December 1994 Report No. UMCEE 94-38 Summary Report on Semi-Active Base Isolation Control by I-Hong Chen Henri P. Gavin Robert D. Hanson A report on research sponsored by National Science Foundation Grant No.NSF-BCS-9201787 Department of Civil and Environmental Engineering The University of Michigan Ann Arbor, MI 48109 - 2125

Contents Acknowledgement....................................... 1 Introduction........................................ 2 Section I Semi-Active Damping Control.......................... 4 System A: Bilinear System................................... 4 System B: Semi-Active Stiffness System...................... 6 System C: Linear System................................... 7 Overall Comments............................................. 8 Section II Semi-Active Stiffness Control........................10 System A: Semi-Active Stiffness 5% Fix Damping Case.10 System B: V*BS for Different Damping......................11 Overall Comments...........................................12 Conclusion................................................. 13 References................................................................. 15 Tables & Plots Bilinear System Damping Control........................... (I)-(A)-* Semi-Active Stiffness System Damping Control.......... (I)-(B)-* Linear System Damping Control............................ (I)-(C)-* Semi-Active 5% Fix Damping Stiffness Control...... (II)-(A)-* V*BS Stiffness Control....................................... (II)-(B)-* Program Flow-Chart and Listing..................................... 16

Acknowledgement This work was supported by a grant from the National Science Foundation under Award No. BCS-9201787 as part of the Coordinated USA Research Program on Structural Control for Safety, Performance, and Hazard Mitigation. Any opinions, findings, and conclusions or recommendations expressed in this report are those of the author and do not necessarily reflect the views of the National Science Foundation. 1

Introduction Isolating structures from ground motions is gaining popular acceptance as a technique for protecting structures from earthquake hazards (NEHRP, 1994 ). In essence, base isolation systems decouple the structure from the seismic disturbance, and reduce the energy transmission from the ground to the structure and from the structure to the ground. Because passive base isolation systems limit the transfer of energy leaving the structure as well as the transfer of energy entering the structure, it has been proposed that the structural response can be improved by adjusting the isolator's properties based upon the instantaneous direction of energy transfer (Hanson and Firmansjah, 1992). The direction of energy transfer is the same sign as the product of the ground velocity (GV) and the base shear (BS). To minimize the energy transferred to the structure, the properties of the isolation interface can be adjusted to minimize the forces in the isolation interface whenever energy being transferred to the structure. Therefore, one rule for controlling the isolator's properties is to specify maximum stiffness or damping when (GV*BS) > 0 and to specify minimum stiffness or damping otherwise. Because the system is non-linear and that the excitation is random, digital simulation are used to evaluate these control rules in this report. Two other control rules are also investigated in this study. These two control rules replace (GV*BS) in the first control rule by (V*BS) and (V*U), where (V) is the (relative) velocity of the structure with respect to the ground, and (U) is the deformation of the isolator. These control rules are of practical interest because (U) and (V) are relative quantities and are easier to measure than absolute ground velocity. 2

Because the compliance in a base-isolated structure is concentrated at the isolation interface, a base isolated structure is modeled as a SDOF oscillator in this study. The stiffness and damping properties of the SDOF model is that of the isolation system. The main purpose of this study is to investigate how four peak response parameters (base shear (BS), relative displacement (U), energy input (El), and total kinetic and potential energy ( EKS)) are influenced by modulating the stiffness or damping properties of the isolation interface. This report summarizes semi-active control computer simulation results of a single degree of freedom system subjected to the El Centro earthquake record. The candidate control algorithms are based on the sign of 1) Base Shear (BS) times Ground Velocity (GV); 2) Base Shear (BS) times Relative Velocity (V); and 3) Relative Velocity (V) times Relative Displacement (U). The products (BS)(GV), (BS)(V), and (V)(U) are referred to as "control parameters" in this report. The report is divided into two main sections. The section I examines the effectiveness of specifying the damping rate as a function of the sign of a chosen control parameter. Section II examines the result of specifying the stiffness as a function of the sign of the control parameter. 3

Section I Semi-Active Damping Control The damping control cases are summarized in Table 1. This table indicates the level of the damping specified when the control parameter is positive and negative. Note that Cases 1 and 2 are similar except that the "polarity" of the control rule is reversed (as are Cases 3 and 4). The entry "0 - 200 %" indicates that several levels of damping were considered in this specified range. Table 1: Variable Damping Test Cases Case Sign of Control Parameter (+) (-) 1 - 200 %ofCch 5% of Ccl 2 5% of Cch 0 - 200 % of Cct 3 0- 200 % of Cch 20 % of Ccl 4 20 % of Cch 0 - 200 % of Ccl Cch is critical damping of a linear SDOF system having the high stiffness of a two stiffness (i.e. bi-linear) system and Ccl is critical damping of a linear SDOF system having the low stiffness of a two-stiffness system. For example, if the two stiffness system has stiffnesses Kh and K1, then Ch = 2KM and Cc, = 2 KkM where (M) is the mass of the SDOF system. Three different systems will be discussed in this section. They are a bilinear hysteretic system, a semi-active stiffness control system, and a linear elastic system. System A: Bilinear System Description of the system: The system discussed here is a bi-linear hysteretic system with stiffness of Kh =390 kips/in and K1 =39 kips/in. For each stiffness, the system carries a passive damping value related to the stiffness of the branch of the hysteresis loop. 4

That is, the passive damping ratio is assumed to be a constant multiple of 1/(2kim) where k is 39 kips/in or 390 kips/in. The weight of the mass is 10 kips. In this system, supplemental damping is controlled. That is, the stiffness of the system follows bi-linear hysteretic behavior according to their specified yield force, while the supplemental damping can be switched actively between two values according to the sign of the control parameter ( GV*BS, V*BS, or V*U). The specified yield forces used in this study are 50 kips and 300 kips. For each yield force four cases are simulated using each control parameter (GV*BS, V*BS, or V*U). These cases are summarized in Table 1 and described below. Case 1) Set the system damping to 5% of 2Vkm (k=39 kip/in) when the control parameter is negative; vary the system damping to 0%, 5%, 9%, 15%, 20%,....200% of 2/km (k=390 kip/in) when the control parameter is positive. In this way we get curves for peak base shear, peak displacement, total energy input, and peak energy content for each control parameter under different yield force levels. Case 2) Set the system damping to 5% of 2x/km (k=390 kip/in) when the control parameter is positive; vary the system damping to 0%, 5%, 9%, 15%, 20%,....200% of 2x/km (k=39 kip/in) when the control parameter is negative. Case 3) Set the system damping to 20% of 2/km (k=39 kip/in) when the control parameter is negative; vary the system damping to 0%, 5%, 9%, 15%, 20%,....200% of 24kkm (k=390 kip/in) when the control parameter is positive. Case 4) Set the system damping to 20% of 2x/km (k=390 kip/in) when the control parameter is positive; vary the system damping to 0%, 5%, 9%, 15%, 20%,....200% of 2 /km (k=39 kip/in) when the control parameter is negative. For detailed results of the simulations please refer to pages (I)-(A)-*. 5

Observations: When the yield force level is lower, base shear, energy input and energy content response are smaller; however, the displacement is larger. From the results, it seems that using V*BS as the control parameter will provide somewhat better overall results over all ranges of damping. If we want a better overall result for combining semiactive damping control and bilinear hysterestic stiffness, it is recommended that we use a higher level of yield force with V*BS as the control parameter, and keep the controlled damping below 40% of the critical damping. System B: Semi-Active Stiffness System Description of the system: The system discussed here is a semi-active control system for both damping and stiffness. The weight of the system is 10 kips. The stiffness is always 390 kip/in when the control parameter is positive and 39 kip/in when the control parameter is negative. Here we simulate the following 4 cases while the stiffness is always switched between 390 kip/in and 39 kip/in. Case 1) Set the system damping to 5% of 2V/kn (k=39 kip/in) when the control parameter is negative; vary the system damping to 0%, 5%, 9%, 15%, 20%,....200% of 2V/km (k=390 kip/in) when the control parameter is positive. In this way we get curves for peak base shear, peak displacement, total energy input, and peak energy content for each control parameter, as damping is changed. Case 2) Set the system damping to 5% of 2V/k (k=390 kip/in) when the control parameter is positive; vary the system damping to 0%, 5%, 9%, 15%, 20%....200% of 2Vkkm (k=39 kip/in) when the control parameter is negative. 6

Case 3) Set the system damping to 20% of 2Vkm (k=39 kip/in) when the control parameter is negative; vary the system damping to 0%, 5%, 9%, 15%, 20%,....200% of 2/km (k=390 kip/in) when the control parameters is positive. Case 4) Set the system damping to 20% of 2/jkm (k=390 kip/in) when the control parameter is positive; vary the system damping to 0%, 5%, 9%, 15%, 20%,.....200% of 2/J-m (k=39 kip/in) when the control parameter is negative. For detailed results of the simulations please refer to page (I)-(B)-*. Observations: For base shear and energy input, using GV*BS as the control parameter provides the best result in these cases. For the displacement, however, the result is about 3 times higher than using (V*BS or V*U) as the control parameter. If V*BS or V*U are used, base shear and displacement are almost insensitive to the amount of controlled damping used when the damping range is lower than 30%. As for energy content, it seems insensitive to the damping for all control parameters. The best control damping range is around 20% to 40% critical damping if the base shear is our main interest. (The peak displacement will keep decreasing as damping increases.) System C: Linear System Description of the system: The system discussed here is a fixed stiffness and semiactive damping control system. The mass is 10 kips. The stiffness of the system is always 390 kip/in. The damping of the system is switched between two values according to the sign of the control parameters. Here we simulate the following 4 cases with the stiffness remaining constant at 390 kip/in. 7

Case 1) Set the system damping to 5% when the control parameter is negative; vary the system damping to 0%, 5%, 9%, 15%, 20%,....200% when the control parameter is positive. In this way we get curves for peak base shear, peak displacement, total energy input, and peak energy content for each control parameter. Case 2) Set the system damping to 5% when the control parameter is positive; vary the system damping to 0%, 5%, 9%, 15%, 20%,....200% when the control parameter is negative. Case 3) Set the system damping to 20% when the control parameter is negative; vary the system damping to 0%, 5%, 9%, 15%, 20%,....200% when the control parameter is positive. Case 4) Set the system damping to 20% when the control parameter is positive; vary the system damping to 0%, 5%, 9%, 15%, 20%,....200% when the control parameter is negative. For detailed results of the simulations please refer to page (I)-(C)-*. Observations: Semi-active damping control improves the response only for low levels of controlled damping in these cases. For base shear, if the fixed damping is 5%, then active control can reduce the base shear up to one half compared to the uncontrolled with 5% damping system. If the fix damping is 20%, then active control can hardly improve the performance compared to the uncontrolled 20% damping system. All the three control parameters provided similar results. The best control switch target damping range is around 20% to 40% critical damping if the base shear is our main interest. (The displacement will decrease as the damping increases.) Overall Comments 1. The displacement and energy content decrease as the damping increases. 8

2. Overall, the best range in semi-active damping control is 20 % to 40% of critical damping in these studies. 3. From these simulations it appears that bi-linear hysteretic systems with lower yield forces result in improved peak base shear but increased peak relative displacement under the effect of the control strategy. 4. The reversal of the polarity of the damping control rule does not result in dramatic changes in the system behavior. This suggests that the three control parameters (GV*BS), (V*BS), and (V*U) are not the appropriate control parameters for damping control. 5. It seems that if we perform only semi-active damping control, the improvement in base shear response from a fixed damping system (i.e. a system without control) will reduce as the fixed damping increases. The improvement is not that significant if the stiffness is constant. Therefore, the next part of the report focuses on the stiffness control only. 9

Section II Semi-Active Stiffness Control In this section, the system with 5% critical damping is discussed first in order to see which control algorithm will yield the best overall result. The reason for using 5% critical damping is that the damping of most existing structures is around 3% to 5%. After the control algorithm was selected, different damping cases were tried in order to observe the sensitivity to damping. System A: Semi-Active Stiffness 5% Fix Damping Case Description of the system: The system discussed here is a fixed damping and semiactive stiffness control system. The damping of the system is 5% of 2 km (k=390 kip/in). The mass of the system is 10 kips. When the control parameter is positive, the stiffness of the system is 390 kip/in; when it is negative, the stiffness of the system is pk*390 kip/in, where pk is the stiffness ratio,and varies from 0.01, 0.1, 0.2, 0.3,....to 1.0. When pk= 1.0, the system has no control ( linear SDOF with k=390kip/in, mg=l0 kips, c=5% critical damping = (0.05) 2km ). For detailed results of the simulations please refer to page (II)-(A)-*. Observations: If (BS*GV) is used as the control parameter, then the base shear will have a sharp drop, but displacement will increase when the stiffness ratio pk is small. This kind of behavior is not desirable. If we use V*BS or V*U, all the response parameters (base shear, displacement, and energy content) will improve ( decrease) as the stiffness ratio becomes smaller. However, for stiffness ratios below 0.2, only marginal improvement in the value of peak base shear, peak displacement, and peak energy content are observed. Therefore, overall V*BS seems to provide the best control result. The difference between using V*BS and using V*U is very small. 10

System B: V*BS for Different Damping % Because V*BS yields the best overall stiffness control result, it will be used here as the only control parameter. The goal is to find out how the system will respond under different damping conditions. Description of the system: The system considered here is a fixed damping and semiactive stiffness control system. The mass of the system is 10 kips. Fix the damping of the system to 3% of 24kam (k=390 kip/in). When V*BS is positive, the stiffness of the system is 390 kip/in; when it is negative, the stiffness of the system is pk*390 kip/in, where pk is the stiffness ratio, and varies from 0.01, 0.1, 0.2, 0.3,....to 1.0. Similarly, we change the damping to 5%, 10%, 15%, 20%, 30%, 40%, 50%,-75%, 100%, 150%, 200% of critical damping. For detailed results of the simulations please refer to page (II)-(B)-*. Observations: The performance improvement due to semi-active stiffness control decreases as the passive damping increases. (i.e. If we have a system with 3% critical damping and 5% critical damping, the semi-active stiffness control has a greater effect in the 3% case than in the 5% case.) Semi-active stiffness control can reduce peak response quantities (base shear, relative displacement, energy input, total energy) to levels comparable to a passive system damped to 30% - 50% of critical without the accompanying increase in base shear that high passive damping entails. The response will improve (displacement, energy input, and energy content decreases) as damping increases except for the base shear. When the damping is higher than 30%, the base shear increases as the damping increases. 11

Overall Comments 1. From these studies, it seems that semi-active stiffness control improves the performance only when the system damping is less than 30% critical. If the damping of the system is higher than 30%, then the semi-active stiffness control is almost ineffective. 2. In the cases considered in this report, it seems that stiffness ratio, pk, of around 0.1 to 0.3 will provide the best control result. 12

Conclusion Based on the simulation results, the following conclusions can be drawn. 1. It seems that the use of relative velocity times base shear (V*BS) as the control parameter provides the best results for semi-active stiffness control. If we use ground velocity times base shear (GV*BS), even though we can minimize the energy input, the overall response (including displacement) is not always the best. 2. The effect of the semi-active stiffness control decreases with increased passive damping. For passive damping above 30%, the semi-active stiffness control has little effect. 3. For semi-active damping control using the mentioned algorithms, in order to obtain the best overall control result, it is recommended that 20% to 40% of critical damping be set as the maximum system damping. If a higher value of maximum damping were chosen, the response will only become more undesirable. 4. It seems that semi-active stiffness control is more effective than semi-active damping control. The semi-active stiffness control with 3% critical damping can reduce the base shear by about 65%; while the semi-active damping control with minimum damping of 5% can reduce the base shear by about 50%. The most effective stiffness ratio, pk, to be used in semi-active stiffness control seems to be around 0.1 to 0.3. For both types of control, the smaller the passive damping is (damping value between 0% to 30% critical damping), the more effective the active control is. 5. Semi-active stiffness control of a lightly damped structure reduce peak response quantities ( displacement, energy content, total energy input) to levels comparable to a structure damped with 30% passive damping, without the accompanying increase in base shear associated with high damping. 13

Hopefully, the results of this study will be useful in the decision making for applying semi-active control. Also, some reference values are provided for parameters to be used in semi-active control. 14

References 1. 1994 Edition NEHRP Recommended Provisions for the Development of Seismic Regulations for New Buildings. FEMA 222/ January 1994. 2. Hanson, Robert D., and Firmansjah, Jodi, "Energy Concerns for Active Response Control," Proc. Japan National Symposium/workshop on Structural Response Control, July 1992. 15

Section I, System A, Case 1, Base Shear Description: Here provide IFix k&c for comparison I, represent the case without controling (Fixed damping ratio according to 390 kip/in, i.e. keep the same damping even in the range of 39 kip/in) (Different from the other columns, the 30% point means bilinear sys with 30% damping, no change in k&c.) The GV*BS,fy=50 column: when GV*BS is negative provide 5% damping according to39 kip/in (FIX), when GV*BS is positive provide c% damping according to 390 kip/in (VARY). The yield force of bilinear system is 50 kips. _ 7 - i I (30% point means when neg. GV*BS c=5% acc. to 39 kip/in; when pos. GV*BS c=30% acc. to 390 kip/in) Base shear (Bilinear 390, 39) Fix soft 5% (*.005) C(%) Fix k&c GV*BS,fy=50 tGV*BS,fy=300 V*BS,fy=50 V*BS,fy=300 V*U,fy=50 V*Ufy=300 0 3144 3201 410 3011 429 295j 434 5 1976 - 294! 411 266 417 291 413 9 1465 2841 41 1 277 454 304 455 1 5 10811 274 4271 316 527 3861 527 201 9451 2731 444 362 624 415 603 25 8541 4131 466 407 739 445 761 30 791 465 497 475.838 531 906 40 894 398 597 612 101 8 691 1195 50 974 4811 725 727 1179 907 1397 75 1095 658 1020 933 1434 1523 1726 100 1154 1394 1037 1054 1583" 1843 1884 150 1205 1987 1711 1166 2023 2235 2150 200 1235 2411 2126 1226 2155 2421 2469 3500 T- - -. —--—. —-- CL 3000 —----- ----— FT.- —, —-T- -.. --,Fix k&c 2500 —\-':: - - GV*BS,fy=50'I I,./.......... — GV*BS,fy=300 3 2000 —---- ------.::500 +-\ —------------ - ----- ------!' O V*BS,fy=50 ino 15001\] \y^?j-' - - V*BS,fy=300 1 500 - - - - - 0- - - - - - - - - -L V*B,fy=300 5100 j_^^ 0^- -— ~ -—' — ~ -- -- -- V*U,fy=50 100 C / Cch 100 *g,,, [ * V*U,fy=300 C c I I 7 I I I I i (I)-(A)-BS1

Section I, System A, Case 2, Base Shear Description: |Here provide IFix k&c for comparison I, represent the case without controling (Fixed damping ratio according to 390 kip/in, i.e. keep the same damping even in the range of 39 kip/in) (Different from the other columns, the 30% point means bilinear sys with 30% damping, no change in k&c.) I 1 The GV*BS,fy=50 column: when GV*BS is positive provide 5% damping according to390 kip/in(FIX), when GV*BS is negative provide c% damping according to 39 kip/in (VARY). The yield force of bilinear system is 50 kips.. (30% point means when neg. GV*BS c=30% acc. to 39 kip/in; when pos. GV*BS c=5% acc. to 390 kip/in) Base shear (Bilinear 390, 39) Fix stiff 5% (005.*) c(%) Fix k&c IGV*BS,fy=50 GV*BS,fy=300 V*BS,fy=50 V*BS,fy=300 V*U,fy=50 V*U,fy=300 0 3144 340 418 290 424 312 421 5 1976 294 411 266 417 291 413 9 1465 270 412 262 423 266 418 15 1081 242 417 236 4211 257 419 20 945 2371 424 237 4181 233 423 25 854 244 443 235 418 218 421 30 791] 258 463 228 419 218 425 40 8941 291 5021 228 422 239 446 50 974 324 542 226 4199 254 481 75 10951 389 686 222 422 2921 513 100 11541 499 828 265 416 388 609 150 12051 688 1083 339 617 401 733 3500 r —- -----------------------— c —------- 3500 T 3000 -- - -- - - - - -- - - -- - - - - -- - - - - --- - - * Fix k&c I2500 j\8 3 5' I GV*BS,fy=50 j \ ---- -GV*BS,fy=300 5 2000 ---- ------ ------ ------ ------ ------ H \ -;{ — V*BS,fy=50 cn I. \,, D 15002 1500 ------ ---------------—, —------- ----—, C \', V*BS,fy=300.=-1000 -- - - i - -. ^ V*U,fy=50 500 i - _^ _ - I -_ - ^^^ * V*U,fy=300':.... --. AM 0 I I _LI' I 0 Lr OU 0 o) 00 0 o. 0o0 0 *. 0c, C0 ) I o Nr,- LO ) 100 C / Ccl II II I I I I 7 (I)-(A)-BS2

Section I, System A, Case 3, Base Shear I I I I I Description: IHere provide jFix k&c for comparison |, represent the case without controling (Fixed damping ratio according to 390 kip/in, i.e. keep the same damping even in the range of 39 kip/in) (Different from the other columns, the 30% point means bilinear sys with 30% damping, no change in k&c.) -- The GV*BS,fy=50 column: when GV*BS is negative provide 20% damping according to39 kip/in (FIX) when GV*BS is positive provide c% damping accordinq to 390 kip/in (VARY). The yield force of bilinear system is 50 kips. (30% point means when neg. GV*BS c=20% acc. to 39 kip/in; when pos. GV*BS c=30% acc. to 390 kip/in) Base Shear (Bilinear 390, 39) Fix soft 20% (*.020) __ I _I I C(%) Fix k&c GV*BSfy=50 GV*BS,fy=300 V*BS,fy=50 V*BS,fy=300 V*U,fy=50 V*U,fy=300 0 3144 267 424 298 424 268 441 5 1976 237 424' 237 418 233 423 9 1465____ 233'_____45 9 1 4651 233 423 256 453 287 454 15 10811 234 422 317 525 362 528 20 9451 235 421 366 599 3971 588 25 8541 250 4450 408 715 419 690 30 791 290 499 99476.798 499..872 40~ 894 381 586 605 978 645 1163 50 974 479 656 71 6 11i1 0 845 1362 75 1095 731 902 91 8 13231 1455 1 659 100 1154 10031 1263 1031 14321 1770 1823 150 1205i 1465 1 710 1145 15141 2189 2106 200 1235I 18181 2234 1204 1676 2362 2185 3500 --- --- - ----—'- -- -------- 3000 --— __ —__ _ Fix k&_ 3500 -T ------------ ------ — *-'Fix k&c 1 2500 ------------ - - - - --- - - - - -G- - — BS,fy=50 2500 \ /t —---- GV*BS,fy=300 f2000 - - -- I 2.. \ ^ /& — V*BS,fy=50 1500 -- gu, \ J / -- - V*BS,fy=300 1000 --- -- V*U,fy=50 500.... -— V*U,fy=300 o ) LO ) LO. — OC C) C) 0 ~ N 1.0 co 1. 0 ~ 0l 0 OC0 CCl C) c LO i 0 oO 0 0 100 C / Cch I ~I......!... I I _I (I)-(A)-BS3

Section I,System A, Case 4, Base Shear Description: Here provide Fix k&c for comparison 1, represent the case without controling (Fixed damping ratio according to 390 kip/in, i.e. keep the same damping even in the range of 39 kip/in) (Different from the other columns, the 30% point means bilinear sys with 30% damping, no change in k&c.) The GV*BS,fy=50 column: when GV*BS is positive provide 20% damping according to390 kip/in(FIX) when GV*BS is negative provide c% damping according to 39 kip/in (VARY). The yield force of bilinear system is 50 kips. i. I I I _ (30% point means when neg. GV*BS c=30% acc. to 39 kip/in: when pos. GV*BS c=20% acc. to 390 kiD/in) Base shear (Bilinear 390, 39) Fix stiff 20% (020.*)_ _____ c(%) Fix k&c GV*BS,fy=50 GV*BS,fy=300 V*BS,fy=50 V*BS,fy=300 V*U,fy=50 V*U,fy=300 0 3144 288 462 360 649 417 611 5 1976 273 444 362 624 415 603 9 1465 280 432 362 626 405 591 15 1081 267, 415 359 603' 4061 588 20 945 2351 421 366 599 3971 588 25 854 244 439 358 600 390] 588 30 791 258 457 358 592 386 588 40 8941 295 494 355 584 369 586 50 9741 324 532 354 581 365 585 75 1095 393 646 355 580 348 610 100 11 541 500 770 3581 581 380 678 150 1205 680 965 350 571 421 813 2001 1235 818 1039 351 569 480 921 _. 1.._ I _ _.. _ 3500 - - 3000 —--------- ----— x1 --- *-Fix k&c 2500 ---------------------- ---- GV*BS,fy=50 ~ \............-~ * GV*BS,fy=300 2000- - - - <> \ -- - V*BS,fy=50 1500 --- ---------- co' \ _ * — V*BS,fy=300 Q - - - --- - - 1000 -.-..- V*U,fy=50, -o - - *- -,- ^" — U - - - - 500 V*Ua4.-' -— IiL - V*U,fy=300 5 0 0' —4~:=='9m=~-L — -_ __l _-__]_____. 0C LO O LO 0 LO 000 C C0 C) 0'- m N 100 C / Ccl I II 0 7 1 II II I I II I (I)-(A)-BS4

Section I, System A, Case 1, Displacement Description: Here provide IFix k&c for comparison I, represent the case without controling (Fixed damping ratio according to 390 kip/in, i.e. keep the same damping even in the range of 39 kip/in) (Different from the other columns, the 30% point means bilinear sys with 30% damping, no change in k&c.) r The GV*BS,fy=50 column: when GV*BS is negative provide 5% damping according to39 kip/in (FIX), when GV*BS is positive provide c% damping according to 390 kip/in (VARY). The yield force of L bilinear system is 50 kips. (30% point means when neg. GV*BS c=5% acc. to 39 kip/in; when pos. GV*BS c=30% acc. to 390 kip/in) Displacement (Bilinear 390, 39) Fix soft 5% (*.005) c(%) Fix k&c GV*BS,fy=50 GV*BS,fy=300 V*BS,fy=50 V*BS,fy=300 V*U,fy=50 V*U,fy=300 0 8.06 6.971 3.558 6.583 4.08 6.417 4.23 5 5.041 6.308 3.587 4.754 3.204 5.389 3.083 9 3.6821 6.078 3.584 3.803 2.953 4.474 2.7 [ 15 2.683] 5.81 3.553 3.032 2.772 4.031 2.474 20i 2.259j 5.5551 3.515 2.785 2.563 3.668 2.291 25 1.9351 5.2811 3.496 2.532 2.3151 3.251 2.197 30 1.6841 4.996 3.474 2.518 2.028 2.959 1.978 40 1.33 4.414 3.397 2.176 1.653 2.445 1.972 50 1.119 3.937 3.272 1.806 1.414 2.111 1.532 75 0.876 3.798 2.991 1 1.129 1.47 1.256 100 0.747 4.743 2.894 0.939 0.985 1.146 1.145 150 0.5721 4.846 2.802 0.981 0.859 0.83 0.913 200 0.4561 4.927 2.647 0.5191 0.675 0.674 0.727 \ ---- Fix k&c 7. - - - c, -= GV*BS,fy=50 5 — n-~ - 6 ----------. o \,.. _'......:',', —',-: *-..GV*BS,fy=300...' — - - - -...... --: —:V*BS,fy=300 1 1 ------------------— r —-s —----— I O=0-0 V*U,fy=300 II I I O i Io I i C I I0 0' t I I O LO) ) L)O 0O O O O 0 ) O O O NOJ N C) to NP 0 LO 0 100- C Cch 100 C / Cch (I)-(A)-DISP1

Section I, System A, Case 2, Displacement I -1 -1 Description: IHere provide Fix k&c for comparison, represent the case without controling (Fixed damping ratio according to 390 kip/in, i.e. keep the same damping even in the range of 39 kip/in) (Different from the other columns, the 30% point means bilinear sys with 30% damping, no change in k&c.) The GV*BS,fy=50 column: when GV*BS is positive provide 5% damping according to390 kip/in(FIX), when GV*BS is negative provide c% dampina accordina to 39 kio/in (VARY). The vield force of bilinear system is 50 kips. (30% point means when neg. GV*BS c=30% acc. to 39 kip/in; when pos. GV*BS c=5% acc. to 390 kip/in) Displacement (Bilinear 390, 39) Fix stiff 5% (005.*) c(%) Fix k&c GV*BS,fy=50 GV*BS,fy=300 V*BS,fy=50 V*BS,fy=300 V*U,fy=50 V*U,fy=300 0 8.06 7.565 3.795 5.332 3.375 5.911 3.288 5 5.041 6.3081 3.587 4.754 3.204 5.389 3.083 9 3.682 5.493 3.445 4.65 3.363 4.763 3.236 15 2.683 4.488 3.261 4.298 3.303 4.534 3.261 20 2.259 3.822 3.134 4.265 3.248 4.219 3.351 25 1.935 3.539 3.023 4.262 3.252 3.79 3.33 30 1.684 3.3111 2.926 4.041 3.261 3.6 3.431 401 1.33 2.959 2.764 4.038 3.353 3.2' 3.95 50 1.1199 2.776 2.636 4.004 3.289 3.2351 3.936 75 0.876 2.691 2.418 3.882 3.356 3.2121 4.245 100 0.747' 2.647 2.28 3.838 3.226- 3.603 3.868 150L 0.572 2.6391 1.94 3.449 2.992 4.071 3.987 2001 0.456 2.673 1.676 3.475 3.347 4.448 2.892 __,__,___=___7___ [ ______ I __ I,....... GV*BS,fy=300 8 -1^ ^ ^ T — ^ -. —-— ~ - ---— BS —50'i;~ 3 -'*-'":'"~~" Fix k&c 13 \\ hC D, | I GV*UBS,fy=50 Q)Q) s Aeh<..~.,...l...:; | + GV*BSfy=300 2ura ~"_ -'"^ ^ — A —- V*U,fy=50 1 ------------- -- ---------------— I.....- *V*U,fy=300 0 0 i4 I i) LO 1I I i O I") 3) U.) O l O O 0 1) 0 0 0 100 C / Ccl (I)-(A)-DISP2

Section I, System A, Case 3, Displacement I I I Description: |Here provide Fix k&c for comparison 1, represent the case without controling (Fixed damping ratio according to 390 kip/in, i.e. keep the same damping even in the range of 39 kip/in) (Different from the other columns, the 30% point means bilinear sys with 30% damping, no change in k&c.) The GV*BS,fy=50 column: when GV*BS is negative provide 20% damping according to39 kip/in (FIX) when GV*BS is positive provide c% damping according to 390 kip/in (VARY). The yield force of bilinear system is 50 kips. G I I I c i (30% point means when neg. GV*BS c=20% acc. to 39 kip/in; when pos. GV*BS c=30% acc. to 390 kip/in) Displacement (Bilinear 390, 39) Fix soft 20% (*.020) 1 _ c(%) Fix k&c GV*BS,fy=50 GV*BS,fy=300 V*BS,fy=50 V*BS,fy=300 IV*U,fy=50 V*U,fy=300 0 8.06 4.33 3.0921 6.494 3.956 5.725 4.396 5 5.041 3.8221 3.134; 4.265 3.248 4.219 3.351 9 3.682 3.7641 3.102 3.422 2.8991 3.829 2.789 15 2.683 3.7631 3.032 3.089 2.844J 3.709 2.403 20 2.259 3.763 2.981 2.399 2.591 3.184 2.306 25 1.935 3.7741 2.923 2.539 2.774 3.044 2.107 30 1.684 3.7561 2.858 2.011 2.564 2.738 1.966 40 1.33 3.673 2.6911 1.655 1.596 2.205 1.716 50 1.119 3.597 2.54 1.504 1.332 2.122 1.692 75 0.876 3.49 2.467 1.181 1.043 1.389 1.21 100 0.747 3.507 2.381 0.87 0.9531 1.132 1.114 150 0.5721 3.459[ 2.165 1.045 0.7331 0.907 0.896 200 0.4561 3.3821 2.059T 0.623 0.581 0.669 0.717 9 _ __ —- I ____ __ __ I.I.. I I 8 — 1 —---. --------- -... 8_..-\ — " —.... i —'i - =~*- Fix k&c 7 -L\- -,- -- - -,- -, — -. -- -. - - - -=- - arc~ <>a~~ \t` /~ ----- GV*BS,fy=50 E -- -< — \- — * —* GV*BS,fy=300 C V*BS,fy=50 ~L -' ""^-^ —-— g-D —{ —--—' ----- V*BS,fy=300 2 V*U,fy=50 0I ~ t t t I$I., I I I f I~' ^^ - --,I*-V*U,fy=300 LO 0 LO 0 LO LO 0 0 0 O1-C Ckl CI ~1 LO -- 0 LO 0 cm 100 C / Cch (I)-(A)-DISP3

Section I, System A, Case 4, Displacement Description: Here provide IFix k&c for comparison, represent the case without controling (Fixed damping ratio according to 390 kip/in, i.e. keep the same damping even in the range of 39 kip/in) (Different from the other columns, the 30% point means bilinear sys with 30% damping, no change in k&c.) The GV*BS,fy=50 column: when GV*BS is positive provide 20% damping according to390 kip/in(FIX) when GV*BS is negative provide c% damping according to 39 kip/in (VARY). The yield force of bilinear system is 50 kips. I 1 (30% point means when neq. GV*BS c=30% acc. to 39 kip/in: when pos. GV*BS c=20% acc. to 390 kiD/in) 1- Displacement (Bilinear 390, 39) Fix stiff 20% (020.*) c(%) Fix k&c GV*BS,fy=50 GV*BS,fy=300 V*BS,fy=50 V*BS,fy=300 V*U,fy=50 V*U,fy=300 0 8.061 6.1 67 3.762 2.872 2.519 3.676 2.258 5 5.0411 5.555. 3.515 2.785 2.563 3.668 2.291 9 3.682 4.964! 3.348 2.617 2.428 3.441 2.407 15 2.683 4.2991 3.129 2.421 2.585 3.4911 2.282 20 2.2591 3.7631 2.9811 2.399 2.591 3.184 2.306 251 1.935 3.3671 2.8491 2.394 2.456 3.169 2.367 30 1.684 3.0881f 2.739 2.443 2.601 3.095 2.384 40 1.33 2.743k 2.561 2.363 2.643 2.8 2.41 50 1.119j 2.4257 2.43 2.329 2.594 2.536 2.336 75 0.876 2.0637 2.225 2.297 2.548 2.05 2.588 100 0.747 2.0031 2.122 2.1 64 2.651- 2.38 2.221 150 0.572 2.0091 1.8211 2.269 2.413 2.951 2.435 200 0.456 2.0881 1.709 2.048 2.498 3.325 2.588 9 - - - --- - - --- - - I - - - \8"iI~~~~~~ — * -- Fix k&c 7 ri^~~ \ — D —~ GV*BS,fy=50 0) \^\ — ~ —V*BS,fy=50 T 3-''........''-' ^ -- - r —--- - - - - - - - -, CD.-^S^^^ ^iF-^ ^^^^^^ V*BS,fy=50 =^^~-.- ^ ---- GV*BS,fy=300 0 ---—,:-... —.... E I -.... ~:.-e-__... V*Ufy=300' CJ CN) LO U) N 0 100 C / Ccl (i)-(A)-DISP4

Section I, System A, Case 1, Energy Input Description: Here provide Fix k&c for comparison, represent the case without controling (Fixed damping ratio according to 390 kip/in, i.e. keep the same damping even in the range of 39 kip/in) (Different from the other columns, the 30% point means bilinear sys with 30% damping, no change in k&c.) r The GV*BS,fy=50 column: when GV*BS is negative provide 5% damping according to39 kip/in (FIX), when GV*BS is positive provide c% damDina accordina to 390 kip/in (VARY). The vield force of bilinear system is 50 kips. i I -. (30% point means when neg. GV*BS c=5% acc. to 39 kip/in; when pos. GV*BS c=30%,acc. to 390 kip/in) Energy Input (Bilinear 390, 39) Fix soft 5% (*.005) c(%) Fix k&c GV*BS,fy=50 IGV*BS,fy=300 V*BS,fy=50 V*BS,fy=300 V*U,fy=50 V*U,fy=300 0__ 17288 4760 5628 4374 5361 4267 5489 5 13023 4273 5685 4737 6275 4771 6083 _ 9 10868 4143 5794 4963 6906 5021 6656 51 1 10150 41 09o 5934 5365 7663 5103 7277 20 9937 4123 6028 5777 8194 5136 7739 25 9634 4145 6107 6098 8601 5396 8072 30 9326 4158 6186 6291 8856 5544 8562 40 8759 4153 6334 6678 9154 5888 8869 50 8237 4135 6444 6804 9272 628 9 9585 100 6277 4478 6709 6395 8585- 7720 8987 150 5042 5222 6545 5598 7073 7325 7468 200 4210 5001 6279 4962 6215 6486 6463 _ _ I I I I I.6 1 _. _ 18000 T —---- - - - - --- -, 16000 --, —------— s —----- ------ -- ---- \ 16000 -! I =\ — * Fix k&c c 14000 —----- <... -.. iGV*BS,fy=50 7 12000 —----------------------------------'0 >.... — GV*BS,fy=300 10000 — - _c Ir^S^^^ -'^i\ -— o V*BS,fy=50 8000 -''*' V*BS,fy=300,, 6000 - -r V*U,fy=50 4000.... 2000 -------- --------- --- -: —--' 0 I I t I I I, 1 I i 1 1 1 o c LtO tO o 0 C ) C) 0 o — 1 C'J CO) ~' L) "- 0 LO 0 M llqr LO r0 ~T.- a C 100 C / Cch i (I)-(A)-E 1

Section I, System A, Case 2, Energy Input Description: Here provide Fix k&c for comparison, represent the case without controling (Fixed damping ratio according to 390 kip/in, i.e. keep the same damping even in the range of 39 kip/in) I 7 i i (Different from the other columns, the 30% point means bilinear sys with 30% damping, no change in k&c.) The GV*BS,fy=50 column:when GV*BS is positive provide 5% damping according to390 kip/in(FIX), when GV*BS is negative provide c% damping according to 39 kip/in (VARY). The yield force of bilinear system is 50 kips. T (30% point means when neg. GV*BS c=30% acc. to 39 kip/in; when pos. GV*BS c=5% acc. to 390 kip/in) Energy Input (Bilinear 390, 39) Fix stiff 5% (005.*) c(%) Fix k&c GV*BS,fy=50 GV*BS,fy=300 V*BS,fy=50 V*BS,fy=300 V*U,fy=50 V*U,fy=300 0 17288 4191 5386 4738 6260 4954 6001 5 13023 4273 5685 4737 6275 4771 6083 91 10868 4334 5923 4635 6283 4662 6168 15 10150 4532 6242 4542 6304 44911 6284 20 9937 4713 6474 4497 6312 45361 6362 25 9634 4856 6689 4458 6302 45521 6408 30 9326 4969 6880 4427 6298 4594 6528 40 8759 5228 7202 4394 6383 4666 6854 50 8237 5576 7456 4391 6387 46871 6930 75 7138 6146 7924 4308 6508 47111 7421 1001 6277 6533 8177 4280 6543- 5175 7544 150 5042 6962 8360 4168 6611 5520i 7875 200 4210i 7082 8286 1 4113 6792 5436i 7699 18000 T- -- ----- - ------ ---- --- 16000 - --. - ------------ -- I \ =, *- Fix k&c C 14000 — \. —---------—.... ------ 1< 2000- GV*BS,fy=50. 12000 I —— l —-------- -------------- ---— i 12000,:^', -::':'',,; — GV*BS,fy=300 = W _-. — __ —_ V*BS,fy=50 8000 --— t --- I:..,,,~- V*BS,fy=300 6000 I,,,,,V*Ufy=50 20 0 0 L-~ — - -- - --- --- --- ---- --- --- __________ V*U,fy=300 0 Lo o LO 0 L 00 0 C) 00 0 o - d 4 3 o ~ o- o C o 100 t U) Ccl 100 C / Ccl (I)-(A)-E12

I I I Section I, System A, Case 3, Energy Input Description: Here provide Fix k&c for comparison, represent the case without controling (Fixed damping ratio according to 390 kip/in, i.e. keep the same damping even in the range of 39 kip/in) (Different from the other columns, the 30% point means bilinear sys with 30% damping, no change in k&c.) i I - I -.0 I The GV*BS,fy=50 column: when GV*BS is negative provide 20% damping according to39 kip/in (FIX),., _ IWO. — I'"" -,!A~ ~ when GV*BS is positive provide c% damping according to 390 kip/in (VARY). The yield force of bilinear system is 50 kips. I I (30% point means when neg. GV*BS c=20% acc. to 39 kip/in; when pos. GV*BS c=30% acc. to 390 kip/in) Energy Input (Bilinear 390, 39) Fix soft 20% (*.020) c(%) IFix k&c IGV*BS,fy=50 GV*BS,fy=300 V*BS,fy=50 V*BS,fy=300 V*U,fy=50 V*U,fy=300 0 17288 4817 64161 3922 5477 4037 5846 5 13023 4713 6474 4497 6312 4536 6362.91 10868 4621 6546 4893 6873 49461 6769 1 5 10150 4571 6650 5449 7633 5163i 7381 20 9937 45491 6726 5815 8108 5489 7811 25 9634 4538 6792 6080 8453 5719 8186 30 93261 4513 6852 6288 88653 5872 8513 40 8759 4449 6947 6541 8870 6234 8972 50 8237 4386 7022 6642 8961 6267 9033 75 7138 4193 7100 6508 8594 7360 9447 100 6277 4115i 7094 6104 7980- 7598 8758 150 5042 4016 6899 5316 66131 6911 7380 200f 4210 _ 3962 6669 4632 5621 6412 6444! I 10' 4 21 56 321 66 I69 18000 T — - ----------- - ---- ---- ----- ---- -- 16000 -, —\.,Fix k&c 14000 ------ - - ---- - ---- -. - - - - -;. ----— |. <1000 -- GV*BS,fy=50 12000 -- --- ---.,.* GV*BS,fy=300 = 10000 - - - - - - 000 r- — ~ V*BS,fy=50 | 86A ^^ — "-000 iz —'- * V*BS,fy=300 6000 ------- i} 0-(-0 i -~=-g -— r - 0- { > ~ —-e —---- V*U,fy=50 4000 < - - - I — -- 2000 -.~ —..- V*U,fy=300 2 0 --- - I I I I I I I O L LO 0 LO C ) ) LO I) 0 C) r Ci C o COI' LO Nr. o )L 0 1 CJ 100 C / Cch t,,!, I, I I II (I)-(A)-E13

Section I, System A, Case 4, Energy Input Description: Here provide Fix k&c for comparison I, represent the case without controling (Fixed damping ratio according to 390 kip/in, i.e. keep the same damping even in the range of 39 kip/in) (Different from the other columns, the 30% point means bilinear sys with 30% damping, no change in k&c.) - The GV*BS,fy=50 column: when GV*BS is positive provide 20% damping according to390 kip/in(FIX) when GV*BS is negative provide c% damping according to 39 kip/in (VARY). The yield force of bilinear system is 50 kips. I_ I- I (30% point means when neg. GV*BS c=30% acc. to 39 kip/in; when pos. GV*BS c=20% acc. to 390 kip/in) Energy Input (Bilinear 390, 39) Fix stiff 20% (020.*)] C(%) Fix k&c GV*BS,fy=50 IGV*BS,fy=300 V*BS,fy=50 V*BS,fy=300 V*U,fy=50 V*U,fy=300 0 17288 40731 5750 5691 8208 5140 7694 5 13023 4123 6028 5777 8194 5136 7739 9 10868 4218 6229 5827 8173 5303 7766 15 10150 4422 6512 5834 8107 5404 7795 20 99371 4549 6726 5815 8108 5489[ 7811 25 96341 4705_ 6916 5805 8066 5560 7820 30 93261 48011 7085 5772 8.046 5567 7819 40 87591 5115 7372 57541 7983 5615 7822 50 82371 53921 76031 57381 7953 5696 7849 75 71381 59391 7997 5726 7860 5759 7958 100 6277 6322 8200 5678 7788 5761 7884 150 5042 6761 8277 5643 7668 5962 7891 200 4210 69321 8067 5606 7578 5823 7752 18000 T -- ------- -- - 16000 ---- \ -- -- Fix k&c 14000 - - < ~ — 0- GV*BS,fy=50 GV*BSfy32000 _ * GV*BS,fy=300 10000 --- ------------ -- -------- 2' _~ -- -o V*BS,fy=50 8000 -- - 0 _' - - —'1"<>; -- - V*BS,fy=300 m 6000 -~= W --- V*U,fy=50 2 000- V*U,fy=300 0 C0 Lo O LO C) L C) 0 0 C0 ) 00 C: Co (%i C) ~1 io In 0 o 0 *^CM ~CM CT d ~ OC' 100 C / Ccl i (I)-(A)-E14

Section I, System A, Case 1, Energy Content Description: Here provide Fix k&c for comparison, represent the case without controling (Fixed damping ratio according to 390 kip/in, i.e. keep the same damping even in the range of 39 kip/in) (Different from the other columns, the 30% point means bilinear sys with 30% damping, no change in k&c.) r The GV*BS,fy=50 column: when GV*BS is negative provide 5% damping according to39 kip/in (FIX), when GV*BS is positive provide c% damping according to 390 kip/in (VARY). The yield force of L bilinear system is 50 kips. _ 7 (30% point means when neg. GV*BS c=5% acc. to 39 kip/in; when pos. GV*BS c=30% acc. to 390 kip/in) KE + SE (Bilinear 390, 39) Fix soft 5% (*.005) I [ T I K.Uf50 V*U~ 0 u,I c(%) Fix k&c!GV*BS,fy=50 GV*BS,fy=300 V*BS,fy=50 V*BS,fy=300 V*U,fy=50 V*U,fy=300 0 17288 1520 653 1278 665 1206 670 5 7689 1332 647 1031 711 1090 730 9 4759 1335 675 849 793 947 829 15 28661 1265 726 650 894 7551 948 20 21711 1195 760 654 975 672 1030 25 17941 1125 791 601 1061 631 1134 30 15721 1056 814 569 1033 607 1138 40 13351 929 8421 613 117.2 646 1096 50 12151 839 860 648 1234 713 1264 75 1074! 874 903 705 12941 7731 1299 100 10071 9321 953 7921 1324- 8281 1292 150 9351 1146 871 881 1194 842 1195 200 9441 1162 882 889 1203 888 1224 _ 1 000 - - - - - - _ - - -- - - - - - - -_ _ 18000 T-r - - -,- - - -- - - - - - - - - - - 16000 T —------- ------ ----— ~ —, —--—, —---- 6 00-*0 Fix k&c < 14000 \ —------------ -—. —----.c 1 \,- -- GV*BS,fy=50' 12000 ---------------- c- \ 12000, — GV*BS,fy=300 c \ < >- V*BS,fy=50 ) 8000 ---- - -- >, \....... I _A- V*BS,fy=300 4 6000 -t. — I — 200 — A — V*U,fy=500 4000 - ------------------------------ 100 C Cch I....CM C CO t 1. OOO (I)-(A)-EKS1

Section I, System A, Case 2, Energy Content Description: IHere provide IFix k&c for comparison, represent the case without controling (Fixed damping ratio according to 390 kip/in, i.e. keep the same damping even in the range of 39 kip/in) (Different from the other columns, the 30% point means bilinear sys with 30% damping, no change in k&c.) The GV*BS,fy=50 column: when GV*BS is positive provide 5% damping according to390 kip/in(FIX), when GV*BS is negative provide c% damping according to 39 kip/in (VARY). The yield force of bilinear system is 50 kips. I.J I I. (30% point means when neg. GV*BS c=30% acc. to 39 kip/in; when pos. GV*BS c=5% acc. to 390 kip/in) i KE + SE (Bilinear 390, 39) Fix stiff 5% (005.*) c(%) Fix k&c GV*BS,fy=50 GV*BS,fy=300 V*BS,fy=50 V*BS,fy=300 V*U,fy=50 V'U,fy=300 0 17288 1628 661 1113 719 1249 731 5 7689 13321 647 1031 711 1090 730 9 4759 11581 658 912 697 1027 694 15 2866 956 673 929 678 852 691 20 2171 858 700 897 683 866 666 25 1794 788 733 914 693 760 653 30 15721 724 763 861 719 755i 674 40 13351 647 828 852 723 7191 754 50 1215 628 879 854 758 652 782 75[ 1074i 5991 996 845 886 611 862 100 10071 5771 10931 813 1094- 751 874 150 935 6051 1194 719 1454 8061 914 200 944 679 1253 634 1666 9161 908 18000 ---- I 18000 - —, — ---- ------- - - ---- - - -----:'\ —,..; GV*BS,fy=50 Ys 12000 i-t —-\ ---- ----- ---------------- -------- [ _-| \12000 ___-'- -';,,, | *.- GV*BS,fy=300 1 0000 - ------- ---- - -r -- - - -- ---- I o 8 - V*00 BS 300 w - - V*U,fy=50 -1 4-~-~-~ t \. -- V*U,fy=300 2000 0' r] I I t I,t t - I 1 I0 o O0 LCO o L) o o LO 0o o I IC4 0c O' t 1 I o - 0 0C 100 C / Ccl I t I I, I I' I I" (I)-(A)-EKS2

I I I Section I, System A, Case 3, Energy Content Description: |Here provide Fix k&c for comparison, represent the case without controling (Fixed damping ratio according to 390 kip/in, i.e. keep the same damping even in the range of 39 kip/in) (Different from the other columns, the 30% point means bilinear sys with 30% damping, no change in k&c.) The GV*BS,fy=50 column: when GV*BS is negative provide 20% damping according to39 kip/in (FIX) when GV*BS is positive provide c% damping according to 390 kip/in (VARY). The yield force of bilinear system is 50 kips. I I I (30% point means when neg. GV*BS c=20% acc. to 39 kip/in; when Dos. GV*BS c=30% acc. to 390 kio/in) KE + SE (Bilinear 390, 39) Fix soft 20% (*.020) c(%) Fix k&c GV*BS,fy=50 GVBS,fy=300 V*BS,fy=50 VBS,fy=300 V*U,fy=50 V*U,fy=300 0 17288 1013i 708 1328 673 1007 728 5 7689 858 700 897 683 866 666 9_ 4759 842 714 716 744 918 782 1 5 2866 875 764 636 851 694 885 20 2171 _ 893 799 625 929 665 978 25 17941 900 831 559 9966 624 1046 30 1572 898 852 557 94481 590 1095 40 1335 877 895 605 1105 619 1101 50 12155 857 921 618 11631 692 1092 75 1074 823 953 670 1209 745 1258 100 1007 823 963 767 1239 813 1238 150 935 805 993 871 1149 781 1140 200 944 779 984 889 1110 875 1183 18000 T'' —---- - ---- ----- -' ——' —-- - 16000 --- --. —--- -... — - ----::-;::;,. j ix cjFix k&c < 14000 -\ —----- - ----—.. —---.c \. —, D- GV*BS,fy=50 12000' 1000 \''' GV*BS,fy=300 1 0000 T.. r. —--— r....-t- -- ------- 8000 - |-:. -,.. V*BS,fy=50 O 8000 t-.....I. — --- 6 0\ — A —--' i- i VV*BS,fy=300 j? 6 00 - --- --- ------ ---- ---- ---------- ------ U5 *,- -',V*U,fy=50 4000., * V*U,fy=300 2000 0 0 I I I, I O0 0 LO LO 0 LO 000 LO 000 CV cO C1 ~C LC c 0 LC 100 C / Cch I.1 1. 1 1 1.. I (I)-(A)-EKS3

Section 1, System A, Case 4, Energy Content Description: Here provide Fix k&c for comparison, represent the case without controling (Fixed damping ratio according to 390 kip/in, i.e. keep the same damping even in the range of 39 kip/in) (Different from the other columns, the 30% point means bilinear sys with 30% damping, no change in k&c.) t" The GV*BS,fy=50 column: when GV*BS is positive provide 20% damping according to390 kip/in(FIX) when GV*BS is negative provide c% damping according to 39 kip/in (VARY). The yield force of bilinear system is 50 kips. I I- _.. 1(30% point means when neg. GV*BS c=30% acc. to 39 kip/in; when pos. GV*BS c=20% acc. to 390 kip/in) I KE + SE (Bilinear 390, 39) Fix stiff 20% (020.') 7 c(%) Fix k&c GV*BS,fy=50 GV*BS,fy=300 V*BS,fy=50 V*BS,fy=300 V*U,fy=50 V*U,fy=300 0 17288 1362 756 648 1025 676 1036 5 7689 1195 760 654 975 672 1030 9 4759 1060 767 640 952 658 999 15 2866 966 7833 603 936 6581 991 20 2171 893 799 625 929 6651 978 25 1794 819 812 602 922 6461 968 30 1572 _ 718 820 603 904 6511 952 40 13351 653j 841 583 893 6231 919 501 12151 6081 852 5791 866 597j 886 75 1074 554 915 5791 901 544 846 100 10071 540 1007 576 972- 548 823 150 9351 592 1105 591 1070 667 920 200 9444 667 1147 587 _ 1178 702 995 18000 T — -------------- -- - 16000 -. —------ ------- --- 160 00-:':i=Fix k&c < 14000 -.C _.'''.' D i f: I I i — n-~I- GV*BS,fy=50 -5t 12000 -\ --—: —-1 —--------- --- ----- ------ ----- XE \ 1200 — GV*BS,fy=300 ( 10000 ------- - --- - 8o \,t --- V*BS,fy=50 0 8000 >'-' V*BS,fy=300 | 6000 --- — V --------------------------- ----—' - 6000: I,........ V*U,fy=50 4000 1 2 00 0 ------—...-.. —S * V*U,fy=300 2000 --- 0 O0 f 0) )L 0 0 ) 000 0 ) 0 00 o s cn s O o o o tn oC o o c- CJ Ce) tU NI 0 U) 0 CM 100 C / Ccl (I)-(A)-EKS4

L i I Section I, System B, Case 1, Base Shear Description: I I Here provide Fix k&c for comparison, represent the case without controling. (Fixed damping ratio and stiffness to 390 kip/in. Different from the other columns.) (The 30% point means the system has k=390 kip/in, c=30% critical damping; i.e. SDFS without control.) The V*BS(change) column: when V*BS is negative use k=39 kip/in, and c=5% acc. to 39 (FIX); when V*BS is positive use k=390 kip/in, and c=c% acc. to 390. (VARY) (The 30% point means when V*BS neg. k=39kip/in, c=5%; when pos. k=390kip/in, c=30%) I Base shear (Two stiffness 390, 39) Fix soft 5% (*.005) c(%) Fix k&c GV*BS V*BS V*U 0 3144 809 800 781 5__ 19761 609 785 753 9_____ 1465 501 725 746 151 1081 368 732 747 20_ l945 303 740 748 25 854 359 758 747 30 791 419 829 781 40 894 549 977 883 50 974 620 10651 1127 75 1095 1143 1209 1517 100 1154 1649 1238]- 1748 150 1205 1235 1251 2078 2001 1235 1603 1449 2407 3500 ----------- -------------------- 3000 --- - -------- -------'2500'~... 2500 — \ -------- - - -- - - - Fix k&c i 2000 t —- -- - -— \'-'' —------------- L, GV*BS 20 15 00.. __. —_ —.... —---------- GV*BS 1500 - --- - -- - - - V*, 5000 C /- c.-. —. —Q — 0 -— i —--' —------- i, —----— i -.. o LO Go u) 0 L) 0 0 0 LO 0 0 0 C'.. C,) 0 LO). 0a U) 0 100 C / Cch (I)-(B)-BS1

Section I, System B, Case 2, Base Shear L I I I Description: I I Here provide Fix k&c for comparison, represent the case without controling. (Fixed damping ratio and stiffness to 390 kip/in. Different from the other columns.) (The 30% point means the system has k=390 kip/in, c=30% critical damping; i.e. SDFS without control.) The V*BS(change) column: when V*BS is negative use k=39 kiD/in, and c=c% acc. to 39 (VARY) when V*BS is positive use k=390 kip/in, and c=5% acc. to 390. (FIX) (The 30% point means when V*BS neg. k=39kip/in, c=30%; when pos. k=390kip/in, c=5%) Base shear (Two stiffness 390, 39) Fix stiff 5% (005.*) c(%) Fix k&c GV*BS V*BS V*U 0 3144 661.5 769 769 5 1976 608.7 785 753 9 1465 535.9 805 743 15 1081 400.5 765 757 20 945 292.3 801 728 25 854 249.7 795 737 30 791 256.5 808 762 40 894 290.41 752 745 50 974 318.4 788 773 75 1095 371.6 743 780 100 1154 448.3 777- 788 150' 1205 632.8 742 684 200 1235 779.4 742 724 3500 - - 3000 ---- ------------ - --- 25.00 _. Fix k&c. 2000 —.. i;c n i i50 - - - - - - - -- - - - - - - - ----- - - GV*BS 1000 \ -- ------. c 0 fI I I I - I 2 500 - -------- - ----------------- - -- Ol020000- OJ 0. CO,- )..0 0 L0 0 1500 tLo LO —-L —- -- ----- ----- I C / 10 0 0 t ~~~~~ — q - ----.100 C / Ccl I i (I)-(B)-BS2

I Section I, System B, Case 3, Base Shear Description: I I I Here provide Fix k&c for comparison, represent the case without controling. (Fixed damping ratio and stiffness to 390 kip/in. Different from the other columns.) (The 30% point means the system has k=390 kip/in, c=30% critical damping; i.e. SDFS without control.) The V*BS(change) column: when V*BS is negative use k=39 kip/in, and c=20% acc. to 39 (FIX); when V*BS is positive use k=390 kip/in, and c=c% acc. to 390. (VARY) -~~~sps — I_ (The 30% point means when V*BS neq. k=39kip/in, c=20%; when pos. k=390kip/in, c=30%) L.L Base shear (Two stiffness 390, 39) Fix soft 20% (*.020) c(%) Fix k&c GV*BS TV*BS V*U 0 3144 338.5 803 806 5 1976 292.3 801 728 91 1465 271.6 747 724 15 1081 255.8 761 707 20 945 245.5 790 698 25 854 271.3 844 700 30 791 355.8 877 737 40 894 461.1 969 853 50 974 568.8 1017 1068 75 1095 975.8 11101 1467 1001 11 54 1267.4 1147- 1696 1501 1205 1981.1 1204 2028 200! 1235 2472 12541 2353 3500 T —---- ----- 250f00..... 3000 -—, -,, --, --—, -—. t:00 I I - 2500 \:F -- * Fix k&c X 2000 -- -- ---------- GV*BS —-- --.- - __ Q -- *BS a 1500 ------------------ V*BS 1000 _ 5oo00. —-------— " — -------- — _ - --- --- ----- 500 —0 -I —-_- -- - -i- -i- *-* o oCM o 100 C / Cch (I)-(B)-BS3

Section I, System B, Case 4, Base Shear Description: Here provide Fix k&c for comparison, represent the case without controling. (Fixed damping ratio and stiffness to 390 kip/in. Different from the other columns.) (The 30% point means the system has k=390 kip/in, c=30% critical damping; i.e. SDFS without control.) The V*BS(change) column: when V*BS is negative use k=39 kiD/in, and c=c% acc. to 39 (VARY) when V*BS is positive use k=390 kip/in, and c=20% acc. to 390. (FIX) (The 30% point means when V*BS neg. k=39kip/in, c=30%; when pos. k=390kip/in, c=20%) Base shear (Two stiffness 390, 39) Fix stiff 20% (020.*) c(%) Fix k&c GV*BS V*BS V*U 0 3144 335.7 781 781 5 1976 302.8 740 748 9 1465 341.7 750 752 1 5 1081 300.2 785 719 20 945 245.5 790 698 251 854 234.3 799 697 30 791 252.3 812 707 40 894 358.4 812 663 50 974 388.3 808 664 751 1095 378.6 816 603 1001 1154 455.3 817 678 1501 1205 638.8 816 633 200t 1235 783.6 804 598 I....... ~... I 3500 _ -- ---- —..._ — __ _ _.. _. ____.. _.. 20- \ i i: — _-!Fix k&c i - * ~, * *,, i...: 2 000 t —- ------.. -25 00.... I r -. \ - - Fix k&c \ C',',,''':'- 1 0-E 0r-^ 5 G. V*BS 1000 ----------- V*- _ t^ —-I- ----- ------ ---- ----------- 0 0 o L Q U) I. 0 1 0 0 0 LI 0 0 0 N CI c 0 C) ". N CD0 U) - 100~~~~~o.. c J 100 C / Ccl (I)-(B)-BS4

L I Section I, System B, Case 1, Displacement Description: I.. Here provide Fix k&c for comparison, represent the case without controling. (Fixed damping ratio and stiffness to 390 kip/in. Different from the other columns.) (The 30% point means the system has k=390 kip/in, c=30% critical damping; i.e. SDFS without control.) The V*BS(change) column: when V*BS is negative use k=39 kip/in, and c=5% acc. to 39 (FIX); when V*BS is positive use k=390 kip/in, and c=c% acc. to 390. (VARY) (The 30% point means when V*BS neg. k=39kip/in, c=5%; when pos. k=390kip/in, c=30%),,,, ___~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ P. -- - - - -. - - - - - - -. - - - Displacement (Two stiffness 390. 39) Fix soft 5% (*.005) t c(%) Fix k&c GV*BS V*BS V*U 0 8.06 9.391 2.596 2.615 5 5.041 8.631 1.918 2.451 9 3.682 8.175 1.715 2.236 15 2.683 7.366 1.639 1.953 20 2.259 6.591 1.486 1.911 251 1.935 5.818 1.369 1.541 30 1.684 5.11 1.341 1.508 40 1.33 4.275 1.285 1.432 50 1.119 4.383 1.125 1.279 75 0.876 4.578 1.147 1.087 1001 0.747 4.677 0.838 — 0.994 1501 0.572 4.442 0.615 0.794 2001 0.456 3.09 0.561_ 0.662 10 -...- -.- -.I -—. — - - 190 -" —-------------------------- --- --- ----- ------- ---------------..,. 7 0E'::::' I I I: I " 7 ll.. I.-' Fix k&c —'t t —...... GV*BS 3 ------- -- ----------- --- T —----- ---- -- - oD Lo 0 LO 0 LO 0 0 0 LO 0 0 - -—, —— 0 LO 0 100 C -- V*BS 1 \ i I I I I I I i (I)-(B)-DISP1

Section I, System B, Case 2, Displacement Description: l IHere provide Fix k&c for comparison, represent the case without controling. (Fixed damping ratio and stiffness to 390 kip/in. Different from the other columns.) (The 30% point means the system has k=390 kip/in, c=30% critical damping; i.e. SDFS without control.) The V*BS(change) column: when V*BS is negative use k=39 kip/in, and c=c% acc. to 39 (VARY) when~~~~~ v*Si -stv'uek30kpi, an ~c5 c. to 30. (FX j when V*BS is positive use k=390 kip/in, and c=5% acc. to 390. (FIX) (The 30% point means when V*BS neg. k=39kip/in, c=30%; when pos. k=390kip/in, c=5%) Displacement (Two stiffness 390, 39) Fix stiff 5% (005.*) c(%) Fix k&c GV*BS V*BS V*BS V*U 0 8.06 9.615 2.479 2.48 5__1 5.041 8.631 1.91 8 2.451 9 ____ 3.682 7.826 2.319 2.329 1 5 2.683 6.66 1.627 2.4 20 2.259 5.804 2.2 2.176 25 1.935 5.097 1.866 2.245 30 1.684 4.489 2.218 2.306 40 1.33 3.604 1.627 2.174 50 1.119 3.007 1.794 2.182 75 0.876 2.508 1.627 2.04 100 0.747 2.28 2.059- 2.009 150 0.572 1.556 1.914 1.743 200 0.456 1.424 1.941 1.912 97 - - - - - - — L - - 7 I I -I.- Fix k&c _ 9____________ 6 --------- - - -------------- -- ---- 7 t - - - - - - -- - - - - - - - - - - - - -- -.... --,E, 5 \ I, \, <~ GV*BS 5 4._'-,,X,,,,,: o V*U: - 2 i ------ --- _ 1,,,.,,, -, _.... -— _-_:iZ~ - -_.... * _,,,, ------ 0 -- O -— i — O — - O O O O L —------ O O O ov L 0) C) LO 0 LO) 0 0 L O C0 CJ C'J C1T T-) C 0 100 C / Ccl I... - I I i i (I)-(B)-DISP2

Section I, System B, Case 3, Displacement Description: Here provide Fix k&c for comparison, represent the case without controling. (Fixed damping ratio and stiffness to 390 kip/in. Different from the other columns.) (The 30% point means the system has k=390 kip/in, c=30% critical damping; i.e. SDFS without control.) The V*BS(change) column: when V*BS is negative use k=39 kip/in, and c=20% acc. to 39 (FIX); when V*BS is positive use k=390 kip/in, and c=c% acc. to 390. (VARY) (The 30% point means when V*BS neg. k=39kip/in, c=20%; when pos. k=390kip/in, c=30%) Displacement (Two stiffness 390, 39) Fix soft 20% (*.020) c(%) Fix k&c GV*BS V*BS V*U 0 8.06 6.037 2.492 2.535 5 5.041 5.804 2.2 2.176 9 3.682 5.679 1.469 2.035 1 5 2.683 5.472 1.631 1.91 20 2.259 5.214 1.218 1.753 25 1.935 4.957 1.171 1.516 30 1.684 4.669 1.385 1.411 401 1.33 4.103 1.097 1.311 501 1.119 4.041 1.023 1.254 75i.. 0.876 4.45 0.91 1.048 100 0.747 4.705 0.919_ 0.973 150 0.572 4.452 0.582 0.781 2001 0.456 4.536 0.698 0.647 _0__________ I ________ 9 8 - - - - - - - - - - - - - - - - - - - _11 _ -7 - - -L- - - - - - - - --- - -- -- - -- - - r - L- - -L - - -,L _ *- 6' 1 I --- --- Fix k&c _ \ i "" ~ "" -- @ ov_ Co E5 VU \, I I I I (0 — k-1 CJ C\ 1 C I f r 0 I) ~ 4; —— i —-i —i-i- i- -\ —........V*BS...., x 3,,. V U i!. 1 I t I I I, I t t I I I I 100 C / Cch II I I I (I)-(B)-DISP3

Section I, System B, Case 4, Displacement I I I L Description: _ Here provide Fix k&c for comparison, represent the case without controling. (Fixed damping ratio and stiffness to 390 kip/in. Different from the other columns.) (The 30% point means the system has k=390 kip/in, c=30% critical damping; i.e. SDFS without control.) The V*BS(change) column: when V*BS is negative use k=39 kip/in, and c=c% acc. to 39 (VARY) ~-A when V*BS is positive use k=390 kip/in, and c=20% acc. to 390. (FIX) (The 30% point means when V*BS neg. k=39kip/in, c=30%; when pos. k=390kip/in, c=20%) Displacement (Two stiffness 390, 39) Fix stiff 20% (020.*) c(%) Fix k&c GV*BS V*BS V*U 0 ~8.06 6.733 2.038 2.404 ~5 5.041 6.591 1.486 1.911 9 3.682 6.302 1.6 1.99 1 5 2.683 5.755 1.352 1.874 20 2.259 5.214 1.218 1.753 25 1.935 4.632 1.83 1.828 30 1.684 4.232 1.583 2.009 40__. — 1.33 3.441 1.509 1.765 50 1.119 2.867 1.62t 1.76 75 0.876 2.383 1.305 1.518 100 0.747 2.07 1.306 1.715 150 0.572 1.6 1.305 1.5 200 0.456 1.24 1.34 1.712 9 T- - - - — "- " - - 1.2 8,. i,..,-. L L —- L-..-.. -...... -....-...-.. T I, *, *, *, 87 -- L — > — -— L —-------- -- L —------ -- -- ~ 4 ------------------ V*BS 1 I —- r- --- ------------- I- - -- - - ---------- H Q i,,, *, —, \*D -- - - - _- - - - - - - - - L — - --- - -- - - - - - - - - r --- _ — V_ _ _ o-~~c cm q) iI U) - C0 I 0 100 C / Ccl 100 C / Col (I)-(B)-DISP4

Section I, System B, Case 1, Energy Input Description: I I -... Here provide Fix k&c for comparison, represent the case without controling. (Fixed damping ratio and stiffness to 390 kip/in. Different from the other columns.) (The 30% point means the system has k=390 kip/in, c=30% critical damping; i.e. SDFS without control.) The V*BS(change) column: when V*BS is negative use k=39 kip/in, and c=5% acc. to 39 (FIX); when V*BS is positive use k=390 kip/in, and c=c% acc. to 390. (VARY) (The 30% point means when V*BS neg. k=39kip/in, c=5%; when pos. k=390kip/in, c=30%) Energy Input (TWO stiffness 390, 39) FIX soft 5% (.005) I c(%) Fix k&c GV*BS V*BS V*U 0 17288 2089 5654 5397 51. 13023 1796 6885 5795'9 " 10868 1638 7207 6248 __151 ____ 10150 1380 7472 6541 20, 9937 1150 7643 6841 25! 9634 946 7703 7172 301 9326 782 7758.7377 40' 8759 730 7743 7470 50 8237_ 715 7731 7735 75 7138 1045 7089 8003 100, 6277 1099 6613- 7938 150 5042 _10271 5590 7062 200 4210 638 4637 6133 0.__. l ________._______6__________63_. 18000 T —- --- --------,,,,,,,,:, i l 16000 -... -. - 14000- ----, ------ I,.... T 12000 t —-- ~ — ------------- ---- ----------- ------ Fix k&c "S 14000,0. —-- -L___,,.- _- _ _. -— _-__ - -- -L -— _- _ _L__GV*B 12000 Fixk&c -- 1 000-0 _: ___.-: —*-:iT-.-..- - - - - - ----- - ------ - - GV*BS C 600-0 I- --- ------- - O-VU Ul i, 4000 ----- - - ------- V* - 6000 o V*, 4000 2000 - -: ------------- - --- ------ - -- - --- 2 0 0 0_ C-~~_:Q_:.._-. —]....:i^Q_-_.....8-~-............. 0 I, oL) 0) I) 0C LO 0 0 0 L ) 0 0 0 - Cm C' C' ) t tO- 0 U) tO 100 C / Cch I~I I I..I... 1 7 1 I I I I I I (I)-(B)-EI 1

Section I, System B, Case 2, Energy Input Description: I Here provide Fix k&c for comparison, represent the case without controling. (Fixed damping ratio and stiffness to 390 kip/in. Different from the other columns.) 7 (The 30% point means the system has k=390 kip/in, c=30% critical damping; i.e. SDFS without control.) The V*BS(chanae) column: when V*BS is neaative use k=39 kin/in. and c=c% acc- to 39 (VARY) when V*BS is positive use k=390 kip/in, and c=5% acc. to 390. (FIX) (The 30% point means when V*BS neg. k=39kip/in, c=30%; when pos. k=390kip/in, c=5%) Energy Input (Two stiffness 390, 39) Fix stiff 5% (005.*) c(%) Fix k&c GV*BS V*BS V*U 0 17288 2945 5898 5727 5 13023 3120 6885 5795 9 10868 3260 7444 6014 1 5 10150 3541 7788 5809 20 9937 3819 7639 5982 25 9634 4093 7624 5922 3 0 9326 4289 7615 5956 40 8759 4562 7626 6030 50 8237 4816 7580 6180 75t 7138 5377 7518 6723 100 6277 5788 7435' 6722 150 5042 6089 7283 6593 200 4210 6282 7082 6516 18000 --- ---------------- ------ 16 00 0'T - - - - - - - - - -- - - - -: —--, 14000..-. <I~~~I 12000 ----------- - - - --- Fix k&c 10000 - ----: ---- - —'-' —-—. — —' —-- -V*BS 12000 1 - - - - -VBS -. Fix k&, 6000 T —--—': —- ----— 0-: —- --- ---. *.B, 8000 --- - -- -... -.:::. —:. V:BS 2000 {-V —------------------- II I,......I I I > o )0) o) U) 0 > 0 ) 0 0 0 C 100 C I 0 U) c 100 C / Ccl (I)-(B)-E12

Section I, System B, Case 3, Energy Input Description: I Here provide Fix k&c for comparison, represent the case without controling. (Fixed damping ratio and stiffness to 390 kip/in. Different from the other columns.) (The 30% point means the system has k=390 kip/in, c=30% critical damping; i.e. SDFS without control.) The V*BS(change) column: when V*BS is negative use k=39 kip/in, and c=20% acc. to 39 (FIX); when V*BS is positive use k=390 kip/in, and c=c% acc. to 390. (VARY)(The 30% point means when V*BS neg. k=39kip/in, c=20%; when pos. k=390kip/in, c=30%) Energy Input (Two stiffness 390, 39) Fix soft 20% (*.020) c(%) Fix k&c GV*BS V*BS V*U 0 172881 3289 5634 5622 5 13023 3819 7639 5981 9 10868 3870 7839 6270 151 10150 3932 7589 6547 20j 9937 3975 7601 6912 25 9634 3999 7543 7067 30 9326 4077 7358 7199 401 8759 4032 7152 7407 50 8237 3941 6744 7568 75 7138 4582 6265 7940 1001 6277 4709 57221. 7794 150 5042 4873 4709 6965 200 4210 4671 4085 6042 18000 T 16 000 I 16000 --- ------------------ -. —-. 8 14000 i-r — I-s — ---- VB'S,',i —-"'-' —_....' —-' — < 14000 12000 ---—'- ----—. —- -------- ----- ------ Fixk&c 00 CI Cch — 1 6000 g- -_- ----------------— - — >_ - l —, — > — V*U _ U::: 1 [1 —s 4 0 0 0 T - — C-: —!- — ~ <}- -.: —, —-- -, —-...... I I I I I I uo i i I I I I i I i I i~ ~ IriII I~ ~ ~ ~~~~~~~~~~~.' I- OJ I I _~~~ (I)-(B)-E13

Section I, System B, Case 4, Energy Input I Description: Here provide Fix k&c for comparison, represent the case without controling. (Fixed damping ratio and stiffness to 390 kip/in. Different from the other columns.) (The 30% point means the system has k=390 kip/in, c=30% critical damping; i.e. SDFS without control.) The V*BS(change) column: when V*BS is negative use k=39 kip/in, and c=c% acc. to 39 (VARY) when V*BS is positive use k=390 kip/in, and c=20% acc. to 390. (FIX) I (The 30% point means when V*BS neg. k=39kip/in, c=30%; when pos. k=390kip/in, c=20%) Energy Input (Two stiffness 390, 39) Fix stiff 20% (020.*) c(%) Fix k&c GV*BS V'BS V*U 0 17288 3277 6721 6554 5 13023 3459 7643 6841 _9 10868 3616 7697 6696 151 101501 3747 77161 6765 20 ____ 9937_ 3975 676016912 25 9634 4119 7492 6619 30 9326 4243 7479 6749 40 8759 4416 7400 6621 501 8237 4594 7365 6654 75 7138 5110 7229 6623 100 6277 5544 7267 -6675 150 5042 6123 7239 6666 2001 42101 _ 6429. 7283 6488 I! I I I _ _________...._.,., 18000 T —------ -. —------ - - 16000'5 10000 ---— _a-.I —--------- -Q O ----- - GV*BS 1 0000 —.-.._ —__-_. __. -.. —. - GV*BS 86000; —--- ------ - -— * V*BS Q) 6000. V*U i! i ~! i - i! ii 4000 ------- -- -- -- -------—, —-, —--- 0,,, -, i,,,i - i t I 2000 I 0,. i i,, i,, oUL 0) LO0 LO 0. 0 0 0 LO 0 0 0 _ O - CJ 1- 1 1 1 1'. 01 t) 0 <- 9- CCM 100 C / Ccl I,t, 7 i (I)-(B)-E14

Section I, System B, Case 1, Energy Content Description: I I Here provide Fix k&c for comparison, represent the case without controling. (Fixed damping ratio and stiffness to 390 kip/in. Different from the other columns.) (The 30% point means the system has k=390 kip/in, c=30% critical damping; i.e. SDFS without control.) The V*BS(change) column: when V*BS is negative use k=39 kip/in, and c=5% acc. to 39 (FIX); when V*BS is positive use k=390 kip/in, and c=c% acc. to 390. (VARY) (The 30% point means when V*BS neg. k=39kip/in, c=5%; when pos. k=390kip/in, c=30%) KE +SE (Two stiffness 390, 39) Fix soft 5% (*.005) C(%) Fix k&c GV*BS V*BS V*U 0 17288 3239 1113 1130 5 7689 3120 1194 1 094 9 4759 3099 1133 1055 15 2866 3326 1076 1019 20 2171 3459 10411 1055 251 1794 3530 1035 1110 30 1572 3534 1013 1078 40 1335 3471 01017 996 50 21215 3461 949 955 751 1074 4197 964 929 100' 1007 4325 877 — 909 150' 935 4682 948 917 200 __944 4281 1007 974 18000.......,.... —-... —-—.. 1 8000 T 16000 —, ------ - 14000 ---- ---- ----- - 12000 - ----------- ------ Fix k&c I 10000 t —\ —-- ------ --- -— 1 — -—.- ---- --- -— 1 -D GV*BS O i - \ 8 8000 ---, —-------- -— V —-------- --- ------ V*BS 6000 --- v 64000 ---- - 240 0 0 + —-—, —-, —-. —-- --' — _ 2000 I I I I i I i i I i i i o 0 O L ) 0 L O 0 0 0 I 0 0 0o 1 C C C O I" 0 L O 0 1. CMJ 100 C / Cch (I)-(B)-EKS1

I I I I Section I, System B, Case 2, Energy Content Description: I. I Here provide Fix k&c for comparison, represent the case without controling. (Fixed damping ratio and stiffness to 390 kip/in. Different from the other columns.) (The 30% point means the system has k=390 kip/in, c=30% critical damping; i.e. SDFS without control.) The V*BS(change) column: when V*BS is negative use k=39 kip/in, and c=c% acc. to 39 (VARY) when V*BS is positive use k=390 kip/in, and c=5% acc. to 390. (FIX) (The 30% point means when V*BS neg. k=39kiD/in. c=30%: when DOS. k=390kiD/in. c=5%) KE +SE (Two stiffness 390, 39) Fix stiff 5% (005.*) c(%) Fix k&c GV*BS V*BS V*U 0 17288 2106 1068 1067 5 7689 1796 1194 1094 9 4759 1566 1144 1116 1 5 2866 1268 1203 1100 201 2171 1080 1159 1157 25 1794 957 1182 1117 30 15721 868 11651 1083 401 1335 750 1161 1103 501 1215 680 1182 1173 75f 1074 569 1184 1298 100! 1007 529 11641 1211 1501 935 519 1150 800 2001 944 581 1192 1000 18000 T- --------------- -- ----- I i I i I I! I,,,,,.,.. 16000- --- -- ------ --------. < 14000 - -----. C \ I I I I I I j __ 12000 - - --- -- Fix k&c ~ \ - 1000 O I \I 0 8000 0-~ ------ -- - ----- *- G —-- ---- V*BS UJ -- - ------ V*BS I - I i i: IL 4 6000 V*u 4000 - - 4000 -- ----- ---- - - --- - - - ------- ---- --------- 100 C / Ccl F F I F F I I (l)-(B)-EKS2

Section I, System B, Case 3, Energy Content Description: Here provide Fix k&c for comparison, represent the case without controling. (Fixed damping ratio and stiffness to 390 kip/in. Different from the other columns.) (The 30% point means the system has k=390 kip/in, c=30% critical damping; i.e. SDFS without control.) The V*BS(change) column: when V*BS is negative use k=39 kip/in, and c=20% acc. to 39 (FIX); when V*BS is positive use k=390 kip/in, and c=c% acc. to 390. (VARY) I (The 30% point means when V*BS neg. k=39kip/in, c=20%; when pos. k=390kip/in, c=30%) KE +SE (Two stiffness 390, 39) Fix soft 20% (*.020) c(%) Fix k&c 72GV'BS V*BS __V*U 0 17288 1160 1 177 1160 5 7689 1080 1159 1157 9 4759 1037 1207 1072 1 5 12866 973 1061 1064 20 1 2171 900 1119 1033 25 1794 832 1081 1063 30 1572 762 1003 1081 40 1335 728 985 1004 50 1215 753 1035 975 75_ 1074 895 929 933 00 100 1007 939 922 907 150 935 1004 957 882 200 944 1044 1009 970 I I 18000 T —------ 16000 ---- ----- ----- ----------- - < 14000 } 12000 -, Fix k&c = 12000 r - - - - - ~ 10000 I - -G —- GV*BS O 8000 - ---------------- ------ ---- -- V*BS 4 000 - --- -- - ----- I - 1 _' B I 0 o2 I.' 0 0L 0 C 0 LO C, 0 _ c cm c' O N" 0 LO 0o _...... I...... - C. 100 C / Cch I (I)-(B)-EKS3

Section I, System B, Case 4, Energy Content L Description: Here provide Fix k&c for comparison, represent the case without controling. (Fixed damping ratio and stiffness to 390 kip/in. Different from the other columns.) (The 30% point means the system has k=390 kip/in, c=30% critical damping; i.e. SDFS without control.) The V*BS(change) column: when V*BS is negative use k=39 kip/in, and c=c% acc. to 39 (VARY) when V*BS is positive use k=390 kip/in, and c=20% acc. to 390. (FIX) r (The 30% point means when V*BS neg. k=39kip/in, c=30%: when Dos. k=390kio/in. c=20%) KE +SE (Two stiffness 390, 39) Fix stiff 20% (020.*) c(%) Fix k&c GV*BS V*BS V*U 0 17288 1160 1046 1052 5 7689 1149 1041 1055 9,_. 4759 1097 1041 1010 151 2866 996 1087 1018 20 _' 2171 900 1119 1033 25 1794 807 1033 1053 30 1572 789 1042 1039 40 1335 711 1059 1070 50 1215 650 1050 1082 75 1074 531 1063 1077 100 1007 486 1062 1076 150 935 5521 1065 1008 2001 944 592 1042 852 18000 Tr 16000 ----- -—, —---—, — - II I 7 I I 12000 ----- - I...x C _',, i,,,,,, = i 10000 -1- -------- -.-J..___ —-— ___,.,.. -- GV*BS -! - \ o 8000.... ------.... 64000 ----------- ---------------------- V*BS L m I C M C n - 62000 - — ), O _ _ _ L- -j_-_'_ _ _ _ __ _' _ V U _ 4 4100 C O IZ3 0) U) C) U) 0 0 0 ) 0 0 0, N~ 04 C) ~ U N 0 U) 0 100 C / Ccl = (I)-(B)-EKS4

Section I, System C, Case 1, Base Shear Description: Here the stiffness always the same 390 kip/in. Here provide Fix k&c for comparison, represent the case without controling. (Different from the other columns, the damping ratio is always the same) I (The 30% point means the system has k=390 kip/in and c=30% critical. i.e. SDFS without control.) The V*U(same) column: when V*U is negative c=5%(FIX); when positive c=c%(VARY). (The 30% point means when V*U is neg. c=5%, k=390; when pos. c=30%, k=390.) Base shear (Same stiffness 390) Fix soft 5% (*.005) c(%) Fix k&c GV*BS V*BS V*U 0 3144 2357 2505 2481 5 1976 1976 1997 1997 91..L. 1465 1757 1635 1664 1 5 1081 1517 1267 1325 20 945. 1372 1180 1230 25 854 1274 1117 1168 30 791 1218 1051 1130 40 894 1124 1167 1242 50 974 1118 1295 1410 75 1095 1552 1460 1637 100 1154 1862 1515 1796 150 1205 2558 1645 2118 200 1235 3331 1720 2207 3500 -- - - -- - - - 3000 ----------- -------------- 2500- f S- I I I t\ / — ~ Fix k&c r 0 -GV*BS. 2300 ---- ---------—, -,....-... -.... GV*BS _ ooo....._._.. ^^^^^11-G V ---------------- _ O - I I,' I I I, o,?-.... 0 O,, 0 0 0 0 -0 ~ ---— l —---------------— i 500' _ t i CM C: l, z, O, o 0 LO M I. 0 LO 10 C CD0 ) I. 0 — c'J C'J C) ~ L.O N 5 0.O 0 100 C / Cch (I)-(C)-BS1

Section I, System C, Case 2, Base Shear Description: Here the stiffness always the same 390 kip/in. Here provide Fix k&c for comparison, represent the case without controling. (Different from the other columns, the damping ratio is always the same) I (The 30% point means the system has k=390 kip/in and c=30% critical. i.e. SDFS without control.) The V*U(same) column: when V*U is negative c=c%(VARY); when positive c=5%(FIX). (The 30% point means when V*U is neg. c=30%, k=390; when pos. c=5%, k=390.) Base shear (Same stiffness 390) Fix stiff 5% (005.*) c(%) Fix k&c GV*BS V*BS V*U 0 3144 2619 2413 2413.5 1976 1976 1997 1997 9 1465 1636 1752 1703 151 1081 1291 1450 1353 20] 945 1166 1305 1158 25 854 1116 1238 1067 301 791 1096 1192 972 40 894 1151 1084 830 50 _974 1285 977 768 75 1095 1138 1311 920 100 1154 1620 1581- 1027 150 1205 1922 1912 848 200 1235 2191 2004 827 3500 - -- i []. I I I. I, 3 000 -. — - - - - - -- - - - - 3000 2500. -\\ -- Fix k&c -~.,, i,,,,. 5 2000 - - -. - - - - - - -..- - - GV*BS 1500. —---------- -- V*BS 5 0,::.,-,- - -,- -, —..., —-- - O - I I, I I I I I I I I 500 -..... 0 I! I,,, I I'N cm C C' U) "- 0 L O 0 100 C / Ccl [.... 1.... 1 (I)-(C)-BS2

Section 1, System C, Case 3, Base Shear Description: Here the stiffness always the same 390 kip/in. Here provide Fix k&c for comparison, represent the case without controling. (Different from the other columns, the damping ratio is always the same) (The 30% point means the system has k=390 kip/in and c=30% critical. i.e. SDFS without control.) The V*U(same) column: when V*U is negative c=20%(FIX); when positive c=c%(VARY). (The 30% point means when V*U is neg. c=20%, k=390; when pos. c=30%, k=390.) Base shear (Same stiffness 390) Fix soft 20% (*.020) c(%) Fix k&c GV*BS V*BS V*U 0 3144 1289 1484 1318 5 1976 1166 1305 1158 91 1465 1092 1168 1061 r 1 5 1081 1008 1022 969 20 9451 944 954 954 251 854 888 896 938 301 791 838 845 920 40 ____894_ _770j 9741 1086 50 974 788 10681 1261 75 1 0951 897 1198 1508 1001 1 154 1 199 1236- 1644 150 1205 1748 1256 2012 2001 1235 2292 1257 2183 3500 - -- 3000 --------- --- --- -,,,,,, 2500- Fix k&c g 2000 T — i —- --- --- - - --- - --- — f - —: - Q2000 T t —............................, GV*BS 1500 ----------------- V*BS m:fI I IT I' ~ vu V*U 500 500 ------------------- -------- ------- 5 I,,100 C Cch 0 143 (') 13 ) IZ') 0 0 ) 0 o3 o 100 C / Cch (I)-(C)-BS3

Section I, System C, Case 4, Base Shear Description: Here the stiffness always the same 390 kip/in. Here provide Fix k&c for comparison, represent the case without controling. (Different from the other columns, the damping ratio is always the same) (The 30% point means the system has k=390 kip/in and c=30% critical. i.e. SDFS without control.) The V*U(same) column: when V*U is negative c=c%(VARY); when positive c=20%(FIX). (The 30% point means when V*U is neg. c=30%, k=390; when pos. c=20%, k=390.) Base shear (Same stiffness 390) Fix stiff 20% (020.*)_ c(%) Fix k&c GV*BS V*BS V*U 0 3144, 1740 1325 1326 5 1976 1372 1180 1230 9 1465 1175 1085 1146 15 1081 1016 996 1038 20 945 944 954 954 25 854 910 918 883 30 791i 894 879 821 40 8941 964 826 _784 50 974 1072 773 863 75 1095 1121 733 992 100 11541 1298 822 1054 150 1205 1750 1063 793 200 1235 2209 1809 848._. 1 _.....,..._.._ _.. 3500 - --.,.,.,!,!, i! ~: s i,,, 3000 --- ---- -- -- --.. - I — - L.2500 — \ —---- - ------------------- X._Q- \.,F*- Fix k&c 2000 -- ------- -- - L V*BS ~~ 2000....... i I GV*BS a,,,1500 \ -------------- -------- -- V*BS m- n- -o?^ O V*U 500 ---- -- ---- --- --- --- --- -- a —-----— 1 1000- -x-~-~ t t 1 Q, - 500 -,,..,,,, 1 C, O, I! I I1 I I Ic - 100C/Ccl H F~~~~~~~~~~C (I)-(C)-BS4

Section 1, System C, Case 1, Displacement Description: Here the stiffness always the same 390 kip/in. Here provide Fix k&c for comparison, represent the case without controling. (Different from the other columns, the damping ratio is always the same) (The 30% point means the system has k=390 kip/in and c=30% critical. i.e. SDFS without control.) The V*U(same) column: when V*U is negative c=5%(FIX); when positive c=c%(VARY). (The 30% point means when V*U is neg. c=5%, k=390; when pos. c=30%, k=390.) Displacement (Same stiffness 390) Fix soft 5% (*.005) 1 c(%) Fix k&c GV*BS V*BS V*U 0 8.06 6.012 6.431 6.365 5 5.041 5.041 5.094 5.095 9 3.682 4.48 4.112 4.187 15 2.683 3.8681 3.13 3.278 20 2.259 3.51 2.798 2.916 25 1.935 3.253 2.526 2.639 30 1.684 3.111 2.257 2.427 40 1.33 2.87 1.88 2.047 50__ 1.1 1 9 2.646 1.593 1.74 75__ 0.876 2.157 1.259 1.407 100i 0.747 2.119 1.049- 1.189 150 0.572 2.151 0.764 0.899 200 0.456 2.1 75 0.594 0.719 9......,,, 7 - --' — -- -- -, —, -- -—, —- -—, —-- -—. -',\ —---—, ----—:,,, -----—, -—,, —---- - Fix k&c ~) I I I I _D 5 + \4 - - - -r-~ -.,.. -,,,. GV*BS..,.,,,,,.,V*BS -- 0 I I II I I 5 - - - - - - -- - - - - - - - - - - - - - - - - - - - - o L O 0 LO 0 LO 0 0 0 uLO 0 c cmJ Cn) l LOu N- LC-) O cmJ 100 C / Cch - (I)-(C)-DISP1

Section I, System C, Case 2, Displacement Description: Here the stiffness always the same 390 kip/in. Here provide Fix k&c for comparison, represent the case without controling. (Different from the other columns, the damping ratio is always the same) (The 30% point means the system has k=390 kip/in and c=30% critical. i.e. SDFS without control.) The V*U(same) column: when V*U is negative c=c%(VARY); when positive c=5%(FIX). (The 30% point means when V*U is neg. c=30%, k=390; when pos. c=5%, k=390.) Displacement (Same stiffness 390) Fix stiff 5% (005.*) c(%) Fix k&c GV*BS V*BS V*U 0 8.06 6.717 6.155 6.155 5 5.041 5.041 5.094 5.095 9 3.682 4.113 4.469 4.347 15 2.683 3.15 3.7 3.453 20 2.259 2.756 3.3281 2.954 25 1.935 2.37 3.1621 2.725 30 1.684 2.3351 3.044 2.482 40 1.33 2.049 2.766 2.118 50o 1.119 1.82 2.494 1.935 75_ 0.876 1.358 2.211 1.904 100 0.747 1.315 1.925- 1.645 150 0.572 1.128 2.019 2.159 200 0.456 1.097 1.675 2.102 8 -- ---- ------— r —-r —-r —-r —-r —-r —-r —9 L I L - - - --- ------—;- -—; —--— Fix k&c \,....,...... -5 - -- r --- —'- r'- --- GV*BS - e; GV*BS 1 -------------------------—, - L -,, ----------------- ------,,, O - I I I rI I "I I - V o ) LO 0 0 o 0 0 0 o u) 0 0 0 c, CJ ) I U) I" 0 L.) 0 100 C / Cci ~...... (I)-(C)-DISP2

Section I, System C, Case 3, Displacement Description: Here the stiffness always the same 390 kip/in. Here provide Fix k&c for comparison, represent the case without controling. (Different from the other columns, the damping ratio is always the same) (The 30% point means the system has k=390 kip/in and c=30% critical. i.e. SDFS without control.) The V*U(same) column: when V*U is negative c=20%(FIX); when positive c=c%(VARY). (The 30% point means when V*U is neg. c=20%, k=390; when pos. c=30%, k=390.) Displacement (Same stiffness 390) Fix soft 20% (*.020) c(%) Fix k&c GV*BS V*BS V*U 0 8.06 3.046 3.807 3.382 5 5.041 2.756 3.328 2.954 9 3.682 2.465 2.941 2.672 1 5 2.683 2.406 2.542 2.413 20 2.259 2.259 2.282 2.283 25 1.935 2.127 2.03 2.126 30 1.684 2.01 1.808 1.97 40B 1.33 1.807 1.463 1.694 50i 1.119 1.719 1.252 1.457 75 0.876 1.63 0.951 1.251 100 0.747 1.575 0.814 1.088 1501 0.572 1.487 0.617 0.8329 200j 0.4561 1.432 0.49 0.676..9..', - - -,, - - - 8 ------—'" —----- ---- --- 6 - ---------- --------— Fix k&c C) aS 4 --- - -- --------- — 6_., --------' —--- - V*BS 23 " —-' —-------------......- V*U 1 --- -—, —----------------- --... 100 C / Cch 0 ~~~I I I ICch (I)-(C)-DISP3

Section I, System C, Case 4, Displacement Description:. Here the stiffness always the same 390 kip/in. Here provide Fix k&c for comparison, represent the case without controling. (Different from the other columns, the damping ratio is always the same) (The 30% point means the system has k=390 kip/in and c=30% critical. i.e. SDFS without control.) The V*U(same) column: when V*U is negative c=c%(VARY); when positive c=20%(FIX). (The 30% point means when V*U is neg. c=30%, k=390; when pos. c=20%, k=390.) Displacement (Same stiffness 390) Fix stiff 20% (020.*) c(%) Fix k&c GV*BS V*BS V*U 0 8.06 4.464 3.136 3.137 5 5.041 3.49 2.798 2.916 9 3.682 2.978 2.576 2.72 1_ 5 2.683 2.525 2.374 2.474 20 2.259 2.259 2.282 2.283 2_5 1.935 2.06 2.206 2.124 3_0 1.684 1.908 2.1 21 1.987 400 1.33 1.691_ 2 1.657 50 1 1.119 1.533 1.784 1.591 75, 0.876 1.257 1.719 1.399 100! 0.747 1.195 1.564' 1.378 150 0.572 1.107 1.473 1.719 200 0.456 1.109 1.624 1.853 t - - r - - - - 8 - -- ---- -------,... _ - \ * r - - - I * I - I I IO 64- --- -- ------------------- ----------- -- --— = Fix k&c - - - r r - - - - - -r- - - r —-r —- -r - - - r- - -r GV*BS ~~a) r~~~"o,,,.-.- vu ——' —-------- -------- —'; V* I.,,,.,,,, I. v - I, I ) I,10 C I C l -CMCM C o o oo C o o o 100 C /Ccl (I)-(C)-DISP4

Section I, System C, Case 1, Energy Input Description: Here the stiffness always the same 390 kip/in. Here provide Fix k&c for comparison, represent the case without controling. (Different from the other columns, the damping ratio is always the same) I (The 30% point means the system has k=390 kip/in and c=30% critical. i.e. SDFS without control.) The V*U(same) column: when V*U is negative c=5%(FIX); when positive c=c%(VARY). (The 30% point means when V*U is neg. c=5%, k=390; when pos. c=30%, k=390.) Energy Input (Same stiffness 390) Fix soft 5% (*.005) _ c(%) Fix k&c GV*BS V*BS V*U 0 17288 14597 14005 13837 5 13023 13023 12733 12729 9 10868 12044 11821 12008 151 10150 10908 10767 10876 20 9937 10184 11039 11241 25 9634 10240 11085 11351 30 _9326 10241 10987 11329 40! 8759 10170 10520 10883 501 8237 10045 10102 10512 75 7138 9668 91711 9686 100 6277 9220 8268- 8921 1501 5042 8374 6775 7512 2001 4210 8019 5735 6447 18000 T —------------- ------ - --- 16000 - ------ --- - ------ --- - - 14000 —: -- cm 14000.............. * 12000 -- Fix k&c = 10000 t. —- -.,- -- GV*BS 8 8000 ---------- - ------- ------- V*BS 6000 V*U 4 2000....' —-' —- —'... -.-. LLJ 2000.. / Cch.. O C O C. O O o M o o o 0 — C o, Ir LO I — O - - T 100 C / Cch (I)-(C)-El1

Section I, System C, Case 2, Energy Input Description: Here the stiffness always the same 390 kip/in. Here provide Fix k&c for comparison, represent the case without controling. (Different from the other columns, the damping ratio is always the same) (The 30% point means the system has k=390 kip/in and c=30% critical. i.e. SDFS without control.) The V*U(same) column: when V*U is negative c=c%(VARY); when positive c=5%(FIX). (The 30% point means when V*U is neg. c=30%, k=390; when pos. c=5%, k=390.) Energy Input (Same stiffness 390) Fix stiff 5% (005.*)_~ c(%) Fix k&c GV*BS V*BS V*U 0 __17288 15226 15022 15028 _ 5 13023 13023 12733 12729 9 10868 116751 11424 11214 15 10150 10184 10069 9436 20 9937 9925 9278 9307 25 9634 9857 9196 9165 30 9326 9745 9029 8973 40 87591 9556 8740 8648 50 o 8237 9125 8602 8333 751 _7138 8037 8239 7563 100 6277 8094 7966 6949 150 5042 7205 7487 6289 2001 4210 6487 6828 5847 18000 T —- -- -' — -------------' _ *,, I,, I. i 16000 - - - - -- -- - - - -- -- 6' 14000' -- ---------.. - I 14000 y? 12000 ---- ---------- ---------------- ------ — *-Fix k&c 12000 -.'S 1 0000 -------— G,,_~-~-:-L -—: —--------.. ——; - GV*BS 8000t —---- ----------------------------------—. > oo~I, i''... I I u 2 o o ~o. I 1 6 0cI,', —-------- - i 0 CCMCMCT torNo Co 100 C /Ccl 1-IL~ (I)-(C)-E12

Section I, System C, Case 3, Energy Input Description: Here the stiffness always the same 390 kip/in. Here provide Fix k&c for comparison, represent the case without controling. (Different from the other columns, the damping ratio is always the same) (The 30% point means the system has k=390 kip/in and c=30% critical. i.e. SDFS without control.) The V*U(same) column: when V*U is negative c=20%(FIX); when positive c=c%(VARY). (The 30% point means when V*U is neg. c=20%, k=390; when pos. c=30%, k=390.) Energy Input (Same stiffness 390) Fix soft 20% (*.020) c(%) Fix k&c GV*BS V*BS V*U 0 17288 10117 9129 8998 5 13023 9925 9278 9307 9 10868 9978 9568 9496 1 51 10150 9993 9868 9802 20 9937 9937 9938 9936 25i 9634 9844 9839 9967 30i 9326 9727 9684 9937 40 87591 9488 9357 9829 50 8237 9275 8933 9658 75 7138 8809 7959 9045 100 6277 8372 7060' 8376 150 5042 7652 5741 7189 200 4210 7124 4747 6240 18000 -...... 18000 ^ —---------- --- ----- -- ---------- 16000 I..... 14000 —-, —-- ----,,, -.........;........' 12000 -— \ -- - --- - ---------- Fix k&c 10000 t - GV*BS C 8000 ----- - V*BS 6000 0 2000 ---— ~) —-1 —- - --------— i —------ 0 T — C I CM C) 1 LC) LO 0 LO O 100 C / C. ch 100 C / Cch (I)-(C)-E13

Section I, System C, Case 4, Energy Input Description: Here the stiffness always the same 390 kip/in. Here provide Fix k&c for comparison, represent the case without controling. (Different from the other columns, the damping ratio is always the same) (The 30% point means the system has k=390 kip/in and c=30% critical. i.e. SDFS without control.) The V*U(same) column: when V*U is negative c=c%(VARY); when positive c=20%(FIX). (The 30% point means when V*U is neg. c=30%, k=390; when pos. c=20%, k=390.) Energy Input (Same stiffness 390) Fix stiff 20% (020.*) c(%) Fix k&c GV*BS V*BS V*U 0.. 17288 11476 11832 11832 5 13023 10184 1 1039 11241 9 10868 10283 10586 10752 1 5 10150 10131 1 0151 10261 20 9937 9937 9938 9936 25 9634 9748 9734 9621 30 9326 9576 9542 9316 401 8759 9289 9200 8747 50 8237 9011 8918 8314 75 7138 82311 8445 7363 100_ 6277 7862 7945 6753 150i 5042 6990 7475 6226 200 4210 6198 6907 5808 I 18000 T -- ------- ----- 16000 ----------- ----- ------ ------ ------ c4 14000 -— \ —-I- ----- - ----- -L - ---------- ------ - 14000 <, ——, —-----—, — - - - ------ - y 12000 -----— Fix k&c 10000 1 ------- - -- -- GV*BS 8000 --------- V*BS 6000 ------------------- ---- -----—: —-o -o — v*u 4000........ 2000 ------ ---------- --. —--- -200 00.100 C / Ccl O — I I I I I I I I I I I (I)-(C)-E14

Section I, System C, Case 1, Energy Content Description: Here the stiffness always the same 390 kip/in. Here provide Fix k&c for comparison, represent the case without controling. (Different from the other columns, the damping ratio is always the same) (The 30% point means the system has k=390 kip/in and c=30% critical. i.e. SDFS without control.) The V*U(same) column: when V*U is negative c=5%(FIX); when positive c=c%(VARY). (The 30% point means when V*U is neg. c=5%, k=390; when pos. c=30%, k=390.) KE + SE (Same stiffness 390) Fix soft 5% (*.005) c(%) Fix k&c G S V*BS V*U 0 17288 10273 10696 1 0439 5 7689 7689 7662 7661 9 4759 6358 5880 6057 1 5 2866 5035 4282 4565 201 2171 4311 3447 3593 251 1794 3805 2841] 3005 301 1572 3444 24231 2605 40! 1335 2984 1925 2068 50 1215 2731 16871 1848 75 1074 2302 1409 1568 100 1007 2070 1257 — 1365 150 935 1967 1153 1241 200 944 1961 1134 1192 18000 T- - U 120 16000 T —--- -- -.. ----- -- -- --. —.. --------- - 14 00 0 -- - --- " - - --— r _ ----—, ---—,, ----— r - --- < 14000 *H 12000 ------ -- Fix k&c 0.a5 10000 -\ ——, —--—, ----—, ——,-, —-, -—, —-, —-- - - GV*BS': \\ o 8000 - -------. —- - —.-. V*BS D 6000V* " 4000 -------------:... —------- 12000 -..-. —--.:;,-' —-' - I I I I I I I I _ O L 0 o 0 ) 0 0 C) D ) 0:) 0. c J -— C m u - I Io) 0 - CM 100 C / Cch (I)-(C)-EKS1

Section I, System C, Case 2, Energy Content Description:.... Here the stiffness always the same 390 kip/in. Here provide Fix k&c for comparison, represent the case without controling. (Different from the other columns, the damping ratio is always the same) (The 30% point means the system has k=390 kip/in and c=30% critical. i.e. SDFS without control.) The V*U(same) column: when V*U is negative c=c%(VARY); when positive c=5%(FIX). (The 30% point means when V*U is neg. c=30%, k=390; when pos. c=5%, k=390.) KE + SE (Same stiffness 390) Fix stiff 5% (005.*) c(%) Fix k&c GV*BS V*BS V*U 0 17288 12557 11368 11374 5 7689 7689 7662 7661 9 4759 5629 5969 5719 15 2866 3854 4262 3821 20 2171 2999 3471 2943 25 1794 2449 2816 2305 30 1572 2075 2324 1918 40 1335 1503 1865 1530 50 1215 1389 1553 1348 75 1074 1086 1293 1332 1001 1007 1029 1257 1325 150 935 980 1330 1630 200 944 948 1341 1524 18000 T — ------ ---- - ----- - 16000 - - - -- - - -- - - < 14000 -- --------- -------- ___________,,.......... - 12000 - -- - - - - - - - - - * Fix k&c S 10000 - ---,- ----- GV*BS 0 2000 ------- O L 100 0 1 I0 0 0 1 0 0 0C CMj C) -1 t O 1 O 100 C / Ccl (I)-(C)-EKS2

Section I, System C, Case 3, Energy Content Description: Here the stiffness always the same 390 kip/in. Here provide Fix k&c for comparison, represent the case without controling. (Different from the other columns, the damping ratio is always the same) (The 30% point means the system has k=390 kip/in and c=30% critical. i.e. SDFS without control.) The V*U(same) column: when V*U is negative c=20%(FIX); when positive c=c%(VARY). (The 30% point means when V*U is neg. c=20%, k=390; when pos. c=30%, k=390.) KE + SE (Same stiffness 390) Fix soft 20% (*.020) c(%) Fix k&c GV*BS V*BS V*U 0 17288 3694 3835 3038 5 7689 2999 3471 2943 9 14759 2652 3092 2706 1 5. 2866 2330 2496 2382 20 2171 2171 2152 2152 25 1794 2070 1889 1954 30 1572 2002 171 5 1823 40 1335 1 913 1490 1612 50 1121 5 1854 1354 1473 75' 1074 1776 1190 1268 1001 1007 1725 1133 1185 1501 935 1608 1076 1099 200 944 1526 1033 1130 18000 -T -... 16000 -' —--—' —----- -- ------ ---, -- -' ------, 14000 -... —-- - -- -.-...... 12000 - Fix k&c 1000 - t - - - - - -- - --- -- -- GV*BS 8000- -- -- - - -~V*BS 4000 2000 -- 0) \ - _ 18000 -, _.__._._ _ _ _ _' V*BS rULJ~~~~ LO 0 ) ~Q~ 6~000t100 C Cch 4000............. o O o o o'"'' —':"-: -o o —-- 0 I t I t (I)-(C)-EKS3

Section I, System C, Case 4, Energy Content Description: I Here the stiffness always the same 390 kip/in. Here provide Fix k&c for comparison, represent the case without controling. (Different from the other columns, the damping ratio is always the same) I (The 30% point means the system has k=390 kip/in and c=30% critical. i.e. SDFS without control.) The V*U(same) column: when V*U is negative c=c%(VARY); when positive c=20%(FIX). (The 30% point means when V*U is neg. c=30%, k=390; when pos. c=20%, k=390.) KE + SE (Same stiffness 390) Fix stiff 20% (020.*)___ c(%) IFix k&c_ GV*BS V*BS V*U 01 17288 6204 4761 4761 _5 ____ 7689 4311 3447 3593 9 4759 3452 2856 3112 155 2866 3620 2377 2489 201 2171 2171 21521 2152 251 1794 1861 1989 1872 30 " 1572 1645 1865 1693 401 1335 1383 1676 1576 50 1215 1241 1659 1497 751 1074 _1093 1436 1349 100 10071 1038 1386- 1289 1501 935 984 1259 1279 200 944 9410 1239 1326 0.I I I I.,,,,.,... ) 8 — - ---- - - - - - - - - - V-S 18000 T -........ —. —_ iI,, I I t I I, I.1 14000 -,.............................................. ~ 12000 ------ ------------------------------- Fix ~ 80000 ---- -- -- -- - - - -- --- --- -- * r ------ -DV*BS 0 8000 ------- V*BS 6 000 ---------- --- i I - 6,000.*..... U j o u) 0 L) 0 ) 0 0 0 ) 0 0 0 0'" 0 >0041000 2000 _j 0 I CM CY LO C> l ) 0 O U, t..... I I I..I 100 C / Ccl (I)-(C)-EKS4

Section II, System A, Base Shear I [ [ [ [ [ [ [! I J j Description: Fix the system damping to 5% critical of 390 kip/in. When GV*BS, Vrel*BS, Vrel*Urel is negative, then change the system k to (pk*390); if positive then k=390. (pk=1 is the case without any control) Two ssstiffness: stiff 390k/in; soft (pk*390) Fix the damping 5% of stiff system (only change the stiffness) Base Shear_______ stiff ratio (pk) GV BS Vrel * BS Vrel * Urel soft damping ratio 0.01 169.2 800 777 50.00% 0.1 381 773 742 15.81% 0.2 608 822 776 11.18% 0.3 702 824 861 9.13% 0.4 773 935 953 7.91% 0.5 782 1064 1064 7.07% 0.6 884 1177 1209 6.45% 0.7 1 01 5 1233 1310 5.98% 0.8 1302 1447 1502 5.59% 0.9 1606 1715 1718 5.27% 1_____ _ 19761 1 997 1997 5.00% I I. _ _ 2000 - *s-^^/ / 1800-,/ — L-., -,,, -,. 1 - - -- 1 1 1600 - -, -,, -,0- - - - - - - - - - - - - - 1400 -.. 1200 -— _ 1000 —--------- 600 -. 400 200 - --- GV * BS - Vrel * BS -*- - Vrel * Urel j I i C0~ C c C) Lc CO r 0ness Ro Stiffness Ratio p ~ (Il)-(A)-BS

Section II, System A, Displacement Description: I ___________ Fix the system damping to 5% critical of 390 kip/in. When GV*BS, Vrel*BS, Vrel*Urel is negative, then change the system k to (pk*390); if positive then k=390. (pk=l is the case without any control) Two ssstiffness: stiff 390k/in; soft (pk*390) Fix the damping 5% of stiff system (only change the stiffness) Displacement stiff ratio (pk) GV*BS Vrel * BS Vrel * Urel soft damping ratio 0.01 5.01 2.44 2.89 50.00% 0.1 6.51 1.63 2.28 15.81% 0.2 5.79 2.01 2.19 11.18% 0.3 3.92 1.82 2.2 9.13% 0.4 3.49 2.14 2.43 7.91% 0.5 3.27 2.51 2.71 7.07% 0.6 3.54 2.84 3.09 6.45% 0.7 3.69 3.06 3.34 5.98% 0.8 4.13 3.63 3.83 5.59% 0.9 4.54 4.34 4.38 5.27% 1 5.04 5.09 5.1 5.00% I _ _ _ _ _ _ _ _ _ _ _ _ _ I I _ _ _ _ _ _ _ 7 6 5 c ~4 E 0) 23 2.. _ - t. _ _ - -- -- - -_ - --- -- - - -- -------- ------ \ -OJCI ) q LO (0 D co 0 - o o 0 c0 0 0 c 0 0 Stiffness Ratio p ---- GV * BS ---- Vrel * BS -* -- Vrel * Urel 1 0 (II)-(A)-DISP

Section II, System A, Energy Input I I Description: I. Fix the system damping to 5% critical of 390 kip/in. When GV*BS, Vrel*BS, Vrel*Urel is negative, then change the system k to (pk*390); if positive then k=390. (pk=1 is the case without any control) Two ssstiffness: stiff 390k/in; soft (pk*390) Fix the damping 5% of stiff system (only change the stiffness) _ Energy Input stiff ratio (pk) GV* BS Vrel * BS Vrel * Urel soft damping ratio 0.01 1650 7287 5486 50.00% 0.1 3586 7689 5955 15.81% 0.2 6010 7646 6389 11.18% 0.3 4209 7802 7047 9.13% 0.4 4334 8306 7700 7.91% 0.5 4666 8723 8110 7.07% 0.6 6457 9312 8479 6.45% 0.7 7668 9194 9269 5.98% 0.8 8463 9562 9524 5.59% 0.9 10337 11085 11133 5.27% 1 13023 12733 12729 5.00% I I I I 14000 --------- C 10000- - -- -- -----.s,,,^,,-,,,,G GV* BS 4 8000 - - ------ I- ['Vre — Vrel * BS Vrel Urel 4000 --- 12000,-1, ----------- ---------------- ---- 10 0 0-, --- -0 0- 0- 0-D 0-r 0 800 0GV BS 0 Stiffness Ratio p i, ~, \, i I,'' LU /: I u Vrel * BS / I I I t, t I t I 2 0 0 0 iZ/ — - -' OJ 03 ~ Lf) I —- (I:) 0 Stiffness Ratio p (I11)-(A)-E! I I I i I I I

Section II, System A, Energy Content. 1 Description: Fix the system damping to 5% critical of 390 kip/in. When GV*BS, Vrel*BS, Vrel*Urel is negative, then change the system k to (pk*390); if positive then k=390. (pk=1 is the case without any control) Two ssstiffness: stiff 390k/in; soft (pk*390) Fix the damping 5% of stiff system (only change the stiffness) KE +SE___ stiff ratio (pk) GV* BS Vrel* BS Vrel * Urel soft damping ratio 0.01 128 1144 1177 50.00% 0.1 1233 1225 1104 15.81% 0.2 1558 1160 1046 11.18% 0.3 1293 1394 1040 9.13% 0.41 1324 1411 1276 7.91% 0.5 1384 1569 1551 7.07% 0.6 1802 1883 1992 6.45% 0.7 2418 2510 2351 5.98% 0.8 3183 3553 3688 5.59% 0.9 5035 5286 5303 5.27% 1 7688 7662 7661 5.00% CM c L) C.; O 0 C) a) LU 6) uJ 0 A A r% duuu 7000.... 6000.....: —-------—:... — i. I I''''. I I I i I'''' / 5000 0 -- -i 3000 —....: __-_ —.- - —,-,. I.... I E- I 4.......,...,- - 3000 - - - ------ 2000 ------------ ------- — ^ -- ---------- 1000,,,. I I I I I I! -- -- GV * BS ------ Vrel * BS'* — Vrel * Urel.L v r - 0T-' O. r.. 0- 0 C ) Stiffness Rati o p Stiffness Ratio p r (1 )-(A)-EKS

Section II, System B, Base Shear I Description: I _ _ Here change the stiffness while damping stay the same. Each line represent one damping condition. The c% column (ea. 3%....200%): means the dampina of the svstem was FIXED to c% accordina to - _,- - I - - -I - _ _ -_ -_ -_ __........ _ _ _ -_ - - a _.... 390 kip/in. When Vrel*BS is pos. k=390; when neg. k=pk*390.(VARY) Two ssstiffness: stiff 390k/in; soft (pk*39p) I I Fix the damping to different % of stiff system (only change the stiffness) Base Shear' SR(pk) 3% 5% 10% 15% 20% 30% 40% 50% 75% 100% 150% 200% 0.01 814 800 787 795 821 897 969 1016 1097 1148 1197 1250 0.1 774 773 766 773 816 886 969 1023 1090 1149 1201 1252 0.2 841 8221 757 751 792 877 954 1024 1096 1153 1200 1256 0.3 940 824 788 746 767 866 951 1007 1101 1144 1198 1263 0.4 1054 935 823 762 739 856 952 1006 1099 1148 1206 1260 0.5 1169 1064 843 784 753 831 929 1008 1102 1145 1203 1263 0.6 1288 1177 951 787 766 828 925 994 1090 1148 1204 1234 0.7 1379 1233 1006 873 775 802 913 988 1101 1147 1197 1232 0.81 1707 1447 1076 949 808 794 894 991 1097 1156 1202 1237 0.9 1994 1715 1204 990 900 796 889 989 11051 1157 1203 1240 1 2343 1997 1359 1056 954 803 887 985 1090 1148 1206 1249 2500. - -. ---- 3%'' 5 % 2000 --------------- ----- - 10% t /)? /' 15% ~' 1500- -... )50,, —---------- ------------------- -- —. —/. 0% "': --' P, /" - $-20% a), _. -. --- -30% 51000 CO A-?~ -^^~ ^A ~-* ^ -jT — ^-^-^ ^ —^ 40% - 5 —---- 0% 500- 75% 10 100% I: - --- 150% 1- o+.- rC -C'l lO U) to N CO co M. o o* 0 o I 0; 0 0o 200% Stiffness Ratio p I,, I 0 I I I I 0 F I I i (I1)-(B)-BS

Section II, System B, Displacement Description:- t!. Here change the stiffness while damping stay the same. Each line represent one damping condition. The c% column (eg. 3%,...200%): means the damping of the system was FIXED to c% according to 390 kip/in. When Vrel*BS is pos. k=390; when neg. k=pk*390.(VARY) Two ssstiffness: stiff 390k/in; soft (pk*390) I __ Fix the damping to different % of stiff system (only change the stiffness) Displacemenl I I SR(pk) 3% 5% 10% 15% 20% 30% 40% 50% 75%j 100% 150% 200% 0.01 2.37 2.44 2.68 5.84 2.39 1.95 1.69 1.21 2.57 3.9 1.94 0.86 0.1 2.09 1.63 1.7 2.05 1.3 1.24 1.18 1.15 1.5 1.22 1.26 1.11 0.2 1.76 2.01 1.53 1.41 1.24 1.2 1.09 1.06 1.16 0.96 1.24 1.03 0.3 2.32 1.82 1.7 1.42 1.2 1.09 1.03 0.97 0.85 0.89 0.83 0.67 0.4 2.5 2.14 1.74 1.62 1.32 1.16 1.31 0.96 0.83 0.72 0.75 0.64 0.5 2.84 2.51 1.86 1.53 1.39 1.23 1.36 1.04 0.98 0.69 0.59 0.63 0.6 3.18 2.84 2.19 1.62 1.5 1.26 1.21 1.08 0.9 0.73 0.56t 0.56 0.7 3.45 3.06 2.38 1.99 1.6 1.28 1.12 1.06 1.01 0.67 0.54 0.45 0.8 4.32 3.63 2.6 2.23 1.79 1.41 1.18 1.07 0.87 0.71 0.6 0.45 0.9 5.07 4.34 2.96 2.39 2.08 1.54 1.23 1.07 0.97 0.77 0.56 0.47 1 5.99 5.09 3.4 2.62 2.28 1.72 1.34 1.13 0.97 0.6 0.52 6 - - --- -- - - - - - -- - - -, 6''''''',' /' * 3% 10% Coo -A —-- 40% 1 - - -- — tiff ess X 7 I - 01 +-_-__-__________________ = - 0 0 0 0 0 0' 200% 0o 2 0%?i~~~~~~~~~~~~i 000%I. ~ 6 o ~ 200% Stiffness Ratio p (II)-(B)-DISP

Section II, System B, Energy Input Description: I I I {' I I I' Here change the stiffness while damping stay the same. Each line represent one damping condition. The c% column (eg. 3%,...200%): means the damping of the system was FIXED to c% according to 390 kip/in. When Vrel*BS is pos. k=390; when neg. k=pk*390.(VARY) I -j Two ssstiffness: stiff 390k/in; soft (pk*399p) - Fix the damping to different % of stiff system (only change the stiffness)_ Energy Input'..._ SR(pk) 3% 5% 10% 15% 20% 30% 40% 50% 75% 100% 150% 200% 0.01 7275 7287 7184 7115 6925 6749 6505 6362 5759 5239 4368 3757 0.1 7366 7689 7611 7476 7293 6995 6713 6433 5881 5328 4443 3790 0.2 7187 7646 8064 7900 7695 7311 6945 6644 6036 5435 4522 3825 0.3 7663 7802 8195 8152 8006 7507 7183 6856 6099 5543 4577 3888 0.4 8056 8306 8281 8377 8250 7817 7357 7033 6266 5651 4669 3898 0.5 8737 8723 8595 8574 8512 8120 7597 7216 6355 5750 4714 3985 0.6i 8708 9312 9078 8832 8722 8317 7848 7417 6524 5807 4788 4001 0.7 93871 9194 9402 9168 8964 8548 8105 7633 6662 5934 4843 4085 0.8 10223 9562 9641 9534 9270 8842 8335 7873 6817 6051 4907 4122 0.9112123 11085 9799 9795 9604 9080 8548 8053 6939 6156' 4977 4172 1114276112733 10403 10087 9938 9330 8734 8237 7100 62581 5047 4228 i.II........ t i i. t 16000 F - =T * 3%. 14000i —---------- -....... —------—.. -- - 5 i 1 0% 14000 12000'. --— * 10% ~.~: I i''', o~//' * 1 15% -8000 A 20% I ~' _ _ + ^ —---- -t —--- 3 0% w x )K )K )K )K — 40% 6 8000 - - -30%0150% 4 000.._ -- ------ ----- 4.0 [ -X__X 75% 2000k-i-.. —. x.. —---.. --- -----— o 2000 t 0 I i i I i I 150% N co I,* LO O cO I d d C3 4 (0! " - CO 0"). o 0 o o o o o o o- 200% Stiffness Ratio p 1~~~.......... (11I)-(B)-EI

Section II, System B, Energy Content I i -1 u Description: Here change the stiffness while damping stay the same. Each line represent one damping condition. The c% column (eg. 3%,...200%): means the damping of the system was FIXED to c% according to 390 kip/in. When Vrel*BS is pos. k=390; when neg. k=pk*390.(VARY) Two ssstiffness: stiff 390k/in; soft (pk*39) ) ____ Fix the damping to different % of stiff system (only change the stiffness) KE+SE I _ SR(pk) 3% 5% 10% 15% 20% 30% 40% 50% 75% 100% 150% 200% 0.01 1205 1144 1120 1079 1092 1027 1001 943 943 929 959 1010 0.1 1204 1225 1107 1080 1054 992 1040 1011 921 953 978 997 0.2 1248 1160 1145 1144 1112 1016 1018 1047 912 944 973 996 0.3 1240 1394 1113 1140 1148 1052 1010 985 928 892 921 975 0.4 1532 1411 1176 1097 163 1072 1103 994 904 915 956 975 0.5 1884 1569 1398 1187 1125 1040 1125 1007 960 893 902 976 0.6j 2243 1883 1510 1294 1160 1110 1070 1013 9431 921 901 964 0.7 2941 2510 1842 1482 131 183 1098 1050 1006 917 887 946 0.8 4443 3553 2380 1784 1511 1242 1138 1 086 1005 949 910 940 0.9 6783 5286 3163 2227 1766 1383 1226 1156 1066 985 918 944 1 10140 7662 4260 2848 2152 1549 1334 1238 1105 1027 942 938 12000 -- - -- - -- - -- - - - - -- - -- - L- - 3% ---- 5% 10000 ----- ------- - 10% 8000 15% 8000 ------: ----------- ------- --------- / C= i, ~ /, - * ~-A 20% C 6000 ------------------- oT - ---- 40% 0 30% 0 II'''' II4 C 4000 0 t —-------------------- --- 7150%; - C C o t ) CI'rl o o II o o5 o Co > C C — 200% Stiffness Ratio p (II)-(B)-EKS

Program Flow-chart and Listing Program Flow-chart Every program is developed according to the following flow-chart: Read input data from data file Calculate system response through Subroutine Response Subroutine Response includes the follows: Calculate miscellaneous constants(damping ratio,period etc.), initial conditions Select appropriate integrate step, and calculate the exciting forces Use Subroutine Solve to calculate the displacement, velocity, acceleration, etc. using the exciting forces [Use Subroutine Base to calculate the base shear using the results from Sub Solve Overshooting the time whenever the control parameter changes sign, then recalculate base shear, velocity, acceleration, displacement,etc. Use Subroutine State to perform semi-active control according to the algorithms Do the necessary adjustments(base shear,etc.) due to state change Use Subroutine Energy to calculate the energy level Procede to output, including peak values and other detailed data Repeat the calculation for the next integral interval Program Listing An input sample data and three sets of programs used to perform the simulation are provided for reference. These three programs include the semi-active damping control bilinear system (I-A), semi-active stiffness system (I-B), and semi-active stiffness control for different damping (II-B) using (V*BS) as control parameter. 16

ACTIVE DAMPER 10.0 390.C 1000 0.020 0.100 0.180 0.260 0.340 0.420 0.500 0.580 0.660 0.740 0.820 0.900 0.980 1.060 1.140 1.220 1.300 1.380 1.460 1.540 1.620 1.700 1.780 1.860 1.940 2.020 2.100 2.180 2.260 2.340 2.420 2.500 2.580 2.660 2.740 2.820 2.900 2.980 3.060 3.140 3.220 3.300 3.380 3.460 3.540 3.620 3.700 3.780 3.860 3.940 4.020 4.100 4.180 4.260 4.340 4.420 4.500 4.580 4.660 4.740 4.820 4.900 4.980 0.00 -0.001 -0.01C -0.011 -0.018 -0.011 -0.013 0.003 -0.01E -0.031 -0.017 0.024 0.05C 0.024 0.065 0.041 -0.08C -0.006 0.072 0.147 0.094 0.123 -0.202 -0.178 -0.137 -0.002 0.162 0.308 0.236 -0.189 0.011 0.17E -0.175 -0.068 -0.15C -0.053 -0.01C -0.073 0.019 -0.038 0.057 0.022 0.134 -0.133 0.06E -0.11E -0.013 -0.011 0.062 0.00 0.122 0.00: -0.01E 0.06E 0.16E 0.17S -0.03S -0.25C -0.093 0.134 0.02S 0.18 -0.10o -0.12' SYSTEM 1.5 386.0 (8F10.3) 0.040 0.120 0.200 0.280 0.360 0.440 0.520 5 0.600 L 0.680? 0.760 I 0.840 0.920 1 1.000 1.080 1.160 1.240 1.320 1.400 1.480 1.560 1.640 1.720 1.800? 1.880 1.960 2.040 2.120 2.200 2.280 2.360 2.440 > 2.520 2.600 2.680 2.760 2.840 2.920 3.000 3.080 7 3.160 3.240 3.320 3.400 3 3.480 3 3.560 3.640 3.720 3.800 3.880 3.960 4.040 4.120 4.200 4.280 4.360 4.440 4.520 7 4.600 1 4.680 3 4.760 3 4.840 L 4.920 7 5.000 0.05 -0.011 -0.012 -0.009 -0.020 -0.008 -0.019 0.014 -0.021 -0.017 -0.007 0.026 0.042 0.034 0.074 0.041 -0.061 0.014 0.101 0.117 0.085 0.033 -0.206 -0.178 -0.110 0.037 0.199 0.325 -0.122 -0.111 0.054 0.058 -0.103 -0.201 -0.125 -0.027 -0.044 -0.061 0.043 -0.004 0.090 0.024 0.137 -0.070 -0.108 -0.077 -0.068 0.002 0.023 0.021 0.150 0.026 0.015 0.097 0.197 0.127 -0.032 -0.205 -0.033 0.184 0.045 0.249 -0.110 -0.214 0.05 0.060 0.140 0.220 0.300 0.380 0.460 0.540 0.620 0.700 0.780 0.860 0.940 1.020 1.100 1.180 1.260 1.340 1.420 1.500 1.580 1.660 1.740 1.820 1.900 1.980 2.060 2.140 2.220 2.300 2.380 2.460 2.540 2.620 2.700 2.780 2.860 2.940 3.020 3.100 3.180 3.260 3.340 3.420 3.500 3.580 3.660 3.740 3.820 3.900 3.980 4.060 4.140 4.220 4.300 4.380 4.460 4.540 4.620 4.700 4.780 4.860 4.940 5.020 0.001 -0.010 -0.014 -0.009 -0.016 -0.004 -0.020 -0.005 -0.026 -0.020 0.003 0.034 0.036 0.042 0.066 0.006 -0.049 0.031 0.124 0.095 0.091 -0.150 -0.184 -0.183 -0.079 0.080 0.245 0.347 -0.241 -0.076 0.091 -0.267 -0.059 -0.166 -0.102 -0.004 -0.085 -0.034 0.068 0.001 0.115 0.069 0.207 -0.055 -0.151 -0.057 -0.033 0.030 -0.003 0.058 0.176 0.030 0.021 0.114 0.188 -0.122 -0.113 -0.186 0.016 -0.006 0.100 0.171 -0.092 -0.164 1.0 0.080 0.160 0.240 0.320 0.400 0.480 0.560 0.640 0.720 0.800 0.880 0.960 1.040 1.120 1.200 1.280 1.360 1.440 1.520 1.600 1.680 1.760 1.840 1.920 - 2.000 2.080 2.160 2.240 2.320 2.400 2.480 2.560 2.640 2.720 2.800 2.880 2.960 3.040 3.120 3.200 3.280 3.360 3.440 3.520 3.600 3.680 3.760 3.840 3.920 4.000 4.080 4.160 4.240 4.320 4.400 4.480 4.560 4.640 4.720 4.800 4.880 4.960 5.040 -0.009 -0.013 -0.013 -0.015 -0.007 -0.007 -0.013 -0.033 -0.017 0.015 0.047 0.027 0.054 0.061 -0.052 -0.025 0.051 0.155 0.090 0.101 -0.210 -0.175 -0.165 -0.044 0.118 0.277 0.286 -0.166 -0.018 0.120 -0.157 0.024 -0.171 -0.076 0.019 -0.096 -0.011 -0.010 0.035 0.138 0.070 -0.094 0.007 -0.109 -0.022 -0.034 0.049 -0.025 0.084 0.043 -0.006 0.051 0.147 0.201 -0.055 -0.168 -0.134 0.083 -0.017 0.144 -0.140 -0.048 -0.172

5.060 5.140 5.220 5.300 5.380 5.460 5.540 5.620 5.700 5.780 5.860 5.940 6.020 6.100 6.180 6.260 6.340 6.420 6.500 6.580 6.660 6.740 6.820 6.900 6.980 7.060 7.140 7.220 7.300 7.380 7.460 7.540 7.620 7.700 7.780 7.860 7.940 8.020 8.100 8.180 8.260 8.340 8.420 8.500 8.580 8.660 8.740 8.820 8.900 8.980 9.060 9.140 9.220 9.300 9.380 9.460 9.540 9.620 9.700 9.780 9.860 9.940 10.020 10.100 10.180 10.260 -0.132 -0.055 -0.116 -0.082 -0.040 0.089 0.030 0.137 0.065 0.050 -0.011 -0.007 0.026 0.010 0.008 0.016 0.008 -0.002 -0.031 -0.018 -0.011 -0.011 0.024 0.019 0.016 -0.043 0.032 -0.021 -0.006 0.024 0.044 -0.002 0.026 0.043 0.037 -0.025 -0.044 -0.021 -0.041 -0.027 -0.022 0.031 0.029 0.014 -0.136 -0.084 -0.006 0.009 0.059 0.113 -0.024 -0.068 0.109 0.068 -0.084 -0.037 0.163 0.002 -0.021 -0.003 0.076 0.002 -0.008 -0.006 -0.044 0.021 5.080 5.160 5.240 5.320 5.400 5.480 5.560 5.640 5.720 5.800 5.880 5.960 6.040 6.120 6.200 6.280 6.360 6.440 6.520 6.600 6.680 6.760 6.840 6.920 7.000 7.080 7.160 7.240 7.320 7.400 7.480 7.560 7.640 7.720 7.800 7.880 7.960 8.040 8.120 8.200 8.280 8.360 8.440 8.520 8.600 8.680 8.760 8.840 8.920 9.000 9.080 9.160 9.240 9.320 9.400 9.480 9.560 9.640 9.720 9.800 9.880 9.960 10.040 10.120 10.200 10.280 -0.113 -0.122 -0.073 -0.166 -0.015 0.048 0.045 0.163 0.021 0.024 -0.023 0.015 -0.004 0.023 0.021 -0.003 0.004 0.004 -0.043 -0.013 -0.009 -0.010 0.036 -0.027 0.005 -0.022 0.042 -0.008 0.005 0.008 0.050 -0.002 0.037 0.040 0.042 -0.041 -0.046 -0.050 -0.031 -0.027 -0.008 0.036 0.031 0.039 -0.137 -0.066 -0.009 0.017 0.088 -0.112 -0.097 -0.056 0.169 0.013 -0.117 0.003 -0.027 0.015 -0.060 0.008 0.081 0.006 0.017 0.004 -0.036 0.053 5.100 5.180 5.260 5.340 5.420 5.500 5.580 5.660 5.740 5.820 5.900 5.980 6.060 6.140 6.220 6.300 6.380 6.460 6.540 6.620 6.700 6.780 6.860 6.940 7.020 7.100 7.180 7.260 7.340 7.420 7.500 7.580 7.660 7.740 7.820 7.900 7.980 8.060 8.140 8.220 8.300 8.380 8.460 8.540 8.620 8.700 8.780 8.860 8.940 9.020 9.100 9.180 9.260 9.340 9.420 9.500 9.580 9.660 9.740 9.820 9.900 9.980 10.060 10.140 10.220 10.300 -0.078 -0.123 -0.055 -0.087 0.032 0.020 0.080 0.189 0.032 -0.009 -0.025 0.038 -0.043 -0.013 0.039 -0.011 -0.010 0.009 -0.025 -0.002 -0.003 0.000 0.072 -0.013 -0.022 -0.004 0.012 -0.021 0.014 -0.001 0.019 0.005 0.053 0.057 0.010 -0.042 -0.006 -0.054 -0.032 -0.035 0.009 0.035 0.011 -0.087 -0.121 -0.045 -0.018 0.005 0.122 -0.037 -0.067 -0.003 0.096 -0.010 -0.117 0.055 0.003 0.054 -0.017 0.039 0.060 -0.041 0.058 -0.012 -0.026 0.087 5.120 5.200 5.280 5.360 5.440 5.520 5.600 5.680 5.760 5.840 5.920 6.000 6.080 6.160 6.240 6.320 6.400 6.480 6.560 6.640 6.720 6.800 6.880 6.960 7.040 7.120 7.200 7.280 7.360 7.440 7.520 7.600 7.680 7.760 7.840 7.920 8.000 8.080 8.160 8.240 8.320 8.400 8.480 8.560 8.640 8.720 8.800 8.880 8.960 9.040 9.120 9.200 9.280 9.360 9.440 9.520 9.600 9.680 9.760 9.840 9.920 10.000 10.080 10.160 10.240 10.320 -0.052 -0.117 0.006 -0.097 0.066 -0.003 0.105 0.130 0.038 -0.017 -0.016 0.059 -0.013 -0.005 0.052 0.001 -0.004 -0.006 -0.024 0.021 -0.011 0.007 0.079 -0.004 -0.047 0.016 -0.016 -0.014 0.027 0.020 0.009 0.009 0.055 0.077 -0.021 -0.048 0.018 -0.037 -0.027 -0.031 0.028 0.036 0.022 -0.137 -0.106 -0.026 -0.015 0.027 0.172 -0.045 -0.061 0.038 0.041 -0.053 -0.081 0.119 -0.006 0.081 -0.018 0.058 0.031 -0.046 0.009 -0.029 -0.011 0.116

10.340 10.420 10.500 10.580 10.660 10.740 10.820 10.900 10.980 11.060 11.140 11.220 11.300 11.380 11.460 11.540 11.620 11.700 11.780 11.860 11. 940 12.020 12.100 12.180 12.260 12.340 12.420 12.500 12.580 12.660 12.740 12.820 12.900 12.980 13.060 13.140 13.220 13.300 13.380 13.460 13.540 13.620 13.700 13.780 13.860 13.940 14.020 14.100 14.180 14.260 14.340 14.420 14.500 14.580 14.660 14.740 14.820 14.900 14.980 15.060 15.140 15.220 15.300 15.380 15.460 15.540 0.074 -0.022 -0.034 0.037 -0.032 -0.073 -0.001 -0.017 0.038 -0.006 -0.005 -0.023 -0.060 -0.027 -0.112 -0.048 0.021 0.095 0.126 0.207 -0.068 -0.126 -0.075 -0.088 -0.054 0.059 0.060 0.020 0.044 -0.015 0.004 -0.003 0.052 0.023 0.059 0.096 -0.035 -0.027 -0.039 0.003 -0.014 -0.034 -0.007 0.035 -0.037 -0.055 0.015 -0.036 0.009 0.141 -0.009 0.055 -0.019 -0.021 -0.059 0.010 0.009 -0.008 -0.003 0.049 -0.001 -0. 011 -0.022 -0.002 0.023 0.044 10.360 10.440 10.520 10.600 10.680 10.760 10.840 10.920 11.000 11.080 11.160 11.240 11.320 11.400 11.480 11.560 11.640 11.720 11.800 11.880 11.960 12.040 12.120 12.200 12.280 12.360 12.440 12.520 12.600 12.680 12.760 12.840 12.920 13.000 13.080 13.160 13.240 13.320 13.400 13.480 13.560 13.640 13.720 13.800 13.880 13.960 14.040 14.120 14.200 14.280 14.360 14.440 14.520 14.600 14.680 14.760 14.840 14.920 15.000 15.080 15.160 15.240 15.320 15.400 15.480 15.560 0.024 -0.089 0.008 0.008 -0.024 -0.081 0.007 -0.042 0.062 -0.048 0.013 -0.043 -0.052 -0.055 -0.089 -0.034 0.044 0.108 0.135 0.125 -0.056 -0.120 -0.082 -0.089 0.005 0.032 0.053 0.050 0.024 -0.008 -0.015 0.018 0.047 0.028 0.060 0.035 -0.043 0.008 -0.008 -0.071 0.008 -0.027 -0.004 0.097 -0.101 -0.033 0.052 -0.070 0.064 0.121 -0.023 0.040 -0.002 -0.031 -0.027 0.014 -0.056 0.025 -0.025 0.079 -0.020 0.005 -0.048 0.017 0.038 0.035 10.380 10.460 10.540 10.620 10.700 10.780 10.860 10.940 11.020 11.100 11.180 11.260 11.340 11.420 11.500 11.580 11.660 11.740 11.820 11.900 11.980 12.060 12.140 12.220 12.300 12.380 12.460 12.540 12.620 12.700 12.780 12.860 12.940 13.020 13.100 13.180 13.260 13.340 13.420 13.500 13.580 13.660 13.740 13.820 13.900 13.980 14.060 14.140 14.220 14.300 14.380 14.460 14.540 14.620 14.700 14.780 14.860 14.940 15.020 15.100 15.180 15.260 15.340 15.420 15.500 15.580 -0.037 -0.099 0.026 -0.006 -0.038 -0.053 -0.004 -0.008 0.067 -0.036 0.038 -0.069 -0.041 -0.064 -0.078 -0.020 0.062 0.115 0.162 0.045 -0.070 -0.106 -0.086 -0.088 0.022 0.024 0.036 0.035 0.009 -0.002 -0.032 0.043 0.049 0.040 0.083 0.005 -0.042 0.043 0.014 -0.081 -0.012 -0.031 0.011 0.091 -0.082 -0.013 -0.002 -0.052 0.085 0.076 0.008 0.005 0.001 -0.052 -0.018 0.022 -0.056 0.042 -0.002 0.063 -0.025 0.024 -0.037 -0.008 0.061 0.051 10.400 10.480 10.560 10.640 10.720 10.800 10.880 10.960 11.040 11.120 11.200 11.280 11.360 11.440 11.520 11.600 11.680 11.760 11.840 11.920 12.000 12.080 12.160 12.240 12.320 12.400 12.480 12.560 12.640 12.720 12.800 12.880 12.960 13.040 13.120 13.200 13.280 13.360 13.440 13.520 13.600 13.680 13.760 13.840 13.920 14.000 14.080 14.160 14.240 14.320 14.400 14.480 14.560 14.640 14.720 14.800 14.880 14.960 15.040 15.120 15.200 15.280 15.360 15.440 15.520 15.600 -0.027 -0.060 0.052 -0.021 -0.056 -0.034 -0.001 0.008 0.026 -0.025 0.024 -0.067 -0.031 -0.092 -0.059 0.002 0.078 0.120 0. 182 -0.014 -0.100 -0.093 -0.087 -0.090 0.025 0.049 0.020 0.029 0.008 0.008 -0.024 0.045 0.020 0.051 0.081 -0.012 -0.028 -0.023 0.045 -0.025 -0.025 -0.020 0.030 0.018 -0.075 0.003 -0.050 -0.038 0.129 0.023 0.018 -0.008 -0.012 -0.074 0.004 0.044 -0.025 0.018 0.025 0.034 -0.022 -0.003 -0.020 0.001 0.052 0.066

15.620 15.700 15.780 15.860 15.940 16.020 16.100 16.180 16.260 16.340 16.420 16.500 16.580 16.660 16.740 16.820 16.900 16.980 17.060 17.140 17.220 17.300 17.380 17.460 17.540 17.620 17.700 17.780 17.860 17.940 18.020 18.100 18.180 18.260 18.340 18.420 18.500 18.580 18.660 18.740 18.820 18.900 18.980 19.060 19.140 19.220 19.300 19.380 19.460 19.540 19.620 19.700 19.780 19.860 19.940 0.069 -0.067 0.012 -0.034 0.007 -0.035 0.048 -0.007 -0.021 0.012 0.021 -0.015 -0.003 -0.028 -0.018 -0.019 0.070 0.052 -0.015 0.022 -0.053 -0.031 -0.032 -0.032 -0.043 -0.014 0.089 0.008 0.003 0.021 0.007 -0.016 0.011 -0.010 0.005 0.018 0.035 0.024 0.005 -0.064 0.028 -0.011 -0.023 0.017 0.017 -0.029 -0.008 0.025 -0.029 0.034 -0.001 -0.036 -0.049 -0.019 -0.007 15.640 15.720 15.800 15.880 15.960 16.040 16.120 16.200 16.280 16.360 16.440 16.520 16.600 16.680 16.760 16.840 16.920 17.000 17.080 17.160 17.240 17.320 17.400 17.480 17.560 17.640 17.720 17.800 17.880 17.960 18.040 18.120 18.200 18.280 18.360 18.440 18.520 18.600 18.680 18.760 18.840 18.920 19.000 19.080 19.160 19.240 19.320 19.400 19.480 19.560 19.640 19.720 19.800 19.880 19.960 0.017 -0.039 -0.013 -0.022 -0.006 -0.009 0.061 -0.079 0.003 0.034 0.020 -0.035 0.017 -0.039 -0.018 -0.012 0.092 0.019 -0.007 0.002 -0.072 -0.015 -0.047 -0.044 -0.037 -0.007 0.079 0.001 0.011 0.008 0.011 -0.019 -0.012 -0.006 0.006 0.022 0.039 0.012 0.003 -0.060 0.028 -0.022 0.003 0.026 -0.014 -0.031 0.013 0.016 -0.032 0.058 -0.014 -0.040 -0.041 -0.006 -0.017 15.660 15.740 15.820 15.900 15.980 16.060 16.140 16.220 16.300 16.380 16.460 16.540 16.620 16.700 16.780 16.860 16.940 17.020 17.100 17.180 17.260 17.340 17.420 17.500 17.580 17.660 17.740 17.820 17.900 17.980 18.060 18.140 18.220 18.300 18.380 18.460 18.540 18.620 18.700 18.780 18.860 18.940 19.020 19.100 19.180 19.260 19.340 19.420 19.500 19.580 19.660 19.740 19.820 19.900 19.980 -0.017 -0.023 -0.036 -0.001 -0.012 0.007 0.058 -0.062 0.035 0.032 0.018 -0.034 -0.010 -0.025 -0.004 0.009 0.087 0.002 0.002 -0.013 -0.059 -0.001 -0.040 -0.050 -0.028 0.051 0.078 -0.013 0.011 -0.006 0.015 -0.001 -0.031 0.000 0.010 0.026 0.048 -0.008 -0.025 -0.042 -0.002 -0.042 0.008 0.033 -0.033 -0.034 0.038 -0.004 -0.011 0.043 -0.027 -0.041 -0.041 0.004 -0.012 15.680 15.760 15.840 15.920 16.000 16.080 16.160 16.240 16.320 16.400 16.480 16.560 16.640 16.720 16.800 16.880 16.960 17.040 17.120 17.200 17.280 17.360 17.440 17.520 17.600 17.680 17.760 17.840 17.920 18.000 18.080 18.160 18.240 18.320 18.400 18.480 18.560 18.640 18.720 18.800 18.880 18.960 19.040 19.120 19.200 19.280 19.360 19.440 19.520 19.600 19.680 19.760 19.840 19.920 20.000 -0.053 -0.003 -0.052 0.014 -0.033 0.031 0.033 -0.044 0.030 0.026 0.002 -0.015 -0.026 -0.022 -0.003 0.035 0.077 -0.019 0.013 -0.033 -0.047 -0.018 -0.035 -0.048 -0.026 0.073 0.045 -0.002 0.020 -0.007 -0.001 0.016 -0.031 0.002 0.014 0.031 0.040 -0.013 -0.057 -0.007 -0.006 -0.053 0.014 0.040 -0.030 -0.025 0.041 -0.016 0.010 0.015 -0.035 -0.049 -0.036 -0.002 0.013

C PROGRAM FOR CASE I-A C *** Use Vrel* BSrel for controlling C *** Bilinear stiffness C C************************************************************ IMPLICIT DOUBLE PRECISION (A-H,O-Z) CHARACTER*20 FMT CHARACTER*10 HED C C DYNAMIC ANALYSIS OF SINGLE DEGREE OF FREEDOM SYSTEMS C WITH THE FOLLOWING FORCE-DEFORMATION MECHANICAL CHARACTERISTICS C SIGN BASE-SHEAR.EQ. SIGN GROUND VELOCITY: MIN.STIFFNESS C SIGN BASE-SHEAR.NE. SIGN GROUND VELOCITY: MAX.STIFFNESS C C PROGRAMMED BY JODI FIRMANSJAH, CORRECTED AND EXTENDED BY I-HONG CHEN C C SOME KEY VARIABLES C XMASS = MASS C STIFF = MAXIMUM STIFFNESS C PK = RATIO OF MINIMUM STIFFNESS TO MAXIMUM STIFFNESS C DAMP1 = DAMPING RATIO OF MAXIMUN STIFFNESS SYSTEM C DAMP2 = DAMPING RATIO OF MINIMUM STIFFNESS SYSTEM C DELTAT = INTEGRATION INTERVAL C XOUT = OUTPUT INTERVAL C C KOUNT = NO. GROUND ACCELERATION RECORD C FACTOR = MAGNIFICATION FACTOR C FY = YIEDING FORCE OF BILINEAR SYS FOR BOTH T & C C COMMON /BLK5/ DF,FC,FT,FY,FYC1,FYT1,UC,UT,KEY,KEYO COMMON /BLK1/ XMASS,STIFF,PSTIFF,ST,FACTOR,C1,C2,HED COMMON /BLK2/ DAMP1,DOUT,PK,DAMP2,KOUNT COMMON /BLK3/ DELTAT,P1,P2,DP,U1,U2,Fl,F2,Tl,T2,V1,V2,A1,A2 COMMON /BLK8/ RU,F1C,F2C COMMON /ACCL/ TT(2000),PP(2000) COMMON /RESP/ UU(100000),VV(100000),AA(100000),RR(100000), 1 TO(100000),CC(100000) COMMON /BLK9/ BSMAX,BSMIN,DISMAX,DISMIN, EDMAX,EIMAX, 1 EKSMAX, EKTMAX COMMON /TIME/ TBSMAX,TBSMIN,TDIMAX,TDIMIN,TEDMAX,TEIMAX, 1 TESMAX,TETMAX CHARACTER*24 INP C C OPEN EXTERNAL FILES C WRITE(*,5) 5 FORMAT(' input file') READ(*,10) INP 10 FORMAT(a24) C OPEN (5, FILE=INP) OPEN(6,FILE='out200.020') OPEN(1,FILE='file200. 020') OPEN(7,FILE='file7200.020') OPEN(10,FILE='state200.020') OPEN(ll,FILE='dis200.020') OPEN(12,FILE='bs200.020' ) OPEN (13,FILE='gv200.020' ) OPEN(UNIT=14,FILE='sg200.020') OPEN(2,FILE='eks200.020') OPEN(18,FILE='ekt200.020') OPEN(17,FILE='ed200.020') OPEN(21,FILE='stiff200.020')

OPEN(UNIT=15,FILE='ei200.020') OPEN(20,FILE='max200.020') C C READ HEADING AND SYSTEM INFORMATION C READ(5,1000) HED 1000 FORMAT(3A10) READ(5,1005) XMASS,STIFF,PK,DAMP1,DAMP2,DELTAT,XOUT,FY 1005 FORMAT(8F10.2) IF (XOUT.EQ.0.D0) XOUT=1.DO C C READ LOAD INFORMATION C READ(5,1015) KOUNT,DT,FACTOR,fmt 1015 FORMAT(lI5,2F10.2,a20) IF (FACTOR.EQ.0.DO) FACTOR=1.DO IF (DT.NE.0.DO) GO TO 30 READ(5,FMT) (TT(I),PP(I),I=1,KOUNT) GO TO 40 30 TT(1)=0.D0 DO 35 I=2,KOUNT TT(I)=I*DT 35 CONTINUE READ(5,fmt) (PP(I),I=1,KOUNT) C 40 C C C C C C DOUT=XOUT*DELTAT NOUT=(TT(KOUNT)-TT(1))/DOUT RESPONSE CALCULATION CALL RESPON(DELTAT) STOP END SUBROUTINE RESPON(DELTA) IMPLICIT DOUBLE PRECISION (A-H,O-Z) CALCULATE THE RESPONSE TIME HISTORIES CHARACTER*10 HED C C C COMMON COMMON COMMON COMMON COMMON COMMON COMMON COMMON COMMON 1 COMMON COMMON 1 COMMON 1 /BLK5/ DF,FC,FT,FY,FYC1,FYT1,UC,UT,KEY,KEYO /BLK1/ XMASS,STIFF,PSTIFF,ST,FACTOR,C1,C2,HED /BLK2/ DAMP1,DOUT,PK,DAMP2,KOUNT /BLK3/ DELTAT, P,P2,DP,U1,U2,F1,F2,Tl,T2,V1,V2,Al,A2 /BLK8/ RU,F1C,F2C /BLK4/ GA1,GA2,GVl,GV2,EI, ES,EH,ED,EK,ET,UB,UR,EKS,EKT /BLK7/ KPR /ACCL/ TT(2000),GA(2000) /RESP/ UU(100000),VV(100000),AA(100000),RR(100000), TO(100000),CC(100000) /BASE1/ BB(100000),GV(100000),SS(100000),KD(100000) /BLK9/ BSMAX,BSMIN,DISMAX,DISMIN,EDMAX,EIMAX, EKSMAX, EKTMAX /TIME/ TBSMAX,TBSMIN,TDIMAX,TDIMIN,TEDMAX,TEIMAX, TESMAX,TETMAX COMPUTE MISCELLANEOUS CONSTANTS W1 =DSQRT(STIFF/XMASS) PERIOD1=8.DO*ATAN(1.0)/W1 C1 =2.DO*W1*XMASS*DAMP1 PSTIFF=PK*STIFF

W2 =DSQRT(PSTIFF/XMASS) PERIOD2=8.D0*ATAN(1.0)/W2 C2 =2.DO*W2*XMASS*DAMP2 C YIELDING DISPL. FT=FY FC=-FY UT=FT/STIFF UC=FC/STIFF C ELASTO-PLASTIC YIELDING FORCE FYT1=UT*(STIFF-PSTIFF) FYC1=UC*(STIFF-PSTIFF) DF=FT-FC C C ECHO-PRINT INPUT QUANTITIES C WRITE(1,2068) WRITE(6,2000) WRITE(6,2005) 1 WRITE(6,2020) WRITE (6,2030) WRITE(6,2035) WRITE(6,2045) WRITE(6,2055) WRITE(6,2060) HED XMASS,STIFF,PK,W1,PERIOD1,DAMP1,W2,PERIOD2, DAMP2 DELTA,DOUT FACTOR (TT(I),GA(I), I=1,KOUNT) HED C C C C INITIALIZE BSMAX=0.DO BSMIN=0.DO DISMAX=0.DO DISMIN=0.DO EDMAX=0.DO EIMAX=0.DO EKSMAX=0.DO EKTMAX=0.DO TBSMAX=0.DO TBSMIN=0.DO TDIMAX=0.DO TDIMIN=0.DO TEDMAX=0.DO TEIMAX=O.DO TESMAX=O.DO TETMAX=O.DO RU=0.DO MCYC=500 KODY=1 KPR=0 A1=-GA(1)*FACTOR EI=0.DO EKT=0.DO ED=0.DO ES=0.DO EH=0.DO ET=0.DO GA1=GA(1)*FACTOR GA2=0.DO GV1=0.DO C

GV2=0.D0 BS1=0.DO BS2=0.D0 P1=-XMASS*FACTOR*GA(1) C=C2 T1=TT(1) C F1=0.DO F2=0.D0 FlC=0.DO F2C=0.DO U1=0.DO U2=0.D0 V1=0.DO V2=O.D0 II=1 KK=1 KEY=0 C C COMPUTE RESPONSE HISTORY C (A) DETERMINING THE CURRENT INTEGRATION STEP C SIZE AT BEGINNING C DT=DELTAT IF (DT.GT.(TT(2)-TT(1))) DT=TT(2)-TT(1) DELTAT=DT T2=T1+DT KCHEK=0 KODP=KODY KEY0=KEY C C STARTING PLACE EXCEPT THE FIRST TIME STEP C (B) UPDATING THE CURRENT INPUT-EXCITATION C DIGITIZATION INTERVAL AT WHICH THE CURRENT C INTEGRATION STEP RESIDES C 20 IF (T2.LE.TT(II)) GO TO 25 IF (T2.GT.TT(II).AND.T2.LE.TT(II+1)) GO TO 30 KCHEK=0 II=II+1 IF (II.GE.KOUNT) GO TO 400 GO TO 20 25 II=II-1 GO TO 20 C C (C) INTERPOLATED LOADS AT THE TWO ENDS OF C CURRENT INTEGRATION STEP C 30 IF (KCHEK) 35,35,40 35 TP=TT(II) TQ=TT(II+1) AP=GA(II)* FACTOR AQ=GA(II+1)* FACTOR DGR= (AQ-AP) /(TQ-TP) DP=-XMASS*DGR KCHEK=1 C 40 P2=-XMASS* (AP+DGR* (T2-TP)) C DGA=DGR*DT GA2 =GA1 +DGA DGV=GA1*DT+DGA*DT/2.0 GV2=GV1+DGV DGU=GV1*DT+GA1*DT*DT/2.0+DGA*DT*DT/4.0 IF (GV1.EQ.0.D0.OR.GV1.EQ.GV2) GO TO 90 DTG=GV1/ (GV1-GV2) *DT

IF (DTG.GE.DT.OR.DTG.LE.0.D0) GO TO 90 DT=DTG T2=T1+DTG P2=-XMASS*(AP+DGR*(T2-TP)) DGA=DGR*DT GA2=GA1+DGA DGV=GA1*DT+DGA*DT/2.0 GV2=GV1+DGV DGU=GV1*DT+GA1*DT*DT/2.0+DGA*DT*DT/4.0 GV2=0.DO C C CALCULATE RESPONSE AT THE END OF CURRENT C INTEGRATION TIME STEP C 90 CALL SOLVE(DT,DA2,C) CALL BASE(BS2,C,DA2,DT,DU) U2=U1+DU DV=A1*DT+DA2*DT/2.0 V2=V1+DV C C Overshooting the time when V2=0 C U2=U1+DU DV=A1*DT+DA2*DT/2.0 V2=V1+DV IF (V2.EQ.0.D0) GO TO 153 IF ((V1*V2).GE.0.DO) GO TO 153 NCYC=0 DTP=0.DO DTQ=DT VP=V1 C 9100 DT=0.5D0*(DTP+DTQ) CALL SOLVE(DT,DA2,C) CALL BASE(BS2,C,DA2,DT,DU) U2=U1+DU DV=A1*DT+DA2*DT/2.0 V2=V1+DV IF (DABS(V2).LE.0.001D0.OR.DABS(DTP-DTQ).LE.0.00001D0) THEN V2=0.DO GO TO 153 ENDIF NCYC=NCYC+ 1 IF (NCYC.LE.MCYC) GO TO 9105 WRITE(*, 995) 995 FORMAT(' COULD NOT COMPUTE THE OVER SHOOT FACTOR WITHIN', 1' PERMISSIBLE NO. OF ITERATIONS') STOP C 9105 IF ((VP*V2).GT.0.DO) GO TO 9110 DTQ=DT GO TO 9100 9110 DTP=DT VP=V2 GO TO 9100

c C Overshooting the time BS2=0 c 153 IF (BS2.EQ.0.D0) GO TO 125 IF ((BS1*BS2).GE.0.DO) GO TO 125 NCYC=0 DTP=0.DO DTQ=DT BSP=BS1 C 100 DT=0.5DO*(DTP+DTQ) CALL SOLVE(DT,DA2,C) CALL BASE(BS2,C,DA2,DT,DU) U2=U1+DU DV=A1*DT+DA2*DT/2.0 V2=V1+DV IF (DABS(BS2).LE.0.01D0.OR.DABS(DTP-DTQ).LE.0.00001D0) THEN BS2=0.DO F2=-F2C GO TO 120 ENDIF NCYC=NCYC+ 1 IF (NCYC.LE.MCYC) GO TO 105 WRITE(*,95) 95 FORMAT(' COULD NOT COMPUTE THE OVER SHOOT FACTOR WITHIN', 1' PERMISSIBLE NO. OF ITERATIONS') STOP C 105 IF ((BSP*BS2).GT.0.DO) GO TO 110 DTQ=DT GO TO 100 110 DTP=DT BSP=BS2 GO TO 100 C 120 GA2=GA1+DGR*DT GV2=GV1+ (GA1+GA2) *DT/2.DO T2=T1+DT 125 P2=P1+DP*DT C C RU=0.DO IF ((KEY.EQ.KEYO).AND. (KEY.NE.O)) RU=DU C C CALL STATE(KODY,KODP,C, SG) C IF (KODP.EQ.KODY) GO TO 140 C C FROM LOW STIFFNESS TO HIGH STIFFNESS C IF (KODP.EQ.1.AND.KODY.EQ.0) THEN FCP=F2C F2C=V2*C1 AP=A1+DA2 EI=EI+(GA1+A1 + GA2+AP)*XMASS*DGU/2.0 A2= (P2-F2C-F2)/XMASS ET=ET+(F1+F2)*DU/2.DO ED=ED+(F1C+FCP)*DU/2.DO DU=0.DO DGU=0.DO

c GO TO 150 ENDIF C C FROM HIGH STIFFNESS TO LOW STIFFNESS C FCP=F2C F2C=V2*C2 AP=A1+DA2 EI=EI+(GA1+A1 + GA2+AP)*XMASS*DGU/2.0 A2=(P2-F2C-F2)/XMASS C ACOR=(FP+FCP-F2C-F2)/XMASS ET=ET+(F1+F2)*DU/2.DO ED=ED+(F1C+FCP)*DU/2.DO DU=0.DO DGU=0.DO GO TO 150 C 140 A2=A1+DA2 150 CALL ENERGY (XMASS,ST,C,DU,DGU,DT,PSTIFF,STIFF) C C PROCEED TO OUTPUT C IF (KPR.NE.10) GO TO 155 WRITE(6,2070) T2,KK,EI,EK,ED,ES,EH,UB,UR,GA2,GV2 WRITE(7,3068) T2,U2,V2,A2,F2,EI,EK,ED,ES,EH,EKS WRITE(11,3068) T2,U2 WRITE(15,3068) T2,EI WRITE(21,3068) U2,F2 WRITE(17,3068) T2,ED WRITE(2,3068) T2,EKS WRITE(18,3068) T2,EKT KPR=0 C Calculate maximum value IF (U2.GT.DISMAX) THEN DISMAX=U2 TDIMAX=T2 ENDIF IF (U2.LT.DISMIN) THEN DISMIN=U2 TDIMIN=T2 ENDIF IF (ED.GT.EDMAX) THEN EDMAX=ED TEDMAX=T2 ENDIF IF (EI.GT.EIMAX) THEN EIMAX=EI TEIMAX=T2 ENDIF IF (EKS.GT.EKSMAX) THEN EKSMAX=EKS TESMAX=T2 ENDIF

IF (EKT.GT.EKTMAX) THEN EKTMAX=EKT TETMAX=T2 ENDIF C C UPDATING INTEGRATION TIME STEP AND STRUCTURAL C RESPONSE QUANTITIES FOR THE NEXT TIME STEP C 155 F1=F2 F1C=F2C BS2=F2+F2C BS1=BS2 C P1=P2 T1=T2 C A1=A2 V1=V2 U1=U2 C GA1=GA2 GV1=GV2 C TO(KK)=T2 UU(KK)=U2 VV(KK)=V2 AA(KK)=A2 RR(KK)=F2 CC(KK)=F2C C BB(KK)=BS2 GV(KK)=GV2 SS(KK)=SG KD(KK)=KODY C DT=DELTAT DTT=TT(II+1)-T1 IF (DTT.EQ.0.DO) GO TO 160 IF (DT.GT.DTT) DT=DTT 160 T2=T1+DT KODP=KODY KEYO=KEY KK=KK+1 GO TO 20 C C PRINT RESPONSE TIME HISTORY AND SUMMARIES C 400 WRITE(6,2090) WRITE(6,2095) (TO(I),UU(I),VV(I),AA(I),RR(I),I=1,KK,10) C WRITE(6,2100) WRITE(6,2105) (TO(I),BB(I),GV(I),SS(I),KD(I),I=1,KK,10) C WRITE (20,3068) TBSMAX,BSMAX WRITE (20,3068) TBSMIN,BSMIN WRITE (20,3068) TDIMAX,DISMAX WRITE (20,3068) TDIMIN,DISMIN WRITE (20,3068) TEDMAX,EDMAX WRITE (20,3068) TEIMAX,EIMAX WRITE (20,3068) TESMAX,EKSMAX WRITE (20,3068) TETMAX,EKTMAX 2000 FORMAT(1H,52(1H-),/,

1 2 53H DYNAMIC RESPONSE OF SINGLE DEGREE OF FREEDOM SYSTEMS,/, 1H,52(1H-),//,1H,8A10) 2005 FORMAT(19H 1 29H 2 29H 3 29H 4 29H 5 29H 6 29H 7 29H 8 29H 9 29H 2020 FORMAT(24H 1 29H 2 29H SYSTEM DESCRIPTION,/,1H,42(1H-),/, MASS.....................,E14.6,/, STIFFNESS................,E14.6,/, STRAIN HARDENING RATIO...,E4.6,/, NATURAL FREQUENCY.........E14.6,/, PERIOD................... E14.6,/, DAMPING.................. E14.6,/, SHIFT NATURAL FREQUENCY...,E14.6,/, SHIFT PERIOD.............. E14.6,/, SHIFT DAMPING..............E14.6) SOLUTION SPECIFICATIONS,/,1H,42(1H-),/, ANALYSIS TIME STEP........,E14.6,/, OUTPUT TIME STEP........E14.6,/) 2030 FORMAT(1H,15(1H-),/,16H LOADING HISTORY,/,1H,15(1H-),//, 1 15H LOAD FACTOR =,E14.6) 2035 FORMAT(//,4(10X,4HTIME,2X,12HACCELERATION)) 2045 FORMAT(4(5X,F9.4,2X,E12.5)) 2055 FORMAT(1H,8A10) 2060 FORMAT( ENERGY TIME HISTORY'/, 1' TIME STEPS INPUT KINETIC DAMPING 2' STRAIN HYSTE. UNBAL. EQUILIBRIUM 3'GROUND GROUND GROUND'/, 4'NO. ENERGY ENERGY ENERGY 5' ENERGY ENERGY ENERGY RATIO 6'ACCELERATION VELOCITY DISPLACEMENT'/,lX,140(1H-)) 2068 FORMAT(' OUTPUT TIME HISTORIES IN THE ORDER? TIME,', 1'DISPLACEMENT, VELOCITY, ACCELERATION, RESISTANCE,', 2'INPUT ENERGY,'/,' KINETIC ENERGY, HYSTERETIC ENERGY,', 3'DAMPING ENERGY, HYSTERETIC ENERGY DUCTILITY,', 4'RESIDUAL DUCTILITY.,'//) 2070 FORMAT(F8.4,I7,6F12.4,F12.6,3F13.4) 3068 FORMAT(F8.4,11F12.5) 2090 FORMAT(' RESPONSE TIME HISTORY'/, 1' TIME DISPLACEMENT VELOCITY 2'ACCELERATION RESISTANCE'/, X,78(1H-)) 2095 FORMAT(F9.5,5X,F12.4,5X,F12.4,5X,F12.4,5X,F12.4) 2100 FORMAT(' BASE-SHEAR TIME HISTORY'/, 1' TIME BASE-SHEAR GROUND-VELOCITY 2' SIGN KODY'/,1X,77(1H-)) 2105 FORMAT(F9.5,3F17.4,I14) C RETURN END C SUBROUTINE SOLVE(DT,DA,C) IMPLICIT DOUBLE PRECISION (A-H,O-Z) CHARACTER*10 HED COMMON /BLK5/ DF,FC,FT,FY,FYC1,FYT1,UC,UT,KEY,KEYO COMMON /BLK1/ XMASS,STIFF,PSTIFF,ST,FACTOR,C1,C2,HED COMMON /BLK3/ DELTAT,P1,P2,DP,U1,U2,Fl,F2,T1,T2,V1,V2,Al,A2 COMMON /BLK8/ RU,F1C,F2C C ST = STIFF IF (KEY.EQ.-1) ST=PSTIFF IF (KEY.EQ. 1) ST=PSTIFF EFMAS=XMASS+C*DT/2.DO+ST*DT*DT/4.DO EFLOD=(DP-C*A1-ST*(V1+Al*DT/2.D) ) *DT DA=EFLOD/EFMAS DV=A1 *DT+DA*DT/2.DO DU=V1*DT+A1*DT*DT/2.DO+DA*DT*DT/4.DO

VV=V1+DV IF (KEY.EQ. 0) RR=FT-(UT-U1-DU)*(STIFF) IF (KEY.EQ. 1) RR=FYT1+PSTIFF*(Ul+DU) IF (KEY.EQ. -1)RR=FYC1+PSTIFF*(Ul+DU) AA= (P1+DP*DT-C*VV-RR)/XMASS DA=AA-A1 DV=A1*DT+DA*DT/2.DO V2=V1+DV DU=Vl*DT+A1*DT*DT/2.DO+DA*DT*DT/4.DO U2=U1+DU IF (U2.GT.UC.AND. U2.LT.UT) KEY=0.O IF (U2.GE.UT) THEN IF (V2.GT. 0.0) KEY=1 IF (V2.LE. 0.0) THEN KEY=0 UT=U2 UC=U2- (FT-FC) /STIFF FT=FYT1+UT*PSTIFF FC=FT-DF ENDIF ENDIF IF (U2.LE.UC) THEN IF (V2.LT. 0.0) KEY=-1 IF (V2.GE. 0.0) THEN KEY=0 UC=U2 UT=U2+(FT-FC) /STIFF FC=FYC1+UC*PSTIFF FT=FC+DF ENDIF ENDIF C*********************************** C RETURN END C SUBROUTINE BASE(BS,C,DA,DT,DU) IMPLICIT DOUBLE PRECISION (A-H,O-Z) CHARACTER*10 HED COMMON /BLK5/ DF,FC,FT,FY,FYC1,FYT1,UC,UT,KEY,KEYO COMMON /BLK1/ XMASS,STIFF,PSTIFF,ST,FACTOR,C1,C2,HED COMMON /BLK3/ DELTAT,P1,P2,DP,U1,U2,Fl,F2,T1,T2,V1,V2,A1,A2 COMMON /BLK8/ RU,F1C,F2C C DV=A1*DT+DA*DT/2.DO DU=V1*DT+Al*DT*DT/2.DO+DA*DT*DT/4.DO C IF (KEY.EQ. 0) F2=FT-(UT-U1-DU)*(STIFF) IF (KEY.EQ. 1) F2=FYT1+PSTIFF*(Ul+DU) IF (KEY.EQ. -1)F2=FYCl+PSTIFF*(Ul+DU) F2C=F1C+C*DV BS=F2+F2C RETURN END C SUBROUTINE ENERGY(XMASS,ST,C,DU,DGU,DT,PSTIFF,STIFF) IMPLICIT DOUBLE PRECISION (A-H,O-Z) COMMON /BLK5/ DF,FC,FT,FY,FYC1,FYT1,UC,UT,KEY,KEYO COMMON /BLK2/ DAMP1,DOUT,PK,DAMP2,KOUNT

COMMON /BLK3/ DELTAT,P1,P2,DP,U1,U2,Fl,F2,T1,T2,V1,V2,A1,A2 COMMON /BLK8/ RU,F1C,F2C COMMON /BLK4/ GA1,GA2,GV1,GV2,EI,ES,EH,ED,EK,ET,UB,UR,EKS,EKT C C COMPUTE TIME HISTORY OF ENERGY INPUT, STORED, AND DISSIPATED C BY SINGLE DEGREE OF FREEDOM SYSTEM WITH STRAIN HARDENING C C RECOVERABLE STRAIN ENERGY (ES), HYSTERETIC ENERGY (EH), DAMPING C ENERGY (ED) AND KINETIC ENERGY (EK) C AT1=Al+GA1 AT2=A2+GA2 EI=EI+(AT1+AT2)*XMASS*DGU/2.0 ED=ED+(F1C+F2C)*DU/2.DO ET=ET+(F1+F2)*DU/2.DO ES=ES+(F1+F2)*DU/2.DO-DABS(RU)*FYT1 EH=ET-ES VT=GV2+V2 EK=0. 5D0*XMASS*VT*VT EKS=ES+EK EKT=ET+EK C C COMPUTE ENERGY OUT-OF-BALANCE RATIO C UB=EI-ES-EH-ED-EK UR=UB/EI 1000 C WRITE(*,1000) T2,EI,EK,ED,ES,EH,UB,UR FORMAT(10F12.5) RETURN END C SUBROUTINE STATE(KODY,KODP,C,SQ) IMPLICIT DOUBLE PRECISION (A-H,O-Z) CHARACTER*10 HED COMMON COMMON COMMON COMMON COMMON COMMON 1 /BLK1/ /BLK3/ /BLK8/ /BLK4/ /BLK7/ /BLK9/ XMASS,STIFF,PSTIFF,ST,FACTOR,C1, C2,HED DELTAT, P1, P2,DP,U1,U2,F1,F2,Tl,T2,V1,V2,Al,A2 RU,F1C,F2C GA1,GA2,GV1,GV2,EI,ES,EH,ED,EK,ET,UB,UR,EKS,EKT KPR BSMAX,BSMIN,DISMAX,DISMIN, EDMAX, EIMAX, EKSMAX,EKTMAX TBSMAX,TBSMIN,TDIMAX,TDIMIN,TEDMAX,TEIMAX, TESMAX,TETMAX COMMON /TIME/ 1 C TEMP1=F1+F1C TEMP2=F2+F2C SP=TEMP1*V1 SQ=TEMP2*V2 C IF (SP) 10,100,200 10 IF (SQ) 20,30,40 20 KODY=1 ST=PSTIFF C=C2 GO TO 400 30 KODY=0 ST=STIFF C=C1

IF (TEMP2.EQ.0.DO.AND.V2.EQ.O.DO) THEN KODY=1 ST=PSTIFF C=C2 ENDIF GO TO 400 40 KODY=0 ST=STIFF C=C1 GO TO 400 C 100 IF (SQ) 120,130,140 120 KODY=1 ST=PSTIFF C=C2 GO TO 400 130 KODY=0 ST=STIFF C=C1 IF (TEMP1.GE.0.DO.AND.TEMP2.GE.0.DO.AND.V1.GE.0.DO.AND.V2.GE. + 0.DO) THEN KODY=1 ST=PSTIFF C=C2 ENDIF IF (TEMP1.LE.0.DO.AND.TEMP2.LE.0.DO.AND.V1.LE.O.DO.AND.V2.LE. + 0.DO) THEN KODY=1 ST=PSTIFF C=C2 ENDIF GO TO 400 140 KODY=0 ST=STIFF C=C1 GO TO 400 C 200 IF (SQ) 220,230,240 220 KODY=1 ST=PSTIFF C=C2 GO TO 400 230 KODY=1 ST=PSTIFF C=C2 IF (TEMP1.GE.0.DO.AND.TEMP2.EQ.0.DO.AND.V1.GE.0.DO.AND.V2.EQ. + 0.DO) THEN KODY=0 ST=STIFF C=C1 ENDIF IF (TEMP1. LE. 0.DO.AND.TEMP2. EQ. 0.DO.AND.V1.LE. 0.DO.AND.V2. EQ. + 0.DO) THEN KODY=0 ST=STIFF C=C1 ENDIF GO TO 400 240 KODY=0 ST=STIFF C=C1 C 400 KPR=KPR+1 IF (KPR.NE.10) GO TO 700 KKKK=1 IF (KODY.EQ.1) KKKK=-1

WRITE(12,750) T2,TEMP2 WRITE(13,750) T2,GV2 WRITE(14,600) T2,KKKK IF (TEMP2.GT.BSMAX) THEN BSMAX=TEMP2 TBSMAX=T2 ENDIF IF (TEMP2.LT.BSMIN) THEN BSMIN=TEMP2 TBSMIN=T2 ENDIF 600 FORMAT(F15.3,I5) C 700 WRITE(10,750) T2,F1,GV1,F2,GV2,KODP,KODY 750 FORMAT(5F15.3,2I5) C RETURN END

C PROGRAM FOR I-B C *** Use Vrel* BS for controlling C (HERE THE STIFFNESS ONLY HAVE TWO VALUES) C IMPLICIT DOUBLE PRECISION (A-H,O-Z) CHARACTER*20 FMT CHARACTER*10 HED C C DYNAMIC ANALYSIS OF SINGLE DEGREE OF FREEDOM SYSTEMS C WITH THE FOLLOWING FORCE-DEFORMATION MECHANICAL CHARACTERISTICS C SIGN BASE-SHEAR.EQ. SIGN GROUND VELOCITY: MIN.STIFFNESS C SIGN BASE-SHEAR.NE. SIGN GROUND VELOCITY: MAX.STIFFNESS C C PROGRAMMED BY JODI FIRMANSJAH, CORRECTED AND EXPANDED BY I-HONG CHEN C C SOME KEY VARIABLES C XMASS = MASS C STIFF = MAXIMUM STIFFNESS C PK = RATIO OF MINIMUM STIFFNESS TO MAXIMUM STIFFNESS C DAMP1 = DAMPING RATIO OF MAXIMUN STIFFNESS SYSTEM C DAMP2 = DAMPING RATIO OF MINIMUM STIFFNESS SYSTEM C DELTAT = INTEGRATION INTERVAL C XOUT = OUTPUT INTERVAL C C KOUNT = NO. GROUND ACCELERATION RECORD C FACTOR = MAGNIFICATION FACTOR C COMMON /BLK1/ XMASS,STIFF,PSTIFF,FACTOR,C1,C2,HED COMMON /BLK2/ DAMP1,DOUT,PK,DAMP2,KOUNT COMMON /BLK3/ DELTAT,P1,P2,DP,U1,U2,Fl,F2,Tl,T2,Vl,V2,A1,A2 COMMON /BLK8/ RU,F1C,F2C COMMON /ACCL/ TT(2000),PP(2000) COMMON /RESP/ UU(100000),VV(100000),AA(100000),RR(100000), 1 TO(100000),CC(100000) COMMON /BLK9/ BSMAX, BSMIN, DISMAX,DISMIN, EDMAX, EIMAX, 1 EKSMAX,EKTMAX COMMON /TIME/ TBSMAX,TBSMIN,TDIMAX,TDIMIN,TEDMAX,TEIMAX, 1 TESMAX,TETMAX CHARACTER*24 INP C C OPEN EXTERNAL FILES C WRITE(*,5) 5 FORMAT(' input file') READ(*,10) INP 10 FORMAT(a24) C OPEN (5, FILE=INP) OPEN(6,FILE='out000.009') OPEN(1,FILE='filelO00.009') OPEN(7,FILE='file7000.009') OPEN(10,FILE='stateOOO.009') OPEN(ll,FILE='dis000.009') OPEN(12,FILE='bs000.009') OPEN(13,FILE='gv000.009') OPEN(UNIT=14,FILE='sg00 O.009') OPEN(2,FILE='eks000. 009') OPEN(18,FILE='ekt000.009') OPEN(17,FILE='edO00.009') OPEN(UNIT=15,FILE='eiOOO.009') OPEN(20,FILE='max00 O.009')

C READ HEADING AND SYSTEM INFORMATION C READ(5,1000) HED 1000 FORMAT(3A10) READ(5,1005) XMASS,STIFF,PK,DAMP1,DAMP2,DELTAT,XOUT 1005 FORMAT(7F10.2) IF (XOUT.EQ.0.D0) XOUT=1.D0 C C READ LOAD INFORMATION C READ(5,1015) KOUNT,DT,FACTOR,fmt 1015 FORMAT(lI5,2F10.2,a20) IF (FACTOR.EQ.0.DO) FACTOR=1.DO IF (DT.NE.0.D0) GO TO 30 READ(5,FMT) (TT(I),PP(I),I=1,KOUNT) GO TO 40 30 TT(1)=0.DO DO 35 I=2,KOUNT TT(I)=I*DT 35 CONTINUE READ(5,fmt) (PP(I),I=1,KOUNT) C 40 C C C C C C C DOUT=XOUT*DELTAT NOUT=(TT(KOUNT)-TT(1))/DOUT RESPONSE CALCULATION CALL RESPON(DELTAT) STOP END SUBROUTINE RESPON(DELTA) IMPLICIT DOUBLE PRECISION (A-H,O-Z) C C C CALCULATE THE RESPONSE TIME HISTORIES CHARACTER*10 HED COMMON COMMON COMMON COMMON COMMON COMMON COMMON COMMON 1 /BLK1/ XMASS,STIFF,PSTIFF,FACTOR,C1,C2,HED /BLK2/ DAMP1,DOUT,PK,DAMP2,KOUNT /BLK3/ DELTAT,P1,P2,DP,U1,U2,Fl,F2,Tl,T2,V1,V2,Al,A2 /BLK8/ RU,F1C,F2C /BLK4/ GA1,GA2,GV1, GV2,EI, ES,EH,ED,EK,ET,UB,UR,EKS,EKT /BLK7/ KPR /ACCL/ TT(2000),GA(2000) /RESP/ UU(100000),VW(100000),AA(100000),RR(100000), TO(100000),CC(100000) /BASE1/ BB(100000),GV(100000),SS(100000),KD(100000) /BLK9/ BSMAX,BSMIN,DISMAX,DISMIN,EDMAX,EIMAX, EKSMAX,EKTMAX /TIME/ TBSMAX,TBSMIN,TDIMAX,TDIMIN,TEDMAX,TEIMAX, TESMAX,TETMAX COMMON COMMON 1 COMMON 1 C C C COMPUTE MISCELLANEOUS CONSTANTS W1 =DSQRT(STIFF/XMASS) PERIOD1=8.DO*ATAN(1.0)/W1 C1 =2.DO*W1*XMASS*DAMP1 PSTIFF=PK*STIFF W2 =DSQRT(PSTIFF/XMASS) PERIOD2=8.DO*ATAN(1.0)/W2 C2 =2.DO*W2*XMASS*DAMP2

c c ECHO-PRINT INPUT QUANTITIES WRITE(1, 2068) WRITE(6,2000) WRITE (6, 2005) 1 WRITE(6,2020) WRITE (6,2030) WRITE(6,2035) WRITE(6, 2045) WRITE(6, 2055) WRITE (6,2060) HED XMASS, STIFF,PK, W, PERIOD, DAMP1, W2, PERIOD2, DAMP2 DELTA,DOUT FACTOR (TT(I),GA(I), I=1,KOUNT) HED C C C INITIALIZE BSMAX=0.DO BSMIN=0.DO DISMAX=.DO DISMIN=0.DO EDMAX=0.DO EIMAX=0.DO EKSMAX=0.DO EKTMAX=0.DO TBSMAX=.DO TBSMIN=0.DO TDIMAX=O.DO TDIMIN=O.DO TEDMAX=.DO TEIMAX=O.DO TESMAX=0.DO TETMAX=O.DO RU=O.DO MCYC=500 KODY=1 KPR=0 A1=-GA(1) *FACTOR EI=O.DO EKT=O.DO ED=O.DO ES=O.DO EH=O.DO ET=O.DO GA1=GA(1) *FACTOR GA2=0.DO GV1=0.DO GV2 =.DO BS1=O.DO BS2=0.DO P1=-XMASS*FACTOR*GA(1) ST=PSTIFF C=C2 T1=TT(1) F1=0.DO F2=0.DO F1C=O.DO F2C=0.DO U1=0.DO U2=.DO V1=O.DO

V2=0.D0 II=1 KK=1 C C COMPUTE RESPONSE HISTORY C (A) DETERMINING THE CURRENT INTEGRATION STEP C SIZE AT BEGINNING C DT=DELTAT IF (DT.GT.(TT(2)-TT(1))) DT=TT(2)-TT(1) DELTAT=DT T2=T1+DT KCHEK=0 KODP=KODY C C STARTING PLACE EXCEPT THE FIRST TIME STEP C (B) UPDATING THE CURRENT INPUT-EXCITATION C DIGITIZATION INTERVAL AT WHICH THE CURRENT C INTEGRATION STEP RESIDES C 20 IF (T2.LE.TT(II)) GO TO 25 IF (T2.GT.TT(II).AND.T2.LE.TT(II+1)) GO TO 30 KCHEK=0 II=II+1 IF (II.GE.KOUNT) GO TO 400 GO TO 20 25 II=II-1 GO TO 20 C C (C) INTERPOLATED LOADS AT THE TWO ENDS OF C CURRENT INTEGRATION STEP C 30 IF (KCHEK) 35,35,40 35 TP=TT(II) TQ=TT(II+1) AP=GA(II) *FACTOR AQ=GA(II+1) *FACTOR DGR= (AQ-AP) /(TQ-TP) DP=-XMASS*DGR KCHEK=1 C 40 P2=-XMASS* (AP+DGR* (T2-TP)) DGA=DGR*DT GA2=GA1+DGA DGV=GA1*DT+DGA*DT/2.0 GV2=GV1+DGV DGU=GV1*DT+GA1*DT*DT/2.0+DGA*DT*DT/4.0 IF (GV1.EQ.0.DO.OR.GV1.EQ.GV2) GO TO 90 DTG=GV1/ (GV1-GV2) *DT IF (DTG.GE.DT.OR.DTG.LE.0.DO) GO TO 90 DT=DTG T2=T1+DTG P2=-XMASS*(AP+DGR*(T2-TP)) DGA=DGR*DT GA2=GA1+DGA DGV=GA1*DT+DGA*DT/2.0 GV2=GV1+DGV DGU=GV1*DT+GA1*DT*DT/2.0+DGA*DT*DT/4.0 GV2=0.DO C C CALCULATE RESPONSE AT THE END OF CURRENT C INTEGRATION TIME STEP C 90 CALL SOLVE(DT,DA2,ST,C) CALL BASE(BS2,ST,C,DA2,DT,DU)

c C Overshooting the time when V2=0 C U2=U1+DU DV=A1*DT+DA2*DT/2.0 V2=V1+DV IF (V2.EQ.0.D0) GO TO 153 IF ((V1*V2).GE.0.DO) GO TO 153 NCYC=0 DTP=0.DO DTQ=DT VP=V1 C 9100 DT=0.5DO*(DTP+DTQ) CALL SOLVE(DT,DA2,ST,C) CALL BASE(BS2,ST,C,DA2,DT,DU) C CALL BASE SHOULD BE ABLE TO OMMIT U2=U1+DU DV=A1*DT+DA2*DT/2.0 V2=V1+DV IF (DABS(V2).LE.0.001DO.OR.DABS(DTP-DTQ).LE.0.00001D0) THEN V2=0.DO GO TO 153 ENDIF NC NCYC=NCYC+1 IF (NCYC.LE.MCYC) GO TO 9105 WRITE(*,995) 995 FORMAT(' COULD NOT COMPUTE THE OVER SHOOT FACTOR WITHIN', 1' PERMISSIBLE NO. OF ITERATIONS') STOP C 9105 IF ((VP*V2).GT.O.DO) GO TO 9110 DTQ=DT GO TO 9100 9110 DTP=DT VP=V2 GO TO 9100 C C Overshooting the time BS2=0 c 153 IF (BS2.EQ.0.DO) GO TO 125 IF ((BS1*BS2).GE.0.DO) GO TO 125 NCYC=0 DTP=0.DO DTQ=DT BSP=BS1 C 100 DT=0.5D0*(DTP+DTQ) CALL SOLVE(DT,DA2,ST,C) CALL BASE(BS2,ST,C,DA2,DT,DU) U2=U1+DU DV=A1*DT+DA2*DT/2.0 V2=V1+DV IF (DABS(BS2).LE.0.01DO.OR.DABS(DTP-DTQ).LE.0.00001DO) THEN BS2=0.DO F2=-F2C GO TO 120 ENDIF NCYC=NCYC+ 1 IF (NCYC.LE.MCYC) GO TO 105 WRITE(*,95) 95 FORMAT(' COULD NOT COMPUTE THE OVER SHOOT FACTOR WITHIN', 1' PERMISSIBLE NO. OF ITERATIONS')

STOP C 105 IF ((BSP*BS2).GT.0.D0) GO TO 110 DTQ=DT GO TO 100 110 DTP=DT BSP=BS2 GO TO 100 C 120 GA2=GA1+DGR*DT GV2=GV1+ (GA1+GA2) *DT/2.DO T2=T1+DT 125 P2=P1+DP*DT CALL STATE(KODY,KODP,ST,C,SG) C IF (KODP.EQ.KODY) GO TO 140 C C FROM LOW STIFFNESS TO HIGH STIFFNESS C IF (KODP.EQ.1.AND.KODY.EQ.0) THEN RU=0.DO FCP=F2C F2C=V2*C1 AP=A1+DA2 EI=EI+(GA1+A1 + GA2+AP) *XMASS*DGU/2.0 A2= (P2-F2C-F2)/XMASS C ACOR= (FP+FCP-F2C-F2)/XMASS ET=ET+(F1+F2)*DU/2.DO ED=ED+(F1C+FCP)*DU/2.DO DU=.DO DGU=0.DO C GO TO 150 ENDIF C C FROM HIGH STIFFNESS TO LOW STIFFNESS C FP=F2 FCP=F2C F2=U2 * PSTIFF F2C=V2*C2 AP=A1+DA2 EI=EI+(GA1+A1 + GA2+AP)*XMASS*DGU/2.0 A2= (P2-F2C-F2)/XMASS C ACOR=(FP+FCP-F2C-F2)/XMASS ET=ET+(Fl+FP)*DU/2.DO ED=ED+(F1C+FCP)*DU/2.DO RU=0.DO DU=0.DO DGU=0.DO GO TO 150 C 140 A2=A1+DA2 IF(KODY.EQ.0.DO.AND.KODP.EQ.0.DO) RU=RU+DU 150 CALL ENERGY(XMASS,ST,C,DU,DGU,DT,PSTIFF,STIFF) C

C PROCEED TO OUTPUT IF (KPR.NE.10) GO TO 155 WRITE(6,2070) T2,KK, EI, EK, ED,ES,EH,UB,UR,GA2,GV2 WRITE(7,3068) T2,U2,V2,A2,F2,EI,EK,ED,ES,EH,EKS WRITE(11,3068) T2,U2 WRITE(15,3068) T2,EI WRITE(17,3068) T2,ED WRITE(2,3068) T2,EKS WRITE(18,3068) T2,EKT KPR=0 C Calculate maximum value IF (U2.GT.DISMAX) THEN DISMAX=U2 TDIMAX=T2 ENDIF IF (U2.LT.DISMIN) THEN DISMIN=U2 TDIMIN=T2 ENDIF IF (ED.GT.EDMAX) THEN EDMAX=ED TEDMAX=T2 ENDIF IF (EI.GT.EIMAX) THEN EIMAX=EI TEIMAX=T2 ENDIF IF (EKS.GT.EKSMAX) THEN EKSMAX=EKS TESMAX=T2 ENDIF IF (EKT.GT.EKTMAX) THEN EKTMAX=EKT TETMAX=T2 ENDIF C C UPDATING INTEGRATION TIME STEP AND STRUCTURAL C RESPONSE QUANTITIES FOR THE NEXT TIME STEP C 155 F1=F2 F1C=F2C BS2=F2+F2C BS1=BS2 C P1=P2 T1=T2 C A1=A2 V1=V2 U1=U2 C GA1=GA2 GV1=GV2 C TO(KK)=T2 UU (KK)=U2 W (KK)=V2 AA(KK)=A2 RR(KK) =F2

CC (KK)=F2C C BB(KK)=BS2 GV(KK) =GV2 SS(KK)=SG KD(KK)=KODY C DT=DELTAT DTT=TT(II+1)-T1 IF (DTT.EQ.0.DO) GO TO 160 IF (DT.GT.DTT) DT=DTT 160 T2=T1+DT KODP=KODY KK=KK+1 GO TO 20 C C PRINT RESPONSE TIME HISTORY AND SUMMARIES C 400 WRITE(6,2090) WRITE(6,2095) (TO(I), UU(I),VV(I),AA(I),RR(I),I=1,KK,10) C WRITE(6,2100) WRITE(6,2105) (TO(I),BB(I),GV(I),SS(I),KD(I),I=1,KK,10) C WRITE WRITE WRITE WRITE WRITE WRITE WRITE WRITE (20,3068) (20,3068) (20,3068) (20,3068) (20,3068) (20,3068) (20,3068) (20,3068) TBSMAX,BSMAX TBSMIN,BSMIN TDIMAX, DISMAX TDIMIN,DISMIN TEDMAX,EDMAX TEIMAX,EIMAX TESMAX,EKSMAX TETMAX,EKTMAX 2000 FORMAT(1H,52(1H-),/, 1 53H DYNAMIC RESPONSE OF SINGLE DEGREE OF FREEDOM SYSTEMS,/, 2 1H,52(1H-),//,1H,8A10) 2005 FORMAT(19H SYSTEM DESCRIPTION,/,1H,42(1H-),/, 1 29H MASS..................... E14.6,/, 2 29H STIFFNESS...............,E14.6,/, 3 29H STRAIN HARDENING RATIO...,E14.6,/, 4 29H NATURAL FREQUENCY........ E14.6,/, 5 29H PERIOD...................... E14.6,/, 6 29H DAMPING.................. E14.6,/, 7 29H SHIFT NATURAL FREQUENCY...,E14.6,/, 8 29H SHIFT PERIOD.............. E14.6,/, 9 29H SHIFT DAMPING............,E14.6) 2020 FORMAT(24H SOLUTION SPECIFICATIONS,/,1H,42(1H-),/, 1 29H ANALYSIS TIME STEP....... E14.6,/, 2 29H OUTPUT TIME STEP.......,E14.6,/) 2030 FORMAT(1H,15(1H-),/,16H LOADING HISTORY,/,1H,15(1H-),//, 1 15H LOAD FACTOR =,E14.6) 2035 FORMAT(//,4(10X,4HTIME,2X,12HACCELERATION)) 2045 FORMAT(4(5X,F9.4,2X,E12.5)) 2055 FORMAT(1H,8A10) 2060 FORMAT(' ENERGY TIME HISTORY'/, 1' TIME STEPS INPUT KINETIC DAMPING 2' STRAIN HYSTE. UNBAL. EQUILIBRIUM 3'GROUND GROUND GROUND'/, 4' NO. ENERGY ENERGY ENERGY 5' ENERGY ENERGY ENERGY RATIO 6'ACCELERATION VELOCITY DISPLACEMENT'/,lX,140(1H-)) 2068 FORMAT(' OUTPUT TIME HISTORIES IN THE ORDER? TIME,', 1'DISPLACEMENT, VELOCITY, ACCELERATION, RESISTANCE,', 2'INPUT ENERGY,'/,' KINETIC ENERGY, HYSTERETIC ENERGY,', 3'DAMPING ENERGY, HYSTERETIC ENERGY DUCTILITY,', I I

4'RESIDUAL DUCTILITY.,'//) 2070 FORMAT(F8.4,I7,6F12.4,F12.6,3F13.4) 3068 FORMAT(F8.4,11F12.5) 2090 FORMAT(' RESPONSE TIME HISTORY'/, 1' TIME DISPLACEMENT VELOCITY 2'ACCELERATION RESISTANCE'/, X,78(1H-) ) 2095 FORMAT(F9.5,5X,F12.4,5X,F12.4,5X,F12.4,5X,F12.4) 2100 FORMAT(' BASE-SHEAR TIME HISTORY'/, 1' TIME BASE-SHEAR GROUND-VELOCITY 2' SIGN KODY'/,1X,77(1H-)) 2105 FORMAT(F9.5,3F17.4,I14) C RETURN END C SUBROUTINE SOLVE(DT,DA,ST,C) IMPLICIT DOUBLE PRECISION (A-H,O-Z) CHARACTER*10 HED COMMON /BLK1/ XMASS,STIFF,PSTIFF,FACTOR,C1,C2,HED COMMON /BLK3/ DELTAT,P1,P2,DP,U1,U2,Fl,F2,T1,T2,V1,V2,A1,A2 COMMON /BLK8/ RU,F1C,F2C C EFMAS=XMASS+C*DT/2.DO+ST*DT*DT/4.DO EFLOD=(DP-C*Al-ST*(V1+A*DT/2.DO) )*DT DA=EFLOD/EFMAS DV=A1*DT+DA*DT/2.DO DU=V1*DT+A1*DT*DT/2.DO+DA*DT*DT/4.DO C VV=V1+DV RR=F1+ST*DU AA=(P1+DP*DT-C*VV-RR)/XMASS DA=AA-A1 C RETURN END C SUBROUTINE BASE(BS,ST,C,DA,DT,DU) IMPLICIT DOUBLE PRECISION (A-H,O-Z) CHARACTER*10 HED COMMON /BLK1/ XMASS,STIFF,PSTIFF,FACTOR,C1,C2,HED COMMON /BLK3/ DELTAT,P1,P2,DP,U1,U2,F1,F2,T1,T2,V1,V2,A1,A2 COMMON /BLK8/ RU,F1C,F2C C DV=A1*DT+DA*DT/2.DO DU=V1*DT+A1*DT*DT/2.DO+DA*DT*DT/4.DO F2=F1+ST*DU F2C=F1C+C*DV BS=F2+F2C C RETURN END C SUBROUTINE ENERGY(XMASS,ST,C,DU,DGU,DT,PSTIFF,STIFF) IMPLICIT DOUBLE PRECISION (A-H,O-Z) COMMON /BLK2/ DAMP1,DOUT,PK,DAMP2,KOUNT COMMON /BLK3/ DELTAT,P1,P2,DP,U1,U2,Fl,F2,T1,T2,V1,V2,A1,A2 COMMON /BLK8/ RU,F1C,F2C COMMON /BLK4/ GA1,GA2,GV1,GV2,EI,ES,EH,ED,EK,ET,UB,UR,EKS,EKT C C COMPUTE TIME HISTORY OF ENERGY INPUT, STORED, AND DISSIPATED C BY SINGLE DEGREE OF FREEDOM SYSTEM WITH STRAIN HARDENING

c C RECOVERABLE STRAIN ENERGY (ES), HYSTERETIC ENERGY (EH), DAMPING C ENERGY (ED) AND KINETIC ENERGY (EK) C AT1=A1+GA1 AT2=A2+GA2 EI=EI+(AT1+AT2) *XMASS*DGU/2.0 ED=ED+(F1C+F2C)*DU/2.DO ET=ET+(F1+F2)*DU/2.DO ES=0.5*PSTIFF*U2*U2 + 0.5*(STIFF-PSTIFF)*RU*RU EH=ET-ES VT=GV2+V2 EK=0.5D0*XMASS*VT*VT EKS=ES+EK EKT=ET+EK C C COMPUTE ENERGY OUT-OF-BALANCE RATIO C UB=EI-ES-EH-ED-EK UR=UB/EI WRITE(*,1000) T2,EI,EK,ED,ES,EH,UB,UR 1000 FORMAT(10F12.5) C RETURN END C SUBROUTINE STATE(KODY,KODP,ST, C, SQ) IMPLICIT DOUBLE PRECISION (A-H,O-Z) CHARACTER*10 HED COMMON /BLK1/ XMASS,STIFF,PSTIFF, FACTOR,C1, C2, HED COMMON /BLK3/ DELTAT,P1,P2,DP,U1,U2, F,F2,T1,T2,V1,V2,A1,A2 COMMON /BLK8/ RU,F1C,F2C COMMON /BLK4/ GA1,GA2,GV1,GV2,EI,ES,EH,ED,EK,ET,UB,UR,EKS,EKT COMMON /BLK7/ KPR COMMON /BLK9/ BSMAX,BSMIN,DISMAX,DISMIN,EDMAX,EIMAX, 1 EKSMAX, EKTMAX COMMON /TIME/ TBSMAX,TBSMIN,TDIMAX,TDIMIN,TEDMAX,TEIMAX, 1 TESMAX,TETMAX C TEMP1=F1+F1C TEMP2=F2+F2C SP=TEMP1*Vl SQ=TEMP2*V2 C IF (SP) 10,100,200 10 IF (SQ) 20,30,40 20 KODY=1 ST=PSTIFF C=C2 GO TO 400 30 KODY=0 ST=STIFF C=C1 IF (TEMP2.EQ.0.D0.AND.V2.EQ.0.D0) THEN KODY=1 ST=PSTIFF C=C2 ENDIF GO TO 400 40 KODY=0 ST=STIFF

C=C1 GO TO 400 C 100 IF (SQ) 120,130,140 120 KODY=1 ST=PSTIFF C=C2 GO TO 400 130 KODY=0 ST=STIFF C=C1 IF (TEMP1.GE..DO.AND.TEMP2.GE..DO.AND.V1.GE..DO.AND.V2.GE. + 0.DO) THEN KODY=1 ST=PSTIFF C=C2 ENDIF IF (TEMP1.LE.0.DO.AND.TEMP2.LE.0.DO.AND.V1.LE.0.DO.AND.V2.LE. + 0.DO) THEN KODY=1 ST=PSTIFF C=C2 ENDIF GO TO 400 140 KODY=0 ST=STIFF C=C1 GO TO 400 C 200 IF (SQ) 220,230,240 220 KODY=1 ST=PSTIFF C=C2 GO TO 400 230 KODY=1 ST=PSTIFF C=C2 IF (TEMP1. GE. 0.DO.AND.TEMP2.EQ. 0.DO.AND.V1.GE.0.DO.AND.V2.EQ. + 0.DO) THEN KODY=0 ST=STIFF C=C1 ENDIF IF (TEMP1.LE. 0.DO.AND.TEMP2.EQ. 0.DO.AND.V1.LE. O.DO.AND.V2.EQ. + 0.DO) THEN KODY=0 ST=STIFF C=C1 ENDIF GO TO 400 240 KODY=0 ST=STIFF C=C1 C 400 KPR=KPR+1 IF (KPR.NE.10) GO TO 700 KKKK=1 IF (KODY.EQ.1) KKKK=-1 WRITE(12,750) T2,TEMP2 WRITE(13,750) T2,GV2 WRITE(14,600) T2,KKKK IF (TEMP2.GT.BSMAX) THEN BSMAX=TEMP2 TBSMAX=T2 ENDIF

IF (TEMP2.LT.BSMIN) THEN BSMIN=TEMP2 TBSMIN=T2 ENDIF 600 FORMAT(F15.3,I5) C 700 WRITE(10,750) T2,Fl,GV1,F2,GV2,KODP,KODY 750 FORMAT(5F15.3,215) C RETURN END

C PROGRAM FOR II-B c ===================Here keep damping constant ie cl=c2 c (ONLY CHANGE STIFFNESS STIFF & PSTIFF ) C C *** Use Vrel* BS for controlling C (HERE THE STIFFNESS ONLY HAVE TWO VALUES) C IMPLICIT DOUBLE PRECISION (A-H,O-Z) CHARACTER*20 FMT CHARACTER*10 HED C C DYNAMIC ANALYSIS OF SINGLE DEGREE OF FREEDOM SYSTEMS C WITH THE FOLLOWING FORCE-DEFORMATION MECHANICAL CHARACTERISTICS C SIGN BASE-SHEAR.EQ. SIGN GROUND VELOCITY: MIN.STIFFNESS C SIGN BASE-SHEAR.NE. SIGN GROUND VELOCITY: MAX.STIFFNESS C C PROGRAMMED BY JODI FIRMANSJAH, CORRECTED AND EXPANDED BY I-HONG CHEN C C SOME KEY VARIABLES C XMASS = MASS C STIFF = MAXIMUM STIFFNESS C PK = RATIO OF MINIMUM STIFFNESS TO MAXIMUM STIFFNESS C DAMP1 = DAMPING RATIO OF MAXIMUN STIFFNESS SYSTEM C DAMP2 = DAMPING RATIO OF MINIMUM STIFFNESS SYSTEM C DELTAT = INTEGRATION INTERVAL C XOUT = OUTPUT INTERVAL C C KOUNT = NO. GROUND ACCELERATION RECORD C FACTOR = MAGNIFICATION FACTOR C COMMON /BLK1/ XMASS,STIFF,PSTIFF,FACTOR,C1,C2,HED COMMON /BLK2/ DAMP1,DOUT,PK,DAMP2,KOUNT COMMON /BLK3/ DELTAT,P1,P2,DP,U1,U2,Fl,F2,Tl,T2,Vl,V2,A1,A2 COMMON /BLK8/ RU,F1C,F2C COMMON /ACCL/ TT(2000),PP(2000) COMMON /RESP/ UU(100000),VV(100000),AA(100000),RR(100000), 1 TO(100000),CC(100000) COMMON /BLK9/ BSMAX,BSMIN,DISMAX,DISMIN,EDMAX,EIMAX, 1 EKSMAX,EKTMAX COMMON /TIME/ TBSMAX,TBSMIN,TDIMAX,TDIMIN,TEDMAX,TEIMAX, 1 TESMAX,TETMAX CHARACTER*24 INP C C OPEN EXTERNAL FILES C WRITE(*,5) 5 FORMAT(' input file') READ(*,10) INP 10 FORMAT(a24) C OPEN(5,FILE=INP) OPEN(6,FILE='outO01') OPEN(1,FILE='filelO01') OPEN(7,FILE='file7001') OPEN(10,FILE='state001') OPEN(11,FILE='dis001') OPEN(12,FILE='bs001') OPEN(13,FILE='gvO1' ) OPEN(UNIT=14,FILE='sgO01') OPEN(2,FILE='eks001') OPEN(18,FILE='ektO01') OPEN(17,FILE='edOOl')

OPEN(UNIT=15,FILE='ei001') OPEN(20,FILE='maxO01') C C READ HEADING AND SYSTEM INFORMATION C READ(5,1000) HED 1000 FORMAT(3A10) READ(5,1005) XMASS,STIFF,PK,DAMP1,DAMP2,DELTAT,XOUT 1005 FORMAT(7F10.2) IF (XOUT.EQ.0.D0) XOUT=1.DO C C READ LOAD INFORMATION C READ(5,1015) KOUNT,DT,FACTOR, fmt 1015 FORMAT(1I5,2F10.2,a20) IF (FACTOR.EQ.0.DO) FACTOR=1.DO IF (DT.NE.0.D0) GO TO 30 READ(5,FMT) (TT(I),PP(I),I=1,KOUNT) GO TO 40 30 TT(1)=0.DO DO 35 I=2,KOUNT TT(I)=I*DT 35 CONTINUE READ(5,fmt) (PP(I),I=1,KOUNT) C 40 DOUT=XOUT*DELTAT C C C RESPONSE CALCULATION C CALL RESPON(DELTAT) C C STOP END C SUBROUTINE RESPON(DELTA) IMPLICIT DOUBLE PRECISION (A-H,O-Z) CALCULATE THE RESPONSE TIME HISTORIES C C C CHARACTER*10 HED COMMON COMMON COMMON COMMON COMMON COMMON COMMON COMMON 1 /BLK1/ /BLK2/ /BLK3/ /BLK8/ /BLK4/ /BLK7/ /ACCL/ /RESP/ XMASS,STIFF,PSTIFF,FACTOR,C1,C2,HED DAMP1,DOUT,PK,DAMP2,KOUNT DELTAT, P1,P2,DP,U1,U2,Fl,F2,T1,T2,V1,V2,Al,A2 RU,F1C,F2C GA1,GA2,GV1,GV2,EI,ES,EH,ED,EK,ET,UB,UR,EKS,EKT KPR TT(2000),GA(2000) UU(100000),VV(100000),AA(100000),RR(100000), TO(100000),CC(100000) / BB(100000),GV(100000),SS(100000),KD(100000) COMMON /BASE1/ C C C COMMON /BLK9/ BSMAX,BSMIN,DISMAX,DISMIN,EDMAX,EIMAX, 1 EKSMAX,EKTMAX COMMON /TIME/ TBSMAX,TBSMIN,TDIMAX,TDIMIN,TEDMAX,TEIMAX, 1 TESMAX,TETMAX COMPUTE MISCELLANEOUS CONSTANTS W1 =DSQRT(STIFF/XMASS) PERIOD1=8.DO*ATAN(1.0)/W1 C1 =2.DO*W1*XMASS*DAMP1 PSTIFF=PK*STIFF W2 =DSQRT(PSTIFF/XMASS) PERIOD2=8.DO*ATAN(1.0)/W2

c C LET C2 = C1 C2 =2.DO*W1*XMASS*DAMP1 C C ECHO-PRINT INPUT QUANTITIES WRITE(1,2068) WRITE(6,2000) WRITE(6,2005) 1 WRITE(6,2020) WRITE(6,2030) WRITE(6,2035) WRITE(6,2045) WRITE(6,2055) WRITE(6,2060) HED XMASS,STIFF,PK, W, PERIOD, DAMP1,W2,PERIOD2, DAMP2 DELTA,DOUT FACTOR (TT(I),GA(I),I=1,KOUNT) HED C C C INITIALIZE BSMAX=0.DO BSMIN=0.DO DISMAX=.DO DISMIN=0.DO EDMAX=0.DO EIMAX=0.DO EKSMAX=. DO EKTMAX=. DO TBSMAX=0.DO TBSMIN=0.DO TDIMAX=O.DO TDIMIN=O.DO TEDMAX=.DO TEIMAX=0.DO TESMAX=.DO TETMAX=.DO RU=O.DO MCYC=500 KODY=1 KPR=0 Al=-GA(1) *FACTOR EI=0.DO EKT=O.DO ED=0.DO ES=0.DO EH=.DO ET=0.DO GA1=GA(1) *FACTOR GA2=0.DO GV1=0.DO GV2=0.DO BS1=O.DO BS2=0.DO P1=-XMASS*FACTOR*GA(1) ST=PSTIFF C=C2 T1=TT(1) F1=0.DO F2=0.DO F1C=O.DO F2C=0.DO

U1=0.D0 U2 =.D0 V1=0O.DO V2=0.D0 II=1 KK=1 C C COMPUTE RESPONSE HISTORY C (A) DETERMINING THE CURRENT INTEGRATION STEP C SIZE AT BEGINNING C DT=DELTAT IF (DT.GT.(TT(2)-TT(1))) DT=TT(2)-TT(1) DELTAT=DT T2=T1+DT KCHEK=0 KODP=KODY C C STARTING PLACE EXCEPT THE FIRST TIME STEP C (B) UPDATING THE CURRENT INPUT-EXCITATION C DIGITIZATION INTERVAL AT WHICH THE CURRENT C INTEGRATION STEP RESIDES C 20 IF (T2.LE.TT(II)) GO TO 25 IF (T2.GT.TT(II).AND.T2.LE.TT(II+1)) GO TO 30 KCHEK=0 II=II+1 IF (II.GE.KOUNT) GO TO 400 GO TO 20 25 II=II-1 GO TO 20 C C (C) INTERPOLATED LOADS AT THE TWO ENDS OF C CURRENT INTEGRATION STEP C 30 IF (KCHEK) 35,35,40 35 TP=TT(II) TQ=TT(II+1) AP=GA(II)*FACTOR AQ=GA(II+1)* FACTOR DGR=(AQ-AP)/(TQ-TP) DP=-XMASS*DGR KCHEK=1 C 40 P2=-XMASS*(AP+DGR*(T2-TP)) c DGA=DGR*DT GA2=GA1+DGA DGV=GA1*DT+DGA*DT/2.0 GV2=GV1+DGV DGU=GV1*DT+GA1*DT*DT/2.0+DGA*DT*DT/4.0 IF (GV1.EQ.0.DO.OR.GV1.EQ.GV2) GO TO 90 DTG=GV1/(GV1-GV2)*DT IF (DTG.GE.DT.OR.DTG.LE.0.DO) GO TO 90 DT=DTG T2=T1+DTG P2=-XMASS*(AP+DGR*(T2-TP)) DGA=DGR*DT GA2=GA1 +DGA DGV=GA1*DT+DGA*DT/2.0 GV2 =GV1 +DGV DGU=GV1*DT+GA1*DT*DT/2.0+DGA*DT*DT/4.0 GV2=0.DO C C CALCULATE RESPONSE AT THE END OF CURRENT

C INTEGRATION TIME STEP C 90 CALL SOLVE(DT,DA2,ST,C) CALL BASE(BS2,ST,C,DA2,DT,DU) C C Overshooting the time when V2=0 C U2=U1+DU DV=A1*DT+DA2*DT/2.0 V2=V1+DV IF (V2.EQ.0.DO) GO TO 153 IF ((V1*V2).GE.0.DO) GO TO 153 NCYC=0 DTP=0.D0 DTQ=DT VP=V1 C 9100 DT=0.5DO*(DTP+DTQ) CALL SOLVE(DT,DA2,ST,C) CALL BASE(BS2,ST,C,DA2,DT,DU) U2=U1+DU DV=A1*DT+DA2*DT/2.0 V2=V1+DV IF (DABS(V2).LE.0.001DO.OR.DABS(DTP-DTQ).LE.0.00001D0) THEN V2=0.D0 GO TO 153 ENDIF NCYC=NCYC+1 IF (NCYC.LE.MCYC) GO TO 9105 WRITE(*,995) 995 FORMAT(' COULD NOT COMPUTE THE OVER SHOOT FACTOR WITHIN', 1' PERMISSIBLE NO. OF ITERATIONS') STOP C 9105 IF ((VP*V2).GT.0.DO) GO TO 9110 DTQ=DT GO TO 9100 9110 DTP=DT VP=V2 GO TO 9100 C C Overshooting the time BS2=0 c 153 IF (BS2.EQ.0.DO) GO TO 125 IF ((BS1*BS2).GE.0.DO) GO TO 125 NCYC=0 DTP=0.DO DTQ=DT BSP=BS1 C 100 DT=0.5DO*(DTP+DTQ) CALL SOLVE(DT,DA2,ST,C) CALL BASE(BS2,ST,C,DA2,DT,DU) U2=U1+DU DV=A1*DT+DA2*DT/2.0 V2=V1+DV IF (DABS(BS2).LE.0.01DO.OR.DABS(DTP-DTQ).LE.0.00001D0) THEN BS2=0.DO F2=-F2C GO TO 120 ENDIF NCYC=NCYC+ 1

IF (NCYC.LE.MCYC) GO TO 105 WRITE(*,95) 95 FORMAT(' COULD NOT COMPUTE THE OVER SHOOT FACTOR WITHIN', 1' PERMISSIBLE NO. OF ITERATIONS') STOP C 105 IF ((BSP*BS2).GT.0.DO) GO TO 110 DTQ=DT GO TO 100 110 DTP=DT BSP=BS2 GO TO 100 C 120 GA2=GA1+DGR*DT GV2=GV1+(GA1+GA2) *DT/2.DO T2=T1+DT 125 P2=P1+DP*DT CALL STATE(KODY,KODP,ST,C,SG) C IF (KODP.EQ.KODY) GO TO 140 C C FROM LOW STIFFNESS TO HIGH STIFFNESS C IF (KODP.EQ.1.AND.KODY.EQ.0) THEN RU=0.DO FCP=F2C F2C=V2*C1 AP=A1+DA2 EI=EI+(GA1+A1 + GA2+AP)*XMASS*DGU/2.0 A2= (P2-F2C-F2)/XMASS ET=ET+(F1+F2)*DU/2.DO ED=ED+(F1C+FCP)*DU/2.DO DU=.DO DGU=0.DO C GO TO 150 ENDIF C C FROM HIGH STIFFNESS TO LOW STIFFNESS C FP=F2 FCP=F2C F2=U2 * PSTIFF F2C=V2*C2 AP=A1+DA2 EI=EI+(GA1+A1 + GA2+AP) *XMASS*DGU/2.0 A2= (P2-F2C-F2)/XMASS C ACOR= (FP+FCP-F2C-F2) /XMASS ET=ET+(F1+FP) *DU/2.DO ED=ED+(FC+FCP) *DU/2.DO RU=0.DO DU=.DO DGU=0.DO GO TO 150 C 140 A2=Al+DA2

IF(KODY.EQ. 0.DO.AND.KODP.EQ.0.D0) RU=RU+DU C 150 CALL ENERGY(XMASS,ST,C,DU,DGU,DT,PSTIFF,STIFF) C C PROCEED TO OUTPUT C IF (KPR.NE.10) GO TO 155 WRITE(6,2070) T2,KK,EI,EK,ED,ES,EH,UB,UR,GA2,GV2 WRITE(7,3068) T2,U2,V2,A2,F2,EI,EK,ED,ES,EH,EKS WRITE(11,3068) T2,U2 WRITE(15,3068) T2,EI WRITE(17,3068) T2,ED WRITE(2,3068) T2,EKS WRITE(18,3068) T2,EKT KPR=0 C Calculate maximum value IF (U2.GT.DISMAX) THEN DISMAX=U2 TDIMAX=T2 ENDIF IF (U2.LT.DISMIN) THEN DISMIN=U2 TDIMIN=T2 ENDIF IF (ED.GT.EDMAX) THEN EDMAX=ED TEDMAX=T2 ENDIF IF (EI.GT.EIMAX) THEN EIMAX=EI TEIMAX=T2 ENDIF IF (EKS.GT.EKSMAX) THEN EKSMAX=EKS TESMAX=T2 ENDIF IF (EKT.GT.EKTMAX) THEN EKTMAX=EKT TETMAX=T2 ENDIF C C UPDATING INTEGRATION TIME STEP AND STRUCTURAL C RESPONSE QUANTITIES FOR THE NEXT TIME STEP C 155 F1=F2 F1C=F2C BS2=F2+F2C BS1=BS2 P1=P2 T1=T2 A1=A2 V1=V2 U1=U2 GA1=GA2 GV1=GV2 TO(KK) =T2 UU (KK)=U2 VV (KK)=V2 AA (KK) =A2 RR(KK)=F2

CC(KK)=F2C BB(KK)=BS2 GV(KK) =GV2 SS(KK)=SG KD(KK)=KODY DT=DELTAT DTT=TT(II+1)-T1 IF (DTT.EQ.0.DO) GO TO 160 IF (DT.GT.DTT) DT=DTT 160 T2=T1+DT KODP=KODY KK=KK+1 GO TO 20 C C PRINT RESPONSE TIME HISTORY AND SUMMARIES C 400 C WRITE(6,2090) WRITE(6,2095) (TO(I), UU(I), VV(I),AA(I) WRITE(6,2100) WRITE(6,2105) (TO(I),BB(I),GV(I),SS(I),RR(I), I=1,KK, 10),KD(I),I=1,KK,10) 400 WRITE WRITE WRITE WRITE WRITE WRITE WRITE WRITE (20,3068) (20,3068) (20,3068) (20,3068) (20,3068) (20,3068) (20,3068) (20,3068) TBSMAX,BSMAX TBSMIN,BSMIN TDIMAX,DISMAX TDIMIN,DISMIN TEDMAX,EDMAX TEIMAX, EIMAX TESMAX,EKSMAX TETMAX,EKTMAX 2000 FORMAT(1H,52(1H-),/, 1 53H DYNAMIC RESPONSE OF SINGLE DEGREE OF FREEDOM SYSTEMS,/, 2 1H,52(1H-),//,1H,8A10) 2005 FORMAT(19H SYSTEM DESCRIPTION,/,1H,42(1H-),/, 1 29H MASS..................... E14.6,/, 2 29H STIFFNESS.............,E14.6,/, 3 29H STRAIN HARDENING RATIO...,E14.6,/, 4 29H NATURAL FREQUENCY........ E14.6,/, 5 29H PERIOD................... E14.6,/, 6 29H DAMPING.................. E14.6,/, 7 29H SHIFT NATURAL FREQUENCY...,E14.6,/, 8 29H SHIFT PERIOD.............. E14.6,/, 9 29H SHIFT DAMPING...........,E14.6) 2020 FORMAT(24H SOLUTION SPECIFICATIONS,/,1H,42(1H-),/, 1 29H ANALYSIS TIME STEP.......,E14.6,/, 2 29H OUTPUT TIME STEP....... E14.6,/) 2030 FORMAT(1H,15(1H-),/,16H LOADING HISTORY,/,1H,15(1H-),//, 1 15H LOAD FACTOR =,E14.6) 2035 FORMAT(//,4(10X,4HTIME,2X,12HACCELERATION)) 2045 FORMAT(4(5X,F9.4,2X,E12.5)) 2055 FORMAT(1H,8A10) 2060 FORMAT(' ENERGY TIME HISTORY'/, 1' TIME STEPS INPUT KINETIC DAMPING 2' STRAIN HYSTE. UNBAL. EQUILIBRIUM 3'GROUND GROUND GROUND'/, 4' NO. ENERGY ENERGY ENERGY 5' ENERGY ENERGY ENERGY RATIO 6'ACCELERATION VELOCITY DISPLACEMENT'/,lX,140(1H-)) 2068 FORMAT(' OUTPUT TIME HISTORIES IN THE ORDER? TIME,', 1'DISPLACEMENT, VELOCITY, ACCELERATION, RESISTANCE,', 2'INPUT ENERGY,'/,' KINETIC ENERGY, HYSTERETIC ENERGY,', 3'DAMPING ENERGY, HYSTERETIC ENERGY DUCTILITY,', 4'RESIDUAL DUCTILITY.,'//) 2070 FORMAT(F8.4,I7,6F12.4,F12.6,3F13.4) 3068 FORMAT(F8.4,11F12.5) I I

2090 FORMAT(' RESPONSE TIME HISTORY'/, 1' TIME DISPLACEMENT VELOCITY 2'ACCELERATION RESISTANCE'/,lX,78(1H-)) 2095 FORMAT(F9.5,5X,F12.4,5X,F12.4,5X,F12.4,5X,F12.4) 2100 FORMAT(' BASE-SHEAR TIME HISTORY'/, 1' TIME BASE-SHEAR GROUND-VELOCITY 2' SIGN KODY'/,lX,77(1H-)) 2105 FORMAT(F9.5,3F17.4,I14) C RETURN END C SUBROUTINE SOLVE(DT,DA,ST,C) IMPLICIT DOUBLE PRECISION (A-H,O-Z) CHARACTER*10 HED COMMON /BLK1/ XMASS,STIFF,PSTIFF,FACTOR,C1,C2,HED COMMON /BLK3/ DELTAT,P1,P2,DP,U1,U2,F1,F2,T1,T2,V1,V2,A1,A2 COMMON /BLK8/ RU,F1C,F2C C EFMAS=XMASS+C*DT/2.DO+ST*DT*DT/4.DO EFLOD=(DP-C*Al-ST*(V1+A1*DT/2.DO) ) *DT DA=EFLOD/EFMAS DV=A1*DT+DA*DT/2.DO DU=V1*DT+A1*DT*DT/2.D0+DA*DT*DT/4.DO C VV=V1+DV RR=F1+ST*DU AA= (P1+DP*DT-C*VV-RR)/XMASS DA=AA-A1 C RETURN END C SUBROUTINE BASE(BS,ST,C,DA,DT,DU) IMPLICIT DOUBLE PRECISION (A-H,O-Z) CHARACTER*10 HED COMMON /BLK1/ XMASS,STIFF,PSTIFF,FACTOR,C1,C2,HED COMMON /BLK3/ DELTAT,P1,P2,DP,U1,U2,F1,F2,T1,T2,V1,V2,A1,A2 COMMON /BLK8/ RU,F1C,F2C C DV=A1*DT+DA*DT/2.DO DU=V1*DT+A1*DT*DT/2.DO+DA*DT*DT/4.DO F2=F1+ST*DU F2C=F1C+C*DV BS=F2+F2C C RETURN END C SUBROUTINE ENERGY(XMASS,ST,C,DU,DGU,DT,PSTIFF,STIFF) IMPLICIT DOUBLE PRECISION (A-H,O-Z) COMMON /BLK2/ DAMP1,DOUT,PK,DAMP2,KOUNT COMMON /BLK3/ DELTAT,P1,P2,DP,U1,U2,F1,F2,T1,T2,V1,V2,A1,A2 COMMON /BLK8/ RU,F1C,F2C COMMON /BLK4/ GA1,GA2,GV1,GV2,EI,ES,EH,ED,EK,ET,UB,UR,EKS,EKT C C COMPUTE TIME HISTORY OF ENERGY INPUT, STORED, AND DISSIPATED C BY SINGLE DEGREE OF FREEDOM SYSTEM WITH STRAIN HARDENING C C RECOVERABLE STRAIN ENERGY (ES), HYSTERETIC ENERGY (EH), DAMPING C ENERGY (ED) AND KINETIC ENERGY (EK)

c AT1=A1+GA1 AT2=A2+GA2 EI=EI+(AT1+AT2) *XMASS*DGU/2.0 ED=ED+(F1C+F2C)*DU/2.DO ET=ET+(F1+F2)*DU/2.DO ES=0.5*PSTIFF*U2*U2 + 0.5*(STIFF-PSTIFF)*RU*RU EH=ET-ES VT=GV2+V2 EK=0.5D0*XMASS*VT*VT EKS=ES+EK EKT=ET+EK C C COMPUTE ENERGY OUT-OF-BALANCE RATIO C UB=EI-ES-EH-ED-EK UR=UB/EI WRITE(*,1000) T2,EI,EK,ED,ES,EH,UB,UR 1000 FORMAT(10F12.5) C RETURN END C SUBROUTINE STATE(KODY,KODP,ST,C,SQ) IMPLICIT DOUBLE PRECISION (A-H,O-Z) CHARACTER*10 HED COMMON /BLK1/ XMASS,STIFF,PSTIFF,FACTOR,C1,C2,HED COMMON /BLK3/ DELTAT,P1,P2,DP,U1,U2,F1,F2,T1,T2,Vl,V2,A1,A2 COMMON /BLK8/ RU,F1C,F2C COMMON /BLK4/ GA1,GA2,GV1,GV2,EI,ES,EH,ED,EK, ET,UB,UR, EKS,EKT COMMON /BLK7/ KPR COMMON /BLK9/ BSMAX,BSMIN,DISMAX,DISMIN,EDMAX,EIMAX, 1 EKSMAX,EKTMAX COMMON /TIME/ TBSMAX,TBSMIN,TDIMAX,TDIMIN,TEDMAX,TEIMAX, 1 TESMAX,TETMAX C TEMP1=Fl+F1C TEMP2=F2+F2C SP=TEMP1 *V1 SQ=TEMP2 *V2 C IF (SP) 10,100,200 10 IF (SQ) 20,30,40 20 KODY=1 ST=PSTIFF C=C2 GO TO 400 30 KODY=0 ST=STIFF C=C1 IF (TEMP2.EQ.0.DO.AND.V2.EQ.0.DO) THEN KODY=1 ST=PSTIFF C=C2 ENDIF GO TO 400 40 KODY=0 ST=STIFF C=C1 GO TO 400 C 100 IF (SQ) 120,130,140 120 KODY=1

ST=PSTIFF C=C2 GO TO 400 130 KODY=0 ST=STIFF C=C1 IF (TEMP1.GE..D0.AND.TEMP2.GE..DO.AND.V1.GE..DO.AND.V2.GE. + 0.D0) THEN KODY=1 ST=PSTIFF C=C2 ENDIF IF (TEMP1.LE.0.DO.AND.TEMP2.LE.0.DO.AND.V1.LE.0.DO.AND.V2.LE. + 0.DO) THEN KODY=1 ST=PSTIFF C=C2 ENDIF GO TO 400 140 KODY=0 ST=STIFF C=C1 GO TO 400 C 200 IF (SQ) 220,230,240 220 KODY=1 ST=PSTIFF C=C2 GO TO 400 230 KODY=1 ST=PSTIFF C=C2 IF (TEMP1.GE. 0.DO.AND.TEMP2.EQ. 0.DO.AND.V1.GE. 0.DO.AND.V2. EQ. + 0.DO) THEN KODY=0 ST=STIFF C=C1 ENDIF IF (TEMPl.LE. 0.DO.AND.TEMP2.EQ. 0.DO.AND.V1. LE. 0.DO.AND.V2.EQ. + 0.DO) THEN KODY=0 ST=STIFF C=C1 ENDIF GO TO 400 240 KODY=0 ST=STIFF C=C1 C 400 KPR=KPR+1 IF (KPR.NE.10) GO TO 700 KKKK=1 IF (KODY.EQ.1) KKKK=-1 WRITE(12,750) T2,TEMP2 WRITE(13,750) T2,GV2 WRITE(14,600) T2,KKKK IF (TEMP2.GT.BSMAX) THEN BSMAX=TEMP2 TBSMAX=T2 ENDIF IF (TEMP2.LT.BSMIN) THEN BSMIN=TEMP2 TBSMIN=T2 ENDIF

600 FORMAT(F15.3,I5) 700 WRITE(10,750) T2,Fl,GV1,F2,GV2,KODP,KODY 750 FORMAT(5F15.3,215) C RETURN END