1. Concepts about the science of "Strength of Materials" tasks, consistency, uniformity, priority, brief history

SomeImportantDefinitions

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  At a point on a beam where shear force changes its sign, the point is known as the maximum bending moment position.
  
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  At a point where the bending moment changes, the point of contra flexure is known.
  
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  At a span where the shear force value is completely zero and the bending moment constant is called a pure bending span.
  

16.Twisting of a circular cross section. Finding stresses and deformations (torque moment, effort stresses, distribution, pole: moment of inertia, moment of resistance; twist angle, singularity, relative).
When a circular cross-section undergoes twisting, several parameters can be analyzed to determine the stresses and deformations. Here are the key factors involved:

1. 
   Torque moment (T):
   
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     The torque moment applied to the circular cross-section.
     
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     It causes the cross-section to twist.
     
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     It is denoted by T.
     
2. 
   Shear stress (τ):
   
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     Shear stress is developed within the circular cross-section due to twisting.
     
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     The distribution of shear stress is non-linear, and it varies with the radial distance from the center.
     
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     The maximum shear stress occurs at the outermost fibers, while the inner fibers experience lower shear stresses.
     
3. 
   Polar moment of inertia (J):
   
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     Polar moment of inertia is a property of the cross-sectional shape that influences the resistance to twisting.
     
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     It is denoted by J.
     
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     For a circular cross-section, J = (π/32) * D^4, where D is the diameter.
     
4. 
   Angle of twist (θ):
   
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     The angle of twist represents the total rotation of the cross-section due to the applied torque moment.
     
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     It is denoted by θ.
     
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     The relationship between the angle of twist and torque moment is given by T = G * J * θ / L, where G is the shear modulus and L is the length of the section.
     
5. 
   Moment of resistance (R):
   
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     The moment of resistance represents the resistance of the cross-section to twisting.
     
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     It is denoted by R.
     
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     R = τ * J, where τ is the shear stress and J is the polar moment of inertia.
     
6. 
   Singularity:
   
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     A singularity occurs at the center of the cross-section where the shear stress is zero.
     
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     The shear stress distribution increases linearly from the center to the outer fibers.
     
7. 
   Relative deformations:
   
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     Relative deformations describe the relative displacement of fibers within the cross-section due to twisting.
     
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     The fibers at the outermost portion of the section undergo greater deformations compared to the inner fibers.
     

To analyze the stresses and deformations in more detail, it is necessary to apply specific formulas and calculations based on the given parameters and material properties of the circular cross-section. The above information provides a general overview of the factors involved in twisting a circular cross-section.