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Analysis of the Internal Forces of the Rail Supports for the Serviceability of Concrete Slab Track Bridge

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(1)

Received October 18 2012, Revised January 30 2013, Accepted May 31 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)

 ǣŠ––’ǣȀȀ†šǤ†‘‹Ǥ‘”‰ȀͳͲǤͳʹ͸ͷʹȀ•…‡ǤʹͲͳ͵Ǥ͵͵ǤͶǤͳ͵Ͳ͵ ™™™Ǥ•…‡Œ‘—”ƒŽǤ‘”Ǥ”

㔖㘪Ὢ㡶#⡪ᵖ⏊#።ᦂ#ጎᶇⴖ#♪Ⱨ⛯#ሾ㝞Ἲ#Ⳃ㬚#᷆ⴺ#⽾⽾ⷎ⮎⛚ⴖ#

ⵏⱧᷣ#㬲⛛

ౖஜ෭

Choi, Jun-Hyeok*

Analysis of the Internal Forces of the Rail Supports for the Serviceability of Concrete Slab Track Bridge

ABSTRACT

In this study, the reference values for the internal forces of the rail supports caused by a wheel load, a unit vertical displacement, a unit end rotation in examination of the serviceability of concrete slab track bridge were obtained. In analysis, the analysis models of which the rail was continuously and discretely supported by elastic springs were used. The internal forces of the rail supports from the analysis were compared with the results provided in the DS 804 regulations and agreed with well. In addition, the effects of the space between the rail supports and the stiffness of fastener on the internal forces of the rail supports were investigated.

Key words : Concrete slab track, Serviceability, Continuous support model, Discrete support model, Compressive force, Uplifting force

Ⅹಾ

ᅙᩑǍᨱᕽ۵⎹Ⓧญ✙ᜍ௹ቭȅࠥෝaḡ۵Ʊప᮹ᔍᬊᖒá☁ᨱᯩᨕ݉᭥⇶⦹ᵲ, ݉᭥ᙹḢ݉₉, ݉᭥⫭ᱥᨱ᮹⧕ၽᔾࡹ۵౩ᯝḡḡᱱ ᮹᯲ᬊಆᨱݡ⦽ʑᵡsᮥǍ⦹ᩡ݅. ⧕ᕾႊჶᨱᯩᨕᕽ۵౩ᯝᯕ┥ᖒᜅ⥥ยᨱ᮹⧕ᩑᗮᱢᮝಽḡḡࡹ۵༉ߙŝᯕᔑᱢᮝಽḡḡࡹ۵༉ߙ ᯕᯕᬊࡹᨩ݅. ⧕ᕾđŝ᨜ᨕḥ౩ᯝḡḡᱱᨱᕽ᮹᯲ᬊಆᮡ⎹Ⓧญ✙ȅࠥ᮹ᔍᬊᖒá☁ᨱᕽₙ᳑ࡹŁᯩ۵DS 804 ʑᵡᨱᱽ᜽ࡽsŝእ Ʊࡹᩡᮝ໑, əđŝ۵᯹ᯝ⊹⦹ᩡ݅. ੱ⦽, ౩ᯝḡḡᱱ᮹eĊŝℕđᰆ⊹᮹vᖒᯕ౩ᯝḡḡᱱᨱᕽ᮹᯲ᬊಆᨱၙ⊹۵ᩢ⨆ᮥᇥᕾ⦹ᩡ݅.

áᔪᨕ ⎹Ⓧญ✙ᜍ௹ቭȅࠥ, ᔍᬊᖒ, ᩑᗮḡḡ༉ߙ, ᯕᔑḡḡ༉ߙ, ᦶ⇶ಆ, ᇡᔢಆ

1. ᕽು

⎹Ⓧญ✙ ȅࠥ۵ ᯱiࠥᔢ ȅࠥ᪡ እƱ⦹ᩍ vᖒᯕ ⓍŁ ȅࠥ᮹ ᄡ⩶ᯕ ᯲ᮝ໑, ᮁḡšญ ᯲ᨦᯕ qᗭࡹŁ ᩕ₉ᬕ⧪᮹ ᦩᱥᖒŝ

Łᗮ⪵ ⊂໕ᨱᕽ ᮁญ⦹݅۵ ᰆᱱॅಽ ᯙ⦹ᩍ ↽ɝ Õᖅࡹ۵ ݡᇡᇥ᮹ ℁ࠥיᖁᨱᕽ ᱢᬊࡹŁ ᯩ݅.

ȅࠥෝḡḡ⦹۵יၹᵲƱపᨱ۵☁Ŗᯕӹ░ձŝ۵ݍญᩕ₉᮹ᵝ⧪, ᪉ࠥ᮹ᄡ⪵, ḡၹ᳑Õ᮹₉ᯕ॒ᨱ঑ෙᱶ, ࠺ᱢ⦹ᵲᯕ

᯲ᬊ⦹໑, əಽᯙ⦽Ʊపŝȅࠥᨱᕽ᮹ᄡ᭥ၰᄡ⩶ᯕၽᔾࡽ݅. ✚⯩, ƱపǍe᮹Ʊbᇡ᪡Ʊݡᇡ᮹ḡḡᇡĞĥ໕ᨱᕽ۵ḡḡᇡ᮹

vᖒ᮹ ₉ᯕಽ ᯙ⧕ ᩕ₉᮹ ᵝ⧪ᦩᱥᖒ, ᜚₉q, ᮁḡᅕᙹ᪡ šಉࡽ ȅࠥ᮹ ᔍᬊᖒᯕ Ⓧí ԏᦥḩ ᙹ ᯩ݅.

⎹Ⓧญ✙ȅࠥ᮹Ğᬑᯱiȅࠥ᪡۵ݍญᔍᬊᖒ⪶ᅕෝ᭥⦽ᱽ⦽Ƚᱶॅᯕ໦⪶⦹ḡᦫᦹᮝӹ, ↽ɝᨱ۵ƱపᔢᇡǍ᳑ၰȅࠥ᮹

–”—…–—”ƒŽ‰‹‡‡”‹‰ ĵܓėॡ

(2)

Table 1. Static and Dynamic Actions on a Superstructure of Bridge

Type Static Actions Dynamic Actions

Axial load - Direct acting force due to axial load

Vertical gap Pier rotation due to the temperature difference between rail and bridge

Pier rotation due to the temperature difference between front and rear sides of a pierPier rotation due to starting and breaking loads

Vertical deformation due to axial load End rotation

Dead loads, creep and shrinkage

Temperature difference between top and bottom surfaces of a superstructure

Settlement of footing Train axial load

ᄡ᭥ᨱ঑ෙȅࠥǍ᳑᮹ʑ܆ᮁḡ᪡ᩕ₉ᵝ⧪ᦩᱥᖒ⪶ᅕෝ᭥⧕ᕽ

౩ᯝḡḡᱱᨱᕽ᮹ᦶ⇶ಆ(compressive force) ၰᇡᔢಆ(uplifting force)ᨱݡ⦽ᔍᬊᖒá☁ႊჶၰʑᵡᮥࠦᯝ᮹ₙŁʑᵡᯙDS 804 (2000)ෝᵡᬊ⦹ᩍᱢᬊ⦹Łᯩ݅(⦽ǎ℁ࠥ᜽ᖅŖ݉, 2008).

ǎԕᨱᕽ۵⎹Ⓧญ✙ȅࠥ᮹ᔍᬊᖒá☁ෝ᭥⦽ʑⅩᩑǍಽᕽ

DS 804 ʑᵡᨱᱽ᜽ࡽȅࠥ᮹ᔍᬊᖒᩢ⨆ᯙᯱᨱݡ⦽ᩑǍ᪡

݅᧲⦽᳑Õᨱݡ⦽ᔍᬊᖒá☁⊂໕ᨱᕽ᮹Ʊప᮹Ñ࠺ᨱݡ⦽

ᩑǍđŝॅᯕᅕŁࡹᨩ݅(ၶ⪮ʑ, 2009; ၶ⪮ʑ᫙, 2009; ᖒ޶ൂ

᫙, 2008).

DS 804 ʑᵡᨱ᮹⦽ᔍᬊᖒá☁۵݅᧲⦽⦹ᵲ᳑Õᨱ᮹⧕

ၽᔾࡹ۵ƱపᔢᇡǍ᳑᮹ᄡ᭥ෝ݉₉᪡⫭ᱥᮝಽǍᇥ⦹Ł, əಽ ᯙ⦽ ౩ᯝ ḡḡᱱ ၰ ౩ᯝᨱᕽ᮹ ᯲ᬊಆᯕ ᔍᬊ⦽ĥ ჵ᭥ԕᨱ

ᯩࠥಾ ⦹۵ äᯕ݅. ᯕ ŝᱶᨱᕽ ౩ᯝ ḡḡᱱᨱᕽ᮹ ᯲ᬊಆᮡ

ჵᬊ Ǎ᳑⧕ᕾ ⥥ಽəఉ ੱ۵ ✚ᱶ ⧕ᕾ ⥥ಽəఉᮥ ᯕᬊ⦹ᩍ

ᙹ⧪ࡹŁᯩ݅. ə్ӹə్⦽⧕ᕾ⥥ಽəఉᮥᔍᬊ⦹Ñӹ݅᧲⦽

᳑Õᮥ༉ߙย⦹ᩍๅჩ⧕ᕾᮥᙹ⧪⦽݅۵äᮡๅᬑᅖᰂ⦹Ł

ჩÑಽᬕᯝᯕ໑, ᝅྕᯱॅᨱí۵ᯕ్⦽ŝᱶᮥᯕ⧕⦹Łᙹ⧪⦹

ʑ௡ ๅᬑ ᨕಅᬕ ᝅᱶᯕ݅.

঑௝ᕽ, ᅙᩑǍ۵⎹Ⓧญ✙ȅࠥaᇡᖅࡽƱప᮹ᔍᬊᖒᖅĥʑ ჶ ᱽ᜽ෝ ᭥⦽ ʑⅩ ᩑǍಽᕽ ᖅĥ᜽ ᱢᬊࡹŁ ᯩ۵ DS 804 ʑᵡ᮹ᱽ᜽sᮥ݅ෙ⧕ᕾႊჶᮥᯕᬊ⦹ᩍ⧕ᕾ⦹Łəđŝෝ  እƱ, á᷾⦹ᩡ݅. ⧕ᕾႊჶᮡȅࠥᩎ⦺ᨱᕽ᯹᦭ಅḥ┥ᖒḡḡࡽ

ᩑᗮᅕ༉ߙᮥᱢᬊ⦹ᩡᮝ໑, ᯕᔑḡḡᅕ༉ߙᨱᕽ۵5ᩑ༉ູ✙

ႊᱶ᜾ᮥᱢᬊ⦹ᩡ݅. ⧕ᕾᮡ݉᭥⇶⦹ᵲ, ݉᭥ᙹḢ݉₉, ݉᭥

⫭ᱥᨱ᮹⧕ၽᔾࡹ۵౩ᯝḡḡᱱ᮹᯲ᬊಆᮥǍ⦹ᩡᮝ໑, ౩ᯝḡ ḡᱱ᮹eĊŝℕđᰆ⊹᮹ vᖒᯕ౩ᯝḡḡᱱᨱᕽ᮹᯲ᬊಆᨱ

ၙ⊹۵ᩢ⨆ᮥӹ┡ԕᨩ݅. ⇵⬥ᩑǍᨱᕽ۵⎹Ⓧญ✙ȅࠥƱప᮹

ᔍᬊᖒᨱᩢ⨆ᮥၙ⊹۵ᄡᙹ᪡⦹ᵲ᳑Õᨱ঑ෙᔍᬊᖒ⊂໕ᨱᕽ ᮹ Ʊప ၰ ȅࠥ᮹ Ñ࠺ᨱ ݡ⧕ ᱽ᜽ࢁ ĥ⫮ᯕ݅.

2. ⎹Ⓧญ✙ȅࠥ᮹ᔍᬊᖒ

⎹Ⓧญ✙ȅࠥaᇡᖅࡽƱప᮹ȅࠥၰℕđᰆ⊹ᨱၽᔾࡹ۵

᯲ᬊಆᮡḡḡᇡ᮹vᖒ₉ᯕaⓍŁƱపᔢᇡǍ᳑᪡ȅࠥe᮹

ᔢݡᄡ᭥aⓍíၽᔾࡹ۵☁ŖⴇƱపᱲᗮᇡ, ݅ෙĞe᮹ᔢᇡ

Ǎ᳑aᱲᗮࡹ۵ƱbᇡᨱᕽaᰆⓍíӹ┡ӽ݅. ⎹Ⓧญ✙ȅࠥ

Ʊప᮹ᔍᬊᖒᖅĥ۵ᩍ్aḡᱶ, ࠺ᱢ⦹ᵲᨱ᮹⧕ၽᔾࡹ۵

ƱపᔢᇡǍ᳑ၰȅࠥ᮹ᄡ⩶ੱ۵ᄡ᭥ಽᯙ⦽౩ᯝၰℕđᰆ⊹ᨱ ᕽ᮹᯲ᬊಆᯕ✚ᱶ⦽⨩ᬊ⦽ĥෝչḡᦫࠥಾ⦹۵äᯕ݅. ᩍʑ ᕽ, Ʊప᮹ᔢᇡǍ᳑᮹ᄡ⩶ᮥᯝᮝ┅۵ᵝ᫵⦹ᵲᮡTable 1ᨱ

ӹ┡ԙ ᱶ, ࠺ᱢ⦹ᵲᯕ໑, Ʊప᮹ ᔢᇡǍ᳑᪡ ȅࠥᨱ ၽᔾࡹ۵

ᄡ⩶ၰᄡ᭥᮹ၽᔾ᫵ᯙᮡ౩ᯝᨱḢᱲ᯲ᬊ⦹۵ᩕ₉᮹⇶⦹ᵲŝ

ƱపᔢᇡǍ᳑ḡᱱe᮹ᙹḢ݉₉ၰƱపᔢᇡǍ᳑᮹⫭ᱥᄡ᭥ಽ

Ǎᇥ⦽݅. ੱ⦽, ౩ᯝၰℕđᰆ⊹ᨱၽᔾࡹ۵᯲ᬊಆᮡℕđᰆ⊹᮹

ℕđಆၰ┥ᖒ➉ऽ᮹⨩ᬊᄡ᭥, ౩ᯝᦶ⇶ಆᨱݡ⦽⨩ᬊ⦽ĥ

ᯕ⦹ᩍ᧝ ⦽݅.

ᔍᬊᖒá☁ŝᱶᨱᕽƱపŝȅࠥǍ᳑᮹ʑ⦹⦺ᱢ᳑Õ, ᱶᱢ

ၰ࠺ᱢ⦹ᵲ, ౩ᯝၰℕđᰆ⊹᮹vᖒᮡᖅĥ݉ĥᨱᕽᯕၙđᱶࡹ

ᨕᯩᮝအಽ, ƱపᔢᇡǍ᳑ၰȅࠥ᮹݉᭥⇶⦹ᵲ, ݉᭥ᙹḢ݉₉,

݉᭥⫭ᱥᄡ᭥ᨱ᮹⦽ᄡ᭥ੱ۵᯲ᬊಆᮥǍ⦹໕Eqs. (1)ⴇ(4)᮹

ӹ┡ԙၵ᪡zᯕ᯲ᬊ⦹ᵲ᮹ᱢᱩ⦽᳑⧊ᮝಽℕđᰆ⊹ᨱၽᔾ⦹

۵ ᦶ⇶ಆŝ ᇡᔢಆᮥ ĥᔑ⧁ ᙹ ᯩ݅.

ŸƓá ŋƂìƑƒſƒŸƓŋÞƁƑì ſì ſÎß â ŋƂìƂƗƌŸƓŋÞƁƂì ſì ſÎß (1) âĺƂìƑƒſƒŸƓ ĺÞƁƑì ſì ſÎß â ĺƂìƂƗƌŸƓĺÞƁƂì ſì ſÎß

â ćÎ××

ªƂ

ŸƓƎÞƁƂì ſß

ŸƁá ŋƂìƂƗƌŸƁŋÞƁƂì ſì ſÎß â ĺƂìƂƗƌŸƁĺÞƁƂì ſì ſÎß â ćÎ××

ªƂ

ŸƁƎÞƁƂì ſß

(2)

ŋƂìƑƒſƒá

ā

şŋƑƒſƒ, ŋƂìƂƗƌá

ā

şŋƂƗƌ (3)

ĺƂìƑƒſƒá

ā

şĺƑƒſƒ, ĺƂìƂƗƌá

ā

şĺƂƗƌ (4)

ᩍʑᕽ, ŋƂìƑƒſƒ, ŋƂìƂƗƌ : ᱶ, ࠺ᱢ⦹ᵲᨱ᮹⦽݉᭥⫭ᱥᄡ᭥

᮹ ⧊(•)

(3)

j–•Š™Œ›ŒGš“ˆ‰

mˆš›Œ•Œ™

yˆ“

(a) TrackSubgrade System

l“ˆš›ŠGz—™•Ž

yˆ“

(b) Analysis Model

Fig. 1. Continuous Support Model of TrackSubgrade System

yˆ“ x

’

  Ÿ

Fig. 2. Model for a Vertical Wheel Load Application

ĺƂìƑƒſƒ, ĺƂìƂƗƌ : ᱶ, ࠺ᱢ⦹ᵲᨱ᮹⦽݉᭥ᙹḢ݉₉

᮹ ⧊(ƋƋ) ş : ᇡᇥᦩᱥĥᙹ

ªƂ : ᩕ₉⇶⦹ᵲᨱ᮹⦽౩ᯝḡḡᱱᨱ ᕽ᮹ ᯲ᬊ⦹ᵲ(Ɖ§)

ŸƓŋ, ŸƓ ĺ, ŸƓ Ǝ: ݉᭥⫭ᱥᄡ᭥(1•),݉᭥ᙹḢ݉

₉(1ƋƋ), ݉᭥ ⇶⦹ᵲ(100Ɖ§) ᨱ᮹⦽౩ᯝḡḡᱱᨱᕽ᮹ᇡᔢಆ (Ɖ§)

ŸƁŋ, ŸƁĺ, ŸƁƎ : ݉᭥⫭ᱥᄡ᭥(1•),݉᭥ᙹḢ݉

₉(1ƋƋ), ݉᭥ ⇶⦹ᵲ(100Ɖ§) ᨱ᮹⦽౩ᯝḡḡᱱᨱᕽ᮹ᦶ⇶ಆ (Ɖ§)

ƁƑ, ƁƂ : ℕđǍ᮹ ᱶᱢ ၰ ࠺ᱢvᖒ

(Ɖ§îƋƋ)

ſ, ſÎ : ౩ᯝ ḡḡᱱe᮹ eĊ(ƋƋ)

3. Ǎ᳑⧕ᕾ

⎹Ⓧญ✙ȅࠥaᇡᖅࡽƱప᮹⧕ᕾ༉ߙยᨱᯩᨕŁಅࡹᨕ

᧝⧁Ǎ᳑᫵ᗭ۵Ʊప᮹ၼ⋉, Ñ޵, ᔢᇡᜍ௹ቭ, ℕđᰆ⊹, ౩ᯝ ᯕ݅. ⧕ᕾ᮹݉ᙽ⪵ෝ᭥⧕ᕽƱప᮹Ñ޵᪡ᔢᇡᜍ௹ቭ۵⦹ᵲ

ᮥḢᱲၼ۵౩ᯝᨱእ⦹ᩍᔢݡᱢᮝಽvᖒᯕๅᬑⓍŁǎᇡᱢ ᯙᄡ⩶ᯕӹ⃹ḱᯕᦥᵝ᯲ᮝအಽȅࠥǍ᳑ෝḡḡ⦹۵ḡᱱᮝಽ

aᱶ⦽݅. ƱపḡeᯕʕĞᬑᔢᇡǍ᳑᮹⃹ḱᨱ᮹⧕ȅࠥᨱࠥ

ᄡ᭥ෝၽᔾ᜽┅ḡอ, ᔍᬊᖒá☁ǍeᯕƱపḡᱱᇡᇡɝᯕအ ಽᔢᇡǍ᳑ᯱℕ᮹ᄡ⩶ᨱ᮹⦽ᩢ⨆ᮡᨧ۵äᮝಽaᱶ⦽݅.

ℕđǍ۵✚ᱶ⦽⦹ᵲᯕᔢᨱᕽℕđǍ᮹ʑ܆ᮥᔢᝅ⦹íࡹအಽ

┥ᗭᖒÑ࠺ᮥӹ┡ԕӹℕđǍ᮹ᔍᬊ⦽ĥෝᦶ⇶ಆᨱᕽ۵౩ᯝ

➉ऽ᮹ᄡ⩶, ᯙᰆᨱݡ⧕ᕽ۵ၙญᦶ⇶ࡽ⦹ᵲᯕᔢᝅࡹʑᱥʭ ḡಽ ᱶ᮹⦹အಽ ℕđǍ᮹Ñ࠺ᮡ ┥ᖒჵ᭥ԕᨱᯩ۵äᮝಽ

aᱶ⦽݅.

ᯕ్⦽aᱶᨱʑⅩ⦹ᩍ⧕ᕾ༉ߙยᮡƱపᔢᇡǍ᳑۵Ğĥ໕, ℕđᰆ⊹۵┥ᖒᜅ⥥ย᫵ᗭ, ౩ᯝᮡᩑᗮࡽᅕ᫵ᗭಽ⦹ᩍ, čŁ⦽

Ğĥ໕ᨱ┥ᖒᜅ⥥ยᮝಽḡḡࡽᩑᗮᅕಽ༉ߙย⦹ᩡ݅. ℕđᰆ⊹

ෝӹ┡ԕ۵ᜅ⥥ย᫵ᗭ۵ᩑᗮᱢᮝಽᇥ⡍ḡḡࡽ༉ߙ(Continuous Support Model, CSM)ŝ ℕđᰆ⊹᮹ ᭥⊹ᨱ ḡḡࡽ ᯕᔑḡḡ

༉ߙ(Discrete Support Model, DSM)ಽ Ǎᇥ⦹ᩡ݅.

⧕ᕾ᜽ȅࠥ᮹݉໕✚ᖒ⊹۵UIC 60 ౩ᯝ⦽}ᨱݡ⦽݉໕ᱢ

š á ÔíÓÕÓ Z Î×ÐƋƋÏ,݉໕2₉༉ູ✙¢ á Ðí×ÒÒ Z Î×ÔƋƋÑ, ౩ᯝ᮹ ┥ᖒĥᙹ۵ž á ÏÎ× ©ſᮥ ᱢᬊ⦹ᩡ݅.

3.1 ઴ু஺஺࣪ࡦ܄

┥ᖒḡḡᩑᗮᅕ༉ߙᮡ౩ᯝ᮹᮲ಆĥᔑ᜽ᯝၹᱢᮝಽᔍᬊࡹ

۵⧕ᕾ༉ߙᯕ݅. ʙᯕaݡ݉⯩ʕ౩ᯝⴇ⋉༊ᅕᨱᕽℕđᰆ⊹᮹

eĊᮡᔢݡᱢᮝಽṈᮝအಽ౩ᯝᮡFigure 1ᨱӹ┡ԙၵ᪡zᯕ

ℕđᰆ⊹ᨱ ᮹⧕ ᩑᗮᱢᮝಽ ḡḡࡽ äᮝಽ aᱶࡽ݅.

3.1.1 ۚ଍ౠ෇ண

౩ᯝḡḡᱱᨱၽᔾࡹ۵᯲ᬊಆᮥĥᔑ⦹ʑ᭥⧕ྙ⨭ᯱഭ(Kerr, 2009)ෝ ₙŁ⦹໕, Figure 2᪡ zᯕ ᩑᗮḡḡࡽ ᅕᨱ Ḳᵲ⦹ᵲ

ªa᯲ᬊ⧁ভ౩ᯝᨱၽᔾࡹ۵ᄡ᭥۵Eq. (5)᪡zᯕᵝᨕḥ݅.

ƗÞƖß á ćÏÎ

ªćƉĸƃàĸƖފ–šĸƖ ⚐•ĸƖß (5)

ᩍʑᕽ,ĸ۵

ö

Ñ ććў¢Ɖ ,Ɖ۵ℕđᰆ⊹᮹vᖒ(ƉƑ)ᮥḡḡᱱeĊ ᮝಽӹ٩݉᭥ʙᯕݚḡḡᱱvᖒ, Ɩ۵⦹ᵲᰍ⦹ᱱᮝ ಽ ᇡ░᮹ Ñญᯕ݅.

౩ᯝᨱᕽ ၽᔾࡹ۵ ᯲ᬊಆ©Ɛᮡ ᩑᗮᱢᮝಽ ᇥ⡍ࡽ ၹಆᨱ

॒eĊᮝಽ႑⊹ࡽ౩ᯝḡḡᱱe᮹ÑญſෝŒ⦽äŝzᮝအಽ

Eq. (6)ᮝಽ ĥᔑࡽ݅.

©Ɛá ſ_ Əá ſ _ Ɖ_ Ɨ

á ćÏÎ ſ ĸª ƃàĸƖފ–šĸƖ⠚• ĸƖß

(6)

(4)

Fig. 3. Vertical Reaction Forces of the Rail Supports by a Wheel Load (Î××Ɖ§) in CSM

Table 2. Maximum Internal Forces of the Rail Supports by a Wheel Load(Î××Ɖ§) in CSM

Stiffness Maximum Compressive Force(kN) Maximum Uplifting Force(kN)

ƉƑ (kN/mm) ſ á ÓÒ×ƋƋ ſ á Ó××ƋƋ ſ á ÒÒ×ƋƋ ſ á ÓÒ×ƋƋ ſ á Ó××ƋƋ ſ á ÒÒ×ƋƋ

20 -34.01 -32.03 -30.00 1.47 1.38 1.30

25 -35.96 -33.86 -31.73 1.55 1.46 1.37

30 -37.64 -35.44 -33.20 1.63 1.53 1.43

35 -39.12 -36.84 -34.51 1.69 1.59 1.49

40 -40.44 -38.09 -35.68 1.75 1.65 1.54

45 -41.65 -39.23 -36.75 1.80 1.69 1.59

50 -42.76 -40.27 -37.73 1.85 1.74 1.63

55 -43.79 -41.24 -38.64 1.89 1.78 1.67

60 -44.76 -42.15 -39.49 1.93 1.82 1.71

౩ᯝḡḡᱱᨱ᯲ᬊ⦹۵↽ݡᦶ⇶ಆ©Ɛ씈Ÿᮡ⦹ᵲᯕᰍ⦹ࡹ۵

Ɩ á ×ᯙ᭥⊹ᨱᕽၽᔾ⦹໑, ᯕෝEq. (6)ᨱݡ᯦⦹໕Eq. (7)ᮥ

᨜۵݅.

©Ɛ씈Ÿá ćÏÎſĸª (7)

Figure 3ᮡEq. (6)ᮥᯕᬊ⦹ᩍ⇶⦹ᵲª á Î××Ɖ§ᯕ᯲ᬊ⧁

ভÑญᨱ঑ෙ౩ᯝᨱᕽၽᔾࡹ۵᯲ᬊಆᮥӹ┡ԙäᮝಽ౩ᯝᨱ ᕽ᮹ᦶ⇶ಆᮡ⦹ᵲᯕᰍ⦹ࡹ۵᭥⊹ᨱᕽaᰆⓑᦶ⇶ಆᯕၽᔾ⦹

Ł⦹ᵲ᯲ᬊᱱᨱᕽᨕ۱ᱶࠥਉᨕḥ᭥⊹ᨱ↽ݡᇡᔢಆᯕӹ┡ԉ

ᮥ ᦭ ᙹ ᯩ݅.

౩ᯝḡḡᱱᨱ᯲ᬊ⦹۵↽ݡᇡᔢಆᮡ౩ᯝᨱၽᔾ⦹۵᯲ᬊಆ ᮹ ࠥ⧉ᙹa 0 ᯕ ࡹ۵ ḡᱱ᮹ sᯕအಽ Eq. (6)ŝ Eq. (8)ᮥ

ᯕᬊ⦹ᩍ ĥᔑࢁ ᙹ ᯩ݅.

ćƂƖ

Ƃ©ƐÞƖß

á × (8)

Eq. (8)ಽᇡ░↽ݡᇡᔢಆᯕၽᔾ⦹۵᭥⊹۵Eq. (9)ಽĥᔑࡹ

໑, ᯕෝEq. (6)ᨱݡ᯦⦹໕, ↽ݡᇡᔢಆᮡEq. (10)ᨱӹ┡ӽ

ၵ᪡ zᯕ ↽ݡ ᦶ⇶ಆ᮹ 4.32%a ࢉᮥ ᦭ ᙹ ᯩ݅.

Ɩ á ćĸņ (9)

©Ɠì ”ˆŸá à ćϪ ſĸƃàņá à ×í×ÑÐÏ©Ɛ씈Ÿ (10)

ੱ⦽, ᇡᔢಆᯕၽᔾ⦹۵Ǎeᮡ౩ᯝᨱᕽၽᔾࡹ۵᯲ᬊಆᯕ

0ᯕࡹ۵ჵ᭥᮹sᯕအಽEq. (6)ᮝಽᇡ░Eq. (11)ᯕǍ⧕ḥ݅.

౩ᯝᨱᕽᇡᔢಆᯕၽᔾ⦹۵ℌჩṙǍeᮡEq.(12)᪡zᮝ໑, ౩ᯝḡḡᱱe᮹Ñญಽӹ٥໕ᇡᔢಆᯕ ᯲ᬊ⦹۵ℕđᰆ⊹᮹

᭥⊹ෝ ᦭ ᙹ ᯩ݅.

ⴅƖ á ćĸÎ

Þ

Ƈņ à ćÑņ

ß

ÞƇ á ÎìÏìÐìzß (11) ⴅ ᇡᔢಆ ၽᔾ Ǎe : ƖÎg ƖÏá ćÑĸÐņ

g ćÑĸÔņ (12)

Table 2۵݉᭥⇶⦹ᵲÎ××Ɖ§a᯲ᬊ⧁ভ౩ᯝᨱᕽ᮹ၽᔾࡹ

۵↽ݡᦶ⇶ಆŝ↽ݡᇡᔢಆᮥℕđᰆ⊹᮹vᖒ(ƉƑ)ŝḡḡᱱe ᮹Ñญ(ſ)ᨱݡ⧕ӹ┡ԙđŝᯕ݅. ↽ݡᦶ⇶ಆŝ↽ݡᇡᔢಆᮡ

ℕđᰆ⊹᮹vᖒᯕ⍅ḩᙹಾ, əญŁ౩ᯝḡḡᱱe᮹Ñญa⍅ḩ ᙹಾ ⍅ḥ݅.

3.1.2 ۚ଍৤஻ۚఙ

݉᭥ᙹḢ݉₉ಽᯙ⦽౩ᯝḡḡᱱ᮹ၹಆᮥĥᔑ⦹ʑ᭥⧕

ᙹḢ⦹ᵲᮥၼ۵ᩑᗮḡḡᅕᨱݡ⦽⧕ᕾᯕುᮥᯕᬊ⦽݅. ᩑᗮḡ

(5)

X

xd’ UUU

Y Z [ \ ]

UUU XN UUU

YN [N ZN ]N \N UUU UUU

yˆ“

’

X

Fig. 4. Model for the Vertical Displacement between the Rail Supports

Fig. 5. Vertical Reaction Forces of the Rail Supports by the Vertical Displacement(ÎƋƋ) in CSM

Table 3. Maximum Internal Forces of the Rail Supports by the Vertical Displacement(ÎƋƋ) in CSM

Stiffness Maximum Compressive Force(kN) Maximum Uplifting Force(kN)

ƉƑ (kN/mm) ſ á ÓÒ×ƋƋ ſ á Ó××ƋƋ ſ á ÒÒ×ƋƋ ſ á ÓÒ×ƋƋ ſ á Ó××ƋƋ ſ á ÒÒ×ƋƋ

20 -6.61 -6.80 -6.99 6.61 6.80 6.99

25 -8.02 -8.27 -8.53 8.02 8.27 8.53

30 -9.38 -9.70 -10.02 9.38 9.70 10.02

35 -10.69 -11.08 -11.48 10.69 11.08 11.48

40 -11.96 -12.42 -12.89 11.96 12.42 12.89

45 -13.19 -13.72 -14.27 13.19 13.72 14.27

50 -14.39 -14.99 -15.61 14.39 14.99 15.61

55 -15.55 -16.23 -16.93 15.55 16.23 16.93

60 -16.68 -17.44 -18.22 16.68 17.44 18.22

ḡᅕ༉ߙᨱᕽ۵ḡᱱ᮹ᄡ᭥ಽᯙ⦽౩ᯝḡḡᱱᨱᕽ᮹ၹಆᮡ

ḢᱲᱢᮝಽǍ⧕ḩᙹᨧ݅. ə௹ᕽḡᱱ᮹݉᭥ᄡ᭥ෝᯝᮝ┅۵

ߑ⦥᫵⦽॒a᮹⦹ᵲᮥ⧕ݚḡḡᱱᨱa⦹۵äᮝಽ⧕ᕾ⦹ᩡ݅.

݉᭥ᙹḢ݉₉aFigure 4ᨱӹ┡ԙၵ᪡zᯕᩍ్ḡḡᱱᨱ

ၽᔾ⦹۵Ğᬑ౩ᯝḡḡᱱᨱᕽ᮹ၹಆᮡ॒a⦹ᵲᰍ⦹᭥⊹ෝ

ᙽ₉ᱢᮝಽ᪏ĉa໕ᕽ⦹ӹ᮹॒a⦹ᵲᮥᰍ⦹⦽đŝෝᵲℊ᜽

┕ᮝಽ៉Ǎ⧁ᙹᯩ݅. ᩍʑᕽ, ℕđᰆ⊹۵݉ᯝᯱᮁࠥ᮹┥ᖒ

ᜅ⥥ยᮝಽ༉ߙย⦹ᩡᮝအಽ݉᭥ᙹḢ݉₉, ᷪ┥ᖒᜅ⥥ย᮹

݉᭥ ᄡ᭥ᨱ ᮹⦽ ॒a⦹ᵲᮡ ℕđᰆ⊹᮹ vᖒŝ ࠺ᯝ⦽ sᯕ

ࡽ݅.

Figure 4ᨱᕽᙹḢ݉₉᮹ᬑ⊂౩ᯝ᮹॒a⦹ᵲᯕ᯲ᬊ⦹۵

౩ᯝḡḡᱱᮥƇಽ⦹Ł, ᙹḢ݉₉᮹᳭⊂౩ᯝḡḡᱱᮥƈ௝Ł

⦹໕, ⦹ӹ᮹ ॒a⦹ᵲ ᯲ᬊᨱ ݡ⧕ ౩ᯝ ḡḡᱱᨱᕽ᮹ ၹಆᮡ

Eq. (6)ᮥᯕᬊ⦹ᩍĥᔑࢁᙹᯩᮝ໑, ᬑ⊂ᇡᇥ᮹౩ᯝḡḡᱱᨱ

݉᭥ᙹḢ݉₉aၽᔾ⧁Ğᬑ౩ᯝḡḡᱱ᮹ၹಆᮡEqs. (13)ⴇ (15)᪡zᯕb౩ᯝḡḡᱱᨱᕽ᮹ၹಆᮥᵲℊ᜽┕ᮝಽᕽǍ⧁

ᙹ ᯩ݅.

©ƐÎáƇ á Î

ā

ƌ ćÏÎſĸ ƉƑƃàĸ ſފ–šĸ ſ⠚• ĸ ſß (13)

©ƐÏáƇ á Î

ā

ƌ ćÏÎ ſĸƉƑƃàÏĸſފ–š Ïĸſ⠚• Ïĸſß (14)

{ {

©Ɛƈá

ā

Ƈ á Îƌ ćÏÎſĸ ƉƑƃàƈĸſފ–š ƈĸſ⠚• ƈĸſß (15)

Figure 5۵݉᭥ᙹḢ݉₉ᨱ᮹⦽౩ᯝḡḡᱱᨱᕽ᮹ၹಆᮥ

ӹ┡ԙäᮝಽ݉᭥ᙹḢ݉₉aၽᔾࡽḡḡᱱŝ݉₉aၽᔾࡹḡ

ᦫᮡᯙᱲ⦽౩ᯝḡḡᱱᨱᕽ᮹ၹಆᮡⓍʑ۵zŁᇡ⪙۵ၹݡႊ

⨆ᯕ݅. ᷪ, ↽ݡ ᦶ⇶ಆŝ ↽ݡ ᇡᔢಆᮡ Ⓧʑ۵ zŁ ᇡ⪙۵

ၹݡᯕ໑, ݉₉a ၽᔾࡹ۵ ℌ ჩṙ ౩ᯝ ḡḡᱱᨱᕽ ӹ┡ԉᮥ

᦭ ᙹ ᯩ݅.

݉᭥ᙹḢ݉₉ᨱ᮹⦽↽ݡᦶ⇶ಆŝ↽ݡᇡᔢಆᮥℕđᰆ⊹᮹

vᖒŝ౩ᯝḡḡᱱe᮹Ñญᨱ঑௝ĥᔑ⦽đŝෝTable 3ᨱ

ӹ┡ԕᨩ݅. ౩ᯝḡḡᱱᨱᕽ᮹↽ݡᦶ⇶ಆŝ↽ݡᇡᔢಆᮡℕđ ᰆ⊹᮹vᖒᯕ⍅ḩᙹಾ⍅ḡ໑, ౩ᯝḡḡᱱe᮹eĊᯕ⍅ḩᙹಾ

᯲ᦥḡ۵ äᮥ ᦭ ᙹ ᯩ݅.

(6)

yˆ“

’

X

UUU

Y Z [ \ ]

UUU XN UUU

YN ZN [N

\N UUU ]N

UUU

X x x x x x xY Z [ \ ] XVXWWW

ˆ ˆ ˆ ˆ ˆ ˆ ˆ

x

Fig. 6. Model for the End Rotation of the Rail Supports

Fig. 7. Vertical Reaction Forces of the Rail Supports by the End Rotation(ÎîÎ×××) in CSM

Table 4. Maximum Internal Forces of the Rail Supports by the End Rotation(ÎîÎ×××) in CSM

Stiffness Maximum Compressive Force(kN) Maximum Uplifting Force(kN)

ƉƑ (kN/mm) ſ á ÓÒ×ƋƋ ſ á Ó××ƋƋ ſ á ÒÒ×ƋƋ ſ á ÓÒ×ƋƋ ſ á Ó××ƋƋ ſ á ÒÒ×ƋƋ

20 -4.29 -4.21 -4.13 1.05 1.00 0.95

25 -5.07 -4.97 -4.87 1.27 1.21 1.15

30 -5.79 -5.70 -5.58 1.46 1.42 1.35

35 -6.46 -6.38 -6.26 1.64 1.61 1.54

40 -7.10 -7.03 -6.92 1.81 1.78 1.72

45 -7.71 -7.65 -7.54 1.96 1.95 1.90

50 -8.28 -8.24 -8.14 2.09 2.10 2.06

55 -8.83 -8.80 -8.72 2.22 2.24 2.21

60 -9.36 -9.34 -9.27 2.33 2.37 2.36

š š š š š š š š š

T[ yˆ“TZ TY TX  RX RY RZ R[

’ ’ ’ ’ ’ ’ ’ ’ ’

x

UUU UUU UUU

UUU

Fig. 8. Discrete Support Model 3.1.3 ۚ଍ۚऀฎୢ

Ʊప݉ᇡ᮹݉᭥⫭ᱥᮡFigure 6ᨱӹ┡ԙၵ᪡zᯕƱప

݉ᇡḡḡᱱᮥʑᵡᮝಽ⫭ᱥb1/1000ᨱ᮹⧕౩ᯝḡḡᱱᨱᕽ᮹

ᙹḢᄡ᭥aၽᔾࡽ݅. ౩ᯝḡḡᱱᨱᕽ᮹᯲ᬊಆᨱݡ⦽ĥᔑŝᱶ

ᮡ݉᭥ᙹḢ݉₉᮹⧕ᕾŝᱶŝ࠺ᯝ⦹໑॒a⦹ᵲอᰍĥᔑࡽ݅.

ᷪ, ౩ᯝḡḡᱱ᮹ᙹḢᄡ᭥۵݉ᇡ⫭ᱥb1/1000ŝ౩ᯝḡḡᱱᨱ ᕽ݉ᇡ⫭ᱥʑᵡᱱʭḡ᮹ÑญƇſ᮹Œŝzᮝ໑, əভ᮹ᄡ᭥ᨱ

⧕ݚ⦹۵॒a⦹ᵲᮡ౩ᯝḡḡᱱᨱᕽ᮹ᙹḢᄡ᭥ᨱℕđᰆ⊹᮹

vᖒᮥ Œ⦽ äŝ z݅.

঑௝ᕽ, ᩑᗮḡḡᅕ᮹౩ᯝḡḡᱱᨱᕽ᮹ၹಆᮡ݉᭥⫭ᱥᨱ

᮹⦽ b ౩ᯝ ḡḡᱱᨱᕽ᮹ ၹಆᮥ ༉ࢱ ᵲℊ⦽ äᯕအಽ Eqs.

(16)ⴇ(18)ಽ ӹ┡ԝ ᙹ ᯩ݅.

©ƐÎáƇ á Î

ā

ƌ ćÏ×××Î ĸ ſƉƑƃàĸſފ–š ĸſ⠚• ĸſß (16)

©ƐÏáƇ á Î

ā

ƌ ćÏ×××Î ĸ ÏſƉƑƃàÏĸſފ–š Ïĸſ⠚• Ïĸſß (17)

{ {

©Ɛƈá

ā

Ƈ á Îƌ ćÏ×××Î ĸ ƇſƉƑƃàƈĸſފ–š ƈĸſ⠚• ƈĸſß (18)

Figure 7ᮡ݉᭥݉ᇡ⫭ᱥᨱ᮹⦽౩ᯝḡḡᱱᨱᕽ᮹ၹಆ᮹

ᇥ⡍ෝӹ┡ԙäᯕ݅. ↽ݡᦶ⇶ಆᮡ݉ᇡ⫭ᱥᯕ᜽᯲ࡹ۵ḡᱱᨱ ᕽaᰆ Ⓧí ӹ┡ӹ໑ə ḡḡᱱᨱᕽ ᧞eਉᨕḥ ḡḡᱱᨱᕽ

↽ݡ ᇡᔢಆᯕ ӹ┡ԉᮥ ᦭ ᙹ ᯩ݅.

Table 4۵ℕđᰆ⊹᮹vᖒŝ౩ᯝḡḡᱱ᮹eĊᨱ঑௝݉᭥

݉ᇡ⫭ᱥᨱ᮹⦽౩ᯝḡḡᱱ᮹᯲ᬊಆᮥĥᔑ⦹ᩍӹ┡ԙđŝᯕ

݅. ↽ݡᦶ⇶ಆᮡℕđᰆ⊹᮹vᖒᯕ⍅ḱᨱ঑௝⍅ḡ۵äᮝಽ

ӹ┡ԍᮝӹ౩ᯝḡḡᱱeĊᨱ঑ෙ₉ᯕ۵᯲݅. ੱ⦽↽ݡᇡᔢಆ

ᮡℕđᰆ⊹᮹vᖒᯕ⍅ḩᙹಾ⍅ḡ໑౩ᯝḡḡᱱe᮹Ñญa

⍅ḩᙹಾ ⍅ḡӹ ᦥᵝ ׳ᮡ vᖒᨱ ݡ⧕ᕽ۵ ᯲ᦥḡ۵ äᮝಽ

ӹ┡ԍ݅.

3.2 ଲॺ஺஺࣪ࡦ܄

ᯕᔑḡḡᅕ༉ߙ᮹⧕ᕾᮡ݅ᙹ᮹┥ᖒḡḡᜅ⥥ย᭥ᨱ״ᩍḥ

ᩑᗮᅕಽᕽ3ᩑ ༉ູ✙ႊᱶ᜾ᮥ ᯕᬊ⦽݅. Figure 8ᮡᯥ᮹᮹

(7)

Table 5. Maximum Internal Forces of the Rail Supports by a Wheel Load(Î××Ɖ§) in DSM

Stiffness Maximum Compressive Force(kN) Maximum Uplifting Force(kN)

ƉƑ (kN/mm) ſ á ÓÒ×ƋƋ ſ á Ó××ƋƋ ſ á ÒÒ×ƋƋ ſ á ÓÒ×ƋƋ ſ á Ó××ƋƋ ſ á ÒÒ×ƋƋ

20 -33.95 -31.98 -29.97 1.42 1.42 1.32

25 -35.87 -33.80 -31.68 1.43 1.42 1.42

30 -37.53 -35.36 -33.15 1.60 1.37 1.43

35 -38.98 -36.74 -34.44 1.69 1.53 1.41

40 -40.28 -37.97 -35.60 1.73 1.63 1.40

45 -41.46 -39.09 -36.65 1.74 1.69 1.52

50 -42.54 -40.11 -37.62 1.73 1.73 1.60

55 -43.54 -41.06 -38.51 1.70 1.74 1.67

60 -44.47 -41.95 -39.34 1.66 1.74 1.70

ḡᱱჩ⪙aᇡᩍࡽ5}᮹┥ᖒḡᱱᮝಽ॒eĊḡḡࡽᩑᗮᅕෝ

ӹ┡ԙ݅. ḡᱱeÑญ۵॒eĊᯕ໑, ᵲᦺḡᱱᇡᨱḲᵲ⦹ᵲᯕ

᯲ᬊ⦽݅Ł⧁ভᵲᦺḡᱱᨱݡ⦽ᩑᗮᅕᨱᕽ᮹༉ູ✙ႊᱶ᜾ᮡ

3ᩑ༉ູ✙ႊᱶ᜾ᨱ᮹⧕Eq. (19)ಽӹ┡ԝᙹᯩ݅. ੱ⦽b

ḡᱱᮡ┥ᖒᜅ⥥ยᮝಽḡḡࡹᨕᯩᮝအಽəḡᱱᨱᕽ᮹ᄡ᭥۵

Eq. (20)ᮝಽ ᵝᨕḥ݅.

¦Ƈ àÎćӞ¢ſ â ϦƇćО¢ſ â ¦Ƈ âÎćӞ¢ſ (19)

á ćſ

ƗƇà ƗƇ àÎ

â ćſ

ƗƇà ƗƇ âÎ

ƗƇá ćƉƑ

ŸƇ

(20)

ᯥ᮹᮹ḡᱱᨱᕽ᮹ၹಆᮡᯙᱲ⦽ḡᱱ᮹༉ູ✙šĥ᜾ᮝಽᇡ

░Eq. (21)ಽӹ┡ԝᙹᯩ݅. ᩍʑᕽ, ªƇ۵᫙ᇡ᯲ᬊ⦹ᵲᯕ໑,

ŸƇ۵ ᯕᔑḡḡᅕ ༉ߙᨱᕽ᮹ ḡḡᱱ ၹಆᯕ݅.

ŸƇá ćſ

¦Ƈ àÎà ϦƇâ ¦Ƈ âÎ

â ªƇ (21)

Eq. (21)ᮥ Eq. (20)ᨱ ݡ᯦⦹໕

ƗƇá ćƉƑſ

¦Ƈ àÎà ϦƇâ ¦Ƈ âÎ â ćƉƑ

ªƇ

(22)

ᯕ ᵝᨕḡŁ, Eq. (22)ෝ Eq. (19)ᨱ ݡ᯦⦹Ł ᱶญ⦹໕

Eq. (23)ŝ zᮡ 5}᮹ ḡᱱᨱ ݡ⦽ ᩑᗮ ༉ູ✙ ႊᱶ᜾ᯕ

᨜ᨕḥ݅.

¦Ƈ àÏâ

Þ

ćĹÎ àÑ

ß

¦Ƈ àÎâ

Þ

ćĹÑ âÓ

ß

¦Ƈâ

Þ

ćĹÎ àÑ

ß

¦Ƈ âÎâ¦Ƈ âÏ

á à ſÞ©Ƈ àÎà Ï©Ƈâ©Ƈ âÎß (23)

ᩍʑᕽ, Ĺá ć ƉƑſРӞ¢ᯕ݅.

Eq. (23)ᮡᯥ᮹ḡᱱᨱݡ⦽5ᩑ༉ູ✙ႊᱶ᜾ᮝಽᕽḡᱱ᮹

}ᙹaฯᮡĞᬑ᮹༉ູ✙ႊᱶ᜾᮹⧕۵Eq. (24)ŝzᯕๅ✙ฎ ᜅෝᯕᬊ⦹ᩍǍ⧁ᙹᯩ݅. ᩍʑᕽĞĥ᳑Õᮡḡᱱ᮹}ᙹa

∊ᇥ⧁ভ⦹ᵲᱱᮝಽᇡ░ມญਉᨕḥ᧲Ҿ݉ᨱᕽ᮹༉ູ✙ෝ

0ᮝಽ aᱶ⦽݅.

š ¦ á › ª (24)

ᩍʑᕽ, š۵༉ູ✙ႊᱶ᜾᮹ĥᙹๅ✙ฎᜅ,›۵ḡᱱၹಆᨱ

ݡ⦽ ĥᙹ ๅ✙ฎᜅ, ¦, ª۵ bb ༉ູ✙᪡ ᫙ᇡ ᯲ᬊ⦹ᵲᨱ

ݡ⦽ ๅ✙ฎᜅಽ Eqs. (25)ⴇ(27)ŝ z݅.

š á ƙ

Ɯ

ƚ

Î ćĹ{ {××× Î àÑÎ×× ćĹćĹÑ âÓÎ àÑ{Î× ćĹćĹćĹÎ àÑ ÎÑ âÓÎ àÑ{Î ćĹćĹćĹÎ àÑ ÎÑ âÓÎ àÑ{ ćĹćĹÎ àÑ Î × zÑ âÓ{× ćĹÎ àÑ Î z{×× { |× z× zƛƝ

ƞ

(25)

(8)

Table 6. Maximum Internal Forces of the Rail Supports by the Vertical Displacement(ÎƋƋ) in DSM

Stiffness Maximum Compressive Force(kN) Maximum Uplifting Force(kN)

ƉƑ (kN/mm) ſ á ÓÒ×ƋƋ ſ á Ó××ƋƋ ſ á ÒÒ×ƋƋ ſ á ÓÒ×ƋƋ ſ á Ó××ƋƋ ſ á ÒÒ×ƋƋ

20 -6.57 -6.76 -6.97 6.57 6.76 6.97

25 -7.99 -8.23 -8.49 7.99 8.23 8.49

30 -9.35 -9.66 -9.98 9.35 9.66 9.98

35 -10.66 -11.04 -11.42 10.66 11.04 11.42

40 -11.93 -12.38 -12.83 11.93 12.38 12.83

45 -13.16 -13.68 -14.21 13.16 13.68 14.21

50 -14.36 -14.95 -15.56 14.36 14.95 15.56

55 -15.52 -16.19 -16.87 15.52 16.19 16.87

60 -16.66 -17.41 -18.17 16.66 17.41 18.17

Table 7. Maximum Internal Forces of the Rail Supports for the End Rotation(ÎîÎ×××) in DSM

Stiffness Maximum Compressive Force(kN) Maximum Uplifting Force(kN)

ƉƑ (kN/mm) ſ á ÓÒ×ƋƋ ſ á Ó××ƋƋ ſ á ÒÒ×ƋƋ ſ á ÓÒ×ƋƋ ſ á Ó××ƋƋ ſ á ÒÒ×ƋƋ

20 -4.21 -4.14 -4.11 1.07 1.03 0.98

25 -4.96 -4.87 -4.8 1.28 1.24 1.19

30 -5.68 -5.58 -5.48 1.46 1.43 1.39

35 -6.37 -6.26 -6.13 1.64 1.61 1.57

40 -7.02 -6.91 -6.77 1.8 1.78 1.74

45 -7.64 -7.54 -7.39 1.94 1.94 1.9

50 -8.23 -8.14 -8 2.08 2.08 2.06

55 -8.8 -8.72 -8.58 2.2 2.22 2.21

60 -9.34 -9.27 -9.15 2.31 2.35 2.35

› á ƙ

Ɯ

ƚ

× à ſ Ïſ à ſ × × × × zƛƝ

ƞ

× × à ſ Ïſ à ſ × × × z

× × × à ſ Ïſ à ſ × × z

× × × × à ſ Ïſ à ſ × z

{ { { { { { { { |

(26)

¦á Ē ē Ĕ

ĕ ĕ

¦Î

¦Ï

¦Ð

¦Ñ { Ĝ ĝ Ğ

ĕ ĕ

, ªá

Ē ē Ĕ

ĕ ĕ

ªÎ

ªÏ

ªÐ ªÑ { Ĝ ĝ Ğ

ĕ ĕ

(27)

3.2.1 ۚ଍ౠ෇ண

ᯕᔑḡḡᅕ༉ߙᨱᕽ݉᭥⇶⦹ᵲ(Î××Ɖ§)ᨱ᮹⧕ၽᔾࡹ۵

౩ᯝḡḡᱱᨱᕽ᮹ၹಆᮥ ℕđᰆ⊹᮹vᖒŝ౩ᯝḡḡᱱe᮹

eĊᨱݡ⧕ĥᔑ⦹ᩍTable 5ᨱӹ┡ԕᨩ݅. ᩍʑᕽ, ḡḡᱱᮡ

Ğĥ᳑Õ᮹ᩢ⨆ᮥၼḡᦫࠥಾ⦹ʑ᭥⦹ᩍ20}᮹౩ᯝḡḡᱱᨱ

ݡ⧕ ĥᔑ⦹ᩡ݅.

౩ᯝḡḡᱱᨱᕽ᮹ၹಆᮡᩑᗮḡḡᅕ༉ߙ᮹⧕ᕾđŝ᪡ᮁᔍ

⦹໑, ↽ݡᦶ⇶ಆᮡℕđᰆ⊹᮹vᖒŝ౩ᯝḡḡᱱe᮹eĊᯕ

⍅ḩᙹಾⓍíӹ┡ԍᮝ໑, ↽ݡᇡᔢಆࠥ࠺ᯝ⦹݅. ə్ӹℕđᰆ

⊹᮹ vᖒᯕ 45kN/mm ᯕᔢᨱᕽ۵ ↽ݡ ᇡᔢಆ᮹ qᗭ⦹Ñӹ

᧞e ᵥᨕऽ۵ äᮝಽ ӹ┡ԍ݅. ᯕ్⦽ ᯕᮁ۵ ↽ݡ ᇡᔢಆᯕ

౩ᯝḡḡᱱᯕ ᦥܭ ౩ᯝḡḡᱱ ᔍᯕᨱᕽ ၽᔾ⦹۵Ğᬑ ౩ᯝ

ḡḡᱱᨱᕽĥᔑࡽsᮡ↽ݡᇡᔢಆᅕ݅᧞e᯲ᮡsᮥӹ┡ԝ

ᙹ ᯩ݅.

3.2.2 ۚ଍৤஻ۚఙ

ᯕᔑḡḡᅕ༉ߙᨱ᮹⧕݉᭥ᙹḢ݉₉ᨱ᮹⦽౩ᯝḡḡᱱᨱᕽ ᮹ၹಆᮡ┥ᖒᜅ⥥ย᮹݉᭥ᄡ᭥ᨱ᮹⦽॒a⦹ᵲᮥᯕᬊ⦹ᩍ

ĥᔑ⦹ᩡᮝ໑ ə đŝෝ Table 6ᨱ ӹ┡ԕᨩ݅.

݉᭥ᙹḢ݉₉ᨱ᮹⦽౩ᯝḡḡᱱᨱᕽၹಆᮡ↽ݡᦶ⇶ಆŝ

↽ݡᇡᔢಆᮡⓍʑ۵zŁႊ⨆ᮡၹݡᯕ݅. ↽ݡᦶ⇶ಆŝ↽ݡ

(9)

Table 8. Comparison with Internal Forces of the Rail Supports by a Wheel Load

Stiffness Maximum Compressive Force(kN) Maximum Uplifting Force(kN) ƉƑ (kN/mm) CSM

(A)

DSM (B)

DS804 (C)

(A-C) /C (%)

(B-C) /C (%)

CSM (A)

DSM (B)

DS804 (C)

(A-C) /C (%)

(B-C) /C (%)

20 -34.01 -33.95 - - - 1.47 1.42 - - -

25 -35.96 -35.87 - - - 1.55 1.43 - - -

30 -37.64 -37.53 -37.53 0.11 0.01 1.63 1.60 1.59 0.04 0.50 35 -39.12 -38.98 -38.98 0.14 0.00 1.69 1.69 1.69 0.00 0.05 40 -40.44 -40.28 -40.28 0.16 0.00 1.75 1.73 1.73 0.02 0.05 45 -41.65 -41.46 -41.46 0.19 0.00 1.80 1.74 1.74 0.06 0.02 50 -42.76 -42.54 -42.54 0.22 0.00 1.85 1.73 1.81 0.04 4.65 55 -43.79 -43.54 -43.54 0.25 0.01 1.89 1.70 1.89 0.00 10.24

60 -44.76 -44.47 - - - 1.93 1.66 - - -

Table 9. Comparison with Internal Forces of the Rail Supports by a Vertical Displacement

Stiffness Maximum Compressive Force(kN) Maximum Uplifting Force(kN)

ƉƑ (kN/mm) CSM (A)

DSM (B)

DS804 (C)

(A-C) /C (%)

(B-C) /C (%)

CSM (A)

DSM (B)

DS804 (C)

(A-C) /C (%)

(B-C) /C (%)

20 -6.61 -6.57 - - - 6.61 6.57 - - -

25 -8.02 -7.99 - - - 8.02 7.99 - - -

30 -9.38 -9.35 -9.37 0.13 0.25 9.38 9.35 9.37 0.13 0.25

35 -10.69 -10.66 -10.70 0.06 0.38 10.69 10.66 10.70 0.06 0.38 40 -11.96 -11.93 -11.90 0.52 0.25 11.96 11.93 11.90 0.52 0.25 45 -13.19 -13.16 -13.20 0.07 0.29 13.19 13.16 13.20 0.07 0.29 50 -14.39 -14.36 -14.40 0.10 0.28 14.39 14.36 14.40 0.10 0.28 55 -15.55 -15.52 -15.50 0.32 0.15 15.55 15.52 15.50 0.32 0.15

60 -16.68 -16.66 - - - 16.68 16.66 - - -

ᇡᔢಆᮡ ℕđᰆ⊹᮹ vᖒᯕ ⍅ḩᙹಾ ⍅ḥ݅. ə్ӹ ࠺ᯝ⦽

vᖒᨱᕽ౩ᯝḡḡᱱ᮹eĊᯕⓕᙹಾəsᮡ᯲ᦥḡ۵äᮝಽ

ӹ┡ԍᮝ໑, ə₉ᯕ۵ℕđᰆ⊹᮹vᖒᯕⓕᙹಾ⍅ḱᮥ᦭ᙹ

ᯩ݅.

3.2.3 ۚ଍ۚऀฎୢ

ᯕᔑḡḡᅕ༉ߙᨱᕽ݉᭥݉ᇡ⫭ᱥ(1/000)ᨱ᮹⦽౩ᯝḡḡᱱ ᮹ၹಆᮡ౩ᯝḡḡᱱᨱᕽ᮹ᙹḢᄡ᭥ᨱݡ⦽॒a⦹ᵲᮥᯕᬊ⦹

ᩍ ĥᔑ⦹ᩡᮝ໑, ə đŝෝ Table 7ᨱ ӹ┡ԕᨩ݅.

↽ݡᦶ⇶ಆᮡℕđᰆ⊹᮹vᖒᯕ⍅ḩᙹಾ᷾a⦹໑, ౩ᯝ

ḡḡᱱe᮹ Ñญa ᷾a⧁ᙹಾ ↽ݡᦶ⇶ಆᮡ ᧞e ᷾a⦹ӹ

ə₉ᯕ۵Ⓧḡᦫ݅. ੱ⦽, ↽ݡᇡᔢಆᮡℕđᰆ⊹᮹vᖒᯕ

ⓕᙹಾ᷾a⦽݅. ℕđᰆ⊹᮹vᖒᯕ᯲ᮡĞᬑᨱ۵౩ᯝḡḡᱱ ᮹ eĊᯕ ⍅ḩᙹಾ ⍅ḡ۵ äᮝಽ ӹ┡ԍᮝӹ, ℕđᰆ⊹᮹

vᖒᯕⓑĞᬑᨱ۵౩ᯝḡḡᱱ᮹eĊ᮹ᩢ⨆ᮡᦥᵝ᯲ᮡ

äᮝಽ ӹ┡ԍ݅.

4. ⧕ᕾđŝ᮹እƱ

౩ᯝḡḡᱱᨱᕽ᮹ၹಆᮥĥᔑ⦹ʑ᭥⦽⧕ᕾႊჶ᮹ᱢᬊᖒá☁

ෝ᭥⦹ᩍᩑᗮḡḡᅕ༉ߙŝᯕᔑḡḡᅕ༉ߙᨱ᮹⦽⧕ᕾđŝෝ

እƱ⦹ᩡᮝ໑, DS 804 ʑᵡᨱᕽᱽ᜽ࡽsᮥʑᵡᮝಽᔢݡ᪅₉ෝ

ᱽ᜽⦹ᩡ݅. DS 804ᨱᱽ᜽ࡽsᮡₙsᮡᦥܩӹᝅྕᨱᕽ⎹Ⓧญ✙

ȅࠥ᮹ᔍᬊᖒá☁ᨱᱢᬊࡹŁᯩŁ⧕ᕾႊჶ᮹₉ᯕᨱ঑ෙ⧕ᕾđ ŝ᮹₉ᯕᱶࠥෝ݉ᙽእƱ⦹۵༊ᱢᮝಽ۵እƱ⧁ᙹᯩᮥäᮝಽ

❱݉ࡽ݅. እƱsᮡ౩ᯝḡḡᱱe᮹eĊſ á ÓÒ×ƋƋ,ℕđᰆ⊹᮹

vᖒƉƑá Ò×Ɖ§îƋƋᨱ ݡ⦽ ⧕ᕾ đŝᯕ݅.

(10)

Table 10. Comparison with Internal Forces of the Rail Supports by a End Rotation

Stiffness Maximum Compressive Force(kN) Maximum Uplifting Force(kN) ƉƑ (kN/mm) CSM

(A)

DSM (B)

DS804 (C)

(A-C) /C (%)

(B-C) /C (%)

CSM (A)

DSM (B)

DS804 (C)

(A-C) /C (%)

(B-C) /C (%)

20 -4.29 -4.21 - - - 1.05 1.07 - - -

25 -5.07 -4.96 - - - 1.27 1.28 - - -

30 -5.79 -5.68 -5.83 0.73 2.50 1.46 1.46 1.47 0.45 0.43

35 -6.46 -6.37 -6.48 0.24 1.71 1.64 1.64 1.65 0.38 0.79

40 -7.10 -7.02 -7.10 0.02 1.12 1.81 1.80 1.82 0.67 1.30

45 -7.71 -7.64 -7.69 0.20 0.65 1.96 1.94 1.96 0.16 0.88

50 -8.28 -8.23 -8.26 0.25 0.36 2.09 2.08 2.10 0.37 1.10

55 -8.83 -8.80 -8.81 0.22 0.17 2.22 2.20 2.22 0.22 0.92

60 -9.36 -9.34 - - - 2.33 2.31 - - -

4.1 ۚ଍ౠ෇ண

⧕ᕾ ༉ߙᨱ ঑ෙ ݉᭥⇶⦹ᵲᨱ᮹⦽ ౩ᯝ ḡḡᱱᨱᕽ᮹

ၹಆ ĥᔑđŝෝTable 8ᨱ ӹ┡ԕᨩ݅. ↽ݡᦶ⇶ಆᮡᩑᗮ

ḡḡᅕ༉ߙᨱᕽDS 804 ʑᵡ᮹sŝ ᧞e᮹₉ᯕaᯩᮝӹ

ə ₉ᯕ۵ๅᬑ ᯲ᮝ໑, ᯕᔑ ḡḡᅕ༉ߙᮡ࠺ᯝ⦽sᮥᅕᩍᵡ

݅. ↽ݡᇡᔢಆ᮹Ğᬑ۵ᩑᗮḡḡᅕ ༉ߙ᮹Ğᬑ۵DS 804ᨱ

ᱽ᜽ࡽsŝᯝ⊹⦹໑, ᯕᔑḡḡᅕ ༉ߙ᮹ĞᬑDS 804 ʑᵡ᮹

sŝ እƱ⧁ ভ ℕđ ᰆ⊹᮹ vᖒᯕ ᧞ 50kN/mm ᯕᔢᨱᕽ

₉ᯕaⓍí ӹ┡ӹ໑݅ෙǍeᨱᕽ۵࠺ᯝ⦹݅. ᯕ్⦽ᬱᯙ

ᮡ ౩ᯝ ḡḡᱱᨱᕽ᮹ ĥᔑࡽ sŝ ↽ݡ ᇡᔢಆᯕ ӹ┡ӹ۵

᭥⊹a݅ෝᙹ ᯩʑভྙᮝಽ❱݉ࡽ݅. ঑௝ᕽ, ݉᭥⇶⦹ᵲᨱ

᮹⦽ ౩ᯝ ḡḡᱱᨱᕽ᮹ ၹಆᮡ ᖅĥ᜽ ᧞e᮹ ᦩᱥ⊂ sᮥ

ᱢᬊ⦹ᩍᩑᗮḡḡᅕ ༉ߙᨱ᮹⦽⧕ᕾđŝෝᱢᬊ⧁ᙹᯩ݅Ł

❱݉ࡽ݅.

4.2 ۚ଍৤஻ۚఙ

Table 9۵⧕ᕾ༉ߙᨱ঑ෙ݉᭥ᙹḢ݉₉ᨱ᮹⦽౩ᯝḡḡᱱ ᨱᕽ᮹ၹಆᮥእƱ⦽đŝᯕ݅. əđŝ, ᩑᗮḡḡᅕ༉ߙŝᯕᔑḡ ḡᅕ༉ߙᨱ᮹⦽⧕ᕾđŝ۵DS 804 ʑᵡᨱᱽ᜽ࡽsŝ᧞e᮹

⠙₉a ᯩᮝӹ Ñ᮹ ᯝ⊹⦹۵ äᮝಽ ӹ┡ԍ݅.

4.3 ۚ଍ۚऀฎୢ

⧕ᕾ ༉ߙᨱ ঑ෙ ݉᭥ ݉ᇡ ⫭ᱥᨱ ᮹⦽ ౩ᯝ ḡḡᱱᨱᕽ᮹

ၹಆᮥ እƱ⦹ᩍ Table 10ᨱ ӹ┡ԕᨩ݅. ə đŝ, ᩑᗮḡḡᅕ

༉ߙᨱ ᮹⦽ ⧕ᕾđŝᅕ݅ ᯕᔑ ḡḡᅕ ༉ߙᨱ ᮹⦽ ⧕ᕾđŝ ᮹ ᔢݡ᪅₉a ᧞e ޵ Ⓧí ӹ┡ԍᮝӹ ə ᪅₉۵ ↽ݡ 1.7%ᯕ

⦹ಽ ⧕ᕾ༉ߙᨱ ঑ෙ ⧕ᕾđŝ᮹ ₉ᯕ۵ ᦥᵝ ᯲ᮡ äᮝಽ

ӹ┡ԍ݅.

5. đು

ᅙᩑǍᨱᕽ۵⎹Ⓧญ✙ȅࠥƱప᮹ᔍᬊᖒá☁ŝᱶ᮹ʑᅙ

݉ĥಽ ౩ᯝ ḡḡᱱᨱᕽ᮹ ↽ݡ ᦶ⇶ಆŝ ↽ݡ ᇡᔢಆᨱ ݡ⦽

ʑᵡsᮥ ĥᔑ⦹ᩡᮝ໑, ə ԕᬊᮥ ᫵᧞⦹໕ ݅ᮭŝ z݅.

(1) ౩ᯝḡḡᱱᨱᕽ᮹ၹಆᮡȅࠥᩎ⦺ᨱᕽᵝಽᔍᬊࡹᨕḡ۵

ᩑᗮ ḡḡᅕ ༉ߙᮥ ᯕᬊ⦹ᩍ ĥᔑࢁ ᙹ ᯩᮭᮥ ᅕᩡᮝ໑, ᯕᔑḡḡᅕ༉ߙᮥᯕᬊ⦽ᯕುᱢ⧕ᕾႊჶᮥᱽ᜽⦹ᩡ݅.

⧕ᕾ ༉ߙᨱ঑ෙ ⧕ᕾđŝ᮹እƱđŝ, ݉᭥⇶⦹ᵲ, ݉᭥

ᙹḢ݉₉, ݉᭥݉ᇡ⫭ᱥᨱݡ⦽౩ᯝḡḡᱱᨱᕽ᮹ၹಆᮡ

ᩑᗮḡḡᅕ༉ߙŝᯕᔑḡḡᅕ⧕ᕾ༉ߙ, DS 804 ʑᵡᨱᕽ

ᱽ᜽ࡽ sŝ Ñ᮹ ᯝ⊹⦹ᩡ݅.

(2)݉᭥⇶⦹ᵲᨱ᮹⦽౩ᯝḡḡᱱ᮹↽ݡᦶ⇶ಆᮡȅࠥ᮹vᖒ ĥᙹಽᇡ░ e݉⯩ ĥᔑࢁ ᙹ ᯩᮝ໑, ↽ݡ ᇡᔢಆᮡ ↽ݡ

ᦶ⇶ಆ᮹4.32%ಽӹ┡ԍ݅. ੱ⦽, ౩ᯝḡḡᱱᨱᕽ᮹↽ݡ

ᦶ⇶ಆŝ↽ݡᇡᔢಆᮡℕđᰆ⊹᮹vᖒŝ౩ᯝḡḡᱱe᮹

eĊᯕ ⍅ḩᙹಾ Ⓧí ӹ┡ԍ݅.

(3) ݉᭥ᙹḢ݉₉ᨱ᮹⦽↽ݡᦶ⇶ಆŝ↽ݡᇡᔢಆᮡⓍʑ۵

zŁႊ⨆ᮡၹݡᯕ໑, ℕđᰆ⊹᮹vᖒᯕ⍅ḩᙹಾ, ౩ᯝḡḡ ᱱ᮹eĊᯕ᯲ᮥᙹಾ⍅ḥ݅. ݉᭥݉ᇡ⫭ᱥᨱ᮹⦽౩ᯝ

ḡḡᱱᨱᕽ᮹↽ݡᦶ⇶ಆŝ↽ݡᇡᔢಆᮡℕđᰆ⊹᮹vᖒŝ

౩ᯝḡḡᱱ᮹eĊᯕ⍅ḩᙹಾ⍅ḡ۵äᮝಽӹ┡ԍᮝӹ, ౩ᯝ ḡḡᱱ᮹ eĊ᮹ ᩢ⨆ᮡ ᦥᵝ ᯲ᮡ äᮝಽ ӹ┡ԍ݅.

qᔍ᮹ɡ

ᯕ םྙᮡ 2012֥ࠥ ᇡ⃽ݡ⦺Ʊ Ʊእḡᬱ ᩑǍእᨱ ᮹⦹ᩍ

ḡᬱࡽ ᩑǍ᮹ đŝᯕ໑, ᩑǍእ ḡᬱᨱ qᔍऽพܩ݅.

(11)

References

Park, H.-K., Jang, S.-Y., Yang, S.-C. and park, Y.-G. (2009). “A parametric study on the serviceability of concrete slab track on railway bridges.” Journal of Korean Society for Railway, The Korean Society for Railway, Vol. 12, No. 1, pp. 95-103 (In Korean).

Sung, D.-Y., Kim, Y.-H., Park, Y.-G. and Kim, S.-I. (2008). “The parameter study of serviceability review of end track on railway bridge installed concrete slab track.” 2008 Autumn Conference of Korean Society for Railway, The Korean Society for Railway, 2008. 11, pp. 117-124 (In Korean).

Arnold D. K. and Seo. S.-B.(translation) (2009). Fundamental of

track dynamics 1, 2, Book Gallery, Korea (In Korean).

Park, H.-K. (2009). An analysis of parameters on serviceability of concrete slab track fasteners at railway bridge deck ends, Ph.D.

Dissertation, Dept. of Railway Construction Engineering Graduate School of Railroad, Seoul National University of Technology, Seoul, Korea (in Korean).

Yang. S.-C. (2008). A study on the improvement of performance for concrete track interface, Research Report, Korea Railroad Research Institute, Korea Rail Network Authority, Korea (In Korean).

DS 804 App. 29. (2009). Bridge deck ends, check for serviceability limit state of superstructure, Regulation for Railway Bridges and Other Civil Constructions, Deutch Bahn.

(12)

수치

Table 1. Static and Dynamic Actions on a Superstructure of Bridge
Fig. 1. Continuous Support Model of TrackSubgrade System
Table 2. Maximum Internal Forces of the Rail Supports by a Wheel Load( Î××Ɖ§ ) in CSM
Fig. 5. Vertical Reaction Forces of the Rail Supports by the Vertical  Displacement( ÎƋƋ ) in CSM
+6

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