Question: When the force $P$ reached $1,540$ 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.
The average shearing stress is ________ psi.
1. **State the problem:**
We need to find the average shearing stress on the wooden specimen when the force $P = 1,540$ lb causes failure along the dashed shear surface.
2. **Formula for average shearing stress:**
The average shearing stress $\tau$ is given by:
$$\tau = \frac{F}{A}$$
where $F$ is the force causing the shear and $A$ is the area of the shear surface.
3. **Identify given values:**
- Force $F = 1,540$ lb
- Length of shear surface $L = 3$ in.
- Thickness (or width) $t = 0.6$ in.
4. **Calculate the shear area $A$:**
$$A = L \times t = 3 \times 0.6 = 1.8 \text{ in}^2$$
5. **Calculate the average shearing stress:**
$$\tau = \frac{1,540}{1.8}$$
6. **Simplify the fraction:**
$$\tau = \frac{\cancel{1,540}}{\cancel{1.8}} \approx 855.56 \text{ psi}$$
7. **Final answer:**
The average shearing stress along the surface at failure is approximately **855.56 psi**.