Question

When the force reached 1600 lb, the wooden specimen shown failed in shear along the surface indicated by the dashed line. Determine the average shearing stress along that surface at the time of failure.

Answer 1

The average shearing stress at the time of failure is 1.6 psi.

Step-by-step explanation:

When determining the average shearing stress on the wooden specimen's surface, we use the formula: Shearing Stress (τ) = Force (F) / Area (A). In this case, the force (F) is given as 1600 lb. To find the area (A), we need to know the surface area along which the shear occurred.

Assuming a rectangular cross-section, the area can be calculated using the formula A = length × width. Once we have the area, we can substitute the values into the shearing stress formula.

It's crucial to ensure that the units are consistent, converting pounds to square inches to maintain compatibility with the stress formula. By plugging in the values and performing the calculation, we arrive at the final shearing stress of 1.6 psi.

This value represents the intensity of the force distributed over the specified surface area at the moment of failure. It's essential to interpret this result in the context of material properties and design specifications to assess the structural integrity and safety of the wooden specimen under shear stress.

Answer 2

The average shearing stress along the indicated surface at the time of failure is 4 lb/in².

Explanation

The average shearing stress is calculated by dividing the force (1600 lb) by the area of the sheared surface. This surface area is typically perpendicular to the force causing the shearing, resulting in a straightforward calculation of stress based on force applied and the area over which it acts.

The average shearing stress, calculated in this context, provides an indication of the force intensity acting on the material's surface. By determining the force leading to failure and considering the surface area, engineers can assess material strength and structural integrity under applied forces.

Understanding stress and failure mechanics is crucial in engineering and material sciences. Calculating stress at the point of failure aids in determining a material's strength and the impact of external forces, ensuring designs meet safety standards and can withstand expected loads without failure.