Feasibility study to improve the life of buckling restrained braces and fragility curve analysis for a steel frame with buckling restrained braces

Improving the performance of buckling restraint braces and having uniformity in their performance in a particular structural system can further improve the life of a system. In order to achieve this, demand of the buckling restraint braces needs to be altered by altering their size and effect of changing on structural response needs to be studied in detail. The paper aims at evaluating the feasibility of changing the size of the buckling restrained brace as being a method to increase the overall performance of the system. The paper uses a software PERFORM 3D for modeling and simulating the structure is first subjected to ground motion histories from the Kobe and Northridge earthquakes. Nonlinear time history analysis is then performed on the structure. Fragility curves were then developed to further confirm the improved performance of the system. The structure was subjected to one hundred earthquakes. Peak ground acceleration values for each of the hundred simulations varied from 0.1 to 1 with an increase of 0.1. The results showed that increasing the size of the buckling restrained braces only altered the structural response parameter like interstory drift, displacement, velocity, moment rotations by a small margin and hence it can be used as a method to improve the buckling restrained brace performance. The fragility curves further confirmed the improved performance of the buildings using buckling restrained braces.

FEASIBILITY STUDY TO IMPROVE THE LIFE OF BUCKLING RESTRAINED BRACES AND FRAGILITY CURVE ANALYSIS FOR A STEEL FRAME WITH BUCKLING RESTRAINED BRACES by Anurag Ghatole A thesis submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Master of Science in Civil Engineering Department of Civil and Environmental Engineering The University of Utah December 2009 Copyright © Anurag Ghatole 2009 Rights Reserved All T H E U N I V E R S I T Y OF U T A H G R A D U A T E S C H O OL of a thesis submitted by Anurag Ghatole This thesis has been read by each member of the following supervisory committee and by majority vote has been found to be satisfactory. Chair: Kevin Wong THE UNIVERSITY UTAH GRADUATE SCHOOL SUPERVISORY COMMITTEE APPROVAL 03 - 2 f - 20CJCj T H E U N I V E R S I T Y OF U T A H G R A D U A T E S C H O OL FINAL APPROVAL To the Graduate Council of the University of Utah: I have read the thesis of Anurag Ghatole jn j t s f i n a ] fo rm and have found that (1) its format, citations, and bibliographic style are consistent and acceptable; (2) its illustrative materials including figures, tables, and charts are in place; and (3) the final manuscript is satisfactory to the supervisory committee and is ready for submission to The Graduate School. Date Kevin Wong Chair: Supervisory Committee Approved for the Major Department Approved for the Graduate Council David S. Chapman Dean of The Graduate School THE UNIVERSITY UTAH GRADUATE SCHOOL FIN AL READING APPRO V AL in its final form Chair/Dean ~c.-:.J SO. ca. ~--. ABSTRACT Improving the performance of buckling restraint braces and having uniformity in their performance in a particular structural system can further improve the life of a system. order to achieve this, demand of the buckling restraint braces needs to be altered by altering their size and effect of changing on structural response needs to be studied in detail. The paper aims at evaluating the feasibility of changing the size of the buckling restrained brace as being a method to increase the overall performance of the system. The paper uses a software PERFORM 3D for modeling and simulating the structure is first subjected to ground motion histories from the Kobe and Northridge earthquakes. Nonlinear time history analysis is then performed on the structure. Fragility curves were then developed to further confirm the improved performance of the system. The structure was subjected to one hundred earthquakes. Peak ground acceleration values for each of the hundred simulations varied from 0.1 to 1 with an increase of 0.1. The results showed that increasing the size of the buckling restrained braces only altered the structural response parameter like interstory drift, displacement, velocity, moment rotations by a small margin and hence it can be used as a method to improve the buckling restrained brace performance. The fragility curves further confirmed the improved performance of the buildings using buckling restrained braces. In further TABLE OF CONTENTS ABSTRACT iv LIST OF TABLES vi LIST OF FIGURES vii ACKNOWLEDGEMENTS ix CHAPTER 1. INTRODUCTION 1 Literature Review 4 2. PROBLEM STATEMENT 10 3. FEASIBILITY STUDY AND FRAGILITY ANALYSIS 15 4. RESULTS 19 Feasibility Results 19 Fragility Curve Results 28 5. CONCLUSIONS 41 6. RECOMMENDATIONS 43 REFERENCES 44 ABSTRACT ... .. .. .. .... .... .... ... ............ ..... ................. .... ... ....... .. .................... .... .... ... ....... iv ... ... .... .... .. ....... ..... ..................... ..... ... ..................... ... .......... ... .... ...... ................. .. ................ .. ............................... ..... .. ..... .... ............... ... .......................... . .. ... .. ......... .... .. ... ............. ... I. .. ........... ....... .... ..... ... ... ..... ... ... ..... ..... ... ....................... ... ................ I .. ...... .......... ...... ....... .... ...... ...................... ... .. ..... ... ..... ....... ..... ... .. ... .............................. ....... .... .. ..... ........................ ... ANALySIS ..... ...... ............ ... .... ........ ..... ... ... ............ .. .................................... ... ..... ... .......... ....... ........................ Res ults ........ ............................. ...... ... .. .. ..... ... ...... .... .... ...... .. ........ .. Fragility Curve Results .. ... .... ........ ........ .. ........ .... .... ..... ................... .. .. ... ......... 28 5. CONCLUSIONS .... ... ... .... ... ........ .. ...... ........ .... ... .. ......................................... ......... .41 6. RECOMMENDA TIONS .............................................. ................................ .. ......... .43 REFERENCES .... .. ...... ............ ....... ............ ........ ... .... .. .... .. ....... ........... .................... ..... 44 LIST OF TABLES Properties 2. Properties of Buckling Restraint Braces Considered for Simulations.... 16 1. Beam Member Properties.......... .......... ..... .... ........... .... . ......... 12 LIST OF FIGURES Fig no. Figure name Page No. 1 Typical cross section of CoreBrace brand of buckling restrained braces Interstory drift 3 Idealized buckling control mechanism 4 4 Force-Displacement graph for buckling restrained brace considered for fragility analysis 12 5 Six-story moment resisting steel frame with hinge locations and other details 13 6 Frame showing the buckling restraint brace arrangement 14 7 Graph for displacement response for Kobe earthquake 20 8 Displacement response for Northridge earthquake 20 9 Velocity response for Kobe earthquake 22 10 Velocity response for Northridge earthquake 22 11 Acceleration response for Kobe earthquake 23 12 Acceleration response for Northridge earthquake 23 13 Interstory drift response for Kobe earthquake 24 14 Interstory drift response for Northridge earthquake 24 15 Plastic rotation response for hinges in columns for Kobe in positive x-direction 25 16 Plastic rotation response for hinges in columns for Kobe in negative x-direction 25 Core Brace braces..... . .... .... ....... ........ .... ..... ...... ........ ..... ........ ...... 2 2 lnterstory drift..... . .. ............ . ... ..... . .. ................ . .. ............ 3 mechanism.......... .... .... ........ ......... for fragility analysis.................... .... ............ ..................... 12 details. .. ... ..... . .......... ... ... .... .. .. . ..... ... ... ..... . ... ... .. ..... arrangement... ...... . ..... earthquake.................. earthquake.......... ............ ............ ...................... earthquake.... ................ ......... II earthquake...................... ........ earthquake.................... ... I3 interstory earthquake........................... interstory earthquake.. .................... direction...................... . ... ... ...... .. .. .. ...... ..... ...... direction...................................................... direction negative x-direction .... 26 19 Plastic rotation comparison graphs for Kobe earthquake 27 earthquake of BRBs earthquake earthquake of BRBs earthquake of BRBs earthquake 0.5% 1 % 39 fragility 2% viii 17 Plastic rotation response for hinges in columns for Northridge in positive x-direction. .. .. . .. ....... .. .. .. . .. . ... .. .. . .. . .. . .. .. ... .. . . . ... . ... 26 18 Plastic rotation response for hinges in columns for Northridge in . .... .. ........ ................. : ...... :: .. : .. :............. earthquake...... .. ... .... 20 Plastic rotation comparison graphs for Northridge earthquake...... ... 27 21 Force displacement graphs for different types ofBRBs used for Kobe earthquake................................. ..... ............ ....... .. ... 29 22 Force displacement graphs for different types of BRBs used for Northridge earthquake.................................. .. .. ................. 31 23 Moment rotation graphs for different types ofBRBs for Kobe earthquake.. . ...... .... . .. . ......... .................. . .. ............. ........ . 33 24 Moment rotation graphs for different types ofBRBs for Northridge earthquake..... .. ............ .. .. .. . ............ ....................... . ... .... 36 25 Comparison of fragility curves for a steel moment frame and a BRBF for immediate occupancy drift limit of 0.5%................... .... .... 38 26 Comparison of fragility curves for a steel moment frame and a BRBF for life safety drift limit of 1%............. ............................. ... ... 39 27 Comparison of fragi lity curves for a steel moment frame and a BRBF for collapse prevention drift limit of 2%.................. .... .. ....... .. 40 ACKNOWLEDGEMENTS I would like to thank my advisor and teacher Dr. Kevin K.F. Wong for all the efforts he put in with this research and for everything he has taught me during this course. I cannot thank him enough when I look back at the effort he has put in day in day out with this research. His command over the subjects he taught was impeccable and the best I have experienced so far in my educational career. He has been the driving force and has helped me through difficult times during the research with utmost patience and has always shown a path which led me to my goal. I would also like to thank Dr. Paul Tikalsky for his continued support and how professional should we be in order to be the best. I feel blessed to have him as my without my having to asking twice for anything I needed with the course or my research. His support has been a major reason for a stress free course for me. teacher and researcher. I would also like to thank Dr. Larry Reaveley for his support and guidance. CoreBrace, company dealing in buckling restrained braces, for providing me with data that proved J. guidance through the course. As a teacher he has been an inspiration and an example of teacher and department head. As department head he supported me in every way possible I would also like to thank Dr. Chris Pantelides for being an active and dynamic I would also like to especially thank Mark Daniels from Core Brace, a local very useful in the research. CoreBrace patiently and promptly provided data whenever required making the whole process a lot easier. Finally, I would like to thank my parents, family and friends for their continued love and support throughout the course. I thank them for having undying faith. I would like to also thank my American family, the Arringtons, for making my life comfortable here and for accepting me as their own. I would like to thank my friend Richa and her family for their love and support all throughout the course of my studies. .. . comfortable x CHAPTER 1 INTRODUCTION research has been conducted since then to improve its performance. While its purpose is better understand the behavior of BRBFs when subjected to seismic loading. In different BRB sizes and to improve the performance. Buckling restrained braces are members with a steel core coated with non-bonding 1. They have gained popularity in the United States and other countries around the world recently because of their basic property of yielding both in tension and compression. Another advantage of BRBs is that they add stiffness to the structure, resulting in possible reduction in the framed member sizes while achieving the same performance The buckling restrained brace (BRB) was invented in the 1970s, and active mainly to provide stiffness to framed structures, only limited research on the structural dynamic response of buckling restraint braced frames (BRBFs) has been performed until recently to fully exploit the benefits of having BRBs installed. This research attempts to ofBRBFs particular, the main objective is to evaluate the BRBF performance when the locations of installing BRB are limited for architectural reasons - open ground floor space. Numerical simulations were conducted to understand the responses of BRBF using non­bonding material covered by mortar grout inside a steel casing as shown in Figure I. 2 Unbonding material Steel Casing Mortar Flat core plate or cruciform plate Figure 1: Typical cross section of CoreBrace brand of buckling restrained braces. level. This research also aims at evaluating the feasibility of increasing the efficiency of BRB by increasing the area of steel core in a BRB. A Perform-3D computer model was developed for the numerical simulation of the nonlinear structural response. The moment-resisting steel frame was modeled and the hinge locations were defined. Different sizes of BRBs were examined to see the difference in responses. These to increase the efficiency of BRBs. The details for different types of BRBs were provided by CoreBrace, major suppliers and installers of buckling restraint braces. A feasibility study was performed to study structural responses, which include displacement, velocity, acceleration and interstory drift. In addition, plastic rotations, moment rotations and force displacement responses were investigated in the research. The structure was subjected to ground motion records for Kobe (January 17th, 1995, Japan) and Northridge (January 17, 1994, California, USA) earthquakes. limit when subjected to specified ground motion intensity. Fragility curves are a tool for JjJ~~~ti~~- I: changes also helped in studying the feasibility of increasing the area of steel core section Fragility is the probability of response of a structure to exceed a certain critical 3 performance based design. They capture the nonlinearity and uncertainty in evaluation and design processes (Bozidar Stojadinovic et al. 2005). In this research, the fragility curves were developed for the BRBF to evaluate its performance. One hundred simulated earthquake ground motions were used to develop the fragility curves. The acceleration ground motions were modeled as a nonstationary Gaussian random process with zero mean. The performance limits were based on the interstory drift responses. Interstory drift is the ratio of difference between upper story drift and lower story drift to the height of the floor, as shown in Figure 2. The performance limits based on interstory drifts specified by FEMA356 were used, where these limits for immediate occupancy, life safety, and collapse prevention are 0.005, 0.01, and 0.02, respectively. In the fragility analysis, the peak ground acceleration intensities varied from 0.1 to 1.0 for each of the hundred earthquakes. The number of values above each performance level was counted to determine the probability of exceedance. The best-fitted log-normal distribution based on the least square method was then used to plot the curves. Upper story drift (USD) Floor Height (L) Interstory Drift USD-LSD L Lower story drift (LSD) Figure 2: Interstory drift. at. fragility evalua~e .performa~ce .. 0.01 , j. LSD Dnft = --- ­L 2004).To understand the working of the buckling restrained braces, theoretically, we can consider a compression member subjected to compressive forces, laterally bracing the member at regular intervals such that the unbraced length of the member is equal to zero (Hussain et al. 2007) as shown in Figure 3. BRBs are generally members in which compression buckling has been reduced or ideally been eliminated. While understanding the concept of BRB in protecting structures is important, most of the research has been done on small structures in order to formulate design procedures. Detailed research has been done but it has been suggested that further research is needed to ascertain the fragility parameters of different types of configuration for frames using BRBs (Andrews et al. 2008). P P 'mm. > A Decoupled axial stress and Euler Buckling Figure 3- Idealized buckling control mechanism. 4 Literature Review BRBs were first tested in 1970s. The first of its kind structural arrangement resembling a BRB was a shearwall encased with a metal strip inserted diagonally (Xie p Balanced Hysteresis 5 The standards of BRBFs as prescribed by American Institute of Steel Aby, Aby g(t) Gaussian random processes with zero mean (Wang and Wong 2005). Recent research on 3-story and 6-story BRBFs suggests better performance of BRBFs but lacks comparison of the BRBFs with the performance of a steel moment idea about the behavior of these systems. But for a probabilistic evaluation of these Construction (AISC) state that the maximum required deformation of the brace corresponding to 2.0 times the design story drift from neutral position in both directions should not be less than 10 times ~by, where ~by is the initial yield length of the brace. While the earthquake data used in most of the research done to date has been typically recorded from earthquakes in the past, some results have used earthquake data randomly generated using various methods like equivalent linearization method (ELM) (Andrews et al. 2008) or modeling them as stochastic processes based on parameters for the structure (Tantala et al. 2002). This paper uses ground acceleration ag (t) modeled as a non-stationary Gaussian random processes with zero mean (Wang and Wong 2005). resisting frame or any normal steel frame (Sabelli and Mahin 2002). Also, the number of ground motion records, if increased, can lead to a better probabilistic approach. The interstory drift response values if compared with the response of frame not using BRB can give a better picture of the performance advantages of the BRBFs. The research gives a good approach to evaluate BRBFs by comparing the parameters such as displacement, acceleration, and interstory drift. Efficiency of BRBFs can be addressed using this approach effectively. Another study shows that using a dual system of a special moment frame and buckling restrained braces in a system is a better option than using just BRBs in a system, thus suggesting that the choice of a dual system can increase structural performance (Kiggins et al. 2006). Most of the testing on BRBFs gives a good idea about the behavior of these systems. But for a probabilistic evaluation of these 6 previous research and better control on strain in the system has been observed (Kumar and Kumar 2006). But identifying the BRBs with higher demand in a frame and changing them would mean we have better control on the economics of the changes required. Also, analyzing a structure with a limitation of not having a BRB on one of the floors gives an opportunity to look at how the behavior would change for a system with such a limitation. Choosing a frame with the limitation of not using BRB at the ground floor in this thesis gives us the opportunity to look at the importance of providing BRBs on the first floor. It also gives us an opportunity to evaluate the frame responses of story in a frame that might be called a partial dual system since one of the floors does not have a dual of another research initiative that suggest that due to the residual strain in BRBFs after earthquakes the BRBs might require replacement (Fahnestock and of BRB will help in deciding if they require replacement. Also, these parameters may help in increasing the life span of the BRBF as a whole. Thus the evaluation of critical parameters that affect the performance of a BRB, such as the area of steel core section, length of brace, and total length of brace, can be of prime importance. This thesis deals with the core area as results, a number of tests need to be carried out, which is difficult to achieve considering the cost of each test. Hence sustainable methods like computer simulations need to be developed, primarily to carry out these tests on a larger number of specimens and have a probabilistic result on behavior patterns of structures using BRBs (Tsai and Weng 2003). Testing different BRBs in the same frame using hybrid simulation has been achieved in system. There are results Sause 2007). Evaluating parameters for increasing the efficiency affect perfonnance a parameter for influencing the efficiency of BRBFs. It not evaluated. Thus, comparison and evaluation of BRBs according to their parameters might prove to be helpful in understanding the behavior of BRBFs (Sabelli and Mahin 2002). limits sustained by the frames. The damage limits as per FEMA 356 are defined for steel Immediate Occupancy (IO) - At this damage limit the structure shows minor local permanent distortion of members (FEMA 2000). being intact (FEMA 2000). Depending on the performance criteria the fragility curves were plotted. To as the random variable, lognormal distribution has the probability density function of the 7 Uniformity in quality of BRBs manufactured by different providers can also affect the system response and in case of replacements it may limit the options of the concerned party. might also prompt the need to provide a secondary bracing system if Performance limits for BRBFs have been specified by FEMA based on the drift moment frames as follows: 10) yielding at a few places, without any fractures, and minor buckling or observable Life Safety (LS) - At this damage limit hinges form at various locations in the structure, local buckling is observed in some beam elements, severe joint damage is seen and a few fractured moment connections might also be seen but the shear connection are intact at this point of damage, with partial fracture in a few elements (FEMA 2000). Collapse Prevention (CP) - At this damage limit extensive distortion of beam and column panels is seen and many moment connections fail with shear connections still minimize the error, lognormal distribution was used to plot the fragility curves. Using x 8 form: - (ln(*HQ2 the cumulative distribution function for lognormal distribution is given by 1 1 4 - + -erf 2 2 \n(x) - ju a42 where \i is the mean of natural logarithm for the values of variable x > 0, and o is the standard deviation of natural logarithm for the values of variable x> 0. Therefore, the mean and variance of the lognormal distribution can be computed as: E{X) = e^2'2 Var(X) = (e? - l ) e w in which case the standard deviation becomes StdDev{X) = ^Var(X) = ^ + ° 2 / 2 ^ ° 2 - l 1 (In(x)-Il l 2cr2 f(x;f.1 ,a) = e . xcr.J2TI ~+~erIln(x)- f.1] 2 2 J L aJ2 Il x> (j O. 9 The difference between lognormal distribution and normal distribution is the various forces acting independently of one another. In normal distribution the forces are additive whereas they are multiplicative in lognormal distribution (Limpert et al. 2001). Evaluating the parameters that affect the performance of a BRB in a BRBF is an important research topic. Comparing the responses with a moment resisting frame will further confirm better performance of BRBF. Also the probability of exceedance of performance based design limits when compared with a steel moment resisting frame using a medium like fragility curves, which is a probabilistic way of depicting the performance exceedance values, gives a better idea of the performance. It also requires us to get the results from a greater number of ground motion records. frame CHAPTER 2 PROBLEM STATEMENT It also magnifies the responses, which helps recording even the marginal changes by The 6DOF structural model is shown in Figure 5, where there are 40 potential plastic the columns. These plastic hinges are assumed to deform in an elastic-plastic behavior (Zhe Wang and Kevin K. F. Wong et al.). All the joints have been assigned constraints in the direction of the unit force applied for the nonlinear time history analysis to be carried on the structure. The properties of the BRB used were taken from the tests done for a buckling restraint brace company, CoreBrace. The bracing length was 179.75 inches the cross-sectional area was considered to be 5 sq.in. The force displacement graph is as shown in Figure 4. The beams are designed to fail by flexure and not by shear failure. The model of a six-story moment-resisting steel frame, shown in Figure 5, is selected as the example. The architect demands open space on the first floor, inducing a soft story, thus also helping us evaluate the effect of a soft story in a building with BRBs. amplifying responses of the structure. The floor masses of 1081.6 kips per floor are selected to give a long first period of vibration of 1.237 seconds. In this study, the structural damping is assumed to remain unchanged during the entire analysis process. hinge locations (PHL), with 6 PHLs on the beams per floor, and 4 PHLs at the base on ofthe 11 Cyclic degradation and strength loss have not been considered in the plastic hinge definitions. Sections used and section properties and geometry of the structure is provided in Table 1. For feasibility study five different BRBs were tried. Design data were provided by CoreBrace. BRBs on floor 1 and floor 2 seemed to have the highest demand when earthquake responses were compared. Only these BRBs were replaced since the aim of the feasibility study conducted was to decrease this demand and observe its effect on the structural response. The structural responses of the structure for all the BRBs were obtained by running the simulations for Kobe and Northridge earthquakes. The data obtained were then compared for all the five BRBs to see how the response varies with increase in size of BRBs. The structural responses included displacement, velocity, acceleration, interstory drift, plastic rotations at hinge locations and force displacement relationship graphs for buckling restrained braces. CB-5i was chosen for fragility analysis based upon the results from feasibility study. Figure 4 shows the force-displacement graph for CB-5L The structure was then tested for a hundred earthquakes developed earlier for developing fragility curves. The peak ground acceleration (PGA) was varied from 0.1 to 1 in increments of 0.1 and applied to a structure with BRBs. Interstory drift response was used for developing fragility curves. The data were then processed to obtain lognormal distribution curves for fragility curves. Similar procedure was followed for developing fragility curves for a frame without BRBs. The frame with BRBs and a frame without BRBs have been shown in Figure 5 and Figure 6. Design properties of the beam in the frame are as per Table 1. I. ofthe ofBRBs. 5i. I ofthe 12 fragility 1: TYPE Z(in3) Mp(in-kip) Me q + Me q"(in-kip) W36 x210 29987.19 30925.39 W36xl50 20914.91 19976.71 21853.12 W36xl35 508.801 18321.57 17383.36 19259.78 W27 x94 10010.48 10948.69 12 F-D rel'ltionshil) for buckling re~1r.lint brace used 900 ,.---------------_.------ 3.75, 800.5 800 700 "'""' 600 'Q" , ;g 500 Q" i's" ~ OO r-. 300 200 100 0 0 0.5 1.5 2.5 3 3.5 Dispi:H'ement (in) Figure 4: Force-Displacement graph for buckling restrained brace considered for fragility analysis. Table. 1: Beam Member Properties (prepared with data from Wong et al. 2005) Zein:»~ Mp(in-kip) Me/ (in-kip) Meq-(in-kip) 832.65 29048.98 W36 x150 580.781 W36 x135 277.916 9072.275 13 K> W27x94 36 ^ ^ 3 7 W27x94 U TO o 29 W36xl35 30 o 23 W36xl50 24 OO -=1- o 17 W36x210 IS O 11 W36x210 12 OO O W36x210 38 ^ ,39 W27x94 - -OrtJ- 31 W36xl35 O-O 25 W36xl50 26 OO OO 19 W36x210 13 W36x210 14 OO W36x210 -25L Vjy, OO OO OO -251 40 O 3 33 W36xl35 O 27 W36xl50 28 O H W36x210 O 15 W3<5x210 16 O W3dx210 -25L O 3 Lvl. 84' details. 13 35 37 39 -0 -0-0 ./"'"'... .r..-."\ 0 Lv!. (""") 'N N (""") 0-. "<1" , "<I" 0. (""") (""") - q q q q - 8;: 8;: 8;: 8;: .;,W36x135 ...... ~3J W36x135 , 32 -0'33 W36x135 34 ~ ~ ~ .0- ~ ~ ' Lv!. 70' W36x150 .--, ",,W36x150 26 "" W36x150 -0 -v rv "\..J" -0 0 Lv!. 56' t"- V) V) t"- V) V) V) V) N ' ''<I" '?i N ~ ~ ~ "<I" "<I" -"<I" "-<I" 8;: 8;: 8;:, 8;: .() 18 .(). h 20 /'"', .--,'21 W36x21O 22 0- ~ ~ ~ ~ ~ Lv!. 42' 1.4 ~ 1 5 W36x210 ~ Lv!. 28' ~ ~ ~ ~ ~ 5 6.--, ~ 7 ~ ",,9 W36x210 10 r-. -0 -v tv v rv v Lv!. 14' (""") C) C) (""") 00 C) C) 00 '" 'f) V) N q q q q 8;: 8;: 8;: 8;: ~ 0 2 <)3 04 / // /'/ // '/ // 25 25 25 Figure 5: Six-story moment resisting steel frame with hinge locations and other detail s. Figure Frame showing the buckling restraint brace arrangement. 14 W27x94 YV.27x94 W27x94 Lvi. 84' M M -0- -0- >< >< .". ~~ .". ~ ~ 1N36x135 W36x135 1N36xJ35 Lvi. 70' 1N36x150 1N36x150 Lvi. 56' ~ ~ "M" "M" J; ~~ J; ~ ~ 1N36x21O W36x210 1N36x21O Lvi. 42' 1N36x210 1N36x210 Lvi. 28' 1N36x210 1N36x210 Lvi. 14' L..:......:..---'25'---..:......:.L..:......:...--~~5'---":""":"O'..:......:.../---25'------'-"' 6: FEASIBILITY STUDY AND FRAGILITY ANALYSIS The effect of change of size of BRBs in a system contributing high demands to the structural response has not been an active research topic. In order to make a structure more economical or in order to increase the efficiency of BRBs this study can potentially prove to be helpful. The size of the BRBs used in a system can be an important factor in further reducing the initial cost of the system. This part of the thesis aims at studying the effect of replacing the BRBs with high demands with heavier BRBs. The idea behind the study was to understand the correlation between change in the sizes of BRBs in the system and the change in response of the structure. This was achieved by identifying floor 1 and floor 2 BRBs as BRBs having high demand and trying five different BRBs at these locations. Properties of the BRBs considered are provided in Table 2. The stiffness of BRBs used in most research is underestimated by considering the work point to work point stiffness (KLWP). Thus, a stiffness factor has been proposed which is to be multiplied by the a factor which accounts for stiffness from work point to work point including the transition zones and connection regions (KWP). These factors were provided by CoreBrace. Structural response parameters were recorded for each of the BRBs. The simulations were run for ground motion records of the Kobe and Northridge earthquakes. CHAPTER 3 ofthe identifying stiffness ofBRBs Kwp). Table 2: Properties of Buckling Restraint Braces Considered for Simulations. Name (in) L c Lysc (in) As c (in2) Pysc (kip) K W p KWP/K-LWP Ay (in) CB-5 272 1/16 224 14/16 198 12/16 5.00 190 633.96 1.51 0.23 CB-10 257 15/16 185 12/16 154 4/16 10.00 380 1490.06 1.77 0.18 CB-15 255 8/16 174 11/16 159 15.00 570 2054.66 1.63 0.19 CB-20 253 3/16 172 10/16 156 10/16 20.00 760 2762.55 1.64 0.18 CB-5i 272 1/16 224 14/16 179 12/16 5.00 222 1126.55 1.55 0.1975 Lb- Length of BRB from tip to tip, Lc - Length of casing Lysc - Yield length of the core section, Ay- Yield deformation for BRB As c Kw p - Stiffness of BRB work point to work point Kiwp- Pvsc- 16 Lb Le Lyse Ase Pyse Kwp (in) Kwp/KLwP ~y (in) tl16 1O 12116 11116 3116 10116 1116 14116 12116 Le- Lyse ~y- Asc - Area of steel core sections, Kwp- Klwp- Stiffness from work point to work point including transition and connection regions. Pyse- Yield force of BRB 17 The Fragility analysis was carried out by subjecting the structure to a hundred ground motion records generated as Gaussian random process with zero mean. The method can be explained as follows. cf>{t) by stationary random process S(t) (Zhe Wang and Kevin K. F. where ^4,2?, C , Z) and E are constants, and ^(/0 ) is the normalizing factor which is equal to maximum value of (j>{t) that occurs at t = t0. The stationary process S(t) in Eq. (1) is assumed to have zero mean and possesses a two-sided power spectral density function known as the Clough-Penzien spectrum: (i) here, the Yeh and Wen (1990) formulation of (f){t) is used col+{2^gcogcof (CD2-co2)2 +(2Ccosco)2 (co2-co2)2 +(2£FCOFCD) 0 17 Ground motion acceleration is derived by multiplying a deterministic temporal modulation function ¢(t) by stationary random processS(t) (Zhe Wang and Kevin K. F. Wong et al. 2007): ag (t) = ¢(t) x S(t) 1) ¢(t) t B ¢(t) = A , e-Ct } ¢(t) D+t'- 0 (2) A, B ,,D ¢(to) ¢(t) that occurs at t = to' The stationary process S(t) in Eq. (3) 18 where <D0 represents the spectrum level (normalized to unit mass) of the broadband excitation at the base, co and £ represent the characteristic frequency and damping ratio of the ground, respectively, and f and Ctf represent the characteristic frequency and damping ratio of the subfilter, respectively (Zhe Wang and Kevin K. F. Wong et al.). The ground motion records were then normalized to peak ground acceleration values of 1. The structure was then subjected to a hundred earthquakes. The peak ground acceleration intensities varied from 0.1 to 1 for each of the hundred earthquakes. The number of values of interstory drift responses above the performance level determined probability of exceedance. Lognormal distribution was then used to minimize the error and plot the curves. 1>0 COg Sg coJ sJ repr~sent.frequency Feasibility Results X - direction, X - the displacement responses of the frame without BRB. The Kobe response shows a big difference of about 5 inches between the maximum displacement by the frames with the BRBs and the frames not using BRBs. The Northridge response on the other hand shows how badly the soft story affects the response of the structure, with the BRBF responses on the first three floors almost matching the responses of the frame not using BRB. CHAPTER 4 RESULTS The structural responses suggest that there is a marginal difference observed after replacing the BRBs with higher demand BRBs. The displacement responses are as shown in graph in Figure 7. The graph suggests that the response changes marginally for all the BRBs tested. Since all the BRBs are installed to have an effect in the positive x­direction, the negative displacement or the displacement in the negative X- direction seems to have more variation. Response was considered only in the direction of the BRBs because the effect of change in BRBs can only be observed in positive direction. Similar results can be seen for the Northridge earthquake in the graph shown in Figure 8. The soft story effect cannot be seen affecting the Kobe displacement response but the Northridge response clearly shows the soft story effect. The graphs also show the difference between Kobe •--0 (in) 20 PositiveDisplacement (in) - • -CBoiMAX -B-CB-5iMIN CB-5 MAX CB-5 MIN -K-CB-10MAX - • -CB-10MIN -I-CB-15 MAX CB-15MIN CB-20MAX -•-CB-20MIN No BFB max No BRB Min Northridge -15 -10 -5 0 NegativeDisplacement 10 15 20 • CB-51 MAX •CB-5iMIN •CB-5 MAX •CB-5 MIN -*-CB-10MAX -•- CB-10MIN -+-CB-13MAX CB-15MIN CB-20 MAX -C B - 2 0 MIN -•-No BRB MAX Positive Displacement (in) NO BRB MIN 20 ...-CB·5iMAX .... CB·5iMIN -.-CB·5MAX ~CB· 5 MIN -+'-CB·I 0MAX is _ CB·I 0MIN o ~ ------~~~--~~~--~----~------------ ~CB·1 5 11l!\X - CB·1 5MIN - CB·201M.x ....... CB·_ NoBRBma-:: ·15 ·10 ·5 o 5 10 15 20 -'-NoBRBMin Negative Displacement (in) PositiveDisplacemellt (in) Figure 7: Graph for Displacement response for Kobe earthquake. ....... CB·5iMA.'C - CB·5i:MIN ..... CB·5MAX -*-CB·5MIN -+-CB·I0 MA..'C j - CB·IOMIN ~ ----~~--------~r---------~~----------- -+-C'B·15 MAX - CB·1 5MIN - C'B·10 :MA.'C -+-CB·10 MIN .15 1 0 o 5 - NoBRB MAX Nf'lativeDisphlcemfnt (in) PosltiveDlsphlCf'IIlfllt (in>-*-NoBRB MIN Figure 8: Displacement response for Northridge earthquake. 21 Velocity responses show similar results for both the earthquakes as shown in the graph in Figure 9 and Figure 10 for Kobe and Northridge. The change observed is again marginal. The acceleration responses for both the earthquakes are as shown in Figure 11 and Figure 12. The frames not using BRBs show a completely different and a higher acceleration response. The observed interstory drift response is as shown in Figure 13 and Figure 14. The results and behavior again vary marginally for frames with BRB. But an important observation in the case of the Northridge response was the drift of the first floor going close to 0.03 which further confirms the soft story response and also shows how ineffective the frame is if BRB is not installed on the ground floor. Plastic rotation responses for hinges at the column base are as shown in Figure 15 and Figure 16. Both the maximum and minimum responses for the Kobe earthquake vary marginally except for the response from the frame with no BRBs which seem to be half of the values of frame with BRBs. Figure 17 and Figure 18 show the maximum and minimum plastic rotation response for the Northridge earthquake. The behavior here is the same as the behavior shown by the plastic rotation response for the Kobe earthquake. 19 and Figure 20. The values are absolute maximum values of plastic rotation. The plastic rotation values for hinges in beams in frames without BRBs clearly have a very high value of plastic rotation. The plastic rotation comparison results for each hinge with all types of BRBs suggest that only a marginal change occurs in most cases except the frames with no BRBs which show a significant change over the values as compared to frames with BRBs. The comparison graphs for other hinges located in beams are as shown in Figure Kobe •100 -50 Negative Velocity (in sec) 50 100 Positive Velocity (in sec) •CB-5 i MAX . CB-5 i MIN •CB-MAX •CB-5 MIN •CB-10MAX •CB-10 MIN •CB-15 MAX •15 CB-20MAX earthquake. Northridge CB-5iMAX CB-5 i MIN CB-5 MAX •CB-5 MIN •CB-10 MAX •CB-10 MIN •CB-15 MAX •CB-15 MIN CB-20 •CB-20 MIN Negative in in earthquake. ~CB- 5 iMAX _ 5iMIN -.-5 rvLA.x ~CB- 5 1\lIIN so ~CB-IO :MAX ~ ----------4B~----+-~----~~---------- ..... l 0 -+O-- CB-l 5 MIN -o ~o - in/in/Figure 9: Velocity response for Kobe earthquake. Northrhlge ~ -----4:--II"-----------4--f---------__ I.----­~ ----~~----+4---~~--- ·80 -60 -40 -20 o 20 40 60 Negat.ive Velocity (in/sec) Positive Velocity (in/sec) Figure 10: Velocity response for Northridge earthquake. ~CB· 5iMAX _ CB·5iMIN -.-CB·5MAX "'*-CB· 5 MIN ~CB·I O IvIAX ..... CB·I Ol\lIIN -+-CB·rvIAX - CB·l 5 MIN - CB·MAX ~CB·20MIN 22 23 0 •1 -0.5 0 Negative Acceleration (in'sec2) 0.5 1 Positive Acceleration (in sec2) CB-5iMAX CB-5iMIN CB-5 MAX CB-5 MIN CB-10 MAX CB-10 MIN CB-15 MAX CB-15 MIN CB-20 MAX CB-20 MIN BRB MAX BRB MIN 11: earthquake. i o -1 -0.5 0 Negative Acceleration (in sec2) 15 Positive Acceleration (in sec2) -•-CB-5 I MAX - • -CB- 5 1 M IN CB-5 MAX - * - C B - 5 M IN -4-CB-10 MAX - • -CB-10 MIN -h-CB-15 MAX CB-15 MIN CB-20 MAX -•-CB-20 MIN - • -No BRB MAX No BRB MIN earthquake. Kobe ~ .. ~~~----------6-+--------------~~~-- i5 o ~ --~~~~.----------~+-----------~~+------ -I o ~CB- 5 i ~liL",{ . _ -'-5MAX ~CB- 5 MIN --!o'-l 0 ..... l 0 ~CB-1 5MAX - 1 5MIN - 20MAX ~CB- 20 MIN _ BRBMAX Accelerat.ion in/sec2) _ BRBMIN in/Figure 11 : Acceleration response for Kobe earthquake. Northridge i5 o ~ -------I ~+------3-+_--------.:a~ __ ---------- ~CB- 5 i MAX ~CB- 5 iMIN -'-5MAX ~CB- 5 MIN ~CB-I O MAX CB-IOMIN ~CB-1 5MAX - 1 5MIN - 20MAX ~CB- 20 MIN ---No BRB M ... \.X o 0.5 1 1.5 -a-NoBRBMIN in/Positi\'e in/sec:!) Figure 12: Acceleration response for Northridge earthquake. Kobe -0.03 -0.02 -0.01 0.03 ~ -•-CB-5 MAX •CB-5 MIN •CB-10 MAX •CB-10 MIN •CB-15 MAX •CB-15 MIN CB-20 MAX •CB-20 MIN •No BRB MAX No BRB MIN earthquake. -0.04 -0.03 -0.02 -0.01 Negative Drift Ratio 0.02 0.04 Positive Drift Ratio • 5 i MAX ••5 MAX •CB-5 MIN •CB-10MAX •CB-10 MIN •CB-15 MAX •15 MIN 20MAX •20 MIN •MAX o o ~ ------------~I~~~+---~)~--~--------- -+-CB-5iMAX _ CB-5iMIN ..... 5MAX ~CB- 5:MIN ~CB-I 0l\1AX ~CB-I OMIN ~CB-1 5MAX - 15MIN - 20?vLA.X -+- CB-~ O MIN o 0.01 0.02 0.03 _ NoBRBMAX Negative Drift Ratio Positive Drift Ratio Figure 13: Interstory drift response for Kobe earthquake. Northridge is o ~ -----------1~"~~--~~"~---------- -O . O~ o 0.01 O . O ~ 0.03 O . O~ -+-CB-5i?vLA.X _ CB-5iMIN ..... CB-5MAX -CB-5MIN ~CB-I 0MAX ~CB-I 0MIN ~CB-1 5?vLA.X - CB-15MIN - CB-20?vL<\'X -+-CB-20?VUN _ No BRB ?vL<\'x No BRB MIN Figure 14: Interstory drift response for Northridge earthquake. 24 0.03 1 0.025 3 • 1 unite 1 max • hinge 2 max lunge 5 max 1 in me 4 max CB-5i CB-5 CB-10 CB-15 CB-20 No BRB Types of BRBs i lunge 1 nun i hinge 2 min hinge3 min i hinge 4 min Types of BRBs 25 Kobe .-.. ~ 0.025 ~ -=- = 0.02 ~ Q~ 0.015 ~ (,> 0.01 ill hin.~e 1 ma.'I: • hinge 2 ma.'I: :: "~" 0.005 ~ 0 • hinge3 ma.'I: • hillge4 ma.'I{ C'B-10 1 5 Typf's or Figure 15: Plastic rotation response for hinges in columns for Kobe in positive x-direction. Kobe 0 .-.. ~ ~ -0.005 -=Q= - • hinge 1 min :: .~.. -0.01 • hin.ge 2 min Q ~(,> • hinge3 min :: ;I! ~ -0.015 • hinge 4 min ~ -0.02 or Figure 16: Plastic rotation response for hinges in columns for Kobe in negative x-direction. 26 • hinge 1 max a hinge 2 max hinge3 max • hinge 4 max CB-5i CB-5 CB-10 CB-15 CB-20 No BRB Types of BRBs "2 m -0.005 9 i -001 • w 1 -0.02 • i -0.025 -0.03 a hinge 1 nun • hinge 2 nun hinge3 nun nun Types BRBs 26 Northridge 0.035 .- 'e 0.03 ~ -=- 0.025 = ~ : 0.02 .~.. ma~ ~ 0.015 ~ • l ma~ --<oJ 0.01 ~ ~ 0.005 ~ 0 • ma~ ma~ I0 1 5 lO NoBRB Figure 17: Plastic rotation response for hinges in columns for Northridge in positive x-direction. Northridge 0 .- 'e ~ -=- ~ 0.01 • min -~ -0.015 min ~ ~<oJ -0.02 • min i ~ • hinge 4 min ~ of Figure 18: Plastic rotation response for hinges in columns for Northridge in negative x-direction. 27 GRAPHS i £ 0.03 O /111 e 0.02 -ynh ^ / i | 40 36 32 28 24 2 0 16 12 8 39 35 31 2^ 23 19 15 n 7 fflNGE NUMBER 4 0 3 6 32 28 2 4 2 0 i 6 „ 3 9 35 31 27 23 19 15 „ HINGE NUMBER 11 ,-. ~ e'I: .::.. 1;il Z 0.03 0 ~ 0.02 ~ r- 0.01 0 ~ u 0 E= ~ ~ ~ PLASTIC ROTATION COMPARISON GR.J.\PHS FOR KOBE EARTHQUAKE 2-t 20 16 12 8 27 11 lUNGE Figure 19: Plastic rotation comparison graphs for Kobe earthquake. PLASTIC ROTATION COMPARISON GRAPHS FOR NORTHRIDGE EARTHQUAKE . CB-5i .CB-5 - CB-I0 . CB-15 . CB-20 - No BRB ~ 0.03 o r------------------______ CB - 5i E= 0.02 ;",: r----------.~~----------_. CB-5 r- ~ 0.01 U _____ _ ~ 0 ~~:;::~~~~~~~~if~:~-~:i:i:~:~-tiiijl~'Ei'i]~~~ ~ '0 ---- •••• ~ .. 36 28 24 20 16 12 8 ~ 39 2 11 lUNGE 7 . CB-1 5 Figure 20: Plastic rotation comparison graphs for Northridge earthquake. 27 The marginal changes in most of the responses suggest that initial stiffness of the BRBs is not important for structural responses like displacement, interstory drift, velocity and moment rotation but it does affect the acceleration responses since the maximum acceleration is achieved when the structure is in its elastic limit. As the responses differ by only a small amount the lowest BRB was selected for the fragility analysis. The force displacement graphs for all the BRBs tried on floor 1 are as shown in Figure 21 and Figure 22. The x-axis is displacement in inches and y-axis is force in kips. Moment rotation graphs for hinge number four for all the BRBs tried are shown in Figure 23 and Figure 24. The difference in responses of the BRBs is very significant but the structural response seems to be unaffected by the change in most of the responses. Fragility Curve Results The advantages of BRBs in frame start to show their significance at the lowest level of damage in a structure. The probability of exceeding a 0.5% interstory drift or the immediate occupancy drift limit reduces significantly in BRBFs as shown in Figure 25. The probability of failure starts to rise above 0 at a PGA of 0.1 as compared to 0.2 PGA for the BRBF. At 0.2 PGA the probablity of the IO drift limit exceedance rises to about 60% in the steel moment frames, which is a significant improvement in the performance of BRBF as compared to the normal frame. The probability of exceedance of the IO drift limit rises to 100% at 0.4 PGA and 0.6 PGA for steel moment frames and BRBF, respectively. Thus providing a valuable improvement in performance. 28 ofthe I 10 10 respectively. Thus providing a valuable improvement in performance. Force displacement graph for CB-5i for Kobe 400 r ^ 0 0 _ Displacement displacement graph 400 -600 Displacement (in) Figure 21: Force displacement graphs for different types of BRBs used for Kobe earthquake. ---------- - - .- --- - -400- 1 ------------------------------~60&_L------------­Displacement (in) Force displ.uement gr,ll)h for CB-5 for Kobe -----------------------4~&_r_-------- 1 (a) 29 30 Force displacement graph f o r CB-10 f o r Kobe 8 0 0 -SOO-Displacenient (in) Force (lisphit eraent graph for CB-15 for Kobe 8 0 0 r - 8 0 0 Displacement (in) Force displacement graph for CB-20 for Kobe 1 5 0 0 - 1 5 0 0 1 Displacement (in) Figure 21: Continued Q: - ;g 2:! disl,lacement gn11)h for IO for Kobe --- -- --- seo- · ~-~------''''' Displllc,ement (111) disldacement gr~l))h 15 Kobe ------ seo- ---- .----- -1. 5 -----seo­Displ( lcement (disl)lacenlent gr'll)h ----- -- --l-~eo- - - -l-!'OO­Displacement ((b) 30 1 1 31 Force d i s p l a c e m e n t graph f o r CB-5i f or Northridse -800 Displacement (Force displacement graph f o r C B - 5 f o r Northridge 60O o -600 (Force displacement g r a p h f o r C B - 1 0 f or Northridge 1000 •1000 Figure 22: Force displacement graphs for different types of BRBs used for Northridge earthquake displacenlent gr.ll)h for for Northridge ------.------. ---:690- -----------------. ~ c ~ ---------~~_7_,~~~~-------~----- 5 ~ - -3- --3 ~~~---=-490 ~- - -69 ± ----- - - S90 - ---- Disp lacement (in) disl)lacement gral)h for CB-for Northridge ------------,69~~------------- -------------4B~~---------=_---- -3 3 ==--__ -==:------ - -499--1--- -- --6e9--L Displacement (in) disl)lacement gra()for CD-tO for N orth."idge -----------+GGG-.-------------- --------------·~lBG·9_~------------- Displacement (in) (a) displacement graph f o r for Northridge 1000 T -tooo-J Displacement (in) displacement graph f o r C B - 2 0 Northridge 1 Sflfi 1O00 - f s o o y / ^ • & 0, 8-2 - 1 5 / -1 f-0.5 ( ) 0.5 1 / 1.5 2 ^ -1500 Displacement (in) Figure 22: Continued Force disl)iacement gral)" for CB-15 Northridge -·--------------·------Hffif)-·--------·-------- --.---. ------.. - ~---- ------------~~--~--~~~~~---------------.~-------- v -----------4~---~--~~~9~L----------------r---------­<..;> 8- T3------~~~----~~~~JH~~~~~--------I~~~~~------~ ~ - ----------------------~19rr-~-------------------------­Disp iacemellt (in) Force disl)lacement gral)h for CB-20 for Northridge --- ---- -.--. .-.- ----1-599- --- .-- -.---------- ~ ~ ----------~------.u~---H~~--------------~--------- ~2 2 8 ~----~~--~~~--~~ Hrr-+-----~~--~~----~----~ ~~~==== Dl..,placemen t (in) (b) 32 Hinge 4 25000 1 i 5000 ;>ooo *O0O~ & • " 'J2 l _ i Moment ( ' I I I r -0:00? i >O00- )00G -o o r 0.00? 0 rr 0.015 07 n o:o -x 1 u -1 JUUU 5000 ' - Rotation (R ad) Moment rotation graphs for Hinge 4 using CB-5 for 2-5000- ~ ~ - ">OAAA 1 c 000 eoe- 000- 0 000 , 000 000- it 01 -0.003- H 0.005 ~ 0 DT 0.01 2 0:0 i -2-5000 Rotation (Kad) Moment rotation graphs for Hinge" using CB-5i for Kobe 33 ----'2~5eeel-,---~------------­? --;riiiiiiOiiO. -.-"1 ;;;;l:~-AA 1-JoIfi1Io Ii)ali-;j-\ii-iifiii"'_ _~ ~::::::::=-;;;;;;;;;;;;;;;;;;;;;;:~- ---------­' X ---1----1 ~{)oe-fl-;I-"II-------I--If--------l---I---'-­~- - -i1-----IL-l:Ief},'~'J+_m_---_l_l----_l-_I_--­5 ~1----~eee-·U+4U----!~~----~~-+--- § A :::S_o.T lU-1'+---:_ftV .'. v'o-~oe'9A-Iirl-m--ftUI .-. ttnUU_~ )---I;uT.r") nl --- (J.OT) I-(J. _ 0:-025 - 11-----1 · 000'- .... -1-.111-----'- --------+- 1------- --1------~I~{)efGH~~-----l--l---__ - --l- 4I---- _ 'vvv ---~2~OO(}A. -1-_______________ _ Rntiltinn Rild) rot"ltion Hinge" Kobe .-::;- ---~25ee,f}-",.------------------: -:;: _1C\C\C\C\_ :.0:2. . ------- ------1-: [hVie e-- ~ lf~ee,~I~-I--------fl------.. ----4---- g Inn ::o:s . 'v0~~I_4+----~I_---~--~--- 1- .~----- --------- '----..::!:.- -------- - O_Vl -V_ VU~7 eeI+-JGIrlI--tH- '(J.(}(lS--u /1 (J.OT ---O:l _ (1)25 --- ----H 000- - ----- ------- -------- --+--EeeAf}-~~----~---~4---~--- -----}5eee---'------------------ Rotatioll Rad) (a) Figure 23: Moment rotation graphs for different types of BRBs for Kobe earthquake. 34 O «-i <5 graphs Hinge 4 10 25000 | .-^OQO 0.01 15000 100* '0 5000 0 -0J)05->0n0 - I O O h O -15000 - 20000 -25000 O/005 0:01 0.013 0 02 0 025 Rotation (13000 o. o •-i 2 0.0+0.0it "0.1)05OC0 i\ 400(0 mm 150(0 100(0 50(0 0 O.0O5 0.01 0r0t5 € O: ~ O . 0 2 5 -25000 (Figure Continued Moment rotation gr;'ll)hs for Hinge'" using CB-I0 for Kobe ~ ==;::::;::~:~n'O,~ny,~:~:;:~;:~::::~~~~~~~~~:~~~~~~~~~~~~;====== ~ ---r----r-+5o~fIO-~~_1r_~---t-------~----------~~----- ~ --~--_+-4!~G'O~:18.~~~-+----~---------+-------~~-~----­ § --+---~~50~&-+~~+---~--------~--------~~-----­::: E ---- ~--- ---- 0---1---1---+-----1-------------- ---------- - f--~---- -0 _0 1 -v. O:'i~O'~·I3_iI\tr_~_t1v'-l-. fvtvft :·5 +---'V'l-.. 1o -~t----IHvy,.. v tTtrj ----tl.- viY. i----(1) 2 5 --1-----I---tOO,~:~8~~-I--+----~--------~--------~-I------- -- ---- -~HO (}- -- --- ------ -------------- -------1-- ------- _ v 'v ---------±2500G-GL-------------------------------------­Rotntion (Rad) Moment rotation graphs for Hinge 4 using CB-15 for Kobe ~ --------------~2~5·oe,~~ ,--------------------------------- 0:;=. . ---,-=r"-'f\I/iI,'(\. ..- r-,.;;;~~==:::::::::==p;;;;;;;;;;;;:;:;;;;;:;;::;__- ~- --------~---l-~~_+_1_1----_I__-------I_------_+_+----- ~ -------~---I_+!OOc{-~-~_+_1_1~--_I__------~------_+_+----- § :::E ------ ------- ------- --~ ~- 1--- - 1---- ------------ ---------- ---- f----. --------~--~~:O{-.+_+_1_1~--+_-------I_------_+_+----- -0 _01 5 -O:-&t8. e-~(\' iGOO5- 8.8! i 8 . &!-5-{-t+.G)"'I-~8H-.,e25 --------~--~~QUI,(\~~+-+_--~------~------~~--- ------ ----- -1-50u&- 1---I-- ------- ,---------- f-------- -- ------.- ~ ";UU' v Rotation (Rad) (b) 23: 35 Moment rotation graphs for Hinge 4 using CB-20 for Kobe 25000 s 15000 10000 5000 -0 015 - >01 0 fl.QCBDOO I 10000 -; ^ 0 5 - O r O i 0 : 0 1 > 0:( 2 - 6 025 --0:03 -15000 -25000 Moment rotation graphs for Hinge 4 using CB-5i for o 2 -0.03 •0.02 25000 i •20W-. 15000 10000 5000 0 »O.Oi 5000 H - -10000 •15000 e.oi O.02- 0:03 -2'OOOU^ ^25000 Figure Continued. Momentrot'ltion gn11)hs 20 ~ ----------~2~5~o·on~,_~--------------------------------- . :;: ., /\/\/\/\ ~ ---r=~~~~==~--~~~~-- ~ l' GGI~/\+-4rflr--~----__ --4r--~~--~----- -----r--~~lBee/\~+-~+r-------------_;----;_--~------- --+-- t-t---:>.-eee-+--t-tt-------I-- -ll---ll---- -----~--~+-----o ---- +----. -- ---_. - -- . - _ .. _-- ----_. 0. (}f-5~ . v ~ - . eooee-lt--t-:IIi:-·o&.'--&.-el--HG. +. GI ,~+f\---I HF'---+IHG~O 3 ---~~~~ea~- -I--+~------~-1--1---- ----·~--~~~~'eQn.Qn- -+_1~.~.-- l - --- -- - -+--- + ------ _ vvvv -:!5000 Rotation (Rad) gral)hs Si Northridge -.s ooe " l}Mf-) 1-500" ------ - :H)OOO - - c--- --- .- e -~ G e - &.-e~ -&.-el-..§OO " n .. V.J v -~ v . v _ - ~ GooG • .:-ooe - _ vvv ., <: . _\1\/\ Rotation (Rad) (c) 23: ---- &.-03 Moment rotation graphs for Hinge 4 using CB-5 -30000-1- o -0.03 10000 0" •0.02 -Q-0 1-1Q000 -iuuutr 01 •30000, 1 Rotation (Rad) 0.02 0.03 Moment rotation graphs for Hinge 4 using CB-10 a. M O - 0 . . Q 1 . . - 0 02 30000 i 2oa ~iooDt> 0 --noma? 0 . 1 L 0.Q2., 0 . 0 3 •30000 Rotation (Rad) Figure 24: Moment rotation graphs for different types of BRBs for Northridge gral)hs u~ing for Northridge ~ -----------------}9900~-------------------- I 0.. g - 'ClCillnn, -- 10000 I v" 0 .Qi_ ___ -0.,1)2 __- 0.01_10000- -- ~- ~02 f----.0~0 3 -g o ~ -0. IH _ vvvv 3000" , RotatIon (Rad) gra))hsfor IO for Northridge 5900~ ,.., "" " ... T H) IV ,... v () ()., -OO J_ie ~ () hi () n, IV _ v 'v -}ooeo (a) () .D3 ofBRBs earthquake. 36 37 graphs Hinge 4 15 0.03 -0 02 25000 ism 15< 00 ~m oo 5( 00 -0 - K K 00 •15t 00 -20000 •25000 o n 0.02 0.03 Moment rotation Northridge v I S 25000 5 000 )()()() i?opo - 0.03 H H 0.01 0.02 0.03 0.04 -10000 -150 >0 •25000 Rotation (Rad) Moment rotation gral,hs for Hinge'" using CB-IS for Northridge '::' -------·--------2-§-oofJ-'- .----- -.--.. - .----.- g..:~.;.: -----.-- r.-_-------c---- ---.~ -.~- -~-~g.... '" ~,f1"lO\1'\ ~f-----.-----.--.+-~ -~I.-~---~--~--~-'~- 1---.­- 2 w oo·~--~-+--~----~- o ~ f).{'H-'+---lI--.J-- t-----t-- ~ n v -0 . OJ·~-f----;;-jvfl-. fvt'_- -~- vf)-.fvT t-O'· oO·HI\·---+--uA-,t 1H...I --I-- ...U..H .. u¥_)-- -I---Iu'H."l:-u3 .--1-----.---------- ·--to 00 ----- -- - 1--- -1-.------1---. ---~--------~) O&-~--~-+-~----~-- ~-g '':'\:1'-'"" ___________ ~O&&-AL-------------- -Rotation (Rad) Momentrot,ltion graphs for Hinge 4 using CB-20 for N ortluidge ~O[)O ---+----------·~~0 : 8 <3 ----- --- §o~o----- - --- _. --.--.- ---- ------------- ~ o 0 _ f)-tT1J r-+~- ·fH)-"-2- ~-O~ :>-0 ~O-It---II-+'fHH-- f---G-:-O-_' -~--------- OQVhln-~~-I~II---~---------I------ I _________ ·~on&-L--------------- Rul<lliulI (RiIll) (b) Figure 24: Continued 38 Immediate Occupancy Drift Limit Peak Ground Accelerations Figure 25: Comparison of fragility curves for a steel moment frame and a BRBF for immediate occupancy drift limit of 0.5%. For this life safety performance limit the probability of exceeding a 1% interstory drift reduces significantly in BRBF as shown in Figure 26. The probability of failure starts to rise above the minimum value at a PGA of 0.2 as compared to 0.4 PGA for the BRBF. At 0.4 PGA the probablity of the LS drift limit exceedance rises to about 60% in the steel moment frames, which is a significant improvement in the performance of BRBF as compared to the normal frame. The probability of exceedance of the LS drift limit rises to 100%. at 0.7 PGA and 1.0 PGA for steel moment frames and the BRBF, respectively, suggesting that the curve is flatter than the previous one indicating lower probability of exceedance of this performance limit. L! <lJ ~ <: 0.8 "0 <lJ <lJ V i;J 0.6 ..... 0 § OA ;, ;<,: O.! 9 p:; 0 0.2 -0.2 Immedhlte OCCUI)~n~J LiD1~t 0,4 0.6 0.8 (h ound AcceleJat.iolls 1.2 -+-BRBF _ Steel Moment Frame 100% and 1.0 PGA for steel frames and the BRBF, flatter 39 S t eel M oment 1.2 Figure 26: Comparison of fragility curves for a steel moment frame and a BRBF for life safety drift limit of 1%. A significantly flat curve as shown in Figure 27 suggests a truly enhanced performance for structure at the perfomance level of collapse prevention, for which the drift limit has been specified as 2%. The probability of failure starts to rise above the minimum value at a PGA of 0.4 as compared to 0.65 PGA for the BRBF. At 0.65 PGA the probablity of the CP drift limit exceedance rises to about 60% in the steel moment frames, which is a significant improvement in the performance of BRBF as compared to the normal frame. The probability of exceedance of the CP drift limit rises to about 95% at 1.0 PGA and 5 5% at 1.0 PGA for steel moment frames and BRBF, respectively. The curves are much flatter, as expected, than the curves for other performance limit criteria. 1.2 v '=0j: "E 0.8 u u \:l 0.6 '+a-< ~ 0.4 ~ '" 0 ') ~ .a. p.., 0 -0.2 0.2 Life Safety Drift Limit 0.4 0.6 0.8 Peak Ground Accelerations ""'-BRBF _Steel !vlomellt Frame 1 %. PGA ofexceedance 55% curves are much flatter, as expected, than the curves for other performance limit criteria. Collapse rrevention Drift Limit Ground Accelerations Figure 27: Comparison of fragility curves for a steel moment frame and a BRBF for collapse prevention drift limit of 2%. 1 II 0.8 ~ r';" II 0.6 '-' ~ <..., 0 UA §' .0 0.2 .'0" '::> ~ 0 -0.2 ColL"llue Prevention 0.:: 0." 06 0.3 Peak Grollud A,celeratiollS 1.2 ~BRBF _Steel Moment Frame 2%. 40 CHAPTER 5 CONCLUSIONS 1) The change in structural response for a change in BRB size of four times the required cross-sectional area is marginal and hence can be considered for a valid factor for studying the effect of the increase in size on a structural system. 2) Providing higher size so that the life of the BRB can be further increased does seem to be a feasible option since the structural response changes marginally even with an increase in area of about four times the required area and the demand of BRB decreases drastically with this increase. elastic limit. 4) The fragility analysis further confirms the superior performance of structure under consideration. The probability of failure in steel moment frames increases by about 60% at each damage limit. Also discussions with local companies dealing in buckling restrained braces suggest that BRBF are lighter since the required performance limits are met at lower member sizes thus making the structure more economical. 5) The thesis provides a way to use PERFORM 3D for nonlinear time history analysis and develop fragility curves using the results from it. 3) The Initial stiffness of the BRBs does not affect most of the structural responses except acceleration since the maximum acceleration occurs when the structure is in its 42 6) The BRBF without a BRB at the first floor has responses which match to a great extent the responses of frames not using BRBs. 7) The results also hold good for other types of BRBs in PERFORM 3D as the crossectional properties like shape of the steel core do not change in the software. The only crossectional property input is the area of the steel core. ofthe CHAPTER 6 RECOMMENDATIONS 1) Stiffness of BRBs is underestimated. Some results from CoreBrace, a Company dealing in BRB construction and consulting show that the stiffness used in analysis is underestimated and a multiplying factor of 1.2 to 2.5 can be applied to the stiffness. Further research on BRBs is recommended to confirm this. These factors are calculated for BRBs provided by CoreBrace. 2) Further research is recommended to understand the behavior of structure when buckling restrained brace sizes are altered. 3) Not providing BRB on any floor in a BRBF can induce a soft story response and hence make the strcuture as unstable as a frame not using BRB and hence should be avoided. RECOMMENDA TrONS REFERENCES 1. Xie, Q., "State of the Art of Buckling-restrained Braces in Asia," Journal of Constructional Steel Research, V. 61, No. 6, June 2005, pp. 727-748. 2. Sabelli, R., Mahin, S., and Chang, C , "Seismic Demands of Steel Braced Frame Engineering Structures, 5, 2003, pp. 655-666. 3. AISC (American Institute of Steel Construction) "Seismic Provisions for Structural Steel Buildings," Chicago, 2005. 4. Andrews, B. M., Fahnestock, A. L., and Song J., NSEL (Newmark Structural Engineering Laboratory) report, 2008. 5. Tantala, M. W., and Deodatis, G., "Development of Seismic Fragility Curves for Tall Buildings," 15th ASCE Engineering Mechanics Conference, Columbia University, New York, 2002. 6. Hussain, S., Benschoten, V. P., Satari, M., and Lin, S., Coffman Engineers, Inc., "Buckling Restrained Braced Frame (BRBF) Structures: Analysis, Design and Approvals Issues," Proceedings of the 75th SEAOC Annual Convention, Long Beach, CA, 2006. 7. Wang, Z., and Wong, K., "Energy Evaluation of Inelastic Structures Subjected to Random Earthquake Excitations," The Structural Design of Tall and Special Buildings, John Wiley & Sons, V. 18, No. 5, 2009, pp. 559-571. 8. "Manual for PERFORM-3D Nonlinear Analysis and Performance Assessment for 3D Structures," Computers and Structures Inc. Berkeley, CA, V. 4, August 2006. 9. Wong, K., and Wang, Y., "Energy- Based Damage Assessment on Structures During Earthquakes," The Structural Design of Tall and Special Buildings, John Wiley & Sons, V. 10, No. 2, 2001, pp. 135-154. 10. Wong, K. K. F., and Wang, Y., "Probabilistic Structural Damage Assessment and Control Based on Energy Approach," The Structural Design of Tall and Special Buildings, John Wiley & Sons, V. 10, No. 4, 2001, pp. 283-308. 11. Fahnestock, A. L., Sause, R., and Ricles, M. J., "Seismic Response and Performance of Buckling-Restrained Braced Frames," Journal of Structural Engineering, V.133, No.9, Sept. 2007, pp. 1195-1204. C., Buildings with Buckling-Restrained Braces," V. 25, No. 5, April Structural ofInelastic Buildings, 5, Special Engineering, 45 12. Kiggins, S., and Uang, C-M., "Reducing Residual Drift of Buckling Restrained Braced Frames as a Dual System," Engineering Structures, V. 28, No.l 1, September 2006, Pages 1525-1532. 13. Tsai, C , Weng, Y.,T., Lin, M. L., Chui-Hsin Chen, C. H., Lai M. L., and Hsiao P. C, "Pseudo Dynamic Tests of a Full-Scale CFT/BRB Composite Frame: Displacement Based Seismic Design and Response Evaluations," Earthquake Engineering & Structural Dynamics, John Wiley & Sons,V.37, No.7, 2008, Pages 1081-1098. 14. Kumar, G. R., Kumar, S. R. S., and Kalyanaraman, V., "Behavior of Frames With Non-Buckling Bracings Under Earthquake Loading," Journal of Constructional Steel Research, V. 63, No. 2, Feb. 2007, Pages 254-262. 15. Limpert, E., Stahel, A. W., and Abbt, M., "Log-Normal Distributions Across The Sciences: Keys And Clues," American Institute of Biosciences, V.51, No.5, May 2001, Pages 341-352. 11 , c., C., DynamicTests ofa Displacement Structural Steel