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A carpenter glues a pair of cylindrical wooden logs by bonding 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
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- fails only because of criterion 1
- fails only because of criterion 2
- fails because of both criteria 1 and 2
- does not fail.
Correct Option: C
Normal stress on inclined plane
σ = σx cos² θ
= 4 × cos²30 = 3 MPaShear stress on inclined plane τ = sin2θ 2
= 2 × sin 60° = 1.73 MPa
Since both the stress exceeds the given limits, answer is option (c).
