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A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of $\theta = 30^{\circ}$ as shown in the figure.

The glue used at the interface fails is

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

  1. fails only because of criterion $1$
  2. fails only because of criterion $2$
  3. fails because of both criterion $1$ and $2$
  4. does not fail
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