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# The grain of a wooden member forms an angle of 15° with the vertical. For the state of stress shown, determine (a) the inplane shearing stress parallel to the grain, (b) the normal stress perpendicular to the grain.

Question-AnswerCategory: Strength of MaterialsThe grain of a wooden member forms an angle of 15° with the vertical. For the state of stress shown, determine (a) the inplane shearing stress parallel to the grain, (b) the normal stress perpendicular to the grain.
Beer Johnston asked 12 months ago

The grain of a wooden member forms an angle of 15° with the vertical. For the state of stress shown, determine (a) the inplane shearing stress parallel to the grain, (b) the normal stress perpendicular to the grain.

1 Answers
Mazurek Gravity answered 12 months ago

Step No: 1

a)
Draw the diagram representing the stresses acting on the planes.

Step No: 2

As there is no direct stress acting along x and y direction, the stresses in that direction will be zero.

Calculate the in-plane shearing stress  parallel to the grain by using the equation,

Here,  is the shear stress acting along  plane,  is the direct stress acting along x direction, and  is the direct stress acting along y direction.
Substitute  for  for  for , and  for .

Therefore, the in-plane shearing stress parallel to the grain is .

Step No: 3

b)
Calculate the normal stress  perpendicular to the grain by using the formula.

Substitute  for  for  for , and  for .

Therefore, the normal stress acting perpendicular to the grain is .

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