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A carpenter glues a pair of cylindrical wooden logs by banding their end faces at an angle of θ = 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

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

Correct answer: fails because of both criteria 1 and 2

Solution

Both criteria are violated under the applied tensile stress of 4 MPa. The normal stress exceeds the maximum limit of 2.5 MPa, and the shear stress also exceeds the limit of 1.5 MPa due to the angle of the logs, leading to failure according to both criteria.

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