PileCap.exe User Manual
Contents
1. Fig 7 Plan view of piles in input grid The plan view can be zoomed in or out in order to get a suitable picture resolution A grid with 1 m grid line spacing can be turned on and of as can the Pile ID s also be The center of the plan view is always the center of the cap This is the horizontal projection of the pile cap origin that is where the loads acting on the cap are assumed to be situated more about that below at the description of the Cap Load form The cap dimensions can be changed using the leftmost up down buttons above the view However these dimensions have no influence of the calculation results Pile and soil material data When the geometrical data of each pile has been defined it s time to define the material properties of the piles and also the soil surrounding the piles This is done by calling up the form called Pile Elastic Constants see figure 8 In order to calculate the cap response of external loads the sum of all piles contributions to the cap stiffness must be assembled Therefore the relationship between forces and moments and the corresponding translations and rotations for each pile top must be evaluated This is what the form in fig 8 is for The values used in the calculation are the ones in the uppermost boxes Since there are 6 degrees of freedom 3 translations and 3 rotations for the pile top there should be 6 boxes but since symmetrical conditions for each pile top are assumed the numbe2. Open Project Save Project Bredenberg Teknik adress Trindelvagen 4 phone 46 708 120 138 copyright Bredenberg Teknik 2007 21611 Limhamn fax 46 40 970315 wey bredenbergteknik se Sweden mail hakan bredenberg teba com Fig 10 The File Option at the menu bar From this list it is possible to make the same type of Open Save operations as described above Any attempt to load an input data file not compatible with the type assumed will result in an error alert from the program It is recommended that input data files are created using PileCap exe and that the input data file are kept in the format used by PileCap exe Calculated data Ok now the PileCap exe has got enough info about your pile group So let us analyse it easiest part of the manual Jus the press Calculate button between the two frames at the top of the start6 page When you do so a considerable amount of numerical analysis is done for you It involves matrix inversion pivoting and lots of number crunching In case anything goes wrong during the calculation an error message is generated However if the input data files have passed the tests the program generates and the pile group is reasonably stable in a physical sense the calculation should not raise any error flags A successful calculation gives a green status light for the status box at the calculation frame at in the Start form Stiffness matrix flexibility matrix cap displacements The pr
3. Bredenberg Teknik uppdate 2007 08 23 The user can save his files where ever he wants in his system However it is recommended to maintain a systematic way of building a folder structure in order to make it easy to find and use stored data files The picture below is shown as a recommend structure Leta i PileCap e ce Elastic Pile Constants Senast General data anv nda dok Geometric Data Skrivbord 9 Mina dokument Project Data a Den har datorn ur Cc Mina 7 OoOO E n tverksplatser Filnamn ha Filformat Project Data Files pcp Avbryt ZL Fig 4 Recommended folder structure for storing data for Pile Cap calculations If the user tries to open a Project Data File which is not such a file an error message is displayed and the load is cancelled The file extension pcp is checked as well as a header written into every Project Data File saved When a valid Project Data File has been loaded the name of the file is shown in upper case letters in the frame containing the names of the loaded data files Further the names of the individual input data files contained in the Project Data file are displayed in the frame Returning to the Start page the bottom frame contains some information about Bredenberg Teknik the copy right holder of PileCap exe At the upper right corner on the Start form the usual min max and stop buttons are found If the stop button is pressed a
4. you will find that un unstable configuration of piles as for example only a few vertical piles with hinged connection to the cap cap be analyzed applying only a very small soil support to one of the piles in the group A division by zero situation e g a horizontal pile can not yield a result by there will be no crash to your desktop and the error messages are not intimidating Not by purpose anyhow The results of the equilibrium check are displayed by pressing the Equilibrium Check button on the Startup form Pile Cross Section capacity check When the axial load and the bending moments at the pile top has been calculated it s time to check whether the pile cross section can take these load effects Usually this is checked using an interaction formula Ns Nd Ms Md lt 1 where Ns axial load Nd axial load capacity Ms bending moment acting together with the axial force Md moment capacity Usually reduction factors are added in order to consider local buckling and other effects affecting the bearing capacity of the cross section However the basic formula for a section subjected to both a normal force for piles usually a compressive force and a connected bending moment is the one shown above For a 3D pile group the individual piles will usually have bending moments in three directions two bending moments Mx and My acting around the two horizontal axis s x and y respectively and a twisting moment Mz The mome
5. PileCap exe In order to print out data on paper or sending them to some application converting data into Adobe pdf format f r mailing them somewhere the use of some application taking care of information on screen is assumed One solution not demanding any software other than components supplied with a standard Windows installation is as follows Bring up the forms to be printed Press the PrintScreen command Start Paint and press Paste to copy the screen image to the Paint canvas Cut the part you are interested in of the pasted image Start new don t save and paste The copied part will appear alone Print mail and store the image as required Onrwns In order to make a pdf of the image you need a pdf converter Many freeware such applications ca be found for free on the internet or be purchased from Adobe in case you will go for the full functionality of the pdf file format Bredenberg Teknik uppdate 2007 08 23 page 21 21 PileCap exe User www bredenbergteknik se
6. cap The difference is calculated and presented An example is shown in fig 15 Pile Cap Equilibrium Check 10 x Input Cap Loads and Moments LoadCase Fx kN Fy kN Fz kN Mx kNm l My kNm Mz kNm LastFal A 75 00 98 00 1940 00 284 00 902 00 0 00 LastFal B l 0 00 0 00 2000 00 0 00 oof 0 00 Back Calculated Cap Loads and Moments sum of pile reactions moved to cap origin M z kNm 02 1 4210854715202 14 Difference abs Given abs Back Calculated LoadCase Fx Fox kN Fy Fy kN Fz F z kN Mx M kNm My M y kNm Mz M z kNm LastFal A 2 8421709430404E 14 0 0 O _2 27373675443232E 13 1 4210854715202E 14 LastFal B 7 105427357601E 15 3 33452188793935E 14 6 82121026329536E 13 8 5265128291212E 14 1 136868377216 16E 13 a Fig 15 Equilibrium check Cap Loads back calculated loads and differences Form fig 15 it there are errors in the magnitude of 10 14 or less This is pretty close to zero which is the correct value of course For engineering purposes such a small resulting truncation error means that the results of the calculation are validated The reason exact zero is not obtained is that the computer uses a limited number of digits doing the math The double precision math and the numerical method used a re very powerful when dealing with marginally stable pile groups If you are interested in testing the abilities of PileCap exe in this respect
7. confirmation message box is shown in order to avoid unintentional escape from the program The Start form can be minimised maximised moved and area modified the standard Windows way These facilities are handy when arranging the different forms on the screen when a pile group design is in progress Input Data Input data are supplied by means of four different Input Data files for a Project These Input files are File Extension Example General Data gat Pgroup2 gdt Geometrical Data geo Group 9 geo Material Data ela New Piles ela www bredenbergteknik se Cap Load Data dt LoadCase IV ldt Project Data pcp ProjA11 pcp The organisation of input data contained in the first four input files is described below together with the functionality of the respective input forms The content of a project data file is an assembly of the data in the four basic files The Project File Open Save facilities makes it easy to load or save all project data in a single sequence whereas the individual data in each of the four Input Data sets can be edited using the respective input form The user can save his files where ever he wants in his system However it is recommended to maintain a systematic way of building a folder structure in order to make it easy to find and use stored data files The file format for all Input Data files is simple ASCII files txt files They can be edited by using any text editor as for example Notepad However such e
8. rwerse of StitfnercMatrix ist is6 e ie Oe ef le 4 0817373201 et 6316589611 18268 07 2 45792336900487E 07 4 31126776411551E 06 7 390627966361 032E 07 2 467980289361861E 06 550391543731707E 05 3 83324005816521E 07 7 25376044651937E 06 2 32408652520237E 07 5 905483069561 96E 06 4 31126776411551E 06 2 32408652520238E 07 9 22826804233524 08 6 43827227135714E 09 8 76337174262783E 07 2 84051 7381 88889E 07 7 90627966361 036 07 5906483069561 SEE 06 9 096000887931 23 08 1 7797791724484 06 2 84051 733188383 07 2 2624192492775 05 is JIS Matrix check multiply eee n aeei other elements 0 deviations are dus to truncation errors is4 i 5 i 6 1 hee 4215099407E m 93346579551637E 19 2 22769665127881E 19 1 41114630221382E 17 1 34305544116642E 17 8 46694134075399E 7 1 97757046893258E L 2 77979272629916E 17 203610838652173E 18 1 458251921993E 17 i 3 1 76687684665458E 16 1 2146960683395E a 9 554531 64502851E 18 1 59904997365035E 17 3 2729353081 S062 1 8 i 4 7 11846488872514E 17 8 71155445592103E 16 2 819899736351 65E zH 1 5 19570009845788E 18 5 07406616723216E 17 i 5 9 84320047345277E 16 2 34133459148245E 16 3 30800247220694E 17 1 84111081415195E 17 1 856519716263549E 18 6 3 11030498231 779E 18 7 48312650644362E 17 1 52169458974235E 18 6 25125754610379E 18 6 31039545704454E 19 1 Z mm sot rad 1 000 rot rad 1000 10lZ_rad 1000 4 0528
9. 000 0 0000000 134 1058385 00000000 8 0000000 0 00 9 Fig 13 Pile reaction forces and moments at the pile cap interface Pile Cap Pile Displacements z lol xj Pile Displacements translations mm och rotations rad 1000 1 93298228477667 396695481160048 0214719950474373 1 89607532118483 395766047169199 _6 325589971 41786 02 1 6883739722003 3 96695479392507 0 884080715127865 3 84734173027533 1 93992522090811 1 20391808759087 4 12544151035257 1 828941 110828 0179131785109075 58 381442829025342 1 94845247935035 1 68418042236706 OA co mag io dd 4 32212282045813 1 82828439470616 _ 0810936175061846 A AY do 2 20085317239311 4 136288568501 39 0 678416554967 RR S 1 87491120150133 4 14613708046539 1 93157314812329 234411524458305 4 12709257618798 1 41944166240533 0 974334310247075 1 00495344204229 0 762865427118905 1 24876432081589 1 03043203738305 0 710268028345663 1 14716633012141 1 00495349100599 1 20807247135949 0 67331341661442 1 09958973762142 1 08277987185028 0 481825679067955 2 7 0 934017426041508 1 4088539042439 1 13197911365554 a 0 0 2 8 1 23895101715748 0 535609686057542 0613195420803994 al 0 0 2 EJ 1 27969072383495 0508321586415794 1 28661606129576 o 0 ol z Fig 14 Pile translations and rotations at the pile cap interface Like the input data forms a warning is given if the user presses the close button for any of the forms
10. 6 0 76 w8 LastFal A 166584 oof oaj 0 41 nt LastFal B 1553 oof 038 0 38 vertikal LastFal B a oof 064 064 n2 LastFal B 18573 oof 045 045 w3 LastFal B 192 oof oss ooo ed LasraB 0 00 20525 00 0 50 w5 LastFal B 247 56 00 0 60 n6 LastFal B 0 00 13411 00o 033 0 33 w7 LastFal B 0 00 281 38 0 00 0 69 0 69 vertikal LastFal B 0 00 204 49 ooo 0 50 0 50 rr 8 LastFal B N wojo f 0o ojo Fig 17 Pile cross section check form The capacity of pile 9 seems too low red On this form the values of resulting bending moment Ms as outlined above is calculated Then the interaction quotient is calculated If gt 1 it is displayed in red The value is calculated for every pile in the pile group and also for each load case The capacity values Nd and Md can be input to boxes above the grid se e fig 17 The calculation is invoked by pressing the UpDate button A status box displays red when a change input data of Nd or Md ahs been made and an Update calculation is to be done In case a value gt 1 is displayed the capacity of the pile section must usually be increased In case of a steel tube pile this can be accomplished by increasing the diameter and or the wall thickness of the tube for exa mple Further cross section examination The horizontal forces Fx and Fy at the pile head will cause a bending moment in the pile at sections below the pile cap int
11. 8384546302 1 00431108280476 0 487078977706861 0 622130251637262 6 5671 2922558874 02 0 765549011633043 0 99983860031 3428 0 274384984033021 0 184565360868705 0 181920017758626 Fig 11 Stiffness matrix flexibility matrix and pile cap displacements The stiffness matrix is made visible by clicking the Stiffness button on the Start form An example is shown in fig 11 Below the stiffness matrix on this form there are also the flexibility matrix the check matrix and the cap displacements The flexibility matrix is the inverse matrix S a of the stiffness matrix The check matrix is calculated by the matrix multiplication s s which shall yield the 6 6 identity matrix I in which all diagonal elements are equal to 1 and all others 0 A look at figure 11 shows that the off diagonal elements of the check matrix are not really zero but instead something like 10 to 10 The reason is truncation errors since real number multiplication is carried out using a limited nu mber of digits However a number that small is in most pile cap calculations something that can be considered zero As can be seen from fig 11 the results are given with lots of decimals In order to make grids presenting the output easier to read the number of decimals can be decreased using the www bredenbergteknik se Bredenberg Teknik uppdate 2007 08 23 up down button at the upper right corner of the form For example letting the number of decimals tick down to
12. PileCap exe User Manual General The PileCap exe PC program is used for the analysis of 3 D pile groups cast into a rigid cap The soil and the pile top conditions fixed or hinged can be considered in the calculations The number of piles and loading cases are only restricted by the resources of the user Pile Soil Load data are input by means or a user friendly interface and modifications of the task are easy to implement In this way the optimum design of a pile group within given conditions can be obtained in an interactive manner fast and effective The method for analysis direct stiffness method is well proven for pile group design The output is all the time checked for numerical stability and accuracy meaning the user can feel confident that the results calculated In case of attempts to analyse an instable structure the application will issue a warning Soil and pile properties are easy and hands on to input It is possible to design a pile group with every pile different from their neig hbours although this is of course never the case in practice Nevertheless the ability to analyse a pile group with one or several piles different from the others is many times of great value Pile group analysis after installation and checking the piles when unenviable deviations from original design usually shown up is one example The input data as well as the output can be stored for repeated use The user can build a library of data an
13. SJ Do you really want to close the Form We Fig 4 Confirmation request when attempt ing to close an Input Data form Should the form be closed this way anyhow the data on the form are lost however if they have been saved they can easily be retrieved using the Open button on all Input Data forms It is recommended that input data are saved frequently On each Input form there is also a status box The status box turns green when the data in the text boxes have been Saved If a box is changed the status box will turn red alerting the user the data should be saved in order not to be lost in case the form is closed Below follows a description of the functionality of each of the four Input Data forms General Data Input form Pressing the button General Data opens up an Input Form for such data see Fig 5 FE PileCap General Data f x Title Title of Project DARE 07 21 08 Client Project Client Time 2007 08 21 Pile Cap ID Pile Cap ID Set Time and Date Name Operator Name Comment Project Comments Status Data Save Ml Open Save Fig 5 Form for Input of General Data The title bar contains the name of the input form in this case General Data Then there are a set of input text boxes where the user can input project data The time and date taken from the user system can be put into the corresponding text boxes pressing the button labelled Set Time and Date The Open and Sav
14. a soil and pile properties Cap Load Data File none 4 input cap load data 5 calculate Calculation Status EH 6 asses results change and re analyse Open Project Save Project Bredenberg Teknik adress Trindelv gen 4 phone 46 708 120 138 copyright Bredenberg Teknik 2007 21611 Limhamn fax 46 40 970315 www bredenbergteknik se Sweden mail hakan bredenberg telia com Fig 1 PileCap exe start form On this form there are several items aimed at guide the user through the design process On the topmost bar the program version is displayed The menu row below shows the three items File Help and About The Help option simply points to this manual The About choice can give detailed information about the system where PileCap exe is run This facility is useful in tracing eventual difficulties running the application The content of the File option is described later Below the title row and some general information using the appl ication there are two main frames containing Input Data and Calculated Data respectively In between there is a command button making analysing the Input Data to happen The function of each button is outlined later Next below there are two frames The left one gives a schematic description of the usual calculation flow The frame to the right contains the names of the input data files loaded This frame also holds a status box coloured green when a successful
15. and Save as also the control buttons up to the right have the same functionality as is the case for the other Input Forms Pile Cap Load Data The loads acting at the cap are input into the last of the four input forms se figure 9 lolx 2 issrare of E of Positive axes for forces Fx y 2 are shown Save Insert Row Delete Row Load Cases 2 Status Data Save i Positive direction for moments Mx y 2 right Fig 9 Pile Cap Load form The loads are related to an origin usually chosen as the gravity centre of the cap There are 6 generalised forces 3 forces and 3 moments The directions of the positive axis are shown in a picture to the right of the input data grid Vertical loads z axis are parallel to the direction of gravity usually If so the x y directions establishes the horizontal plane The respective moment is assumed positive turning right wise when looking in the respective axis In the form info about sign conventions is given in the picture to the right of the input grid This part of the form can be removed when the user has understood the force direction rules In case he will return to this form without a clear memory of the direction signs used the picture may serve as a reminder Any number of load combinations can be loaded The active number is shown at the right in the control frame below the grid The functionality of the Open and the Save buttons as well as the Stat
16. calculation has been performed using the Input Data loaded When some Input has changed and a calculation has not yet been done the status box is red Bredenberg Teknik uppdate 2007 08 23 Below the right frame is a frame containing 3 command buttons The rightmost button marked Exit offers the user the choice to stop the program The leftmost button labelled Open Project opens up a dialogue enabling the user to load a complete set of Input Data Files see Figure 2 Load Project Data File 21 x laat Project Data z FASE a I f Recent E Skrivbord P lkomm R54 gt Project Data Files pcp z Fig 2 Dialogue box for loading a Project Data File a set of Input Data Files The function of this input box follows the standard Windows way to handle file input and is not further explained here The button Save Project opens up a similar dialogue box making it possible for the user to save the assembly of loaded Input Data files into a Project Data File containing the assembly figure 3 Save Project Data File as Spara i jo Project Data x DE Project Data Files pcp gt natverksplatser New Project hd mat 4 Fig 3 Dialogue box for saving a Project Data File an assembly of Input Data Files As is the case with the Input Dialogue this is standard Windows stuff and no fu rther explanation is given here Consult the Windows manual if necessary www bredenbergteknik se
17. d thereby simplify the pile group design commonly performed The PileCap exe is designed to run under MS Windows XP or later Calculation method The method used for the analysis is described in detail in Appendix A In short the calculation flow is as follows for a single pile calculate the forces and mome nts required at a pile top to give top the translations and rotations 1 in the 6 possible directions 3 translations 3 rotations The coordinate system used is one with one axis parallel to the pile axis transform these forces and moments to a coordinate system the axis parallel to the axis of the pile cap the transformed forces and moments are moved to the origin of the pile cap the process is repeated for all piles The contributions of all piles are summed in a stiffness matrix 6x6 at the pile cap origin The element of the matrix expresses the force and moment respectively to give the pile cap a specified translation rotation when loaded in a specific way the loads 3 forces 3 moments are applied to the pile cap origin Using the stiffness matrix assembled the corresponding translations displacements of the pile cap origin are calculated the translation and rotation of a pile top is calculated using the cap movements These are expressed in the pile cap coordinate system The cap is assumed perfectly rigid the pile top movements are transformed into the coordinate system of the pile The pile directi
18. diting may result in corrupted files resulting in an error message when trying to make a calculation or otherwise handling such a faulty file Avoiding such editing eliminates the risk of such errors If the user tries to open an Input Data File which is not a valid such a file an error message is displayed and the load is cancelled The file extension is checked as well as a header written into every Input Data File saved Each Input Data form contains two buttons labelled Open and Save They operate the same way as described above for Project Data files The forms for the Input Data files can be minimised maximised moved and re shaped the standard Windows way This makes it possible to tailor the screen to the outfit that is best suited for the analysis being made As for example when inputting geometrical data describing the location and direction of individual piles it is practical to make the geometrical input form and the pile plan view form visible side by side Doing so the user gets an immediate check that each pile are given correct coordinate and direction values If the user presses the X button at the upper right corner of an Input Data form a confirmation request message is shown in order to avoid unintentional loss of data contained in the form see fig 4 as a bonus you learn some Swedish Ja Yes and Nej No PileCap General Data ZX Pd Tf this Form is closed all data loaded in the Form will be lost
19. e button Upload all boxes Upload is done to the row pointed at It should be mentioned that it is possible to use different stiffness properties for every pile in a group However usually it is assumed that all piles have the same stiffness characterises FJ Pile Cap Elastic Pile Constants Typer Type ID k11 k22 kN m k15 k51 kNm rad k24 k42 kNm rad k33 kN m m k44 k55 kNm rad _k66 kNm rad m 0 0 0 2187000 0 0 Status Data Save JE Save Insert Type Delete Type Number of types fant mene ai k15 k51 k24 k42 k33 k44 k55 fal kNm rad IkNm rad KN m m teva kN m note minus sign for 1 m pile kN rad for 1 m pile 321 0 0 1159725 0 ol Force moment kij gives displacement rotation 1 in direction when applied in direction i To upload single boxes to grid use Ctrl C use Ctrl V Upload all boxes m Pile cross section r Calculated section data r Pile Material m E moduli HE amp square massive Width or Diameter mm Inner concrete E moduls pile GPa 21 diameter mm 235 steel p i j mod i 200 O circular massive Meaca ET E modulus soil kPa 4 Calculated Elastic Length m 4 15 tube emph Moment of C melas inertia cm4 25415 wood tube concrete filled Twist moment factor cm4 2 J pile fixed into cap Fig 8 Pile and soil material data elastic properties The Open
20. e buttons gives the user the option to Open and Save files containing General Data by opening up dialogues as described above at the description of the functions of the Start Form The function of the status box has also been described as well as the control buttons in the upper rightmost corner Note that there is no exit button on the form Usually the text boxes are filled and the data saved and the form is then minimised and maybe kept in this shape until the session is ended However in case the user wants to close the form instead of minimising it this ca be accomplished by clicking the X up right and confirm the intention to close the form Geometric Pile Data The next input form to be filled is the form where the geometrical data for each pile in the group is typed The form is activated by pressing the corresponding button in the input frame The geometrical data input form is shown in fig 6 Bredenberg Teknik uppdate 2007 08 23 Pile nr Pile ID tini 1450 n 470 650 ss 400 1270 1420 Status Data Save E Save Insert Row Delete Row Draw plan Number of Pies 10 Rs GR ht Saeed Fig 6 Form for Input of pile geometrical data Data are typed into the cells in the grid A completed cell input should be confirmed by pressing keyboard Enter Piles can be inserted and deleted using the Insert and Delete buttons The rightmost part of the form gives a description of the inp
21. erface The resultant of these two forces Hmax is calculated in the same manner as for the bending moments that is Hmax sqr Fx 2 Fy 2 See also fig 16 The resultant Hmax is calculated in PileCap exe and displayed in column 3 on the form shown in figure 17 The bending moment at the pile top will decrease downwards the pile whereas the bending moment from the horizontal force Hmax will increase downwards until a peak I reached and after that the moment will decrease The value of this moment depends on the soil and the pile properties The two bending moments will interact and a maximum is reached at some www bredenbergteknik se depth This is the section of peak interaction factor The shear is zero where the bending is max Note also that the interface section between the pile and the cap must be analyzed taking the shear Fs on the stresses into account together with the stresses caused by the resulting bending and the twisting moment and the axial force In practice this can be difficult to validate for some types of piles This dilemma is sometimes solved by assuming that the piles are ball point connected to the cap and thus no moments will occur Further the influence of the soil is neglected With these assumptions the piles are loaded by an axial force only making the analysis easier to carry out Considering that both numerical models and calculation tools are c ommonly available such an over simplification appea
22. imary calculation result is the stiffness S matrix for the pile cap It is a 6 6 symmetrical positive definite matrix containing the forces and moments required to translate and rotate the cap one length unit for translation and one radian for moments respectively The 6 6 order of the matrix reflects the 6 degrees of freedom 3 translations 3 rotations the cap can do The element Sij of the stiffness matrix is thus the force moment Bredenberg Teknik uppdate 2007 08 23 required to give a translation rotation equal to 1 length rotation unit The stiffness matrix is symmetrical EH Pile Cap StiffnessMatrix FlexMatrix ControMatrix and Cap Displacements StiffnessMatrix S l art lannat adataid aadnk Kohi ET chad dacs dane aes es ener number ot decals Z Hf 52067 42491 Soule 2 EE 21 755 6441907853 255787 699633533 6178 67445043598 2 86365050755692E 03 38733 3011448462 11329 77231 60088 158733 030682438 11047 8888849776 2452 48016959659 21755 6441907853 11323 7723160088 20951 39 27394147 211373 4377 15569 107557 162195308 4652 67030410219 15700 55898907398 158733 030582438 211373 437715569 1265245 30038582 1125523 339972586 59367 651 2644782 255787 699633538 11047 8886849776 107557_162196308 125523 339972585 2428032 21424039 46845 991 919891 6178 67446043599 2452 48016968659 4652 67030410219 59367 651 2644782 46845 991313891 49015 8515955838 Flexibility Matrix S1
23. nd the pile displacement grid visible se fig 13 and fid 14 Again the number of decimals can be set by an up down button situated upper right Note that the moments and the rotations for hinged pile cap connections are 0 as in the figures shown www bredenbergteknik se Bredenberg Teknik uppdate 2007 08 23 In the pile force grid the maximum and the minimum axial force are shown in bold red and bold blue font respectively PileCap Pile Loads xf Pile Loads forces kN and bending moments kNm Fee rumba ct deca 7 Load Case pile Fx kN Fy kN Fe kN Mx kNm My km Makmal 0 0000000 0 000000 46 9592532 0000000 oooooo0 OOK 0 0000000 00000000 13 8340653 0 001 9 000000 00000000 193 3484524 000 00000000 0 0000000 263 2968858 0 001 es Esa 5 00000000 0 0000000 391761214 0 0000000 000 5 0 0000000 0 0000000 368 3302584 0 000000 000 7 0 0000000 0 0000000 177 3517415 0 000000 0 001 8 0 0000000 0 000000 148 3697006 0 000000 0 00 ee 00000000 0 0000000 422 4350475 0 001 00000000 00000000 zoaze 0 oooooo00 8 0000000 0 00 0 0000000 0 0000000 166 8386689 0 001 2 ae a 2 0 0000000 0 0000000 155 3356178 0 000000 0 001 a3 0 000000 0 000000 254 2054435 0 000000 0 00 a 0 000000 0 000000 185 1293448 0 000000 0 00 A 5 0 0000000 0 0000000 197 2229900 0 0000000 0 00 a 6 00000000 0 0000000 205 2500033 000 00000000 00000000 247 5638322 0 001 aaa ae 00000
24. nt Ms to feed into the interaction formula is the resulting moment from Mx and My that is Ms sqr Mx 2 My 2 That is the resultant of the two moments if they are looked at as vectors se fig 16 Fig 16 Resulting bending moment from Mx and My The influence of the twisting moment Mz must also be considered when the cross section is checked The moment Mz gives shear stresses in the section These stresses are combined with stresses caused by compression tension and the other two bending moments National building codes have rules how to take such situations into consideration PileCap exe has a facility to make the calculation of the necessary pile cross section capacity This option is activated by pressing the Cross Section button on the Start Up form A new form is the displayed se fig 17 Bredenberg Teknik uppdate 2007 08 23 frmPileCap_PileCapacityCheck Pen Ol x N Fx Pile cross section capacity Nd axial capacity KN Md moment capacity kNm Hmax Fx Fy Mmax Mx2 My Nd kN 410 00 Md kNm 50 00 E Update LoadCase Pile nm Hmax kN N KN Mmax kNm N Nd M Md N Nd M Md PileID LoadCaselD 0 00 0 11 0 00 m1 A oof 138 ooo 003 0 00 0 03 vertikal LastFal A 0 47 m2 LastFal A 064 n3 LastFal 0 10 rr 4 LastFal A 09 0 90 w5 LastFal A 1735 000 043 0 43 w6 LastFal A 48 37 00 036 0 36 n7 LastFal A 42244 OSs 1 03 vertikal LastFal A 310 43 00 07
25. on and slope provides input data for the transformation finally the pile forces and moments are calculated using the relationship between movements and forces moments established in the first item mentioned in the list the process is repeated for all piles in the pile group It is then assessed whether the movements and forces moments are acceptable Usually the design must be modified and reanalysed a couple of times before a satisfactory result is obtained Further when the piles have been installed there are usually deviations as for example in slope and direction who s influence must be analysed and maybe must also additional piles be installed meaning further calculations It is obvious that the calculation process demands a vast amount of numerical calculations Fortunately this can be handed over to a computer a PC doing Win XP Doing so the question arises how reliable are the results The computer uses a limited number if digits in its number crunching In PileCap exe all calculations are carried out in so called floating point double precision meaning the results are as accurate as possible Further the reactions at each pile top are transformed and moved back to the pile cap origin where they are compared to the applied loads forces and moments The difference is due to numerical truncations during all the calculations performed and the residual vector difference between applied and back calculated load is a measu
26. presenting calculated data Should however an unintentional close be done this is not critical since the calculation can be repeated just by pressing the Calculation b utton on the Start form again Equilibrium check On screen there are a lot of pile loads and pile top displacements displayed How do you know they are accurate Well actually you ca nt unless you get some support If there are huge and obvious errors it s safe to conclude the calculated data are not reliable But if there are errors say 10 30 its generally not possible to figure out something is wrong www bredenbergteknik se The stiffness matrix the flexibility matrix and the calculation of the product of these will give one indication of the reliability of the results displayed The fact that the matrix inversion was possible to carry out means that the pile group analyzed is stable from an engineering point of view that is there is no direction in the cap coordinate system where a infinitely small force moment will give a huge unlimited translation rotation Further as a check maybe easier to understand an equilibrium check is made se figure 15 All the calculated forces and moments at each pile top are rotated into the cap coordinate system and the corresponding force and moment at the cap origin is calculated The contribution from each pile is accumulated and when all piles have been calculated this way the sum is compared to the loads applied to the
27. r of stiffness factors are reduced The stiffness factor kij defines the force moment required in direction THU CHH l to give the pile to a translation rotation equal to 1 length unit one radian in direction j 66457 CHH l The direction of i and j are defined in the appendix describing the numerical method for the analysis For example k33 is the force applied to the pile top which causes a unit compression of the pile at the pile top 08 23 uppdate 2007 The form shown in fig 8 is created to simpl ify the evaluation of the factors kij Often the soil resistance around the piles is neglected and then only factor kij to be considered is the axial stiffens In the form a different cross section shape the side diameter length and the pile material can be selected and the corresponding stiffness calculated The E modulus can be selected as standard values or modified using text box input In case the user wants to consider soil resistance around the piles recommended PileCap exe offers the option to do that by the input of a soil E modulus see rightmost input frame The kij values are then calculated assuming the piles are equivalent to semi infinite beams in a Winkler linear spring environment In case another way to calculate the stiffness factors are preferred by the user maybe factors evaluated from a load test this can be accomplished by typing in the factors and then upload them by pressing th
28. re of the accuracy of the analysis It should be mentioned that numerical stability mirrors the physical stability of a pile group For example a pile group with only vertical piles when subjected to a horizontal force responds with an infinite translation no matter how small the force is Thus such a pile group can not be analysed by the direct stiffness method described above However by cheating a little by applying a small amount of lateral soil resistance even such pile groups can be analysed Start Page At start the PileCap exe displays it s Start Up for figure 1 f PileCap exe ver 2 12 uppdate 2007 08 09 Bredenberg Teknik Fie Help About PileCap exe analyses a 3 D pile group Below the installed components are shown Press the component to be used At File other options are found as for example Save and Open datattiles Click the component icon to show the form To hide the form click the icon again m Input data m Calculated Data General Data EH Pile Plan View Calculate Geometric Pile Data mn Elastic Pile Constants Pile Loads Stiffness Matrix Flex Matrix and Cap Displacements Cap Load Data Pile Displacements Loaded data files and calculation status Calculation flow Project Data File none J General Data File none 1 input general data Geometric Pile Data File none 2 input geometrical data Elastic Pile Data File none 3 input elastic pile dat
29. rs hardly justified There is no longer any reason to treat piles different than other structural members for building structures as far as analysis of structural issues are considered A closer look down along the pile In order to simplify the calculation of the peak bending moment the option Pile Bending Moment is given in the Cross Section Analyse form shown in fig 17 The bending moment down along the pile is made se fig 18 The calculated bending moments are assuming the pile acts as a beam in an semi infinite elastic surrounding Fig 18 Bending moments caused by a moment and a horizontal force at the pile top The resulting horizontal force and the resulting bending moment are assumed to act in the same vertical plane The corresponding bending moments are shown in figure 19 These results ca be used for design of pile groups and other engineering structures possessing same characteristics as a pile group a for example elements bolted together in order to avoid welding Modifying Input data When an calculation run has been made modification of input data as for example additional piles changing cap load data changing pile and soil data and so on can be analysed without saving any data Bring up the form s where the changes are required hit Enter to get rid of any yellow grid markers and make a new calculation Used this way PileCap exe is a very powerful design tool Presentation of results Distribution of results from
30. us box different states green red has bees described above Menu bar the File option As mentioned above the File option at the menu bar have a special function Pressing the File item a drop down list is presented as shown fig 10 PileCap exe ver 2 12 uppdate 2007 08 09 Bredenberg Teknik 10 x File Help About New Pile Group Open Project Data Fie eXe analyses a 3D pile group Open General Data File Open Geometric Pile Data File Open Elastic Pile Data File ts are shown Press the component to be used At File other options are found as for example Save and Open data files Open Cap Load Data File show the form To hide the form click the icon again Save Project Data File Calculated Data Save General Data File Save Geometric Pile Data File Ee Pile Plan View Save Elastic Pile Data File Save Cap Load Data File Stiffness Matrix Flex Matrix and Cap Displacements Pile Loads iC Pile Displacements m Loaded data files and calculation status Calculation flow Project Data Fie none i General Data File none 1 input general data Geometic Pile Data Fle none 2 input geometrical data Elastic Pile Data Fie none 3 input elastic pile data soil and pile properties Cap Load Data File PALKOMM R54 TVA LASTFALL LDA 4 input cap load data 5 calculate Calculation Status a 6 asses results change and re analyse
31. ut data This can be a handy reminder in case the user does not make pile group calculations very often but this part of the form is usually removed during a design session by resizing the form The data to be filled in are as follows from left to right Pile ID Any description the user wants to input to label the pile Type a pointer to the material characteristics of the pile see next form material properties x y z coordinates of the pile top related to the cap coordinate system note millimetres n slope of the pile expressed as n 1 as for example 4 1 Input 0 zero for a vertical pile alpha direction of the pile degrees projected to onto the horizontal plane L pile length where elastic compression is supposed to occu note millimetres m factor defining how the pile top is connected to the cap Fixed is m 1 Hinged is m 0 The function of the Open and the Save buttons have been described above as well as the control buttons in the upper rightmost corner and the Status box down left In the control frame at the bottom of the form the number of active piles in the grid is shown to the right To the left of this info there is a button labelled Draw plan Clicking this button shows a plan view of the piles fed into the grid on the Geometrical Data input form see figure 7 File Cap Pile Plan loj x Length CapX m 6 Zoom 28 IV ishe Length Cap Y m 5 y IT show Pile ID
32. zero gives the example shown in fig 11 the following look s Pile Cap StiffnessMatrix FlexMatrix ControlMatrix and Cap Displacements StiffnessMatrix S ees Element Si means force KN in direction T corresponding to cap displacement 1 m in drechon Also moment kNm in rotation direction T giving rotation 1 rad in rotation drechon Y rumiber of decimals 0 Fig 12 Same as fig 11 but with zero decimals In the 3 d grid the check matrix it is now seen that the diagonal elements are all 1 and the others zero However information about the elements of the flexibility matrix not often required though and the pile cap displacements require more decimals than zero in order to find out actual values This is easily done with the up down button up right The last grid shows the translations millimetres and the rotations radians of the cap The values are calculated as u S F where F is a column vector holding the forces F1 F2 F3 and the moments M1 M2 M3 acting at the cap origin As for the grids above the numbers of decimals shown are set by means of the up down button at the upper right corner of the form The first column of the grid gives the number of the load case corresponding to the loads and displacements Pile loads pile displacements Next two calculation show buttons that can be clicked at the Start Up form makes the pile load grid a
Download Pdf Manuals
Related Search