ᵓ㐀ᕤᏛㄽᩥ㞟Vol. 67A (2021 ᖺ 3 ᭶) ᅵᮌᏛ
㠀✺ฟᆺ㧗ຊ࣎ࣝࢺ࢚ࣥࢻࣉ࣮ࣞࢺ᥋ྜ࠾ࡅࡿ
࣎ࣝࢺ㍈ຊ᥎ᐃ㛵ࡍࡿゎᯒⓗ◊✲
Analytical study on estimating bolt axial force of flush endplate connection
ᮡᮏᝆ┿†㸪ᒣཱྀ㝯ྖ*
Yuma Sugimoto, Takashi Yamaguchi
†ಟኈ㸦ᕤ㸧㸪᪥ᮏᏛ⾡ᨭ⯆≉ู◊✲ဨ DC㸪㜰ᕷ❧Ꮫ㸪Ꮫ㝔ᕤᏛ◊✲⛉㒔ᕷ⣔ᑓᨷ
㸦ࠛ558-8585 㜰ᕷఫྜྷ༊ᮡᮏ 3-3-138㸧
*༤㸦ᕤ㸧㸪㜰ᕷ❧Ꮫᩍᤵ㸪Ꮫ㝔ᕤᏛ◊✲⛉㒔ᕷ⣔ᑓᨷ㸦ࠛ558-8585 㜰ᕷఫྜྷ༊ᮡᮏ 3-3-138㸧
Recently, the demands of flush endplate connections have been increased in the field of bridge structures. However, no estimation-methods are proposed of the bolt axial force in such connections. This study proposes a new estimation method of the bolt axial force in flush endplate connections by FE analysis. Firstly, prying force coefficient and joint stiffness formulas are derived from the analysis of joint elements which can simulate the bolt force increment of flush endplate connections. Secondly, formulas for acting force in lower flange, horizontal stiffener and web are also obtained from girder analysis with a lower flange that has the low-Young’s-modulus-region. Finally, the new estimation method for a bolt axial force is established by these proposed formulas.
Key Words: high strength bolt, endplate connection, FE analysis, tensile type joint
࣮࣮࢟࣡ࢻ㸸㧗ຊ࣎ࣝࢺ㸪࢚ࣥࢻࣉ࣮ࣞࢺ᥋ྜ㸪FEゎᯒ㸪ᘬᙇ᥋ྜ ᗎㄽ ㏆ᖺ㸪㒊ᮦࡢ⤌ࡳ❧࡚㛫ࡢ▷⦰ࢆ┠ⓗ㸪㧗ຊ࣎ࣝ ࢺ࢚ࣥࢻࣉ࣮ࣞࢺ᥋ྜ㸦௨ୗ㸪࢚ࣥࢻࣉ࣮ࣞࢺ᥋ྜ㸧ࡀ ⅏ᐖࡢ⥭ᛴᶫࡸᕤ⏝௬ᱞᶫ㐺⏝ࡉࢀ࡚࠸ࡿ1), 2)㸬≉ 㸪᱆ࡢᕤሙಖ⟶㸪㐠ᦙ㸪⌧ሙ࡛ࡢ௬⨨ࡁࡢࡋࡸࡍࡉ ࡽ㸪࢚ࣥࢻࣉ࣮ࣞࢺࡀୖୗࣇࣛࣥࢪࡽ✺ฟࡋ࡚࠸࡞࠸ ᅗ㸫1 ࡢ㠀✺ฟᆺ࢚ࣥࢻࣉ࣮ࣞࢺ᥋ྜ㸦௨ୗ㸪㠀✺ฟᆺ ᥋ྜ㸧ࡢ㟂せࡀ㧗ࡲࡗ࡚࠾ࡾ㸪ᮏ◊✲࡛ࡣࡇࡢࡼ࠺࡞㠀 ✺ฟᆺ᥋ྜ╔┠ࡍࡿ㸬㗰ᶫࡢ᱆᥋ྜ㒊࠾ࡅࡿ㠀✺ ฟᆺ᥋ྜࡣ᥋ྜ㒊๛ᛶࢆ☜ಖࡍࡿࡓࡵᅗ㸫1 ♧ࡍỈ ᖹࣜࣈࡢタ⨨ࡀᚲせࡉࢀ࡚࠸ࡿ3)㸬 㠀✺ฟᆺ᥋ྜࡣ᥋ྜ㒊స⏝ࡍࡿ᱆ࡢ᭤ࡆ࣮࣓ࣔࣥࢺ ࡢቑຍక࠸࣎ࣝࢺࡢ㍈ຊࡀቑຍࡍࡿ㸬ࡇࡢࡓࡵ㸪᥋ྜ 㒊ࡢ࣎ࣝࢺ㍈ຊ᥎ᐃࡀ㔜せ࡛࠶ࡿࡀ㸪ḟ♧ࡍ2 ࡘࡢၥ 㢟Ⅼࡽ㠀✺ฟᆺ᥋ྜࡢ࣎ࣝࢺ㍈ຊ᥎ᐃࡣ⌧≧㞴ࡋ࠸㸬 a. ࢚ࣥࢻࣉ࣮ࣞࢺࡢኚᙧࡼࡾ㸪࢙࢘ࣈ㸪ୗࣇࣛࣥࢪ ࠾ࡼࡧỈᖹࣜࣈࡽ᥋ྜ㒊ఏ㐩ࡍࡿ㍈᪉ྥస⏝ຊ㸦௨ ୗ㸪ᘬᙇຊ㸧ࡀ㸪᥋ྜ㒊స⏝ࡍࡿ᱆ࡢ᭤ࡆ࣮࣓ࣔࣥࢺ ࡢቑຍక࠸㸪㠀⥺ᙧⓗኚࡍࡿ㸬 b. 㠀✺ฟᆺ᥋ྜࡣᅗ㸫2 (b)ࡢ L ᥋ྜࡢᶵᵓࢆ᭷ࡍࡿࡀ㸪 ࣎ࣝࢺ㍈ຊࢆ᥎ᐃࡍࡿୖ࡛㔜せ࡞௵ពⲴ㔜࠾ࡅࡿ࡚ࡇ ຊಀᩘࢆồࡵࡿࡓࡵࡢ⟬ᐃᘧࡣᅗ㸫2 (a)ࡢ T ᥋ྜࢆᑐ ㇟ࡋ࡚࠾ࡾ㸪௵ពⲴ㔜࠾ࡅࡿL ᥋ྜࡢ࡚ࡇຊಀᩘ ࢆồࡵࡿࡓࡵࡢ⟬ᐃᘧࡣᏑᅾࡋ࡞࠸㸬 ᮏ◊✲ࡣୖグࡢၥ㢟Ⅼࢆࡩࡲ࠼㸪㠀✺ฟᆺ᥋ྜ࠾ࡅ ࡿ࣎ࣝࢺ㍈ຊࡢ᥎ᐃἲࢆᥦࡍࡿࡇࢆ┠ⓗࡋ࡚࠸ࡿ㸬 ᅗ㸫1 㠀✺ฟᆺ࢚ࣥࢻࣉ࣮ࣞࢺ᥋ྜࡢ Ỉᖹ䝸䝤 㧗ຊ䝪䝹䝖 ୖ䝣䝷䞁䝆 ୗ䝣䝷䞁䝆 䜶䞁䝗 䝥䝺䞊䝖 †㐃⤡ⴭ⪅ / Corresponding author E-mail: [email protected]
ࡲࡎ㸪㠀✺ฟᆺ᥋ྜయࡢFE ゎᯒࡼࡾ㸪᭱ึ㝆 అࡍࡿ࣎ࣝࢺࢆ᫂ࡽࡍࡿࡶ㸪᭤ࡆ࣮࣓ࣔࣥࢺቑ ศᑐࡍࡿୗࣇࣛࣥࢪ㸪Ỉᖹࣜࣈ࠾ࡼࡧ࢙࢘ࣈࡢᘬᙇຊ ࡢቑῶࡘ࠸࡚ᩚ⌮ࡍࡿ㸬ḟ㸪㠀✺ฟᆺ᥋ྜ࡛᭱ึ 㝆అࡍࡿ࣎ࣝࢺࡢ㍈ຊቑຍࢆ⌧࡛ࡁࡿせ⣲⥅ᡭࡑࡢ ᙉᗘኚᙧホ౯ᘧࢆᥦࡍࡿ㸬ࡉࡽ㸪ୗࣇࣛࣥࢪࡢࣖࣥ ࢢ⋡ࢆᒁᡤⓗኚࡉࡏࡓ᱆ࡢ FE ゎᯒࡼࡾ㸪ୗࣇࣛ ࣥࢪഃ࢙࢘ࣈ࣭Ỉᖹࣜࣈഃࡢ๛ᛶࡢ㐪࠸ࡀᘬᙇຊ ࠼ࡿᙳ㡪ࢆ᫂ࡽࡍࡿ㸬᭱ᚋࡇࢀࡽࢆࡲࡵ࡚㠀✺ ฟᆺ᥋ྜࡢ࣎ࣝࢺ㍈ຊ᥎ᐃἲࢆᥦࡍࡿ㸬 ᮏ◊✲࡛⏝ࡍࡿ࡞ኚᩘ୍ぴࢆ⾲㸫1 ♧ࡍ㸬 Ỉᖹࣜࣈࢆ᭷ࡋࡓ㠀✺ฟᆺ࢚ࣥࢻࣉ࣮ࣞࢺ᥋ྜࡢຊ Ꮫⓗᣲື ᑐ㇟᱆ ᮏ❶࡛ࡣ㠀✺ฟᆺ᥋ྜࡢ FE ゎᯒࢆᐇࡋ㸪㠀✺ฟᆺ ᥋ྜ࡛᭱ึ㝆అࡍࡿ࣎ࣝࢺࢆ᫂ࡽࡍࡿ㸬ࡲࡓ㸪᭤ ࡆ࣮࣓ࣔࣥࢺቑศᑐࡍࡿୗࣇࣛࣥࢪ㸪Ỉᖹࣜࣈ࠾ࡼࡧ ࢙࢘ࣈࡢᘬᙇຊࡢቑῶࢆᩚ⌮ࡍࡿ㸬 ᮏ◊✲࡛ᑐ㇟ࡍࡿ᱆ࢆ⾲㸫2 ♧ࡍ㸬᱆ࡣ Type A, B, C ࡢ 3 ࣃࢱ࣮ࣥࢆ⏝ពࡋ㸪Type A ࡣ⥭ᛴ௬タᶫ1)ࡢ ᱆᩿㠃࡛ᶫ㛗60m ࡢ 2 ᱆ᶫࢆ㸪Type B ࡣᛂᛴᶫ2)ࡢ ᱆᩿㠃࡛ᶫ㛗36m ࡢ 2 ᱆ᶫࢆ㸪Type C ࡣᕤ⏝ᱞᶫ ࡋ࡚ᐇ㝿⏝ࡉࢀ࡚࠸ࡿ᱆᩿㠃ࡢ୍ࡘ࡛㸪ᶫ㛗 30m ࡢ 4 ᱆ᶫࢆࡑࢀࡒࢀᐃࡋ࡚࠸ࡿ㸬᱆ࡢᙉࡣ㸪 㐨㊰ᶫ♧᪉᭩4)㸦௨ୗ㸪㐨♧㸧ࡢタィィ⟬࡛ồࡲࡿࠕᶓಽ ࢀᗙᒅࠖ㸪ࠕ㒊ᮦࡢᒁ㒊ᗙᒅࠖ㸪ࠕࣇࣛࣥࢪ㝆అࠖࡢᢠࣔ ࣮࣓ࣥࢺࡢ᭱ᑠ್ࡋ㸪Type A, B, C ࡢᙉࡣࡑࢀࡒࢀ ࠕᶓಽࢀᗙᒅࠖ㸪ࠕୖࣇࣛࣥࢪࡢᒁ㒊ᗙᒅࠖ㸪ࠕࣇࣛࣥࢪ㝆 అ࡛ࠖỴᐃࡋࡓ㸬࡞࠾㸪⾲㸫2 ୰ࡢᙉ࣮࣓ࣔࣥࢺ Mgyࡣ Ᏻ⋡ࡸᢠಀᩘࡣ⪃៖ࡋ࡚࠾ࡽࡎ㸪Ỉᖹࣜࣈ᩿㠃ࢆ⪃ ៖ࡏࡎ⟬ฟࡋ࡚࠸ࡿ㸬 㠀✺ฟᆺ᥋ྜࡢゎᯒࣔࢹࣝ࠾ࡼࡧゎᯒࢣ࣮ࢫ 㠀✺ฟᆺ᥋ྜࡢゎᯒࣔࢹࣝࢆᅗ㸫3 ♧ࡍ㸬ゎᯒࡣ ỗ⏝᭷㝈ゎᯒࢥ࣮ࢻAbaqus 20165)ࢆ⏝ࡋ㸪ᙎረᛶ᭷㝈 ኚゎᯒࢆᐇࡋࡓ㸬ゎᯒࣔࢹࣝࡣᨭ㛫㛗4,000mm ࡢ I ᱆࡛㸪ᑐ⛠ᛶࢆ⪃៖ࡋࡓ1/ 2 ࣔࢹࣝࡋ㸪ࡡࡌࢀࡸ㠃እ ኚࡘ࠸࡚ࡣ⪃៖ࡋ࡞࠸㸬 ゎᯒࣔࢹࣝࡣ᱆㸪࢚ࣥࢻࣉ࣮ࣞࢺ㸪Ỉᖹࣜࣈ㸪㧗ຊ ࣎ࣝࢺࢭࢵࢺ(M24F10T)ࡽᵓᡂࡉࢀ࡚࠾ࡾ㸪㧗ຊ࣎ࣝ ࢺࢭࢵࢺࡣ࣎ࣝࢺ㢌㸪ࢼࢵࢺ㸪㍈㒊㸪ᗙ㔠ࢆ୍యࡉࡏ㸪 ㍈㒊ࢆࡧᚄ㸪ࢿࢪ㒊ࢆJIS ࡢࢿࢪ㒊᭷ຠ᩿㠃✚6)ࡋ ࡚ࣔࢹࣝࡋ࡚࠸ࡿ㸬࡞࠾㸪M24F10T ࡣ㐨♧4)࡛つᐃࡉ ࢀ࡚࠸ࡿ㧗ຊ࣎ࣝࢺࡢ୰࡛㸪SHTB ࢆ㝖࠸࡚᭱ࡶ㝆అ㍈ ຊࡀ㧗࠸࣎ࣝࢺ࡛㸪M24F10T ࡢ㠀✺ฟᆺ᥋ྜࡢ㐺⏝ᛶ ࡘ࠸࡚ࡶ᳨ウࡍࡿ㸬Ỉᖹࣜࣈࡢᶫ㍈᪉ྥࡢ㛗ࡉࡣ࣎ࣝ ᅗ㸫2 T ᥋ྜ L ᥋ྜ ⾲㸫1 ᮏ◊✲࡛⏝ࡍࡿ࡞ኚᩘ ⾲㸫2 ᮏ◊✲࡛ᑐ㇟ࡍࡿ᱆ࡢㅖඖ Af, Ah, Aw :ୗࣇࣛࣥࢪ㸪Ỉᖹࣜࣈ㸪࢙࢘ࣈ᩿㠃✚ (mm2) bh, bv :Ỉᖹ᪉ྥ㖄┤᪉ྥࡢbᑍἲ (mm)ࠉᅗ㸫5, ⾲㸫5ཧ↷ Bf, Bh :᱆ࣇࣛࣥࢪ㸪Ỉᖹࣜࣈᖜ (mm) B0, By :ึᮇ࣎ࣝࢺ㍈ຊ㸪㝆అ࣎ࣝࢺ㍈ຊ (kN) d :㧗ຊ࣎ࣝࢺᚄ㸦ࡧᚄ㸧 (mm) eh :Ỉᖹ᪉ྥࡢ⦕➃㊥㞳 (mm)ࠉᅗ㸫5, ⾲㸫5ཧ↷ H :᱆㧗 (mm) K1, K2 :せ⣲⥅ᡭࡢ㞳㛫๛ᛶ㸪㝆అ๛ᛶ (kN/mm) ᅗ㸫15ཧ↷ M :స⏝᭤ࡆ࣮࣓ࣔࣥࢺ (kNm) Mgy :ᙉ࣮࣓ࣔࣥࢺ (kNm)ࠉ⾲㸫2ཧ↷ n1 :1⾜┠ࡢ࣎ࣝࢺᮏᩘ Pel :せ⣲⥅ᡭస⏝ࡍࡿⲴ㔜 (kN) Pgy :Mgy1⾜┠࣎ࣝࢺస⏝ࡍࡿⲴ㔜 (kN) ᅗ㸫5ཧ↷ Ps, Py :せ⣲⥅ᡭࡢ㞳㛫⪏ຊ㸪㝆అ⪏ຊ (kN) ᅗ㸫15ཧ↷ ph :Ỉᖹ᪉ྥࡢ࣎ࣝࢺࣆࢵࢳ (mm)ࠉᅗ㸫5, ⾲㸫5ཧ↷ SFh, SFf, SFw:Ỉᖹࣜࣈ㸪ୗࣇࣛࣥࢪ㸪࢙࢘ࣈస⏝ࡍࡿᘬᙇຊ(kN) te, tf, th, tw :࢚ࣥࢻࣉ࣮ࣞࢺ㸪ࣇࣛࣥࢪ㸪Ỉᖹࣜࣈ㸪࢙࢘ࣈཌ (mm)
Type A 1) Type B 2) Type C
᱆᩿㠃 (mm) ᱆㧗 H (mm) 2000 1500 1027 䝣䝷䞁䝆ᖜ Bf (mm) 400 500 350 䝣䝷䞁䝆ཌ tf (mm) 22 19 25 䜴䜵䝤ཌ tw (mm) 11 11 8 ᮦ㉁ SM570 SM490Y SM490Y ᶓಽ䜜ᗙᒅ䈜㻞 ඛ⾜ ୖ䝣䝷䞁䝆䛾ᒁ㒊ᗙᒅ ඛ⾜ 䝣䝷䞁䝆㝆అ ඛ⾜ 8610.74 4856.46 3467.14 ᙉ䝰䞊䝯䞁䝖䈜1 Mgy (kNm) 䈜1 : ᙉ䝰䞊䝯䞁䝖䛾⟬ฟ䛻䛒䛯䜚䠈Ᏻ⋡䜔ᢠಀᩘ䛿⪃៖䛧䛶䛔䛺䛔䠊 䈜2 : ᅽ⦰䝣䝷䞁䝆䛾ᅛᐃ㛫㊥㞳䛿⥭ᛴ௬タᶫ䛾ᶓ᱆㛫㝸4500mm1)䛸䛧䛶䛔䜛䠊 11 1956 22 22 400 500 350 11 8 19 19 1462 977 25 25 (a) T ᥋ྜ (b) L ᥋ྜ
ᅗ㸫3 㠀✺ฟᆺ᥋ྜࡢゎᯒࣔࢹࣝ᥋ྜ㒊ࡢ࣓ࢵࢩࣗศࡢ≧ἣ ᅗ㸫4 ゎᯒ⏝ࡋࡓᮦᩱᵓᡂ๎ ࢺ㍈ຊᙳ㡪ࡍࡿࡀ㸪࣎ࣝࢺ㍈ຊࢆ᮰ࡉࡏࡿࡓࡵࡢỈ ᖹࣜࣈ㛗ࡉࡣᮍゎ࡛᫂࠶ࡿ㸬ᐇᵓ㐀࡛ࡣᅗ㸫1 ࡢࡼ࠺㸪 Ỉᖹࣜࣈࡣ᥋ྜ㒊㏆ഐࡢࡳタ⨨ࡉࢀࡿࡀ㸪Ỉᖹࣜࣈ㛗 ࡉࡀ୍ᐃ௨ୖ࡞ࢀࡤ࣎ࣝࢺ㍈ຊቑศࡣ᮰ࡍࡿ⪃࠼㸪 ᮏ◊✲࡛ࡣ㸪⡆༢ࡢࡓࡵ᱆㛗ࢃࡓࡗ࡚Ỉᖹࣜࣈࢆタ ⨨ࡋࡓ㸬ࡲࡓ㸪᥋ྜ㒊๛ᛶࢆ᱆๛ᛶ௨ୖࡍࡿࡣ㸪 ᘬᙇഃࡢỈᖹࣜࣈࡼࡾࡶୗഃࡢ࢙࢘ࣈୗࣇࣛࣥࢪ᩿㠃 ࢆ⪃៖ࡏࡎ⟬ฟࡋࡓ᩿㠃ḟ࣮࣓ࣔࣥࢺࡀ㸪᱆ࡢ᩿㠃 ḟ࣮࣓ࣔࣥࢺ௨ୖ࡞ࡿᚲせࡀ࠶ࡿ 3)㸬ࡇࢀࢆ‶ࡓࡍ ࡓࡵ㸪ᮏ◊✲࡛ࡣỈᖹࣜࣈཌࢆୗࣇࣛࣥࢪཌࡢ1.5 ಸ࡛ ⤫୍ࡋࡓ㸬 ࢚ࣥࢻࣉ࣮ࣞࢺ㸪࣎ࣝࢺࢭࢵࢺ㸪Ỉᖹࣜࣈ㸪ୗࣇࣛࣥ ࢪࡣ8 ⠇Ⅼపῶ✚ศࢯࣜࢵࢻせ⣲㸪࢙࢘ࣈୖࣇࣛࣥࢪ ࡣ4 ⠇Ⅼపῶ✚ศࢩ࢙ࣝせ⣲ࢆ⏝ࡋࡓ㸬࢚ࣥࢻࣉ࣮ࣞ ࢺ㧗ຊ࣎ࣝࢺࡢせ⣲ࢧࢬࡣ1 ㎶ 5mm ࡛㸪ࡑࢀ௨እ ࡢ㒊ᮦࡢせ⣲ࢧࢬࡣ1 ㎶ 10mm ࡋ㸪Ỉᖹࣜࣈୗࣇ ࣛࣥࢪࡢᯈཌ᪉ྥࡢศࡣ᭱ప3 ศࡋ࡚࠸ࡿ㸬 ࢚ࣥࢻࣉ࣮ࣞࢺ㛫ࡢ᥋ゐ㠃ࡣቃ⏺㠀⥺ᙧᛶࢆ⪃៖ࡋ࡚ ࠾ࡾ㸪᥋ゐ㠃ࡢ᥋⥺᪉ྥࡢࡍࡾᣲືࡢᐃᘧࡣ࣌ࢼ ࣝࢸἲࢆ⏝࠸࡚㸪ᦶ᧿ಀᩘ0.4 ࢆ࠼࡚࠸ࡿ㸬୍᪉㸪 ᥋ゐ㠃ࡢἲ⥺᪉ྥࡢ᥋ゐ࣭㞳㛫ᣲືࡢᐃᘧࡣࣛࢢࣛ ࣥࢪࣗᮍᐃᩘἲ࠾ࡅࡿ๛᥋ゐࣔࢹࣝࢆ⏝࠸࡚࠸ࡿ㸬 ࡇࢀࡽࡢせ⣲ศ᥋ゐ᮲௳ࡼࡾ㸪㠀✺ฟᆺ᥋ྜࡢ ࣎ࣝࢺ㍈ຊቑศኚ㔞ࡢᐇ㦂್ゎᯒ್ࡀ୍⮴ࡍࡿࡇ ࢆᩥ⊩7)࡛☜ㄆࡋ࡚࠸ࡿ㸬 ゎᯒࡣ࣎ࣝࢺ㍈ຊᑟධẁ㝵᭤ࡆ࣮࣓ࣔࣥࢺస⏝ẁ㝵 ࡢ2 ẁ㝵ࢃࡅ࡚࠸ࡿ㸬࣎ࣝࢺ㍈ຊࡣ⥾⤖ຊࣔࢹࣝ8) ࡼࡾ࠼㸪࣎ࣝࢺ㍈㒊M24F10T ࡢタィ㍈ຊ(238kN)ࢆ ᑟධࡋࡓ㸬ᮏゎᯒ࡛ࡣ᱆➃㒊ࡢ୰❧㍈⨨㓄⨨ࡋࡓཧ ↷Ⅼ㸪᱆ᙉ࣮࣓ࣔࣥࢺMgyࡢ0.88 ಸࡢ࣮࣓ࣔࣥࢺ Ⲵ㔜ࢆస⏝ࡉࡏ㸪⣧᭤ࡆࢆ⌧ࡋࡓ㸬ཧ↷Ⅼ᱆➃㒊ࡣ MPC㸦Multi-Point Constraints㸧ࡼࡾ㸪ཧ↷Ⅼࡢືࡁᛂ ࡌ࡚᱆➃㒊ࡀ๛య⛣ື࣭ᅇ㌿ࡍࡿ᮲௳ࢆ࠼ࡓ㸬ࡇࡇ࡛㸪 0.88 Mgyࡣ㸪࢚ࣥࢻࣉ࣮ࣞࢺ᥋ྜࡀ௬ᱞᶫ㐺⏝ࡉࢀࡓ ࡼࡾ㸪ᕤࡢᏳ⋡ࡢࡾቑࡋࢆ⪃៖ࡋࡓ᱆ࡢ ᙉ (1.5 Mgy / 1.7)ࢆᐃࡋ࡚࠾ࡾ㸪ࡇࡢ್ࡣᅵᮌศ㔝ࡢ᥋ ྜ㒊タィ࡛⪃࠼ࡽࢀࡿ᭤ࡆ࣮࣓ࣔࣥࢺࡢ್࡛᭱࠶ࡿ㸬 ゎᯒ⏝࠸ࡓᮦᩱᵓᡂ๎ࢆᅗ㸫4 ♧ࡍ㸬᱆Ỉᖹ ࣜࣈࡣᙎᛶయ㸪࢚ࣥࢻࣉ࣮ࣞࢺࡣSM490Y ࡛࣐ࣝࢳࣜࢽ ᆺ9)ࢆ㸪㧗ຊ࣎ࣝࢺࡣF10T ࡛᪤ ᐇ㦂2)ࡢᮦᩱヨ㦂⤖ ᯝࡽᚓࡽࢀࡓረᛶᇦࡢᛂຊ̺ࡦࡎࡳ᭤⥺ࢆᘧ(1)ࡢ ࡁ๎࡛㏆ఝࡋࡓᵓᡂ๎ࢆබ⛠್ኚ᭦ࡋࡓࡶࡢࢆ⏝ ࡋࡓ㸬ᘧ(1)୰ࡢ C, n ࡣᮦᩱヨ㦂⤖ᯝࡼࡾồࡲࡿᐃᩘ࡛ࡑ ࢀࡒࢀ1320㸪0.049 ࡋࡓ㸬
( )
nC
V
H
(1) 䝰䞊䝯䞁䝖Ⲵ㔜0.88Mby 䜴䜵䝤ཌ୰ᚰ䛻ᑐ⛠᮲௳ ᱆➃䛻MPCᣊ᮰ A BA䠖ux, uy, uz, θy, θz ᅛᐃ B䠖ux, uy, θy, θz ᅛᐃ
㉥ᯟ㒊ᣑ 1⾜┠ 2⾜┠ 0 100 200 300 400 500 600 700 800 900 1000 1100 0 0.05 0.1 0.15 0.2 0.25 Tr ue s tr es s σt (N /m m 2) True strain εt(ʹ10-6) SM490Y (t ≤ 40mm) SM490Y (40mm < t ≤ 75mm) F10T 䝲䞁䜾⋡ E (N / mm2) 䝫䜰䝋䞁ẚ μ 㝆అⅬ σty (N / mm2 ) ᘬᙇⲴ㔜 σtu (N / mm2 ) 355.6 535.1 335.6 500.6 904.0 1003.6 SM490Y (t ≤ 40mm) 200000 0.3 SM490Y (40mm < t ≤ 75mm) F10T ⾲㸫3 㠀✺ฟᆺ᥋ྜࡢゎᯒࢣ࣮ࢫ᥋ྜ㒊ࡢᖹ㠃ᅗ ࢣ࣮ࢫྡ A24 A48 B24 B48 C24 C48
᱆ࢱࣉ Type A Type B Type C
࢚ࣥࢻ ࣉ࣮ࣞࢺཌ te (mm) 24 48 24 48 24 48 ࣎ࣝࢺิᩘ 2 3 2 n1By / Pgy 0.41 0.77 0.43 ᖹ㠃ᅗ 㸦༢ : mm㸧 128 50 37.5 50 50 25 450 72 49 141.5 141.5 141.5 128 86.5 86.5 50 28.5 50 50 19 5.550 72 72 50.5 5.5 50 133.4 133.4 133.4 133.4 A24, A48 B24, B48 C24, C48 Sym. 72 72.5 22 50 50 33 50 128 133.4 Sym. Sym. Sym. Sym. Sym.
ᅗ㸫5 n1ByPgyࡢ⪃࠼᪉ (༢㸸mm) ⾲㸫3 㠀✺ฟᆺ᥋ྜࡢゎᯒࢣ࣮ࢫࢆ♧ࡍ㸬ࣃ࣓࣮ࣛ ࢱࡣ᱆ࢱࣉ࢚ࣥࢻࣉ࣮ࣞࢺཌ࡛㸪᱆ࢱࣉࡣ⾲㸫2 ࡢType A ࡽ Type C㸪࢚ࣥࢻࣉ࣮ࣞࢺཌࡣ࣎ࣝࢺᚄࡢ 1 ಸ 2 ಸࡢ 2 ࣃࢱ࣮ࣥࢆ⏝ពࡋࡓ㸬࣎ࣝࢺิᩘࡣ M24 ࣎ࣝࢺࡀ㓄⨨࡛ࡁࡿ᭱ࡢิᩘ࡛㸪ࣇࣛࣥࢪᖜࡢไ⣙ ࡽỴᐃࡋ࡚࠸ࡿ㸬ࡲࡓ㸪⾲㸫3 ࡣ 1 ⾜┠࣎ࣝࢺࡢ㝆అ ㍈ຊࡢ⥲㸦n1By㸧Mgy1 ⾜┠࣎ࣝࢺ࿘㎶ࡢ⿕ ᥋ྜ㒊స⏝ࡍࡿᘬᙇຊPgyࡢẚ㸦௨ୗ㸪㝆అ㍈ຊ㸫 ᙉẚ㸧ࢆ♧ࡋ࡚࠸ࡿ㸬ᅗ㸫5 n1ByPgyࡢ⟬ฟ᪉ἲ ࢆ♧ࡍ㸬Pgyࡣ᭤ࡆ࣮࣓ࣔࣥࢺࡼࡿᛂຊศᕸࡽ⟬ฟ ࡉࢀ㸪ᛂຊศᕸࡢ⟬ฟ࠶ࡓࡗ࡚ࡣỈᖹࣜࣈࢆ⪃៖ࡋࡓ ᱆ࡢ᩿㠃ḟ࣮࣓ࣔࣥࢺࢆ⏝ࡋ࡚࠸ࡿ㸬Type A, B, C ࡛ 㝆అ㍈ຊ㸫ᙉẚࡣࡑࢀࡒࢀ0.41, 0.77, 0.43 ࡞ࡗࡓ㸬 ࣎ࣝࢺ㍈ຊ ᅗ㸫6 ᭤ࡆ࣮࣓ࣔࣥࢺ㸫࣎ࣝࢺ㍈ຊ㛵ಀࢆ♧ࡍ㸬⦪ ㍈ࡣ࣎ࣝࢺ㍈ຊࢆ㝆అ࣎ࣝࢺ㍈ຊ࡛㝖ࡋࡓ↓ḟඖ㍈ຊ㸪 ᶓ㍈ࡣస⏝࣮࣓ࣔࣥࢺࢆᙉ࣮࣓ࣔࣥࢺ࡛㝖ࡋࡓ↓ḟඖ ࣮࣓ࣔࣥࢺࡋࡓ㸬ỈᖹࡢⅬ⥺ࡣ㝆అ㍈ຊࢆ⾲ࡋ࡚࠸ ࡿ㸬࠶ࡿ1 ᮏࡢ࣎ࣝࢺࡀ㝆అ࣎ࣝࢺ㍈ຊ฿㐩ࡋࡓࡁ ࢆ᥋ྜ㒊ࡢ㝆అࡋ㸪ࡑࡢࡁࡢ᭤ࡆ࣮࣓ࣔࣥࢺࢆ㝆అ ࣮࣓ࣔࣥࢺᐃ⩏ࡍࡿ㸬ᅗ୰࡛㸪᥋ྜ㒊タィ㸦⏝㝈⏺㸧 ࡛⪃៖ࡉࢀࡿ࣮࣓ࣔࣥࢺ⠊ᅖ㸦0.44 Mgy ࡽ 0.88 Mgy㸧ࢆ ⅊Ⰽ࡛ሬࡾࡘࡪࡋ࡚࠸ࡿ㸬ࡇࡇ࡛㸪0.44 MgyࡣᏳ⋡1.7 ࢆ⪃៖ࡋࡓ᱆ࡢᙉࡢ75%ࢆᐃࡋ࡚࠾ࡾ㸪㐨♧4)ࡢ᥋ ྜ㒊ࡢ㝈⏺≧ែ1 ࡛⪃៖ࡉࢀࡿ᭤ࡆ࣮࣓ࣔࣥࢺࡢ᭱ᑠ್ ࡛࠶ࡿ㸬ࡲࡓ㸪࣎ࣝࢺ␒ྕࡣᅗ㸫5 ♧ࡍࡼ࠺㸪ࠕBࠖ ࡢ࠶⥆ࡃᩘᏐࡀ࣎ࣝࢺ⾜ࢆ⾲ࡋ࡚࠾ࡾ㸪᭱ᚋࡢᩘᏐ ࡀ࣎ࣝࢺิࢆ⾲ࡋ࡚࠸ࡿ㸬 ࢣ࣮ࢫB11 ࣎ࣝࢺࡀ᭱ึ㝆అࡋ࡚࠾ࡾ㸪㠀✺ฟᆺ ᥋ྜ࡛ࡣ㸪࢙࢘ࣈୗࣇࣛࣥࢪࡢᕪ㒊ࡽ᭱ࡶ㏆࠸࣎ ࣝࢺࡀ᭱ึ㝆అࡍࡿ㸬ࡇࡢ⤖ᯝࡽ㸪B11 ࣎ࣝࢺ╔ ┠ࡋࡓせ⣲⥅ᡭࡢᙉᗘኚᙧホ౯ᘧࡼࡾ㸪㠀✺ฟᆺ᥋ྜ ࡢ㝆అ࣎ࣝࢺ㍈ຊࢆ᥎ᐃࡍࡿࡇࡀ࡛ࡁࡿ⪃࠼ࡽࢀࡿ㸬 ࡓࡔࡋ㸪A48 ࢣ࣮ࢫ࡛ࡣ㸪B11 ࣎ࣝࢺ B12 ࣎ࣝࢺࡢ㍈ ຊࡀࡰᆒ➼ቑຍࡋ࡚࠸ࡿ㸬ࡇࢀࡣType A ࡢ⦕➃㊥㞳 ehࡀࡁࡃ㸪B12 ࣎ࣝࢺࡶୗࣇࣛࣥࢪࡽẚ㍑ⓗࡁ ࡞ᘬᙇຊࡀస⏝ࡋࡓࡓࡵ࡛࠶ࡾ㸪⦕➃㊥㞳ehࡀ࣎ࣝࢺࣆ ᅗ㸫6 ᭤ࡆ࣮࣓ࣔࣥࢺ㸫࣎ࣝࢺ㍈ຊ㛵ಀ ࢵࢳph௨ୖ࡞ࡿሙྜࡣ2 ิ┠௨㝆ࡢ࣎ࣝࢺ㍈ຊ↷ᰝࡶ ᚲせ࡞ࡿ㸬 A, C ࢩ࣮ࣜࢬࡣ 0.44 Mgy㏆࡛࣎ࣝࢺࡀ㝆అࡍࡿ㸬ࡇ ࢀࡣType A, C ᱆࡛ࡣ㸪M24F10T ࣎ࣝࢺࢆ⏝ࡋ࡚ࡶ ᥋ྜ㒊タィᚲせ࡞⪏ຊࢆ☜ಖ࡛ࡁ࡞࠸ࡇࢆ♧ࡋ࡚࠸ ࡿ㸬ࡇࡢࡓࡵ㸪㠀✺ฟᆺ᥋ྜ࡛ࡣM27 ௨ୖࡢኴᚄ࣎ࣝࢺ ࡢ⏝ࢆ᳨ウࡍࡿᚲせࡀ࠶ࡿ㸬 ⾲㸫3 ࡢ㝆అ㍈ຊ㸫ᙉẚࡑࢀࡒࢀࡢࢣ࣮ࢫࡢ↓ḟ ඖ㝆అ࣮࣓ࣔࣥࢺࢆẚ㍑ࡍࡿ㸪B ࢩ࣮ࣜࢬࡣ㝆అ㍈ ຊ㸫ᙉẚࡀ↓ḟඖ㝆అ࣮࣓ࣔࣥࢺࡼࡾࡶᑠࡉࡃ࡞ࡿ㸬 ࡇࢀࡣ㝆అ㍈ຊ㸫ᙉẚࡼࡾ࣎ࣝࢺ㍈ຊࢆ᥎ᐃࡍࡿ ༴㝤ഃࡢホ౯࡞ࡿྍ⬟ᛶࡀ࠶ࡿࡇࢆ♧ࡋ࡚࠸ࡿ㸬 1⾜┠→ 2⾜┠→ 䝣䝷䞁䝆 Ỉᖹ䝸䝤 䜴䜵䝤 tf 100 (2bv ) tw 50 (bh) 72 (ph) eh th n1㽢By䠖1⾜┠䝪䝹 䝖䛾㝆అ㍈ຊ䛾ྜィ 1 / 2 th Bf Pgy䠖Mgy䛻㉥ᩳ⥺ 㒊䛻స⏝䛩䜛ᘬᙇຊ B11 B12 B13 B21 B22 B23 72 (ph) 1ิ┠ ↓ 2ิ┠ ↓ 3ิ┠ ↓ (a) A ࢩ࣮ࣜࢬ (b) B ࢩ࣮ࣜࢬ (c) C ࢩ࣮ࣜࢬ 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 0.00 0.20 0.40 0.60 0.80 1.00 B / By M / Mgy B24 B11 B24 B12 B24 B13 B24 B21 B48 B11 B48 B12 B48 B13 B48 B21 0.44~0.88Mgy B48 : 0.74Mgy B24 : 0.66Mgy 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 0.00 0.20 0.40 0.60 0.80 1.00 B / By M / Mgy C24 B11 C24 B12 C24 B21 C24 B22 C48 B11 C48 B12 C48 B21 C48 B22 0.44~0.88Mgy C24 : 0.41Mgy C48 : 0.44Mgy 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 0.00 0.20 0.40 0.60 0.80 1.00 B / By M / Mgy A24 B11 A24 B12 A24 B21 A24 B22 A48 B11 A48 B12 A48 B21 A48 B22 0.44~0.88Mgy A48 : 0.44Mgy A24 : 0.41Mgy
ᅗ㸫7 ᭤ࡆ࣮࣓ࣔࣥࢺ㸫ᘬᙇຊ㛵ಀ ᅗ㸫8 ࢙࢘ࣈᘬᙇຊࢆồࡵࡿࡓࡵࡢᛂຊཧ↷⨨ ᅗ㸫9 ᥋ྜ㠃ࡢ㞳㛫㸦A48 ኚᙧಸ⋡ 20 ಸ㸧 ୗࣇࣛࣥࢪ࣭Ỉᖹࣜࣈ࣭࢙࢘ࣈస⏝ࡍࡿᘬᙇຊ ᅗ㸫7 ᭤ࡆ࣮࣓ࣔࣥࢺ㸫ᘬᙇຊ㛵ಀࢆ♧ࡍ㸬ᘬᙇຊ ࡣ࢚ࣥࢻࣉ࣮ࣞࢺᯈࡽᶫ㍈᪉ྥ10mm 㞳ࢀࡓ᩿㠃࡛ ィ ࡋ࡚࠸ࡿ㸬ୗࣇࣛࣥࢪỈᖹࣜࣈࡢᘬᙇຊࡣ㸪╔┠ ᩿㠃࠾ࡅࡿ㍈᪉ྥ⠇Ⅼຊࡢྜィ㔞ࢆィ ࡋࡓ㸬࢙࢘ࣈ ࡢᘬᙇຊࡣᅗ㸫8 ♧ࡍࡼ࠺㸪10mm 㛫㝸࡛ィ ࡋࡓ ࢙࢘ࣈࡢ✚ศⅬ࠾ࡅࡿ㍈᪉ྥᛂຊࡢ⥲ᖹᆒᑐ㇟ ࡍࡿ᩿㠃✚Aw_1ࡢ✚ࡽồࡵ࡚࠸ࡿ㸬ࡇࡇ࡛㸪Aw_1ࡣ௨ ୗ࡛ồࡵࡽࢀࡿ㸬 _1= ×(100 + ) w w h A t t (mm2) (2) ᅗ㸫7 ࡢ⦪㍈ࡣゎᯒࡽᚓࡽࢀࡓᘬᙇຊࢆᱱ⌮ㄽィ⟬ ࡛ồࡵࡓᘬᙇຊ࡛㝖ࡋࡓ↓ḟඖᘬᙇຊࡋ㸪ᶓ㍈ࡣ ࡛ᐃ⩏ࡋࡓ↓ḟඖ࣮࣓ࣔࣥࢺࡋࡓ㸬↓ḟඖᘬ ᙇຊࡀ1 ௨ୖ࡛࠶ࢀࡤゎᯒ್ࡀᱱ⌮ㄽ್ࡼࡾࡶࡁ࠸㸬 ᅗ㸫7 ࡼࡾᘬᙇຊࡣ᭤ࡆ࣮࣓ࣔࣥࢺࡢቑຍక࠸㸪㠀 ⥺ᙧⓗኚࡋ࡚࠸ࡿ㸬ࢣ࣮ࢫ࡛ୗࣇࣛࣥࢪࡢᘬᙇຊ ࡣ1 ࡼࡾࡶᑠࡉࡃ㸪᭤ࡆ࣮࣓ࣔࣥࢺࡢቑຍక࠸㸪ୗࣇ ࣛࣥࢪᘬᙇຊࡣῶᑡࡍࡿ㸬୍᪉㸪࢙࢘ࣈỈᖹࣜࣈࡢᘬ ᙇຊࡣ1 ௨ୖ࡞ࡿഴྥ࠶ࡾ㸪ୗࣇࣛࣥࢪࡢᘬᙇຊࡀ ࢙࢘ࣈỈᖹࣜࣈศᢸࡉࢀ࡚࠸ࡿ㸬㠀✺ฟᆺ᥋ྜ࡛ࡣ ᅗ㸫9 ࡢࡼ࠺㸪ୗࣇࣛࣥࢪഃࡀ L ᥋ྜ㸪࢙࢘ࣈഃࡸỈ ᖹࣜࣈഃࡀT ᥋ྜࡢᶵᵓࡋ࡚ኚᙧࡋ㸪࢙࢘ࣈഃࡸỈᖹ ࣜࣈഃẚ㍑ࡋ࡚ୗࣇࣛࣥࢪഃࡢ᥋ྜ㒊๛ᛶࡀపࡃ࡞ࡿ㸬 ࡇࡢࡓࡵ㸪ୗࣇࣛࣥࢪస⏝ࡍࡿᘬᙇຊࡀ㸪ୗࣇࣛࣥࢪ ഃࡼࡾࡶ᥋ྜ㒊๛ᛶࡢ㧗࠸࢙࢘ࣈࡸỈᖹࣜࣈఏ㐩ࡋࡓ ⪃࠼ࡽࢀࡿ㸬ࡲࡓ㸪᭤ࡆ࣮࣓ࣔࣥࢺࡀᑠࡉ࠸⠊ᅖ࡛࢘ ࢙ࣈỈᖹࣜࣈࡢ↓ḟඖᘬᙇຊࢆẚ㍑ࡍࡿ㸪࢙࢘ࣈ ࡢ↓ḟඖᘬᙇຊࡀࡁ࠸㸬ࡇࢀࡣ㸪࢙࢘ࣈୗࣇࣛࣥ ࢪࡀ㐃⥆ࡋ࡚࠾ࡾ㸪ୗࣇࣛࣥࢪࡽ࢙࢘ࣈᘬᙇຊࡀఏ 㐩ࡋࡸࡍ࠸ࡓࡵ⪃࠼ࡽࢀࡿ㸬ࡲࡓ㸪࢚ࣥࢻࣉ࣮ࣞࢺཌ ࡀࡁ࠸㸪ゎᯒ࡛ࡢᘬᙇຊࡣᱱ⌮ㄽ್㏆ࡃ࡞ࡿ㸬 ࡇࢀࡣ㸪࢚ࣥࢻࣉ࣮ࣞࢺཌࡢቑຍࡼࡾୗࣇࣛࣥࢪഃࡢ ᥋ྜ㒊๛ᛶࡀࡁࡃ࡞ࡿࡓࡵ࡛࠶ࡿ㸬 A, C ࢩ࣮ࣜࢬ࡛᭤ࡆ࣮࣓ࣔࣥࢺࡀࡁࡃ࡞ࡿ㸪࢙࢘ ࣈỈᖹࣜࣈࡢ↓ḟඖᘬᙇຊࡀ1 ࢆୗᅇࡿࡀ㸪ࡇࢀࡣ 1 ⾜┠࣎ࣝࢺࡀ࡚㝆అࡋ㸪ᘬᙇຊࢆ 2 ⾜┠࣎ࣝࢺࡀศ ᢸࡍࡿࡓࡵ࡛࠶ࡿ㸬 ᘬᙇຊࡣ࣎ࣝࢺ㍈ຊࡢ᥎ᐃᚲせ࡛࠶ࡿࡀ㸪㠀✺ฟᆺ ᥋ྜࡢୗࣇࣛࣥࢪ㸪Ỉᖹࣜࣈ࠾ࡼࡧ࢙࢘ࣈࡢᘬᙇຊࡣ᭤ ࡆ࣮࣓ࣔࣥࢺቑศᑐࡋ࡚㠀⥺ᙧⓗኚࡍࡿ㸬ࡇࡢࡓ ࡵ㸪࣎ࣝࢺ㍈ຊ᥎ᐃἲࡣ㸪L ᥋ྜ T ᥋ྜࡢ๛ᛶẚࢆ ⪃៖ࡋࡓᘬᙇຊࡢ᥎ᐃᘧࡀᚲせ⪃࠼ࡽࢀࡿ㸬 㠀✺ฟᆺ᥋ྜࡢ࣎ࣝࢺ㍈ຊ᥎ᐃࡢࡓࡵࡢせ⣲⥅ᡭ ࡑࡢᙉᗘኚᙧホ౯ᘧ せ⣲⥅ᡭࡢゎᯒࣔࢹࣝࣔࢹࣝ⠊ᅖ 㠀✺ฟᆺ࢚ࣥࢻࣉ࣮ࣞࢺ᥋ྜ࡛ࡣ㸪࢙࢘ࣈୗࣇࣛࣥ ࢪᕪ㒊ࡽ㏆࠸ B11 ࣎ࣝࢺࡀ᭱ึ㝆అ㍈ຊ฿㐩 ࡍࡿࡇࡽ㸪ࡇࡢ࣎ࣝࢺ╔┠ࡋࡓせ⣲⥅ᡭࢆᥦࡍ ࡿ㸬ᅗ㸫10 㠀✺ฟᆺ᥋ྜࡽྲྀࡾฟࡍせ⣲⥅ᡭࢆ♧ 䜴䜵䝤 ୗ䝣䝷䞁䝆 σw_1 σw_11 bw1 = 100mm I䠖ୗ䝣䝷䞁䝆ୖ㠃䛛䜙Ỉ ᖹ䝸䝤ୖ㠃䜎 䛷䛾㛫䛾 䜴 䜵 䝤 ㍈ ᪉ ྥ ᛂ ຊ 䜢 10mm㛫㝸䛷ィ II䠖I䛷ồ䜑䛯ᛂຊ䛾ᖹ ᆒ್䛸䜴䜵䝤᩿㠃✚Aw_1 䛾✚䛛䜙䜴䜵䝤ᘬᙇຊ 䜢ồ䜑䜛䠊 Ỉᖹ䝸䝤 th (a) A ࢩ࣮ࣜࢬ (b) B ࢩ࣮ࣜࢬ (c) C ࢩ࣮ࣜࢬ 0 0.5 1 1.5 2 2.5 0.00 0.20 0.40 0.60 0.80 1.00 Te ns ile L oad (F E m odel / T heor y) M / Mgy
A24 Flange A24 Stiffener A24 Web A48 Flange A48 Stiffener A48 Web
0 0.5 1 1.5 2 2.5 0.00 0.20 0.40 0.60 0.80 1.00 Te ns ile L oad (F E m odel / T heor y) M / Mgy B24 Flange B24 Stiffener B24 Web B48 Flange B48 Stiffener B48 Web 0 0.5 1 1.5 2 2.5 0.00 0.20 0.40 0.60 0.80 1.00 Te ns ile L oa d (F E m ode l / T he or y) M / Mgy C24 Flange C24 Stiffener C24 Web C48 Flange C48 Stiffener C48 Web (a) 0.22Mgy (b) 0.44Mgy࣎ࣝࢺ㝆అ ୗ䝣䝷䞁䝆ഃ䛛 䜙㞳㛫䛜⏕䛨䜛䠊 T᥋ྜ L᥋ྜ 䝪䝹䝖㝆అ䜒ୗ䝣䝷䞁䝆ഃ 䛾㞳㛫䛜䛝䛔䠊
ᅗ㸫10 㠀✺ฟᆺ᥋ྜࡽྲྀࡾฟࡍせ⣲⥅ᡭ (A24) ᅗ㸫11 せ⣲⥅ᡭࡢゎᯒࣔࢹ࣓ࣝࢵࢩࣗศࡢ≧ἣ ᅗ㸫12 㠀✺ฟᆺ᥋ྜࡢୗࣇࣛࣥࢪ㍈᪉ྥᛂຊศᕸ ( B24, 0.88Mgy ) ᅗ㸫13 㠀✺ฟᆺ᥋ྜ L せ⣲ࡢ࣎ࣝࢺ㍈ຊࡢẚ㍑ ࡍ㸬ୗࣇࣛࣥࢪ࢙࢘ࣈࢆྵࡴL せ⣲㸪Ỉᖹࣜࣈ࢘ ࢙ࣈࢆྵࡴT せ⣲ࡢ 2 ࡘࡢせ⣲⥅ᡭࢆ௬ᐃࡋࡓ㸬L せ⣲ ࡣ㠀✺ฟᆺ᥋ྜࡢ࣎ࣝࢺ㍈ຊࢆ᥎ᐃࡍࡿ┠ⓗ࡛㸪T せ⣲ ࡣL せ⣲ࡢ๛ᛶẚࢆồࡵ㸪ୗࣇࣛࣥࢪ㸪Ỉᖹࣜࣈ࠾ࡼ ࡧ࢙࢘ࣈస⏝ࡍࡿᘬᙇຊࢆ᥎ᐃࡍࡿ┠ⓗ࡛సᡂࡋࡓ㸬 ᅗ㸫11 せ⣲⥅ᡭࡢゎᯒࣔࢹ࣓ࣝࢵࢩࣗศ≧ἣࢆ ♧ࡍ㸬㠀⥺ᙧ᭷㝈ኚゎᯒࢆ⾜࠸㸪ᮦᩱᵓᡂ๎㸪᥋ྜ㠃 ࡢ᥋ゐ᮲௳㸪㧗ຊ࣎ࣝࢺࡢࣔࢹࣝࡘ࠸࡚ࡣ ❶ࡢ㠀 ✺ฟᆺ᥋ྜࡢゎᯒࣔࢹࣝྠᵝࡋࡓ㸬せ⣲ࡣ࡚8 ⠇ Ⅼ✚ศࢯࣜࢵࢻせ⣲࡛㸪࢚ࣥࢻࣉ࣮ࣞࢺࡣ1 ㎶ 4mm㸪 㧗ຊ࣎ࣝࢺࡣ1 ㎶ 2mm ࡛ࡑࢀࡒࢀศࡋ࡚࠸ࡿ㸬ゎᯒ ࡣ2 ẁ㝵ศࡅ㸪ࡲࡎ㸪 ❶ྠࡌ᪉ἲ࡛࣎ࣝࢺタィ ㍈ຊࢆᑟධࡋ㸪ࡑࡢᚋ㸪せ⣲⥅ᡭࡢ➃㠃ࡢ⠇Ⅼᙉไ ኚࢆ࠼ࡿࡇ࡛ᘬᙇⲴ㔜ࢆ⌧ࡋࡓ㸬 L せ⣲ࡣୗࣇࣛࣥࢪ೫ᚰ᭤ࡆࡀ⏕ࡌࡿࡓࡵ㸪㍈᪉ྥ ࡢୗࣇࣛࣥࢪ㛗ࡉࡀ⥅ᡭ⪏ຊᙳ㡪ࡍࡿࡇࡀ▱ࡽࢀ ࡚࠸ࡿ10)㸬L せ⣲ࡢୗࣇࣛࣥࢪ㛗ࡉࢆỴᐃࡍࡿࡓࡵ㸪 㠀✺ฟᆺ᥋ྜࡢୗࣇࣛࣥࢪ㍈᪉ྥᛂຊ╔┠ࡍࡿ㸬ᅗ㸫 12 B24 ࢣ࣮ࢫࡢୗࣇࣛࣥࢪ㍈᪉ྥᛂຊศᕸࢆ♧ࡍ㸬 ᅗࡣ㸪ୗࣇࣛࣥࢪ㠃እ᭤ࡆࡢᙳ㡪ࡀࡁ࠸㸪ୗࣇࣛࣥ ࢪཌ࢚ࣥࢻࣉ࣮ࣞࢺཌࡢᑠࡉ࠸ B24 ࢣ࣮ࢫࢆ♧ࡋ࡚ ࠸ࡿ㸬ᅗ୰ࡢᛂຊ್ࡣ╔┠᩿㠃࠾ࡅࡿࣇࣛࣥࢪᖜࡢ せ⣲ࡢᛂຊ್ࢆᖹᆒࡋࡓ್࡛࠶ࡿ㸬࢚ࣥࢻࣉ࣮ࣞࢺ ࡽ150mm ⨨ࡲ࡛ࡣ㠃እ᭤ࡆࡢᙳ㡪࡛㸪ୗࣇࣛࣥࢪୖ ഃࡢᛂຊࡀୗഃࡢᛂຊࡼࡾࡶࡁ࠸ࡀ㸪࢚ࣥࢻࣉ࣮ࣞࢺ ࡽ400mm ⨨࡛ࡣ㸪ୗࣇࣛࣥࢪୗഃࡢᛂຊࡀୖഃࡢ ᛂຊࡼࡾࡶࡁࡃ㸪㠃እ᭤ࡆࡢᙳ㡪ࡣᑠࡉࡃ࡞ࡿ㸬ࡇࡢ ⤖ᯝࡼࡾ㸪L せ⣲ࡢୗࣇࣛࣥࢪ㛗ࡉࡣ 400mm ࡋࡓ㸬 㠀✺ฟᆺ᥋ྜせ⣲⥅ᡭࡢ࣎ࣝࢺ㍈ຊࡢẚ㍑ ᅗ㸫13 㠀✺ฟᆺ᥋ྜせ⣲⥅ᡭࡢ࣎ࣝࢺ㍈ຊ㸫ᘬ ᙇຊ㛵ಀࡢẚ㍑ࢆ♧ࡍ㸬ỈᖹࡢⅬ⥺ࡣ㝆అ࣎ࣝࢺ㍈ຊࢆ ⾲ࡋ࡚࠸ࡿ㸬⦪㍈ࡣ࣎ࣝࢺ㍈ຊ࡛㸪ᶓ㍈ࡣL せ⣲ࡢⲴ㔜 Pel㸪ࡲࡓࡣ㠀✺ฟᆺ᥋ྜࡢ1 ิ┠࣎ࣝࢺస⏝ࡍࡿ࢙࢘ ࣈୗࣇࣛࣥࢪࡢᘬᙇຊPf1+wࡋ࡚࠸ࡿ㸬ࡇࡇ࡛㸪Pf1+w ࡣᘧ (3)ࡼࡾồࡲࡿ㸬 _1 1 _1 _ 1 1 2 1000 f f w fa w w mean f A P SF A A
V
§ · ¨ ¸ ¨ ¸ © ¹ (3) ࡇࡇ࡛㸪 ⥺ᑐ⛠ ୗ䝣䝷䞁䝆 Ỉᖹ䝸䝤 䜴䜵䝤 Tせ⣲ Lせ⣲ 1 / 2 th 1 / 2 ph Ỉᖹ䝸䝤 ୗ䝣䝷䞁䝆 䜴䜵䝤 䜴䜵䝤 ⥺ᑐ⛠ ⥺ᑐ⛠ ⥺ᑐ⛠ 䜴䜵䝤ཌ୰ᚰ䛻ᑐ⛠᮲௳ 䜴䜵䝤 Lせ⣲㸸ୗࣇࣛࣥࢪ Tせ⣲㸸Ỉᖹࣜࣈ ᯈཌ୰ᚰ䛻ᑐ⛠᮲௳䠄Tせ⣲䠅 㧗ຊ࣎ࣝࢺ ࢚ࣥࢻࣉ࣮ࣞࢺ 䜴䜵䝤䛸ୗ䝣䝷䞁䝆䜎䛯䛿Ỉᖹ䝸䝤➃㒊 䛾⠇Ⅼ䛻Z᪉ྥ䛾ᙉไኚ䜢䛘䜛䠊 ➃㠃䛾⠇Ⅼ䜢ᅛᐃ 0 20 40 60 80 100 120 140 160 180 0 50 100 150 200 250 300 350 400 450 St re ss in longi tudi na l di re ct ion ( N /m m 2)Distance from endplate (mm)
Upper side Lower side
Upper side Lower side
(a) A24 (b) A48
(c) B24 (d) C24 200 250 300 350 400 450 0 100 200 300 400 Bo lt ax ia l fo rc e B (k N ) Tensile load Pel , Pf1+w(kN) 㠀✺ฟᆺ᥋ྜB11 Lせ⣲ 200 250 300 350 400 450 0 100 200 300 400 Bo lt ax ia l fo rc e B (k N ) Tensile load Pel , Pf1+w(kN) 㠀✺ฟᆺ᥋ྜB11 Lせ⣲ 200 250 300 350 400 450 0 100 200 300 400 B olt a xia l fo rc e B (k N ) Tensile load Pel , Pf1+w(kN) 㠀✺ฟᆺ᥋ྜB11 Lせ⣲ 200 250 300 350 400 450 0 100 200 300 400 Bo lt ax ia l fo rc e B (k N ) Tensile load Pel , Pf1+w(kN) 㠀✺ฟᆺ᥋ྜB11 Lせ⣲
ᅗ㸫14 㠀✺ฟᆺ᥋ྜ L せ⣲ࡢ ࣎ࣝࢺ㝆అࡢኚᙧᅗ㸦A24 ኚᙧಸ⋡ 10 ಸ㸧 ⾲㸫4 せ⣲⥅ᡭࡢゎᯒࣃ࣓࣮ࣛࢱ Af 㸸 ୗࣇࣛࣥࢪ᩿㠃✚ (mm2) SFfa 㸸 ゎᯒࡢୗࣇࣛࣥࢪᘬᙇຊ (kN) σwa_mean 㸸 ゎᯒࡢ࢙࢘ࣈࡢᖹᆒᛂຊ (N / mm2) Af_1 㸸 L せ⣲ࡢୗࣇࣛࣥࢪ᩿㠃✚ (mm2)
_1 f w h h f A t p b ut (4) ᅗ㸫13 (a), (c)ࡼࡾ㸪A24 B24 ࡣ㠀✺ฟᆺ᥋ྜࡢ B11 L せ⣲ࡢ࣎ࣝࢺ㍈ຊࡣ㸪㝆అ࣎ࣝࢺ㍈ຊࡲ࡛ࡼࡃ୍⮴ ࡍࡿ㸬ࡇࢀࡣᅗ㸫14 ♧ࡍࡼ࠺㸪Ỉᖹࣜࣈࡽ B11 స⏝ࡍࡿᘬᙇຊ㸦ᅗ㸫14 (a)㸧㸪L せ⣲ࡢ࡚ࡇຊ㸦ᅗ 㸫14 (b)㸧ࡢࡁࡉࡀ୍⮴ࡋࡓࡓࡵ࡛࠶ࡿ㸬Ỉᖹࣜࣈࡽ ࡢᘬᙇຊࡀ࡚ࡇຊࡼࡾࡶࡁ࠸ሙྜࡣ㸪ᅗ㸫13 (b)ࡢ ࡼ࠺㠀✺ฟᆺ᥋ྜࡢB11 ࡀ L せ⣲ࡢ࣎ࣝࢺẚ࡚ ᪩ᮇ㝆అࡋ㸪㏫ࡢሙྜࡣ㸪ᅗ㸫13 (d)ࡢࡼ࠺ L せ⣲ ࡢ࣎ࣝࢺࡀB11 ࡼࡾ᪩ᮇ㝆అࡍࡿ㸬ࡲࡓ㸪ᅗࡣ┬␎ࡋ ࡓࡀ㸪B48 C48 ࡣࡑࢀࡒࢀᅗ㸫13 (d)ᅗ㸫13 (b)ఝ ࡓᣲືࢆ♧ࡋࡓ㸬㝆అ࣎ࣝࢺ㍈ຊࡲ࡛ࡢ㠀✺ฟᆺ᥋ྜ L せ⣲ࡢⲴ㔜 Pf1+w, Pelࡢ᭱ㄗᕪࡣ⣙9%࡛㸪Ỉᖹࣜࣈ ࡢᘬᙇຊL せ⣲ࡢ࡚ࡇຊࡢᑠࢆ⪃៖ࡍࡿࡇ࡛㸪 ࡉࡽ⢭ᗘⰋࡃ࣎ࣝࢺ㍈ຊࢆ᥎ᐃ࡛ࡁࡿ⪃࠼ࡽࢀࡿ㸬 せ⣲⥅ᡭࡢゎᯒࢣ࣮ࢫ せ⣲⥅ᡭࡢᙉᗘኚᙧホ౯ᘧࢆᥦࡍࡿ┠ⓗ࡛㸪ࣃ࣓ࣛ ࢺࣜࢵࢡゎᯒࢆᐇࡍࡿ㸬⾲㸫4 ኚࡉࡏࡿゎᯒࣃࣛ ࣓࣮ࢱࢆ♧ࡍ㸬ࣃ࣓࣮ࣛࢱࡣ࣎ࣝࢺᚄ㸪࢚ࣥࢻࣉ࣮ࣞࢺ ཌ㸪࢙࢘ࣈཌ㸪ୗࣇࣛࣥࢪཌ㸪⥅ᡭᙧᘧ࡛࠶ࡿ㸬 ࣃ࣓ࣛࢺࣜࢵࢡゎᯒ࡛⪃៖ࡍࡿ㧗ຊ࣎ࣝࢺ㛵㐃ࡍࡿ ᑍἲ್ࢆ⾲㸫5 ♧ࡍ㸬㧗ຊ࣎ࣝࢺࡣ㐨♧࡛つᐃࡉࢀ࡚ ࠸ࡿᦶ᧿᥋ྜ⏝࣎ࣝࢺM20㹼M24 ຍ࠼㸪ኴᚄ࣎ࣝࢺࡢ M27, M30 ࡶᑐ㇟ࡍࡿ㸬⿕᥋ྜ㒊⾲㠃ࡽ࣎ࣝࢺ୰ᚰࡲ ࡛ࡢ㊥㞳bh, bv㸦௨ୗ㸪b ᑍἲ㸧ࡣᶫᱱ⏝㧗ຊ࣎ࣝࢺᘬᙇ ᥋ྜタィᣦ㔪 11)㸦௨ୗ㸪タィᣦ㔪㸧࡛つᐃࡉࢀ࡚࠸ࡿ 50mm ࢆᇶᮏࡍࡿ㸬ࡓࡔࡋ㸪M27, M30 ࡘ࠸࡚ࡣ㸪Ỉ ᖹࣜࣈࣇࣛࣥࢪ㛫⥾ࡵࡅᕤලࡀධࡿࡼ࠺b ᑍἲ ࢆ60mm ࡋࡓ㸬⦕➃㊥㞳 ehࡘ࠸࡚㸪࢚ࣥࢻࣉ࣮ࣞࢺ ⦕➃ࡣ⮬ື࢞ࢫษ᩿⦕ࡲࡓࡣᅽᘏ⦕ࢆ௬ᐃࡋ㸪㐨♧࡛つ ᐃࡉࢀࡿ᭱ᑠ㊥㞳ࡋࡓ㸬࣎ࣝࢺࣆࢵࢳphࡣ࣎ࣝࢺᚄࡢ 3 ಸ࡛タᐃࡋ࡚࠸ࡿ㸬M27, M30 ࡢ⦕➃㊥㞳࣎ࣝࢺࣆࢵ ࢳࡣᩥ⊩12)ࢆཧ⪃㸪࠸ࡎࢀࡶ᭱ᑠ㊥㞳࡛Ỵᐃࡋࡓ㸬 ࢚ࣥࢻࣉ࣮ࣞࢺཌࡢ᭱ᑠ್ࡣ࣎ࣝࢺᚄྠࡌࡋࡓ㸬 ࡇࢀࡣᶫᱱ⏝㧗ຊ࣎ࣝࢺタィᣦ㔪㸦㸧13)࡛つᐃࡉࢀࡿ ࢚ࣥࢻࣉ࣮ࣞࢺࡢ᭱ᑠᯈཌ࡛࠶ࡿ㸬ࡲࡓ㸪࣎ࣝࢺᚄࡀ2.5 ಸࡼࡾࡁ࠸ᯈࢆ⥾ࡅ࡛ࡁࡿ࣎ࣝࢺࡣධᡭࡀ㞴ࡋ࠸ࡓ ࡵ㸪᭱ࡢ࢚ࣥࢻࣉ࣮ࣞࢺཌࡣ࣎ࣝࢺᚄࡢ2.5ಸࡋࡓ㸬 ࢙࢘ࣈཌୗࣇࣛࣥࢪཌࡢẚࡘ࠸࡚㸪0.25, 0.5, 0.75 ࡞ࡿࡼ࠺࢙࢘ࣈୗࣇࣛࣥࢪཌࢆタᐃࡋࡓ㸬0.5 ࡣ Type A ࡢ࢙࢘ࣈཌୗࣇࣛࣥࢪཌࡢẚ࡛㸪Type B, C ࡢ࢘ ࢙ࣈཌࣇࣛࣥࢪཌࡢẚ 0.32 0.58 ࢆ⥙⨶࡛ࡁࡿࡼ࠺ 㸪᭱ᑠ್0.25㸪್᭱ 0.75 ࢆタᐃࡋࡓ㸬࡞࠾㸪๓᳨ ウ࡛T せ⣲ࡢ⪏ຊ㞳㛫㔞ࡣ࢙࢘ࣈୗࣇࣛࣥࢪཌࡢẚ ࡢᙳ㡪ࢆཷࡅ࡞ࡗࡓࡓࡵ㸪T せ⣲ࡣ࢙࢘ࣈᯈཌ 11mm㸪 ୗࣇࣛࣥࢪᯈཌ22mm ࡢࢣ࣮ࢫࡢࡳࢆ⏝ពࡋࡓ㸬ࡉࡽ㸪 ⥅ᡭᙧᘧ㸦L せ⣲㸪T せ⣲㸧ࢆࣃ࣓࣮ࣛࢱຍ࠼㸪ྜィ 80 ࡢゎᯒࢣ࣮ࢫࢆ⏝ពࡋࡓ㸬 せ⣲⥅ᡭࡢᙉᗘኚᙧホ౯ᘧࡢ᳨ウ᪉㔪 ゎᯒࡽᚓࡽࢀࡓせ⣲⥅ᡭࡢⲴ㔜̺㞳㛫㛵ಀࢆᅗ㸫15 ♧ࡍ㉥⥺ࡢࢺࣜࣜࢽ㛵ಀ࡛⌮ࡍࡿ㸬ࢺࣜࣜࢽ ࡢ➨ 1 ໙㓄ࡣཎⅬࡽ㞳㛫⪏ຊࡲ࡛ࡢ༊㛫ࡢ⥺๛ᛶ 㸦௨ୗ㸪㞳㛫๛ᛶ㸧࡛K1ࡋ㸪➨2 ໙㓄ࡣ㞳㛫⪏ຊࡽ 㝆అ⪏ຊࡲ࡛ࡢ༊㛫ࡢ⥺๛ᛶ㸦௨ୗ㸪㝆అ๛ᛶ㸧࡛K2㸪 㝆అ⪏ຊ௨㝆ࡢ໙㓄ࡣ0 ࡍࡿ㸬ࡇࡇ࡛㸪㞳㛫⪏ຊࡣᅗ 㸫15 ࡢⲴ㔜㸫࣎ࣝࢺ㍈ຊ᭤⥺ࡢ 0.8㹼0.9By㛫ࡢࢹ࣮ࢱࡢ ᅇᖐศᯒࡼࡾồࡲࡿ➨2 ḟ໙㓄ࡢ┤⥺ึᮇ࣎ࣝࢺ㍈ ຊࡢ┤⥺ࡢⅬࡢⲴ㔜ࡋࡓ14)㸬㝆అ⪏ຊࡣ࣎ࣝࢺ㍈ ຊࡀ㝆అ㍈ຊ฿㐩ࡋࡓࡢⲴ㔜ࡍࡿ㸬㞳㛫⪏ຊ㝆 ࣃ࣓࣮ࣛࢱ ⠊ᅖ ࣎ࣝࢺᚄ d (mm) 20, 22, 24, 27, 30 ࢚ࣥࢻࣉ࣮ࣞࢺཌ te / d 1.0, 1.5, 2.0, 2.5 ࢙࢘ࣈཌ / ୗࣇࣛࣥࢪཌ tw / tf (tw, tf (mm)) 0.25, 0.5, 0.75 (8, 32), (11, 22), (12, 16) ⥅ᡭᙧᘧ L せ⣲㸪T せ⣲ ⾲㸫5 ⏝ࡍࡿ㧗ຊ࣎ࣝࢺ㛵㐃ࡍࡿᑍἲ್ 䝪䝹䝖ᚄ d (mm) 㐨♧䛷䛾 つᐃ bᑍἲ bv, bh (mm) ⦕➃㊥㞳 eh (mm) 䝪䝹䝖䝢䝑䝏 ph (mm) ᮦ㉁ タィ㍈ຊ B0 (kN) 20 28 60 165 22 32 66 205 24 37 72 238 27 45 81 310 30 50 90 379 ኚᩘ⨨ ᭷ ↓ 50 60 F10T (S10T) → → 䝣䝷䞁䝆 Ỉᖹ䝸䝤 䜴䜵䝤 tf tw bh ph ph eh th bv bv bv 1⾜┠ 2⾜┠ (a) 㠀✺ฟᆺ᥋ྜ (b) L せ⣲ Ỉᖹ䝸䝤 ୗ䝣䝷䞁䝆 ୗ䝣䝷䞁䝆 Ỉᖹ䝸䝤䛛䜙䛾ᘬᙇຊ ᥋ྜ㠃㛫䛻స⏝䛩䜛 䛶䛣ຊ
ᅗ㸫15 せ⣲⥅ᡭࡢ⪏ຊ๛ᛶࡢᐃ⩏ ᅗ㸫16 ᥎ᐃ್ゎᯒ್ࡢẚ㍑㸦㞳㛫⪏ຊ Ps㝆అ⪏ຊPy㸧 అ⪏ຊࡣ࣎ࣝࢺ㍈ຊⲴ㔜ࡢ㛵ಀࡽỴࡲࡿࡓࡵ㸪せ⣲ ⥅ᡭࡢ࡚ࡇຊಀᩘࡀ㔜せ࡞ࡿ㸬ࡇࡇ࡛㸪Ⲵ㔜P ࣎ ࣝࢺ㍈ຊB ࡢ㛵ಀࡣ࡚ࡇຊಀᩘ p ࢆ⏝࠸ࡓḟᘧ࡞ࡿ㸬
(1
)
B
p P
(5) K1, K2ࢆỴࡵࡿࡓࡵࡢ㞳㛫㔞ࡣせ⣲⥅ᡭࡢୗࣇࣛࣥࢪ 㸦Ỉᖹࣜࣈ㸧㸫࢙࢘ࣈᕪ㒊ࡢ᥋ྜ㠃㛫ࡢ㞳㛫㔞ࢆ⏝࠸ ࡿ㸬L せ⣲ T せ⣲ࡢ࡚ࡇຊಀᩘ pL, pT㸪㞳㛫๛ᛶKL_1, KT_1࠾ࡼࡧ㝆అ๛ᛶKL_2, KT_2ࢆ㔜ᅇᖐศᯒࡼࡾᐃᘧ ࡋ㸪せ⣲⥅ᡭࡢᙉᗘኚᙧホ౯ᘧࢆᥦࡍࡿ㸬 せ⣲⥅ᡭࡢ࡚ࡇຊಀᩘ FE ゎᯒ⤖ᯝࡢ㔜ᅇᖐศᯒࡼࡾ㸪せ⣲⥅ᡭࡢ࡚ࡇຊ ಀᩘࢆồࡵࡿ㸬タィᣦ㔪11)ࡢ࡚ࡇຊಀᩘࡣⲴ㔜ึᮇ ࣎ࣝࢺ㍈ຊࡢᑠ㛵ಀ࡛ホ౯ᘧࡀ␗࡞ࡿࡀ㸪ᮏ◊✲ࡢ࡚ ࡇຊಀᩘࡣᘧ(5)ࢆኚᙧࡋࡓḟᘧ࡛⤫୍ࡍࡿ㸬 1 B p P (6) ᅇᖐศᯒ࠺↓ḟඖኚᩘࢆᘧ (7)~(11)♧ࡍ㸬 π1~π4ࡣ࣎ࣝࢺᚄd ࢆศẕࡋ㸪π1, π3, π4ࡣ⾲㸫4 ࡛ኚ ࡉࡏࡓ࢚ࣥࢻࣉ࣮ࣞࢺཌte㸪ࣇࣛࣥࢪཌtf㸪࢙࢘ࣈཌtwࢆ ศᏊࡋࡓ㸬ࡲࡓ㸪⾲㸫5 ࡛ bhࡀ50mm 60mm ࡛ኚ ࡍࡿࡓࡵ㸪bhࢆศᏊࡋࡓπ2ࢆタᐃࡋࡓ㸬ࡉࡽ㸪௵ព Ⲵ㔜࡛ࡢ࡚ࡇຊಀᩘࡢ⟬ฟࢆ⾜࠺ࡓࡵ㸪Ⲵ㔜ࢆึᮇ ࣎ࣝࢺ㍈ຊ࡛㝖ࡋࡓπ5ࢆタᐃࡋ࡚࠸ࡿ㸬 1 e t d S (7) 2 h b d S (8) 3 f t d S (9) 4 w t d S (10) 5 0 P BS
(11) タィᣦ㔪11)ࡢT ᥋ྜࡢ࡚ࡇຊಀᩘᘧࡣ π 5ࡢ3 ḟᘧ ࡛㸪⢭ᗘࡀⰋ࠸ࡇࡽᮏ◊✲ࡶࡇࢀೌ࠺㸬L せ⣲ T せ⣲ࡢ࡚ࡇຊಀᩘᘧࢆᘧ(12)㸪ᘧ(13)♧ࡍ㸬 3 2 1 5 2 5 3 5 4 L L L L Lp
D S
D S
D S D
(12) PL_y, PT_y PL_s, PT_s B0 0.8By By KL_1 , KT_1 Bolt Force (kN) Lo ad ( kN ) L oad (kN ) Separation at A (mm) KL_2 , KT_2 PL_s, PT_s: L, Tせ⣲䛾㞳㛫⪏ຊ (kN) PL_y, PT_y: L, Tせ⣲䛾㝆అ⪏ຊ (kN) KL_1 , KT_1 : L, Tせ⣲䛾㞳㛫๛ᛶ (kN / mm) KL_2 , KT_2 : L, Tせ⣲䛾㝆అ๛ᛶ (kN / mm) 0.9By 㟷 ⥺ 䛿0.8-0.9By㛫 䛾 䝕 䞊 䝍 䛾ᅇᖐศᯒ䜘䜚ồ䜎䜛Ⲵ㔜-䝪 䝹䝖㍈ຊ᭤⥺䛾2ḟ໙㓄┤⥺䠊 㞳㛫Ⲵ㔜䛿Ⲵ㔜-䝪䝹䝖㍈ຊ᭤⥺䛾2ḟ໙ 㓄┤⥺䛸ึᮇ䝪䝹䝖㍈ຊ䛸䛾Ⅼ䛾Ⲵ㔜䠊(a) PL_s (b) PL_y (c) PT_s (d) PT_y
0 100 200 300 400 500 600 0 200 400 600 Estim ation PL_ y (k N ) FE model PL_y(kN) 0 100 200 300 400 500 600 0 200 400 600 E stim ation PL_ s (k N ) FE model PL_s(kN) 0 100 200 300 400 500 600 0 200 400 600 Estim ation PT_ s (k N ) FE model PT_s(kN) 0 100 200 300 400 500 600 0 200 400 600 Estim ation PT_ y (k N ) FE model PT_y(kN)
ᅗ㸫17 ᥎ᐃ್ゎᯒ್ࡢẚ㍑㸦㞳㛫๛ᛶ K1㝆అ๛ᛶK2㸧 3 2 1 5 2 5 3 5 4 T T T T T
p
D S
D S
D S D
(13) ࡇࡇ࡛㸪αL1~αL4ࡣπ1~π4ࢆㄝ᫂ኚᩘࡋࡓ㔜ᅇᖐศᯒ ࡼࡾ௨ୗࡢࡼ࠺ồࡲࡿ㸬 0.608 0.578 0.418 0.514 3.103 1 1 2 3 4 Le
D
S
u
S
u
S
u
S
u
(14) 0.475 0.415 0.310 0.391 3.783 2 1 2 3 4 Le
D
S
u
S
u
S
u
S
u
(15) 0.348 0.248 0.203 0.267 3.400 3 1 2 3 4 Le
D
S
u
S
u
S
u
S
u
(16) 0.229 0.112 0.116 0.155 2.080 4 1 2 3 4 Le
D
S
u
S
u
S
u
S
u
(17) ࡲࡓ㸪T せ⣲ࡢࣃ࣓ࣛࢺࣜࢵࢡゎᯒ࡛ࡣ tftwࢆ୍ᐃ ࡋ࡚࠸ࡿࡓࡵ㸪αT1~αT4ࡣπ1, π2ࡢࡳࢆㄝ᫂ኚᩘࡋࡓ 㔜ᅇᖐศᯒࡼࡾḟᘧ࡞ࡿ㸬 1.730 0.640 1.357 1 1 2 Te
D
S
u
S
u
(18) 1.285 0.452 2.505 2 1 2 Te
D
S
u
S
u
(19) 0.860 0.282 2.579 3 1 2 Te
D
S
u
S
u
(20) 0.534 0.166 1.621 4 1 2 Te
D
S
u
S
u
(21) ࡓࡔࡋ㸪ᘧ(12)㸪ᘧ(13)ࡢ࡚ࡇຊಀᩘࢆᘧ(5)௦ධࡋ࡚ ᚓࡽࢀࡓ࣎ࣝࢺ㍈ຊB ࡀึᮇ࣎ࣝࢺ㍈ຊ B0௨ୗࡢሙྜ ࡣ㸪࣎ࣝࢺ㍈ຊࢆึᮇ࣎ࣝࢺ㍈ຊ⨨ࡁ࠼ࡿ㸬ᘧ(14)~ ᘧ(21)ࡢ⮬⏤ᗘㄪᩚ῭ࡳỴᐃಀᩘࡣ᭱ᑠ࡛ 0.90 ࡛࠶ࡗࡓ㸬 ࡲࡓ㸪ᥦࡋࡓ࡚ࡇຊಀᩘࡽồࡲࡿ㞳㛫⪏ຊPs㸪㝆 అ⪏ຊPyゎᯒ್ࡢẚ㍑ࢆᅗ㸫16 ♧ࡍ㸬ᅗ୰ࡢ 2 ᮏ ࡢᩳ⥺ࡣㄗᕪ+10%-10%ࡢ┤⥺࡛࠶ࡿ㸬PL_s, PL_y, PT_s PT_yࡢゎᯒ್᥎ᐃ್ࡢㄗᕪࡣࡑࢀࡒࢀ᭱12.2%, 4.9%, 15.1%, 1.7%࡞ࡗࡓ㸬 㞳㛫๛ᛶ㝆అ๛ᛶ FE ゎᯒࡢ㔜ᅇᖐศᯒࡼࡾ㞳㛫๛ᛶ㝆అ๛ᛶࡢ᥎ ᐃᘧࢆồࡵࡿ㸬㞳㛫๛ᛶ㝆అ๛ᛶࡢ᥎ᐃᘧ⏝ࡍࡿ 㞳㛫⪏ຊ㝆అ⪏ຊࡢ↓ḟඖ㔞ࢆࡑࢀࡒࢀୗグ♧ࡍ㸬 6 0 s P BS
(22) 7 0 y P B S (23) 㞳㛫⪏ຊPs㝆అ⪏ຊPyࡣ ࡛ᥦࡋࡓ࡚ࡇຊ ಀᩘࡽồࡵࡿ㸬㔜ᅇᖐศᯒࡢ⤖ᯝ㸪L せ⣲ࡢ㞳㛫๛ᛶ KL_1ࡣπ1~π4π6ࢆຍ࠼ࡓᘧ(24)࡛㸪㝆అ๛ᛶ KL_2ࡣࡉࡽ π6ࢆຍ࠼ࡓᘧ(25)࡛ࡑࢀࡒࢀ⾲ࡍࡇࡀ࡛ࡁࡿ㸬 1.509 1.399 0.889 0.318 _1 1 2 3 4 0.334 5.983 6 L K eS
S
S
S
S
u u u u u (24) 0.173 0.767 0.394 0.669 0.532 _ 2 1 2 3 4 6 2.967 5.317 7 L K eS
S
S
S
S
S
u u u u u u (25) T せ⣲ࡢ㞳㛫๛ᛶ KT_1ࡣπ1, π2 , π4, π6ࢆㄝ᫂ኚᩘࡋࡓ ᘧ(26)࡛㸪㝆అ๛ᛶ KT_2ࡣπ7ࢆຍ࠼ࡓᘧ(27)࡛⾲ࡍ㸬 1.515 1.784 0.220 5.567 _1 1 4 6 T KS
uS
uS
ue (26) 0.379 1.145 0.551 3.613 4.700 _2 1 4 6 7 TK
S
u
S
u
S
u
S
u
e
(27) ᘧ(24)~(27)ࡢᅇᖐᘧࡢ⮬⏤ᗘㄪᩚ῭ࡳỴᐃಀᩘࡣ᭱ᑠ ࡛0.94 ࡛࠶ࡗࡓ㸬ࡲࡓ㸪ᅇᖐᘧࡽồࡲࡿ㞳㛫๛ᛶ㸪㝆 అ๛ᛶゎᯒ್ࡢẚ㍑ࢆᅗ㸫17 ♧ࡍ㸬ᅗ୰ࡢ 2 ᮏࡢ ᩳ⥺ࡣㄗᕪ㸩10%-10%ࡢ┤⥺࡛࠶ࡿ㸬KL_1, KL_2, KT_1 KT_2ࡢゎᯒ್᥎ᐃ್ࡢㄗᕪࡣࡑࢀࡒࢀ᭱ 12.0%, 13.8%, 12.8%, 3.0%࡞ࡗࡓ㸬 ୗࣇࣛࣥࢪ๛ᛶᘬᙇຊศᢸࡢ㛵ಀ ゎᯒࣔࢹࣝ࠾ࡼࡧゎᯒࢣ࣮ࢫ ᮏ❶࡛ࡣ㸪ୗࣇࣛࣥࢪࡢ୍㒊࡛ࣖࣥࢢ⋡ࢆኚࡉࡏࡓ ᱆ࡢFE ゎᯒࢆᐇࡋ㸪๛ᛶẚୗࣇࣛࣥࢪ࣭Ỉᖹࣜࣈ࣭ ࢙࢘ࣈస⏝ࡍࡿᘬᙇຊࡢ㛵ಀࢆᐃ㔞ⓗ᫂ࡽࡋ㸪 せ⣲⥅ᡭస⏝ࡉࡏࡿࡓࡵࡢᘬᙇຊࡢ᥎ᐃᘧࢆᥦࡍࡿ㸬 ᅗ㸫18 ゎᯒࣔࢹࣝࢆ♧ࡍ㸬ゎᯒࡣᙎᛶᚤᑠኚゎᯒ (a) KL_1 (b) KL_2 (c) KT_1 (d) KT_2 0 1 2 3 4 5 6 7 8 9 10 0 2.5 5 7.5 10 Estim ation KT_1 (k N / m ) FE model KT_1 (kN / m) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.25 0.5 0.75 1 E stim ation KT_2 (k N / m ) FE model KT_2 (kN / m) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.5 1 1.5 2 E stim ation KL_1 (k N / m ) FE model KL_1 (kN / m) 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.125 0.25 0.375 0.5 E stim ation KL_2 (k N / m ) FE model KL_2 (kN / m)ᅗ㸫18 ୗࣇࣛࣥࢪࡢࣖࣥࢢ⋡ࢆኚࡉࡏࡓ᱆ࣔࢹࣝ ⾲㸫6 ኚࡉࡏࡿࣃ࣓࣮ࣛࢱ ࣃ࣓࣮ࣛࢱ ⠊ᅖ ๛ᛶẚ γ 1.0, 0.75, 0.5, 0.45, 0.4, 0.35, 0.3, 0.25, 0.2, 0.15, 0.1, 0.05, 0.04, 0.03, 0.02 Ỉᖹࣜࣈ⨨ 2bv (mm) 100, 120 Ỉᖹࣜࣈཌ th / tf 1.0, 1.5, 2.0
᱆ࢱࣉ Type A, Type B, Type C
ᅗ㸫19 せ⣲⥅ᡭࡢ๛ᛶẚ γ ࡢ㢖ᗘศᕸ ᅗ㸫20 ๛ᛶẚᘬᙇຊࡢ㛵ಀ ࡋ㸪Ⲵ㔜᮲௳㸪ቃ⏺᮲௳࠾ࡼࡧせ⣲ࡣ ❶ࡢゎᯒࣔࢹ ࣝྠࡌ࡛࠶ࡿ㸬ୗࣇࣛࣥࢪᨭ㛫୰ኸ㒊ࡢࣖࣥࢢ⋡ࢆኚ ࡉࡏࡿࡇ࡛㸪㠀✺ฟᆺ᥋ྜࡢୗࣇࣛࣥࢪഃ࢙࢘ࣈ㸪 Ỉᖹࣜࣈഃࡢ๛ᛶࡢ㐪࠸ࢆ⌧ࡍࡿ㸬ࣖࣥࢢ⋡ࢆኚࡉ ࡏࡿ⠊ᅖ㸦௨ୗ㸪๛ᛶኚ㒊㸧ࡣᶫ㍈᪉ྥ100mm㸪ᶫ ㍈┤ゅ᪉ྥࡣୗࣇࣛࣥࢪᖜࡋࡓ㸬ᶫ㍈᪉ྥࡢ100mm ࡣ⾲㸫3 ࡢ A48, B48, C48 ࢣ࣮ࢫࡢ࢚ࣥࢻࣉ࣮ࣞࢺ⥲ཌ 96mm ࢆᅄᤞධࡋ࡚Ỵᐃࡋࡓ㸬⾲㸫6 ゎᯒ࡛ኚࡉ ࡏࡿࣃ࣓࣮ࣛࢱࢆ♧ࡍ㸬๛ᛶẚγ㸪Ỉᖹࣜࣈ⨨ 2bv㸪Ỉ ᖹࣜࣈཌ㸪᱆ࢱࣉࡢ4 ࡘࢆࣃ࣓࣮ࣛࢱࡋࡓ㸬 ๛ᛶẚγ ࡣ๛ᛶኚ㒊ࡢࣖࣥࢢ⋡ Efࢆ୍⯡㒊ࡢࣖࣥࢢ ⋡E (2.0105 N / mm2)࡛㝖ࡋࡓ್ࡋ㸪L せ⣲ࡢ๛ᛶ K L T せ⣲ࡢ๛ᛶ KTࡢẚࡰ➼ࡋ࠸௬ᐃࡍࡿ㸬 f L T E K E K J | (28) (KL, KT) ࡢ⤌ࡳྜࢃࡏࡋ࡚⪃࠼ࡽࢀࡿࡢࡣ㸪(KL_1, KT_1), (KL_2, KT_1), (KL_2, KT_2) ࡢ 3 ㏻ࡾ࡛࠶ࡿ㸬 ❶ࡢゎᯒ ࡛ᚓࡽࢀࡓせ⣲⥅ᡭࡢ๛ᛶẚࡢศᕸࢆᅗ㸫19 ♧ࡍ㸬L せ⣲ T せ⣲ࡢ๛ᛶẚ γ ࡢ᭱ᑠ್㸪್᭱ࡣࡑࢀࡒࢀ 0.034, 0.473 ࡞ࡗࡓ㸬ࡇࡢࡓࡵ㸪⾲㸫6 ୰ࡢ๛ᛶẚ γ ࡢ ࣃ࣓࣮ࣛࢱࡣ᭱ᑠ್ࢆ0.02 ࡋ㸪0.02~0.05 ࡢ㛫ࡣ 0.01 ้ࡳ㸪0.05~0.5 ࡢ㛫ࡣ 0.05 ้ࡳ㸪せ⣲⥅ᡭࡢ๛ᛶẚ࡛ࡣ ほ ࡉࢀ࡞࠸0.5~1.0 ࡢ㛫ࡣ 0.25 ้ࡳ࡛ኚࡉࡏ࡚࠸ࡿ㸬 Ỉᖹࣜࣈ⨨ࡣୗࣇࣛࣥࢪୖ㒊ࡽỈᖹࣜࣈୗ㠃ࡲ࡛ ࡢ㊥㞳࡛㸪⾲㸫5 ୰ࡢ bvࡢ2 ಸ࡛⾲ࡉࢀࡿ㸬Ỉᖹࣜࣈ ⨨ࡢ100, 120mm ࡣࡑࢀࡒࢀ M20~M24 ࢆ᥇⏝ࡋࡓሙྜ 㸪M27, M30 ࢆ᥇⏝ࡋࡓሙྜࡢ bvࡽỴᐃࡋ࡚࠸ࡿ㸬 Ỉᖹࣜࣈཌࡣୗࣇࣛࣥࢪཌᑐࡋ࡚1, 1.5, 2 ಸࡢ 3 ࣃ ࢱ࣮ࣥࢆ⏝ពࡋ㸪⾲㸫2 ࡢ 3 ࣃࢱ࣮ࣥࡢ᱆ࢱࣉࢆຍ࠼ ྜィ270 ࡢゎᯒࢣ࣮ࢫࢆసᡂࡋࡓ㸬 ๛ᛶẚȚᘬᙇຊࡢ㛵ಀ ᅗ㸫20 ๛ᛶẚᘬᙇຊࡢ㛵ಀࢆ♧ࡍ㸬⦪㍈ࡣゎᯒࡢ ᨭ㛫୰ኸࡢᘬᙇຊࢆᱱ⌮ㄽィ⟬ࡽồࡲࡿᘬᙇຊ࡛㝖ࡋ ࡓ↓ḟඖᘬᙇຊࡋ㸪ᶓ㍈ࡣ๛ᛶẚγ ࡋ࡚࠸ࡿ㸬ゎ ᯒ࡛ࡢ࢙࢘ࣈࡢᘬᙇຊSFwaࡣᅗ㸫8 ࡛♧ࡋࡓ㍈᪉ྥᛂຊ ࡢᖹᆒ್᩿㠃✚ࡢ✚ࡽồࡵ࡚࠾ࡾ㸪㍈᪉ྥᛂຊࡣᨭ 㛫୰ኸ࡛ィ ࡋࡓ㸬 ᅗ㸫20 ࡼࡾ㸪๛ᛶẚࡀᑠࡉࡃ࡞ࢀࡤୗࣇࣛࣥࢪస⏝ ࡍࡿᘬᙇຊࡣῶᑡࡋ㸪Ỉᖹࣜࣈ࢙࢘ࣈస⏝ࡍࡿᘬᙇ ຊࡣቑຍࡍࡿ㸬ࡲࡓ㸪Ỉᖹࣜࣈ࢙࢘ࣈࡢ↓ḟඖᘬᙇ ຊࢆẚ㍑ࡍࡿ࢙࢘ࣈࡢ↓ḟඖᘬᙇຊࡀࡁࡃ࡞ࡾ㸪 㠀✺ฟᆺ᥋ྜࡢᅗ㸫7 ࡢഴྥ୍⮴ࡍࡿ㸬 㠀✺ฟᆺ᥋ྜ࠾ࡅࡿᘬᙇຊࡢ᥎ᐃᘧ 㔜ᅇᖐศᯒࡼࡾ㸪๛ᛶẚγ ᑐࡍࡿ↓ḟඖᘬᙇຊ ࡢᘧࢆồࡵࡿ㸬ᅗ㸫20 ࡢ᭤⥺ᙧ≧ࡣ log (γ)ࡢ 2 ḟ㛵ᩘ࡛ ⾲⌧࡛ࡁࡿ⪃࠼㸪௨ୗࡢࡼ࠺ᐃᘧࡋࡓ㸬
^
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21 log 2log 1 ha h h hb SF SF E J E J (29)
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21 log 2log 1 fa f f fb SF SF E J E J (30)
^
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21 log 2log 1 wa w w wb SF SF E J E J (31) ࡇࡇ࡛㸪 SFha : Ỉᖹࣜࣈࡢᘬᙇຊ㸦ゎᯒ್㸧(kN) 䝲䞁䜾⋡䜢ኚ䛥䛫䜛⠊ᅖ ୗ䝣䝷䞁䝆 Ỉᖹ䝸䝤 䜴䜵䝤 䝰䞊䝯䞁䝖Ⲵ㔜0.88Mby 䜴䜵䝤ཌ୰ᚰ䛻ᑐ⛠᮲௳ A
A䠖ux, uy, uz, θy, θz ᅛᐃ B䠖ux, uy, θy, θz ᅛᐃ
B 0 0.5 1 1.5 2 2.5 3 3.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Te nsile L oad (F E model / Theory ) Stiffness ratio γ Ỉᖹ䝸䝤 ୗ䝣䝷䞁䝆 䜴䜵䝤 ᱆䝍䜲䝥: Type A Ỉᖹ䝸䝤⨨2bv: 100 Ỉᖹ䝸䝤ཌth/ tf: 1.5 0 5 10 15 20 25 30 Frequency Stiffness ratio γ KL_2 / KT_1KL_2 / KT_1 KL_1 / KT_1KL_1 / KT_1 KL_2 / KT_2KL_2 / KT_2
ᅗ㸫21 ᥎ᐃ್ゎᯒ್ࡢẚ㍑㸦↓ḟඖᘬᙇຊ㸧 SFhb : Ỉᖹࣜࣈࡢᘬᙇຊ㸦ᱱ⌮ㄽ್㸧(kN) SFfa : ୗࣇࣛࣥࢪࡢᘬᙇຊ㸦ゎᯒ್㸧(kN) SFfb : ୗࣇࣛࣥࢪࡢᘬᙇຊ㸦ᱱ⌮ㄽ್㸧(kN) SFwa : ࢙࢘ࣈࡢᘬᙇຊ㸦ゎᯒ್㸧(kN) SFwb : ࢙࢘ࣈࡢᘬᙇຊ㸦ᱱ⌮ㄽ್㸧(kN) ࡲࡓ㸪γ = 1 ࡢࡁ㸪↓ḟඖᘬᙇຊࡣ 1 ࡞ࡿࡢ࡛㸪ᘧ (29)~(31)ࡢᐃᩘ㡯ࡣ 1 ࡋ࡚࠸ࡿ㸬βh1, βh2, βf1, βf2, βw1, βw2 ࡢ㔜ᅇᖐᘧᚲせ࡞↓ḟඖኚᩘࢆ௨ୗ♧ࡍ㸬 8 h f t t S (32) 9 v b H
S
(33) 10 w f t t S (34) βh1, βh2, βf1, βf2, βw1, βw2,ࡣ π8~π10ࢆ⏝ࡍࡿࡇ࡛㸪ḟ ࡢᘧ࡛⾲ࡍࡇࡀ࡛ࡁࡿ㸬 1 0.0096 8 0.1000 9 0.0067 10 0.0292 h E S S S (35) 2 0.0098 8 0.0070 9 0.0364 10 0.0638 h E S S S (36) 1 0.0008 8 0.0368 9 0.0003 10 0.0253 f E S S S (37) 2 0.0084 8 0.2489 9 0.010 10 0.1100 f E S S S (38) 1 0.020 8 0.2832 9 0.074 10 0.1090 w E S S S (39) 2 0.0071 8 0.4054 9 0.4227 10 0.5424 h E S S S (40) ᥦࡋࡓᅇᖐᘧࡽồࡲࡿ↓ḟඖᘬᙇຊゎᯒ್ࡢ ẚ㍑ࢆᅗ㸫21 ♧ࡍ㸬ᅗ୰ࡢ 2 ᮏࡢᩳ⥺ࡣㄗᕪ+10%-10%ࡢ┤⥺࡛࠶ࡿ㸬ᅗ㸫21 ࡢࣉࣟࢵࢺࡢ┦㛵ಀᩘࡣ࠸ࡎ ࢀࡶ0.99 ௨ୖ࡞ࡗࡓ㸬ࡲࡓ㸪Ỉᖹࣜࣈ㸪ୗࣇࣛࣥࢪ࠾ ࡼࡧ࢙࢘ࣈࡢ↓ḟඖᘬᙇຊࡢゎᯒ್᥎ᐃ್ࡢㄗᕪࡣ ࡑࢀࡒࢀ᭱4.9%, 14.0%, 9.9%࡛࠶ࡗࡓ㸬 㠀✺ฟᆺ᥋ྜࡢ࣎ࣝࢺ㍈ຊ᥎ᐃἲ ࣎ࣝࢺ㍈ຊ᥎ᐃἲ࣎ࣝࢺ㍈ຊࡢ↷ᰝ᪉ἲ ᅗ㸫22 㠀✺ฟᆺ᥋ྜࡢ࣎ࣝࢺ㍈ຊ↷ᰝࡢࣇ࣮ࣟࢆ ♧ࡍ㸬ࡲࡎ㸪᱆᩿㠃タィ࣮࣓ࣔࣥࢺMdࢆỴᐃࡋࡓᚋ 㸪᥋ྜ㒊ㅖඖࢆ௬Ỵᐃࡍࡿ (I, II)㸬ࡑࡢᚋ㸪せ⣲⥅ᡭࡢ 㞳㛫⪏ຊPL_s, PT_s㝆అ⪏ຊPL_y, PT_yࢆồࡵ (III)㸪㞳㛫๛ᛶKL_1, KT_1㝆అ๛ᛶKL_2, KT_2ࢆ⟬ฟࡍࡿ (IV)㸬⧞ ࡾ㏉ࡋィ⟬ࡢࡓࡵࡢ࣮࣓ࣔࣥࢺቑศ㔞ΔM ࢆỴᐃᚋ (V)㸪 VI~XIII ࡢ⧞ࡾ㏉ࡋィ⟬ࡼࡾタィ࣮࣓ࣔࣥࢺ Mdࡲ࡛ࡢ ࣎ࣝࢺ㍈ຊB ࢆ᥎ᐃࡍࡿ㸬ࡇࡇ࡛㸪࣮࣓ࣔࣥࢺቑศ㔞 ΔM ࡣ㸪1 ᅇࡢ⧞ࡾ㏉ࡋィ⟬࡛╔┠࣎ࣝࢺ B11 㸪⣙ 1kN ࡢ Ⲵ㔜ࢆ࠼ࡿ᪉㔪࡛㸪ḟᘧ࡛Ỵᐃࡋࡓ㸬 ΔM = 1 (kN)H (m)n1 (41) ࡲࡓ㸪ᘧ(41)࡛⟬ฟࡉࢀࡿ࣮࣓ࣔࣥࢺቑศ㔞 ΔM ࢆ⏝ ࠸ࡓ⧞ࡾ㏉ࡋィ⟬࡛㸪㝆అ࣎ࣝࢺ㍈ຊ฿㐩ࡍࡿࡢ᭤ ࡆ࣮࣓ࣔࣥࢺ್ࡀ༑ศ᮰ࡍࡿࡇࢆ☜ㄆࡋ࡚࠸ࡿ㸬 ⧞ࡾ㏉ࡋィ⟬ࡢ᭱ึࡣ㸪Ỉᖹࣜࣈ㸪ୗࣇࣛࣥࢪ㸪࢙࢘ ࣈࡢᘬᙇຊSFh_i, SFf_i, SFw_iࢆ⟬ฟࡍࡿ(VI)㸬⧞ࡾ㏉ࡋィ
⟬1 ᅇ┠ (i = 1)ࡢ SFh_i, SFf_i, SFw_iࡣγ = 1 ࢆᘧ(29), (30),
(31)௦ධࡋࡓࡁࡢ SFha, SFfa, SFwa➼ࡋࡃ࡞ࡿ㸬⧞ࡾ
㏉ࡋi ᅇ┠(i >1)ࡢ SFha_i, SFfa_i, SFwa_iࡣ㸪i-1 ᅇ┠ࡢ SF
ha_i-1, SFfa_i-1, SFwa_i-1XIII ࡛ồࡵࡽࢀࡓỈᖹࣜࣈ㸪ୗࣇࣛࣥ
ࢪ㸪࢙࢘ࣈࡢᘬᙇຊቑศΔSFh, ΔSFf, ΔSFwࢆຍ࠼ࡿࡇ࡛ ⟬ฟࡍࡿ㸦ᘧ(42), (43), (44)㸧㸬࡞࠾㸪ΔSFh, ΔSFf, ΔSFwࡣ㸪 ⧞ࡾ㏉ࡋィ⟬i-1 ᅇ┠ࡢ VIII ࡛ồࡲࡿ γ ΔM ࢆᘧ(29), (30), (31)௦ධࡋࡓࡁࡢ SFha, SFfa, SFwa➼ࡋ࠸㸬 _
= Δ
+
_ -1 h i h h iSF
SF
SF
(42) _= Δ
+
_ -1 f i f f iSF
SF
SF
(43) (a) Ỉᖹࣜࣈ (b) ୗࣇࣛࣥࢪ (c) ࢙࢘ࣈ 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Es tim ati on FE model 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Es tim ati on FE model 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Es tim ati on FE model_
= Δ
+
_ -1w i w w i
SF
SF
SF
(44) ḟ㸪L せ⣲ T せ⣲స⏝ࡍࡿⲴ㔜 SFL, SFTࢆ⟬ฟࡍࡿ(VII)㸬L せ⣲ T せ⣲స⏝ࡍࡿⲴ㔜 SFL, SFTࡣ SFha_i, SFfa_i, SFwa_iࢆ⏝࠸࡚ḟᘧ࡛ồࡵࡿ㸬
_ _ + 2 + = × + 2 2 w i w h h L f i f SF t b p SF SF B (45) _ _ + 2 + = × + 2 2 w i w h h T h i h SF t b p SF SF B (46)
ḟ㸪VII ࡛ồࡵࡓ SFL, SFTIII ࡛ồࡵࡓ PL_s, PL_y, PT_s , PT_yࡢᑠ㛵ಀࢆ᮲௳ศᒱ⏝ࡋ㸪๛ᛶẚγ ࢆ⟬ ฟࡍࡿ (VIII) 㸬ࡑࡋ࡚㸪L せ⣲ࡢ࡚ࡇຊಀᩘ pLL せ ⣲స⏝ࡍࡿⲴ㔜SFLࢆᘧ(4)௦ධࡍࡿࡇ࡛࣎ࣝࢺ㍈ ຊࢆ᥎ᐃࡍࡿ㸬ࡓࡔࡋ㸪L せ⣲ࡢ࡚ࡇຊ SFLpLࡼࡾ ࡶỈᖹࣜࣈࡽB11 ࣎ࣝࢺస⏝ࡍࡿᘬᙇຊ SFh_1ࡀ ࡁ࠸ሙྜ㸪ᅗ㸫13(b)♧ࡍࡼ࠺ L せ⣲࡛᥎ᐃࡍࡿ࣎ࣝ ࢺ㍈ຊࡀ㠀✺ฟᆺ᥋ྜࡢ࣎ࣝࢺ㍈ຊࡼࡾࡶపࡃ㸪࣎ࣝࢺ ㍈ຊࡢ᥎ᐃ್ࡀ༴㝤ഃ࡞ࡿྍ⬟ᛶࡀ࠶ࡿ㸬ࡇࡢࡓࡵ㸪 SFh_1ࡀSFLpLࡼࡾࡶࡁ࠸ሙྜࡣ࣎ࣝࢺ㍈ຊࢆḟᘧ࡛ ᥎ᐃࡍࡿ㸬 _1
=
L+
hB SF
SF
(47) ࡇࡇ࡛㸪 _1 + 2 + = × 2 2 w h h ha h h t b p SF SF B (48) ᚓࡽࢀࡓ࣎ࣝࢺ㍈ຊ㝆అ࣎ࣝࢺ㍈ຊByࢆẚ㍑ࡋ(X)㸪 ࣎ࣝࢺ㍈ຊࡢ᥎ᐃ್ࡀ㝆అ࣎ࣝࢺ㍈ຊࢆ㉸࠼ࡿሙྜࡣ᥋ ྜ㒊ㅖඖࢆᗘ᳨ウࡍࡿ(II)㸬VI~XIII ࡲ࡛ࡢィ⟬ࢆ⧞ࡾ ㏉ࡋ࣮࣓ࣔࣥࢺࡀタィ࣮࣓ࣔࣥࢺ Md௨ୖ࡞ࡗࡓሙྜ ࣎ࣝࢺ㍈ຊࡢ↷ᰝࢆࡍࡿ㸬࡞࠾㸪ᮏ↷ᰝἲࡣ㸪࣎ ࣝࢺᚄ20~30mm㸪࢚ࣥࢻࣉ࣮ࣞࢺཌࡣ࣎ࣝࢺᚄࡢ 1~2.5 ಸ㸪᱆ࡢ࢙࢘ࣈ㸫ୗࣇࣛࣥࢪཌẚࡀ0.25~0.75 ಸࡢ⠊ᅖ ࡛㐺⏝࡛ࡁࡿ㸬 ࣎ࣝࢺ㍈ຊ᥎ᐃἲゎᯒࡢẚ㍑ 㠀✺ฟᆺ᥋ྜࡢゎᯒ⤖ᯝୗグࡢ3 ✀㢮ࡢ࣎ࣝࢺ㍈ຊ ᥎ᐃἲࢆẚ㍑ࡍࡿ㸬 ᥎ᐃἲ1㸸ᩥ⊩ 2)࡛⏝࠸ࡽࢀࡓ㠀✺ฟᆺ᥋ྜࡢ࣎ࣝࢺ ㍈ຊ᥎ᐃἲ࡛㸪ᅗ㸫22 ࡢ VIII㸪IX ࢆ⪃៖ࡏࡎ㸪࣎ࣝࢺ㍈ ຊࡣᅗ㸫5 ࡢ㉥ᩳ⥺㒊స⏝ࡍࡿᘬᙇຊࢆ 1 ⾜┠ࡢ࣎ࣝ ࢺᮏᩘn1࡛㝖ࡍࡿࡇ࡛⟬ฟࡍࡿ㸬 ᥎ᐃἲ2㸸ᅗ㸫22 ࡢ VIII ࢆ⪃៖ࡏࡎ㸪IX ࡢࡳࢆ⪃៖ࡋ ࡚࣎ࣝࢺ㍈ຊࢆ᥎ᐃࡍࡿ㸬ࡘࡲࡾ㸪L せ⣲స⏝ࡍࡿⲴ 㔜SFLࡣᱱ⌮ㄽィ⟬ࡼࡾồࡵ㸪๛ᛶẚγ ࡢᙳ㡪ࡣ⪃៖ࡋ ࡞࠸㸬 ᥎ᐃἲ3㸸ᅗ㸫22 ࡢ VIII㸪IX ࢆ⪃៖ࡋ࡚࣎ࣝࢺ㍈ຊࢆ ᥎ᐃࡍࡿ㸬 ᅗ㸫23 ࣮࣓ࣔࣥࢺ̾࣎ࣝࢺ㍈ຊ㛵ಀࡢゎᯒ್᥎ᐃ ್ࡢẚ㍑ࢆ♧ࡍ㸬⦪㍈ࡣ࣎ࣝࢺ㍈ຊࢆ㝆అ࣎ࣝࢺ㍈ຊ ࡛↓ḟඖࡋࡓ↓ḟඖ㍈ຊ࡛㸪ᶓ㍈ࡣస⏝࣮࣓ࣔࣥࢺ ࢆᙉ࣮࣓ࣔࣥࢺ࡛㝖ࡋࡓ↓ḟඖ࣮࣓ࣔࣥࢺࡋࡓ㸬 ᅗ㸫23 ୰ࡢ᥎ᐃ್ࡣ᥎ᐃἲ 1 ᥎ᐃἲ 3 ࡽồࡲࡿ࣎ࣝ ࢺ㍈ຊࢆ♧ࡋ࡚࠸ࡿ㸬 ᥎ᐃἲ1 ࡣ㝆అ㍈ຊ(B / By =1)ゎᯒ್Ⰻ࠸ᩚྜࢆ ♧ࡍࢣ࣮ࢫࡶᏑᅾࡍࡿࡀ㸪ᅗ㸫23 (c)࡛ࡣ㸪᥎ᐃἲ 1 ࡀゎ ᯒ್ࡼࡾࡶప࠸↓ḟඖ࣎ࣝࢺ㍈ຊࢆ♧ࡋ㸪༴㝤ഃࡢホ ౯ࢆ࠼ࡿ㸬 ᥎ᐃἲ3 ࡣ࡚ࡇຊࡢᙳ㡪ࢆ⪃៖ࡍࡿࡇ࡛㸪ึᮇ࣎ ࣝࢺ㍈ຊࡽࡢ❧ࡕୖࡀࡾࡸ㠀⥺ᙧⓗ࡞࣎ࣝࢺ㍈ຊࡢቑ ຍࢆ⾲⌧࡛ࡁ࡚࠾ࡾ㸪࣎ࣝࢺ㍈ຊࡢ᥎ᐃ್ࡀゎᯒ್௨ୖ ࡞ࡿഴྥࡀ☜ㄆ࡛ࡁࡓ㸬 ᅗ㸫24 ࣎ࣝࢺ㝆అ࣮࣓ࣔࣥࢺࡢゎᯒ್᥎ᐃ್ ࡢẚ㍑ࢆ♧ࡍ㸬⦪㍈ࡣ࣎ࣝࢺ㝆అࡢ࣮࣓ࣔࣥࢺࡢゎᯒ ್ࢆ᥎ᐃ್࡛㝖ࡋࡓ↓ḟඖ㔞ࡋ㸪ゎᯒ್ࡣ⾲㸫3 ࡢゎ ᯒࢣ࣮ࢫࡢ⤖ᯝ࡛࠶ࡿ㸬↓ḟඖ㔞ࡀ1 ௨ୖ࡛࠶ࢀࡤ㸪ゎ ᯒ್ࡀ᥎ᐃ್ࡼࡾࡶࡁࡃ㸪Ᏻഃࡢホ౯࡞ࡿ㸬 ᥎ᐃἲ1 ࡣ B24, B48, C24 ࡛↓ḟඖ㔞ࡀ 1 ᮍ‶࡞ࡾ㸪 ᅗ㸫22 㠀✺ฟᆺ᥋ྜࡢ࣎ࣝࢺ㍈ຊ↷ᰝ I. ᱆᩿㠃䛸 タィ䝰䞊䝯䞁䝖Md 䛾Ỵᐃ II. 䜶䞁䝗䝥䝺䞊䝖ཌ䠈Ỉᖹ䝸䝤ཌ䠈 䝪䝹䝖ᚄ䠈䝪䝹䝖ᮏᩘ䛾௬Ỵᐃ III. PL_s, PL_y, PT_s, PT_y䛾⟬ฟᘧ(5), ᘧ(12), ᘧ(13) IV. KL_1, KL_2, KT_1, KT_2䛾⟬ฟ ᘧ(24), ᘧ(25), ᘧ(26), ᘧ(27) V. M = ΔM , i = 1 ΔM = 1(kN)㽢H(m) 㽢n1, γ = 1 γ = KL_1 / KT_1 γ = KL_2 / KT_1 γ = KL_2 / KT_2 SFL≤ PL_s SFT≤ PT_s SFL> PL_s SFT≤ PT_s SFL> PL_s SFT> PT_s VI. SFh_i, SFf_i, SFw_i䛾⟬ฟ
i = 1䛾ሙྜ䠈ᘧ(29), ᘧ(30),ᘧ(31) i > 1䛾ሙྜ䠈ᘧ(42), ᘧ(43),ᘧ(44) No B = (1+pL)SFL XIII. ΔM䛸ᘧ(29), ᘧ(30),ᘧ(31) 䛛䜙 ΔSFh, ΔSFf, ΔSFw䜢⟬ฟ B = SFh _1 + SFL p㽢SFL< SFh _1 p㽢SFL≥ SFh _1 X. B ≤ By Yes No XI. M ≥ Md Yes VIII. Ỉᖹ䝸䝤䞉䜴䜵䝤䞉ୗ䝣䝷䞁䝆ᘬ ᙇຊ䜢⿵ṇ䛩䜛䛯䜑䛾๛ᛶẚ䛾⟬ฟ IX. 䛶䛣ຊಀᩘ䜢⏝䛔䛯䝪䝹䝖 ㍈ຊ䛾⟬ฟ XII. M = M + ΔM i = i +1 VII. SFL, SFT 䛾⟬ฟ ᘧ(45), ᘧ(46)
ᅗ㸫23 ゎᯒ್᥎ᐃ್ࡢẚ㍑㸦࣎ࣝࢺ㍈ຊ㸧 ᅗ㸫24 ゎᯒ್᥎ᐃ್ࡢẚ㍑ 㸦㠀✺ฟᆺ᥋ྜࡢ㝆అ࣮࣓ࣔࣥࢺ㸧 ༴㝤ഃࡢホ౯࡞ࡿࢣ࣮ࢫࡀᏑᅾࡍࡿ㸬᥎ᐃἲ2, 3 ࡣ ࡚ࡢࢣ࣮ࢫ࡛↓ḟඖ㔞ࡣ1 ࢆୖᅇࡾ㸪Ᏻഃ࡞ࡿ㸬 ࡲࡓ㸪᥎ᐃἲ2 ࡢ↓ḟඖ㔞ࡣ 1.15~1.32 ࡢ㛫࡛ศᕸࡋ㸪᥎ ᐃἲ3 ࡢ↓ḟඖ㔞ࡣ 1.1~1.25 ࡢ㛫࡛ศᕸࡋ࡚࠸ࡿ㸬ࡘࡲ ࡾ㸪๛ᛶẚγ ࢆ⪃៖ࡋࡓ᥎ᐃἲ 3 ࡣ γ ࢆ⪃៖ࡋ࡞࠸᥎ᐃ ἲ2 ࡼࡾࡶ⣙ 5%ゎᯒ್㏆࠸್ࢆ♧ࡋࡓ㸬 ᥎ᐃἲ3 ࡢ㝆అ࣮࣓ࣔࣥࢺࡣ 10~25%ࡢㄗᕪࡀ⏕ࡌࡿ㸬 ᅗ㸫13 ࡼࡾయ᥋ྜ L せ⣲ࡢ࣎ࣝࢺ㍈ຊቑศࡣࡰ ➼ࡋࡃ㸪ᥦࡋࡓ࡚ࡇຊಀᩘ㸪㞳㛫๛ᛶ㸪㝆అ๛ᛶ㸪 ᘬᙇຊࡢ᥎ᐃᘧࡶ15%௨ෆࡢ⢭ᗘ࡞ࡿࡇࡽ㸪᥎ᐃ ἲ3 ࡢㄗᕪࡣᘧ(28)࡛♧ࡋࡓࣖࣥࢢ⋡ࡢẚ๛ᛶࡢẚࡀ ➼ࡋࡃ࡞࠸ࡓࡵ⏕ࡌ࡚࠸ࡿ⪃࠼ࡽࢀࡿ㸬᥎ᐃ್ࡢ⢭ ᗘྥୖࡣ㸪ᘧ(28)࡛♧ࡋࡓࣖࣥࢢ⋡ẚ๛ᛶẚࡢ㛵ಀ ࢆ᫂ࡽࡍࡿᚲせࡀ࠶ࡾ㸪ࡇࢀࡣᚋࡢㄢ㢟࡛࠶ࡿ㸬 ࡲࡵ ᮏ◊✲ࡣ㸪ࡲࡎ㠀✺ฟᆺ᥋ྜࡢ FE ゎᯒࡼࡾ㸪࣎ࣝ ࢺ㍈ຊ᥎ᐃἲ࡛╔┠ࡍࡁ࣎ࣝࢺ㸪᭤ࡆ࣮࣓ࣔࣥࢺቑ ศᑐࡍࡿୗࣇࣛࣥࢪ㸪Ỉᖹࣜࣈ࠾ࡼࡧ࢙࢘ࣈࡢᘬᙇຊ ࡢቑῶࢆ᫂ࡽࡋࡓ㸬ḟ㸪㠀✺ฟᆺ᥋ྜ࡛᭱ึ㝆 అࡍࡿ࣎ࣝࢺࡢ㍈ຊቑຍࢆ⌧࡛ࡁࡿせ⣲⥅ᡭࢆ⪃ࡋ㸪 ⪃ࡋࡓせ⣲⥅ᡭࡢᙉᗘኚᙧホ౯ᘧࢆᅇᖐศᯒࡼࡾᥦ ࡋࡓ㸬ࡲࡓ㸪ୗࣇࣛࣥࢪࡢࣖࣥࢢ⋡ࢆ୍㒊ኚࡉࡏࡓ ᱆ࡢ FE ゎᯒࢆᐇࡋ㸪ᘬᙇຊせ⣲⥅ᡭࡢ๛ᛶẚࡢ㛵 ಀࢆ᫂ࡽࡋ㸪᭱ᚋ㸪ࡇࢀࡽࡢ⤖ᯝࢆࡲࡵࡿࡇ ࡛㸪㠀✺ฟᆺ᥋ྜࡢ࣎ࣝࢺ㍈ຊ᥎ᐃἲࢆᥦࡋࡓ㸬ᚓࡽ ࢀࡓ࡞⤖ㄽࢆ௨ୗ♧ࡍ㸬 1) 㠀✺ฟᆺ᥋ྜ࡛ࡣ㸪࢙࢘ࣈࣇࣛࣥࢪᕪ㒊ࡽ᭱ ࡶ㏆࠸࣎ࣝࢺࡀ᭱ึ㝆అ࣎ࣝࢺ㍈ຊ฿㐩ࡍࡿ㸬 ࡲࡓ㸪㠀✺ฟᆺ᥋ྜࡢỈᖹࣜࣈ㸪ୗࣇࣛࣥࢪ࠾ࡼࡧ ࢙࢘ࣈస⏝ࡍࡿᘬᙇຊቑศࡣ㸪᭤ࡆ࣮࣓ࣔࣥࢺቑ ศᑐࡋ࡚㠀⥺ᙧᛶࢆ࿊ࡍࡿ㸬ࡇࢀࡣ㸪L ᥋ྜࡢᶵ ᵓࢆ᭷ࡍࡿୗࣇࣛࣥࢪഃ T ᥋ྜࡢᶵᵓࢆ᭷ࡍࡿ ࢙࢘ࣈ㸪Ỉᖹࣜࣈഃࡢ᥋ྜ㒊ࡢ๛ᛶࡀస⏝ຊᛂࡌ ࡚ኚࡍࡿࡓࡵ࡛࠶ࡿ㸬 2) ࢙࢘ࣈࣇࣛࣥࢪᕪ㒊ࡽ᭱ࡶ㏆࠸࣎ࣝࢺࡑ ࡢ࿘㎶ࡢ࢙࢘ࣈୗࣇࣛࣥࢪࢆࣔࢹࣝࡋࡓ L せ ⣲ࡼࡾ㸪㠀✺ฟᆺ᥋ྜࡢ࢙࢘ࣈࣇࣛࣥࢪᕪ㒊 ㏆ഐࡢ࣎ࣝࢺ㍈ຊቑຍࢆ 10%௨ෆࡢㄗᕪ࡛⌧࡛ ࡁࡓ㸬 3) L せ⣲ T せ⣲ࡢ࡚ࡇຊಀᩘࡢ᥎ᐃᘧࢆ FE ゎᯒ ⤖ᯝࡑࡢᅇᖐศᯒࡼࡾࡑࢀࡒࢀᥦࡋࡓ㸬ᥦ ࡋࡓ࡚ࡇຊಀᩘࡢ᥎ᐃᘧࡣ࣎ࣝࢺᚄࡀM20~M30㸪 ࢚ࣥࢻࣉ࣮ࣞࢺཌࡀ࣎ࣝࢺᚄࡢ1~2.5 ಸࡢ⠊ᅖ࡛ 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1 2 3 4 5 6 Mom ent at bolt y iel d (F E m odel / Estim at ion) ᥎ᐃἲ㻝 ᥎ᐃἲ㻞 ᥎ᐃἲ㻟 A24 A48 B24 B48 C24 C48
(a) A24 (b) A48
(d) B48 (c) B24 (e) C24 (f) C48 0.6 0.7 0.8 0.9 1 1.1 1.2 0 0.22 0.44 0.66 0.88 B / B y M / Mgy ゎᯒ್ ᥎ᐃἲ1 ᥎ᐃἲ3 0.6 0.7 0.8 0.9 1 1.1 1.2 0 0.22 0.44 0.66 0.88 B / By M / Mgy ゎᯒ್ ᥎ᐃἲ1 ᥎ᐃἲ3 0.6 0.7 0.8 0.9 1 1.1 1.2 0 0.22 0.44 0.66 0.88 B / B y M / Mgy ゎᯒ್ ᥎ᐃἲ1 ᥎ᐃἲ3 0.6 0.7 0.8 0.9 1 1.1 1.2 0 0.22 0.44 0.66 0.88 B / By M / Mgy ゎᯒ್ ᥎ᐃἲ1 ᥎ᐃἲ3 0.6 0.7 0.8 0.9 1 1.1 1.2 0 0.22 0.44 0.66 0.88 B / B y M / Mgy ゎᯒ್ ᥎ᐃἲ1 ᥎ᐃἲ3 0.6 0.7 0.8 0.9 1 1.1 1.2 0 0.22 0.44 0.66 0.88 B / B y M / Mgy ゎᯒ್ ᥎ᐃἲ1 ᥎ᐃἲ3
⏝࡛ࡁ㸪L せ⣲ T せ⣲ࡢ㝆అ⪏ຊࢆ 5%௨ෆࡢㄗ ᕪ࡛᥎ᐃ࡛ࡁࡓ㸬 4) L せ⣲ T せ⣲ࡢ㞳㛫๛ᛶ㝆అ๛ᛶࡢ᥎ᐃᘧࢆ FE ゎᯒ⤖ᯝࡑࡢᅇᖐศᯒࡼࡾࡑࢀࡒࢀᥦࡋ ࡓ㸬㞳㛫๛ᛶࡢ᥎ᐃᘧࡣㄗᕪ10%௨ෆ㸪㝆అ๛ᛶࡢ ᥎ᐃᘧࡣㄗᕪ15%௨ෆ࡛᥎ᐃ࡛ࡁࡓ㸬 5) ୗࣇࣛࣥࢪࡢࣖࣥࢢ⋡ࢆ୍㒊పୗࡉࡏࡓ᱆ࡢ FE ゎ ᯒ࡛㸪ୗࣇࣛࣥࢪࡢᘬᙇຊࡀᱱ⌮ㄽ್ࡼࡾࡶᑠࡉࡃ㸪 ࢙࢘ࣈỈᖹࣜࣈࡢᘬᙇຊࡀᱱ⌮ㄽ್ࡼࡾࡶࡁ ࠸㠀✺ฟᆺ᥋ྜࡢᣲືࢆ⌧࡛ࡁࡓ㸬ࡲࡓ㸪L せ⣲ T せ⣲ࡢ๛ᛶẚ γ ࢆᇶࡋࡓỈᖹࣜࣈ㸪ୗࣇࣛࣥ ࢪ࠾ࡼࡧ࢙࢘ࣈࡢᘬᙇຊࡢ᥎ᐃᘧࢆࡑࢀࡒࢀᥦ ࡋࡓ㸬ᥦࡋࡓ᥎ᐃᘧࡼࡾᘬᙇຊࢆㄗᕪ10%௨ෆ ࡛᥎ᐃ࡛ࡁࡿ㸬 6) ࡚ࡇຊಀᩘ㸪㞳㛫๛ᛶ㸪㝆అ๛ᛶ࠾ࡼࡧᘬᙇຊࡢ ᥎ᐃᘧࢆࡶ࣎ࣝࢺ㍈ຊࡢ᥎ᐃἲࢆᥦࡋࡓ㸬ᥦ ࡋࡓ᥎ᐃἲ࡛ồࡵࡽࢀࡿ࣎ࣝࢺ㍈ຊࡣึᮇ࣎ࣝ ࢺ㍈ຊࡽࡢ❧ࡕୖࡀࡾࡸ㠀⥺ᙧⓗ࡞࣎ࣝࢺ㍈ຊ ࡢቑຍࢆ⾲⌧࡛ࡁࡿ㸬ࡲࡓ㸪ᥦࡋࡓ᥎ᐃἲ࡛࣎ࣝ ࢺ㝆అࡢ࣮࣓ࣔࣥࢺࢆ᥎ᐃࡍࡿ㸪⣙10~25%Ᏻ ഃࡢ㝆అ࣮࣓ࣔࣥࢺࡀᚓࡽࢀࡿ㸬 ㅰ㎡ ᮏ◊✲ࡣJSPS ⛉◊㈝㸦ㄢ㢟␒ྕ㸸20J15702㸧ࡢຓᡂࢆ ཷࡅ࡚ᐇࡋࡲࡋࡓ㸬ࡇࡇཌࡃ࠾♩⏦ࡋୖࡆࡲࡍ㸬 ཧ⪃ᩥ⊩ 1) 㕥ᮌ㸪⋢㉺㝯ྐ㸪ἑ⏣㐨ᙪ㸸⥭ᛴ௬タᶫࡢ㛤Ⓨࡘ ࠸࡚㸪ᶫᱱᇶ♏ 11 ᭶ྕ㸪Vol. 49㸪pp.46-51㸪2015. 2) ᒲᒣ⣖㸪ᮡᮏᝆ┿㸪ᮾ༤ᖺ㸪Ụ㢌୕㸪ᮡ⏣ᆂဢ㸪 ᒣཱྀ㝯ྖ㸸௬ᱞᶫ㒊ᮦࢆά⏝ࡋࡓ⥭ᛴ௬タᶫࡢ᱆㐃 ⤖ᵓ㐀㛵ࡍࡿᐇ㦂ⓗ◊✲㸪ᵓ㐀ᕤᏛㄽᩥ㞟 Vol.64A㸪 ᅵᮌᏛ㸪pp.594-604㸪2018. 3) ᒲᒣ⣖㸪ᮡᮏᝆ┿㸪ᒣཱྀ㝯ྖ㸸Ỉᖹࣜࣈࢆ᭷ࡍࡿ࢚ ࣥࢻࣉ࣮ࣞࢺ᥋ྜࡢ᭤ࡆᙉᗘ࠾ࡼࡧࡑࡢ࣎ࣝࢺ㍈ຊ ⡆᫆ホ౯ἲ㛵ࡍࡿ◊✲㸪㗰ᵓ㐀ㄽᩥ㞟㸪Vol.27, No.106㸪᪥ᮏ㗰ᵓ㐀༠㸪pp. 61-74㸪2020. 4) ᪥ᮏ㐨㊰༠㸸㐨㊰ᶫ♧᪉᭩࣭ྠゎㄝ᭩ II 㗰ᶫ࣭㗰㒊 ᮦ⦅㸪ၿ㸪2017.
5) Dassault Systems: Abaqus Online Documentarion, 2016. 6) ᪥ᮏつ᱁༠㸸ᦶ᧿᥋ྜ⏝㧗ຊ࣎ࣝࢺ࣭භゅࢼࢵࢺ࣭ ᖹᗙ㔠ࡢࢭࢵࢺ㸪JIS B 1186-2013, 2013. 7) ᮡᮏᝆ┿㸪ᒲᒣ⣖㸪ᒣཱྀ㝯ྖ㸸᥋ྜ㠃ึᮇ㝣ࢆ ᭷ࡍࡿ࢚ࣥࢻࣉ࣮ࣞࢺ᥋ྜࡢᣲືࡑࡢ⌧ゎᯒᡭ ἲ㸪ᅵᮌᏛᖹᡂ30 ᖺᗘ➨ 73 ᅇᖺḟᏛ⾡ㅮ₇ㅮ₇ ᴫせ㞟㸪I-201㸪2018. 8) ⋢㉺㝯ྐ㸪▼ᑿ┿㔛㸪ᶓⰾ㍤㸪ᒣᓮḟ㑻㸪Ỉཱྀ▱ ᶞ㸸㧗ຊ࣎ࣝࢺᦶ᧿᥋ྜࡢ࣎ࣝࢺ㍈ຊᑟධ╔┠ࡋࡓ ゎᯒࣔࢹࣝ㛵ࡍࡿ◊✲㸪㗰ᵓ㐀ㄽᩥ㞟㸪Vol. 21㸪No. 84㸪᪥ᮏ㗰ᵓ㐀༠㸪pp.95-110㸪2014. 9) ᪥ᮏ㗰ᵓ㐀༠ 㗰ᶫࡢྜ⌮ᵓ㐀࣭タィἲ◊✲ጤဨ /ྜ⌮ᵓ㐀࣭タィጤဨ㸸㗰ᶫࡢᙉᗘタィࡢྜ⌮㸪 JSSC ࢸࢡࢽ࣏࣮࢝ࣝࣞࢺ No.98㸪2013. 10)㕥ᮌᗣኵ㸪ᒣཱྀ㝯ྖ㸪⏣ಇ⾜㸸㧗ຊ࣎ࣝࢺ L ᆺᘬᙇ ⥅ᡭࡢ⤊ᒁᙉᗘ⥅ᡭ㠃᥋ゐຊࡢኚ≉ᛶ㛵ࡍࡿ ᇶ♏ⓗ◊✲㸪ᅵᮌᏛㄽᩥ㞟㸪No. 780, I-70, pp.87-96, 2005. 11)᪥ᮏ㗰ᵓ㐀༠㸸ᶫᱱ⏝㧗ຊ࣎ࣝࢺᘬᙇ᥋ྜタィᣦ㔪㸪 2004. 12)ᅵᮌᏛ 㗰ᵓ㐀ጤဨ㸸㧗ຊ࣎ࣝࢺᦶ᧿᥋ྜ⥅ᡭࡢ タィ࣭ᕤ࣭⥔ᣢ⟶⌮ᣦ㔪㸦㸧㸪2006. 13)᪥ᮏ㗰ᵓ㐀༠㸸ᶫᱱ⏝㧗ຊ࣎ࣝࢺᘬᙇ᥋ྜタィᣦ㔪 㸦㸧㸪1993. 14)ఀ⸨┤᫂㸪ୖຌ୍㸪ὠ᳃ຮ㸪୰ᓥⱱኖ㸪㕥ᮌ㇏ᮁ㸸 ࢫࣉࣜࢵࢺࢸ࣮ࢆ⏝࠸ࡓ㧗ຊ࣎ࣝࢺᘬᙇ᥋ྜࡼ ࡿH ᙧ㗰ᰕ࣭ࡣࡾ᥋ྜ㒊ࡢຊᏛⓗᛶ≧㛵ࡍࡿᐇ㦂ⓗ ◊✲ ࡑࡢ 3㸪᪥ᮏᘓ⠏ᏛᏛ⾡ㅮ₇᱾ᴫ㞟㸪 pp.1179-1180㸪1991. 㸦2020 ᖺ 9 ᭶ 15 ᪥ཷ㸧 㸦2021 ᖺ 2 ᭶ 1 ᪥ཷ⌮㸧
