Home

Lateral torsional buckling analysis BTII

1. EI Formulas 1 1 El y 6 Ely ls Torsion spring constant 6 21000 8360 3 21000 8360 100 500 10533KNm rad BTII Lateral torsional buckling analysis 45 46 Reference literature 1 2 3 4 9 6 7 8 9 10 11 12 13 F d ration Europ enne de la Manutention section XI Rules for the design of series lifting equipment Local girder stresses FEM 9 341 10 1983 W F Chen T Atsuta Theory of Beam Columns Vol 2 Space Behaviour and De sign McGraw Hill New York 1976 Traglastermittlung ebener Stabwerke mit r umlicher Beanspruchung Mitteilung Nr 81 3 Institut f r konstruktiven Ingenieurbau Ruhr Universit t Bochum 1981 J Lindner Der Einflu von Eigenspannungen auf die Traglast von l Tr gern Habilita tionsschrift professorial dissertation Technical University of Berlin 1972 Abbreviated version in Der Stahlbau 43 1974 p 39 45 and 86 91 J Lindner Berichte aus Forschung und Entwicklung DASt 15 1986 and Stabilisie rung von Biegtr gern durch Drehbettung eine Klarstellung Stahlbau 12 1987 p 365 373 J Lindner J Scheer H Schmidt Hrsg Stahlbauten Erl uterungen zu DIN 18800 Teil 1 bis Teil 4 Beuth Kommentare Beuth Berlin K ln Ernst amp Sohn Berlin 1993 P Osterrieder Traglastberechnung von r umlichen Stabtragwerken bei gro en Verformungen mit finiten Elementen Dissertation University of Stuttgart
2. flange and applies at a distance ey to the outer edges of the flange sides BTII Lateral torsional buckling analysis 30 Superpositions The calculation of the system is based on load case combinations They are generated in accordance with the combination rules stipulated by EN 1990 Load case combinations include the load cases via coefficients into the calculation These coefficients correspond to the partial safety factors for the actions Load case combinations are assigned to a design situation and a limit state independently of each other The partial safety factors for the actions are determined via the load combination factors The partial safety factors for the resistances are determined by the design situation and the limit state Load case combinations Value Description No Consecutive number of the superposition Designation Name of the superposition min x Smallest coordinate for the trolley travel max x Highest coordinate for the trolley travel Criterion Criterion for the decisive load position Design Design situation as per EN 1990 Limit state Limit state as per EN 1990 Type of Imperfections 1 parabolic 2 sinusoidal Imperfections Displays a dialog for the input of the imperfections Factors Displays a dialog for the input of the superposition factors Notes concerning moving loads When the Moving load option was selected in the Load parameter menu areas where the wheel loads move must be defi
3. simultaneously The load cases are not taken into account directly They are included in the calculation via superposition factors that correspond to the partial safety factors on the action side Load case definition Input options Value Description Load case Consecutive number of the load case Designation Name ofthe load case Type Allows to specify whether the load case should contain the lower or the upper values or the difference of the upper and lower values of the loads 1 lower value 2 upper value 3 upper lower values Action Index of the action that is assigned to the load case Alternative Alternative group loads in an alternative group exclude each other Self weight Tick the corresponding check box to include the self weight automatically to gether with this load case Type of point 0 static point load load 1 moving point load Load cases can include static and moving point loads independently of each other if the load parameters have been set accordingly Loads Allows you to edit the loads assigned to the load case Functions available via the tool bar Symbol Shortcut Description a Adds a load case at the end of the list Ctrl I Inserts a load case above the active list item gt Ctrl D Deletes the active load case Fr n Deletes all load cases F5 Displays a dialog for the definition of the loads This input option is only available if the inclusion of moving loads was set in the load pa
4. 1983 Chr Petersen Statik und Stabilt t der Baukonstruktionen Vieweg amp Sohn Braun schweig 1981 G Powell R Klingner Elastic Lateral Buckling of Steel Beams in Proceedings ASCE J of Structural Division 96 1970 pp 1919 1932 S Rajasekaran Finite Element Analysis of Thin Walled Members of Open Cross Sections Structural Engineering Report No 34 Department of Civil Engineering University of Alberta Edmonton Canada Sept 1971 K Roik J Carl J Lindner Biegetorsionsprobleme gerader d nnwandiger St be Ernst amp Sohn Berlin M nchen D sseldorf 1972 H Rubin U Vogel Baustatik ebener Stabwerke in Stahlbau Handbuch Band 1 Stahlbau Verlags GmbH K ln 1982 U Vogel W Heil Traglast Tabellen Published by Beratungsstelle f r Stahlverwen dung Stahleisen GmbH D sseldorf 1981 Frilo Structural analysis and design
5. be limited to the 1 25 fold value of the elastic limit bending moment This reduction can be dispensed with if the system consists of single span beams and continuous beams with constant cross sections over their total length Partial internal forces method according to Kindmann See Plastic ultimate resistance IAW DIN 18800 1 Equivalent bar method IAW DIN 18800 2 This option allows you select among two different methods for the verification of the lateral stability against torsional buckling with biaxial loading either including or not axial forces You can also select both verification methods Method of calculation Second order analysis The second order analysis is based on iteration The first step in each calculation is a first order analysis The resulting internal forces form the basis of the next iteration step to calculate the geometric stiffness matrix describing the non linear behaviour As typical in civil engineering the modification of the internal forces is not considered in the following iteration steps for the generation of the geometric matrix Disregard of the modification of the main deflection This corresponds to the freezing of the axial bar forces after the first iteration step in connection with the two dimensional stability problem The iteration ends with the a iteration step If the defined loads are greater than the lateral buckling or lateral torsional buckling loads the load deformation problem can be solve
6. combination with the analysis as per NEN EN 1993 1 1 and NBN EN 1993 1 1 Equation for the permanent and the transient design situation Specifies which equation should be used for the structural safety analysis in the permanent or transient design situation Only in combination with the analysis as per NEN EN 1993 1 1 and NBN EN 1993 1 1 Specifications concerning the load introduction Load introduction stresses due to loading on the lower flange When underslung overhead cranes travel along the beam on wheels or trolleys the crane wheel loads or trolley loads apply eccentrically to the beam web Therefore secondary flange bending stresses occur in the proximity of the load application point in two directions The application calculates the local load introduction stresses for double T sections on the basis of the experimental and theoretical examinations of Hannover and Reichwald and superimposes these stresses with global axial beam stresses in accordance with the von Mises yield criterion The following options are available for this calculation No calculation A point load in z direction is considered as a force entity Calculation w o consideration of the load position The decisive load position underneath the travelling crane is calculated without consid eration of the secondary flange bending stresses A point load in z direction is interpreted as two force entities one acting on the left and the other on the right lower fla
7. concerning the calculation in reference 1 The superposition of global and local stresses is limited to the node points where the point loads apply to the flanges It is analysed separately for each flange side the top and bottom edge of the flange at the web flange transition points 3 4 at the load application points points 2 5 as well as at the flange edges points 1 6 The variable flange thickness of cross sections with inclined flanges section type 5 can optionally be taken into account According to 1 local stresses in the length direction of the beam ox can be reduced by 75 before superimposing them with the axial beam stresses The comparison stresses in the specified points in accordance with the von Mises yield criterion can optionally be calculated with or without consideration of shear stresses resulting from the Saint Venant s torsional moment portion BTII Lateral torsional buckling analysis 43 44 Lateral buckling of frame systems Problem The equivalent bar method as per DIN 18800 2 is an alternative calculation method for the verification of load bearing systems in second order analyses with inclusion of deformations This simplified verification is based on ideal bifurcation loads which are calculated on the straight beam in BTII The calculation of the ideal bifurcation loads is performed separately for each of the failure modes lateral buckling and lateral torsional buckling This approach has pr
8. rameter section BTII Lateral torsional buckling analysis 25 26 Loads Value Type Dir Ple Pri Flag ey ez Distances Remark Description Load types 1 to 8 Load direction 2 in direction of the y axis 3 in direction of the z axis Left load ordinate Distance to the left beam edge Right load ordinate Length of a load section Specifies how the distance to the load application point is defined See load appli cation points Distance of the load application point to the reference point in y direction Distance of the load application point to the reference point in z direction Click on the Edit button to display the dialog for the definition of the distances to the reference point with graphic support Comments concerning the load Frilo Structural analysis and design Load type ji Cancel 1 Uniformly distrib uted load 2 Concentrated load point load 3 Concentrated moment point moment 4 Trapezoidal load 5 Triangular load 6 Trapezoidal load over lo 7 Torsional region moment 8 Axial force The option displays the insert row for a load If you have already defined a load in this row it is deleted when you select this option A linear load that applies constantly over the total length of the beam A concentrated load apply ing at the distance a from the left beam edge A moment applying at a distance a from the left beam e
9. specified by the user no node is generated and the support string or individual load is displaced to the next closest node If this displacement is not acceptable for the analysis the user must subsequently adjust the minimum element extension accordingly and perform a new calculation Variable cross sections The application allows you to couple asymmetric cross sections You should note in this connection that the relative location of the centre of gravity and that of the shear centre do not coincide if different shapes of cross sections are used Since internal forces and defor mations refer partly to the centre of gravity and partly to the shear centre the principle of equilibrium in the strict sense is violated in the nodes This problem can be neglected with haunched beams however Thin walled open sections This option allows the user to define any open cross section in a freely selectable local system of coordinates Bearing capacity analysis E P IAW DIN 18800 1 This option allows you to utilize plastic bearing capacity reserves in a second order analysis First BTII performs a calculation of the three dimensionally pre deformed system After this the values of the yield function are calculated at each element end in accordance with DIN 18800 P 1 Eq 41 and Eq 42 using the extension for warping moments specified in 6 In addition to this the limiting values for the referenced shear forces vy Vy Vpl y and vz Vz Vpl
10. you must define high but not too high spring stiffnesses As a rule stiffness should be lt 10 In order to ensure the numerical stability of the calcula tion discrete stiffnesses intended as shift fixities should not be greater than strictly neces sary You can check this by verifying the kinematic constraint conditions in the cross section BTII Lateral torsional buckling analysis 19 Foundations Definition of foundation regions The term foundation in this context refers to continuous supporting conditions Foundation regions must be located inside the beam and must not overlap As with discrete elastic supporting conditions you can define a distance of the foundation region to the reference point Input values Value Description From x First coordinate of the foundation region Tox Last coordinate of the foundation region Type Type of foundation 0 elastic foundation 1 shear field stiffness cy Foundation modulus for translational foundation in y direction with type 0 elastic foundation with type 1 shear field stiffness Flag Control parameter for the specification of the distance of the application point of the cy foundation to the reference point 0 absolute distance to the reference point 1 factor to be multiplied with the section height Z cy Distance of the cy foundation to the reference point in z direction or factor for this distance CZ Foundation modulus for translational foundation in z direction wi
11. z are determined as required by DIN 18800 P1 Element 757 BTII Lateral torsional buckling analysis Settings The menu item gt Edit gt Settings displays a dialog for the adjustment of general settings and calculation parameters You can access this dialog also by double clicking on the menu item gt Settings Dimensions This dialog allows you to set dimensions and calculation parameters discretisation analyses and adjust output settings Dimensions This option allows you to set the desired units for dimensions forces etc The number of decimal places is set by the application according to selected unit The selected units apply also to the output Calculation parameters This option allows you to set the parameters for the discretisation of the system and the verification of the cross sectional bearing capacity Output profile In this section the user defines the profile for the output of the sections the system the loads and the results The output profile allows you to define the scope of the output Frilo Structural analysis and design System inputs Material and calculation parameters Design standard Allows you to select the design standard that constitutes the basis of the structural safety analysis When you select a national version of EN 1993 1 1 also the corresponding Na tional Appendix is used Material Steel grade Allows you to select the steel grade The following steel grades are curren
12. 0n n0nanun nun nun nun nnnnnnnnn nun nenn 39 Purlins with torsionally elastic support by the roof skin 22u0022000220002nnn ernennen 39 Trusses with torsionally elastic support by purlins 10 2 0 ccc ccc eecceeeeceeeeeeese esse eeseeesaeeeaaes 39 Trusses with elastic translational support at the top chord by purlins 39 Trusses with elastic torsional support by columns ccc cecccceecceeeeeeeeeeeeeeeceeeeeeeeaeeeaees 40 Beam with elastic warping SUPpOtt u220022002e0enenenenenenennnnnnnnnnnnnnnnenenenenenenenenennnnnnnnnnenn 40 Beam with shear field SUDPOMT cccceccceccceececeeeeseeceeeeeeeeeeaeeesseceseeeeseeeeseeeeseeetaeeetseeees 42 Lateral torsional buckling with a fixed axis Of rotation cccccccseccceeeceeeeeeaeeeeeeeeseeeeseeees 42 Torsion with solid cross S CTtIONS cccccccceecceecceseceeeceueceeeceeessueeceeesaeeseeecaeesaeecseesaeesaees 43 Stresses due to local beam loading 200022002220020n0nnenn anne nenne nenn ennnnenenneneneennnenn 43 Lateral buckling of frame systems 2220022402200022nnennnnennnnennnnennnnnnenennenennnne nenne nennen 44 Reference literature 2 2 2 einige trate ie a ee abi bass 46 BTII Lateral torsional buckling analysis Application options General scope of application The BTII application allows you to perform analyses of the ultimate and serviceability limit
13. LAIN CECI earann a E E 24 Specifications concerning the safety concept cece cecceeeeeeseeeeeeeesaeeesaeeesaeeeseneeseeeees 24 Specifications concerning the load introduction cccceececceeceeeeeeeeseeeeesaeeeeaeeeeeaaeeesees 24 Lodd CASES ee en re ee ee en 25 Load ease deiihlionease ee ei iled 25 LOG Se es ee ee ee ae 26 Definition of the distances to the reference point 0022200220000nnennnnnnnnnennnnennenenn 28 SUDELPOSIIONSens2288 1 2 ee een e 30 IMDEHEeIIOnS reani mre ee tice en ene ete nt Cee ere nee eee E ere 31 SUBELDOSNION TAGS ee taeda tena 32 Generating load case combinations s0242400200000080n0 neuen nenne nnnnne nennen nenne nnnnnenennnn 33 Design and analysis use ee 34 Galeulation paramelersa u nn nn 34 DISCESA UOM nanna ee 34 Types 6 gre 1g f Whol gt ic soturi a ea be ee eee 35 WethOd Ol Ealeulalon sen ee ee ee 35 OCLC ARE SPEER BEREELSFER a E EE a O REDE SEDEFRARELNT HERRN ER 37 Output of the results on the screen 2222002200020000nnne nenne nenn onennnnennnnnnn nenne nenne nenne nennen 37 Output of the system and the results for documentation 0022000220002nn0 nenn enennenenn 38 JEO PrO N One ee acne Cre NaN DN eR ME reer en MC a ee 38 Frilo Structural analysis and design SYSICHI ee ee ee ee 38 BOSSE ee ae eee eee ele 38 FRE SUS Se el este dg ea a ee 38 Notes concerning practical applications 2022002u002n
14. Lateral torsional buckling analysis BTIl User manual for Frilo design applications S Bending Torsion Theorem BTII 02H 2011 Position DEMO33 Project Frilo Examples Graphics File Edit Options wiew Help DEU RSG te evo 33 BB AQRA Sn M a M Mz OM 1 Ge T Gye Ae A gt Mm Superposition v Grafic of deformation v Sy System input gt Material gt Dimensions gt Supports gt Elast foundations amp Hinges E Text 2 43 Load input Load parameters Load cases Superpositions El Text 2 43 Settings Dimensions Calculation parameters Run computation Sy Output B Hs Output settings E Sections for output E System E Loads E Results Word I Screen amp Printer B Print preview 2 43 Tools Carrying capacity ST Projects EShinput Friedrich Lochner GmbH 2011 Frilo on the web www frilo com E mail info frilo com BTII manual 1 2011 BTII Lateral torsional buckling analysis 10 05 2011 09 40 L Contents Application oBLONS a een a 4 Basis Of Cal Cla OWN ccc rie ase ocean ee a 6 General notes Concerning BTIl scccceeeeeeeeeeeeeeeeeeeseeeeeneeseeneeeeeneesenneeeaenenseneeseeneeseaneess 7 SENOS tezaues Seecicaycnc tun cemaeacccutcearestccsgncoucageescsauaccanceesavaeadsnceaaesteeuesnacdstesatsamcageeceidiaccdacetsanteasunis 8 System INPUTS aa ea a E r 9 Material and calculation parameters ccccccceecceeeceeeceeeceeecee
15. N 1993 1 1 and takes the corresponding National Appendix into account The following National Appendices are available DIN EN 1993 1 1 NA NORM B 1993 1 1 NA to BS EN 1993 1 1 NEN EN 1993 1 1 NB NBN EN 1993 1 1 ANB CSN EN 1993 1 1 NA System definition The BTII application allows you to define any bar system composed of straight bars including cross sectional jumps and or haunches simple and double symmetrical T sections with and w o top flange angles U sections thin walled closed sections and any type of thin walled open cross sections discrete three dimensional supporting conditions with a distance to the shear centre definable as rigid supports or supports with discrete spring stiffness continuous three dimensional supporting conditions such as elastic foundation or shear field foundation also with a distance to the shear centre beam sections connected with shear force joints and moment joints Frilo Structural analysis and design Special notes concerning the system definition The material shows elastic behaviour The modulus of elasticity and the shear modulus are constant over the total beam The z axis is the symmetry axis for single symmetrical cross sections The finite elements have constant cross sections Haunches are calculated by approxi mation Loads load cases superpositions and deformations In BTII linearly variable line loads and point loads in direction of or a
16. ained by setting the virtual work of the elastic foundation equal to that of the shear field i S y8 v dx TER v dx When assuming a sinusoidal horizontal shift of the top chord with n half waves over the length of the beam E ee vv sin it follows ga NT a ern First perform the calculation of the elastic foundation c with n 1 Verify subsequently the elastic foundation on the basis of the shift of the top chord caused through this and or repeat the calculation with n gt 1 This approximation is sufficient in many cases of practical application Lateral torsional buckling with a fixed axis of rotation The problem of lateral torsional buckling with a fixed axis of rotation at a distance z from the shear centre often occurs in practice You can describe it in BTII as follows Define an elastic translational foundation in y direction with a stiffness 10E 8 to 10E 10 at the distance zo from the centre of gravity The resulting shift and torsion in regard to the centre of gravity and the shear centre are equal to zero along the pre set fixed axis of rota tion You can also use eccentric discrete springs to provide fixity C against lateral shift in the y or z direction at any point in the cross section For this purpose you ought to define high but WH not too high spring stiffnesses As a rule the stiffnesses should y be lt 10E 16 In order to ensure the numerical stability of the calculation discrete stiff
17. angles The reference point is the centre of the clear web height Z Thin walled open section The reference point is given by the zero point of the implicitly defined system of coordinates BTII Lateral torsional buckling analysis T section The reference point is the centre of the clear web height i Z User defined U section The reference point is the centre of the clear web height OR Z Square hollow section Round hollow section Steel dimensions This menu item allows you to define a cross section via its dimensions Select first the type of cross section double T U square etc The corresponding input fields for the dimensions are displayed The resistances are calculated by the application and displayed in the lower half of the screen Name Clicking on this button enables the Name field and you can edit the name of the cross section Read Clicking on this button loads a section definition file that you have previously saved with via the Write button Write Clicking on this button saves section definition data in an ASCII file Display all section values The option displays a window showing the structural design and geometry val ues Single syrrmeiriaa Edi dan Double T section with double Tsection top flange anges nnn pa 194 LOC 16 Frilo Structural analysis and design Structural values I A W This menu allows the user to define the
18. ant in practice you cannot describe the exact deformations of the general buckling torsion problem in a single closed system Therefore the beam is verified in accordance with the finite elements method which means that it is divided into a number of sections of different lengths finite elements The number of sections is pre set by the user The state of deformation within an element is described with the help cubic polynomials for the shift perpendicular to the bar axis and the distortion The elements are linked via the nodes in between them The elements have 6 degrees of freedom each at the left and right node Shift vand w in the y z direction Torsion Ox Oy Oz around the x y z axis Warping x Node loads and node deformations Cross sections in the system of coordinates Frilo Structural analysis and design General notes concerning BTII Moving loads You can optionally define node loads in the form of a load train The limit load positions for the first wheel in travelling direction must be specified by the user You can select among various criteria to define the target for the decisive load position For each load position a linear or non linear calculation of the beam is performed depending on the defined target If you select the maximum axial stress as a target value for the deci sive load position you can choose among two alternative criteria These are either the absolute maximum axial beam st
19. astic translational foundation in y direction with the stiffness 10 to 101 at the distance z to the shear centre The resulting shift and torsion in regard to the centre of grav ity and the shear centre are equal to zero along the pre set fixed axis of rotation Calculation of the foundation constants If the application S713 Shear Field Stiffness is installed on your computer you can launch it by pressing the F5 key in either of the input fields ctheta cy cz ST13 allows you to calcu late the foundation constants for trapezoidal sheet metal structures The application calculates the torsion spring c9 KNm m the ideal shear stiffness S kN as well as the translational foundation cy KN m These values allow you to take the stabilising effect of trapezoidal steel sheet sections into account In addition to this the application verifies the fixity against lateral shift and torsion If the verification is not successful an additional lateral stability verification is required In practice the verification whether the rotational foundation is sufficient is hardly ever successful A lateral torsional buckling analy sis is required in most cases The spring constants calculated by S773 can be transferred to the relevant applications such as BTII You should note in this connection however that the calculation in S773 is based on the simplified assumptions of DIN 18800 2 El 308 and El 309 These assumptions presume a constant doub
20. cross section Double symmetrical and single Double T with top flange angles symmetrical I section LCR a i ih a EN 1 F E T sections Solid cross section y TZ 2 U section as per DIN 1026 and user Thin walled open section defined U section M x 1 2 3 BTII Lateral torsional buckling analysis 13 14 Square hollow section Round hollow section 8 1 Reference points on the cross section If the shear centre of a standard section is known it is always the reference point of this section The following rules apply to user defined cross sections The reference point of single symmetrical l and T sections and single symmetrical I sections with top flange angles is always the centre of the clear web height The reference point of user defined U sections is the shear centre in horizontal direction and the centre of the clear flange height in vertical direction The reference point of thin walled open sections is given by the zero point of the coordi nate system which is implicitly defined when the user enters the cross section Double T section U section as per DIN 1026 The reference point is the shear centre The reference point is the shear centre s O M y 5 ya S 0 M Frilo Structural analysis and design Single symmetrical I section The reference point is the centre of the clear web height ya oo GF Poo Z Double T with top flange
21. cross section via the values for the structural calcu lation ly z It A Aqy z by hz and the values for the stress analysis Wy top Wz left W torsion Aty z The decisive resistance moments must also be specified If no values are entered no stress analysis is performed for the corresponding cross section BTII Lateral torsional buckling analysis Supports Definition of discrete supporting conditions Supports in this connection refer to discrete supporting conditions that are realised as rigid or elastic translational or torsional fixities Rigid supports in direction of the global degrees of freedom are defined by specifying 1 in the corresponding columns For elastic supports the absolute value of the spring stiffness must be entered Input values Value O O At x Cy OM m4 ee Cz theta x theta y theta z theta xy Distances Functions available via the tool bar Symbol Shortcut Description Ff 4 HH Hu 18 Description Distance of the support from the left beam edge Supporting condition for shift in y direction Supporting condition for shift in z direction Supporting condition for torsion around the x axis Supporting condition for torsion around the y axis Supporting condition for torsion around the z axis Supporting condition for warping Definition of the distances to the reference point Adds a supporting condition at the end of the list Ctrl I Inserts a supporting condit
22. d but the equilibrium becomes unstable in this state The determinant of the system stiffness matrix is negative in this case Therefore BTII aborts the calculation and displays a corresponding message If a load level was defined that is only slightly below the load level of the lowest eigenvalue smallest torsional buckling load deformations increase considerably In this case the results are useful only under certain conditions because the theoretical basis still describes the equilibrium of the deformed system but assumes only small deformations The forces and moments calculated in the 2 order analysis are already referenced to the major axis system Therefore no transformation is required for the subsequent stress ex amination Warping torsion Torsional loading on thin walled open sections is distributed via Saint Venant s torsion Mtp primary torsional moment and warping torsion Mts Secondary torsional moment The larger the fixity against cross section warping the larger the portion that is distributed via warping torsion and vice versa The fixity depends on the shape of the cross section and the behaviour of the torsional moments With solid cross sections and circular hollow cross sections for instance warping fixity is low The same applies to the area of torsional mo ments with constant behaviour Accordingly the load distribution via Saint Venant s torsion prevails In contrast to this the distribution via warping torsio
23. dge A linear load linearly vari able over the length applying at a distance a from the left beam edge A triangular load variable over the total length of the beam A trapezoidal load variable over the total length of the beam A torsional region moment applying over a length ata distance a from the left beam edge An axial force linearly variable over the length applying at a distance a from the left beam edge BTII Lateral torsional buckling analysis 2 28 Functions available via the tool bar Symbol Shortcut Description Adds a load at the end of the list Ctrl I Inserts a load above the active list item Ctrl D Deletes the active load Deletes all loads H 4 HH Hu en F5 Displays a dialog for the input of the distances Definition of the distances to the reference point Some loads extend over a particular area of the beam The distances are defined consis tently over the total area If required several loads must be entered The following rules apply to the input of distances 1 Linear loads extending in both directions y and z direction types 1 4 5 6 can be defined via a distance in the y direction and in the z direction These kinds of loads can produce a torsional moment 2 Point loads can be defined only via one distance in the load direction Therefore point loads cannot produce torsional moments except when applying to open polygonal cross s
24. do not comply with the combination rules of EN 1990 however BTII Lateral torsional buckling analysis 33 Design and analysis Calculation parameters The menu option gt Settings Calculation parameters allows you to set the parameters for the discretisation of the system and the analysis procedure Discretisation Minimum element extension min dx Specifies the minimum length of a finite element in the discretisation of the system The user can control the number of elements by specifying minimum and maximum element exten sions Minimum number of elements on the beam ne Specifies the minimum number of finite elements in the discretisation of the system The real number of elements could be considerably higher The quotient of the beam length and the minimum number of elements gives orientation for the element length in the beam sections As a rule the user should define between 5 and 15 elements in order to ensure that with average shift gradients the difference in the deformations is less than 5 compared to the exact solution The number of required elements depends on the gradient of the bending curve With steep gradients such as those of point loads individual springs and stiffness jumps and with elastic foundation in combination with stability critical loading the number of elements must be increased If you are unsure about the number of required elements simply perform a new calculation with refined eleme
25. e inclusion of imperfection half waves BTII Lateral torsional buckling analysis 31 32 Notes concerning the course of imperfection half waves The course of the imperfection half waves should correspond to the lowest mode shape of lateral buckling or lateral torsional buckling According to 6 you can alternatively define the imperfection in such a manner that the modal component is sufficiently great to achieve an approximation of the load deformation curve to the 1st eigenvalue Notes concerning verification as per DIN 18800 2 The amplitudes should be determined on the basis of the buckling curves a b c d as per DIN 18800 Part 2 and the direction of deflection y or z You should note in connection with the elastic elastic verification method as per DIN 18800 P 2 that the imperfection may be reduced to 2 3 according to table 3 In addition to this you may reduce the initial bow imper fections by 50 in the lateral stability verification according to Element 202 Functions available via the tool bar Symbol Shortcut Description a Adds a imperfection half wave at the end of the list Ctrl I Inserts a imperfection half wave above the active list item gt Ctrl D Deletes the active imperfection half wave rf Deletes all imperfection half waves Superposition factors No Consecutive number of the load case Load case Name of the load case Factor The factor for the inclusion of the load case in the load case comb
26. e s material b Projection can directly be modelled IT Saint Venant s torsional moment of inertia lo warping moment of inertia lu projection E modulus of elasticity G shear modulus C ec et m C Gly tanh Aly W Frilo Structural analysis and design c Column connection h beam height distance between the centres of h gravity of the flanges Ir Saint Venant s torsional moment of inertia of the ger OS column ee Open sections l Lic gt 5 x 3 Closed sections A S 2 The variables refer to 0 I Ge ap a Be a eh ur un Ve ee N ee lu a eo mag i Y 4 I I I 4 Si length of the i rectangle ti width of the i rectangle Am surface of the cross section enclosed by the section centre line Examples Ls t gt Tr y i H L b 4 oat to 2 2 ee 2bt ntz 4b hh t 2 b h BTII Lateral torsional buckling analysis 41 Beam with shear field support Purlins under roof plates are supported rigidly or elastically against lateral shift through the shear field stiffness at the height of the top chord In the current version BTII does not provide any options to describe the shear field effect exactly An approach by approximation can be achieved by converting the shear field stiffness S to an equivalent elastic foundation with the stiffness Cy applying at the top chord c The conversion is obt
27. e stresses resulting from the local load introduction and superim poses these stresses with the global beam stresses Local beam loading due to the opera tion of underslung overhead cranes is considered for double T beams with or w o top flange angles Calculation and analysis Verification of the cross sectional bearing capacity on the basis of elastic or plastic cross section values The calculation in accordance with DIN 18800 1 verifies the b t ratio on which the e e or e p verification is based In the calculation in accordance with EN 1993 1 1 the cross sections are classified Verification of the system s bearing capacity in a second order buckling torsion analysis or in a structural safety analysis on the basis of bifurcation loads for the failure modes lat eral buckling torsional bucking and lateral torsional buckling The analyses are subject to the following restrictions The BTII application only considers cross sections of class 1 to 3 The verification of a cross section of class 4 is not implemented in the current version Interfaces to BTIl A number of FRILO applications support the BTII interface which provides for the transfer of the system and the loads to BTII BTII Lateral torsional buckling analysis Basis of calculation The theoretical fundamentals of this application are described in detail in the reference literature particularly in reference 7 and 10 In the majority of the cases relev
28. ections 3 Point loads in z direction can be included as wheel loads acting on the lower flange Half of the value is assigned to the right flange and half of the value to the left flange The cor responding option must be set in the load parameters Note If a beam is composed of different cross sections you should be aware that the reference points may vary and with them the decisive distances to the centre of gravity or the shear centre of the cross section in question Frilo Structural analysis and design Load distances without loading on the lower flange Value Description Absolute The distance to the reference point is od distance defined via an absolute value ez or factor h Relative The distance to the reference point is Nele distance defined via a factor to be multiplied with the height of the cross section ez Distance of the load to the reference point in the z direction flag 0 Factor Factor for the distance of the load to the rE reference point in the z direction flag 1 ey The load applies at a distance ey to the reference point of the cross section Illustration Te f h 0 5 h X Load distances with loading on the lower flange Value Description ez the distance to The distance to the reference point is the reference point defined via an absolute value ey the distance to The load is defined as lower flange the outer edge ofthe loading with F 2 on each flange side
29. eeeeeeseeeseeeseesueeseeseesaeeeseeeaes 9 Designs and Ardasneea a 9 MAGETAN r seele ae 9 Analysis of the system s bearing capat ity uuusssuensseeneneenennennnnnnnnnnennnnennenennnneneennnenn 9 Analysis of the cross sectional bearing capatity uusnuuuunennnnnenneenennnenenne nenne nnnnne nen 10 Dimiensions an ans een ade nate Mode cee teed 11 EVER EOIR ne earl ee ere TEE need 11 EIOSSSELLONS ee een 12 Stress points OM the cross seclion anne an 13 Reference points on the cross section cccccecccceececeeceseeeceeeeeeeeeeauceseueesauceseueeseeeeaaaes 14 Steel dimensions s un ts neu nen 16 Structural W AU OS KA Vene 17 SUP POLL E E ee ee el ee eee ee 18 Definition of discrete supporting conditions 2 2022200222000en0nnnn nenne nenne nennenennenenn 18 Distances of discrete supporting conditions 022200222002200nnnnnnnnnnennn nenn enennenenn 19 Notes concerning the input of spring stiffnesses uu024400042nnennenne nenne nenne nnnnnnn nen 19 FOUNOALONS rate reisen leeren ee amceesoechacce 20 Definition of foundation regions 22u00222400nnnneenennnnnennnnnnnnn nenne nnennenennn nennen ernennen 20 DISTANCES of foundations faint seen ee 21 Notes concerning the input of fOUNCATIONS ccceececceeeeceeeeeeeeeeeeeeeeesaeeeesaeeeeseaeeesaeeeees 22 es a 216 I 1 ho serene tai ARENA et Pte eS tein tone eee en Be 23 INDUL OF LOADS 2er 24 Load A
30. he deformation diagrams freeman e pe e pe e pe o peere m femme 3 pen nem a om a Shear force behaviour in the selected point of the cross section Comparison stress behaviour in the selected point of the cross section Deformations The selectable options are shift distortion warping and 3D representation Pi ur T a oO Imperfections The selectable options are imperfection initial sway imperfec tion and 3D representation Kinematics figure BTII Lateral torsional buckling analysis 3 Load cases The loads assigned to the generated load cases are only displayed on the screen if the load case input dialog is active If so the loads associated to the currently active entry in the load case table are shown The displayed load values are those entered by the user Superpositions The loads assigned to the generated load case combinations are only displayed on the screen if the superposition input dialog is active If so the loads associated to the currently active entry in the superposition table are shown The displayed load values are the ones used in the superposition Imperfections The imperfections assigned to the generated load case combinations are only displayed on the screen if the superposition input dialog is active The imperfections associated to the currently active entry in the superposition table are shown You can define the scope of the output via the output profile Output of the sy
31. ination See also Automatic generation of load case combinations Note The superposition factor corresponds to the partial safety factor for actions in accordance with the partial safety concept Frilo Structural analysis and design Generating load case combinations General Under normal conditions superposition factors are defined in accordance with typical design practices In addition to this the user can benefit from the automatic generation of load case combinations This dialog allows you to generate load case combinations for all design situations and limit states in accordance with the combination rules of EN 1990 The settings concerning the safety concept in the Load parameter menu are taken globally into consid eration for the generation of the load case combinations Design situation Select the design situation for which you like to generate the load case combinations Limit states Select the limit state for which you like to generate the load case combinations Automatic generation of load case combinations The following combination rules as per EN 1990 apply to the combination of design situation and limit state Limit state i u Eq 6 10a and Eq 6 10b Eq 6 10a and Eq 6 10b P T Accidental A Eq 6 11a or Eq 6 11b E nn Quasi permanent qp The user can generate combinations of design situation and limit state that are not imple mented via an equation These combinations
32. ion above the active list item Ctrl D Deletes the active supporting condition Deletes all supporting conditions F5 Displays a dialog for the definition of distances Frilo Structural analysis and design Distances of discrete supporting conditions Click on the Edit button to display the dialog for the definition of the distances Value Description z Cy y Cz Distance of the elastic support to the reference point in y direction z Cy Distance of the elastic support to the reference point in z direction This input option is only available if a spring value was defined in direction of the correspond ing translational degree of freedom Notes concerning the input of spring stiffnesses Discrete spring stiffnesses describe the stiffnesses of the components connected to the examined beam e g purlins on top of beams horizontal beams on top of wall columns tension rods for purlins etc by approximation The application allows also the eccentric location of springs to provide fixity against lateral shift in y or z direction The locations are defined via their distance to the reference point The reference point depends on the defined section type however See Reference points of the cross sections The application converts the distances to the shear centre You can also use eccentric discrete springs to provide fixity against lateral shifts in the y or z direction at any point of the cross section For this purpose
33. ion factors for the bearing resistances which are required for the stability analysis BTII Lateral torsional buckling analysis 10 Analysis of the cross sectional bearing capacity Elastic elastic e e The design values of the internal forces calculated in accordance with the theory of elasticity are used to determine the axial and shear stresses acting on the cross section in accordance with the mechanics of materials These stresses are compared to the design value of the yield strength The structural safety of the cross section is ensured when the loading in all cross sectional parts is smaller or in the worst case equal to the design values of the resis tances The plastic bearing reserves are not taken into account When the calculation is performed as per EN 1993 1 1 the equations are based on the elastic cross sectional values This method is suitable for cross section classes 1 to 3 Elastic plastic e p The internal forces and deformations are calculated on the basis of the theory of elasticity The resistances are determined with utilization of the plastic bearing capacity The structural safety of the cross section is ensured when the design values of the internal forces do not exceed the limit internal forces in the plastic state There are three methods available for this verification 1 Analysis as per DIN 18800 1 Para 7 5 3 DIN 18800 1 describes in paragraph 7 5 3 a verification method for the struct
34. ion of imperfection half waves Vo Wo I o0 1 half wave 2 half Value Description Area Consecutive number of the imperfection half wave Dir Direction of the amplitude of the imperfection half wave 0 Cancellation of the input 1 Pre distortion around the x axis 2 Imperfection in y direction 3 Imperfection in z direction From x Coordinate of the front end of the imperfection region from the left beam edge Tox Coordinate of the rear end of the imperfection region from the left beam edge Amplitude y Amplitude of the imperfection half wave in the centre of the imperfection Vo region in y direction Amplitude z Amplitude of the imperfection half wave in the centre of the imperfection Wo region in z direction Amplitude theta xX Amplitude of the imperfection half wave in the centre of the imperfection 9x0 region around the x axis Inclusion of imperfections in the second order analyses only lf geometric and structural imperfections should be calculated in second order analyses geometric equivalent imperfections must be taken into account These are initial sway imper fections caused by angles of bar rotation for sway systems and initial bow imperfections in the form of sinusoidal or parabolic half waves for non sway systems Even though geometric equivalent imperfections are not defined in the form of an imperfect system geometry in design practice but for reasons of simplification via static equivalent loads BT allows th
35. le T cross section and beam supports on both sides of the beam Foundation regions extending over different cross sections must be divided accordingly When you transfer data from BTII to ST13 the cross section in the middle of the foundation region is considered to be relevant You can edit the cross section in S713 to modify it subsequently Frilo Structural analysis and design Pinned joints BTII allows you to define shear force and moment joints A degree of freedom is treated as a pinned joint if you set a check mark in the corresponding column To define amoment joint for My for instance tick the check box in the theta column Input values Value Atx V Ww theta x theta y theta z theta xy Description Distance of the joint to the left beam edge Shear force joint in y direction Shear force joint in z direction Moment joint around the x axis Moment joint around the y axis Moment joint around the z axis Warping joint Functions available via the tool bar Symbol ba HH Hu en Shortcut Description Adds a joint at the end of the list Ctrl l Inserts a joint above the active list item Ctrl D Deletes the active joint Deletes all joints BTII Lateral torsional buckling analysis 23 24 Input of loads Load parameters Specifications concerning the safety concept Consequence classes Allows you to define the consequence class the safety concept should be the based on CC1 CC2 or CC3 Only in
36. lect edit cross section is displayed allowing you to edit a previously defined cross sec tion Functions available via the tool bar Symbol Shortcut Description a Adds a cross section at the end of the list re Ctrl I Inserts a cross section above the active list item 2 Ctrl D Deletes the active cross section A Deletes all cross sections Selecting editing a cross section The dialog allows you to enter a new cross section or edit an existing one You can access the editing dialog via the cross section dialog F5 key In the left area of the screen the available input options are displayed F L section file Steel dimensions Structural values single or double symmetrical You can display the hidden submenu of the option F L section file for instance by clicking on the symbol or the 1 key In the right area of the screen you can either select the desired section or enter the dimen sions or the structural values Clicking OK confirms the entered values and closes the section selection window Reading writing cross sections You can save across section that you have defined via its dimensions for instance in an ASCII file by pressing the Write button and load this file by pressing the Read button The storage path is freely selectable The Name button activates the name field and you can edit the name of the corresponding cross section Frilo Structural analysis and design Stress points on the
37. n is predominant particularly at jumps in the torsional moments behaviour and at warping restraints BTII Lateral torsional buckling analysis 35 36 Axial warping stresses in the longitudinal direction of the bar and warping moments also referred to as bending moments occur due to warping fixity In stress analyses on open cross sections warping stresses resulting from warping torsion must therefore be considered in addition to the axial stresses caused by the axial force and the bending moments The equation for the total axial stresses is as follows N M M Mo Ox ee y Z 0 N axial force My Mz bending moments around the y or z axis on the deformed cross section M warping moment also indicated with Mw or B A cross sectional area Wy Wz section moduli around the y or z axis Io warping moment of inertia also indicated with Iw or C wo standard main warping also indicated with wy Equivalent bar analyses When using the equivalent bar method for the stability examination BT performs an eigen value calculation by applying the linear subspace method Frilo Structural analysis and design Output Output of the results on the screen Selection of the results to be shown in graphics The calculation results are displayed for the load case combinations not the individual load cases You can select the relevant load case combinations via the tool bar Another tool bar allows you to select the presentation of t
38. nce with the equivalent bar method is much more difficult in this case because you have to adjust the structural system of the equivalent bar via load conditions in such a manner that the effective length corresponds to that of the entire system To do this you have to calcu late corresponding spring stiffnesses The equivalent bar verification for lateral buckling requires a system modified in the described way It is particularly difficult to determine the corresponding rotational and translations springs and requires the consultation of expert literature This verification method and the prepara tive work involved are quite elaborate in comparison to the calculation of the frame system in second order analyses In the following examples the lateral buckling stability of the frame columns will be exam ined You will learn how to calculate the torsion spring constant and which structural system you have to enter in BTIl Frilo Structural analysis and design Example pinned and restrained frame Taken from Petersen Statik und Stabilit t der Baukonstruktionen 2 edition 1982 Publ Vieweg Verlag p 340 table 5 3 In the present example the lateral buckling stability of the frame column is examined q 10 0 kN m q 10 0 kN m IPE 300 IPE 300 I2 10 0 4 C 0 8 0 single storey sway frames with C 0 5 0 single storey sway frames with restrained column bases pinned column bases Parameters Effective length Cl 3
39. ned on the beam for each superposition To define such a travelling area the smallest and the greatest permissible x coordinate must be specified for the front wheel in travelling direction Limit load positions may be defined in such a manner that individual wheels are beyond the beam Functions available via the tool bar Symbol Shortcut Description Adds a load case combination at the end of the list Ctrl I Inserts a load case combination above the active list item Ctrl D Deletes the active load case combination Deletes all load case combinations i ki HH Hu Displays a dialog for the input of the imperfections Displays a dialog for the automatic generation of the load case combinations Frilo Structural analysis and design Imperfections General BTIl allows you to define imperfections in the directions of the both cross sectional major axes y and z as well as initial sway imperfections around the longitudinal axis of the bar In order to reduce input work in connection with the inclusion of imperfections you simply need to specify the zero points of the half waves and their amplitudes On the basis of these specifications the application calculates the magnitude of the imperfections in all node points in between the zero passages of the half waves The equivalent imperfection loads required for the 2 order analysis result from the multiplication of the imperfections with the geometric stiffness matrices Definit
40. nesses intended as shift fixities should not be greater than strictly necessary You can check this by verifying the kinematic constraint conditions in the cross sec tion z Frilo Structural analysis and design Torsion with solid cross sections The calculation of beams with solid cross sections such as glued laminated girders or pre stressed concrete girders requires particular attention in regard to the load distribution of torsional loading On thin walled open cross sections typical in steel construction the load is distributed via Saint Venant s torsion and warping torsion cross sectional warping fixity whereby the distribution depends mainly on the beam length and the type of loading On solid cross sections typical in reinforced concrete and timber construction the load portion distributed via warping torsion is very low and can therefore be neglected In BTII you can take this fact into account by setting the warping moment of inertia of the cross sections to zero when entering the data In this case the warping bimoments determined in the calculation of the internal forces acting on the bar end are equal to zero Stresses due to local beam loading When flange bending stresses apply due to the operation of underslung overhead cranes the global stresses calculated in accordance with the beam bending theory must be super imposed with the local bending stresses BTII handles this calculation as described in the notes
41. nge with a distance ey to the outer flange edge Calculation with consideration of the load position The decisive load position underneath the travelling crane is calculated with consideration of the secondary flange bending stresses The decisive load position results from the su perposition of the axial beam stresses with the load introduction stresses in x direction Point loads in z direction are handled as described above Type of point load If you have selected the option Moving load you must set the desired criterion of the decisive load position in the selection window The available criteria for the decisive load position are the minimum or maximum internal forces or the greatest absolute axial stress or comparison stress If you select the maximum axial stress as a criterion for the decisive load position you can choose among two additional options These are either the absolute maximum axial beam stress or the greatest absolute stress considering the load introduction stresses if the corre sponding option was selected If you select the comparison stress as a criterion for the decisive load position this criterion also includes the secondary flange bending stress in x direction if applicable Frilo Structural analysis and design Load cases Loads are always defined in combination with load cases This means that all loads assigned to the same load case are always caused by the same action and always considered to act
42. nts If the results differ considerably perform another calculation with even more refined elements Discretisation of the system The beam is described by its areas and one or more cross sections This allows the user to define cross section jumps and haunches For the calculation however the beam must be divided into sections with constant cross sections Haunches are represented by a suitable number of similar cross sections with gradually increasing sizes In the discretisation process the node mesh is first generated from the front and rear end coordinates of the beam regions Due to the fact that BTII displaces node loads supporting conditions region borders as well as the zero points of the imperfection half waves auto matically to the next closest node additional section borders have to be defined in these points This will only happen however if the distance between the section border to be inserted and the existing section borders exceeds the specified minimum size The minimum size is defined via the minimum element extension Frilo Structural analysis and design Types of analyses Elastic ultimate resistance This option allows you to specify whether the shear stresses resulting from Saint Venant s torsion and warping torsion should be considered in the calculation of the comparison stress Plastic ultimate resistance IAW DIN 18800 1 DIN 18800 1 EI 755 specifies that limit bending moments in the plastic state should
43. oven its worth for beam and column systems that typically comply with the Euler bucking modes Where frame systems are concerned the calculation is often based on second order analyses The second order analysis provides for lateral buckling in the plane of the frame under normal conditions The lateral torsional buckling failure mode must be examined separately however This examination is based on a simplified verifica tion in accordance with the equivalent bar method Equivalent bars for lateral torsional buckling analyses In order to verify a bar in a sway or non sway frame system in accordance with the equiva lent bar method you have to extract it from the total system A single span beam with fork supports is assumed for the examination of the lateral torsional buckling failure mode The bar end moments which result from the calculation of the basic frame in a first or second order analysis are applied to the single span beam in accordance with the behaviour of the internal forces The span moments can be calculated in first order analyses The load bifur cation factor is calculated numerically for the structural system generated this way producing the basic value M iy for the equivalent bar method Equivalent bars for lateral buckling examinations Under normal conditions the verification of the lateral stability of frame systems is included in the second order calculation of the internal forces The simplified verification in accor da
44. ress or the greatest absolute stress considering the load introduction stresses described below The application calculates automatically deforma tions internal forces and stresses for the decisive load position in first and second order analyses Local beam loading When underslung overhead cranes travel along the beam on wheels or trolleys the crane wheel loads or trolley loads apply eccentrically to the beam web Therefore secondary flange bending stresses occur in the proximity of the load application point in two directions The application calculates local load introduction stresses on the basis of 1 and superim poses them with the global beam stresses in accordance with the von Mises yield criterion The experimental and theoretical examinations by Hannover and Reichwald form the basis for the consideration of local beam loading caused by the operation of underslung overhead cranes in the BTII application In the current version this type of calculation can be per formed on double T beam cross section types Coordinates for supports springs and concentrated point loads The locations of supports discrete springs concentrated loads element borders as well as zero points of imperfection half waves are defined by specifying the x coordinate Internally the application generates nodes at supports springs loads and deformation zero points If the distance of a node to the relevant point is smaller than the minimum element extension
45. round the y z axis as well as bending torsional and warping moments can optionally be defined Loads that pro duce axial forces cannot be put out directly To compensate for this restriction you can define constant or linear variable axial force curves Additional bending moments that result from an offset of the centre of gravity must be defined explicitly by the user The loads are assigned to load cases All loads that are member of the same load case are considered to act always simultaneously The load case defines the action that produces the loads and indicates in addition how it is to be handled in the automatic generation of the load case combinations The user can generate load case combinations either automatically with the help of an assistant or define them manually on the basis of typical design practices For second order analyses imperfections are taken into account To include them in the form of initial bow or initial sway imperfections you simply need to specify the zero points and the amplitudes of the sinusoidal or parabolic half waves Moving loads You can optionally define node loads in the form of a load train Local beam loading When overhead underslung cranes travel along the beam on rails or wheels crane wheel loads or trolley loads apply eccentrically to the beam web Therefore secondary flange bending stresses occur in the proximity of the load application point in two directions The application calculates th
46. section measured from the left beam edge Tox X coordinate of the end of the beam section measured from the left beam edge Index referring to the cross section assigned to the left edge of the beam section Index referring to the cross section assigned to the right edge of the beam section bo Length of the beam section You can divide the beam into several sections This allows you to describe cross sectional jumps and haunches Haunches can be defined for the following section types Standard sections User defined double symmetrical sections User defined single symmetrical I sections User defined single symmetrical I sections with top flange angles User defined U sections Functions available via the tool bar Symbol Shortcut Description M Adds a beam section at the end of the list mis Ctrl Inserts a beam section above the active list item gt Ctrl D Deletes the active beam section Mr Deletes all beam sections Te F5 Displays the cross section selection dialog BTII Lateral torsional buckling analysis 11 Cross sections Defining new cross sections Click into the next empty table cell in the column Name Press the F5 key or type ina name for the cross section The dialog Select edit cross section is displayed offering sev eral options to select or define a cross section Editing cross sections Click onto the name of the cross section that you like to edit Press the F5 key The dialog Se
47. sheet must be taken into account in addition See also Lindner 5 Trusses with torsionally elastic support by purlins The spring stiffnesses are calculated as described above It must be distinguished between centre trusses and edge trusses Trusses with elastic translational support at the top chord by purlins The stiffness of the horizontal equivalent spring results from the compliance of the horizontal roof structure in the edge spans If required also the slip in the connectors must be taken into account For more information concerning the calculation of equivalent stiffnesses in different types of structural framework see Rubin Vogel 12 for instance BTII Lateral torsional buckling analysis 39 40 Trusses with elastic torsional support by columns Est modulus of elasticity of the column IStz moment of inertia of the column around the z axis h height of the column section a restraint value depending on the support of the column base around the weak axis a 4 restrained a 3 pinned The supporting effect is low under normal conditions Beam with elastic warping support AE ilar oy by The free warping fixity increases the torsional stiffness of beams with thin walled open cross sections In the following we are going to give you some information about the calculation of discrete warping springs Cw in three frequent cases of warping fixity a End plate G shear modulus of the end plat
48. states of steel bar systems with any types of supports The steel bars may have open or closed cross sections with thin walled members The most important features of BTII are the following Calculation of internal forces elastic deformations and axial and shear stresses on uni formly or three dimensionally loaded beam systems with consideration to warping torsion in second order buckling torsion analyses Calculation of the ideal bifurcation loads for the lateral buckling and lateral torsional buckling failure modes as well as determination of the slenderness ratios and the reduc tion factors for stability analyses in accordance with the equivalent bar method Optional definition of moving loads to examine crane runways for instance in the ulti mate and serviceability limit states Calculation of secondary flange bending stress considered as local beam loading due to eccentric loading on the lower flange Special applications Purlins supported by the roof skin with or without pin joints Ledgers supported by purlins or trapezoidal steel sections Columns supported by the wall lining and or bracing Stability verifications of craneway beams with or without horizontal bracing Determination of the ideal bifurcation loads for the calculation of buckling slenderness ratios in concrete and timber construction Design standards The BTII application performs structural safety analyses in accordance with DIN 18800 and E
49. stem and the results for documentation Output profile The output profile offers comprehensive adjustment options that allow the user to control the scope of the documentation Output sections The application determines automatically the verification points at which the design values stresses and structural safety verifications are put out The user can define additional output sections by specifying the corresponding x coordinates System This option allows you to specify the parameters that should be put out for the system Loads This option allows you to specify the loads that should be put out and select whether they should be put out as text or graphic Results This option allows you to set the desired output parameters separately for each superposi tion Frilo Structural analysis and design Notes concerning practical applications Purlins with torsionally elastic support by the roof skin Forf skin Centre punins Edge pirin Lirection of span of the roof gd gd E ED modulus of elasticity of the roof skin ID moment of inertia of the roof skin per length unit The transfer of the moment between the purlin and the roof due to contact or loading on the connectors is to be verified See also Vogel Heil 13 If the moment to be transferred exceeds the contact moment created by the drift of the load application point to the flange edge the compliance of the connection between the purlin and the trapezoidal
50. th type 0 elastic foundation in z direction with type 1 no specification Flag Control parameter for the specification of the distance of the application point of the cz foundation to the reference point O absolute distance to the reference point 1 factor to be multiplied with the top flange width y cz Distance of the cz foundation to the reference point in y direction or factor for this distance ctheta Foundation modulus for the rotational foundation around the x axis Distances Click on the Edit button to display the dialog for the definition of the distances to the reference point with graphic support Frilo Structural analysis and design Functions available via the tool bar Symbol Shortcut Description E m k HH Hu en and rotational foundation Distances of foundations Adds a foundation region at the end of the list Ctrl I Inserts a foundation region above the active list item Ctrl D Deletes the active foundation region Deletes all foundation regions F5 Displays a dialog for the definition of the distances Launches the FLS73 application if correctly installed and licensed FLS13 allows you to calculate the values for translational shear field Foundation regions extend over a particular area of the beam The distances are defined uniformly over the total region If required several foundation regions must be defined Graphic representation The graphic representation of the selected foundation region ei
51. ther shows the total region or a discrete point on the beam Tick the option x coordinate to display the representation at the point xO Otherwise the entire foundation region is shown Distance in z direction a k Value Description Absolute The distance to the reference point is defined z ey Factor h distance via an absolute value 7 Relative The distance to the reference point is defined distance via a factor to be multiplied with the height of the cross section Z cy The distance of the cy foundation to the refer Vz ence point in z direction Factor The factor for the distance to the reference point in z direction Illustration BTII Lateral torsional buckling analysis Taten f h 0 5 h 21 Distance in y direction Value Description Absolute The distance to the reference point is defined distance via an absolute value Relative The distance to the reference point is defined distance via a factor to be multiplied with the height of the cross section y cz The distance of the cy foundation to the refer ence point in y direction cz Factor The factor for the distance to the reference Vz point in y direction Notes concerning the input of foundations Defining a fixed axis of rotation The problem of lateral torsional buckling with a fixed axis of rotation at a distance z from the shear centre often occurs in practice You can describe it in BTII as follows Define an el
52. tly implemented Hot rolled non alloy structural steel Hot rolled structural steel normalized Hot rolled structural steel thermo mechanically rolled Hot rolled weatherproof structural steel High temperature steel Hot finished hollow sections User defined steels Steel quality Allows you to select the steel quality depending on the selected steel grade User defined If you have selected User defined steels among the steel grade options a dialog for the definition of the user defined parameters is displayed Analysis of the system s bearing capacity 1 order analyses Internal forces deformations and stresses are calculated in first order analyses The bearing capacity of the system cannot be verified in this type of analysis 2 order analyses Internal forces deformations and stresses are calculated in second order buckling torsion analyses whereby the imperfections are taken into account Evidence of the system s bear ing capacity is established via the verification of the cross sectional bearing capacity Equivalent bar method When using the equivalent bar method for the examination of the lateral buckling and lateral torsional buckling behaviour BTII performs an eigenvalue calculation by applying the linear subspace method The resulting ideal bifurcation loads Nxiy Nxizand Myiy are used to calcu late the corresponding effective slenderness ratios These ratios allow the calculation of the relevant reduct
53. ural safety of double symmetrical I sections This method is extended by the terms for torsion and warping However it is limited to the analysis of standardised or user defined double symmetrical I sections 2 Analysis as per EN 1993 1 1 Para 6 The structural safety verification of cross sections is stipulated in EN 1993 1 1 Para 6 The terms elastic elastic method and elastic plastic method are not included in EN 1993 1 1 The related verification equations take the classification of the cross sec tions into account and refer to the elastic or plastic cross sectional values that are de termined by the class of the cross section classes 1 to 4 When you select the elastic plastic verification method the verification equations are based on the plastic cross sec tional values This method is suitable for cross sections of the classes 1 and 2 3 Partial internal forces method according to Kindmann The partial internal forces method by Kindmann allows you to verify any type of hvh beam hvh refers in this connection to a cross section of the horizontal vertical horizontal type This means that any type of cross section with two or three limbs flanges and webs perpendicular to each other can be verified on the basis of plastic limit internal forces Frilo Structural analysis and design Dimensions System definition Definition of the beam sections System sketch Om Dun O O O X coordinate at the beginning of the beam

Lateral torsional buckling analysis BTII

Contents

Download Pdf Manuals

Related Search

Related Contents