Stress And Strain

Stress

Stress is defined as "force per area".

Direct Stress or Normal Stress

Stress normal to the plane is usually denoted "normal stress" and can be expressed as

σ = F_n / A         (1)
where
σ = normal stress ((Pa) N/m², psi)
F_n = normal component force (N, lb_f)
A = area (m², in²)

Shear Stress

Stress parallel to the plane is usually denoted "shear stress" and can be expressed as

τ = F_p / A         (2)
where
τ = shear stress ((Pa) N/m², psi)
F_p = parallel component force (N, lb_f)
A = area (m², in²)

Strain

Strain is defined as "deformation of a solid due to stress" and can be expressed as

ε = dl / l_o = σ / E         (3)
where
dl = change of length (m, in)
l_o = initial length (m, in)
ε = unitless measure of engineering strain
E = Young's modulus (Modulus of Elasticity) (Pa, psi)

Hooke's Law -  Modulus of Elasticity (Young's Modulus or Tensile Modulus)

Most metals have deformations that are proportional with the imposed loads over a range of loads. Stress is proportional to load and strain is proportional to deformation expressed by the Hooke's law like

E = stress / strain = (F_n / A) / (dl / l_o)         (4)
where
E = Young's modulus (N/m²) (lb/in², psi)

Modulus of Elasticity or Young's Modulus are commonly used for metals and metal alloys and expressed in terms 10⁶ lb_f/in², N/m² or Pa. Tensile modulus are often used for plastics and expressed in terms 10⁵ lb_f/in² or  GPa


Please note: The above article is taken from www.engineeringtoolbox.com. Please do refer to them for further info.


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