Question

Calculate the biaxial stresses σ1 and σ2 for the biaxial stress case, where ε1 = .0020 and ε2 = –.0010 are determined experimentally on an aluminum member of elastic constants, E = 71 GPa and v = 0.35. Also, determine the value for the maximum shear stress.

Answer 1

i) σ1 = 133.5 MPa

σ2 = -2427 MPa

ii) 78.89 MPa

Step-by-step explanation:

Given data:

ε1 = 0.0020 and ε2 = –0.0010

E = 71 GPa

v = 0.35

i) Determine the biaxial stresses σ1 and σ2 using the relations below

ε1 = σ1 / E - v (σ2 / E) -----( 1 )

ε2 = σ2 / E - v (σ1 / E) -------( 2 )

resolving equations 1 and 2

σ1 = E / 1 - v^2 { ε1 + vε2 } ---- ( 3 )

σ2 = E / 1 - v^2 { ε2 + vε1 } ----- ( 4 )

input the given data into equation 3 and equation 4

σ1 = 133.5 MPa

σ2 = -2427 MPa

ii) Calculate the value of the maximum shear stress ( Zmax )

Zmax = ( σ1 - σ2 ) / 2

= 133.5 - ( - 2427 ) / 2

= 78.89 MPa