BRBF Designer Report - Civil & Environmental Engineering
Contents
1. Co SeisDemand4 287 788 kip 2 E 168 14ft ColSeisDemand2 BraceForce3 Co SeisDemand3 514 713 kip 2 AnalyzeWidth nalyzeWi 14 2 148 ColSeisDemandl 2 ColSeisDemand2 766 853 kip 2 AnalyzeWidth nalyzeWi 14897 2 ColumnGravityDemandl 311 8 The values to the left were obtained in a hidden tab the BRBF Designer spreadsheet titled Gravity Demand Look at this tab if you desire to know how they were obtained Load combination 5 was used ASCE 7 10 pg 127 ColumnGravityDemand2 249 4kip ColumnGravityDemand3 186 3kip ColumnGravityDemand4 121 9kip ColumnGravityDemand5 54 9kip ColumnTotalDemandl ColSeisDemand ColumnGravityDemand1 1078 653 kip ColumnTotalDemand2 ColSeisDemand2 ColumnGravityDemand2 764 113 kip ColumnTotalDemand3 ColSeisDemand3 ColumnGravityDemand3 474 088 kip ColumnTotalDemand4 ColSeisDemand4 ColumnGravityDemand4 222 756 kip ColumnTotalDemand ColSeisDemand5 ColumnGravityDemand5 54 9 kip Therefore the following shapes shall be used for the brace columns Story 1 W14x61 Capacity 571 2k The shapes and values to the left were obtained via an autosizer in the BRBF spreadsheet that picks the lightest W shape for t2. 120 355 kip 194 324 kip 285 643 kip F5 Vp Cyx5 285 288 kip SumFx1 Fy3 Fy4 5 944 124 kip SumFx2 Fy3 Fy5 885 61 kip SumFx3 F 4 Fy5 765 255 kip SumFx4 Fy 4 5 570 931 kip SumFx5 lt 285 288 kip SumFxlperBracedBay a __ 236 031 kip XBracedBays SumFx2 SumFx2perBracedBay 221 403 kip XBracedBays SumFx3 SumFx3perBracedBay 191 314 kip XBracedBays SumFx4 SumFx4perBracedBay 142 733 kip XBracedBays 32 SumFx5 SumFxSperBracedBay 71 322 kip XBracedBays e 2 188 Fenai i SumFxlperBracedBay 5 2 2 AnalyzeWidth 2 anem 2 14ft SumFx2perBracedBay 2 2 AnalyzeWidth 2 cd 2 14ft SumFx3perBracedBay 5 2 2 AnalyzeWidth 2 2 160 ForceinBraced SumFx4perBracedBay 2 2 AnalyzeWidth 2 AnalyzeWidth 7 2 148 5 2 AnalyzeWidth 2 In this example we will use SteelCorefy 38ksi ForceinBracel RequiredCoreAreal eie 5 894 in 9 SteelCoref y ForceinBrace2 RequiredCoreArea2 4 157402 9 1 y ForceinBrace3 RequiredCoreArea3 411 02 9 SteelCoref y ForceinBrace4 RequiredCoreArea4 Tes 3 309 in 9 SteelCoref 33 I
3. 16 Figure 2 12 OpenSees when it has completed its analysis eee 16 Figure 2 13 Table displaying drift and displacement 18 Figure 2 14 Animation plot of the story displacements 19 2 I5 Dnft vs m Plot aoe dd a eiae 2l Figure 2 16 Displacement vs Time Plot uei ie rr tire Letti oe deren 2l Figure 2 17 Hysteretic plot created from OpenSees 22 Figure 2 18 Table displaying maximum forces and deformations from a hysteretic plot 22 Figure 2 19 Animation Hysteretic Plots aae coder endisse ee 23 Figure 2 20 a First Story Column Axial Force vs Time and b the Corresponding i E EG 24 Figure 2 21 a Brace Axial Force vs Time and b the Corresponding Table 25 1 INTRODUCTION 1 1 What is a BRBF Structure Many different systems are used in structures to resist lateral loads such as what an earthquake would induce One of these systems is buckling restrained braced frames BRBF s which involves having special diagonal braces in the frames of the structure These braces are different from ordinary braces in that they are encased in a concrete core to prevent them from buckling when experiencing compressive forces Two journal articles relating to BRBF structures are provided in the Reference section of this report 1 2 OpenSees Earthquake analysis requi
4. MathCAD Design Example ssccscoscsssssssssssssssscsessscssssssessesssssssseasers 4 How the spreadsheet functions ccssccssssccssssscssssccssscccssscsssssssseesees 4 1 How the Auto SIzer works 4 2 Importing Results Works eene 4 3 How the Animation Plots Work eese TABLE OF CONTENTS iii 0000000000000000000000000 000000000000000000000000 m 1 7 s Improvements 5 1 Brace CODD g TdtoHs andes A ee 41 5 2 Additional Parthquakes soos edes 41 iv LIST OF FIGURES Figure 2 1 Screenshot of the Cover Page ide 3 Figure 2 2 Screenshot of the Bay Geometry Tab 4 Figure 2 3 Screenshot of the Brace Geometry 6 Figure 2 4 Screenshot of the Story Geometry 7 Figure 2 5 Screenshot of Gravity Loads and Seismic Wt 8 Figure 2 6 Screenshot of the Seismic Loads 9 Figure 2 7 Screenshot of the First Part of ELF Brace and Column Design Tab 11 Figure 2 8 Screenshot of the Second Part of the ELF Brace and Column Design 12 Figure 2 9 Screenshot of the P Delta Column Design 14 Figure 2 10 Screenshot of OpensSees Tab iniecta 15 Figure 2 11 OpenSees when the user has entered source
5. Figure 2 13 Table displaying drift and displacement results Max drift is the maximum amount of drift a given story experiences during an earthquake This has a limit of 2 596 as stated in ASCE 7 10 Table 12 12 1 If any of these values exceed 2 596 the spreadsheet will automatically flag that respective cell yellow Residual drift is the amount of drift a given story has after the earthquake is over This drift has no limit from ASCE 7 10 Max displacement and residual displacement are equivalent to max and residual drift but for displacement This tab then displays the Story Displacement Plot as shown in Figure 2 14 This is the first of two animation plots in the spreadsheet The y axis is the stories of the building The x axis is the displacement in inches When the user clicks the play button gt the plot will start animating When running the plot will show the building shake throughout the duration of the 18 earthquake The animation also shows the extra time at the end As mentioned previously extra time is when the earthquake is over but the building is still shaking but is slowly coming to a stop Show every time steps Story 10 Displacement in 14 Story Displacement Plot 10 E 2 0 096 Figure 2 14 Animation plot of the story displacements Other buttons are also available the fast forward button the rewind button 14 and the pause button 11 The pause butt
6. 1 201 567 kip 162 688 kip 140 579 kip 113 174 kip 52 408 kip ForceinBrace5 RequiredCoreArea5 1 532 in 9 SteelCoref Therefore we will use 2 1 2 12 CoreArea2 Sin mo CoreArea3 4 5in 2 CoreArea4 3 5 2 5 2in Now we will calculate the actual forces in the braces We will assume that all braces will reach their max force at the same time Because this is a chevron configuration and not a two story x configuration all braces will be in compression at the time of their max force because with BRBF s compression forces are bigger than tension forces Because the force is compression it has to be multiplied by the amplication factor beta Beta 1 1 Omega 1 36 Strain Hardening fymax 46ksi BraceForcel 1 Omega Beta 412 896 kip Compression BraceForce2 CoreArea2 fy max Omega Beta 344 08 kip Compression BraceForce3 CoreArea3 fy max Omega Beta 309 672 kip Compression BraceForce4 4 Omega Beta 240 856 kip Compression BraceForce5 CoreArea5 f Omega Beta 137 632 kip Compression ymax ColSeisDemand5 Okip 14ft ColSeisDemand4 5 100 856 2 AnalyzeWidth nalyzeWi 2 168 ColSeisDemand3 BraceForce4
7. For information on how the spreadsheet auto sizes the columns see section 4 1 A demand 13 to capacity ratio column N is computed here as well as the previous tab Refer to Figure 2 9 for a screenshot of the second part of this tab Total Columns in Building 36 Target Column Depth 14 in Number of Braced Bays in X Direction average gravity column for that story for the sake of doing a p P Delta Columns perBracedBay 7 delta column analysis Note Only load combo 2 is being considered Restore Column Formulas Assume Weak Axis story Height at Dead Live Reduction Snow Column Column Column Column Dem Cap Total A Total I reed TotalZ Loads Loads Factor Loads Demand Demand Shape Capacity Ratio a Area Loads Area Inertia I z ft ft psf psf psf psf k in in in ir in 4 14 0 659 80 20 0 60 12 0 56 7 157 9 62 20 137 9 63 3 14 0 659 90 60 0 54 33 0 70 0 157 9 62 20 137 9 63 2 14 0 659 90 60 0 46 27 0 68 3 318 13 88 45 316 17 121 1 14 0 659 90 60 0 42 25 0 67 6 318 13 88 45 316 17 121 Figure 2 9 Screenshot of the P Delta Column Design Tab Lastly the spreadsheet uses the shape s that were auto sized and looks up the cross sectional area the moment of inertia and the plastic modulus for each It also multiplies these values by the number of p delta columns per braced bay to obtain a total area moment of inertia and plasti
8. pg 90 eqn 12 8 2 sec 12 7 2 Figure 2 6 Screenshot of the Seismic Loads Tab The long period is defaulted to 8 seconds The user is free to change this value if they desire although doing so won t affect most structures Values for this parameter are obtained from ASCE 7 seismic design maps Values for the parameters R Ca C and x are all obtained from tables in ASCE 7 and are all constant for BRBF structures so they need not be changed by the user The parameter is obtained from the height of the structure and the and x parameters The values is obtained from the Sps value using ASCE 7 table 12 8 1 The 9 building s period T is calculated by multiplying Ta and together The parameter is obtained using ASCE 7 equation 12 8 2 and taking into consideration ASCE 7 equations 12 8 3 12 8 4 and 12 8 5 With these values the base shear can finally be obtained by multiplying the total seismic weight of the structure by Cs 2 7 ELF Brace and Column Design The first part of this tab is where the spreadsheet comes up with the distribution of the base shear to each story Fx using the Equivalent Lateral Force procedure outlined in ASCE 7 chapter 11 The Fx values are then summed up to obtain the story shears Fx This value is then divided by the number of braces in the direction of analysis to get the force acting on each braced bay The spreadsheet then calculates the axial force in the brace and comes up wit
9. ASCE 7 Equation 11 4 4 This results in a Seismic Design Category of D from IBC Table 1613 5 6 1 125 X T C76 0712 1 4 Tg Cy 1 081 81528 C 0 127 R le ASCE 7 Table 1 5 2 Using risk category III ASCE 7 Table 12 2 1 For BRBF structures ASCE 7 Table 12 2 1 For BRBF structures ASCE 7 Table 12 8 2 For BRBF structures ASCE 7 Table 12 8 2 For BRBF structures ASCE 7 Equation 12 8 7 ASCE 7 Table 12 8 1 ASCE 7 pg 90 0 067 max 044 81528 1 01 0 045 ASCE 7 Equation 12 8 2 30 C max min C C9 C 3 0 067 Vp TotalSeismicWeight C 944 124 kip Equivalent Lateral Force Method 18ft 18ft 14ft 32ft 18ft 148 14ft 46 ft 188 140 148 168 628 188 148 140 168 148 768 1807 41 685 TET 32 87 591 hy3 46 139 913 62 205 663 li gi 7607 1779 967 466 wxhx1 SeisWtl h 124722 138 kip wxhx2 SeisWt2 h gt 256536 44 kip wxhx3 SeisWt3 h 3 414199 248 kip wxhx4 SeisWt4 h 608845 711 kip wxhx5 SeisWt5 h lt 608089 94 kip Totalwxhx wxhxl wxhx2 wxhx3 wxhx4 wxhx5 2012393 477 kip wxhx 0 062 vxl Totalwxhx 31 wxhx2 T 0127 0 206 LE 0 303 5 22 0 302 58 514 kip Fy
10. and the perimeter of the building The floor area is for one floor of the building all floors will have the same area The floor area and perimeter both include the concrete overhang in their calculations The spreadsheet will also display the total X direction width of the building as well as the Y direction width And finally the spreadsheet will automatically display an image in the form of a chart of the building layout that is to scale which can be used to get an idea of what the building looks like according to the user s inputs The user will be able to easily see how many bays are present in the X and Y directions along with the size of each bay 2 3 Brace Geometry The user can input how many total braces there are in each direction on this tab This is very important since it directly affects the load that will go to each brace Because OpenSees only analyzes one brace and not an entire building the user must decide which direction to analyze and what width of bay to analyze To completely understand how well the building will withstand an earthquake multiple analyses should be run in each direction and testing different bay widths Refer to Figure 2 3 for a screenshot of this tab It should be noted that the chevron configuration is the only operational option at the moment This is something that needs to be addressed at a later time See the improvements needed section of this report Total Number of Braced Bays in X Dir
11. code run faster However it is important to have error handling functionality like this to prevent the calculations from accidentally being left off 39 5 IMPROVEMENTS NEEDED 5 1 Brace Configurations At the present time only the Chevron brace configuration has an OpenSees template written The Two Story X and Single Bay configurations currently run just as a Chevron configuration would run These need to have templates written for them to work properly Functionality then needs to be added to the spreadsheet to make the text file know what configuration was selected by the user 5 2 Additional Earthquakes On the OpenSees tab the user can select an earthquake that OpenSees will run in its analysis Currently the drop down menu on has two earthquake options Loma Prieta and Northridge There are actually six earthquakes listed off to the right on this tab One of these Mexico City doesn t have a record in the spreadsheet The significance of the two that are in the drop down menu are that they have a spectra file which OpenSees needs The other records have a ground motion but still need a spectra while Mexico City needs both Lastly OpenSees always uses the Loma Prieta earthquake at the present even if the user selects Northridge Somewhere in the text files that OpenSees reads there is code that is overwriting the user s selection The spreadsheet is making the correct change when the user selects an earthquake the code just
12. column AX The play button and the pause button 11 are two separate buttons that are actually right on top of each other Initially the pause button is hidden and the play button is visible 38 When the play button is pressed the code hides the play button and unhides the pause button and vice versa when the pause button is pressed How the plots animate is quite simple It all happens in the For loop The DoEvents line makes everything work This makes the plot animate fast and smooth This also is required for the pause functionality The value of 1 is incremented by the value that the user specified in the Show every X time steps cell The With statements are where the plot is actually animating It changes what cells the plot is looking at based on the current value of i Other methods were experimented with and this method was found to be the fastest Another method was having the plot look at the same cells throughout the animation but having those cells change their value This method is not nearly as fast because the spreadsheet is required to calculate the value in the cells every loop which slows everything down The For loop is also given some error handling functionality Errors happen when the user changes spreadsheet tabs while the plot is animating The error handling functionality will stop the animation and will turn calculations back on Many functions in the BRBF Designer turn calculations off temporarily to make the
13. is near impossible for the user to reach a useful conclusion from the text files alone However these data can be imported into a spreadsheet to be summarized in tables or plotted on graphs This way the user can better understand the results from his or her analyses 2 USER S MANUAL 2 1 Cover Page The purpose of this tab is to give the user general instructions for how to use the spreadsheet This tab shows the user where he or she can download OpenSees It also explains what the different cell colors mean See Figure 2 1 for a screenshot of this tab BRBF Designer By Kelly Christensen and Dr Richards Instructions This spreadsheet is built for designing and analyzing a BRBF building in OpenSees Open System for Earthquake Engineering Simulation OpenSees is a program used to simulate structures under eathquakes It can be downloaded at http opensees berkeley edu OpenSees user download php This spreadsheet was designed with a step by step mentality Each tab is a step in the process of desinging a BRBF structure Procede left to right through the tabs to design your building The following is helpful information while using this spreadsheet cells are input cells Enter dimensions parameters sizes etc in these cells green cells are calculation result cells Do not enter anything into these cells Yellow cells are flagged cells They mean what you entered is invalid or a capacity is insufficient
14. usehd directions and advice Figure 2 1 Screenshot of the Cover Page Tab 2 2 Geometry This tab is used to input the size of the building that will be run in OpenSees A rectangular building is required but that is basically the only limitation for the bay geometry The user has many aspects of freedom including different number of bays in the X and Y directions 3 the width of each bay and the slab overhang The spreadsheet has input cells which can be used to set the width of all X direction or all Y direction bays If the user desires individual bay s to have a different width from the others he or she can directly input the width into the cell below for that bay This design allows for a very quick setup of a building if all or most bays are to be the same width Note that changing the width of an individual bay overwrites the formula in the cell For this reason this tab has a button to restore the formulas in all the X and Y bay width cells Refer to Figure 2 2 for a screenshot of this tab Number of Bays in X Dir Number of Bays in Y Dir X Direction Bay Width ft Y Direction Bay Width ft Concrete Slab Overhang 2 ft See Total Floor Area ft Restore Formulas Perimeter ft X Dir Bay Widths ft 4 5 1 2 3 Building Layout Of WN Y Dir Bay Widths ft Figure 2 2 Screenshot of the Bay Geometry Tab 4 The spreadsheet automatically calculates the floor area in feet squared
15. 7 section It then comes up with a demand to capacity ratio for the column that was automatically selected 4 2 How Importing Results Works There are many ways that a spreadsheet can import data from a text file Some methods are faster than others The method that the BRBF Designer uses is the result of much experimentation There may be methods that are faster or there may not be however this method is quite fast The spreadsheet first opens finds specific text files in the Results folder that is in the same file location as the spreadsheet itself It opens these files one at a time using a For loop in a separate excel window Using a variable named lastrow the spreadsheet determines how many rows of data there are to be imported Then it simply sets specific cells in the BRBF spreadsheet equal to the data in the separate window It does not copy and paste the data as this would take longer which is especially a problem when there are a lot of data to import such as this Also notice that the spreadsheet does not loop through the data cells one by one to import them It completes the process in one big selection thereby minimizing needless calculations and functions 43 How the Animation Plots Work First off the data for the plots is in cells that are to the right of the main viewing area For the Story Displacement Plot the data starts in column CQ column AY is where the drift data begins The Hysteretic Plot data begins in
16. BRBF Designer Report Kelly Christensen A project submitted to the faculty of Brigham Young University in partial fulfillment of the requirements for the degree of Master of Science Paul Richards Committee Chair Fernando Fonseca Kevin Franke Department of Civil and Environmental Engineering Brigham Young University March 2015 Copyright 2015 Kelly Christensen All Rights Reserved ABSTRACT BRBF Designer Report Kelly Christensen Department of Civil and Environmental Engineering BYU Master of Science Structural seismic analysis can be lengthy and complicated Nonlinear analyses can be performed to accurately compute the response a structure has to an earthquake A program called OpenSees is an excellent way to run a nonlinear analysis Due to usability issues a spreadsheet called BRBF Designer was created to assist users in running OpenSees This spreadsheet was made to design a BRBF structure any structure utilizing another lateral force resisting system cannot be designed in this spreadsheet This spreadsheet greatly shortens the time one must spend when using OpenSees When using this spreadsheet one should proceed through the tabs going from left to right About the first half of the spreadsheet is used for designing the structure in question This includes designing the geometry and number of stories and inputting the loads and seismic parameters When the design is complete the user will then run the nonlinear ana
17. OpenSees gt as can be seen in Figure 2 11 The user will then type source dynamic tcl in the command line prompt and hit Enter OpenSees will run its analysis at this point which could take several seconds It is recommended that this analysis is not run from a 15 flash drive because the time it will take to complete will be much longer OpenSees will display information as it progresses through its analysis The user will know it is finished when OpenSees gt displayed at the bottom as shown in Figure 2 12 C Users Kelly Desktop OpenSees OpenSees exe E OpenSees Open System For Earthquake Engineering Simulation Pacific Earthquake Engineering Research Center 2 4 4 reu 57745 Copyright 1999 2013 The Regents of the University of California All Rights Reserved CCopyright and Disclaimer http www berkeley edu OpenSees copyright html gt OpenSees gt source dynamic tcl_ Figure 2 11 OpenSees when the user has entered source dynamic tcl C Users Kelly Desktop OpenSees OpenSees exe edm 25 amping defined Building Period 2 6489854933933254 losest spectral period orresponding accel 80 2383568634240746 7 caleFactor is 947591539 867474 tory drift recorders defined 4261626166 6 6 459 4 6 6 load 4261626266 6 6 459 4 B B load 4201020300 6 6 459 4 B A load 4201020400 6 6 459 4 O A and analyzed pattern UniformExcitation 28 1 accel Series dt 8 018080 filePath GMfil
18. SA ft 2 1 Story Height ft Figure 2 4 Screenshot of the Story Geometry Tab The spreadsheet automatically determines the total building height which does not include the parapet height A building elevation which is to scale is also provided to give the user an idea of how tall the building is compared to its X direction width 2 5 Gravity Loads and Seismic Wt The design loads are entered on this tab including the floor dead and live loads the roof dead and live loads the snow loads and the wall loads These loads affect the seismic weight of the structure which is calculated automatically The individual story seismic weights are shown with white fill and a border while the total structure s seismic weight is displayed in the green cell below The individual story seismic weights are converted to units of kip sec 2 in then passed to the OpenSees input text file Refer to Figure 2 5 for a screenshot of this tab Floor Dead Load psf Exterior Wall Dead Load psf Floor Live Load psf table 4 1 Partition Wall Load psf including partitions Roof Dead Load psf Roof Live Load psf table 4 1 Snow Load psf 4 0 0 1 897 3 277 2 3 2 134 4 0 0 431 2 P 2 134 4 0 0 431 2 1 2 134 4 0 0 431 2 Story Floor Wt Roof Wt Ext Wall Partition Seismic k k k Total Seismic Wt 29583 k Figure 2 5 Screenshot of Gravity Loads and Seismic Wt Tab 2 6 Seismic Loads The purpose of this tab is to come up with t
19. Total Number of Braced Bays in Y Dir may be required o fully understand your building Analyze X Dir or Y Dir Location of Braces in Building For column gravity demands Ra Figure 2 3 Screenshot of the Brace Geometry Tab Width of Bay to be Analyzed The spreadsheet will automatically list only the bay widths that are available in the direction X or Y chosen The user can also specify if the braces are located on the exterior or the interior of the building which will only affect the gravity loads on the columns Lastly the user must specify what orientation of brace they are using Two Story X Chevron or Single Bay This greatly affects the demand on the braces and the columns 2 4 Story Geometry This tab is where the user inputs how many stories the building has The spreadsheet limits the design to 40 stories Similar to the Bay Geometry tab a global story height can be entered and it will apply to all stories Individual story heights may be entered into the designated cells for any story A button is provided for this tab as well that will restore the 6 formulas in the story height cells A parapet height is also available for input which increases the seismic weight of the structure Refer to Figure 2 4 for a screenshot of this tab Number of stries 4 Story Height Parapet Height below and the button may be used to restore the formulas Restore Formulas Ez Total ft ft Height 4 E
20. bottom and select Unhide and pick the Gravity Demand tab 11 With the total column demand calculated the column for each story is then auto sized The column shapes will auto size according to the target column depth cell R2 which should be specified by the user This depth refers to the depth of the W shape the spreadsheet will auto size e g a target column depth of 14 will auto size W14 s The auto sizing takes place off to the right of the main information For information on how the spreadsheet auto sizes the columns see section 4 1 The column titled Column Shape displays the result of the auto sizer which is the lightest column shape that works Refer to Figure 2 8 for a screenshot of the second part of this tab Target Column Depth in Formulas Restore Column Formulas Brace Column Column Column Comp Seismic Gravity Total Force Demand Demand Demand Column Column Dem Cap Beam Shape Capacity Ratio Shape Total Single Column weight 22 968 Ib Figure 2 8 Screenshot of the Second Part of the ELF Brace and Column Design Tab 12 After auto sizing the spreadsheet comes up with a demand to capacity ratio column This ratio is close to 1 when the selected shape nearly failing The ratio will be greater than 1 if it is failing The demand capacity cells will become yellow if the ratio is greater than for a given story This may happen when the user selec
21. c modulus for each story These numbers are passed to OpenSees for analysis 2 9 OpenSees At this point the user is ready to run OpenSees The user may select an actual earthquake from the drop down box for OpenSees to analyze the structure with The extra time may be specified by the user This is the time that OpenSees will wait for the structure to stop vibrating after the earthquake has stopped Unfortunately the larger the number the more data the spreadsheet has to import which takes up memory 14 The user can now create the OpenSees tcl files These files are named BRBF OSInput tcl and dynamic tcl These files are created by pulling inputs and calculations from all the previous tabs These files will be created in the same location that the spreadsheet is in For information on how the spreadsheet creates tcl files see section 4 2 Refer to Figure 2 10 for a screenshot of this tab Analysis Earthquake Station Extra Time 30 Acceleration g Import Results Time sec Duration ES sec Max Acceleration 00215 Results folders filepath must be Figure 2 10 Screenshot of the OpenSees Tab The final thing that must be done before running OpenSees is the user s Results folder must be cleared of all data Now with the Results folder cleared and the tcl files created OpenSees can be run The user must launch the executable OpenSees exe The command line will say
22. calculations the spreadsheet performs The MathCAD example is now presented BRBF Design Example This example is to accompany the BRBF Designer spreadsheet designed by Kelly Christensen and Dr Richards Geometry NumXBays 6 NumY Bays 5 For X bay widths we will use ft 26 26 30 30 26 26 For Y bay widths we will use ft 30 24 30 30 30 TotalX Width 1648 TotalY Width 144ft ConcOverhang 2ft TribFloorArea TotalXWidth 2 ConcOverhang TotalY Width 2 ConcOverhang 2486482 Perimeter 2 TotalXWidth TotalYWidth 4 ConcOverhang 6328 We will have 4 total braces in the X Direction and 4 total in the Y Direction as well We will analyze the X Direction which has braced bay widths of 26 ft The braces are on the exterior of the building and we will use the Chevron configuration The building looks as follows 21 Building Layout XBracedBays 4 YbracedBays 4 AnalyzeWidth 26ft We will do a 5 story building with some different story heights We will have an 18ft main floor and so on as follows For story heights we will use ft 18 14 14 16 14 NumStories 5 TotalHeight 18ft 14ft 148 168 14ft 76 ft ParapetHeight 4ft Loads FloorDead 90psf FloorLive 60psf This includes partition walls 28 RoofDead 80psf RoofLive 20psf Snow 30psf ExteriorWallDead SOpsf PartitionWall 10psf Seismic Weight FloorWeight TribFloorArea Floo
23. e and Column Design and the P Delta Column Design tabs The spreadsheet auto sizes shapes for columns in these instances The actual auto sizing takes place off to the right of the main information starting at column AL of the spreadsheet The spreadsheet starts by pulling the height and total demand from the main information for convenience It writes out all possible column shapes horizontally for the given target column depth cell R2 For each shape a capacity is calculated for each story Each story needs to have its own calculation because the stories may have different heights which will cause the column to have a different capacity If the calculated capacity for a given shape is less than the demand the cell will be blank This is an important part of the next step the spreadsheet makes The spreadsheet then picks the lightest shape that works This happens in the column titled Story Selected Shape column BZ The formula in this column looks at the minimum capacity value in its story The min function automatically ignores blank cells which is why cells where the capacity was less than the demand were left blank Once it has identified the minimum value on its row it returns the value in 9 row of the corresponding column which is the shape name e g W14X68 The next thing it does is it runs the shape on the odd stories up to the story above in column CA This is for splicing purposes as mentioned in the User s Manual 3
24. es CNP166 dat factor 366 1493787031192 Ground Motion Done End Time 54 990000 tory drift is 08 0152947 125126 0 0180536 192396 residual drifts are 06175022 6 60539366 6 616018 6 6131581 umStoryDriftList lt 1 152947 gt lt 2 125126 gt lt 3 0 0180536 gt lt 4 6192396 gt umResidualDriftList 1 66175622 gt lt 2 0 00539366 gt lt 3 610618 gt lt 4 6 6131581 gt verage story drift demands 0 015294 6125126 618 536 6192396 verage residual drift demands 9 991 25922 8 00539366 6 616018 6 6131581 verage plus story drift demands 9 915294 125126 0 0180536 80 0192396 verage plus residual drift demands 8 88175822 8 88539366 8 818818 8 8131581 OpenSees gt Figure 2 12 OpenSees when it has completed its analysis 16 With the analysis complete the Results folder is populated with data such as brace deformations and forces column forces and story drifts This data needs to be imported into the spreadsheet for post processing The user will now click the Import Results button to do this The user s Results folder must be in the same location as the spreadsheet or the spreadsheet will fail to import the data this is explained further in the orange text box below the Import Results button The importing process can take anywhere from 10 seconds to over a minute The time it takes depends on how much data there is to import which is a function of how tall the structure is and
25. gets overwritten 41 REFERENCES Fahnestock L A Sause R and Ricles J M 2007 Seismic Response and Performance of Buckling Restrained Braced Frames Journal of Structural Engineering 133 9 1195 1204 Lin B Chuang M and Tsai K 2009 Object oriented development and application of a nonlinear structural analysis framework Advances in Engineering Software 40 1 66 82 42
26. h a required brace core area After that a brace cross sectional area in is then auto sized for each story Refer to Figure 2 7 for a screenshot of the first part of this tab 10 Steel core ER ksi Overstrength factor strain hardening w 1 36 Steel core min 38 ksi Overstrength factor compressive effects 1 1 Steelcoremax f 46 Restore in Story Height Height E Braced aru Bay ft ft k k k 251 206 260 1 65 0 230 596 498 8 124 7 142 917 646 7 161 7 63 081 712 1 178 0 687 801 Figure 2 7 Screenshot of the First Part of the ELF Brace and Column Design Tab The second part of this tab comes up with a column shape for each story It is designed to have certain shape run for two stories for splicing purposes For example if W14X68 is used for the first story the spreadsheet will also use that shape for the second story It will then pick a new shape for the third and fourth stories and so on In order to pick a column it comes up with a seismic demand and a gravity demand seismic demand and sums the two The seismic demand is calculated while taking the brace orientation Two Story X Chevron or Single Bay into account which was selected by the user on the Brace Geometry tab The gravity demand is calculated in a different tab that is hidden If one desires to see the calculation he or she may unhide the tab To do so right click the tabs at the
27. hat maximum load to the column This tab will help the designer see if that assumption will result in over designing the columns Shown in Figure 2 20 a is the First Story Column Axial Force vs Time plot This displays the force that the first story column experiences throughout the earthquake There is a plot for the left and the right column of the frame This force is solely the force caused by the earthquake this does not include gravity loads The red marker shows the maximum force Figure b is a table of pertinent information relating to the First Story Column Axial Force vs Time plot It shows the maximum force and the time when the column experiences that force The other two items in the table will be discussed later Time sec 0 10 20 30 40 50 400 200 0 Q 200 400 a Time When Max Weighted Column Column Average Average Force Max Force Force Ratio Force Ratio sec 20 74 233 4 94 9 96 0 b Figure 2 20 a First Story Column Axial Force vs Time and b the Corresponding Table Next are the brace plots one of which can be seen in Figure 2 20 a These are shown with a blue line where the column plots are shown with a red line These plots are essentially the 24 same as the column plots they show the axial force vs time for the left and right braces of each story The blue marker shows when the brace is experiencing its maximum force The red marker
28. he design base shear of the building The user inputs the Risk Category Site Class and 5 and S values The spreadsheet uses the Risk Category to come up with the Seismic Design Category and the Importance Factor The Site Class and S and 51 values are used to come up with Fa and values which are used to determine Sms and values which ultimately lead to Sps and Spi values The design spectrum is plotted using the Sps and Spi values Refer to Figure 2 6 for a screenshot of this tab Risk Category Site Class Mapped Accel at short Period 5 Mapped Accel at T 1 sec 5 E Site Coefficient Fa 1 021 Site Coefficient Fs 1 553 Spectral Accel at short Period Sms 1 223 g Spectral Accel atT 1sec S 0 694 g Design Accel at short Period 5 Design Accel atT 1sec Sp 0463 Seismic Design Category 100 8 5 Long Period T Importance Factor l Response Modification Factor R Deflection Amp Factor Approx Period Parameter G 0 03 Approx Period Parameter x 0 75 Approx Period T 0 614 sec Upper Limit Coefficient 1 4 Period T sec Seismic Response Coefficient 0 067 Total Seismic Weight Ww 10583 k Seismic Base Shear k ASCE 7 10 Reference table 1 5 1 table 11 4 1 table 11 4 2 eqn 11 4 1 eqn 11 4 2 eqn 11 4 3 eqn 11 4 4 table 1 5 2 table 12 2 1 8 for BRBF table 12 2 1 5 for BRBF table 12 8 2 0 03 for BRBF table 12 8 2 0 75 for BRBF eqn 12 8 7 table 12 8 1
29. he target depth the user specifies The column capacity equations taught in CE En Story 1 W14x61 Capacity 571 2k 421 were used Story 1 W14x61 Capacity 514 1k 35 Story 1 W14x109 Capacity 1241 5k Story 1 W14x109 Capacity 1126 9k P Delta Column Design ColumnDemandl 60 5kip ColumnDemand2 60 9kip ColumnDemand3 61 6kip ColumnDemand4 63 2kip ColumnDemands 56 2kip The values to the left were obtained via basic tributary area and load calculations These values are for their respective story only not a cumulative total The average of these values is passed to OpenSees for the P Delta column load The total columns in the building for a single story is 42 The tributary area used to obtain these values is estimated by taking the total floor area and dividing by the number of columns 42 thus obtaining an average tributary area This tab autosizes a column shape for the P delta columns and passes the cross sectional area moment of inertia and the plasic modulus to OpenSees Since there are 4 braces in the X Direction there are 8 5 p delta columns per brace this number is multiplied by the section properties that are passed to OpenSees 36 4 HOW THE SPREADSHEET FUNCTIONS 41 How the Auto Sizer works There are two tabs in the BRBF Designer spreadsheet that have auto sizers that is functionality that automatically picks the optimal steel shape for a member Those tabs are the ELF Brac
30. how fast the user s computer is The spreadsheet is not only importing data during this time it is also formatting plots and tables on the next three tabs Once the data is imported the spreadsheet no longer needs OpenSees It can run all results on its own 2 10 Story Drifts amp Displacements The remainder of the spreadsheet is dedicated towards helping the user more clearly understand OpenSees results The raw results are just lists of numbers The numbers are extremely valuable but very difficult for users to truly understand or draw conclusions from Thus this spreadsheet is not only a great tool to help users design a structure for OpenSees to run but also display the results in a more readable format This tab is the first of three meant for displaying OpenSees results Firstly this tab displays a table which includes information drifts and displacements for each story as shown in Figure 2 13 Drift is how far a given story horizontally displaces during an earthquake expressed as a percentage of the story height Displacement is how far a given story horizontally displaces during an earthquake expressed in inches As opposed to drift displacement is a cumulative sum of the story displacements therefore the roof will have a high value because it is a sum of all the stories below it 17 Drift Limit ISI ASCE 7 10 Table 12 12 1 Max Residual Max Residual Drift Drift Disp Disp ft 26 26 in in Story Height
31. is the force the brace is experiencing when the first story column is at its maximum force The corresponding table Figure 2 21 b displays the value of the brace s maximum force the blue cell and the force of the brace when the column force is at its maximum the red cell Lastly it displays the ratio between the two forces which is the red cell divided by the blue cell The closer this ratio is to 100 the more valid the original assumption is 200 0 200 a Force k Force Max Force When Force Ratio k Column Max k 68 0 61 0 90 b Figure 2 21 a Brace Axial Force vs Time and b the Corresponding Table Referring back to figure 2 19 b the Average Force Ratio is simply the average of all the brace Force Ratios see Figure 2 20 b The Weighted Average Force Ratio is the same thing but weighted according to the story s brace size The original assumption was that all the braces are at their maximum force when determining the design load of the columns If these average force ratios are near 100 then the assumption is very valid In this case the averages are 94 9 and 96 0 This shows that the original assumption is quite valid and the columns should be designed using the maximum load from the braces 25 3 MATHCAD DESIGN EXAMPLE A detailed MathCAD example was created to show the entire design process for a 5 story BRBF structure and to display the
32. isplaying maximum forces and deformations from a hysteretic plot Below the story hysteretic plots is the animation Hysteretic Plot see Figure 2 19 This plot functions the same way the previous animation plot works Refer to section 2 10 for how to use an animation plot and section 4 4 for information on how the animation plots work The only 22 aspect different with this animation plot in comparison to the Story Displacement Plot is the user may select what hysteretic plot to view This is done in the blue cell above the plot on the left side Left and right braces for each story are available to view Show every ast Story Lefe time steps Hysteretic Plot v o T 0 5 0 Deformation in Jump tof o sec Figure 2 19 Animation Hysteretic Plot Two small tables are shown to the right of the animation plot One is the same table that is present for each hysteretic plot which shows the maximum force and deformation The other plot displays the current force and deformation from what is currently displayed on the animation plot As the plot runs these values will continuously change 23 2 12 Column amp Brace Forces The purpose of this tab is to compare the first story column axial force to the axial force in the braces The reason this is important is because when the column is designed all braces are assumed to be loaded to their max and thus transferring t
33. lysis in OpenSees using the text files that the spreadsheet creates The OpenSees results must then be imported into the spreadsheet The rest of the spreadsheet is dedicated to analyzing the results from OpenSees The results consist of drift and displacement tables hysteretic plots and column brace axial force plots Animation plots for story displacement and hysteretic plots are also included Because some of the calculations that the spreadsheet performs are convoluted a MathCAD design example is provided A section is also included for how the spreadsheet functions with some of the more complicated features LIST OF FIGURES rcr l OND 1 1 Whatis BRBF ib OH p 1 2 OPENS EES wt pute ence te eed 1 3 Spreadsheet s Usefulness with 2 User s Manual DE ESL MM E E 2 1 2 27 CICORIGIDy 2 3 Brace Geometty 2 4 Story Geometr Y 25 Gravity Loads and Seismic 2 6 Seismic iere ie aed idu nouit do di 2 7 ELF Brace and Column Design 2 8 P Delta Column os ott idet AI UP e pede 2 0 PES CC ADU RM PUE 2 10 Story Drifts amp Displacements ordo tre potete e eie dec tinet pnaes 2 11 Hysteretic Plots entr 2 12 Column amp Brace Forces
34. on becomes available only when the animation plot is playing The fast forward button will take the plot to the very end and stop it This can be useful 19 if the user wants to see what the building looks like after the earthquake is over The rewind button will take the plot back to the very beginning and will stop the animation if it is running This is useful if the user wants to watch the animation again The pause button obviously pauses the animation and shows the play button again The animation can resume right where it left off by pushing the play button again The user can change the number in the Show every x time steps blue cell to speed up or slow down the plot If a 5 is entered in this cell for example the plot will only showing every 5 time steps Enter in a higher number to speed up the animation and a lower number to slow it down If too high of a number is entered in this cell the plot can start to look less smooth because is skipping so many time steps The user is also use the blue horizontal scroll bar directly beneath the plot to skip to a certain point in the animation Another way to achieve this is the Jump to x seconds cell The user can enter a value in the blue cell and push Enter and the plot will skip to that time in the animation Refer to section 4 4 for information on how the animation plots work To the right of the Story Displacement Plot are the Drift vs Time and the Displacement vs Time plo
35. rDead 2237 76 kip RoofWeight TribFloorArea RoofDead 1989 12 kip 188 148 ExteriorWallWeightl Perimeter 77 ExteriorWallDead 505 6 kip ExteriorWallDead 442 4 kip 14ft 14ft ExteriorWallWeight2 Perimeter 20 14ft 168 2 ExteriorWallWeight3 Perimeter ExteriorWallDead 474 kip 16ft 14ft ExteriorWallWeight4 Perimeter ExteriorWallDead 474 kip 14ft ParapetHeight ExteriorWallDead 284 4 kip ExteriorWallWeight5 Perimeter PartitionWeight TribFloorArea PartitionWall 248 64 kip SeisWtl FloorWeight ExteriorWallWeightl PartitionWeight 2992 kip SeisWt2 FloorWeight ExteriorWallWeight2 PartitionWeight 2928 8 kip SeisWt3 FloorWeight ExteriorWallWeight3 PartitionWeight 2960 4 kip SeisWt4 FloorWeight ExteriorWallWeight4 PartitionWeight 2960 4 kip SeisWt5 RoofWeight ExteriorWallWeight5 2273 52 kip TotalSeismicWeight SeisWtl SeisWt2 SeisWt3 SeisWt4 SeisWt5 14115 12 kip Seismic Loads Risk Category will be III and Site Class will be D We will use the location of the Clyde Building for this example which has the following Ss and S1 values obtained from earthquake usgs gov 29 5 1 198g 447g F 1 021 1 553 Suis S F 1 223 g SMI SLF 0 694 g wjn ASCE 7 Table 11 4 1 ASCE 7 Table 11 4 2 ASCE 7 Equation 11 4 1 ASCE 7 Equation 11 4 2 ASCE 7 Equation 11 4 3
36. res a nonlinear approach rather than using linear computations This is because earthquakes cause large displacements in a structure and because the braces yield during an earthquake which causes their behavior to change Of the many programs that can run nonlinear analyses OpenSees was chosen for this project due to its versatility OpenSees stands for Open System for Earthquake Engineering Simulation It is an open source program that simulates the seismic response of structural and geotechnical systems OpenSees is capable of running a dynamic nonlinear analysis to simulate a structure s response to a real earthquake ground motion This analysis is the focus of the BRBF Designer spreadsheet 13 Spreadsheet s Usefulness with OpenSees As useful as OpenSees is it is purely an analysis tool It reads text files for input and runs an analysis The text files are a major disadvantage of OpenSees due to the amount of time the user has to spend creating them and the large possibility of typographical errors This is what makes a spreadsheet useful when using OpenSees Essentially the first half of the BRBF Designer spreadsheet is a design tool The user enters information for the building he or she wants to be analyzed and the spreadsheet will come up with data such as seismic weight brace and column sizes at each story and p delta loads Another disadvantage of OpenSees is the results because they are simply text files with columns of numbers It
37. ts a shape to overwrite the auto sizer It also can happen when a poor target column depth is selected and the auto sizer comes up with column shapes and some don t work 2 8 P Delta Column Design This main purpose of this tab is to come up with the moment of inertia for the gravity columns on each story It take an approach that is somewhat accurate The total columns in the building per story are determined The number of braced bays in the direction of interest which was selected on the Brace Geometry tab is listed The p delta columns per braced bay is obtained by dividing the total number of columns by the number of braced bays then subtracting two because we don t count the two columns in the braced bay Then the average tributary area for each of those columns is determined by dividing the total floor area by the total columns in the building This isn t the exact tributary area for each column since each column is be different This is just the average tributary area for the columns Now that the spreadsheet has a tributary area loads are determined to ultimately come up with a column demand Dead live and snow loads are pulled from the Gravity Loads and Seismic Wt tab Live loads are reduced according to ASCE 7 10 standards A column demand is then obtained for each story using only load combination 2 from ASCE 7 10 This column demand is used to auto size a column shape in the same manner as the previous tab see section 2 7
38. ts which can be seen in Figures 2 15 and 2 16 The blue cell above the plots can be changed to be any of the stories of the building Doing so will update these plots to show the data for the selected story These plots can be useful for the user to see how much drift or displacement the building had at any point in time during the earthquake It can also be useful to view the Story Displacement Plot animation while paying attention to the Story Displacement Plot to easily see when big displacements will happen 20 1 00000 0 50000 0 00000 0 50000 1 00000 1 50000 2 00000 1st Story Drift 30 Time sec Figure 2 15 Drift vs Time Plot Displacement in 2 00000 1 50000 1 00000 0 50000 0 00000 0 50000 1 00000 1 50000 2 00000 2 50000 3 00000 1st Story Displacement 30 Time sec Figure 2 16 Displacement vs Time Plot 21 2 11 Hysteretic Plots This tab displays hysteretic plots for the left and right brace of each story in the building An example of one can be seen in Figure 2 17 Each hysteretic plot has a corresponding table which displays the maximum axial forces and deformations an example of which can be seen in Figure 2 18 lt o x lt 0 Deformation in Figure 2 17 Hysteretic plot created from OpenSees Results Max Max Force Deform k in Compression 192 5 1 691 Tension 186 0 1 221 Figure 2 18 Table d
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