せ⣙ ࠉ๓ሗࡑࡢ 1 ࡛ࡣ 㕲➽ࢥࣥࢡ࣮ࣜࢺ༊㛫㕲㦵༊㛫ࡢቃ⏺㓄ࡉࢀ㕲㦵㒊ᮦ⁐᥋ࡉࢀࡓ㗰〇ࣉ࣮ࣞࢺࢆ᭷ࡍ ࡿᇙ㎸ࡳᙧᘧࡢ」ྜᱱࡘ࠸࡚ ᙎᛶᇦ࠾ࡅࡿ㒊ᮦ๛ᛶࡢホ౯ࣔࢹࣝࡢᐃᘧࢆ⾜࠸ ࣔࢹࣝࡀ࠼ࡿホ౯್ ࡢᛶ㉁ࡢ⢭ᰝࢆヨࡳࡓࠋᮏሗࡑࡢ 2 ࡛ࡣ ྠࡌホ౯ࣔࢹࣝࡢホ౯ᑐ㇟ࢆ㠀ᙎᛶᇦࡲ࡛ᣑᙇࡋ࡚๓ሗྠᵝࡢࣃࣛ ࣓ࢺࣜࢵࢡ࣭ࢫࢱࢹࢆ⾜࠺ࡇ࡛ ᮏ」ྜᱱࡢ㒊ᮦ๛ᛶࡢ㠀ᙎᛶᇦ࠾ࡅࡿᛶ㉁ࡶ᳨ウࡀຍ࠼ࡽࢀ࡚࠸ࡿࠋ ࠉࡣࡌࡵ ࠉࡑࡢ 2 ࡛ࡣ ࡑࡢ 1 1)࡛ᙎᛶᇦࡘ࠸࡚ゐࢀࡽࢀࡓホ ౯ࣔࢹࣝ㛵ࡋ ࡑࡢ㠀ᙎᛶᇦࡢホ౯᪉ἲࡢᐃᘧ࠾ ࡼࡧᛶ㉁ࡢ⢭ᰝࢆヨࡳࡿࠋ 㸬ホ౯ࣔࢹࣝࡢ㠀ᙎᛶᙧᇦ࠾ࡅࡿᐃᘧࡑࡢᛶ㉁ ࠉ㠀ᙎᛶᇦ࠾ࡅࡿ㒊ᮦ๛ᛶࡢホ౯ ࠉホ౯ࣔࢹࣝࡢ㠀ᙎᛶᇦ࠾ࡅࡿ㒊ᮦ๛ᛶࡣ, ྛᵓᡂせ ⣲ࡢࡑࢀࡒࢀ㠀⥺ᙧᛶࢆ࠼, ┦㔜ࡡྜࢃࡏࡿࡇ ࡛ホ౯ࡍࡿࠋࡍ࡞ࢃࡕ, ࡲࡎ RC 㐀ᱱࡢ㒊ᮦ๛ᛶࡣ , ㏻ᖖࡢ RC 㐀ᱱྠᵝ , RC つ‽ 2)‽ࡌࡓࢺࣜࣜࢽ ᆺࡢపୗࢆ࿊ࡍࡿࡶࡢࡍࡿࠋࡇࢀࡣ, ᅗ 1 ( b ) ୰ࡢ ᭤ࡆࡦࡧࢀ࣮࣓ࣔࣥࢺ rcMc , 㝆అ࣮࣓ࣔࣥࢺ rcMy , 㝆 అⅬ࠾ࡅࡿ๛ᛶపୗ⋡Dy ࢆ , ࠸ࡎࢀࡶ RC つ‽2)ࡀ ᐃࡵࡿḟᘧ ( 1 ) 㹼ᘧ ( 3 ) ࡼࡗ࡚ồࡵࡽࢀࡿࡇࢆព ࡍࡿࠋ ࠉࡇࡇ, c VB ࡣࢥࣥࢡ࣮ࣜࢺࡢᮦᩱᙉᗘ , rcZe ࡣ᭷➽ࡢ ሙྜࡢ᩿㠃ಀᩘ2), a t ࡣᘬᙇ㕲➽ࡢ᩿㠃✚ , r Vy ࡣ㕲➽ࡢ 㺕㺎㺺㺎㺢㺼 ᇙ㎸ࡳᙧᘧࡢ」ྜᱱ, 㒊ᮦ๛ᛶ , 㦵᱁᭤⥺ , ࢺࣜࣜࢽࣔࢹࣝ ┠ḟ 1. ࡣࡌࡵ 2. ホ౯ࣔࢹࣝࡢ㠀ᙎᛶᇦ࠾ࡅࡿᐃᘧࡑࡢᛶ㉁ 3. ࡲࡵ 㝆అᙉᗘ, rcd ࡣ RC ༊㛫ࡢ᭷ຠࡏ࠸ , n ࡣ㕲➽ࢥࣥࢡ ࣮ࣜࢺࡢᮦᩱ๛ᛶẚ, pt ࡣ RC ༊㛫ࡢᘬᙇ㕲➽ẚ , rcD ࡣ RC ༊㛫ࡢᱱࡏ࠸࡛࠶ࡿࠋ࡞࠾㝆అⅬ࠾ࡅࡿ๛ᛶపୗ ⋡ Dy ࢆồࡵࡿᘧ ( 3 ) ୰ࡢࢩࢫࣃࣥ a ࡘ࠸࡚ࡣ , RC ༊㛫ࡢ㛗ࡉrcl ࡀࡇࡢ a ┦ᙜࡍࡿࡇࡍࡿ3)ࠋࡲࡓࡇ ࡢ๛ᛶపୗ⋡ Dy ࡘ࠸࡚ࡣࡉࡽ , ᘧ ( 3 ) ࡢ㐺⏝⠊ᅖ ࡋ࡚ࠕࢩࢫࣃࣥẚ 2.0 㹼 5.0 ࠖࡀ RC つ‽࡚ᐃࡵࡽ ࢀ࡚࠸ࡿ2)ࡀ, ᮏㄽᩥ࡛ࡣ㐣ཤࡢ᳨ウ⤖ᯝ4)ࢆᫎࡉࡏ, ࢩࢫࣃࣥẚࡢ್ࡢᑠࢆၥࢃࡎᘧ ( 3 ) ࢆ᥇⏝ࡍࡿࠋ ࠉࡲࡓ᭤ࡆࣂࢿࡣ, ᅗ 1 ( c ) ࡀ⾲⌧ࡍࡿࡼ࠺ RC 㐀ᱱ ྠᵝࡢࢺࣜࣜࢽᆺࡢ㠀ᙎᛶᛶࢆ♧ࡍࡶࡢࡍࡿࠋࡇ ࢀࡣ, ࡑࡢ 11) ࡛ᐃ⩏ࡋࡓ㏻ࡾ , ࡇࡢኚᙧᡂศࡀ RC ༊㛫 㰯ඛ࠾ࡅࡿ S 㒊ᮦࡢ๛యᅇ㌿ゅẚࡋ , ࡘࡑࡢ ๛యᅇ㌿ゅࡀ RC ༊㛫ࡢኚᙧࡢ㐃⥆᮲௳ࢆ㉳Ⅼồ ࡵࡽࢀ࡚࠸ࡿࡓࡵ࡛࠶ࡿࠋࡍ࡞ࢃࡕᅗ 1 ( c ) ࡣ , ⮬⏤➃ స⏝ࡍࡿࡏࢇ᩿ຊ Q S 㒊ᮦࡢ๛యᅇ㌿ࡼࡿኚᙧ ┦ᙜࡍࡿ s Gr ࡀ , RC 㐀ᱱࡢ๛ᛶపୗྠᮇࡋ࡚ᣲື ࡍࡿࡼ࠺ᥥࢀࡓࠕ࣮࣓ࣔࣥࢺ㒊ᮦኚᙧゅࡢ㛵ಀࠖ ࡛࠶ࡾ, RC 㐀ᱱࡢ᭤ࡆࡦࡧࢀ࣮࣓ࣔࣥࢺ࠾ࡼࡧ㝆అ ࣮࣓ࣔࣥࢺᑐᛂࡍࡿⅬࡀ, ࡑࢀࡒࢀ rcMc ࠾ࡼࡧ rcMy ( s ln / l ) ࢆࡌࡿࡇ࡛ᚓࡽࢀ࡚࠸ࡿࠋ ࠉ࡞࠾ S 㐀ᱱࡢ㠀ᙎᛶᇦࡘ࠸࡚ࡣ , ᅗ 1 ( d ) ♧ࡍ㏻ ࡾ, ㏻ᖖࡢ S 㐀ᱱఱࡽኚࢃࡿࡇ࡞ࡃ , 㝆అ࣮࣓ࣔࣥ U.D.C 624. 012. 016 : 624. 042. 2
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ࠉᑠ⃝ࠉ₶
ࠉ୰⏣ࠉᐶ
rcMc= 0.56√cσB×rcZe rcMy= 0.9 at rσy rcd αy= 0.043 + 1.64 n pt+ 0.043 a rcD rcd rcD 2 ᅗ㸯ࠉホ౯ࣔࢹࣝࡑࡢᵓᡂせ⣲ࡢ㠀ᙎᛶᇦ࠾ࡅࡿᣲື ( b )RC 㐀ᱱ ( c )᭤ࡆࣂࢿ ( a )ホ౯ࣔࢹࣝ l r S s RC ༊㛫➃䛻స⏝䛩䜛 ᭤䛢䝰䞊䝯䞁䝖 㒊ᮦኚᙧゅ D RC ༊㛫㰯ඛ䛻స⏝䛩䜛 ᭤䛢䝰䞊䝯䞁䝖 㒊ᮦኚᙧゅ D S rc S rc My Mc rc rc R rc s rR l l s n n DyrcS r S s Dy r S s RC ༊㛫➃䛻స⏝䛩䜛 ᭤䛢䝰䞊䝯䞁䝖 㒊ᮦኚᙧゅ M My Mc fa R S S' = Mfa Mno 䕰 Qy rc 䕰 Qy rc l s ln sl D' S 㒊ᮦኚᙧゅ Mp s My s RC ༊㛫㰯ඛ䛻స⏝䛩䜛 ᭤䛢䝰䞊䝯䞁䝖 Mno e S s 䕰rcQy R s e 䕰rcQu ( d )S 㐀ᱱ ( 1 ) ( 2 ) ( 3 )ࢺረᛶ࣮࣓ࣔࣥࢺ࡛㒊ᮦ๛ᛶࢆኚࡉࡏࡿ㦵᱁᭤ ⥺ࡋ࡚ࣔࢹ࡛ࣝࡁࡿࡇࡍࡿࠋ ࠉ㠀ᙎᛶᇦ࠾ࡅࡿᮏホ౯ࣔࢹࣝࡢᛶ㉁ ࠉᮏ」ྜᱱࡼࡗ࡚ᵓ⠏ࡉࢀࡿᯫᵓࡢ㸰ḟタィࢆ⾜࠺ ሙྜ ᙜヱᯫᵓࢆᵓᡂࡍࡿྛ㒊ᮦࡢ᳨ウࡣ ࡑࢀࡒࢀ ࡀᙎᛶᇦࢆ㉸࠼ࡓ㠀ᙎᛶᇦ࡛ᣲືࡍࡿࡇࢆ๓ᥦᐇ ࡉࢀࡿࠋࡇࡢ㐣⛬࠾࠸࡚ ᅗ 1 ࡢࡼ࠺⾲⌧ࡉࢀ ࡿᮏホ౯ࣔࢹࣝࡢᵓᡂせ⣲ࡢኚᙧࡢ࠺ࡕ RC 㐀ᱱࡢࡑ ࢀ㛵ࡋ࡚ࡣࡼࡾៅ㔜࡞⌮ゎࡀᚲせ࡞ࡿࠋ ࠉࡇࡢᵓᡂせ⣲ࡣ ࠕ୍㒊࠶ࡿ࠸ࡣ㒊 S 㒊ᮦࡀᇙ ㎸ࡲࢀࡓ RC ༊㛫ࠖࢆᢳ㇟ࡋࡓࡶࡢ࡛࠶ࡿࡓࡵ ᙜ ヱ㒊ࡢタィ࠶ࡗ࡚ࡣ ࠕ RC S 㒊ᮦࡀᇙ㎸ࡲࢀ࡚ ࠸ࡿᙳ㡪ࠖࢆ㐺ษᫎࡉࡏࡓ᳨ウࡀồࡵࡽࢀࡿ5)ࠋ ᪤ከࡃࡢሗ࿌ࡀⅭࡉࢀ࡚࠸ࡿࡼ࠺ ࡇࡢ࠺ࡕ≉ RC ࡣ S 㒊ᮦࡀᇙ㎸ࡲࢀࡿࡇࡢᙳ㡪ࡀࡏࢇ᩿ᙉᗘ ࡲ࡛ཬࡪࡉࢀࡇࢀࡲ࡛ࡶάⓎ࡞㆟ㄽࡀ㔜ࡡࡽࢀ࡚ ࠾ࡾࡓ࠼ࡤ6),7) 㕲➽ࢥࣥࢡ࣮ࣜࢺ㐀ᘓ≀ࡢ㠎ᛶಖドᆺ⪏ 㟈タィᣦ㔪࣭ྠゎㄝᘧ8)㸦௨ᚋ ࠕ㠌ᛶᣦ㔪ᘧࠖ␎グ㸧 ࢆಟṇࡍࡿࣉ࣮ࣟࢳࡀ✀ࠎᥦࡉࢀ࡚࠸ࡿࠋ ࠉࠕ RC 㐀ᱱࡢኚᙧ ࡼࡾៅ㔜࡞⌮ゎࡀᚲせ࡞ࡿࠖ ᡤ௨ࡣ ࡇࡢࡼ࠺⏝ࡉࢀࡿ㠌ᛶᣦ㔪ᘧࡀ ᅗ 2 ࡢࡼ ࠺࡞ᴫᛕ࡛ࠕ᭤ࡆ㝆అᚋࡏࢇ᩿◚ቯࠖࢆ⾲⌧ࡋ࡚࠸ࡿⅬ ࠶ࡿࠋࡇࡢࡏࢇ᩿タィἲ࡛ࡣ ᭤ࡆ㝆అᚋࡢረᛶኚᙧ ࡢ㐍ᒎక࠺ࡏࢇ᩿ᙉᗘࡢపୗࡀረᛶࣄࣥࢪࡢᅇ㌿ゅࡢ 㛵ᩘࡉࢀ࡚࠸ࡿ8)ࠋ ࠉᮏ」ྜᱱࡀࠕ S 㒊ᮦඛࢇࡌ࡚ RC ༊㛫➃࡚᭤ࡆ 㝆అࡍࡿࠖሙྜ RC ࡢࡏࢇ᩿タィࡇࡢᙳ㡪ࢆᫎࡉ ࡏ ᭤ࡆ㝆అᚋࡢࡏࢇ᩿ᙉᗘࡢపୗࢆṇࡋࡃ⪃៖ࡋ࡞ ࡅࢀࡤ࡞ࡽ࡞࠸ࡇࡣゝ࠺ࡲ࡛ࡶ࡞࠸ࠋࡑࡋ࡚ࡑࡢ㝿 ࡢᅗ 1 ୰ࡢረᛶኚᙧ⬟ຊ rc Rp ࡣ ࠕ」ྜᱱయࡢ㒊ᮦኚ ᙧゅ R ࡛ࠖࡣ࡞ࡃࠕ᭤ࡆ㝆అᚋࡢ RC ༊㛫ࡢ㒊ᮦኚᙧ ゅrc R ࠖࢆᇶㄪ⟬ᐃࡍࡁ⪃࠼ࡿࡢࡀ⮬↛࡛࠶ࡿࠋ ࠉ୍᪉ᐇົୖࡣ ࡓ࠼ࡤᯫᵓタィ࠶ࡗ࡚ 㒊ᮦࡢ ┠ᶆᵓ㐀ᛶ⬟10)ࡀࠕ」ྜᱱయࡢረᛶኚᙧ⬟ຊࠖࡋ ࡚タᐃࡉࢀࡿࡇࡶᐃࡍࡁ࡛࠶ࡾ ࡇࡢሙྜ ࠕ」 ྜᱱయࡢ㒊ᮦኚᙧゅ R RC ༊㛫ࡢ㒊ᮦኚᙧゅ rc R ࡢ㛵ಀࠖᇶ࡙࠸ࡓ㆟ㄽࡀᮃࡲࢀࡿࡇ࡞ࡿࠋ ࠉ௨ୖࡼࡾࡇࡇ࡛ࡣ ᮏ」ྜᱱࡢ㸰ḟタィ ≉ࡏࢇ ᩿◚ቯࡢ᳨ウ㝿ࡋ࡚ࡢᡂ⇍ࡋࡓ㆟ㄽࡢᐇ⌧ࢆ┠ⓗ ᮏホ౯ࣔࢹࣝࡀ࠼ࡿ㠀ᙎᛶᇦࡢኚᙧࡘ࠸࡚ ࣔࢹࣝ యྛᵓᡂせ⣲ࡢ┦㛵ಀ㛵ࡍࡿ᳨ウࢆ⾜࠺ࠋ ࠉ➨໙㓄༊㛫࠾ࡅࡿホ౯ࣔࢹࣝయࡢ㒊ᮦ๛ᛶ ࠉ๓ᥖᅗ 1 ࡣ ホ౯ࣔࢹࣝ RC 㐀ᱱ ᭤ࡆࣂࢿࡢ➨ ໙㓄༊㛫ࡢᵝ┦ࢆࡼࡾヲ⣽ᥥ࠸ࡓ࣮࣓ࣔࣥࢺ㸫㒊 ᮦኚᙧゅ㛵ಀ࡛࠶ࡿࠋࡇࡢᅗ 1 ୰ぢࡿ Dy ࡣ ᘧ ( 3 ) ♧ࡋࡓ㏻ࡾ RC つ‽2)ࡀᐃ⩏ࡍࡿ㝆అⅬ࠾ࡅࡿ๛ ᛶపୗ⋡࡛࠶ࡿࡀ ࡇࢀࡣඖ᮶ ➨໙㓄༊㛫ෆࡢ௵ ពࡢⅬࢆ ྠᵝࠕ㒊ᮦᙎᛶ๛ᛶ๛ᛶపୗ⋡ D ࢆ ࡌࡓ⥺๛ᛶࠖࡼࡗ࡚≉ᐃࡍࡿࡇࢆពᅗࡋ࡚ᑟධ ࡉࢀࡓಀᩘ࡛࠶ࡿ2)ࠋࡍ࡞ࢃࡕ RC 㐀ᱱࡢ㦵᱁᭤⥺ࢆ ♧ࡋࡓᅗ 1 ( b ) ࡛࠶ࢀࡤ ᭤ࡆ㝆అⅬ࠾ࡅࡿ⥺ ๛ᛶࢆ Dy rc S ➨໙㓄༊㛫ෆࡢ௵ពࡢⅬ࠾ࡅࡿ ⥺๛ᛶࢆD rc S ⾲⌧ࡋࡓሙྜࡢ Dy D ࡣ ᘧ ( 4 ) ࡼࡗ࡚㛵㐃ࡅࡽࢀࡿ2)ࠋ ࠉᮏホ౯ࣔࢹࣝ࠾࠸࡚ࡣ ๓グࡢࡼ࠺ࠕ RC 㐀ᱱ ᭤ࡆࣂࢿࡀ๛ᛶపୗ⋡ Dy ࢆඹ᭷ࡍࡿࠖࡢ௬ᐃࡀ タࡅࡽࢀ࡚࠸ࡿࡀ ࡇࡢ௬ᐃࡣྠ ࠕ RC 㐀ᱱ ᭤ࡆࣂࢿࡀ ➨໙㓄༊㛫ෆࡢ௵ពࡢⅬࢆᐃࡵࡿ๛ᛶ పୗ⋡ D ࡶඹ㏻ࡉࡏࡿࠖࡇࢆពࡍࡿ9)ࠋࡍ࡞ࢃࡕ ホ౯ࣔࢹࣝయࡀᅗ 1 ( a ) ୰ࡢࠐ༳♧ࡍࡼ࠺࡞ࠕ㦵 ᱁᭤⥺ୖࡢ➨໙㓄༊㛫ෆࡢ௵ពࡢⅬ┦ᙜࡍࡿࠖኚ ᙧ≧ែ࠶ࡿ ࡇࢀࢆᵓᡂࡍࡿ RC 㐀ᱱ᭤ࡆࣂࢿ ࡢኚᙧࡶࡑࢀࡒࢀࡢ㦵᱁᭤⥺ࡢ➨໙㓄༊㛫ෆࡢⅬ࡛ ≉ᐃࡉࢀࡿ≧ែ࠶ࡾ ࡘࡇࢀࡽⅬࡣ ᘧ ( 4 ) ࡼࡗ࡚࠼ࡽࢀࡿྠ୍ࡢ๛ᛶపୗ⋡ D ࢆྛࠎࡢ㒊ᮦ ᙎᛶ๛ᛶࡎࡿࡇ࡛ᐃࡵࡽࢀࡿ㛵ಀ࠶ࡿࠋࡋࡓ ࡀࡗ࡚ RC ༊㛫➃ࡢ᭤ࡆ㝆అࡀඛ⾜ࡍࡿሙྜ S 㐀 ᱱࡀ⤊ጞᙎᛶᣲືࢆಖࡘࡇࢆ⪃៖ࡍࡿ 」ྜᱱ యࡀᅗ 1 ( a ) ࡢࡼ࠺࡞➨໙㓄༊㛫ෆࡢ௵ពࡢኚᙧ≧ ែ࠶ࡿ㝿ࡢྛᵓᡂせ⣲ࡢᵓᡂ㛵ಀࡣ ᘧ ( 5 ) ࡋ࡚ ᩘᘧ⾲グ࡛ࡁࡿࡇ࡞ࡿࠋ ࠉᘧ ( 5 ) ࡼࡾ ホ౯ࣔࢹࣝయࡀ➨໙㓄༊㛫࠶ࡿ ሙྜࡢྛᵓᡂせ⣲ࡢኚᙧrc G s Gr s Ge ࡀồࡵࡽࢀࡿࡓ ࡵ ࡇࢀࢆྜ⟬ࡍࡿࡇ࡛ 㠀ᙎᛶᇦ࠾ࡅࡿయࡢ ࡓࢃࡳG ࡀᘧ ( 6 ) ࡋ࡚ᚓࡽࢀࡿࠋ ࠉD = 1 ࡢ ࡑࡢ 1 ࡛ᐃ⩏ࡋࡓ㒊ᮦᙎᛶࡓࢃࡳ୍⮴ ࡍࡿᘧ ( 6 ) ࡣ ᮏ」ྜᱱయࡢ⮬⏤➃ࡓࢃࡳࢆᙎᛶᇦ 㝈ᐃࡍࡿࡇ࡞ࡃ⾲⌧ࡍࡿ୍⯡ᘧ┦ᙜࡋ ࡉࡽ ྠᘧ ( 6 ) ࡋࡓ㏻ࡾ ࡇࡢ G ࢆࢩࢫࣃࣥ l ࡛㝖ࡍ ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ Mfa=αrcSrcR Mno=αsSr sRr Mno= sSe sRe ⇔ ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ rcR = Mfa αrcS= rcδ rcl sRr= Mno αsSr= Mfa αsSr sln l = sδr sln sRe= Mno sSe = Mfa sSe sln l = sδe sln δ =rcδ +sδr+sδe=Q lrcl αrcS + sln2 αsSr + sln2 sSe =R l 1 α= 1 + 1 αy− 1 1 − rcMc Mfa 1 −rcMc rcMy ᅗ㸰ࠉ㠌ᛶᣦ㔪࠾ࡅࡿࡏࢇ᩿◚ቯࣔࢹࣝ 㒊ᮦኚᙧゅ 䛫䜣᩿ᙉᗘ ረᛶኚᙧ⬟ຊ 䛫䜣᩿◚ቯ Ry rc rcRu Rp rc R rc Q 䛫䜣᩿ຊ ᭤䛢㝆అ ᭤䛢䜂䜃䜜 ( 4 ) ( 5 ) ( 6 )
1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ( - ) 1.0 0.8 0.6 0.4 0.2 ( - ) rc / s r / s e / slb / rcl = 0.69 rcl / l = 0.30 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ( - ) 1.0 0.8 0.6 0.4 0.2 ( - ) rc / s r / s e / slb / rcl = 0.80 rcl / l = 0.30 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ( - ) 1.0 0.8 0.6 0.4 0.2 ( - ) rc / s r / s e / slb / rcl = 0.92 rcl / l = 0.30 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ( - ) 1.0 0.8 0.6 0.4 0.2 ( - ) rc / s r / s e / slb / rcl = 1.00 rcl / l = 0.30 ࡇ࡛ 㒊ᮦኚᙧゅ R ࡶ୍⯡ᘧࡋ࡚ᐃ⩏࡛ࡁࡿࠋᅗ 1 ( a ) ୰ࡢ S' ࡣ 」ྜᱱయࡢ㦵᱁᭤⥺࠾࠸࡚ ᮦ ➃᭤ࡆ࣮࣓ࣔࣥࢺ Mfa యࡢ㒊ᮦኚᙧゅ R ࡛ᐃࡲࡿ ࠐ༳ࢆᣦࡋ♧ࡍ⥺๛ᛶ┦ᙜࡋ ࡇࢀࢆࠕホ౯ࣔࢹ ࣝయࡢ㒊ᮦᙎᛶ๛ᛶ S ๛ᛶపୗ⋡ D' ࢆࡌࡿࡇ ࡛ồࡵࡽࢀࡿࠖࡋࡓሙྜࡢ D' ࡣ ᘧ ( 7 ) ࡞ࡿࠋ ࠉD = 1 ࡢ D' ࡶ 1 ࡞ࡾ ホ౯ࣔࢹࣝయࡢ㒊ᮦ ๛ᛶࡣᙎᛶ๛ᛶ S 1) ୍⮴ࡍࡿࠋ ࠉࠉయኚᙧᵓᡂせ⣲ࡢኚᙧࡢ㛵ಀ ࠉᅗ 1 ( a ) ♧ࡋࡓᮏ」ྜᱱయࡢᵓᡂ㛵ಀࡣ ᘧ ( 7 ) ࡢ D' ࢆά⏝ࡋࡓ⥺๛ᛶࢆ⏝࠸ࡿࡇ࡛ ᘧ ( 8 ) ࡢࡼ ࠺ࡑࡢᙎᛶᇦࡽ㠀ᙎᛶᇦࡲ࡛ࡢᣲືࢆ㐃⥆ⓗ⾲ ⌧࡛ࡁࡿࠋ ࠉࡍ࡞ࢃࡕᘧ ( 8 ) ࡼࡗ࡚ ᮏ」ྜᱱࢆ㸯ᮏࡢ➼㉁ᮦ ゎ㔘ࡋ ホ౯ࣔࢹࣝࢆᵓ⠏ࡍࡿࡇ࡞ࡃ⡆᫆ ࡑ ࡢᮦ➃᭤ࡆ࣮࣓ࣔࣥࢺ Mfa ᑐࡍࡿᵓᡂ㛵ಀࢆ㠀ᙎᛶᇦ ࡲ࡛⾲⌧ࡍࡿࡇࡶ࡛ࡁࡿࠋ ࠉࡋࡋ࡞ࡀࡽᅗ 1 ( a ) ᅗ 1 ( b ) ࡢᑐẚࡽ᫂ࡽ࡞ ࡼ࠺ RC ༊㛫➃ࡢ㈇ᢸ᭤ࡆ࣮࣓ࣔࣥࢺ Mfa ᑐࡋ ホ౯ࣔࢹࣝయ RC 㐀ᱱࡢࡑࢀࡒࢀࡀ࠼ࡿኚᙧࡣ ୧⪅ࡢ㒊ᮦ๛ᛶࡀ␗࡞ࡿࡓࡵ୍⮴ࡍࡿࡇࡣ࡞࠸ࠋࡋ ࡓࡀࡗ࡚ ᮏ」ྜᱱࡢ㸰ḟタィ㝿ࡋ RC ࡢࡏࢇ᩿タ ィ๓ᥖᅗ 2 ࡢᴫᛕࢆᫎࡉࡏࡿࡣ ࡓ࠼ࡤࠕ⤊ ᒁࡢ」ྜᱱయࡢ㒊ᮦኚᙧゅ R ࡽ RC ༊㛫ࡢ㒊ᮦ ኚᙧゅrc R ࢆᑟฟࡋࡓ࠺࠼࡛ࡑࡢረᛶኚᙧ⬟ຊ rc Rp ࡘ ࠸᳨࡚ウࡍࡿࠖࡀせࡉࢀࡿ➼ࡀᐃࡉࢀ ࡑࡢࡓࡵ ࡣ ホ౯ࣔࢹࣝయࡢኚᙧᵓᡂせ⣲ࡑࢀࡒࢀࡢኚᙧ ࡢ┦㛵ಀࢆṇࡋࡃᢕᥱ࡛ࡁࡿ⎔ቃࡀᩚࡗ࡚࠸ࡿࡇ ࡀᮃࡲࡋ࠸ࠋ ࠉࡑࡇ࡛ ホ౯ࣔࢹࣝయࡢࡓࢃࡳ G ࠾ࡼࡧ㒊ᮦኚᙧ ゅ R ᑐࡍࡿྛᵓᡂせ⣲ࡢᐤศࢆࡑࢀࡒࢀࠕࡓࢃࡳ ࡢᡂศẚࠖ࠾ࡼࡧࠕ㒊ᮦኚᙧゅࡢᡂศẚࠖᐃ⩏ࡍࡿ ᘧ ( 5 ) ᘧ ( 6 ) ᇶ࡙࠸࡚ࡑࢀࡒࢀࢆḟࡢᘧ ( 9 ) ࠾ࡼ ࡧᘧ ( 10 ) ࡋ࡚⾲⌧࡛ࡁࡿࠋ ࠉᘧ ( 9 ) ࠾ࡼࡧᘧ ( 10 ) ࡣࡶ ᮦ㍈᪉ྥࡢᗄఱᏛ ⓗ᮲௳ྛᵓᡂせ⣲ࡢ㒊ᮦᙎᛶ๛ᛶ ࠾ࡼࡧ๛ᛶపୗ ⋡ D ࡽᵓᡂࡉࢀ࡚࠸ࡿࠋࡍ࡞ࢃࡕྛᡂศẚࡣ ࡲࡎ ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ rcδ δ = sSr sSe lrcl sSr sSe lrcl +rcSsSe sln2+ α rcSsSr sln2 sδr δ = rcS sSe sln2 sSr sSe lrcl +rcSsSe sln2+ α rcSsSr sln2 sδe δ = α rcS sSr sln2 sSr sSe lrcl +rcSsSe sln2 + αrcSsSr sln2 ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ rcR R = sSr sSe l2 sSr sSe lrcl +rcSsSe sln2+ α rcSsSr sln2 sRr R = rcS sSe lsln sSr sSe lrcl +rcSsSe sln2+ α rcSsSr sln2 sRe R = α rcS sSr lsln sSr sSe lrcl +rcSsSe sln2+ αrcSsSr sln2 ᅗ㸱ࠉ๛ᛶపୗ⋡ D ࡢῶక࠺ࡓࢃࡳࡢᡂศẚࡢ᥎⛣ 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ( - ) 1.0 0.8 0.6 0.4 0.2 ( - ) rc / s r / s e / slb / rcl = 0.92 rcl / l = 0.20 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ( - ) 1.0 0.8 0.6 0.4 0.2 ( - ) rc / s r / s e / slb / rcl = 0.92 rcl / l = 0.30 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ( - ) 1.0 0.8 0.6 0.4 0.2 ( - ) rc / s r / s e / slb / rcl = 0.92 rcl / l = 0.40 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ( - ) 1.0 0.8 0.6 0.4 0.2 ( - ) rc / s r / s e / slb / rcl = 0.92 rcl / l = 0.50 ( b )rc l ࡢᙳ㡪 ( a )s lb ࡢᙳ㡪 Mfa= SR ⇔ Mfa= αS R ( 8 ) ( 9 ) ( 10 ) α= sSr sSe lrcl +rcSsSe sln 2 + rcSsSr sln2 sSr sSe lrcl +rcSsSe sln2+ α rcSsSr sln2 α ( 7 )
1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ( - ) 1.0 0.8 0.6 0.4 0.2 ( - ) rcR / R sRr / R sRe / R slb / rcl = 0.69 rcl / l = 0.30 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ( - ) 1.0 0.8 0.6 0.4 0.2 ( - ) rcR / R sRr / R sRe / R slb / rcl = 0.92 rcl / l = 0.50 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ( - ) 1.0 0.8 0.6 0.4 0.2 ( - ) rcR / R sRr / R sRe / R slb / rcl = 0.92 rcl / l = 0.40 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ( - ) 1.0 0.8 0.6 0.4 0.2 ( - ) rcR / R sRr / R sRe / R slb / rcl = 0.92 rcl / l = 0.30 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ( - ) 1.0 0.8 0.6 0.4 0.2 ( - ) rcR / R sRr / R sRe / R slb / rcl = 0.92 rcl / l = 0.20 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ( - ) 1.0 0.8 0.6 0.4 0.2 ( - ) rcR / R sRr / R sRe / R slb / rcl = 0.80 rcl / l = 0.30 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ( - ) 1.0 0.8 0.6 0.4 0.2 ( - ) rcR / R sRr / R sRe / R slb / rcl = 0.92 rcl / l = 0.30 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ( - ) 1.0 0.8 0.6 0.4 0.2 ( - ) rcR / R sRr / R sRe / R slb / rcl = 1.00 rcl / l = 0.30 ᮦ㍈᪉ྥࡢᗄఱᏛⓗ᮲௳ྛᵓᡂせ⣲ࡢ㒊ᮦᙎᛶ๛ᛶ ࡼࡗ࡚ࡑࡢึᮇ್ ࡘࡲࡾᙎᛶᇦ࠾ࡅࡿ┦㛵ಀ ࡀ☜ᐃࡉࢀ ࡑࡢᚋ RC ༊㛫➃࠾ࡅࡿ᭤ࡆࡦࡧࢀ ࡢⓎ⏕ࢆ㉳Ⅼ ࡑࡢ್ࢆ 1 ࡽᚎࠎῶࡉࡏࡿ๛ ᛶపୗ⋡ D ࡼࡗ࡚㠀ᙎᛶᇦ࠾ࡅࡿᣲືࡀグ㏙ࡉࢀ ࡿᛶ㉁࠶ࡿࠋ ࠉᅗ 3 ௨ୖࢆ㋃ࡲ࠼ ࡑࡢ 1 ࡛ࡢࣃ࣓ࣛࢺࣜࢵࢡ࣭ ࢫࢱࢹ࠾ࡅࡿᶓ㍈⦪㍈┦ᙜࡍࡿ slb rcl rcl l ࡢኚືక࠺ࠕᮏ」ྜᱱࡢࡓࢃࡳࡢᡂศẚࡢ๛ᛶపୗ ⋡D ࡢῶᚑࡗࡓ᥎⛣ࠖࢆ♧ࡍࠋ࠸ࡎࢀࡢࢢࣛࣇࡶ ࡑࡢ 1 ྠ୍ࡢඹ㏻ᅉᏊࢆ๓ᥦࡋࡓ࠺࠼࡛ ୖẁࡢ ᅗ 3 ( a ) ࠾࠸࡚ࡣ rcl l ࢆ 0.30 ୍ᐃಖࡗࡓ≧ែ ࡛ slb rcl ࡀ ୗẁࡢᅗ 3 ( b ) ࠾࠸࡚ࡣ slb rcl ࢆ 0.92 ୍ᐃಖࡗࡓ≧ែ࡛ rcl l ࡀቑࡋ࡚࠸ࡃ୰࡛ࡢࡓࢃ ࡳࡢᡂศẚࡢ᥎⛣ࡀᅗ♧ࡉࢀ࡚࠸ࡿࠋࡇࡢ㝿 ᶓ㍈ࡀࠕ D = 1 ࡞ࡗ࡚⥺๛ᛶᙎᛶ๛ᛶࡀ୍⮴ࡍࡿⅬ㸦ᙎᛶ 㝈㸧ࢆ㉳Ⅼῶࡋ࡚࠸ࡃࠖࡼ࠺᥇ࡽࢀ࡚࠸ࡿࡓࡵ ᅗ 3 ࠾࠸࡚ࡣ ࡑࡢ 1 ࡛᫂ࡽࡉࢀࡓᙎᛶᇦࡢᛶ ㉁ࡀᙎᛶ㝈┦ᙜࡍࡿ D = 1 ࡢᡂศẚࡋ࡚⾲ࡉࢀ࡚ ࠾ࡾ ࡑࡢẚ⋡ࡀࡑࡢᚋ ᭤ࡆࡦࡧࢀ ᭤ࡆ㝆అࢆ ⤒࡚᥎⛣ࡋ࡚࠸ࡃᵝࡀྍどࡉࢀ࡚࠸ࡿࡇ࡞ࡿࠋ ࠉࡣࡌࡵᅗ 3 ( a ) ࡽぢ࡚࠸ࡃ ࢢࣛࣇ㛫ࡢ┦㐪 ࡀṤ࡞ࡃ ྛࡓࢃࡳࡢᡂศẚࡀ ኚືᅉᏊ࡛࠶ࡿ slb rcl ᑐࡋ࡚㕌ឤ᥎⛣ࡋ࡚࠸ࡿࡇࡀ⌮ゎࡉࢀࡿࠋ ࡍ࡞ࢃࡕ ྛᵓᡂせ⣲ࡢኚᙧࡣ slb rcl ࡣࡰ↓㛵 ಀ ࠕᙎᛶ㝈㏆࠸㡿ᇦ࠾࠸࡚ࡣ S 㐀ᱱࡢࡓࢃࡳ s Ge ࡀ✺ฟࡋ࡚ࡁࡃ ࡘ࠸࡛᭤ࡆࣂࢿࡢኚᙧ s Gr RC 㐀ᱱࡢࡓࢃࡳ rc G ࡢ㡰ホ౯ࣔࢹࣝయࡢࡓࢃࡳ G ᑐࡍࡿᐤᗘࢆᑠࡉࡃࡋ࡚࠸ࡃࠖᛶ㉁ ࠕホ౯ࣔࢹ ࣝࡋ࡚ࡢኚᙧࡀ㐍⾜ࡋ࡚ᙎᛶ㝈ࡽ㐲ࡊࡿࡘࢀ ࡚ RC 㐀ᱱ᭤ࡆࣂࢿࡀయࡢࡓࢃࡳ༨ࡵࡿྜࡀ ቑࡋ࡚࠸ࡃࠖᛶ㉁ࢆಖࡗ࡚࠸ࡿࠋ๓⪅ࡣࡑࡢ 1 ぢ ࡓᛶ㉁ྜ⮴ࡋ࡚࠸ࡿⅬ࡛ ᚋ⪅ࡣࠕ๛ᛶపୗ⋡ D ࡢ ῶᚑࡗࡓ RC 㐀ᱱ᭤ࡆࣂࢿࡢ㒊ᮦ๛ᛶࡢపୗ కࡗ࡚ࡇࢀࡽࡢᵓᡂせ⣲ࡢᡂศࡀୖ᪼ࡋ S 㐀ᱱࡢࡓ ࢃࡳࡀ┦ᑐⓗᑠࡉࡃ࡞ࡿࠖࡢㄆ㆑ྜ⮴ࡍࡿⅬ࡛ ጇᙜ࡞⤖ᯝุ᩿ࡉࢀࡿࡀ ࡑࡢᵝ┦ slb rcl ࡍ࡞ ࢃࡕ RC ༊㛫ᇙࡵ㎸ࡲࢀࡿ S 㒊ᮦࡢ㛗ࡉࡼࡿᙳ㡪 ࡀᫎࡉࢀࡿࡇࡀ࡞࠸ࡇࢆ ࡇࢀࡽࡢࢢࣛࣇࡣ♧ ࡋ࡚࠸ࡿࠋ ࠉࡘ࠸࡛ ኚືᅉᏊrc l l ࡢᙳ㡪ࡘ࠸࡚♧ࡋࡓᅗ 3 ( b ) ࡽࡣ ๓グࡢࠕᙎᛶ㝈㏆ഐ࡛ࡢᡂศẚࡢᑠ㛵ಀࠖ ࠕኚᙧࡢ㐍⾜క࠺ RC 㐀ᱱࡢᙎᛶࡓࢃࡳ rc G ᭤ࡆࣂࢿ ࡢᙎᛶኚᙧ s Gr ࡢᐤศࡢቑഴྥࠖࡀᅗ 3 ( a ) ࡛ぢࡓࡑ ࢀ୍⮴ࡋ࡚࠸ࡿ୍᪉࡛ ࡇࢀࡽࡢഴྥᑐࡍࡿኚືᅉ Ꮚ rc l l ࡢᙳ㡪ࡀ㢧ࢃࢀ࡚࠸ࡿࡇࡀ┳ྲྀࡉࢀࡿࠋࡍ࡞ ࢃࡕ ࡑࡢ 1 ࡛ࡶぢࡓࡼ࠺ ᮏホ౯ࣔࢹࣝ࠾࠸࡚ࡣ rc l l ࡀࡁࡃ࡞ࡗ࡚ rc l ࡀ㛗ࡃ࡞ࡿ㸦 sln ࡀ▷ࡃ࡞ࡿ㸧 ࡘࢀ࡚ RC 㐀ᱱࡢᙎᛶࡓࢃࡳ rc G ᭤ࡆࣂࢿࡢᙎᛶኚᙧ s Gr ࡀࡁࡃ࡞ࡗ࡚ S 㐀ᱱࡢᙎᛶࡓࢃࡳ s Ge ࡀᑠࡉࡃ࡞ࡿ ᛶ㉁࠶ࡿࡓࡵ ࡲࡎᙎᛶ㝈࠾ࡅࡿᡂศẚࡢᑠ㛵ಀ ࡑࡢᙳ㡪ࡀዴᐇᫎࡉࢀ࡚࠸ࡿࠋຍ࠼࡚ ࡇࡢ RC 㐀ᱱࡢᙎᛶࡓࢃࡳ rc G ᭤ࡆࣂࢿࡢᙎᛶኚᙧ s Gr ࡢᣲື ╔┠ࡍࡿ ๓ᥖᅗ 3 ( a ) ྠᵝ ࠕ๛ᛶపୗ⋡ D ࡢῶ ᅗ㸲ࠉ๛ᛶపୗ⋡ D ࡢῶక࠺㒊ᮦኚᙧゅࡢᡂศẚࡢ᥎⛣ ( b )rc l ࡢᙳ㡪 ( a )s lb ࡢᙳ㡪
కࡗ࡚ቑࡍࡿࠖഴྥࢆඹ㏻ࡉࡏࡘࡘ ࡇࢀࡽࡢቑ ࡀࠕ rc l l ࡀࡁࡃ࡞ࡗ࡚ rc l ࡀ㛗ࡃ࡞ࡿ㸦 s ln ࡀ▷ࡃ࡞ࡿ㸧 ࡘࢀ⦆៏࡞ࡾ┤⥺ᣲື㏆࡙ࡃഴྥ࠶ࡿࠖࡇࢆ ㄞࡳྲྀࡿࡇࡀ࡛ࡁࡿࠋ ࡘ࡙ࡃᅗ 4 ( a ) ࠾ࡼࡧᅗ 4 ( b ) ࡣ ࡓࢃࡳࡢᡂศẚྠ ᵝ ᘧ ( 10 ) ࡼࡗ࡚ồࡵࡽࢀࡿ㒊ᮦኚᙧゅࡢᡂศẚ ๛ᛶపୗ⋡ D ࡢῶࡢ㛵ಀࡘ࠸࡚ᐇࡋࡓᮦ㍈᪉ ྥࡢᗄఱᏛⓗ᮲௳ᑐࡍࡿࣃ࣓ࣛࢺࣜࢵࢡ࡞᳨ウࡢ⤖ ᯝࢆ♧ࡍࡶࡢ࡛࠶ࡿࡀ ࡇࡇࡽࡶࡓࢃࡳࡢᡂศẚ ࡰྠᵝࡢഴྥࡀ☜ㄆࡉࢀ࡚࠸ࡿࠋࡍ࡞ࢃࡕ RC 㐀ᱱ ࡢ㒊ᮦኚᙧゅ rcR ᭤ࡆࣂࢿࡼࡿ㒊ᮦኚᙧゅ s R r ࡣ ᙎᛶ㝈㏆ഐ࡚ホ౯ࣔࢹࣝయࡢ㒊ᮦኚᙧゅ R ࡼࡾࡶ ᑠࡉࡃホ౯ࡉࢀ 㠀ᙎᛶᇦ࡚ࡑࢀࡒࢀࡢᐤศࢆ ቑࡉࡏ࡚࠸ࡃࡀ ࡑࡢᣲືࡣslb rcl ᑐࡋ㕌ឤ࡛ rcl l ᑐࡋᩄឤ࡞ᛶ㉁ࢆ᭷ࡋ࡚࠸ࡿࠋゝࡍࢀࡤ RC 㐀ᱱ ࡢ㒊ᮦኚᙧゅ rc R ᭤ࡆࣂࢿࡼࡿ㒊ᮦኚᙧゅ s R r ࡣ ᙎᛶᇦ࠾࠸࡚ホ౯ࣔࢹࣝయࡢ㒊ᮦኚᙧゅ R ࡼࡾ ࡁࡃ࡞ࡿࡇࡣ࡞࠸ࡶࡢࡢ RC ༊㛫ࡢ㛗ࡉ rc l ࡀ㛗࠸ ᮲௳ୗ࡛㠀ᙎᛶᇦ࠶ࡿሙྜࡣ S 㐀ᱱࡢ㒊ᮦኚᙧ ゅ s Re ࢆ㉸࠼ࡿᐤࢆぢࡏࡿྍ⬟ᛶࡶ࠶ࡿࠋࡲࡓࡑࢀࡒ ࢀࡢᐤᗘࡣ RC ༊㛫ࡢ㛗ࡉ rc l ከ࡞ᙳ㡪ࢆཷࡅ ࡿ୍᪉࡛ S 㒊ᮦࡢᇙ㎸ࡳ㛗ࡉ s lb ࡛ࡣไᚚ࡛ࡁ࡞࠸ᛶ㉁ ࠶ࡿࡓࡵ タィᐇົ࠾࠸࡚ ≉㠌ᛶᣦ㔪ᘧ8)ࢆ ⏝ࡍࡿሙྜࡣ ࡇࡢᛶ㉁ࢆศព㆑ࡍࡿᚲせࡀ ࠶ࡿ⪃࠼ࡽࢀࡿࠋ ᅗ 4 ࠾࠸࡚ࡉࡽ␃ពࡍࡁࡣ ᙎᛶᇦ㏆࠸≧ ែࡢ S 㐀ᱱࡢ୍㒊 ᡂศẚࡀ 1 ࢆ㉸࠼࡚࠸ࡿࡶࡢࡀ ᏑᅾࡍࡿⅬ࠶ࡿࠋᘧ ( 5 ) ♧ࡋࡓ㏻ࡾ S 㐀ᱱ࡛ࡣ ᙎᛶࡓࢃࡳ s Ge ࢆ sln ࡛㝖ࡋ࡚㒊ᮦኚᙧゅ s Re ࡀồࡵࡽ ࢀࡿ୍᪉࡛ ホ౯ࣔࢹࣝయ࡛ࡣ ᘧ ( 6 ) ࡋ࡚ࡓࢃ ࡳ G ࢆࢩࢫࣃࣥ l ࡛㝖ࡋ࡚㒊ᮦኚᙧゅ R ࡀồࡵࡽࢀ ࡿࠋࡓࢃࡳࢆ㒊ᮦ㛗࡛㝖ࡋ࡚↓ḟඖࡍࡿࡇࡢ㐣⛬ ࠾࠸࡚ᇶ‽࡞ࡿ㛗ࡉࡀ␗࡞ࡿࡇ㉳ᅉࡍࡿࡇࡢ⤖ ᯝࡣ ࠕᮏホ౯ࣔࢹࣝ࠶ࡗ࡚ࡣ యࡢ㒊ᮦኚᙧゅ ࡼࡾࡶ S 㐀ᱱࡢ㒊ᮦኚᙧゅࡀࡁࡃ࡞ࡗ࡚࠸ࡿሙྜࡀ ࠶ࡿࠖࡇࢆྠ♧၀ࡍࡿࠋࡍ࡞ࢃࡕ 」ྜᱱࡢᵓ 㐀タィ㝿ࡋ యࡢ㒊ᮦኚᙧゅ R ࡢࡳ╔┠ࡋ࡚ྛ ᵓᡂせ⣲ࡢኚᙧ㓄៖ࡋ࡞࠸ࡇࡣࠕ S 㒊ᮦࡋ࡚ࡢ ኚᙧࣞ࣋ࣝࡢ㐣ᑠホ౯ࠖࡘ࡞ࡀࡿྍ⬟ᛶࡀ࠶ࡿࡓࡵ ᐇົୖࡣࡇࡢⅬࡶศㄆ㆑ࡋ࡚࠾ࡃࡇࡀᚲせ⪃ ࠼ࡽࢀࡿࠋ 㸬ࡲࡵ ࠉ㕲㦵㒊ᮦ⁐᥋ࡉࢀࡓ㗰〇ࣉ࣮ࣞࢺࡀ㕲➽ࢥࣥࢡ ࣮ࣜࢺ༊㛫㕲㦵༊㛫ࡢቃ⏺㓄ࡉࢀࡓᇙ㎸ࡳᙧᘧࡢ 」ྜᱱࡢ㒊ᮦ๛ᛶࢆホ౯ࡍࡿࣔࢹࣝࢆᵓ⠏ࡋ ࣔࢹࣝ ࡢᛶ㉁ࡢ⢭ᰝࢆヨࡳࡓࠋᮏホ౯ࣔࢹࣝࡀ᭷ࡍࡿᛶ㉁ࡢ ▱ᜳ ࡞ࡽࡧࡑࡇࡽᚓࡽࢀࡿࠕᐇ㝿ࡢタィ᭷ ⏝࡞▱ぢࡢ࿊♧ࠖࢆ┠ⓗࡋࡓ㆟ㄽࡢ⤖ᯝࢆࡲࡵࡿ ௨ୗࡢࡼ࠺࡞ࡿࠋ ( 1 ) ᮏ」ྜᱱࡢ㒊ᮦ๛ᛶࡣ ᪤ ࡢᇙ㎸ࡳᙧᘧࡢ 」ྜᱱࡢホ౯ᡭἲ‽ࡌࡓኚᙧᣲືゎᯒࡢࣉ ࣮ࣟࢳ6)ࢆ㋃くࡋࡘࡘ ቃ⏺ࣉ࣮ࣞࢺࡢᙳ㡪ࢆ ⪃៖ࡢ࠺࠼ ỗ⏝ࣉࣟࢢ࣒ࣛࡢぶᛶࢆ☜ಖ ࡋ࡞ࡀࡽࣔࢹࣝࡍࡿࡇ࡛ᙎᛶᇦࡽ㠀⥺ᙧ ᇦࡲ࡛ホ౯࡛ࡁࡿࠋ ( 2 ) ᮏ」ྜᱱయࡢ㒊ᮦኚᙧゅ R ࡣ ᙎᛶᇦ࠶ࡗ ࡚ࡶ㠀ᙎᛶᇦ࠶ࡗ࡚ࡶ RC ༊㛫ࡸ S ༊㛫ࡢ㒊 ᮦኚᙧゅࡢᙳ㡪ࡀ」㞧ᫎࡉࢀࡓ್ࢆࡿࠋ ࡑࢀᨾ 」ྜᱱయࡢ㒊ᮦኚᙧゅ R ᐇ㝿 RC ༊㛫࠾ࡼࡧ S ༊㛫⏕ࡌ࡚࠸ࡿ㒊ᮦኚᙧゅ ࡣ㞳ࡀᏑᅾࡍࡿࡓࡵ ྛ༊㛫ࡢヲ⣽タィ㝿 ࡋ࡚ࡣ ࡇࡢᕪ␗ࢆṇࡋࡃᢕᥱࡋᫎࡉࡏࡿᚲ せࡀ࠶ࡿࠋ ࡞࠾ᮏㄽᩥ࡛ࡣ,ࠕ S 㒊ᮦඛࢇࡌ࡚ RC ༊㛫➃ࡀ᭤ ࡆ㝆అࡍࡿࠖሙྜ≉ࡋ࡚ㄽࢆᒎ㛤ࡋ࡚ࡁࡓࡀ, ᮏホ ౯ࣔࢹࣝࡣ, ࡑࡢᵓᡂࡽ᫂ࡽ࡞ࡼ࠺ , S 㒊ᮦࡢ᭤ ࡆ㝆అࡀඛ⾜ࡍࡿሙྜࡶᐜ᫆ᑐᛂࡍࡿࡇࡀ࡛ࡁ ࡿࠋࡓࡔࡋ, ᪤㏙ࡓࡼ࠺ , ᮏホ౯ࣔࢹࣝࡣ , ᮏ」 ྜᱱࡢ᭤ࡆኚᙧࡢ㏣㊧ࡢࡳ≉ࡋ࡚࠸ࡿࡓࡵ, ᐇ㝿ࡢ タィ㝿ࡋ࡚ࡣࡏࢇ᩿ኚᙧࡢᙳ㡪ࢆࡶ⟬ධࡋࡓ᳨ウࢆ ⾜࠺ᚲせࡀ࠶ࡿࠋࡲࡓࡶࡕࢁࢇ, ቃ⏺ࣉ࣮ࣞࢺ➼ࢆṇࡋ ࡃタィࡋ࡚, ᮏホ౯ࣔࢹࣝᵓ⠏ࡢ㝿タࡅࡓ๓ᥦ᮲௳ࢆ ☜ಖࡋ࡞ࡃ࡚ࡣ࡞ࡽ࡞࠸ࠋ ࠉཧ⪃ᩥ⊩ బ⸨Ⰻ , ᑠ⃝₶ , ୰⏣ᐶ : 㕲㦵㒊ᮦ⁐᥋ࡉࢀࡓ㗰〇ࣉ࣮ࣞࢺࡀ㕲➽ࢥࣥࢡ࣮ࣜࢺ༊㛫㕲㦵༊㛫ࡢቃ⏺㓄ࡉࢀࡓᇙ㎸ ࡳᙧᘧࡢ」ྜᱱࡢ㒊ᮦ๛ᛶホ౯ࣔࢹࣝࠉ㸫ࡑࡢ㸯ࠉ㠀ᙎᛶᇦ࠾ࡅࡿホ౯ࣔࢹࣝࡢᛶ㉁㸫, ᮾᛴᘓタᢏ⾡◊✲ᡤሗ , No. 46, pp. . 2021. 2 ᪥ᮏᘓ⠏Ꮫ : 㕲➽ࢥࣥࢡ࣮ࣜࢺᵓ㐀ィ⟬つ‽࣭ྠゎㄝ , 2010 బ⸨Ⰻ, ᑠ⃝₶, 2 ྡ : 㕲㦵㒊ᮦ⁐᥋ࡉࢀࡓ㗰〇ࣉ࣮ࣞࢺ࡛㕲➽ࢥࣥࢡ࣮ࣜࢺ༊㛫ࢆᙉࡋࡓᇙ㎸ࡳᙧᘧࡢ」ྜᵓ㐀 ᱱࡢ㒊ᮦ๛ᛶࡢホ౯ᡭἲ, ࢥࣥࢡ࣮ࣜࢺᕤᏛᖺḟㄽᩥ㞟 , Vol. 35, No. 2, 2013 బ⸨Ⰻ, ᑠ⃝₶, ୰⏣ᐶ : 㕲➽ࢥࣥࢡ࣮ࣜࢺ༊㛫㕲㦵༊㛫ࡢቃ⏺㗰〇ࣉ࣮ࣞࢺࡀ㓄ࡉࢀࡓᇙ㎸ࡳᙧᘧࡢ」ྜᱱࡢ㒊 ᮦ๛ᛶホ౯ᡭἲࡢ㐺⏝ᛶ, ࢥࣥࢡ࣮ࣜࢺᕤᏛᖺḟㄽᩥ㞟 , Vol. 38, No. 2, 2016
5) ᪥ᮏᘓ⠏Ꮫ : 㗰ࢥࣥࢡ࣮ࣜࢺᵓ㐀᥋ྜ㒊ࡢᛂຊఏ㐩ᢠᶵᵓ , 2011 6) 㕥ᮌⱥஅ , すཎᐶ : ᮦ➃㒊 RC 㐀୰ኸ㒊㕲㦵㐀࡛ᵓᡂࡉࢀࡿ」ྜᵓ㐀ᱱࡢࡏࢇ᩿⪏ຊኚᙧᛶ⬟ , ᪥ᮏᘓ⠏Ꮫᵓ㐀⣔ㄽᩥ㞟 , ➨ 73 ᕳ , ➨ 631 ྕ , 2008 7) 㔠ᮏΎ⮧ , ┿℩ఙ , ᒣ㔝㎶ᏹ : 㕲➽ࢥࣥࢡ࣮ࣜࢺᰕ᥋ྜࡉࢀࡓ㕲㦵ᱱ➃㒊ࢆ㕲➽ࢥࣥࢡ࣮ࣜࢺ࡛ᕳ࠸ࡓΰྜᵓ㐀ᱱࡢ⪏ຊ ホ౯, ᪥ᮏᘓ⠏Ꮫᵓ㐀⣔ㄽᩥ㞟 , ➨ 76 ᕳ , ➨ 659 ྕ , 2011 8) ᪥ᮏᘓ⠏Ꮫ : 㕲➽ࢥࣥࢡ࣮ࣜࢺ㐀ᘓ≀ࡢ㠌ᛶಖドᆺ⪏㟈タィᣦ㔪 , 1999. 9) బ⸨Ⰻ , ᑠ⃝₶ , ୰⏣ᐶ : 㕲㦵㒊ᮦ⁐᥋ࡉࢀࡓ㗰〇ࣉ࣮ࣞࢺࢆ᭷ࡍࡿᇙ㎸ࡳᙧᘧࡢ」ྜᵓ㐀ᱱࡢ㒊ᮦ๛ᛶࡢホ౯ᡭἲ ࡑࡢ㠀⥺ᙧᛶ㛵ࡍࡿ୍⪃ᐹ, ᪥ᮏᘓ⠏ᏛᏛ⾡ㅮ₇᱾ᴫ㞟㸦㏆␥㸧, ᵓ㐀 III, 2014 10) ᪥ᮏᘓ⠏Ꮫ : ྜᡂᵓ㐀タィつ‽ , 2014
A DESIGN MODEL FOR STRUCTURAL BEHAVIOR OF A STEEL BEAM WITH REINFORCED
CON-CRETE ENCASED ENDS STRENGTHENED WITH STEEL PLATE WELDED TO STEEL MEMBER
FORMULATION OF THE MODEL AND ITS CARACTERISTICS IN INELASTIC REGION
-R. Sato, J. Ozawa, and H. Nakata
This paper proposes a design model for structural behavior of a steel beam with reinforced concrete encased ends. The steel beam with reinforced concrete encased ends has steel plates installed at boundaries between reinforced concrete regions and steel region, which are not only connected to rebars with nuts but also welded to steel member to strengthen reinforced concrete regions. Aimed at being introduced into practical use, the design model complies with the existing system of structural design in Japan. Normally, the deformation of steel beam with reinforced concrete encased ends is devided into three constituents as a previous VWXG\$QG WKH GHVLJQ PRGHO LV IRUPHG E\ DVVHPEOLQJ WKUHH FRPSRQHQWV LH UHLQIRUFHG FRQFUHWH EHDP FRPSRQHQW DQG ÀH[XUDO spring component and steel beam component, that give the three constituents of elastic deformation mentioned above. Due to the similar composition of embedded steel column base and the steel beam with reinforced concrete ends, constitutive equation for deformation of each component is formulated by solving elastic curve equations set up based on an existing mechanical model for embedded steel column base. Moreover, the model is also possible to simulate structural behaviors in inelastic deformation by add-LQJQRQOLQHDULW\WRHDFKFRPSRQHQW%HVLGHVH൵HFWVRIJHRPHWULFFRQGLWLRQDORQJPHPEHUD[LVD൵HFWHGE\VKHDUVSDQOHQJWKRI reinforced concrete region, and embedded length of steel member were evaluated by analysis results through the design model. 7KHIROORZLQJ¿QGLQJVKDYHEHHQREWDLQHGIURPWKHSUHVHQWVWXG\ %DVHGRQPRGL¿FDWLRQRISUHYLRXVVWXG\VWUXFWXUDOEHKDYLRURIWKHVWHHOEHDPZLWKUHLQIRUFHGFRQFUHWHHQFDVHGHQGV VWUHQJWKHQHGZLWKVWHHOSODWHFDQEHHYDOXDWHGE\WKHSURSRVHGPRGHOFRQVLGHULQJH൵HFWRIVWHHOSODWH 7KHDQDO\VLVUHVXOWVVKRZWKDWOHQJWKRIUHLQIRUFHGFRQFUHWHUHJLRQKDVDFRQVLGHUDEOHLQÀXHQFHRQPHPEHUVWL൵QHVV RIVWHHOEHDPZLWKUHLQIRUFHGFRQFUHWHHQGV7KHPHPEHUVWL൵QHVVLQFUHDVHVZLWKDQLQFUHDVLQJOHQJWKRIUHLQIRUFHG concrete region.
( 3 ) Drift angle of the steel beam with reinforced concrete encased ends has complicated relationship between that of reinforced concrete region and of steel region. It makes disagreement between integrated drift angle and other drift angle occurs in reinforced concrete region or steel region. Thus, it is needed to recognize this disagreement in order to UHÀHFWWKHLQÀXHQFHWRFRQVLGHUDWLRQVIRUGHWDLOVDERXWWKHVHUHJLRQVLQFDVHRISUDFWLFDOVWUXFWXUDOGHVLJQ
