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-Answer › Category: Strength of Materials › 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.

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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.

Question Tags: Chapter 7

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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 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.