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Mohr circle

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Mohr circle

  1. 1. (1) (3) (2) (3)
  2. 2. (𝜎 π‘›βˆ’ 𝜎 π‘₯ + 𝜎 𝑦 2 )2 + 𝜏 𝑑 2 = ( 𝜎 π‘₯ βˆ’ 𝜎 𝑦 2 )2 + 𝜏2 (𝜎 π‘›βˆ’π‘Ž)2 + 𝜏 𝑑 2 = 𝑅2 π‘€β„Žπ‘’π‘Ÿπ‘’; π‘Ž = 𝜎 π‘₯ + 𝜎 𝑦 2 𝑅 = ( 𝜎 π‘₯ βˆ’ 𝜎 𝑦 2 )2 + 𝜏2 π‘Ž π‘Žπ‘›π‘‘ π‘Ÿπ‘Žπ‘‘π‘–π‘’π‘  𝑅 𝑖𝑛
  3. 3. (𝜎 π‘₯, 𝜏) 𝜎 π‘₯ (𝜎 𝑦, 𝜏) 𝜎 𝑦 = 𝜎 π‘₯ + 𝜎 𝑦 2
  4. 4. = 𝜎π‘₯ βˆ’ 𝜎 𝑦 2 = ( 𝜎 π‘₯ βˆ’ 𝜎 𝑦 2 )2 + 𝜏2 𝜎π‘₯ βˆ’ 𝜎 𝑦 2 = ( 𝜎π‘₯ βˆ’ 𝜎 𝑦 2 )2 + 𝜏2
  5. 5. (𝜎π‘₯, 𝜏) 𝐸(𝜎 𝑦, 𝜏)
  6. 6. 𝜎 π‘₯ 𝜎π‘₯ βˆ’ 𝜎 𝑦 2 𝜏 𝜎π‘₯ βˆ’ 𝜎 𝑦 2 𝜎π‘₯ + 𝜎 𝑦 2 𝜏 𝜎 𝑛
  7. 7. 𝜎π‘₯ βˆ’ 𝜎 𝑦 2 𝜏 𝜏 𝑑 𝜎 π‘₯ 𝜎π‘₯ + 𝜎 𝑦 2 𝜏 π‘‘πœŽ 𝑛 𝜎π‘₯
  8. 8. 𝜎 𝑛 𝜏 𝑑 π‘Ÿ
  9. 9. 1
  10. 10. 𝜎π‘₯ 𝜎 𝑦 𝜏 𝜎1 𝜎2 𝜏 π‘šπ‘Žπ‘₯
  11. 11. 2
  12. 12. 𝜎π‘₯ 𝜎 𝑦 𝜏 𝜎1 𝜎2 𝜏 π‘šπ‘Žπ‘₯
  13. 13. 3
  14. 14. 𝜎π‘₯ 𝜎 𝑦 𝜏 𝜎1 𝜎2 𝜏 π‘šπ‘Žπ‘₯ 2πœƒ1 2πœƒ2 2πœƒ1 = 72 + 180Β° = 252Β° 2πœƒ2 = 72Β° or 432Β°
  15. 15. 4
  16. 16. 𝜎π‘₯ 𝜎 𝑦 𝜏 𝜎𝜎 𝑛 𝜏 π‘šπ‘Žπ‘₯

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