ᇹ‫ׅ‬ᢊែ೛࠿༿⇝∙∃⇞⇌∆ᛯ૨‫إ‬ԓᨼ‒ ‫ם‬ங‫˟ܖ‬ㄽᩥࢩ࣮ࢺ⿵ᙉᕤἲ࡟࠾ࡅࡿ⿵ᙉຠᯝ࡜෌⿵ᙉᕤ࡟ࡼࡿవᑑ࿨ࡢẚ㍑
୕ୖᾈ*㸪⸨⏣ᗈᚿ**㸪஭அୖ㈼୍***㸪ᘅ℩ΎὈ****㸪ᇼᕝ㒔ᚿ㞝****** ༤ኈ ᕤᏛ , ୕஭ఫ཭ᘓタ ᰴ , ᢏ⾡◊✲ᡤ㸦ࠛ270-0132 ༓ⴥ┴ὶᒣᕷ㥖ᮌ 518-1㸧
** ኱ᡂࣟࢸࢵࢡ ᰴ , Ⴀᴗᮏ㒊㸦ࠛ160-6112 ᮾி㒔᪂ᐟ༊す᪂ᐟ 8-17-1㸧
*** ࣇ࢓࢖࣋ࢵࢡࢫ ᰴ , ᅵᮌ㒊㸦ࠛ162-0845 ᮾி㒔᪂ᐟ༊ᕷ㇂ᮏᮧ⏫ 1 ␒ 1 ྕ㸧**** ᰴ ஭ἑタィ, ᢏ⾡㒊㸦ࠛ581-0019 ኱㜰ᗓඵᑿᕷ༡ᑠ㜰ྜ⏫ 5-8-30㸧***** ᕤ༤, ኱㜰ᕤᴗ኱Ꮫྡ㄃ᩍᤵ㸦ࠛ522-0056 ᙪ ᰿ ᕷ 㛤 ฟ ௒ ⏫ 1488-11 㸧࢔࣑ࣛࢻࢩ࣮ࢺ⿵ᙉᕤἲࡢࢩ࣮ࢺᮦ࡟ࡣ㸪a)⧄⥔ࢆ⦪ᶓ࡟⧊ࡾ㎸ࡴ Type 㹒࡜㸪b)୍᪉ྥࡢࡳ࡟ᙉᗘࢆࡶࡘࢩ࣮ࢺࢆୖୗ࡟᮰ࡡࡿ Type S ࡀ࠶ࡿ㸬ࡑࢀࡒࢀ࡟➼᪉ᛶయࡸ␗᪉ᛶయ࡛ࡢኚ఩㛵ᩘࢆ㐺⏝ࡋ࡚㸪ࢩ࣮ࢺ⿵ᙉࡉࢀࡿᦆയᗋ∧ࡢᙎᛶࡓࢃࡳ࡟ࡼࡿ⿵ᙉຠᯝ࡟╔┠ࡍࡿ㸬୧ࢱ࢖ࣉ࡛ࡢึᮇ᫬ࡸ෌⿵ᙉ᫬ࢆᑐ㇟࡟㸪࡝ࡢ⛬ᗘࡢᘏ࿨໬ࡀᅗࢀࡿࡢ࠿ࢆẚ㍑ࡋ㸪Type T ࡀ Type Sࡼࡾࡶඃࢀ࡚࠸ࡿࡇ࡜ࢆ♧ࡍ㸬࣮࣮࢟࣡ࢻ㸸␗᪉ᛶయ㸪ࢩ࣮ࢺ⿵ᙉᕤ㸪⿵ᙉຠᯝ㸪෌⿵ᙉᕤ㸬ࡣࡋࡀࡁ᥎ᐃࢆࡶ࡜࡟㸪࡝ࡢ⛬ᗘࡢᘏ࿨໬ࡀᮇᚅ࡛ࡁࡿࡢ࠿ࢆຊᏛⓗぢᆅ࠿ࡽ᳨ウࡍࡿ㸬 ᦆയᗋ∧ࡢ࢔࣑ࣛࢻࢩ࣮ࢺ⿵ᙉᕤἲࡢࢩ࣮ࢺᵓ㐀ᶵ⬟࡟╔║ࡋ࡚㸪a)ணࡵ⧄⥔ࢆ⦪ᶓ࡟⧊ࡾ㎸ࡳ஧᪉ྥ࡟ᙉᗘ㸬ኚ఩㛵ᩘࡢᇶ♏ᘧ࡜ኚ఩ࡢ㛵ಀᘧࢆⓎ᥹ࡍࡿ⭷せ⣲ࢱ࢖ࣉࢆ Type T㸪b)୍᪉ྥࡢࡳ࡟ᙉᗘ
ࢆ♧ࡍࢩ࣮ࢺ 2 ᯛࢆ஫࠸࡟┤஺ࡉࡏࡿ࡜࡜ࡶ࡟ୖୗ᪉ྥ
␗᪉ᛶⷧᯈ⌮ㄽ࡛ࡢ Huber ࡢᥦ᱌ᘧ࡜➼᪉ᛶయࡢᵓᡂ
࡟᮰ࡡ࡚ᒙᵓ㐀ࢆ࡞ࡍࢱ࢖ࣉࢆ Type S ࡜ྡ௜ࡅࡿ㸬ຊᏛ๎ࢆᛕ㢌࡟㸪┤஺␗᪉ᙎᛶయࡢᙎᛶᐃᩘࢆ⨨ࡁ᥮࠼ࡿ㸬ⓗ࡟ࡣࡑࢀࡒࢀࡀᶞ⬡࡛ྵᾐࡋࡓ Type T ࡣ➼᪉ᛶయ࡛㸪 ౛࠼ࡤ x ᪉ྥࡢᙎᛶᐃᩘ Ex ӌ y ᪉ྥࡢᙎᛶᐃᩘ Ey ࡜࡞ࡿ୕ḟඖࡢ Huber ᆺ␗᪉ᛶయ࡛ࡢᵓᡂ๎ࡣᘧ(1)ࡢࡼ࠺
Type S ࡣᒙ≧ࡢ␗᪉ᛶయ࡜ぢ೴ࡍࡇ࡜ࡀ࡛ࡁࡿ㸬࡟♧ࡉࢀࡿ㸬ᮏ◊✲࡛ࡣ㸪ձ␗᪉ᛶⷧᯈ⌮ㄽ࡟࠾ࡅࡿ Huber ࡢᥦ᱌ᘧ 1)࡜୕ḟඖ➼᪉ᛶయࡢᵓᡂ๎ࢆᛕ㢌࡟⨨ࡁ㸪┤஺␗᪉=( +2 ) +√+,=√,
ᛶయ 2)ࡢ⊂❧࡞ 9 ಶࡢᙎᛶᐃᩘࢆపῶࡋࡓ␗᪉ᛶయ ௨=√+ ( +2 ) +√,=,
ୗ㸪Huber ᆺ␗᪉ᛶయ࡜࠸࠺ ࡢኚ఩㛵ᩘࢆㄏᑟࡋ㸪ࡇࡢ=+√+( +2 ) ,=√(1)㛵ᩘ⩌ࡀᨃ㔜ㄪ࿴ᙧ࡜ᨃㄪ࿴ᙧࡢ㛵ᩘ࡟ᖐ╔ࡍࡿࡇ࡜ࢆᥦ♧ࡍࡿ㸬ղType T ࡟ᑐࡋ࡚ࡣ➼᪉ᛶయ࡛ࡢ Galerkin- ࡇࡇ࡛㸪 , : ➼᪉ᛶయࡢ࣓ࣛࡢᐃᩘ㸪 = Ey / Exvector ࡜ Boussinesq 㛵ᩘࢆ⏝࠸㸪ᙉ㍈᪉ྥࢆ஫࠸࡟┤஺
ᘧ(1)ࡢᙎᛶᐃᩘࡣ࢚ࢿࣝࢠ࣮ṇ್ࡢ᮲௳ࢆ‶ࡓࡍ࡜ࡉࡏ࡚ከᒙ⣔せ⣲࡜࡞ࡿ Type S ࡟ࡣ㸪Huber ᆺ␗᪉ᛶయ࡜ࡶ࡟㸪Ș=1 ࡢ࡜ࡁ➼᪉ᛶయࡢᵓᡂ๎࡟ᖐ╔ࡍࡿࡇ࡜ࡣࡢኚ఩㛵ᩘࢆୖୗࡢⷧᒙ࡟ࡑࢀࡒࢀ㐺⏝ࡋ㸪ࡇࢀࡽࢆゝ࠺ࡲ࡛ࡶ࡞࠸㸬
Fourier ⣭ᩘᒎ㛤ࡍࡿ㸬ճ㍯Ⲵ㔜ࡢ㉮⾜⑂ປ࡟ࡼࡿࡦࡧ๭
ᘧ(1)ࢆᛂຊࡢࡘࡾྜ࠸ᘧ࡟௦ධࡋ࡚㸪ኚ఩࡛⾲ࡉࢀࡿࢀᦆയᗋ∧ࡢ⿵ᙉၥ㢟ࢆྲྀୖࡆ㸪ᗋ∧ୗ㠃࡟ Type T ࡸNavier ࡢᘧࢆồࡵࡿ㸬
Type S ࡀ᪋ࡉࢀࡿࢩ࣮ࢺ⿵ᙉᕤࢆ౛࡟㸪ᗋ∧ࡢࡓࢃࡳࡸ
( +2 ) +√ᛂຊ࡟㛵ࡍࡿኚືࢆㄪ࡭ࡿ㸬≉࡟⿵ᙉ๓ᚋ࡛ࡢࡓࢃࡳ࡟
++√ ( + )╔║ࡋ㸪Type T ࡸ Type S ࡢ⿵ᙉᕤἲ࡟ࡼࡿ⿵ᙉຠᯝ࠿=− ,+( + )ࡽ㸪Type T ࡜ Type S ࡢࡑࢀࡒࢀࡢᒙᩘࡀ࡝ࡢᵝ࡞㛵ಀ࡟+ {√+ ( +2 ) +√}√ ( + )
࠶ࡿࡢ࠿ࢆ᳨ドࡍࡿ㸬մᩥ⊩ 3)ࡢᡭἲࢆ⏝࠸࡚㸪Type T+√ ( + )=− ,࡜ Type S ࡛ࡑࢀࡒࢀࢩ࣮ࢺ⿵ᙉࡉࢀࡿᦆയᗋ∧ࡢవᑑ( + )+√ ( + )࿨᥎ᐃࢆヨࡳ㸪ࡉࡽ࡟ึᮇ⿵ᙉ᫬࠿ࡽᩘᖺ⤒㐣ᚋ࡟෌⿵++√+( +2 )=−(2)ᙉᕤࡀ᪋ࡉࢀࡿሙྜ࡟ࡘ࠸࡚ࡶ㸪෌⿵ᙉᕤᚋ࡛ࡢవᑑ࿨

-5-

: x, y, z ᪉ྥࡢ≀యຊ㸪ࡇࡇ࡛㸪X, ,: x, y, z ᪉ྥࡢኚ఩㸪, ,   = /,=, 㺃㺃㺃/ ⊂❧࡞≀యຊ X, , ࡟ᑐᛂࡍࡿᙧ࡛㸪Huber ᆺ␗᪉ᛶయ࡛ࡢ࣋ࢡࢺࣝᙧᘧࡢኚ఩㛵ᩘࡀ㸪ᘧ(2)࠿ࡽㄏᑟࡉࢀࡿ㸬౛࠼ࡤ Huber ᆺ␗᪉ᛶయ࡛ࡢኚ఩㛵ᩘࡢ z ᪉ྥᡂศ ࡜ࡢᇶ♏ᘧ㸪࡞ࡽࡧ࡟ኚ఩࡜ࡢ㛵ಀᘧࡣ␗᪉ᛶࣃ࣓࣮ࣛ
ࢱ α ࡸ β ࢆ፹௓࡟ࡋ࡚ḟᘧ࡛ᚓࡽࢀࡿ㸬ᅗ㸫1 ᗙᶆ࠾ࡼࡧᙧ≧ࡇࡇ࡛㸪 Mode-M ExӌEy (+√++√+)= −2 ( + )/( + 2 ) ,(3)

=0

2=−

+√

2=−−2

= ( + 2 )/( + )[,+√]

 Mode-D Ex㸼Ey +++)= −2 ( + )/( + 2 ) ,(3)’=02=−+2=−−2= ( + 2 )/( + )[=+√for Mode-M=+for Mode-D

౛࠼ࡤMode-M࡛ࡢኚ఩ ࡜ᛂຊ ࡣḟࡢࡼ࠺࡟ᚓࡽࢀࡿ㸬(4)2+/ ,    ch = cosh 㸪sh = sinh ,C ~ C ࡣ∧ࡢୖୗ㠃࡛ࡢቃ⏺᮲௳ࡼࡾỴᐃࡉࢀࡿ✚ศᐃᩘ㸬,+ /( + 2 )(=2/ , ( m, = 0,1,2,㺃㺃㺃) ,=,,++ /( + 2 )](4)’ࡇࡇ࡛㸪β = Ex 㸭Ey(6)ྠᵝ࡟Mode-D࡟ࡘ࠸࡚ࡢኚ఩ ࡜ᛂຊ ࡶồࡵࡽࢀࡿ㸬2 ௚ࡢ≀యຊ X, ࡟ᑐᛂࡍࡿኚ఩㛵ᩘࡢ x , y ᪉ྥᡂศ( , )ࡸ( , )ࡶྠᵝ࡟ᑟࡃࡇ࡜ࡀ࡛ࡁࡿ㸬α =1 ࡢ࡜ࡁኚ఩㛵ᩘ ࡣ Galerkin-vector ࡢ z ᪉ྥᡂศ࡟㸪ࡲࡓኚ఩㛵ᩘ ࡣ Boussinesq 㛵ᩘࡢ z ᪉ྥᡂศ࡟ᖐ╔ࡋ㸪௚ࡢ㛵ᩘ( , ) ࡜( , ) ࡶࡑࢀࡒࢀ Galerkin-vector ࡸBoussinesq 㛵ᩘࡢ x ࡜ y ᪉ྥᡂศ࡜୍⮴ࡍࡿ㸬࡞࠾ᘧ(1)࡜␗࡞ࡿᙎᛶᐃᩘࢆ௵ព࡟㑅ᢥࡍࢀࡤ㸪࢚ࢿࣝࢠ࣮ṇ್ࡢ᮲௳ࢆ‶㊊ࡋ࡞࠸࠿㸪࠶ࡿ࠸ࡣᚓࡽࢀࡓኚ఩㛵ᩘࡣᘧ(3)ࡢࡼ࠺࡞ศ㞳ᙧᘧ࡟ࡣ࡞ࡽࡎ㸪↹㞧࡞ 6 㝵ᆺࡢ೫ᚤศ᪉⛬ᘧ࡟␃ࡲࡿࡇ࡜ࢆ☜࠿ࡵ࡚࠸ࡿ㸬= −∑ ∑[C ch + C sh
+C { ch − 2(1 − 2 )sh }+C { sh − 2(1 − 2 )ch }]∙ sinsin,= ∑ ∑[C sh + C ch
+C { sh + (1 + 2/ 2 )ch }+C { ch + (1 + 2/ 2 )sh }+√/(C ch +C sh )]∙ 2 sinsin= −∑ ∑[C ch + C sh+C { ch − 2(1 − 2 )sh }+C { sh − 2(1 − 2 )ch }]∙ sinsin,= ∑ ∑[C sh + C ch+C { sh + 1 + 2 /∙ / 2 ch}

/ 2 sh}+C {ch+ /(C ch+ 1+2 /+C sh∙ 2 sin∙)]sin(6)’

㸬ࡦࡧ๭ࢀᦆയᗋ∧࡬ࡢ㐺⏝㸬ኚ఩㛵ᩘࡢ⣭ᩘ⾲♧ᅗ㸫1 ࡟♧ࡍᗋ∧ࡢ㝮ゅⅬ࡟ x , y ᗙᶆࢆ㸪∧୰ኸ㠃࡟z ᗙᶆࢆ⨨ࡅࡤ㸪ኚ఩㛵ᩘ ࡜ ࡢ Fourier ⣭ᩘᒎ㛤ࡣ௨ୗࡢᘧ࡛୚࠼ࡽࢀࡿ㸬= ∑ ∑ 〔C ch+Cch= ∑ ∑ 〔 C ch+ C shsh〕 sinsin㸪+ C sh〕 coscos

(5)

+C-6-

 ㍯Ⲵ㔜 98kN ㍕Ⲵ㠃✚ 200mm500mm ࡀ㸪඲࿘༢⣧ᨭᣢࡢᗋ∧୰ኸ࡟స⏝ࡍࡿሙྜࢆ᝿ᐃࡍࡿ㸬ᗋ∧ࡢᦆയᗘࢆవᑑ࿨᥎ᐃࣉࣟࢢ࣒ࣛ 3)࠿ࡽồࡵ㸪ᗋ∧ࡢᦆയ⛬ᗘ࡟ᛂࡌࡓࡦࡧ๭ࢀᐦᗘ 2m/m2 ࡢ඲᩿㠃᭷ຠ᫬ࡢ㡿ᇦ࡜ᘬᙇࡾ↓ど᫬ࡢ 4m/m2 ࡢ㡿ᇦࢆ௦⾲౛࡜ࡋ࡚ྲྀୖࡆࡿ㸬୺➽᪉ྥࡢࢫࣃࣥࢆ 2.5m㸪㓄ຊ➽᪉ྥࡢࢫࣃࣥࢆ 5m
࡜ࡍࡿᗋ∧ࡢㅖඖࢆ⾲㸫1 ࡟ࡲ࡜ࡵࡿ ᅗ㸫2 㸬ᦆയᗋ∧࡟ Type T ┠௜㔞 870g/ m2㸪බ⛠ཌ 0.24mm ࡜ Type S ┠⾲㸫1 ᗋ∧ࡢㅖඖྡཌࡉ mm⛠ᙎᛶಀᩘ kN/mm2 ࣏࢔ࢯࣥẚ࢔ࢫࣇ࢓ࣝࢺ⯒⿦

80

2.00.4RC ᗋ∧ ὀ㸯㸧200

ᶞ⬡ᒙ

1.0

2.00.4

Type T0.24

Ex = Ey =118.00.3

඲᩿㠃᭷ຠ᫬ 19.110.2

ᘬᙇࡾ↓ど᫬ 9.66

Ey = 97.66,
Ex = 0.009766
Type S
Ey = 0.009766,ᙉ㍈᪉ྥ x0.24
Ex = 97.66
ὀ㸯㸧RC ᗋ∧ࡣ᥮⟬ᙎᛶಀᩘࢆ♧ࡍ㸬ᙉ㍈᪉ྥ y0.240.3

ᅗ㸫2 ィ⟬ࣔࢹࣝᗋ∧⾲㸫2 ᗋ∧୰ኸⅬ࡛ࡢࡓࢃࡳ࡜ᛂຊࡢẚ㍑ x=2500mm㸪y=1250mm
ࡦࡧ๭ࢀᐦᗘ 2m/m2ᦆയᗘType Tࢩ࣮ࢺྡ⛠ᒙᩘmm

N/mm2N/mm2ࡦࡧ๭ࢀᐦᗘ 4m/m2

Type SType T

Type S

12

12

12

1

2

0.578

0.566

0.583

0.576

0.950

0.915

0.965

0.943

0.573

0.561

0.578

0.571

0.940

0.905

0.955

0.933

-2.060-2.032-2.071-2.053-1.600-1.564-1.612-1.589

2.520

2.437

2.555

2.510

2.201

2.073

2.257

2.185

-2.630-2.596-2.645-2.621-2.079-2.038-2.099-2.074

2.952

2.860

2.988

2.930

2.567

2.425

2.625

2.533

⾲㸫3 ㍯Ⲵ㔜➃㒊࡛ࡢࡓࢃࡳ࡜ᛂຊࡢẚ㍑ x=2500mm㸪y=1500mm
ࡦࡧ๭ࢀᐦᗘ 2m/m2

ᦆയᗘType Tࢩ࣮ࢺྡ⛠ᒙᩘ
mmN/mm2ὀ  ᛂຊ

ࡦࡧ๭ࢀᐦᗘ 4m/m2

Type SType TType S

1212

12

12

0.537

0.525

0.541

0.534

0.881

0.848

0.895

0.874

0.534

0.523

0.539

0.532

0.875

0.843

0.889

0.869

-0.376-0.374-0.377-0.376-0.352-0.349-0.351-0.351-0.012-0.022-0.007-0.013-0.020-0.038-0.012-0.022ࡢୖẁࡢ್ࡣᗋ∧୰ኸ㠃ࢆ♧ࡍ௜㔞 720g/ m2㸪බ⛠ཌ 0.24mm ࡢࢩ࣮ࢺ⿵ᙉᕤࢆ᪋ࡍ㸬ᩥᏐ T ࡣ⦪ᶓ⧄⥔ࡀ⦅ࡳ㎸ࡲࢀࡿ஧᪉ྥࢩ࣮ࢺࢆ㸪ᩥᏐS ࡣ୍᪉ྥࡢࡳ࡟ᙉᗘࢆⓎ᥹ࡍࡿࢩ࣮ࢺࢆୖୗ࡟᮰ࡡࡿ୍᪉ྥࢩ࣮ࢺࢆព࿡ࡍࡿ㸬ᮏㄽᩥ࡛ࡢࢩ࣮ࢺᒙᩘࢆ TypeT ࡛ࡣᶞ⬡ᒙ+ࢩ࣮ࢺᒙࢆ 1 ᒙศ࡜ࡋ㸪Type S ࡛ࡣᶞ⬡
ᒙ+⦪᪉ྥࢩ࣮ࢺ㸩ᶓ᪉ྥࢩ࣮ࢺࢆ 1 ᒙศ࡜ࡋ࡚ᢅ࠺㸬ࡲࡓ⾲㸫1 ࡢ␗᪉ᛶࣃ࣓࣮ࣛࢱ α =104 ࡢ್ࡣ㸪୺➽᪉ྥ

-7-ࡢᛂຊ ࡟ẚ࡭㸪㓄ຊ➽᪉ྥࡢᛂຊ ࡸ᤟ࡾ࡟㛵ࡍࡿࡏࢇ᩿ᛂຊ ࡢ᢬ᢠࡀᑠࡉࡃ࡞ࡿࡇ࡜ࢆ♧ࡋ࡚࠸ࡿ㸬∧ࡢ୰ኸⅬ࡜Ⲵ㔜➃㒊࡟࠾ࡅࡿᦆയᗋ∧ࡢୖ㠃 ⾲୰ࡢୖẁ ࡜ୗ㠃 ୗẁ ࡛ࡢኚ఩ =ࡓࢃࡳ ࡜ᛂຊࡢẚ㍑ࢆ⾲㸫2 ࡜ 3 ࡟♧ࡍ㸬࡞࠾⣭ᩘࡢ㡯ᩘ m,n ࡣ 150 ࡜ 100 ࡛࠶ࡿ㸬࠸ࡎࢀࡢࡦࡧ๭ࢀᐦᗘ࡛ࡶࢩ࣮ࢺᒙᩘࡢቑຍ࡟ࡘࢀ࡚㸪ࡓࢃࡳࡸᛂຊࡣḟ➨࡟ῶᑡࡍࡿࡀ㸪ྠࡌᒙᩘ࡛࠶ࢀࡤ

⾲㸫4 ᗋ∧ୖ㠃࡛ࡢࡓࢃࡳ⿵ᙉ⋡ࡢẚ㍑ x =2500mm㸪y =1250mm
ࡦࡧ๭ࢀᐦᗘ 2m/m2

ᦆയ ᗘType TT0T1

T2

T3

T0T1

T2

T3mm

0.591

0.578

0.566

0.554

0.988

0.950

0.915

0.883

mm

--

0.013

0.025

0.037

--

0.038

0.073

0.105

%

--

2.200

4.230

6.261

--

3.846

7.389

10.628Type S

S0S2S4S6S0S2S4S6mm

0.591

0.576

0.561

0.548

0.988

0.943

0.903

0.862mm

--

0.015

0.030

0.043

--

0.045

0.085

0.126%

--

2.538

5.076

7.276

--

4.555

8.603

12.75

∆
∆

/

∆
∆

ࡦࡧ๭ࢀᐦᗘ 4m/m2/

⾲㸫5 ྛ Type ࡢᅇᖐᘧ࡜┦㛵ಀᩘྡ ⛠ࡦࡧ๭ࢀᐦᗘ 2m/m2ࡦࡧ๭ࢀᐦᗘ 4m/m2

Type T

yTS=2.081xTS+ 0.051, R = 0.9996

yTS=3.543xTS+ 0.152, R = 0.9985

Type S

ySS=1.218xSS+ 0.068, R = 0.9988

ySS=2.115xSS+ 0.132, R = 0.9993

ὀ㸧⾲୰ R ࡣ┦㛵ಀᩘࢆព࿡ࡍࡿ㸬ᗋ∧୰ኸⅬ࡛ࡢ⤖ᯝࡣ⾲㸫4 ࡢࡼ࠺࡟⾲ࡉࢀࡿ㸬࡞࠾ୗῧᏐࡣᒙᩘࢆ♧ࡋ㸪0 ࡣ↓⿵ᙉ᫬ࢆព࿡ࡍࡿ㸬⾲㸫4 ࡢ⿵ᙉ⋡࡜ᒙᩘ࡜ࡢ㛵ಀࡣ⾲㸫5 ࡢᅇᖐ┤⥺ᘧ࡛ᩚ⌮ࡉࢀࡿ ᅗ㸫3 㸬┦㛵ಀᩘ R ࡣ࠸ࡎࢀࡶ 0.7 ௨ୖ࡛࠶ࡿࡢ࡛㸪ᶆᮏⅬࢆࡼࡃ⥙⨶ࡋ࡚࠸ࡿࡢࡀุࡿ㸬౛࠼ࡤࡦࡧ๭ࢀᐦᗘ 2m/m2ࡢሙྜ㸪ྠࡌ⿵ᙉຠᯝ y T= yS ࢆᚓࡿ Type S ࡢᒙᩘ xS ࡣxT=1 ࡟ᑐࡋ㸪xS = 2.081/1.218 xT + 0.051- 0.068 /1.218(7)= 1.709 xT - 0.0140Ҹ1.695      ࡜࡞ࡿ㸬ࡲࡓࡦࡧ๭ࢀᐦᗘ 4m/m2 ࡛ࡣ㸪ᅗ㸫3 ࡓࢃࡳ⿵ᙉ⋡࡜㈞௜ᒙᩘࡢ㛵ಀ

Type T ࡢ್ࡼࡾࡶ Type S ࡢ᪉ࡀ኱ࡁࡃ࡞ࡿ㸬ࡲࡓ୰ኸ㠃࡛ࡢࡏࢇ᩿ᛂຊ ࡢ Type S ࡢ್ࡣ Type T ࡜࡯ࡰ୍⮴ࡍࡿࡀ㸪ᗋ∧ୗ㠃࡛ࡢ⏺㠃ᛂຊࡣ Type T ࡢ᪉ࡀ Type S ࡼࡾࡶ኱ࡁࡃ࡞ࡗ࡚࠸ࡿ㸬ࡇࡢࡇ࡜ࡣ Type S ࡢ௜╔᢬ᢠࡀ
ᑠࡉࡃ㸪RC ᗋ∧ࡢศᢸࡍࡿ๭ྜࡀ Type T ࡟ẚ࡭࡚㧗ࡃ࡞ࡗ࡚࠸ࡿࡇ࡜ࢆఛࢃࡏ࡚࠸ࡿ㸬㸬ྛࢩ࣮ࢺ࡟࠾ࡅࡿࡓࢃࡳࡢ⿵ᙉຠᯝ࡜➼౯ᒙᩘ ᦆയᗋ∧ࡢవᑑ࿨⟬ฟ࡟࠾࠸࡚㸪౛࠼ࡤᗋ∧ୖ㠃 u ࡛ࡢάⲴ㔜ࡓࢃࡳࢆ᥇⏝ࡋ㸪ࢩ࣮ࢺ⿵ᙉᕤ࡟ࡼࡿ⿵ᙉຠᯝ
ࢆㄪ࡭ࡿࡓࡵ࡟㸪ࡓࢃࡳࡢ⿵ᙉ⋡∆ / ࢆᑟධࡍࡿ㸬-8-xxSS==3.543/2.115
3.543/2.115xxTT++0.0202/2.115
0.0202/2.115+0.010Ҹ1.685
(8)=1.675xT(8)=1.675 x T + 0.010Ҹ1.685 ࡜ᚓࡽࢀࡿ㸬 Type S ࡢ➼౯࡞ᒙᩘࡣ Type T ࡢ 1 ᒙ࡟ᑐࡍࡿẚ⋡࡛⣙ 1.69~1.70 ಸ࡜࡞ࡿ㸬ࡇࡢࡇ࡜࠿ࡽ Type S ࡢ➼౯ᒙᩘࡣḟࡢせᅉ࡟ᨭ㓄ࡉࢀࡿ㸬a Type T ࡜ྠࡌᙎᛶᐃᩘ࡜ࡍࡿሙྜࡢ Type S ࡜ࡢẚ
㍑࠿ࡽ㸪ࢩ࣮ࢺᵓ㐀ࡢᕪ␗࡟ࡼࡿᵓ㐀≉ᛶࡀồࡵࡽࢀࡿ㸬xT=1࡟ᑐࡍࡿxSࡢ➼౯ᒙᩘࡣ1.42࡜ᚓࡽࢀ㸪Type T ࡢ⭷స⏝࡟ࡼࡿຠᯝࡣ 1.42 ಸ࡜᥎㔞ࡉࢀࡿ㸬b Type S ࡢ┠௜㔞ࡀ Type T ࡜ྠࡌ┠௜㔞࡜ࡍࡿሙྜ࡛ࡢᕪࡣ┠௜㔞ẚࡢࡳ࡜࡞ࡿࡢ࡛㸪ᚋ⪅࡟ᑐࡍࡿ xS ࡢ್ࡣ 1.21(Ҹ870/720)ಸ࡜࡞ࡿ㸬c Type S ࡢ➼౯ᒙᩘࡣ Type T ࡢ 1.69 ಸ࡜ồࡵࡽࢀࡿ㸬㏆ఝⓗ࡟ࡣ a ࡜ b ࡢ್ࢆ⏝࠸࡚㸪 ࢩ࣮ࢺࡢᵓ㐀≉ᛶ
್ 1.42  ┠௜㔞ẚ 1.21 Ҹ1.72 ಸ࡜㢮᥎࡛ࡁࡿ㸬⾲㸫6 ෌⿵ᙉ᫬࡛ࡢవᑑ࿨ẚ㍑
Type Tࢩ࣮ࢺྡ⛠Type S෌⿵ᙉ᫬ᮇ ᖺ

357

357

᥮⟬ᙎᛶᐃᩘ Er kN/mm2

14.89

12.82

11.14

14.96 ~ 12.86

12.92 ~ 10.26

11.27 ~ 8.35

෌⿵ᙉ๓ࡢࡓࢃࡳ

mm㸧

0.69320.77330.85340.6982 ~ 0.7811 0.7783 ~ 0.9164 0.8584 ~ 1.052

෌⿵ᙉᚋࡢࡓࢃࡳmm㸧

0.67500.75030.82530.6872 ~ 0.7669 0.7644 ~ 0.8966 0.8412 ~ 1.026

ࡓࢃࡳࡢ⿵ᙉ⋡ %

2.6

3.0

3.3

1.6 ~ 1.81.8 ~ 2.2

2.0 ~ 2.5

వᑑ࿨ ᖺ

46.8

44.6

42.3

25.9 ~ 46.1

23.5 ~ 43.8

21.2 ~ 41.4

⾲㸫7 వᑑ࿨ࡢᅇᖐᘧࢩ࣮ࢺྡ⛠ᅇᖐᘧ

Type T

Lr = 50.192  1.125 x , R= 0.9999

Type S

Lr = 29.41 1.175 x , R= 0.9999㹼Lr = 49.62  1.175 x , R= 0.9999

࡜௬ᐃࡍࡿ㸬Type S ࡢ㍯Ⲵ㔜㉮⾜࡟ࡼࡿヨ㦂⤖ᯝࡀ୙࡛᫂࠶ࡿࡢ࡛㸪Type S ࡛ࡢຎ໬㐣⛬ࡣᘧ(10)ࡢᅇᖐᘧࡢ⠊ᅖෆ࡟␃ࡲࡿ࡜ண ࡉࢀࡿ㸬= 1.0 ~1.69 0.04005t + 0.578

(10)ࡑࡢ⤖ᯝ࡜ຎ໬㐣⛬ࢆᅗ㸫4 ࡟♧ࡍ࡜㸪Type S ࡣᩳ⥺ࡢ⠊ᅖෆ࡟཰ࡲࡿ㸬Type S ࡢవᑑ࿨ࡣ⣙ 13~22 ᖺࡢ⠊ᅖෆ࡟࠶ࡿ࡜᥎ᐃࡉ
ࢀ㸪Type T ࡼࡾࡶ▷࠸ࡇ࡜ࡀุࡿ㸬ࡋ࠿ࡋ Type T ࡜ TypeS ࡢᵓ㐀≉ᛶࡢᕪ␗ࢆ⪃៖ࡍࢀࡤ㸪Type S ࡢవᑑ࿨ࡣ⣙13 ᖺ㏆ഐ࡟࠶ࡿ࡜᥎ ࡉࢀࡿ㸬ḟ࡟ึᮇ⿵ᙉᕤࡢᩘᖺᚋ࡟ྛ Type ࡀ 2 ᒙᵓ㐀࡜࡞ࡿ෌⿵ᙉᕤࡀ᪋ࡉࢀࡿሙྜࢆ⪃࠼ࡿ㸬Type S ࡛ࡢవᑑ࿨㛗ࡉ 13 ᖺࢆ຺᱌ࡋ࡚㸪౛࠼ࡤ෌⿵ᙉ᫬ᮇࢆ୧ Type ࡜ࡶึᮇ⿵ᙉᚋ 3 ᖺ㸪5 ᖺ࠾ࡼࡧ 7 ᖺ࡟タᐃࡍࡿ㸬෌⿵ᙉᚋࡢ
Type T ࡜ Type S ࡛ࡢึᮇ⿵ᙉ᫬ࢆ㉳Ⅼ࡜ࡍࡿ 2 ᒙ㈞ࡾ
⿵ᙉᕤ᫬ࡢຎ໬ᅇᖐᘧࡣᘧ(11)࡛♧ࡉࢀࡿ㸬ᅗ㸫4 Type T ࠾ࡼࡧ Type S ࡢవᑑ࿨㸬ึᮇ⿵ᙉᕤ࡜෌⿵ᙉᕤ࡛ࡢవᑑ࿨᥎ᐃ
Type T ࡢ㍯Ⲵ㔜㉮⾜ヨ㦂ࡢ⤖ᯝ 3)࠿ࡽ㸪᚟ඖຊ≉ᛶ࡟㛵㐃ࡍࡿࡓࢃࡳࡢᙎᛶᡂศࢆᢳฟࡋ㸪ࡇࡢࡓࢃࡳࡀᗋ∧ࡢ౑⏝㝈⏺≧ែ࡟⮳ࡿࡲ࡛ࡢ⑂ປ࡟ࡼࡿຎ໬ᅇᖐᘧࢆᑟ
ࡅࡤ 3)㸪⾲㸫1 ࡟♧ࡍᗋ∧ࡢࡦࡧ๭ࢀᐦᗘࡀ 2m/m2 ࡛㸪౛࠼ࡤᖺ㛫 6 ୓ྎࡢ㐣✚㍕㌴ࡢ஺㏻㔞ࡀ࠶ࡿ࡜ࡁࡢຎ໬
ᅇᖐᘧࡣᘧ(9)࡜࡞ࡿ㸬= 0.04005t + 0.573           (9)ࡇࡇ࡛㸪 : ࡓࢃࡳ㸪t : ᖺᩘ㸪ୖῧᏐ 1 ࡣึᮇ⿵ᙉᕤࢆ㸪ୗῧᏐ T ࡣ Type T ࢆ♧ࡍ㸬ᅉࡳ࡟ึᮇ⿵ᙉᕤ᫬࡛ 1 ᒙ㸪ࡲࡓࡣ 2 ᒙ㈞ࡾࡉࢀࡓ
Type T ࡛ࡢవᑑ࿨ࡣࡑࢀࡒࢀ 22 ᖺ࡜ 50.2 ᖺ࡛࠶ࡗࡓ㸬 ຎ໬ᅇᖐᘧࡣᙎᛶᡂศ࡟౫Ꮡࡍࡿࡇ࡜࠿ࡽ Type S ࡛ࡢᅇᖐᘧࡢ໙㓄ࢆ㸪Type T ࡢ 1 ᒙศ࡟┦ᙜࡍࡿಸᩘ
1.69 Ҹᵓ㐀≉ᛶ/┠௜㔞ẚ ࢆ Type T ࡢ໙㓄࡟஌ࡌࡓ್

-9-= 0.01779 t  t0 +,= 1.0 ~1.69  0.01779 t  t0 +





(11)

ࡇࡇ࡛㸪 , :ࡑࢀࡒࢀ෌⿵ᙉ┤ᚋࡢ Type T ࡜ Type Sࡢࡓࢃࡳ㸪t0:෌⿵ᙉ᫬ᮇࡢᖺᩘ㸪ୖῧᏐ 2 ࡣ෌⿵ᙉᕤࢆ♧ࡍ㸬ࡑࡢ⤖ᯝࢆ⾲㸫6 ࡟ࡲ࡜ࡵ㸪෌⿵ᙉ᫬ᮇࡀ 5 ᖺ࡛ࡢྛType ࡢຎ໬㐣⛬࡜వᑑ࿨ࢆᅗ㸫5 ࡟♧ࡍ㸬Type T ࡢຎ໬⤒㊰ࡣ㸪ึᮇ⿵ᙉᕤ᫬ձЍ5 ᖺ⤒㐣᫬ղЍ෌⿵ᙉᕤ᫬ղ’Ѝ౑⏝㝈⏺᫬ճࢆ㎺ࡾ㸪ึᮇ᫬࡟ 2 ᒙ㈞ࡾ⿵ᙉᕤࡍࡿవᑑ࿨ 50.2 ᖺࡢ⣙ 90%⛬ᗘ࡟⮳ࡿ㸬ྠᵝ࡟➼౯ᒙᩘ 1.69 ࢆ᥇⏝ࡍࡿሙྜࡢ Type S ࡣ㸪ձЍմЍմ’Ѝյࡢຎ໬㐣⛬࡜♧ࡉࢀ㸪ึᮇ᫬ࡢ 2 ᒙ㈞ࡾ࡛ࡢవᑑ࿨
29.4 ᖺࡢ⣙ 80%࡜࡞ࡿ㸬Type S ࡢవᑑ࿨ࡣ㸪Type T ࡢ⣙
50%⛬ᗘ࡟␃ࡲࡿ࡜᥎ ࡉࢀࡿ㸬ᅗ㸫5 ෌⿵ᙉ᫬ᮇࡀ 5 ᖺ࡛ࡢྛ Type ࡢຎ໬㐣⛬࡜వᑑ࿨ྛ Type ࡜ࡶ෌⿵ᙉ᫬ᮇࡀ᪩ࡅࢀࡤ᪩࠸⛬㸪෌⿵ᙉᕤࡢవᑑ࿨࡟୚࠼ࡿᙳ㡪ࡣ኱ࡁࡃ࡞ࡗ࡚࠸ࡿ㸬⿵ᙉ๓ᚋࡢࡓ࡜
ࡣ࠸ࡎࢀࡢ⿵ᙉ᫬ᮇ࡛ࡶ Type S ࡢ᪉ࡀࢃࡳType T ࡼࡾࡶ኱ࡁࡃ㸪Type S ࡢ᭤ࡆ᢬ᢠࡀᑠࡉ࠸ࡇ࡜ࢆ♧၀ࡋ࡚࠾ࡾ㸪ࡓࢃࡳࡢ⿵ᙉ⋡࡟㛵ࡋ࡚ࡶ Type T>Type S࡜࡞ࡾ㸪Type T ࡢ᪉ࡀ⿵ᙉຠᯝࡀ㧗࠸ࡇ࡜ࡀㄞࡳྲྀࢀࡿ㸬ࡲࡓ Type T ࡢవᑑ࿨ࡣ 3 ᖺ,5 ᖺ࠾ࡼࡧ 7 ᖺࡢ࡝ࡢ᫬ᮇ
࡛ࡶ Type T>Type S ࡜ᚓࡽࢀ㸪ࡑࢀࡒࢀ 1.0~1.8 ಸ,1.0~1.9ಸ࠾ࡼࡧ 1.0~2.0 ಸ࡜㛗ࡃ࡞ࡿ㸬ࡲࡓྛ Type ࡛ࡢ෌⿵ᙉᕤࢆ᪋ࡍ᫬ᮇ x ࡜వᑑ࿨ Lr ࡢ㛵ಀࢆ⾲ࡍᅇᖐᘧࢆ⾲㸫7 ࡟♧ࡍ㸬Type S ࡢవᑑ࿨ࡣ Lr=29.41-1.175x ࡜ Lr=49.62-1.175x
ࡢ⠊ᅖෆ࡟࠶ࡿ࡜᥎ ࡉࢀࡿ㸬ึᮇ⿵ᙉᕤ࡜෌⿵ᙉᕤ࡛ࡢẚ㍑࡟ࡼࢀࡤ㸪Type T ࡢ⿵ᙉᕤἲࡢ᪉ࡀ㸪Type S ࡢᕤἲࡼࡾࡶඃࢀࡓᘏ࿨⟇࡛࠶ࡿ࡜ุ᩿ࡉࢀࡿ㸬㸬ࡲ࡜ࡵ ᚓࡽࢀࡓ▱ぢࢆ௨ୗ࡟ิグࡍࡿ㸬ձ ␗᪉ᛶⷧᯈ⌮ㄽࡢ Huber ࡢᥦ᱌ᘧ࡜➼᪉ᛶయࡢᵓᡂ
๎ࢆࡶ࡜࡟㸪⊂❧࡞≀యຊ࡟క࠺ Huber ᆺ␗᪉ᛶయࡢᵓᡂ๎࠿ࡽ࣋ࢡࢺࣝᙧᘧࡢኚ఩㛵ᩘࡀᑟ࠿ࢀ㸪Ș=1 ࡢ᫬ࡇࢀࡽࡣ➼᪉ᛶయࡢኚ఩㛵ᩘ࡟ᖐ╔ࡍࡿ㸬ղ ୍᪉ྥࡢࡳ࡟ᙉᗘࢆࡶࡘ⦪࣭ᶓࢩ࣮ࢺࢆୖୗ࡟㔜ࡡ㸪
Type T ࡜ྠࡌᙎᛶᐃᩘࢆࡶࡘሙྜࡢ Type S ࡛ࡢࡓࢃࡳࡣ㸪஧᪉ྥࢩ࣮ࢺࡢ Type T ࡼࡾࡶ 1.42 ಸ኱ࡁࡃ㸪Type T ࡣ⭷స⏝ຠᯝࢆⓎ᥹ࡋ࡚࠸ࡿࡇ࡜ࡀุࡿ㸬ճ ࢩ࣮ࢺᒙᩘࡢቑຍ࡟ࡘࢀ࡚㸪RC ᗋ∧ࡢୖୗ㠃࡛ࡢࡓࢃࡳࡸᛂຊࡣ࡜ࡶ࡟ῶᑡഴྥࢆ♧ࡍ㸬ࡋ࠿ࡋᗋ∧୰ኸ㠃࡛ࡢࡏࢇ᩿ᛂຊȫyz ࡣ Type T ࡜ Type S ࡛ᕪࡣ࡞࠸ࡀ㸪ᗋ∧ୗഃࡢ⏺㠃࡛ࡣ Type T ࡢ᪉ࡀ Type Sࡼࡾࡶ኱ࡁ࠸㸬ྠࡌᒙᩘࡢሙྜ㸪Type S ࡛ࡢᗋ∧ࡢศᢸຊࡣ Type T ࡟ẚ࡭࡚኱ࡁࡃ࡞ࡾ㸪ࡓࢃࡳࡸᛂຊ
ࡀ Type T ࡼࡾࡶቑ኱ࡋ࡚࠸ࡿࡇ࡜࡜➢ྜࡍࡿ㸬մ ඲᩿㠃᭷ຠ᫬࡜ᘬᙇࡾ↓ど᫬࡛ࡢࡓࢃࡳ࡟㛵ࡍࡿ⿵ᙉຠᯝ࡟ࡼࢀࡤ㸪Type T ࡢ 1 ᒙศࡣ Type S ࡢ⣙ 1.7ᒙศ࡟┦ᙜࡍࡿ㸬յ Type T ࡜ Type S ࡢᵓ㐀≉ᛶࡢᕪ␗ࢆ຺᱌ࡍࢀࡤ㸪෌⿵ᙉᕤ࡟ࡼࡿ Type T ࡢవᑑ࿨ࡣ Type S ࡟ẚ࡭࡚㛗ࡃ࡞ࡾ㸪ᴫࡡ 1.8㹼2.0 ಸ௨ୖࡢᘏ࿨໬ࡀᮇᚅ࡛ࡁࡿ࡜᥎ᐹࡉࢀࡿ㸬㸬࠶࡜ࡀࡁ Type T ࡣ Type S ࡟ẚ࡭࡚㸪⭷ຠᯝࢆⓎ᥹ࡍࡿᵓ㐀≉ᛶࢆࡶࡘ Type T ࡢ᪉ࡀ RC ᗋ∧࡜ࡢ௜╔ᛶ⬟ࡶ㧗ࡃ㸪⿵ᙉᚋࡢ RC ᗋ∧ࡢ᭤ࡆ᢬ᢠࡸᘬᙇࡾ᢬ᢠຊ࡟ᐤ୚ࡋ㸪᪤Ꮡᗋ∧࡬ࡢ㈇ᢸࡀᑠࡉࡃ࡞ࡿ㸬෌⿵ᙉᕤࢆ᪋ࡍ≧ἣୗ࡟࠾࠸࡚ࡶ Type T ࡣ Type S ࡼࡾࡶ㛗࠸ᘏ࿨ຠᯝࢆࡶࡓࡽࡍ࡜᥎ ࡛ࡁࡿ㸬௒ᚋࡣᮏ◊✲ࡢኚ఩㛵ᩘࢆά⏝ࡋ࡚㸪⦪࣭ᶓࢩ࣮ࢺࡢ┠௜㔞ࡀ஫࠸࡟␗࡞ࡿ➼ࡢ␗᪉ᛶ≧ࢆ࿊ࡍࡿከᒙ⣔ᵓ㐀࡬ࡢ㐺⏝ࢆᅗࡿணᐃ࡛࠶ࡿ㸬ཧ⪃ᩥ⊩1) Timoshenko,S.P. and Woinowsky-Krieger,S.: Theory ofPlates and Shells, 2nd ed. ,McGraw-Hill,New York,1955.
2) K.Sonoda and T.Horikawa: Displacement functions for an
orthotropic elastic body and their applications to thick plateproblems, Theo.Appl.Mech.,Vol.29,pp.117-126,1979.
3) ୕ୖ ᾈ,஭அୖ㈼୍,௒⏣ᩥ⏨,Ἑ㔝୍㈨,ᘅ℩ΎὈ,ᇼᕝ㒔ᚿ㞝㸪࢔࣑ࣛࢻ⧄⥔ࢩ࣮ࢺ࡟ࡼࡿ⿵ᙉ᫬࡜෌⿵ᙉ᫬࡛ࡢవᑑ࿨᥎ᐃࣉࣟࢢ࣒ࣛࡢ㛤Ⓨ㸪➨ඵᅇ㐨㊰ᶫᗋ∧ࢩ࣏ࣥࢪ࣒࢘ㄽᩥሗ࿌㞟,pp.295~300,2014㸬㸦2018 ᖺ 7 ᭶ 20 ᪥ཷ௜㸧- 10 -