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Sagot :
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
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
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