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Mohr circle
1.
(1) (3) (2) (3)
2.
(𝜎 𝑛− 𝜎 𝑥
+ 𝜎 𝑦 2 )2 + 𝜏 𝑡 2 = ( 𝜎 𝑥 − 𝜎 𝑦 2 )2 + 𝜏2 (𝜎 𝑛−𝑎)2 + 𝜏 𝑡 2 = 𝑅2 𝑤ℎ𝑒𝑟𝑒; 𝑎 = 𝜎 𝑥 + 𝜎 𝑦 2 𝑅 = ( 𝜎 𝑥 − 𝜎 𝑦 2 )2 + 𝜏2 𝑎 𝑎𝑛𝑑 𝑟𝑎𝑑𝑖𝑢𝑠 𝑅 𝑖𝑛
3.
(𝜎 𝑥, 𝜏)
𝜎 𝑥 (𝜎 𝑦, 𝜏) 𝜎 𝑦 = 𝜎 𝑥 + 𝜎 𝑦 2
4.
= 𝜎𝑥 − 𝜎
𝑦 2 = ( 𝜎 𝑥 − 𝜎 𝑦 2 )2 + 𝜏2 𝜎𝑥 − 𝜎 𝑦 2 = ( 𝜎𝑥 − 𝜎 𝑦 2 )2 + 𝜏2
5.
(𝜎𝑥, 𝜏) 𝐸(𝜎 𝑦,
𝜏)
6.
𝜎 𝑥 𝜎𝑥 −
𝜎 𝑦 2 𝜏 𝜎𝑥 − 𝜎 𝑦 2 𝜎𝑥 + 𝜎 𝑦 2 𝜏 𝜎 𝑛
7.
𝜎𝑥 − 𝜎
𝑦 2 𝜏 𝜏 𝑡 𝜎 𝑥 𝜎𝑥 + 𝜎 𝑦 2 𝜏 𝑡𝜎 𝑛 𝜎𝑥
8.
𝜎 𝑛 𝜏 𝑡 𝑟
9.
1
10.
𝜎𝑥 𝜎 𝑦
𝜏 𝜎1 𝜎2 𝜏 𝑚𝑎𝑥
11.
12.
2
13.
𝜎𝑥 𝜎 𝑦
𝜏 𝜎1 𝜎2 𝜏 𝑚𝑎𝑥
14.
3
15.
𝜎𝑥 𝜎 𝑦
𝜏 𝜎1 𝜎2 𝜏 𝑚𝑎𝑥 2𝜃1 2𝜃2 2𝜃1 = 72 + 180° = 252° 2𝜃2 = 72° or 432°
16.
4
17.
𝜎𝑥 𝜎 𝑦
𝜏 𝜎𝜎 𝑛 𝜏 𝑚𝑎𝑥
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