Advanced Mechanics of Materials and Applied Elasticity

Subject classification: this is an engineering resource.
Subject classification: this is a physics resource.

Equation of Advanced Mechanics of Materials and Applied Elasticity

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Chapter 1:Analysis of Stress

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three-dimensional state of stress

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prismatic bars of linearly elastic material

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  • axial loading  
  • torsion  
  • bending  
  • shear  
  torque.
  vertical shear force from bending force.
  moment of inertia about neutral axis(N.A.).
  polar moment of inertia of circular cross section.
  distance from the center of torque to the point.
  first moment about N.A. of the area beyond the point at which \tau_{x,y} is calculated.

thin-walled pressure vessels

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  • cylinder  
 
  • sphere  
  tangential stress in cylinder wall.
  axial stress in cylinder wall.
  membrane stress in sphere wall.
  internal pressure.
  wall thickness.
  mean radius.

axially loaded members

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differential equations of equilibrium

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plane-stress transformation

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(2-dimensional stress, neglect the stress in the z coordinate.)

 

 

 

Stress tensor

 constant.

 

 

 

 

principal stresses in plane

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