Stress - Mechanics of Materials

Stress is defined as a force per unit area.

Normal stress(σ) acts perpendicular to the longitudinal axis of a member.

Shear stress( ) acts tangent to the area.

State of Stress: a volumetric element of material from the member and is characterized by σx, σy, σz, xy, xz , and yz

Units of stress are Pascals (Pa). 1Pa = N/m^2 , psi, or Kilopound(Kip)

Assumptions for determining the average stress distribution:

• Uniform deformation
• The force applied to the member is along the centroidal axis
• The member remains straight before and after loading
• The member is homogeneous: having the same physical and mechanical properties throughout the volume of the member

σ = P / A

• σ is the average normal stress
• P is the internal resultant normal force
• A is the area of the cross section

avg = V / A

• avg is the average shear stress
• V is the internal resultant shear force, determined from equations of equilibrium
• A is the area at that section

Factor of Safety: ensures the safety of members by determining the maximum shear and normal stresses that are safe for a member to hold

F.S. = Ffail / Fallowable

• F.S. is the factor of safety and is always greater than 1 to avoid the member from potential failure
• Ffail can either be σ or failure
• Fallowable can either be σ or allowable

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