Research Reports of Kumamoto-NCT. Vol. 4 （2012）
ᣢ⸳ߩ࠾࡞ࡦࡠᯅߩ᭴ㅧ․ᕈߦߟߡ
ጤဝ ⷐ
㧖The Report of Structure Characteristic of Existing Nielsen-Lohse Bridges
Kaname Iwatsubo㧖
The Nielsen bridge proposed by O.F.Nielsen(Sweden) in 1922 is formed that use of the cable on tensional hanger, and is constructed after 1967 in Japan. The Nielsen-Lohse bridge has the structure form of a parallel arch rib or a basket handle arch rib, and it shows the fine sight and good strength as a bridge. Many researches about the seismic performance of a steel bridge are made, and the seismic design method is becoming up. It is required to develop the method of raising the ultimate strength and the earthquake-proof performance about existing Nielsen-Lohse bridges. Especially, the basket handle arch type erected in three dimensions must investigate the relationship of between axial force and bending moment of arch rib member, and the influence of hanger as tension member to refine the performance under big earthquake. However, there is little research which investigated the performance on seismic load or ultimate strength behavior of the Nielsen-Lohse bridge. In this report, to decide the parameter for structural analysis, it shows the investigated result about the structure characteristic of the constructed Nielsen-Lohse bridges.
ࠠࡢ࠼㧦࠾࡞ࡦࡠᯅ㧘ࠕ࠴ᯅ㧘㍑ᯅ㧘⠴㔡⸳⸘㧘⠴⩄ജ
Keywords㧦Nielsen-Lohse Bridge, Arch Bridge, Steel Bridge, Seismic Design, Ultimate Strength
㧝. ߪߓߦ 2012 ᐕ 3 ߦ〝ᯅߩᛛⴚၮḰࠍ␜ߒߡࠆ〝ᯅᣇ ᦠ߇ᡷ⸓ߐࠇߚ(1)ޕ࿁ߩᡷ⸓ߢߪ㧘⛽ᜬ▤ℂߦ㑐ߔࠆⷙቯ ߿᭴ㅧ⸳⸘ߩวℂൻࠍ⋡ᜰߒߚⷙቯߥߤ߇ណ↪ߐࠇߡ ࠆޕ⠴㔡⸳⸘ߦ㑐ߒߡߪ㧘2011 ᐕ 3 11 ᣣߦ⊒↢ߒߚ᧲ᣣ ᧄᄢ㔡ἴߩ⚻㛎߆ࠄ⠴㔡ᕈ⢻ᾖᩏߩߚߩ㔡ᵄᒻ߇ᄌᦝ ߐࠇߚޕߎࠇࠄߩⷙቯߪᣂ⸳ᯅߩߺߥࠄߕ㧘ᓟߩᣢ⸳ᯅ ߩ⠴㔡ᒝߢ߽↪ߐࠇࠆߚ㧘᭽ޘߥᯅߩ㔡ᤨേ ࠍ⺞ߴߡ߅ߊߎߣߪ㊀ⷐߥ⺖㗴ߢࠆޕ⪺⠪ߪߎࠇ߹ߢߦ ㍑᭴ㅧ‛ߩ⚳ዪേߦ㑐ߔࠆ⎇ⓥࠍⴕߞߡ߈ߡࠆ߇㧘ᣢ ᓔߩ⎇ⓥࠍ⺞ߴߡߺࠆߣ࠾࡞ࡦࡠᯅߦߟߡߩ⎇ ⓥ߇ዋߥߎߣ߇ಽ߆ߞߚޕߘߎߢᧄႎ๔ߢߪ᭴ㅧࡄ ࡔ࠲ࠍቯߔࠆߚߩ⾗ᢱߣߒߡ㧘ᣢ⸳ߩ࠾࡞ࡦ ࡠᯅߩ᭴ㅧߩ․ᓽࠍ⺞ߴߚ⚿ᨐࠍႎ๔ߔࠆޕ 㧞. ࠾࡞ࡦࡠᯅߦߟߡ ࠕ࠴ᯅߩ࠾࡞ࡦᒻᑼߪ㧘1922 ᐕߦࠬ࠙ࠚ࠺ࡦߩ O.F.Nielsen ߦࠃߞߡឭ᩺ߐࠇߚᯅᒻᑼߢ㧘ᣣᧄߢ߽ 1966 ᐕߩ㏜Ꮉᯅ㧔᳓▤ᯅ㧕ߢೋߡណ↪ߐࠇߚ(2)ޕਅ〝ᯅ߿ਛ〝 ᯅߢណ↪ߐࠇߡࠆ࠾࡞ࡦᒻᑼߩ․ᓽߪ㧘ษࠅ᧚ߦࠤ ࡉ࡞߿ࡠ࠶࠼ࠍ↪ߒߡࠆὐߢࠅ㧘ࠝࡊࡦߥⷞ⇇ ࠍ⏕ߢ߈ࠆޕᚒ߇࿖ߢߪࠕ࠴ࡉߣᩴߦゲജߣᦛ ߍࡕࡔࡦ࠻߇↪ߔࠆࡠᒻᑼߣ૬ߖߡ㧘࠾࡞ࡦ ࡠᯅߣߒߡᄙߊᑪ⸳ߐࠇߡࠆޕߐࠄߦᧄᒻᑼߩ․ᓽ ߣߒߡ㧘ࠕ࠴ࠢ࠙ࡦㇱߩࠕ࠴ࡉ㑆㓒ࠍࠕ࠴ၮㇱ ߩ㑆㓒ࠃࠅ߽⁜ߚࡃࠬࠤ࠶࠻ࡂࡦ࠼࡞ᒻᑼ߇ណ↪ߐࠇࠆ ߎߣ߽ᄙᯅᒻᑼߢࠆޕ ࿑1 ߪᾢᧄ⋵⏴ᧁߦ᨞߆ࠆᬞᯅߢࠆޕᬞᯅߩ ⻉రࠍ 1 ߦ␜ߔ߇㧘ᯅߩⷙᮨߣߒߡߪᮡḰ⊛ߥⷙᮨߢ ࠆޕᧄᯅߢߪࡔࡦ࠹࠽ࡦࠬᕈࠍ㊀ⷞߒߡ⠴ᕈ㍑߇↪ ࠄࠇߡ߅ࠅ㧘ߐ߮ቯൻഥಣℂ᧚߇ႣᏓߐࠇߡࠆޕ⠴ ᕈ㍑ߪ㍑᧚⥄り߆ࠄ⊒↢ߔࠆቯ㍕ߢᖡ⾰ߥ⣣㘩៊்ࠍ 㒐ᱛߔࠆ᧚ᢱߢࠆߚ㧘ႣⵝߩႣࠅᦧ߃߇ਇⷐߣߥࠅ ࠗࡈࠨࠗࠢ࡞ࠦࠬ࠻߇ૐᷫߢ߈ࠆ㍑᧚ߢࠆޕ ࠕ࠴ᯅߪࠕ࠴ࡉㇱ᧚ߢᦛ✢߇ᒝ⺞ߐࠇߡࠆߚ ⟤ⷰߦఝࠇߡ߅ࠅ㧘ࠕ࠴ലᨐߦࠃࠅఝࠇߚ㕙ౝߩ⠴⩄ജ ࠍߔࠆޕߒ߆ߒߥ߇ࠄ㔡ᤨ⩄㊀ߩࠃ߁ߦ㕙ᄖᣇะߩ⩄ ㊀߇↪ߒߚ႐วߪ㧘ࠕ࠴ࡉోߩ㕙ᄖᐳዮ߇⊒↢ߔ ࠆߚ㧘ᮮ᭴ࠍㆡಾߦ㈩⟎ߔࠆߎߣߢ⠴㔡ᕈ⢻ߩะࠍ࿑ ߞߡࠆޕߘߩὐ㧘ࡃࠬࠤ࠶࠻ࡂࡦ࠼࡞ᒻᑼߩ࠾࡞ࡦ ࡠᯅߢߪ㧘㕙ᄖᣇะߦᢳߐߖߚ᭴ㅧᒻᑼߣߒߡࠆ ߚ㧘㕙ᄖᐳዮߩ⠴⩄ജ߽㜞ᒻᑼߢࠆ(3),(4)ޕᧄႎ๔ߢߪ ᯅ࠺࠲ࡌࠬ(5)ࠍ↪ߡ㧘ᯅߩ⠴⩄ജߦ㑐ଥ߇ࠆᯅ ోߩኸᴺ⻉రߦߟߡ⺞ߴߡࠆޕ 㧖 ᑪ▽␠ળ࠺ࠩࠗࡦᎿቇ⑼ ޥ866-8501 ᾢᧄ⋵ઍᏒᐔጊᣂ↸ 2627 Dept. of Architecture and Civil Engineering,
2627 Hirayama, Yatsushiro-shi, Kumamoto, Japan 866-8501
⺞ᩏႎ๔
熊本高等専門学校 研究紀要 第 4 号（2012） 㧟. ࠺࠲ಽᨆ 3.1 ৻⥸⊛ߥ࠾࡞ࡦࡠᯅߩ᭴ㅧ⻉ర ᢥ₂(5)ߩ࠺࠲ࡌࠬ߆ࠄ࠾࡞ࡦᒻᑼࠍ⺞ߴࠆߣ 182 ᯅᒰߒߚޕᢥ₂(6)ߢߪ৻⥸⊛ߥ࠾࡞ࡦࡠᯅߩ ᭴ㅧ⻉రߣߒߡ2 ߦ␜ߔኸᴺࠍቯ⟵ߒߡࠆޕߎࠇࠄߪ㧘 ਛࠄ߇ߘࠇ߹ߢߦⴕߞߚ⺞ᩏ⎇ⓥߩᚑᨐࠍరߦ␜ߒߡ ࠆ(7)ޕએਅ㧘ᣢ⸳ߩᯅ࠺࠲ߦߟߡ2 ߦ␜ߔᮡḰࠨࠗ ࠭ߣᲧセߒߥ߇ࠄ․ᓽࠍ␜ߔޕ 3.2 ࠺࠲ಽᨆ (1)ᑪ⸳ᐕߣᓘ㑆㐳 ࿑ 3 ߦᑪ⸳ᐕߣᓘ㑆㐳(L)ߩ㑐ଥࠍ␜ߔޕᄙߊߩᯅ߇ 260m એਅߩᓘ㑆ߢᑪ⸳ߐࠇߡ߅ࠅ㧘260m ࠍ߃ߚᯅ߽ ฃߌࠄࠇࠆޕᑪ⸳ਛߩᯅ߇ᓘ㑆㐳292m ߩ╙㧞㖸ᚭ ᄢᯅ㧔ᐢፉ⋵㧕(8)ߢ㧘ᦨ߽㐳ᓘ㑆㐳ߪ305m ߩᣂᧁᵤᎹᄢ ᯅ(9)ߢߞߚޕ߹ߚ㧘ᑪ⸳ߐࠇߚᓘ㑆㐳ߩᐔဋߪ129m ߢ ࠅ㧘৻⥸⊛ߥࠕ࠴ᯅߩㆡ↪ࠬࡄࡦߣห᭽ߢߞߚޕ (2)᭴ㅧᒻᑼ ࠾࡞ࡦࡠᯅߩታ❣ߢߪ㧘2 ᧄߩࠕ࠴ࡉࠍᐔⴕ ߦ㈩⟎ߔࠆᐔⴕᒏߩᒻᑼߣࠕ࠴ࡉࠍߌߚࡃࠬࠤ࠶࠻ ࡂࡦ࠼࡞ߩᒻᑼ߇ࠅ㧘1 ᧄߩࠕ࠴ࡉࠍߔࠆනᒏߩᒻ ᑼ߽ࠆޕᐔⴕᒏߩᒻᑼߪ㧞ਛߩࠕ࠴ࡉߩ㕙ౝᢳ ⷺ㧔ǰ㧕߇ 90qߦ⋧ᒰߒ㧘90qએᄖߪࡃࠬࠤ࠶࠻ࡂࡦ࠼࡞ ᒻᑼߣߥࠆޕ࿑ 4 ߦోᯅߩᒻᑼߩഀวࠍ␜ߔ߇㧘ඨᢙ ߇ࡃࠬࠤ࠶࠻ࡂࡦ࠼࡞ᒻᑼࠍណ↪ߒߡࠆߎߣ߇ಽ߆ࠆޕ ߹ߚ㧘࿑3 ߣ࿑ 4 ࠃࠅ㧘ฦ⒳ߩᒻᑼߦㆡ↪ᓘ㑆ࠍ⺞ߴߡ ߺࠆߣ㧘ߤߩᓘ㑆㐳ߢ߽ࡃࠬࠤ࠶࠻ࡂࡦ࠼࡞ᒻᑼ߇ណ↪ߐ ࠇߡ߅ࠅ㧘ࡃࠬࠤ࠶࠻ࡂࡦ࠼࡞ᒻᑼߩㆡ↪㒢⇇㧔ᦨᄢᓘ㑆 㐳㧕ߪήࠃ߁ߢࠆޕ (3)ᓘ㑆㐳ߣࠗ࠭ߣߩ㑐ଥ ࿑5 ߦߪᓘ㑆㐳(L)ߣࠗ࠭(f)ߣߩ㑐ଥࠍ␜ߒ㧘࿑ 6 ߦᓘ 㑆㐳ߣࠗ࠭Ყ(f/L)ߣߩ㑐ଥࠍ␜ߔޕߎߎߢߩࠗ࠭Ყߣ ߪ㧘ࠗ࠭㧔f㧕ࠍᓘ㑆㐳㧔L㧕ߢ㒰ߒߚ୯ߢࠆޕ ࿑㧡ࠃࠅ㧘ᓘ㑆㐳߇㐳ߊߥࠆߦߟࠇߡࠗ࠭(f)ߪ㜞ߊߥ ߞߡࠆߎߣ߇ಽ߆ࠆޕ࿑ਛߩᑼߪᦨዊੑਸ਼ᴺࠍ↪ߡ 1 ᰴᑼߢቯᑼൻߒߚᑼߢࠆ߇㧘߶߷⋥✢ㄭૃ᧪ߡࠆޕ ߹ߚ࿑6 ࠃࠅ㧘߶ߣࠎߤߩᯅ߇ 2 ߦ␜ߔࠗ࠭Ყߩ㑆 ߢᑪ⸳ߐࠇߡࠆߎߣ߇ಽ߆ࠆޕࡃࠬࠤ࠶࠻ࡂࡦ࠼࡞ᒻᑼ
1 ᬞᯅߩ⻉ర 㧔Table 1 Spec of Tsubaki Bridge㧕
ᯅ ⒳ ࠾࡞ࡦᯅ㧔ਛ〝㧕 ࠕ࠴ࡉ㑆㓒 11 m
ᯅ 㐳 104 m ࠕ ࠴ ࠗ ࠭ 18 m
ᓘ 㑆 㐳 99 m ᮮ ᭴ ᧄ ᢙ 8 ᧄ
ᐥ RC ᐥ ࠕ࠴ࡉᢿ㕙 ▫ᒻᢿ㕙
ቢ Ꮏ ᐕ 1991 ᐕ ㍑ ᧚ ⠴ᕈ㍑
࿑1 ᬞᯅ㧔Fig1 Tsubaki Bridge㧕
৻⥸⊛ߥ࠾࡞ࡦࡠᯅߩኸᴺ⻉ర
㧔Table 2 General Spec of Nielsen-Lohse Bridge㧕
㗄 ⋡ ⻉ ర ࠕ࠴ࠬࡄࡦ㧔ᓘ㑆㐳㧘L㧕 260m એਅ ࠗ࠭ߣᓘ㑆㐳ߣߩᲧ㧔f/L㧕 1/5㨪1/8 ࠕ࠴ࡉߩ㕙ౝᢳⷺ㧔ǰ㧕 65q㨪90q ᐔဋᮮ❬߉᧚㑆㓒㧔d㧕 30m એਅ ᦨᄢᮮ❬߉᧚㑆㓒㧔dmax㧕 36m એਅ ࠤࡉ࡞㑆㓒㧔a㧕 5㨪13m ⒟ᐲ ษࠅ᧚ߩ㕙ౝᢳⷺ㧔Ǿ㧦৻ቯ㧕 60q⒟ᐲ ࿑3 ᑪ⸳ᢙߩផ⒖
(Fig 3 Trend of the Number of Construction)
࿑2 ৻⥸⊛ߥ࠾࡞ࡦࡠᯅߩ⸃ᨆࡕ࠺࡞
(Fig 2 General Nielse-Lohse Bridge Analysis Model) (a)㕙࿑
(b)ᐔ㕙࿑ (c)ᢿ㕙࿑
Basket-Handle Arch
Parallel Arch Single Arch
࿑4 ᭴ㅧᒻᑼߩഀว㧔Fig 4 Arch Type㧕 P
Research Reports of Kumamoto-NCT. Vol. 4 （2012） ࠾࡞ࡦࡠᯅߩ᭴ㅧ․ᕈ㧔ጤဝⷐ㧕 ߣᐔⴕᒏᒻᑼߣߩᲧセߢ߽ᄢ߈ߥᏅߪฃߌࠄࠇߥޕߎ ࠇࠄߩ⚿ᨐࠃࠅ㧘ᑪ⸳ߐࠇߚ࠾࡞ࡦᒻᑼߩᄙߊߪ㧘2 ߦ␜ߔ▸࿐ߢᑪ⸳ߐࠇߡ߅ࠅ㧘ߘࠇ߹ߢߩᑪ⸳ࠍෳ⠨ ߦኸᴺ߇ቯߐࠇߡࠆߎߣ߇ផ᷹᧪ࠆޕ (4)ᓘ㑆㐳ߣࠗ࠭ߣߩ㑐ଥ ᰴߦࡃࠬࠤ࠶࠻ࡂࡦ࠼࡞ᒻᑼߩᯅߦߟߡ㧘ࠕ࠴ ࡉߩᢳⷺߦߟߡᢛℂߒߚ⚿ᨐࠍ␜ߔޕࡃࠬࠤ࠶࠻ࡂࡦ ࠼࡞ᒻᑼߢߪ㧘ࠕ࠴ࡉ㑆㓒(B)ߣᓘ㑆㐳(L)㧘ࠕ࠴ࠗ ࠭(f)ߦࠃߞߡᢳⷺ(ǰ)߇ቯߐࠇࠆޕ࿑ 7 ߦᓘ㑆㐳ߣᢳ ⷺߣߩ㑐ଥ࿑ࠍ␜ߒ㧘࿑ 8 ߦࠕ࠴ࡉ㑆㓒ߣᢳⷺߣߩ 㑐ଥࠍ␜ߔޕ࿑ਛߩ⎕✢ߪ 2 ߦ␜ߔᢳⷺߩਅ㒢୯ߢ ࠆ65qࠍ␜ߒ㧘৻ὐ㎮✢ߪᐔဋᢳⷺࠍ␜ߒߡࠆޕ ࿑7 ࠃࠅ߶ߣࠎߤߩᯅ߇ 65qએߩᢳⷺࠍߒߡ ࠆߎߣ߇ࠊ߆ࠅ㧘ᓘ㑆㐳߇㐳ߊߡ߽ࠗ࠭ࠍ㜞ߊߔࠆߎߣ ߦࠃߞߡ㧘ᢳⷺࠍ65qએߦ⚊ߡࠆޕ߹ߚ࿑ 8 ࠃࠅ㧘 ࠕ࠴ࡉ㑆㓒߇ᐢ߶ߤ߈߇ᄢ߈ߊߥߞߡࠆะ߇ ࠆޕࠕ࠴ࡉߩᢳⷺ߇ዊߐߊߥࠆߣ㧘ࠕ࠴ࡉߩ ၮㇱઃㄭߩㇱ᧚ജߦᓇ㗀ࠍਈ߃ࠆߣ⠨߃ࠄࠇࠆߚ㧘ၮㇱ ઃㄭߩᢿ㕙⸳⸘߇㊀ⷐߦߥࠆߣ⠨߃ࠄࠇࠆޕ 3.3 ᶏᄖߩ ࿑㧥ߪࠬࡍࠗࡦߩࡄ࡞ࡑ࠺࡞ࠝᯅߢࠆ(10),(11)ޕᓘ 㑆㐳ߪ130m ߢࠗ࠭ߪ 25m ߢࠅ㧘ࠕ࠴ࡉߦߪᦨᄢ ෘ50mm ߩ㍑▤ࠍ↪ߒߡࠆޕࠕ࠴ࡉߩᢳⷺ㧔ǰ㧕 ߪ 78.8qߢࠅ㧘ߎࠇ߹ߢߩᣣᧄߢߩታ❣ߣߪᄢ߈ߥᏅߪ ήޕߒ߆ߒߥ߇ࠄᧄᯅߩ․ᓽߣߒߡ㧘ࡃࠬࠤ࠶࠻ࡂࡦ࠼ ࡞ᒻᑼߢࠕ࠴ࡉ㑆ߦK ࠻ࠬߩᮮ❬߉᧚ࠍലᨐ⊛ߦ ㈩⟎ߒ㕙ᄖᐳዮ߳ߩኻ╷ࠍⴕߞߡࠆޕߘߩ⚿ᨐ㧘㐽ᢿ㕙 ߢࠆ㍑▤ߩᢿ㕙․ᕈߣวࠊߐࠅ㧘㕖Ᏹߦࠬࡦ࠳ߥᯅ ߣߥߞߡࠆޕ ࿑10 ߪࠗࡦᎹߦដ߆ࠆ Tri-Countries Bridge ߢࠆ(12)ޕ ᧄᯅߪᱠᯅߢࠆ߇㧘ᓘ㑆㐳 229.4m ߦኻߒߡࠗ࠭ߪ 23m ߣᚳᐔߥ࠾࡞ࡦᒻᑼࠍណ↪ߒߡࠆޕᧄᯅߩฬ೨ ߩ↱᧪ߪ࠼ࠗ࠷㧘ࡈࡦࠬ㧘ࠬࠗࠬߦ߹ߚ߇ࠆᯅߦࠃࠆޕ ᭴ㅧߩ․ᓽߣߒߡ㧘ർߪ㧞ᧄߩ㧢ⷺᒻ▫ᒻᢿ㕙ㇱ᧚ࠍ 0 0.05 0.1 0.15 0.2 0.25 0.3 0 50 100 150 200 250 300 350 400 Arch Span (m) Single Arch Prarel Arch Basket-Handle f/L=1/5 f/L=1/8 Table 2 Arch Rise Ra o (f/L) ࿑6 ᓘ㑆㐳ߣࠗ࠭Ყߩ㑐ଥ
㧔Fig 6 Relation of Arch Span and Arch Rise Ratio㧕
50 55 60 65 70 75 80 85 90 0 50 100 150 200 250 300 350 Arch Span L (m) 䉝䊷䉼䊥䊑ᢳⷺ㩷θ䋨ᐲ䋩 Average Line θ=75.98° θ=65° Table 2 ࿑7 ᓘ㑆㐳ߣࠕ࠴ࡉᢳⷺߩ㑐ଥ
㧔Fig 7 Relation of Arch Span and Inclination Angle㧕
࿑8 ࠕ࠴ࡉ㑆㓒ߣࠕ࠴ࡉᢳⷺߩ㑐ଥ
㧔Fig 8 Relation of Interval of Arch Rib and Inclination Angle㧕
࿑9 ࡄ࡞ࡑ࠺࡞ࠝᯅ㧔ࠬࡍࠗࡦ㧕(10),(11)
㧔Fig 9 Palma del Rio Bridge (Spain)㧕
࿑10 Tri-Countries Bridge㧔࠼ࠗ࠷㧘ࡈࡦࠬ㧘ࠬࠗࠬ㧕(12)
㧔Fig 10 Tri-Countries Bridge (Germany, France, Switzerland)㧕
࿑5 ᓘ㑆㐳ߣࠗ࠭ߩ㑐ଥ
㧔Fig 5 Relation of Arch Span and Arch Rise㧕
熊本高等専門学校 研究紀要 第 4 号（2012） ਗߴߡု⋥ߥࠕ࠴ࡉࠍᒻᚑߒ㧘ධߪ㍑▤ࠍ↪ߒߡ ࡃࠬࠤ࠶࠻ࡂࡦ࠼࡞ߦㄭᒻ⁁ࠍߒߡࠆޕ 㧠. ߹ߣߣᓟߩᬌ⸛⺖㗴 4.1 ߹ߣ ᣢᓔߩ⎇ⓥᢥ₂ࠍᢥ₂(13)ߩᢥ₂ᬌ⚝࠺࠲ࡌࠬࠍ↪ ߡ⺞ߴߡߺߚߣߎࠈ㧘ᧁቇળߦ㑐ଥߔࠆ⊒ߣߒߡߪ 43 ઙߩᢥ₂߇ᬌ⚝ߐࠇ㧘ߘߩઁߩቇදળ߽ࠆߣ 60 ઙߩ ᢥ₂߇ᬌ⚝ߐࠇߚޕ⚦ߪ⋭⇛ߔࠆ߇㧘ߘߩඨᢙㄭߊ߇ࠤ ࡉ࡞㧔ษࠅ᧚㧕ߩᒛജߦ㑐ߔࠆౝኈߣ㧘ታᯅߩᣉᎿႎ๔ ߢߞߚޕᲧセ⊛ᱧผ߇ᵻᯅᒻᑼߢࠆߚ㧘ߎߩࠃ ߁ߥะ߇㗼⪺ߦߥߞߚ߽ߩߣផኤߢ߈ࠆ߇㧘ᯅߩ⠴⩄ ജߦ㑐ߔࠆ⎇ⓥ߇ዋߥߎߣ߇ಽ߆ߞߚޕ․ߦ㔡ᤨߩേ ⊛േߦߟߡ⺞ߴߚ⎇ⓥߪ߆ߢߞߚޕએߩ⚿ᨐࠃ ࠅ㧘ߎࠇ߹ߢߩᑪ⸳ታ❣ߩ࠺࠲ಽᨆߣᢥ₂ᬌ⚝ࠍㅢߓߡ ್ߒߚߎߣࠍⷐ⚂ߔࠆߣᰴߩࠃ߁ߦߥࠆޕ 1) ߎࠇ߹ߢߩᑪ⸳ታ❣ߢߪ㧘 2 ߦ␜ߔ৻⥸⊛ߥ࠾࡞ ࡦᒻᑼߣߒߡㆡ↪ߢ߈ࠆኸᴺߢᑪ⸳ߐࠇߡࠆޕ 2) ᣂ⸳ߩᯅߢ߽ㆊߩᣉᎿታ❣ࠍෳ⠨ߦߒߡࠆ߽ߩ ߣ⠨߃ࠄࠇ㧘․ᱶߥᒻ⁁ߪዋߥޕ 3) ᓘ㑆㐳(L)߇㐳ߊߥࠆߦߟࠇߡࠗ࠭(f)߽㜞ߊߥࠆะ ߇ࠆ߇㧘ࠗ࠭Ყ(f/L)ߩ߫ࠄߟ߈ߪዋߥޕ 4) ࠕ࠴ࡉߩᢳⷺ(ǰ)ߪᓘ㑆㐳(L)ࠃࠅ߽ࠕ࠴ࡉ 㑆㓒(B)ߩᓇ㗀߇ᄢ߈ޕߚߛߒ㧘ࠕ࠴ࡉ㑆㓒ߪ㧘 〝ߩຬߦᏀฝߐࠇࠆߚ㧘ߎߩὐߪ᭴ㅧ⸘↹ߩᤨ ὐߢ⚂᧦ઙ߇ઃߊ߽ߩߣ⠨߃ࠄࠇࠆޕ 5) ࠾࡞ࡦᒻᑼߩ㊀ⷐߥⷐ⚛ߢࠆࠤࡉ࡞㧔ษࠅ᧚㧕 ߩᒛജߦ㑐ߔࠆᣉᎿታ❣ߩႎ๔ߦ㑐ߔࠆᢥ₂ߪᄙᢙ⊒ ߐࠇߡࠆޕ 6) ࠾࡞ࡦࡠᯅߩ⠴⩄ജ․ᕈ߿㔡ᤨേࠍ⺞ߴ ߚ⎇ⓥ⊒ߩᢥ₂ߪዋߥޕ 7) ᶏᄖߢߪࠕ࠴ߩ․ᕈߣษࠅ᧚ࠍലᨐ⊛ߦ↪ߒߡࠬ ࡦ࠳ߥᯅ߇ᑪ⸳ߐࠇߡࠆޕ 4.2 ᓟߩ⺖㗴 ߩᯅ⸳⸘ߪ㜞ᐲൻߒߡ߅ࠅ㧘ⶄ㔀ߥᄖ⊛↪㧔⩄ ㊀㧕ߦኻߔࠆᬌ⸛߇น⢻ߣߥߞߡ߈ߡࠆޕߐࠄߦ᧲੩ḧ ࠥ࠻ࡉ࠶ࠫߢណ↪ߐࠇߡࠆࠃ߁ߥ㜞ᒝᐲ㍑ߩ↪߇ น⢻ߣߥߞߡ߈ߡ߅ࠅ㧘᭴ㅧᒻᑼߩวℂൻ߇น⢻ߣߥࠅߟ ߟࠆޕߒ߆ߒߥ߇ࠄ㧘᧲ᣣᧄᄢ㔡ἴߩⵍἴࠍᢎ⸠ߣ ߒߡ㧘㔡ᤨേ߿ᯅߩ⚳ዪ⁁ᘒࠍᬌ⸽ߒߟߟ㧘ലᨐ⊛ ߥ⠴㔡ኻ╷ࠍⴕߞߡߊߴ߈ߢࠆޕߐࠄߦᣂߒ᭴ㅧᒻ ᑼߩ㐿⊒ߪ㧘ᣣᧄߩᯅᛛⴚߩ⊒ዷߩߚߦߪᔅⷐߢࠆޕ ࿁ขࠅߍߚ࠾࡞ࡦࡠᯅߪ㧘᭴ㅧㇱ᧚ࠍ㧟ᰴర ⊛ߦ㈩⟎ߒߡࠆὐߣ㧘ࠤࡉ࡞ࠍᵴ↪ߒߡࠆὐ߇․ᓽ ߢࠆޕߎࠇࠄߩ․ᓽࠍᵴ߆ߔߎߣߢ㧘⠴㔡ᕈ㧘⟤ⷰߦఝ ࠇ㧘ߐࠄߦวℂ⊛ߥ⸳⸘ߦၮߠߚᯅߩഃㅧ߇น⢻ߦߥ ࠆߣ⠨߃ࠄࠇࠆޕߐࠄߦࠤࡉ࡞ࠍ↪ߒߚᒝᣇᴺߪ㧘 㗴ߣߥߞߡࠆ⠧ൻߒߚᣢ⸳ᯅߩ࠾ࡘࠕ࡞ߥ ߤߦ߽ォ↪ߢ߈ࠆ߽ߩߣ⠨߃ߡࠆޕᓟߪߎߩὐߦ⌕⋡ ߒߥ߇ࠄ⎇ⓥࠍㆀⴕߔࠆ੍ቯߢࠆޕ 㧔ᐔᚑ24 ᐕ 9 25 ᣣฃઃ㧕 㧔ᐔᚑ24 ᐕ 10 25 ᣣฃℂ㧕 ෳ⠨ᢥ₂ (1) ᣣᧄ〝ᯅળ㧦ޟ〝ᯅ␜ᣇᦠ Τ㍑ᯅ✬ޠ (2012)㧚 (2) ේ↰ᒾ㧘᫃Ꮉᐽ↵㧘ᷓ↰ቿผ㧦ޟ30 ᐕࠍ⚻ㆊߒߚ࠾ ࡞ࡦࡠᯅߩ⺞ᩏޠ㧘ᧁቇળ╙ 57 ࿁ᐕᰴቇ ⴚ⻠Ṷળ╙1 ㇱ㧘Vol.57㧘Σ-290㧘pp.579-580 (2002)㧚 (3) ർ↰ବⴕ㧘ਛඳ㧘ศᎹ♿㧘㒋㊁㓷ೣ㧦ޟ࠾࡞ࡦ ࡠᯅࠕ࠴ࡉߩᐳዮߦኻߔࠆวℂ⊛⸳⸘ᴺߦ ߟߡޠ㧘᭴ㅧᎿቇ⺰ᢥ㓸㧘Vol.34A㧘pp.315-326 (1988)㧚 (4) 㒋㊁㓷ೣ㧘ർ↰ବⴕ㧘㠽㊁ᤩ〈㧦ޟ࠾࡞ࡦࡠ ᯅߩജቇ․ᕈߣߘߩ⠴⩄ജޠ㧘᭴ㅧᎿቇ⺰ᢥ㓸㧘 Vol.49A㧘pp.93-104 (2003)㧚 (5) ᣣ ᧄ ᯅ ᑪ ⸳ ද ળ 㧦ޟ ᯅ ᐕ 㐓 ࠺ ࠲ ࡌ ࠬ ޠ 㧔http://www.jasbc.or.jp/kyoryodb/index.cgi㧕㧚 (6) ᧁቇળ㧦ޟᐳዮ⸳⸘ࠟࠗ࠼ࠗࡦ[2005 ᐕ ]ޠ㧘 pp.320-327 (2005)㧚 (7) ਛඳ㧦ޟ㍑วᚑᯅߩㅴᱠࠍᡰ߃ࠆ⻉ᛛⴚޠ㧘ጊ ᶏၴ㧘pp.165-180 (1999)㧚 (8) ⊛႐ᱞᢥ㧘᪀၂⺈㧘ጟᷡᔒ㧘▤৻㧦ޟ╙㧞㖸ᚭᄢ ᯅߩᣉᎿޠ㧘ᯅߣၮ␆㧘Vol.46㧘No.1㧘pp.11-16 (2012)㧚 (9) ⮮Ỉᖗ㧘⧃ේᩕᴦ㧘ᮮጊື㧘ਛᤋม㧦ޟᣂᧁᵤᎹ ᄢᯅߩታᯅタ⩄⹜㛎ޠ㧘ᧁቇળ╙ 51 ࿁ᐕᰴቇⴚ⻠ Ṷળ╙1 ㇱ(A)㧘Vol.51㧘A342㧘pp.684-685 (1996)㧚
(10) Francisco Millanes, Miguel Ortega, Antonio Carnerero : “Palma del Río Arch Bridge, Córdoba, Spain”, Structural Engineering International, Vol.20, No.3 pp.338-342 (2010)㧚
(11) ᯅߣၮ␆ ᶏᄖᢥ₂ࠣ࡞ࡊ㧦ޟࠬࡍࠗࡦߩࡄ࡞
ࡑ࠺࡞ࠝᯅߩ⸳⸘ᣉᎿޠ㧘ᯅߣၮ␆㧘Vol.46㧘
No.9㧘pp.42-43 (2012)㧚
(12) Uwe Häberle : “Tri-Counties Bridge between Weil am Rhein, Germany and Hüningen, France”, Structural Engineering International, Vol.20, No.3 pp.321-324 (2010)㧚
(13) ᧁ ቇ ળ 㧦ޟ ᚲ⬿ ᢥ ₂ ᦠ ᬌ ⚝ ࠺ ࠲ ࡌ ࠬ ޠ 㧔http://www.jsce.or.jp/㧕㧚
(14) Per Tveit : “An Introduction to the Optimal Netwok Arch”, Structural Engineering International, Vol.17, No.2 pp.184-187 (2007)㧚 (15) ↰ਛసᒄ㧘ർ↰ବⴕ㧦ޟᒢ႟ᕈ㒢ᄌ⸃ᨆߦࠃࠆ࠾ ࡞ࡦࡠᯅ߅ࠃ߮ᢳᒛᯅߩ⠴⩄ജᾖᩏᴺߦ ߟߡޠ㧘㍑᭴ㅧ⺰ᢥ㓸㧘Vol.8㧘No.30㧘pp.39-49 (2001)㧚 (16) ർ↰ବⴕ㧘ਛඳ㧘⍹ፒᶈ㧘ᳯญᘕ㧦ޟ㍑࠾࡞ ࡦࡠᯅ㧘߅ࠃ߮ࡔࡦ㍑ᯅ⣉ߩ㒢⇇⁁ᘒߦ 㑐ߔࠆၮ␆⊛⎇ⓥޠ㧘᭴ㅧᎿቇ⺰ᢥ㓸㧘Vol.42A㧘 pp.91-98 (1995)㧚 (17) ᪢↰⡡㧘⏷ᳯᥙ㧘ᷰㄝ㧘㒋↰ᄢ⬿㧦ޟ࠾࡞ࡦ ᯅߩᢳ᧚ᒛജ⺞ᢛߦߟߡޠ㧘ᧁቇળ╙ 46 ࿁ᐕᰴ ቇⴚ⻠Ṷળ╙1 ㇱ㧘Vol.46㧘Σ-335㧘pp.708-709 (1991)㧚 (18) ㊁ᵏᅤ㧦ޟᣢ⸳ᯅ〝ᑼࠕ࠴ᯅߦ߅ߌࠆ᭴ㅧࡄ ࡔ࠲ߩ⺞ᩏޠ㧘ᧁቇળ⺰ᢥ㓸 A1㧔᭴ㅧ㔡Ꮏ ቇ㧕㧘Vol.67㧘No.2㧘pp.320-325 (2011)㧚
