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Program AMSES Frame2D User`s Manual

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1. Name R 30 50 Color NS Figure 2 7 Entering data for a new cross section 15 1999 2002 Ainet Elements on the screen are painted by their cross section color by default User s manual 2 2 AMSES Frame2D solution 3 The cross section should be named too Any name can be used However it is wise to use a meaningful name like R 50 30 A unique cross section color should be also selected 4 After the cross section was defined close the window with the OK button 5 Weare back in the cross section editor window Notice that the new cross section R 50 30 appears in the cross section list box Index 1 was assigned to this cross section automatically We have no control over indices in the current version of program 6 After we have defined the cross section we MUST close the cross section editor with the OK button All modifications and new cross section entries will be lost if we press Cancel After the cross section editor window was closed with the OK button both elements change their color to the color of the new cross section Remember both elements point to the cross section 1 This is the reason why element colors match the color of cross section 1 Material The material is defined in a similar manner as the cross section 1 Select the Geometry Material command This opens the material editor window Press the New button to create a new material 2 Ina tabbed window
2. 93 8 2 1 Kinematic geometric non linearity 94 8 3 Some illustrative examples E eh OS SPT ORGS BG ee 95 8 3 1 Vertical cantilever sway structure 95 8 3 2 High accuracy horizontal cantilever and bending moment 96 8 3 3 Influence of dummy values for A JorE 97 5 1999 2002 Ainet User s manual CONTENTS 6 1999 2002 Ainet Preface The AMSES Frame2D 2D program is coming into a mature state It s first version was issued in 1999 and I am very pleased that it found a large audience all over the world For many of them it became a must have an indispensable tool The new version was enriched with a set of tools that cover the design of steel and reinforced concrete elements The design was programmed according to the Eurocode 2 reinforced concrete and Eurocode 3 steel design codes Thus the new version is not just a facelift but has many new practical facilities The analysis results are used in design procedure the user only needs to provide some additional information to verify the element design The story of the AMSES Frame2D 2D began several years ago in the beginning of 1994 Back than I came up with an idea of writing a group of simple and easy to use computer programs that shall make the life of structural engineers easier Next year I actually wrote a few simple programs concerned with the reinforced concrete and steel elements d
3. Snow This is another variation of the loads where the snow is the leading action Wind is not included since it acts favorable Snow 1 35G 1 55 0 70 1 50Q 35 1999 2002 Ainet User s manual 3 1 About the structure Serviceability limit states combinations The serviceability limit states are considered too The steel elements will be checked for the stresses that should not exceed fy and local deflections The reinforced concrete foundation beam will be checked for crack widths Having this in mind we can define the following serviceability load cases g Maximal vertical load SLS This case is needed to determine the beam deflection and RC beam cracks VmazS 1 00G 1 00Q 0 65 h Maximal horizontal load This load gives us maximal sway displacements and contact pressures on the right HmazxS 1 00G 1 0 WL 0 70Q 0 651 Concrete creep and shrinkage During the serviceability limit state analysis we can take into account reduced elastic modulus of the concrete due to creep and shrinkage effects Eep 7 In our case 1 c bc 2 2 3 1 4 Load case table All load cases from a to h are collected in a table form All those cases are prepared for the structure which is skewed rightwards The load case table is presented on table 3 1 Almost identical table spreadsheet will be introduced when the problem will be solved using AMSES Frame2D see the figure 3 9 on page 44 Some abbrevia
4. Krajnc User s manual CONTENTS 8 1999 2002 Ainet CHAPTER 1 Getting started The easiest and the quickest way to get familiar with AMSES Frame2D is to read this chapter Two examples are revealed in detail The first example is a simple continuous reinforced concrete beam A static analysis is performed first and this is followed by the design of one of its elements In the second example a more complex case of steel frame that is lied on the reinforced concrete foundation beam is considered Here several actions and load cases are applied and designs of several elements are carefully considered If you are an experienced computer guru you can skip to section 2 starting on page 11 Others may find next section interesting 1 1 Folder tree description During the installation process you have selected the basic folder The manuals as sume you have selected the default option the Program Files AMSES folder Several additional subfolders are also created and their content is briefly presented below Frame2D holds all executable and DLL files needed to run the AMSES Frame2D pro gram Frame2D Misc holds several support files mostly in textual form These files are startup tips error messages and some internally used working files Frame2D Help includes all files of the AMSES Frame2D help system Frame2D Examples includes several examples mostly from the manual Common The folder only hosts two subfolders Common
5. Load case Type S W Skew leftwards Skewness ml Load case 1 Ultimate 1 50 1 50 Load case 2 Serviceability 1 00 1 00 Skew rightwards Skewness wl Load case 3 Ultimate 1 50 1 50 Load case 4 Serviceability 0 20 1 00 Table 5 2 An example os load case sequence when skewness load cases are used Skew rightwards Reset previous imperfection angle Afterwards skew the structure for 74 radians in the negative direction clockwise All load case factors are ignored and no other calculations are done Load case 3 Calculate the load case using specified factors and skewed geometry ObteZni primer 4 Calculate the load case using specified factors and skewed geom etry Etc Comment If you want to reset the imperfection angle define Skewness load case and specify 1 0 for the angle AMSES Frame2D will translate this into zero skew 5 3 Concrete creep time depended effects This section is mostly intended for concrete structures If you are designing a steel structure you may want to skip it The concrete is one of the most often used building materials But it is also one of the most problematic materials as far as material models are concerned It has visco elasto plastic behaviour suffers from shrinkage effect and its characteristics are time temperature and moisture depended As a result every author that had studied the behaviour of concrete proposed its own material model It is very difficult
6. Stin 0 0 000 010 020 030 040 050 O88 O70 080 090 1 00 2 F Check ultimate limit states nap wk 02 F Check serviceability limit st U Ultimate Serviceability obo obo 080 100 Select S Clear All Gas wk 02 Figure 2 22 Crack width bar chart The chart shows that no crack is wider than 0 1 mm 28 1999 2002 Ainet User s manual 2 2 AMSES Frame2D solution Design of the second element The design of the second element is almost identical There is not need to describe it here We believe that you are able to do it yourself and we leave this as an exercise 2 2 6 Printout We came almost to the end All we have to do is to print the results Before we do the actual printout we can preview the output on the screen by clicking on the L icon or by selecting the File Print Preview command Press the L and list the pages with PeUp and PgDn keys You should see a screen like one on the figure 2 23 LC1 G Q ui Bending Moments My Figure 2 23 Predogled rezultatov na zaslonu In order to print the results press the amp icon or issue the File Print command Before printing the program asks which pages to print In our case keep the default all pages and press the OK button 29 1999 2002 Ainet Check this box if T non horizontal text labels are not printed properly User s manual 2 2 AMSES Frame2D solution Output contents When we are work
7. The com mand is undone and initial situation is restored right The level of Undo Redo commands is unlimited All important commands are recorded by the system Comment Commands are undone redone even if we switch to a different view or workspace The switch is not recorded by the system This means that some com mands can be undone but we will not be able to see the change on the screen 4 5 View related commands There are several commands which are used to change the appearance of current view The commands can be found on the View menu or on the top toolbar figure 4 5 RARRAAR D RE to 680 Figure 4 5 View related toolbar 4 5 1 Zoom commands In many cases a structure that we are analysing is so big that individual elements appear too small if the whole structure is shown on the screen To overcome this problem zoom commands were built in AMSES Frame2D The commands can be found in the View Zoom menu or in the view toolbar The following zoom commands are available 4 Zoom in makes the structure 50 larger A Zoom out makes the structure 50 smaller EA Zoom window allows us to select the part of the structure to be enlarged E Zoom previous returns zoom back to its previous state a kind of zoom undo GX Zoom next reverses the last zoom previous command a kind of zoom redo Com mands El and 4 are not limited to one level GX Zoom all shows complete structure on the screen amp Zoom extents fit
8. 0 1 3 En Left click a cell to editits value Right click a cell to select a row Figure 2 19 Correctly completed window for positive reinforcement 2 In the spreadsheet we enter 2 under column n 3 Under Fi we enter 20 under x start bar start point in relative coordinates we enter 0 and under x end bar end point in relative coordinates we enter 1 4 For the Concrete Cover we specify 3 cm and the window should look like one on the figure 2 19 5 Close the window by pressing OK Longitudinal negative bars We will set the negative reinforcement in an almost identical way Let s take two 20 mm bars for the start The concrete cover is 2 cm 1 Issue the Design Negative Bars command 2 In the spreadsheet under letter n enter 2 under Fi enter 20 under x start enter 0 and under x end enter 1 3 Into the Concrete Cover field enter 2 cm 4 Press OK to close the window Concrete cover is thickness of the concrete measured from the cross section edge to the edge of the nearest stirrup or longitudinal bar 25 1999 2002 Ainet User s manual 2 2 AMSES Frame2D solution Stirrups Stirrups are defined in a similar way too Here we have an extra column in the spread sheet the distance between stirrup links Let s assume 2 times 10 mm stirrups Around the support areas 0 0 0 2 and 0 8 1 0 we set them 7 5 cm apart In the field area 0 2 0 8 w
9. but such load is favorable it reduces bending moments in the RC beam and is therefore neglected We assume that the beam takes the uniform load of 25 kN m Additionally 10 kN horizontal concentrated force acts on the left node The figure 3 3 illustrates the situation Due to simple geometry there is only one most unfavorable position of the live load 1 However in the future we intend to issue a simple tool that will handle actions in the Eurocode 32 O 1999 2002 Ainet User s manual 3 1 About the structure 20 kN m E g E Z 13 kN m Figure 3 2 Distribution of the permanent action and self weight G 25 kN m Figure 3 3 Distribution of the live load Q S Snow load In general two different snow loads needs to be assessed In the first load S1 the snow is evenly distributed over the beam In the second load S2 only half of the beam is covered with the snow and we take only half of te initial snow intensity See figure 3 4 9 kN m 4 5 kN m Figure 3 4 Both snow loads
10. line from the list During the reinforcement material selection the material list was changed and there fore AMSES Frame2D deleted the all analysis results Hence the analysis must be repeated Press the Bl icon or issue the Solve Solve command New analysis results are calculated Now we issue the Design This Element command or press the Bi but ton to verify the limit states The program makes all possible design calculations and shows results in a compact form on the screen The screen looks like the figure 2 21 26 1999 2002 Ainet User s manual 2 2 AMSES Frame2D solution Cross section cm R 30 50 0 0 h 50 00 000 010 020 030 040 O50 060 O70 080 O90 1 00 b 30 00 TE Element supports 2 pa width 5 w left 20 00 cm right 20 00 cm Concrete C 30 37 Reinforcement RS 400 o elos lo t s o o o a y t o B S 2 un a a t 2 Y o o co t o to S o a Positive on oo gt M Check ultimate limit states FN Check serviceability limit st U Ultimate S serviceability UP G Q ult S G Q displ 010 020 030 0 40 050 060 070 080 O90 1 00 Select U Clear AIl Figure 2 21 Once all required information is available we can verify the design Results are presented in a bar chart All bars should be below 1 As we see at some areas the cross section capacity is exceeded Red colored bars mean nothing good On th
11. permanent snow 1 35G 1 505 0 90W 2 permanent wind 1 35G 0 905 1 50W 3 serv permanent snow 1 00G 1 005 0 50W 4 serv permanent wind 1 00G 0 205 1 00W Comment Safety factors used in both examples will not suit your situation and your building codes Check out you building codes to find the right factors for your problem 5 2 Equivalent imperfections Logically This section belongs into the geometry chapter but we can benefit more if the equivalent structural imperfection is treated as a special kind of load case This is why it is located here A good design practice requires that in the ultimate limit state consideration shall be given to the effects of the imperfections in the geometry of the unloaded structure Where significant any possible unfavorable effect of such imperfections must be taken into account Different building codes estimate the structural imperfection differently However almost all of them define the structural imperfection angle for which the structure is inclined from the vertical horizontal axis figure 5 1 The usual measure for the angle is defined in a form 1 X where X is some number defined by the codes Positive angle skews the structure in counter clockwise direction and negative angle skews the structure in clockwise direction 5 2 1 How to simulate the imperfection To handle the initial imperfection you may follow one of two
12. towards the subgrade Figure C shows the case where element stiffness is small comparing to the subgrade stiffness and only the middle part of the element moves towards the ground while element ends are lifted off the ground The relation between the displacement w and subgrade reaction is defined by the equation 7 1 k x K w x b 7 1 K subgrade coefficient kN m w displacement m b contact width between the beam and subgrade m and k x subgrade reaction in the point z expressed in kN m Since tension between subgrade and the beam is not possible we must slightly modify the previous equation _ J K w x b w x gt 0 towards the subgrade Mla 0 w x lt 0 lift of the subgrade 2 89 Some parts of element on elastic ground may be lifted off the ground AMSES Frame2D internally splits each element on elastic ground into three finite elements to reduce the displacements error Convergence rate is linear quite a few iterations are needed if element lift off occurs User s manual 7 1 Some theory A SS eee ____ 3333SSSSSSSSSSSSS Figure 7 1 Illustration of the element laid on elastic subgrade As we can see the pressure has bilinear behaviour it is linear if the beam moves toward ground and constant zero if beam is lifting off the ground If we want to handle both cases B and C from the figure 7 1 an element must be able to identify all x points whe
13. 0 8 3 w Y We see that equations are independent and may be treated as simple differential equa tions Second order theory People were not happy with the first order theory especially with the simplification of term cosy 1 A better approximation is cos w 1 y 2 which after neglecting small terms y and e a yields the equations 8 5 and 8 6 W Ee 1 2 wtp 0 8 5 0 8 6 This theory is limited to moderate rotations The equations are depended in the case of pure bending we also have horizontal displacements Co rotational theory The second order theory is better than the first order theory but large displacements are still problematic To overcome this problem a co rotational theory was derived This theory takes global rotation Y const of the finite element into account equations 8 7 and 8 8 ul e 1 2 cos Y w sin V 8 7 8 8 94 1999 2002 Ainet User s manual 8 3 Some illustrative examples Exact kinematical equations The co rotational theory is very good but not so good as the exact theory which is used in AMSES Frame2D There are no simplifications of initial Reissner equations here equations 8 1 and 8 2 and as far as the kinematics is concerned the element does not have any limitations 8 3 Some illustrative examples In this section we will take a look at three simple but illustrative examples e The first example is a vertical
14. DB holds database files which describe material and cross sectional char acteristics 51 Common 5 CB Common Doc stores documents which are downloaded from the Internet site www ain re a a E rame sp si msgsys a My Projects is the default location where your files are stored You can use any other O Help location of course O Misc User s manual 1 2 Setting up the character set 1 2 Setting up the character set AMSES Frame2D uses ANSI Western character set by default If you are using some special character set like Central European Baltic Cyrillic etc then it is good idea to set it right away 1 Run the program 2 Select the Tools Character Set command and a list of available character sets appears 3 Select the character set you want to use Now the selected character set is active and special characters should appear correctly The selection is stored permanently which means you do not need to define the char acter set ever again 1 3 File extensions When a structure you are working on is stored on a disk two files are created which differ by their extension The AMP and AMS extensions are used e The AMP extension is bound with a project file The project file is a relatively short file which stores all file names used in current project e The AMS extension is bound with working files structure files They hold ac tual data of the structure geometry load analysis and design results When an e
15. Load vector Load position Start load End load C World Local Fx jo kN m p kN m Typical wind Fz fis kN m E KN m SE 1 Direction Local My E kNm m kNm m Position Local Relative load position on element Load name Start at End at Rel jo a 1 Optional Abs jo cm 600 cm PE Cancel Help Figure 2 10 The linear load window In this case local coordinate system matches the world coordinate system which makes the load direction and load position irrelevant 4 Press OK to complete the operation A load schema appears on the selected element The second element gets the same load too In principle we could repeat the above procedure however there is a short cut 18 1999 2002 Ainet User s manual 2 2 AMSES Frame2D solution 1 Hold down the Shift key and click on the second element The second element accepts the last entered linear load immediately there is no need to fill the linear load dialog 2 11 1 gt Q 2 gt 15 kN m 15 KN M Figure 2 11 The continues beam and load of action G We have just defined the action G A similar procedure is used to define the load of action Q 1 Select the Q item in the tree and double click it to open its action window 2 Press the icon to switch into linear load entry mode and then click the element one 3 In the linear load window enter 35 kN m under Fz field and make sure that other fields are set to zero Na
16. Typical loads that fit into this group are self weight of structure installations equipment pre stressing etc Variable actions Q Typical loads that fit into this group are traffic load variable load snow load wind load temperature load etc Accidental actions A Loads that fit into this group are rare but have high inten sity explosions fire hit of a conveyance etc Earthquake action EA Dynamic load of an earthquake or its static equivalent Individual actions can be further divided into subgroups this depends mostly on the problem we solve In the most cases variable actions Q are subdivided into new actions S snow actions W wind actions several positions of the live load Q1 Q2 Itis up to the engineer how she he will define the actions 71 Action is a term for a group of loads User s manual 5 1 Basic definitions 5 1 3 Load cases Load cases combine A load case combines different actions into a realistic load combination Each action different actions in the combination gets its own safety factor The values of safety factors are defined by building codes A load case can be written in the following symbolic way Load case action 1 factor 1 action 2 factor 2 action n factor n AMSES Frame2D assigns a limit state type for each load case Limit states are states beyond which the structure no longer satisfies the design performance requirements Two basic kinds of limit sta
17. be verified man A cow 1 ually Our displacement reaches ratio 355 A brief resume The beam cross section satisfies both limits states and has a slight reserve in capacity and displacements You may consider replacing current HE 360 A cross section with HE 340 A The procedure is simple 1 Click the 15 icon and select the HE 360 A cross section 2 Press the Edit button 3 In the sections list browse for the HE 340 A cross section 4 Press OK twice to close both windows 54 1999 2002 Ainet User s manual 3 2 AMSES Frame2D solution 5 The cross section has changed and the internal forces and design results are lost Click the B icon to calculate new internal forces 6 Click the 8 to redesign the beam The left column element 1 The procedure to design this element is almost identical to the procedure used on the beam element The only difference can be found in the supports and the load application position This element has no intermediate supports and it has neutral load position Additionally we will not take effective support width into account 1 Expand the Steel item and double click the Element 1 line 2 Select the Design Steel Design Data command 3 Move load application position into the indifferent state 4 Press OK to close the window 5 Press the Select U button to include all ultimate load cases into the design verification The results are shown on the screen As you can see the s
18. cantilever subject to vertical and horizontal load at the free end This sample clearly demonstrates non linear effects on sway structures e The second example shows high accuracy of the non linear element used in AM SES Frame2D e The third example demonstrates that non linear elements require meaningful cross section and material data but linear elements do not So if you play with non linear elements and you get odd results make sure that you have specified correct cross section dimensions and material 8 3 1 Vertical cantilever sway structure We have two eight meters long cantilevers made of steel 5235 and IPE 240 hot rolled cross section The free ends of cantilevers were loaded with axial forces of 50kN and lateral forces of 10kN The left cantilever was modeled using linear element and the right cantilever was modeled using non linear element The figure 8 1 shows the can tilevers and their load 50 kN 50 kN z y z W o gt Alllgads AllIdads a A Figure 8 1 Cantilevers and their load The results of analysis are presented on the figure 8 2 Bending moments were calcu lated at safety factor of 1 50 The results for linear element can be easily verified 10 kN 8 m 1 50 factor 120 kNm which is the same result as shown on the left can tilever Surprisingly we got significantly larger results for the right cantilever which 95 1999 2002 Ainet Note that the program correctly a
19. case AMSES Frame2D uses a special kind of load case skewness This load case allows the designer to set the initial imperfection of the structure All load cases that follows are acting on skewed geometry until a new skewness load case is introduced Hence the sequence of the load cases is important In our case we start with the skewness load case We skew the structure to the right and appropriate ULS and SLS load cases follows If the structure or the load is non symmetric then we should also skew the structure to the left using a new skewness load case and a new set of ULS and SLS load cases that follow However in our case we have symmetric situation and it is enough to consider load and skewness for one side only a Initial imperfection Eurocodes demand that initial imperfection is taken into account during the analysis The initial imperfection is based on a fact that it is virtually impossible to make a structure perfectly vertical It also includes effects that arise from residual stresses and 34 1999 2002 Ainet User s manual 3 1 About the structure other deviations from the ideal material characteristics Due to these imperfections additional internal forces appear in the real structure and they need to be considered in the analysis too Eurocodes provide formulas based on number of stories and bays of a frame The result of the formula is an equivalent imperfection angle for which the structure must be inclin
20. clicks away Click on the S Serviceability tab and the content of the screen is changed Both charts are empty since no load case is selected Click the Select S button to select all serviceability load cases After a moment both charts are shown and the screen should look like the figure 3 19 Cross section cm HE 360 A h 35 00 b 30 00 tw 1 00 tf 1 75 Relative load position used in LT calculation is 1 00 unfavourable r 2 70 Element supports width left 13 00 cm 250 right 13 00 cm Y Y Supports Z Z Supports LT Supports v x VO s Vis VV Y ox V 000 020 040 060 0 80 100 000 0 20 040 0 60 080 10o o 00 0 20 040 060 080 1 00 Steel 235 209 Check ultimate limit states F Check serviceability limit states Stresses kN cm2 U Utimate Serviceability 1 400 1 5004 116674 1 10004 Deflections u L 1 2000 Select S Clear All Figure 3 19 The situation of the serviceability limit state design of the beam ele ment 3 The top chart shows envelope of the stresses for selected load cases Cross sections classified into class 1 and 2 may develop a plastic hinge in ultimate limit states how ever in the serviceability limit states the stresses must not cross the fy limit The bottom chart displays envelope of local displacements in the 7 form Please note that global displacements especially horizontal displacements must
21. e select the View Workspace Design workspace command 19 Project Continues beam We see similar workspace changes as in previous cases Windows have disappeared pos ee n l ul and the tree has changed In our case both elements are made of reinforced concrete 5 Reinforced Concrete material Hence they are located in the Reinforced Concrete folder If we expand the CEE folder we see both element names Double click on the 01 Element item opens the res reinforced concrete element design window shown on the figure 2 14 8 Not designed The window is split into several sections We are already familiar with the tree on the left We use it to select individual elements AMSES Frame2D enables us to design only certain cross section shape and material combinations Element that can t be designed are put into special Not designed folder Currently we can design rectangles 21 1999 2002 Ainet User s manual 2 2 AMSES Frame2D solution AMSES Frame2D Continues beam Reinforced Concrete Design of Element 1 E l0 x E Fle Edit view Design Solve Tools Window Help la x osBsaRra jes Bros es jaja 22 29 900 RAS Ja 1 05 19 Project Continues beam Bi Cross section cm 2 Bars are not defined Structure Continues beal B R 30 50 E 0 0 E Design Resume FA h 50 00 ooo 010 020 030 040 050 060 070 0680 0
22. elements in the same way they differ in their colors only Although they are almost the same on the outside they are significantly different on the inside The non linear element is more complex and precise The difference between elements can be noticed in structures which are slender and have significant displacements e g sway frames Since non linear analysis fulfils equilibrium equations in deformed state we get more precise results than results obtained by linear analysis The non linear element used in AMSES Frame2D is very reliable and heavily tested We believe that there is no reason to use linear elements ever again except for the beam on elastic ground and this is true for any kind of structure you analyse The program allows you to mix linear and non linear elements in the same structure The non linear analysis will be used if at least one non linear element is used in the structure Although element mixing is possible it is not recommended since results of the analysis are not so precise as they would be if only non linear elements were used Comment The second order theory has limitations but kinematically exact element is without any limitations This means that large strain large displacements dis cussion is irrelevant here and you may use AMSES Frame2D s element without any hesitations 8 2 Three kinds of non linearities There is a little confusion about terms used in linearity and non linearity discu
23. forces F Shear forces are quite interesting figure 8 7 We should not forget that axial and shear forces for the non linear element are shown on undeformed geometry but are calcu lated on deformed geometry and their orientation is valid for deformed geometry 98 1999 2002 Ainet User s manual 8 3 Some illustrative examples AN Figure 8 8 Axial forces Fy Axial forces the effect of the rope is clearly visible on the figure 8 8 The linear element has no axial forces while the non linear has quite significant axial forces 1 2 lt 4My 0 3333 i A My 0 3333 Rul ae IN EXO a o D lt 1 My 0 147 7 _My 0 147 x4 196 Be Exa 196 i 1 c wm a Figure 8 9 Displacements uz The figure 8 9 shows the displacements They are totally unrealistic in the linear case but very precise and logical in non linear case 99 1999 2002 Ainet User s manual 8 3 Some illustrative examples 100 1999 2002 Ainet Bibliography 1 CEN Eurocode 2 Design of concrete structures Part 1 General rules and rules for buildings European Commitittee for Standardization 1991 2 CEN Eurocode 3 Design of steel structures Part 1 1 General rules and rules for buildings European Commitittee for Standardization 1992 3 CEN Eurocode 1 Basis of Design and Actions on Structures Part 1 Basis of Design European Commitittee for Standardiz
24. ja aja so 90 RRRADAAB EF n 19 Project Continues beam E Structure Continues beal Geometry B Elements 1 4 Nodes amp Cross sections tq Materials 4 RE vad ab dba o l NX gt gt x 0m z 0m FAVA amp 050 Be M Da k 0m z 0m Standard E 1A Figure 2 4 The first element is drawn We repeat the procedure to draw the second element 1 Move pointer over node 2 and click it Note When the pointer is over a node it slightly changes its shape a small black dot appears This indicates that the mouse click will not create a new node but it will use the existing node instead 2 Move the pointer to the right and locate coordinate 12 0 3 When the pointer is in place click left mouse button Now you should see two elements as presented in the figure 2 5 0 E n a es ee O RO Figure 2 5 Both elements are in place Comment While moving the mouse do not keep left mouse button pressed A line a rectangle etc are drawn in a slightly different way you may be used to First mouse button is clicked Next the pointer is positioned to the desired place Finally mouse button is clicked again and this completes the operation This approach differs from the approach that most windows programs use AutoCAD uses similar approach for example 14 O 1999 2002 Ainet User s manual 2 2 AMSES Frame2D solution Suppo
25. may be needed to find equilibrium You should not confuse this with the convergence rate of elastic non linear elements which have quadratic convergence 90 1999 2002 Ainet User s manual 7 1 Some theory 7 13 Nodal supports Element on elastic ground resists in a direction which is perpendicular to the element axis It has no resistance in direction which is parallel to the element axis This means that in most cases additional nodal supports are needed A case like this is given in the figure 7 2 In this case the structure is unstable if nodal support on the right is omitted it can not resist against horizontal forces ZSSSSSSSEEEEEE Figure 7 2 An example of structure that requires nodal support On the other hand we can construct structures that need not to be supported with classical node supports One example is given on figure 7 3 AMSES Frame2D will handle structures like this if the coefficient of subgrade reaction is properly set In the case shown on the figure the sum of vertical load must be positive If lift off load dominates over the gravity load the structure becomes unstable w M MAI WA Figure 7 3 An example of structure without nodal supports As the last example we show a pile which has ground support on both sides and vertical node support at the bottom In this case lifting off the ground is not possible and therefore the problem is linear See the figure 7 4 SS333333
26. of people the appearance of the struc ture Eurocode 1 gives a detailed explanation on limit states As far as AMSES Frame2D is concerned a more detailed definition is not needed For the serviceability load cases we may additionally specify the creep and shrinkage coefficient fp that is used during the analysis and design crack width Skewness is a special Skewness load case type simulates equivalent imperfections of the structures by type of load case skewing the structure for prescribed angle Creep This kind of load case is obsolete It will be removed in next program versions 5 1 4 Safety factors Each building code has its own approach for defining safety factors However they can be divided into two basic groups 72 1999 2002 Ainet User s manual 5 1 Basic definitions Load case Type Pe G S W primary snow Ultimate primary wind Ultimate 10 ied supplementary Ultimate displacements Serviceability Table 5 1 An example of global safety factors e Codes that use global safety factors e Codes that use partial safety factors Each approach has its own story which is complicated and beyond the scope of this manual Here is given a recipe which tells how to use AMSES Frame2D for either group of building codes Global safety factors When a global safety factor approach is used it means that each action used in a load case is multiplied with the sa
27. option Additionally you may completely remove some load cases from the output Important Design results will be printed only if the Print design results is checked In most cases we get significantly shorter output after these settings are applied Note Before you actually print the results itis wise to take a preview on the screen If you want to change something correct the settings and preview again You may also consider to redirect the output into a postscript file or a pdf file and burn a CD instead of print out a pile of paper 57 1999 2002 Ainet User s manual 3 2 AMSES Frame2D solution Setup Output Content CC aleta a a la la CCA ek peek oe peepee i EN C P Envelope EN My Envelope Figure 3 21 Recommended settings for the output 58 1999 2002 Ainet CHAPTER 4 Basics In this chapter we will reveal some of the AMSES Frame2D properties and details which make the program powerful elegant and useful 4 1 Coordinate system AMSES Frame2D uses a bit unusual coordinate system The main axis are x and z as shown on the figure 4 1 The program is using two coodinate systems global and local negative i pozitive rotation rotation L local coordinate system W global world Zy coordinate system Figure 4 1 The illustration of global world and local coordinate system The dot ted line indicates the positive sid
28. select the Concrete tab and a page presented on the figure 2 8 appears Create New Material k 21x General Steel Concrete Reinforcement Steel Materials by design codes Material name C 30 37 Code Eurocode 2 Material c 30 37 Material color sd modus 200 faena none kNicme ll le el ao KN cm2 Density 2450 kg m3 tenais rent Nome These settings are optional and informative only E Cancel Help Figure 2 8 Entering data for the new material In most cases it is enough to select one from the database 3 Selection from the database is handy Choose the building codes first Eurocode 2 and then browse for the C 30 37 Additionally select a material color that uniquely identifies the material 16 1999 2002 Ainet User s manual 2 2 AMSES Frame2D solution 4 Our material is defined Close the window by pressing OK 5 We are brought back to the material editor window Notice that the new material C 30 37 appears in the material list box Index 1 was assigned to this material automatically 6 After the material was defined we must close the editor pressing the OK button All modifications and the new material will be lost if we press Cancel Now we are back to the geometry window This time the elements on the screen remain unchanged If we want to see elements painted in their material colors we must issue the View Show Material command or press the button on the ge
29. the View Workspace Loads command 2 Double click the Action Load case Manager line on the three and a spreadsheet appears The topmost row defines actions while the leftmost column defines load cases 3 Rename the Action 1 cell into G and the Action 2 cell into Q 4 In oder to enter the next two actions the spreadsheet needs to be expanded Press the icon twice to add two more columns The same effect can be ob tained using the Load Manager Add Action command 5 Rename the new columns into S and W Actions are now defined Each action gets its own window where we define its load At this moment we could start putting loads onto the frame Nevertheless let s define the load cases and load factors first All we have to do is to copy numbers from the table 3 1 into the spreadsheet 42 1999 2002 Ainet User s manual 3 2 AMSES Frame2D solution 1 Rename the Load case 1 cell into Skew rightwards The first load case defines the skewness of the structure Such skewness is then used in subsequent load cases until a new skewness is defined We are going to skew the structure for p TE A negative value must be used since the skew is a consequence of the clockwise rotation which is a negative rotation Click on the Limit state cell and click the arrow to open the list box Select the Skewness type To bring selection into effect click outside the cell Once this was done the cell turns gray Click on the gray
30. the figure 3 10 2 4 ALT TIT IT TIL IE i YY aomm PIII Ii eit iii dt lt _ lt lt 4 kN m 4 kN m lt lt SS PELE ETE LETT Loree TITEL TI Figure 3 10 The load of the action G Action Q The live load was introduced on page 33 figure 3 3 It consists of one uniform load and one concentrated force Before the load can be specified action Q window must be opened 1 Double click the Q line on the three A new window opens which corresponds to the action Q 2 Select the icon and click on the top beam 3 The linear load window opens Enter 25 kN m into the Fz field and choose cor rect coordinate systems Our live load behaves as a self weight 4 Close the window 5 Select the icon and click on the node 2 6 The concentrated load window opens Enter 10 KN into the Fx field and hit OK button to exit The live load Q is now completed 45 1999 2002 Ainet User s manual 3 2 AMSES Frame2D solution Action S Initially two different snow situations were considered but we realized that in our case only the first one can be mandatory See page 33 figure 3 4 Let s define the snow load 1 Double click the S line on the three A new window opens which corresponds to the action S 2 Select the icon and click on the top beam 3 The linear load window opens Enter 9 KN m into the Fz field and choose correct coordinate systems both loa
31. the load needs to be trans formed Let s denote the load as 5 s m AMSES Frame2D transforms this load internally into the local coordinate system p where p denotes the load in lo cal coordinate system Let a denotes the angle between local x axis and global x axis The transformation can be written using the expression 5 1 This expression is build into the program Dr Se sin a s sinacosa Pz Szs8inacosa t S cos a 5 1 Mp Ms Here we should bear in mind that the s component is used very rarely while the m almost never Self weight direction global position local The self weight is a gravity load hence the global direction is used The weight refers to the length of element which means that it lies in the local coordinate system The figure 5 5 illustrates the situation i m Coordinate system Load direction Word Local Load position C Word Local Typical self weigh 2 1 Direction Word Position Local Figure 5 5 A load with global direction and local position Self weight dead load is a typical case Since the load direction is given in global coordinates the transformation 9 9z My p is needed expression 5 2 Pe Ge COSA gzsina Pz Gxsina g cosa 5 2 Mp My 79 1999 2002 Ainet User s manual 5 4 Load and coordinate systems 5 4 3 Temperature difference load We may assign to an element a temperature difference A positi
32. to select multiple nodes 2 Select the Edit Move command or press the ES icon This starts the move opera tion 3 Click on a reference point 4 Move the reference point to a new location Notice that nodes and referred el ements are moving along the mouse pointer If you stop the movement a tip window will display the difference between the current point and the first refer ence point 5 Click on the second reference point to finish the move operation There is an alternative way to move a single node to a new coordinate This way is usually used to specify a precise location of the node 1 Right click the node and select the Properties menu item 65 1999 2002 Ainet The E icon switches into the rectangle selection mode Don t forget we can undo the delete command The 5 start the move operation User s manual 4 9 Some element specific commands 2 Select the Coordinates amp Name tab 3 Enter new coordinates of the node 4 Press the Apply button to assign new coordinates to the node 4 9 Some element specific commands AMSES Frame2D Two kinds of finite elements are currently used in AMSES Frame2D linear element uses two kinds of and non linear element Both types are used in the same way and they look the same inea nn from the outside However they differ on the background theory Generally non linear elements give more realistic results especially in the case of sway frames But linear eleme
33. 3 A load with local direction and local position Wind load represents a typical case As far as finite element is concerned it accepts the load without any internal transfor mation Snow load direction global position global The snow load is a gravity load hence the global coordinate system is used for the direction The load refers to the x axis unit of global coordinate system basement line The intensity of the load expressed in per global x axis is always the same no matter how steep is a roof The figure 5 4 illustrates the situation Generally only the vertical komponent s is given its position is expressed in per global x axis units However when the horizontal component sx is given as well it is expressed in per global z axis units And when the distributed moment m is specified as well it always refers to the local x axis 1 This claim is not 100 correct Some building codes declares different values for the snow load that depend of the roof steepness But the load is still expressed in per global x axis units 78 1999 2002 Ainet User s manual 5 4 Load and coordinate systems Coordinate system 10 kN m Load direction y Word C Local Load position Word Local Typical snow 2 1 Direction W orld Position World Figure 5 4 A load with global direction and position Snow load is a typical case Finite element can t accept this kind of load directly and
34. 33335 SSSSSSSSSSESE Figure 7 4 An example of a pile supported on both sides of the element 7 14 Approximate values for the coefficient of subgrade reaction The best way to get coefficient of subgrade reaction is to ask one of the qualified per sonnel geo mechanics engineer for example to provide it She he will take a look at the building site take some ground samples or even drilling will be necessary to get 91 1999 2002 Ainet User s manual 7 1 Some theory Rigidness Very compressible Semi compressible Compressible Semi rigid Rigid Rock Material type sand clay sand clay sand gravel compact clay compact sand gravel incompressible clay aggregated sand and gravel monolith solid rock K kN cm 0 001 0 005 0 005 0 05 0 05 0 1 0 1 0 2 0 1 1 1 5 Table 7 1 Approximate values for the coefficient of subgrade reaction a good picture However if you know that ground is compact and homogenous you may consider values from the following table Please note that these values are approximate and more precise values are usually required Several articles state that coefficient of subgrade reaction is not solely a ground characteristics and depends on the beam breadth too Terzaghi 1959 92 1999 2002 Ainet CHAPTER 8 Linear and non linear elements 8 1 General AMSES Frame2D uses two types of elements linear and non linear You work with both
35. 90 1 00 EE Reinforced Concrete ae b 30 00 o 1 0 5 Steel Element supports 2 Bars are not defined 3 Timber width D 00 a D Not designed left 0 00 cm Z 000 010 020 030 040 050 O80 070 O80 090 1 00 right 0 00 cm i5 fet Concrete C 30 37 g Bars are not defined sz Reinforcement Not defined P 00 t gt a 000 010 0 20 030 O40 050 060 O70 080 090 1 00 Ye Y Check ultimate limit states E2 Check serviceability limit st The design of this element is not possible due to the U Ultimate S serviceability following reason s UP G Q ult 1 Reinforcement material is either not selected or it 8 G Q displ is wrong 2 Bottom reinforcement is not defined There are uncovered areas 0 00 1 00 3 Bottom reinforcement is not defined There are uncovered areas 0 00 1 00 4 Stirrups are not defined There are uncovered areas 0 00 1 00 gt 0 15L 14 19 For Help press F1 Select U Clear All MOD Standard 4 Figure 2 14 Initial look of the reinforced concrete design window and T shaped cross sections made of reinforced concrete and tubes boxes and I shaped cross sections made of steel Let s focus back to the figure 2 14 The window is quite empty and the program has reported that it can t check the ultimate and serviceability states due to missing infor mation We must provide information about the reinforcement material longitudinal bars dispo
36. G This opens the load window for se lected action According to the figure the top beam gets uniform load of 20 kN m 1 Select the linear load icon or issue the Add Uniform Force command Note uniform load is just a special case of linear load 2 Click on the top beam and linear load window appears Enter 20 kN m into the Fz field select World for the Load direction and Local for the Load position 3 Confirm the entry by pressing OK Both columns are loaded with 4 kN m The procedure is almost identical here 3 Weare dealing with the gravity load here Since the gravity load always points downwards the load direction refers to the global coordinate system However the intensity of the load depends on the beam length hence the position of the load refers to the local coordinate system 44 1999 2002 Ainet User s manual 3 2 AMSES Frame2D solution 1 Click on the left column and enter 4 kN m into the Fz field The load direction and the load position settings are already in place the self weight illustration shall be visible Press OK to close the window 2 The right column gets the same load To copy the last load hold down the SHIFT key and click on the right column Both columns are loaded now Remember You can use Edit Undo to reverse the last command We still need to load the bottom beam The beam is loaded with 13 kN m You can try this for yourself When you are finished your screen should look like
37. If a selected object is clicked it is removed from the selection toggle behaviour 64 1999 2002 Ainet User s manual 4 7 Objects deletion Rectangle selection A selection can be also made using a stretching rectangle Here is the procedure 1 Switch the program into the rectangle selection mode Use the icon or issue the Edit Select Window command 2 Click to define the first point of the stretching rectangle 3 Move the pointer to locate the second rectangle point A stretching rectangle appears on the screen 4 Click on the second point to define the rectangle All objects located entirely inside the stretching rectangle are selected Comment Youcan hold down the SHIFT key during the rectangle selection too All newly selected objects will be merged with any previously selected objects 4 7 Objects deletion It is simple to delete an object Select an object a node or element and hit the Del key or select the Edit Delete command If a node is deleted all elements that refer to the node are deleted too The same is true for nodal and element load if a node or element is deleted their load will be deleted too We can undo the delete command 4 8 How to move a node We can move one node several nodes or even all structure at the same time Here is the procedure we have to follow 1 Be sure that we are in the selection mode Select all nodes we want to move Do not forget to hold down the SHIFT key
38. N e et dd an Et 72 5 14 Safety factors acron i Gave whe Se ee mare ele nes 72 5 2 Equivalent imperfections vii sews Mad Due at Sn 74 5 2 1 How to simulate the imperfection 2 244424 ee Bs 74 5 3 Concrete creep time depended effects 76 5 4 Load and coordinate systems ey eevee eS PRK a ne Re ee a 77 5 4 1 Concentrated load 77 542 Distributed load 77 5 4 3 Temperature difference load insista ia ee rare mere 80 5 4 4 Prescribed nodal displacements 81 6 General program settings options 83 Gel MIES A NE Aims tacts Satie tiled ge Blak Sk gee psig CA BN 0 83 Oa PRECISION A ee ie eke es ne we ep ee ONE i 83 6 35 Grid amp Snap Umts ies ee ia Sey ra ee ere reed 84 64 Personalize e 3 2 degoa aes ed Avge d a Bag eh es Koai 85 65 Symbol A Vion et eae SES Ue rate Pts 85 6 6 Analysis Lee E O Ma de a ile Soka ad 86 4 1999 2002 Ainet User s manual CONTENTS 7 Element on elastic ground 89 File SOME thE SE ere RS Bk EA Bees ce 89 7 1 1 Displacements error spas Sas Bates es 90 7 12 The solution of the problem is non linear 90 7 1 3 Nodal supports y to pe aid ren ea ls 91 7 1 4 Approximate values for the coefficient of subgrade reaction 91 8 Linear and non linear elements 93 81 Ge neral5 ct Saks mick ta eal Gent watt Be hele ot eel Not cee aa eee 93 8 2 Three kinds of non linearities
39. Program AMSES Frame2D User s Manual Ainet Projektiranje Ale Krajnc s p Ul heroja Roj ka 70 SI 3000 Celje Slovenia Document version 2 00 6 unrevised version Updated on 24th April 2002 1 e mail info amses com User s manual 2 1999 2002 Ainet Contents 1 Getting started 11 Folder tree description ae Wee ra per e EVES Be Ee AES 1 2 Setting up the character Seb 4 na eh Pol BG Botte d 153 sFile sextensSiOns 2 3 23 228 meme ba oe els A alin a eg ape DEN ee be 1 3 1 Renaming ale eB Rah Be BPR dd ala 2 Continuous RC beam 2 1 Problem definition 2 2 AMSES Frame2D solution 2 2 1 Starting a new document yla Dune nine ea 2 2 2 Defining the geometry aoaaa 2 2 3 Actions and load cases LR Analysis AAA AAA RDA Nan SN NES 2 20 a da AAA de Sh iho aod one Pet Se Let en Le ying Sh deli 2 26 Printout 2 sae 0 Gk a As Gee BO wee Be ne 2 2 7 Shortconclusion 3 Steel Frame 3 1 About the Structure voi be nas M Se wd Ps JLL Geometry pee wet ee ee ADA GES 3 1 2 Actions load groups Lee a ES ag 313 Load case ii a eb a den Bla pueraa aa 314 Load case table cue ae at ira de Ar Reel ee K 3 2 AMSES Frame2D solution 3 2 1 Opening anew document structure 3 2 2 Structure geometry sus mutants Sales ne den 3 2 3 Load actions and l
40. The left one is labeled as S1 and the right one as S2 Due to our simple geometry we can realize that the second case S2 can never be mandatory and can be omitted Hence we will use only the first action 51 gt S 33 1999 2002 Ainet User s manual 3 1 About the structure W Wind load The wind can act from two different sides hence two symmetric wind pressure dis tributions are assumed The distribution for the wind blowing from the left side to wards the right side is given on the figure 3 5 We get a symmetric picture when the wind blows from the right 3 12 kN m 2 15 kN m 1 17 kN m 50 250 400 g Pid Pi 2 JZ z 5 Figure 3 5 Wind load distribution load when the wind blows from the left W All major actions are now described and we can focus on their combinations 3 1 3 Load cases In order to get a load case we combine individual actions multiplied with partial safety factors Load cases try to simulate some extreme conditions under which the structure can find itself during its lifetime ultimate limit states Additionally load cases try to simulate rare frequent and quasi permanent conditions which can be met under regular structure operation serviceability limits states Thus each load case gets its individual set of partial safety factors load factors Initial imperfection as a load
41. VETICA e Selection color is the color used to indicate a selected object 85 1999 2002 Ainet User s manual 6 6 Analysis Node We can choose following graphical elements for a node e Line the line color color of the edge of a node circle e Label text the text color used for a node label e Label area color of the circle and label background Element Similar attributes can be set for an element e Linear element color of the linear element line rectangle edge e Non linear element color of the non linear element line rectangle edge e Label text the text color used for an element label e Label area color of the label background Draw element as rectangle In the geometry workspace elements are drawn as rectangles by default The color of the rectangle interior presents either element material or element cross section If you uncheck the Draw element as rectangle check box the element will be drawn as a thin line The second option may be useful on low resolution monitors The figure 6 1 presents both possibilities Figure 6 1 Elements drawn as rectangles left and elements drawn as thin lines right 6 6 Analysis This page is used to specify some analysis parameters Do not change the settings if you are not sure about what are you doing 86 1999 2002 Ainet User s manual 6 6 Analysis Non linear analysis settings The following parameters governs the behavior of the non line
42. a rotation of node 2 reflects to the element 4 only A bending moment in any element can t be transferred to any other element connected to node 2 Thus the second option is equivalent to the first The node 2 acts like a true pinned node There is only one slight difference In the second option rotation of node 2 is used and has its own equation in the stiffness matrix Additionally if a bending moment is put on the node 2 the load will be accepted by the element four and no warnings will be produced We find the second option better mainly because it does not raises false warnings 69 1999 2002 Ainet User s manual 4 9 Some element specific commands 70 1999 2002 Ainet CHAPTER 5 Load 5 1 Basic definitions When we talk about load we use a few terms which are often used throughout the manual These terms are load action and load case They are compatible with the termi nology used by Eurocodes 5 1 1 Load Load is a generic name for everything that has a static or dynamic influence on a structure Typical loads are actual self weight actual dead load actual traffic load actual temperature load actual prescribed displacements reactions earthquake force explosion etc 5 1 2 Action Action represents a group of actual loads which have some common characteristic Loads can be classified in many different ways The most often used classification is presented below Permanent actions G
43. ace area element length units 77 1999 2002 Ainet User s manual 5 4 Load and coordinate systems e Snow load Gravity determines the direction of the snow load Hence the global coordinate system is used for the direction Intensity of the snow load is usually given in per ground surface area baseline lenght This means that the load position refers to the global coordinate system as well e Self weight The load direction of the self weight is also governed by gravity Hence the global coordinate system However the load intensity is expressed in per element length units and element s local coordinate system must be used to define the load position Now let us take a closer look at each of distributed load coordinate system combina tion We named the combinations by the most typical load However other kind of loads may use the same coordinate system combination Wind load direction local position local The wind is actually a pressure that always acts perpendicular to the structure surface hence it has local direction This is true when viscose forces are considered too large roof areas and strong wind The pressure refers to the local x axis unit which means that it lies in the local coordinate system too The figure 5 3 illustrates the situation ry 2 r Coordinate system Load direction C Word Local Load position C World Local Typical wind SE 1 Direction Local Position Local Figure 5
44. ar analysis Maximal number of iterations prevents an endless calculation In most cases only a few iterations are needed to obtain the equilibrium The default settings are 10 iterations Rarely when elements on elastic ground are used this limit may be to severe and a larger value may be selected Relative displacement precision is a parameter that serves as an analysis termi nation criteria for a load case The load case analysis is terminated when rela tive difference of two subsequent solutions nodal displacements is smaller than displacement precision parameter Value of 0 0001 may be used for the ordinary structures Degree of interpolation polynomial This is used for non linear elements only The default value is four Specify greater value to get higher precision and longer calculation times We do not recommend values less than four unless you want to experiment Element results Number of internal points can be set here The results are always calculated at the beginning and at the end of an element However this is not enough and results must be calculated in some internal points too The default setting is set to 9 internal points which gives us 10 intervals Comment The results are also calculated in some special points which are related to the load that acts on the element Such points are concentrated force application points and start and end points of distributed loads 87 1999 2002 Ainet User s manua
45. ar ele ment compared with results that were obtained using other theories first order sec ond order and co rotational Numbers in parentheses represents number of finite elements used to model the problem 96 1999 2002 Ainet User s manual 8 3 Some illustrative examples first solution Second soli 4 E 100 kNiom A 1cm 1 1cmt L 100 cm Figure 8 4 The problem disposition load and illustration of both analytical solu tions Element type theory kinem eq type Analytical First order 157 080 146 741 314 159 Second order 157 080 146 741 a 314 159 Co rotational 2 64 119 0 718 Co rotational 10 63 663 0 002 AMSES Frame2D 1 63 662 0 000 Table 8 1 Results of the test using different kinematic theories The first order theory fails completely We do not get any horizontal displacement but we should and we get an enormous vertical displacement but we shouldn t The second order theory is just slightly better Both displacements are wrong com pletely but at least we got some horizontal displacement True second order theory is of no use here The co rotational theory managed to solve the first problem with sufficient accuracy but we had to apply more than one finite element The program failed to solve the second problem the rigid body rotations were too large AMSES Frame2D non linear element based on exact theory solved both problems with out any problems and with v
46. ars 2 Add new row New bar 3 Enter 3 under n 20 under Fi 0 8 under x start and 1 0 under x end 4 Add new row gumb New bar 5 Enter 1 under n 20 under Fi 0 9 under x start and 1 0 under x end 6 Close the window by pressing the OK button Finally the limit ultimate states requirements are fulfilled Serviceability limit states At the end we must verify the serviceability limit states At this stage of program development we check the crack width only Let s switch to the serviceability limit states checks Press the S Serviceability tab or press the icon In the list of load cases select all load cases that needs to be verified against crack widths In most cases only serviceability load cases are verified We can select them one by one or all of them by pressing the Select S button Once load cases are selected a bar chart appears on the screen figure 2 22 Bars rep resents width of the cracks Since the criteria whether a crack is within limits or not changes from case to case the program does not do any judgement here It merely shows the crack width and allows designer to decide 40 0 Cross section cm Ed 2 20 0 R 30 50 h 50 00 D 000 010 020 030 040 050 060 070 080 090 1 00 b 30 00 Element supports width gt left 20 00 cm right 20 00 cm Concrete C 30 37 Reinforcement RS 400 0 0 000 010 020 030 040 050 060 O70 080 090 1 00 D Positive Negative
47. ateral torsional support at both ends only Nonlinear elements will be used to model the steel frame Hence buckling coefficients of individual elements do not need to be specially considered and we can assume to 31 User s manual 3 1 About the structure take ky 1 0 for all elements This assumption includes local material and geometrical imperfections while the global imperfection is already taken into account during the analysis due to initial imperfection and non linear elements steel frame 370 4L RC beam Le 700 Me gt Figure 3 1 Mathematical model geometry of the steel frame 3 1 2 Actions load groups The steel frame is subject of several actions which are listed below e G permanent and self weight action e Q variable action e S snow action e W wind action In next few steps we will briefly analyse individual actions Unfortunately a detailed analysis is beyond the scope of this manual G Permanent action and self weight dead load Standard weights were assigned to individual elements The beam takes the self weight and weight of the composite slab The columns take the weight of the fa cade elements and the self weight while the concrete beam only takes the self weight Based on this data we calculated loads shown on the figure 3 2 O Variable load Live load acts on the top beam only Actually a load acts on the foundation beam
48. ation 1993 4 E Reissner On one dimensional finite strain beam theory the plain problem J Appl Math Phys ZAMP 23 pages 795 804 1972 101
49. basic approaches e Using the first approach we define equivalent horizontal forces that simulate the inclination skewness of the structure The horizontal forces are applied on nodes at each storey and they act on the ideally straight structure By the ideal structure we mean a structure which is not inclined due to imperfections This approach is assumed by most building codes The drawback of this approach can be found in the fact that we must calculate the horizontal forces that are related to the vertical load on each storey 74 1999 2002 Ainet Refer to your building codes correct factors User s manual 5 2 Equivalent imperfections positive rotation negative rotation Figure 5 1 Illustration of equivalent imperfection a Geometry is skewed right wards negative angle b Geometry is skewed leftwards positive angle e Usign the second approach we specify the inclined skewed geometry of the structure Since the structure is skewed the effects of imperfections are in effect and there is no need to calculate equivalent forces Unfortunately this approach requires high precision on specifying node coordinates which is tedious job We derived an approach which is equivalent to the second one but where an user is not required to specify precise coordinates of skewed structure All she he has to do is to specify the imperfection angle and AMSES Frame2D will do the rest it will skew t
50. by selecting the Geometry Shrink Node command In the case of a long structure the nodes will be too small and we will expand them by selecting the Geometry Expand Node command We can use these commands several times in a sequence Commands shrink and expand annul each other If we issue the first command 3 times and then the second command 3 times we will get the same size of the nodes and symbols as they were at the beginning These commands effects the output too The rule of thumb is that if the picture on the screen looks nice the printout will look nice as well Redraw a view The View Redraw command completely redraws the current view This is useful if the drawing on the screen is corrupted for some reason 4 6 Objects selection There are only three visible objects a node an element and a load In many cases we need to select an object or several objects first and we issue some command on the selection afterwards Single object selection 1 Switch the program into the selection mode by pressing the ES icon located on a toolbar between a view and tree pane or by selecting the Edit Select command 2 Position mouse pointer over the object and click it The object will change the color indicating that it is selected Selecting more than one object The procedure for selection of several objects is similar first two steps are the same Now hold down the SHIFT key and click other objects Object are added to the selection
51. ce Element passes the cross section resistance test if all bars are smaller than 1 0 The color of bars differs according to the exploration rate light blue for interval 0 00 0 50 Pr green for interval 0 50 0 70 as yellow for interval 0 70 0 90 A orange for interval 0 90 1 00 A red for values gt 1 000 Obviously bars should never be red In our case we reach the yellow area Besides the individual cross section whole element stability must be checked as well Basically three kind of checks are made for each element and they vary according to the distribution of internal forces and supports This may result in a few dozens stability checks for each element The result of the most relevant check is presented on the bottom of the screen in a textual form The color of the text refers to the score 1 Values 0 1 refer to class 1 values 1 2 refer to class 2 values 2 3 refer to class 3 and values greater than 3 refer to class 4 5 Besides F we can meet letters W and O as well The letter W stands for the web and indicates cross sections where the web has the highest slenderness The letter O may be met in the welded boxes It stands for the outstand part of the flange 53 1999 2002 Ainet User s manual 3 2 AMSES Frame2D solution In our case all stability checks were passed and the worst cases scores 0 878 hence the text in yellow Serviceability limit state design Serviceability checks are just a few
52. cell to open the skewness window figure 3 8 In our case we enter 260 into the Horizontal field for the angle while we leave the axis location as it is 4 Confirm the entry by pressing OK 10 Define Skewness of the Structrue x Horizontal Vertical 1 1 Angle TS Angle eooo Z center jo m Xcenter 0 m ae Note Effects of the skewness are not visible on the screen the structure will not be drawn in the skewed shape Skewness is used in the analysis only Cancel Help Figure 3 8 The skewness window In reality we skew the structure by prescribing the angle of the skew Rename the second load case from Load case 2 into V max This is an ultimate load case Hence select the Ultimate P amp T from the Limit State column The Fi creep Skew cell shall remain empty Enter load factors that correspond from the table 3 1 G 1 35 Q 1 50 S 0 90 W 0 00 Add new load case by issuing the Load Manager Add Load case command or by pressing the E icon Rename the new row into V min select the Ultimate P amp T limit state and enter corresponding factors into cells See table 3 1 2 The skewness effect can be visualized Issue the Solve Solve command which calculates internal forces and displacements The same command also calculates the initial skewness To see the results switch to the results workspace View Workspace Results and double click the 01 S
53. cribe the physical quantities of the structure and about its approximate size Since this example is defined in 12 1999 2002 Ainet User s manual 2 2 AMSES Frame2D solution metric units we recommend you to keep default settings Don t worry you will learn how to work with the Imperial units later Our structure is 12 meters wide and about 0 5 meters high Figure 2 2 shows the wizard s first page Press the Next button to move to the second page Basic Information Step 1 of 2 2 xj Unit type Metric C Imperial US amp UK You can use any units you like Later you can change default settings any time using the Tool Options command r Structure size ight 05 m El Height 0 5 m Width 12 m You can change these settings later using the Geometry Extents command width Note The global coordinate system you will work with has Z axis pointed downwards This means thatthe structure grows in a negative direction Finish Cancel Help Figure 2 2 The initial size of structure 3 The second page is used to describe the structure The description is optional and AMSES Frame2D will use it as a comment When working on real struc tures we recommend you to take a few seconds and enter the structure descrip tion 4 After the data was entered close the wizard using the Finish button Comment From the height and width given in the wizard the program reserves appropriate wo
54. d direction and load position must be in global coordinate system 4 Press OK to close the window Action W Figure 3 5 on page 34 shows the distribution of wind that we must define for this action Here we will take into account that the wind acts always perpendicular to an element Hence both the load direction and load position refer to the local coordinate system 1 Double click the W line on the three A new window opens which corresponds to the action W 2 Select the icon and click on the top beam where we must define three differ ent loads The linear load window opens 3 Select local for load position and load direction Enter 3 12 kN m into the Fz field 4 Since this load refers only to the left part of the beam we must specify the load start and end position This can be entered using relative or absolute coordinates We will use absolute coordinates here Enter 50 cm into the Abs row under the End at column 5 Press OK to close the window 6 Click on the top beam once again and enter the 2 15 kN m into the Fz field 7 This load starts at x 50 cm and ends at x 300 cm Enter 50 cm into the Abs row under the Start at column and enter 300 cm under the End at column 8 Press OK to close the window 9 The remaining of the beam is loaded with 1 17 KN m Click on the beam and enter 1 17 kN m into the Fz field 10 The load starts at x 300 cm and lasts up to the end Enter the 300 cm into the Abs
55. e flange from the top list and the HE 360 A from the bottom list Pick the green color for this cross section bream Close the window by pressing the OK button Finally we need the foundation beam cross section Press the New button and select the T tab Enter 60 cm into the Depth field 80 cm into the Breadth field 40 cm for the Web thickness and 25 cm for the Flange thickness Label the cross section as T beam and pick the yellow color for it Close the window by pressing the OK button This puts us back to the cross section window Click OK once more to complete the cross section input All elements on the screen are colored in red the color of columns We need to change the cross section of both beams 1 Move the cursor over the top steel beam and press the right mouse button to display the pop up menu Select the Properties menu item and the element property window appears Select the Cross section tab and browse for the HE 360 A in the list Click on the Apply button to make the new selection active The beam on the screen if it is visible turns green Click on the pin icon to make the property window pinned on the screen Click on the bottom foundation beam and repeat the procedure Here we must select the T beam cross section Do not forget to hit the apply button to accept the changes Now we can close the property window 40 1999 2002 Ainet User s manual 3 2 AMSES Frame2D sol
56. e of the element 4 1 1 Global coordinate sistem The global coordinate system is used mainly to describe the geometry of the structure and to declare directions for some of the loads The x axis is horizontal and points 59 Node 3 x 1 8 m 2 4 4 m Note negative sign User s manual 4 2 Unit conversions rightwards while the z axis is vertical and points downwards Such orientation has some advantages First all gravity loads are positive and second the same coordinate system is used by Eurocodes Unfortunately there is one disad vantage the structure grows into negative direction E g If the origin is located at foundations then the top of the building has a negative z coordinate Rotation The figure 4 1 also defines positive counterclockwise and negative clockwise rota tions This definition is valid for both coordinate systems 4 1 2 Local coordinate sistem The local coordinate system is related to an element and is defined by the element di rection The local z axis points from the start node to the end node AMSES Frame2D identifies the element direction with an arrow at the end node The local z axis is ad justed to the local x axis The positive side of the element positive local z coordinate is marked with a dotted line that runs along the element figure 4 2 The positive side is important during the analysis where we must define the positive and negative rei
57. e set them 15 cm apart 1 Select the Design Edit Stirrups command 2 Press the New bar button 3 In the spreadsheet under column n enter 2 under Fi enter 10 under e enter 7 5 under x start enter 0 and under x end enter 0 2 This completes the 0 0 0 2 area 4 Repeat the procedure for the field area Press the New bar button Under n enter 2 under Fi enter 10 under e enter 15 under x start enter 0 2 and under x end enter 0 8 5 Only the third area is missing Pres the New bar button Under n enter 2 under Fi enter 10 under e enter 7 5 under x start enter 0 8 and under x end enter 1 0 The stirrup window is now complete and should look like the figure 2 20 Stirrups editor E xj Stirrups editor F The element does not have any shear reinforcement n Fi mm e cm xstart xend J y New bar 2 10 75 0 02 2 10 15 02 0 8 Delete 2 10 75 0 8 1 x must be given in relative coordinates 0 1 Left click a cell to edit its value Right click a cell to select a row Figure 2 20 The look of the stirrup window after the stirrup information was en tered 6 Close the window by pressing OK Ultimate states calculation Now almost everything is ready In order to perform the ultimate limit states calcula tion we must select which load cases should be used in design Press the Select U button to select all ultimate limit state or simply select the U G Q uls
58. ections If we add a new element which intersects one or more existing elements nodes will be created at all intersections and the intersecting elements will be split at the intersection points The load that was originally put on the elements is split too This default behavior can be altered if we hold down the SHIFT key while we are drawing a new element In this case the new element will be drawn over existing elements and nodes will not be created at intersections The figure 4 6 illustrates both situations 66 1999 2002 Ainet User s manual 4 9 Some element specific commands Figure 4 6 Existing elements left A new element crosses the existing elements Hence two new nodes and four new elements are created middle SHIFT was pressed while the new element was drawn Hence the new element bypasses exiting ones right 4 9 3 Releasing degrees of freedom There are two general approaches for releasing individual degrees of freedom at the element edges e Condensation of element stiffness matrix e Applying a special kind of node called linked node We have used the linked node principle since it is easier to implement it in the pro gram code and because the linked nodes can successfully solve some additional prob lems The disadvantage of this principle can be found in a fact that we can not release axial and shear forces on non horizontal elements In practice this does not present a problem but it is a clear d
59. ed skewed from the vertical The structure must be skewed into direction which increases the internals forces When in doubt the structure should be skewed in both directions To follow ideas from the Eurocode the program AMSES Frame2D defines special load case where we define the initial imperfection This load case does not calculate any forces but simply skews the structure for given angle The same skewness is used in the load cases that follows until a new skew angle is specified Therefore the skewness load case is the usually the first one In our case the structure is skewed for angle 34 rightwards b Maximal vertical load The structure is skewed and on this structure we put a combination of actions that gives maximal vertical load Vmax 1 35G 1 50Q 0 60 1 505 c Minimal vertical load This is the opposite from the previous load case The minimal vertical load is obtained by the following combination Vmin 1 00G 1 50W L d Maximal horizontal load wind is not the leading action A candidate for a maximal horizontal load is obtained if we take the maximal vertical load and add the wind action where the wind is not the leading action Hmaz 1 35G 1 50Q 0 60 1 505 0 6 1 50WL e Wind from the left Another candidate for the horizontal load is the variation of the previous load case where the wind load is the leading action Wind 1 35G 1 50WL 0 70 1 50Q 0 60 1 505
60. ed only a few features of AMSES Frame2D Another example was prepared to show more features and to make you familiar with the steel members design A simple three element frame was constructed The frame founda tion is a RC beam on elastic ground During the analysis and design we will meet most of the essential program features e simple and efficient handling of geometric imperfection e using a precise non linear finite element e beam on elastic ground tension zone is excluded automatically e design of steel elements according to Eurocode 3 3 1 About the structure 3 1 1 Geometry The structure geometry is presented by figure 3 1 It consist of two columns rigidly connected by a beam Both columns have pin connections on RC beam Precise di mensions of elements are not know at this point Initially we can assume that columns are made of HE 240 A hot rolled profiles while the beam is made of HE 360 A Mate rial S235 is assumed for all steel elements The RC beam is of a T shaped cross section depth 60 breadth 80 flange 25 web 40 and it is made of concrete C30 37 The wide part of the beam lies on the ground The reinforcement grade is 5400 f 40 kN cm The subgrade characteristics are given by the subgrade reaction coefficient 0 015 KN cm The geometric imperfection angle is assumed to be ziy Beam has lateral and torsional support at both ends and one additional support at the middle Both columns have l
61. een should look like the figure 3 7 37 1999 2002 Ainet User s manual 3 2 AMSES Frame2D solution Steel frame Let s draw the left column first 1 Make sure that the Ys icon is currently active Steel element should be modeled using non linear finite elements 2 Move the cursor to the coordinate x z 0 0 m and click left mouse button 3 Move the cursor upwards and click on the x z 0 3 7 m coordinate to finish the element Repeat the above procedure for the right column The only difference is that the left column is at x 7 m Once the second column is in place the beam can be drawn The beam connects nodes 2 and 4 1 Click on the node 2 2 Move pointer to the node 4 and click again The steel frame is now completed If you find the elements nodes and labels too large you can make them smaller by pressing the icon a few times Beam on elastic ground There are two issues about the beam on elastic ground that need to be mentioned e The beam must be modeled using linear elements e The local coordinate system of the beam is very important The T shaped cross section has its web always on the positive side and the flange on the negative side In order to make the flange lying on the ground the element must be drawn from right to left Therefore 1 Select the linear element click on the 4 icon 2 Move the pointer over the node 3 and click 3 Move the pointer over the node 1 and clic
62. elongs to the element In our case this is one half of the actual support width 20 cm for either side 3 Close the window by pressing OK Left right support size settings x C Disable support width effects conservative approach Enable support width effects r Support width Width from support center line to the inner side of support usually this is half of the total support width Press Help for more details Atelement start Atelement end 20 lem 20 cm IMPORTANT NOTES 1 Ifyou are unsure about widths of supports you should specify zero width nN Ifyou do notwantto cut the bending moment around supports specify a NEGATIVE value Any value will do the trick This MUST be used if no support is present CANTILEVER case Figure 2 15 Support widths for our continues beam element A support width reduces shear forces and bending moments Reinforcement material The base cross section material was already defined Here we need to define an addi tional material used for reinforcement following given procedure 1 Select the 15 in the middle toolbar or issue the Design Edit amp Select Materials command A window opens where we select the base material and rein forcement material for our element See figure 2 16 Select element materials xj List of concrete materials List of reinforcing steel Cancel Help Note Ifthe listis empty create edit suitable material first You need at
63. ent you want to load The temperature load window appears 80 1999 2002 Ainet User s manual 5 4 Load and coordinate systems 3 Enter the values of temperature difference into the appropriate fields The fields are labelled as Neg z and Pos Z which refers to the negative and positive element side respectively 4 Enter the load name optional and close the window with the OK button The load always applies to the whole element To use the temperature load correctly we must know the direction of the element The temperature load is in strong relation with the element material and cross section properties Temperature Load 21x m Temperature load Neg Ez fo ac Pos 2 f 0 d Name Unknown Cancel Help Figure 5 7 The temperature difference load window We must enter the difference for the positive and negative side of element Both sides can have the same differences of course 5 44 Prescribed nodal displacements Prescribed displacements can be assigned to the supported nodes only 1 Select the icon or issue the Add Prescribed Displacement command 2 Click the node you want to prescribe an displacement 3 Enter the size of the displacement Note you can only assign displacements rotation to supported degrees of freedom 4 Press OK to close the window Comment We can put concentrated force and prescribed displacement on the same node Both loads will be correctly acc
64. epted and processed however their combination will not be drawn on the screen It will be replaced with the Mix U F message AMSES Frame2D will not allow you to put the prescribed displacements on an un supported node but you can fool it and prescribe a displacement for unsupported degree of freedom Example Select a node and support all degrees of freedoms Prescribe displacements and remove the supports afterwards In such a case AMSES Frame2D ignores all prescribed displacements for unsupported directions and it issues several warnings 81 1999 2002 Ainet User s manual 5 4 Load and coordinate systems 82 1999 2002 Ainet CHAPTER 6 General program settings options AMSES Frame2D lets you to fine tune some settings to meet your specific needs Op tions are set in a special tabbed window To open the window issue the Tools Options command Each tab represents a group of specific options 6 1 Units The units page is used to specify the units you want to work with Any mixture of units can be used there is no need to select compatible units AMSES Frame2D will take all necessary steps for unit conversions Selected units are stored on your disk as default units for all subsequent structures Selected units will be used in the output too Units are separated by their physical meaning The Load Metric Default button will set the units that are most practical for the metric system they are build into program and
65. er My Envelope into the Name field 4 Select the leading quantity My O1 Specify which load cases shall be included in the envelope In our case all Ulti mate load cases are included hence turn on the Ultimate checkbox oO It is also advisable to keep the automatic load case selection turned on In this case all ultimate limit states are automatically included into the envelope If the Manual selection is in effect we have to pick load cases one by one 7 Bottom lists show which load cases are selected and which are not Note Some times it is necessary to click on the Automatic button even if it is already selected in order to activate the automatic selection Envelope of contact pressures We still need to define an envelope of contact pressures The procedure is almost identical 1 Press Add New button to define a new envelope 2 Enter C P Envelope into the Name field 3 Select the contact pressure option for the leading quantity 48 1999 2002 Ainet User s manual 3 2 AMSES Frame2D solution 4 Check the Serviceability option and clear the Ultimate option in the load case filter 5 Keep the automatic selection of load cases turned on Envelopes are now defined and we can look at the results In order to browse the envelope results we need to expand the Envelope branch on the tree Once the branch is expanded a list of envelope names appears Double click an envelope name to open the results wi
66. erial name field Pick pink color for the reinforcement 41 1999 2002 Ainet User s manual 3 2 AMSES Frame2D solution 12 Press OK to close the window 13 Close the material main window to complete the definition of materials Press the OK button After the material definition the screen does not change The element colors still refer to the cross sections To alter this situation press the icon on the top toolbar or issue the View Show Material command Now the elements are viewed in their material colors The bottom beam color is wrong It is dark red steel while it should be light gray concrete 1 Right click on the foundation beam element and select the Properties command 2 Select the Material tab from the element properties window 3 Display the material list and select the C 30 37 material for the main material and RS 400 for the reinforcement 4 Do not forget to hit the Apply button to put the changes into effect The beam should turn light gray 3 2 3 Load actions and load cases To describe the load of the structure we must start with the action and load case definition first Both were defined in the initial section of the chapter and they were summarized in the table 3 1 on page 37 AMSES Frame2D uses a similar table to define actions and load cases The final result for our case is presented on the figure 3 9 on page 44 1 Switch AMSES Frame2D into the load workspace This can be done by issuing
67. ering the geometry of the structure a new document structure needs to be open and some basic information needs to be given 1 Start AMSES Frame2D and open a new document structure by issuing the File New command A window opens where we define the name of the structure and the folder where the file will be stored Press the OK button 2 Select metric units and enter the structure extends in order to reserve appropriate drawing area Our structure is about 4 m tall and 7 m wide Proceed with the Next button 3 Enter relevant information about the structure this is optional and close the window by pressing the Finish button Once the process is completed the geometry workspace appears and the geometry window is opened It is wise to maximize it to make the drawing easier 3 2 2 Structure geometry The figure 3 1 shows the frame geometry This is a simple orthogonal frame The up per part consists of three steel elements while the bottom part consist of a reinforced concrete beam that lies on the elastic ground It is important to select non linear elements to model the upper part of the structure Element on the steel elements while the foundation beam needs to be modeled using linear elements elastic ground must Foundation beam lies on the elastic ground and AMSES Frame2D allows such simu oca A lation for linear elements only See chapter 7 on page 89 for more details Once the geometry is set the situation on the scr
68. ery high accuracy 8 3 3 Influence of dummy values for A I or E Non linear elements are very sensitive to the geometrical properties E A and 1 but linear elements are not To illustrate this fact the following example was prepared figure 8 5 Both elements are fully supported and have exactly the same attributes The length of both elements is 200 cm elastic modulus E 1000 kN cm and geometric properties are chosen as A 1 cm and 1 1 cm Both elements are loaded with linear load of 97 1999 2002 Ainet User s manual 8 3 Some illustrative examples B gt LI i gt E TIT Ti iii tiem O RD gb Mi 2 gt r 7 1 KN M Figure 8 5 The disposition top element is linear and the bottom element is non linear 1kN m As you see A and J are non realistic If we choose E 1 kN cm non linear element will produce useless results In addition here are the results Bending moments are shown on the figure 8 6 0 3333 0 3333 0 06649 EC 51 ce qa due cd en gt CA 116 03324 RA gt E Figure 8 6 Bending moments My As we can see the linear element calculated results that we are used to but they are completely wrong Namely I is so small that element behaves as a rope rather than as a beam sk LS d Figure 8 7 Shear
69. es Results of the design are presented on the figure 3 20 Reinfarcement RS 4nn Check ultimate limit states 1 Cross section cm ee Tbeam E 0 0 h 60 00 0 00 0 10 0 20 0 30 0 40 0 50 0 60 0 70 0 80 0 90 1 00 b 80 00 NI tw 40 00 2500 es Element supports width 2 0 00 010 0 20 0 30 0 40 0 50 0 60 0 70 0 80 0 90 1 00 left 0 00 cm o 100 oncrete C 30 F gt Concrete C 30 37 8 00 a ooo 0 10 0 20 0 30 0 40 0 50 0 60 0 70 0 80 0 90 1 00 0 F Check serviceability limit states 0 8 U Utimate S serviceabity Shear Design Figure 3 20 Results of the reinforced concrete design of the beam Serviceability limit states The ultimate limit states are under control but we must not forget to verify the ser viceability limit states too 1 Press the S Serviceability tab 2 Press the Select S button Opps the crack widths are too large more than 0 3 mm Here we have two solutions We may add more reinforcement or try to utilize more bars with smaller diameter or both Try replacing 4 28 bars with 7 21 bars The reinforcement area has actually de creased a little bit however the cracks are now smaller than 0 3 mm and we may ac cept this solution depends on the environment aggressiveness If this is not enough more reinforcement is needed 3 2 8 Output settings When we deal with more than one or two elements we may consider to optimize the q
70. esign These programs were warmly accepted by users however I felt that this is not what I wanted in the first place It turned out that programs are good on their own but they are not so good when they have to communicate with other programs At that moment I realized that most of the structural engineering software is outdated from the user interface point of view This led me into a conclusion that integrated computer aided structural engineering design will be possible only if most of the software is written from scratch Everyone knows that it is practically impossible to write all structural engineering software from scratch It wouldn t have much sense too Many of the packages avail able today are very useful though clumsy One of the Murphy s laws says something like 20 of tasks are used 80 of time According to my experience I am a struc tural engineer and experience of many of my colleagues the Murphy was right This means that we do not need to rewrite all the software to significantly speed up our work the 20 will be just fine In the beginning of 1997 I gathered a group of developers and supporters and we started our work The project goal was to write that 20 of the software we use almost all the time We named our project as AMSES project Today I am proud that our first product has reached the mature state and I wish that you will find this software useful enough to register it and support our further work Ale
71. essions or diagrams in the relevant codes EC2 In our case we assume creep coefficient de 2 2 Since the ultimate limits states are simulations for extreme loading situations which occur seldom and last only for a short period they are not prone to the creep effects On the other hand the service ability limit states simulate situations which occur often and can last for longer period Hence creep effects must be considered too Please see Eurocode 1 3 and Eurocode 2 1 for more details 2 2 AMSES Frame2D solution The continues beam geometry materials and its load are well defined and we can start solving the problem The problem will be solved in several steps 1 Starting a new document structure 2 Defining the geometry 3 Actions and load cases 4 Action load 5 Analysis 6 Design of individual elements according to EC2 7 Printout 2 2 1 Starting a new document Run the AMSES Frame2D program if it is not already running Before a new structure can be analyzed a new document had to be opened 1 To open a new document select the File New command A window appears asking for a file name and a location where the file should be stored Enter the Continues Beam into the Structure name field and keep current settings for the Location field Close the window with the OK button 2 A simple wizard is used to collect some basic information about the structure The first page asks about units that we use to des
72. gn and a list of load cases appears When the list of load cases is visible double click the line named as G Q uls This opens result window for the selected load case If this is the first opened window then bending moments are presented The toolbar in the middle holds several icons which can be described as shot cuts to 19 display bending moments display axial forces tension is positive Fel display shear forces us display nodal displacements and reactions display local element displacements 4 display rotations make diagrams larger comparing to the structure size Y make diagrams smaller comparing to the structure size toggles result labels on off The toggle effects the printed output too All these commands can be also reached via the Diagram menu 1 35 Stalni vpliv G 1 50 Spremenljivi vpliv Q Enote kNm Figure 2 13 Results bending moments of the first load case Results of the second load case G Q sls can be opened if you double click appro priate line in the tree To see desired internal force or displacements simply select corresponding button on the middle toolbar 20 1999 2002 Ainet User s manual 2 2 AMSES Frame2D solution Specifying number of calculation points AMSES Frame2D calculates internal forces at the both element ends at load applica tion points and at equidistant points across the element The number of equ
73. h a large number of load cases In order to have one look over all load cases or over a subset of load cases we define an envelope for a particular quantity an internal force displacement contact pressure Usually bend ing moment M is selected for the leading quantity Any number of envelopes can be defined Let us define two envelopes e Envelope of bending moments M We will include all ultimate limit state load cases e Envelope of contact pressures Here we will include only serviceability load cases 47 1999 2002 Ainet User s manual 3 2 AMSES Frame2D solution Envelope of bending moments An envelope is defined in a so called Envelope Manager 1 To open the Envelope Manager window find the corresponding line in the tree and double click it Note Maybe you need to scroll down the tree to see the line The window is shown on figure 3 12 Envelopes _ Leading quantity Sal Load case filter r Load case selection My Envelope C My Cfi Y Ultimate Automatic CP Envelope C Fx C ux I Serviceability C Manual C Fz uz I Creeping y contact Sipe pressure IE Srewmees Load cases used in envelope ee Selected Not selected Name My Envelope Add New Delete LE EA Figure 3 12 The Envelope Manager window The window shows values and set tings needed to define the envelope for bending moments 2 Define a new envelope press the Add New button Ent
74. he structure put on the load and calculate results all behind the scenes Furthermore it allows you to specify different initial imperfections for different load cases Namely the structure may be non symmetric and you can not know in advance which skew direction will lead to the right effect The skewness load case We defined a special load case and named it Skewness It can be defined in the Ac tion LoadCase Manager window The skewness load case is a special load case that simply skews the structure for a given angle All subsequent load cases are than eval uated on the skewed geometry You can define any number of skewness load cases Example Let s consider six load cases presented in the table 5 2 To simplify the example only two action are used AMSES Frame2D will interpret the table 5 2 as follows Skew leftwards Incline the structure for ziz radians in the positive direction counter clockwise All load case factors are ignored and no other calculations are done Load case 1 Calculate the load case using specified factors and skewed geometry Load case 2 Calculate the load case using specified factors and skewed geometry More load cases may follow here The skewed geometry is used until another skewness load case is met 75 1999 2002 Ainet In general you can not know which skewed direction will give more unfavourable effect User s manual 5 3 Concrete creep time depended effects
75. hile the others support the beam in z direction only All supports have the same width of 40 cm The beam cross section is rectangle Its depth is 50 cm and breadth is 30 cm The beam is made of concrete C30 37 a quality specified by Eurocode 2 1 The beam is subject of two uniform loads permanent load 15 kN m and traffic load 30 kN m The permanent load is member of action G and the traffic load is member of action Q These two actions are combined into two load cases The first load case represents the ultimate limit state and the second represents the serviceability limit state We named the first one G Q uls and the second G Q sls Results of both load cases will be used later by design process See table 2 1 The beam is made of reinforced concrete When a concrete is subject of long term load it suffers from creep and shrinkage effects The shrinkage and creep mainly de pends on the ambient humidity the dimensions of the element the composition of 11 User s manual 2 2 AMSES Frame2D solution Load case G Q G Q uls 1 35 1 50 G Q sls 1 00 1 00 Table 2 1 Actions load cases and load factors the concrete the maturity of the concrete when the load first applied the duration and magnitude of loading EC2 takes this into account using a simplified approach It simply reduces the concrete elastic modulus by factor 1 e Here e denotes the creep coefficient which is obtained from expr
76. idistant points can be specified by the user For the sake of design it is wise to select maximum number of equidistant points regardless to increased computing time and memory re quirements 1 Issue the Tools Options command 2 Select the Analysis tab 3 Inside the Element results frame enter 19 which equals to 20 equidistant inter vals across the element 4 Close the window pressing OK The program remembers this setting and it will be applied for all subsequent cases 2 2 5 Element design Analysis results seem logical and we can move forward to element design AMSES Frame2D does not really design elements but it checks if they are capable bear the load The principle here to specify and verify Some properties are specified first and its verification follows We find such approach very useful Namely an engineer develops a special feeling for realistic results The engineer is still in charge here It is he or she which decides what properties a cross section should have not a computer program In our case we will choose number of reinforcement bars and its disposition Once this is done the computer program will tell whether our selection fulfils the building code requirements The reinforcement is defined on element per element basis in the design workspace We invoke the design workspace by one of the following actions e Click on the tab f below the tree on the left e click the icon If in the main toolbar
77. ified See figure 3 15 2 The Load application position is already correctly selected it is unfavorable The same is true for the shear web stiffeners we don t have any We only have to tell that the beam has an additional ZZ weak axis and torsional support in the middle 3 Press the ZZ weak axis button and a new window opens figure 3 16 In this window we specify support positions and buckling koeficient between subse quent supports usually 1 0 In this case an additional support is needed 4 Increase number of supports to 3 Click up arrow once or enter number 3 5 Enter 0 5 into the empty field that appeared in the Rel pos row 50 1999 2002 Ainet User s manual 3 2 AMSES Frame2D solution Steel element design data xi Intemediate supports and buckling lengths a a a a a V x VIV x V x VV x Y T 7 r T 7 0 0 0 50 1 00 0 0 0 50 1 00 0 00 0 50 1 00 YY strong axis ZZ weak axis LT lateraHorsional Load application position Distance between shear stiffners Unfavourable Indifferent Favourable Stifmers are not present OI Cc 0 K l m C Di il JO Ji 1 Fi Distance between stiffners cm OK Cancel Help Figure 3 15 Steel design data window Here we specify additional geometric in formation about individual steel element Supports and buckling lengths x I C Elemen
78. ing on large cases we get a significant amount of the printout To reduce the printout we use the Tools Output Settings command This command opens a special tabbed window where we are able to define what shall be printed The most important are the Results and Geometry amp Load tabs We should exclude all tables and figures that are not needed After the change it is wise to restart the print preview This will tell us if the new setting were correct Comment Some printer drivers do not process non horizontal text e g vertical reactions properly This error can be avoided by selecting the Tools Output Settings command On the General page you will find the Check this box if checkbox Check the box and close the window by pressing OK to correct this error The printer output should work properly However the print preview will be wrong 2 2 7 Short conclusion Your first structure has been successfully analyzed and designed We also printed the results You can handle other structures in a similar manner Before you start using AMSES Frame2D on regular basis we recommend you to read the rest of the manuals There you will find many details that will enable you to use the program more efficiently The next chapter covers similar topic as this one but deals with steel elements forming a simple frame 30 1999 2002 Ainet CHAPTER 3 An example of steel a frame and a beam on the elastic ground The previous example has reveal
79. is area the cross section capacity is ex ceeded and we must either specify more reinforcement or make the cross section larger In our case we will fix the stirrups first The chart shows that more stirrups are needed in the 0 7 0 8 area In this area we have stirrups 15 cm apart Let s reduce the field area to 0 2 0 7 and increase the end support area to 0 7 1 0 1 Issue the Design Edit Stirrups command or double click the stirrups chart on the top 2 Alter the second row in the spreadsheet Under field x end enter 0 7 In the third row alter the x start field Enter 0 7 3 Close the window The stirrup situation is now fine Still we must fix the longitudinal bars Let s deal with the positive reinforcement first We will add an additional bar along the complete element and two more bars 20 mm over the 0 1 0 7 area 1 Select the Design Edit Positive Bars command 2 In the first row change the n from 2 to 3 3 Press the New bar button and enter the following data into the new row 2 under n 20 under Fi 0 1 under x start and 0 7 under x end 4 Close the window 27 1999 2002 Ainet User s manual 2 2 AMSES Frame2D solution The positive reinforcement seem to be OK now We still need to fix the negative one To put it into the order we will add three bars over the 0 8 1 0 area and one more bar over the 0 9 1 0 area 1 Open the negative reinforcement editor Design Edit Negative B
80. isadvantage from the educational point of view How do the linked nodes work The best way to answer this question is to look at an example Let s suppose that we want to release bending moment at the end of a beam that is connected to a col umn The situation is presented on the figure 4 7 In this case we insert an additional hidden node 2 which has some of its degrees of freedom linked to the node 1 The node 2 is called the linked node and the node 1 is called the master node in this example 2 linked node 1 master node Figure 4 7 Illustration of the linked node example Master and linked node usually almost always have the same coordinates In order to speak about the linked node the hidden linked node must have some degrees of 67 1999 2002 Ainet The program uses hidden linked nodes to release internal forces Element displacements can be released only if the element lies parallel to world x axis Rotations can be released in any case The 3 icon toggles releases at the end of an element User s manual 4 9 Some element specific commands freedom linked with the master node If a degree of freedom is linked bound then any change of the degree of freedom on the master node will be identical in the linked node too In this case both nodes refer to the same equation in the stiffness matrix If a linked node has all its degrees of freedom linked with a ma
81. k once more to complete the beam The element must have green frame which indicates that it is a linear element 4 We must assign springs bi linear to the element To do this select the 1 icon from the toolbar 5 Click on the beam and a window opens figure 3 6 6 Enter the 0 015 kN cm value for the subgrade coefficient and select the negative side as shown on the figure 7 Press OK to close the window 38 1999 2002 Ainet User s manual 3 2 AMSES Frame2D solution Elastic Ground Data x m Elastic ground support coefficient 0 015 kN cm3 Elastic ground support type C No ground supp Cancel C Both sides C Positive side Help Negative side Figure 3 6 A window where subgrade coefficient and its position are specified Supports If we look at the structure as a rigid body we realize that the structure is not sta ble The elastic springs supports the structure at the bottom but they do not prevent the movement in the horizontal direction Hence additional supports are needed as shown on the figure 3 1 page 32 1 Select the icon from the toolbar on the right and click the node 1 This makes the structure stable 2 Nevertheless select the ll icon and click the node 3 to make the both sides sup ported Element releases Currently both columns are rigidly connected to the foundation beam This is not in correspondence with the figure 3 1 on page 32 We need to relea
82. kew rightwards line Finally select the Uy icon to view the displacements 43 1999 2002 Ainet User s manual 3 2 AMSES Frame2D solution 11 Repeat this procedure for all other load cases The only thing we should take care about is that the V max S and H max S have different limit state They are Serviceability load cases This is important from the design point of view Limite state Fi creep Skew G Q S W FT Skew rightwards Skewness Z 1 260 pat Y max Ultimate PET 1 350 1 500 0 900 pat V min Ultimate P amp T 1 000 1 500 pat H max Ultimate PRT 1 350 1 500 0 900 0 900 est Wind Ultimate P amp T 1 350 1 050 0 900 1 500 est SNOW Ultimate PET 1 350 1 050 1 500 E Y max S Serviceability 1 000 1 000 0 600 E H maxs Serviceability 1 000 0 700 0 600 1 000 Figure 3 9 The look of the action load case spreadsheet after the entry was com pleted 3 2 4 Load actual load of individual actions Actions have been already defined in the section 3 1 2 which start on page 32 We will load the frame elements and nodes according to the schemas presented in the section Action G The load disposition for this action is presented on page 33 figure 3 2 To arrange the load in accordance with the figure the following procedure should be followed 1 Make sure that the tree on the left has the Action branch expanded If this is not the case click on the in front of the branch 2 Double click on the action denoted by
83. l 6 6 Analysis 88 1999 2002 Ainet CHAPTER 7 Element on elastic ground Structural analysis always requires some idealizations of structure under considera tion The same is true for the foundations too Foundation idealizations in the sence of rigid fixed pinned and movable nodes are sometimes adequate but there are also many cases when they are not This is especially true in situations where upper part of the structure lies on beams which are laid directly on the ground Relationships be tween foundation ground and structure may be quite complex here To solve many of problems of this type this chapter introduces a special kind of finite element element on elastic ground 7 1 Some theory Element on elastic ground is a special kind of finite element that serves as a link between the upper structure and the foundation ground subgrade As its name suggests it implies that the behaviour of the subgrade is elastic In order to use such an element we must know the coefficient of subgrade reaction k This coefficient tells us how big is the contact pressure p between the beam element and the subgrade if the element moves perpendicular towards the subgrade for one length unit w The mathematical model of this situation is presented on the figure 7 1 The figure 7 1 shows two typical results Figure A shows initial state Figure B shows the case where the element stiffness is large enough to push complete element
84. least z one Concrete and one Reinforcement Steel material 15 Material Figure 2 16 A window used to define concrete and reinforcement material Rein forcement material is not known yet 2 The concrete material is already given Only the reinforcement is missing In order to select one we must create it first Press the S Material button and the material editor windows opens 3 We need a new reinforcement material Hence press the New button 23 1999 2002 Ainet User s manual 2 2 AMSES Frame2D solution 4 Select the Reinforcement Steel tab 5 Our material shall be RS 400 Its yield strength is 40 KN cm2 or 400 MPa Name the material as RS 400 which should be entered into the Material name field figure 2 17 Specify the material color and press OK to close the window Create New Material 24x General Steel Concrete Reinforcement Steel Reinforcement steel information is Material name AS 400 given according to European Standard prEN 1992 1 Meterial color 0O Elastic 7 Class modulus MPa Classes of Convenience EN 10080 Coef of thermal F 2E 5 E A eps uk 2 5 expansion ake C B eps uk 5 0 Yield strength 400 MPa C Clepsuk 7 5 Density 7850 kg m3 When in doubt select class A These settings are optional and informative only Figure 2 17 A material editor window 6 We are back to the material editor Close this
85. me one global factor Note that most modern building codes utilize partial safety factor approach Different global factors are usually used for different load combinations We will show this on an example Let us suppose that three actions have been defined e G permanent action e S snow action e W wind action Now suppose that building codes prescribe a global safety factor of 1 50 for the pri mary load case and 1 33 for the supplementary load case Knowing this we can set up the four load cases we can set up any number of load cases 1 Load case 1 50 G 1 50 S 0 00 W 2 Load case 1 50 G 0 00 S 1 50 W 3 Load case 1 33 G 1 335 1 33 W 4 Load case 1 00 G 1 00 S 1 00 W The load cases above can be presented in a tabular form table 5 1 Note that only one factor but zero is used for each load case 73 1999 2002 Ainet Geometry imperfection must be included in the analysis User s manual 5 2 Equivalent imperfections Partial safety factors Partial safety factors are used in most modern building codes e g Eurocodes The basic rule here is that each action used in a load case has its own factor Since many different factors are used one should have building codes at hand for a quick refer ence Example Let us assume that we have the same three actions as in the global safety factor case Knowing this we set up the four load cases we can set up any number of load cases 1
86. me the load as traffic load 4 Close the dialog with OK The element one has its linear load defined 5 Hold down the Shift key and click the element two Now the second element has the same load as the first one The screen should match the figure 2 12 1 2 gt gt O 1 2 A 35 KN M 35 KN M b Figure 2 12 The continues beam and action load Q This completes the load definition 2 2 4 Analysis This is the easiest part Simply press the B icon on the standard toolbar or issue the Solve Solve command We can issue this command anytime If anything goes wrong during the calculation error messages are displayed in the message window which is located at the bottom of the screen To browse the analysis results we need to switch into results workspace We can do this in three ways e Click the 4 tab below the three pane 19 1999 2002 Ainet 19 Project Continues beam i Structure Continues beai El Load cases 02 G Q displ E Envelope Manager 1 Envelopes User s manual 2 2 AMSES Frame2D solution e click the 4 toolbar icon e select the View Workspace Results command The contents of the screen changes after the switch The load windows have disap peared menus toolbars and the three have changed Now we see the results workspace layout Results of each load case are presented in a separate window To open a result window we must expand the Load cases branch Click on the plus si
87. nalyses both cantilevers although they have no common nodes or elements User s manual 8 3 Some illustrative examples ural ps ERA Figure 8 2 Bending moments shown for both cantilevers Linear and non linear analysis were used for left and right cantilever respectively is made of non linear element Since non linear analysis takes displacements into ac count axial load contributes to bending moment too This makes non linear result 25 6 larger The figure of displacements presents similar situation Free edge of linear element moves 31 34 cm towards the X axis direction while non linear element moves 40 85 cm Displacement of the right cantilever is larger due to larger bending moments inside the element The non linear displacement exceeds the linear displacement for 30 3 Figure 8 3 Displacements shown for both cantilevers Linear and non linear anal ysis were used for left and right cantilever respectively 8 3 2 High accuracy horizontal cantilever and bending moment The aim of this example is to show high precision of AMSES Frame2D non linear finite element The figure shows 8 4 the disposition of the element and moment load The moments are calculated as M 2 and M 42 The analytical solution of the first moment results in a half circle while the second moment results in a perfect circle The table reveals 8 1 results we got using only ONE AMSES Frame2D non line
88. nch is always empty while the Not designed branch holds ele ments that do not fit into any other branch and can t be designed by AMSES Frame2D Expand the Steel item and double click element 3 The situation on screen changes and it looks like the figure 3 14 Alternatively double click the Design resume item This opens a window where all elements are presented Now double click the top beam element to open its design window Cross section cm Z Z Supports HE 360 A h 35 00 v x K v v y v b 30 00 0 00 020 040 0 60 0 80 1 00 0 00 020 0 40 060 080 100 0 00 0 20 040 060 0 80 1 00 tw 1 00 tf ee Relative load position used in LT calculation is 1 00 unfavourable r 2 Element supports width left 0 00 cm right 0 00 cm 4 0 Y Y Supports LT Supports Steel S 235 30 Classification F Check ultimate limit states M Check serviceability limit states U Uttimate S serviceabiity Shear amp CS Resistance Element stability was not checked Select U Clear All Figure 3 14 Initial look of the steel element design window Supports The beam geometry has not been completely defied yet Namely the beam has an additional lateral torsional support at the middle Here is the procedure for its definition 1 Select the Design Steel Design Data command to open the window where addi tional information about beam supports can be spec
89. nd y axis Fortunately in vast majority of cases we want to release rotations only In order to release an element simply press the icon This puts us in the toggle y release mode Now all we have to do is to click on an element end where we want to release the rotation 4 9 4 Pinned node simulation AMSES Frame2D does not support pinned nodes directly If we must model such node we need to simulate it There are two options Option 1 As it is shown on the figure all elements that are connected to the node 2 use linked nodes which are linked to the master node 2 All linked nodes have their rotational degree of freedom released In this case rotation referred as in the node 2 is not used This will be noticed by AMSES Frame2D during stiffness matrix set up and a warning will be issued Solving Warning 1017 No equation was assigned for degree of freedom Ry in node 2 If we put moment load on node 2 we will get even more warnings Namely there is no way for the structure to resists such a load Note that the structure will be calculated properly despite the warning the moment load will be ignored 68 1999 2002 Ainet User s manual 4 9 Some element specific commands Option 2 The second option is similar with one difference One of the elements element 4 does not have linked node and it is directly connected to the node 2 All other elements are connected via linked nodes This means that
90. ndow and browse the results in the same way as you browsed the load cases Figure 3 13 shows the results for contact pressures f a ml eer SA P tf A ane 0 01055 3 77 AT 0 01234 410 01203 0 0138 Figure 3 13 Envelope of contact pressures Boxed numbers pressures are given in kN m units 3 2 6 Design of steel elements Once the structure is stable and the internal forces are calculated we can design its elements Note that envelopes we have just defined have nothing in common with the design During the design each element is verified against all selected load case individually Before the design takes place it is wise to define groups of elements that shall have the same cross section properties In our case we have already done this both columns have the same cross section the top beam has its own as well as the bottom beam Top beam element 3 Now it is time to perform design for each element We will start with the top beam The design takes place in the design workspace Select the View Workspace Design command or press the 12 icon to switch into the workspace 49 1999 2002 Ainet User s manual 3 2 AMSES Frame2D solution In the tree you can see several branches which hold individual elements The Steel branch holds elements which can be verified against rules and principles of Eurocode 3 steel design the Reinforced concrete branch holds elements verified against Eu rocode 2 the Timber bra
91. nforcement Figure 4 2 An example of local coordinate systems Dotted lines represent positive side of the elements positive side of the local z axis 4 2 Unit conversions AMSES Frame2D has a unique feature which can not be found in any other similar program It can automatically convert between units of the same physical base This enables us to enter data in units that we are most familiar with These units are then automatically converted into the units needed by the analysis When the analysis is finished units are converted back to the desired units Example Assume that we use cm for distance and kN for forces If we want to enter some force per distance unit then most computer programs require the kN cm unit However this is an impractical unit since loads expressed in kN cm are very small and we do not have the right feeling for them To overcome this shortcoming AMSES 60 1999 2002 Ainet User s manual 4 2 Unit conversions Frame2D accepts any unit kN m kN cm or even klbf in All we have to do is to select the correct unit before we enter its intensity 4 2 1 How to use the unit conversion AMSES Frame2D uses the unit conversion feature wherever it is possible In order to use this feature correctly we have to follow one rule Select the unit first and enter its value later In most cases default uni
92. nts are useful too They are typically used to model beam on elastic sub grade problems Linear elements are also often used in educational process Since both elements are used in the same way we do not distinguish between them in this section Each element has following properties e An index that uniquely defines an element e An element name any name can be used It is used as a comment e Indices of start node and end node which define the element position e Material index which refers to material properties e Cross section index which refers to cross section properties e Releases of individual degrees of freedom at either side of the element e Elastic ground properties that are used when the element is laid on the elastic subgrade Winkler halfspace Note This feature can be used with linear ele ments only 4 9 1 Orthogonal elements When we work on a structure which has orthogonal elements we may turn on a feature which prevent us to draw inclined elements The feature is called ortho mode We can toggle the When the ortho mode is turned on elements are drawn either in horizontal or in ver ortho mode while we tical direction regardless to current mouse position If we want do define inclined are dragging a new a e element elements we simply turn the ortho mode off by pressing the icon in the middle tool bar or by selecting Geometry Orto Mode The icon behaves like a toggle 4 9 2 Element inters
93. oad cases 3 24 Load actual load of individual actions 3 2 5 Analysis y eee AA Eee A ene 3 2 6 Design of steel elements ei iaa 3 2 7 Design of reinforced concrete beam 32 8 Outputseftings s Gs a O Sl So E a ts 10 10 10 User s manual CONTENTS 4 Basics 59 4 1 Coordinat syst ni Bor esters Both cots Re bean wa ee Be S 59 41 1 Global coordinate sistem 59 41 2 Local coordinate sistem 60 402 UNIECONVETSIONS 23 54 int da an Se a Be Ee 60 42 1 How to use the unit conversion 61 43 Object properties 0 ls ur da ro AEE Be rei ete 62 44 Undo REd System sn gt eE a Des ee soin users 62 45 View related commands 63 4 5 1 Zoom 0 0 cee ee 63 4 5 2 Other view commands 64 46 Objects selections e rod aes a De gs need 64 47 Objects deletion 24x e565 Pode e Eee SAN AAA 65 48 How to move anode 65 4 9 Some element specific commands vii a 66 4 9 1 Orthogonal elements ida AA BEE 66 4 9 2 Element intersections 66 4 9 3 Releasing degrees of freedom iii sets 67 4 9 4 Pinned node simulation 68 5 Load 71 5 1 Basic definitions 71 D Lil o Load AA a 71 DiL22 CACHO ic 32 ak ee a id a See eee 71 51 3 load cases Mi at ne rx to ME
94. ometry toolbar Cross section and material are defined and we can move forward to define actions loads and load cases 2 2 3 Actions and load cases In order to define a load we must invoke the Loads workspace first This can be done in one of the three ways e By pressing the 8 button on the standard toolbar e by selecting the 8 tab under the three in the left pane e by selecting the View Workspace Loads command We notice significant change on the screen Elements have disappeared menus tool bars and three in the left pane have changed This is the default load workspace lay out In next step we will define actions and load cases Actions and load cases are defined in a special spreadsheet like window 1 Double click the Actions Load Cases Manager line which is located at the top of the tree on the left or select the line and press Alt Enter key This opens the spreadsheet window 2 Enter action names load case names and load factors as defined at the beginning of this chapter table 2 1 When we are finished our spreadsheet should look like one on the figure 2 9 Limite state Fi creep Skew G Q ULT 25 G Q UI Ultimate PRT 1 350 1 500 EY G displ Serviceabiity 2 200 1 000 Figure 2 9 The spreadsheet window after the entry has been completed 3 Cells in the column Fi creep Skew have special meaning In this case they define the creep coefficient of the concrete For the short term loads ultima
95. one by pressing the OK button 7 Now the reinforcement material is defined and appears on the reinforcement list We must select highlight it Being on the list it does not mean anything A material must be highlighted in order to be selected even if it is the only material in the list The figure 2 18 reveals the correct selection for our element 8 Close the window The program has noticed the new reinforcement material Now it complains for the longitudinal bars and stirrups only Select element materials xj List of concrete materials List of reinforcing steel Cancel ele Note Ifthe listis empty create edit suitable material first You need atleast one Concrete and one Reinforcement Steel material 15 Material Figure 2 18 Reinforcement material is defined and selected highlighted Longitudinal positive bars Our next task is to define the quantity and disposition of the longitudinal bars and stirrups The principle is the same in all cases 24 1999 2002 Ainet User s manual 2 2 AMSES Frame2D solution For start we assume two 20 mm bars along the whole element The concrete cover is 3 cm 1 Select the Design Positive Bars command A window like shown in the figure 2 19 appears Reinforcement bar editor E xi m Reinforcement bar editor 8 Row1 Row2 3 Row3 n Fifmm xstt xen New bar 2 20 0 1 Delete Concrete Cover x must be given in relative coordinates
96. put Zeros are extra sensitive In many cases values that should be zero are displayed as e g 1 432532E 14 The Threat values smaller than 1 E X as zeros option allows us to overcome the undesired effect above Values as 1 432532E 14 will be filtered out and replaced with a true zero on the output which is what we wanted on the first place Comment If we are working on a small structures and if we selected such units that produce results of very small magnitude we have to either turn the filtration off or replace the threshold value with an appropriate 6 3 Grid Snap Units The grid and snap units page is mostly related to the geometry workspace The grid and snap settings help us to draw the structure element and nodes On this page we can fine tune the snap and grid settings Units type Metric or Imperial units can be selected Metric units are selected by default Grid amp Snap The major and minor steps are set here We have to select the unit size of the step in selected units and color of the step marker The step size settings depend on the unit type Following values can be used for metric and imperial unit system respectively e Metric system cm and m may be selected for the step unit The step size can be 100 50 10 5 4 2 1 1 2 1 4 1 5 and 1 10 of the selected step unit e Imperial system in and ft may be selected for the step unit The step size can be 12 6 4 3 2 1 1 2 1 3 1 4 1 6 and 1 12 of selec
97. re w x 0 and exclude lifted parts of the element In general this is a tricky job especially for non linear elements Namely it is difficult to identify all zeroes of the w x since w x may be complicated function which consists of several high degree polynomials Therefore we decided to use linear elastic finite element that has analytic solution for w x which is a polynomial of third degree For this polynomial we can easily identify all x points for which w x 0 7 1 1 Displacements error Since the element on elastic ground is based on the linear elastic element some error is present in the displacement w x According to the Galerkin method finite ele ment method the error can be minimized if more finite elements are used AMSES Frame2D automatically splits every element on elastic ground into tree hidden finite elements to minimize such error The splitting is not visible from the outside it is done internally All you can notice is that more degrees of freedom are used by calcu lation as one would expect 7 1 2 The solution of the problem is non linear Although the element on elastic ground is linear the solution of the problem may not be linear If the case C lift off the ground happens several iterations are needed to calculate contact areas properly In the case B only one iteration is needed to obtain the solution In the case C the convergence rate is linear This means that quite a few iterations
98. rking space The origin is set to the bottom left corner which means that top right corner lies in positive x direction and in negative z direction of the world coordinate system As you can see the z axis of the world coordinate system points downwards 2 2 2 Defining the geometry Maximize the main window and the working view This will help you to track precise mouse movements When the window is maximized it should look like the figure 2 3 The continuous beam is made of two elements Both elements are six meters long You start drawing the first element at the origin 0 0 1 Move mouse pointer over the origin coordinate 0 0 We can see current mouse pointer coordinate if we take a look at right side of the status bar Press left mouse button to start drawing the first element 2 Move mouse pointer to the right Notice that a thin line is drawn from the origin to the pointer Move the pointer to the coordinate 6 0 3 Press left button and you will get the first element The figure 2 4 presents the situation you should see on the screen two unsupported nodes and an element 13 1999 2002 Ainet Hold a mouse movement for a while to display a small tip window which will provide useful information User s manual 2 2 AMSES Frame2D solution AMSES Frame2D Continues beam Geometry E E I0 x D File Edit View Geometry Solve Tools Window Help le xj osusnra gt ema o eea a e
99. row below the Start at column The end position is already in place 11 Press OK to close the window 46 1999 2002 Ainet User s manual 3 2 AMSES Frame2D solution Both columns are loaded too The left column takes 0 78 kN m while the right one takes 1 37 kN m 1 Click on the left column enter 0 78 kN m into the Fz field and press OK to close the window 2 Now click on the right column and enter 1 37 kN m into the Fz field When you press OK to close the window the wind load is completed If everything went well your screen should look like the figure 3 11 We have just defined the last action and we can move on to the analysis 2 14 O 3 O PAAZ Km A TT 2 15 kN im T f K W LTT TTT T117 kNm TT TTT ZH Ziz aor RH N m o 0 RE A LEA O Ca Figure 3 11 The load of the action W wind load 3 2 5 Analysis The geometry and load of the structure are completely defined and we can calcu late internal forces and displacements To view them we must move to the Results workspace Issue the View Workspace Results to move there The tree shows load cases that we have defined in the spreadsheet Since the analysis has not been performed yet all windows are empty In order to perform the analysis issue the Solve Solve command After the command had completed the job we can browse results for each individual load case Envelopes Sometimes we have to deal wit
100. rts Both elements are in place Now we will support them by changing individual nodes into supports 1 Locate the support toolbar on the right side and press on the a icon which represents a fixed pinned support 2 Click on the node 1 Right after the click the node changes its shape to the shape of the selected support 3 Select the 4 icon on the support toolbar a movable pinned support 4 Click on nodes 2 and 3 The screen should look as shown on the figure 2 6 Figure 2 6 Supported continues beam Cross section In this step we will define cross section of both elements When a new element is created it binds itself with a default cross section If the default cross section does not exist it automatically binds itself with a cross section that has index 1 even if such cross section does not exist So far we did not define any cross sections and for this reason all elements point to a non existing cross section 1 1 Select the Geometry Cross section command This opens the cross section edi tor window Press the New button to create a new cross section 2 Ina tabbed window select the Rectangle tab and enter cross section dimensions depth 50 cm and breadth 30 cm as shown on the figure 2 7 Create New Cross Section 21x General Rectangle Circle ouble sym T Tube Box Depth A 1500 cm2 312500 m i250 cm3 lz 112500 cmd
101. s e concentrated load forces and moment e distributed linear load uniform load is just a special case of linear load e temperature difference load e load influenced by prescribed displacements 5 4 1 Concentrated load A concentrated load can be put on a node or on an element When it is put on a node its values F in F refer to the global coordinate system However when a load is put on an element we can choose the coordinate system figure 5 2 No gt 20 kN M e y y 10 kN e 30 kNm ES Figure 5 2 A concentrated load in the global coordinate system left and the same load in the element local coordinate system right The dotted line declares the positive direction of local z axis 5 4 2 Distributed load A distributed load can be put on an element only A special care need to be taken for correct selection of coordinate system for the load direction and load position Internally the program uses local coordinate system for both direction and position and the program will perform all necessary transformations automatically As far as coordinate systems are concerned we meet three different basic types of distributed load e Wind load Wind pressures always act perpendicular to the surface element Thus their direction is local z axis When viscous wind forces are also con sidered rarely they act parallel to the surface local x axis The load is also expressed in per structure surf
102. s the structure extents on the screen Each zoom command is a transparent command It can be issued while some other command is active E g you can zoom while dragging a new element 63 1999 2002 Ainet The button toggles the node labels The A button toggles the element labels The D icon expands the size of the nodes labels and symbols The D icon shrinks the size of nodes labels and symbols The R icon switches into the selection mode Hold down the SHIFT key to add new selection to the existing selection User s manual 4 6 Objects selection 4 5 2 Other view commands There are couple of useful view commands that can not be easily categorized and for this reason they are presented here Node labels The View Show Node Index command is a toggle First it turns the node labels off the screen If we repeat it it will bring node labels back Element labels The View Show Element Index command is a toggle for the element labels Label size Icons amp and are used to change the size of symbols nodes element thickness labels and size of text on the screen and output They are very useful in cases where the size of a node is relatively big or small when compared to the whole structure This usually happens when the structure is very small a small truss or the structure is very big or long a long bridge In the case of a small structure nodes and symbols will be too big and we will reduce them
103. se rotations of both columns at the foundation beam connection The following procedure will release the columns 1 Click on the 2 to turn on the rotation bending moment release 2 Click on the low part of the column 1 near connection to the foundation beam A special symbol that indicates the rotational release appears 3 Click on the low part of the element 2 to release the rotations of the second col umn too Cross sections We have three kind of cross sections a both columns have the same dimensions b steel beam has a cross section of its own as well as the foundation beam c Let s define them here and modify them later if necessary 1 Issue the Geometry Cross Section command A window opens 39 1999 2002 Ainet User s manual 3 2 AMSES Frame2D solution 10 11 12 13 14 15 Let us define the column cross section first Press the New button and select the double sym tab Check the Standard sections box and a list of standard hot rolled sections ap pears Select the HE EU wide flange from the top list and the HE 220 A from the bottom list The cross section needs a color Pick up the red one Close the window by pressing the OK button Now we need to define the beam cross section Press the New button and select the double sym tab Check the Standard sections box and a list of standard hot rolled sections ap pears Select the HE EU wid
104. sifies 52 1999 2002 Ainet User s manual 3 2 AMSES Frame2D solution Cross section cm Tey Suppo rts HE 340 A i h 33 00 pu Y b 30 00 0 00 020 040 0 60 080 1 00 tw 0 95 tf 1 65 Relative load position used in LT calculation is 1 00 unfavourable r 2 70 Element supports width left 13 00 cm right 13 00 cm Z Z Supports 7v x V x V 0 00 020 040 060 0 80 1 00 LT Supports V x Or V 0 00 020 040 060 080 100 w Steel 235 N eo Classification F Check ultimate limit states Check serviceability limit states U Ultimate Is Serviceabilty UP V max PE ttl MDN A M 11 PET p EPMA EL E EE E 30 0 40 0 50 0 60 0 70 0 80 0 90 1 00 Shear amp CS Resistance ili w IH odo 010 020 Element was classified into class 1 All stability checks have passed The compentent check is axial compression and lateral tolsional stability check 0 973 lt 1 0 in load case UP V max Select U Clear All Figure 3 18 The situation of the ultimate design of the beam element 3 all cross sections into class 1 The letter F in the bars stands for the flange which means that the flange has the highest slenderness in the cross section The bottom chart displays exploration rate of cross section resistance Dotted bars refer to shear resistance while solid bars refer to complete resistan
105. sition positive and negative bars and stirrups We will also need the support width at both element ends Specifying the support width can significantly reduce bending moments at the intermediate support Namely the theoretical length of the element can be quite larger than clear element length Eurocode 2 allows us to take this into account Support width Theoretical element length used in analysis goes from the mid point of the left support to the mid point of the right support Since the clear length is smaller than theoretical length used in the analysis the calculated internal forces are slightly higher than the real ones By defining the support width we can compensate this shear forces and bending moments peaks at both element ends 1 Issue the Design Edit Support Width command or press the 3 icon located in the middle toolbar 2 A window appears figure 2 15 Here we enter width of the element supports at both sides Caution This is not the width of the complete support we enter just 1 The term support is used here in its general sence Besides the true support this term also covers cases of connections say beam to column connection If a beam is under consideration it is evident that the clear length of the beam is smaller than theoretical length In this case we could specify one half of the column depth as the beam support width 22 1999 2002 Ainet User s manual 2 2 AMSES Frame2D solution the portion that b
106. ssions To make things a little more clear as far as this document is concerned we will make a few definitions e Kinematic geometric non linearity is related to the kinematical equation used to formulate the finite element e Material non linearity is related to the stress strain formulation material model 93 Non linear elements give better results than linear elements User s manual 8 2 Three kinds of non linearities e Other non linearities Non linear boundary conditions are the most typical repre sentatives here We have already met one beam on elastic ground The bilinear behaviour of the subgrade is nothing but a non linear boundary condition 8 2 1 Kinematic geometric non linearity This non linearity is related to the kinematic equations of the planar element The kinematic equations derived by Reissner 4 are given below 1 u 1 e cosw 0 8 1 w l e sinp 0 8 2 where u x is displacement in the x direction w x is displacement in the z direction e x is extensional strain and y x is rotation of the centroid axis at x AMSES Frame2D uses the exact formulation 8 1 and 8 2 in its non linear element First order theory First order theory is obtained by limiting itself to small displacements rotations and deformations where we get cosy 1 and sing y Additionally term e y is very small and can be neglected The simplified kinematic equations now become 8 3 and 8 4 u e
107. ster node they occupy only three equations in the stiffness matrix Actually the linked node is redundant since it has no degree of freedom of its own If one degree of freedom e g rotation y is released while others are linked to the master node than both nodes occupy four equations The master node occupies three equations and the linked node occupies one rotation y If all degrees of freedom are released in the linked node than there is no connection between master and linked node and the linked node behaves as an ordinary node They occupy six equations This is more a theoretical than a practical case Degrees of freedom of a node always refer to the world coordinate system For this reason we can release local u displacement and local u displacement only if the el ement lies horizontally The element local coordinate system is parallel to the world coordinate system If local uz or u displacement ware released on an inclined ele ment then coordinate systems are not parallel and the results of calculation will be wrong E g if we release u displacement axial force than you will still get some axial force in the element although it should be zero Releasing rotations Rotations bending moments M can be released in any case even for inclined el ements Why y axis of the local coordinate system is always parallel to the y axis of world coordinate system and therefore no transformation is needed for rotations arou
108. tability check has failed This means that a stronger cross section needs to be selected or an additional torsional support provided The right column element 2 The design procedure for the right column is identical to the previous one 3 2 7 Design of reinforced concrete beam The foundation beam is designed in the very same way as it was presented in the first example continues beam Nevertheless there if one important thing to keep in mind The local coordinate system of the foundation beam points rightwards This means that you must pay attention about the positive and negative side of the beam the beam is turned upsidedown E g the stirrups you define and see on the left are on the right in the reality Ultimate limit states 1 Expand the Reinforced concrete branch and double click the 04 Element 2 We have already defined and selected the reinforcement material If you forgot to do this you can do it now Click the 15 icon and select the RS 400 material 3 Define stirrups 10 mm e 12 cm for areas 0 0 0 2 and 0 8 1 0 and e 20 for area 0 2 0 8 4 The negative reinforcement is minimal Define four 12 bars that run over com plete beam and specify 5 cm concrete cover 55 1999 2002 Ainet User s manual 3 2 AMSES Frame2D solution 5 Define four 28 bars over complete area for the positive reinforcement Define 5 cm of concrete cover 6 Press the Select U button to select ultimate load cas
109. te load cases the creep is not used hence the cell is empty However in long term loads serviceability we use value 2 2 17 1999 2002 Ainet Press the 15 button to see elements painted in material colors User s manual 2 2 AMSES Frame2D solution Action load Each action has a window of its own and we must open it before we can put any load on it In our case we will open the G window and define its load first 1 Expand the Actions branch on the tree You see a list of all actions defined in this structure 2 Select item G and press Alt Enter or double click the item A corresponding action window opens displaying a thin structure geometry ready to take some load Action G consists of uniform load distributed over both elements Note that AMSES Frame2D treats the uniform load as a special kind of linear load To define a load a load type must be selected first 1 Press the icon on the toolbar or select the Add Linear Force command to switch into linear load entry mode 2 Click on the first element 3 A dialog window appears asking about the intensity of the linear load The figure 2 10 shows the dialog after load intensity has been entered Enter 15 kN m into the Fz field set other fields to zero and name the load as Self weight Element Linear Load 2 xj Load vector type Coordinate system gt Uniform C Linear Load direction C Word Local
110. ted unit 84 1999 2002 Ainet User s manual 6 4 Personalize Grid options We can specify which step points are visible on the geometry window Three options are given e Show major only displays major points only e Show major amp minor displays major and minor points e Hide both does not display any points Important The mouse input is always adjusted to the minor steps weather the step points are displayed on the screen or not Note If the grid is too dense the minor or even major grid points will not be shown on the screen This usually happens to the minor points when working on large struc tures 6 4 Personalize This page is used to collect some information about you and your company Author name your name Enter your name or name of the person who will use AM SES Frame2D most often Each time you start a new document structure the entered name will be used as the author name automatically Company name Enter name of the company you are working for You can also leave the field empty if you like This version does not allow specifying the company logos 6 5 Symbol settings The symbol settings options refer mostly to the symbols used to define elements of the structure General The following options are considered as general e Font The font typeface used for the labels and text which is drawn on the screen We recommend a typeface without serifs ARIAL TAHOMA VER DANA TREBUSHET HEL
111. tes are used Ultimate structural Ultimate Ultimate limit states are associated with structural collapse of with other collapse or failure form of structural failure They generally concern the safety of the structure and its content and the safety of the people Load cases combine actions that may occur simultaneously into following situa tions e Ultimate P amp T Persistent and Transient situations Here are merged an dominant action and combination of other actions This is the most com mon subtype of the ultimate limit state e Ult Accidental Accidental situations Permanent actions together with frequent values of the dominant variable action plus quasi permanent val ues of other variable actions are combines with the design value of the ac cidental action e Ult Seismic Seismic situation Here we combine permanent actions to gether with quasi permanent values of variable actions and the seismic ac tion Reinforced concrete design applies different safety factors for different ultimate limit states For this reason it is advisable to choose correct ultimate limit state subtype Serviceability Serviceability Serviceability limit states correspond to conditions beyond which spec service requirements ified service requirements for a structure or structural element are no longer met RO Typically the serviceability requirements concern the functioning of construc tion works or parts of them the comfort
112. the Load Imperial Default button will set units that are most practical for the imperial system 6 2 Precision This page defines the numbers format We can specify number of significant digits and the format type We can ask the program to delete all redundant zeros too Two different precisions are used in the AMSES Frame2D e The working precision is used during the entering sessions in most dialog win dows e The output precision is used for the printer output In both cases we define the same parameter format minimal numbers of significant digits and option to delete redundant zeroes The following formats can be used Smart This format tries to present the output in a human friendly form Frankly speaking we have to polish this algorithm a little more 83 User s manual 6 3 Grid amp Snap Units Fixed Number of decimal places is prescribed and scientific format is avoided if pos sible Scientific All numbers are presented in the scientific exponential format The delete redundant zeros removes any meaningless zeroes form the number This makes the output more compact and readable Filtration of small values The structural analysis is numerically intensive process with many arithmetic opera tions This usually introduces a small amount of error in the final results especially when non linear elements are used The amount of such error is minimal however it produces some undesired side effects in the out
113. tions are used in the table Their meaning is as follows e ULS P T ultimate limit state for the cases of persistent amp transient type This is the most frequently used type e ULS S ultimate limit state of seismic type This ULS type requires differ ent material partial safety factors lower for the reinforced concrete materials Hence cross sections have larger resistance e SLS serviceability limit state For the time being we do not distinguish be tween different kinds of SLS By defining the table we have all the information needed to perform the calculation using AMSES Frame2D 36 1999 2002 Ainet User s manual 3 2 AMSES Frame2D solution Load case Type Pe G Q S W a Skew rightwards b V max ULS P T 1 35 0 90 c V min ULS P T 1 50 d H max ULS P T e Wind ULS P T f Snow MSN P T g V max S h H maxS Table 3 1 Load cases trier types and partial safety factors 3 2 AMSES Frame2D solution Let s take a look at the AMSES Frame2D solution We recommend you to run the program and follow the step by step instructions from the manual Most of the proce dures that were introduced in our first example are also used here They are repeated here in a more condensed form The final solution can be found in the file ProgramFiles AMSES Frame2D Examples SteelFrame amp 3 2 1 Opening a new document structure Before ent
114. tis fully supported buckling effects are not possible Supports positions and buckling coefficients are given below 1 0 K V 1 0 K 000 010 020 0 30 040 050 0 60 0 70 080 090 1 00 Number of supports F q Figure 3 16 lected axis 6 Hit OK to close the window Support conditions supports and buckling coefficients for the se 7 We must repeat the procedure for the torsional lateral support Press the LT lateral torsional button 8 Increase number of supports to 3 and enter 0 5 into the new field 9 Press OK to close the window 10 Press OK once more to return to the steel design window Effective support width The mathematical model of the structure is idealized in a wire frame model This model neglects the actual depth of elements and replaces the cross section shape with geometric properties As a consequence most elements length is slightly longer than the actual one which leads to larger values for the inter nal forces To compensate such effects and reduce internal forces at the element end we may take into account the effect of the effective support width or the depth of the 51 1999 2002 Ainet User s manual 3 2 AMSES Frame2D solution connecting element In usual case the effective width is one half of the actual width see the figure 3 17 However there may be cases where such width is different zero for example When the effecti
115. to write a computer program that will be able to take into account all concrete specific details Most of the building codes are aware of this fact and they usually require that time dependent effects shall be taken into account where significant Eurocodes also say Creep and shrinkage normally need only be considered for the serviceability limit state except where their influence in the ultimate limit state are likely to be significant Well this does not help much since no criteria for significance are given AMSES Frame2D uses concrete creep and shrinkage information during the analysis and design crack width calculation The procedure uses reduced elastic module of concrete Ecy which is defined as E Bop In this expression y gt 0 represents creep coefficient that reduces elastic module of the concrete An evaluation of the can be found in relevant building codes The typical values lie within the 0 3 interval 76 1999 2002 Ainet User s manual 5 4 Load and coordinate systems Creep coefficient can be entered into the Fi creep Skew column of the load case action spreadsheet This value will be used during the analysis and design Creep coefficient is applied to the serviceability load cases mostly Namely ultimate load cases simulate extreme but short situations where creep does not have enough time to develop a significant effect 5 4 Load and coordinate systems AMSES Frame2D uses four different load
116. ts suit our needs but sometimes we need to enter a physical value in some other unit Let us illustrate the conversion feature using the following scenario The default force unit is KN and default moment unit is kNm Yet we got the following concentrated force data Fx 5000 N Fz 10000 N and My 30000 kNcm The unit conversion feature enables us to enter such data directly 1 Click on the kN label of the Fx field A list of related units pops up see figure 4 3 2 Select the N Newton unit Notice that Fx and Fz units are changed after the popup menu selection 3 Enter 5000 into the Fx field and 10000 into the Fz field 4 Click on the kNm label of the My field and select the kKNcm unit instead 5 Enter 30000 into the My field Concentrated Force 21x m Force vector Coordinate system Fx KN cm World MN mega Newton a kN kilo Newton N klbf kilo pound force Load name name bf pound force Unknown coca m9 Figure 4 3 An example of unit conversion feature in action Default kN unit was replaced with the N Newton unit In this example units of the Fx and FZ field were related When we change the force unit of the Fx field the unit of the Fz field is changed as well This is a common practice within the program On each window most units that have the same physical base are linked 61 1999 2002 Ainet Select the unit first and enter its value later The change of
117. uantity of the output It turns out that we do not need to print all tables and figures some may be omitted Let s take a look how to fine tune the output This can be done using the Tools Output Settings command 56 1999 2002 Ainet User s manual 3 2 AMSES Frame2D solution Select the General tab and make sure that the At least 3 pictures per page option is selected This option commands AMSES Frame2D to condense the pictures as much as possible Select the Geometry amp Load tab We can spare a page or two if we decide not to print tables of loads besides the load schemas Uncheck the Tables option within the Print frame Select the Results tab Options stated here have the most influence on the output quantity As far as internal forces are concerned we do not need both pictures and tables Therefore uncheck Displacements Reactions Internal forces and Envelopes to remove tables from the output Figure 3 21 shows the Results page with modified settings e In the case of ultimate limit state load cases we are mostly interested in internal forces and not in displacements rotations and local displacements which can be unchecked under the Ultimate column In the case of serviceability limit cases we are mostly interested in displacements and reactions hence we uncheck everything but this option e Envelopes are used in rare cases Mostly you will be interested in bending mo ment and thus uncheck everything but the My
118. unit in one field automatically reflects in a change of all linked fields Press Apply to accept the changes The El icon is a shortcut for the Edit Undo command User s manual 4 3 Object properties 4 3 Object properties AMSES Frame2D uses a few major objects nodes elements nodal loads element loads and results Each of these objects possesses important attributes which can not be all presented on the screen However they can be presented in a special window called property window The property window is opened if we are in the selection mode and if we double click the object Property windows usually consist of several pages in which we can modify the object attributes There are a few simple rules about property windows that we should keep in mind e Double click an object to open its property window e Right click an object to pop up a menu The last menu item is the Properties item If we select it the property window appears e Recent changes of object properties are accepted and stored only after the 7 Apply button is pressed The button is located on the left side of the property window e The Al button keeps the property window on the screen If we click on some other object the property window stays on the screen and properties of newly selected object appear in the property window e If property window is pinned than several objects of the same type can be se lected simultaneously The modified attributes
119. ution A acusa oe eee eee ds Figure 3 7 Situation on the screen after the geometry and cross section were de fined Materials This structure uses thee different materials a structural steel a concrete and a rein forcement steel We need to define all three here The structural steel of the steel elements has S 235 grade the foundation beam is made of C30 37 grade concrete and of S400 reinforcement For the sake of analysis the reinforcement is not really needed However it is needed later during the design stage and it is wise to define it at this point as well 1 2 10 11 Select the Geometry Material command A window opens Press the New button and select the Steel tab to declare a structural steel mate rial Select the Eurocode 3 2 from the Code list and material S 235 from the material list Pick the dark red color for the selected steel Press OK to close the window In order to define the concrete press the New button again and select the Con crete tab Pick the Eurocode 2 from the top list and C 30 37 from the bottom Select light gray color and close the window The reinforcement material is still missing Hit the New button once more Select the Reinforcement Steel tab Note Steel and Reinforcement steel are com pletely different material types and they must never be interchanged Enter 40 kN cm or 400 MPa into the Yield strength field and RS 400 into the Mat
120. ve difference means that the element is warmer than some reference environment while a negative differ ence means that the element is colder than the environment Further more we can specify different temperature difference on each side of the element and assume linear distribution of the temperature difference across the cross section Let us take a brief example A 10 m long simple supported beam is made of hot rolled IPE 360 steel cross section The beam is loaded with three temperature differ ence loads Due to beam simple supports internal forces do not appear however the deflections do 1 Negative side of the beam gets 30 C difference and the positive side gets 10 C difference The figure 5 7 shows the window where the load was entered 2 Negative side of the beam gets 10 C difference while the positive side gets 30 C 3 Both sides get 20 C difference Analysis results are presented on the figure 5 6 We used a non linear element The example file can be found in ProgramFiles AMSES Frame2D Examples Temperature amp u 8 355 cm zy 20 u 0 24 cm Figure 5 6 A beam loaded with three different temperature loads Temperature load window In order to put a temperature difference load on an element follow the procedure given below 1 Select the Add Temperature Load command or press the t button on the toolbar 2 Click the elem
121. ve supporting width is given AMSES Frame2D cuts the internal forces on the supported areas hence slightly smaller internal forces are used in the design Figure 3 17 Effective supporting width for the beam column connection case and intermediate support of the continues beam case If we are not sure about specifying the support widht we can always assume zero width which is a conservative assumption Element 3 gets 13 cm of support width on both ends 1 Select the Design Element support width command The support width window is opened 2 Enable support width effects 3 Enter 13 cm into both fields 4 Hit OK to close the window Ultimate limit state design The beam geometry is completely set now Let s check ultimate load cases for our beam 1 Make sure that the U Ultimate tab is selected Below the tab you see list of the load cases 2 Select those load cases you want to include in the design Press the Select U button to select all ultimate load cases in one step 3 After a few moments results appear on the screen figure 3 18 If you do not see the results press the Bi icon to recalculate internal forces and then the Mi icon to initiate the design The top chart shows the class of each cross section Since several load cases are con sidered the highes value is shown for particular point Eurocode 3 declares four dif ferent classes The values bars you see on the screen are all below 1 which clas
122. will be applied to all selected objects Example We selected elements 5 7 and 9 Now we can change the material cross section properties releases etc to all elements in one singe step Note that there are a few attributes that are unique to each element and the program will not allow you to modify them when more than one element is selected e Some objects e g nodal and element loads do not allow multiple selection e When the property window is not pinned a mouse click outside the window closes it 4 4 Undo Redo system A very complex system which allows us to undo or to redo individual commands is build in AMSES Frame2D The system keeps track of all issued commands that are related to the structure Commands like zoom workspace switching etc are ignored by the Undo Redo system If we realize that the last command or a few of last commands was wrong we can simply undo the command by pressing the El icon or by typing the Alt Backspace key combination The program will take care for the necessary actions and will restore the previous situation The figure 4 4 illustrates the system behaviour We can also change our mind deciding that the undone command was a good one after all All we have to do is to hit the 4 icon or press the Ctrl Y combination and the command will be redone 62 1999 2002 Ainet User s manual 4 5 View related commands Figure 4 4 Initial state left A command spoils the situation middle
123. xisting project is opened the program loads the AMP project file first The AMP file holds information about all working files structural files included in the structure In the next step all working files are loaded one by one 1 3 1 Renaming a file You should keep in mind that working files AMS extensions should not be renamed outside the program e g in Explorer If you change the AMS file name information that is written in related AMP file will not match the new file name and the program will raise an error when you will try to open it In order to rename a file open the file with AMSES Frame2D and apply the File Save As command 10 O 1999 2002 Ainet CHAPTER 2 Continuous RC Beam a Quick Tour The quick tour is a tutorial which briefly demonstrates some major AMSES Frame2D capabilities In the tour you will solve your first problem and when the tour completes you will gather enough knowledge to solve some simple tasks on your own 2 1 Problem definition We will analyse and design a simple symmetric reinforced concrete continues beam which has two fields The beam geometry is shown on the figure 2 1 a 30 Nm 9 15 Nm G dd 25 cm 6 00 m qn 6 00 m 7 2 Figure 2 1 Geometry and load of continues beam The beam is made of two 6 m wide fields The leftmost support is fixed w

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