tonus - Scad
Contents
1. Use the Numbering button 5 to have the vertices numbered in the section s view 1 3 13 Table of strips The table of strips is very similar to the table of vertices Fig 13 Each row of the table contains information about one strip The information consists of Nos of vertices at the beginning and end of a strip accompanied by connection checkboxes and of a thickness of the strip T The table can be filled in either automatically as you use graphic tools to add strips or directly by entering s dmm coordinates of new strips to it In the latter case you should click the button before you can specify a strip this will add a new row to the table in which you specify the data for the new strip If a strip is stiffly attached to other strips at its vertex its respective connection checkbox wil be turned on when you add strips with graphic tools the checkboxes are turned on by default A disabled checkbox means there is no connection between this particular strip and other ones that come into the same vertex cO 020 Iss II LS Oo c 0 M Fig 13 A table of strips By default the thickness of every new strip is set equal to a value specified with the Thickness button a The thickness can be modified when adding new strips or by editing in the table To change the thickness of multiple strips select the respective rows in the table and click the Fill Thickness button El2. ppm If necessary a selected table of profiles can be exported as RIF file to a word processing application associated with this format the Report button w If a catalogue or database rather than a group of profiles is selected for printing then all profile tables of that catalogue database will be printed out The setup of the view print mode the Settings button 3 ELE CELER EET ED E EE Rae HHHHHHHHHHHHRHHHHHHHHHHHIHH f PEPPAR BEEEE 2 follows the same conventions as those the applications described earlier Fig 23 Viewing a profile 22 User manual endices Bt 200 1 Fig 24 23 wv K gt The Find dialog box To search for a profile that matches certain geometric characteristics the Find button use a dialog box under the respective name Fig 24 In the text fields of the Search criteria group you put down characteristics minimum and maximum of a profile to use as search criteria Clicking the OK button will start the search If one or more profiles matching the specified characteristics are found their names will be displayed in the Search results list As you select one of the found profiles in the list and click the Go button the selected profile will be highlighted in
3. If the Snap To Grid mode Is enabled then the vertices will snap to a nearest coordinate grid node The new vertices will be added to the table of vertices Use this action to add new vertices without adding any strips To do it point at a desired location 1 3 7 Delete a vertex When this action is invoked you need just to point at a vertex with the mouse and left click to delete it All strips than join it will be deleted together with the vertex The vertices and strips will be deleted also from the tables 1 3 8 Snap to grid When this mode is active vertices being added will snap i e will be automatically moved to a coordinate grid node nearest to the pointer 8 User manual Tonus 1 3 9 Smooth an angle BE ff Smoothing radius Fx An angle can smoothed by inscribing a circular arc of a given radius in it After you invoke the action point at a corner of the contour with the mouse wait for the E smoothing action cursor to appear and left click In the Rounding Radius dialog box that opens Fig 9 specify a Fig 9 The Rounding Radius radius and click the OK button Fig 10 a shows a section in dialog box the form of a contour with its corners smoothed and Fig 10 b shows the same section with the Show Thickness mode ow ve enabled The number of points vertices on a circular arc is i set on the Other tab of the Settings d
4. 211 Channel UPN NF A 45 202 Channel UPN A NF A 45 202 Channel UAP NF A 45 255 Channel UAP A NF A 45 255 Pipe rectangular Pipe round DIN 2448 List of sections of ARBED Equal angle per 56 77 26 User manual List of welded profile assortments Welded double T per TU Y 01412851 001 95 List of sections in the Indian assortment Equal angle Double T ISLB List of sections in the Japanese assortment 27 User manual Appendices SS List of sections in the assortments of zinked steel cables per GOST Cable locked coil load bearing with two layers of Z shaped wire and a TK type core GOST 18901 73 Cable double lay LK RO type TY 14 4 902 78 Cable locked coil load bearing with one layer of Z shaped wire and a TK type core GOST 3090 73 Cable locked coil with one layer of wedge and Z shaped wire and a TK type core GOST 7675 73 Cable locked coil with layers of wedge and Z shaped wire and a TK type core GOST 7676 73 Reinforcement cables of Class K 7 per GOST 13840 68 Reinforcement cables of Class K 19 per TU 14 4 22 71 Reinforcement of Class A VI per GOST 5781 82 28 User manual References 3 1 References E A Beilin A version of a unified theory of torsion of thin walled bars having open closed and partially closed profiles Researches on mechanics of structural constructions and materials Collected topical works of universities Leningrad Civ
5. be actually moved to the specified point after you click the Apply button Fig 11 The Coordinate Origin dialog box 1 3 12 Table of vertices To add delete or edit the coordinates of existing vertices you can use a table placed on the table panel and opened when you click the respective button on the toolbar A number of buttons is used to control the table editing process the buttons are found under the table itself Fig 12 The table can be filled in either automatically as you use graphic tools to add vertices and strips or directly by entering coordinates of new vertices to it In the latter case you should click the button before you can specify a vertex this will add a new row to the table in which you enter the coordinates for the new vertex 10 User manual Tonus The results of editing the table will be displayed in the working area only after you click the Apply button vj To delete vertices you select the respective rows in the 2201 2 346 table and then click the button vertices in the von section s view will be highlighted but deleted only when you 11000 20000 click the button vi To remove the highlighting from the 18000 wo selected vertices click the button To select one or more successive rows place the pointer v X X N onto No of a row click and hold the left mouse button and drag the pointer to the last row you want to delete Fig 12 A table of vertices S SP y
6. do the action select a tab of respective measures Length Area etc The conversion procedure depends on whether the units are simple such as length area or time or compound such as pressure velocity or specific weight 222 To convert simple unit you just enter a number in one 22 E 2 9 of the text fields Its respective values in all the other units will WTHNO n be displayed automatically If the unit is compound select units 117200 Mis to convert from in the drop down lists of one row and select 1772 ma units to convert to in the lists of the other row Next enter a number in the edit field of the first row and see the conversion result in the second row field Nc B Pon H Fig 21 The Convert Units Of Measurement dialog box 2 3 3 21 User manual Appendices 2 3 4 Rolled profile catalogue browser The browser can be started from the SCAD Office folder on the desktop and used to browse through rolled steel profile databases catalogues The browser s w
7. the section table User manual Appendices MES 2 4 List of assortments databases of rolled profiles shipped with the software package Channel with oblique webs per GOST 8240 89 Double T for columns K per GOST 26020 83 Double T with oblique webs per 8239 89 Double T of additional series D per GOST 26020 83 Double T normal B per GOST 26020 83 Roll formed equal web channel per GOST 8278 83 of steels C255 C275 Double T wide flange per GOST 26020 83 T shape for columns KT per TU 14 2 685 86 Angle equal per GOST 8509 93 T shape ShT per TU 14 2 685 86 Pipes electric welded longitudinal per GOST 10704 91 Angle unequal per GOST 8510 86 Channel with parallel web faces per GOST 8240 89 Pipes per GOST 10704 91 shortened Pipes steel seamless hot formed Roll formed equal web channel per GOST 8278 83 of steels C239 C245 les Channel with oblique webs per GOST 8240 97 List of sections of the GOST abridged database Channel B per GOST 5267yu1 90 Double T for columns K per GOST 26020 83 mns Square pipes per TU 36 2287 80 Rectangular pipes per TU 67 2287 80 Channels economical with parallel web faces per GOST 8240 97 Channels of lightweight series with parallel web faces per GOST 8240 97 Channels special per GOST 8240 97 Channel with parallel web faces per GOST 8240 97 3 E 24 User manual Appendices List of sections of the assortment of Chelyabinsk Inte
8. In the Thickness dialog box that appears specify a new value and click the Apply button To delete selected strips table rows use the Delete button x To select one or more successive rows place the pointer onto a No of a row click and hold the left 11 User manual Tonus mouse button and drag the pointer to the last row you want to delete The results of editing the table will be displayed in the working area only after you click the Apply button Use the Numbering button to have the strips numbered in the section s view 1 3 14 Flexural center blue This button turns on the visibility of a section s flexural center 1 3 15 Show no thickness Depending on whether this button is depressed or not the working area will display either a whole section if the button s depressed or just a contour of it that is the median lines of the strips Figs 14 a and 14 b respectively Dral die I Lia mam um b Fig 14 A section displayed in the working area 1 3 16 Snap to vertices If this is enabled the distance measurement will be bound to nearest vertices i e only the distances between vertices of a section can be measured 12 User manual Tonus 1 3 17 Standard sections Standard sections To create a section you can use a set of standard parametric sections profiles Use the Create Standard Section item from the File menu This will open a dialog box Fig 15 which contains a
9. Jo 0 6 Z m dydz Q The Moz U11 quantities are central moments of inertia with respect to the Z Y axes and cetrifugal moment of inertia respectively 2 1 2 Principal moments of inertia a slope of principal axes The principal moments of inertia are calculated by this formula I I L LY BUSES LI 7 2 idi This is a slope of the principal axes of inertia a arctg In the last formula you should substitute to its right part to find a slope of the axis of the maximum moment of inertia to find a slope of the minimum inertia moment axis substitute Note The Konsul application does not confine you to working with an area bounded by polygons curves are also allowed these may appear when you use the Smooth an angle or Make a round orifice actions In the latter case the application will replace the curve by a polygonal line to do the calculation 2 1 3 Radii of inertia 1 P J 2 j tu P 1 Sale 4S5 A A A A 14 User manual Appendices MEE 2 1 4 Moduli of section Axial moduli of section 1 W W 2 W 2 W where Umax Umin Vmax Vmin are respective maximum distances from points of the section s exterior boundary to the U V axes on one and the other sides Polar modulus of section max where pmax is a maximum distance from points of the section to its center of mass The I quantity is called a polar
10. SCAD Group Structure CAD software pack tor Windows NCAD TONUS application is used to build thin walled sections and calculate their geometric characteristics User manual Tonus Table of contents 1 3 ONUS 4 1 1 Window of the application 5 1 2 5 1 3 Creating a section 6 Appendices 14 2 1 Definitions of geometric characteristics 14 2 2 File formats 18 2 3 Service 1 20 2 4 List of assortments databases of rolled profiles shipped with the software package 24 29 User manual Tonus 1 Tonus The Tonus application is used to build thi
11. cing and the Angle 0 degree slope of the grid in degrees with respect to the horizontal axis The grid is rotated about the coordinate origin X Cancel Fig 4 The Grid Properties dialog box 6 User manual Tonus Note that the grid spacing and its slope can be varied as many times as needed during the creation of the section s interior contours or editing of the exterior one The grid will be displayed as soon as you finish entering its properties Fig 5 Its visualization is turned on and off by the Grid button i on the toolbar Bem deere nl mm Fig 5 grid displayed in the working area 1 3 2 Overall dimensions ie A section is created on a coordinate grid the overall abii dimensions of which match those of the section The overall o dimensions are specified in the dialog box under the same nr 215 100 mm arie i didus name Fig 6 in units of measurement defined on the Fig 6 The Overall Dimensions respective tab of the Settings dialog box dialog box A rectangle that bounds the section a dimension box Fig 7 is displayed in the working area Values of the section s overall dimensions are displayed in the first field of the Status Bar As long as no element is created in the sections area the status bar will display the specified dimensions As you add elements to the section the field will display the actual current overall dimens
12. cipal axes that act in the section u v are coordinates of a point in the section s principal axes 17 User manual Appendices I 2 2 File formats 2 2 1 Konsul application The application is capable of importing sections created by other software In particular Konsul can import files of the CON format which can be created for example by the SCAD system 5 CON files are plain text ones of the following structure 0 asection is defined as a set of polygons first polygon is an exterior contour and the next ones if any define orifices interior contours o each polygon both exterior and interior must be defined in the following format e first line is an integer number n defining the number of vertices in the polygon e next go n lines each one containing three floating point numbers coordinates of a vertex in the section s plane and a radius of the rounded corner in that vertex the latter number may be absent when there is no rounding All sizes are specified in meters The numbers in a line are separated by spaces The decimal separator is a period Example A section shown in Fig 18 is described in the CON format as follows 3 0 000 0 000 3 000 1 000 6 000 1 000 S 9 000 0 000 10 000 3 000 10 000 6 000 9 000 9 000 6 000 10 000 3 000 10 000 0 000 9 000 1 000 6 000 4 CT p 3 000 3 000 6 000 3 000 6 000 6 000 3 000 6 000 Fig 18 18 User manual Appendices 2 2 2 T
13. file thin walled bars more than to closed profile ones A theory for analysis of bars of this type for the open and closed profile case was developed by V Z Vlasov 2 and A A Umansky 6 7 see also 4 The Tonus application lets you deal with any arbitrary including mixed open closed profiles it makes use of a version of a unified theory of thin walled bars suggested by E A Beilin 1 Unlike the Section Builder and Konsul applications this software implements another approach to the creation of a cross section model The application assumes that a section is thin walled and is being built of strips the user specifies a thickness of each strip and a position of its median line Fig 2 4 User manual Tonus 1 1 Window of the application The Tonus application window Fig 3 contains a menu a toolbar a working area with scrollbars when necessary a table panel and a status bar 4 TONUS Tonus N File Edit Settings View Window Help Ds Py H 81 1 11 0 1 27 E 18 A xl No hi E mm mm 1 20 2 20 70 Ea 35 30 B5 90 5 80 70 80 10 7 65 10 8 65 45 9 40 45 10 40 65 60 65 p Mo From vertex To vertex Thickne H E PARREREN Ei EEE oo 1 MN Siu 4 7 oo m M miu a s 555558 E EE 5 7 ma c
14. grated Iron And Steel Works List of sections of old assortments Angle equal per OST 14 1926 Angle equal per OST 14 1932 Angle unequal per OST 15 1926 Double T H beam per OST 16 193 Channel with oblique webs per OST 17 1933 H beams per OST 10016 39 Angle unequal per OST 15 1932 Channel per OST 10017 39 Channel with oblique webs per OST 17 1926 Double T Universal Beams to BS4 Double T Universal Columns to BS4 Double T Universal Bearing Piles to BS4 Angle equal per OST 10014 39 Angle unequal per OST 10015 39 Double T ASTM Shapes List of sections of Great Britain assortments standard profiles Double T H beam per OST 16 1926 Double T Euronorm IPE Sections Pipe rectangular EN10210 UK List of sections of Great Britain assortments imported profiles Double T Euronorm HE Sections Pipe rectangular EN10210 OS Pipe round EN10210 OS no List of sections in OTUA Equal angle NF A 45 009 Unequal angle NF A 45 010 Double T with oblique webs NF A 45 210 Double T with parallel webs NF A 45 206 25 User manual Pipe square EN10210 OS Appendices Double T with parallel webs NF 45 206 Double T with parallel webs NF A 45 206 Double T with parallel webs NF A 45 206 Double T with parallel webs NF A 45 211 Double T with parallel webs NF A 45 211 Double T with parallel webs NF A 45 211 Double T with parallel webs NF A 45
15. ialog box a B pe pm dames almi xd Daum 5 RE rint Rs BE Fesh re en i lod P m Fig 10 An example of a section with its angles smoothed 9 User manual Tonus 1 3 10 Move a group of selected vertices This action is used to move a group of vertices selected with a rectangular marquee To do the move action follow these steps V invoke the action i capture the vertices to be moved with the rectangular marquee drag the marquee into a new position together with the vertices it captures To confirm the new position of the vertices left click 1 3 11 Move the coordinate origin This action is used to move the coordinate origin to a point with known coordinates to a vertex or to the center of mass of a section Fig 11 The application can calculate such things as the moments of inertia with respect to a custom coordinate system not only the principal axes therefore the capability of moving the coordinate origin can be useful in geometric analysis If you need to move the coordinate origin to the center of Fa iD RUSO Pe 2324 mass or to a particular vertex click the red cross button or y 48 174 mm choose No of the vertex from the drop down list respectively z 58250 mm X Cancel This will put the required coordinates into the edit fields The coordinate origin will
16. il Engng Inst 1991 pp 57 74 In Russian V Z Vlasov Selected works Vol 2 Moscow USSR Acad Sci Publishing House 1963 In Russian G Y Janelidze On a theory of thin and thin walled bars Appl Math And Mech 1949 XIII N6 597 608 In Russian G Y Janelidze Y G Panovko Statics of elastic thin walled bars Moscow OGIZ Publishers 1948 208 p In Russian V S Karpilovsky et al SCAD Office The SCAD computing system V S Karpilovsky E Z Kriksunov A V Perelmuter M A Perelmuter Moscow ASV Publishers 2004 596 p In Russian A A Umansky Bending and torsion of thin walled aircraft constructions Moscow Oboronizdat 1939 112 p In Russian A A Umansky Analysis of thin walled curvilinear beams Proc Sci Conf of Zhukovsky Air Force Academy Vol 2 1944 In Russian A P Filin Applied mechanics of deformable solids Strength of materials with basics of continua theory and structural mechanics Vol 2 Moscow Nauka 1978 616 p In Russian V S Karpilovsky E Z Kriksunov Malyarenko M A Mikitarenko Perelmuter M A Perelmuter V G Fedorovsky SCAD Office Implementation of SNiP codes in computer aided design applications Moscow ASV Publishers 2004 288 p In Russian
17. indow Fig 22 contains a list of the databases and a table of profile properties To see a table of profiles of a certain type you should open a list of profiles of a respective database and choose the name of a group of your desired profiles in it To get a picture of a profile of particular dimensions you should open the profile group s list and choose a desired Ms n E profile in it Fig 23 i e n menm c rane 1 dz Pans eee There are checkboxes to the left from the profile names Gi nee e es ee in the list which are enabled by default Disabling a checkbox mie s NERA DNE dd 1 i will exclude profiles thus indicated from a list which will be used for proportioning in the steel construction section check mode 152 me however the disabled profile can still be used to associate ted fates eee iim E 1 1 Te stiffness properties with elements ELE tir i z U DI ER 7 menaa harm 7s 0 12 006 17 900 32 000 08 000 1 PL 25900000 1000 TTE Mem The profile tables can be sorted in an ascending order of various characteristics To choose a characteristics use the Sort drop down list By default the order in which the profiles follow one another in the list will conform to that in the standard or the catalogue Fig 22 The profile browser s window
18. ions of it 5 L c Ford Eres done mm m Fig 7 Overall dimensions displayed in the working area 1 3 3 Strips The strips are line segments If the Snap To Grid mode is active depressed the vertices of the segments will snap to a nearest grid node automatically as soon as they are added To add a vertex place the pointer onto a desired point of the working area within the overall dimensions and left click to confirm the creation of the new vertex To interrupt the process right click 7 User manual Tonus You can have tables of vertex coordinates and properties of strips displayed to the left from the working area use the Table Of Vertices and Table Of Strips buttons respectively As you add a new strip the table will be supplemented with information about new objects vertices and strips 1 3 4 Delete a strip H a 2 n When this action is invoked you can delete any of the strips that make up the section s walls To do it point at the strip and left click The strip will be deleted automatically from the table of strips too 1 3 5 Assign thickness Clicking this button will open the Thickness dialog box Fig 8 the edit field in which is used to specify a segments thickness wf K thickness for your section s wall The said value will be mm assigned by default to all newly added strips x Cancel Fig 8 The Thickness dialog box 1 3 6 Vertices with the mouse and left click
19. list of standard sections a picture of a selected one a legend of its properties and a few fields to enter numerical values of those To add a section do the following V choose a desired section from the drop down list rae m enter numbers in the fields as the chosen model requires 30 000 mm click the OK button Am The last action will close the dialog and the working area 20 000 mm of the Tonus application will display the section that has been just created Fig 16 The following set of standard parametric sections is available in the application Fig 15 The Standard Sections dialog box Seni 11 pr MU Fig 16 A section created with Tonus 13 User manual Appendices MEN 2 Appendices 2 1 Definitions of geometric characteristics 2 1 1 Moments of inertia To calculate some of the geometric characteristics such as an area moments of inertia a location of a center of mass we actually calculate moments of an area 2 covered by a section that is we deal with quantities like this z dydz Q For example at p q 0 this expression becomes the area of the section A Sometimes it is necessary to calculate a moment normalized by the area A that is a quantity like this aa For example the a quantities will be coordinates of the section s center of mass At p q 22 centered central moments are of interest Hy
20. moment of inertia 2 1 5 Core distances 2 1 6 Torsional stiffness Lets consider a function o y z in the Q area a stress function or Prandtl s function which satisfies the equation 2 0 and also 0 on the boundary of Q in the case when is singly connected In case of a multiply connected area i e if there are orifices we assume that 0 on the exterior boundary of the area and it is constant on every interior boundary Lj 1 n the constants Ui i71 n being such that the following relationships hold fas 20 Li where Q is an area bounded by the contour L The quantity 7 39 9 dz Sua is called a torsional moment of inertia i l 2 1 7 Flexural center The coordinates of the flexural center in principal central axes can be determined by these formulas 1 dy dz 1 z J Q where o y z is Saint Venant s torsion function or a displacement function This function is harmonic in the area Ao 0 and satisfies the following condition on the boundary COS COS AZ Also 15 User manual Appendices 00 ds 0 2 1 8 Shear areas of a section Suppose Fig 17 depicts a section and its Y Z axes are principal ones Let Q z mbna A shear area with respect to the Y axis is a quantity 2 Zi 2 b z In the same way a shear area
21. n acos atan can be presented in degrees or radians respectively Only parentheses are allowed for grouping arguments together these can be nested as deeply as desired _ NOD Fig 20 The calculator s window y 0 xs 0 amp E Example The following formula 1 2 sin 0 43 6 7 6 8 3 0 003 should be written as follows 1 2 sin 0 43 6 7 sqrt 6 8 0 003 1 5 There is an additional option of using three independent variables x y z in formulas Values for the variables will be specified in respective edit fields This makes it possible to perform a series of similar calculations with different parameters For example to use this mode with the following formula 1 2 sin x 6 7 6 8 20 User manual Appendices write it as 1 2 sin x 46 7 sqrt 6 8 y 1 5 The application lets you also write a symbolic expression in the formula edit field that ar amp E depends on the variables x y z and then enable one of the selection buttons d dz to get a symbolic expression for the respective partial derivative 2 3 2 Converter of measurement units This converter be started both from the SCAD Office program group with the icon and from the Tools menu The application converts between data specified in different units of measurement Fig 21 To
22. n c o7 HELL Ll 111 E g 8 mu 8 7 LL LL LLL EHE 7 Status bar gx gu 10 7 10 10 11 7 l N zi SN Tonus Ready Overall dimension 67x87 mm 100 3 767 Fig 3 A general view of the Tonus application s window 1 2 Cursors All actions are performed in the working field with specific cursors different shapes of the mouse pointer The shape depends on what action is in progress at a certain moment Below you can see a list of the actions and their respective cursor shapes Jn add strips display stress values in arbitrary points of a section __ delete strips add a vertex smooth round angles 8 delete a vertex delete a group of strips delete a group of vertices move vertices m measure a distance between two points within given overall dimensions The mouse pointer can be used to determine a distance between two arbitrary points of a section 5 User manual Tonus or the working area To do it discard an action active at the moment un press its button place the pointer onto first point and left click Drag the pointer to the second point while holding the button The right part of the status bar will display the distance between the points the accuracy of this indication will depend on a precision specified in the Units Of Measurement tab of the Settings dialog box Coordinates of the current cursor s
23. n walled sections and calculate their geometric characteristics Thin walled bars can be found in a great variety of structures used in various fields of engineering In some cases a thin walled bar model simulates a structure as a E whole such as a multi storey building with load bearing i walls or a span of a bridge while in other cases this model can be used to simulate important load bearing components b b of a structure s framework In the science of structural mechanics a bar refers to a body that has the maximum overall dimension of its cross section Dmax much smaller than its length i b In a solid bar the smallest size of its cross section tmin has the same order of magnitude as by Fig 1 a In a L thin walled bar fmin lt lt Dmax so obviously tmin lt lt L where L is the length of the bar s cross section contour 8 Fig 1 b Usually a bar is considered to be thin walled if the a 6 following inequalities hold t b 0 1 b l 0 1 Fig 1 A key difference in the behavior of a thin walled bar under a load from that of a solid bar is that the plane sections hypothesis can be violated in the case of the thin walled bar A typical example is an unrestrained torsion of an open profile bar a pipe with a longitudinal cut or a deformation of a double tee loaded by a bimoment at its butt Fig 2 Ee A deviation from the plane sections hypothesis is a feature immanent to open pro
24. onus application TNS files are plain text files A section is defined by a set of vertices and segments First line in a file specifies two numbers of the section s dimensions The next line contains an integer n that defines the number of vertices Next go lines with coordinates of the vertices Each line consists of two floating point numbers separated by spaces Then a line stands that contains an integer m to define the number of segments This line must be followed by m lines of segment descriptions Each line that describes a segment contains five numbers First two numbers are integers they are respective Nos of start and end vertices the vertices are numbered starting from 0 The second couple of integers each can be either or 1 defines whether the respective ends of a segment are connected to their vertices The last number in the line is a thickness of the segment All sizes are specified in meters The numbers in a line are separated by spaces The decimal separator is a period Example A section shown in Fig 19 is described in the TNS format as follows 100 0 LOO 25 0 75 0 35 0 7540 45 0 75 0 FaU T5930 65 0 75 0 Fig 19 55 0 65 0 45 0 65 0 35 0 65 0 453 0 75 0 9 0101 1 0 Lx Ll lo led 2 l L0 4 1 4 10 TUE up 5 6111 0 6 711 1 0 TALL Lag 8 2 1 1 1 0 19 User manual Appendices MEN 2 3 Service tools 2 3 1 Formula calculator As you work with the software package sometimes y
25. ou need to perform certain relevant auxiliary calculations The Tools menu contains items for invoking additional calculators a standard MS Windows one if it has been installed together with the system and a special calculator Fig 20 that processes user specified formulas This calculator is used to perform calculations by formulas that one can specify in a text edit field The following rules should be observed when entering a formula e names of functions are entered in lowercase Roman letters e the fractional and the integral parts of a number are separated by a period e arithmetic operations are specified by the symbols raising to a power for example 2 5 2 5 2 5 can be written also as 2 5 3 The following mathematical functions can be used in the formulas floor the greatest integer not greater than the EDUC argument 22 8 cos 34 145 311 tan uu tangent i NN t sin sine 0 p cos cosine asin arc sine acos arc cosine atan arc tangent exp exponent ceil the least integer greater than the argument tanh hyperbolic tangent sinh hyperbolic sine cosh hyperbolic cosine log natural logarithm log10 decimal logarithm abs absolute value sqrt square root Depending on the state of the Degrees Radians switch buttons arguments of the trigonometric functions sin cos tan and results of inverse trigonometric functions asi
26. position will be displayed in the second field of the status bar 1 3 Creating a section You are recommended to follow these steps to create a section P specify sizes overall dimensions of the section Ht define properties of the coordinate grid E V set the strip thickness E V add vertices and strips FA smooth angles if necessary E The vertices and strips can be added both in the graphical mode and in a tabular form After you add a new vertex its coordinates will checked for coincidence with those of previously added vertices The coincident vertices are those the distance between which is less than or equal to a value specified in the Accuracy field on the Other tab of the Settings dialog box If the vertices are coincident the newer one will be deleted and the strip will get the older one as its vertex When strips are added or vertices moved the strips may happen to cross one another In that case both a crossed strip and a crossing one will be divided into parts automatically and a new vertex will appear at the point of their intersection The fact of intersection is analyzed using the given accuracy value 1 3 1 Coordinate grid Grid settings 4 x Properties of a coordinate grid are specified in the o Grid Properties dialog box Fig 4 which opens after youu j iu invoke the respective action The edit fields of this dialog let z 0 mm you specify a horizontal and vertical grid spa
27. with respect to the Z axis can be defined 2 1 9 Plastic moduli of section Let be an area occupied by the section Let Q be a part of the Q area lying on one side of the principal axis U A plastic modulus of section for bending with respect to the U axis is a quantity Waa 2 vdo Qo In the similar way a plastic modulus with respect to the V principal axis can be defined 2 1 10 Sectorial characteristics A bimoment sectorial moment of inertia of a solid section is L o y 2 dy dz where o y z is Saint Venant s torsion function In a thin walled section the sectorial moment is defined by V Z Vlasov s theory see 2 1 16 User manual Appendices Note that the sectorial characteristics are usual in the thin walled bar theory developed by V Z Vlasov 2 However G Y Janelidze 3 has shown that the above formulas obviously applicable to all sections conform with the accuracy 1 O h p to the concepts of the biboment and the sectorial static moment of Vlasov s theory where h is a thin walled section s thickness and pis its radius of curvature 2 1 11 Normal stresses You are required to specify components of integral forces in the section i e the N component of an integral force vector and the M M components of an integral moment of forces with respect to the section s center of mass The normal stress at a point is equal to A 1 1 where N M M are the respective normal force and moments in prin
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