Evaluation of Compressive Strength of Assembled Column System Reinforced with Cross-Arms and Stayed Struts

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** ℎᵝݡ⦺Ʊ ☁༊Ŗ⦺ŝ ᕾᔍ ([email protected])

Received August 1, 2013/ revised September 4, 2013/ accepted October 1, 2013

Copyright ⵑ 2013 by the Korean Society of Civil Engineers

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0)

ǣǣȀȀǤǤȀͳͲǤͳʹ͸ͷʹȀǤʹͲͳ͵Ǥ͵͵Ǥ͸Ǥʹͳ͸ͻ ǤǤǤ

⟖㦇⵪#⇍#♪⵪Ḛ#⊲ᇓ᧚#⸮ύᏮᨣ⢚⡢㜚ⴖ#⬓㍓ᇓᦂ#㦇ᆾ

׌լਐȵࢮ෮૳

Kim, Kyung Sik*, Park, Hyun Yong**

Evaluation of Compressive Strength of Assembled Column System Reinforced with Cross-Arms and Stayed Struts

ABSTRACT

The compressive strengths of simply supported columns may be significantly increased by reinforcing them with an assemblage of cross-arms and stayed struts connecting both ends of the columns and the cross-arm members. The purpose of the stayed struts and cross-arms is to introduce partial restraints against translation and rotation, thereby decreasing the effective buckling length of the column. In this study, buckling strengths of the assembled column system have been quantitatively evaluated from the theoretical methods based on both the equivalent spring model and the stiffness matrix formulation. And the results were compared with those from elastic/inelastic analysis using a finite element analysis package program, ABAQUS, for verification purpose. Expected compressive strength curves have been proposed for the assembled column system as a function of slenderness ratio of the simply supported column.

Key words : Assembled column system, Compressive strength, Equivalent spring model, Stiffness matrix, Finite element analysis

Ⅹಾ

݉ᙽḡḡࡽʑࣆᇡᰍ᮹ᵲe᭥⊹ᨱᙹ⠪ᰍෝᖅ⊹⦹Ł, əᙹ⠪ᰍ᮹᧲݉ŝʑࣆᇡᰍᔢ⦹݉ᮥᜅ✙ౠᮝಽbbᩑđ⦹ᩍᅕvࡽ᳑พʑࣆ᜽

ᜅ▽ᮡእᅕv݉ᙽʑࣆᇡᰍᨱእ⦹ᩍəᦶ⇶vࠥaᔢݚ⯩⨆ᔢࢁᙹᯩ݅. ᙹ⠪ᰍaᖅ⊹ࡽʑࣆ᮹ᵲeḡᱱᨱᕽᙹ⠪ၰ⫭ᱥᯱᮁࠥෝᱽ

⦽⦹ᩍʑࣆ᮹ᮁ⬉᳭Ǖʙᯕෝᵥᯕ۵⬉ŝෝ☖⧕vࠥ⨆ᔢᯕǍ⩥ࡽ݅. ᅙᩑǍᨱᕽ۵ʑࣆᇡᰍᯕ᫙᮹Ǎᖒ᫵ᗭෝᜅ⥥ยᮝಽ⊹⪹⦽॒a ᜅ⥥ย༉ߙʑჶ, ᯱᮁࠥෝ↽ᗭ⪵⦹ᩍ݉ᙽ⪵᜽┉Ǎ᳑ĥᨱݡ⦽vᖒ⧪಍ʑჶ, əญŁჵᬊᮁ⦽᫵ᗭ⧕ᕾ⥥ಽəఉᮥ⪽ᬊ⦽┥ᖒ/እ┥ᖒ⧕

ᕾʑჶᮥᱢᬊ⦹ᩍᅕvࡽ᳑พʑࣆ᜽ᜅ▽᮹ᦶ⇶vࠥෝᱶపᱢᮝಽᔑᱶ⦹ŁəđŝෝእƱ⦹ᩡ݅. ᅕvݡᔢᯕࡹ۵݉ᙽʑࣆ᮹ᖙᰆእađ ᱶࡹ໕᳑พʑࣆ᜽ᜅ▽ᮥǍᖒᮥ☖⧕⨆ᔢࢁᙹᯩ۵ʑݡᦶ⇶vࠥෝᔑᱶ⧁ᙹᯩ۵ᦶ⇶vࠥłᖁᯕᱽᦩࡹᨩ݅.

áᔪᨕ᳑พʑࣆ, ᦶ⇶vࠥ, ॒aᜅ⥥ย༉ߙ, vᖒ⧪಍, ᮁ⦽᫵ᗭ⧕ᕾ

1. ᕽು

ᙹ⠪ᰍ(cross-arms) ၰᔍᰍ(stayed strut)ಽᅕvࡽ᳑พʑࣆ᜽ᜅ▽ᮡᜅ✙ౠŝᙹ⠪ᰍಽǍᖒࡹ۵Ǎ᳑᳑⧊ᯕ⇵aᇡ₊ࡹᨕ݉ᙽḡḡ ʑࣆ᮹ᦶ⇶vࠥෝᔢݚ⯩⨆ᔢ᜽┍ᙹᯩ۵Ǎ᳑᜽ᜅ▽ᯕ݅. ᯝၹᱢᮝಽʑࣆᇡᰍ۵ᦶ⇶ಆᨱᱡ⧎⦹໑ᯝᱶⓍʑ᮹ᦶ⇶ಆᨱࠥݍ⦹໕

᳭Ǖᯕၽᔾ⦹íࡽ݅. ᦶ⇶ᇡᰍ᮹᳭Ǖvࠥ۵᧲݉᮹Ğĥ᳑Õᨱ᮹⧕đᱶࡹ۵ᮁ⬉ʙᯕĥᙹKෝ⡍⧉⦹۵ᇡᰍ᮹ᖙᰆእ᮹⧉ᙹಽ

⢽⩥ࡽ݅.

ĵܓėॡ

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Fig. 1. Compressive Strength Curve in AISC

(a) 3-Dimensional View (b) 2-Dimensional View Fig. 2. Assembled Column System with Cross-Arms and Stayed Struts

Fig. 3. Example for Assembled Column System (Andrade et al. 2003)

ၙǎ᮹AISC (2001, 2011)ᨱᕽ۵ᖅĥ༊ᱢᮝಽᖙᰆእ(slenderness ratio)᮹Ⓧʑᨱ঑௝┥ᖒᩢᩎŝእ┥ᖒᩢᩎᮝಽǍᇥ⦹ᩍࢱ}᮹

łᖁᮝಽǍᖒࡽʑࣆvࠥłᖁᮥFig. 1ŝzᯕᱽᦩ⦹ᩡ݅(Segui, 2007). Fcr,FyၰFe۵ᦶ⇶vࠥ, ⧎ᅖvࠥəญŁ᪅ᯝ్(Euler)

᳭Ǖvࠥෝ᮲ಆ₉ᬱᮝಽᱥ⪹⦽sॅᮥbb᮹ၙ⦽݅. ᨙɪࡽ

AISCᨱᕽ۵ ┥ᖒ᳭Ǖᩢᩎ᮹ ᦶ⇶vࠥಽᕽ ᪅ᯝ్ ᳭Ǖvࠥ᮹

88%ᙹᵡᮥ ᯙᱶ⦹Ł ᯩŁ, ə ভ እ┥ᖒ ᳭Ǖᩢᩎŝ᮹ ᖙᰆእ

Ğĥsᮝಽ۵ÑíÔÎö^ć^îƗᮥᱽᦩ⦹Łᯩ݅. ᩍʑᕽE۵ᰍഭ᮹

┥ᖒĥᙹෝ ӹ┡ԙ݅.

┥ᖒᩢᩎᨱᕽᦶ⇶ᇡᰍaaḡ۵┥ᖒ᳭Ǖvࠥ۵᪅ᯝ్᳭Ǖ Ŗ᜾ᨱᕽ᦭ᙹᯩॐᯕᖙᰆእ᮹ᱽŒᨱၹእಡ⦹ḡอ᧲݉ᨱᕽ᮹

Ğĥ᳑Õၰᵲeḡᱱ᮹ቭ౩ᯕᝒ(bracing) ⬉ŝ॒ᨱ᮹⧕ə

ᦶ⇶᳭Ǖvࠥෝᔢݚᙹᵡ⨆ᔢ᜽┍ᙹᯩ݅. ᧲݉⯭ḡᦶ⇶ᇡᰍ᮹

᳭Ǖ༉ऽ(buckling mode)۵݉ᯝłශ(single curvature)ᮥᅕᯕ ۵⮉᳭Ǖ⩶ᔢᮥᅕᯕḡอ, ʙᯕႊ⨆ᮝಽᵲe᭥⊹ᨱᙹ⠪ᄡ᭥ෝ

Ǎᗮ⦹۵⬂ႊ⨆ቭ౩ᯕᝒᯕ ᳕ᰍ⦽݅໕᳭Ǖ༉ऽ۵ᯕᵲłශ (double curvature)ᮥᅕᯕ۵⮉᳭Ǖ⩶ᔢᮥᅕᯕ໕ᕽ┥ᖒ᳭Ǖv

ࠥ۵4႑ಽ᷾a⦹íࡽ݅. ੱ⦽⬂ႊ⨆ᄡ᭥Ǎᗮᨱ݅⇵aᱢᮝಽ

⫭ᱥᯱᮁࠥʭḡǍᗮ⦹íࡹ໕┥ᖒ᳭Ǖvࠥ۵ᯕುᱢᮝಽ8.18႑ ʭḡ᷾a⦹íࡽ݅. ᯕ్⦽ႊჶᮝಽᦶ⇶ᇡᰍ᮹ᵲeḡᱱǍᗮ᳑

Õᮥ⇵aᱢᮝಽ᳑ᖒ⦹ᩍᱥℕʑࣆǍ᳑ᨱݡ⦽ᦶ⇶᳭Ǖvࠥෝ

⨆ᔢ᜽┍ᙹᯩ݅۵}ֱᮝಽᇡ░ᅕvࡽ᳑พʑࣆ᜽ᜅ▽ᯕᱽᦩ

ࢁ ᙹ ᯩ݅.

Ǎ᳑ྜྷ᮹⩥ᰆᩍÕᔢᦶ⇶ᇡᰍ, ᷪʑࣆ᮹ᵲe᭥⊹ᨱ⬂ႊ⨆

ቭ౩ᯕᝒ᮹ ᖅ⊹a ᇩa⦹ᩍ Ǎᗮᮥ ᅕᰆ⧁ ᙹ ᨧ۵ Ğᬑᨱ۵

ʑࣆᇡᰍ ᯱℕ᮹ ᦶ⇶ಆᨱ ᮹⧕ ḡḡࡹ۵ ᙹ⠪ᰍ(cross-arm)᪡

ᔍᰍ(stayed strut)ಽǍᖒࡽǍᗮᰆ⊹ෝFig. 2᪡zᯕᖅ⊹⧁

ᙹᯩ݅. ʑࣆᇡᰍ᮹ᵲeḡᱱᨱႊᔍႊ⨆ᮝಽ݅ᙹ᮹ᙹ⠪ᰍෝ

ᖅ⊹⦹Łbbᙹ⠪ᰍ᮹↽᫙⊂ŝʑࣆᇡᰍ᮹ᔢ⦹᧲݉ᮥᜅ✙ౠ ᮝಽᩑđ⦽ᅕv᜽ᜅ▽ʑࣆᮡʑࣆᇡᰍ᮹ᵲe⦽ḡᱱᨱᕽอ

ᖅ⊹ࡹအಽ݉ᯝᙹ⠪ᰍ᜽ᜅ▽ᮝಽᇩฑ݅. ᯕভ⬉ᮉᮥ׳ᯕʑ

᭥⧕ᜅ✙ౠᇡᰍᨱʕᰆಆᯕ᯦ࠥࡹʑࠥ⦹ḡอᜅ░ౠᨱၙญ

᯦ࠥࡽᯙᰆಆᮡʑࣆᇡᰍ᮹ᦶ⇶ᮝಽᱡ⧎ࡹအಽᱥℕ᮹ᦶ⇶᜽

ᜅ▽ᮝಽᅕᦥvࠥෝᱡ⦹᜽┍ᙹᯩᮝအಽᵝ᮹⧕᧝⦽݅. ʑࣆᇡ ᰍᵲeḡᱱᨱᯩ۵ᙹ⠪ᇡᰍ۵ᜅ✙ౠ᮹ᯙᰆಆᨱᦶ⇶ᮝಽᱡ⧎

⦹íࡹ໕ᕽʑࣆᇡᰍ᮹Ğĥ᳑Õᨱᩢ⨆ᮥᵝᨕ᳭Ǖvࠥෝ⨆ᔢ

᜽┅íࡽ݅. Fig. 2ᨱᅕᯙᔍᰍၰᙹ⠪ᰍಽᅕvࡽ᳑พʑࣆ᜽ᜅ

▽᮹┥ᖒ᳭Ǖvࠥ۵ᅕv᜽ᜅ▽ᯕᨧ۵݉ᙽ ʑࣆᇡᰍᯝভ᪡

እƱ⦹໕ᔢݚᙹᵡ⨆ᔢࡽ݅. ə౨ḡอə⨆ᔢᱶࠥ۵ᵝʑࣆ

ᇡᰍ᪡ᙹ⠪ᰍ᮹ʙᯕእ, ᵝʑࣆ/ᙹ⠪ᰍ/ᔍᰍ᮹vᖒၰvࠥ, ᔍᰍ ᨱ᯦ࠥࡹ۵Ⅹʑʕᰆಆ᮹Ⓧʑ॒݅᧲⦽ๅ}ᄡᙹ(parameter)᮹

ᩢ⨆ᮥ ၼ۵݅.

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(a) Mode 1 (b) Mode 2 Fig. 4. Buckling Modes of Assembled Column System ᯕ్⦽᳑พʑࣆ᜽ᜅ▽ᮡÑݡ⦹Ñӹ, Ł⊖Ǎ᳑ྜྷ᮹᜽Ŗᵲ

a᜽ᖅಽᔍᬊࡹ۵ᦶ⇶ᇡᰍᨱᱢᬊࢁᙹᯩ݅. ᝅᱽᱢᬊࡽᔍಡෝ

ᅕ໕ Fig. 3ᨱᕽ ᅕᯙ ၵ᪡ zᯕ ቭ௝ḩ᮹ ญᬑߑᯱօᯕ൉(Rio de Janeiro)ᨱᯩ۵“Rock in Rio ⳓ” ᜅ┡ॵᬡᯕᯩ݅(Andrade et al. 2003). ᯕᜅ┡ॵᬡᮡḡᇶʭḡ׳ᯕa36mᯕ݅. ׳ᮡḡᇶ᮹

Ǎ᳑۵݉໕ᯕⓍÑӹ᜽Ŗᗮࠥ᮹ᇩᯕᯖᮥᵝ۵ḡᵝ᜽ᜅ▽ᮥ

᫵Ǎ⦹ʑᨱᨵḡܩᨕॅᮡᅕvࡽ᳑พʑࣆ᜽ᜅ▽ᮥ₥┾⦹ᩡ݅.

ᅙ᳑พʑࣆ᜽ᜅ▽᮹ᦶ⇶vࠥ۵ᙹ⠪ᰍ᮹ʙᯕၰvᖒŝᔍᰍ ᮹ ݉໕ᱢŝvᖒᨱ ၝq⦽ ᩢ⨆ᮥၼí ࡹ۵ߑ, Fig. 4(a)ᨱᕽ

ᅕᯙၵ᪡zᯕᙹ⠪ᰍၰᔍᰍaᗭ᫵᮹vࠥᨱၙ⊹ḡ༜⦹໕

ᔢ⦹ݡ⋎ᯙ᳭Ǖ༉ऽಽ ၽ⩥ࡹᨕᦶ⇶vࠥa᷾aࡹʑ۵⦹ӹ

ə⬉ᮉᯕԏíࡽ݅. อ᧞ᙹ⠪ᰍ᪡ᔍᰍaᱢᱶᙹᵡ᮹ᗭ᫵vࠥෝ

aḥ݅໕᳑พʑࣆ᜽ᜅ▽ᮡFig. 4(b)ᨱᅕᯙၵ᪡zᯕᔢ⦹ᩎݡ

⋎ᯙ᳭Ǖ༉ऽෝӹ┡ԕ໑ᙹ⠪ᰍᖅ⊹ḡᱱᨱݡ⦽ʑࣆᇡᰍ᮹

ᙹ⠪ᄡ᭥Ǎᗮ᳑Õᮥᝅ⩥᜽┍ᙹᯩ݅. Fig. 4᮹Mode 2ᨱᕽ۵

ʑࣆŝᙹ⠪ᰍaอӹ۵ ḡᱱᨱᕽ⫭ᱥᄡ᭥aၽᔾࡹ۵äᮝಽ

ཹᔍ⦹ᩡḡอᙹ⠪ᰍ᮹⮉vᖒၰᔍᰍ᮹ᯙᰆ/ᦶ⇶vᖒᮥ⨆ᔢ᜽

┉݅໕⫭ᱥᄡ᭥ʭḡᱽᨕࡹᨕᱥℕʑࣆ᜽ᜅ▽᮹ᦶ⇶vࠥ۵޵

ᬒ ⨆ᔢࢁ ᙹ ᯩ݅.

ᔍᰍಽᅕvࡽᦶ⇶ᇡᰍ᜽ᜅ▽ᨱݡ⦽ʑⅩᱢᯙᱲɝႊ᜾ᮡ

Chu and Berge (1963) əญŁMauch and Felton (1967) ॒᮹

ၽ⢽ᨱᕽᗭ}ࡹᨩ݅. ᯕॅᮡᦶ⇶ᇡᰍᨱᯙᰆᇡᰍෝᅕ᳑ᱢᮝಽ

ᖅ⊹⦹ᩍʑࣆ᜽ᜅ▽ᮥǍᖒ⦹໕ᯙᰆᇡᰍ᮹ᩎ⧁ᨱ᮹⧕ʑࣆ᜽

ᜅ▽᮹ᦶ⇶vࠥaᯝᱶᇡྙ⨆ᔢࢁᙹᯩ݅۵}ֱᮥŖ⦺ᱢᯙ

ႊჶᮝಽᱥ}⦹ᩡ݅. ᯕ⬥1970֥ᵲၹᯕ⬥⋱ӹ݅᪉┡ญ᪅

ḡᩎᮥᵲᝍᮝಽᙹ⠪ᰍၰᔍᰍಽᅕvࡽ᳑พʑࣆ᜽ᜅ▽ᨱݡ⦽

⪽ၽ⦽ᩑǍaḥ⧪ࡹᨩ݅. Smith et al. (1975)ᮡ݉ᯝᙹ⠪ᰍ (single crossarm)᪡ᔍᰍಽᅕvࡽ᳑พʑࣆ᜽ᜅ▽ᮡእᅕv݉ᙽ ʑࣆݡእᦶ⇶vࠥ᷾aእᯙTSI (theoretical strength increase) ᮹ ᔢ⦽sᯕ 8.18ᨱ ᯕෝ äᮝಽ ᩩ⊂⦹ᩡŁ, ᳭Ǖ༉ऽᨱ ঑ෙ

ᦶ⇶vࠥᔑᱶᮥ ⧕ᕾᱢ ႊჶᮝಽ ᜽ࠥ⦹ᩡ݅. ੱ⦽ ᩩᱽ⧕ᕾᮥ

☖⧕ʑࣆᇡᰍ᪡ᙹ⠪ᰍ᮹↽ᱢʙᯕእa6ᯕࢉᮥᅕᩡ݅. Hafez et al. (1979)ᮡ Smith et al. (1975)᮹ ᯕುᮥ ĥ᜚⦹ᩍ ޵ᬒ

ᱶƱ⦽⧕ᕾᱢ⧕ෝ}ၽ⦹ᩡ۵ߑ, ᯕॅᮡ⃹ᮭᮝಽᔍᰍᨱ᯲ᬊ⦹

۵ᯙᰆಆ᮹Ⓧʑa᳑พʑࣆ᜽ᜅ▽᮹ᦶ⇶vࠥ᷾aᨱḢᱲᱢᮝ ಽʑᩍ⦽݅۵ᔍᝅᮥᯙḡ⦹Łᯕᯙᰆಆ᮹Ⓧʑaᦶ⇶vࠥෝ

ᔑᱶ⦹۵ᵝ᫵ๅ}ᄡᙹaࡽ݅۵äᮥ᷾໦⦹ᩡ݅. Hathout et al. (1979)ᮡ݉ᯝᙹ⠪ᰍᅕv᜽ᜅ▽ʑࣆᨱᕽᙹ⠪ᰍ᮹}ᙹෝ

3}ੱ۵4}ಽᄡ⪵᜽┅໑ᅕvࡽ᳑พʑࣆ᜽ᜅ▽᮹ᦶ⇶vࠥ

᷾a᮹⬉ᮉᮥá☁⦹ᩍᙹ⠪ᰍ᮹}ᙹa4}ᯝভ޵ᬒ⬉ᮉᱢᯕ௝

۵ᔍᝅᮥၽ⢽⦹ᩡ݅. Temple (1977)ᮡᮁ⦽᫵ᗭ⧕ᕾ᮹ɝeᯕ

ࡹᨩ޹ๅ✙ฎᜅǍ᳑⧕ᕾʑჶᮥᱢᬊ⦹ᩍ᜽ᜅ▽᮹┥ᖒᦶ⇶v

ࠥ᮹⧕ᕾᱢ⧕ෝᮁࠥ⦹ᩡ݅. ੱ⦽ᅕ-ʑࣆ(beam-column)᫵ᗭᨱ

ݡ⦽ᦩᱶ⧉ᙹ(stability function)ෝ⪽ᬊ⦹ᩍvᖒ⧪಍(stiffness matrix)᮹ ᮁࠥᨱ ⪽ᬊ⦹ᩡ݅.

1980֥ݡॅᨕᕽ۵ʑ᳕᮹ᅕv᜽ᜅ▽ʑࣆ᮹vࠥ᷾aᨱݡ⦽

ᝅ⨹ᱢá᷾ၰᝅྜྷᱽ᯲ᨱݡ⦽ྙᱽᱱᮥḡᱢ⦹۵ᩑǍaၽ⢽ࡹ

ᨩ݅. Wong and Temple (1982)ᮡ ᯙᰆಆᮥ ၼ۵ ᅕv᜽ᜅ▽

ʑࣆ᮹ᱽ᯲ᨱᯩᨕⅩʑđ⧉(initial imperfection)ᯕ⧎ᔢ᳕ᰍ⦽

݅۵ ᔍᝅᨱ ᵝ༊⦹ᩍ ᯕುᱢᯙ ᦶ⇶vࠥa Ⅹʑ đ⧉ᨱ ᮹⧕

qᗭࡹ۵ŝᱶᮥᱶపᱢᮝಽᇥᕾ⦹ᩡ݅. ə్ӹᯕॅ᮹ᩑǍᨱᕽ

ŁಅࡽⅩʑđ⧉ᮡᙹ⠪ᰍᨱǎ⦽ࡹᨕ᜽ᜅ▽ᱥℕ᮹Ⅹʑđ⧉ᨱ

ݡ⦽ၝqࠥᇥᕾᮡᰍݡಽᯕ൉ᨕḡḡ༜⦹ᩡ݅. Temple et al.

(1984)ᮡʑ᳕᮹ᝅ⨹ᨱ᮹⦽ᦶ⇶vࠥaᔍᰍ᮹ᯙᰆಆᯕᗭᝅࡹ

۵᜽ᱱ᮹vࠥಽᱶ᮹ࡹᨕ᪵݅۵äᮥ⪶ᯙ⦹ᩡ݅. ੱ⦽vࠥᔑᱶ ᮹ᯝšᖒᯕđᩍࡹᨩ݅۵ᔍᝅᮥḡᱢ⦹ŁMode 1ᨱᕽ᪅༊⦽

⊂(concave side)᮹ ᔍᰍᨱ ᯙᰆಆᯕ ᗭᝅࡹ޵௝ࠥ ᅝಾ⦽ ⊂ (convex side) ᔍᰍa⧎ᅖࢁভʭḡᦶ⇶᜽ᜅ▽ᮡvࠥaᮁḡࢉ

ᮥᅕᩡ݅. Smith (1985)۵ᅕvࡽ᳑พʑࣆ᜽ᜅ▽ᯕ↽ݡvࠥ

Ǎ⩥ᮥ ᭥⧕ᕽ ᙹ⠪ᰍᨱ ᯲ᬊ᜽⍽᧝ ⧁ ↽ᗭ ᯙᰆಆ᮹ Ⓧʑෝ

ᱽᦩ⦹ᩡ݅.

ᯕ⬥᧞e᮹Ŗ႒ʑෝÑℱ2000֥ݡॅᨕᅕv᜽ᜅ▽ʑࣆᨱ

ݡ⦽ᩑǍaᅕ݅ḥᅕࡽႊჶುၰǍℕ⪵ࡽᖅĥჶ॒᮹ԕᬊᮝಽ

ၽ⢽ࡹᨩ݅(Chan et al. 2002, Steirteghem et al. 2005, Araujo et al. 2008, Saito and Wadee 2008; 2009a; 2009b). Kim (2011)

ᮡSmith et al. (1985)ᨱ᮹⧕ࠥ⇽ࡹᨩ޹⧕ᕾᱢ⧕ෝᮁ⦽᫵ᗭ⧕

ᕾᮥ ☖⧕ á☁⦹ᩡ݅.

(4)

(a) Elastic Boundary (b) Free Body Diagram Fig. 5. Equivalent Spring Model

(a) Forces in Cross-Arms (b) Deformation in Strut Fig. 6. Force-Displacement Relationship in Mode 1

Fig. 7. Equilibrium at Junction of Cross-Arm and Strut ᅙᩑǍᨱᕽ۵ᅕ-ʑࣆ(beam-column) ᇡᰍಽᕽ᮹ᵝʑࣆᇡᰍ

᪡ᙹ⠪ᰍ, ᯕෝᩑđ⦹۵ᔍᰍෝᜅ✙ౠ(strut) ᇡᰍಽ₥┾⦹ᩍ

ᜅ✙ౠ-ᅕ-ʑࣆ᮹ ᔢ⪙᯲ᬊᨱ ɝÑ⦹ᩍ ᳑พʑࣆ᜽ᜅ▽ᨱ ݡ⦽

⧕ᕾᮥᙹ⧪⦽݅. ┥ᖒ᳭Ǖvࠥᔑᱶᮥ᭥⧕ࢱaḡ⧕ᕾႊჶᯕ

ᱢᬊࡽ݅. ℌṙ۵ᜅ⥥ย༉ߙᨱɝÑ⦹ᩍᮁࠥࡽḡ႑ၙᇥႊᱶ᜾

᮹⧕ᮥᯕᬊ⦹۵ᯕುᱢ⧕ᕾʑჶᯕŁ, ࢹṙ۵⥥౩ᯥၰ✙్ᜅ

᫵ᗭ᮹ vᖒ⧪಍ᮥ ᯕᬊ⦽ ๅ✙ฎᜅ ⧕ᕾʑჶᯕ݅. ᙹ⊹ᩩᱽෝ

ᱽ᜽⦹ᩍᮁ⦽᫵ᗭᨱʑⅩ⦽ჵᬊǍ᳑⧕ᕾ⥥ಽəఉᯙABAQUS

ෝᯕᬊ⦹ᩍ┥ᖒၰእ┥ᖒ᳭Ǖvࠥෝ⪶ᯙ⦹Ł, ᯕುᱢ⧕ᕾʑჶ ŝ ᙹ⊹ᱢ ⧕ᕾᱢ ʑჶᨱ ᮹⦽ ⧕ෝ እƱ⦽݅.

2. ॒aᜅ⥥ย༉ߙ

ᅙ ᱩᨱᕽ۵ Fig. 2ᨱ ᅕᯙ ᅕvࡽ ᳑พʑࣆ᜽ᜅ▽ᮥ 2₉ᬱ

⠪໕Ǎ᳑ྜྷಽᕽ⧕ᕾ⦽݅. Fig. 4ᨱᕽᅕᯙၵ᪡ࢱaḡ᳭Ǖ༉ऽ

ᵲᨱᕽℌჩṙ༉ऽಽӹ┡ӹ۵݉ᯝłශ༉ऽᷪ, Mode 1᮹

᳭Ǖvࠥෝ⧕ᕾᱢᮝಽᮁࠥ⦹ʑ᭥⧕᳑พʑࣆ᜽ᜅ▽᮹݉ᙽ⪵ࡽ

༉ߙᮥŁಅ⦽݅. Fig. 5(a)ᨱᕽ۵᳑พʑࣆ᜽ᜅ▽ᨱᕽᙹ⠪ᰍ᪡

ᔍᰍaᱽÑࡹŁᙹ⠪ᰍ ᭥⊹ᨱᜅ⥥ยᯕᇡ₊⦽ᵲe┥ᖒḡḡ

༉ߙᮥᅕᩍᵡ݅. ᩍʑᕽ᳭Ǖ᜽ၽᔾ⦹۵ʑࣆ᮹⬂ᄡ᭥ᨱᱡ⧎⦹

۵ᔍᰍ᪡ᙹ⠪ᰍ۵┥ᖒᜅ⥥ยḡḡಽݡᝁ⧁ᙹᯩ݅. ᅙǍ᳑ĥᨱ ᕽ ⯹᮹ ⠪⩶ᔢ┽ෝ ᅕᩍᵝ۵ ᯱᮁྜྷℕࠥ۵ Fig. 5(b)᪡ z݅.

ᅙᱩᨱᕽ۵ᅙǍ᳑ĥᨱݡ⦽ḡ႑ႊᱶ᜾ᮥᯕᬊ⦹ᩍ᳭Ǖvࠥෝ

⪶ᯙ⦹Ł, ᵲ᫵ ๅ}ᄡᙹ ᵲ ⦹ӹᯙ ᜅ⥥ยᔢᙹ ᜾ᮥ ᮁࠥ⦹Ł

ᜅ⥥ยᔢᙹa ᳭Ǖvࠥᨱ ၙ⊹۵ ⬉ŝᨱ ݡ⦹ᩍ ᔕ⠕ᅙ݅.

ᵲe┥ᖒḡḡʑࣆ༉ߙᨱᕽ᳭Ǖvࠥ۵┥ᖒᜅ⥥ยᔢᙹ(ƉƑƎ) ᮹⧉ᙹಽ⢽⩥ࡽ݅. Fig. 6ᮡᅕvࡽ᳑พʑࣆ᜽ᜅ▽᮹᳭Ǖ⩶ᔢ

Mode 1 ᔢ┽ᨱᕽᙹ⠪ᰍᨱ᯲ᬊ⦹۵⯹ŝᜅ✙ౠᔍᰍ᮹ᄡ᭥పᮥ

ӹ┡ԕᨩ݅. ©۵ ᳑พʑࣆ᜽ᜅ▽ᨱ ᯲ᬊ⦹۵ ⇶⦹ᵲᯕ໑, ĺ_Ɓ۵

ʑࣆᇡᰍ᮹ᵲeḡᱱᨱᕽᙹ⠪ᄡ᭥ෝӹ┡ԙ݅. ʑࣆᵲeḡᱱᨱ ᕽ ᩑđࡽ ᜅ⥥ย᮹ Łᱶḡᱱᨱᕽ᮹ ၹಆÏª_Ɗᮡ Fig. 6(a)ᨱᕽ

ᅕᩡॐᯕ ݅ᮭŝ zᯕ ⢽⩥ࡽ݅.

ÏªƊáÞƆâĢ_Ɔß^àÞƆà Ģ_Ɔß^{á ÏĢ}Ɔ (1)

Eq. (1)ᨱᕽª_Ɗᮡʑࣆᇡᰍ᮹ᔢ⦹᧲݉ᨱᕽᙹ⠪ၹಆ, _Ɔ۵

ʑࣆᇡᰍᄡ⩶ᱥᙹ⠪ᰍaၼ۵ᦶ⇶ಆ, əญŁĢƆ۵ʑࣆᇡᰍ᮹

ᄡ⩶⬥ᙹ⠪ᰍᨱၽᔾ⦹۵⯹᮹ᄡ⪵పᮝಽᕽ, Fig. 7ᨱᕽ⪶ᯙ⧁

ᙹ ᯩॐᯕĢƆ۵ Eq. (2)ಽ ⢽⩥ࢁ ᙹ ᯩ݅.

ĢƆá ÏĢ ķ (2)

(5)

Table 1. Properties Used in Example Analysis

Column elastic modulus, _Ɓ

204 (GPa) Cross-arm elastic modulus, _Ɓſ

Strut elastic modulus, _Ƒ

Column length, _¥Þ^{á Ïŕ}Ɓß ^{4900 (mm)}

Cross-arm length, ŕ_Ɓſ ŕ_ƁZ×íÎÕ

Outer diameter of column and cross-arm, _Ɓìƍ/_Ɓſìƍ 57.2 (mm) Inner diameter of column and cross-arm, _ƁìƇ/_ƁſìƇ 44.5 (mm)

Diameter of strut, _Ƒ 6 (mm)

Cross-sectional area of column and cross-arm, _Ɓ/_Ɓſ 1014 (mm²) Cross-sectional area of strut, _Ƒ 28.27 (mm²) Moment of inertia of column and cross-arm, ¢_Ɓ/¢_Ɓſ 332986 (mm⁴)

Yield strength, _Ɨ 0.355 (GPa)

ᩍʑᕽĢ۵ʑࣆ᮹ᄡ⩶⬥ၽᔾ⦹۵ᜅ✙ౠᇡᰍ᮹⇶ಆᄡ⪵

పᯕ݅. Eq. (2)᮹᯦ࠥᨱᯩᨕᬑ⧎᮹ĥᙹ2۵ʑࣆᇡᰍᬑ⊂᮹

ᯙᰆᔢ┽ᨱᯩ۵ࢱ}᮹ᔍᰍอᯕŁಅࡹᨩᮭᮥஜ⦽݅. ʑࣆᇡᰍ

᳭⊂ᨱ᭥⊹⦹۵ࢱ}᮹ᔍᰍ۵ᦶ⇶ᔢ┽ᨱᯩ۵ߑ, ᔢݡᱢᮝಽ

ⓑᖙᰆእෝaḡ۵ᔍᰍᯱℕ۵⇶ႊ⨆ᦶ⇶ᨱݡ⦽ᱡ⧎܆ಆᮥ

ᔢᝅ⦹ᩡ݅Ł aᱶ⦹ᩍ vᖒ᮹ ᔑᱶᨱ Łಅࡹḡ ᦫᦹ݅. ⦽⠙, Eq. (2)ෝ Eq. (1)ᨱ ݡ᯦⦹໕

ÏªƊá ÑĢ ķ (3)

ෝ᨜Ł, ᜅ✙ౠᇡᰍᨱݡ⦽⇶ಆŝ⇶ႊ⨆ᄡ⩶ప᮹ᔢššĥෝ

ᯕᬊ⦹໕ ݅ᮭ ᜾ᮥ ᨜۵݅.

ĺƑá ć_Ƒ_Ƒ Ģŕ_Ƒ

(4)

ᩍʑᕽĺƑ۵ᜅ✙ౠ⇶ႊ⨆ᄡ⩶పᯕŁ,ŕƑ,_Ƒ ၰƑ۵ᜅ✙ౠᇡ ᰍ᮹ʙᯕ, ┥ᖒĥᙹ, ݉໕ᱢᮥbbӹ┡ԙ݅. ⦽⠙, Fig. 6(b)ᨱᕽ

ᅕᯙၵ᪡zᯕၙᗭᄡ᭥ᯕುᨱɝÑ⦹ᩍᜅ✙ౠᇡᰍ᮹ʙᯕᄡ⪵

ෝ ݅ᮭŝ zᯕĺ_Ɓķಽ ӹ┡ԝ ᙹ ᯩ݅.

ĺ_Ƒá ĺ_Ɓķ (5)

ᩍʑᕽĺ_Ɓ۵ʑࣆᇡᰍᵲeḡᱱᨱᕽᙹ⠪ᄡ᭥ෝӹ┡ԙ݅. Eqs.

(4) and (5)ಽᇡ░ ݅ᮭ ᜾ᮥ ᨜۵݅.

Ģ á ćŕ_Ƒ

_Ƒ_Ƒ

ĺ_Ɓķ (6)

Eq. (6)ᮥ Eq. (3)ᨱ ݡ᯦⦹໕, ÏªƊá Ñćŕ_Ƒ

_Ƒ_Ƒ

ĺƁ^Ïķ (7)

ᮥ᨜Ł↽᳦ᱢᮝಽEq. (7)ಽᇡ░ၹಆÏªƊŝᙹ⠪ᄡ᭥ĺƁ᮹

šĥෝ đᱶ⦹۵ ᔢᙹƉ_ƑƎ۵

rƉ_ƑƎá ÑćŕƑ

ƑƑ

^Ïķ (8)

ಽ ᮁࠥࢁ ᙹ ᯩ݅.

ʑࣆ᮹ ʙᯕ LᮥŕÎŝŕÏಽ bb ӹ٥۵ ḡᱱᨱ ᜅ⥥ยᔢᙹ

ĺƁෝaḡ۵ᜅ⥥ยᯕ᭥⊹⦹۵ᵲe┥ᖒḡḡʑࣆǍ᳑ĥᨱݡ⦽

ᯥĥ᳭Ǖ⦹ᵲPෝǍ⦹ʑ᭥⦹ᩍTimoshenko (1961)۵ḡ႑ၙᇥ

ႊᱶ᜾ᨱ ᮹⧕ ݅ᮭŝ zᮡ ᜾ᮥ ᱽᦩ⦹ᩡ݅.

à ć©Ɖ_ƑƎŁÞ^ƊÎâƊ_Ïß

ŁƊÎŁƊÏ

â ć©Þ^ƊÎâƊ_Ïß

ƊÎƊÏ

à ćƉÎ á×_ƑƎ (9)

ᩍʑᕽ, ŁÎá

ö

^ć^ć^©^Î^¢^Î ^, ^Ł^Ï^á

ö

^ć^ć^©^Ï^¢^Ï

Fukumoto (1982) ੱ⦽vᖒ⧪಍Ŗ᜾⪵ᨱ᮹⧕ᜅ⥥ยᔢᙹa

⡍⧉ࡽ ݅ᮭŝ zᮡ ᜾ᮥ ᮁࠥ⦹ᩡ݅.

Î à

Þ

^ć^Ɗ^¥^Î^Ɗ^Ï^{à ć}^Ɖ^©^ƑƎ

ßÞ

^ć^Ł^Ł^Î^Î^Ɗ^Î^{â ć}^Ł^Ł^Ï^Ï^Ɗ^Ï

ß

^{á ×} ⁽¹⁰⁾

Eq. (9)᪡Eq. (10)ᮡᕽಽ݅෕ḡอ₉ᯕaᨧ۵⧕ෝᱽŖ⦽݅.

Fig. 5(a)ᨱᕽᅕᯙၵ᪡zᯕᅙᩑǍᨱᕽŁಅࡽᅕvࡽ᳑พʑࣆ

᜽ᜅ▽ᨱᕽ۵ʑࣆᇡᰍ᮹ʙᯕෝᱩၹᮝಽӹ٥۵ᵲᦺḡᱱᨱᙹ

⠪ᰍa᭥⊹⧕ᯩᮝအಽƊÎá Ɗ_Ïá ŕ_Ɓ ၰŁÎá Ł_Ïá Łಽ⊹⪹⧁

ᙹᯩ݅. ᯕෝEqs. (9) and (10)ᨱݡ᯦⦹ᩍᱶญ⦹໕Eqs. (11) and (12)ෝ bb ᨜۵݅.

à ć©ƉƑƎÏŁŕƁ

ÏŁŕ_Ɓ

â ćÏ©ŕƁ

ŕ_Ɓ^Ï

à ćƉÎ á×ƑƎ (11) Î à ćŁŕƁ

ÏŁ

Þ

^ć^ŕ^¥^Ɓ^Ï^{à ć}^Ɖ^©^ƑƎ

ß

^{á ×} ⁽¹²⁾

(6)

Theory (Min.) = 27.9kN, Theory (Max.)=228.4kN Fig. 8. Buckling Strength vs. Spring Constant

Fig. 9. Buckling Strength vs. Cross Sectional Area of Strut

Fig. 10. Buckling Strength vs. Length Ratio

ᵲe┥ᖒḡḡ ʑࣆǍ᳑ĥᨱ ᱢᬊᮥ ༊ᱢᮝಽ ᮁࠥࡽ ᜅ⥥ย

ᔢᙹ ၰ ᯥĥ⦹ᵲᨱ ݡ⦽ ᜅ⥥ยvᖒ᮹ ᩢ⨆ᮥ ᦭ᦥᅕʑ ᭥⧕

ᬱ⩶všᇡᰍෝݡᔢᮝಽᩩᱽ⧕ᕾᮥᙹ⧪⦹ᩡ݅. ᩩᱽᨱᔍᬊࡽ

ᇡᰍ᮹ ⊹ᙹ ၰ ᰍഭᔢᙹ۵ Table 1ŝ z݅.

Fig. 8ᮡ Table 1ᨱ ᅕᯙ ᩩᱽ᮹ ʑࣆᇡᰍ᮹ ᙹ⠪ᰍ ᭥⊹ᨱ

ᜅ⥥ยᮥᱽŖ⦹ᩡ݅Łaᱶ⧩ᮥ ভᜅ⥥ยᔢᙹ᮹ᄡ⪵ᨱ঑ෙ

┥ᖒ᳭Ǖvࠥ᮹ᄡ⪵ෝᅕᩍᵡ݅. ᜅ⥥ยᔢᙹa‘0’ᯝভ۵ᯝၹᱢ ᯙ᧲݉݉ᙽḡḡʑࣆ᮹᪅ᯝ్᳭Ǖvࠥ᪡zḡอ, ᯕ⬥əsᯕ

⍅ḩᙹಾᦶ⇶vࠥaᕽᕽ⯩᷾a⦹ᩍ᪅ᯝ్᳭Ǖvࠥ᮹8.18႑ ᮹ sᨱ ᙹಕ⦹۵ äᮥ ⪶ᯙ⧁ ᙹ ᯩ݅. ᯕ ᯕುᱢᯙ ↽ݡsᮡ

ʑࣆᇡᰍ᮹ ᵲeᇡᇥ, ᷪ ᜅ⥥ย᭥⊹ᨱᕽ ⬂ႊ⨆ ᄡ᭥ ၰ ⫭ᱥ

ᯱᮁࠥʭḡǍᗮ⧩ᮥভ᮹┥ᖒ᳭Ǖvࠥsᯕ݅. Fig. 8ᨱᕽTheory (Min.)ᮡ᪅ᯝ్┥ᖒ᳭Ǖ⦹ᵲᮥ, Theory (Max.)۵ᵲeĞĥ᳑Õ ᯕŁಅࡽ┥ᖒ᳭Ǖ⦹ᵲᮥ᮹ၙ⦽݅. Eqs. (11) and (12)۵ᕽಽ

݅ෙ ᜾ᯕḡอ ə ⧕۵ ᯝ⊹⦽݅۵ äᮥ ੱ⦽ ⪶ᯙ⧁ ᙹ ᯩ݅.

Fig. 9۵ᔍᰍᯙᜅ✙ౠᇡᰍ݉໕ᱢᄡ⪵ᨱ঑ෙᩩᱽ᳑พʑࣆ

᜽ᜅ▽ᨱݡ⦽┥ᖒ᳭Ǖvࠥ᮹ᄡ⪵ෝᅕᩍᵡ݅. ᜅ⥥ยᔢᙹ۵

Eq. (8)ಽ ĥᔑ⦹ᩡŁ, Eq. (12)ᨱ ᅕᯙ Fukumoto (1982)᮹

᜾ᮝಽ⧕ෝǍ⦹ᩡ݅. Fig. 9ᨱᕽᅕᯙ᳑พʑࣆ᜽ᜅ▽᮹ᦶ⇶v

ࠥP᮹ᄡ⪵➉▕ᮡFig. 8ᨱᅕᯙᜅ⥥ยᔢᙹᨱݡ⦽ᄡ⪵➉▕ŝ

ᯝ⊹⦽݅. Fig. 10ᮡᙹ⠪ᰍ᪡ʑࣆᇡᰍ᮹ʙᯕእᨱ঑ෙ᳑พʑࣆ

᜽ᜅ▽᮹┥ᖒ᳭Ǖvࠥෝӹ┡ԙäᯕ݅. ᅕvࡽ᳑พʑࣆ᜽ᜅ▽

ᨱᕽᙹ⠪ᰍ᪡ʑࣆᇡᰍʙᯕእ(ŕƁſ/_ŕ_Ɓ)a0.2ʭḡɪĊ⯩᷾a⦹

݅aᯕ⬥ಽ۵ᦶ⇶vࠥ۵᷾a⦹ḡᦫŁᙹಕ⧕a۵äᮥ⪶ᯙ⧁

ᙹ ᯩ݅.

3. vᖒ⧪಍Ǎᖒᨱ᮹⦽Łᮁ⊹⧕ᕾ

ᅙᱩᨱᕽ۵ᦿᕽᗭ}ࡽᙹ⠪ᰍၰᔍᰍಽᅕvࡽ2₉ᬱ⠪໕

᳑พʑࣆ᜽ᜅ▽ᨱݡ⦽vᖒ⧪಍ᮥǍᖒ⦹ŁŁᮁ⊹⧕ᕾʑჶᮝಽ

┥ᖒ᳭Ǖvࠥෝ⪶ᯙ⦹Ł, 2ᰆᨱᕽᗭ}ࡽᜅ⥥ย༉ߙ᮹ḡ႑ႊᱶ

᜾ᮝಽǍ⦽vࠥ᪡እƱ·á☁⦽݅. vᖒ⧪಍ᨱ᮹⦽Łᮁ⊹⧕ᕾႊ

ჶᮡǍ᳑ྜྷᮥ᫵ᗭ᪡ᱩᱱᮝಽӹ٥ᨕb᫵ᗭษ݅᫵ᗭvᖒ⧪಍

(element stiffness matrix, k_n)ෝǍᖒ⦹Ł, ᱥℕǍ᳑ྜྷᨱݡ⦽

vᖒ⧪಍(global stiffness matrix, K)ಽ ᳑⧊⦹ᩍ ⯹ŝ ᄡ᭥᮹

šĥᨱᕽ᳭ǕvࠥෝǍ⦹۵ႊჶᯕ݅. Mode 1᮹┥ᖒ᳭Ǖvࠥอ

ᔑᱶᯕa܆⧩޹ᜅ⥥ย༉ߙŝ۵ݍญ, ᅙ⧕ᕾʑჶᨱᕽ۵Ğĥ᳑

Õᮥ ݅෕í ⦹ᩍ Mode 1ŝ Mode 2᮹ ┥ᖒ᳭Ǖvࠥෝ bb

⠪a⧁ᙹᯩ݅. Fig. 11ŝzᯕᅕvࡽ᳑พʑࣆ᜽ᜅ▽᮹5}᮹

ᱩᱱŝ8}᮹᫵ᗭ, əญŁᯱᮁࠥ۵bᱩᱱᨱ3}ᦊ, ⅾ15}ᯙ

Ǎ᳑ĥಽ ݉ᙽ⪵⦹ᩍ ᖅᱶ⦹ᩡ݅.

ᅙ ᩑǍᨱᕽ ᱢᬊࡽ 2ᱩᱱ ᇡᰍ᮹ ᯱᮁࠥ ⢽ʑෝ Fig. 12ᨱ

ᅕᩡ݅. ᔍᰍᯙ 1, 3, 6, 8ჩ ᜅ✙ౠᇡᰍ۵ 4X4᮹ ✙్ᜅ᫵ᗭ

vᖒ⧪಍, ᙹ⠪ᰍᯙ4, 5ჩᇡᰍ۵6X6᮹⥥౩ᯥ᫵ᗭvᖒ⧪಍ಽ

(7)

(a) Nodes and Members (b) DOF Fig. 11. Simplified Structural System for Matrix Formulation

Fig. 12. DOF for Two-Node Element

Ǎᖒ⦹ᩡ݅. ᦶ⇶᳭Ǖ᮹ݡᔢᯙʑࣆ2, 7ჩᇡᰍ۵⇶ႊ⨆ಆၰ

ʑ⦹እᖁ⩶ᯕ Łಅࡽ 6X6 ⥥౩ᯥ᫵ᗭ vᖒ⧪಍ᯕ Łಅࡹᨩ݅.

bᇡᰍᨱᔍᬊࡽ᫵ᗭᄥvᖒ⧪಍ᮥEqs. (13) ~ (15)ᨱӹ┡ԕᨩ

݅(McGuire ॒). ᯕ్⦽᫵ᗭvᖒ⧪಍ᮡ᳑⧊(assemble)᮹ŝᱶ

ᮥÑℱ13X13᮹ᱥℕǍ᳑ĥvᖒ⧪಍ᯕ᪥ᖒࡽ݅. Łᮁ⊹⧕ᕾᮥ

☖⧕ ᯥĥ⇶⦹ᵲᮥ ᔑᱶ⧁ ভᨱ۵ᔢᬊ ᙹ⦺⥥ಽəఉ Maple᮹

ʑ܆ᮥ ⪽ᬊ⦹ᩡ݅.

ý ćƉ_ƒá ćŕ_Ƒ

ƑƑ

ƙ

Ɯ

ƚ

^Ï ^{¬ à}^¬^Ï ^{à ¬ à¬}^Ï^Ï ^{à ¬}^¬^¬^Ï^Ï^ƛ^Ɲ

ƞ

⁽¹³⁾

ᩍʑᕽ, ¬ á ľ

á ľ

ý ćƉ_ſá ćŕ_Ɓſ

Ɓſ

ƙ

Ɯ

ƚ

^{ſ ƀ à ć}^{Ɓ ć}^Ó¢^ŕ^Ñ¢^Ó¢^Ɓſ^ŕ^Ɓſ^Ɓſ^Ɓſ^Ɓſ^{à ƀ}^{¬ à ſ}^ć^Ó¢^ŕ^Ɓſ^ſ^Ɓſ^{¬ à ć}^{à ƀ}^{à Ɓ}^Ó¢^ŕ^ƀ^Ɓ^Ɓſ^Ɓſ^Ï¢^{à ć}^{à ć}^ć^ć^Ó¢^Ó¢^ŕ^ŕ^Ñ¢^Ó¢^Ó¢^Ɓſ^Ɓſ^ŕ^ŕ^Ɓſ^Ɓſ^Ɓſ^Ɓſ^Ɓſ^Ɓſ^Ɓſ^Ɓſ^¬^¬^ƛ^Ɲ

ƞ

⁽¹⁴⁾

ᩍʑᕽ, ſ á _Ɓſ^Ïâ ćŕ_Ɓſ^Ï ÎÏ¢Ɓſ

¬^Ï

ƀ á

Þ

^Ɓſ^{à ć}^ÎÏ¢^ŕ^Ɓſ^Ï^Ɓſ

ß

^¬

Ɓ á Ɓſ¬^Ïâ ćŕƁſÏ

ÎÏ¢_Ɓſ

^Ï

ý ćƉƁá ćŕ_Ɓ

_Ɓ ƙ

Ɯ

ƚ

^{Ƃ ƃ à ć}^{Ƅ ć}^Ó¢^ŕ^Ñ¢^Ó¢^Ɓ^ŕ^Ɓ^Ɓ^Ɓ^Ɓ^{à ƃ}^{¬ à Ƃ}^ć^Ó¢^ŕ^Ɓ^Ɓ^Ƃ^{¬ à ć}^{à ƃ à ć}^{à Ƅ}^Ó¢^ŕ^ƃ^Ƅ^Ɓ^Ɓ^{à ć}^ć^Ó¢^ć^Ó¢^ŕ^ŕ^Ï¢^Ñ¢^Ó¢^Ó¢^Ɓ^ŕ^ŕ^Ɓ^Ɓ^Ɓ^Ɓ^Ɓ^Ɓ^Ɓ^Ɓ^Ɓ^¬^¬^ƛ^Ɲ

ƞ

à ćŕ©_Ɓ ƙ

Ɯ

ƚ

^{Î ×}^ć^Ò^Ó ^ć^ć^Ïŕ^Î×^ÎÒ^ŕ^{× à Î ×}^Ɓ^Ɓ^Ï ^{× à ćÒ}^{× à ć}^Î ^ćÒ^×^Ó^Î×^ŕ^Ó^Ɓ ^{à ć}^{à ć}^ć^ć^Ïŕ^Î×^ÎÒ^ŕ^×^×^Ð×^ŕ^Î×^Ɓ^ŕ^Ɓ^Ï^Ɓ^Ɓ^Ï^ƛ^Ɲ

ƞ

⁽¹⁵⁾

ᩍʑᕽ, Ƃ á _Ɓ^Ïâ ćŕ_Ɓ^Ï ÎÏ¢Ɓ

¬^Ï

ƃ á

Þ

^Ɓ^{à ć}^ÎÏ¢^ŕ^Ɓ^Ï^Ɓ

ß

^¬

Ƅ á Ɓ¬^Ïâ ćŕƁÏ

ÎÏ¢_Ɓ

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(8)

Fig. 13. Compressive Strength by Matrix Formulation

Fig. 14. Strength Comparison from Equivalent Spring Model and

Stiffness Matrix Method Fig. 15. Buckling Strength from ABAQUS Analyses

Fig. 4ᨱᕽᅕᯙ᳭Ǖ⩶ᔢᨱᕽ, Mode 1ᮥǍ⩥⦹ʑ᭥⦽Ğĥ᳑

Õᮝಽ1, 9, 13, 14ჩᯱᮁࠥෝǍᗮ⦹ᩡŁ, Mode 2ෝǍ⩥⦹ʑ

᭥⦽Ğĥ᳑Õᮝಽ۵1, 7, 13, 14ჩᯱᮁࠥෝᖁ┾⦹ᩍǍᗮ⦹ᩡ݅.

Fig. 13ᮡᔍᰍ݉໕ᱢ᮹Ⓧʑᄡ⪵ᨱ঑ෙMode 1 ၰMode 2ᨱݡ⦽Łᮁ⊹⧕ᕾᨱ᮹⦽ᦶ⇶vࠥෝᅕᩍᵡ݅. ᔍᰍ᮹⇶ႊ⨆

vᖒ, ᷪ݉໕ᱢᯕ᯲ᮥভ۵Mode 1᮹vࠥa᳑พʑࣆ᜽ᜅ▽᮹

vࠥෝḡ႑⦹ḡอᔍᰍ᮹vᖒᯕ⍅ḡ໕Mode 2᮹vࠥaᱥℕǍ

᳑ĥ᮹ vࠥෝ ḡ႑⦹í ࡽ݅.

Fig. 14۵2ᱩᨱᕽᜅ⥥ย༉ߙᨱݡ⦽ḡ႑ႊᱶ᜾᮹⧕ಽࠥ⇽

⦽Mode 1ᨱݡ⦽ᦶ⇶vࠥ᪡᮹እƱෝᅕᩍᵡ݅. ᔍᰍ᮹vᖒᯕ

ᔢݡᱢᮝಽ ᯲ᮥ Ğᬑ ࢱ aḡ ႊჶᨱ ᮹⦽ ⧕۵ ᯹ ᇡ⧊⦹۵

Ğ⨆ᮥᅕᯕḡอᔍᰍ᮹vᖒᯕᯝᱶ⦽sᯕᔢᮝಽ᷾a⦹໕ᕽ

ࢱႊჶᨱ᮹⦽⧕᮹₉ᯕaჭᨕḡʑ᜽᯲⧉ᮥ⪶ᯙ⧁ᙹᯩ݅.

ᔍᰍᨱᱢᬊࡽ✙్ᜅ᫵ᗭ᮹݉໕ᱢᯕ⍅ḡ໕ᕽə⇶ႊ⨆vᖒᯕ

ʑࣆᇡᰍၰᙹ⠪ᰍಽᱢᬊࡽᅕ᫵ᗭ᮹vᖒᨱɝᱲ⦹໕ᕽǍ᳑ĥ

᮹ᄡ⪵aᇩa⦝⦽äᮝಽᅕᯙ݅. ᷪ, ᔍᰍ᮹vᖒᯕ᷾a⦹໕ᕽ

᳑พʑࣆ᜽ᜅ▽ᮡʑᅙᱢᯙʑࣆǍ᳑ĥᯕ௝ʑᅕ݅۵ʑࣆᇡᰍ, ᙹ⠪ᰍ, ᔍᰍಽǍᖒࡽŉ᳑Ǎ᳑ĥಽ⠪aࢁᙹᯩ݅. ᯕ్⦽ŉ᳑Ǎ

᳑ĥ۵ʑᅙᱢᮝಽʑࣆǍ᳑ĥᯙᜅ⥥ย༉ߙǍ᳑ĥᅕ݅۵׳ᮡ

ᦶ⇶vࠥa ᩩᔢࡽ݅Ł ⧁ ᙹ ᯩ݅.

4. ᮁ⦽᫵ᗭჶᨱɝÑ⦽እᖁ⩶/እ┥ᖒ⧕ᕾ

ᅙᱩᨱᕽ۵ᮁ⦽᫵ᗭჶᨱɝÑ⦽እᖁ⩶/እ┥ᖒ⧕ᕾʑჶᮝಽ

ᅕvࡽ ᳑พʑࣆ᜽ᜅ▽᮹ ᦶ⇶vࠥෝ á☁⦽݅. ᅙ ᩑǍᨱᕽ۵

ჵᬊǍ᳑⧕ᕾ➉┅ḡ⥥ಽəఉᯙABAQUS (2004)ෝᯕᬊ⦹ᩡ

݅. ABAQUS۵ᖁ⩶┥ᖒ⧕ᕾʑჶᯙŁᮁ⊹⧕ᕾᨱ᮹⦽᳭Ǖ⦹

ᵲᮥ ᔑᱶ⧁ ᙹ ᯩᮥ ᐱ ᦥܩ௝, Modified Riks Algorithmᨱ

ɝÑ⦹ᩍእᖁ⩶᳭Ǖၰ❭ƕ⧕ᕾᮥእƱᱢᦩᱶࡹíǍ⩥⦽݅.

ᬑᖁ┥ᖒ⧕ᕾᮥ☖⦹ᩍ᳭Ǖvࠥෝ⪶ᯙ⦹Ł, ᦿᕽࢱaḡႊჶᨱ ᕽđᱶࡽ┥ᖒ᳭Ǖvࠥ᪡እƱ·á☁⦽݅. ੱ⦽እ┥ᖒ⧕ᕾᮥ☖⦹

ᩍⅩʑđ⧉ᨱ঑ෙ᳭Ǖvࠥ᮹₉ᯕෝá☁⦽݅. ݉ᙽʑࣆᇡᰍෝ

⬉ᮉᱢᮝಽᅕv⦹ᩍ᳑พʑࣆ᜽ᜅ▽ᮥǍᖒ⦹ᩡᮥভ᮹Ǎ⩥a܆

⦽ᦶ⇶vࠥෝ❭ᦦ⦹Ł⨆ᔢࡽ᳭Ǖvࠥෝᱶపᱢᮝಽ⪶ᯙ⦽݅.

⠪໕ԕǍ᳑ྜྷಽᕽ᳑พʑࣆ᜽ᜅ▽᮹ʑࣆᇡᰍ۵40}᮹ᅕ᫵

ᗭ, ᙹ⠪ᰍ۵20}᮹ᅕ᫵ᗭ, ᔍᰍ۵b1}᮹✙్ᜅ᫵ᗭaᯕᬊࡹ

ᨕᱥℕǍ᳑ĥa༉ߙยࡹᨩ݅. ʑࣆᇡᰍၰᙹ⠪ᰍ᮹᫵ᗭᙹෝ

޵ ۹ᩍࠥ vࠥᔑᱶᨱ۵ ⇵aᱢᯙ ᩢ⨆ᮥ ᵝḡ ᦫ۵݅۵ äᮥ

⧕ᕾᮥ☖⧕⪶ᯙ⦹ᩡ݅. ᅙᰆᨱᕽᔍᬊࡽᙹ⊹ᩩᱽᩎ᜽Table 1᮹ ྜྷᖒ⊹ෝ ᄡ⧉ᨧᯕ ᔍᬊ⦹ᩡᮝ໑ Ğĥ᳑Õᮡ Fig. 11(b)ᨱ

ᅕᯙ ၵ᪡ z݅.

Fig. 15۵ᖁ⩶┥ᖒ⧕ᕾʑჶᯙEigenvalue ⧕ᕾᵲSubspace

ႊჶᮥ ᯕᬊ⦹ᩍ ᔑᱶࡽ äᮝಽ៉ ᔍᰍ݉໕ᱢ ᄡ⪵ᨱ ঑ෙ b

᳭Ǖ༉ऽ᮹ᦶ⇶vࠥ᮹ᄡ⪵ෝӹ┡ԙ݅. ᔍᰍ݉໕ᱢᯕ⍅ḩᙹಾ

(9)

Fig. 16. Strength Comparison from Stiffness Matrix Method and ABAQUS Analyses

Fig. 17. Mode 1 Compressive Strength Comparison

᳑พʑࣆ᜽ᜅ▽᮹┥ᖒ᳭Ǖvࠥa᷾a⦹Ł, ḡ႑᳭Ǖvࠥ۵Mode 1ᨱᕽMode 2ಽၵѱ݅۵äᮥ⪶ᯙ⧁ᙹᯩ݅. ᯕđŝ۵Fig.

13ᨱᅕᯙၵ᪡zᯕvᖒ⧪಍Ǎᖒᮥ☖⧕᨜ᮡᦶ⇶vࠥ᮹Ğᬑ᪡

ᮁᔍ⦽Ğ⨆ᮥᅕᯙ݅. እƱ༊ᱢᮝಽFig. 16ᨱࢱđŝෝᵲℊ⦹ᩍ

݅᜽ ᅕᩡ݅. Mode 1᮹ ᳭Ǖvࠥ۵ ᔍᰍ݉໕ᱢ 30 mm² ᅕ݅

᯲ᮡᩢᩎᨱᕽᇡ⧊⦹۵Ğ⨆ᯕᯩḡอ, Mode 2᮹Ğᬑᨱ۵ᱥ

ᩢᩎᨱÙℱࢱđŝᨱᔢݚ⦽₉ᯕෝᅕᯙ݅. əᯕᮁ۵ABAQUS ಽ ⧕ᕾ⦽ ᔍᰆʑࣆᮡ ᵝʑࣆ᮹ ᫵ᗭa 40}, ᙹ⠪ᰍ᮹ ᫵ᗭ۵

20}ಽ៉᳭Ǖၽᔾ᜽Mode 2᮹⩶ᔢᮥᱢᱩ⯩⢽⩥⧁ᙹᯩḡอ, vᖒ⧪಍ᮥᯕᬊ⦽vࠥᔑᱶ ႊჶᨱᕽ۵ᇡᰍ᮹ᙹaᱽ⦽ࡹᨕ

Mode 2᮹᳭Ǖ⩶ᔢᮥᱽݡಽǍ⩥⦹ʑᨕಅᬕ໕ᯕᯩŁđŝᱢᮝ ಽᝅᱽᅕ݅vᖒᯕ׳ᯕ⠪aࡹᨩ݅Łᅝᙹᯩ݅. ʑࣆᇡᰍၰ

ᙹ⠪ᰍ᮹᫵ᗭᙹෝ∊ᇥ⯩᷾a᜽┉⬥vᖒ⧪಍ᮥᯕᬊ⦹ᩍMode 2᮹┥ᖒ᳭Ǖvࠥෝᔑᱶ⦽݅໕ᅕ݅ᱶ⪶ࠥෝ׳ᯝᙹᯩᮥäᮝಽ

ᩩᔢࡽ݅. ə్ӹ݉8}᮹᫵ᗭಽeఖ⪵᜽┉༉ߙಽᕽࠥᝅᱽಽ

ᱢᬊࢁa܆ᖒᯕ׳ᮡᩢᩎᨱᕽḡ႑vࠥෝᔑᱶ⧁ᙹᯩ݅۵ᔍᝅᮡ

e⠙ᖒ ⊂໕ᨱᕽ ⠪aၼᮥอ⦹݅Ł ᅕᯙ݅.

Fig. 17ᮡ2, 3ᱩᨱᕽđᱶࡽMode 1᮹᳭ǕvࠥෝABAQUS ಽ⧕ᕾ⦽᳭Ǖvࠥ᪡⧉̹ӹ┡ԙäᯕ݅. ᵲe┥ᖒḡḡǍ᳑ĥᯙ

॒aᜅ⥥ย༉ߙŝvᖒ⧪಍Ǎᖒჶᮝಽᔑᱶࡽ᳭ǕvࠥŝእƱ⧕

ᅕ໕ᔢݡᱢᮝಽ᯲ᮡᔍᰍ݉໕ᱢᨱ۵᯹ᇡ⧊⦹Łᯩᮭᮥ⪶ᯙ⧁

ᯩ݅. 30 mm²ᯕᔢ᮹ᔍᰍ݉໕ᱢᩢᩎᨱᕽ۵ABAQUS⧕ᕾᨱ

᮹⦽vࠥ۵ᦿᕽᨙɪࡽࢱaḡႊჶᨱ᮹⦽vࠥᔍᯕᨱᇥ⡍⦹Ł

ᯩ݅. ᔍᰍ᮹݉໕ᱢᯕᯝᱶᙹᵡᯕ⦹ᯝĞᬑ᳭Ǖvࠥ᮹ᔑᱶᨱ

ᯩᨕ ᖙ aḡ ႊჶ ༉ࢱ ᝁ഑⧁ ᙹ ᯩ۵ ᙹᵡᮝಽ ❱݉ࡽ݅.

݅ᮭᮝಽʑ⦹እᖁ⩶ᖒၰᰍഭ᮹⧎ᅖᯕŁಅࡽእ┥ᖒ᷾ᇥ⧕

ᕾ(inleastic incremental analysis)ᮝಽɚ⦽ᦶ⇶vࠥෝᔑᱶ⦹Ł,

┥ᖒ᳭Ǖvࠥ᪡ እƱ⧕ ᅙ݅. ᅕvࡽ ᳑พʑࣆ᜽ᜅ▽᮹ ᫵ᗭ᪡

ᰍഭၰĞĥ᳑Õᮡ┥ᖒ⧕ᕾ᮹ᖅᱶŝz݅. ᔍᰍಽ༉ߙยࡹ۵

✙్ᜅ᫵ᗭᨱ۵⍡ᯕት⃹ౝᦶ⇶ᨱ۵ᱡ⧎⦹ḡ༜⦹Łᯙᰆᨱอ

ᱡ⧎⦹ࠥಾ‘No Compression’ ᪖ᖹᮥᱢᬊ⦹ᩡ݅. እ┥ᖒ⧕ᕾ

ႊჶᮝಽABAQUSᨱᕽᱽŖࡹ۵Riks Analysis ᪖ᖹᮥᱢᬊ⦹Ł

ʑࣆᇡᰍʙᯕ᮹1/1000 sᮥⅩʑđ⧉(initial imperfection)ᮝಽ

ᖅᱶ⦹ᩍ ᙹ⧪⦹ᩡ݅.

Fig. 18ᮡ┥ᖒ⧕ᕾŝእ┥ᖒ⧕ᕾ᮹bModeᨱݡ⦽᳭Ǖvࠥ

ෝᅕᩍᵡ݅. ᳑พʑࣆ᜽ᜅ▽᮹┥ᖒ᳭Ǖvࠥaእ┥ᖒ᳭Ǖvࠥ

ᨱእ⧕݅ᗭ׳ᯕ⠪aࡹᨩᮭᮥ᦭ᙹᯩ݅. əᯕᮁ۵┥ᖒ᳭Ǖvࠥ

۵ᖁ⩶┥ᖒ⧕ᕾႊჶᯙŁᮁ⊹⧕ᕾ᮹đŝಽ៉ᔍᰍaᯙᰆᔢ┽

ᯙḡᦶ⇶ᔢ┽ᯙḡෝǍᇥ⦹ḡᦫŁ༉ࢱvᖒ⧪಍᮹Ǎᖒᨱၹᩢ

ࡽ݅. እ┥ᖒ⧕ᕾᨱᕽ۵ᯙᰆᔢ┽ᨱᯩ۵ᔍᰍอᯕᱡ⧎⦹۵ᔢ┽

ᨱᕽ᳑พʑࣆ᜽ᜅ▽᮹ᦶ⇶vࠥađᱶࡹအಽ4}᮹ᔍᰍvᖒᯕ

༉ࢱ Łಅࡽ ┥ᖒ᳭Ǖvࠥᨱ እ⧕ ԏᮡ vࠥa ࡽ݅.

Fig. 19۵ᔍᰆʑࣆ᮹እ┥ᖒ⧕ᕾᨱᕽⅩʑđ⧉᮹Ⓧʑᨱ঑ෙ

ɚ⦽ᦶ⇶vࠥෝӹ┡ԩ݅. x⇶ᨱӹ┡ԙᄡ᭥۵⇶ႊ⨆⦹ᵲᰍ⦹

ḡᱱᨱᕽ᮹ʑࣆႊ⨆ᄡ᭥ෝ᮹ၙ⦽݅. Ⅹʑđ⧉᮹Ⓧʑᨱ঑௝

ɚ⦽ᦶ⇶vࠥ۵ ၝq⦹í ၹ᮲⦽݅۵ ᔍᝅᮥ ⪶ᯙ⧁ ᙹ ᯩ݅.

᳑พʑࣆ᜽ᜅ▽᮹ᅕv⬉ŝ۵ʑࣆᇡᰍ᮹᳭Ǖ⩶ᔢᯕእݡ⋎

(Mode 2)ᮝಽӹ┡ԁভ᮹ᅕvࡽǍ᳑a↽ᱢ⪵ࡽ݅Ł⧁ᙹ

ᯩ݅. Fig. 18ᮥ⡍⧉⦹ᩍᦿᕽᩍ్aḡႊჶᨱ᮹⦽ᦶ⇶vࠥ

ᔑᱶᮥ☖⧕ᔍᰍ᮹݉໕ᱢ, ᷪᜅ✙ౠvᖒᯕ׳ᮥᙹಾ᜽ᜅ▽᮹

ᦶ⇶vࠥ۵ ḡᗮᱢᮝಽ ⨆ᔢࡽ݅۵ ᔍᝅᮥ ⪶ᯙ⦹ᩡ݅. ə్ӹ

ᔍᰍ᮹vᖒᯕᯝᱶᙹᵡᨱᯕ෕໕əᯕᔢsᮥ⨆ᔢ᜽⍽ࠥ᜽ᜅ▽

᮹ᦶ⇶vࠥ᷾a۵Ñ᮹ᨧÑӹๅᬑ᧞⦽ᙹᵡᯥᮥ᦭ᙹᯩ݅.

⦽ĥ⬉ᬊ⊂໕ᨱᕽᔍᰍ᮹vᖒᮥྕ⦽⯩᷾a᜽┅۵äᮡ᮹ၙa

ᨧᮝအಽᱢᱩ⦽↽ᱢ⪵᮹ŝᱶᯕ⦥᫵⦹݅. ᅙᩑǍᨱᕽ۵Fig.

18ᨱᕽᅕᯙ᳑พʑࣆ᜽ᜅ▽᮹vࠥłᖁᨱᕽḡ႑vࠥaMode 1ᨱᕽMode 2ಽᱥ⪹ࡹ۵ᱱᮥ‘Optimum Point’௝ᱶ᮹⦽݅.

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Fig. 18. Compressive Strengths form Elastic and Inelastic Analyses

Fig. 19. Effect of Initial Imperfection (Elastic Buckling Strength = 207.3 kN)

Fig. 20. Optimum Points for Various Column Lengths

Fig. 21. Expected Compressive Strength vs. Slenderness Ratio

ᯕᱱᮝಽᇡ░ᱶ⧕ḡ۵ᦶ⇶vࠥෝPoptಽӹ┡ԕŁ᪅ᯝ్᳭Ǖv

ࠥ ݡእ ⨆ᔢࢁ ᙹ ᯩ۵ ʑݡᦶ⇶vࠥ(expected compressive strength)ෝ❱݉⦹۵ʑᵡᮝಽ⪽ᬊ⦽݅. ੱ⦽ᯕᱱᮝಽǍ⧕ḡ۵

ᔍᰍ݉໕ᱢᮥAoptಽ⢽⩥⦹ŁPoptෝǍ⩥⦹ʑ᭥⦽⦥᫵vᖒ᮹

ʑᵡᮝಽ⪽ᬊ⦽݅. ᦶ⇶vࠥa⨆ᔢࢁᙹᯩ۵ᱶࠥෝᱶపᱢᮝಽ

᦭ᦥᅕʑ᭥⧕ʑࣆᇡᰍ᮹ʙᯕᄡ⪵᜽┅໕ᕽ‘Optimum Point’ෝ

⠪a⦹ᩡ݅. Fig. 20ᨱ۵bʑࣆᇡᰍ᮹ʙᯕ᪡əᨱ঑ෙᔍᰍ݉໕ ᱢᮥᄡ⪵᜽⍽₟ᦥԙ‘Optimum Point’᮹᭥⊹ෝᅕᩍᵡ݅. ┥ᖒ

⧕ᕾŝእ┥ᖒ⧕ᕾᮝಽࠥ⇽ࡽ‘Optimum Point’ᨱ⧕ݚ⦹۵ʑᵡ vࠥPoptෝʑࣆᇡᰍᖙᰆእᨱ঑௝Fig. 21ᨱӹ┡ԕᨩ݅. እ┥ᖒ

⧕ᕾ᮹ĞᬑⅩʑđ⧉᮹ᙹᵡᮥʑࣆʙᯕ᮹1/1000ŝ1/10000ᮥ

Łಅ⦹ᩍእƱ⦹ᩡ݅. ᅕvࡽ᳑พʑࣆ᜽ᜅ▽ᮡʑᅙᱢᮝಽ݉ᙽ ʑࣆᮥᅕv⦹۵≉ḡᯕအಽʑࣆᇡᰍ᮹⧎ᅖಆʭḡอᱽ᜽⦹ᩡ

݅. ᦿᕽᨙɪ⦹ᩡॐᯕᔍᰍvᖒᯕ⍅Კʑࣆᇡᰍၰᙹ⠪ᰍvᖒᨱ

ɝᱲ⧁ᱶࠥಽᅕvࡹ໕ʑࣆǍ᳑ĥ۵ŉ᳑Ǎ᳑ĥಽ✚ᖒᮥᅕᯕ ໕ᕽ ↽ݡ ᦶ⇶ಆᮡ ʑࣆᇡᰍ ᯱℕ᮹ ⧎ᅖಆᮥ Ⅹŝ⦹í ࡽ݅.

᳑พʑࣆ᜽ᜅ▽᮹ᦶ⇶vࠥPopt۵Ⅹʑđ⧉ᯕ1/1000ᯝভ۵᪅ᯝ

్᳭Ǖvࠥݡእ᧞5~6.3႑, 1/10000ᯝভ۵᧞6.7~7.1႑ᙹᵡᮝ ಽ ӹ┡ԍ݅.

5. đುၰ๛ᮭั

݉ᙽʑࣆᇡᰍ᮹ ᵲe ᭥⊹ᨱ ᙹ⠪ᰍ᪡ ᜅ✙ౠᔍᰍಽ Ǎᖒࡽ

Ǎᗮᰆ⊹ෝᖅ⊹⦹ᩍᅕvࡽ᳑พʑࣆ᜽ᜅ▽ᮡ ᅕvࡹḡᦫᮡ

݉ᙽʑࣆ᮹ Ğᬑᨱ እ⧕ ə ᳭Ǖvࠥෝ ᔢݚᇡᇥ ⨆ᔢ᜽┍ ᙹ

ᯩᮭᮥ⪶ᯙ⦹ᩡ݅. ᅕvࡽ᳑พʑࣆ᜽ᜅ▽᮹ᦶ⇶vࠥෝᱶపᱢ ᮝಽᔑᱶ⦹ʑ᭥⦹ᩍʑࣆᇡᰍĞĥǍᖒ᫵ᗭෝᜅ⥥ยᮝಽ⊹⪹

⦽॒a᮹ᜅ⥥ย༉ߙʑჶ, ᯱᮁࠥෝ↽ᗭ⪵⦹ᩍ݉ᙽ⪵ࡽǍ᳑ĥ

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ᨱݡ⦽vᖒ⧪಍ʑჶ, əญŁჵᬊᮁ⦽᫵ᗭ⧕ᕾ⥥ಽəఉᮥ⪽ᬊ

⦽ ┥ᖒ/እ┥ᖒ ⧕ᕾʑჶᮥ ᱢᬊ⦹ᩡ݅. ᙹ⊹ᩩᱽ ⧕ᕾđŝ ᖙ

aḡ⧕ᕾႊჶ༉ࢱᜅ✙ౠᔍᰍ᮹݉໕ᱢᯕʑࣆᇡᰍၰᙹ⠪ᰍ᮹

݉໕ᱢᅕ݅ᯝᱶᙹᵡᯕ⦹ಽ᯲ᮥĞᬑ┥ᖒ᳭Ǖvࠥᩩ⊂ᯕ᯹

ᇡ⧊⦽݅۵äᮥ⪶ᯙ⦹ᩡ݅. ᪅ᯝ్᳭Ǖvࠥ᪡እƱ⦹ᩡᮥভ, ᅕvࡽ᳑พʑࣆ᜽ᜅ▽ᮡᅕvࡹḡᦫᮡ݉ᙽʑࣆᨱእ⦹ᩍ7႑ʭ ḡ᳭Ǖvࠥa⨆ᔢࢁᙹᯩᮭᮥੱ⦽⪶ᯙ⦹ᩡ݅. ᅙᩑǍᨱᕽ۵

ᅕvݡᔢᯕࡹ۵݉ᙽʑࣆ᮹ᱽᬱᯕđᱶࡹ໕᳑พʑࣆ᜽ᜅ▽Ǎ ᖒᮥ☖⧕⨆ᔢࢁᙹᯩ۵ᦶ⇶vࠥ᮹ʑᵡᮝಽʑݡᦶ⇶vࠥෝ

ᱽ᜽⦹ᩡ݅. ʑݡᦶ⇶vࠥ۵Ⅹʑđ⧉ᯕ1/1000ᯝভ۵᪅ᯝ్

᳭Ǖvࠥݡእ᧞5~6.3႑, 1/10000ᯝভ۵᧞6.7~7.1႑ᙹᵡᮝಽ

ӹ┡ԍ݅.

ᅙᱽᦩ᜽ᜅ▽ᮡᖙᰆእaⓑ݉ᙽʑࣆᇡᰍෝݡᔢᮝಽᦶ⇶v

ࠥ⨆ᔢᮥ༊ᱢᮝಽ⦹ŁᯩᮝအಽᩢǍ᜽ᖅ᮹ᇡᰍᅕ݅۵Õᖅ⩥

ᰆ॒ᨱᕽᯥ᜽Ǎ᳑ྜྷ॒ᮥᅕ᪥⦹۵໕ᨱᕽ⪽ᬊᖒᯕᩩᔢࡽ݅.

እ┥ᖒ⧕ᕾᮝಽᅕᯙၵ᪡zᯕᅙ᳑พʑࣆ᜽ᜅ▽ᮡⅩʑđ⧉ᨱ

᮹⦽vࠥqᗭaᩩᔢࡹအಽ⩥ᰆᱢᬊ᜽ᨱ۵ᨥĊ⦽᜽Ŗšญa

᫵Ǎࡽ݅.

qᔍ᮹ɡ

ᯕםྙᮡ2012֥ࠥℎᵝݡ⦺ƱᩑǍᰆ⦺ḡᬱᨱ᮹⦽ä᯦ܩ݅.

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