降伏加勁阻尼裝置之實驗與理論分析研究

(1)

ࢫЄΐݏܡκ྅ཉ̝၁រᄃநኢ̶ژࡁտ

߉ځே

઼ϲ੼ฯௐ˘ࡊԫ̂ጯᒉޙ̍඀ጯր

ԇ͛՗

઼ϲ๔ৈԫఙጯੰഀ៍నࢍᄃგநր

ၡ! ࢋ

ҲࢫЄૻޘ᐀Մ(LYS100)׍ѣᐹள۞ิّĂͷጾѣྵܜ۞Ҳೈᒖি౻৔ᗼ (low cycle fatique)ု׻Ăͧ˘ਠ็௚ඕၹϡ A36 ᐀Մ׍Հ੼۞ᑕតർ̼தĂٙ

ͽਕҹڇԊొऴᕇٙౄј۞Ԋొ৔ᗼĂѣӀٺ๬ّঐਕ፟ט̝ଠטĂЯѩΞᇃ ھᑕϡٺΐݏܡκ྅ཉ(added damping and stiffness, ADAS)̝ܛᛳঐਕ̮І

̚ĄϤٺҲࢫЄ᐀ՄдࢫЄޢ۞ᑕ˧-ᑕតᙯܼ۞൴णĂ̙Тٺ૱ϡ۞ A36 ᐀ ՄĂࡶͽᑕϡٺ A36 ঐਕጡ۞ᗕቢّሀё̶ֽژሀᑢĂ൑ڱϒቁͅߍ΍Ҳࢫ Є᐀ՄঐਕጡĂצـᖬྶࢦүϡ˭ኑᗔ۞ܧቢّҖࠎĄЯѩώ͛೩΍ͽ࣒ϒ͛

ͩሀё(Wen’s model)ĂሀᑢҲࢫЄ᐀Մঐਕጡ̝˧ጯҖࠎĄགྷϤᇴࣃሀᑢᄃ၁ រඕڍ۞ͧྵᙋ၁Ăώ͛ٙଯጱ̝࣒ϒ͛ͩሀёĂΞͽϒቁሀᑢҲࢫЄ᐀ΐݏ ܡκ྅ཉ̝Ᏽ႖ҖࠎĄ

ᙯᔣෟĈҲࢫЄ᐀ՄঐਕጡăᏵ႖Җࠎă࣒ϒ͛ͩሀёăܧቢّҖࠎĄ

EXPERIMENTAL AND ANALYTICAL INVESTIGATION OF LOW YIELD ADDED DAMPING AND STIFFNESS

Ming-Hsiang Shih

Department of Construction Engineering

National Kaoshiang First University of Science and Technology Kaoshiang, Taiwan 824, R.O.C.

Wen-Pei Sung

Department of Landscape Design and Management National Chin-Yi Institute of Technology

Taichung, Taiwan 411, R.O.C.

Key Words: low yield steel absorber, hysteresis energy dissipation, modified Wen’s model, nonlinear behavior.

ABSTRACT

The advantages of LYS are fine ductility, longer endurance of low cycle fatigue and higher rate of strain hardening that can overcome local fracture problems in steel plate. It is a very good material to apply for Added Damping and Stiffness, ADAS. The bilinear model for an A36 energy absorber cannot be used to analyze this newly developed device

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that of ordinary steel. Therefore, Wen’s Model is revised and extended to accurately simulate the complex nonlinear strain hardening behavior of seismic resistance of rhombic LYS under reciprocating loading tests. A comparison between numerical simulation and experimental results verifies that Wen’s model, modified, proposed in this research, can successfully simulate the hysteresis energy dissipation behavior of rhombic low yielding steel plate.

˘ă݈! ֏

ܕѐֽĂ͵ࠧЧгЯгዩጱ࡭ޙ᎝ඕၹ໑ຫ۞९ּᆸ

΍̙቎Ăтң೩̿ፋវඕၹ۞࡝ዩਕ˧ಶјࠎிٙ៘ϫ۞

ࡁտኝᗟĄࠎ྿ѩϫ۞Ăഴዩᄃ࿣ዩඈඕၹଠטԫఙ̙ᕝ

۞జ೩΍ᄃࡁտ[1]Ąдኜк۞ඕၹଠטԫఙᄃ̮І̚Ăΐ ݏܡκ྅ཉ(added damping and stiffness, ADAS)Яጾѣᘦ ؠ۞ঐਕҖࠎăᄦүјώҲຆ̈́щ྅ᖎٽඈᐹᕇĂ၁ᅫᑕ ϡٺ̍඀˯۞ΞҖّ࠹၆೩੼Ăϫ݈д઼̰̏ѣ၁ᅫ̝ᑕ ϡ९ּ[2]ĄѩγĂ̚᐀ٙ᎕ໂࡁ൴۞າёטዩ᐀Մ––Ҳࢫ Є᐀(LYS100)Ăॲፂ͛ᚥ[3,4]൴னҲࢫЄ᐀̝ໂࢨᑕ˧ࠎ ࢫЄᑕ˧۞ 3 ࢺνΠĂ҃ໂࢨᑕត෹࿅ 50%ࡗࠎ็௚ඕၹ

᐀Մ۞ 1.5~2 ࢺĂࠎ˘ໂָ̝טዩ᐀ՄĄ౵ܕд઼̰̈́͟

ώ̏૟ҲࢫЄ᐀ڕᑕϡٺధк̙Тԛё̝טዩඕၹ˯

[5,6]Ą઼̰҃ጯ۰˵അ૟ҲࢫЄ᐀Մᑕϡٺิّ୆ᇣ̚Ă ඕڍពϯдͅᖬྶࢦүϡ˭ĂҲࢫЄ᐀Մቁ၁ጾѣᘦؠ۞

ঐਕड़ڍ[7]ĄЯѩĂࡶ૟ҲࢫЄ᐀ᑕϡٺΐݏܡκ྅ཉ

˯Ăѣड़гඕЪ׌۰̝ᐹᕇĂᑕਕᆧซΐݏܡκ྅ཉٺഴ ዩ˯۞ड़ਕĄ

᐀ ڕ Մ फ़ д ซˢ ܧ ቢ ّ ቑ ಛޢ Ă ົ ൴ Ϡ ᑕត ർ ̼ (strain harding)ҖࠎĂГΐ˯ᕝࢬᇦѡᑕ˧̶Ҷ۞ᇆᜩĂౄ

јΐݏܡκ྅ཉ̝˧ůតԛҖࠎ۞ೡࢗត଀࠹༊ኑᗔĄЯ ѩ Ԇ Б ᇅ ๬ ّ (elastic-perfectly plastic model) ă ᗕ ቢ ّ (elastic-linear work-harding model) ඈ ᖎ ̼ ۞ ᇴ ጯ ̶ ژ ሀ ёĂ૱జϡֽೡࢗΐݏܡκ྅ཉ۞Ᏽ႖Җࠎ[8]ĄϤՄफ़ྏ

រ̈́ΐݏܡκ྅ཉّ̝ਕീྏඕڍ൴னĂҲࢫЄ᐀Մ̝ᑕ

˧ůᑕតѡቢត̼Ă֭൑˘ਠ૱ϡ A36 ᐀Մ׍ѣځព̝ࢫ Єᑕ˧πέ[3,4]ćѩγĂҲࢫЄ᐀Մᑕϡٺΐݏܡκ྅ཉ

۞˧ጯҖࠎᄃ A36 ᄦݡѣٙमளĂࡶͽᗕቢ̶ّژሀёĂ ሀᑢҲࢫЄ᐀ΐݏܡκ྅ཉĂ൑ڱϒቁͅߍ΍׎၁ᅫ̝˧

ጯҖࠎĄЯѩችҹᅞି଱[9]അͽ๬ّ˧ጯ៍ᕇĂ೩΍˘ჯ ញჯሀёĂሀᑢඈШّർ̼(isotropic hardening)পّځព۞

ҲࢫЄ᐀ՄĂֶ֭ѩሀݭซ˘ՎՐ଀ҲࢫЄΐݏܡκ྅ཉ

̝ـᖬᏵ႖ҖࠎĄϤٺ๬ّ˧ጯࠎྵኑᗔ۞நኢĂ၆ٺ၁ ᅫଂְనࢍ۞̍඀रྵ̙ٽೠଠᄃᑕϡĂٙͽವՐ˘࣎ᖎ ಏͷЪந۞̶ژሀёĂត଀࠹༊ࢦࢋĄ1976 ѐ Y. K. Wen

൴ण΍۞͛ͩሀё(Wen’s model)Ă͹ࢋᖣϤα࣎ᖎಏ۞ଠ טણᇴĂՐ΍Ч჌̙Т۞Ᏽ႖ҖࠎĂЯѩኑᗔၹІ̝ܧቢ

ّ˧ጯҖࠎĂ͛ͩሀёࠎໂָ̝ሀᑢ̍׍[10,11]Ą̙࿅͛

ͩሀёĂ̪൒൑ڱԁචͅߍ΍ҲࢫЄ᐀ΐݏܡκ྅ཉٙ׍

ѣ̝ᑕតർ̼পّĄࠎ˞ሀᑢҲࢫЄ᐀ΐݏܡκ྅ཉĂצ ـᖬྶࢦүϡ˭̝ܧቢّ˧ጯҖࠎĂ֭ᑕϡٺඕၹજ˧

̶ژ̚ĂͽෞҤҲࢫЄ᐀ΐݏܡκ྅ཉٙ׍ѣ۞טዩड़ ਕĂЯѩώ͛૟ͽ͛ͩሀёࠎૄᖂĂඕЪඈШّർ̼ఢ

݋Ă೩΍˘इᖎಏ҃Ъந۞ᇴጯሀёĂ֭੨Ъ၁រᇴፂ ᙊҾ̶ژሀё۞ЧีણᇴĂͽሀᑢҲࢫЄ᐀ΐݏܡκጡ

۞Ᏽ႖ҖࠎĄ

˟ăҲࢫЄ඼ԛΐݏܡκጡᄃ׎ـᖬྶࢦྏរ

ϫ݈౵૱ᑕϡ̝ΐݏܡκ྅ཉࠎ X ԛ[12]̈́ˬ֎ԛ[13]

׌჌Ă׌۰̝үϡҖࠎ̈́ᄦү௡྅˯࠰хд˘ֱયᗟĂּ

тค˧ᄃஙତ۞ᇆᜩĄЯѩώࡁտࠎԼච˯̝ࢗ৿ᕇĂЯ

҃൴णనࢍ΍າё඼ԛ᐀ڕĂтဦ 1 ٙϯĂ׎͚ٚळ۞ݭ ёĂтဦ 2 ٙϯĄѩԼ։̝ΐݏܡκ྅ཉ׍˭ЕᐹᕇĈ 1. ඼ԛ᐀ڕӀϡԛې၆Ⴭ۞পّயϠᙷҬ׽ؠბ۞ड़

ᑕĂԆБ̙ᅮஙତĂтѩܮ̙ົயϠЯஙତ̙։ٙౄј

۞ᇆᜩĂٙͽΞซ˘ՎࢫҲ̮Іᄦү˯۞јώĄ 2. ඼ԛ᐀ڕঐਕጡ׌ბ̝͚ٚ͞ё࠰ࠎᅘତĂЯѩ̙ົய

Ϡค˧Ą

3. ඼ԛ᐀ڕᄃ X ԛ׶ˬ֎ԛ᐀ڕ࠹ТĂٺ᐀ڕ˯Տ˘ᕇ

࠰׍ѣ࠹Т̝ѡதត̼Ăਕֹ᐀ڕ˯Տ˘ᕝࢬӮ̹г྿

זࢫЄĂᔖҺԊొऴᕇ۞யϠĄ

Я඼ԛΐݏܡκ྅ཉ׍ѣ˯̝ࢗᐹᕇĂГΐ˯ҲࢫЄ

᐀Մٙጾѣ۞পّĂυΞᆧΐፋវඕၹ̝ิّᄃঐਕҖ ࠎĂ҃ѩ඼ԛΐݏܡκ྅ཉٺඕၹۏ̝྅ཉဦĂтဦ 3 ٙ ϯĄЯѩώࡁտ૟੫၆ҲࢫЄ඼ԛ᐀ڕĂซҖҜொ႙ᆧ̝

ـᖬྶࢦྏរĂͽ˞ྋҲࢫЄ඼ԛΐݏܡκ྅ཉ̝ૄώҖ ࠎĄ

1. ྏរ͞ڱ

ྏរ።඀ࠎซҖҜொଠט̝ـᖬΐྶྏរĂҜொଠט ณͽҲࢫЄ඼ԛ᐀ڕ̝நኢࢫЄҜொŔ_y0ࠎૄώณĂ֭ͽ ϒ࢑ 0.5Ŕy0ăŔ_y0ă1.5Ŕy0ă2Ŕy0ă3Ŕy0ă4Ŕy0ă8Ŕy0ă 12Ŕy0ă16Ŕy0…̝Ҝொณֽа߉˧˟ѨĂۡזҜொณ྿

40Ŕy0 ( ࡗࠎ 88mm )ॡĂӈซҖॎ಼ࠎ 40Ŕy0̝ฉഇّྏ

រĂΐྶ።඀тဦ 4 ٙϯĂώ၁រֹٙϡ̝߉˧ր௚ࠎ MTS100 ጟڵᑅ࡭જጡĄྏរซҖ̚ྶࢦࣃᄃҜொࣃ̝ณ

ീĂϤ࡭જጡ˯۞ఈࢦࢍ(load cell)ᄃҜொࢍ(LVDT)౅࿅

MTS407 ଠטጡณീ҃଀Ă၁រ྅ཉဦĂтဦ 5 ٙϯĄ

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40mm

D30 R40

80mm 40 mm 360

mm 100mm

580mm 640mm

300mm

(a) (b)

ဦ 1! ඼ԛ᐀ڕ͎̇

(a)

(b)

ဦ 2 ҲࢫЄ᐀Մঐਕጡ̝၁វ໰ͯ

2. ྏរඕڍ

(˘) ೧ዚё඼ԛ᐀ڕঐਕ྅ཉ

૟ྏវበ̶ཱིҾࠎ LYS-1ăLYS-2 ᄃ LYS-3Ăˬ௡೧ ዚёঐਕ྅ཉྏរྤफ़̝Ᏽ႖ਫ਼઻Ăೱზјಏͯ᐀ڕૻޘ

̝Ᏽ႖ਫ਼઻ဦĂтဦ 6 ٙϯĂ൴னঐਕ࠹༊ᘦؠͷˬ௡ೀ

ͼࢦЪд˘੓ĄΩγĂϤྏរ̝Ᏽ႖ਫ਼઻൴ன LYS-1 дҜ

ொࡗ྿ Ų30mm ޢĂҭ LYS-2 ̈́ LYS-3 ื྿ Ų45mmĂᏵ ႖ਫ਼઻யϠ˯ೳ̝ᖼԶĂ׎˧ณ૟ᐌҜொณᆧΐ҃ត̂Ă

఺჌ன෪ߏЯ᐀ڕតԛณ͉̂Ăֹ଀᐀ڕᅘତ఍யϠ࢑ᝈ

৏̝ቡ߇Ăтဦ 7 ٙϯĄ఺჌ன෪ٺ͛ᚥ[14]̝ˬ֎ԛঐ ਕ᐀ڕّ̝ਕീྏྏរĂ˵൴Ϡ࿅ᙷҬଐڶĄ

(˟) ໣ᇿё඼ԛ᐀ڕঐਕ྅ཉ

K- K

A

(a)

(b) A-A

ဦ 3 ඼ԛࢫЄΐݏܡκ྅ཉٺඕၹۏ̝྅ཉဦ

100 50

0

-50

-100

(mm)

ဦ 4 Ҝொ႙ᆧଠט።඀ဦ

ဦ 5 ၁រ྅ཉྎဦ

(4)

60 40 20 0 -20 -40 -60

12 8 4 0 -4 -8 -12 -2.7 -1.8 -0.9 0 0.9 1.8 2.7

-100 -50 0 50 100

(kN) Moment, kN-m

(mm) LYS-1

LYS-2 LYS-3

PUSH

PULL

ဦ 6 ೧ዚёྏរᏵ႖ਫ਼઻(ಏͯ᐀ڕ)

ဦ 7 ᐀ڕᅘତ఍யϠ࢑ᝈ৏ϯຍဦ

Ϥ ೧ ዚ ё ̝ ၁រ ඕ ڍ Ξ ൴ னᏵ ႖ ਫ਼ ઻ ٺ Ҝொ ณ ྿ 30mm~45mm ॡĂ᐀ڕ˧ณ൴ϠᐌҜொᆧΐ҃ត̂۞ᔌ ๕Ă҃ͷ᐀ڕ˵யϠԊొऴᕇ۞ன෪ĂЯѩྏវበཱི LYS-4

̈́ LYS-5 ̝ତЪ͞ёԼࠎ໣ᇿёĄϤဦ 8 ໣ᇿёྏរ̝Ᏽ ႖ਫ਼઻൴னĂѩ௟ొԼ։ቁ၁ਕᔖҺ೧ዚёٙౄј۞࢑ᝈ

৏ன෪ĄѩγĂࠎ˞ͧྵҲࢫЄ᐀(LYS100)ᄃ˘ਠ૱ϡ᐀

Մ(A36)ᑕϡٺΐݏܡκ྅ཉ̝ҖࠎमளĂЯѩซҖ˘௡໣

ᇿё A36 ඼ԛΐݏܡκ྅ཉّ̝ਕീྏĄϤဦ 9 Ξ៍၅΍

ҲࢫЄ඼ԛΐݏܡκ྅ཉ۞ඈШّർ̼ன෪Ăྵ A36 ඼ԛ ΐݏܡκ྅ཉځពĄ

ˬăநኢሀё

˘࣎ԆፋͷЪந۞ᇴጯ̶ژሀёυืࢋਕͅᑕ΍᐀

Մٕטዩ྅ཉώ֗ٙ׍ѣ̝ർ̼পّĂтѩ̖Ξѣड़ͷϒ ቁгͅߍ΍Մफ़дצـᖬྶࢦүϡॡ̝ܧቢّҖࠎĄώࡁ տᑕϡ͛ᚥ[11]ٙ೩̝ѡቢᑢЪ͞ڱĂ੨Ъ඼ԛΐݏܡκ

྅ཉྏរྤफ़ĂᑢЪ΍͛ͩሀё౵ָણᇴࣃĄ͛ͩሀёϡ ٺሀᑢΐݏܡκ྅ཉд׽ؠ಼ޘ۞ـೇតԛ˭̝ܧቢّҖ ࠎĂ͛ёሀё၆ٺͽ֕જർ̼পّྵ׍ຍཌྷ̝ A36 ᐀Մܡ

60 40 20 0 -20 -40 -60

12 8 4 0 -4 -8 -12 -2.7 -1.8 -0.9 0 0.9 1.8 2.7

-100 -50 0 50 100

(kN) Moment, kN-m

(mm) LYS-4

A36-1 PUSH

PULL

ဦ 8 ໣ᇿёྏរᏵ႖ਫ਼઻(ಏͯ)

60 40 20 0 -20 -40 -60

12 8 4 0 -4 -8 -12 -2.7 -1.8 -0.9 0 0.9 1.8 2.7

-100 -50 0 50 100

(kN) Moment, kN-m

(mm) LYS-4 PUSH

A36-1

Curvature, 1/m

ဦ 9 ҲࢫЄ᐀ᄃ A36 ̝Ᏽ႖ਫ਼઻ͧྵ

κጡĂ̪൒׍ѣ։р̝ሀᑢड़ڍĂтဦ 10(a)ٙϯćҭ၆ٺ ඈШർ̼পّځព۞ҲࢫЄ᐀ՄܡκጡĂ͛ͩሀё݋൑ڱ ԆБೡࢗ΍ѩ჌ඈШർ̼ҖࠎĂтဦ 10(b)ٙϯĄЯѩΞ

ۢĂ͛ͩሀёਕૉሀᑢ΍֕જർ̼ᔌ๕ځព۞ർ̼ҖࠎĂ ҭߏ၆ඈШർ̼Җࠎྵځព۰Ăᑕ၆׎̟ͽ࣒ϒĄ

1. ͛ͩሀё

͛ͩሀё(Wen’s model)[10]Ξሀᑢ׍π໣ѡቢ߱۞Ᏽ ႖ҖࠎĂЯѩ͛ͩሀёሀᑢၹІ̝ܧቢّҖࠎĂࠎໂָ۞

ᏴፄĄ͛ͩሀёٙؠཌྷ̝Ᏽ႖аೇ˧ R(t)ᄃҜொ x ̝ᙯܼ

т˭ٙϯĈ

( ) 0 (1 ) 0

R t =υK x+ −υ K q (1)

1

n n

q&=αx&−β x q& ⁻ q−γx q& (2)

׎̚Ĉ

(5)

60 40 20 0 -20 -40 -60

-100 -50 0 50 100

α = 1.0, β = γ = 0.05

(kN)

(mm) 60

40 20 0 -20 -40 -60

-100 -50 0 50 100

α = 1.0, β = γ = 0.04

(kN)

(mm) A36-1

LYS-4 (a) A36

(b) LYS100

ဦ 10 ͛ͩሀёሀᑢᄃྏរᏵ႖ਫ਼઻̝ͧྵ(ฉഇّྶࢦ)

x ࠎր௚̝ҜொćR(t)ࠎ၆ᑕ̝аೇ˧ć K0 ࠎր௚ܐؕݏޘćɪࠎࢫЄ݈ޢݏޘͧć

q ࠎ ᖼ ೱ Ҝ ொ ត ̼ ב ᇴ (transformed displacement variable)ć

ɗăɘăə̈́ n ࠎଠטᏵ႖ਫ਼઻ԛېត̼۞ણᇴĄ Ϥ(1)ă(2)̝ᇴࣃྋĂΞ൴னɗăɘăə̈́ n ඈαีܼ

ᇴĂ׍ѣ˭ЕّኳĈ

(˘) q ࣃ۞ቑಛĂӈ౵̂ᇅّҜொณĂצͽ˯αܼᇴ̝௡

ЪᇆᜩĂт͞඀ё(3)ٙϯĈ

1 n

q α

β γ

 

≤  +  (3)

(˟) n ࣃᇆᜩܧቢّᖼԶΗशĂn ࣃດ̂Ă݋ٙ଀۞Ᏽ႖ѡ ቢດܕٺԆБᇅ๬ّćn ࣃດ̈Ă݋ᖼԶᔌٺπቤĂ Яѩ༊n≥1.0ॡĂ͞ࠎᘦؠĄ

͞඀ё(1)ă(2)ٙؠཌྷ͛ͩሀёϡٺሀᑢ˘ਠ᐀Մ̝ܧ ቢّҖࠎĂΞ଀΍ᄃ၁រณീࣃ࠹༊˘࡭۞ඕڍĄҭϤٺ

40 30 20 10 0 -10 -20 -30 -40

-100 -75 -50 -25 0 25 50 75 100 (mm)

(kN)

= (KP/K0)- K₀

KP

1 l

LYS-5 LYS-4

ဦ 11 ҲࢫЄΐݏܡκ྅ཉ̝Βඛቢត̼

ඈШّർ̼পّځព۞ҲࢫЄ᐀ՄܡκጡĂ͛ͩሀё൑ڱ ԆБೡࢗ΍ѩ჌ඈШّർ̼ҖࠎĂЯѩ͛ͩሀёυืΐͽ

࣒ϒĄ

2. ࣒ϒ͛ͩሀё

ࠎ˞ϒቁೡࢗҲࢫЄ᐀ΐݏܡκ྅ཉĂ၁ᅫצـᖬྶ

ࢦүϡ˭̝ܧቢّҖࠎĂυื૟ඈШّർ̼፟טΐˢ͛ͩ

ሀёĄϤҜொ႙ᆧ̝ـᖬྶࢦ၁រ̚ĂЧೈᒖ౵̂ࣃాቢ

҃ ј ۞ Β ඛ ቢ Ă ൴ ன Ҳ ࢫ Є ᐀ ΐ ݏ ܡ κ ጡ ۞ ᙝ ࠧ ࢬ (bounding surface)ർ̼ҖࠎܕҬٺᗕቢّត̼Ăтဦ 11 ٙ ϯĄ

Яѩ઄నҲࢫЄ᐀ΐݏܡκ྅ཉᙝࠧࢬ̝ඈШّർ

̼ఢ݋ត̼т˭Ĉ

( )

0 max 0

max 0

0 max 0

,

y y

y

y y y

if

µ if

 ∆ ∆ ≤ ∆

∆ = 

∆ + ∆ − ∆ ∆ ≥ ∆



(4)

׎̚Ĉ

ɂ_y0 ࠎܐؕࢫЄҜொć

ɂ_maxࠎྶࢦ።ॡٙ̚གྷ።࿅۞౵̂Ҝொ඗၆ࣃć ɢ ࠎώ͛ٙؠཌྷ̝ᗕቢّർ̼בᇴௐ˟ۡቢ߱׶

ܐؕۡቢ߱୆தͧᄃ֕જർ̼தɪ̝मࣃĄ

Ϥ͛ᚥ[11]ɗăɘᄃə၆ૻޘ̈́ݏޘ۞ᇆᜩ଀ۢĂצ

˧̮І̝ᇅّݏޘϤɗࣃՙؠĂ҃ࢫЄҜொณ(ϺӈࢫЄࢬ Ηश)Ϥɗăɘᄃə̝׶۞ͧࣃՙؠĂт˭ёٙϯĈ

0

Ke=K ⋅ (5) α

1/ n y

α β γ

 

∆ =  +  (6)

׎̚Ĉ

Ke ࠎͽ͛ͩሀёሀᑢ̝̮І۞ܐؕݏޘĄ

Ϥ၁រྤफ़ۢĂΐݏܡκ྅ཉ̝ᇅّݏޘࡗரܲ޺ؠࣃĂ

ٙͽɗࣃᑕٺតԛ።ॡ̚ჯ޺̙តĄТॡ၁រྤफ़˵ព ϯĂࢫЄҜொณ૟ᐌ඾౵̂Ҝொณ҃೩੼ĂЯѩืԼតɘ

(6)

Ϥ Eq.(14)аᕩٙ଀ నؠણᇴᑢЪ

ྏវበཱི Kp/K0

ɂy0 mm

ɢ ɪ

ɗ ɘ ə error ɗ ɘ ə error LYS-1 0.133 4.6 0.101 0.032 1.006 0.134 0.084 0.10 1.000 0.163 0.054 0.01 LYS-4 0.131 4.4 0.1 0.031 1.001 0.176 0.052 0.06 1.000 0.182 0.046 0.07 LA2-1 0.06 5.9 0.031 0.029 1.002 0.128 0.041 0.07 1.000 0.125 0.042 0.08 A36-1 0.095 11.9 0 0.095 1.001 0.054 0.030 0.12 1.000 0.056 0.028 0.12

ᄃə̝׶۞ࣃĂֹ̝ᐌ඾౵̂តԛณ۞ᆧΐ҃ഴ͌ćЯѩ ώ͛ؠཌྷ˘࣎າ۞ણᇴɝĂ༊үɘ̈́ə۞ࢷ̄Ăٙͽ࣒ϒ

຋̶͞඀ё(2)Ă଀˭Е͞඀ёĈ

( ⁿ¹ ⁿ)

q&=αx&−η β x q& ⁻ +γx q& (7)

0 n y

y

η

∆ −

= ∆  (8)

׎̚Ĉ

ɂ_y ࠎܡκጡϫ݈۞ࢫЄҜொĂт͞඀ё(4)ٙϯć ɂ_y0 ࠎܐؕࢫЄҜொĄ

ืপҾڦຍ۞ߏĂɝົᐌ඾តԛ።ॡ҃ԼតĂͷ׎ࣃ̬ٺ 0 ᄃ 1 ̝มĄ

αăણᇴᙊҾ

૟Ҝொᖼೱតᇴ຋̶͞඀ё(7)ੵͽၹІតԛ၆ॡม

̝຋̶ĂΞ૟ࣧࠎ၆ॡม຋̶۞͞඀ё(7)Ă΃ೱј၆Ҝொ

຋̶۞͞඀ёĂт˭ёٙϯĈ

( ( ) ⁿ¹ ⁿ)

q dq sign x q q q

dx α η β ⁻ γ

′ = = − ⋅ & + (9)

҃˯ё̝ᗓ೸̼͞඀ёĂт˭ٙϯĈ

[ ( ( ) ⁿ¹ ⁿ) ^]

i i i i i i i

q α η β sign x q ⁻ q γ q x

∆ = − ⋅ & + ∆ (10)

ซ˘Վؠཌྷˬ࣎តᇴĈ

1i i

y = ∆ (11a) x

( ( ) ¹ )

2

n

i i i i i i

y = η ⋅sign x& q ⁻ q ∆x (11b)

( )

3

n

i i i i

y = η q ∆ (11c) x

݋͞඀ё(10)јࠎĈ

1 2 3

i i i i

q αy βy γy

∆ = − − (12)

ЯѩĂɂqiࠎ y1iăy2iăy3i۞ቢّבᇴĂ׎౵ָܼᇴɗă ɘăəΞ౅࿅౵̈˟ࢷڱՐ଀Ą׎ઇڱ੅ኢт˭Ĉ

၁រᇴፂ̝Ҝொᆧณྤफ़ӈࠎ(11)ёٙืࢋ۞ɂxićа

ೇ˧ Ri΃ˢё(1)̚ĂࢍზྍՎូ۞ qiࣃт˭ёٙϯĈ

(1 )⁰0

i i

i

R K x

q K

υ υ

= −

− (13)

K0̈́ɪࣃĂืॲፂྏរྤफ़Ҥზ҃଀ĂΪื࢜΃ᇴ ѨĂӈќᑦז̙᏾۞ඕڍĄҌٺ(11b)̈́(11c)ё̚۞ɝiࣃĂ

݋ֶ઄న۞ർ̼ܼᇴɢ΃ˢ xiࣃĂϤ͞඀ё(4)ҿᕝྍՎូ

۞ࢫЄҜொɂyiĂ֭΃ˢ(8)ёՐ΍ɝiࣃĄֶԔ૟Տ˘Վូ

۞ xiăqḯɝi΃ˢ(11a-c)ё̚ĂΞ଀Տ˘Վូ۞ y1iăy2i

̈́ y3iĂ઄న q0ࠎߙ˘̏ۢࣃĂ֭ᑕϡ౵̈˟ࢷڱՐ΍ӈ ΞĂ౵ޢྋ˭Еᓑϲ͞඀௡Ĉ

2

1 1 2 1 3 1

2

2 2 3 2

2

3 3

.

i i i i i i i

i i i i i

i i i

y y y y y y q

y y y y q

sym y y q

α β γ

 − −    ∆ 

   = −   ∆ 

 

   

   − ∆ 

 

∑ ∑ ∑ ∑

∑ ∑ ∑

∑ ∑ ⁽¹⁴⁾

͞඀ё(14)ё̝ྋĂӈࠎ౵ָ࣒ϒ͛ͩሀёણᇴɗăɘ̈́

əĄ

̣ă౵ָ̼ঐਕጡણᇴ

ࠎរᙋώ͛ٙ೩΍࣒ϒ͛ͩሀё۞ዋϡّ̈́үࠎ͟

ޢ̶ژྍঐਕጡ۞ֶፂĂώ͛૟ͽ၁រྤफ़̈́ͽ˯ࢗᙊҾ

͞ڱĂՐ΍౵ਕ΃ܑ᐀ڕঐਕጡ۞࣒ϒ͛ͩሀёણᇴĂ֭

ޙϲ˘इዋϡ۞ࢍზ͞ёĄ

ࢵА૟ͽҜொ႙ᆧ̝ـᖬྶࢦྏរඕڍซҖᑢЪĂٙ

Ր଀̝ણᇴགྷ࿅௚ࢍ͞ڱĂ଀΍πӮࣃޢĂӈؠཌྷࠎ౵ָ

ણᇴĂٙ଀̝౵ָણᇴࣃĂтܑ˘ٙϯĄᙯٺ࣒ϒሀё۞

ዋϡّĂ૟ͽᑢЪ̝ᄱमӮ͞ॲүؠณ੅ኢĂ֭ͽྏរඕ ڍ̝ᇾ໤ઐमүֶፂĄ

ॲፂҜொ႙ᆧྏរྤफ़ĂᙊҾٙՐ଀̝౵ָણᇴࣃĂ

΃ˢ࣒ϒ͛ͩሀёޢĂٙ଀̝ᑢЪѡቢтဦ 12 Ҍဦ 15 ٙ ϯĂဦ̶̚Ҿពϯ˞ྏរྤफ़(experimental)ă౵ָᑢЪѡ ቢ(optimal)ֶ̈́ώ͛೩΍۞ఢ݋Ăٙؠણᇴ̝ሀᑢඕڍ (trial)ĄѣᙯᙊҾྤफ़ᕇᇴ̝ᕜפ͞ёĂϤٺ೧ዚёྏរ̚

(LYS-1ăLYS-2 ̈́ LYS-3)дតԛณྵ̂ॡĂᏵ႖ਫ਼઻̝˧

(7)

20 15 10 5 0 -5 -10 -15 -20

(kN)

(mm)

-30 -20 -10 0 10 20 30

LYS-1 Experimental Optimal Trial

ဦ 12 ྏវ LYS-1 ̝ᑢЪඕڍ

30

20

10

0

-10

-20

-30

-40 -20 0 20 40

Experimental Optimal Trial

(kN)

(mm) LYS-4

ဦ 13 ྏវ LYS-4 ̝ᑢЪඕڍ

ᄃҜொᙯܼЯ࢑ᝈ৏யϠ˯ೳ۞ᖼԶᕇĂЯѩ೧ዚё่פ

݈ࢬϏצ࢑ᝈ৏ᇆᜩ̝ྤफ़ᕇᙊҾᑢЪĄ҃໣ᇿё̝၁រ ᔵ൑࢑ᝈ৏۞ᇆᜩĂҭ྅ཉдྵ̂ҜொॡĂϺЯೀңܧቢ

ّயϠ˧ณ˯ೳ̝ன෪Ăٙͽ໣ᇿёϺ่פዋЪ̝ྤफ़ᕇ ᙊҾĄ

ଂဦ 12~ဦ 15 ۢĂώఢ݋ᄃ౵ָણᇴඕڍ࠹मࠤ຋Ă

׎ዋϡّΞ଀ᙋ၁

̱ăඕኢᄃޙᛉ

ॲፂ၁រඕڍ଀ۢĂҲࢫЄ᐀ڕঐਕ྅ཉ൑ڱᑕϡሀ ᑢ A36 ᐀ՄҖࠎ̝ᗕቢّሀёĂϤـᖬҜொ႙ᆧྏរ൴ன ҲࢫЄ᐀ڕ̝ࢫЄҜொᐌ౵̂Ҝொ҃ᆧΐĂͷӔ˘ᗕቢّ

ត̼Ąٙͽώ͛ٙଳϡ̝ᗕቢّർ̼בᇴ̈́າણᇴɝĂ֭

ֶҜொ።ॡ࣒ϒ͛ͩሀё̝ࢫЄҜொࣃĂᒔ଀ͽ˭Еೀᕇ

300

200

100

0

-100

-200

-300

-50 -25 0 25 50

(kN)

(mm) LA2-1

ဦ 14 ྏវ LA2-1 ̝ᑢЪඕڍ

50 40 30 20 10 0 -1 -20 -30 -40 -50

-40 -20 0 20 40

(kN)

(mm) A36-1

ဦ 15 ྏវ A36-1 ̝ᑢЪඕڍ

׍វඕኢĈ

1. ၆ٺ LYS100 ঐਕ᐀ڕĂ׎ඈШّർ̼ܼᇴɢࣃĂࡗࠎ

֕જّർ̼ܼᇴɪࣃ۞ 3 ࢺĂͷ׌۰̝׶ඈٺࢫЄޢݏ ޘ Kpᄃܐؕݏޘ K0̝ͧĄϤώ͛ٙ଀̝ඕڍĂޙᛉɢ ࣃనࠎ 0.1Ă҃ɪࣃ݋నࠎ 0.03Ą

2. ၆ٺ A36 ঐਕ᐀ڕΞ૟ɢࣃనࠎ 0Ăɪࣃనࠎ 0.09~0.1 มĄ҃ LYS235 ݋Ξ૟ɢࣃᄃɪࣃనࠎ࠹Т̝ࣃĂ׎ࣃ ࡗࠎ 0.03Ą

3. ၁ᅫሀᑢҜொ႙ᆧ̝ـᖬྶࢦඕڍ൴னĂԼតɘᄃə̝

ͧࣃĂ၆ሀᑢٙ଀̝Ᏽ႖ਫ਼઻ᇆᜩ̙̂Ăҭื̂ٺ 1Ą Ϥ࢜΃̝ඕڍĂޙᛉ LYS100 ᐀ڕɘᄃə̝ͧࣃ౵рд 3 ͽ˯Ă҃ A36 ᐀ڕɘᄃə̝ͧࣃ౵рд 1 ͽ˯Ą

ॲፂᙊҾඕڍሀᑢ᐀ڕঐਕጡצـᖬྶࢦүϡ˭̝

Җࠎ଀ۢĂώ͛ٙ೩΍̝࣒ϒ͛ͩሀёĂΞՐ଀᐀ڕٺЇ ຍྶࢦүϡ˭̝Ᏽ႖ঐਕҖࠎĂ׍ѣ̙᏾̝ᑢЪड़ڍĂЯ

(8)

κ྅ཉ̝ᇴࣃ̶ژĄ

௑ཱི৶͔

Ke ͛ͩሀёሀᑢ̝̮І۞ܐؕݏޘ K0 ր௚ܐؕݏޘ

q ᖼೱҜொត̼בᇴ

R(t) ၆ᑕ̝аೇ˧

ɪ ࢫЄ݈ޢݏޘͧ

x ր௚̝Ҝொ

ɗ,ɘ,ə,n ଠטᏵ႖ਫ਼઻ԛېត̼۞ણᇴ

µ ώ͛ٙؠཌྷ̝ᗕቢّർ̼בᇴௐ˟ۡቢ߱׶

ܐؕۡቢ߱୆தͧ ᄃ֕જർ̼தɪ̝मࣃ ɂ_y ܡκጡϫ݈۞ࢫЄҜொ

ɂ_y0 ܐؕࢫЄҜொ

ɂ_max ౵̂Ҝொ඗၆ࣃ

ણ҂͛ᚥ

1. Housner, G. W., Masri, S. F., and Thiel, C. C., “Structural Control: Past, Present and Future,” Journal of Engineering Mechanics, Vol. 123, No. 9, pp. 897-971 (1997).

2. ችૣᎸăᔨϲֽăౘ୻ே׶ౘߦЇĂĶૻ̼ёΐݏܡκ ጡٺ̍඀၁ચ˯̝ᑕϡķĂௐ̣بඕၹ̍඀ࡁ੅ົĂ໨

ᐝĂௐ 127-134 ࢱ(2000)Ą

3. ߉ځேăԇ͛՗׶ో׎ࠡĂĶҲࢫЄૻޘ᐀Մّ̝ਕរ ᙋķĂᎸ̂̍඀ጯΏĂௐ˩˟סĂௐ˘ഇĂௐ 65-70 ࢱ (2001)Ą

4. ߉ځேăԇ͛՗ăో׎ࠡ׶ӕ੼ᖳĂĶҲࢫЄ඼ԛ᐀ڕ

̝࡝ዩّਕࡁտķĂ˿̍͢඀ԫఙĂௐαסĂௐαഇĂ ௐ 1-10 ࢱ(2001)Ą

5. Tanaka, K., and Sasaki, Y., “Hysteretic Performance of Shear Panel Dampers of Ultra Low-Yield-Strength Steel for Seismic Response Control of Buildings,” 12thWCEE,

6. ԇ͛՗ăୖୁᐑă഑ ٤͈׶เ͛ЍĂĶໂҲࢫЄૻޘ

᐀ᑕϡٺ੼ᆸޙ᎝̝࡝ዩր௚ķĂ˿̍͢඀ԫఙĂௐα סĂௐ˘ഇĂௐ 11-23 ࢱ(2001)Ą

7. ౘϒྕăͳᐅර׶เ୹ซĂĶҲࢫЄ᐀ᄦิّ୆ᇣၹՄ

̝Ᏽ႖Җࠎᄃᕝෘ̝࿰ҤķĂௐ̣بඕၹ̍඀ࡁ੅ົĂ ௐ 1711-1718 ࢱ(2000)Ą

8. Soong, T. T., and Dargush, G. F., “Passive Energy Dissipation Systems in Structural Engineering,” State University of New York at Buffalo, USA (1997).

9. ችҹᅞă׹ࣰ̚ĂĶˬ֎ԛ᐀ڕঐਕጡ̝๬ّሀݭķĂ

઼ϲέ៉̂ጯгዩ̍඀ࡁտ͕̚ĂಡӘበཱི CEER, R83-4-04 (1994)Ą

10. Wen, Y. K., “Method for Random Vibration of Hysteretic System,” Journal of Engineering Mechanics ASCE, Vol.

102, No. 2, pp. 249-263 (1976).

11. Sues, R. H., Mau, S. T., and Wen, Y. K., “System Identification of Degrading Hysteretic Restoring Forces, ”Journal of Engineering Mechanics, Vol. 114, No.

5, pp. 833-846 (1988).

12. Whittaker, A. S., Bertero, V. V., Thompson, C. L., and Alonso, J. L., “Seismic testing of Steel Plate Energy Dissipation Devices,” Earthquake Spectra, Vol. 7, No. 4, pp. 563-604 (1991).

13. Tsai, C. S., and Chung, L. L., “RADAS As A Damper for Seismic Mitigation,” Proceedings of the Second World Conference on Structural Control, Kyoto, Japan (1998).

14. ችҹᅞă߸Ԡෞ׶ᛂ໚पĂĶӣΐݏܡκ྅ཉၹߛ̝࡝

ዩྏរࡁտķĂ઼ϲέ៉̂ጯгዩ̍඀ࡁտ͕̚ĂಡӘ በཱི CEER.R81-09 (1992)Ą

2002 ѐ 12 ͡ 19 ͟! ќቇ 2003 ѐ 05 ͡ 20 ͟! ܐᆶ 2003 ѐ 06 ͡ 05 ͟! ኑᆶ 2003 ѐ 06 ͡ 17 ͟! ତצ