Earthquake Response Analysis of Buildings

(1)

(2)

(3)

(4)

(5)

(6)

(7)



(8)

𝛿 𝑡 = 0,02

(9)

𝑉𝑠

( 𝑇1) 𝑞 = 2,0

𝑎𝑔 40𝐻𝑧 𝑚/𝑠2

(10)

𝑞

(11)

(12)

 C

𝑡 ℎ_𝑖 𝐴_𝑐 𝐴_{𝑙𝑜𝑜𝑝} 𝑐_𝑟𝑒𝑓^′ 𝑐_𝑐𝑟 𝐸₅₀^𝑟𝑒𝑓 𝐸_𝐷 𝐸_𝑆 𝐸_𝑜𝑒𝑑^𝑟𝑒𝑓 𝐸_𝑢𝑟^𝑟𝑒𝑓 𝐹_𝑏 𝐹_𝑖 𝐺^∗ 𝐺_𝑠 𝐺_𝑡 [𝐾]

𝐾₀ [𝑀]

𝑅_𝑖𝑛𝑡 𝑅_𝛾 𝑆_𝑑 (𝑇) 𝑆_𝑒(𝑇) 𝑇₁ 𝑇_𝐵 𝑇_𝐶 𝑇_𝐷 𝑉_𝑠,30 𝑉_𝑠 𝑊_𝐷

(13)

𝑎_𝑣𝑔 𝑓₁

𝑝_𝑟𝑒𝑓 𝑝_𝑟𝑒𝑓= 100 𝑘𝑝𝑎

𝑢̇ (𝑡) 𝑢̈ (𝑡) 𝑢_𝑖 𝑣_𝑖 𝛾̇

𝛾_0,7 𝛾_𝐼 𝛾_𝑐 𝛾_𝑒𝑓𝑓 𝛾_𝑠𝑎𝑡 𝛾_{𝑢𝑛𝑠𝑎𝑡} 𝛿_𝑡

𝜆_𝑠 Length of share wave 𝜈_𝑢𝑟

𝜎₁^′ 𝜎₃^′ 𝜏_𝑐 𝜔_𝑛 𝑐 𝑑 𝑓 𝑔 G

𝑘 𝑚 𝑚 𝑚 𝑛 𝑝 𝑞

(14)

𝜂 𝜈 𝜉 𝜌 𝜏 𝜑 𝜓 𝜔

(15)

(16)

(17)

(18)

•

𝑇₁ 𝑞

(19)

𝑇₁

(20)

•

• NS-EN 1998

•

(21)

(22)

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(24)

𝑚𝑢̈(𝑡) + 𝑐𝑢̇ + 𝑘𝑢 = 𝑝

𝑢̈ + 2𝜉𝜔_𝑛𝑢̇ + 𝜔_𝑛²𝑢 = 0

𝜔_𝑛 = √𝑘 𝑚 𝜉 = 𝑐

2𝑚𝜔_𝑛 = 𝑐 𝑐_𝑐𝑟 𝑐_𝑐𝑟 = 2𝑚𝜔_𝑛 = 2√𝑘𝑚 =2𝑘

𝜔_𝑛 𝜔_𝑛

𝜉 𝑐_𝑐𝑟 𝑐

𝑐 < 𝑐_𝑐𝑟 𝜉 < 1

𝑐 = 𝑐_𝑐𝑟 𝜉 = 1

𝑐 > 𝑐_𝑐𝑟 𝜉 > 1

(25)

(26)

(27)

𝐺

𝜏 = 𝐺 ∗ 𝛾 + 𝜂 ∗ 𝛾̇

𝐺 𝜏 𝛾 𝛾̇

𝜂

𝑢 (𝑧, 𝑡) 𝛾 =𝜕_𝑢(𝑧, 𝑡)

𝜕_𝑧 𝑎𝑛𝑑 𝛾̇ =𝜕_𝛾(𝑧, 𝑡)

𝜕_𝑡 = 𝜕_𝑢²(𝑧, 𝑡)

𝜕_𝑧∗ 𝜕_𝑡

(28)

𝐺_𝑠 𝛾

𝐺_𝑠 = 𝜏_𝑐 𝛾_𝑐 𝜏_𝑐

𝛾_𝑐

𝛾 𝐺

𝜉

𝐺_𝑠𝑒𝑐 𝐺_𝑠𝑒𝑐

𝜉

(29)

𝜉 =4 ∗ 𝜋 ∗ 𝑊_𝑠 =

2 ∗ 𝜋 ∗ 𝐺_𝑠𝑒𝑐∗ 𝛾_𝑐²

𝑊_𝐷 𝑊_𝑠 𝐴_{𝑙𝑜𝑜𝑝}

𝐺_𝑠𝑒𝑐 𝜉

(30)

𝐺

𝐺_𝑚𝑎𝑥 = 𝜌 ∗ 𝑉_𝑠²

𝑉_𝑠 𝐺_𝑚𝑎𝑥

(31)

𝐹_𝑚𝑎𝑥 = 𝑚 ∗ 𝑃𝑆𝐴 =𝑃𝑆𝐴 𝑔 ∗ 𝑤 𝑔

(32)

𝑘 𝜉

𝑘 𝑇

𝑇 = 2𝜋√𝑚 𝑘



𝐸₅₀= 𝐸₅₀^𝑟𝑒𝑓∗ ( 𝜎₃^′+ 𝑎 𝑝_𝑟𝑒𝑓+ 𝑎)

𝑚

𝐸_𝑢𝑟 = 𝐸_𝑢𝑟^𝑟𝑒𝑓∗ ( 𝜎₃^′+ 𝑎 𝑝_𝑟𝑒𝑓+ 𝑎)

𝑚

𝐸_𝑜𝑒𝑑= 𝐸_𝑜𝑒𝑑^𝑟𝑒𝑓∗ ( 𝜎₁^′+ 𝑎 𝑝_𝑟𝑒𝑓+ 𝑎)

𝑚

𝐺₀ = 𝐺₀^𝑟𝑒𝑓( c ∗ cos(𝜑) − 𝜎₃^′∗ sin (𝜑) c ∗ cos(𝜑) + 𝑝^𝑟𝑒𝑓∗ 𝑠𝑖𝑛(𝜑))

𝑚

𝐺₀^𝑟𝑒𝑓 = 𝐸₀^𝑟𝑒𝑓 2 ∗ (1 + 𝜐_𝑢𝑟)

(33)

𝑚 𝐸₅₀^𝑟𝑒𝑓 𝐸_𝑜𝑒𝑑^𝑟𝑒𝑓 𝐸_𝑢𝑟^𝑟𝑒𝑓 𝜈_𝑢𝑟

𝑝_𝑟𝑒𝑓 𝑝_𝑟𝑒𝑓 = 100 𝑘𝑝𝑎

(34)

The Hardin-Drnevich relationship is perhaps t

𝐺_𝑠

𝐺₀ = 1 1 + |𝛾

𝛾_𝑟|

𝛾_𝑟 =𝜏_𝑚𝑎𝑥 𝐺₀ 𝜏_𝑚𝑎𝑥

𝐺₀

𝛾_𝑟 = 𝛾_0,7 𝐺_𝑠

𝐺_𝑠

𝐺₀ = 1 1 + 𝑎 | 𝛾

𝛾_0,7|

𝐺_𝑠 𝐺₀.

𝐺₀

(35)

𝜏 = 𝐺_𝑠∗ 𝛾 𝐺_𝑠

𝜉 = 𝐸_𝐷 4𝜋𝐸_𝑠 𝜉

𝐸_𝐷

𝐸_𝑠 𝛾_𝐶

𝐺_𝑠/𝐺₀ 𝐺_𝑡/𝐺₀ 𝐺_𝑡

(36)

𝜉

(37)

 

[𝐶] = 𝛼[𝑀] + 𝛽[𝐾]

𝑀 𝐾 𝛼 𝛽

𝛼 + 𝛽𝜔² = 2𝜔𝜉 𝜔 = 2𝜋𝑓

𝛼 = 2𝜔₁∗ 𝜔₂∗𝜔₁∗ 𝜉₂− 𝜔₂∗ 𝜉₁ 𝜔₁²− 𝜔₂² 𝛽 = 2 ∗𝜔₁∗ 𝜉₁− 𝜔₂∗ 𝜉₂

𝜔₁²− 𝜔₂² 𝜔

𝜉 𝜉 = 1

𝑢₀

(38)



𝑓₁ = 𝑉_𝑠 4𝐻

𝑥_𝑚𝑖𝑛 𝑥_𝑚𝑎𝑥

(39)

𝑥_𝑚𝑖𝑛 𝑥_𝑚𝑎𝑥

𝑦_𝑚𝑖𝑛

(40)

𝑅_{𝑖𝑛𝑡𝑒𝑟} 𝑅_{𝑖𝑛𝑡𝑒𝑟}

𝛿𝑡 = Δ𝑡 𝑛 ∗ 𝑚

𝑡 𝑛 𝑚





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𝜆𝑠 = 𝑉_𝑠 𝑓_𝑚𝑎𝑥

𝜆𝑠 8

(43)

50%

𝐺^∗ = 𝐺(1 + 𝑖2𝜉)

𝐺^∗ = 𝐺(1 − 𝜉²+ 𝑖2𝜉)

(44)

𝜉

𝜔 𝐺^∗ 𝜔

𝑊_𝑑 = 4𝜋𝑊_𝑠𝜉 = 2𝜋𝜉𝐺𝛾_𝑐²𝜔

𝜉 𝜔

|𝐺^∗| 𝜉

|𝐺^∗| = 𝐺√1 + 4𝜉²

(45)

𝜉

𝐺^∗= 𝐺 {(1 − 2𝜉²) + 2𝜉_𝑗√1 − 𝜉²}

𝐺^∗ = 𝐺{(1 − 2𝜉²) + 4𝜉²(1 − 𝜉²)} = 𝐺

𝑊_𝑑 =1

2𝜔𝛾_𝑐²∫ 2𝐺𝜉√1 − 𝜉²𝑑𝑡

𝑡+2𝜋 𝜔 𝑡

= 2𝜋𝐺𝜉√1 − 𝜉²𝛾_𝑐² 𝜉

(46)

𝐺^𝑖 𝜉^𝑖

𝛾_𝑚𝑎𝑥 𝛾_𝑒𝑓𝑓 𝛾_𝑚𝑎𝑥

𝛾_𝑒𝑓𝑓 = 𝑅_𝛾∗ 𝛾_𝑚𝑎𝑥 𝑅_𝛾

𝐺_𝑖+1 𝜉_𝑖+1 𝛾_𝑒𝑓𝑓

(47)

𝑉_𝑠

𝑉𝑠, 30

𝑉_𝑠,30= 30 Σ_𝑖=1,𝑁 ℎ_𝑖

𝑣_𝑖 ℎ_𝑖 𝑣_𝑖

𝑖 − 𝑡ℎ

𝑉_𝑠

𝛾_𝐼)

(48)

𝛾_𝐼

𝑎_𝑔 = 𝛾_𝐼∗ 𝑎_𝑔𝑅 𝑎_𝑔𝑅

𝑎_𝑔𝑅 = 0,8 ∗ 𝑎_{𝑔40 𝐻𝑧}

𝑎_{𝑔40 𝐻𝑧} 𝑓 = 40 𝐻𝑧 𝑇 = 0,025 𝑠

0 ≤ 𝑇 ≤ 𝑇_𝐵: 𝑆_𝑒(𝑇) = 𝑎_𝑔∗ 𝑆 ∗ [1 + 𝑇

𝑇_𝐵(𝜂 ∗ 2,5 − 1)]

𝑇_𝐵 ≤ 𝑇 ≤ 𝑇_𝐶: 𝑆_𝑒(𝑇) = 𝑎_𝑔∗ 𝑆 ∗ 𝜂 ∗ 2,5 𝑇_𝐶 ≤ 𝑇 ≤ 𝑇_𝐷: 𝑆_𝑒(𝑇) = 𝑎_𝑔∗ 𝑆 ∗ 𝜂 ∗ 2,5 [𝑇_𝐶

𝑇] 𝑇_𝐷 ≤ 𝑇 ≤ 4𝑠: 𝑆_𝑒(𝑇) = 𝑎_𝑔 ∗ 𝑆 ∗ 𝜂 ∗ 2,5 [𝑇_𝐶∗ 𝑇_𝐷

𝑇² ]

𝑎_𝑔 𝑇_𝐵 𝑇_𝐶 𝑇_𝐷

𝜂 𝜂 = 1

(49)

𝜂 = √ 10

(5 + 𝜉) ≥ 0,55 𝜉

𝑇_𝐵 𝑇_𝐶 𝑇_𝐷

(50)

(𝑆_𝑣𝑒)

0 ≤ 𝑇 ≤ 𝑇_𝐵: 𝑆_𝑣𝑒(𝑇) = 𝑎_𝑣𝑔∗ [1 + 𝑇

𝑇_𝐵(𝜂 ∗ 3,0 − 1)]

𝑇_𝐵 ≤ 𝑇 ≤ 𝑇_𝐶: 𝑆_𝑣𝑒(𝑇) = 𝑎_𝑣𝑔∗ 𝜂 ∗ 3,0 𝑇_𝐶 ≤ 𝑇 ≤ 𝑇_𝐷: 𝑆_𝑣𝑒(𝑇) = 𝑎_𝑣𝑔∗ 𝜂 ∗ 3,0 [𝑇_𝐶

𝑇] 𝑇_𝐷 ≤ 𝑇 ≤ 4𝑠: 𝑆_𝑣𝑒(𝑇) = 𝑎_𝑣𝑔∗ 𝜂 ∗ 3,0 [𝑇_𝐶∗ 𝑇_𝐷

𝑇² ] 𝑇 𝑇_𝐵 𝑇_𝐶 𝜂

𝑎_𝑣𝑔

𝑎_𝑣𝑔/ 𝑎_𝑔

(51)

𝑞

𝑞 ≤ 1,5

𝑞 > 4,0

𝑞 = 4,0

0 ≤ 𝑇 ≤ 𝑇_𝐵: 𝑆_𝑑(𝑇) = 𝑎_𝑔 ∗ 𝑆 ∗ [2 3+ 𝑇

𝑇_𝐵(2,5 𝑞 −2

3)]

𝑇_𝐵 ≤ 𝑇 ≤ 𝑇_𝐶: 𝑆_𝑑(𝑇) = 𝑎_𝑔 ∗ 𝑆 ∗2,5 𝑞 𝑇_𝐶 ≤ 𝑇 ≤ 𝑇_𝐷: 𝑆_𝑑(𝑇) = {= 𝑎_𝑔∗ 𝑆 ∗2,5

𝑞 ∗ [𝑇_𝐶 𝑇]

≥ 𝛽 ∗ 𝑎_𝑔

}

𝑇_𝐷 ≤ 𝑇: 𝑆_𝑑(𝑇) = {= 𝑎_𝑔∗ 𝑆 ∗2,5

𝑞 ∗ [𝑇_𝐶∗ 𝑇_𝐷 𝑇² ]

≥ 𝛽 ∗ 𝑎_𝑔

} 𝑇 𝑇_𝐵 𝑇_𝐶 𝜂 𝑆

𝛽

(52)

𝐹_𝑏

𝑇₁ ≤ {4 ∗ 𝑇_𝐶 2,0 𝑠}

𝐹_𝑏 = 𝑆_𝑑(𝑇₁) ∗ 𝑚 ∗ 𝜆

𝑆_𝑑 (𝑇₁) 𝑇₁

𝑇₁ 𝑚

 𝑇1 ≤ 2 = 0,85

= 1,0

𝑇₁ = 𝐶_𝑡∗ 𝐻 ³⁴

𝐶_𝑡 0,085 0,075

0,050 𝐶_𝑡

𝐶_𝑡 =0,075

√𝐴_𝑐

𝑇₁

𝑇₁ = 2√𝑑 𝑑

𝑇₁

𝑇₁ = 2𝜋√∑ 𝑚_𝑖∗ 𝑢_𝑖²

∑ 𝐹_𝑖∗ 𝑢_𝑖

𝑚_𝑖 "𝑖 𝑢_𝑖 "𝑖 𝐹_𝑖 "𝑖

(53)

𝑚 ∗ 𝑢̈ (𝑡) + 𝑐 ∗ 𝑢̇(𝑡) + 𝑘 ∗ 𝑢(𝑡) = 0

𝑚 ∗ 𝑢̈ (𝑡) + 𝑐 ∗ 𝑢̇(𝑡) + 𝑘 ∗ 𝑢(𝑡) = − 𝑚 ∗ 𝑢̈ _𝑔 = 𝑝_𝑒𝑓𝑓(𝑡) 𝑢(𝑡) = 1

𝜔𝑉(𝑡)

𝑉(𝑡) = ∫ 𝑢̈_𝑔 (𝑡) ∗ 𝑠𝑖𝑛𝜔(𝑡 − 𝜏)𝑒^{−𝜉𝜔(𝑡−𝜏)}

𝑡

0

𝑆_𝑣(𝜉, 𝜔) = |𝑉(𝑡, 𝜉, 𝜔|_𝑚𝑎𝑥

𝐹_𝑚𝑎𝑥 = 𝑘 ∗ 𝑢_𝑚𝑎𝑥 = 𝑘 1

𝜔𝑆_𝑣(𝜉, 𝜔) = 𝑘

𝜔²𝑆_𝑑(𝜉, 𝜔) = 𝑚 ∗ 𝑆_𝑑(𝜉, 𝜔)

(54)

(55)

(56)

50%

(57)

(58)

(59)

_𝑠𝑎𝑡 20 𝑘𝑁/𝑚³

 _{𝑢𝑛𝑠𝑎𝑡} 20 𝑘𝑁/𝑚³

𝐸₅₀^𝑟𝑒𝑓 6815 𝑘𝑁/𝑚² 𝐸_𝑜𝑒𝑑^𝑟𝑒𝑓 6815 𝑘𝑁/𝑚² 𝐸_𝑢𝑟^𝑟𝑒𝑓 20446 𝑘𝑁/𝑚²

𝑚 0,8

𝑐 _𝑟𝑒𝑓^′ 10 𝑘𝑁/𝑚²

 (𝑝ℎ𝑖) 18 

 (𝑝𝑠𝑖) - 

_0,7 0,700E-3

𝐺₀^𝑟𝑒𝑓 66450 𝑘𝑁/𝑚²

 0,2

0,6910

𝑅_{𝑖𝑛𝑡𝑒𝑟} 0,8

𝐺₀^𝑟𝑒𝑓 𝐺_𝑢𝑟^𝑟𝑒𝑓

(60)

• 𝐺₀^𝑟𝑒𝑓= 𝐺₀ = 𝐺_𝑚𝑎𝑥 𝑉_𝑠

• 𝐺_𝑢𝑟^𝑟𝑒𝑓 ^𝐺⁰

𝑟𝑒𝑓

𝐺_𝑢𝑟^𝑟𝑒𝑓 = (2,5 𝑡𝑜 10)𝑔𝑜𝑖𝑛𝑔 𝑓𝑟𝑜𝑚 ℎ𝑎𝑟𝑑 𝑡𝑜 𝑠𝑜𝑓𝑡 𝑠𝑜𝑖𝑙𝑠

• 𝐸_𝑢𝑟^𝑟𝑒𝑓

𝐺_𝑢𝑟^𝑟𝑒𝑓 = 𝐸_𝑢𝑟^𝑟𝑒𝑓 2 ∗ (1 + 𝜐_𝑢𝑟)

• 𝐸_𝑜𝑒𝑑^𝑟𝑒𝑓 𝐸_𝑢𝑟^𝑟𝑒𝑓= 3 ∗ 𝐸_𝑜𝑒𝑑^𝑟𝑒𝑓

(61)

(62)

(63)

(64)

(65)

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(70)

(71)

𝛿 _𝑡 = 0,02

(72)

(73)

(74)

(75)

(76)

(77)

(78)

(79)

1,20

(80)

𝑃𝑜𝑤𝑒𝑟 (𝑈𝑥) 𝑃𝑜𝑤𝑒𝑟 (𝑎𝑥)

(81)

𝑎_𝑔 = 0,288 𝑔 𝑆 = 1,65 𝑞 = 1,5 𝐻 = 15 𝑚 𝐶_𝑡= 0,075

𝐺𝑟𝑜𝑢𝑛𝑑 𝑡𝑦𝑝𝑒 − 𝐸 𝑇_𝐵= 0,10 𝑠 𝑇_𝐶 = 0,30 𝑠 𝑇_𝐷 = 1,40 𝑠

𝐻

𝑚 = 72360 𝑘𝑔 𝜆 = 0,85 𝑇₁ = 0,572 𝑠 𝑆_𝑑 = 0,416 𝑚/𝑠² 𝐹_𝑏 = 25,6 𝑘𝑁

𝑇₁ = 0,714 𝑠 𝑆_𝑑 = 0,333 𝑚/𝑠² 𝐹_𝑏 = 24,1𝑘𝑁

(82)

𝑇₁ = 0,833 𝑠 𝑆_𝑑 = 0,285 𝑚/𝑠² 𝐹_𝑏 = 20,6 𝑘𝑁

(𝑚)

𝐻 = 12 𝑚 𝑚 = 60480 𝑘𝑔 𝑇₁ = 0,484 𝑠 𝑆_𝑑 = 0,491 𝑚/𝑠² 𝐹_𝑏 = 25,3 𝑘𝑁

𝑇₁ = 0,714 𝑠 𝑆_𝑑 = 0,333 𝑚/𝑠² 𝐹_𝑏 = 20,1 𝑘𝑁

(83)

75,6 𝑘𝑁 64,3 ∗ 10 + 75,6 = 718,6 𝑘𝑁

723,6 𝑘𝑁. 𝑡𝑜𝑛 𝑘𝑁 10

9,8 (22 𝑘𝑁/𝑚)

(25,6 𝑘𝑁/𝑚)

(84)

(𝑅_𝑖𝑛𝑡)

(85)

(86)

𝑅_𝑖𝑛𝑡 𝑅_𝑖𝑛𝑡 = 0,6

1 𝑘𝑁/𝑚 𝑅_𝑖𝑛𝑡 = 0,8

2,3 𝑘𝑁/𝑚

2,6 𝑘𝑁/𝑚 30 𝑘𝑁/𝑚

𝑇₁

(87)

𝑇₁

𝑇₁ 𝑇₁

𝑇₁[𝑠] 𝑆_𝑑 [𝑚/𝑠²] 𝐹_𝑏 [𝑘𝑁/𝑚]

Alternative 1 - 𝑇₁ , Eq 0,572 0,416 25,6 𝑇₁ , Eq 0,525 0,452 27,8

𝑇₁

(88)

(89)

𝑞 𝑞 = 1,5

𝑞 𝑞

𝑞 = 1,0 𝑞 = 1,5 𝑞 = 2,0

(90)

𝑆₁ 𝑆₂

𝑇₁ 𝑇₁

𝑇₁

(91)

(92)

(93)

v= z u= w*z v’= v - u h’= v’ * K0

G0

G0ref G0 = G/

𝛾 = 20 𝑘𝑁/𝑚³ 𝑐^′ =  𝑘𝑁/𝑚² 𝜑^′ = 18°

𝐾₀ = 1 − 𝑠𝑖𝑛𝜑 = 0,691 𝑝_𝑟𝑒𝑓 = 100 𝑘𝑁/𝑚²

𝑚 = 0,8 𝐺𝑊 = 5,0 𝑚 𝜌 = 𝛾

𝑔 = 2038,7 𝑘𝑁/𝑚³ 𝜈 = 0,2

(94)

𝐺₀^𝑟𝑒𝑓 = 66450 𝑘𝑁/𝑚² 𝐺_𝑢^𝑟𝑒𝑓 = 𝐺₀^𝑟𝑒𝑓

7,8 = 8519 𝑘𝑁/𝑚²

𝐸_𝑢𝑟^𝑟𝑒𝑓= 𝐺_𝑢^𝑟𝑒𝑓 (2 ∗ (1 + 𝜐)) = 20446 𝑘𝑁/𝑚² 𝐸₅₀^𝑟𝑒𝑓 = 𝐸_𝑢𝑟^𝑟𝑒𝑓

3 = 6815 𝑘𝑁/𝑚² 𝐸_𝑜𝑒𝑑^𝑟𝑒𝑓 = 𝐸₅₀^𝑟𝑒𝑓 = 6815 𝑘𝑁/𝑚²

(95)

𝛿𝑡

𝛿𝑡 = Δ𝑡

𝑛 ∗ 𝑚 = 52,78

5278 ∗ 1= 0,01

(96)

•

• 𝑓₂

• ^𝑓²

𝑓₁ 𝑓₂

• 

• 𝑓₁ 𝑓₂

𝑓₁ = 𝑉_{𝑠,𝑎𝑣𝑒𝑟𝑎𝑔𝑒}

4 ∗ 𝐻 = 165,4

4 ∗ 15= 2,75 𝐻𝑧 𝑓₂

𝑓₁ =0,79

2,75= 0,28 → 𝑓₂ = 1 𝐻𝑧

(97)

(98)

(99)

(100)

(101)

(102)

(103)

(104)

(105)

(106)

(107)

𝑉𝑠

(108)

(109)

𝑎_{𝑔 40 𝐻𝑧} 𝑎_𝑔 𝛾_𝐼

 β



𝑆 𝑇_𝑩 𝑇_𝑪 𝑇_𝑫 𝑞

𝐻 𝐶_𝑡 𝑇_𝟏

 𝑆_𝑑 𝐹_𝑏

𝑇_𝟏



(110)

(111)

 β



𝑇_𝟏



(112)

(113)

 β



𝑇_𝟏



(114)

(115)

𝟏

𝑇₁ = 2√𝑑 = 2√0,069 = 0,52 𝑠

( 𝑇₁)

𝑇₁ = 2𝜋√𝑀

𝐾 = 2𝜋√ 𝐹_ℎ

𝑔 ∗ 𝐾 = 2𝜋√𝑑

𝑔 ≅ 2√𝑑

𝐹_ℎ (𝑔)

(116)

𝒒 = 𝟐, 𝟎

𝑞 𝐻 𝐶_𝑡 𝑇_𝟏 𝑚



𝑞 = 2,0

(117)

m₁ = 108,0 𝑘𝑁/𝑚 𝑚_𝟐= 129,6 𝑘𝑁/𝑚 𝑚₃ = 129,6 𝑘𝑁/𝑚 𝑚₄ = 129,6 𝑘𝑁/𝑚 𝑚₅ = 151,2 𝑘𝑁/𝑚

𝐵𝑎𝑠𝑒 𝑝𝑙𝑎𝑡𝑒 = 75,6 𝑘𝑁/𝑚 𝑇𝑜𝑡𝑎𝑙 = 723,6 𝑘𝑁/𝑚

𝑚₁ = 108,0 𝑘𝑁/𝑚 𝑚₂ = 129,6 𝑘𝑁/𝑚 𝑚₃ = 129,6 𝑘𝑁/𝑚 𝑚₄ = 129,6 𝑘𝑁/𝑚 𝑚₅ = 108,0 𝑘𝑁/𝑚 𝑇𝑜𝑡𝑎𝑙 = 604,8 𝑘𝑁/𝑚

(118)

(119)

𝑎_{𝑔 40𝐻𝑧} 𝑚/𝑠²

(120)

(121)

(122)

𝑎𝑥 𝑢𝑥

(123)