This document discusses analytical methods for determining stresses on oblique sections of bodies subjected to direct stress in two perpendicular directions or simple shear stress. It presents equations for calculating the normal stress, shear stress, maximum shear stress, resultant stress, and direction of resultant stress on such oblique sections based on the applied stresses and the section orientation. It also contains example problems applying these analytical methods.

1. BIBIN CHIDAMBARANATHAN
STRESS ON AN OBLIQUE
SECTION OF A BODY SUBJECTED
TO DIRECT STRESS IN TWO
MUTUALLY PERPENDICULAR
DIRECTIONS
1 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/11

2. BIBIN CHIDAMBARANATHAN
ANALYTICAL
METHOD
2 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/11

3. STRESS ON AN OBLIQUE SECTION OF A BODY
SUBJECTED TO DIRECT STRESS IN TWO MUTUALLY
PERPENDICULAR DIRECTIONS
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4. 4 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/11

5. 5 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/11

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7. Stress on an oblique section of a body subjected to
direct stress in two mutually perpendicular directions
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8. Normal stress across the section AB
𝜎𝑛 =
𝜎𝑥 + 𝜎𝑦
2
−
𝜎𝑥 − 𝜎𝑦
2
cos 2𝜃
Shear stress (tangential stress) across the section AB
𝜏 =
𝜎𝑥 − 𝜎𝑦
2
sin 2𝜃
Maximum shear stress
𝜏𝑚𝑎𝑥 =
𝜎𝑥 − 𝜎𝑦
2
Resultant stress
𝜎𝑅 = 𝜎𝑛
2
+ 𝜏2
Direction of Resultant stress
𝜃 = tan−1
(
𝜏
𝜎𝑛
)
8 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/11

9. BIBIN CHIDAMBARANATHAN
PROBLEMS
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10. 10 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/11

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14. 14 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/11

15. BIBIN CHIDAMBARANATHAN
GRAPHICAL
METHOD
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18. 18 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/11

19. BIBIN CHIDAMBARANATHAN
PROBLEMS
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20. 20 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/11

21. 21 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/11

22. 22 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/11

23. 23 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/11

24. BIBIN CHIDAMBARANATHAN
STRESS ON AN OBLIQUE
SECTION OF A BODY SUBJECTED
TO SIMPLE SHEAR STRESS
24 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/11

25. BIBIN CHIDAMBARANATHAN
ANALYTICAL
METHOD
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26. Stress on an oblique section of a body subjected to
simple shear stress
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27. 27 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/11

28. 28 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/11

29. 29 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/11

30. Stress on an oblique section of a body subjected to
simple shear stress
30 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/11

31. Normal stress across the section AB
𝜎𝑛 = 𝜏𝑥𝑦 sin 2𝜃
Shear stress (tangential stress) across the section AB
𝜏 = −𝜏𝑥𝑦 Cos 2𝜃
Resultant stress
𝜎𝑅 = 𝜎𝑛
2
+ 𝜏2
Direction of Resultant stress
𝜃 = tan−1
(
𝜏
𝜎𝑛
)
31 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/11

32. Thank You
32 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/11