# 18. 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 Materials18. 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.

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. Step No: 1

a)
Draw the diagram representing the stresses acting on the planes. Step No: 2

As there is no shear stress acting on the xy plane, the shear stress is equal to 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 .