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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
[2018, Set-1]
  • a)
    fails only because of criterion 1
  • b)
    fails only because of criterion 2
  • c)
    fails because of both criteria 1 and 2
  • d)
    does not fail.
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A carpenter glues a pair of cylindrical wooden logs by bonding their e...
Normal stress on inclined plane
σ = σx cos2θ
= 4 × cos2 30 = 3 MPa
Shear stress on inclined plane

= 2 × sin 60° = 1.73 MPa
Since both the stress exceeds the given limits, answer is option (c).
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Most Upvoted Answer
A carpenter glues a pair of cylindrical wooden logs by bonding their e...
Normal stress on inclined plane
σ = σx cos2θ
= 4 × cos2 30 = 3 MPa
Shear stress on inclined plane

= 2 × sin 60° = 1.73 MPa
Since both the stress exceeds the given limits, answer is option (c).
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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 ifCriterion 1 : the maximum normal stress exceeds 2.5 MPaCriterion 2 : the maximum shear stress exceeds 1.5 MPaAssume that the interface fails before the logs fail. When a uniform tensile stress of 4 MPa is applied, the interface[2018, Set-1]a)fails only because of criterion 1b)fails only because of criterion 2c)fails because of both criteria 1 and 2d)does not fail.Correct answer is option 'C'. Can you explain this answer?
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