical evaluation options comprise eigen modes natural vi bration modes large deflections evolutionary structural optimization cross section optimization and iterative elimination o
43. center points of the beam Their distance to the mesh vertices is smaller than that of the collocation points on the beam axis Thus all the mesh load gets reduced to point loads A finer resolution of the loaded mesh would remedy that The right side of figure Shows what data the Mesh load component collects The input plug Vec expects a vector or list of vectors that define 52 Beamlds LCase O local to mesh O global O global proj Zz Yy Figure 45 Simply supported beam loaded with point loads dark orange that approxi mate a given evenly distributed surface load on a mesh the surface load Its physical units are kilo Newton per square meter kN m7 The orientation of the load vector depends on the checkbox selected under Orientation see also figure 46 local to mesh X component 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
44. cities Load values Figure 77 Moment M green about the local beam Y Axis and shear force V blue in local Z direction 6 6 9 Resultant Section Forces The Res S Force component retrieves axial forces N resultant bending moments M and shear forces V for all beams and load cases See fig 78 for the definition of N V and M The sequence of element results corresponds to the sequence of beams Thus the data can be used for cross section design of radially symmetric elements Figure 79 shows a simply supported beam with two load cases presented in one picture The beam consists of two elements 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 undeformed beam axis The results at the output plugs N and M in fig are 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 third index from the right is zero The second index from the right refers to the load case the first two lists contain results for load case zero the last two for load case one The last index 85 Figure 78 Normal force N shear force V and resultant moment M at a cross section with local coordinate axes XYZ Force and bending moment components
45. cts transverse shear deformation v UM r He lt v CU PRA Fae A T s into Figure 20 The MeshToShell component turns meshes into shells 6 1 9 Disassemble Beam Beam Beam Id Pts Axis CroSec Joints Mat is active Disassemble Bending LCoSys ecce loc ecce glo Figure 21 A beam decomposed into its individual parts When interested in the information contained in a beam component feed it into the DisassembleBeam component see fig 21 It is necessary to provide the list of points that correspond to the list of nodes of the model This is due to the fact that beams can reference their nodes via index 29 6 1 10 Make Beam Set Beam Id Pt 4 Set ld w os Set J Beam Model J MinSLen cies Swatch J Color e A Info gt C cCroSec Material PA Beam Id 4 Set Set Id 10 Mass D yo Set p d LDist MinSLen 91D Color Smal gt Figure 22 Beam sets can be used to group beams The Make Beam Set component provides a practical way for grouping different elements under one identifier see fig 22 Beam sets need not be disjoint The Beam Id plug expects a list of strings with beam identifiers beam indexes other beam set identifiers or a regular expression Regular expressions have amp as their first character by definition Set Id expects a string which serves as identifier of the new set
46. ctures 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 zx is an eigen mode as can be computed with Karamba Vibration modes g of structures result from the solution of the generalized Eigenvalue gt problem This has the form C z w M 2Z 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 2z 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 115 ON OOBWN FE include the effect of mass inertia will be referred to as natural vibration modes See sec for how to calculate them A 5 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 T
47. d 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 e g stresses use a color spectrum from blue to white to red by default One can customize the color range by handing 5 over a list of RGB values to the Colors plug There have to be at least four 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 167 In case you want to change the coloring defaults set them in the karamba ini file 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 empty 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 amp and adhere to the conventions for regular expressions as used in C The identifier of each element of the model is compared to each item of the given string list In case a list entry matches the element identifier the element will be displayed Length Segment m 09 04 Upper Result Threshold 100 00 O Lower Result Threshold 0 00
48. d connection lines signify different dimensionality of the data that flows through them 4 If no results show check whether preview is enabled on the ModelView BeamView or ShellView component 105 5 If the Analyze component reports a kinematic structure do the follow Ing Check the supports for forgotten support conditions 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 Save your model before doing that Large models can take a long time to calculate If the first few eigen modes seemingly show an un deflected struc ture there might be beams in the system that rotate about their lon gitudinal axis Enable Local Axes in the ModelView component and move the slider for scaling Deformation in order to check this 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 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 throws a fem
49. d to select single load cases for display Select all in order to view all ex isting load definitions of all load cases simultaneously Use the force slider to scale the size of the load symbols double clicking on its knob lets you change the value range and its current value ModelView 1 00 J we v 4 S mal m a ES E D D IN x Figure 43 Simply supported beam with three loads and three load cases 50 6 4 1 Point Load The component Point Load lets you define loads on points These get attached to their points either by node index or coordinate Feed a cor responding 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 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 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 For more information on loads and some typical values see section 6 4 2 Mesh
50. d source point see fig 97 104 Both components User Iso Lines and User Stream Lines work similar to the IsoLines see section 6 6 12 and Principal Stress Lines on Shells components see section respectively The only difference lies in the fact that for each node of the model which includes also nodes that only connect to beams a value input plug Vals or vector input plug TVecs tangent to the flow needs to be supplied 7 Trouble shooting Do not panic in case some Karamba components turn red upon feeding them with your model Read the error message It usually contains information that helps you further The very efficient way of tracking errors is to divide and conquer 1 Split the model in half 2 Check both parts 3 Scrutinize the part that does not work 4 See whether you can find an error in it 5 If not take that part as your new model and proceed to point 1 7 1 Karamba does not work for unknown reason This is the recommended procedure 1 If a component turns red read its runtime error message 2 In case that more than one item is plugged into an input check the incoming data via a panel component 3 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 dimensionality of the data Another method is to enable Draw Fancy Wires in the View menu Differently outline
51. d to separate thousands which then needs to be adapted as well The setting may be changed under Windows via regional settings in system settings All lines in the table that start with 32f are comments Feel free to define your own materials All physical units in the table are assumed to be metric irrespective of the user choice at installation 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 6 4 Load Currently Karamba supports seven kinds of loads point mesh gravity uniformly distributed pretension temperature loads and prescribed dis placements at supports An arbitrary number of point mesh etc loads and one gravity load may be combined to form a load case of which again an arbitrary number may exist Figure shows the definition of loads with 49 ReadMatTable Figure 42 List of materials resulting from the ReadMatTable component reading the default data base of materials Selection of the default Steel via MatSelect the help of Gravity and Point Load components On the bottom of the ModelView component see section there is a drop down list unfold it by clicking on the Load case Selection menu header which can be use
52. del is determined under utilized elements removed and so on This iterative procedure stops when a target volume or number of remaining structural elements is reached The above algorithm can be viewed as a way of tracing the internal force flow through a structure and removing those elements that do not form part of it That is what the ForceFlowFinder FFF component does see fig of a cantilever after applying FFF Yet its main emphasis does not lie on structural optimization but on harnessing the flow of forces for design purposes The ForceFlowFinder component replaces the ESO and BESO components of previous Karamba releases It works on beam and truss elements only Shells are currently not included in the algorithm a See eee 7 S N 7 E MES XN NY N AN e Y ie ee e i i l y 1 os ool a Figure 60 Cantilever with initially regular mesh after application of the ForceFlowFinder component Figure 61 shows the ForceFlowFinder component at work On the left side one can see the initial geometry which is a triangular mesh derived from a surface 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 opti mized structure reduced to 45 of its initial mass in the course of 20 design iterations 65 He
53. delView component to thin them out if necessary 6 Export Karamba is not meant to be a substitute for a full blown structural engineer ing finite element software package Instead it aims at providing flexibility in testing different structural designs that the more traditional FE applications lack We therefore started to implement interfaces to those traditional civil engineering packages At the moment Karamba supports data exchange with RStab5 RStab6 RStab7 and Robot Interfaces to other applications will be added in near future 6 7 1 Export Model to DStV Communication between Karamba and RStab or Robot works via DAStV file which is a STEP derivative In order to create an exchange file place a Export Model to DStv component on you definition and feed it with a model via the Model plug The Path plug lets you chose a name for the exchange file RStab names 94 cross sections and materials depend on the selected language Therefore set RStab to English before importing Karamba DAStV files The output plug DAStV returns the export file as a list of strings which can be viewed with a Panel component Check the output of the Info plug to see whether Karamba encountered problems during export The different versions of RStab interpret some aspects of DAStV data differently For example distributed projected loads will not be imported correctly in all versions of RStab Therefore you shou
54. dth Lower Width Height y CroSec f Family Upper Thick Lower Thick Web Thick Family Name Figure 6 left definition of a beam cross section 1 Middle definition of a shell cross section 2 Right selection of a cross section from the cross section library 3 Arbitrary I hollow box filled trapezoid and hollow circular cross sections can be defined for beams an element wise variable height for shells Cross sections get attached to elements via element names B and S in fig 6 Alternatively cross sections can be chosen from a library 4 6 Supports Tx Ty Tz Rx Ry Rz O000 Figure 7 Component for creating supports 14 Supports suppress translations or rotations at nodes An activated button appears black and means either zero translation T in the direction of the global x y or z axis or zero rotation R about the corresponding global axis A node index or position can be used to specify the location of a support Supply a plane as input for specifying locally oriented support conditions 4 7 Loads LCase Figure 8 definitions of gravity load 1 point load 2 uniformly distributed load on a beam 3 and distributed load on a mesh 4 Fig 8 shows examples for defining loads on parts of a structural model The input plug LCase can be used to set the number of the load case in which the load acts This enables different load s
55. e SElem and RElem output data remember their spot in the original list of elements Joining them results in the original order of elements 6 1 14 Support 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 forbidden 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 26 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 three trani la lons A oe Bib y aif gt xX i Lh tee to blions je Figure 26 Metaphor for the six degrees of freedom
56. e deformed mesh e Faster model assembly and generation of mesh loads aS compared to the previous version of Karamba e A component for the retrieval of distributed cross section forces for Shells Principal moment and normal force directions on shells Separation of graphical user interface and underlying functionality of most Karamba components This makes it easier to use Karamba in scripts These bugs got fixed e The layer position of shell results was corrected e A problem with infinite loops in the calculation of flow lines was re solved e Snapping nodes of elements do not cause errors and problems with mesh loads any more e A bug that led to deviations in the display of principal stresses from the correct direction was removed Due updating to NET Framework 4 0 Karamba 1 0 5 does not run on Rhinoceros 4 any more sorry 2 1 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 license agreement that comes with Karamba in case of further questions 3 Installation These are the prerequisites for installing Karamba e Rhino 5 0 e Grasshopper version 1 0 5 of Karamba was tested on GH 0 9 0056 In case you do not possess Rhino download a fully featured free trial version from http www rhino3d com download html Grasshopper which is
57. e spans between two 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 see section 6 5 2 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 nodes 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 Activation status of be
58. e the zone of highest stress Thus the distribution of colors will not change You can define individual color ranges for all quantities in the karamba ini file A Legend component lets you inspect the meaning of the colors The mesh of the rendered image is available at the Mesh output of the BeamView component Two sliders control the mesh size of the rendered beams First Length Segment of ModelView determines the size of sec tions along the middle axis of the beams Second Faces Cross section of 83 BeamView controls the number of faces per cross section Figure 76 Mesh of beams under dead weight with Render Color Margin set to 5 It is instructive to see which parts of a beam are under tension or com pression Activate the Stress checkbox in menu Render Settings in order to display the stresses in longitudinal beam direction Red like brick means compression blue like steel tension In some models there may exist small regions with high stresses with the rest of the structure having comparatively low stress levels This results in a stress rendering that is predominantly white and not very informative With the sliders for Result Threshold of the ModelView you can set the percentage of maximum tensile and com pressive stress at which the color scale starts Compressive stress values beyond that level appear yellow excessive tensile strains green see figure 76 Display
59. ed into the definition after the ModelView component 5 9 Utilities Detect Collisions Counts the number of intersections between the model and a given mesh Get Cells from Lines Creates closed cells from a graph and vertices on a user supplied plane Line Line Intersection Intersects given lines and returns resulting end points and pieces Mesh Breps Takes multiple Breps and generates a unified mesh from Al la Za them The algorithm takes account of common edges and predefined points This lets one define positions for supports or point loads on shells 22 F i m Nearest Neighbors Connects each node of one set to a given number of nearest neighbor nodes or neighbors within a specified distance of another set Multi dimensional Nearest Neighbors Performs a multidimensional nearest neighbor search on a two sets of vectors Remove Duplicate Lines Eliminates identical lines Remove Duplicate Points Eliminates identical points Element Felting Felts elements of a model by connecting them at their mutual closest points Mapper Applies mappings like Simple Stitch to a model Interpolate Shapes Interpolates between a base geometry 0 0 and given shape s 1 0 Proximity Stitch Connects beam sets by a preset number of el ements whose maximum inclination can be controlled via min max offset limits from their starting point Simple Stitch Connects beam sets by a preset number of elements
60. emperature changes materials expand or shorten alpha T sets the increase of strain per degree Celsius of an unrestrained element For steel the value is 1 0 5 1 08 5 1 0 10 0 00001 Therefore an unrestrained steel rod of length 10 m lengthens by 1 mm under an increase of temperature of 10 C alphaT enters calculations when temperature loads are present In order to be registered with the model the resulting material needs to be plugged into the Assemble Model component 6 3 2 Material Selection The MatSelect component in the menu subsection Material lets you se lect a material by name or index from a given list of materials see fig 40 or fig 42 The names of materials are not case sensitive A 74 in a material name means that the rest of the line is a comment amp starts a regular expression in that case material names are case sensitive Mat expects a list of materials the input plug Name material names Element identifiers given through the MatSelect component add to those already given for a material see fig 40 6 3 3 Read Material Table from File Karamba comes with a table of predefined materials The csv file Material properties csv resides in the Karamba folder inside the Libraries directory By default the ReadMatTable component takes this file and creates a 48 ee E F G H 1 E G gamma alphaT fyd
61. en forms the thin red lines in 93 of a simply supported beam serve as the shape dimensions of the design space 10In other words a mapping is a functor 101 Galapagos is used to determine the position in that design space which results in minimum deflection under a single load at mid span It is clear think of a hanging model that the optimum shape has a sharp kink under the load and is otherwise straight Fig shows the result of the optimization run which resembles the ideal shape to a large degree A sharper bend underneath the load could be achieved by including more shape dimensions in the design space Figure 93 Result of shape optimization thick red line for a simply supported beam under mid span single load using the first 30 eigen forms the thin red lines as axes of the design space 6 8 11 Proximity Stitch Figure 94 Proximity Stitch mapping with the same set up as in fig but fifteen random connections instead of two The Proximity Stitch is a tamed Simple Stitch see sec 6 8 12 In case of n beam sets a tuple of n parameters describes one connection All parameters are in the range 0 1 The first value p sets the relative location li on the first beam set All following parameters pn relate to the restricted interval l 1 minOf fset ln_1 maxO f fset Here minOffset and maxOff set can be defined by the user The narrower the interval they define the 102 more reg
62. en 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 further 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 52 one immediately notices that only beam center axes are shown In order to see beams or shells in a rendered view add a BeamView or ShellView component after the ModelView See sections and 6 6 18 for details 6 5 2 Analyze Large Deformation Before the advent of digital modeling people like Heinz Isler or Antoni Gaudi helped themselves with physical models for generating curved geometries A popular method was to use the shape of meshes or elastic membranes hanging from supports see fig 53 In Karamba the behavior of hanging models can be simulated with the help of the Analyze Large Deformation component Figure shows a geometry derived from an initially flat mesh under evenly distributed point loads Karamba handles geometric non linearity by an incremental approach 59 ST MUN EW Las at elie l i at vii r Nite WE 4 i 7 AAA A aphid DAN e E f d j i 4 i 14 Xi 3 ri hijil Y 4A 4 x SON he i 8 j eh bo
63. ent Cross sections materials and eccentricities previously defined for this beam identifier apply to these In case no identifier is given neighboring elements snap to the point in the middle of their shortest connection line The felting algorithm proceeds from the first element to the last always testing against all currently existing elements Therefore newly generated connection elements may be the source of further connections The algorithm operates directly on the Karamba model and is therefore quite fast 6 8 9 Mapper Assemble 0 Model jE Q Mapping a Model Gia oeo ECC SimpleStitch Figure 91 The Mapper component applies mappings to a given model In this case there is one mapping that connects two beam sets with elements whose position is con trolled by the parameters given to the mapper A Mapper is a component that takes a Karamba model and modifies it according to some generic rules defined by mappings based on parameters Supplied by the user It acts directly on the Karamba model so the process of transferring Grasshopper geometry to a Karamba model is dispensed with 100 The resulting gain of speed can be important when running optimization tasks with e g Galapagos Fig 91 shows a definition where a mapper applies a mapping called Simple Stitch on a given model which originally consists of two elements A and B The input plug Params receive
64. er Sources and Seg L have the same meaning as for the Force Flow Lines on Shells component see sec 6 6 11 The load case to examine as well as load case factors can be set with a ModelView component plugged into the definition ahead of the Isolines on Shells component By default all load cases get Superimposed using unit load factors Isolines are straight lines within each shell element This may result in Slightly rugged poly lines Set the Smooth input plug to true in order to flatten them out The Line output plug will then return splines instead of lists of line like curves They result from using the calculated iso points as control points For curved shell geometries this has the disadvantage that those splines no longer stay exactly on the shell surface This may give you a hard time trying to intersect different groups of such lines In the property submenu you can select the result value to be displayed first or second principal stress Sig1 Sig2 first or second principal bending moments m1 m2 utilization Util resultant displacement Disp or shell thickness Thick The Lines output data structure corresponds to that of the Force Flow Lines on Shells component Each number in the output plug Value cor 90 responds to one piece of tsoline from the Lines output 6 6 13 Principal Force Directions on Shells a u k
65. ere are the Family and Name plug e Family Each cross section belongs to a family When doing cross section optimization see section 6 5 7 Karamba selects only profiles that belong to the same family as the original section Families can be composed of arbitrary section types e Name the identifier of a cross section need not be unique Enable CroSec names in ModelViews RenderSettings submenu in order to view them 6 2 2 Shell Cross Section Each element of a shell can be given an individual constant thickness Fig shows a Shell consisting of two elements Meshes form the basis for defin ing a shell geometry see section and specify the sequence of faces i e shell elements The list of element thicknesses in fig 30 corresponds to that order In case that there are more mesh faces than thickness speci fications the last value 6 cm in this case acts as the default value Make sure to graft the Heights input when you want to define a list of shell cross sections Otherwise one cross section results where one would expect several Figure 30 Shell made up of two elements with different thicknesses When rendering the shell cross sections see fig thicknesses get linearly interpolated between the nodes The cross section height at each node results from the mean thickness of shell elements attached to it The input plugs Family and Name have the same meaning as described
66. erties that relate to beam and shell elements can be defined with the BeamView and ShellView component The viewing options get stored in the model Settings of View components thus stick with the model and remain valid further down the data stream until changed by another View component 7 4 When adding a ModelView to the definition it is sometimes 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 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 11 50 Model Model res disp cm Mesh 0 00e 00 Curves def Mesh def Curves ModelView BeamView Legend C Legend T 1 16e 00 1 54e 00 Cross section O Displacement O O Utilization Axial Stress Faces Cross section 15 00 Figure 66 Partial view of a model The ModelView component features five plugs on its left side Model expects the model to be displayed LC Factor can be used to scale individual load cases see further below LC Index lets one select the visible load case The value in LC Index will be added to the load case selected in the drop down list of ModelView all counts as 1 If the resulting number is larger than the number of available load cases the ModelView turns re
67. es Select translations or rotations fd which should be prescribed For load cases with no displacements prescribed this will create a support 20 5 7 Material Material Properties Sets the characteristic parameters of a material Material Selection Lets you select a material by name regular ex pression or index from a list of materials Read Material Table from File Reads a list of materials from a table given in csv format 27 uy Ya Results sl Sd Deformation Energy Retrieves deformation energies of the elements of the model Model View Lets you inspect the general properties of the model 3 gt Nodal Displacements Returns nodal displacements translation s rotations in global x y and z direction rotations about global and z axis Principal Strains Approximates the principal strain directions from the model deformation at arbitrary points X y Reaction Forces Returns reaction forces and moments at supports Utilization of Elements Returns the utilization of elements for each load case The utilization of beams is calculated according to EC3 see section A 6 for shells the maximum Van Mises Stress serves as the basis 1 means 100 ian Beam Displacements Returns displacements along elements trans lations rotations in global x y and z direction rotations about global x y and z axis Beam View Lets you inspect beam properties section forces cross sections d
68. ess lines because the latter lack the property of constant force between adjacent lines The Shell Force Flow Lines component lets you create force flow lines in arbitrary points of shells see fig 81 There exist seven input plugs e Model The model from which you want to create FF lines By default the results of all load cases get Superimposed with factor 1 Use a 88 ModelView component to select specific load cases or to impose load factors other than 1 Layer In case of bending the stress state of shells and therefore the FF lines change over the cross section height A value of 1 denotes the lower 1 the upper shell surface and 0 the middle layer The default value in 0 e ForceDirs Expects a vector or list of vectors that defines the direction of force This direction gets projected on each element in order to define the local force flow directions Elements perpendicular to the ForceDir vector are skipped Multiple such directions can be defined for different regions ForceDirPos For each vector in ForceDirs a position can be defined The force direction at an arbitrary point on the shell corresponds to the ForceDir vector with the closest ForceDirPos Source Defines points on the shell where FF lines shall originate You can feed points on or near the shell into this plug It is also possible to use lines that intersect the shell In case of multiple
69. et you limit the list according to maximum cross section height and width The submenu which unfolds when clicking on the black select bar offers further options for narrowing the search country of origin general shape and family name iden 0 28 25 CroSecRSelect ReadCSTable Figure 36 Selection of a range of cross sections from among a given list 6 2 9 Cross Section Selector The component CroSecSelect deals with selecting cross sections by name or index from a list of cross sections Provide the name s or index es of desired cross sections in the Name lind plug Cross section names are not case sensitive All characters coming after count as remark It is possible to use regular expressions for selection In this selection is case sensitive and amp has to be provided as first character List indexes start from zero CroSecSelect lets you specify beams via the Elem Id plug which shall be assigned a specific cross section The Assemble component sets the cross sections of elements accordingly 6 2 10 Generate Cross Section Table An entry in a cross section table consists of a row which contains 44 Figure 37 Cantilever with four different kinds of cross section taken from the standard cross section table e country country of origin e family name of the group to which the cross section belongs see sec 6 2 1 e name name of the specifi
70. etermination of section forces at nSample points along all beams using the initial cross section 2 For each element or given set of elements selection of the first sufficient entry from the family to which each cross section belongs 3 If no changes were necessary in step two or the maximum number of design iterations is reached the algorithm stops Otherwise it returns to step one using the cross sections selected in step two In statically indeterminate structures the section forces depend on the stiffness i e cross section of the members This necessitates the iterative procedure described above DI NADO AAAA a TA II Figure 64 Cross section optimization with the OptiCroSec component on a cantilever discretized with shell elements When performing thickness optimization on shells the list structure for defining a cross section family plays a crucial role In fig one can see the example of a cantilever The optimization results in thicker shells at the top and bottom edge of the built in side When defining a list of shell cross sections one needs to supply a list of lists of thicknesses and corresponding cross section names Each sub list specifies the element thicknesses of one shell see section 6 2 2 70 After ensuring safety against structural failure a second optional step fol lows where Karamba tries to approach a user supplied maximum deflection Behind the scenes Karamba iteratively adapts temporarily t
71. etermine the principal strain directions plane stress is assumed The conversion of first output plug VT1 and second principal strains output plug VT2 to vectors occurs in such a way that they align with the average displacement of the triangle that defines the corresponding strain state The size of the vectors emanating from VT1 and VT2 can be scaled by providing a factor in the input plug Scale The principal strains are tangents to the principal stress lines of a struc ture Use e g Daniel Hambleton s SPM Vector Components see wiw grasshopper3d com group spmvectorcomponents to retrieve these lines from the strain vector field 6 6 5 Reaction Forces Figure 71 Beam under axial and transverse point load Reaction forces and moments for both load cases The Reaction Forces component gives access to the reaction forces and moments at supports It expects a model at its input plug and returns via RF and RM a tree containing reaction forces in kN and reaction mo ments in Nm as three dimensional vectors The two rightmost dimensions correspond to LoadCase Support The support reactions are ordered in such a way that the indexes of the nodes they attach to form an ascending se quence In case of locally oriented supports reaction forces refer to the local coordinate system 6 6 6 Utilization of Elements Figure 72 Simply supported beam under axial and transverse point load Uti
72. f tension or compression ele ments For each calculation option exists a corresponding component which takes a model as input calculates it and adds the results to the model data 4 10 Visualization Ed p lt Model Model Model Model d E gt Mesh Q LC Factor ee Mesh vee e esl D Q LC Index Model po Curv LegendC D Q Colors def Curves J Legend CP LegendT p d Id def Model D LegendT J Render settings S Section Forces an Deformation Filled El Displacement O 5 60 Numbers El Utilization O Reactions Scale Princ Stress 1 O i 1 00 Princ Stress2 O teats 020 mO MO mo Van Mises Stress O a xo wo ve O Layer of results 0 63 Princ Stress 1 2 O o4 Local axes O 1 00 E o o Supports E O 0 20 o m Joints 1 00 Faces Cross section O 12 00 Figure 11 There are three components for visualizing the model ModelView BeamView and Shell View Karamba comes with three components for visualizing the structural model see fig 11 1 ModelView Sets the basic visualization properties like scaling factor of displacements sizes of symbols number of displayed load case 16 2 BeamView visualizes beams 3 ShellView visualizes shells Each of these components contains submenus which can be unfolded by clicking on the black caption bar The numerical range of sliders can be set by double clicking on
73. f the load case in which dis placements 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 possible to have displacement boundary conditions active in one load case and completely disabled in others For load cases not mentioned in LCase the PreDisp component will act like a simple support with fixed degrees of freedom equal to zero Plane LCase Y Supp Trans Rot Tx Ty Tz Rx Ry Rz 9000000 Figure 51 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 either in global coordinates or in the coordinate system defined by the plane fed into the Plane input plug Translations are to be given in meter rotations in degree The X component of the rotation vector describes a rotation about the coordinate systems X axis The term displacement as used throughout this manual includes translations and rota tions 3In order to find out the index of a specific node enable the node tag checkbox in the ModelView component See section 6 1 5Jon how to predefine the index of specific nodes 57 A positive value means that the node rotates counter clockwise if the X axis points towards you Analog definitions apply to rotati
74. fig 29 They know about the elements or element sets they belong to by their Elemids property This is a list of strings containing element identifiers see 6 1 5 or regular expressions that match a group of element identifiers elem ids Upon assembly all elem ids are compared to all Elemids entries of a cross section In case of correspondence the cross section is attached to the element An empty string which is the default value signifies that the cross section shall be applied to all elements If two cross sections refer to the same element then that which gets processed later by the assemble component wins It makes no sense to attribute beam cross sections to shells and vice versa Karamba ignores any such attempts 6 2 1 Box Profile Circular Profile I Profile and Trapezoid Profile Fig 29 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 In case the position of e g the upper side of a cross section needs to be fixed 38 specify an eccentricity see sec 6 2 6 The corresponding position of the centroid can be retrieved from the Disassemble Cross Section component see sec 6 2 5 Apart from the input plugs that define the cross section geometry th
75. fined element identifiers 5 Analyze the Karamba structural model 6 View the analyzed model with the ModelView component Deflec tions can be scaled multiple load cases can be viewed together or separately The BeamView and ShellView components not shown in fig can be used to generate mesh representations of stresses level of material utilization Karamba is intended to provide an intuitive approach to statical model ing All its components come with extensive help tags and there are lots of examples on the web see http www karamba3d com examples Or http www grasshopper3d com group karamba page example files and in the installation folder which can be easily customized according to ones own needs 4 2 Physical Units On installing Karamba one can specify the family of physical units to be used for input and results The default option is metric e g meters centimeters 12 degree Celsius Newtons but Karamba can also deal with Imperial units e g feet inch degree Fahrenheit kiloponds The set of units to be used can be changed any time by editing the Karamba ini file Depending on the family of units Karamba interprets geometric input either as meters or feet The kind of physical units that components expect to receive shows up in the tool tip which appears when the mouse pointer hovers over an input plug Changing the type of physical units during the creation of a GH definition
76. hase works interactively and costs slightly less than the rest Karamba is fully embedded in the parametric environment of Grasshopper which is a plug in for the 3d modeling tool Rhinoceros This makes it easy to combine parameterized geometric models finite element calculations and optimization algorithms like Octopus or Galapagos Besides the free version for non commercial use only there exists also a pro version of Karamba for commercial use and a trial version Table 1 lists their main features Table 1 Variants of Karamba Karamba beam shell other version elements elements features free unlimited lt 50 limited trial lt 20 lt 50 unlimited pro unlimited unlimited unlimited pro student unlimited unlimited unlimited 1 1 How to obtain a pro or pro student license The commercial license pro without time limitation costs 30 for stu dents and 990 for businesses A pro license with one year validity comes at 390 The pro student version is for non commercial use only In case you plan to use Karamba for university courses please contact us for special conditions One single static license can be installed on two computers A license includes all updates of the current main version i e currently 1 x x For commercial use a network license option exists Being based on the Zoo 5 0 license server of Mc Neel it comes at the same price as a static license Versions of one year and unlimited validity can be purch
77. hat represent a part of a PS line There are 92 usually two parts per line that start off to either side of the starting point In case of more complicated topologies there can be more than two parts These parts populate the second dimension from the right 6 6 17 Shell Forces Sometimes it is of interest to know not only the directions see section but also the value of principal normal forces and moments on shells In such cases the Shell Forces component comes in handy It lists the results in the same order as the Principal Force Directions on Shells component Thus the element centers returned there can be used in com bination with the numeric results Distributed normal forces are negative in case of compression Positive bending moments result in tension on the upper side of a shell The upper side of a shell element is defined by a positive value of the local Z axis When in doubt about the orientation of your shell elements enable the preview of local element axes in the ModelView component see section 6 6 2 6 6 18 ShellView Model Model res disp cm LC Factor M LC Index Colors id a 5 22e 02 def Model U cL 7 82e 02 Cross section 1 04e 01 Deformation Displacement 1 30e 01 155 2 Utilization def Mesh AS Princ Stress 1 0 Princ Stress 2 ry e Van Mises Stress Supports O 0 20 Local axes O 1 00 Layer of results gy 2 00 Princ Stress 1 2 O O 1 00 Joints
78. he yield stress of the materials This may lead to uneconomic results in case of structures where the maximum displacement occurs in a small region whereas the rest of the structure shows a much smaller deformation In order that the iter ative adaption for the maximum displacement works the number of design iterations should be chosen appropriately five is normally sufficient Building codes prescribe different levels of safety against reaching maxi mum displacement and load bearing limits When using external loads on ultimate limit state level one should keep in mind that this is approximately 1 4 times the loads used to check maximum displacement requirements When the given loads surpass the load bearing capacity of the biggest cross section available in a cross section family Karamba issues a warning via the Info output plug There is no guarantee that the iteration procedure for finding the optimal cross sections eventually converges so check the results via the utilization output of the ModelView component Due to the lower bound theorem of plasticity the structure will be sufficient for the given loads at any iteration step although some elements may show overutilization provided that the material is sufficiently plastic like e g steel With increasing number of iterations the statical system tends to become more and more statically determinate The profile selection procedure assumes that the cross sections
79. his is why inertia forces do not play a role in the calculation of buckling shapes Otherwise the phenomena 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 Currently the stiffness matrix calculated in Karamba does not include the Stabilizing or destabilizing effect of axial forces Therefore the resulting eigenvalues do not correspond to the load factors for buckling A 6 Approach Used for Cross Section Optimization Karamba does cross section design by going through the list of cross sections in a group of cross sections called a family It starts at the first entry and proceeds to the next until a cross section is found that is sufficient for the given cross section forces The core routine of the cross section optimization is the function isSuf ficient which is listed below It returns True if the cross section resistance surpasses the acting cross section forces This is the original C listing of the variant for elastic cross section design which makes use of the elastic resisting moments W and W bool ElemSLDimElastic isSufficient ElementStraightLine amp beam const Beam3DProperties props int Ic const assumptio
80. his enables Karamba to handle problems with overly large deflections at the beginning of the incremental procedure Think of an initially straight string Due to its negligible bending stiffness it tends to deform tremendously in the first loading step With no value supplied in MaxDisp external loads get incremented proportionally in each step Aside from cases like mentioned above this results in an approximation of the structures real deflections under the given loads LocPLoads When false the default point loads keep their initial di rection Fig shows what happens if LocPLoads is set to true The point loads co rotate with the points they apply to This leads to a pneumatic shape The direction of line loads is not affected by Loc PLoads Their orientation during form finding corresponds to that given in the Line Load on Element component The two output plugs of the LaDeform component supply the deflected model and the maximum deflection reached in the calculation The local coordinate system of each element gets updated along with its positions By default an elements local Y axis is taken parallel to the global X Y plane If an element reaches a vertical position however its default coordinate system flips the Y axis is then taken parallel to the global 61 Model Inc MaxDisp LocPLoads FindForm l Figure 56 Pneumatic form resulting from point loads that rotate a
81. ies in the plane which is defined by the local X axis and the vector plugged into the Z axis input e Alpha represents an additional rotation angle in degree of the local Z axis about the local X axis 6 1 13 Select Beam IndToBeam gJ o 3 Figure 25 Elements can be selected by using their identifiers All structural elements can be given identifiers i e names These names need not be unique Two elements can have the same name without Karamba complaining By default an element identifier corresponds to the elements index Figure shows how a list of elements can be split into two data trees using their identifiers The Select Beam component expects a list of elements in Elems as well as a list of identifiers or regular expressions in Id Regular expressions need to be prefixed by a 4 They represent a very mighty selection tool In fig 25 one can see three use cases e amp 1 2 a matches any character 1 2 matches one character in the range of 1 to 2 This is equivalent to 12 e amp b matches any identifier that starts with b followed by an arbi trary character e amp 13 matches any identifier that starts with an arbitrary character followed either by 1 or 3 There are two output plugs on the Select Beam component SElem renders the selected elements which match the selection criteria RElem 34 returns the rest The entries of th
82. in section 39 6 2 3 Spring Cross Section 1 00 ing lo 1 00 Figure 31 Spring fixed at one end and loaded by a point load on the other Springs allow you to directly define the stiffness relation between two nodes via spring constants Each node has six degrees of freedom DOFs three translations and three rotations Using the Spring CroSec component lets one couple these DOFs by means of six spring constants A relative move ment uire between two nodes thus leads to a spring force Fi Ci Uj rel IN this equation uire stands for a relative translation or rotation in any of the three possible directions x y Z c is the spring stiffness In Karamba the latter has the meaning of kilo Newton per meter kN m in case of transla tions and kilo Newton meter per radiant kNm rad in case of rotations The input plugs Ct and Cr expect to receive vectors with translational and rotational stiffness constants respectively Their orientation corresponds to the local beam coordinate system to which they apply In case of zero length Springs this defaults to the global coordinate system but can be changed with the OrientateBeam component In case one wants to realize a rigid connection between two nodes the question arises as to which spring stiffness should be selected A value too high makes the global stiffness matrix badly conditioned an can lead to a numerically singular stiffness matrix A value too low results i
83. ining 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 Lines that overlap only partly can not be detected 6 8 5 Remove Duplicate Points Does essentially the same as the component described above only with points instead of lines 6 8 6 Get Cells from Lines This component takes a connectivity diagram and corresponding nodes and determines all closed cells Input plug PI can be used to supply planes that are approximately parallel to the cells The result is a connectivity diagram of the closed cells 98 6 8 7 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 The input plug L Tol sets the tolerance length in meter for finding intersections between lines that do not actually intersect LTol is also the minimum length of segments at the ends of lines e g at T intersections 6 8 8 Element Felting Model Assemble ist EE 2 K Ww Upper Thick I Profile Lower Thick Web Thick Family Name Figure 90 The elements A and B of the original model are co
84. intersections there will be the same number of FF lines e Seg L Intended length of the segments of the resulting FF lines Is 0 5 m by default e dA This parameter sets the accuracy with which the FF lines get determined It is the maximum differential angle between to adjacent pieces of a FF line If this criteria results in pieces of length smaller than Seg L then they will be joined before sent to the output plug Line By default this value is set to 5 deg e theta Here you can define an angle between the FF lines and those lines output at the Line output plug The angle is in deg and defaults to zero The output of the ShellFFlow component consists of lines arranged in a data tree The right most dimension contains the branches of each flow path In case of a e g a plane there are two branches that originate from the given intersection point In case of T like shell topologies this number can grow to three and larger 89 The load case considered is that defined in the nearest upstream ModelView component 6 6 12 Isolines on Shells The Isolines on Shells component lets you do two things First draw con tour lines on shells that connect points of equal principal stresses utilization or resultant displacements see fig 82 Second query results in arbitrary points of the shell Figure 82 Lines of equal first principal stress on a cantilever The input plugs Model Lay
85. isplacement utilization and stresses Is to be plugged into the definition after the ModelView component Section Forces Retrieves section forces along beams and trusses gt Resultant Section Forces Retrieves resultant section forces of beams gt Force Flow Lines on Shells Computes flow lines for forces in given direction at user defined positions 21 Isolines on shells Creates lines that connect points of same value for selected shell results e g principal stresses displacement utilization cross section thickness at user defined positions Also returns values and can thus be used for probing the shell state es Principal Moment Lines on Shells Lets you retrieve the direction and absolute value principal shell cross section forces and moments in the center of each shell face Principal Moment Lines on Shells Returns the principal moment lines that originate from user defined points on shells Principal Stress Directions on Shells Outputs the principal stress directions in the center of each shell element Principal Stress Lines on Shells Returns the principal stress lines that originate from user defined points on shells Principal Stress Directions on Shells Outputs the values of first and second principal normal forces and moments in the center of each Shell element rey Shell View Lets you inspect shell properties displacement utiliza tion principal stresses and Van Mises stress Is to be plugg
86. 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 Remove karamba dll and libiomp5mad dll from the windows folder if they sill exist Search your hard disk for karamba dll and karamba gha files and remove all occurrences by hand 106 e reinstall Karamba If this does not help do the following e Check whether the karamba dll file in the Windows folder is blocked right click on the file and select Properties then security e Make sure that you installed a Karamba version with the correct bitness Karamba 64bit can be used together with Rhinoceros 5 64bit Karamba 32bit with Rhinoceros 5 Be aware of the fact that both versions of Rhino get installed This is plan b if the above does not help e Start Grasshopper e Type GrasshopperDevelopersettings in the Rhino Window and hit ENTER 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 1 3 The StackedStitch components renders structures with overlapping diagonals Beam sets have an orientation You probably use beam sets wi
87. ld always compare the structural response calculated with the exported model in RStab to that obtained with Karamba 6 8 Utilities 6 8 1 Mesh Breps Figure 87 Unified mesh generated from Breps using the MeshBreps component cre ated by Moritz Heimrath Mesh Breps In Karamba the geometry of shells is represented by meshes Each mesh face corresponds to a constant strain finite element The element nodes determine its connectivity to the other parts of the structure Thus point loads supports point masses and the like can only be attached to mesh vertices When two meshes have common boundaries they need to The Mesh Breps component was programmed by Moritz Heimrath 95 have identical vertices there in order to be structurally connected The MeshBreps component ensures the connectedness of meshes gen erated from multiple Breps It also allows to define points on those Breps where mesh vertices shall result Fig 87 shows the unified mesh based on four Breps and one predefined point Figure 88 In and output of the MeshBreps component created by Moritz Heimrath These input plugs control mesh generation see fig 88 Brep List of Breps to be joined and meshed IPts Points on Breps or at their boundaries where mesh vertices shall be generated MRes Target size of mesh faces in meter Edge Refinement Factor Multiplication factor for MkRes that deter mines
88. lization of the cross sections of the elements Use the Utilization of Elements component in order to get the level of 81 utilization for each element in each load case see fig 72 The rightmost index is the load case which comprises a list of one value per element 1 means 100 For beams the calculation approximates the procedure outlined in Eurocode 3 see section A 6 for details The utilization calculated for Shells is the ratio between yield stress and Van Mises Stress in each element of the shell Utilization numbers for beams rendered by this component and the Mod elView are different in case of compression The ModelView component returns the ratio of stress to yield stress as level of utilization whereas the Utilization of Elements component also includes buckling See for example the last two entries on the bottom in fig The second load case is made up of an axial load acting in the middle of the beam As both ends are axially fixed one beam is in tension on in compression The absolute value of the normal force in both elements is the same Yet the beam under compression has a utilization of 0 26 the one under tension only 0 05 6 6 7 Beam Displacements 9 Figure 73 Simply supported beam consisting of two elements under axial and transverse point load List of displacements along the axis three components of translations and rotations for each section and load case In case you want t
89. long with the points they apply to Y axis This may lead to unwanted results when using line loads which flip along with the local coordinate system It is possible to avoid this by defining local axes via the OrientateBeam component In each incremental step the internal forces of the previous step get cleared This is the reason why the resulting deflected model contains no information regarding internal forces 6 5 3 Eigen Modes Figure 57 Left 14 eigen mode with strain display enabled Right EigenMode component in action Karambas EigenMode component allows to calculate eigen modes and cor responding eigen values of structures see figure 57 as used for buckling analysis i e without inertia effects For details on eigen modes and natural 62 modes see section A 5 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 computed 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 Grasshopper has no Cancel button Therefore you should save your model before activating the component The number of different eigen modes in a structure eq
90. miting deflection automatically leads to a safe design If however compressive forces initiate failure col lapse 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 abso lute 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 A 4 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 n n Sighs Karamba makes use of multiple processors 114 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
91. n Grasshopper Libraries Karamba CrossSectionValues csv This table con tains definitions for a range of standard steel profiles Use a text editor or OpenOffice to view or extend the table 7 is used to mark the rest of a line as comment The physical units are always assumed to be metric irrespective of the user settings at installation When opening the Karamba folder you will find three differently named cross section tables CrossSectionValues csv and CrossSectionValues sorted ForHeight csv contain cross sections sorted according to increasing height In CrossSectionValues sortedForWeight csv the area and thus weight per unit of length determines a cross sections relative position within a family When doing cross section optimization see section those two sorting options lead to different results Depending on external requirements they 46 result in structures of minimum cross section height or structural weight 6 3 Material There are two ways for defining materials in Karamba Either select a ma terial by name from a list of materials see section or set mechanical material properties manually see below The Appendix see section contains additional information on me chanical properties of materials Materials like cross sections are autonomous entities which may be plugged into the Assemble component They know about the elements or element sets they apply to by their Elemids
92. n Table from File Reads cross section data from a csv file Ensemble Activate Model Activates the elements of a model according to the activation list Uses soft kill approach for inactive elements Assemble Model Creates a finite element model by collecting given entities points beams shells supports loads cross sections mate De Connected Parts Returns groups of interconnected lines of the model Disassemble Model Decomposes a model into its components Connectivity to Beam Creates beams with default properties from given connectivity diagram Index to Beam Creates beams with default properties from given node indexes Line to Beam Creates beams with default properties from given lines Lines that meet at a common point are by default rigidly con nected with each other Karamba assumes input to be in meter or feet j la o Lal Mesh to Shell Creates shells with default properties from given meshes Quad faces are split to triangles Disassemble Beam Decomposes beams into their components Make Beam Set Puts beams designated by their beam identifier into a group Modify Beam Modifies beam properties like total section height wall thickness of cross section activation state and whether it has bending stiffness or not 19 Orientate Beam Sets the local Z axis of beams according to a given vector and adds a rotation angle DAlpha deg about the longitudinal axis Flips beam direction according t
93. n unwanted relative displacements So you have to find out by trial and error which value gives acceptable results In Karamba the definition of a spring is analogous to creating a cross sec tion This is why the Spring CroSec component offers the possibility to give Springs a cross section family and name The SpringCroSec component at taches spring properties to beams via their identifiers Figure shows a peculiarity one has to be aware of when using springs They are unaware of the relative position of their endpoints This is why the load on the right end of the spring does not evoke a moment at the left 40 fixed end of the spring 6 2 4 Beam Joints Starting node A Tx Ty Tz Rx Ry Rz 000000 End node Tx Ty Tz Rx Ry Rz E S 000000 Figure 32 Beam under dead weight fixed at both supports with a fully disconnected joint at one end resulting in a cantilever A structure usually consists of a large number of load bearing elements that need to be joined together When rigidly connected such a joint has to transfer three section forces one axial force two shear forces and three moments one torsional and two bending moments Depending on the type of material such full connections are sometimes e g for wood hard to achieve costly and bulky A solution to this problem consists in introducing hinges Figure 32 shows a beam under dead weight with fully fixed boundary con ditions at both end points At
94. nZ allow to specify the buckling length of a beam for its local Y and Z axis respectively When specified these values override those from the buckling length calculation of Karamba 6 1 12 Orientate Beam Beam X axis amp Beam Z axis Alpha Figure 24 The orientation of the local beam coordinate system can be controlled with the OrientateBeam component In Karamba the default orientation of the local coordinate system of a beam or truss follows these conventions e The local X axis of red color is the beam axis and points from starting node to end node e The local Y axis green is at right angle to the local X axis and parallel to the global XY plane This specifies the local Y axis uniquely unless the local X axis is perpendicular to the XY plane If this is the case then the local Y axis is chosen parallel to the global Y axis e The local Z axis blue follows from the local X and Y axis so that the three of them form a right handed coordinate system The local coordinate system affects the direction of locally defined loads and the orientation of the element s cross section Use the Orientate Beam component to set the local coordinate system see fig 24 33 e The input plug X axis accepts a vector The local X axis will be oriented in such a way that its angle with the given vector is less than 90 deg This allows to give a consistent orientation to a group of beams e The local Z axis l
95. nd in table Do not take these values too literally For example snow loads vary strongly depending on the geographical 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 section automates this task for surface loads A 3 Tips for Designing Statically Feasible Structures Karamba can be used to analyze the response of structures of any scale When using the Analysis component for assessing the structural behavior be aware of two preconditions First deflections are small as compared to the 112 type of material kN m reinforced concrete 25 0 glass 25 0 steel 18 5 aluminum 271 0 fir wood 3 2 snow loose 1 2 snow wet 9 0 water 10 0 Table 3 Specific weights of some building materials 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 4 Loads for typical scenarios 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 have to increase the load in several steps and
96. nd spares you programming effort but lacks the full flexibility of the Simple Stitch 6 8 13 Stacked Stitch A Stacked Stich component works along the same lines as a Simple Stitch The difference is that it maps the given parameters to a geometry in such 103 Me Elem ode aL Support MPA re E p vu 4 Y lt x D z p Figure 96 Stacked Stitch mapping with the same set up as in fig but fifteen ran dom connections instead of two StackedStitch a way that no two connection elements cross each other see fig 96 The input plug unevenness can be used to fine tune the average irregularity of the result Zero means totally even the connection elements are placed at equal distance along the beam sets in terms of the corresponding beam set parameter The larger the value in unevenness the more irregular the layout of connection elements 6 8 14 User Iso Lines and Stream Lines The components User Iso Lines and User Stream Lines let you draw iso lines and stream lines on arbitrary meshes by defining values and vectors at their vertices e uv O E Figure 97 User defined Iso lines red and stream lines green on a rectangular shell patch The definition Shell UserDefinedIsoAndStreamLines gh in Libraries Karamba Examples TestExamples uses a function which when given a point returns the distance from and direction to a predefine
97. nd supports The component Assemble gathers all the necessary information and creates a statical model from it see figure 14 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 input plug LDist can be used to define the distance of points below which they will be merged to one This helps in dealing with inaccurate geometry Giving a negative value to LDist allows two separate nodes in a model to reside on the same spot This lets you define zero length elements such as springs connecting the two halves of a scissor structure 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 elements and so on At the end of the list the characteristic length of the model is given which is calculated as the distance between opposing corners of its bounding box 24 w co e j w med Assemble Figure 14 The Assemble component gathers data and creates a model from it 6 1 3 Connected Parts When creating a model based on unprecise geometry or using a generative process elements may not be connected to each other as desired The Con nected Parts component see fig takes a model as input and determines its connected parts It considers beams and trusses only Connected groups get listed in a data tree in descending order of
98. nnected resulting in the additional element C Sometimes one has several potentially structural elements neatly posi tioned in space but no connections between them The Element Felting component helps out in such situations by generating connections between neighboring elements see fig 90 The components behavior can be con trolled with these input plugs e Model Karamba model to be dealt with LimDist m The Element Felting component calculates the short est distance between each pair of elements in the model If this distance is less than LimDist a connection will be generated SnapLen m In case that a connection is to be generated the par ticipating elements need to be divided and a connection element intro duced If any of the thus arising elements has a length of less than SnapLen then the element will be removed and its endpoints snap to the older point of the two 99 MaxELen m you can set here a length limit for elements that shall take part in the felting process All element longer than the value of MaxELen will be ignored Startind Lets you limit the felting process to elements with an index larger than or equal Startind MaxNCon This sets the maximum number of new connections to be generated If this value is reached then felting simply stops Beam Id The beam identifier provided her will be attributed to the connections generated by the compon
99. ns no lateral torsional buckling interaction coefficients kyy kyz kzz 1 0 bucklingLength beam id if Ik lt 0 return true real props gt fy real E props gt E real h real Ncry real Ncrz M PI x M_PIx E Ik x Ik h x props gt lyy h x props gt Izz 116 19 20 21 29 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 AT 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 h real lam_y real lam_z real phi_y real phi_z sqrt props gt A x fy h saqrt Ncry h sqrt Ncrz real phi phi_y gt phi_z phi_y phi_z real lam phi_y gt phi_z lam_y lam_z real chi 1 phi sart phixphi lam x lam chi chi gt 1 1 chi real Nrd props gt A x fy real Nbrd chi gt Nrd real Myrd Wy props x fy real Mzrd Wz props x fy real Mtrd props gt Wt fy sqrt 3 0 real Vyrd props gt Ay x fy saqrt 3 0 real Vzrd props gt Az x fy saqrt 3 0 cross section with zero resistance is insufficient if Nrd 0 Nbrd O Myrd O Mzrd 0 Mtrd 0 Vyrd 0 Vzrd 0 4 _insufficiency 1 return false for nodes i and k for int node_ind 0 node_ind lt 2 node_ind VecReal force beam localForce Ic node_ind real N force Node x_t real Vy force Node y_t real Vz force Node
100. o a given x vector Select Beam Selects beams according to a given identifier and puts all incoming beams in two groups selected or rejected The identifier may be the element index name or a regular expression Support Creates supports at nodes of given node indexes or node coordinates Lets you select translations rotations which should be zero and the support orientation with respect to the global coordinate sys tem 5 5 Export Export Model to RStab Exports a model to RStab5 RStab6 RStab7 or Robot by creating a DStV file 5 6 Load Dissemble Mesh Load Splits a mesh load into corresponding line and point loads a Gravity Creates gravity from a specified direction vector for given load cases Line Load on Element Creates a uniformly distributed load on a beam Mesh Load Creates approximately equivalent point and line loads from a surface load on a mesh Point Load Creates point loads at points of given index or position Point Mass Attaches a point mass to a node of given index or po sition Does not result in additional weight only translational inertia Pretension Load Sets pretension loads on beams The elements get deformed and then built into the structure Temperature Load Imposes a temperature difference on an element er y Ele AA with respect to its initial temperature at construction Prescribed Displacement Prescribes displacements at nodes of given node indexes or node coordinat
101. o know how displacements change over the length of a beam use the Beam Displacements component see fig 73 The maxL and NRes input plugs work analogously to those of the Section Forces component see section 6 6 10 6 6 8 BeamView The BeamView components controls the display options related to beams see fig 74 This concerns the rendering of cross section forces resultant 82 Model Model Model LC Factor daan Mesh 5 75 LC Index Curves def Curves DP Colors Legend C Id def Model P Display Scales mmm ee Cross section O Displacement Utilization O 0 73 ModelView BeamView 11 50 Axial Stress O Faces Cross section 15 00 Figure 74 Display of resultant displacements on beam cross section displacements utilization of material and axial stress The Render Settings submenu When activated Cross section Displacement Utilization and Axial Stress result in a rendered view of the model Utilization is calculated as the ratio between the normal stress at a point and the yield stress of the corresponding material Shear and buckling are not considered j z a Es b E Figure 75 Rendered images of the beam Left Cross section option enabled Right Axial Stress enabled The color range of the results starts at the minimum value and stretches to the maximum In case the model consists of one material the zone of highest utilization will also b
102. of a body in three dimensional space Bad choices of support conditions are easy to detect with Karamba In section it is shown how to calculate the eigen modes of a structure This kind of calculation works also in cases of moveable structures rigid 35 body modes if present correspond to the first few eigen modes Model Model D q Deform Scale Mesh D LC Index z Curves D g v Colors emi Legend C p Id LegendT p Tx Ty Tz Rx Ry Rz 000000 Figure 27 Define the position of supports by node index or position Figure shows a simply supported beam The Karamba Ensemble Support component takes as input either the index or the coordinates of the point or a list with indexes or positions of points to which it applies By default the coordinate system for defining support conditions is the global one This can be changed by defining a plane and feeding it into the Plane input plug of the Support component 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 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 circle 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 freedom
103. of beams The group of beams defined by a set can be used for defining geometric mappings In this context a beam set represents a polygon of straight seg ments The order of the elements in the set is defined by the order in which they were entered into the set Such polygons can be split at an arbitrary position see e g section 6 8 12 MinSLen minimum segment length lets you set the minimum length which may result from such a split In case of potentially smaller segments the intersection point snaps to its nearest neighbor In order to group a structure visually beam sets can be given different colors These colors show when Cross section is enabled in the BeamViews Render Settings see section 6 6 8 The identifier of a beam set can be used anywhere instead of a beam identifier In order to be registered with the model beam sets need to be fed into the Set input plug of the Assemble component 6 1 11 Modify Beam By default Karamba assumes the cross section of beams to be steel tubes with a diameter of 14 3 cm and a wall thickness of 0 4 em When two beams meet they are rigidly connected like they were welded together Use 30 the ModifyBeam component 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
104. of cross section forces and moments The Section Forces sub menu lets you plot section forces and moments as curves meshes and with or without values attached All generated curves and meshes get appended to the BeamViews curve and Mesh output The graphical representation is oriented according to the local coordinate axes of the beam and takes the undeflected 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 78 Customize the mesh colors via karamba ini The slider Length Subdivision in sub menu Render Settings of the ModelView component controls the number of interpolation points 84 8 00 8 00 8 00 8 00 Model LC Factor M LC Index Deformation 8 00 8 00 llo O 1 00 Model def Mesh def Curves def Model z o a D BeamView l Legend T Scale O 0 0467 MO Myf mz No vO vz al A stress kN cm2 2 31e 01 2 02e 01 1 74e 01 1 45e 01 1 16e 01 8 68e 00 5 8e 00 2 89e 00 0 00e 00 2 89e 00 5 78e 00 8 68e 00 1 16e 01 1 45e 01 1 74e 01 2 02e 01 2 31e 01 E O m E O Local axes i 1 00 Cross section O Displacement O Utilization O Axial Stress Faces Cross section 2 00 Joints O 1 00 Length Segment m O 0 60 Result Threshold 16 00 Node tags Element tags Element Ids Element axis CroSec names Eccentri
105. ols support symbols local coordinate systems and symbols for joints at the endpoints of elements 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 The Render Settings submenu The slider entitled Length Segment m lets one control the distance at which beam results displacements forces moments etc are plotted It 1 also sets the number of lines that come out of the def Curves output plug In some cases the color display of results gets distorted by the presence of stresse concentrations or utilization peeks They make much of the structure look unstrained with some small patches of color where the peeks are The Upper Result Threshold and Lower Result Threshold sliders let you filter out these extreme values In case of the Upper Result Threshold slider a value of x sets the upper boundary value of the color range in such a way that x of the actual value range is below For the lower threshold it is vice versa Values in the model beyond the given thresholds are given special colors to make them easily recognizable By default the result threshold values given above refer to the value range in percent Sometimes it turns out to be practical to prescribe absolute values as thresholds e g the yield stress of a material The radio button gro
106. on has to lie below the yield stress f of the material In case of materials with high ductility like steel the plastic capacity of cross sections can be exploited Depending on the cross section shape the plastic capacity is 10 to 20 higher than the elastic capacity Set elast to false in order to activate plastic cross section design When enabling plastic cross section design do not 12 be surprised that the ModelView reports utilization levels beyond 100 The reason is that Karamba assumes linear elastic material behavior Grouplds Sometimes constructive logic demands that all elements of a given set have identical cross sections Karamba allows to define beam sets see section 6 1 10 Put the set identifiers into the Grouplds plug to enforce identical cross sections MaxDisp For usability of a structure it is necessary to put a limit on its maximum deflection This can be done using the MaxDisp plug By default its value is 1 which means that the maximum deflection is not considered for cross section design DispIter Maximum number of iterations used to reach the maximum dis placement criteria in case there is one The design iterations for maxi mum displacement come after those for load bearing capacity On the output side the Model plug renders the structure with optimized cross sections Check the Intfo plug in order to see whether any problems occurred during optimization The M
107. onents for analyzing the structural model contains components to create and select cross sec for export of Karamba models to RStab or Robot via DStV components for the definition of material properties contains some extra geometric functionality that makes it easier The colors of Karamba s icons have a special meaning black or white designates the entity or entities on which a component acts components get referenced by a blue symbol Products of Basic knowledge of Rhino and Grasshopper is needed to understand this guide It is recommended to download the Grasshopper Primer from the Grasshopper web site for introductory material on Grasshopper 4 Quick start 4 1 Basic Example Creating a statical model in Karamba consists of six basic stepg see fig This step by step procedure was devised and formulated by Justin Diles 11 ails cl 4 5 6 assemble calculate model model view results Figure 3 Basic example of a statical model in Karamba 1 Create wire frame point geometry or meshes for the structural model with Rhino or GH 2 Convert wire frame or point geometry to Karamba beams meshes to Shells 3 Define which points are supports and which receive loads 4 Assemble the Karamba structural model with points elements sup ports and loads Optional Define custom cross sections and materials and add them as well They reference elements either by index or user de
108. ons about the Y and Z axis Karamba is based on the assumption of small deflections Thus be aware that large prescribed displacements and rotations give rise to incorrect results which can nevertheless be used for shape finding For approximating effects due to large displacements see section 6 5 2 Displacements can only be prescribed if the corresponding displacement degree of freedom is removed from the statical system This means you have to activate 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 supports 6 5 Algorithms 6 5 1 Analyze With geometry supports and loads defined the statical model is ready for pro cessing 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 Model LC Factor 1 00 LC Index Model D Disp hA N G eee 0 82 robe AN gt 0 82 Ltk Colors Model Figure 52 Deflection of simply supported beam under single load in mid span and grav ity Figure Shows a deflected beam The analysis component not only computes the model deflecti
109. ons 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 of each load case see section 6 6 1 for details on work and energy These values can be used to rank structures in the course of a structural 58 optimization procedure the more efficient a structure the smaller the max 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 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 In order to view the deflected model use the ModelView component see section 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 ModelView 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 th
110. or the first and second principal stresses there Thin out results by setting Result Threshold of ModelView needs to be upstream of the data flow to a value of less than 100 Like for isoline and force flow 91 aac ZZA a Y Y vo ig ee AA PSt L Figure 84 Triangular mesh of shell elements and principal stress directions at their cen troids Colors indicate the resultant displacement lines a specific load case or superimposition of load cases can be set via ModelView By default all load case results get added up using unit load factors 6 6 16 Principal Stress Lines on Shells Line l PStress Figure 85 Principal stress lines they are tangent to the first and second principal stress direction The coloring reflects the level of material utilization Principal stress PS lines are tangent to the principal stress directions see fig 85 In the case of a cantilever they either run parallel or at right angle to the free boundaries In the middle where normal stresses due to bending vanish first and second principal stress lines intersect at 90 deg The meaning of the input plugs of the Principal Stress Lines on Shells component correspond to that of the Force Flow Lines on Shells component see sec 6 6 11 for details On the output side Lines1 and Lines2 hold the first and second principal stress lines in data trees the right most di mension holds a list of lines t
111. ow Figure 81 Cantilever consisting of triangular shell elements Flow lines green of force in horizontal direction 6 6 11 Force Flow Lines on Shells Force flow lines or load pathes as they are also sometimes called illustrate the load distribution in structures 3 There is a loose analogy between those force flow FF lines and streamlines in hydromechanics The law of conservation of mass in hydromechanics is matched by the static conditions of equilibrium in a specified direction If there are two FF lines the resultant force between those in a predefined direction stays constant Consider e g the cantilever in fig 81 for which the force flow in horizontal direction is described by the red lines At the supports the force flow lines run nearly horizontal at the upper and lower side where the normal stresses from the supports reach their maximum and thus dominate the resultant force They gradually curve down to the neutral axis where the shear stresses constitute the only contribution to horizontal forces Aside from resulting in nice line drawings those force flow lines can be practical as well 3 e FF lines form eddies in ineffective with respect to the given force di rection parts of a structure or reverse their direction there e In case you want to strengthen a structure with linear elements e g fibres align them with FF lines to get the most effective layout FF lines are not the same as principal str
112. pported 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 k N in the left element and compression 1 5 kN in the right one 6 6 10 Section Forces Sometimes it is desirable to have section forces and moments represented as components in the direction of the local axes of the cross section instead of resultant values Use the S Force component in such a case Its output is similarly structured as that of the Res S Force component described above but its output plugs comprise the force components in local directions see fig 80 The input parameters maxL and NRes determine the number of results along the beam axis maxL can be used to control the maximum distance between results A negative value for maxL means that there is no maximum distance condition NRes sets the number of results along the beams The beams endpoints are automatically included in the output Figure 80 Simply supported beam under axial and transverse point load List of normal forces shear forces and moments for all elements and all load cases along an the elements 87 a SSS SS 4 AA A K gt 52 gt 2 SS RA Model Zz AAA NA e A prey a a ipa 2 A SS A A Layer ForceDirs ForceDirPos ShellForceFl
113. r an element in active true or inactive false The boolean values map directly on the model elements Using a Tree Branch component with a slider connected to a Activate Model component see section lets you inspect the history of the FFF process see fig 61 is active renders a list of true false values one for each element True Signals that the corresponding element is part of the final structure i e active Otherwise it contains a false entry weights List of element or group weights in ascending order in the final structure This can be used as a qualitative check of the result The more evenly distributed the weights the better utilized the structure There will always be force concentrations around supports and external loads which show up as sharp peaks A good way of visualization is to use a Quick Graph component see fig 61 6 5 6 Tension Compression Eliminator The Tension Compression Eliminator component removes elements from a model based on the sign of their axial force These are the available input parameters Iter The removal of tensile or compressive elements works in an iterative fashion The procedure stops either when no changes occur from one 68 E m E o O Ss i Figure 62 The Tension Compression Eliminator component step to another or if the the maximum number of iterations Iter is reached Ind Indexes of the elements that
114. r of iterations within which the target mass of the structure should be reached Is limited by MaxIter 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 MaxIter Maximum number of iterations When set to a value larger than Iter then at least one element will change its activation state during 66 the last MaxIter Iter iterations Sometimes this helps to improve results Factors for weighting forces moments The FFF component lets you se lect weighting factors for the different force and bending components in an element The weight of an element is determined by averaging single force components at its end division by the elements mass and multiplication by the corresponding user given weighting factor The weight of groups results from the average of their members These are the available weighting factors e W Tension factor for axial tension force e WCompr factor for axial compression force e WShear factor for resultant shear force e WMoment factor for resultant moments Overdrive Say in each iteration step there needs to be
115. re the description of the input parameters Model receives the model to be processed Elem Id There are three alternatives concerning this input parameter e No input The whole of the structure will be considered by the FFF e The input consists of one string All elements whose identifiers match take part e A list of strings is given Elements that match a given list entry belong to one group They get collectively activated or deactivated during force path finding A structure may consist of active and non active elements The initial state of a group is determined by the state of the majority of its elements Groups need not be disjoint L Case List of load cases to be considered Zero is the index of the first load case Considering the total effect of several load cases amounts to adding up their individual influences on an element Target ratio of the target mass to the initial mass of a structure When determining the initial mass all elements of the structure irrespective of State of activation count In the target structure only active elements contribute to its mass This enables one to apply FFF components in series Depending on the activation status of the model elements applying FFF will lead to an increase or decrease in the number of active elements The activation status of individual elements can be set by means of the ModifyBeam and ActivateModel components Iter Numbe
116. rror that is hard to detect by visual inspection alone Two lines on the same spot mean double member stiffness in the statical model e L Dist sets the limit distance for two points to be merged into one Lines of length less than that value will be discarded The default value iS 5 mm e Id takes a list of strings as identifiers for beams The default value is an empty string Each beam has a name by default its zero based index in the model Identifiers provide a useful means to group the beams in order to modify or display them Beams that meet at a common point are by default connected rigidly in the statical model like they were welded together See section 6 2 4 on how to define joints at the end of beams The Info output plug informs about the number of removed nodes and beams 6 1 6 Index to Beam 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 21 iA ME w n CO le O S Figure 18 The IndexToBeam component lets you directly define the connectivity infor mation of beams 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 18 accepts a pair of lists of node indexes and produces beams with default properties from it This
117. s see fig 46 The input plug LCase which designates the load case defaults to 0 6 4 4 Pretension Load Karamba lets you define axial pretension Pre tensioning means that the element gets first axially loaded in such a way that it reaches the target strain Then it gets built into the structure Fig 48 shows a beam with 54 both ends fixed subject to a compressive pretension load The unit of dimension of the pretension which gets fed into the eps0 plug is mm m Pre tensioning an element is not the same as applying a pair of opposite forces at its endpoints In case of pretension the axial force in the element depends on its boundary conditions If the structure to which it connects is very stiff then the resulting axial force will be N eo A E In figure 48 the supports are rigid the elements cross section A 25 cm Young s Modulus E 21000 kN cm and ey 0 00015 This results in an axial force of N 78 75 kN and shows up as horizontal support reactions When the rest of the structure does not resist then a pretension load merely results in lengthening or shortening the corresponding element The input plug ElemIds defines the elements where the load acts and L Case the load case 16 19 eps0 0 15 mm m 78 75 x Figure 48 Pre tensioned member fixed at both ends and resulting support reactions 6 4 5 Temperature Load The definition of temperature loads works analogou
118. s are in meters In order to be of immediate use beams come with a number of default values see string output in figure 17 active means that a beam will be included in the statical model The default cross section is a circular hollow profile of diameter 11 4 cm with a wall thickness 26 of 0 4 cm The default material is steel of grade S235 Lines that fall below the length limit given by LDist get automatically removed Unless lines get removed there is a one to one correspondence between the list of input lines and output beams 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 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 Line ToBeam 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 e
119. s compared to the cross section forces This is done for the two endpoints of index zero and one In order to assess the effect of combined loads the Superposition formula in line 58 or 60 is used for axial stress If the normal force is tensile N gt 0 then N is compared to the plastic resisting force Ny see line 29 if compressive then N q enters the picture These formulas correspond to that given in equation 6 41 of EC3 The superposition of the effect of shear in y and z direction and torsional moments is considered in line 63 along the same lines as for the axial stresses The fact that shear and normal stress are considered separately constitutes a simplification The larger of the utilization numbers of shear and normal stress is taken as the resulting cross section utilization see line 66 References 1 J H Argyris L Tenek and L Olofsson Tric a simple but sophisticated 3 node triangular element based on 6 rigid body and 12 straining modes for fast computational simulations of arbitrary isotropic and laminated composite shells Comput Methods Appl Mech Engrg 145 11 85 1997 2 J H Argyris M Papadrakakis C Apostolopoulou and S Koutsourelakis The tric shell element theoretical and numerical investigation Comput Methods Appl Mech Engrg 182 217 245 2000 3 H Moldenhauer Die visualisierung des kraftflusses in stahlbaukonstruk tionen Stahlbau Ernst amp Sohn Verlag f r Architektur und technische
120. s two parameters In the context of the Simple Stitch mapping these parameters give the relative position on the two beam sets A and B where a connection C shall be introduced So a mapping encapsulates an operation and the mapper activates it 10 Currently Karamba offers mappings which mainly deal with connecting existing beam sets by variants of an operation termed stitching The notion comes from the analogy to joining together pieces of cloth These mappings will be explained further below They are rooted in the research project Algorithmic Generation of Complex Space Frames which was conducted at the University of Applied Arts Vienna 6 8 10 Interpolate Shape The Interpolate Shape component allows one to span a design space with basic means one Karamba model acts as origin of that space an arbitrary number of other models define a coordinate axis each Linear interpolation takes place between the model at the origin and those defining the axes A parameter value of 0 0 corresponds to the origin 1 0 to the model defining the corresponding axis Model 7 Model d Fromind 0 NModes Z Evals 9 Pt Beam e Y pH a pH D aaah Model Mapping s Model Iir Support Load CroSec Assemble Material Set LDist InterShap Figure 92 Definition for optimizing the shape of a simply supported beam under mid span single load Fig shows a definition where the first 30 eig
121. slabs these normally make up the majority of mass in high rises in an approximate manner These masses are assumed to have translational inertia only Karamba scales the resulting vibration modes in such a way that their largest component is one They get attached to a model as load cases which can be viewed via a ModelView component The calculation of modal mass and participation factors are based on the modal displacements as scaled in the above described manner The calculation of natural vibrations is computationally more demanding than eigen modes So save your model before activating the compo nent Grasshopper has no Cancel button Vibration modes depend on stiffness and mass number of vibration modes to calculate Figure 59 Simply supported steel beam IPE100 of length 10 m in its 14 natural vi bration mode 6 5 5 Force Flow Finder 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 made 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 those elements of the structure that are least strained and thus least ef 64 fective Again the response of the now thinned out mo
122. sly to defining pretension loads see sec 6 4 4 The difference is that members get built into the structure first then they are subjected to a temperature change The co efficient of thermal expansion see section characterizes the response of a materials to temperature changes E 52 50 52 50 3 ATLoad Z Figure 49 Temperature load on a member which is fixed at both ends 55 6 4 6 Gravity 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 earth quake loads this can rise to 100 this however also depends on the stiffness properties of the structure and underlying soil The gravity component applies to all active elements in the statical model for which gamma see section is not zero The gravity vector defines the direction in which gravity shall act A vector of length one corresponds to gravity as encountered on earth 6 4 7 Point Mass Karamba is capable of calculating the natural vibration modes and frequen cies of structures see sec 6 5 4 For results to match reality the inertia properties of a structure need to be modeled correctly Masses of elements e g beams trusses shells are automati
123. speeds up model generation considerably for there is no need to compare nodes for coincident coordinates The Ind ToBeam component makes it possible to define elements with zero length This proves useful in case you want to connect elements that touch each other but should not be rigidly connected think of a scissor see section 6 2 3 about springs 6 1 7 Connectivity to Beam In Grasshopper meshing algorithms can generate topological connectivity di agrams With the help of the ConToBeam component these may be directly converted to beam structures see figure 19 Figure 19 The ConToBeam component turns connectivity diagrams into sets of beams 6 1 8 Mesh to Shell The Mesh ToShell component takes a triangle or quad mesh and turns it into a group of shell elements see fig 20 Quads get automatically decomposed to triangles Each patch of shells can be given an identifier for later reference when attaching custom material or cross section properties 28 Shell patches are rigidly connected when their nodes lie at a distance less then that given in LDist The Pt input serves the same purpose as in the LineToBeam component see sec By default shells have a thickness of 1 cm and steel as their material The shell elements used in Karamba resemble the TRIC element devised by Argyris and coworkers see 1 for details They are facetted i e flat elements with constant strain in each layer Karamba negle
124. te a given evenly distributed surface load on a mesh red Offending nodes will be listed in its run time error message By default no point loads will be produced The procedure for calculating nodal loads and uniformly distributed beam loads from surface loads consists of the following steps First Karamba calculates the resultant load on each face of the given mesh Then the resultant load of each face gets evenly distributed among its vertices The second step consists of distributing the vertex loads among the nodes of the structure In order to arrive at beam loads additional helper nodes along their axes get generated The mutual distance of those is chosen equal to a third of the mean edge length of the given mesh Each mesh vertex transfers its load to the nearest node In case that there are several nodes within a radius of less than LDist as set at the Assemble component see section 6 1 2 the vertex load gets evenly distributed among them The loads received by the helper nodes along beam axes get summed up and divided by the element length This results in the approximately equivalent uniformly distributed load which is placed on the element From the procedure described one can see that a crude mesh may lead to a locally incorrect distribution of loads Fig 45 shows a similar setting as in fig The difference lies in the additional input of node positions for the generation of point loads These points lie at the end and
125. th opposing directions 7 4 Karamba does not work after reinstalling Grasshoper Upon installing Grasshopper some files of the Karamba package may have been erased Try to reinstall Karamba 7 5 Karamba does not appear nor any of its components seem to be installed In case of multiple versions of Grasshopper on your machine make sure that you installed Karamba to that Grasshopper version which is used by Rhino In 107 Rhino select Tools Options Plug ins from the menu then Grasshopper from the list of plug ins Press the Properties button to check the path to Grasshopper Multiple Grasshopper versions can result if there are more than one users on a machine and each of them installs his or her own Grasshopper 7 6 Karamba seems to get stuck while calculating a model Depending on your computer CPU size of internal memory Karamba can handle models in the order of 10000 elements efficiently If overlong com putation times occur check the number of models you actually calculate Having the path structures of the input data wrong may lead to multiple models In such cases flattening or simplifying the input data helps 1 1 Predefined displacements take no effect Check whether you disabled the correct degrees of freedom in the Condi tions section of the PreDisp component 7 8 The ModelView component consistently displays all load cases Simultaneously If the ModelView component does not seem to react to
126. the right end the joint which is in fact no joint any more completely dissociates the beam from the support there The result is a cantilever The symbols for joints resemble that for supports pink arrows represent translational joints white circles symbolize moment hinges In Karamba joints are realized by inserting a spring between the endpoint of a beam and the node to which it connects This necessitates sufficient support conditions at the actual nodes to prevent them from freely moving around See for example the right node in fig which has to be fully fixed otherwise the system would be kinematic The Crosec Joint component allows to define hinges at a beams starting and end node A list of beam identifiers lets you select the beams where the joint definition shall apply Filled circles mean that the corresponding degrees of freedom represent joints T stands for translation R for rotation Feed the resulting cross section into the CroSec plug of the Assemble component 41 The orientation of the axes of the joints corresponds to the local coordinate system of the beam they apply to 6 2 5 Disassemble Cross Section p U 9 zy O Disassem ble Figure 33 Properties of a given cross section can be retrieved via the Disassemble Cross Section component In some cases e g after optimizing cross sections it may be necessary to retrieve the properties of a cross section Use the Dis
127. the target edge length of faces at Brep boundaries Point Reduction If True vertices in overly dense areas get culled Such regions may result from a distorted UV space in the underlying Brep Points closer than half of MRes to their next neighbor get removed SStep and Slter These two parameters let you control mesh relax ation Triangular finite shell elements give better results when having sides of approximately equal length The smoothing algorithm tries to improve the mesh in that direction It moves each vertex towards the center of gravity of those vertices it connects to During mesh relaxation vertices always remain on the Brep they belong to 96 The output of the MeshBreps component consists of meshes with iden tical vertices at common boundaries The Info output plug provides infor mation regarding the meshing process 6 8 2 Nearest Neighbors Assume you have two lists of points say FromPts and ToPts Further imagine you want to have a network that connects each point of the first set with a predefined number of its nearest neighbors in the second set or to points in set two that lie within a given distance 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 section 6 8
128. their black knob Visualization properties stick to the model and stay valid until they get overruled by another downstream visualization component 4 11 Results Figure 12 Retrieval of numerical results nodal displacements 1 level of material uti lization 2 resultant cross section forces 3 and reaction forces 4 Structural response properties can be used to inform the model and e g optimize it Fig 12 shows some of the available options 5 Quick Component Reference 5 1 License License Returns the program version license information and can be used to manage the license file 5 2 Algorithms pr Analyze Calculates the deflections of a given model Analyze Large Deformation Does incremental geometrically non linear analysis for loads in load case zero tot Natural Vibrations Calculates the natural vibrations of the given i model 17 any ri 1 a Eigen Modes Calculates the eigen modes of the given model ac cording to the special eigenvalue problem Force Flow Finder Optimizes a structure by placing beams along the route which external forces take through the structure Optimize Cross Section Selects optimum cross sections for beams and trusses in the model Tension Compression Eliminator Removes beams or trusses under axial tension or compression By default compression members will be removed 5 3 Cross Section el B a MO 0 ra a z HER Box Profile
129. ts issue a warning message turn orange In case you enable Draw Icons in Grasshoppers View menu deprecated components are marked by a skull 7 14 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 not be cast to some other object In this case replace the old component with a new one and reattach the input plugs accordingly 7 15 The Optimize Cross Section component does not work Make sure that the beams you intend to optimize belong to the same family as those you want them to be selected from 109 7 16 The Optimize Cross Section component returns wrong results Increase the value at the iter input plug The cross section optimization algorithm is an iterative procedure In case you stop too early having limited the maximum number of iterations to a small value the algorithm has no chance to converge and thus returns seemingly wrong results Always check the Info output of the component for information on the solution procedure 7 17 Other problems In case you encounter any further problems please do not hesitate to con tact us at info karamba3d com or via the Karamba group at http www grasshopper3d com group karamba 110 A Background information A 1 Basic Properties of Materials A 1 1 Material
130. two elements The buckling length is determined as the distance between these two nodes It lies on the safe side in case of endpoints held by the rest of the structure against translation When beams are elements of a larger part of a system that buckles e g a girder of a truss then the applied determination of buckling length produces unsafe results In case of a free end the buckling length is doubled Compressive normal force in slender beams reduces their allowable maximum stress below the yield limit Visualizing the level of utilization with the ModelView component will then show values below 100 in the compressive range The OptiCroSec component provides the following set of input plugs Model Model to be optimized Iter Maximum number of design iterations for sufficient load bearing ca pacity The default value is five nSamples Number of points along beams at which their utilization is de termined The default is three ElemIds Identifiers of elements that should be optimized If not specified optimization is carried out for the entire model CroSec Cross section list that contains families of cross sections ordered from most favorite to least desired Family membership of cross sections is given via their family property elast If set to true the default cross section design is done within the elastic range This means that under given loads the maximum resulting stress in a cross secti
131. uals 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 Figure 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 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 WW NN A ih TENN HAS MN A WAAAY WYNN HW VAN MINS WWI WINN VAN WY WW MINS WANN ANN ANN NS AMAN WN AN ANY WWW AVA AA W WYMAN WAANS ZZ WINN YNY ZZAN IAN gt MG al Figure 58 Undeflected geometry upper left corner and the first nine eigen modes of the structure 63 6 5 4 Natural Vibrations In case you want to know how and at which frequency a structure vibrates use the NaturalVibrations component see fig 59 For details on eigen modes and natural modes see section A 5 The mass of beams and trusses enters with the values derived from their material weight Karamba uses consistent mass matrixes for beam elements For truss and shell elements a lumped approach is applied At nodes additional masses see sec 50 can be defined to simulate the effect of e g concrete
132. uation 6 47 x A fy x Asi 2 YM1 No Rd Karamba assumes cross sections of class 1 2 or 3 This means that their most strained fibre yields before local buckling occurs When you define a material Karamba further assumes that the given yield stress f is already reduced by the safety factor ym which in case of steel is 1 0 in many European countries Equation 6 49 of EC3 states that 1 x lt 10 3 B 14 92 X The equivalent code can be found in lines 26 and 27 The values for A and are calculated according to the formulas of EC3 section 6 3 1 2 A ES 4 5 In Karamba A gets calculated for the principal directions of the cross section see lines 19 to 21 and for the principal directions get calculated in lines 22 and 23 The imperfection factors a alpha _ y and a alpha 2 are taken from the cross section tables When using cross sections created within a GH definition then a a 0 3 is assumed The larger of and and the corresponding A see lines 24 and 25 are selected for calculating x in lines 26 and 27 In lines 29 to 35 the resisting moment and forces of the cross section are calculated In case of elastic design the elastic resistance moments W and 118 W come into play otherwise their plastic counterparts Wyp and Wz pi Ay and A are the equivalent shear areas in y and z direction Inside the loop which comprises lines 45 to 75 the cross section resistance i
133. ular the structure 6 8 12 Simple Stitch Figure 95 Simple Stitch mapping with the same set up as in fig 91 but fifteen random connections instead of two A Simple Stitch mapping connects two or more beam sets with truss or beam elements The input plug BeamsSets expects a list of beam sets which get connected in the order as they are listed Double entries of sets are no problem Via NConnect one sets the number of connections There needs to be one parameter per beam set and connection for specifying the mapping The numerical range of parameters should be zero to one zero is the starting position of the beam set one its end In case you fail to provide the mapper with a sufficient number of parameters it will turn red Read its error message in order to see how many parameters are needed The input plug Beam Id can be used to define the name of the connection elements Fig 95 shows a structure with 15 connections resulting from 30 randomly selected parameters This simple variant of stitches is also the most versatile one it gives you great freedom in generating connection patterns by defining the way how a set of parameters is mapped to the set of values that are fed into the Simple Stitch Sections 6 8 11 and 6 8 13 deal with variants of the Simple Stitch which are limiting the scope of possible patters This approach leads to faster convergence in case of optimization with e g Galapagos a
134. up Result Threshold as can be used to switch between relative and absolute thresholds Limiting the value range of utilization values can be confusing If the result thresholds are given in percent then setting the lower threshold to zero and the upper to 100 displays the full range of utilization values If the result thresholds are given as absolute values then a lower threshold of 100 and an upper threshold of 100 limit the color range to the areas where the material resistance is sufficient The Structure Tags submenu The Structure Tags menu contains checkboxes for adding visual informa tion to parts of the model e Node tags attaches node indexes to each node Element tags attaches element indexes to each element Element Ids displays the element identifiers Elements If enabled the def Curves output plug emits the axis of the deformed elements as lines and shows them on the Rhino canvas CroSec names displays the name of the cross section of each element Material names displays the name of the material of each element e Eccentricities visualizes beam eccentricities as blue lines at the end points if active 78 e Load values adds the numerical values of loads or point masses to the corresponding sysmbols The Load case Selection submenu The Load case Selection menu contains a drop down list from which one can choose the load case which should be displayed B
135. update the deflected geometry This can be done with the Large Deformation Analysis component see section 6 5 2 Figure 98 Simply supported beam For typical engineering structures the assumptions mentioned above suffice 113 for an initial design In order to get meaningful cross section dimensions limit the maximum deflection of the structure 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 Asa rough rule of thumb try to limit it to A lt 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 6 1 11 Make sure to include 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 So li
136. y default it is set to all which means that the results of all load cases are superimposed Define load factors by feeding a corresponding list of numbers into the L C Factor input plug The Load case Selection sets the load case to be queried for the shell results components placed further downstream e g Force Flow Lines on Shells Principal Stress Lines on Shells 6 6 3 Nodal Displacements Figure 69 Simply supported beam under axial and transverse point load List of nodal displacements vectors with translations and rotations for each node and load case The NodeDisp component lists the displacements of each node for all load cases Two data trees consisting of vectors make up its output The two rightmost dimensions correspond to Model LoadCase The data for each node at the output plugs Trans and Rot consists of a vector which contains the three translations or three rotations see fig 69 The vectors refer to the global coordinate system Their units are meter and radiant respectively 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 with the X axis pointing towards him or her 19 6 6 4 Approximate Principal Strains ASAS AAA Zs z DAN om AS S ASA gt TX ASA wo Model a Model D e def Model E P PS Point E vT se a i Do

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