MECH 210 080827 - Stress Strain

MECH 210 080827 - Stress Strain - MECH 210 080827 Stress...

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Page 1 of 4 MECH 210 080827 Stress and Strain Stress: applied force per unit area in MPa (= 10 6 N/m 2 ) or psi (= lb f /in 2 ) 1 MPa = 145 psi Engineering Stress = area ional sect cross Original load Applied Normal stress (tensile or compressive), σ = area ional sect cross Originalc surface to lar perpendicu Force = o A F Shear stress, τ = o A F area surface Original force Shear = True Stress = area sectional cross ous Instantane time the at load Applied True normal stress, σ T i A F area sectional cross ous Instantane surface to lar perpendicu Force = = Strain: rate of dimensional change in m / m , in / in , or simply unitless Engineering Strain = length Original length in Change Tensile or compressive strain, ε = o o i o l l l l l length Original force of direction along length in Change - = Δ = where l i is the instantaneous length. Shear strain, ν θ Δ tan h l = = True Strain , ε T = ln (1 + ε ) Relationship between engineering stress and true stress: σ T = σ (1 + ε ) Relationship between engineering strain and true strain: ε T = ln (1 + ε ) The normal stress σ ’ and shear stress ε ’ on a plane at an angle with the applied force: + = = 2 2 cos 1 cos ' 2 θ σ θ σ σ and = = 2 2 sin cos sin ' θ σ θ θ σ ε where θ is the angle between the plane and the surface on which the normal force is applied.
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