The document presents analytical methods for calculating stresses on an oblique section of a body subjected to direct stresses in two perpendicular directions and a shear stress. It defines equations to calculate the normal stress, shear stress, maximum shear stress, resultant stress, and direction of resultant stress on the oblique section. It also provides equations for determining the maximum and minimum principal stresses and directions of maximum shear stress and maximum principal stress. Several example problems are presented to demonstrate applying the analytical methods.

1. BIBIN CHIDAMBARANATHAN
STRESS ON AN OBLIQUE
SECTION OF A BODY SUBJECTED
TO DIRECT STRESSES IN TWO
MUTUALLY PERPENDICULAR
DIRECTIONS ACCOMPANIED BY
A SIMPLE SHEAR STRESS
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2. BIBIN CHIDAMBARANATHAN
ANALYTICAL
METHOD
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3. STRESS ON AN OBLIQUE SECTION OF A BODY
SUBJECTED TO DIRECT STRESSES IN TWO MUTUALLY
PERPENDICULAR DIRECTIONS ACCOMPANIED BY A
SIMPLE SHEAR STRESS
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10. STRESS ON AN OBLIQUE SECTION OF A BODY
SUBJECTED TO DIRECT STRESSES IN TWO MUTUALLY
PERPENDICULAR DIRECTIONS ACCOMPANIED BY A
SIMPLE SHEAR STRESS
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11. Normal stress across the section AB
𝜎𝑛 =
𝜎𝑥 + 𝜎𝑦
2
−
𝜎𝑥 − 𝜎𝑦
2
cos 2𝜃 − 𝜏𝑥𝑦 𝑆𝑖𝑛 2𝜃
Shear stress (tangential stress) across the section AB
𝜏 =
𝜎𝑥 − 𝜎𝑦
2
sin 2𝜃 − 𝜏𝑥𝑦 𝐶𝑜𝑠 2𝜃
Maximum shear stress
𝜏𝑚𝑎𝑥 =
𝜎𝑥 − 𝜎𝑦
2
2
+ 𝜏𝑥𝑦
2
Resultant stress
𝜎𝑅 = 𝜎𝑛
2
+ 𝜏2
Direction of Resultant stress
𝜃𝑅 = tan−1
(
𝜏
𝜎𝑛
)
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12. Maximum principal stress
𝜎𝑝1 =
𝜎𝑥 + 𝜎𝑦
2
+
𝜎𝑥 − 𝜎𝑦
2
2
+ 𝜏𝑥𝑦
2
Minimum principal stress
𝜎𝑝1 =
𝜎𝑥 + 𝜎𝑦
2
−
𝜎𝑥 − 𝜎𝑦
2
2
+ 𝜏𝑥𝑦
2
Direction of Maximum shear stress
𝜃𝑠 =
1
2
tan−1
(
𝜎𝑥 − 𝜎𝑦
2𝜏𝑥𝑦
)
Direction of Maximum principal stress
𝜃𝑝 =
1
2
tan−1
(
2𝜏𝑥𝑦
𝜎𝑥 − 𝜎𝑦
)
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13. BIBIN CHIDAMBARANATHAN
PROBLEMS
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23. Thank You
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