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sertanlavr [38]

3 years ago

9

Calculate the biaxial stresses σ1 and σ2 for the biaxial stress case, where ε1 = .0020 and ε2 = –.0010 are determined experiment

ally on an aluminum member of elastic constants, E = 71 GPa and v = 0.35. Also, determine the value for the maximum shear stress.

1 answer:

Llana [10]3 years ago

3 0

Answer:

i) σ1 = 133.5 MPa

σ2 = -2427 MPa

ii) 78.89 MPa

Explanation:

Given data:

ε1 = 0.0020 and ε2 = –0.0010

E = 71 GPa

v = 0.35

<u>i) Determine the biaxial stresses σ1 and σ2 using the relations below</u>

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

<u>ii) Calculate the value of the maximum shear stress ( Zmax )</u>

Zmax = ( σ1 - σ2 ) / 2

= 133.5 - ( - 2427 ) / 2

= 78.89 MPa

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