The document discusses principal stresses and strains. It describes principal planes as planes where only normal stresses act with no shear stress. Principal stresses are the normal stresses acting on principal planes, while principal strains are the strains produced by principal stresses. It presents two methods - analytical and graphical - for determining stresses on oblique sections, and provides equations for calculating normal stress, shear stress, maximum shear stress, and resultant stress on an oblique section of a body subjected to direct stress in one plane. The document also includes example problems.

1. BIBIN CHIDAMBARANATHAN
PRINCIPAL STRESSES
&
STRAINS
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2. Principal Planes
• Only normal stresses are acting on the plane and shear stresses at the plane is
zero. This is known as Principal Plane
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3. Principal Stresses and Strains
• The normal stresses are applying on the principal plane. This is known as
Principal Stresses.
• Similarly, due to the principal stresses, Plane is producing some strains. And this
strain is known as Principal strain.
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4. Methods For Determining Stresses On Oblique
Section (Principal Stresses and Strains)
There are following methods are used to determine the stresses at the Inclined or
oblique section:
• 1. Analytical method, and
• 2. Graphical method.
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5. Analytical Methods
• 1. A body subjected to Direct stress in one plane.
• 2. A body subjected to Direct stresses in two mutually perpendicular directions.
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6. BIBIN CHIDAMBARANATHAN
STRESS ON AN OBLIQUE
SECTION OF A BODY
SUBJECTED TO DIRECT
STRESSES IN ONE PLANE
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7. BIBIN CHIDAMBARANATHAN
ANALYTICAL
METHOD
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10. 10 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/8

11. Stress on an oblique section of a body subjected to
direct stresses in one plane
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12. Normal stress across the section AB
𝜎𝑛 =
𝜎
2
−
𝜎
2
cos 2𝜃
Shear stress (tangential stress) across the section AB
𝜏 =
𝜎
2
sin 2𝜃
Maximum shear stress
𝜏𝑚𝑎𝑥 =
𝜎
2
Resultant stress
𝜎𝑅 = 𝜎𝑛
2
+ 𝜏2
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13. BIBIN CHIDAMBARANATHAN
GRAPHICAL
METHOD
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14. 14 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/8

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16. 16 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/8

17. BIBIN CHIDAMBARANATHAN
PROBLEMS
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18. 18 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/8

19. 19 BIBIN CHIDAMBARANATHAN, ASP/MECH, RMKCET 5/8

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23. Thank You
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