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S1.09 DEFORMABILIDADE
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Fonte: http://www.geofix.com.br/noticia.php?n=13 ∆σ ∆σ ∆σ ∆σ ≠ ∆σ = ∆σ ∆σ ∆σ ∆σ σ1 Δh1 Δ σ2 Δ σ ∆ Δ σ1; e1 σ2; e2 σ’vm http://www.slideshare.net/rhshah695/research-paper-of-leaning-tower-of-pisa http://www.slideshare.net/rhshah695/research-paper-of-leaning-tower-of-pisa http://www.slideshare.net/rhshah695/research-paper-of-leaning-tower-of-pisa http://www.slideshare.net/rhshah695/research-paper-of-leaning-tower-of-pisa http://www.slideshare.net/rhshah695/research-paper-of-leaning-tower-of-pisa http://www.slideshare.net/rhshah695/research-paper-of-leaning-tower-of-pisa σ • • • σ • • • 𝑶𝑪𝑹 = 𝝈′𝒗𝒎 𝝈′𝒗𝒐 http://www.slideshare.net/rhshah695/research-paper-of-leaning-tower-of-pisa 𝜎′𝑣𝑜 𝜎′𝑣𝑜 < 𝜎′𝑣𝑚 𝜎′𝑣𝑚 𝜎′𝑣𝑜 𝜎′𝑣𝑓 𝜎′𝑣𝑚 Δσ Δσ σ’vf = σ’vo + Δσ 𝜎′𝑣𝑜 𝜎′𝑣𝑓 𝐰 = 𝐇 𝟏 + 𝐞𝟎 . (𝐂𝐫. 𝐥𝐨𝐠 𝛔′𝐯𝐟 𝛔′𝐯𝐨 ) 𝜎′𝑣𝑜 < 𝜎′𝑣𝑚 𝜎′𝑣𝑚 σ’vf = σ’vo + Δσ 𝜎′𝑣𝑜 𝜎′𝑣𝑓 𝐰 = 𝐇 𝟏 + 𝐞𝟎 . (𝐂𝐫. 𝐥𝐨𝐠 𝛔′𝐯𝐦 𝛔′𝐯𝐨 + 𝐂𝐜. 𝐥𝐨𝐠 𝛔′𝐯𝐟 𝛔′𝐯𝐦 ) 𝜎′𝑣𝑜 < 𝜎′𝑣𝑚 𝜎′𝑣𝑚 Δσ σ’vf = σ’vo + Δσ 𝜎′𝑣𝑜 𝜎′𝑣𝑓 𝐰 = 𝐇 𝟏 + 𝐞𝟎 . (𝐂𝐫. 𝐥𝐨𝐠 𝛔′𝐯𝐦 𝛔′𝐯𝐨 + 𝐂𝐜. 𝐥𝐨𝐠 𝛔′𝐯𝐟 𝛔′𝐯𝐦 ) 𝜎′𝑣𝑜 < 𝜎′𝑣𝑚 𝜎′𝑣𝑚 σ’vf = σ’vo + Δσ 𝜎′𝑣𝑜 𝜎′𝑣𝑓 Δσ Δσ 𝜎′𝑣𝑜 = 𝜎′𝑣𝑚 𝐰 = 𝐇 𝟏 + 𝐞𝟎 . (𝐂𝐜. 𝐥𝐨𝐠 𝛔′𝐯𝐟 𝛔′𝐯𝒐 ) 𝜎′𝑣𝑜 𝜎′𝑣𝑓 σ’vf = σ’vo + Δσ 𝜎′𝑣𝑜 < 𝜎′𝑣𝑚 𝐰 = 𝐇 𝟏 + 𝐞𝟎 . (𝐂𝐫. 𝐥𝐨𝐠 𝛔′𝐯𝐟 𝛔′𝐯𝐨 ) 𝐰 = 𝐇 𝟏 + 𝐞𝟎 . (𝐂𝐫. 𝐥𝐨𝐠 𝛔′𝐯𝐦 𝛔′𝐯𝐨 + 𝐂𝐜. 𝐥𝐨𝐠 𝛔′𝐯𝐟 𝛔′𝐯𝐦 ) 𝜎′𝑣𝑜 = 𝜎′𝑣𝑚 𝐰 = 𝐇 𝟏 + 𝐞𝟎 . (𝐂𝐜. 𝐥𝐨𝐠 𝛔′𝐯𝐟 𝛔′𝐯𝒐 ) 𝑼 = 𝒘 𝒘𝒎á𝒙 e1 e2 𝑎𝑣 = − ∆𝑒 ∆𝜎 e1 e2 𝑎𝑣 = − ∆𝑒 ∆ 𝜎 ≈ − 𝑑𝑒 𝑑 𝜎 𝑎𝑣 = − ∆𝑒 ∆ 𝜎 ≈ − 𝑑𝑒 𝑑 𝜎 = 𝑑𝑒 𝑑𝑢 𝒂𝒗 = 𝒅𝒆 𝒅𝒖 𝑘 . (1 + 𝑒) 𝑎𝑣. 𝛾𝑜 . 𝜕2𝑢 𝜕𝑧2 = 𝜕𝑢 𝜕𝑡 𝑐𝑣 . 𝜕2𝑢 𝜕𝑧2 = 𝜕𝑢 𝜕𝑡 𝒄𝒗 = 𝒌 . (𝟏 + 𝒆) 𝒂𝒗. 𝜸𝒐 • • • 𝑐𝑣 . 𝜕2𝑢 𝜕𝑧2 = 𝜕𝑢 𝜕𝑡 𝑈 = 1 − 𝑚=0 ∞ 2 𝑀2 𝑒 − 𝑀2.𝑐𝑣.𝑡 𝐻𝑑 2 𝑇 = 𝑐𝑣. 𝑡 𝐻𝑑 2 𝑼 = 𝟏 − 𝒎=𝟎 ∞ 𝟐 𝑴𝟐 𝒆−𝑴 𝟐.𝑻 𝑐𝑣 . 𝜕2𝑢 𝜕𝑧2 = 𝜕𝑢 𝜕𝑡 𝑻 = 𝒄𝒗. 𝒕 𝑯𝒅 𝟐 𝑻 = 𝝅 𝟒 .𝑼𝟐 𝑻 = −𝟎, 𝟗𝟑𝟑. 𝒍𝒐𝒈 𝟏 − 𝑼 − 𝟎, 𝟎𝟖𝟓 𝑻 = 𝒄𝒗. 𝒕 𝑯𝒅 𝟐 𝑻 = 𝝅 𝟒 .𝑼𝟐 𝑻 = −𝟎, 𝟗𝟑𝟑. 𝒍𝒐𝒈 𝟏 − 𝑼 − 𝟎, 𝟎𝟖𝟓 𝑻 = 𝒄𝒗. 𝒕 𝑯𝒅 𝟐 𝑯𝒅 = 𝑯 𝑻 = 𝒄𝒗. 𝒕 𝑯𝒅 𝟐 𝑯𝒅 = 𝑯 𝟐 𝑼 = 𝒘 𝒘𝒎á𝒙 = 𝑼 = 𝒘 𝒘𝒎á𝒙 ≅ ≅90% 𝒕 = 𝑻.𝑯𝒅 𝟐 𝒄𝒗 𝑯𝒅 = 𝑯 𝑯𝒅 = 𝑯 𝟐
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