Question
A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of of 30° as shown in the figure.
The glue used at the interface fails if
Criterion 1: the maximum normal stress exceeds 2.5 MPa.
Criterion 2: the maximum shear stress exceeds 1.5 MPa.
Assume that the interface fails before the logs fail. When a uniform tensile stress of 4 MPa is applied, the interface
Options :
fails only because of criterion 1
fails only because of criterion 2
fails because of both criteria 1 and 2
does not fail
Answer :
fails because of both criteria 1 and 2
Solution :
Normal stress on inclined plane
T’ = σx*cos²θ
= 4*cos²30 = 3 MPa
Shear stress on inclined plane 𝜏’ = σx sin2θ/2 = 2*sin60°= 1.73 MPa
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