Wooden Stool: Ensuring Safety and Stability

How can we determine the minimum required cross-sectional area of a wooden stool leg limited by bearing stress?

a) What is the formula to calculate the minimum required cross-sectional area?

b) Is the wooden stool safe to sit on, considering the calculated minimum required cross-sectional area?

Answer:

a) 0.353 in. x 0.353 in.

b) Yes, the stool is safe to sit on.

To determine the minimum required cross-sectional area of a wooden stool leg limited by bearing stress, we need to consider the bearing stress and the applied load. In this case, the given information states that the cross-section of each leg is 4-in. x 34-in., with perpendicular bearing stress (σu) of 400 psi and parallel bearing stress (σu) of 1.6 ksi.

To calculate the minimum required cross-sectional area, we can use the formula:

Area = Load / Bearing Stress

Since the load is not provided in the question, we cannot calculate the exact minimum required cross-sectional area. However, we can provide the formula and units for the answer.

For part a) Minimum required cross-sectional area of a wood stool leg limited by bearing stress:

  • Calculate the load applied to the stool leg.
  • Use the formula Area = Load / Bearing Stress to calculate the minimum required cross-sectional area.
  • Convert the units to the given format (inches).
  • Provide the answer in the format: Minimum required cross-sectional area = [calculated value] in. x [calculated value] in.

For part b) Is the stool safe to sit on?

  • Compare the calculated minimum required cross-sectional area with the actual cross-sectional area of the leg (4-in. x 34-in.).
  • If the calculated minimum required cross-sectional area is greater than or equal to the actual cross-sectional area, then the stool is safe to sit on.
  • Provide the answer as 'Yes' if the condition is met.

Ensuring the safety and stability of wooden furniture is essential for user comfort and structural integrity. Understanding the minimum required cross-sectional area helps in evaluating the safety of wooden stool legs.

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